Worked Example: Coastal Management Modelling

Management of coastal aquifers is unforgiving. If too much fresh water is extracted, salt water takes its place. Depending on the location, measurements of historical system behaviour may be scarce or plentiful. However assimilation of these data using a numerical model that attempts to simulate salt water intrusion is nearly impossible because of long run times and a propensity for numerical misbehaviour.

So compromises must be made. Unfortunately, compromises can induce errors in critical model predictions – both on their own, and because parameters of a simplified model may incur bias through history-matching. However history-matching has the ability to reduce the uncertainties of some important model predictions. So simplifications and compromises are alright, as long as any bias that they induce is included in model predictive uncertainty intervals, and as long as these biases are small compared to other sources of uncertainty.

This GMDSI worked example focusses on a coastal aquifer in Southern Portugal. The system is over-exploited. Extraction must therefore be reduced. This poses an optimisation-under-uncertainty problem. How much water can be extracted from the aquifer while still keeping it safe?

Data is far from plentiful. However enough data are available to be useful. Our modelling philosophy is simple in concept, but somewhat difficult to implement. It is this. “Don’t assume anything. If something is unknown, then let it be uncertain. This includes components of the model that are simplifications of reality, but that allow us to assimilate uncertainty-reducing data.”

Our management model is single layer and single density. This is acceptable as the coastal aquifer, though over-exploited, has not yet been damaged by salt water. However, we use a complementary, 2D sectional, stochastic, variable-density model for stochastic parameterisation of the coastal boundary of the management model. This variable-density model simulates conditions on the other side of the coastal boundary – escape of fresh water through a confining layer under pre-development conditions, and encroaching saline water under present conditions.

We use the LUMPREM lumped-parameter soil moisture accounting model to simulate irrigation demand. History-matching is undertaken using PEST_HP and PESTPP-IES. Constrained optimisation of extraction is implemented using PESTPP-OPT and CMAES_HP.