Experiments in Rainfall Estimation with a Polarimetric Radar in a Subtropical Environment
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Cites background from "Experiments in Rainfall Estimation ..."
...The raindrop relation is from Brandes et al. (2002). MAY 2007 B R A N D E S E T A L ....
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223 citations
Cites background or methods from "Experiments in Rainfall Estimation ..."
...Another shape–diameter relation that combines the observations of different authors was recently proposed by Brandes et al. (2002), r 0.9951 0.025 10D 0.036 44D2 0.005 303D3 0.000 249 2D4....
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...The fractional errors of polarimetric rainfall estimation at the S band were examined in recent validation studies performed in Florida (Brandes et al. 2002) and in Oklahoma during JPOLE (Ryzhkov et al. 2003, 2005)....
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...In Florida, the best polarimetric relation R(Z, ZDR) yielded equal to 38% for point estimates of the storm rain accumulations....
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...Another shape–diameter relation that combines the observations of different authors was recently proposed by Brandes et al. (2002),...
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...The fractional errors of polarimetric rainfall estimation at the S band were examined in recent validation studies performed in Florida (Brandes et al. 2002) and in Oklahoma during JPOLE (Ryzhkov et al....
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219 citations
Cites background or methods or result from "Experiments in Rainfall Estimation ..."
...2001; Brandes et al. 2004a,b) have shown that the relation for the southern Great Plains (i.e., Oklahoma) is a little different than the one for a subtropical region (i.e., Florida). Using the SATP method, 2DVD data were processed to refine the – relation for rains in Oklahoma. First, the data were grouped on an R–D0 grid and averaged. Averaged DSDs were then fitted to a gamma distribution by the TMF method. After that, the second-order polynomial least-square fit was used to obtain the mean – relation. The fitted and for the sorted and averaged DSDs are plotted in Fig. 6. The solid line is the fitted curve of circle points, and a dashed line depicts the Florida – relation from Zhang et al. (2001). The dashed line generally has larger values for than the FIG....
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...Previous studies (e.g., Schuur et al. 2001; Brandes et al. 2002, 2004a; Vivekanandan et al. 2004; Zhang et al. 2006) have shown that disdrometer observations are generally consistent with radar observations and that DSD models derived from disdrometer observations generally work well when applied…...
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...However, Brandes et al. (2004b) showed that this approach is sensitive to KDP noise. In addition, KDP is derived from measurements made over many range gates and does not always match ZH and ZDR measurements well at every range gate. Therefore, the addition of KDP may result in a deterioration of the DSD retrieval at a specific range gate, especially if it is not used optimally. Through disdrometer observations, Zhang et al. (2001) and Brandes et al. (2004a) found that is highly related to . The resulting – relationship can be used as a constraint that allows DSDs to be retrieved from dual-polarization or dual-frequency radar measurements. In general, this approach was proven to perform well for DSD retrieval (Vivekanandan et al. 2004; Brandes et al. 2004a,b; Zhang et al. 2006). Nevertheless, there are still several issues that need to be addressed, such as natural DSD variability, sampling errors, and the applicability of the DSD model. The first issue examined in this paper is the quantification of disdrometer sampling errors related to small sampling volumes and limited sampling times. Disdrometer observations contain not only physical variation but also measurement errors. Gertzman and Atlas (1977) and Wong and Chidambaram (1985) presented a detailed analysis of sampling errors based on the assumption of independent Poisson distributions. Rain events, however, may not be independent stationary random processes. Physical variation and sampling errors coexist (e.g., Jameson and Kostinski 1998; Schuur et al. 2001). It is difficult to separate sampling errors from physical variations with a single instrument. Sideby-side comparisons, on the other hand, provide information that allows sampling errors to be quantified. Tokay et al. (2001) compared measurements from a 2-dimensional video disdrometer (2DVD) and an impact disdrometer [the Joss–Waldvogel disdrometer (JWD)]. However, their study focused mainly on the comparison of DSD parameters and rain variables and did not quantify errors. To our knowledge, error quantification for 2DVD observations through side-by-side comparison has not yet been reported. By knowing observational errors and their error correlations for different DSD moments, the error propagation can be estimated for any rain variable estimator based on rain moments (e.g., Zhang et al. 2003). On the other hand, error quantification helps to introduce advanced processing techniques to reduce error effects on DSD modeling or retrieval. It is well known that DSD variability can be reduced by averaging. For example, Joss and Gori (1978) demonstrated that random, time-sequential, and rain-rate sequential averaging will lead to exponential DSDs....
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...Haddad et al. (1997) introduced a parameterization of gamma distribution, which has three mutually independent parameters....
