Abstract. 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.
With the growing use of machine learning (ML) techniques in hydrological applications, there is a need to analyze the robustness, performance, and reliability of predictions made with these ML models. In this paper we analyze the accuracy and variability of groundwater level predictions obtained from a Multilayer Perceptron (MLP) model with optimized hyperparameters for different amounts and types of available training data. The MLP model is trained on point observations of features like groundwater levels, temperature, precipitation, and river flow in various combinations, for different periods and temporal resolutions. We analyze the sensitivity of the MLP predictions at three different test locations in California, United States and derive recommendations for training features to obtain accurate predictions. We show that the use of all available features and data for training the MLP does not necessarily ensure the best predictive performance at all locations. More specifically, river flow and precipitation data are important training features for some, but not all locations. However, we find that predictions made with MLPs that are trained solely on temperature and historical groundwater level measurements as features, without additional hydrological information, are unreliable at all locations.
Abstract. 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) 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.
The depletion of groundwater resources is a widespread phenomenon that can jeopardize both water and food security by making groundwater less accessible, degrading water quality, reducing surface water flow, and compromising the buffering capacity provided by groundwater reserves (Aeschbach-Hertig & Gleeson, 2012). There is abundant documentation of the severity and extent of groundwater depletion, especially in intensively cultivated areas (Bierkens & Wada, 2019;Gleeson et al., 2012). However, undesirable depletion occurs despite knowledge of the problem among water users and despite evidence that effective management and cooperation can reduce the adverse effects of exploitation (Madani & Dinar, 2012b;Ostrom, 1990).Here we address some basic questions about the physical and economic aspects of long-term groundwater depletion. What controls pumping decisions in an unconfined aquifer with multiple wells operated by different users? Can cooperation among the aquifer users increase the benefits and reduce the adverse impacts of pumping? What are the revenue and environmental implications of well yield limitations and regulatory constraints? How are the effects of pumping distributed between storage depletion and reductions in aquifer outflow? These research questions address groundwater depletion issues that are long-standing but have largely remained unresolved, at least in any quantitative sense. Quantitative answers to these questions can provide useful insight about how depletion occurs and how it might be reduced.In order to address our research questions, we need to consider the economically driven pumping decisions made by the agents who use the aquifer (e.g., farmers or irrigation districts) as well as physical processes and policies that may constrain these decisions. One way to include decision-making is to treat pumping rates as time-dependent variables (rather than inputs) that agents continually adjust to maximize particular objectives. This perspective naturally leads to an optimal control formulation of the decision problem. Solutions to this problem describe the pumping and storage histories that can be expected for particular aquifers and management strategies. The optimization process is constrained by physical groundwater flow constraints and by well yield and regulatory constraints that may limit pumping.The constraints required in this decision-driven approach to depletion analysis need to consider local conditions at the well scale, which guide pumping decisions, as well as conditions at larger aquifer scales where the economic and environmental impacts of agent decisions are felt. Consequently, the relevant spatial scales for our
We present an approach that uses a deep learning model, in particular, a MultiLayer Perceptron, for estimating the missing values of a variable in multivariate time series data. We focus on filling a long continuous gap (e.g., multiple months of missing daily observations) rather than on individual randomly missing observations. Our proposed gap filling algorithm uses an automated method for determining the optimal MLP model architecture, thus allowing for optimal prediction performance for the given time series. We tested our approach by filling gaps of various lengths (three months to three years) in three environmental datasets with different time series characteristics, namely daily groundwater levels, daily soil moisture, and hourly Net Ecosystem Exchange. We compared the accuracy of the gap-filled values obtained with our approach to the widely used R-based time series gap filling methods and . The results indicate that using an MLP for filling a large gap leads to better results, especially when the data behave nonlinearly. Thus, our approach enables the use of datasets that have a large gap in one variable, which is common in many long-term environmental monitoring observations.
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