Wide Canvas
  • Home
  • Nature
  • Social Interactions
  • Science & Technology
  • ABOUT

Science and technology

working with nature- civil and hydraulic engineering to aspects of real world problems in water and at the waterfront - within coastal environments

Coastal Ocean Currents off Rivermouths

12/16/2022

0 Comments

 
Picture

. . . the trouble with the world is that the stupid are cocksure and the intelligent are full of doubts. . . This saying from Bertrand Russell (1872 – 1970) is similar to what The Tathagata said in the 152nd verse of the Dhammapada: The man of little learning grows old like a bull. He grows only in bulk, but, his wisdom does not grow. These sayings point one to look deep into things to open one’s wisdom eye, to see the reality of the nature of things – of the existence of uncertainty in the sphere of knowledge (see The Quantum World; Uncertainty and Risk and The World of Numbers and Chances). The necessity of seeing as such – dawns as we continue to learn more – as the horizon of our knowledge continues to expand.

Perhaps – our learning process starts as we begin to develop questions in our mind – like if or when. In computer programming ifs and the answers to such ifs – are used to direct processes in different directions – so does our learning processes. Questions similar like these, reflecting on the past: if I had done things differently . . . if I had been informed differently or were able to see things through my own lens . . . if I had someone powerful on my back . . . so on – and so forth. And intelligent answers to them help us chart future directions. Similarly, such questions can be framed in our mind – at any time – to help examining the pros and cons of making decisions. Sometimes, we fail to ask such questions in time, and mistakes are made – from which recovery becomes difficult. It’s like one of Tagore (1861 – 1941) songs: keno jaminee naa jheta jagelaa naa – saying, why didn’t you wake me up before it was dawn. In one way or another – the consequences of making decisions based on answering ifs –– define the interdependent fluxes in the evolving canvas of life in time, and in the space where one lives – the spacetime.
And as we do so, we begin to realize what Benjamin Franklin (1706 – 1790) once said: . . . without continual growth and progress, such words as improvement, achievement, and success have no meaning . . . Starting from these words of wisdom, let us attempt to understand some dynamics of currents in coastal oceans off rivermouths – focusing on the one, off the mouth of Ganges (Ganga) Brahmaputra River System (GBRS; or the GBM system). Needless to say that such understandings – are very imperative to initiate, manage and execute Civil Engineering on Our Seashore – to achieve sound and sustainable goals. Engineering services are involved in one way or another – in the processes of attaining the 17 interconnected UN declared Sustainable Development Goals (SDG).


Thought of presenting some findings from the 2nd Chapter of my Ph.D. Dissertation – with a note that unlike in An Alluvial River’s Sedimentary Functions, I am keeping the name Brahmaputra River in line with my Dissertation – although its reach in Bangladesh is known as the Jamuna River. Some aspects of this chapter were presented in the Characterizing Wave Asymmetry, with discussions of some theoretical frameworks posted in Nonlinear Waves. This is the only chapter – which I could not manage time to send the manuscript for journal publication. Other chapters are published: Chap 1 (1991), Chap 3 (1995) and Chap 4 (1994). Facilitated by my major Prof WS Moore, the 2nd Chapter benefited from the works and advice of my Dissertation committee member Prof B Kjerfve. Acknowledging them in gratitude – let me move forward to focus on the main contents of this piece – on coastal ocean currents.

In this piece, I am doing this very briefly with some of the interpretations and explanations that accrued from my later experiences and related publications – some of which are summarized and listed in the ABOUT page. Among them, the most relevant publications for this article are: the 1990 IEB Journal Paper on Estuary; the 1991 COPEDEC-PIANC paper; the 1993 Practices and Possibilities; the 1994 Karnafuli River Estuary Hydraulic Behavior; the 1997 Active Delta; the 2001 Suspended Sediment Measurement; the 2002 Geometric Similarity of Deltas; the 2004 Settling Velocity of Natural Sediments; the 2008 Fluid Mud; the 2015 Longshore Transport; and the 2017 Seabed Roughness. It is also enriched by the works done while writing several articles posted in the WIDECANVAS.

Before I begin, a short note on The Coastal Force Fields is helpful. The fields represent a playground of many forcings and responses of different time-scales afforded by different constraints – defined by isobaths and the land-water interface at the shoreline/coastline (see more in the Civil Engineering on our Seashore). Together, the system of forces head to reach dynamic equilibrium (see Natural Equilibrium; Water Modeling).

According to the force fields defined there – GBRS mouth is governed by forces – that are in dominant actions, but differing in the contexts of both space and time - the Metocean Force Field (MOFF), the Extraterrestrial Force Field (ETFF), the Land Drainage Force Field (LDFF) – are all there, together with the Frontal Wave Force Field (FWFF) – which is active in the proximal shoreline and shallow areas. As well important is the Storm Surge that frequents the coastline often. Currents or velocity fields are generated by the development of pressure gradients generated by the highlighted force fields. They are a manifestation of hydrodynamic interactions – of force and response fields – as depicted in the image of Force Fields in a Coastal System.

The Hydro-Geomorphologic Setting – the Processes and Forms.
Let me begin by referring to the attached image (it is enriched by some materials discussed in the Coastal River Delta) – that summarizes some of the key hydro-geomorphologic features and processes of Bangladesh coast. The definitions and delineations have been used by many subsequent authors to describe Bangladesh coastline.
  • The delineation identifies two major groups – the first is the (~) 380-km near-east-west delta of the GBRS, and the second is the (~) 274-km near north-south stretch of the Chattogram coastal region – the Chattogram Coastal Plain (CCP). Following the terms defined in the Force Fields in a Coastal System, the hydrodynamics of these two groups are fundamentally different – with the regular playground of spring-neap ETFF – more so in the eastern channels than in the west. The delta is the showcase of interacting LDFF and MOFF during the four months of the wet-monsoon – roughly from June to September. While the dominance of LDFF is present close to the shore delta fringes – the MOFF dominance is in contagious seas offshore. In the second group CPP – on the other end, MOFF is the dominant process riding on top of ETFF.
  • The first group can be divided into two: the (~) 125-km long coastline of the Ganges Tidal Plain (GTP) in the west, and the (~) 255-km long coastline of the Meghna Deltaic Plain (MDP) in the east. Of these, the first draws only 4% of the GBRS flow – with the delta fringes of multiple interlinked estuaries colonized by extensive mangrove forests – the Sundarbans that stretch from India to Bangladesh. As the name suggests, the GTP is mainly tidal with muddy estuarine channels fringed by narrow and pocket beaches of fine sands at the shoreline.
  • The second draws the other 96% of the GBRS flow – and is the highly dynamic active delta of the GBRS. Horizontal coastal erosion rate to the maximum of 400 m/year, and the vertical sediment accumulation rate to the maximum of 3 m/year were observed (the 1997 paper). The delta is stratified horizontally (the 1990 paper) in current patterns and SST (suspended sediment transport; see the Hydraulics of Sediment Transport for definition) – with seaward residuals in western channels and landward in the east. With such trends of differing residual transport directions associated with stratification, the delta-building processes appear poised to prograde southwestward with gradual of shoaling of eastern channels.
  • Two submarine canyons incise Bangladesh coastal ocean. The first is the Swatch-of-No-Ground (SNG) – or Ganges Canyon in the west (the SNG has a width of 30 km, at 200 m isobath, and penetrates 130 km deep into the continental shelf). A shallow trough – the Hatia Trough (HT) runs parallel and close to the CCP. As discussed further later, these two canyons modulate tidal phenomenon ETFF processes in the Bangladesh coastal ocean.

The Measurements – the Time, Tide, Site and Season.
Let me briefly outline the measurements on which the findings described in this article are based (please refer to Chapter 2 of my 1992 Dissertation for details).
  • A total of three different sets of 13-hour time-series hourly observations cover several stations. Land Reclamation Project survey vessel, M.V. Anwesha was used for observations. A Decca navigation hyperbolic system was used for positioning. The vessel was let to weather-vane – positioned by a bow anchor (with an anchor-chain measuring 3 times the water depth). Velocity was measured by an Ott propeller current meter. A 50 s exposure time was used to obtain the flow velocity. The propellers were calibrated before the measuring campaign in the calibration tank of Bangladesh Water Development Board and were accurate within (+-)2%. With one current meter suspended from a davit located on the mid-section of the ship, measurements were made at three depths (1 m below surface, mid-depth and 1 m above bottom), either starting at the surface or at the bottom, and sampling the mid-depth position during hoisting or lowering. Depending on the depth, 8 to 10 minutes were required for the exercise. The velocity direction was measured by the ship's navigation compass and the deviation from it was noted by a pendulum current meter lowered simultaneously at the level of the current mater.
  • A total 14 measurement sites were covered – in waters between 5 and 20 m isobaths. Of them, 4 are off the GTP – one at the head of SNG with 3 others on the west of it. Three sites are in locations parallel to CCP stretching from the head of HT to Sandwip Channel. The rest 7 measuring stations are located off MDP.
  • The first set of measurements representing a spring tide – covers 5 stations from 27 November to 1 December 1989. Measurements at these stations were repeated the following week (5-9 December) during a neap tide. These sets of measurements during November-December represented GBRS slow falling stage.
  • The second set of measurements representing a mean tide – covers 6 stations during a 22-26 August 1990 period. This set of measurements during August represented GBRS peak stage.
  • On a 17-24 October 1990 period, a third set of measurements cover 6 stations. During this period, the first measurement on 17 October represented a spring tide, and the rest, a mean tide. This set of measurements during October represented rapid falling stage of the GBRS flows. A lone measurement on 15 March 1991 during a spring tide represented a flat low GBRS stage.
  • Among these, the August 1990 measurements represented southwest monsoon while those in October, November-December was during the northeast monsoon. These two seasons represent contrasting wind speed magnitude and directions. Swells having 12-16 s periods were observed at a station, west of SNG during the October 1990 measurements. For a location in the Bay of Bengal near the SNG, sea and swell charts of the U.S. Navy (1965) indicate high seas and swells from southwest in August – moderate seas and swells from Southeast in October – and low or negligible seas and swells from northeast in November and December.

Coastal Water and Wind-driven Circulation.
Here is a gist on the nature of changing seawater salinity (see Coastal Water to know aspects of it) at measured stations, and the wind-driven circulation (see Storm Surge to know aspects of it).
  • The depth-and time-mean (averaged over the semi-diurnal tidal cycle) salinities indicate the enormous influence of GBRS at the measured stations. At no station does the observed salinity exceed 50% of the full strength seawater salinity. Stations sampled in August 1990 during the peak river-discharge period were fresh or mildly brackish.
  • As expected the seawater salinity off the MDP is substantially lower than those stations on both east and west sides – indicating a high influence of GBRS fresh water flow at these stations than others.
  • All the measured stations show a vertically well-mixed situation. Time-mean salinities at 1 m below surface and at 1 m above bottom showed negligible variations over the depth. Absence of vertical density stratification indicates that no estuarine type circulation is present (see aspects of it in Managing Coastal Inlets).
  • Countries bordering northern Indian Ocean experience oscillating monsoon wind systems. The southwest (June through September) and the northeast monsoons (December through February) cause the reversal of circulation in the Bay of Bengal. It can be noted that when wind blows for a long time (for a pendulum day, which is 65 hours for Bangladesh coast; Dissertation) against a coast, a drift current develops and a wind set-up is created at the coast. The wind set-up causes a slope current down the gradient. The drift current is a function of depth and due to frictional resistance at the bottom, is higher near the surface. The combination usually results in a net onshore surface drift current and a net offshore slope current along the bottom.

Submarine Canyons Refract Tide.
The set of measurements in waters between 5 and 20 m isobaths – covering nearly the whole stretch of Bangladesh coastal ocean indicate something very interesting about the refraction of tidal wave by deep submarine canyons.
  • Measurements on the two sides of the SNG reveal that the tidal excursion directions are different on the two sides of the canyon. Most of the shelf areas surrounding the SNG receive tidal forcing from it. While a dominant northeast (rising)–southwest (falling) tidal excursion occurs on the east of SNG, the same on the west is northwest (rising)–southeastward (falling).
  • This pattern, observed for the first time in my Dissertation works – indicates that tide propagating faster through the canyon than the surrounding shelf areas – refracts to either side The result is that the surrounding shelf areas receive tidal forcing generated from the canyon. It appears, however, that this refracting effect of SNG on the tidal motion does not cover the areas as far east to HT. The excursion pattern in stations near HT shows a nearly rectilinear tide propagating through it – and is oriented north-south.
  • Analogous to the refraction of short waves by a submarine trough, a canyon causes divergence of tidal wave energies on both sides of it. The result is a higher amplitude tide on both sides than at its head. The agreement to this observation can be found in co-range tidal lines.
  • Why the tidal waves propagating through SNG and HT are different? Answer to this question becomes apparent from the principles of long wave transformation outlined in the Tsunami and Tsunami Forces piece. On shoaling and funneling of long waves I have written: The phenomena of shoaling and funneling can best be understood by applying the energy conservation principle, often known as the Green’s Law. This simple principle assuming no losses of energy by friction, etc., shows that for a gradually shoaling continental shelf, the ratio of height increase is proportional to the reciprocal of the ratio of depth decrease raised to the 1/4th power. For a channel gradually decreasing in width, the funneling effect is given by the ratio of height increase that is proportional to the reciprocal of the ratio of width decrease raised to the 1/2nd power. In the case of tide propagating through the gradually varying configuration of HT, both the effects of shoaling and funneling are pronounced – resulting in amplification of tide continuing up to Sandwip and Hatia Channels with further effects there (the COPEDEC-PIANC paper). In the case of SNG – the canyon is so deep incised into the continental shelf that the propagating tidal wave virtually does not feel the Green’s Law effects until reaching the head of the canyon. But, there it faces the reflection from the steep canyon wall. The combined effects of loosing energy by reflection and refraction must be the primary reasons why the tidal ranges in areas around SNG are lower (lower than HT areas). However, once the refracted wave spews out from SNG on to the shelf – it becomes subjected to the effects of shoaling – with some amplification and further effects on way into estuaries.
  • The SNG pattern is evident from the observed tidal excursion pattern and explains the general alignment of linear tidal ridges shown by 5 and 10 m isobaths. T Off (1963) described northwest-southeast aligned linear tidal ridges on the west of the SNG reflecting the observed tidal excursion pattern there. In the east, JM Coleman (1969) noted that the distributary mouths and the 5 m isobath are directed toward SNG.
  • Tidal currents aligned to canyon/trough directions are reported to be present in the Indus Trough (EP Shepard and RF Dill 1966). In addition, alternating currents have been measured at the head of different canyons having the frequency of the dominant tidal motion (EP Shepard, NF Marshall, PA McLaughlin and GG Sullivan 1979). More than a century ago, J Fergusson (1863) remarked that the SNG is maintained by the scouring action of the convergence of two tidal currents rotating in opposite sense at the head of the canyon. As revealed in my Dissertation, the rotations of tidal currents are not in opposite sense – but have different excursion patterns.

Tidal Oscillation, Currents and Residuals:
The three sets of described measurements are fairly representative of the river hydrograph and the changing monsoonal wind pattern. In spite of a few exceptions, the data indicate some interesting hydrodynamic characteristics of the surveyed area.
  • A clockwise turning tidal motion is observed at some stations while an erratic pattern is observed at others. The erratic pattern indicates a possible influence of coastal topography. The nearshore stations show rectilinear tidal motion in agreement with the channelised configurations of isobaths at those stations.
  • Tidal motion types are indicated by showing the phase relationships between the observed water levels and the depth-mean tidal currents. An in-phase relation was observed at a station at the head of HT (as far south near Cox’s Bazar) – indicating a progressive wave-type tidal motion there. More shoreward, close to the entrance of Sandwip Channel, however, the tide develops into a standing wave type motion – shown by the phase lead of velocity by about 90o. Near SNG and in other deep waters – the processes of transitioning from progressive to standing wave type were observed with a phase lead of velocity by 1 hour or 29o. Standing wave-type oscillation was observed in inner shelf areas shoreward of 20 m isobath, indicating that coastal reflection of the incoming progressive tidal motion starts becoming effective shoreward from these depth-ranges.
  • Tidal energy shown by variance of the depth-averaged tidal current was found to be a power function of tidal range: V = 0.07 - 0.02T+ 0.13T^2 (V = Variance; T = Tidal range). A depth-mean velocity vector variance of 2.17 m^2/s^2 was observed in Sandwip Channel near the entrance of Karnafuli River during a tidal range of 4.20 m (it is a macro-tidal environment). At the head of SNG for a tidal range of 1.20 m, the depth-mean velocity vector of 0.13 m^2/s^2 was observed (it is a meso-tidal environment). Variance of tidal currents is a measure of kinetic energy.
  • Decomposition of flow vectors into orthogonal components shows that the Northings have higher amplitude, a leading phase and a higher variance than the Eastings. Comparison of the Northings over the vertical, at 1 m below surface and at 1 m above bottom, shows that the bottom velocity has lower amplitude but a leading phase than the surface velocity. The differences suggest that the near-bed sediment can have a different transport direction than the surface transport.

There we have it – a brief synopsis of coastal ocean current dynamics off rivermouths – where the actions of tide, seasonal riverine flow and wind conditions (for details see Chapter 2 of my Dissertation) define the force fields.
This article is dedicated to celebrate the 51st anniversary of Bijoy Dibash – the Day on 16 December 1971 marks the Liberation of Bangladesh from the tyranny of Pakistani rule. Let freedom loving people from around the world come together to breathe the fresh air of emancipation – by being conscientious, heedful and diligent – whenever – wherever – whatever. And let us do that by remembering Charles Dickens (1812 – 1870), the British writer, novelist and social critic: have a heart that never hardens, and a temper that never tires, and a touch that never hurts.

The Koan of this piece: Be mindful what you think, say or do, because the Sun has the habit of not shining on one place for long


. . . . .

- by Dr. Dilip K. Barua, 16 December 2022



0 Comments

Force Fields in a Coastal System

8/25/2021

0 Comments

 
Picture
In this piece let us attempt to see in simple terms – the dynamics of coastal systems through a different scientific angle. This angle is the Force Field Theory (or ENERGY FIELD) first proposed by Michael Faraday (1791 – 1867) in 1845 (see The Quantum World; for a short introduction of the concept). A Coastal Engineer’s works, or widely the works of a Civil Engineer belong to the domain of Gravitational Force Field, GFF – formulated by Isaac Newton’s (1642 – 1727) Universal Law of Gravitation (ULG); and its dynamic characterization by Albert Einstein’s (1879 – 1955) General Theory of Relativity (see Einstein’s Unruly Hair). The GFF is a ubiquitous invisible field that affects everything on the Earth’s gravitation field. It defines all the downslope processes, and establishes the necessity of doing work to create upslope events (see Upslope Events and Downslope Processes). We vividly see the gravitational active force in fast flowing streams – and the gravitational restoration force in waves. In all of a Civil Engineer’s works – the universal gravitational acceleration ‘g’ is present (for all practical purposes, g = 9.81 m/s^2 on Earth’s surface). This value appears in almost every relation – with the mass or density (mass per unit volume) of a substance – together they define the weight of the gravitational force. To be in perspective, while GFF defines the Natural World; as a member of the Quantum Field (QF) family, the EMFF is ubiquitous and defines the world of electromagnetism.