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...However, Brandes et al. (2004b) showed that this approach is sensitive to KDP noise. In addition, KDP is derived from measurements made over many range gates and does not always match ZH and ZDR measurements well at every range gate. Therefore, the addition of KDP may result in a deterioration of the DSD retrieval at a specific range gate, especially if it is not used optimally. Through disdrometer observations, Zhang et al. (2001) and Brandes et al. (2004a) found that is highly related to . The resulting – relationship can be used as a constraint that allows DSDs to be retrieved from dual-polarization or dual-frequency radar measurements. In general, this approach was proven to perform well for DSD retrieval (Vivekanandan et al. 2004; Brandes et al. 2004a,b; Zhang et al. 2006). Nevertheless, there are still several issues that need to be addressed, such as natural DSD variability, sampling errors, and the applicability of the DSD model. The first issue examined in this paper is the quantification of disdrometer sampling errors related to small sampling volumes and limited sampling times. Disdrometer observations contain not only physical variation but also measurement errors. Gertzman and Atlas (1977) and Wong and Chidambaram (1985) presented a detailed analysis of sampling errors based on the assumption of independent Poisson distributions. Rain events, however, may not be independent stationary random processes. Physical variation and sampling errors coexist (e.g., Jameson and Kostinski 1998; Schuur et al. 2001). It is difficult to separate sampling errors from physical variations with a single instrument. Sideby-side comparisons, on the other hand, provide information that allows sampling errors to be quantified. Tokay et al. (2001) compared measurements from a 2-dimensional video disdrometer (2DVD) and an impact disdrometer [the Joss–Waldvogel disdrometer (JWD)]. However, their study focused mainly on the comparison of DSD parameters and rain variables and did not quantify errors. To our knowledge, error quantification for 2DVD observations through side-by-side comparison has not yet been reported. By knowing observational errors and their error correlations for different DSD moments, the error propagation can be estimated for any rain variable estimator based on rain moments (e.g., Zhang et al. 2003). On the other hand, error quantification helps to introduce advanced processing techniques to reduce error effects on DSD modeling or retrieval. It is well known that DSD variability can be reduced by averaging. For example, Joss and Gori (1978) demonstrated that random, time-sequential, and rain-rate sequential averaging will lead to exponential DSDs. Sauvageot and Lacaux (1995), considering “instantaneous” DSDs having strong variability, further studied averaged DSDs of JWD data within a set of rain-rate intervals and found that the rain rate–reflectivity (R–...
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References
1,465 citations
"Experiments in Rainfall Estimation ..." refers methods in this paper
...…velocity was computed from 2 3y 5 20.1021 1 4.932D 2 0.9551D 1 0.079 34Dt 42 0.002 362D , an expression derived from the laboratory measurements of Gunn and Kinzer (1949) and Pruppacher and Pitter (1971). c. Radar–disdrometer comparison Radar reflectivity factor (ZH), differential reflectivity…...
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...an expression derived from the laboratory measurements of Gunn and Kinzer (1949) and Pruppacher and Pitter (1971)....
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1,050 citations
"Experiments in Rainfall Estimation ..." refers methods in this paper
...Radar reflectivity, differential reflectivity, and specific differential phase were determined from the observed DSDs and calculated scattering amplitudes using the T-matrix method (Ishimari 1991) as described by Zhang et al....
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...Radar reflectivity, differential reflectivity, and specific differential phase were determined from the observed DSDs and calculated scattering amplitudes using the T-matrix method (Ishimari 1991) as described by Zhang et al. (2001a)....
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623 citations
"Experiments in Rainfall Estimation ..." refers background in this paper
...The differential reflectivity (ZDR), defined as the ratio of radar reflectivities at horizontal and vertical polarization (Seliga and Bringi 1976), is sensitive to the flattening of raindrops and increases with drop size....
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...Rainfall estimates made with the radar reflectivity (ZH) and differential reflectivity measurement pair respond to size variations and have smaller errors than estimates determined from radar reflectivity alone (Seliga and Bringi 1976; Ulbrich and Atlas 1984)....
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549 citations
"Experiments in Rainfall Estimation ..." refers background in this paper
...Pruppacher and Beard (1970), Green (1975), and Beard and Chuang (1987) examined ‘‘equilibrium’’ shapes, that is, the mean shape of drops falling under the influence of gravity and subject to a balance of forces acting at the water–air interface....
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501 citations
"Experiments in Rainfall Estimation ..." refers background or methods in this paper
...This relation yields axis ratios that are significantly more spherical than were found by Pruppacher and Beard (1970) and Green (1975), particularly for drops with 1 # D # 4 mm....
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...Goddard et al. (1982) compared ZDR values computed from disdrometer observations, using the equilibrium shapes of Pruppacher and Beard (1970), with radar measurements and found that disdrometer-based ZDR values exceeded radar measurements by 0.3 dB on average....
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...Pruppacher and Beard (1970), Green (1975), and Beard and Chuang (1987) examined ‘‘equilibrium’’ shapes, that is, the mean shape of drops falling under the influence of gravity and subject to a balance of forces acting at the water–air interface....
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