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Current modeling approaches for hydrological modeling often rely on eitherphysics-based or data-science methods, including Machine Learning (ML)algorithms. While physics-based models tend to rigid structure resulting inunrealistic parameter values in certain instances, ML algorithms establish theinput-output relationship while ignoring the constraints imposed by well-knownphysical processes. While there is a notion that the physics model enablesbetter process understanding and ML algorithms exhibit better predictiveskills, scientific knowledge that does not add to predictive ability may bedeceptive. Hence, there is a need for a hybrid modeling approach to couple MLalgorithms and physics-based models in a synergistic manner. Here we develop aPhysics Informed Machine Learning (PIML) model that combines the processunderstanding of conceptual hydrological model with predictive abilities ofstate-of-the-art ML models. We apply the proposed model to predict the monthlytime series of the target (streamflow) and intermediate variables (actualevapotranspiration) in the Narmada river basin in India. Our results show thecapability of the PIML model to outperform a purely conceptual model ($abcd$model) and ML algorithms while ensuring the physical consistency in outputsvalidated through water balance analysis. The systematic approach for combiningconceptual model structure with ML algorithms could be used to improve thepredictive accuracy of crucial hydrological processes important for flood riskassessment.

Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processes