Perhaps the dynamics of a coastal system – for that matter of any open system on Earth’s surface – can be viewed for convenience, in terms of external excitation or agitation forces on a system – and its internal balancing responses. Alternatively, this duo represents Action-Reaction Fields – in terms of Newton’s Equation of motion translated into Navier-Stokes Equation (see Seabed Roughness in Coastal Waters). I have presented an early version (shown in the image) of the force-response field concept quite a while ago while giving a seminar at UBC and later at the University of Central Florida – where force and response fields were shown separately defining the dynamics of a coastal system. For simplicity of discussions, I like to discuss the coastal dynamics in terms of five interactive Force Fields: (1) Metocean Force Field, MOFF; (2) Extraterrestrial Force Field, ETFF; (3) Land Drainage Force Field, LDFF; (4) Heat Exchange Force Field, HEFF; and (5) Frontal Wave Force Field, FWFF. The hydro-sediment-seabed dynamics responding to these imposed forces are discussed in these five force fields. I have also included a brief on the Structure Response Field (if structures are present).

A different way of looking at the Force Field Systems is through the Hydrodynamic Entropy as proposed in Entropy and Everything Else. All the force fields impart energy into water – transforming its dynamic characteristics. One very obvious example is the effect of a Frontal Wave Force Field – in transforming the dynamic characteristics of the medium – e.g. an oscillatory wave transforming into a translatory wave – generating the cascade of dissipation processes.

Let me attempt to refresh our understanding of a coastal system – based on pieces posted earlier: Coastal Water and Civil Engineering on our Seashore. A coastal system where the above interactive force fields function – is defined by two vertical boundaries and two horizontal boundaries (see more in Water Modeling piece). The horizontals are the water surface through which it interacts with air – and the seabed, where it interacts with bottom resistance or reactive force. The verticals are: the open water boundary through which it interacts with its neighbors – and the shoreline of the topographical resistance or reactive force. One can also define other systems for the convenience of analysis and purpose (see Entropy and Everything Else).

Metocean Force Field
  • The water surface, a contiguous portion of the water column, or the whole water depth is the playground of MOFF. Atmospheric boundary layer generated by the turbulence of wind pressure and shear-stress – causes the formation of a water boundary layer defined by logarithmic decay of the imparted energy from the water surface down into the water column. Different aspects of this force field are elaborated in the Encyclopedia Chapters, Beaufort Wind Scale; Wave Hindcasting; and in the WIDCANVAS pieces: Ocean Waves; Transformation of Waves; Linear Waves; Nonlinear Waves; Spectral Waves; Waves – Height, Period and Length; Characterizing Wave Asymmetry and Storm Surge. Referring to them may prove useful while trying to understand the actions of MOFF. Further, I have tried to present wave motion dynamics in poetic terms – in the Ocean Waves piece.
  • The MOFF forces the water body to respond in two ways with the GFF acting as the restoring force. To explain the two – I would rely on the Storm Surge piece posted earlier. The two are – the short surface wave and the long storm wave – both are generated by the dynamic pressure or kinetic energy exerted by MOFF; and their magnitudes are proportional to the square of the wind speed (Daniel Bernoulli, 1700 – 1782). The short surface wave transports the gained energy in progressive wave motions. Like the turbulent wind, these waves are highly irregular and spectral. The storm surge – on the other hand results from the hydrodynamic balance between the wind-induced water motion and the resistance of that motion by the coast. The result is the piling up of water at the coast – a standing long wave type oscillation. Along many coasts and bays around the world – MOFF causes seiche or meteo-tide that accentuates the high astronomical tide (see more on Storm Surge and Flood Barrier Systems).
  • Following the wave pieces posted earlier, a clarification of short (or short legged) and long (or long legged) waves are necessary. To do that, let us revisit the 3 fundamental parameters: wave height H (simply the height from trough to crest), local wave length L or wave period T (measured simply from crest to crest, L in space and T in time), and the local still water depth d. A wave is a true short wave – when d/L > 0.5. A wave is a true long wave when d/L < 0.05. In between, a wave transitions from short to the long.
  • Another important effect of MOFF is coastal upwelling and downwelling (see my 2017 Encyclopedia Chapter). These vertical water motions develop from a balance of wind-induced water motion, coastal resistance and the Coriolis Effect (see Characterizing Wave Asymmetry). Costal upwelling has a huge implication on modulating the weather pattern, and in fisheries population and abundance.

Extraterrestrial Force Field
  • The ETFF is caused by the Earth’s only satellite – the Moon, and the source of all our energy – the massive Sun (0.333 million times the mass of the Earth). The GFF of these three celestial masses defines the Earth-Moon-Sun System. An interaction takes place between the spinning Earth’s centrifugal outward force and the inward gravitational force of the system. All masses on Earth respond to the imposed forces – but the massive ocean water responds most (tidal effect on land masses is not effective, because land mass is heavy and rigid to distort; and atmospheric tide is hardly measurable because air density is too light). The result is the swelling of ocean water where outward force is the strongest and depletion where the outward force is the weakest. The generated wave is very large – a periodic rise and fall of the ocean water that has crests on the opposite sides and troughs in between. As the phase of the Earth-Moon-Sun system changes – the generated astronomical tidal wave propagates throughout the ocean. This ocean tide has a very small amplitude but a long period roughly equal to half day (see more on Ocean Waves). The strongest tide results when Moon-Sun acts in unison – resulting in fortnightly spring tide (during the Full and New Moons); and the weakest – the fortnightly neap tide occurs when Moon-Sun forces are out of phase (during the 1st and 3rd Quarters).
  • The generated ocean tide – small in amplitude – propagating into the shallow coastal shelf, gets amplified into higher amplitudes (see more on Transformation of Waves). Further into the coastal basins of different configurations and sizes at different latitudinal distances from the Equator, different components of the tidal wave responds differently to the natural periods of the basins. The result is that each tidal basin shows its unique response to the forced tide – some are high or low, some are semi-diurnal or diurnal in period, yet others are mixed in character. Further, as pointed in earlier pieces, the transformation of a long wave (tide, tsunami and storm surge) – is modulated by the processes of funneling, resonance and shoaling. One spectacular example of such transformation is the vigorous tidal actions – with tides coming from two ends of the Discovery Passage in British Columbia (I had the opportunity to model this tidal phenomena using Mike21 hydrodynamic modeling suite).
  • As outlined before in the Ocean Waves piece, the daily rise and fall of ocean water level attracted human imagination from ancient times, in particular because of its correlation with the phase of Moon. The workable explanations and predictions of the phenomenon, however came much later, and were worked out by many investigators. The notables among them were Galileo Galilei (1564 – 1642), Isaac Newton (1643 – 1727), Pierre-Simon Laplace (1749 – 1827) and Arthur Thomas Doodson (1890 – 1968). Their works led us to see tide as a composite mosaic of many tides – which can be decomposed into harmonic components of different periods, amplitudes and phases (that can be attributed to different generating forces). In very shallow water, some shallow-water harmonic components are highly amplified – giving birth to overtides and compound tides of different periods – different than the parent tide (e.g. my 1991 COPEDEC-PIANC paper). The rise and fall in water level is associated with oscillating horizontal movement of water causing tidal currents.

Land Drainage Force Field
  • In elaborating LDFF, I will rely mostly on WIDECANVAS pieces: Coastal River Delta and Managing Coastal Inlets; on the 2002 ASCE article  Alluvial Deltas; on my Ph.D. Dissertation; on the 1990 IEB journal paper; on the 1995 JCR paper; and on the 1994 and 1990 Elsevier papers. The LDFF – mainly active in river mouths, estuaries and contiguous coastal ocean – comes with three distinct forcing characteristics: (1) the discharge of lighter density fresh/brackish water on to the ambient ocean salt water; (2) the volume and seasonality of this fresh water discharge; and (3) the volume, seasonality of the sediment discharge and sediment granular size distribution. Let us attempt to elaborate these three aspects of LDFF briefly.
  • Density Driven Circulation. In absence of other force fields – riverine/estuarine fresh water flow rides on top of the heavy saline water – creating a stratified water column – with the top fresh water flowing outward into the sea – and bottom saline water moving in to balance the loss of fresh water. This process often with distinct halocline – termed as Estuarine Circulation – is ideal when the receiving coastal ocean is deep. When both MOFF and ETFF are active, the vertical stratification is destroyed by the MOFF induced mixing and circulation – and by tidal pumping of the ETFF. The effects often create horizontal stratification in shallow coastal oceans - with predominance of saline tide on one side, and fresh/brackish water on the other. As revealed in my 1990 works, a spectacular example of the horizontal stratification exists in the low-aspect-ratio (depth/width) coastal ocean at the Ganges-Brahmaputra-Meghna river mouth.
  • Seasonal Fresh Water Discharge. Seasonality of the freshwater outflow has a substantial influence on the river-mouth hydrodynamics – from pushing the freshwater front out into the sea during the high-flow period – to the modification of tidal wave – to letting salt-water to intrude into the lower river reaches during the lean-flow period. As I have shown in my 1995 IEB paper, the Seasonality Index (mean monthly/mean annual) of the Ganges River varies from 0.2 during the dry season to 3.5 during the monsoon. With such a high seasonal fluctuation – and together with actions of other rivers of the Ganges-Brahmaputra-Meghna system, the estuarine front is pushed out into the open ocean during the monsoon (1990 IEB journal paper).
  • Seasonal Sediment Delivery. Sediment transport is a power function of discharge – therefore the same scenarios of seasonality play a role in LDFF. However, there is a certain amount incoherence or hysteresis between water and sediment discharge (the 1995 IEB paper). Additionally, the characteristics of sediment granular distribution are also seasonal – determining the nature of delta progradation.

Heat Exchange Force Field
  • Compared to others, HEFF has a rather subtle – even negligible effect on the coastal hydrodynamics. Therefore no term related to HEFF appears in the general description of the Navier-Stokes Hydrodynamic Equation (e.g. in 2D depth-averaged modeling; but must account for it in 3D modeling). For aquatic lives – however, HEFF is very important – some are dependent on and look for warm waters – while for others cold water is important. Therefore - HEFF appears as an important parameter in the Water Quality Modeling. The water body interacts with the air-temperature above its surface – in gains or losses of heat according to the 2nd Law of Thermodynamics (e.g. high to low, one-way process; see Entropy and Everything Else). This process occurs in the Thermodynamic Force Field or TDFF domain (see The Quantum World) - in molecular diffusion mode. When hydrodynamic actions are strong due to such factors as wind and current - an extra two-way mixing mechanism is added, thus augmenting the TDFF process.
  • The TDFF process primarily gives rise to sharp lines of temperature difference or thermocline in the capacity of micro-circulation. Hydrodynamic actions in turbulent eddies (see Turbulence) is responsible for mixing of thermally stratified water bodies - destroying the thermocline in the process. Also, fast flowing streams or high energy fluid motions do give birth to heat in frictional dissipation of energy at the bed.
  • I only became aware of HEFF when I was working on a project tasked to assess hydrodynamic characteristics of Lynn Canal, Alaska. This deep U-shaped fjord is stratified with distinguishable thermocline. Analyses of long time-series data have revealed how the water column is thermally stratified with the nature of stratification changing shape and gradient responding to seasonal heat gain during Spring-Summer – and heat loss during Autumn-Winter. The investigated area of the Lynn Canal system is characterized by a stable thermal minimum zone at a depth of about 140 m – below which a rather stable layer of positive temperature-gradient (temperature increases with depth) resides – which remain rather irresponsive to the surface heat gain or loss at the surface. The top layer from surface to the thermal minimum, on the other hand is characterized by negative temperature gradient (temperature decreases with depth) – that changes in response to seasonal heat grain or loss. The implication of such a stratification is that dynamic mixing and circulation is confined within the top layer – with the rest of deep water column literally not knowing what happens at the top.

Frontal Wave Force Field
  • The FWFF is the most energetic and dramatic of all the coastal force fields. It generally pertains to the processes of Hydrodynamic Entropy – a term coined in Entropy and Everything Else. It is generated by the sudden release of built-up pressures or accumulated energy (the closest analogy of FWFF is the sonic boom in acoustics) by some triggers. Such accumulation of hydrodynamic energy could occur for many different reasons – impoundment and obstruction are two of them. But basically it happens when the rate of accumulation far exceeds the dissipation processes. The fundamentals of the FWFF are same as what are discussed in the Nature’s Action and Upslope Events and Downslope Processes. Let us attempt to understand the coastal FWFFs in simple terms. The four of them are: Tidal Bore, Tsunami, Flood Barrier Collapse and Storm Surge. Breaking of waves (see The Surf Zone) also creates FWFF – occurring rather regularly, the phenomenon defines beach evolution – in erosion, sedimentation and longshore sand transport. Many episodes of FWFF take people and authorities by surprise – as they are random in occurrence and remain beyond the purview of conventional forecasting.
  • The released FWFF pressure wave containing huge amounts of energy propagates at a celerity or speed of supercritical flow (c = square root of the product of ‘g’ and water depth; at 1-m water depth c = 3.1 m/s; compare that with the tranquil flow speed in the order of 0.5 m/s). The leading edge speed is even higher than supercritical flow ≈ some 1.4 to 2*c. A wave with such a high speed could propagate upstream, and cross and overtake obstacles and transports huge load of debris and sediments. The most spectacular examples of this incredible speed – are the recent 2004 Indonesia tsunami and the 2011 Japan tsunami (many of us witnessed the havoc of them in live coverage). Explained further and see more in Tsunami and Tsunami Forces.
  • Tidal Bore. USGS Circular 1022 (1988) presented a catalogue of world-wide distribution of tidal bores. Tidal bores form during spring tides when the range is the highest. With the combined affects of shoaling and funneling – the propagating tide becomes highly asymmetric so much so that at a certain time maintaining the wave-form becomes unsustainable – the result is the breaking of the accumulated pressures – giving birth to tidal bores. As happens with other long wave transformations – the accumulation lets the integration of all different component tidal frequencies into one pressure wave. The propagating bore with its breaking sound is very spectacular – and the phenomenon has given birth to wave-surfing and tourist attractions – with people flocking together to witness this Nature’s action. While on an investigation vessel, I was once in the middle of tidal bores in a tidal channel in Bangladesh southeast coast. With bores coming from two different directions, very low water suddenly rose to a high level as the bore passed. If one plots the tidal height and current – the sudden rise of these two parameters becomes very vivid. While tidal bores are spectacular to watch, they also pose navigation hazards to small vessels. Tidal bores transports sediments and reshuffles alluvial sand to create islets and scour holes within a very short period of time.
  • Tsunami. Let me highlight this FWFF based on the WIDECANVAS piece, Tsunami and Tsunami Forces and my 2006 Tsunami paper and 2008 ASCE article. Tsunami is a series of impulsive waves generated by sudden rupture of underwater earth’s crust, or by rapid slides of large landmass into water, or by sudden change in local atmospheric pressure (a phenomenon of MOFF). Following the alignment of disturbance, tsunamis radiate out directionally traveling long distances to reach coastal land – far and near. Tsunami characteristics change in response to the configurations of an enclosed basin or harbor. Like all waves, a small tsunami in deep water shoals to monstrous waves as it propagates into the shallow water. After breaking, Tsunami Run-ups flood coastal lands with enormous inbound and outbound speeds causing havoc and destruction. The arrival of Tsunami crest is preceded by the huge draw down or Sea Level Suck Out associated with the Tsunami trough. This phenomenon sucks out things from the shore out into the sea - exposing shoreline features - leaving many aquatic lives stranded in air. It catches offshore boats off-guard - and tragedies happen when people rush out to catch the stranded fishes.    
  • Flood Barrier Collapse. In the Flood Barrier Systems, we have seen different aspects of water barriers. Such barriers are designed to hold the propagating storm surges and other flood waves – to protect areas behind them. The stoppage of propagating waves – lets accumulation and integration of pressures causing a very high turning moment on the barrier systems. The barriers while designed to protect townships and properties – are also like a human-made hazard – in a sense that they pose high risk. But the benefit of taking the risk is worth, because letting the frequent onslaught and inundation has the action of taking a bite on people’s livelihoods. The catastrophic failure of the flood barrier system protecting New Orleans – during Hurricane Katrina in 2005 – is one of the reminders of how vulnerable a flood barrier can be.  
  • Storm Surge. Unlike other waves, storm surge (see more on Storm Surge) generated by Hurricane winds most often does not have a definite wave form – its crest is more pronounced than the trough. It develops, as a Hurricane low pressure system moves along or across on to a shore. The low pressure at the eye of the Hurricane causes reciprocal rise in water level, and together with wind-shear the system causes huge water mass to pile up along the coast – at the right side of the propagating storm in the northern hemisphere. The storm surge (note that a storm surge is not monochromatic, therefore some frequencies may resonate to the basin natural frequency) superimposed on astronomical tide generates the storm tide. The peak storm tide – a superimposition of high tide and peak storm surge – combined with high waves, causes large coastal flooding, erosion and damages.
  • What we have discussed so far is positive storm surge that occurs on the right side of a land-falling Hurricane in the Northern Hemisphere. A negative storm surge, popularly known as the Sea Level Blow Out – also occurs simultaneously on the left side. Spectacular example of this phenomenon was emptying of Tampa Bay during the 2017 Hurricane Irma. Some of the most devastating recent Hurricane storm surges that still haunt people’s memories are the August 23, 2005 Hurricane Katrina on the Louisiana coast at New Orleans, and the October 22, 2012 Hurricane Sandy on the New York and New Jersey coasts. During a project work mission, I got trapped in the middle of a huge cyclonic storm surge that wiped out an entire Bangladeshi coastal village named Urir Char in 1985. Among others, the 2011 WMO Guide to Storm Surge Forecasting (WMO No. 1076) is an excellent source on the science of storm surge.  

These force fields – apart from changing and affecting the Natural setting of Fluid, Solid and Life systems (see Warming Climate and Entropy), have forceful impacts on water-front and in-water civil engineering structures (see Civil Engineering on our Seashore). Aspects of them are discussed in several pieces posted earlier: Wave Forces on Slender Structures; Wave-Structure Interactions and Scour, Tsunami and Tsunami Forces; Flood Barrier Systems; Breakwater; and Uncertainty Propagation in Wave Loadings.

Let me finish this piece with a Koan:
People are the most important institution. Irrespective of the governing system – if those in power fail to uphold the trust and confidence of this institution – of people’s aspiration and wellbeing – then the governance turns into tyranny.


. . . . .


- by Dr. Dilip K. Barua, 25 August 2021



0 Comments

Uncertainty Propagation in Wave Loadings

4/30/2021

0 Comments

 
Picture
Picture
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. Who can be a better person than Ernest Hemingway (1899 – 1961) – to write this in his skillful way of crafting words in a lucid and attractive style? Sayings similar to this have been penned down in several pieces of WIDECANVAS in different contexts – not to advance is to fall back – change and refinement as a show of intelligence – maturity – adaptation . . . etc. But Hemingway touched upon a very important aspect of human mind. That being taken over by superiority or inferiority complex (see aspects of it, in Some Difficult Things) – inhibits a person’s ability to think and function normally. This piece is nothing about these complexes – but on something that define Nature – in this case, the transmission or propagation of errors or uncertainties in wave loadings on coastal structures. Uncertainty (U), in its simplest term, is just the lack of surety or absolute confidence in something.

Uncertainty Propagation (UP) refers to the transfer of uncertainties from the independent variables into the dependent variable – simply put, from the known to the unknown. It is transferred in an equation or relation – from the individual variables on right hand side – into the dependent variable on the left. More commonly the propagation process is referred to as error propagation. The two – error and uncertainty are often used interchangeably. In quantitative terms, while error refers to the difference between the measured and the true value – uncertainty refers to the deviation of an individual measurement from the arithmetic mean of a set of measurements. As we shall see, the magnitude of propagated uncertainty is a function of the type of equation (e.g. linear, non-linear, exponential, logarithmic, etc).

