Estimating Uncertainty in Landslide Segmentation Models

Landslides are a recurring, widespread hazard. Preparation and mitigation efforts can be aided by a high-quality, large-scale dataset that covers global at-risk areas. Such a dataset currently does not exist and is impossible to construct manually. Recent automated efforts focus on deep learning models for landslide segmentation (pixel labeling) from satellite imagery. However, it is also important to characterize the uncertainty or confidence levels of such segmentations. Accurate and robust uncertainty estimates can enable low-cost (in terms of manual labor) oversight of auto-generated landslide databases to resolve errors, identify hard negative examples, and increase the size of labeled training data. In this paper, we evaluate several methods for assessing pixel-level uncertainty of the segmentation. Three methods that do not require architectural changes were compared, including Pre-Threshold activations, Monte-Carlo Dropout and Test-Time Augmentation -- a method that measures the robustness of predictions in the face of data augmentation. Experimentally, the quality of the latter method was consistently higher than the others across a variety of models and metrics in our dataset.

Probing the limit of hydrologic predictability with the Transformer network

For a number of years since its introduction to hydrology, recurrent neural networks like long short-term memory (LSTM) have proven remarkably difficult to surpass in terms of daily hydrograph metrics on known, comparable benchmarks. Outside of hydrology, Transformers have now become the model of choice for sequential prediction tasks, making it a curious architecture to investigate. Here, we first show that a vanilla Transformer architecture is not competitive against LSTM on the widely benchmarked CAMELS dataset, and lagged especially for the high-flow metrics due to short-term processes. However, a recurrence-free variant of Transformer can obtain mixed comparisons with LSTM, producing the same Kling-Gupta efficiency coefficient (KGE), along with other metrics. The lack of advantages for the Transformer is linked to the Markovian nature of the hydrologic prediction problem. Similar to LSTM, the Transformer can also merge multiple forcing dataset to improve model performance. While the Transformer results are not higher than current state-of-the-art, we still learned some valuable lessons: (1) the vanilla Transformer architecture is not suitable for hydrologic modeling; (2) the proposed recurrence-free modification can improve Transformer performance so future work can continue to test more of such modifications; and (3) the prediction limits on the dataset should be close to the current state-of-the-art model. As a non-recurrent model, the Transformer may bear scale advantages for learning from bigger datasets and storing knowledge. This work serves as a reference point for future modifications of the model.

Differentiable modeling to unify machine learning and physical models and advance Geosciences

Process-Based Modeling (PBM) and Machine Learning (ML) are often perceived as distinct paradigms in the geosciences. Here we present differentiable geoscientific modeling as a powerful pathway toward dissolving the perceived barrier between them and ushering in a paradigm shift. For decades, PBM offered benefits in interpretability and physical consistency but struggled to efficiently leverage large datasets. ML methods, especially deep networks, presented strong predictive skills yet lacked the ability to answer specific scientific questions. While various methods have been proposed for ML-physics integration, an important underlying theme -- differentiable modeling -- is not sufficiently recognized. Here we outline the concepts, applicability, and significance of differentiable geoscientific modeling (DG). "Differentiable" refers to accurately and efficiently calculating gradients with respect to model variables, critically enabling the learning of high-dimensional unknown relationships. DG refers to a range of methods connecting varying amounts of prior knowledge to neural networks and training them together, capturing a different scope than physics-guided machine learning and emphasizing first principles. Preliminary evidence suggests DG offers better interpretability and causality than ML, improved generalizability and extrapolation capability, and strong potential for knowledge discovery, while approaching the performance of purely data-driven ML. DG models require less training data while scaling favorably in performance and efficiency with increasing amounts of data. With DG, geoscientists may be better able to frame and investigate questions, test hypotheses, and discover unrecognized linkages.

