Groundwater level forecasting with artificial neural networks: a comparison of long short-term memory (LSTM), convolutional neural networks (CNNs), and non-linear autoregressive networks with exogenous input (NARX)

Abstract

Abstract. It is now well established to use shallow artificial neural networks (ANNs) to obtain accurate and reliable groundwater level forecasts, which are an important tool for sustainable groundwater management. However, we observe an increasing shift from conventional shallow ANNs to state-of-the-art deep-learning (DL) techniques, but a direct comparison of the performance is often lacking. Although they have already clearly proven their suitability, shallow recurrent networks frequently seem to be excluded from the study design due to the euphoria about new DL techniques and its successes in various disciplines. Therefore, we aim to provide an overview on the predictive ability in terms of groundwater levels of shallow conventional recurrent ANNs, namely non-linear autoregressive networks with exogenous input (NARX) and popular state-of-the-art DL techniques such as long short-term memory (LSTM) and convolutional neural networks (CNNs). We compare the performance on both sequence-to-value (seq2val) and sequence-to-sequence (seq2seq) forecasting on a 4-year period while using only few, widely available and easy to measure meteorological input parameters, which makes our approach widely applicable. Further, we also investigate the data dependency in terms of time series length of the different ANN architectures. For seq2val forecasts, NARX models on average perform best; however, CNNs are much faster and only slightly worse in terms of accuracy. For seq2seq forecasts, mostly NARX outperform both DL models and even almost reach the speed of CNNs. However, NARX are the least robust against initialization effects, which nevertheless can be handled easily using ensemble forecasting. We showed that shallow neural networks, such as NARX, should not be neglected in comparison to DL techniques especially when only small amounts of training data are available, where they can clearly outperform LSTMs and CNNs; however, LSTMs and CNNs might perform substantially better with a larger dataset, where DL really can demonstrate its strengths, which is rarely available in the groundwater domain though.

Deep learning shows declining groundwater levels in Germany until 2100 due to climate change

“…The rst 80% of the remaining time series before 2012 were used for training, the following 20% for early stopping (validation set) and for testing during HP optimization (optimization set), using 10% of the remaining time series each (Figure 7B). As acquisition function during HP optimization we chose the sum of Nash-Sutcliffe e ciency (NSE) and squared Pearson r (R²) (compare ref 15 ), because in this study we used mainly these two criteria to judge the accuracy of the nal optimized model in the test section. For each model we used a maximum optimization step number of 150 or stopped after 15 steps without improvement once a minimum of 60 steps was reached.…”

“…In recent years, arti cial neural network (ANN) approaches have proven their usefulness in predicting groundwater levels [9][10][11][12][13][14] , even using a highly transferable approach with purely climatic input parameters (e.g. ref 15 ). In a previous study 15 we showed that 1D-Convolution Neural Networks (CNNs) are a good choice for groundwater level simulation, as they can provide high accuracy and furthermore are fast and reliable.…”

“…ref 15 ). In a previous study 15 we showed that 1D-Convolution Neural Networks (CNNs) are a good choice for groundwater level simulation, as they can provide high accuracy and furthermore are fast and reliable. Unlike physically-based models, which usually require a very good knowledge of local conditions and need to be timeconsumingly built and calibrated, data-driven models such as ANNs are able to predict a target variable using only relevant driving forces.…”

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“…The NARX neural network as a powerful input-output recurrent dynamic model can be utilized to model nonlinear dynamic systems with a high level of stochastic measurements. During the last years, researchers have verified the ability of NARX to successfully predict and model in uncertaintyoriented environments compared to the other methods [26]- [28]. As depicted in Fig.…”

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“…In this study, we use 1D-CNN models as we have shown earlier that these are fast, reliable and excellently suited for modeling hydrogeological time series (Wunsch et al, 2021). Especially compared to LSTMs, which are often the method of choice, they are more stable and significantly faster, while showing similar performance for this specific application.…”