The paper describes the process of induction of equations for the description of vegetation-induced roughness from several angles. Firstly, it describes two approaches for obtaining theoretically well-founded analytical expressions for vegetation resistance. The first of the two is based on simplified assumptions for the vertical flow profile through and over vegetation, whereas the second is based on an analytical solution to the momentum balance for flow through and over vegetation. In addition to analytical expressions the paper also outlines a numerical 1-DV k–e turbulence model which includes several important features related to the influence plants exhibit on the flow. Last but not least, the paper presents a novel way of applying genetic programming to the results of the 1-DV model, in order to obtain an expression for roughness based on synthetic data. The resulting expressions are evaluated and compared with an independent data set of flume experiments

Long short‐term memory (LSTM) networks represent one of the most prevalent deep learning (DL) architectures in current hydrological modeling, but they remain black boxes from which process understanding can hardly be obtained. This study aims to demonstrate the potential of interpretive DL in gaining scientific insights using flood prediction across the contiguous United States (CONUS) as a case study. Two interpretation methods were adopted to decipher the machine‐captured patterns and inner workings of LSTM networks. The DL interpretation by the expected gradients method revealed three distinct input‐output relationships learned by LSTM‐based runoff models in 160 individual catchments. These relationships correspond to three flood‐inducing mechanisms—snowmelt, recent rainfall, and historical rainfall—that account for 10.1%, 60.9%, and 29.0% of the 20,908 flow peaks identified from the data set, respectively. Single flooding mechanisms dominate 70.7% of the investigated catchments (11.9% snowmelt‐dominated, 34.4% recent rainfall‐dominated, and 24.4% historical rainfall‐dominated mechanisms), and the remaining 29.3% have mixed mechanisms. The spatial variability in the dominant mechanisms reflects the catchments' geographic and climatic conditions. Moreover, the additive decomposition method unveils how the LSTM network behaves differently in retaining and discarding information when emulating different types of floods. Information from inputs within previous time steps can be partially stored in the memory of LSTM networks to predict snowmelt‐induced and historical rainfall‐induced floods, while for recent rainfall‐induced floods, only recent information is retained. Overall, this study provides a new perspective for understanding hydrological processes and extremes and demonstrates the prospect of artificial intelligence‐assisted scientific discovery in the future.

Governments face the daunting task of developing policies and making investment decisions for climate change adaptation in an environment that consist of complex, interlinked systems with manifold uncertainties. Instead of responding to surprises and making decisions on ad hoc basis, a structured approach to deal with complex systems and uncertainties can provide indispensable support for policy making. This contribution proposes a structured approach for designing climate adaptation policies based on the concepts of Adaptation Pathways, Adaptive Policy Making, and Real Options Analysis. Such an approach results in incorporation of flexibility that allows change over time in response to how the future unfolds, what is learned about the system, and changes in societal preferences. The approach is illustrated by looking at drainage policies and measures to address flooding in Singapore.

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.

Models of water resources systems are conceived to capture the underlying environmental dynamics occurring within watersheds. All such models can be regarded as working hypotheses, differing in the aspects of process representation and conceptualization. Most of the associated efforts in the water resources research community is dedicated to development of new models that perform well under specific atmospheric conditions and catchment properties. In this context, flexible modeling frameworks are gaining importance as they facilitate the model building process by providing the model building blocks, whereby the hydrologist is free to assemble the model for task at hand. Such flexible models have high degree of transferability, which in turn aid in progressing toward a unified hydrological theory at catchment scale. However, in cases without sufficient insights regarding a catchment characteristics and/or lack of expert's knowledge, one may have to try a large number of model configurations based on available model building blocks to construct an appropriate model for the catchment of interest. Undoubtedly, this may be time consuming and computationally intensive. This paper proposes a novel model building algorithm, which uses the full potential of flexible modeling frameworks by searching the model space and inferring suitable model configurations relying on machine learning. Proposed machine learning algorithm is based on evolutionary computation approach using genetic programming (GP). State‐of‐art GP applications in rainfall‐runoff modeling so far used the algorithm as a short‐term forecasting tool that generates an expected future time series very similar to neural networks application. In this case, the proposed algorithm develops a physically meaningful rainfall‐runoff model. Although at the moment we learn models using two flexible modeling frameworks (SUPERFLEX and FUSE), the model induction toolkit can be armed with any internal coherence building blocks. The model induction capabilities of the proposed framework have been evaluated on the Blackwater River basin, Alabama, United States. The model configurations evolved through the model induction toolkit are consistent with the fieldwork investigations and previously reported research findings.