ThreshNet: Segmentation Refinement Inspired by Region-Specific Thresholding

We present ThreshNet, a post-processing method to refine the output of neural networks designed for binary segmentation tasks. ThreshNet uses the confidence map produced by a base network along with global and local patch information to significantly improve the performance of even state-of-the-art methods. Binary segmentation models typically convert confidence maps into predictions by thresholding the confidence scores at 0.5 (or some other fixed number). However, we observe that the best threshold is image-dependent and often even region-specific -- different parts of the image benefit from using different thresholds. Thus ThreshNet takes a trained segmentation model and learns to correct its predictions by using a memory-efficient post-processing architecture that incorporates region-specific thresholds as part of the training mechanism. Our experiments show that ThreshNet consistently improves over current the state-of-the-art methods in binary segmentation and saliency detection, typically by 3 to 5% in mIoU and mBA.

Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy

Predictions of hydrologic variables across the entire water cycle have significant value for water resource management as well as downstream applications such as ecosystem and water quality modeling. Recently, purely data-driven deep learning models like long short-term memory (LSTM) showed seemingly-insurmountable performance in modeling rainfall-runoff and other geoscientific variables, yet they cannot predict unobserved physical variables and remain challenging to interpret. Here we show that differentiable, learnable, process-based models (called {\delta} models here) can approach the performance level of LSTM for the intensively-observed variable (streamflow) with regionalized parameterization. We use a simple hydrologic model HBV as the backbone and use embedded neural networks, which can only be trained in a differentiable programming framework, to parameterize, replace, or enhance the process-based model modules. Without using an ensemble or post-processor, {\delta} models can obtain a median Nash Sutcliffe efficiency of 0.715 for 671 basins across the USA for a particular forcing data, compared to 0.72 from a state-of-the-art LSTM model with the same setup. Meanwhile, the resulting learnable process-based models can be evaluated (and later, to be trained) by multiple sources of observations, e.g., groundwater storage, evapotranspiration, surface runoff, and baseflow. Both simulated evapotranspiration and fraction of discharge from baseflow agreed decently with alternative estimates. The general framework can work with models with various process complexity and opens up the path for learning physics from big data.

Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solvers

River bathymetry is critical for many aspects of water resources management. We propose and demonstrate a bathymetry inversion method using a deep-learning-based surrogate for shallow water equations solvers. The surrogate uses the convolutional autoencoder with a shared-encoder, separate-decoder architecture. It encodes the input bathymetry and decodes to separate outputs for flow-field variables. A gradient-based optimizer is used to perform bathymetry inversion with the trained surrogate. Two physically-based constraints on both bed elevation value and slope have to be added as inversion loss regularizations to obtain usable inversion results. Using the "L-curve" criterion, a heuristic approach was proposed to determine the regularization parameters. Both the surrogate model and the inversion algorithm show good performance. We found the bathymetry inversion process has two distinctive stages, which resembles the sculptural process of initial broad-brush calving and final detailing. The inversion loss due to flow prediction error reaches its minimum in the first stage and remains almost constant afterward. The bed elevation value and slope regularizations play the dominant role in the second stage in selecting the most probable solution. We also found the surrogate architecture (whether with both velocity and water surface elevation or velocity only as outputs) does not show significant impact on inversion result.

Surrogate Model for Shallow Water Equations Solvers with Deep Learning

Shallow water equations are the foundation of most models for flooding and river hydraulics analysis. These physics-based models are usually expensive and slow to run, thus not suitable for real-time prediction or parameter inversion. An attractive alternative is surrogate model. This work introduces an efficient, accurate, and flexible surrogate model, NN-p2p, based on deep learning and it can make point-to-point predictions on unstructured or irregular meshes. The new method was evaluated and compared against existing methods based on convolutional neural networks (CNNs), which can only make image-to-image predictions on structured or regular meshes. In NN-p2p, the input includes both spatial coordinates and boundary features that can describe the geometry of hydraulic structures, such as bridge piers. All surrogate models perform well in predicting flow around different types of piers in the training domain. However, only NN-p2p works well when spatial extrapolation is performed. The limitations of CNN-based methods are rooted in their raster-image nature which cannot capture boundary geometry and flow features exactly, which are of paramount importance to fluid dynamics. NN-p2p also has good performance in predicting flow around piers unseen by the neural network. The NN-p2p model also respects conservation laws more strictly. The application of the proposed surrogate model was demonstrated by calculating the drag coefficient $C_D$ for piers and a new linear relationship between $C_D$ and the logarithmic transformation of pier's length/width ratio was discovered.

