A Machine Learning Approach for Water Level Residual Correction Using Geospatial Terrain Features

Accurate water level forecasting remains a critical challenge in hydrology, where errors in model predictions may compromise safety and flood defense decisions. This study proposes a machine learning approach that uses geospatial terrain data to correct these residuals. The study presents a LightGBM baseline model using only temporal features and a XGBoost model enhanced with topographic features, including slope, aspect, and elevation statistics derived from 30m DEMs within a 3km radius of 15 diverse National Oceanic and Atmospheric Administration (NOAA) water level stations. The key finding is that the geospatially informed XGBoost model demonstrated a significant 84.38% improvement in MSE for multi-step sequential forecasting compared to the temporal LightGBM baseline, which shows that it was able to overcome the typical challenge of error accumulation in autoregressive tasks. While the simpler LightGBM architecture maintained an advantage for one-step-ahead prediction, the results demonstrate that integrating geospatial data with an appropriate model architecture is very effective for autonomous, long-term residual correction. This study aims to present a framework for incorporating static terrain data into dynamic hydrological forecasting models.

Flooding endangers human life and property, with the Federal Emergency Management Agency (FEMA) estimating that floods cause about $8.2 billion in damages every year in the United States alone. Despite modern advancements in hydrodynamic modeling and machine learning techniques, persistent residuals (errors) between predicted and observed water levels remain a challenge, particularly in complex tidal environments where multiple physical processes may interact nonlinearly.

Current approaches to correcting residuals primarily focus on temporal features, which are variables derived from historical data to capture time-dependent patterns. Examples of these features include autoregressive components and harmonic analysis of tidal constituents such as K1, P1, K2, and S2. While machine learning models such as Long Short-Term Memory (LSTM) and Extreme Gradient Boosting (XGBoost) have shown to be very capable in capturing temporal patterns, they often neglect the potential influence of surrounding terrain characteristics, such as local elevation gradients, slopes, and low-lying regions, on water level errors.

Rather than acting as an alternative to machine learning, digital elevation models (DEMs) serve as a highly complementary data source that can provide this missing spatial context. DEMs are gridded raster datasets that express surface elevation at each pixel, similar to a height map, that permits quantitative extraction of attributes such as slope, aspect, and elevation statistics (min, max, std). By extracting these topographical features, DEMs can supply critical static inputs to machine learning algorithms, which bridges the gap between dynamic temporal forecasting and static terrain analysis. DEMs have been used extensively in other forms of hydrological modeling, such as flood simulation, which shows the importance of topographic features in water behaviour prediction and its potential in residual correction.

This paper investigates a novel approach to water level residual correction by incorporating geospatial elevation data features, including slope, aspect, and other statistical values derived from high-resolution DEMs within a 3-km radius of water stations.

Traditional approaches to water level residual correction have primarily relied on temporal and statistical techniques. Harmonic analysis, implemented in tools like T_TIDE and NS_TIDE, decomposes tidal signals into constituent components to predict and correct residuals. Statistical time-series models such as ARIMA (AutoRegressive Integrated Moving Average) use autoregressive components and differencing to forecast residuals based on past values. However, these methods predominantly focus on temporal patterns and often overlook spatial contextual factors, such as local topography, which may influence residual behaviour.

Machine learning (ML) models have shown to be powerful tools for hydrological modeling and forecasting, where they are able to effectively grasp nonlinear relationships. Techniques like Long Short-Term Memory (LSTM) networks excel in sequence prediction tasks (e.g., streamflow forecasting) by using temporal dependencies. Gradient boosting algorithms (e.g., XGBoost, LightGBM) are increasingly used for regression tasks due to their strength in handling feature interactions.

DEMs have become fundamental in many hydrological studies, where they enable watershed delineation, flood modeling, and bathymetric mapping. Global DEMs like SRTM, NASADEM, and Copernicus DEM (source of DEM data for this study) provide crucial topographical data for extracting terrain features such as slope, aspect, and elevation ranges. However, these advantages do not fully translate to a large-scale coastal context, where tidal harmonics and broad spatial extents may introduce noise and dilute vital local patterns.

This is the main motivation behind using hyper-local terrain features (e.g., within a 3 km radius of a station) in residual correction for water level predictions, as DEMs have extensive utility in basin-scale applications. By restricting the context, the model is able to extract finer details from DEM-derived features (e.g., slope, curvature) and how they can influence water level residuals in coastal environments.

