Tackling water table depth modeling via machine learning: From proxy observations to verifiability

Abstract: Spatial patterns of water table depth (WTD) play a crucial role in shaping ecological resilience, hydrological connectivity, and human-centric systems. Generally, a large-scale (e.g., continental or global) continuous map of static WTD can be simulated using either physically-based (PB) or machine learning-based (ML) models. We construct three fine-resolution (500 m) ML simulations of WTD, using the XGBoost algorithm and more than 20 million real and proxy observations of WTD, across the United States and Canada. The three ML models were constrained using known physical relations between WTD's drivers and WTD and were trained by sequentially adding real and proxy observations of WTD. Through an extensive (pixel-by-pixel) evaluation across the study region and within ten major ecoregions of North America, we demonstrate that our models (corr=0.6-0.75) can more accurately predict unseen real and proxy observations of WTD compared to two available PB simulations of WTD (corr=0.21-0.40). However, we still argue that currently-available large-scale simulations of static WTD could be uncertain within data-scarce regions such as steep mountainous regions. We reason that biased observational data mainly collected from low-elevation floodplains and the over-flexibility of available models can negatively affect the verifiability of large-scale simulations of WTD. Ultimately, we thoroughly discuss future directions that may help hydrogeologists decide how to improve machine learning-based WTD estimations. In particular, we advocate for the use of proxy satellite data, the incorporation of physical laws, the implementation of better model verification standards, the development of novel globally-available emergent indices, and the collection of more reliable observations.

• The paper introduces three XGBoost models leveraging over 20 million real and proxy observations to estimate water table depth across North America.
• The integration of topographic indices in the enhanced model notably improved spatial correlation with existing physical simulations in complex terrains.
• The paper discusses challenges like data uncertainty and overfitting, outlining a promising path for future machine learning applications in hydrological modeling.

Evaluating Machine Learning in Estimating Water Table Depth: An Insightful Study

Introduction and Methodology

Groundwater, as an essential freshwater resource, critically supports ecological, hydrological, and anthropogenic systems. This paper presents three machine learning models trained on more than 20 million real and proxy observations to estimate the water table depth (WTD) across North America. The study utilizes XGBoost, a tree-based machine learning algorithm, and integrates physically-based constraints to mimic natural groundwater influences. The distinct feature of this research lies in the comparative analysis against both real-world observations and existing physically-based models.

Data Sources and Simulation Setup

Three versions of the XGBoost model were developed:

1. V1: Basic Model
   • Trained solely on real observations of WTD.
2. V2: Enhanced with Proxy Data
   • Includes shoreline proxy data indicating where WTD is presumed to be zero, such as along lakes and rivers.
3. V3: Further Enhanced with Terrain Data
   • Incorporates the Height Above Nearest Drainage (HAND) data as additional proxies, particularly beneficial in mountainous regions.

These models were compared against three existing physically-based simulations to evaluate their performance and reliability.

Analysis Results

• Spatial Analysis:
  • The machine learning models generally predict shallower WTD in eastern regions compared to the west. The detailed comparison revealed that V3 remarkably aligns with the topology-driven expectations in mountainous areas, more closely mimicking natural groundwater variability.
• Correlation with Physical Models:
  • V3 showed a higher spatial correlation with the physically-based simulations, potentially indicating its better grasp of underlying physical processes affecting WTD.
• Variable Importance:
  • Climatic variables dominated the influence on V1, while topographical factors, particularly the Topographic Index, critically shaped WTD estimations in V3.

Evaluation Compared to Existing Simulations

When checked against unseen real WTD observations, machine learning models generally exhibited better performance (higher correlation and lower error rates) than physically-based models. V3, despite being less accurate in traditional metrics due to its reliance on high-elevation proxies not well-represented in observation data, showed robust performance in areas with complex geological features.

Implications and Future Directions

The study suggests that future machine learning applications in hydrogeology could benefit significantly from incorporating detailed topographic and hydrologic proxies to train models more aligned with physical realities. This approach builds on the understanding that WTD is influenced not solely by direct human-measurable factors but also by broader ecological and geological frameworks.

Considerations for Future Research

The continuous refinement and validation of machine learning models for hydrological studies will require more comprehensive datasets covering diverse geological settings. Future studies should aim to blend machine learning adaptability with the rigid framework of physically-based models, exploring new methods to incorporate unseen data types that deepen our understanding of subsurface hydrology.

This assessment underscores both the potential and the challenges of utilizing machine learning in large-scale hydrological modeling. As these techniques evolve, they invite a re-examination of how we interpret and predict the behavior of critical water resources under variable environmental conditions. Concerns such as data veracity and model overfitting to existing uncertain data points suggest cautious optimism and a rigorous pathway forward for integrating novel AI techniques in environmental and earth sciences.