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Rainfall–runoff modeling is a complex nonlinear time-series problem in the field of hydrology. Various methods, such as physical-driven and data-driven models, have been developed to study the highly random rainfall–runoff process. In the past 2 years, with the advancement of computing hardware resources and algorithms, deep-learning methods, such as temporal convolutional network (TCN), have been shown to be good prospects in time-series prediction tasks. The aim of this study is to develop a prediction model based on TCN structure to simulate the hourly rainfall–runoff relationship. We use two datasets in the Jingle and Kuye watersheds to test the model under different network structures and compare with the other four models. The results show that the TCN model outperforms the Excess Infiltration and Excess Storage Model (EIESM), artificial neural network, and long short-term memory and improves the flood forecasting accuracy at different foreseeable periods. It is shown that the TCN has a faster convergence rate and is an effective method for hydrological forecasting.

Regional rainfall–runoff modeling is an old but still mostly outstanding problem in the hydrological sciences. The problem currently is that traditional hydrological models degrade significantly in performance when calibrated for multiple basins together instead of for a single basin alone. In this paper, we propose a novel, data-driven approach using Long Short-Term Memory networks (LSTMs) and demonstrate that under a “big data” paradigm, this is not necessarily the case. By training a single LSTM model on 531 basins from the CAMELS dataset using meteorological time series data and static catchment attributes, we were able to significantly improve performance compared to a set of several different hydrological benchmark models. Our proposed approach not only significantly outperforms hydrological models that were calibrated regionally, but also achieves better performance than hydrological models that were calibrated for each basin individually. Furthermore, we propose an adaption to the standard LSTM architecture, which we call an Entity-Aware-LSTM (EA-LSTM), that allows for learning catchment similarities as a feature layer in a deep learning model. We show that these learned catchment similarities correspond well to what we would expect from prior hydrological understanding.

Long short-term memory (LSTM) models are recurrent neural networks from the field of deep learning (DL) which have shown promise for time series modelling, especially in conditions when data are abundant. Previous studies have demonstrated the applicability of LSTM-based models for rainfall–runoff modelling; however, LSTMs have not been tested on catchments in Great Britain (GB). Moreover, opportunities exist to use spatial and seasonal patterns in model performances to improve our understanding of hydrological processes and to examine the advantages and disadvantages of LSTM-based models for hydrological simulation. By training two LSTM architectures across a large sample of 669 catchments in GB, we demonstrate that the LSTM and the Entity Aware LSTM (EA LSTM) models simulate discharge with median Nash–Sutcliffe efficiency (NSE) scores of 0.88 and 0.86 respectively. We find that the LSTM-based models outperform a suite of benchmark conceptual models, suggesting an opportunity to use additional data to refine conceptual models. In summary, the LSTM-based models show the largest performance improvements in the north-east of Scotland and in south-east of England. The south-east of England remained difficult to model, however, in part due to the inability of the LSTMs configured in this study to learn groundwater processes, human abstractions and complex percolation properties from the hydro-meteorological variables typically employed for hydrological modelling.

Deep learning is becoming an increasingly important way to produce accurate hydrological predictions across a wide range of spatial and temporal scales. Uncertainty estimations are critical for actionable hydrological prediction, and while standardized community benchmarks are becoming an increasingly important part of hydrological model development and research, similar tools for benchmarking uncertainty estimation are lacking. This contribution demonstrates that accurate uncertainty predictions can be obtained with deep learning. We establish an uncertainty estimation benchmarking procedure and present four deep learning baselines. Three baselines are based on mixture density networks, and one is based on Monte Carlo dropout. The results indicate that these approaches constitute strong baselines, especially the former ones. Additionally, we provide a post hoc model analysis to put forward some qualitative understanding of the resulting models. The analysis extends the notion of performance and shows that the model learns nuanced behaviors to account for different situations.

