Water budget estimation under parameter uncertainty using Stein Variational Gradient Descent

Increasingly intensive drought periods during the summer months put stresses even on traditionally water-rich regions such as Switzerland. In the particularly dry year of 2018, several Swiss municipalities were forced to place bans on agricultural irrigation, while others were forced to import water from neighbouring catchments to sustain water supply. The preparation for and management during such droughts demands sustainable management plans which are often informed by numerical models providing decision support.

Unfortunately, sustainable water resources management of alpine regions often demands a greater degree of system complexity than usual. This complexity must be reflected in the models used for decision-support: fixed head boundaries must be used cautiously, the aquifer’s depth and properties are often uncertain and highly heterogeneous, and inflow and recharge are similarly difficult to quantify. Considering these diverse sources of uncertainty renders the Bayesian parameter inference problem highly challenging.

Towards this end, we explore a technique known as Stein Variational Gradient Descent (SVGD). This variational method implements a series of smooth transformations resulting in a particle flow, incrementally transforming an ensemble of particles into samples of the posterior. The method has been shown to be able to reproduce non-Gaussian and even multi-modal distributions, provided the underlying posterior is sufficiently smooth.

In this study, we test this algorithm with a groundwater model of the catchment of Fehraltorf implemented in MODFLOW 6. We consider parameter uncertainty for the aquifer depth and topology, its hydraulic parameters, and control variables for recharge and inflow. We report the resulting water table and budget and discuss the optimization performance.