Error Structure of Multiparameter Radar and Surface Measurements of Rainfall. Part III: Specific Differential Phase

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  • 1 University of Alabama in Huntsville, Huntsville, Alabama
  • | 2 Colorado State University, Fort Collins, Colorado
  • | 3 NOAA/ERL, National Severe Storms Laboratory, Norman, Oklahoma
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Abstract

Parts I and II of this three part paper dealt with the error structure of differential reflectivity and X-band specific attenuation in rainfall as estimated by radar and surface disdrometers. In this Part III paper we focus on the error structure of the specific differential phase (KDP, °km−1) measurement in rainfall. This allows us to analyze three estimators of rainfall rate, the first based on the reflectivity factor ZH, the second based on combining reflectivity and ZDR, [R(ZH, ZDR)], and the third based on KDP alone, R(KDP). Simulations are used to model random errors in ZH, ZDR and KDP. Physical variations in the raindrop size distribution (RSD) are modeled by varying the gamma parameters (N0, D0, m) over a range typically found in natural rainfall. Thus, our simulations incorporate physical fluctuations onto which random measurement errors have been superimposed. Radar-derived estimates of R(ZH, ZDR) and R(KDP) have been intercompared using data obtained in convective rainfall with the NSSL Cimarron radar and the NCAR/CP-2 radar. As practical application of the analysis presented here, we have determined the range of applicability of the three rainfall rate estimators: R(ZH), R(ZH, ZDR) and R(KDP). Our simulations show that when the rainfall rate exceeds about 70 mm h−1, R(KDP) performs better than R(ZH, ZDR). This result is valid over a 1 km propagation path. At intermediate rainfall rates around 20 ≲R ≲70 mm h−1, our simulations show that R(ZH, ZDR) gives the least error. However, there are other reasons which make R(KDP) useful; i.e., (i) its stability with respect to mixed phase precipitation, and (ii) the fact that it is a differential phase measurement and thus insensitive to system gain calibration. This last premise suggests an accurate method of system gain calibration based on the rain medium.

Abstract

Parts I and II of this three part paper dealt with the error structure of differential reflectivity and X-band specific attenuation in rainfall as estimated by radar and surface disdrometers. In this Part III paper we focus on the error structure of the specific differential phase (KDP, °km−1) measurement in rainfall. This allows us to analyze three estimators of rainfall rate, the first based on the reflectivity factor ZH, the second based on combining reflectivity and ZDR, [R(ZH, ZDR)], and the third based on KDP alone, R(KDP). Simulations are used to model random errors in ZH, ZDR and KDP. Physical variations in the raindrop size distribution (RSD) are modeled by varying the gamma parameters (N0, D0, m) over a range typically found in natural rainfall. Thus, our simulations incorporate physical fluctuations onto which random measurement errors have been superimposed. Radar-derived estimates of R(ZH, ZDR) and R(KDP) have been intercompared using data obtained in convective rainfall with the NSSL Cimarron radar and the NCAR/CP-2 radar. As practical application of the analysis presented here, we have determined the range of applicability of the three rainfall rate estimators: R(ZH), R(ZH, ZDR) and R(KDP). Our simulations show that when the rainfall rate exceeds about 70 mm h−1, R(KDP) performs better than R(ZH, ZDR). This result is valid over a 1 km propagation path. At intermediate rainfall rates around 20 ≲R ≲70 mm h−1, our simulations show that R(ZH, ZDR) gives the least error. However, there are other reasons which make R(KDP) useful; i.e., (i) its stability with respect to mixed phase precipitation, and (ii) the fact that it is a differential phase measurement and thus insensitive to system gain calibration. This last premise suggests an accurate method of system gain calibration based on the rain medium.

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