EWLR - A New Method for Interpolating Elevation-Driven Variables: Annual Rainfall in Erbil Governorate

Abstract

Accurate spatial estimation of rainfall is critical for hydrological modeling, water resource management, and agricultural planning---particularly in mountainous and semi-arid regions with sparse monitoring networks. This study presents an Enhanced Elevation-Weighted Local Regression (EWLR) model to generate a high-resolution (30~m) annual rainfall surface for Erbil Governorate, northern Iraq. The EWLR model integrates distance weighting, elevation similarity weighting, and orographic enhancement within a locally weighted regression framework. Average annual rainfall, derived from rainy seasons spanning 1997--1998 to 2024--2025 across 19 meteorological stations, along with a 30~m resolution digital elevation model (DEM), were used to construct and validate the model. Hyperparameters were optimized via Leave-One-Out Cross-Validation (LOOCV), and performance was benchmarked against conventional methods including Inverse Distance Weighting (IDW), Kriging, Thin-Plate Spline, and Radial Basis Function interpolation. Results indicate that EWLR outperforms all benchmarks, achieving $R^2 = 0.797$, RMSE $= 120.9$~mm, and MAE $= 87.46$~mm. Rainfall shows a strong positive correlation with elevation ($r = 0.907$, $p < 0.001$), increasing nearly fivefold from lowland plains ($\sim$270~mm) to mountainous areas ($>$1{,}300~mm). The final high-resolution rainfall map captures orographic effects reasonably well, providing a physically consistent, statistically robust dataset suitable for hydrological, climatic, and environmental modeling in data-sparse mountainous regions. The methodology offers a reproducible, elevation-centric framework adaptable to other elevation-driven variables (e.g., temperature lapse rates or snow accumulation) and complex terrains with limited observations.