The study utilized data from 15 diverse NOAA water level stations selected to represent a wide range of environments across the United States. When multiple stations were available within a similar environment, selections were prioritized based on the availability of continuous, verified historical data without significant recording gaps during the four-year study period. These stations provided a robust dataset for creating the proposed residual correction methodology under varying and diverse conditions.

For each station, four years (1460 days) of verified historical water level data, collected at 6-minute intervals from 2021-08-20 to 2025-08-19 were obtained from the NOAA Tides and Currents database. The residual time series, which serves as the target variable for residual correction modeling, was calculated as the difference between observed and predicted water levels, where predicted levels were extracted from NOAA's operational forecast models.

Geospatial data were sourced from the Copernicus Digital Elevation Model (GLO-30), which provides global coverage at 30-meter resolution. For each station, a 3km by 3km raster clip centered on the station coordinates was extracted. This spatial extent was chosen to capture local topographic features without introducing unnecessary computational complexity. The Copernicus DEM was selected for its high vertical accuracy (<4m absolute error) and global consistency, making it suitable for detailed terrain analysis.

Terrain features were derived from each DEM clip using Rasterio for reading raster data and NumPy for geospatial calculations. While these features do not capture the full complexity of hydrodynamic and coastal processes, they act as significant indicators of local terrain structure. For instance, the elevation distributions and percentage of low-lying areas can give insight into the terrain's local water storage potential, thus providing a stable spatial context that allows the model to differentiate distinct coastal environments and potentially introduce a grounding context that the model can rely on for long-term forecasting.

The XGBoost algorithm was selected for this study due to its proven effectiveness in handling tabular data with mixed feature types, its robustness to multicollinearity, and its ability to calculate feature importance, which measures how frequently and effectively each input feature contributes to reducing prediction error during model training, thereby quantifying their significance. These characteristics are crucial for interpreting which terrain and temporal factors most influence residuals.

The dataset was split into a 70% training set and a 30% test set. Hyperparameter tuning was performed via GridSearchCV with 5-fold temporal cross-validation, optimizing for Root Mean Squared Error (RMSE). Key hyperparameters included learning rate, maximum tree depth, number of estimators, subsample ratio, column sample ratio, and the gamma regularization term. The model was implemented using the XGBoost library in Python.

The initial evaluation of the models focused on their core predictive accuracy during training and validation using the conventional one-step-ahead criterion across the entire dataset of 15 stations. The LightGBM (LGBM) model, which serves as the non-geospatial baseline, achieved a strong validation performance, with a root mean squared error (RMSE) of 0.0102 meters and a coefficient of determination (R²) of 0.9920. This indicates that the model was able to capture the dominant temporal patterns in the residual time series. The XGBoost (XGB) model, which incorporates both temporal and geospatial features, demonstrated a similar ability to learn from the training data, where it attained a RMSE of 0.0097 meters and an R² of 0.9928.

These results confirm that both architectures are capable of the one-step-ahead prediction task for which they were trained, with the XGBoost model showing a marginal improvement in RMSE in this specific context. However, it is important to note that this evaluation was performed on the validation split of the original 15-station dataset used for training, where the performance of both models stated above are when they are predicting familiar data.

Feature importance was evaluated using the built-in importance plotting functions of both XGBoost and LightGBM, which rank features by their contribution to reducing the training objective across decision-tree splits, where high importance indicates a feature is repeatedly selected in splits that produce larger decreases in prediction error. However, it is important to note that the feature importance values are not directly comparable across different model architectures, as they have their own internal tree structure, splitting criteria, and generally different numerical scales. Therefore, the magnitude of these feature importance values should only be comparable in relation to other values in the same model.

For the LGBM model, residual_lag1 was the most influential feature (importance 441352.492), followed by rate_of_change_m (4495.545) and residual_lag2 (2935.392). In the XGB model, residual_lag1 also ranked highest (approximately 1044.15), but geospatial features such as elev_mean (3rd place, ≈40.29) and elev_max (4th place, ≈38.25) appeared among the top five predictors, indicating their albeit subtle but consistent role in model predictions.

An interesting observation is that rate_of_change_m was substantially more influential in the LightGBM model as opposed to the XGBoost model, while the relative importance of residual_lag2 remained consistent. This difference likely stems from the role of temporal and spatial context in each model. In the LightGBM model, the rate of change holds value as it informs the model of short-term water level dynamics that allows it to detect rapid transitions in water level residuals that may be driven by external factors, such as tidal phase shifts. However, the XGBoost model is less dependent on the rate of change to provide external context as the geospatial features can also be used to understand environmental factors, making it less reliant on short-term temporal derivatives and instead use both temporal and spatial information to generate predictions. The consistent reliance on lagged residual values on both models suggests that autocorrelation remains a fundamental source of pattern for residual prediction, even with the presence of geospatial features.

