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Machine learning for hydrologic sciences: An introductory overview

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Abstract The hydrologic community has experienced a surge in interest in machine learning in recent years. This interest is primarily driven by rapidly growing hydrologic data repositories, as well as success of machine learning in various academic and commercial applications, now possible due to increasing accessibility to enabling hardware and software. This overview is intended for readers new to the field of machine learning. It provides a non‐technical introduction, placed within a historical context, to commonly used machine learning algorithms and deep learning architectures. Applications in hydrologic sciences are summarized next, with a focus on recent studies. They include the detection of patterns and events such as land use change, approximation of hydrologic variables and processes such as rainfall‐runoff modeling, and mining relationships among variables for identifying controlling factors. The use of machine learning is also discussed in the context of integrated with process‐based modeling for parameterization, surrogate modeling, and bias correction. Finally, the article highlights challenges of extrapolating robustness, physical interpretability, and small sample size in hydrologic applications. This article is categorized under: Science of Water
The nested concepts of artificial intelligence, machine learning, representation learning, and deep learning. Definitions of the four terms are listed in Table 1
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Observed and simulated daily streamflow at USGS Gage 13340600 for two water years. LSTM outperformed RNN during the validation period. Precipitation is partitioned into rain or snow based on minimum temperature being above or below zero. Adapted from Kratzert et al. (2018) under Creative Commons Attribution License
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A random forest (RF) classifier was developed to map irrigated fields at 30 m resolution for a subhumid temperate region. (a) Top 30 (out of 98) important features as identified by RF. Different colors indicate categories of features, such as weather‐sensitive remote sensing indices. (b) National Agriculture Imagery Program (NAIP) aerial image showing irrigated farms with varying sizes. NAIP is shown for visual comparison and not used by the RF classifier. (c) Weather‐sensitive GI calculated from remote sensing images that immediately followed a dry period. (d) Segment of irrigation probability map generated by RF for 2012. Areas not classified as corn or soybeans are shown in dark. Recreated from Xu et al. (2019) under Creative Common CC BY License
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Machine learning has been used in various hydrologic applications in stand‐alone mode or integrated with process‐based modeling. Machine learning can process multitype data to identify hydrologic events and estimate variables (1), approximate hydrologic processes and generate new knowledge regarding the processes (2), aid in parameterization of process‐based models (3), develop fast surrogates (4), and correct the bias of process‐based models (5). The current research frontier is physics informed machine learning that integrates physical knowledge with machine learning to achieve improved prediction accuracy and interpretability (5, 6) (Karpatne et al., 2019; Reichstein et al., 2019). Arrows indicate information flow
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A recurrent neural network (RNN) with LSTM cells. At time step t, xt is the current input, ct is the cell memory, ht is hidden state, it, ft, ot are the input, forget, and output gates, respectively, gt is the cell input activation vector, and denotes element‐wise array multiplication
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Schematic of Gaussian process regression (GPR) showing the (a) prior based on a linear mean function and a squared exponential covariance function, and (b) posterior conditioned on training data. Dark line shows the prior and posterior means, respectively, and gray lines are random samples drawn from the GP. Red open circles are training data points, and they “sculpt” the prior into the posterior
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The architecture of the AlexNet (Krizhevsky et al., 2012) consists of convolution, max‐pooling, local response normalization (LRN), ReLU, and fully connected (FC) layers
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Schematic of trends in training and generalization errors as the model becomes more complex. When the model complexity increases, training error overall tends to decrease while test error starts to increase when the model becomes overfitted, despite temporary fluctuations
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The architecture of (a) a fully connected ANN and (b) a CNN for classifying hand written digits. The ANN has one hidden layer, within which each neuron applies an activation function on the linear combination of inputs x = [x1, …, xp]T, the flattened pixel values of the input image. The CNN applies convolution, pooling, an activation function, followed by a fully connected layer for final output (Section 2.3.2)
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