Diagnosing and Conditionally Correcting X-Band Radar Underestimation in Cyprus: A Cross-Validated Evaluation of Spatial Merging and Machine Learning Approaches

Radar-based Quantitative Precipitation Estimation (QPE) in semi-arid Mediterranean climates is critically challenged by systematic underestimation of shallow precipitation, yet gauge–radar merging frameworks tailored to such environments remain poorly evaluated. This study develops and assesses a merging pipeline for Cyprus, combining X-band polarimetric observations from the Paphos and Larnaca operational radar network with accumulations from a 50-station rain gauge network across 11 rainfall events spanning the 2024 wet season (January and November–December 2024). Four approaches were evaluated: raw radar mosaic, global mean field bias (MFB) correction, spatially varying local inverse distance weighting (IDW) bias correction assessed through leave-one-out cross-validation (LOOCV), and a Random Forest (RF) machine-learning retrieval trained on polarimetric, geometric, and orographic predictors and evaluated through leave-one-event-out cross-validation (LOEO-CV). Raw radar exhibited severe and highly variable underestimation, with station-level bias factors ranging from 1.4 to 200×. Global MFB correction removed systematic offset but, as a single spatially uniform scalar, could not improve spatial correspondence; it was beneficial only where the bias field was spatially coherent. Local IDW correction provided cross-validated reduction in RMSE for most events (commonly 40–53%), but this improvement reflected removal of mean bias rather than recovery of spatial pattern: only 17 January 2024 combined RMSE reduction (24.07 mm to 11.31 mm) with genuine spatial skill (leave-one-out r = 0.850, bias-field coherence r = 0.742), while several events improved in RMSE yet retained near-zero spatial correlation, and 30 and 31 January degraded outright. These results characterise the limits of distance-weighted (IDW) interpolation specifically; whether geostatistical estimators incorporating topographic external drift can restore spatial skill where the present gauge network constrains the bias field remains to be tested. When re-evaluated on the same rainy matched-pair set (N = 2378), the Random Forest reduced 10 min RMSE by only 2.6% relative to the best classical Z-R estimator (from 10.38 mm to 10.10 mm) and reduced the systematic bias from −5.06 mm to −4.25 mm, but did not improve point-to-point spatial correspondence (r ≈ 0), indicating that this mean-regression Random Forest provides effective bias-correction skill without spatial-correspondence skill, leaving the fundamental representativeness gap between CAPPI sampling and gauge point measurements unresolved. Three pre-conditions for local bias correction skill are identified as empirical diagnostics under the sample conditions of this study: a minimum of approximately 40 contributing gauges, a spatially coherent bias field, and a moderate bias range. A formal bootstrap or resampling-based uncertainty estimate for these indicators was not attempted, because eleven events constitute too small a sample for stable resampling statistics; the per-event relationships between the number of contributing gauges, the bias-factor range, the bias-field spatial autocorrelation, and the LOOCV error are therefore presented as the empirical basis for these diagnostic indicators, which should be refined and tested for statistical robustness as longer event records become available. These findings demonstrate that the suitability of spatial merging can be diagnosed from network and bias field properties prior to correction, and that machine-learning retrieval offers complementary value through systematic bias removal where spatial interpolation fails. Probabilistic merging frameworks, denser gauge networks, and ML approaches that explicitly target spatial correspondence are identified as priority developments for eastern Mediterranean QPE.