Uncertainty of a parameter implies that, if it is measured repeatedly – one would find that there is no single value – rather a range of random values accrue that deviate from the arithmetic mean (AM, µ) of the measured set. One needs a method or standardization to characterize the scattered deviations. If the deviations are distributed symmetrically about the arithmetic mean – then a Gaussian (German mathematician Carl Freidrich Gauss, 1777 – 1855) bell-shaped curve can be fitted. One property of such a distribution is defined as the Standard Deviation (SD). This is estimated as the square root of variance (defined as the mean of all deviations squared). If SD is normalized by dividing it with AM – the GD turns into Normal Distribution or ND. The normalized SD, σ/µ, termed as the Coefficient of Variation (CV) – is SD relative to AM. Its distribution follows the symmetry about the mean – and as a fraction or percentage, it covers both sides of the mean. It is like the unit of standard deviation – e.g. 1SD unit saying that 68.2% of the data are scattered on both sides of the mean. A high value of CV is the indication of a large scatter about the mean. CVs are due to nature of the variable in their random response to different forcing functions or kinetic energy (see Turbulence) – and are therefore termed as random uncertainty or simply uncertainty (see more on Uncertainty and Risk). It is the signature characteristic of the variable – and is due to many other factors including the applied measuring or sampling methods.

Not all variables follow the Gaussian distribution (GD), however. For example, a discrete random variable, like an episodic earthquake or tsunami event – are sparse and do not follow the rules of continuity, and is best described by Poisson Distribution (PD, in honor of French Mathematician Simeon Denis Poisson, 1781 – 1840). An ideal example of a continuous variable that follows ND is coastal water level. In this piece, all applied variables are assumed to follow ND. Here are some typical CVs from R Soulsby (1997): water density, ±0.2%; kinematic water viscosity, ±10%; sediment density, ±2%; sediment grain diameter, ±20%; water depth, ±5%; current speed, ±10%; current direction, ±10o; significant wave height, ±10%; wave period, ±10%; and wave direction, ±15o.

Error or uncertainty propagation technique has been in use for long time dating back to the now known method since 1974 (G Dalquist and A Bjorck). The most recent treatment of the subject can be found in BN Taylor and CE Kuyatt (1994) and in AIAA 1998 (The American Institute of Aeronautics and Astronautics). The propagated uncertainty has nothing to do with the scientific merit of a relation or equation; it is rather due to the characteristic or signature uncertainties of the independent variables – which according to the UP principle must propagate or transmit onto the dependent variable.

This piece is primarily based on four pieces posted earlier: Uncertainty and Risk; Wave Forces on Slender Structures; Breakwater; and The World of Numbers and Chances; and three of my papers:
  • 2015: Longshore Sand Transport – An Examination of Methods and Associated Uncertainties.
  • 2011: Role of Parameter Uncertainty in Design Decisions – Analytical Assessment for a Coastal Breakwater and Harbor Entrance Sedimentation. ISOPE-2011-TPC-230, Hawaii (paper not presented).
  • 2008: Wave Loads on Piles – Spectral versus Monochromatic Approach.

Before moving on, let me try to demonstrate how UP principle works – by discussing a simple example. Suppose, we consider an equation, X = Y^2 * Z. Let us say, the variables Y and Z on the right hand side of the equation have known CVs: ± y, and ± z, respectively. How to estimate the CV of X? According to the UP principle, the CV of X can be determined as the square root of x^2 = 2^2*y^2 + z^2. As an example, suppose, y = ±10%, and z = ±5%; then x must be equal to 20.62%.

Further, a pertinent question must be answered. Why Uncertainty? or Why Uncertainty Propagation? The relevance of the questions stems from the quests to develop confidence of the relations or equations one uses to compute and estimate parameters for everything – from the science of Nature to Social Interactions to Engineering and Technology. These relations developed by investigators after painstaking pursuits convey theories and principles mostly on deterministic paradigm. But, things in Nature are hardly deterministic – which means the independent variables on which a relation is based – suffer from uncertainties of some kind due to their stochastic characteristics and variability. These uncertainties associated with the independent variables must be accounted for in the dependent variable or computed unknown parameter. Uncertainty propagation method developed over a period of many years – gives answer to the questions (see more on Uncertainty and Risk, and The World of Numbers and Chances).

In engineering design processes, the traditional method of accounting for uncertainty is done simply by including some redundancy in the system – by the so-called factors of safety – conspicuously described and/or inconspicuously embedded in some practices (for example, using maximum load and minimum strength; and summation of different loads together although they may not occur simultaneously). Further elaboration on coastal design processes can be found in Oumeraci et al (1999), Burcharth (2003) and Pilarczyk (2003). They scaled the processes of design as: Level 0 – deterministic approach; Level I – quasi-probabilistic approach; Level II – approximate probabilistic approach; and Level III – fully probabilistic approach. In the Level 0 approach, parameter uncertainties are not accounted for, instead experience and professional judgment are relied upon to implant redundancy. This practice as a way of developing confidence or assurance – represents in reality – a process of introducing another layer of uncertainty – partly because of heuristics associated with judgments. Or in another interpretation, it amounts to over-designing structure elements at the expense of high cost. For the other three Levels, a load-strength reliability function is defined in different scales to account for parameter uncertainties.

A note on significant wave height uncertainty is warranted. Although a typical ±10% is recommended by Soulsby, in reality the uncertainty can be varied. The reasons can be traced to how the local design significant wave height is estimated. Some likely methods that affect uncertainty are: (1) the duration, resolution and proximity of measurements to the structure; (2) extremal analysis of measurements to derive design waves; (3) in absence of measurements, applied analytical hindcasting or numerical methods to estimate wave parameters; and (4) applied wave transformation routines or modeling. Due to these diverse factors affecting uncertainty, instead of considering one uncertainty, this piece covers a range from10 to 30%.

Uncertainty of Wave Loading on Vertical Pile
This portion of the piece starts with 2008 ISOPE paper and Wave Forces on Slender Structures. Unbroken waves passing across the location of a slender structure (when L/D < 1/5; L is local wave length and D is structure dimension perpendicular to the direction of force) cause two different types of horizontal forces on it. The basis of determining them is the Morison equation (Morison and others 1950). Known as the drag force in the direction of velocity, the first is due to the difference in local horizontal velocity head or dynamic pressure between the stoss and the wake sides of structure. The second, the inertial force is caused by the resistance of structure to the local horizontal water particle acceleration.

Both of the Morison Forces have their roots in Bernoulli Theorem (Daniel Bernoulli; 1700 – 1782) – and as one can imagine, they are a function of water density – and of course, the structure size. The horizontal Drag Force: a function of water density, structure dimension perpendicular to the flow, water particle orbital velocity squared, and a drag coefficient. The horizontal Inertial Force: a function of water density, structure cross-sectional area, water particle orbital acceleration, and an inertial coefficient.

To demonstrate UP of wave loadings at the water surface on a cylindrical vertical pile of 1 meter diameter – this piece relies on the same example wave discussed in Linear Waves; Nonlinear Waves; Spectral Waves; Waves – Height, Period and Length and Characterizing Wave Asymmetry. This wave, H= 1.0 m; T = 10 second; d = 10 m; has a local wave length, L = 70.9 m and Ursell Number (Fritz Joseph Ursell; 1923 – 2012) = 5.1; indicating that the wave can be treated as a linear wave at this depth. Other used and estimated parameters are: water density = 1025 kg/m^3; amplitude of horizontal orbital velocity at surface = 0.56 m/s; and amplitude of horizontal orbital acceleration at surface = 0.44 m/s^2. In addition, while using most typical uncertainties proposed by Soulsby – the Us of wave length, orbital velocity and acceleration have no typical values – therefore they are derived in the 2011 paper and in this piece applying the basic UP principle.

The results of uncertainties in wave loadings are shown in the two presented images – one for the drag force (UDF), the other for inertial force (UIF). They are shown as a function of uncertainties in measured wave heights (U_H) for U_water density = 0.2% and U_linear dimension = 5%, with estimated U_cylindrical pile area = 10%. Since the uncertainties of coefficients (U_Cd and U_Cm) are not known, the images show three cases of them, 10%, 20% and 30%. Here are some numbers for U_H = 10% and 30%.
  • UDF for U_H = 10%. U_orbital velocity = 24.5%. UDF = 50.3% (for U_Cd = 10%); UDF = 53.2% (for U_Cd = 20%); and UDF = 57.7% (for U_Cd = 30%).
  • UDF for U_H = 30%. U_orbital velocity = 37.4%. UDF = 75.7% (for U_Cd = 10%); UDF = 77.6% (for U_Cd = 20%); and UDF = 80.8% (for U_Cd = 30%).
  • UIF at U_H = 10%. U_orbital acceleration = 22.4%. UIF = 26.5% (for U_Cm = 10%); UIF = 31.6% (for U_Cm = 20%); and UIF = 38.7% (for U_Cm = 30%).
  • UIF at U_H = 30%. U_orbital acceleration = 36.1%. UIF = 38.7% (for U_Cm = 10%); UIF = 42.4% (for U_Cm = 20%); and UIF = 48.0% (for U_Cm = 30%).

The shown uncertainties indicate that they increase nonlinearly as the U_H increases; and that nonlinearity associated with drag force is a showcase of higher uncertainty than the corresponding inertial forces.

Uncertainty of Wave Loading on Breakwater Armor Stone
This portion of the piece primarily depends on materials developed and presented in the Breakwater (BW) piece posted earlier, as wells as on my 2011 paper. The state-of-the-art techniques in determining armor stone masses or sizes of rubble-mound breakwater and shore protection measures – rely either on Hudson Equation (RY Hudson 1958) or on VDM Formula (JW Van der Meer 1988). The applicability and relative merits of the two methods are elaborated in the Breakwater piece.

For simplicity of analysis, I will focus on the uncertainty of Hudson Equation. This equation relates Stability Number to the product of a stability coefficient (KD) and a BW side slope factor. The equation provides estimates of median armor stone mass as: a product of the stone density and wave height cubed – divided by the product of KD, side slope factor, and relative stone density cubed. It is assumed that armor stone is forced by H = 1.0 m on the BW seaside slope = 1V:2H; with stone density = 2650 kg/m^3 and water density = 1025 kg/m^3 giving a relative stone density = 2.59. The uncertainties of relative density and side slope factor are not known, they are estimated at 2.01% and 7.1% using basic UP principle.

The crux of the problem appears on defining the KD values. The recommended KDs vary from 1.6 for breaking to 4.0 for non-breaking wave forcing (USACE, 1984). Melby and Mlaker (1997) reported that the KD values have uncertainty of some ±25%. In this piece the uncertainties median armor stone mass U_M50 for KD uncertainties ranging from ±10% to ±25% are investigated. Some estimated numbers are:
  • U_M50 at U_H = 10%. For U_KD = 10%, U_M50 = 33.0%. For U_KD = 25%, U_M50 = 40.2%.
  • U_M50 at U_H = 30%. For U_KD = 10%, U_M50 = 91.1%. For U_KD = 25%, U_M50 = 93.9%.

These estimates show the overwhelming influence of wave height; therefore utmost care is warranted to estimate it – such that local design wave conditions and scenarios are properly investigated and accounted for.

The Koan of this piece on this International Jazz Day:
What seems to be perfect to an ordinary eye – is never finished, never perfect in the creator’s eye. The creative works continuously explore, experiment and search for something – that never comes to the satisfaction of the creator.

.  .  .  .  .

- by Dr. Dilip K. Barua, 30 April 2021





0 Comments

Harbor Sedimentation

11/23/2020

0 Comments

 
Picture
A harbor is a water basin of tranquil or tolerable wave and current climate, and of sufficient water depth in which a maritime or inland vessel (let us use this general term, but when Dead Weight Tonnage or DWT ≥ 500, a vessel is known as a ship) can operate safely. Maritime harbors are selected from the deep shoreline areas sheltered naturally, or are created artificially (see Flood Barrier Systems). The artificial harbors are configured and engineered within an ambient water body at the shoreline by dredging and installing suitable structures (see Breakwater). The purpose in each case is to locate a maritime port or marina within it (see Ship Motion and Mooring Restraints; and Propwash). For the convenience of design and operation, a harbor is classified and distinguished as deep-draft (water depth > 15 ft or 4.6 m), and shallow-draft or small-craft (water depth < 15 ft or 4.6 m). Many artificial harbors have one inlet to allow influx and efflux of water and sediment into the basin (a semi-enclosed basin that allows restricted/controlled entry and exit of matter and energy, see Upslope Events and Downslope Processes); and entry and exit of vessels. The layout of the structure – and the location, width and depth of the approach channel as well as of the harbor itself are designed by addressing such constraints as – ambient wave, current and sediment climates, and the largest allowable vessel designed to call at the port.

In this piece, let us attempt to discuss and understand the sedimentation rates of harbors in simple terms. Sediment transport dynamics and sedimentation pose a complicated problem. But ballpark estimates and numbers are always handy and useful to conceive and study the feasibility of a project. To that end, some methods and pieces of data are selected and blended in this piece. The purpose is to demonstrate the usefulness of some simple analytical models that can be used as a handy tool to picture a high-level impression of possible harbor sedimentation. The magnitude of sedimentation problem can be appreciated if one considers worldwide dredging operations. Maintaining enough water depth within the harbor and keeping the approach channels navigable – are some of the requirements that let flourishing of huge dredging industries. These two major demands, together with the erosion prevention and value-adding beach nourishment works, and others – have yielded the global dredging industry to an annual turnover of some $5.6 billion. I will try to come back to discussing different interesting aspects of dredging at a later time.

Among others, this piece is primarily based on: RB Krone 1962; Delft Hydraulics publications (E Allersma 1982; WD Eysink and H Vermass 1983 and WD Eysink 1989); R Soulsby 1997; USACE 2002 EM 1110-2-1100 (Part III) and 2006 EM 1110-2-1110 (Part II); I Smith 2006; and my own works on fine sediments and sedimentation (Fluid Mud 2008; and Settling Velocity of Natural Sediments 2004) published in the Journal of Hydraulic Engineering, and Journal of Waterway, Port, Coastal and Ocean Engineering, respectively; Seabed Roughness; and two papers presented at the International Symposiums on Coastal Ocean Space Utilization: COSU 1995 and COSU 1993, and my paper at the 24th International Conference on Coastal Engineering, Kobe, Japan, ICCE 1994. The Hydraulics of Sediment Transport and Resistance to Flow posted earlier laid out some fundamentals of sediment behavior and transport.

Configuring the layout of a harbor entrance needs careful optimization exercises and analyses – on the one hand, it has to provide effective diffractive energy dissipation of incoming waves – on the other, it has to minimize the formation and strength of current eddies at the entrance, and sedimentation inside the basin. Filling and emptying tidal currents at a harbor entrance are usually an order of magnitude less than the ambient tidal current. Their magnitudes depend on the size of the basin and entrance. Eddies – more vigorous during changing current directions – are undesirable for at least two primary reasons. The first is to minimize navigation hazards – to vessels entering and leaving the port. The second is to minimize scour and formation of sandy bars. Exercises to engineer a detailed and optimal layout include physical scale modeling and/or numerical modeling. Such exercises, especially the efforts of numerical modeling (see Water Modeling) are becoming increasingly common not only for optimizing harbor entrance layout, but also for visualizing the sediment morphodynamics, sedimentation and other aspects of harbor hydraulics (e.g. Ports 2013 paper).

Before moving on, let us have some words on tidal action. It is assumed that actions attributed to short-waves (see Ocean Waves and Linear Waves) and vessel generated wake-waves are minimal – a valid assumption for all harbors. The main concern of harbor sedimentation processes is the behavior of Suspended Sediment Concentration (SSC) that has a positive gradient from low at top to high at bottom of the water column. As flood and ebb currents reach threshold for erosion and resuspension during a tidal period – sediments are picked up from the seabed and are transported (coarser fraction close to the bed; fines up in the water column) back and forth by the current. Similar but opposite episodes happen, as flood and ebb currents slow down to reach deposition threshold. Suspended sediments have the opportunity to settle down during such slack water periods (SWP) – with more chances for sediments close to the bed than those up in the water column. However, there is often a settlement lag or incoherence between the slack water and actual deposition (see more in my 1990 Elsevier paper).

Let us now dive down into the core issue of this piece. A harbor faces at least two types of major sedimentation problems. The first is the formation of localized shoals or sandbars at and around the entrance due to the scouring actions of eddies, and the sudden drop in flow velocities. These shoals mostly of sandy materials are often attached to the shoreline as a side bar or develop as middle bar(s). They mostly develop when the harbor entrance is located on littoral shores (see Managing Coastal Inlets) – and are usually termed as flood-tidal and ebb-tidal deltas (see Coastal River Delta and Managing Coastal Inlets). The dynamics of such sandy shoals, bars or deltas can best be discerned from the piece on The Hydraulics of Sediment Transport.

The focus of this piece is on the second type of sedimentation problem. It is the sedimentation of fine sediments within the harbor basin. This sedimentation (a phenomenon of suspended sediments having very low settling velocities) is somewhat uniform due to the relatively weak circulation within the harbor basin – but is often less in areas of relatively high currents than in remote areas of stagnant water. It is highly problematic when a harbor is located within Turbidity Maximum (TM) zone (1990 Elsevier paper). The presence of TM in the tide-dominated east shore channels and waterways of the Ganges-Brahmaputra-Meghna (GBM) River mouth has shown very high siltation rates of fine sediments (1997 Taylor & Francis paper). Observations at the mouth of Karnafuli River estuary showed a positive correlation between the Surface Suspended Sediment Concentration (SSSC) and tidal range (TR) – indicating that the resuspension actions of tidal currents are directly related to tidal range. This correlation ends up yielding an exponential relation between SSSC and TR (ICCE 1994). The fitted relation shows, for example, that at mean neap-tidal TR = 1.7 m, SSSC = 154 mg/L; and at mean spring tidal TR = 3.8 m, SSSC = 1912 mg/L.

The gradual but slow filling up of the basin is highly dependent on the concentration of sediment suspended (in textures of fine sand, silt and clay) of influx water. For the convenience of discussion, let us spilt the piece in two: (1) the first is on sedimentation of granular (silt-sized particles) materials; and (2) the second is on sedimentation of silty/clayey materials that are affected by aggregation and flocculation. The provided estimates represent only a high-level first-order magnitude – afforded by some approximations and assumptions. And to be simple yet realistic of a deep-draft harbor, let us use most of the same inlet/basin/tide parameters (inlet depth 15 m; harbor depth 10 m; semi-diurnal tidal period 12.42 hours; and tidal amplitude 1 m) as described in Managing Coastal Inlets – for a large harbor area of 1 million square meter; and an inlet length and width of 100 m and 300 m, respectively. A tide of this amplitude at 15 m water depth, causes a passing peak depth-averaged current of about 0.81 m/s in front of the harbor. A rough estimate shows that for a harbor of this size at this tidal condition – the turnover time (the time required to tidal flushing out 63% of the harbor water volume) is about 3.2 days.