Neural networks have been shown to be extremely effective rainfall-runoff models, where the river discharge is predicted from meteorological inputs. However, the question remains: what have these models learned? Is it possible to extract information about the learned relationships that map inputs to outputs, and do these mappings represent known hydrological concepts? Small-scale experiments have demonstrated that the internal states of long short-term memory networks (LSTMs), a particular neural network architecture predisposed to hydrological modelling, can be interpreted. By extracting the tensors which represent the learned translation from inputs (precipitation, temperature, and potential evapotranspiration) to outputs (discharge), this research seeks to understand what information the LSTM captures about the hydrological system. We assess the hypothesis that the LSTM replicates real-world processes and that we can extract information about these processes from the internal states of the LSTM. We examine the cell-state vector, which represents the memory of the LSTM, and explore the ways in which the LSTM learns to reproduce stores of water, such as soil moisture and snow cover. We use a simple regression approach to map the LSTM state vector to our target stores (soil moisture and snow). Good correlations (R2>0.8) between the probe outputs and the target variables of interest provide evidence that the LSTM contains information that reflects known hydrological processes comparable with the concept of variable-capacity soil moisture stores. The implications of this study are threefold: (1) LSTMs reproduce known hydrological processes. (2) While conceptual models have theoretical assumptions embedded in the model a priori, the LSTM derives these from the data. These learned representations are interpretable by scientists. (3) LSTMs can be used to gain an estimate of intermediate stores of water such as soil moisture. While machine learning interpretability is still a nascent field and our approach reflects a simple technique for exploring what the model has learned, the results are robust to different initial conditions and to a variety of benchmarking experiments. We therefore argue that deep learning approaches can be used to advance our scientific goals as well as our predictive goals.

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.

The most accurate rainfall–runoff predictions are currently based on deep learning. There is a concern among hydrologists that the predictive accuracy of data-driven models based on deep learning may not be reliable in extrapolation or for predicting extreme events. This study tests that hypothesis using long short-term memory (LSTM) networks and an LSTM variant that is architecturally constrained to conserve mass. The LSTM network (and the mass-conserving LSTM variant) remained relatively accurate in predicting extreme (high-return-period) events compared with both a conceptual model (the Sacramento Model) and a process-based model (the US National Water Model), even when extreme events were not included in the training period. Adding mass balance constraints to the data-driven model (LSTM) reduced model skill during extreme events.

Determining rainfall runoff responses of catchments to unprecedented climate conditions is an issue which has largely eluded the hydrologic community for many years. Conceptual rainfall runoff models are used globally to predict runoff for regional water resources management and planning. However, obtaining parameter values suitable for future climate conditions requires approaches that consider conditions beyond historical periods. This paper takes advantage of data from 207 Australian catchments to determine model parameters that most closely produce expected rainfall runoff coefficients (ratio of runoff to rainfall) for a wide range of environmental conditions. This was done for two popular rainfall runoff models, GR4J and Sacramento. In a two‐step process, parameters were first selected that could adequately reproduce observed runoff coefficients across the 207 catchments. Acceptable parameter sets were stored in a library from which, in the second step, parameters were selected for each individual catchment according to various goodness‐of‐fit metrics. Performance of this calibration approach was compared with a classical optimization employed for each catchment (DELO—Differential Evolution Local Optimization). The study found performance trade‐offs using the parameter library based calibration compared to DELO for metrics such as Nash‐Sutcliffe Efficiency and percentage bias. The library‐based calibration exhibited behavior that more closely aligned with expectations under perturbed climate conditions, compared to DELO parameters. Results also showed tolerable estimates of rainfall runoff coefficient using DELO parameters at many sites when rainfall is reduced by no more than 25%. However, there is a high risk of under‐ or over‐estimating runoff coefficients at larger reductions.

Runoff plays an essential part in the hydrological cycle, as it regulates the quantity of water which flows into streams and returns surplus water into the oceans. Runoff modelling may assist in understanding, controlling, and monitoring the quality and amount of water resources. The aim of this article is to discuss various categories of rainfall–runoff models, recent developments, and challenges of rainfall–runoff models in flood prediction in the modern era. Rainfall–runoff models are classified into conceptual, empirical, and physical process-based models depending upon the framework and spatial processing of their algorithms. Well-known runoff models which belong to these categories include the Soil Conservation Service Curve Number (SCS-CN) model, Storm Water Management model (SWMM), Hydrologiska Byråns Vattenbalansavdelning (HBV) model, Soil and Water Assessment Tool (SWAT) model, and the Variable Infiltration Capacity (VIC) model, etc. In addition, the data-driven models such as Adaptive Neuro Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN), Deep Neural Network (DNN), and Support Vector Machine (SVM) have proven to be better performance solutions in runoff modelling and flood prediction in recent decades. The data-driven models detect the best relationship based on the input data series and the output in order to model the runoff process. Finally, the strengths and downsides of the outlined models in terms of understanding variation in runoff modelling and flood prediction were discussed. The findings of this comprehensive study suggested that hybrid models for runoff modeling and flood prediction should be developed by combining the strengths of traditional models and machine learning methods. This article suggests future research initiatives that could help with filling existing gaps in rainfall–runoff research and will also assist hydrological scientists in selecting appropriate rainfall–runoff models for flood prediction and mitigation based on their benefits and drawbacks.