Deep learning based differentiable/hybrid modelling of the global hydrological cycle
Authors: Baghirov Zavud , Kraft Basil , Jung Martin , Körner Marco , Reichstein Markus 
Published: March 2024

The integration of machine learning (ML) and process based modeling (PB) in so-called hybrid models, also known as differentiable modelling, has recently gained popularity in the geoscientific community (Reichstein et al. 2019; Shen et al. 2023). The approach aims to address limitations in both ML (data adaptive but di&#64256;icult to interpret and physically inconsistent) and PB (physically consistent and interpretable but biased). It holds significant potential for studying uncertain processes in the global water cycle (Kraft et al. 2022).
In this work, we developed a differentiable/hybrid model of the global hydrological cycle by fusing deep learning with a custom PB model. The model inputs include air temperature, precipitation, net radiation as dynamic forcings, and static features like soil texture as input to a long short-term memory (LSTM) model. The LSTM represents the uncertain and less understood spatio-temporal parameters which are directly used in a conceptual hydrological model. Simultaneously, we use fully connected neural networks (FCNN) to represent the uncertain spatial parameters. In the hydrological model we represent key water fluxes (e.g. transpiration, evapotranspiration (ET), runoff) and storages (snow, soil moisture and groundwater). The model is constrained against the observation-based data, like terrestrial water storage (TWS) anomalies (GRACE), fAPAR (MODIS) and snow water equivalent (GLOBSNOW).

Building upon previous work (Kraft et al. 2022), we improved the representations of key hydrological processes. We now explicitly estimate vegetation state that is directly used to partition ET into transpiration, soil and interception evaporation. We also estimate rooting-zone water storage capacity&#8212;a key hydrological parameter that is still highly uncertain. To asses the robustness of the estimated parameters, we quantify equifinality by training multiple models with random weight initialisation in a 10-fold cross validation setup.

The model learns reasonable spatial and spatio-temporal patterns of critical, yet uncertain, hydrological parameters as latent variables. For example, we assess and show that the estimations of global spatial patterns on rooting-zone water storage capacity and transpiration versus ET are plausible. Equifinality quantification indicates that the dynamic patterns of the modelled water storages are robust, while there is a large uncertainty in the mean of soil moisture and TWS.

References
Kraft, Basil, Martin Jung, Marco Ko&#776;rner, Sujan Koirala, and Markus Reichstein. 2022. &#8220;Towards Hybrid Modeling of the Global Hydrological Cycle.&#8221; Hydrology and Earth System Sciences 26 (6): 1579&#8211;1614.
Reichstein, Markus, Gustau Camps-Valls, Bjorn Stevens, Martin Jung, Joachim Denzler, Nuno Carvalhais, et al. 2019. &#8220;Deep Learning and Process Understanding for Data-Driven Earth System Science.&#8221; Nature 566 (7743): 195&#8211;204.
Shen, Chaopeng, Alison P Appling, Pierre Gentine, Toshiyuki Bandai, Hoshin Gupta, Alexandre Tartakovsky, Marco Baity-Jesi, et al. 2023. &#8220;Differentiable Modelling to Unify Machine Learning and Physical Models for Geosciences.&#8221; Nature Reviews Earth &amp; Environment 4 (8): 552&#8211;67.