  Current modeling approaches for hydrological modeling often rely on either
physics-based or data-science methods, including Machine Learning (ML)
algorithms. While physics-based models tend to rigid structure resulting in
unrealistic parameter values in certain instances, ML algorithms establish the
input-output relationship while ignoring the constraints imposed by well-known
physical processes. While there is a notion that the physics model enables
better process understanding and ML algorithms exhibit better predictive
skills, scientific knowledge that does not add to predictive ability may be
deceptive. Hence, there is a need for a hybrid modeling approach to couple ML
algorithms and physics-based models in a synergistic manner. Here we develop a
Physics Informed Machine Learning (PIML) model that combines the process
understanding of conceptual hydrological model with predictive abilities of
state-of-the-art ML models. We apply the proposed model to predict the monthly
time series of the target (streamflow) and intermediate variables (actual
evapotranspiration) in the Narmada river basin in India. Our results show the
capability of the PIML model to outperform a purely conceptual model ($abcd$
model) and ML algorithms while ensuring the physical consistency in outputs
validated through water balance analysis. The systematic approach for combining
conceptual model structure with ML algorithms could be used to improve the
predictive accuracy of crucial hydrological processes important for flood risk
assessment.
