Lesson 8 - The Problem of Uncertainty in Contaminant Transport Models

For most real-world systems, at least some of the controlling parameters, processes and events are often uncertain (i.e., poorly understood or quantified) and/or stochastic (i.e., inherently temporally variable). It is for this reason that GoldSim was specifically designed as a powerful probabilistic simulator (probabilistic simulation using GoldSim is discussed in detail starting in Unit 11 of the Basic GoldSim Course).

Although this “problem of uncertainty” applies to any kind of system you may want to simulate (and it is unfortunately often ignored), due to the nature of the systems involved, this issue is especially important when dealing with environmental systems, and particularly so when trying to carry out contaminant transport modelling.

Sources of Uncertainty in Environmental Models

If you give it a little thought, the reasons for the high uncertainty associated with contaminant transport modeling should be clear. Engineered systems (such as a factory or a machine) are, for the most part, well-defined and understood (e.g., you can typically measure the important variables and properties of these systems, may have many similar systems that you can look at to better understand performance, and can often build and test prototypes). They still have uncertainty in their performance (primarily due to exogenous environmental variables that may be important, or perhaps behavior over very long time periods that is difficult to prototype), but this uncertainty is typically not extremely large (and that is why complex machines like airplanes are quite safe and predictable).

For environmental systems, however, we often have a much poorer understanding of the system.  A major reason for this is that they often cannot be easily characterized (i.e., the relevant parameters cannot be easily measured). For example, if trying to predict contaminant transport through groundwater, it is not practical or feasible to completely characterize the subsurface environment and determine the relevant properties (instead, you may have only a handful of data points). This is complicated by the fact that the properties themselves (e.g., hydraulic conductivity, chemical environment) are spatially variable. This spatial variability is important because some of the key parameters controlling mass transport for a contaminant, such as its solubility and partition coefficients to various solids, may be extremely sensitive to local environmental conditions that are difficult to characterize and potentially highly variable (e.g., pH and redox).  Relatively small changes in local environmental conditions could result in order of magnitude changes in these parameters.

Some parameters used to describe contaminant transport are quite difficult to measure at all. An example of this is the dispersivity discussed in Lesson 4. Dispersivity is unusual in that unlike a property like porosity it is not really meaningful to say that it has some value at a particular point in space. This is because its value is typically considered to be scale dependent (due to the concept of macrodispersion discussed previously).  Hence, it can be thought of as a property of the entire system. This, of course, can make it difficult to quantify (doing so may require a large-scale field experiment that may not be feasible or practical).

In some cases, the processes themselves may be poorly understood.  For example, if your model included a pond with many chemical constituents, and during the simulation the pond went dry due to evaporation, concentrations in the pond would be very high (and spatially variable over small distances) and hence the various chemical precipitation reactions taking place while the pond evaporates would be quite difficult to predict accurately.  As a result, the behavior of such a system would have lots of uncertainty.

In many cases, extremely important variables required for predicting performance may be almost entirely unavailable and/or need to be estimated using very poor information.  For contaminant transport models, particularly for existing waste sites, the classic example of this is the source term.  There may be very limited information available regarding what was disposed and when it was disposed.  This imposes a very large uncertainty on any predictive models.

In addition to these issues, it is often not practical or feasible to carry out experiments or evaluate alternative designs for environmental systems you are trying to model. In many cases, it is simply not possible to build and test alternative designs for a proposed system (such as a mine) – the system is simply too large to build and test realistic prototypes. The long time frames involved for some systems also makes this impossible. For example, when disposing of radioactive waste, highly engineered waste packages are often used. Laboratory tests can be carried out on these for months or perhaps years to evaluate their performance.  But their design life is typically thousands of years, and it is very difficult to design experiments to extrapolate performance over such time frames.

Models with long time frames have many other difficulties.  For example, climatic factors (e.g., rainfall) will typically play an important role in environmental models. But predicting future climate for thousands (or even for tens or hundreds) of years in the future is difficult. And, of course, even for very short duration models (months or years), the stochastic nature of weather adds uncertainty to many environmental models.

All of these factors result in very large uncertainties (in some cases, several orders of magnitude) in many of the parameters, processes and events associated with contaminant transport models.

Why Is Dealing with Uncertainty So Important?

Unfortunately, the large uncertainties discussed above are often ignored. If uncertainties are acknowledged at all, the modeler often does so by selecting single values for each parameter, labeling them as “best estimates” or perhaps “worst case estimates”. These inputs are evaluated in the simulation model, which then outputs a single deterministic result, which presumably represents a “best estimate” or “worst case estimate”. They may also carry out some simple sensitivity analyses on some of the parameters.

Unfortunately, dealing with large uncertainties in this way when making predictions about the performance of an environmental system is highly problematic.

Defending “best estimate” approaches is often very difficult. In a confrontational environment (e.g., demonstrating that a particular facility will meet certain regulatory criteria), “best estimate” analyses will typically evolve into “worst case” analyses.  However, “worst case” analyses can be extremely misleading. Worst case analyses of a system are likely to be grossly conservative and therefore completely unrealistic (i.e., by definition, picking lots of unlikely “pessimistic” values will almost certainly have an extremely low probability of actually representing the future behavior of the system). And it is not possible in a deterministic simulation to quantify how conservative a “worst case” simulation actually is (i.e., define its probability). Using a highly improbable estimate to guide policy-making (e.g., “is the design safe?”) is likely to result in very poor decisions.

Due the large uncertainties in the parameters, processes and events associated with contaminant transport models, and the problems with deterministic approaches described above, GoldSim’s modeling philosophy revolves around the belief that explicitly representing these uncertainties (by carrying out probabilistic simulations) is critical. And as we will see in the next Lesson, realistically acknowledging and representing uncertainty has important implications for how you should build and structure your models.