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

Kuai Fang, Daniel Kifer, Kathryn Lawson, Dapeng Feng, Chaopeng Shen

arXiv:2101.01876v1cs.LGstat.ML

TL;DR

Regionalization fits separate models to similar regions, but divides the data available to each model. The paper compares pooled global and local LSTM models for soil moisture and streamflow, finding that pooling outperformed stratification while noting limits in the evidence and scope.

  • Problem

    Regionalization is traditionally used to model homogeneous regions separately, but it leaves each model with fewer observations and limits information sharing across dissimilar regions.

    Source: §1 · p. 2

  • Method

    Using LSTM networks, the study compares pooled global models with region-specific local models for soil moisture and streamflow.

    Source: §2.3.1 · p. 6, §5 · p. 15

  • Results

    Pooling data outperformed stratified separate models for soil moisture and streamflow, with heterogeneous data also associated with improved performance.

    Source: §4 · p. 14, §5 · p. 16

  • Takeaways & Limitations

    The authors recommend trying large, diverse datasets and unified models, while noting stratification may remain useful when critical inputs are missing or model performance is very poor.

    Source: §5 · p. 16

    The multilevel and regularization explanations remain unproved, and latent streamflow processes and simplified routing may make multilevel structure harder to extract.

    Source: §4 · p. 15

Abstract

from arXiv · show

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.

1. Introduction

Hydrologic modeling has traditionally used regionalization to fit separate models to groups of similar data, balancing simpler local relationships against fewer observations per model. This paper explores whether deep learning can instead benefit from pooling data across regions, and tests global versus local models for soil moisture and streamflow.

1. Introduction

  • Regionalization is a longstanding hydrologic practice, including for ungauged-basin prediction, where similar catchments share calibrated parameters and dissimilar basins do not share information.The practice also appears in hydraulic geometry, streamflow, evapotranspiration, and other geoscientific modeling examples.Source: §1 · pp. 1–2
  • Regionalization can simplify local relationships and account for shared latent conditions, but dividing data among more regions leaves fewer observations to constrain each model.The approach therefore depends on whether simplification outweighs the resulting increase in model variance.Source: §1 · p. 2
  • Hierarchical and multilevel models offer a statistical alternative, combining region-specific parameters with global parameters shared across regions.Applying this approach to a new task requires considering how the two parameter types interact in predictions.Source: §1 · pp. 2–3
  • The paper calls it data synergy when a unified deep learning model trained on a large dataset outperforms regionalized, locally trained models.The authors hypothesize that internal representations capture both commonalities and differences between regions.Source: §1 · p. 3
  • The authors compare global and local models for soil moisture and streamflow, asking whether performance gains reflect greater data diversity, greater quantity, or both.Global models include data from more distant regions, while local models use data only from within the region being evaluated.Source: §1 · p. 3

2. Methods and data

The methods section introduces the datasets, deep learning model structure, and experimental designs used in the study.

2. Methods and data

  • The methods section is organized around datasets, model structure, and experimental designs.These topics are presented in that order.Source: §2 · p. 3
  • The first methods subsection presents the datasets leveraged in the study.Source: §2 · p. 3
  • The section then describes the deep learning model structure and specific experimental designs.Source: §2 · p. 3

2.1. Input and target data set

The study investigates soil-moisture and streamflow prediction using satellite, basin-observation, climate-forcing, and geophysical data. The two applications use different targets, sources, and temporal coverage.

2.1. Input and target data set

  • The study investigates data synergy in two hydrologic prediction tasks: soil moisture and streamflow.Source: §2.1 · p. 3

2.1.1. Soil moisture data

  • For soil moisture, SMAP Level 3 radiometer measurements are the target, with April 2015–March 2016 used for training and April 2016–March 2018 for testing.Inputs include climate forcings and static physiographic, soil-property, and vegetation data.Source: §2.1.1 · p. 4

2.1.2. Streamflow data

  • For streamflow, the study uses USGS basin runoff observations from 2,773 basins, with 1979–2009 for training and 2010–2019 for testing.Predictors combine basin-averaged gridMET climate forcings with geographic attributes from GAGES-II.Source: §2.1.2 · p. 4

2.2. Model architecture

The study uses the same LSTM architecture for pixel-level soil-moisture and basin-level streamflow prediction. Models minimize RMSE using AdaDelta.

2.2. Model architecture

  • The study uses LSTM networks to predict soil moisture at pixels and streamflow at basins, with a shared architecture for both tasks.The architecture has a 256-node ReLU linear layer, a 256-node LSTM layer, and a linear output layer.Source: §2.2 · p. 5
  • Models are trained to minimize root-mean-square error (RMSE) using the AdaDelta optimizer.Source: §2.2 · p. 5
  • Training uses 30-day time steps and batch size 100 for soil moisture, versus 365-day steps and batch size 500 for streamflow; all models run for 500 epochs.Source: §2.2 · p. 5

2.3. Experimental design

The design used EPA ecoregions to define study regions and compared global with local models, then tested whether training-data diversity mattered beyond data quantity. Models were evaluated on later periods within regions of interest.