Sedimentation of Suspended Particulates
  • Let us attempt to make a simple first-order estimate for a single inlet harbor that has no freshwater drainage into it. It is assumed the system is well-mixed vertically without any density stratification. In such harbors, the volumetric sedimentation rates can simply be expressed as a linear function of sediment influx, and a factor attributed to the fraction of sediments that actually settles into the basin. It is also a linear and reciprocal function of dry bulk density of the suspended deposits. One can also assign a calibration factor to account for uncertainty of assumptions, approximations, the approach itself, and for the spatial and temporal distributions of sedimentation.
  • The first, the sediment influx is a function of SSC that are transported by the total volume of water exchanged during the tidal cycle. This volume, in turn depends on the tidal prism forced into the harbor, and the horizontal exchange of water induced by passing current at the inlet entrance (a function of passing current, inlet width and depth). The Volumetric Suspended Sediment Concentration (VSSC) is reciprocal to the porosity of water-sediment mixture (the ratio of void volume filled with water to the total volume). When VSSC is multiplied by the density of sediment particulates, the Mass Suspended Sediment Concentration (MSSC) is obtained.
  • The second, the settling factor is a function of (1) particle settling velocity, (2) average basin water depth, (3) threshold velocity for sediment settlement, and (4) the window of time or SWP during a tidal cycle when settling occurs. In this simple example, one silt-sized particulate is considered – the median diameter of which is assumed as 1/32 mm or 0.03125 mm (corresponding to the demarcation defining the coarse and medium silts) – with no sand content. The settling velocity of this fine silty material is 0.084 cm/s (according to Rubey 1933; see 2004).
  • In the density of sediment-water mixture, let us assume the sediment granular density as 2650 kg/m^3 (typical of silty materials of quartz mineral origin) – and the water density as 1025 kg/m^3 (typical of most coastal water; note this density may be high for the some of the considered cases, but the errors caused by using different water densities are very negligible, see Coastal Water). For all-silt suspended sediment, the dry bulk density of the deposit – is a function of these two parameters, as well as of packing.
  • Having laid out these fundamental parameters, let us attempt to make some estimates. The included image shows the annual volume of silt-sized sediment deposits as a function of MSSC. It is applicable for parameters discussed earlier with the assumption that the time window available for settling SWP = 10 min during the tidal cycle. As an example, if an MSSC of 1325 mg/L persists throughout the year, the total annual deposit volume will be about 0.10 million m^3. Such a sedimentation rate is no reflection – however, of the usual differences and variations expected in space (e.g. flowing channel vs sheltered areas) and in time (e.g. spring vs neap tides; and dry vs wet season). Based on actual field conditions, sedimentation volume (which can be discerned from dredged volumes; or from repeated bathymetric surveys) and harbor activities (caused by vessel propwash with consequent erosion, resuspension and deposition of sediments; see Propwash), one can apply a factor to calibrate the estimated sedimentation.

Sedimentation of Aggregated Particulates
This part of the piece is based mostly on my published papers: the 1994 ICCE 24th; and the COSU 1993 and 1995 papers. The published works are based on some site-specific information; and are therefore primarily applicable for situations and conditions in which they were derived. But the approach and methodology can be applied elsewhere with some assumptions for cases – of tide-dominated estuaries, bays and waterways dominated by fine seabed sediments. Let us attempt to see some applications of the gained experience in simple terms. They are supplemented by my discussions in 2004 and 2008 publications.
  • The first approach relies on ICCE 1994 paper and the Fluid Mud 2008 discussion. To be realistic of the annual variability, one needs to consider both spring-neap tidal and seasonal parameters. To that end, the used values are: neap and spring tidal TRs as 1.7 m and 4.0 m, respectively, and the wet and dry season salinities as 2.0 ppt (parts per thousand) and 4.0 ppt, respectively. Another assumption has to be made – it is on SWP during which tidal currents slows down below the sedimentation threshold. Experience tells that neap tidal SWP is longer than the spring tidal SWP; therefore let us assume neap SWP = 15 min and spring SWP = 5 min. Let us also consider the neap and spring tidal SSSC as the initial concentrations required for the relations proposed in 2008. With these assumptions and applied parameters as if they persist throughout the year, the total annual sedimentation volume turns out to be about 0.39 million m^3.
  • The second approach (COSU 1993 and 1995) is primarily based on the modeled sedimentation rates observed in some areas of the GBM mouth – therefore is highly site specific. They were done in contexts of determining the height of sedimentation at which impoldering (a Dutch term referring to the process of reclaiming and developing the silted coastal shores for rice farming – by closing and isolating the area from saline coastal water flooding by installing earthen dikes and sluices) can be initiated. In this case the used relation giving annual sedimentation height relies on initial water depth, and a coefficient. Let me cite examples for two sites – in one, mainly dominated by tide and muddy seabed; and the other dominated by GBM fresh water flow and sand/silty seabed. The measured SSC at the two sites differ by an order of magnitude – the first is about 4230 mg/L, the second is about 126 mg/L. Note that the first area was very sheltered – which means, water flooding the tidal flat and gullies highly laden with SSC was ideal for settling sediments. If one attempts to extrapolate the estimated deposition to the whole harbor basin – applying the assumed conditions and circumstances, the estimated volumes turns out to be 5.42 million m^3 and 0.23 million m^3, respectively.
In summary, the discussed ballpark estimates varying from 0.10 to 0.39 million m^3 – present a clue on what sedimentation to expect when planning the feasibility of a harbor. One referral case in point (see Ports 2013 paper) is the modeled annual sedimentation volume of 0.025 million m^3 – concentrated mostly in entrance areas of the Salt Ponds Inlet harbor (size, 0.1 million m^2) in Virginia, USA. This was the case of a small harbor of sedimentary environment dominated by fine sands, not adequately sheltered from wave actions. The estimate of 5.42 million m^3 – rather unusually high, is an indication of some very calm and stagnant areas – flooded by very high SSC of flocculated sediments. Such a situation is unlikely to happen in harbor conditions.

Before finishing I like to tell a story the Buddha (563 – 483 BCE) told to a congregation of monks and lay people. He did this in context of the 4th Buddhist precept of Right Speech (see Revisiting the Jataka Morals – 2). Once an angry and hateful person used very harsh and abusive words to the Buddha. Instead of getting provoked, the Buddha calmly listened and told the man to take back his abusive outburst. The man was dumbfounded hearing such an unusual reaction. The Buddha then said: Hold it there. If a person gives a gift to another, and if the second person refuses to accept the gift, to whom the gift belongs? The man replied: it belongs to the first person. The Buddha said: so, my friend you must take back the abusive language you have used, because it belongs to you and I refuse to accept it. Then the Buddha delivered some words of wisdom to the congregation: if someone spits against the sky, the spittle returns back to the spitter. So, be mindful. If you use an abusive or unwholesome speech, it gets back at you.

.  .  .  .  .


- by Dr. Dilip K. Barua, 23 November 2020




0 Comments

Breakwater

6/19/2020

0 Comments

 
Picture
Ever since the 1978 failure of a massive breakwater (BW) in Port Sines, Portugal – coastal engineers around the world went back to reviewing the BW design approaches and methods. During my studies at Delft in 1982 – the event and the possible lapses and causes of its failure – came for discussions again and again in coastal engineering lectures. The Sines Deepwater (~ 50 m) BW was designed and constructed of massive 42 tonne armor-layer dolos (dolos are pre-fab concrete units, designed to achieve good interlocks and stability when placed randomly – each unit has three stems, the central and the two twisted ones on ends) to withstand waves up to 100-year extreme of 11 m high significant wave (see Spectral Waves for definition). But near the end of the construction period – a storm that registered a lower wave height, dislodged about 2/3rds of the units – and some subsequent less powerful storms did the rest of the work by destroying the BW.

The risk of failure, the scale and cost of such massive structures – have generated renewed research interests in coastal labs around the world. Physical scale modeling tests – such as those in the massive Delta Flume in Emmeloord (the Netherlands), and in the CERC (Coastal Engineering Research Center) facilities in Vicksburg, Mississippi were some of the examples. The efforts resulted in the refinement of existing formulae and coefficients, and yielded new ones.

In this piece let us attempt to understand some interesting aspects of BW engineering. Engineering literature is full of materials on various aspects of BW planning, loading, stability, designs, and effects assessments. Among them, the following lists have most of the resources one needs for breakwater engineering: (1) Random Seas and Design of Maritime Structures (Y Goda 2000); the USACE (United States Army Corps of Engineers) (2) 1984 Shore Protection Manual (SPM); and its reincarnation, Coastal Engineering Manuals (CEM): (3) the 2002 CEM (EM 1110-2-1100 Part II; Chap 8 – Hydrodynamic Analysis and Design Conditions), (4) the 2006 CEM (EM 1110-2-1100 Part VI; Chap 5 – Fundamentals of Design, and Chap 6 – Reliability Based Design of Coastal Structures); (5) the 2007 Rock Manual (C683, the use of rock in hydraulic engineering, 2nd ed.) of EUROCODE, CIRIA (Construction Industry Research and Information Association) and CUR (Civil Engineering Research and Codes, the Netherlands); the JW Van der Meer publications, starting with his (6) 1988 Ph.D. Diss. (Rock slopes and gravel beaches under wave attack, Delft Univ. of Technology, the Netherlands, Delft Publication No. 396); and his (7) 1992 Delft Lecture Note, Conceptual Design of Rubble Mound Breakwaters; (8) RY Hudson 1958 (Design of quarry-stone cover layers of rubble-mound breakwaters, hydraulic laboratory investigation, Research Report 2-2, Waterways Experiment Station, Vicksburg, MS); and (9) R Iribarren 1938 (Una Formula Para el Calculo de los Digues de Escollera, Technical Report HE 116-295, University of California, Berkeley, CA). On 2D Wave Diffraction Modeling suite: (10) the 2005 Bouss-2D Wave Model in SMS, ERDC/CHL CHETN-I-69/70; (11) the 2007 Delft3D-Wave, TU Delft and Delft Hydraulics; and (12) the 2008 Waves Modules, DHI (Danish Hydraulic Institute). Different aspects of BW engineering are highly elaborate – I will briefly focus on some selected portions of them in simple terms. An overview of civil engineering works on our seashore (see Civil Engineering on our Seashore), and of barrier systems engineering (see Flood Barrier Systems) were posted earlier – that laid out some basics of coastal engineering (CE) works.

A BW generally refers to an in-water self-standing coastal protection or defense structure – shore-attached, detached or offshore. It belongs to the Water Barrier group of structures (see Flood Barrier Systems) in coastal engineering; and may define a system when multiple BWs and functions are integrated together as a package. The purpose of a BW is to diffract, break and obstruct the continuity of an incoming wave – in order to create a tranquil or shadow zone of minimal or no wave activities behind it. Although the term is primarily applied to describe coastal protection or defense structures against wave attack, the underlying concept is similar – for example, in breaking the flow of a river current to protect an inland harbor or river bank erosion from current forcing (collectively known as river training structures). The functional properties of a BW are achieved by designing a suitable layout and dimension – the size of which falls into the definition of a large structure – with its dimension, D scaling with the local wave length, L such that D/L > 1/5 (see Wave Forces on Slender Structures). This means that a BW has a significant presence in the surrounding hydrodynamic field – in diffraction, deflection, reflection, transmission, absorption and scattering of waves, currents and alluvial sediment transports and dispersion. One important aspect of BW configuration – in terms of hydrodynamic loading – is the convergence and divergence of wave energies. The convergence – in particular, at the convex bends and at BW heads – implies that those places must be stronger than the rest of the structure to withstand amplified wave loading.

Breakwater Types and Functions
The necessity for a minimal wave zone can be varied – in port applications, the purpose is to create a harbor where vessels and ships (see Ship Motion and Mooring Restraints) can safely navigate in and out – and moor to load and unload cargoes and people. The second most important necessity is to protect a shore from wave erosion and beach degradation, or to prevent entry of unwanted sediments into a harbor. BWs are classified as two basic types: Floating and Fixed. Floating BWs are pontoons tethered in position either by guide piles, or by chains anchored to the seafloor. A pontoon acts as a deterrent of, or as a low-pass filter to the incident waves (mostly short-periods ~ 4 s) – with the additional use as a loading/unloading platform. They are mostly applied in low wave-climate areas to design marinas where small pleasure boats can be safely secured on several inside finger floats. Different aspects of this type of BW – incident wave attenuation efficiency and transmission are discussed in the Wave Structure Interactions & Scour piece. The primary focus of this piece is Fixed BW.

Breakwaters anchored to and founded on the seabed – as statically or dynamically stable hydraulic structure define a fixed BW. Depending on the scale of project and purpose, as well as on the prevailing hydrodynamic and wave climate, a fixed BW structure can be built by sheet pile walls, caissons (a concrete box or boxes filled with sand), rubble mounds, or combinations of them. Typically, caisson breakwaters can be a vertical face type, a composite type when the caisson sits on top of a raised platform built by rocks/rubbles, a perforated vertical face type (perforations eliminate wave reflection from the vertical wall), and armored caisson type (the seaside of the caisson is protected by rock armor units). Both sheet pile and caisson structures need quarry rock scour protection at seabed.

Fixed BW can be classified according to the magnitude of a Stability Number – defined as a ratio of wave height (H) to the product of armor unit relative density (Δ) and a characteristic dimension (D) of the unit or N_s = H/ΔD. When N_s ≤ 1, it falls into the category of a statically stable monolithic massive defense structure such as caissons and seawalls (in this case D is the height or width of the structure). All other structures including the rubble mounds and the shoreline itself are mostly dynamically stable with N_s > 1 (for rubble mounds, D = D_n50, the 50th percentile nominal rock diameter). In a dynamically stable structure, hydrodynamic forcing is assumed to cause profile changes in various degrees – with the displacements of rocks from a relatively unstable position to new stability. While this process goes on, the integrity of the structure remain largely unaffected or intact. However such structures succumb to failure – when large amounts of armor rocks are broken or are carried away exposing the underlayers and foundational core.

BWs can be designated into four vertical zones according to their exposure to the hydrodynamic loading. They are: the Zone I – the bottom foundational zone below the level of Mean Low Water (MLW); the Zone II – the tidal zone from MLW to the Mean High Water (MHW), loading on this zone is very frequent and determines the longterm structural stability; the Zone III – the higher high water zone from MHW to the design level, wave attack on this zone is less frequent but of high impact; and the top Zone IV subjected to the effects of runup and overtopping.

Shore perpendicular breakwaters attached to the shore are mostly conceived to serve beach management purposes. They are termed as Groins or Groin Systems, and have a range of typical shapes (Straight, T, Y, L, etc.) – the selection of which depend on the purpose and effectiveness. These types of breakwaters interrupt littoral transport, and attenuate the effects of onshore waves. They are usually low crested and are constructed of low-cost quarry rocks and runs. Literature and manuals suggest different planning approaches of such structures. For Groin Systems, the length of each unit is usually transitioned from short at the updrift side to the full length at the downdrift side. The spacing between each Groin usually scales with the length: the spacing is some 2 to 3 times the Groin length.

Shore parallel detached breakwaters – as a way to manage beach erosion and littoral transport – are often identified according to its location with respect to the shoreline. A parameter (L) defining a ratio of breakwater distance from the shoreline (X_off), and the 80% of surf zone width (S_80, note that about 80% of littoral transport occurs within the surf zone; see The Surf Zone processes), or L = X_off/S_80. When L ≤ 0.5, the breakwater is classified as a Beach BW (it protects the foreshore without significantly altering the littoral transport). A Coastal BW is defined when 0.5 < L ≤ 2.0 (intervenes the littoral transport to prevent beach erosion). At L > 2.0, it is known as Offshore BW. This type must be highly robust to withstand high waves and to interrupt and diffract incoming waves.


A fixed BW can also be classified according to the elevation of its crest from the still water level. In broad terms, two types can be identified: the emergent and the low crested breakwaters (LCB). The crest height of an emergent BW is usually high to prevent overtopping or to allow limited spray (breaking waves spray out into air) overtopping – and must take account of design storm surge height, wave set-up, wave run-up, height to compensate BW settlement and a freeboard on top of the design water level. If installed, the concrete cap of an emergent BW (usually used for utilitarian purposes) must be protected against overtopping damages by providing a crown wall. LCBs have various forms and heights depending on the desired limitations of overtopping – and the requirement to achieve certain wave attenuation goals. There are those that allow green overtopping (submerged BW acts as a weir transmitting a portion of the wave energy), and those that emerge and marginally submerge depending on the water level – thus allowing different categories of overtopping.

Wave Diffraction by Configuring the BW Layout
Diffraction is a process of bending the wave energy by obstructing its direct or head-on propagation. Waves lose a portion or all of its energy while bending from the illuminating zone to the shadows. Engineers use this property of wave behavior to design an area of low-energy wave environment so that vessels and ships can moor safely to load/unload cargoes and people – or to protect a shoreline from high energy wave actions and erosions. The ratio of diffracted (Hd) and incident (Hi) wave heights defines the diffraction coefficient, Cd = Hd/Hi.

Characterization of the incident hydrodynamic field in quantitative terms must begin with a clear qualitative understanding of the wave and sediment climate systems of the area. The a-group and b-group of activities shown in the coastal engineering envelope (see Civil Engineering on our Seashore) are the ones to start with. They include: use of longterm timeseries measurements from moored buoy or other platforms (in absence of such measurements, Wave Hindcasting techniques are used, if necessary based on Beaufort Wind Scale) together with analytical and physical and/or numerical modeling.

Before the times of digital computation and numerical modeling, engineers used diffraction diagrams and analytical models to determine diffracted wave heights. The Weigel (RL Weigel 1962) diffraction diagrams included in the SPMs and CEMs, and simple analytical models (Goda and others) are some examples. A simple illustration using the Goda relation, would show that an illuminating (a) 3-m, 8-sec head-on wave at 10-m water depth, would diffract to 0.34 m (Cd = 0.112) in the shadow zone at –60 deg (the direction refers to the direction of wave orthogonal approach).

Modeling activities search for an optimal layout that would diffract the incoming waves to a tolerable height or energy level behind the BW. Physical scale modeling is somewhat a thing of the past as it involves considerable efforts and cost (however massive projects often require it). In contrast, modern practices of optimizing the configuration of a BW layout mostly rely on numerical modeling. First, the regional wave climate is established by wave action modeling – that lays out the boundary conditions for the detailed modeling including the outlines for most probable forcing scenarios. The most effective way of detailed layout optimization is by Mild Slope or Boussinesq (French mathematician and physicist Joseph Valentin Boussinesq; 1842 – 1929) wave modeling – an example of such an application is shown in the attached image. I love the beauty of Boussinesq modeling approach – its phase-resolving capability to analyze the non-linear wave fields close to the shore, etc. I had the opportunity to use it in multiple occasions – the results of one such application are published in my Ports 2013 Conference paper. While the capabilities are real – there are also many limitations and constraints of what a numerical model can or cannot do – therefore one should be careful in interpretations of model results, and their uncertainties. Some aspects of these issues are outlined in the Water Modeling piece. For the sake of brevity, the rest of this piece will primarily focus on rubble mound BW and designing armor rock size.

Rubble Mound Breakwaters
Rubble mound breakwaters represent a triangular (trapezoidal to be exact with thick peak) prism with its base at the seabed and its triangular peak rising to a certain height above or below the still water level (SWL). The thickness of the peak is structurally required to have the dimension of 3 armor rock sizes, often equipped with a concrete cap and a seaside crown wall for an emergent BW. The advantage of a rubble mound is its capacity to absorb and dissipate the wave breaking energy – the dissipation is ensured by the porosity of armor layer.

It is a relatively cost-effective simple structure with the sides laid out in symmetric or asymmetric slope configuration. The slopes must be flatter than the rock angle of repose or internal friction (~ 1V:1.25H). In the case of an asymmetric triangle, the seaward side slope is usually flatter than the harbor side. Let us attempt to see some aspects of this structure in simple terms.