To specifically test the model's ability to generalize to unseen conditions, a separate evaluation was conducted on completely new data from NOAA station 9411340, which was not included in the original training set, using water level data from 2025-08-22 to 2025-08-23. The one-step-ahead prediction results demonstrated strong performance for both models on this unseen station, though with the performance relationship reversed compared to the validation results, where the LGBM model outperforms the XGB model. The LGBM model achieved an RMSE of 0.0085 meters while the XGB model achieved an RMSE of 0.0118 meters. This represents a 28.26% improvement in RMSE for the LGBM model compared to the XGB model on this specific unseen station.

The high accuracy of both models confirms that they are able to effectively use temporal dependencies (e.g., residual_lag1) for immediate residual correction when true historical data is available, though the LGBM model demonstrated better generalization for one-step prediction on this particular unseen station.

In contrast to the one-step-ahead results, the multi-step autoregressive forecasting criterion showed a significant advantage for the XGB model incorporated with geospatial data. The LGBM baseline displayed rapid error accumulation, with its RMSE of 0.4887 meters over a two-day forecast timeframe. In this context, error accumulation refers to the recursive propagation of prediction errors, where an initial error causes later predictions to drift as the erroneous prediction is fed back into the model for subsequent time steps. As the subsequent time steps start to produce errors as well, these errors sum up and compound, causing the model to become more inaccurate over time. In this case, the erroneous predictions occurred almost immediately at the start, and as the errors compounded, the model's performance deteriorated even more as it continued.

The XGB model, however, maintained stability, achieving an RMSE of 0.0763 meters, an 84.38% improvement over the LGBM baseline. This suggests that geospatial features (e.g., terrain elevation and slope statistics) provided a net positive effect that lessens the impact of error accumulation by allowing the model to have topographic context to generate a more well-informed prediction.

The results present a nuanced role of geospatial data in machine learning-based water level residual correction, with the most significant finding being the dependence of model performance on the forecasting criterion. The superior performance of the LightGBM (LGBM) model in the one-step ahead task on unseen data suggests that for immediate correction where the true prior residual is known, a simpler model focused on temporal features is highly effective and also computationally efficient due to its lightweight architecture.

However, the superior performance of the geospatially-informed XGBoost (XGB) model in the multi-step autoregressive task is the key finding of this study. Its ability to maintain an RMSE of 0.0763 meters against the LGBM's 0.4887 meters demonstrates that static terrain features provide a stabilizing context that can help mitigate the problem of error accumulation in recursive prediction. This suggests that geospatial data acts as an “anchor” that may prevent the model's predictions from drifting uncontrollably by allowing the model to have a sense of the physical reality of the station's location, which is a factor that remains constant and reliable over time.

An important consideration is whether the performance differences stem from the geospatial features or the choice of model architecture itself. This study intentionally paired LightGBM with temporal features and XGBoost with the combined feature set based on their inherent architectural complexity and strengths. LightGBM's simpler model architecture makes it very efficient for processing simpler feature sets, making it ideal for capturing patterns in temporal data without overfitting. By contrast, XGBoost's more complex algorithms and robust regularization techniques are better suited to handle the higher-dimensional, more complex feature space created by adding geospatial variables. If the architectures were swapped, using XGBoost on only temporal features might lead to increased overfitting, while applying LightGBM to the full feature set might result in underfitting and failure to capture the subtle but important geospatial patterns. Thus, the current pairing represents a match of model complexity to feature space complexity.

The study demonstrated that the integration of geospatial terrain features with machine learning models presents a promising solution for improving water level residual correction, particularly in multi-step forecasting scenarios. While a simpler LightGBM model excelled at one-step-ahead predictions using temporal features alone, the XGBoost model, enriched with topographic data, achieved a significant 84% improvement in accuracy compared to the LightGBM model during autonomous multi-step forecasting. This key finding highlights the role of static terrain features in providing a stabilizing effect that helps mitigate error accumulation, which is the main challenge in recursive forecasting.

Looking forward, future work should explore the combination of real-time spatial data, such as real-time precipitation and more sophisticated architectures like graph neural networks to capture deeper underlying patterns. Ultimately, this approach intends to take a step toward a more resilient, robust, and accurate forecasting tool that can adapt to the growing challenges of coastal risk management in a world of climate change and global warming.