Basics of GroundWater Modelling Part 3
*Model Calibration
After the first run of a model, model results may differ from field measurements. This is expected because modelling is just a simplification of reality and approximations and computational errors are inevitable. The process of model calibration is aimed at fine-tuning the model results to match the
measurements in the field. In a groundwater flow models, the resulting groundwater head is forced to match the head at measured points. This process requires changing model parameters (i.e. hydraulic conductivity or groundwater recharge) to achieve the best match. The calibration process is important to make the model predictive and it can also be used for inverse modelling.
*Model Verification and Validation
The term “validation” is not completely true when used in groundwater modelling. Oreskes et. al. (1994) asserted it is impossible to validate a numerical model because modelling is only approximation of reality. Model verification and validation is the next step after calibration. The objective of model validation is to check if the calibrated model works well on any dataset. Because the calibration process involves changing different parameters (i. e. hydraulic conductivity, recharge, pumping rate etc.) different sets of values for these parameters may produce the same solution. Reilly and Harbaugh (2004) concluded that good calibration did not lead to good prediction. The validation process determines if the resulting model is applicable for any dataset. Modellers usually split the available measurement data into two groups; one for calibration and the other for validation.
*Sensitivity Analysis
Sensitivity analysis is important for calibration, optimisation, risk assessment and data collection. In regional groundwater models, there are a large number of uncertain parameter. Coping with these uncertainties is time-consuming and requires considerable effort. Sensitivity analysis indicates which parameter or parameters have greater influence on the output.
Parameters with high influence on model output should get the most attention in the calibration process and data collection. In addition, the design of sampling location, and sensitivity analysis can be used to solve optimisation problems.
The most common method of sensitivity analysis is the use of finite difference approximations to estimate the rate of change in model output as a result of change in a certain parameter. The Parameter Estimation Package “PEST” uses this method (Doherty et. al. 1994).
Some other more efficient methods of sensitivity analysis have been used. Automatic differentiation has been used for sensitivity analysis in groundwater models and it produces precise output compared to finite difference approximations (Baalousha 2007).
*Uncertainty Analysis
Uncertainty in groundwater modelling is inevitable for a number of reasons. One source of uncertainty is the aquifer heterogeneity. Field data has uncertainty. Mathematical modelling implies many assumptions and estimations, which increase the uncertainty of the model output (Baalousha and Köngeter 2006). There are different approaches to incorporate uncertainty in groundwater modelling. The most famous approach is stochastic modelling using the Monte Carlo or Quasi Monte Carlo method (Kunstmanna and Kastensb. 2006: Liou, T. and Der Yeh, H. 1997). The problem with
stochastic models is that they require a lot of computations, and thus they are time consuming. Some modifications have been done on stochastic models to make them more deterministic, which reduces computational and time requirements. Latin Hypercube Sampling is a modified form of Monte Carlo Simulation, which considerably reduces the time requirements (Zhang and Pinder 2003).
*Common Mistakes in Modelling
A major mistake in modelling is conceptualisation. If the conceptual model is incorrect, the model output will be incorrect regardless of data accuracy and modelling approach. A good mathematical model will not resurrect an incorrect conceptual model (Zheng and Bennet, 2002).In all models, it is necessary to identify a certain reference elevation for all head so that the model algorithm can converge to a unique solution (Franke et. al. 1987). Boundary conditions should be treated with care, especially in a steady state simulation. Sometimes boundary conditions change during simulation and become invalid. A model with hydraulic boundary conditions will be invalid if stresses inside or outside the model domain cause the hydraulic boundaries to shift or change. Therefore, boundary conditions should be monitored at all times to ensure they are valid. Model parameterisation is a common mistake in modelling. Theoretical values of hydraulic properties or groundwater recharge should never substitute field data and field investigation. Assumptions like isotropy and homogeneity should not be used without support from field investigation. Selection of the model code is important to obtain a good solution. Different codes involve different mathematical settings that suit a certain problem. The selected code should consider characteristics of the area of interest and the objectives of modelling. Models can be well calibrated and match well with the measured values, but have an
incorrect mass balance. This can be a result of an improper conceptual model.
End of Part 3
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