Stability of an Armor Unit. The crucial step in BW engineering is to address the stability of armor rocks or concrete units placed (randomly by dumping, or one-by-one in regular orders) on the rubble mound slope. The hydrodynamic loading of a breaking wave must be balanced by the armor unit weight resting on a slope and held in place by neighboring units and the foundational core. The loading is primarily caused by breaking wave drag and lift forces (inertial forces are negligible, see Wave Forces on Slender Structures). These forces translate to the wave height when breaking water particle velocities become a square root function of H (see Tsunami and Tsunami Forces). In essence, the dynamic stability of armor units depends on a multitude of factors – related to (a) Wave Forcing, (b) Rock Properties and (c) Structural Integrity. They are:
  • Wave Forcing: (1a) water depth or elevation; (2a) water density (see Coastal Water); (3a) foreshore seabed slope; (4a) wave parameters (see Waves – Height, Period and Length); (5a) storm duration or number of waves; (6a) angle of wave attack; (7a) convergence or divergence of the wave field; and (8a) wave breaking type on the slope.
  • Rock Properties: (9b) armor unit density, and strength and durability; and (10b) angularity or shape of the unit.
  • Structural Integrity: (11c) angle of the BW slope; (12c) acceptable damage level or dislocation of units; (13c) permeability of the structure (note the porosity of randomly placed rough quarry rocks varies from 37 to 40%); and (14c) gradation and layering of the interiors rocks including the core, and the strengths and durability of them.
With dependence on so many variables and parameters, it becomes formidable to derive a straightforward formula. Engineers then had to resort to dimensional analysis technique to reduce the variables. This technique yields dimensionless numbers which can be related through laboratory tests and scale modeling. As pointed out earlier, one such number is the Stability Number, N_s = H/ΔD_n50. First breakthrough of finding a useful relation came from Iribarren (1938). He simply focused on non-breaking waves on the BW slope, and related N_s to the product of coefficient, a friction factor and BW slope factor. His investigations revealed something very interesting – that for a non-breaking wave, the downrush force dominates or is more than the uprush. His formula is only of academic interest – because it substantially underestimates the required armor rock size.

Hudson Formula (RY Hudson 1958).
The next breakthrough came from flume tests in the CERC lab facilities at Vicksburg, Mississippi. The derived relation, promoted by SPM manuals and has been in use for long time was the Hudson formula. It simply related N_s to the product of a stability coefficient and slope factor. The formula is based on flume tests relying on the actions of broken waves on non-overtopped permeable core BW slope. SPM manuals prescribed different applicabilities of this formula and provided different tabulated values of the stability coefficient. Although the formula was derived using regular waves, the manual prescribed to use significant wave height (Hs) in the 1977 manual – and changed it to the 10th percentile significant wave height (1.27Hs) in the 1984 manual and in subsequent CEM editions. The limitations of this simple formula are often cited as: (1) probable scale-effects from small model tests; (2) use of regular wave loading only during testing; (3) the effects of wave period and storm duration not accounted for; (4) damage level is not well-defined; and (5) primarily meant for non-overtopped permeable core structure. However, to ensure wide applicability, all these limitations (as we shall see except the wave-period effect) are accounted for, and lumped into the stability coefficient. The example (a) broken wave, when acts on a 1V:2H BW slope, the 1977 formula yield a rough quarry rock armor unit mass of 4.5 tonne with no damage. It nearly doubles to 9.2 tonne when the 1984 formula is used.

Van der Meer Formula (JW Van der Meer 1988).
Van der Meer (VDM) for his PhD thesis conducted elaborate lab tests in the Delta Flume. His derived formula is more complex than Hudson’s. And N_s is related to additional factors – by taking into account of the effect of wave period, wave breaking type, permeability, damage level, and storm duration. VDM formula is tested for wave steepness from 0.005 to 0.06, and with the maximum wave numbers of 7500, at which the forces on the armor unit reach equilibrium (meaning that no more damages could occur with further increase in the number of waves). Let us see how the VDM formula predicts rough quarry rock armor size for the example wave. The (a) wave breaks on the 1V:2H BW slope as a plunging breaker (see The Surf Zone). For 4000 waves on an impermeable core with no damage, the required VDM unit mass is 6.7 tonne (note that this size is smaller than what is required by the 1984 Hudson). If the wave period is increased to (b) 12-sec, the wave breaking type is still plunging, but then the mass increases to 12.7 tonne. For this particular wave forcing, it turns out that the Hudson 1984 formula is conservative for wave periods ≤ 9.7 sec. For heavy storms characterized by long period waves, the VDM formula is appropriate.

Materials. As an alternative to quarry rock, engineers resorted to lab testing to develop different interlocking shapes of concrete units. In most cases, investigations leading to finding such units became necessary when suitable sizes of quarry rocks (most commonly used densities: rock 2.65 tonne/m^3; water 1.025 tonne/m^3; 1 tonne = 1000 kg) could not be identified and found for high wave climate areas – in cost-effectiveness, quantities, qualities and energy dissipation. Concrete units allow engineers to design steep slope (~ 1V:1.5H) rubble mounds, thus affording significant cost savings in relatively deep waters. The units are usually reinforced when the required mass of each unit is heavier than about 10 to 20 tonne (often constrained by the placing equipments and methods). Many countries have developed their own tested shapes, some common examples include (with the year and the countries of development): Tetrapod (France 1950), Tribar (USA 1958), Stabit (UK 1961), Tripod (the Netherlands 1962), Dolos (Republic of South Africa 1963), Seabee (Australia 1978), Accropode (France 1980), Shed (UK 1982), Core-loc (USA 1996), and Xbloc (the Netherlands 2003).

I like to stop at this by noting many other aspects of rubble mound BW engineering that accompany design specs. In brief they include:
  • width of the crest: the specified minimum is some 3 to 4 times D_n50;
  • the thickness of armor layer: minimum 2 layers, 2D_n50. Thicker armor layer ensures more porosity, therefore more energy dissipation but at a high cost. Concrete units have higher porosity (~ tetrapod 50%), therefore ensure more energy dissipation;
  • the gradation of quarry rock armor units, the ranges are: narrow (D_85/D_15 < 1.5); wide (1.5 < D_85/D_15 < 2.5); and very wide (D_85/D_15 > 2.5);
  • among the LCBs there are many options one can tap on: reef breakwater (dynamically stable mostly with permeable core that allow modulated wave transmission), the marginal LCBs that allow both green and spray overtopping, and the low LCBs, weir or sill whose crest remain mostly submerged. Overtopping and wave energy transmission allows smaller armor rocks than the non-overtopped BWs.
  • a recent development in BW engineering is Berm Breakwater (BBW). BBW design takes advantage of forcing the waves to break before it reaches the main BW – by selecting a suitable height of the berm placed on the seaside slope. The berms of BBW are designed to have damages by taking most of the wave breaking load.
  • many BW sections include a toe on the seaside. The toes have two functions – first one is to support the overlying rocks and the foundational underlayers and core – and the second is to take a portion of wave breaking load when waves break at or near the toe level. When the depth of the toe ≤ 0.5 times the water depth, the toe armor unit should have the same spec as that of the BW armor. For higher toe depths lower size toe armor can be used.
  • for many other specs of the rubble mound BW structure including the gradation and filtration requirements of underlayers and core – the CEM and Rock Manual have elaborate guide materials. The rock gradation must satisfy three requirements: (1) stability, and prevention of (2) the loss of fines (3) and the development of pore pressure (by ensuring adequate permeability).
  • Rock sizes and other specs of coastal protection ripraps or revetments are estimated using the similar methods as those of BWs;
  • assessing the effects/impacts of BW systems on the local Fluid, Solid and Life systems;
  • for BWs conceived of risky investments because of their high environmental and failure impacts – an advanced probabilistic analyses and design approach is often followed.

There we have it.
Perhaps some moments of thoughtful reflection and reckoning from all of us are useful – on something as miniscule as a microbe virus yet powerful enough to shatter the confidence in our protective capability of public health. And on something – that opened a terrible flaw in otherwise assumed as civilized systems and norms – but which in reality were nothing but artificial covers on the hidden wounds inflicted by many years of skewed socioeconomic policies promoting asymmetry and inequity. On top of that climate warming is heading towards unsustainable instabilities and trends; and information abuses and malicious internet viruses are at an alarming stage of threatening public security and privacy. With all these, it is no surprise to hear global calls – loud and clear, for the strengths of wisdom, mutual respect and unity.

With that, let me finish this piece with a Koan: Nothing compares with the fury of jealousy, arrogance, anger and hatred – when built within the systems of power or is tolerated – it unleashes the ruthless monster of cruelty and brutality that burns everything it comes close to.

.  .  .  .  .

- by Dr. Dilip K. Barua, 19 June 2020

 


0 Comments

Flood Barrier Systems

1/26/2020

1 Comment

 
Picture
In an earlier piece, Civil Engineering on our Seashore, I have presented and broadly outlined the Coastal Engineering Envelope where several civil engineering measures were shown – that cater to the needs for protecting and developing the seashore. A brief of some 24 different kinds of coastal and port hydraulic structures were listed there. On this piece let us attempt to learn about the Storm Surge Barrier – but in a wider context of Flood Barrier Systems. The barriers as a way of managing water and floods – have two basic engineering components. The first is the dike on low lands, connected to the second component – the gated stream/river/estuary/waterway closure structures. The works represent a system that accounts for many engineering challenges – hydraulic, structural, geotechnical, and risk assessment – as well as impacts on the ambient environment defined by local Fluid, Solid and Life systems (see e.g. Environmental Controls and Functions of a River). In the back drop of Warming Climate with consequent Sea Level Rise, flood barrier systems are becoming increasingly relevant – as one of the management Strategies to cope with the threatening rising sea, and increasingly frequent and intense storm surge.

This piece is built upon materials gleaned from several sources and websites. Unless specified otherwise, they include the following. On river floods: Hydraulic Design of Flood Control Channels, USACE EM 1110-2-1601; Hydrologic Frequency Analysis, USACE EM 1110-2-1415; and Design and Construction of Levees, USACE EM 1110-2-1913. On coastal flood/storm surge: Storm Surge Analysis and Design Water Level Determinations, USACE EM 1110-2-1412; Hurricane and Storm Damage Risk Reduction System Design Guidelines, USACE; and TUDelft (VSSD) Breakwater and Closure Dams (2008, 2nd ed).


​Before jumping on to discussing the flood barrier systems – perhaps it would be instructive to begin by introducing the Water Barrier concept in a broader context. Because all barriers under this generic term, and in the capacities of a hydraulic structure – have one common purpose – that is to protect an area from the onslaught of water actions. These protections can simply be sorted out against the actions of:
  1. wave and current forces and unacceptable agitations;
  2. wave and current induced erosions and scours;
  3. inundation and runup flooding;
  4. propagating flood, storm surge and tsunami waves through channels and waterways;
  5. drainage and navigation blockage of inlets and river mouths by mobile sandbars; and
  6. water-borne suspended sediment depositions in harbors and waterways.
Some common preventative soft and hard engineering measures usually installed for protections against such actions are listed in the Civil Engineering on our Seashore. Perhaps it is helpful to group them pertaining to specific water actions – together with an outline of common assessment routines.
  1. Wave and Current Forces, Agitations, Erosions and Scours: (1) emergent and submerged fixed breakwater; (2) floating breakwater; (3) sill, reef or weir catered to gradually weaken water forces; (4) beach nourishment; (5) a buffer zone of hardy and water tolerant plantations to reduce forces; (6) groin; (7) jetty and training wall to deflect forces; and (8) seawall, bulkhead and revetment; and (8) stone ripraps on banks and beds.
  2. Inundation and Runup by Propagating Flood Waves: (1) on banks or shorelines – stone ripraps, earthen dike or monolithic vertical flood wall with channel closures and sluice outlets; (2) purposely built sand dune; (3) isolating an area to create polders by ring, or partial-enclosure dikes or flood walls with channel closures and sluice outlets; (4) gated barrier on streams, rivers, estuaries and river mouths – designed for actuation in times of unwanted high waters caused by flood waves of all sorts – tide, storm surge and tsunami; (5) managing channel networks through diversion barrages, closure dams and dikes; (6) the crucial step of implementing closure dams; and (7) pumping stations to augment drainage relief of the protected area.
  3. Sedimentation Management: (1) sluice outlet to drain out water and accumulated sediments, together with gates to prevent entry of sediment-laden high-stage water into the protected area; (2) sediment trap dug into channels to be dredged occasionally; (3) updrift to downdrift sediment by-pass to balance accretion-erosion; (4) updrift breakwater to trap sand, and prevent channel sedimentation by breaking the continuity of littoral drift; and (5) occasional dredging of silted basins and channels.
  4. Effects Assessment: It is customary that all modern engineering measures must accompany an assessment of their effects on the Fluid, Solid and Life Systems – with clear identifications of impacted areas on the surrounding – both in short and longterm perspectives. But, many engineering measures failed to take proper account of effects and remedies. The 2012 USGS report (C1375): A Brief History and Summary of the Effects of River Engineering and Dams on the Mississippi River System and Delta – outlined in vivid terms some effects of river engineering and protection works – that totally changed the character and regime of a river – adversely affecting its living dynamic equilibrium process of sustenance. Many such works have been (perhaps even being) installed around the world – without due diligence of assessing their effects and impacts – thus weighing their pros-and-cons on the interdependent Fluid-Solid-Life systems. 
  5. Risk Assessment: Flood barrier systems are a costly investment tasked to protect areas, properties and lives against extreme hydraulic events and forces that have the overwhelming power of destruction. Therefore it is a compelling necessity to complete a risk assessment procedure with due diligence and earnest. The 2012 NAP publication #13393 – Dam and Levee Safety and Community Resilience: A Vision for Future Practice – discusses some of the Flood Barrier safety and risk mitigation issues, and community involvements.
With this brief layout of water barriers, let us move on to discussing the specific issues of flood barriers. Among the many measures identified above, the ones belonging to the group described in 2 are the focus of this piece. Let me first briefly elaborate some key hydraulic basics of this group – then move on to outline some major Storm Surge Barriers – with detailing out some aspects of the Venice MOSE project (image credit: anon).
Flood Barrier Hydraulics
It is necessary to comprehend some key hydraulic technical issues – that are important in aspects of planning, designing, construction, and functions. In all these aspects, different methods and practices are implemented in ways – how a barrier handles the potential and kinetic energies – in eliminating, reducing or modulating their power.
Let us attempt to see them. In barriers installed to prevent flooding due to inundation and runup – potential energy is gradually elevated as the hydraulic head difference increases between the two sides of a barrier. One knows too well that the forces caused by the difference – exerted on an earthen dike, a vertical monolithic wall, or a gated barrier structure – are what cause failures (see Civil Engineering on our Seashore). The threats to their stability and integrity take different dimensions and can be translated into:
  • The first hydraulic issue that comes to one’s mind – is the selection of an upper-envelope extreme event up to which a given barrier system can be designed to withstand and provide protection. Methods and issues related to defining such an event have been discussed in two pieces posted earlier – Uncertainty and Risk; and The World of Numbers and Chances.
  • Among the two modes for flooding, inundation is like the gradual encroachment by a carpet of water with concentration of currents when the dispersing flood-wave faces resistance. In contrast to this, broken-wave runups are forceful in actions with impacts on structures and bed.
  • A standing pressure force develops on the water retaining side of the structure. This pressure representing potential energy causes very high kinetic energy when released (e.g. a 1 m of head difference could generate a flow velocity as high as 4.5 m/s). There are also some dynamic elements to the pressure field – induced by propagating disturbances and/or by surface waves. These forces apply an overturning moment on a vertical wall, and cause pore pressure on an earthen dike. Earthen dikes are designed to minimize the effects of pore water pressure.
  • At a certain moment when the freeboard is less than some tolerable limits, the potentials of overtopping and eventual failure emerge – in particular in the regions of weaknesses. In such cases, the power of concentrated flows continues to erode and topple the barrier until the forces diminish, and the hydraulic head difference between the two sides is levelled off.
  • A vertical wall causes some reflections of the dynamic pressure and surface waves. A sloped earthen dike, on the other hand is dissipative by nature.
  • Areas enclosed by dikes require a drainage sluice outlet gated structure. Most often a flap gate proves to be a very cost-effective alternative. It is a simple structure with gates hinged at the top while the bottom part can flap outward – to let the draining out of accumulated water from inside the protected area. The gates are designed not to flap inward to prevent entry of water from outside.  To cope with adverse drainage-gradients (that often happen at very high tide, but most notably during storm tide when receiving basin water level is higher than the protected area), pumping stations are installed at the drainage outlet structure to pump out accumulated water from inside the protected area.
  • In many flood barrier engineering – a closure dam is required to close the original channel to let the flow divert toward the newly-installed gated-structure. For a uni-directional flow, closing of the original river course is easily done after diversion. For tidal channels, an intensive sequence of activities is required to close the final water-gap. This is mostly accomplished during a short window of neap-tidal slack water. Purposely-built middle islands – together with well-mobilized equipment and workforce are employed to close the gap at one go. While the closing operations continue, the peripheral parts of the dam are protected simultaneously by dumping rocks. I had the opportunity to learn about different aspects of closure dam hydraulic engineering while studying at Delft – working on a group thesis on Asan Bay closure dam in Korea. Also, had the opportunity to be present and witness the labor-intensive works of Feni River Closure Dam in Bangladesh. More on closure dams are available at: TU-Delft 2008, Breakwaters and Closure Dams, 2nd edition; CIRIA Rock Manual 2006, Design of Closure Works (Ch 7). In my 1993 paper {Practices, Possibilities and Impacts of Land Reclamation Activities in the Coastal Areas of Bangladesh. In: Grifman PM and Fawcett JA (Eds), International Perspectives on Coastal Ocean Space Utilization, University of Southern California Sea Grant Publication, pp. 343-356} traditional practices of building large-scale cross-dams or closure dams in Bangladesh were discussed. The 1956-57 Cross-dam 1 and the 1964 Cross-dam 2 – were implemented to close some dying branches of the Meghna Estuary, and some 52,000 ha of land was reclaimed.
  • An important step in flood barrier engineering is to design and construct measures for preventing scour of channel bed. A bed scour is initiated and intensified, because installation of gate-housing structures reduces the channel cross-sectional area – thus increasing the flow velocity, and inducing scour-causing vortices around the gate structures (see Turbulence, and Wave Structure Interactions & Scour). Based on many years of experience, Dutch engineers developed methods and special equipment to place woven straw mattresses on the channel bed. Ballasted by rocks, the mattress acts as a filter to prevent escaping of bed sediments – as well as becomes the prepared foundation on which structures can be placed. This is unique, in a sense that many other methods rely on founding the gate-structure deep into the solid bed on which superstructures are built upon.
  • Engineering of gates on barrier openings have many familiar forms: e.g. gates sliding against structure piers vertically; swing gates hinged to the bottom; swing gates hinged to the bank; rotating drum gates; inflatable gates; gates sliding horizontally; swing flap gates hinged to the top; etc. Some key considerations that lead to the choice of one or the other are: convenience of recess structure for housing the gates when not in operation; strength of the gates and power required to operate them to withstand the design high hydraulic heads, etc.
  • A very important effect of implementing storm surge barriers – is the reduction of tidal prism (see Managing Coastal Inlets). This happens because of the reduced cross-sectional area. Since the behavior of the Fluid (in this case Water) System is changed – the ambient characteristics of the Solid and Life Systems – dependent on water properties and circulation are affected. Therefore a thorough environmental effects assessment is imperative.
Highlights of Some Major Storm Surge Barriers
In the world of modern flood barrier engineering, the first one to occupy the history book is the 32 km long Afsluitdijk closure dam in the Netherlands completed in 1932. This dam separates the shallow IJsselmeer Lake from Wadden Sea. The primary purpose of this dam was to reclaim land from the lake. Starting from this great feat of hydraulic engineering, let me highlight some major storm surge barriers completed around the world.
  • Delta Works, the Netherlands: These works refer to massive barriers, navigation locks and dikes – constructed to control and prevent storm surges entering through several branching delta estuaries of the Rhine-Meuse-Scheldt river system. The works were commissioned after the devastating storm surge flooding of 1953. The last one of the Delta Works was finished in 2010 together with environmental restoration works. The gates on the openings of the barriers vary in technical innovations from sliding to bank-hinged to inflatables. The only sea arm that remains open in the Netherlands is the Western Scheldt that leads to the Antwerp Maritime Port in Belgium. With the threat of rising sea, strengthening of existing structures is on the plan.
  • Thames Barrier, London, England: The same 1953 North Sea storm surge that prompted Delta Works in the Netherlands – was also the reason for initiating the Thames Barrier. Commissioned in 1984, the purpose of the barrier system comprising of the dikes – was to protect low lands of the greater London area from the North Sea high tide and storm surge propagating through Thames Estuary. It was built on the 520 m wide estuary by dividing it in 4 basic segments and 2 navigational spans. The barrier structure openings are equipped with rotating steel drum gates that rest on the channel bed when sleeping, and are rotated to rise in the event of unacceptable forecasts of high tide or storm surge.
  • IHNC Storm Surge Barrier, USA: This barrier (Inner Harbor Navigation Canal) was constructed by US Army Corps of Engineers near New Orleans on the confluence of Gulf Intracoastal Waterway and Mississippi River Gulf Outlet in 2013. The purpose of the barrier was to protect some of the low lying vulnerable areas of greater New Orleans against storm surges from the Gulf of Mexico and Lake Borgne. The barrier system consists of flood walls, bypasses, navigation locks and gated barriers. To reduce the risk of flooding in the greater New Orleans area - a massive $14 billion project - the Hurricane and Storm Damage Risk Reduction System (HSDRRS) is being built by USACE with supports from local and outside consultants. The system is scheduled to be completed in 2023. 
  • Saint Petersburg Dam Complex, Russia: The Saint Petersburg Flood Prevention Facility Complex is a 25 km barrier system – completed in 2011 to protect Saint Petersburg against storm surge coming from the Gulf of Finland. Saint Petersburg is founded on low marshy lands located in Neva Bay – and has seen the onslaught of some 340 devastating floods in the past. The system also forms part of the dike ring road that passes through the gated barrier structure as underwater roadway tunnels. It includes some 30 water purification units designed to maintain the water of Neva Bay healthy.
Among many others in the planning process – a massive storm surge barrier (New York Harbor Storm Surge Barrier) is planned to protect the Lower New York Bay from the onslaught of storm surge coming from the Atlantic through the Outer Harbor.
MOSE Project Venice, Italy
  • Let me begin with a little bit history. Venice marshy islands started to get settled by refugees when they fled from barbarian attacks in the 5th century CE. It gradually became important and powerful as a maritime port and harbor. Venice lagoon gradually silted up by sediments brought in by 3 rivers. At sometime later, the river outfalls were diverted away from the lagoon to prevent sedimentation. In the 20th century, many wells were dug in Venice to extract water for agriculture and industry use. The extraction induced more subsidence of the marshy lands – and was banned only in the 1960s. Present subsidence rate of Venice is about 1 – 2 mm/year.
  • Long waves such as tide, storm surge and tsunami are subjected to transformation as they propagate from open water to constricted areas (see Transformation of Waves) – in the process waves are amplified and distorted. Similar process happens, as the low Mediterranean tide gets amplified as it enters Adriatic Sea to Venice. As an example, in January 2020, a 30 cm tide at Catania, Sicily amplifies to 100 cm at Malamocco, Venice.
  • A term known locally as acqua alta is used to refer to tidal flooding of the Venice city center – tide reaching to + 0.8 above local datum. The analyses of 1872 – 2006 tide records show that acqua alta mostly occurs in the months from October to December due to both astronomical and meteorological phenomena. Since about 1950s, the frequency and intensity of acqua alta have been registering high, due to subsidence as well as the rising sea level of the Adriatic. When tide is + 140 cm, about 90% of Venice is flooded. Low level flooding during high tide are becoming more common – presumably due to rising sea and subsidence.
  • In the backdrop of all these, the MOSE (Modulo Sperimentale Elettromeccanico) flood barrier project was conceived in 2001 and construction began in 2003. It consists of 78 independently moving closure gate elements at 3 inlets (18 at Chioggia; 19 at Malamocco; 20 at Lido-Treporti and 21 at Lido-S. Nicolo). These 3 inlets are located on the barrier island chain that separates Venice Lagoon from the head of Adriatic Sea. The purpose of the project is unique – in a sense that unlike many other major storm surge barrier projects around the world – it is planned to operate rather regularly to lessen the effects of high tides and storm surges penetrating into the Venice lagoon.
  • The rectangular gate elements were designed to rest on seabed recess structure when not active. The resting is ensured by filling the elements with water. Activation of the elements is initiated when the tide is forecasted to reach +110 cm. The elements are raised from their recesses by pumping compressed air into the elements to drain out water. The anticipated completion timeline of the project is 2022. Among the 3 inlets, the Malamocco Inlet is designed to accommodate marine traffic to the Venice Port during the inlet closures.
  • Differences of opinion appeared about the adverse effects of closures – in terms of harming ecology, of very high cost, and of doubts about the effectiveness of the inlet structures. Additionally, concerns were expressed about navigational delays and the cost for such delays on transportation.
It has been a great pleasure writing this piece. Let me finish it with a little Koan: Why let it wither away, some water-of-life on the plant would have worked to let it stand upright and unfold the fragrance of flower.

