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<br />/' <br /> <br />able 1. - Variations in radar-estimated snowfall rate (inch h-1) for <<= 150 and 300 and pbetween 1.7 and 2.3. <br />Ze <<= 150 <<= 300 <br />( dBZ) = 1.7 =2.0 =2.3 = 1.7 =2.0 = 2.3 <br />10 0.008 0.010 0.012 0.005 0.007 0.009 <br />20 0.031 0.032 0.033 0.021 0.023 0.024 <br />30 0.120 0.102 0.090 0.080 0.072 0.067 <br />35 0.237 0.181 0.090 0.157 0.128 0.110 <br /> <br />3 2 Optimization Technique <br /> <br />: 11 individual range bin values of Ze (in dBZ) in SAA development are converted to S by equation (1) <br />f r each volume scan before any averaging is done. That is, S is always averaged and Ze is never <br />~ eraged. Averaging Ze values would result in significant bias because of the nonlinear nature of equation <br />( ). For example, averaging Ze values 10, 100 and 1000 mm6 m-3 (equivalent to 10,20 and 30 dBZ), a <br />p. t unusual range to occur over an hour period, and then using <<= 330 and /3= 2.0 with equation (1), <br />t suIts in an average S value of 0.042 inch hot. But if the conversion to S is first done for each Ze value <br />b fore averaging, the correct value of S = 0.032 inch h-t results. Improper averaging in this example <br />p oduced a significant 31-percent overestimate of S. Unfortunately, the practice of averaging Ze, or even <br />I g Ze' is still found in the literature. <br /> <br /> <br />e basic unit of averaging for the work reported herein is 1 hou~. Obtaining accurate SWE <br />a cumulations for shorter periods is difficult without quite specialized instrumentation, beyond available <br />t sources. The use of 1 hour as the basic unit results in a need to integrate S (calculated from <br />easurements of Ze) forthe several volume scans made each hour. About 6 scans per hour result with <br />~ ear air mode scanning, sometimes used with snowfall, and 10 to 11 scans per hour occur with <br />p ecipitation mode scanning, most commonly used with snowfall. Integrating S requires the assumption <br />b <<and /3 values for equation (1). In practice, many pairs of these values are used in the process <br />Cl scribed below. <br />I <br /> <br />I ppendix A of Super and Holroyd (1996) provides the details of the optimization technique being used <br />t estimate<< and P for given data sets. This technique is based on earlier work by Smith et al. (1975) and <br />~ ntinuing personal communication with Paul Smith. ' <br /> <br />I - <br /> <br />! verage gage SWE accumulation was assumed to be equal to average radar-estimated SWE for the same <br />1 hour duration in this application. This constraint, desirable for hydrologic purposes, results in a unique <br />I <br />y lue of <<for any particular value of p. The process then becomes one of selecting the value of /3 out <br />b a set of input values (typically the range 0.8 to 3.0 was tested at intervals of 0.1) which provided the <br />l' est fit." The best fit was determined by calculating a CTF (criterion function) and selecting its <br />. nimum value. As discussed by Smith et al. (1975), selection of the "best CTF" is more involved than <br />I <br />9 e might suspect. In this analysis, the CTF used was the simple sum of absolute differences between <br />a ailable pairs of hourly gage (or snow board) measurements of snowfall and those estimated by radar <br />t r various <<and P pairs. ' . <br /> <br />6 <br />