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Journal ArticleDOI

Experiments in Rainfall Estimation with a Polarimetric Radar in a Subtropical Environment

01 Jun 2002-Journal of Applied Meteorology (American Meteorological Society)-Vol. 41, Iss: 6, pp 674-685
TL;DR: In this paper, a unique dataset consisting of high-resolution polarimetric radar measurements and dense rain gauge and disdrometer observations collected in east-central Florida during the summer of 1998 was examined.
Abstract: A unique dataset consisting of high-resolution polarimetric radar measurements and dense rain gauge and disdrometer observations collected in east-central Florida during the summer of 1998 was examined. Comparison of the radar measurements and radar parameters computed from the disdrometer observations supported previous studies, which indicate that oscillating drops in the free atmosphere have more spherical apparent shapes in the mean than equilibrium shapes. Radar‐disdrometer comparisons improved markedly when using an empirical axis ratio relation developed from observational studies and representing more spherical drop shapes. Fixedform power-law rainfall estimators for radar reflectivity ( ZH), specific differential phase (KDP), specific differential phase‐differential reflectivity ( KDP, ZDR), and radar reflectivity‐differential reflectivity ( ZH, ZDR) were then determined using the disdrometer observations. Relations were produced for both equilibrium shapes and the empirical axis ratios. Polarimetric rainfall estimators based on more spherical shapes gave significantly improved performance. However, the improvement was largely in bias mitigation. Rainfall estimates with the ZH‐ZDR measurement pair had the highest correlation with rain gauge observations, the smallest range in bias factors from storm to storm, and the smallest root-mean-square error.

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Citations
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Journal ArticleDOI
TL;DR: In this paper, a review of the current status and main outstanding issues related to precipitation forecasting are discussed, providing a basic structure for research coordination aimed at the improvement of modeling, observation and data assimilation applicable to global and regional scales.

336 citations

Journal ArticleDOI
TL;DR: In this paper, a synthetic polarimetric algorithm has been developed for rainfall estimation, which results in significant reduction in the rms errors of hourly rain estimates when compared with the conventional nonpolarimetric relation.
Abstract: As part of the Joint Polarization Experiment (JPOLE), the National Severe Storms Laboratory conducted an operational demonstration of the polarimetric utility of the Norman, Oklahoma (KOUN), Weather Surveillance Radar-1988 Doppler (WSR-88D). The capability of the KOUN radar to estimate rainfall is tested on a large dataset representing different seasons and different types of rain. A dense gauge network—the Agricultural Research Service (ARS) Micronet—is used to validate different polarimetric algorithms for rainfall estimation. One-hour rain totals are estimated from the KOUN radar using conventional and polarimetric algorithms and are compared with hourly accumulations measured by the gauges. Both point and areal rain estimates are examined. A new “synthetic” rainfall algorithm has been developed for rainfall estimation. The use of the synthetic polarimetric algorithm results in significant reduction in the rms errors of hourly rain estimates when compared with the conventional nonpolarimetric relation: 1.7 times for point measurements and 3.7 times for areal rainfall measurements.

289 citations

Journal ArticleDOI
TL;DR: In this paper, a two-dimensional video disdrometer was used to determine the form of particle size distributions (PSDs) and search for useful interrelationships among the governing parameters of assumed distribution forms and environmental factors.
Abstract: Winter-storm hydrometeor distributions along the Front Range in eastern Colorado are studied with a ground-based two-dimensional video disdrometer. The instrument provides shape, size, and terminal velocity information for particles that are larger than about 0.4 mm. The dataset is used to determine the form of particle size distributions (PSDs) and to search for useful interrelationships among the governing parameters of assumed distribution forms and environmental factors. Snowfalls are dominated by almost spherical aggregates having near-exponential or superexponential size distributions. Raindrop size distributions are more peaked than those for snow. A relation between bulk snow density and particle median volume diameter is derived. The data suggest that some adjustment may be needed in relationships found previously between temperature and the concentration and slope parameters of assumed exponential PSDs. A potentially useful relationship is found between the slope and shape terms of the ...

230 citations


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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Journal ArticleDOI
TL;DR: In this paper, a self-consistency approach was proposed to reduce the impact of variability in the drop size distribution and raindrop shape on the quality of the radar reflectivity Z. The proposed scheme was tested on a large polarimetric dataset obtained during the Joint Polarization Experiment in Oklahoma and yielded an accura...
Abstract: Techniques for the absolute calibration of radar reflectivity Z and differential reflectivity ZDR measured with dual-polarization weather radars are examined herein. Calibration of Z is based on the idea of self-consistency among Z, ZDR, and the specific differential phase KDP in rain. Extensive spatial and temporal averaging is used to derive the average values of ZDR and KDP for each 1 dB step in Z. Such averaging substantially reduces the standard error of the KDP estimate so the technique can be used for a wide range of rain intensities, including light rain. In this paper, the performance of different consistency relations is analyzed and a new self-consistency methodology is suggested. The proposed scheme substantially reduces the impact of variability in the drop size distribution and raindrop shape on the quality of the Z calibration. The new calibration technique was tested on a large polarimetric dataset obtained during the Joint Polarization Experiment in Oklahoma and yielded an accura...