.  .  .  .  .


- by Dr. Dilip K. Barua, 26 January 2020

1 Comment

Civil Engineering on our Seashore

2/5/2019

0 Comments

 
Picture
This piece is about the varieties of Coastal Civil Engineering (CCE) works we all see – when visiting seafront to relax, to feel the warmth of ocean in continuous pounding of waves, or when seeing vessels navigating in and out of ports and harbors. These works result from engineering efforts that have three well-known tenets of civil engineering: coastal hydraulic engineering (or simply Coastal Engineering, CE), coastal structural engineering and geotechnical engineering (structural and geotechnical are often lumped together as structures engineering). Coastal hydraulic engineering term is sort of a misnomer – because it not only covers analysis, modeling and determination of hydrodynamic forces caused by water, water level rise and fall, current, wave and bed-level changes – but also includes similar activities due to wind forcing. The combined effects caused by wind and water are known as metocean processes and forces.  
Before moving further it is important to build into our concept the extent of geographical area where civil engineering is referred to as CCE or CE. This area termed as the coastal zone – extends from the inland topographical limit reached by major storm surges and tsunamis to the continental shelf break. Continental shelf mostly of turquoise water, having an average bottom slope of some 1V:100H extends from the shoreline to a seaward line where the slope abruptly dips down into the ocean at about 1V:40H or steeper. This line begins roughly in the region where waves of about ≥ 10 seconds will start feeling the bottom – consequently being subjected to the transformative processes of refraction and shoaling (see Wave Transformation piece on this page). Generally, mariners call the blue ocean beyond continental shelf – high seas. The definitions of inland limit vary among countries – and depend on several criteria such as: technical, legal, administrative, disaster management and hazard insurance – but they all invariably include coastal waterways, river mouths, estuaries and bays. I have discussed many aspects of CE in different pieces on the NATURE and SCIENCE & TECHNOLOGY (S & T) pages. Thought a piece of introductory nature will complement those.
In the US Submerged Land Act (1953) a coastline is defined as: the line of ordinary low water along that portion of the coast which is in direct contact with the open sea and the line marking the seaward limit of inland waters. The same Act defines coastal submerged land under the jurisdiction of coastal States as: navigable waters, and lands beneath, within the boundaries of the respective coastal states out to 3 nautical miles from its coastline. The Outer Continental Shelf Lands Act (OCSLA 1953) defines federal jurisdiction on coastal oceans as: all submerged lands lying seaward of state submerged lands and waters (e.g. outside shelf lands seaward of 3 nautical miles).
Perhaps it is useful to add a brief on the legal definition of Maritime Boundary. Part of this brief is based on my 1994 IEB paper: On the Formulation of Coastal Zone Management Plan for Bangladesh. The following definitions of the boundaries are agreed upon by signatory countries (including the land-locked countries which are given the right to claim maritime transport access through their coastal neighbor) at the UN Convention on the Law of the Sea (UNCLOS 1987). It was developed and refined within the framework of the UN – during a period from 1970 to 1984.
  • To define and demarcate different zones a reference line is required – and this reference line termed as the Base Line (BL) is defined as a delineated shoreline at Mean Low Water (MLW). The BL is delineated to include a country’s nearshore/offshore islands, if any, along with a straight line to enclose bays and estuaries.
  • Inland Water (IW): the waters landward of the BL.
  • Territorial Sea (TS): the seaward water from the BL to the extent of 12 nautical miles (NM) or ~22 km.
  • Exclusive Economic Zone (EEZ): the seaward limit to the extent of 200 NM (~370 km) from the BL. An intermediate Contiguous Zone (CZ) is also defined outside of the TS – seaward to the extent of another 12 NM. One can imagine that with such definitions of BL, TS, CZ and EEZ – each of them represents a series of polylines, roughly mimicking a country’s coastline. A country defining these boundaries owns these waters and has the jurisdictional authority over them: authority to develop and exploit Natural resources (e.g. mineral, fisheries) within its EEZ; authority to control maritime traffic, and to react if a hostile vessel enters its TS without permission. It also has the responsibility to maintain the waters pollution-free and take care of its flora and fauna. A country’s Coast Guard is given the authority to enforce the rights and responsibilities.
Despite the clarity of definitions – legal interpretations differ and disputes often arise – such as the two flashpoints – the Arctic Sea and the South China Sea. As far as the maritime traffic is concerned, the sea beyond the TS – the High Seas belongs to all nations. Note that the definitions of these boundaries have nothing to do with bathymetry (for example, the zone boundary is not affected whether it is a wide or a narrow continental shelf). However, the boundary limit has to be measured along a line perpendicular to the BL. Each country and international organizations issue marine charts showing the demarcated maritime boundaries.
There are other names addressing the same problems of CCE but focusing on some particular aspects: like port and harbor engineering, maritime engineering (coined first in European literature), and marine engineering. The last term is loosely applied in civil engineering to describe in-water works – but its root mainly lies in describing mechanical-electrical engineering, navigation and naval architectural aspects of seafaring vessels. Ocean engineering, oceanographical engineering and offshore engineering terms are also used to describe works in coastal and deep waters. Offshore engineering term is primarily applied to describe isolated in-water works in deep water – like oil terminals and marine pipelines.
There are many definitions of CCE – different in wording but common in contents. Let us attempt to define it in this piece as: CCE refers to the practice of planning, designing and effects assessment of civil engineering works for the protection and preservation of, and developments (water-front townships and cities, recreation, marine transports and installations, and value-adding improvements) within the coastal zone. The history of CE is briefly discussed in the Resistance to Flow on this page – it is a fairly new discipline – the official recognition and definition was launched only about 70 years ago – at the First Conference on Coastal Engineering held in Long Beach, California in 1950. Coming back to the definition – one can see that it relies on the understandings of two other terms: civil engineering, and engineering. There are many definitions of these two terms in literature, but I prefer using the following two.
According to The National Academy of Engineering and National Research Council: engineering is the study and practice of designing artefacts and processes under the constraints of the laws of nature or science and time, money, available materials, ergonomics (it is the process of designing or arranging workplaces, products and systems to satisfy the needs of people who use them) environmental regulations, manufacturability, and repairability. The 2008 ASCE BOK2 (Civil Engineering Body of Knowledge for the 21st Century, 2nd ed.) defines and elaborates civil engineering as: the profession in which a knowledge of the mathematical and physical sciences gained by study, experience, and practice is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the progressive well-being of humanity in creating, improving and protecting the environment, in providing the facilities for community living, industry and transportation, and in providing structures for the use of humanity. Both of these definitions are quite lengthy, but they were developed to cover all different aspects – from both technical and legal perspectives.  
I have written in the Creativity and Due Diligence piece that, CE as a creative profession has the role . . . in the discipline of civil/hydraulic engineering, applied science provides the baseline knowledge on data and analysis, while technology provides tested products and materials. The role of an engineer is to find solutions to a given problem using resources from these two sources. To do it successfully, it is important for engineers to understand the necessary basics of the S & T. Failing in this matter affects the soundness of an engineer’s judgment. Therefore engineers are part of the S & T endeavors by being intricately involved in the development and progress – sometimes working at the forefront, but most often in the practical applications of science and technological advances to the real-world problems . . . And to accomplish that, engineers by and large, and perhaps more than any other profession – spend a significant portion of their time on computing to create acceptable, defensible and implementable solutions in quantitative terms – using slide rule in earlier times (until about 1970s) to the scientific calculators and personal computers in modern times.
Perhaps it is helpful to enumerate some of the sub-disciplines commonly included in the coastal engineering envelope. The first group (a-group) of activities includes those – aimed at establishing critical planning and design conditions and criteria by envisioning the most probable operational and design loading scenarios, uncertainties and risks for various interventions/structures (these structures not only include hard measures of concrete, steel and stones; but also soft structures like beach nourishment and coastal vegetation/tree barriers) based on analysis and modeling of various environmental parameters. This group includes: (1a) hydrodynamics: water level, current, and wave (2a) wind climate and storms (3a) sedimentary climate: coastal geology and sediment transport processes. The second group (b-group) of activities utilizes the first – for planning, designing and assessing the effects and risks of: (1b) coastal zone development and value adding (2b) coast and shore preservation and protection (3b) intakes and outfalls (4b) dredging and spoil disposal (5b) coastal waterfront and marine terminal structures, including marina  (6b) offshore and pipeline structures (7b) port and harbor developments and structures. I have included an image of the coastal envelope showing the discussed disciplines.
An engineering project starts with a very limited knowledge – starting from that the project moves forward to develop criteria, conditions, specifications, etc. in distinct phases of activities. At the first of three phases – the Conceptual Phase (known as Pre-FEED {Front End Engineering and Design} in Oil and Gas Industries) – starting from scratch problems are defined and the project is visualized, they are then translated into a complete solution package (analysis and design sketches, alternatives, economics, etc) – only at a high level by utilizing available regional and site-specific (mostly unavailable) information. This phase is usually preceded by very high level technical feasibility and economic viability studies. At the next phase – known as the Preliminary Phase (FEED in Oil and Gas Industries) – the conceptual package is critically reviewed, a site-specific information base is established by measurements and modeling, new alternatives are generated, and the conceptual package is revised and updated – but the issued design sketches and specifications are not yet ready for implementation. At the Final or Detailed Phase – a final critical review of the preliminary package is undertaken – updated and refined where necessary, usually no new alternatives are generated – construction, monitoring and supervision methodologies are laid out by detailing each nut & bolt – and the final design sketches and specifications are issued for implementation with the consultant having the additional task of selecting a contractor.
The above phases are usually conducted by different engineering consulting firms for better accommodation of talents and ideas, but often the final phase is eliminated entirely for large projects – by combining the final design and construction into a single package. One prominent form of this system is known as the Engineering, Procurement and Construction or EPC method, where the contractor is responsible for the final design, procurement of materials, and delivering the finished functioning product to the client. To assist and oversee the EPC contractor activities – the project owner usually engages a specialist firm known as the Project Management Consultants (PMC). Apart from these, there are many other consulting, contracting and management terms used in different project phases and construction – and they are usually not the same across civil engineering projects – but vary according to types, even from one country to another.           
A little note on design criteria – they refer to the parameters that must be applied as a minimum for designing project elements; and mostly include: (1) environmental metocean forcing functions, (2) configuration and layout, (3) structural material strength, durability, etc (4) structure-geotechnical, (5) construction and construction foot-prints, (6) operation and maintenance, (7) economics, (8) safety and emergency access, (9) ergonomics, and (10) environmental effects. Some of these criteria are established by scientific and engineering analyses; others come from certified standards and codes; and client and regulatory requirements.
         
Having clarified the meanings of different terms let us move on to the rest. Let me begin by listing some of the major works identified with coastal engineering. The list is long – I am tempted to provide a brief outline of some important works that are applied worldwide affording developments of manuals, standards and codes:
  1. beach drain {perforated underground drain placed in the swash zone},
  2. beach nourishment {placement of imported sands to build new beach and/or to counter-balance beach erosion},
  3. breakwater {an in-water self-standing protection structure - shore-attached, detached or offshore - to diffract, break and obstruct waves},
  4. bulkhead {retaining structure to protect coastal inland from wave attack},
  5. dolphin {port structure – usually a cluster of piles for mooring}
  6. floating breakwater {pontoons anchored to seafloor or fixed to guide piles to attenuate mild wave actions; primarily applied to develop Marina where pleasure boats are housed and moored by tying them to finger floats},
  7. groin {shore-perpendicular structure spaced suitably to minimize beach erosion},
  8. jetty {shore perpendicular structure placed on both sides of inlets to keep navigation functional by interrupting longshore transports},
  9. offshore breakwater {submerged or emerged structure to minimize wave action and beach erosion},
  10. pier {port structure extending into water for loading and unloading}
  11. pile structure {series of piles integrated together by pile caps to support superstructure},
  12. pipeline {seabed pipeline to transport liquids and encasing cables},
  13. quay {port structure – paved bank or built-up area for ship mooring, loading and unloading}
  14. revetment/riprap {shore-parallel stones or manufactured concrete slabs laid on coastal slopes to prevent erosion},
  15. sea dike {shore-parallel elevated earth or concrete structure to prevent flooding),
  16. seawall {shore-parallel water-front structure to prevent erosion, overtopping and flooding},
  17. scour protection {primarily stone ripraps to prevent structure undermining by scour},
  18. sluice {drainage outlet generally placed on sea dikes to flush out inland water, and prevent salt-water intrusion},
  19. storm surge barrier {structure placed on inlets, estuaries or river mouths that can be closed during storm surge and tsunami onslaught},
  20. submerged sill/reef {placed in the nearshore to minimize wave action and beach erosion; the same concept is also often configured to facilitate wave surfing},
  21. terminal {fixed or floating marine terminal, platform structure for mooring of ships, loading and unloading}
  22. trestle {port structure – rigid frame of short spans used as a support for loading and unloading}
  23. training wall {structure configured to direct flow to improve navigation and mooring}
  24. wharf {port structure – where vessels can moor alongside for loading and unloading}                   
How does one characterize the failure of a structure – like the listed ones? Failures generally fall into 4 basic types: (a) environmental load failure (the cause for this failure is attributed to the exceedence or unexpected occurrence of design loads and loading conditions), (b) functional or ergonomic failure (although the structural integrity remains intact, the structure fails to provide its designed operations, functions or performance), (c) structural failure and (d) geotechnical failure. The last two could have the following 3 causes: 
  • design failures of the structure – wholly or partly including its foundation – are caused by designed elements’ inabilities to withstand the loads used in the design;   
  • construction failures are caused by incorrect or bad construction and/or use of unspecified low-quality construction materials and methods – in violation of the design and construction specifications;
  • deterioration failures are caused by inadequate or lack of repair and maintenance, specified in the design.
Each of these general failure modes and specific ones – defines the Limit State. A design process examining each state individually – constitutes what is known as the Limit State Design. There are many more features of CE, but for the sake of brevity, I like to stop at this, only to point out one very important aspect. Coastal structures are not like a tall building standing on a dry land – and they should not be treated as such. Because of their exposed location in water or at the water-front, they continuously come under attack by the dynamic and uncertain metocean forcing – from regular to extreme. They must withstand these forces during construction and operational lifetime, as well as face the consequences of uncertain fluid-structure interaction processes, and have to cause minimum impacts on the surrounding environments.
Therefore the role of a coastal engineer is very crucial – not only in the establishment of design and operational conditions and criteria, but also during the process of planning, design and construction. Lack of effective coordination, cooperation and concordance among various disciplines – or perhaps in not recognizing the proper roles required of certain disciplines – could lead to earning bad reputation, and to risks of incurring serious economic losses.       
I like to finish this piece with some lines of poetry written by a seemingly unknown amateur poet, but the poem was made significant by Saint Mother Teresa (1910 – 1997; Nobel Peace Prize 1979; Bharat Ratna 1980; Sainthood 2016) who displayed it in her office.
People are illogical, unreasonable and self-centered
Love them anyway.   
. . .
Give the world the best you have and you’ll get kicked in the teeth
Give the world the best you have anyway.
.  .  .
What motivation went into such portrayals of the societies we live in – and the strength and courage the poet was asking for? One can hardly afford not to like the poem – but perhaps more so by a personality none other than Mother Teresa – because it tells all about her life and experience.


