Hydrologically informed machine learning for rainfall–runoff modelling: towards distributed modelling
Authors: Herath Herath Mudiyanselage Viraj Vidura , Chadalawada Jayashree , Babovic Vladan 
Published: August 2021

Abstract. Despite showing great success of applications in many
commercial fields, machine learning and data science models generally show
limited success in many scientific fields, including hydrology (Karpatne et
al., 2017). The approach is often criticized for its lack of
interpretability and physical consistency. This has led to the emergence of
new modelling paradigms, such as theory-guided data science (TGDS) and
physics-informed machine learning. The motivation behind such approaches is
to improve the physical meaningfulness of machine learning models by
blending existing scientific knowledge with learning algorithms. Following
the same principles in our prior work (Chadalawada et al., 2020), a new
model induction framework was founded on genetic programming (GP), namely the Machine Learning Rainfall–Runoff Model Induction (ML-RR-MI) toolkit.
ML-RR-MI is capable of developing fully fledged lumped conceptual
rainfall–runoff models for a watershed of interest using the building blocks of two flexible rainfall–runoff modelling frameworks. In this study, we extend ML-RR-MI towards inducing semi-distributed rainfall–runoff models. The meaningfulness and reliability of hydrological inferences gained from lumped models may tend to deteriorate within large catchments where the spatial heterogeneity of forcing variables and watershed properties is significant. This was the motivation behind developing our machine learning approach for distributed rainfall–runoff modelling titled Machine Induction Knowledge Augmented – System Hydrologique Asiatique (MIKA-SHA). MIKA-SHA captures spatial variabilities and automatically induces
rainfall–runoff models for the catchment of interest without any explicit
user selections. Currently, MIKA-SHA learns models utilizing the model
building components of two flexible modelling frameworks. However, the
proposed framework can be coupled with any internally coherent collection of building blocks. MIKA-SHA's model induction capabilities have been tested on the Rappahannock River basin near Fredericksburg, Virginia, USA.
MIKA-SHA builds and tests many model configurations using the model building components of the two flexible modelling frameworks and quantitatively identifies the optimal model for the watershed of concern. In this study, MIKA-SHA is utilized to identify two optimal models (one from each flexible modelling framework) to capture the runoff dynamics of the Rappahannock River basin. Both optimal models achieve high-efficiency values in hydrograph predictions (both at catchment and subcatchment outlets) and good visual matches with the observed runoff response of the catchment. Furthermore, the resulting model architectures are compatible with previously reported research findings and fieldwork insights of the watershed and are readily interpretable by hydrologists. MIKA-SHA-induced semi-distributed model performances were compared against existing lumped model performances for the same basin. MIKA-SHA-induced optimal models outperform the lumped models used in this study in terms of efficiency values while benefitting hydrologists with more meaningful hydrological inferences about the runoff dynamics of the Rappahannock River basin.