Bias-Adjusted Attribution Estimation for Rainfall Enhancement Trials
Model-based analyses of rainfall enhancement trial data typically involve modelling log-transformed rainfall using linear mixed models to assess the effectiveness of enhancement methods under real-world conditions. This approach improves on traditional average-based analyses by allowing explicit control for the effects of meteorological and topographical covariates that may affect precipitation amounts. However, a key issue with such analyses is the bias that arises when back-transforming the log-rainfall to the original scale for estimating attribution, defined as the additional raw-scale rainfall attributable to the enhancement method. To address this issue, we propose a new attribution estimator that incorporates theoretically justified, observation-specific bias-adjustment terms. The proposed estimator improves upon existing estimators that rely on arbitrary adjustments, and satisfies a coherence property that ensures zero estimated attribution for observations without enhancement intervention. A proportional random effect block bootstrap is further used to conduct inference on the attribution quantities. Applying both the proposed estimator and an existing estimator to the Oman rainfall enhancement trial from 2013 to 2018, we find statistically significant positive effect of the ground-based ionization technology on downwind rainfall at the 5% significance level, with our proposed estimator indicating a smaller effect than the existing method. A simulation study further support the findings based on the proposed estimator, demonstrating its superior estimation accuracy and improved inferential performance of the associated bootstrap confidence intervals.