Robust data worth analysis with surrogate models in groundwater

Abstract

<p>Physically-based groundwater models allow highly detailed spatial resolution, parameterization and process representation, among other advantages. Unfortunately, their size and complexity make many model applications computationally demanding. This is especially problematic for uncertainty and data worth analysis methods, which often require many model runs.</p><p>To alleviate the problem of high computational demand for the application of groundwater models for data worth analysis, we combine two different solutions:</p><ol><li>a) the use of surrogate models as faster alternatives to a complex model, and</li> <li>b) a robust data worth analysis method that is based on linear predictive uncertainty estimation, coupled with highly efficient null-space Monte Carlo techniques.</li> </ol><p>We compare the performance of a complex benchmark model of a real-world aquifer in New Zealand to two different surrogate models: a spatially and parametrically simplified version of the complex model, and a projection-based surrogate model created with proper orthogonal decomposition (POD). We generate predictive uncertainty estimates with all three models using linearization techniques implemented in the PEST Toolbox (Doherty 2016) and calculate the worth of existing, “future” and “parametric” data in relation to predictive uncertainty. To somewhat account for non-uniqueness of the model parameters, we use null-space Monte Carlo methods (Doherty 2016) to efficiently generate a multitude of calibrated model parameter sets. These are used to compute the variability of the data worth estimates generated by the three models.</p><p>Comparison between the results of the complex benchmark model and the two surrogates show good agreement for both surrogates in estimating the worth of the existing data sets for various model predictions. The simplified surrogate model shows difficulties in estimating worth of “future” data and is unable to reproduce “parametric” data worth due to its simplification in parameter representation. The POD model was able to successfully reproduce both “future” and “parametric” data worth for different predictions. Many of its data worth estimates exhibit a high variance, though, demonstrating the need of robust data worth methods as presented here which (to some degree) can account for parameter non-uniqueness.</p><p> </p><p>Literature:</p><p>Doherty, J., 2016. PEST: Model-Independent Parameter Estimation - User Manual. Watermark Numerical Computing, 6th Edition.</p>