Improved Spectrum Width Estimator Using Multi-Lag Correlation Function in the Alternate Transmission Mode for Polarimetric Weather Radar

Spectrum width (SW) is crucial for warning of severe weather, which is commonly estimated from a ratio of lag-0 to lag-1 autocorrelations (R0/R1). For traditional weather radars, the estimators with higher lags autocorrelation functions (ACFs) have been developed to enhance the performance at low signal-to-noise ratio (SNR) and narrow SW. In the alternate transmission mode, the interval between co-polarimetric signals is twice the pulse repetition time (PRT). Thus, the estimators for traditional radars cannot be applied to the ones with alternate transmission of horizontal and vertical polarized wave (AHV) modes. This article introduces the cross correlation functions (CCFs) to derive multi-lag estimators by least-squares Gaussian fitting of ACFs and CCFs. Moreover, multi-lag estimators are prone to saturate at large SWs, so a hybrid estimator combines the traditional estimator and the multi-lag estimators by comparing the predicted SWs with the SW thresholds. The predicted SWs are calculated by the R0/R2 estimator, and the standard deviation (SD) of the R0/R2 estimator is introduced to identify saturated SWs. SW thresholds at different SNRs and correlation coefficients (CCs) are obtained by minimizing the evaluation metric, which is the weighted sum of biases, SDs, and invalid estimate ratios. Finally, the hybrid estimator is validated via Ku-band weather radar data (surveillance scan mode). The results show that compared with the traditional estimator, the hybrid estimator reduces biases and SDs by about $0.1\sim 0.2$ m/s at SNR <10 dB and SW <2 m/s. Furthermore, the biases and SDs can be reduced by about $0.5\sim 1$ m/s using the hybrid estimator when the radar operates in the Doppler scan mode.