Introduction
The use of computers to model water and sediment transport processes has been around for as long as computers have been (~30 years). A model in this context is a mathematical description of a process or prediction about the end result of a process (or processes), expressed as an equation or series of equations. Quantitative models may be characterised as either analytical or numerical. Analytical models involve simple equations that can be solved rather readily, perhaps using only paper and pencil. Numerical models are much more complex, may involve things called differential equations, and are solved with complex computer codes. A sophisticated graphical user interface (GUI) is now available with all commercially available models. The chief advantage of models is their capacity to describe water and sediment movements and processes across a very wide area. For this reason, models are particularly useful ‘geospatial’ tools that find constructive application in a range of sediment management applications, particularly where there is a requirement to examine the far-field (sediment) impacts of dredging for example, or of marine construction activities.
The sheer mathematical power of modern computers coupled to modern computer graphics (which imbue a particularly glossy and impressive quality to outputs) can persuade non-specialist end users (laymen) to believe or interpret model outputs as definitive. This is dangerous: all contemporary models are, and will only ever be, an approximation of reality, and thus none of the outputs can ever be definitive. This raises the question: “how can non-specialists judge how accurate a given model is?” And a follow on question: “is the model fit for my purpose?” This information is critical where the model is being used to inform or support a particular sediment management initiative. This paper explores why estuary models encounter such difficulties in modeling water and sediment transport in estuaries, and how the non-specialist can understand for themselves the model quality.
Modelling estuaries is not a simple process. Unlike modelling used in other branches of civil engineering (e.g. bridge construction), where there are few surprises and the designs incorporate large safety factors, estuaries are complex systems that operate under the control of many influences, many of which are often poorly understood. The various parameters driving changes in sediment distribution and re-distribution work simultaneously and in unpredictable order, timing and magnitude. Things live in estuarine sediments, too, which complicates things further. There are many surprises. The four most salient problems with models are:
1. Errors in characterisation of the processes being modelled
2. Omission of important processes
3. Lack of knowledge of initial conditions
4. Intrusion of forces that influence events from outside the system
[1] and [2] recur almost universally, to a greater or lesser extent, within all models of sediment transport, and we find particular difficulties when trying to model mud transport in estuaries. As Teisson (1991) states: “The reasons of relative failure in gaining quantitative results do not come from the numerical techniques, which are well experienced today, but from the incomplete knowledge of basic processes such as deposition, erosion and consolidation of muddy sediment,’ and this remains largely true today. For example, research has shown that over 26 separate sedimentological parameters govern mud attributes/transport. This overwhelming complexity precludes modelling from first principles. In spite of this a range of muddy sediment transport models have been formulated, and they have achieved this effectively ignoring many of these parameters and assuming that much of the behaviour of muds in estuarine systems stems from the influence of but a few parameters. It is an axiom of mathematical modelling of natural processes only a sub-set of the various events, large and small, that constitute the process are actually expressed in the equations used. Pragmatic though it might be in either ignoring completely or ranking importance, these modelers have unwittingly reduced the chance that the model will be highly accurate. These issues form a basic impediment to modelling mud transport with a great deal of confide
nce.
An associated issue is that of biology. Very few academic models, and no commercial models, take account of biological aspects and processes. As McCave (1981) noted: “muds are a wonderful medium for life.” Whereas modellers tend to regard expanses of muddy (and sandy) sediments in port environments as abiotic environments devoid of life, the sediments are habitats for a range of flora and fauna, and almost all estuarine sediments are colonised by organisms that include bacteria, worms, shellfish, and macro-algae. Estuarine sediments are notoriously biologically active and biogeochemically reactive. It is naïve to surmise that the presence of the biology does not modify or mediate the transport characteristics of both sands and muds: it does. Aside from the aforementioned inherent complexities of muddy sediments, that we are not yet at the stage where the biological influences on transport are fully understood is also one of the reasons that current models of estuarine sediment transport will never predict sediment transport with very high levels of confidence.
Assessing Models: One Big Grey Area?
Non-specialists will better appreciate models and their application and use in the sediment management arena if they would have a general working knowledge of models, the types of estuary models used, previous successful model applications and a general understanding of model limitations as described above. This would equip the non-specialist with a realistic expectation where models are applied. However, there are two recognisable stages found within all model developments (the processes of model calibration and validation), and most non-specialists should be able to read these and judge for themselves how good a model is.
Whether a model is used for “screening-level” purposes or to make decisions concerning possible remedial actions or environmental compliance, there should be a demonstration that the model and its parameter values are reasonably representative of site conditions. This is achieved through the processes of model calibration and validation. Without these vital steps is not possible to assess whether predictions made with the model are reasonable. Two assessment steps are required:
1. Assessment of model inputs: all models require inputs in order to function. Provision of appropriate inputs to a model is part of the process of model calibration.
2. Assessment of model validation: validation is the process by which predictions from the model are compared to real-world data; critically validation must not use the same data as the calibration exercise.
Checking the Model Calibration
All models require inputs in order to function. Models inputs are parameter values which feature in equations which describe water and sediment transport. For example, a model that predicts the rate of sand transport along a shore face might require a value of the average wave height and direction. Most sediment transport models require information to be inputted on bottom sediment size and density in order to function. All models require a representation (3D map) of the sea bed (bathymetry) in order to function with any degree of robustness at all. A robust model, or at least as robust as we can currently make it, will contain data obtained specifically from the site e.g. wave measurements at the beach location above, or sediment data via collection and subsequent laboratory analysis of samples from the site, high quality bathymetry data are usually available for port areas via the port Hydrographic Department. A less robust model will either use historic values from the site, assume values for these parameters or pick them out of literature for other (similar) sites. The latter is replete with danger, especially for muddy estuarine settings, as the factors which control the transport of muddy sediments are highly site specific and can be, locally, extremely temporally variable.