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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Journal ArticleDOI
TL;DR: In this paper, data from three 2D video disdrometers and an S-band polarimetric radar are used to characterize rain microphysics in Oklahoma and a method of sorting and averaging based on two parameters (SATP) is proposed.
Abstract: In this paper, data from three 2-dimensional video disdrometers (2DVDs) and an S-band polarimetric radar are used to characterize rain microphysics in Oklahoma. Sampling errors from the 2DVD measurements are quantified through side-by-side comparisons. In an attempt to minimize the sampling errors, a method of sorting and averaging based on two parameters (SATP) is proposed. The shape–slope (μ–Λ) relation of a constrained gamma (C-G) model is then refined for the retrieval of drop size distributions (DSDs) from polarimetric radar measurements. An adjustable term that is based on observed radar reflectivity and differential reflectivity is introduced to make the C-G DSD model more applicable. Radar retrievals using this improved DSD model are shown to provide good agreement with disdrometer observations and to give reasonable results, including in locations near the leading edge of convection where poorly sampled large drops are often observed.

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
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Journal ArticleDOI
TL;DR: In this article, the terminal velocities for distilled water droplets falling through stagnant air are accurately determined using a new method employing electronic techniques, and the over-all accuracy of the massterminal-velocity measurements is better than 0.7 per cent.
Abstract: The terminal velocities for distilled water droplets falling through stagnant air are accurately determined. More than 1500 droplets of mass from 0.2 to 100,000 micrograms, embracing droplets so small that Stokes' law is obeyed up to and including droplets so large that they are mechanically unstable, were measured by a new method employing electronic techniques. An apparatus for the production of electrically charged artificial water droplets at a controllable rate is described. The over-all accuracy of the mass-terminal-velocity measurements is better than 0.7 per cent.

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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Book
01 Dec 1990
TL;DR: In this article, the fundamental field equations of wave propagation in homogeneous and layered media waveguides and cavities have been studied, including the effects of a dipole on the conducting earth, inverse scattering radiometry, and interferometry numerical techniques.
Abstract: Fundamental field equations waves in homogeneous and layered media waveguides and cavities Green's functions radiation from apertures and beam waves periodic structures and coupled mode theory dispersion and anisotropic media antennas, apertures and arrays scattering of waves by conducting and di-electric objects waves in cylindrical structures, spheres and wedges scattering of complex objects geometric theory of diffraction and low fequency techniques planar layers, strip lines, patches and apertures radiation from a dipole on the conducting earth, inverse scattering radiometry, noise temperature and interferometry numerical techniques.

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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Journal ArticleDOI
TL;DR: In this paper, the potential use of differential reflectivity measurements at orthogonal polarizations to determine rain-fall rate was examined, which involves measurements of ZH and ZV, the radar reflectivity factors due to horizontally and vertically polarized incident waves respectively.
Abstract: The potential use of differential reflectivity measurements at orthogonal polarizations to determine rain-fall rate is examined. The method involves measurements of ZH and ZV, the radar reflectivity factors due to horizontally and vertically polarized incident waves respectively. The differential reflectivity, ZDR = 10 log (ZH/ZV), which should be precisely determinate, occurs as a result of the distortion of raindrops as they fall at terminal velocity. The approximate theory of Gans for electromagnetic scattering by spheroids is applied to the distorted raindrops. Assuming a general exponential form for the raindrop size distribution, equations are derived relating the distribution parameters to the measurements. The determination of rainfall rate follows directly. Finally, the sensitivity of the distribution parameters to radar inaccuracies is examined, and several methods of implementing the measurements are suggested. It is concluded that good estimates of rainfall rate using a single non-att...

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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Journal ArticleDOI
TL;DR: In this paper, the equilibrium shape of raindrops has been determined from Laplace's equation using an internal hydrostatic pressure with an external aerodynamic pressure based on measurements for a sphere but adjusted for the effect of distortion.
Abstract: The equilibrium shape of raindrops has been determined from Laplace's equation using an internal hydrostatic pressure with an external aerodynamic pressure based on measurements for a sphere but adjusted for the effect of distortion. The drop shape was calculated by integration from the upper pole with the initial curvature determined by iteration on the drop volume. The shape was closed at the lower pole by adjusting either the pressure drag or the drop weight to achieve an overall force balance. Model results provide bounds on the axis ratio of raindrops with an uncertainty of about 1% and very good agreement with extensive wind tunnel measurements for moderate to large water drops. The model yields the peculiar asymmetric shape of raindrops: a singly curved surface with a flattened base and a maximum curvature just below the major axis. A close match was found between model shapes and profiles obtained from photos of water drops for diameters up to 5 mm. Coefficients are provided for computing...

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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Journal ArticleDOI
TL;DR: The internal circulation and shape of water drops falling at terminal velocity in air of 20°C at sea level pressure, and nearly water saturated, were studied by means of a wind tunnel.
Abstract: The internal circulation and the shape of water drops falling at terminal velocity in air of 20°C at sea level pressure, and nearly water saturated, were studied by means of a wind tunnel. Drops with an equivalent radius a0 smaller than 140 um had within the experimental error no detectable deformation from spherical shape. Drops of sizes 140 μm ≤ a0 ≤ 500 μm were slightly deformed into an oblate spheroid. The deviation of these drops from spherical shape was found to be in fair agreement with that theoretically predicted by Imai (1950) and others. The deformation of drops of sizes 0.5 mm < a0 < 4.5 mm was found to be linearly related to the drop size. Such a linear relationship is predicted by the semi-empirical calculations of Savic (1953). By means of a tracer technique it was established that water drops falling at terminal velocity in air have a well developed internal circulation. The flow pattern inside a drop was found to be consistent with the flow pattern of the air around the drop and that predicted theoretically by Hadamard (1911) and by Hamielec and Johnson (1962). The surface velocity at the equator of a drop was found to be about 1/100 of the drop's terminal velocity. The experimentally determined internal velocities were compared with those predicted theoretically by McDonald (1954) from boundary layer theory and by Hadamard (1911) based on Stokes flow.

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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