.  .  .  .  .

- by Dr. Dilip K. Barua, 5 February 2019

0 Comments

Propwash

5/9/2018

0 Comments

 
Picture
This topic is about the consequences of high turbulence and flow velocity that accompany a fixed-pitch screw propulsion ship. Propwash is the term used to describe the high exit velocity a propeller nozzle generates – and in the context of this piece – it is about the propwash effects on a marine terminal during the berthing and unberthing of a ship. The purpose of generating the high exit velocity by a ship is to cause equivalent forward thrust on it – with Newton’s (Isaac Newton, 1643 - 1727) Third Law of Motion in action. Screw propeller blades are twisted in such a way that a rotating propeller produces a high pressure difference by sucking in waters from one side and discharging them to the other to generate the exit velocity required to push a ship forward. The larger the DWT of a ship (see the Ship Motion and Mooring Restraints piece on this page for DWT) the higher is the requirement of propeller powers. But navy and coast guard vessels requiring high speeds, and Tugs tasked to haul barges or to maneuver large vessels during berthing and unberthing – however small they may be – also need to have high propeller powers. For navy and coast guard vessels – the high speed water-jet propulsion system is more of a requirement because the conventional screw propulsion system would just prove inadequate. Let me share some elements of this important port and maritime engineering topic in simple terms – focusing primarily on propwash and its effects.  

Let me begin by focusing on engine thrust that moves a ship ahead. In still ambient water, propeller-induced thrust depends on three important factors – the product of these three describes the efflux – the exiting flux of water from the propeller nozzle. The first is the density of water – which means that with other factors remaining constant – a ship will have somewhat higher thrust in salt water than in fresh water (in addition a ship  will feel somewhat lighter in salt water due to enhanced buoyancy). The second most important parameter – is the diameter of the propeller Dp – the thrust is proportional to the square of Dp, implying that it will increase by 4-fold if Dp is changed, let us say, from 1 m to 2 m. Actually, this dependence comes from the equation of the area of a circle – the area being proportional to the square of the diameter. The concept is utilized by encasing the propeller in a duct or short nozzle to obtain more power for the same engine rpm. Despite the engine thrust being highly dependent on the propeller diameter, there is a limit to its maximum size. One of the reasons is that the diameter must scale with the draft of the ship – otherwise a portion of the propeller will surface and rotate in air. But such surfacing cannot be avoided when a ship rides on rough seas with high roll and pitch motions.  

To describe the third important factor – one needs to take the help of Bernoulli Equation (Daniel Bernoulli, 1700 – 1782). As often pointed out in other pieces, the flow-induced dynamic pressure illustrated by Bernoulli is very important in fluid mechanics – this pressure is proportional to the square of the velocity. Here again, if the velocity is increased, let us say, from 1 m/s to 2 m/s, with other factors remaining constant, the thrust will increase by 4-fold. The exit velocity of an open propeller behaves in a certain way. At a distance of about 0.5*Dp behind the propeller, the exiting jet from an unducted propeller becomes constricted to Do = 0.7*Dp. The maximum jet exit velocity Uo occurs at this location with dissipation taking place further behind.        

Unlike the other two factors (water density and propeller diameter) – one does not know the jet exit velocity a priori. How to estimate it? To answer this question engineers had to conduct series of lab experiments. Delft Hydraulics took the pioneering role in this regard with HG Blaauw and EJ van de Kaa publishing their paper in 1978 – with more subsequent researches coming from other institutions. Remarkable among these, is a review made by MJ Prosser in 1986. Other notable titles dealing with analysis and design recommendations include: EAU (1996); PIANC (1997, 2002 and 2015), Port Designer’s Handbook: Recommendations and Guidelines (CA Thoresen 2003), Design of Marine Facilities for the Berthing, Mooring and Repair of Vessels (JW Gaithwaite 2004), The Rock Manual (CIRIA 2006), HJ Verheij and C Stolker (2007), and K Römisch and E Schmidt (2009). The first theoretical foundations of the behavior of an expanding jet came from ML Albertson and others (1948) and N Rajaratnam (1976). However despite nearly seven decades of scientific research and engineering, one is tempted to say that propwash and its loading on structures and seabed, and interactions – remain inadequately understood.      

In the simplest of all the known empirical relations, the exit velocity Uo is described empirically as the product of propeller revolutions per second n, Dp and a thrust coefficient Kt. The dependence on the thrust coefficient is somewhat weak – but a higher pitch (pitch is the distance traveled by a propeller in one complete revolution in no slip condition. Propeller blades are twisted to have a constant pitch from the root at the hub to the tip. The forward travel of a ship is however less than the nominal pitch determined at 0.7*R, R being the propeller radius. The difference is known as the slip. A note on propeller blade numbers – high numbers are usually optimally chosen to minimize vibration and noise.) ensures a higher Kt. Inclusion of Kt makes things somewhat circular – but to go around that, a rough estimate is possible without using Kt – and investigators have developed Kt tables/nomographs for ducted and unducted propellers as a function of the ratio of propeller pitch to its Dp. Another way to determine Uo is to use the applied engine power – and as can be understood, the applied power during berthing and unberthing is usually less than the capacity – varying from some 10% to 35% of the installed capacity.             

Once Uo is generated, the next important question is what happens to it away from the ship. The afterward behavior of Uo is important because loading on structural elements and seabed depends on it. In the zone of afterward established flow the efflux must mix and dissipate by expanding and entraining the ambient water into the jet boundary. Observations have indicated that in this zone, efflux expands like a cone at an angle of about 12 degrees around the core of maximum velocity. The velocity across the cone decreases from the center following the Gaussian distribution. Along the distance behind the propeller – the whole cone velocity decreases exponentially away from the propeller. At a certain distance behind the propeller, the expanding jet comes in contact with the seabed, causing scour when the sediment pick-up threshold is exceeded.   

To illustrate the effects of an expanding jet on the seabed, I have included an image as an example – applicable for Dp = 2 m, n = 500 rpm, and Kt = 0.37. The estimated jet exit velocity Uo in this case is 16.2 m/s. The distance behind the propeller x and the height of the propeller axis above the flat seabed Zp are both normalized against Dp. The image shows how the jet velocity at the seabed increases and shifts toward the propeller as Zp decreases. At Zp/Dp = 1.0, the maximum is about 3.4 m/s. The change in Zp could occur, for instance due to the tidal rise and fall of water level, or to a small extent due to loading and unloading of a ship. In the example case, the maximum seabed velocities occurred at a distance x, from 5.3 to 6 times the Zp.

The illustrated velocity is a time-averaged quantity – which means that instantaneous turbulence will likely register higher magnitude. Apart from turbulence, the second important one to cause higher velocity – is the effect of rudder behind a single propeller. The rudder splits the jet – and deflects it in one way or another depending on the ship’s heading requirement. At zero rudder deflection, the jet is split into two – one towards the water surface, the other towards the seabed – each making an angle of 12 degrees to the horizontal center – and each spreading at 10 degrees around the core. The implication of rudder deflection (maximum ~ 35 degrees) is that the jet-induced loading and scour phenomena could occur anywhere.

The third is the twin-propeller setting with the rudder in the middle. The jets emanating from the two propellers are merged together at some distance (~ 10*Dp) behind the propeller. Unlike the rudder-behind single propeller setting, the deflecting power of the rudder is different, and the seabed velocity enhancement is expected to be less than the rudder-behind-a-single-propeller. However the propellers are often operated independent of each other, making predictions difficult.

Some other aspects of ship propulsion systems are also important. There are the thrusters – bow and stern – usually having smaller propellers than the main ones – because of this fact they generate less jet exit velocity. Bow thrusters have mostly a transverse setting – meaning that they draw waters from one side to discharge them to the other – to help sidewise maneuvering of the bow. They mostly have high Zp – thus their effects on seabed are not critical – however the horizontal jets could impinge on quay walls or piles to cause substantial loading. Stern thrusters are mostly omni-directional and are located close to the keel, so that their Zp is rather low. They can play a critical role on causing significant seabed loading and scour.  

Ship design and propulsion systems are continually evolving (such as podded propulsors, azimuth thrusters and water jets) requiring refinement of known relations, and finding new ones. The consequences of high speed water jet propulsion systems on structures and seabed, open a different dimension to the propwash and associated loading impacts. Apart from these ship-related factors, there are other factors related to the berthing structure – pile orientation, proximity of the sloped bank behind the piles, vertical face sheet-pile walls, etc. All these factors are likely to complicate the jet loading – making the search for critical design conditions difficult – but one thing is certain, it is the potential conditions of repeated loading and incremental progression of damages – that dominate all design and operational considerations.  

Protecting the seabed against scour-related undermining of the structure foundation for low underkeel clearance setting can be very expensive. For the illustrated case with the maximum seabed velocity of 3.4 m/s, the theoretical median rock diameter is about 0.9 m. Accounting for turbulence factor and other uncertainties associated with rudder, and structural proximity, etc. the required design median rock diameter is likely to be even higher. For such cases, scour protection by bare rock riprap layers can appear impractical. There is an additional danger – it is the sucking-in velocity caused by a propeller with low underkeel clearance, which could suck-in smaller size rocks into the propeller – damaging it. Alternatives such as insitu concrete (such as concrete mattress, grouted rock) and prefabricated mattress (such as concrete block mattress, asphalt mattress, gabion mattress) provide promising options.

Let me now briefly focus on another consequence of high jet exit velocity – and it is the drag force the velocity causes on piles supporting a berthing superstructure. To illustrate it simply, suppose there is an offshore marine terminal – a jacket structure standing on 20 m water. Together with dolphins, its purpose is to facilitate berthing, mooring and loading-unloading of oils or gas. A 10-m draft tanker berthing on this facility, likely un-assisted by Tugs, will berth and unberth at the same location repeatedly. If it is located in the Gulf of Mexico, with very little tidal range, it is highly likely that the tanker propeller jets will cause repeated drag loading at the same heights of the jacket-piles. For a case similar like this, the critical aspect is the localized repeated drag forces causing abrasion and bending of the piles. In this situation, the underkeel clearance is likely to be high; therefore any jet-induced seabed loading and scouring effect on the seabed may turn out to be negligible.

​Let me stop at this – by finishing this piece with a tribute to Stephen Hawking (1942 – 2018) – who despite having debilitating illness did not stop from being active and pursuing his dream for finding a Unified Theory of Everything. He began the 1st paragraph of his book, A Brief History of Time with a little piece of humor:
A well-known scientist (some say it was Bertrand Russell, 1872 – 1970) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits the centre of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: ‘What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.’ The scientist gave a superior smile before replying, ‘What is the tortoise standing on?’ ‘You’re very cleaver, young man, very clever,’ said the old lay. ‘But it’s turtles all the way down!’ 

.  .  .  .  .

- by Dr. Dilip K. Barua, 9 May 2018

0 Comments

Managing Coastal Inlets

3/16/2018

0 Comments

 
Picture
Coastal inlets represent a hydrodynamic connection between two water bodies – the open coastal water on the one hand, and the inland sheltered water body, waterway or lagoon on the other. The name itself suggests that inlets are openings or discontinuities in the shoreline to let oceanic influences such as tide, wave, storm surge and tsunami to propagate inside. They are usually narrow channels that have been historically utilized to install bridges. Another historical significance is that pioneering explorers used the inlets to sail inside into harbors and upriver to discover new lands.  

Four different types are usually distinguished – the geological, the hydrological, the human-made and the alluvial-tidal. The first represents a fixed-shore setting that has been formed during the geological processes – straits and many narrows in fjords are of this type. The second represents delta distributaries – the long outlets draining out the river flow into the ocean. In addition to describing them as Estuaries, hydrodynamics and morphological stabilities of this type are better treated as channels – mostly belonging to the deltaic processes discussed in the Coastal River Delta piece on the NATURE page. The third is a dredged-out channel connecting a closed water body to open water. In most cases, the purpose of opening of such an inlet is to develop marinas by facilitating navigation of pleasure boats to and from the marina.

The fourth type, also known as the tidal inlet – is the natural response of sandy alluvium to establish a connection between the open coastal water and the inland lagoon. Mostly formed or cut during storm surges, they represent a discontinuity in the barrier island along many littoral shores. These inlets are usually a narrow waterway – its length scaling with width – typically varying from 1 to 5 times the width. Literature is full of materials discussing these types of inlets – their stability, sedimentation, navigation, and technical and economic management issues.   

Before moving into discussing further, perhaps spending a little time to clarify the term ESTUARY – the hydrological inlet, would be useful.
  • Let me try to do this based on my 1990 paper: In Search of the Definition of an Estuary published in the BD Journal of the Institution of Engineers. The estuary definition evolved through time starting from investigators like BH Ketchum (1951) and JC Dionne (1963) to the comprehensive syntheses of several papers compiled by the American Association for the Advancement of Science (1967) and the National Academy of Sciences (1977). Dionne’s definition focusing on the St. Lawrence Estuary divides an estuary length into: (1) a marine or lower estuary in free connection with the open sea, (2) a middle estuary subject to strong salt and fresh water mixing, and (3) an upper or fluvial estuary subject to daily tidal action. But the 1967 definition by DW Pritchard focusing primarily on Chesapeake Bay is mostly cited in literature: an estuary is a semi-enclosed coastal body of water which has a free connection with the open sea and within which sea water is measurably diluted with fresh water derived from land drainage. Three terms stand out in this definition: semi-enclosed body of coastal water, open-connection to sea, and measurable dilution.
  • Compared to the Dionne suggestion, tide is excluded from this definition with the understanding that its role is primarily in mixing of waters. In addition the tidal arm of the fresh-water river reach is not considered as an estuary. An additional problem appears with this definition – that in most large river systems like the Amazon, the Ganges-Brahmaputra and the Mississippi, the measurable dilution occurs in open sea water during high river stages – outside their physical land boundary. Therefore according to the Pritchard definition such systems do not have an estuary during this time! In reality estuarial reaches translate back and forth in response to the strength of unidirectional fresh-water flow. To address this problem and by focusing to include large river systems, my suggested definition in the 1990 paper reads as: an estuary is either a semi-enclosed coastal body of water which has a free connection with the open sea or part of the open sea or both, within which sea water is measurably diluted with fresh water derived from land drainage. Basically then, an estuary is any open and/or semi-enclosed coastal water body, where sea water salinity is measurably diluted by fresh-water derived from land drainage.
Moving on – some materials of this piece are based on my Ports2013 paper, presented at the conference in Seattle and published by ASCE: Integrated Modeling and Sedimentation Management: the Case of Salt Ponds Inlet and Harbor in Virginia. {https://doi.org/10.1061/9780784413067.053}. This particular inlet was human-made, dredged to develop a marina in parts of the Salt Ponds water body, and connect it to Chesapeake Bay. In this work, sedimentation problems of Salt Ponds Inlet were addressed by coupled numerical modeling {tide + wave + sediment transport + morphology} together with some analytical approaches – among others by comparing wave and tidal powers.

Inlet opening, closure or its stability depend on four basic oceanic forcings: (1) regular tidal pumping, (2) wave actions and littoral sand mobilization, (3) episodic but seasonal storm actions, and (4) rarer but powerful tsunami events. The effects of the last two can hardly be overemphasized – in addition to cutting new inlets or closing the existing ones, they impose new boundary conditions that are reworked by the regular forces of tide and wave – to achieve new dynamic equilibrium.

Sands are continuously mobilized at the mouth of a tidal inlet by cross-shore and longshore wave actions. If tidal actions do not have the ability to flush out the wave-mobilized sediments, an inlet is doomed to closure. Each year billions of dollars are spent across the world to dredge out sandy shoals of an inlet.

The inland parameters influencing an inlet stability is the size of the lagoon, its inter-connection with other systems and the freshwater that drains into the lagoon. The last but not the least is the textural composition of the littoral material, and the amount of sediment loads. Perhaps discussing more of this topic in 3 groups would help streamlining the rest of this piece.

Cross-sectional Stability of Tidal Inlets. Three easily identifiable features characterize an alluvial tidal inlet system – the ebb-tidal delta on the ocean end, the flood-tidal delta on the bay end, and a relatively narrow deep inlet channel in-between. There had been considerable interests in the cross-sectional stability of tidal inlets – starting from the beginning of 20th century {to name some investigators: LJ LeConte 1906; MP O’Brien (Morrough Parker O’Brien Jr., 1902 – 1988, considered father of coastal engineering) 1931; FF Escoffier 1940; P Bruun and F Gerritsen 1960; JW Johnson 1973; JT Jerrett 1976; MO Hayes 1980}. In its utmost simplicity, the stability was conceived as a simple behavioral model relating the measured inlet cross-sectional area to the tidal prism – as a central fitting, A = CP^n; with a coefficient C and an exponent n on the tidal prism P.

​Tidal prism is the volume of water an ocean tide forces through an inlet to fill the inland basin {the prism can either be estimated by integrating, for example the hourly-tidal-flows through an inlet for the window of rising tide – from trough to crest; or as a product of the inland basin area and the tidal height within the basin}. The coefficient and the exponent are adjustable and verifiable parameters and vary from inlets to inlets – but Jarrett’s analyses show that they are in the order of: C = 3.8*10^-5 to 7.5*10^-4; n = 0.86 to 1.03 in SI unit. They were determined {in general, the coefficient is high when the exponent is low; and vice versa} for all the measured jettied and unjettied inlets along the US coast.

The simple, yet very insightful model have drawn many follow-up works. It turns out that such a relationship can be established for any tide dominated estuarial channels – e.g. the paper I have presented along with my good friend and mentor Fred Koch in 1986 {Characteristic morphological relationship for tide dominated channels of the lower Meghna estuary, UNESCO, BUET} shows such a possibility.

The discussed tidal inlet cross-sectional stability model immediately indicates the following:
  1. first thing to note is its limitations – four obvious ones are: absence of any parameter describing the sediment characteristics, wave actions, freshwater inflow, and flood- and ebb-tidal delta morphodynamics;
  2. that any work of the inland bay – either increasing or decreasing its size will affect the inlet cross-sectional area by such morphological responses as shore-erosion, seabed scour or sedimentation. The effects are not immediate however, but occur within a time-scale characteristic of the system – short for high energy systems than the low energy ones;
  3. that inlet cross-sectional area and morphologies are likely to be different in different tidal regimes (e.g. commonly referred tidal range terminology: micro < 2 m; meso 2 – 4 m; and macro > 4 m); and
  4. fixation effects of the inlet banks by measures such as bridge abutments and rock riprap are not included.
Some aspects of the first characteristic or limitation has been addressed by NC Kraus (1998), who proposed a relation accounting for channel roughness, tidal asymmetry and longshore sand transport.  

Inlet-Bay Hydraulics. Despite providing a first-order understanding of the inlet stability and more, the reality of the problem is much more complex than the simple inlet cross-sectional stability formula. One way to appreciate this is to examine the one-dimensional Saint-Venant hydrodynamic equation applicable in long inlets (French mathematician Adhémar Jean Claude Barré de Saint-Venant, 1797 – 1886). This equation is only solvable by numerical modeling, but an analytical solution to the problem was offered by GH Keulegan (1951) and DB King (1974). This can be very useful to have an improved impression of the inlet current and the bay tidal response.

To illustrate its application, an image is included showing the ocean tide, bay tide and cross-sectional current. It is applicable for: inlet length 5 km; inlet width 3 km; inlet depth 15 m; bay depth 10 m; bay area 300 million square meter; tidal period 12.42 hours; and tidal range 2 m. In this particular example, the bay tide is slightly amplified and lags behind the ocean tide.