2.3. Experimental design

  • EPA ecoregions guided stratification, with three hierarchical levels dividing the conterminous United States into 11, 25, and 105 regions.The selected regions of interest were the six largest level III ecoregions for soil moisture and twelve ecoregions with at least 60 USGS basins for streamflow.Source: §2.3 · p. 5, §2.3.2 · p. 6

2.3.1. Global vs. local experiments.

  • One global LSTM trained on all 18 sub-regions was compared with 18 local models, each trained on its own sub-region and tested on identical pixels or gages.The 18 sub-regions had areas of 1 × 10^5 to 1 × 10^6 km^2; four regions were excluded from streamflow analyses because they had almost no reference basins.Source: §2.3.1 · pp. 5–6

2.3.2. Similar vs. dissimilar experiments

  • Training-data composition experiments compared local, close-neighbor, far-neighbor, and dissimilar data, both with available data amounts and with added data amounts controlled.EPA ecoregion hierarchy served as a proxy for similarity; data-size-controlled comparisons were performed for soil moisture but not streamflow.Source: §2.3.2 · pp. 6–7

2.3.3. Evaluation of model

  • Models were evaluated by temporal generalization on the same pixels or basins: soil moisture used correlation and RMSE, while streamflow used correlation and NSE.Soil moisture was trained from 2015/04/01 to 2017/04/01 and tested from 2017/04/01 to 2018/04/01; streamflow was trained from 1979/01/01 to 2009/01/01 and tested from 2010/01/01 to 2019/01/01.Source: §2.3.3 · p. 7

3. Results and Discussion

Global models generally outperformed local models for both soil moisture and streamflow. Adding more diverse training data improved predictions, and equal-sized soil-moisture comparisons indicate that diversity contributes beyond data quantity.

3.1. Global vs. local experiments

  • For soil moisture, global models averaged RMSE 0.32 versus 0.38 locally and correlation 0.82 versus 0.75, with better RMSE for 87% of pixels and correlation for 95%.The reported global-model advantage was statistically and practically significant.Source: §3.1 · p. 8, Table 2 · p. 9
  • For streamflow, global models averaged correlation 0.84 versus 0.79 and NSE 0.73 versus 0.65; they had higher NSE in 81% of basins and correlation in 84%.Region K was an exception in practice: despite a higher median NSE, global-model error variability was large enough that the local model was preferred.Source: §3.1 · p. 8, Table 2 · p. 9

3.2.1. Dataset size not controlled

  • Soil-moisture RMSE and correlation improved monotonically as increasingly diverse data were added, with the best performance from local + dissimilar data; streamflow gains were smaller and less monotonic.For streamflow, most but not all individual comparisons were significant; pooled ROI comparisons were significant. Some cases showed NSE declines with added far-region data, and diversity did not help poorly performing LSTM models.Source: §3.2.1 · p. 10

3.2.2. Dataset size controlled, streamflow only

  • With equal-sized soil-moisture datasets, pooled results showed that local + far and local + dissimilar each improved over local + close, with no meaningful difference between the two diverse alternatives.The equal-size comparison was possible for soil moisture but not streamflow; the observed differences were smaller than in the uncontrolled-size experiments.Source: Table 5 · p. 13, §3.2.2 · p. 14
  • The experiments indicate that diverse data help through both quantity and characteristics, with quantity having the larger effect; heterogeneity may regularize models, but this is not proven.The authors recommend collecting enough local data for a reasonably performing model before adding outside data, with heterogeneous data preferred; such data are also more plentiful and offer opportunities to build larger datasets.Source: §3.2.1 · p. 10, §3.2.2 · p. 14

4. Further Discussion

Pooling heterogeneous data improved soil moisture and streamflow predictions, with regularization and multilevel representations offered as possible explanations. The authors caution that synergy may vary across problems and that neither explanation is proven.

4. Further Discussion

  • Pooling data outperformed stratification for soil moisture and streamflow, with heterogeneous data potentially reducing overfitting or helping networks capture shared and region-specific patterns.The proposed explanations are not mutually exclusive.Source: §4 · pp. 14–15
  • Streamflow showed less pronounced synergy, which the authors relate to latent processes such as unknown geology and simplified stream-network routing.They caution against generalizing the effect to every stratification scheme or problem.Source: §4 · p. 15
  • The multilevel-model and regularization explanations remain unproven; studying network parameters further would be needed to confirm either theory.Source: §4 · p. 15
  • Deep-learning model complexity is not captured by parameter count alone; regularization methods include weight penalties, dropout, and early stopping.The passage also describes double descent, in which test error can decline, rise, and then decline again as parameter count increases.Source: §4 · p. 15

5. Conclusion

The paper concludes that data quantity and diversity helped LSTM performance in soil moisture and streamflow prediction. It recommends testing unified models on large, diverse datasets while recognizing conditions where stratification may remain useful.

5. Conclusion

  • More data and diversity helped LSTM performance in soil moisture and streamflow prediction, and experiments found no case where adding regions outside the ROI worsened performance.The authors attribute potential benefit to both data quantity and heterogeneity, while noting the mechanism is unknown.Source: §5 · pp. 15–16
  • The authors recommend compiling large datasets from diverse domains and trying a unified model rather than assuming stratification is best.They suggest collecting enough local data for reasonable performance first when collection budgets are limited, then adding heterogeneous sources.Source: §5 · p. 16
  • Stratification may remain useful when deep-learning performance is very poor or critical variables are unknown; transfer learning is suggested for truly non-comparable inputs.The authors do not guarantee that greater diversity will improve performance in every case.Source: §5 · p. 16
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