Improving Radar Rainfall Estimate with Kalman Filter Based Bias Adjustment Methods

Abstract This study evaluates three real-time Kalman filter (KF) approaches—Mean Field (MKF), Site-Specific (SKF), and a novel Lagrangian (LKF)—to correct radar rainfall estimation biases. While the SKF addresses spatial heterogeneity by applying independent filters per gauge, the LKF uniquely utilizes optical flow to advect the bias correction field alongside moving storms. This prevents the erroneous spatial propagation of large correction factors into trailing light rain areas. Evaluated using a dense gauge network in northern China, the LKF demonstrates superior performance, reducing the raw radar’s systemic bias from − 35.0% to -3.5% while minimizing overall errors. However, these performance improvements diminish rapidly beyond a 10 km distance from the training gauges. Furthermore, an analysis of optimized filter parameters reveals a fundamental physical constraint: the KF breaks down when radar measurement variance (S) exceeds the intrinsic process variance (Q). Because these errors are independent, the filter remains effective only when the observed residual variance is less than 2Q. This demonstrates that dynamic algorithmic corrections cannot compensate for fundamentally degraded radar observations.