The illustrated example is only good for preliminary assessment. To better understand the complicated inlet-system processes – a coupled shallow-water numerical model may prove to be the best recourse – like the one described in my Ports2013 paper. Since opening of the Salt Ponds Inlet in 1979, the City of Hampton is required to dredge the inlet every 2 to 3 years to maintain its navigability. This frequency of recurring dredging is quite a burden and has not decreased despite the construction of jetties at the inlet mouth. Presented as a comparison of tide and wave powers – it turns out the tidal prism of the inlet is quite inadequate to flush out the sands mobilized by wave actions – active in the Chesapeake Bay. 
             
Management of Tidal Inlets on Littoral Shores. The problem of such inlets primarily hinges upon keeping them functional, open and navigable – this is necessary because most large inlets cater to the needs of ports, harbors and marinas – for in-and-out sailing of different types of vessels. What issues must one look for sound management of such an inlet? Let me try to highlight some briefly.
  • Requirement of the year-round navigable depth for the highest-draft vessel allowed to call on the port and marina (for deep-draft harbors > 4.6 m; for small-craft harbors ≤ 4.6 m; for marinas according to design specifications). If outer anchorage idling is allowed and available, then a vessel can take advantage of the high tide by riding on it. 
  • Maneuverability of the exiting and entering vessels – overall lengths and widths of the allowable vessel – and maximum currents and vortices within the inlet-bay system. Smaller vessels have low tolerance thresholds of such factors than the large ones.
  • Hydrodynamic actions on the inlet – the tidal pumping (period, range, inlet-bay hydraulics of tidal amplification or attenuation, volume of fresh water inflow), the wave actions on the inlet mouth (wave height and period – their spectral and directional distributions and seasonality); and the frequency and magnitude of extreme events such as storm surge and tsunami. One can classify an inlet as high, medium or low energy inlet based on wave and tidal actions and powers.
  • Textural composition of sediments, in particular in the ebb- and flood-tidal deltas, the inlet and the beach. And the amount of sand mobilized and transported by both longshore and cross-shore processes – their reworking by flood- and ebb-tidal flow.       
  • Ebb- and flood-tidal delta morphodynamics – their identifiable morphological patterns and causal relationships with the forcing hydrodynamic parameters. Morphodynamics of the scour holes that typically develop at the constriction and at the head of jetties and breakwaters.
  • If jetties (these are shore-perpendicular structures made of rocks or sheet piles placed at the updrift and downdrift sides of the inlet) are planned to address the problem – then some new issues appear: (1) most often such structures interrupt the continuity of longshore sand transport – the interruption causes updrift sedimentation and downdrift erosion; (2) what should be their lengths (for example, longer updrift jetty than the downdrift one? and how far should they extend beyond the surf zone?) and height; (3) if sand bypassing (such as by mechanical measures – e.g. pump dredging) is considered to re-establish the continuity of longshore transport – a totally new evaluation and design is required; (4) should weir be installed on the updrift jetty to allow some sand to pass through – only to be collected from pits and sumps for downdrift replenishment; and (5) should the jetties be permeable to some extent, to let some sands to pass through, and implications.
  • Examining the potentials and feasibility of series of groynes (shore-perpendicular) both at updrift and downdrift locations to train the beach morphodynamics such that the inlet will not be overwhelmed by longshore and onshore transports.
  • Examining the potentials and feasibility of reducing the wave actions by installing submerged offshore reefs. Or by installing series of offshore breakwaters both at updrift and downdrift areas beyond the surf zone.
  • If dredging is unavoidable either as a stand-alone measure or as a supporting activity to other measures – then it is important to streamline and customize it, so that recurring costs can be minimized.             
As usual this topic turned out to be another long piece in the WIDECANVAS. Without further adieu, let me finish it with a line of wisdom from Leo Tolstoy (1828 – 1910): there is no greatness where there is no simplicity, goodness and truth. 

.  .  .  .  .

- by Dr. Dilip K. Barua, 16 March 2018

0 Comments

The World of Numbers and Chances

1/19/2018

0 Comments

 
Picture
One must have guessed what I intend to discuss in this piece. People are glued to numbers in one way or another – for the sake of brevity let us say, from the data on finance, social demography and income distribution – to the scientific water level, wave height and wind speed. People say there is strength in numbers. This statement is mostly made to indicate the power of majority. But another way to examine the effectiveness of this statement is like this: suppose Sam is defending himself by arguing very strongly in favor of something. If an observer makes a comment like this, well these are all good, but the numbers say otherwise. This single comment has the power to collapse the entire arguments carefully built by Sam (unless Sam is well-prepared and able to provide counter-punch), despite the fact that numerical generalizations are invariably associated with uncertainties. Uncertainty is simply the lack of surety or absolute confidence in something.    

While the numbers have such powers, one may want to know:
  1. What was the purpose and how were these numbers collected?
  2. What is the attribution map to these numbers?
  3. Are there identifiable patterns in these numbers?
  4. If patterns exist, are they definite?
  5. Are the different sets of numbers correlated or do they belong to some groups?
  6. What is the likelihood of favorable outcomes of certain bins of numbers?
  7. What is the likelihood of favorable outcomes of certain extreme numbers that may not have been sampled yet?
  8. How certain are these likelihoods?
  9. Is the knowledge conveyed by numbers adequate for decision making?

The science that answers all these questions on an uncertainty paradigm is known as statistics. This science is about the stochastic (as opposed to deterministic) world – the world driven by the messages conveyed by random (showing no easily identifiable systematic pattern) numbers, and the chances of favorable outcomes of those numbers. The former refers to, or is generally known as Statistics – the science of collection, organization, presentation and interpretation of numbers or numerical information. The latter as a sub-division of statistics, stands for Probability – the method of evaluating the likelihood of favorable outcomes of an event or hypothesis if sampled many times.

Probability with its root in logic is commonly known as probability distribution because it shows the distribution of a statistical data set – a listing of all the favorable outcomes, and how frequent they might occur (as a clarification of two commonly confused terms: probability refers to what is likely to happen – it denotes the surety of a happening but unsurety in the scale of its likelihood; while possibility refers to what might happen but is not certain to – it denotes the unsurety of a happening). Both of these methods aim at turning the information conveyed by numbers or data into knowledge – based on which inferences and decisions can be made. Statisticians rely on tools and methods to figure out the patterns and messages conveyed by numbers that may appear chaotic in ordinary views.

The term many times originates from the Theory of Large Numbers. Statisticians say that if a coin is tossed for a short period, for instance 10 times – it may yield let us say, 7 heads (70% outcome) and 3 tails (30% outcome); but if tossed many more times, the outcomes of the two possibilities, head and tail is likely to be 50% each – the outcomes one logically expects to see. Following the proof of this observation by Swiss mathematician Jacob Bernoulli (1655 – 1705), the name of the theory was formally coined in 1837 by French mathematician Simeon Denis Poisson (1781 – 1840).

There is a third aspect of statistics – it is known as the Statistical Mechanics (different from ordinary mechanics that deals with one single state) that is mostly used by physicists. Among others, the system deals with equilibrium and non-equilibrium processes, and Ergodicity (the hypothesis that the average over long time of a single state is same as the average of a statistical ensemble – an ensemble is the collection of various independent states).

A few lines on the random and systematic processes. They can be discussed from the view points of both philosophical and technical angles. Randomness or lack of it, is all about perception – irrespective of what the numbers say, one may perceive certain numbers as random while others may see them differently. In technical terms, let me try to explain through a simple example. By building upon the Turbulence piece on the NATURE page, one can say that flow turbulent randomness appears when measurements tend to approximate to near-instantaneous sampling. Let us say, if one goes to the same spot again to measure turbulence under similar conditions; it is likely that the measurements would show different numbers. If the measurements are repeated again and again, a systematic pattern would likely emerge that could be traced to different causes – but the randomness and associated uncertainties of individual measurements would not disappear.

Something more on the randomness. The famous Uncertainty Principle proposed by German theoretical physicist Werner Karl Heisenberg (1901 – 1976) in 1926 changed the way science looks at Nature. It broke the powerful deterministic paradigm of Newtonian (Isaac Newton, 1642 – 1727) physics. The principle says that there can be no certainty in the predictability of a real-world phenomenon. Apart from laying the foundation of Quantum Mechanics, this principle challenges all to have a close look at everything they study, model and predict.                         

Among others, writing this piece is inspired after reading the books: A Brief History of Time (Bantam Books 1995) by British theoretical physicist Stephen Hawking (1942 - 2018); Struck by Lightning – the Curious World of Probabilities by JS Rosenthal (Harper Collins 2005); the 2016 National Academies Press volume: Attribution of Extreme Weather Events in the Context of Climate Change; and the Probability Theory – the Logic of Science by ET Jaynes (Cambridge University Press 2003). A different but relevant aspect of this topic – Uncertainty and Risk was posted earlier on this page indicating how decision making processes depend on shouldering the risks associated with statistical uncertainties.

On some earlier pieces on the NATURE and SCIENCE & TECHNOLOGY pages, I have described two basic types of models – the behavioral and the process-based mathematical models – the deterministic tools that help one to analyze and predict diverse fluid dynamics processes. Statistical processes yield the third type of models – the stochastic or probabilistic models – these tools basically invite one to see what the numbers say to understand the processes and predict things on an uncertainty paradigm. While the first two types of models are based on central-fitting to obtain mean relations for certain parameters, the third type looks beyond the central-fitting to indicate the probability of other occurrences.  

Before moving further, a distinction has to be made. What we have discussed so far is commonly known as the classical or Frequentist Statistics (given that all outcomes are equally likely, it is the number of favorable outcomes of an event divided by the total outcomes). Another approach known as the Bayesian Statistics was proposed by Thomas Bayes (1701 – 1761) – developed further and refined by French mathematician Pierre-Simon Laplace (1749 – 1827). Essentially, this approach is based on the general probability principles of association and conditionality.

Bayesian statisticians assume and use a known or expected probability distribution to overcome, for instance, the difficulties associated with the problems of small sampling durations. It is like infusing an intuition (prior information or knowledge) into the science of presently sampled numbers. [If one thinks about it, the system is nothing new – we do it all the time in non-statistical opinions and judgments.] While the system can be advantageous and allows great flexibility, it also has room for manipulation in influencing or factoring frequentist statistical information (that comes with confidence qualifiers) in one way or another.

Perhaps a little bit of history is desirable. Dating back from ancient times, the concept of statistics existed in all different cultures as a means of administering subjects and armed forces, and for tax collection. The term however appeared in the 18th century Europe as a systematic collection of demographic and economic data for better management of state affairs. It took more than a century for scientists to formally accept the method. The reason for such a long gap is that scientists were somewhat skeptical about the reliability of scattered information conveyed by random numbers. They were more keen on robust and deterministic aspects of repeatability and replicability of experiments and methods that are integral to empirical science.

Additionally, scientists were not used to trust numbers that did not accompany the fundamental processes causing them. Therefore, it is often argued that statistics is not an exact science. Without going into the details on such arguments, it can be safely said that many branches of science including physics and mathematics (built upon theories, and systematic uncertainties associated with assumptions and approximations) also do not pass the exactitude (if one still believes this term) of science.  

In any case as scientists joined, statistical methods received a big boost in sophistication, application and expansion (from simple descriptive statistics to many more advanced aspects that are continually being refined and expanded). Today statistics represents a major discipline in Natural and social sciences; and many decision processes and inferences are unthinkable without the messages conveyed or the knowledge generated by the science of numbers and chances. However, statistically generalized numbers do not necessarily tell the whole story, for instance when it comes down to human and social management – because human mind and personality cannot simply be treated by a rigid number. Moreover, unlike the methods scientists and engineers apply, for instance, to assess the consequences and risks of Natural Hazards on vulnerable infrastructure – statistics-based social decisions and policies are often biased toward favoring the mean quantities or majorities at the cost of sacrificing the interests of vulnerable sections of the social fabric.                        

When one reads the report generated by statisticians at the 2013 Statistical Sciences Workshop (Statistics and Science – a Report of London Workshop on the Future of Statistical Sciences) participated by several international statistical societies, one realizes the enormity of this discipline encompassing all branches of Natural and social sciences. Engineering and applied science are greatly enriched by this science of numbers and chances.                    

In many applied science and engineering practices, a different problem occurs – that is how to attribute and estimate the function parameters for fitting a distribution in order to extrapolate the observed frequency (tail ends of the long-term sample frequencies, to be more specific) to predict the probability of an extreme event (which may not have occurred yet). The applied techniques for such fittings to a distribution (ends up being different shapes of exponential asymptotes) of measurements are known as the extremal probability distribution methods.

They generally fall into a group known as the Generalized Extreme Value (GEV) distribution – and depending on the values of location, scale and shape parameters, they are referred to as Type I (or Gumbel distribution, German mathematician Emil Julius Gumbel, 1891 – 1966), Type II (or Fisher-Tippett distribution, British statisticians Ronald Aylmer Fisher, 1890 – 1962 and Leonard Henry Caleb Tippett, 1902 – 1985) and Type III (or Weibull distribution, Swedish engineer Ernst Hjalmar Waloddi Weibull, 1887 – 1979).

This in itself is a lengthy topic – hope to come back to it at some other time. For now, I have included an image I worked on, showing the probability of exceedence of water levels measured at Prince Rupert in British Columbia. From this image, one can read for example, that a water level of 3.5 m CD (Chart Datum refers to bathymetric vertical datum) will be exceeded for 60% of time (or that water levels will be higher than this value for 60% of time, and lower for 40%). In extreme probability distribution it is common practice to refer to an event in recurrence intervals or return periods. This interval in years says that an event of a certain return period has the annual probability – reciprocal of that period (given that the sampling refers to annual maxima or minima). For example, in a given year, a 100-year event has 1-in-100 chance (or 1%) of occurring.

Another distinction in statistical variables is very important – this is the difference between continuous and discrete random variables. Let me try to briefly clarify it by citing some examples. The continuous random variable is like water level – this parameter changes and has many probabilities or chances of occurring from 0 (exceptionally unlikely) to 1 (virtually certain). In many cases, this type of variables can be described by Gaussian (German mathematician Carl Freidrich Gauss, 1777 – 1855) or Normal Distribution. The discrete random variable is like episodic earthquake or tsunami events – which are sparse and do not follow the rules of continuity, and can best be described by Poisson Distribution.           
When one assembles huge amounts data, there are some first few steps one can do to understand them. Many of these are described in one way or another in different text books – I am tempted to provide a brief highlight here.
  1. A first impression on the quality of data can always be made by deciphering the documentations on the collection platforms, instrumentation, methodology, etc.
  2. Next, it is always helpful to make a plot of the data in order to make a preliminary assessment of scatter or cluster, errors, outliers, shift (could result from datum change, change in the instrumentation configuration, etc.) periodicity, and trend if any. These first two steps are very important for screening and validating the collected information.
  3. The next important step is to do some descriptive statistics – the central tendency (the location parameter – mean, median, and mode), their spread around the center (the scale parameter – the standard deviation, STD) and the shape parameter (symmetry/asymmetry, peak). The simplest and the most prevalent distribution yielding these parameters is the symmetric Normal Distribution – typical of continuous random variables. In this distribution, the larger the standard deviation the larger is the data scatter – with 68%, 95% and 99.8% of data lying within ±1 STD, ±2 STD and ±3 STD of the mean, respectively. In coastal waters, sea-state waves follow a skewed or asymmetric distribution – the Rayleigh Distribution (Lord Rayleigh, 1842 -1919). Whatever distribution is applicable, the data are usually presented in PDF (probability density function), CPD (cumulative probability distribution) or EPD (exceedence probability distribution). The first represents the occurrence probability; the last two are comparative probabilities.    
  4. Most continuous random variables represent a superimposed multiplicity of information belonging to different frequencies, amplitudes and phases. Application of the Fourier Transform (Jean-Baptiste Joseph Fourier, 1768 – 1830) routines is helpful to decompose the data into different components. This is useful for finding out the dominating frequencies, the periodicity or trend in the data.
  5. Depending on the purpose, one can then choose to remove some frequencies from the data by applying an appropriate filter. One such is the Low-Pass Filter (LPF) that passes information of frequencies lower than a cut-off frequency, and attenuates the higher frequencies. The other is the High-Pass Filter (HPF) – passing frequencies higher than a cut-off frequency and attenuating the lower frequencies. Moving average techniques are also applied for similar purposes.
  6. Looking into the stationarity of data is very important. Stationarity simply means that no upward or downward trend is evident in the data when moving averages are applied. Stationarity or non-stationarity has serious implications in future projections (such as GEV distributions – which are based on the assumption that data are stationary), for example of climate change and consequences.  Let me cite one simple example. The water level that one measures at a tidal station has many components – the highest period being the Nodal Period of 18.6 years – this period is caused by the oscillating inclination of the Moon’s orbit relative to the plane of the Earth’s Equator. This factor induces a subtle and small change in the time-series water level data – therefore Mean Sea Level is determined by averaging over this period. It is understandable that any prediction of climate change induced Sea Level Rise trend must take account of such factors to eliminate the undesirable frequencies.      
  7. There are some other analyses – statisticians use to make sense of large amount of multi-variate data, applied especially in climate, social and biological sciences. One of them is known as Cluster Analysis – referring to grouping or clustering, such that data in each group have more similar attributes or characteristics than the ungrouped data. The Principal Component Analysis (PCA) – is one such technique – it is a tool for identifying the patterns in data, and expressing the data in a way to highlight their similarities and differences. Among others, COVARIANCE evaluations are made to determine the strength of data correlation (if COV is 0, +ve or -ve, the variables are uncorrelated, positively correlated, and negatively correlated, respectively).  
This piece ended up into a long one than I anticipated.

Before finishing I like to illustrate a case of conditional probability, applied to specify the joint distribution of wave height and period. These two wave properties are statistically inclusive and dependent; and coastal scientists and engineers usually present them in joint frequency tables. As an example, the joint frequency of the wave data collected by the Halibut Bank Buoy in British Columbia shows that 0.25-0.5 m; 7-8 s waves occur for 0.15% of the time. As for conditional occurrence of these two parameters, analysis would show that the probability of 7-8 s waves is likely 0.52% given the occurrence of 0.25-0.5 m waves; and that of 0.25-0.5 m waves is likely 15.2% given the occurrence of 7-8 s waves.

Here is a piece of caution stated by a 19th century British statesman, Benjamin Disraeli (1804 – 1881): There are three kinds of lies: lies, damned lies, and statistics. Apart from bootstrapping, lies are ploys designed to take advantages by deliberately manipulating and distorting facts. The statistics of Natural sciences are less likely to qualify for lies – although they may be marred with uncertainties resulting from human error, data collection techniques and methods (for example, the data collected in the historic past were crude and sparse, therefore more uncertain than those collected in modern times).

​Data of various disciplines of social sciences, on the other hand are highly fluid in terms of sampling focus, size, duration and methods, in data-weighing, or in the processes of statistical analyses and inferences. Perhaps that is the reason why the statistical assessments of the same socio-political-economic phenomena by two different countries hardly agree, despite the fact that national statistical bodies are supposedly independent of any influence or bias. Perhaps such an impression of statistics was one more compelling reason for statistical societies to lay down professional ethics guidelines (e.g. International Statistics Institute; American Statistical Society).

.  .  .  .  .

- by Dr. Dilip K. Barua, 19 January 2018

0 Comments
<<Previous

    Dr. Dilip K Barua

    Archives

    December 2022
    August 2021
    April 2021
    November 2020
    June 2020
    January 2020
    February 2019
    May 2018
    March 2018
    January 2018
    October 2017
    September 2017
    November 2016
    October 2016
    September 2016
    August 2016
    July 2016
    June 2016
    May 2016
    April 2016

    Categories

    All

    RSS Feed

Powered by Create your own unique website with customizable templates.
  • Home
  • Nature
  • Social Interactions
  • Science & Technology
  • ABOUT