A fundamental first check on whether a model is robust (and therefore may even entertain the prospect of being fit-for purpose) is to seek information on the model inputs. It is also important to understand which parameters have been downgraded or ignored entirely, and why. Clearly, a model based on current, site specific information for most (if not all) the primary process parameters may be judged by a non-specialist end user to have recognised and util
ised the highest quality input data. Some might argue that this approach should be the foundation of Good Practice. Collection of field data from the site is fundamental to development of a robust model. Technology progress, in particular in the areas of sensor accuracy and computer power and computer memory, have transformed the way in which data is collected and transformed also the data quality. The technology exists now to measure most of the input parameters required by estuarine and coastal sediment transport models. The chief sediment transport parameters which can be measured include:
??Flow velocity
??Flow shear
??Flow velocity which first produces sediment movement
??Sediment transport rates at higher flow velocities, plus model coefficients
??Sediment grain size
??Settling velocity (plus model coefficients)
??Sediment concentration
??Bed friction
??Bed roughness
??Mass deposition rate
??Grain density
??Porosity
To this, we should add system variables. These include things like the estuary or shoreline shape, the underlying geology, nearshore wind regimen, riverine sediment supply, water temperature, wave spectrum, beach slope, shoreline angle etc. etc. Many of the system variables are comparatively easy to measure. All (good) reports detailing the use of a model should have a section on the model inputs, outlining where the various inputs have come from and detailing any assumptions based upon a lack of direct data. The non-specialist should at first look for this section, and aim to understand the degree to which the model is supported by site specific data. This will provide a preliminary evaluation on the likely model confidence. Remember, though: a model with inputs derived from site specific measurements is better than one without, but even so remains an approximation of reality. This is chiefly because even collection of field data has to be caveated with assumptions too (measurements can’t be made everywhere and at all times).
End-users may wonder at variable model quality when the technology exists to gather data on most of the model inputs, and this is because for whatever reason (cost, lack of equipment to collect measurements, weather impediments, technological ignorance) a great many models are run using less than adequate data. Modellers respond to this by applying a ‘sensitivity analysis’, which is a means of testing the range of model outputs using a range of model inputs for one or more parameters. For example, a model which predicts the quantity of sediment depositing at a specific location can be run repeatedly with differing values for sediment settling velocity. The problem with this is that whilst a range of model outputs (sediment mass deposited) can be derived, you can never know the actual answer. Better to deploy a settling velocity instrument for a number of days at the site, and then use the real world value[s] for settling velocity.
Checking the Model Validation
Validation is the process in which predictions from the model e.g. predictions of longshore sand transport rate, predictions of sediment thickness deposited etc. are checked i.e. using measurements/data, preferably from the site. Critically validation must not use the data used in the calibration. Without validation there can be no objective appreciation of how close the ‘approximation of reality’ actually is, nor whether the model is ‘fit for purpose’. It is judicious, therefore, from the viewpoint of the non-specialist, also to check to what degree the model has been validated, and to understand how the validation has been performed (e.g. what data have been collected?). For the majority of contemporary models you will discover that models can predict water movements (e.g. current strength, wave height) with high accuracy. Indeed WRc specifies tolerances on [predicted versus actual], which are widely adopted, and provides useful guidance on model validity. There is no generic or specific guidance on acceptable tolerances for the predictive accuracy of sediment transport models. Is a prediction e.g. of longshore sand transport rate or sedimentation thickness, within an order of magnitude tolerable, or is a factor of two tolerable? This leaves sediment transport models on an impoverished standing, and creates a collective difficulty on the part of non-specialists to judge whether a model is suitable for a particular purpose or not. Unfortunately, this issue is beyond the scope of this paper.
Concluding Remarks
There is no doubt that numerical models of water and sediment transport are powerful tools in sediment management. They are applied daily the world over to many different sediment management problems and issues. Indeed, there are many examples of problems that could not be addressed using any other approach. However, in providing sediment managers with highly detailed, glossy outputs (often-times movies and animations of marine processes) it is a small step for the non-specialist to conclude that this is ‘the answer’. Edwards (1995) noted this: “The appearance of hard answers achieved by extensive quantitative analysis and simulation lends an ‘air of certainty to results even when based on certain assumptions’”. The key, therefore, is to understand the model assumptions. The approach advocated here – close inspection of the model calibration-validation procedures – will inform this understanding. We imagine that most non-specialists should be able to undertake this. However, if they simply do not comprehend the model then here, too, is an issue. Models as we have seen are especially complex things, and if you don’t understand the model fundamentally, then you will need to first be bold enough to say so, but – more importantly – find someone that does.
Finally, whilst the thrust of this paper has been on encouraging the non-specialist community to understand better water and sediment transport models for themselves, as a final step (and one would hope as part of a Good Practice Approach on the part of the model commissioner) we would always recommend you to employ an independent modelling expert to review the work. It might cost in the region of Euro 100,000 to commission a model whereas 2 days of a consultant’s time may be Euro 3000. It would be money well spent!
In a box
This article is based on a presentation given by the author at the Ports & Environment Seminar held in Amsterdam in March 2012. For further information contact Kevin Black at KBlack@Partrac.com