Continental-scale streamflow modeling of basins with reservoirs: a demonstration of effectiveness and a delineation of challenges

A large fraction of major waterways have dams influencing streamflow, which must be accounted for in large-scale hydrologic modeling. However, daily streamflow prediction for basins with dams is challenging for various modeling approaches, especially at large scales. Here we took a divide-and-conquer approach to examine which types of basins could be well represented by a long short-term memory (LSTM) deep learning model using only readily-available information. We analyzed data from 3557 basins (83% dammed) over the contiguous United States and noted strong impacts of reservoir purposes, capacity-to-runoff ratio (dor), and diversion on streamflow on streamflow modeling. Surprisingly, while the LSTM model trained on a widely-used reference-basin dataset performed poorly for more non-reference basins, the model trained on the whole dataset presented a median test Nash-Sutcliffe efficiency coefficient (NSE) of 0.74, reaching benchmark-level performance. The zero-dor, small-dor, and large-dor basins were found to have distinct behaviors, so migrating models between categories yielded catastrophic results. However, training with pooled data from different sets yielded optimal median NSEs of 0.73, 0.78, and 0.71 for these groups, respectively, showing noticeable advantages over existing models. These results support a coherent, mixed modeling strategy where smaller dams are modeled as part of rainfall-runoff processes, but dammed basins must not be treated as reference ones and must be included in the training set; then, large-dor reservoirs can be represented explicitly and future work should examine modeling reservoirs for fire protection and irrigation, followed by those for hydroelectric power generation, and flood control, etc.

The data synergy effects of time-series deep learning models in hydrology

When fitting statistical models to variables in geoscientific disciplines such as hydrology, it is a customary practice to regionalize - to divide a large spatial domain into multiple regions and study each region separately - instead of fitting a single model on the entire data (also known as unification). Traditional wisdom in these fields suggests that models built for each region separately will have higher performance because of homogeneity within each region. However, by partitioning the training data, each model has access to fewer data points and cannot learn from commonalities between regions. Here, through two hydrologic examples (soil moisture and streamflow), we argue that unification can often significantly outperform regionalization in the era of big data and deep learning (DL). Common DL architectures, even without bespoke customization, can automatically build models that benefit from regional commonality while accurately learning region-specific differences. We highlight an effect we call data synergy, where the results of the DL models improved when data were pooled together from characteristically different regions. In fact, the performance of the DL models benefited from more diverse rather than more homogeneous training data. We hypothesize that DL models automatically adjust their internal representations to identify commonalities while also providing sufficient discriminatory information to the model. The results here advocate for pooling together larger datasets, and suggest the academic community should place greater emphasis on data sharing and compilation.

Prediction in ungauged regions with sparse flow duration curves and input-selection ensemble modeling

While long short-term memory (LSTM) models have demonstrated stellar performance with streamflow predictions, there are major risks in applying these models in contiguous regions with no gauges, or predictions in ungauged regions (PUR) problems. However, softer data such as the flow duration curve (FDC) may be already available from nearby stations, or may become available. Here we demonstrate that sparse FDC data can be migrated and assimilated by an LSTM-based network, via an encoder. A stringent region-based holdout test showed a median Kling-Gupta efficiency (KGE) of 0.62 for a US dataset, substantially higher than previous state-of-the-art global-scale ungauged basin tests. The baseline model without FDC was already competitive (median KGE 0.56), but integrating FDCs had substantial value. Because of the inaccurate representation of inputs, the baseline models might sometimes produce catastrophic results. However, model generalizability was further meaningfully improved by compiling an ensemble based on models with different input selections.