The Quality Control and Rain Rate Estimation for the X-Band Dual-Polarization Radar: A Study of Propagation of Uncertainty

In this study, the specific differential phase (<mml:semantics>Kdp</mml:semantics>) is applied to attenuation correction for radar reflectivity <mml:semantics>ZH</mml:semantics> and differential reflectivity <mml:semantics>ZDR</mml:semantics>, and then the corrected <mml:semantics>ZH</mml:semantics>, <mml:semantics>ZDR</mml:semantics>, and <mml:semantics>Kdp</mml:semantics> are studied in the rain rate (R) estimation at the X-band. The statistical uncertainties of <mml:semantics>ZH</mml:semantics>, <mml:semantics>ZDR</mml:semantics>, and R are propagated from the uncertainty of <mml:semantics>Kdp</mml:semantics>, leading to variability in their error characteristics. For the attenuation correction, a differential phase shift (<mml:semantics>Phi dp</mml:semantics>)-based method is adopted, while the statistical uncertainties <mml:semantics>sigma(ZH)</mml:semantics> and <mml:semantics>sigma(ZDR)</mml:semantics> are related to <mml:semantics>sigma(Kdp)</mml:semantics> via the relations of <mml:semantics>Kdp</mml:semantics>-specific attenuation (<mml:semantics>AH</mml:semantics>) and <mml:semantics>Kdp</mml:semantics>-specific differential attenuation (<mml:semantics>ADP</mml:semantics>), respectively. For the rain rate estimation, the rain rates are retrieved by the power-law relations of <mml:semantics>R(Kdp)</mml:semantics>, <mml:semantics>R(Zh)</mml:semantics>, <mml:semantics>R(Zh,Zdr)</mml:semantics>, and <mml:semantics>R(Zh,Zdr,Kdp)</mml:semantics>. The statistical uncertainty <mml:semantics>sigma(R)</mml:semantics> is propagated from <mml:semantics>ZH</mml:semantics>, <mml:semantics>ZDR</mml:semantics>, and <mml:semantics>Kdp</mml:semantics> via the Taylor series expansion of the power-law relations. A composite method is then proposed to reduce the <mml:semantics>sigma(R)</mml:semantics> effect. When compared to the existing algorithms, the composite method yields the best performance in terms of root mean square error and Pearson correlation coefficient, but shows slightly worse normalized bias than <mml:semantics>R(Kdp)</mml:semantics> and <mml:semantics>R(Zh,Zdr,Kdp)</mml:semantics>. The attenuation correction and rain rate estimation are evaluated by analyzing a squall line event and a prolonged rain event. It is clear that <mml:semantics>ZH</mml:semantics>, <mml:semantics>ZDR</mml:semantics>, and <mml:semantics>Kdp</mml:semantics> show the storm structure consistent with the theoretical model, while the statistical uncertainties <mml:semantics>sigma(ZH)</mml:semantics>, <mml:semantics>sigma(ZDR)</mml:semantics> and <mml:semantics>sigma(Kdp)</mml:semantics> are increased in the transition region. The scatterplots of <mml:semantics>ZH</mml:semantics>, <mml:semantics>ZDR</mml:semantics>, and <mml:semantics>Kdp</mml:semantics> agree with the self-consistency relations at X-band, indicating a fairly good performance. The rain rate estimation algorithms are also evaluated by the time-series of the prolonged rain event, yielding strong correlations between the composite method and rain gauge data. In addition, the statistical uncertainty <mml:semantics>sigma(R)</mml:semantics> is propagated from <mml:semantics>ZH</mml:semantics>, <mml:semantics>ZDR</mml:semantics>, and <mml:semantics>Kdp</mml:semantics>, showing higher uncertainty when the large gradient presents.