Water Modeling

With this piece I am breaking my usual 3-3-3 cycle of posting the blogs on the NATURE, SOCIAL INTERACTIONS and SCIENCE & TECHNOLOGY pages. The reason is partly due to the comment of one of my friends who said, it is nice reading the Nature and Science & Technology pages. Hope you would share more of your other experiences in theses pages. Well, I have wanted to that but in the disciplined order of 3-3-3 postings. But this does not mean that the practice cannot be changed to concentrate more on the technical pages. Let us see how things go – a professional experience spanning well over 3 decades is long enough to accumulate many diverse and versatile humps and bumps, distinctions and recognitions, and smiles and sadness. 
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This piece can be very long, but I will try to limit it to the usual 4 to 5 pages starting from where I left – some of the model basics described in the Natural Equilibrium blog on the NATURE page, and in the Common Sense Hydraulics blog on this page. To suit the interests of general members of the public, I will mainly focus on the practical aspects of water modeling rather than on numerical aspects.
The title of this piece could have been different – numerical modeling, computational modeling, hydrodynamic modeling, wave modeling, sediment transport modeling, morphological modeling . . . Each of these terms conveys only a portion of the message what a modeling of Natural water means. The Natural waters in a coastal environment are 3-dimensional – in length, width and depth, subjected to the major forces – externally by tide and wave at the open boundaries, wind forcing at the water surface and frictional resistance at the bottom. The bottom can be highly mobile like in alluvial beds, or can be relatively fixed like in a fjord. Apart from these regular forcings coastal waters are also subjected to extreme episodes of storm surge and tsunami.
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While the Natural coastal setting is 3-dimensional, it is not always necessary to treat the system as such in a model. Depending on the purpose and availability of appropriate data, coastal systems can be approximated as 2-dimensional or 1-dimensional. The 2-dimensional shallow-water approximation is possible especially when the aspect ratio (depth/width) is low. When a channel is very long and the aspect ratio is relatively high, it can even be modeled as 1-dimensional.
Apart from these dimensional approximations, some other approximations are also possible because all terms of the governing equations do not carry equal weight. I have tried to highlight how to examine the importance of different terms in a conference presentation (A Dynamic Approach to Characterize a Coastal System for Computational Modeling and Engineering. Canadian Coastal Zone Conference, UBC, 2008). The technique known as scale analysis lets one to examine a complicated partial differential equation by turning it into a discrete scale-value-equation. My presentation showing the beauty of scale analysis is highlighted for the governing hydrodynamics of fluid motion – the Navier-Stokes Equation (Claude-Louis Navier, 1785 – 1836 and George Gabriel Stokes, 1819 – 1903). It was further demonstrated in my Encyclopedia article, Seabed Roughness of Coastal Waters for practical workable solutions.
The technique can also be applied for any other equation – such as the integral or phase-averaged wave action equation, and the phase resolving wave agitation equation. Many investigators deserve credit for developing the phase-averaged wave model – which is based on balancing the wave energy-action. The phase-resolving wave model is based on the formulation by Boussinesq – the French mathematician and physicist Joseph Valentin Boussinesq (1842 – 1929). The latter is very useful in shallow-water wave motions associated with non-linearity and breaking, and in harbors responding to wave excitation at its entrance.   
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To give an idea about the model simulated results, I have included an image taken from one of my Power Points (Littoral Shoreline Change in the Presence of Hardbottom – Approaches, Constraints and Integrated Modeling) presented at the 22nd Annual National Conference on Beach Preservation Technology, St. Pete Beach, Florida, 2009 on behalf of Coastal Tech. It is a depiction of model-simulated south-bound longshore currents that could develop during an obliquely incident storm wave from the northeast. The incident wave is about 4 meter high generated by a Hurricane Frances (September 5th 2004) like storm on the Indian River County shores in Florida. 
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Water modeling is fundamentally different and perhaps more complex – for example, from structural stability and strength modeling and computations. This assertion is true in a sense that a water model first aims to simulate the dynamics of Natural flows to a reasonable level of acceptance, before more can be done with the model – to use it as a soft tool to forecast future scenarios, or to predict changes and effects when engineering interventions are planned.
Water modeling is like a piece of science and art, where one can have a synoptic view of water level, current, wave and sediment transport, and bed morphology within the space of the model domain simultaneously – this convenience cannot be afforded by any other means. If the model results are animated, one can see how the system parameters evolve in response to forces and actions – this type of visuals is rather easy and instructive for anyone to understand the beauty and dynamics of fluid motion. For modelers, the displays elevate his or her intuition helping to identify modeling problems and solutions.        
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Before going further, I would like to clarify the two terms I have introduced in the Coastal River Delta blog on the NATURE page. These two terms are behavioral model and process-based model. Let me try to explain the meaning of these two terms briefly by illustrating two simple examples. The simple example of a behavioral model is the Bruun Rule or the so-called equilibrium 2/3rd beach profile, proposed by Per Bruun in 1954 and refined further by Bob Dean (Robert G. Dean, 1931 – 2015) in 1977. The relation simply describes a planer (no presence of beach bars) beach depth as the 2/3rd power of cross-shore distance – without using any beach-process parameters such as the wave height and wave period. The only other parameter the Rule uses is the sand particle settling velocity. This type of easy-to-understand behavioral models that does not look into the processes exciting the system, exists in many science and engineering applications. The behavioral models capture response behaviors that are often adequate to describe a particular situation – however they cannot be applied or need to be updated if the situation changes.
The simple example of a process-based model is the Chezy Equation (Antoine Chezy, 1718 – 1798) of the uniform non-accelerating flow – that turns out to have resulted from balancing the pressure-gradient force against the frictional resistance force. In this relation velocity of flow is related to water depth, water level slope (or energy slope) and a frictional coefficient. The advantage of a process-based model is that it can be applied in different situations, albeit as an approximation in which it has been derived.           
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Let us now turn our attention to the core material of this piece – the numerical water modeling. The aspects of the scale modeling used to reproduce water motion in a miniature replica of the actual prototype in controlled laboratory conditions are not covered in this piece. These types of models are based on scale laws by ensuring that the governing dimensionless numbers are preserved in the model as in the prototype. I have touched upon a little bit of this aspect in the Common Sense Hydraulics piece on this page.
I have been introduced to programming and to the fundamentals of numerical water modeling in the academic programs at IHE-UNESCO and at the USC. My professional experience started at the Land Reclamation Project (LRP) with the supports from my Dutch colleagues and participating in the hydrodynamic modeling efforts of LRP. Starting with programmable calculators, I was able to develop several hydraulic processing programs and tools – later translating them to personal computer versions.
I must say, however that my knowledge and experience have really taken-off and matured during my heavy involvement with numerical modeling efforts in several projects in Canada, USA and overseas. This started with a model selection study I conducted with UBC for the Fraser River in British Columbia.
A little brief on my modeling experiences. They include the systems: 8 in British Columbia, 1 in Quebec, 1 in Newfoundland and Labrador, 2 in Florida, 1 in Texas and 1 in Virginia. Among the modeled processes were hydrodynamics, wave energy actions, wave agitations, coupled wave-hydrodynamics, and coupled-wave-hydrodynamics-sediment transport-morphologies. The model forcings were tide, wind and wave, storm surge and tsunami. I will try to get back to some of the published works at some other time. Perhaps it is worthwhile to mention here that modeling experience is also a learning exercise; therefore one can say that all hydraulic engineers should have some modeling hand-on experiences, because they let him or her to acquire very valuable insights on hydraulics – simply using available relations to compute forces and parameters may prove incomplete and inadequate.    
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In the Uncertainty and Risk piece on this page, some unavoidable limitations and constraints of models are discussed. Let me try to outline them in some more details. Model uncertainties can result from 8 different sources:

1. representitiveness (difference between the real and the modeled hydraulic situations);
   
2. empiricism (weak relations embedded into the model formulation);
   
3. discretization of the continuum (unavoidable but minimizable);
   
4. iteration to convergence (when the solution residuals could not be completely eliminated);
   
5. rounding-off (when machine calculation rounds-off up to certain digits);
   
6. application (erroneous data usage in developing and running the model);
   
7. modeler (when the modeler has poor understanding of the processes he or she is modeling, and of the model theoretical basics); and
   
8. the numerical code (codes contain thousands of lines and subroutines, therefore it is not unlikely that inadvertent errors creep in).
   

The types of uncertainties indicate that the onus of model performance falls on the shoulders of three: the software being applied, the constraints associated with the quality of data, and the competence of the modeler. Some of the described uncertainties are better managed and minimized in professional commercial software compared to the academic and freely available ones. In addition, commercial software comes with well-developed customized pre- and post-processing tools, thus saving the time and effort of a modeler. Data quality has deeper meanings; it not only means the data accuracy, but also data coverage in space and time – in length and resolution.
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Before a model is ready for application, it requires going through a process of validation. This process of comparing model outputs against corresponding measurements leads to tuning and tweaking of parameters to arrive at acceptable agreements. It is also reinforced with sensitivity analysis to better understand the model responses to parameter changes.  
I have often been asked whether water modeling is worth the efforts and costs. My univocal answer to the question is yes. In this age of quickly improving digital computations, displays, animations and automations, it would be a shame if one thinks otherwise. Science and engineering are not standing still – the capability of numerical models is continually being refined and improved at par with the developments of new techniques in the computing powers of digital machines.
Like all project phases, a water model can be developed in phases – for example, starting with a course and rough model with the known regional data. Such a preliminary model developed by experienced modelers can be useful to develop project concepts and pre-feasibilities, and can also help planning measurements for a refined model required at subsequent project phases.
We have tried to conclude that a model is a soft tool; therefore its performance in simulation and prediction is not expected to be exact. This means that one should be cautious not to oversell or over-interpret what a model cannot do. But even if a water model is not accurate enough to be applied as a quantitative tool, it can still be useful for qualitative and conceptual understandings of fluid motion, in particular as a tool to examine the effectiveness and effects of engineering measures under different scenarios.                     
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Here is an anecdote to ponder:
The disciple asked the master, “Sir, what does digitization mean to social fluidity or continuity?”
The master replied, “Umm! Imagine a digital image built by many tiny pixels to create the totality of it. Each of these pixels is different, yet represents an essential building block of the image puzzle. Now think of the social energy – the energy of the harmonic composite can similarly be high and productive when each building block has the supporting integrity and strength.”

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- by Dr. Dilip K. Barua, 22 September 2016

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