Search

The Gravity Recovery and Climate Experiment (GRACE) satellite and its successor GRACE Follow-On (GRACE-FO) provide valuable and accurate observations of terrestrial water storage anomalies (TWSAs) at a global scale. However, there is an approximately one-year observation gap of TWSAs between GRACE and GRACE-FO. This poses a challenge for practical applications, as discontinuity in the TWSA observations may introduce significant biases and uncertainties in the hydrological model predictions and consequently mislead decision making. To tackle this challenge, a Bayesian convolutional neural network (BCNN) driven by climatic data is proposed in this study to bridge this gap at a global scale. Enhanced by integrating recent advances in deep learning, including the attention mechanisms and the residual and dense connections, BCNN can automatically and efficiently extract important features for TWSA predictions from multi-source input data. The predicted TWSAs are compared to the hydrological model outputs and three recent TWSA prediction products. The comparison suggests the superior performance of BCNN in providing improved predictions of TWSAs during the gap in particular in the relatively arid regions. The BCNN's ability to identify the extreme dry and wet events during the gap period is further discussed and comprehensively demonstrated by comparing with the precipitation anomalies, drought index, ground/surface water levels. Results indicate that BCNN is capable of offering a reliable solution to maintain the TWSA data continuity and quantify the impacts of climate extremes during the gap., Comment: 27 pages, 13 figures

Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In this study, we develop a convolutional adversarial autoencoder (CAAE) to parameterize non-Gaussian conductivity fields with heterogeneous conductivity within each facies using a low-dimensional latent representation. In addition, a deep residual dense convolutional network (DRDCN) is proposed for surrogate modeling of forward models with high-dimensional and highly-complex mappings. The two networks are both based on a multilevel residual learning architecture called residual-in-residual dense block. The multilevel residual learning strategy and the dense connection structure ease the training of deep networks, enabling us to efficiently build deeper networks that have an essentially increased capacity for approximating mappings of very high-complexity. The CCAE and DRDCN networks are incorporated into an iterative ensemble smoother to formulate an inversion framework. The numerical experiments performed using 2-D and 3-D solute transport models illustrate the performance of the integrated method. The obtained results indicate that the CAAE is a robust parameterization method for non-Gaussian conductivity fields with different heterogeneity patterns. The DRDCN is able to obtain accurate approximations of the forward models with high-dimensional and highly-complex mappings using relatively limited training data. The CAAE and DRDCN methods together significantly reduce the computation time required to achieve accurate inversion results.

Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based surrogate method is developed for the forward model to allow us to solve efficiently such high-dimensional inverse problems. The surrogate is trained using limited evaluations of the forward model. Since the relationship between the time-varying inputs and outputs of the forward transport model is complex, we propose an autoregressive strategy, which treats the output at the previous time step as input to the network for predicting the output at the current time step. We employ a dense convolutional encoder-decoder network architecture in which the high-dimensional input and output fields of the model are treated as images to leverage the robust capability of convolutional networks in image-like data processing. An iterative local updating ensemble smoother (ILUES) algorithm is used as the inversion framework. The proposed method is evaluated using a synthetic contaminant source identification problem with 686 uncertain input parameters. Results indicate that, with relatively limited training data, the deep autoregressive neural network consisting of 27 convolutional layers is capable of providing an accurate approximation for the high-dimensional model input-output relationship. The autoregressive strategy substantially improves the network's accuracy and computational efficiency. The application of the surrogate-based ILUES in solving the inverse problem shows that it can achieve accurate inversion results and predictive uncertainty estimates., Comment: 30 pages, 21 figures, submitted to Water Resources Research

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time-dependence of the multi-output responses. In this paper, we propose a deep convolutional encoder-decoder neural network methodology to tackle these issues. The surrogate modeling task is transformed to an image-to-image regression strategy. This approach extracts high-level coarse features from the high-dimensional input permeability images using an encoder, and then refines the coarse features to provide the output pressure/saturation images through a decoder. A training strategy combining a regression loss and a segmentation loss is proposed in order to better approximate the discontinuous saturation field. To characterize the high-dimensional time-dependent outputs of the dynamic system, time is treated as an additional input to the network that is trained using pairs of input realizations and of the corresponding system outputs at a limited number of time instances. The proposed method is evaluated using a geological carbon storage process-based multiphase flow model with a 2500-dimensional stochastic permeability field. With a relatively small number of training data, the surrogate model is capable of accurately characterizing the spatio-temporal evolution of the pressure and discontinuous CO2 saturation fields and can be used efficiently to compute the statistics of the system responses., Comment: 30 pages, 21 figures, submitted to Water Resources Research

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters.