A causal physics-informed deep learning formulation for groundwater flow modeling and climate change effect analysis

Abstract

In this study, we propose and test a formulation for building causal physics-informed hybrid models over traditional physics-informed hybrid models (H-HBVo) and a convolutional neural network (1D-CNN) in groundwater level (GWL) modeling. Two types of models are built based on our formulation and named H-HBV and H-Lin, because they integrate two different hydrological models. The comparison is made in terms of performance and ability to learn cause-and-effect relationships between inputs and outputs. The novelty of this study lies in the CRC (Causal Relationship Constraints) conditions, derived from a mathematical development, that are imposed on the layers of the physics-informed hybrid model to force it to learn causal relationships. The results showed that the 1D-CNN algorithm performed slightly better than the hybrid algorithms, and that the H-Lin and H-HBV algorithms together achieved slightly better results than the traditional hybrid algorithm, H-HBVo. It is also obtained that the algorithms subjected to our formulations (H-Lin and H-HBV) are the ones with satisfactory causality properties and that the integration of domain knowledge is not sufficient to obtain causal and interpretable models within the framework of hybrid algorithms. Subsequently, an analysis of the effect of climate change is carried out for Quebec (Canada) using H-HBV models. The results show that the RCP and SSP scenarios give fairly similar results, i.e. an increase in GWL between 2011 and 2090 with median amplitudes varying between + 5.6 and + 7 cm. In some cases, the amplitude of increase can exceed between + 14 and + 23 cm, and even reach between + 35 and + 70 cm. The results of the climate change analysis are consistent with changes in vertical inflow and potential evapotranspiration, the input variables, for the different climate scenarios, confirming the robustness of our formulation.