On the Estimation of Climatological ZR Relationships

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  • a Iowa Institute of Hydraulic Research, and Department of Civil and Environmental, Engineering, The University of Iowa, Iowa City, Iowa
  • | b Department of Civil Engineering and Operations Research, Princeton University, Princeton New Jersey
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Abstract

A statistical framework for climatological ZR parameter estimation is developed and simulation experiments are conducted to examine sampling properties of the estimators. Both parametric and nonparametric models are considered. For parametric models, it is shown that ZR parameters can be estimated by maximum likelihood, a procedure with optimal large sample properties. A general nonparametric framework for climatological ZR estimation is also developed. Nonparametric procedures are attractive because of their flexibility in dealing with certain types of measurement errors common to radar data. Simulation experiments show that even under favorable assumptions on error characteristics of radar and raingages, large datasets are required to obtain accurate ZR parameter estimates. Another important conclusion is that estimation results are generally quite sensitive to radar and raingage measurement thresholds. For fixed sample size, the simulation results can be used to provide quantitative assessments of the accuracy of ZR model parameter estimates. These results are particular useful for error analysis of precipitation products that are derived using climatological ZR relations. One example is the large-area rainfall estimates derived using the height-area rainfall threshold (HART) technique.

Abstract

A statistical framework for climatological ZR parameter estimation is developed and simulation experiments are conducted to examine sampling properties of the estimators. Both parametric and nonparametric models are considered. For parametric models, it is shown that ZR parameters can be estimated by maximum likelihood, a procedure with optimal large sample properties. A general nonparametric framework for climatological ZR estimation is also developed. Nonparametric procedures are attractive because of their flexibility in dealing with certain types of measurement errors common to radar data. Simulation experiments show that even under favorable assumptions on error characteristics of radar and raingages, large datasets are required to obtain accurate ZR parameter estimates. Another important conclusion is that estimation results are generally quite sensitive to radar and raingage measurement thresholds. For fixed sample size, the simulation results can be used to provide quantitative assessments of the accuracy of ZR model parameter estimates. These results are particular useful for error analysis of precipitation products that are derived using climatological ZR relations. One example is the large-area rainfall estimates derived using the height-area rainfall threshold (HART) technique.

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