Rainfall Parameter Estimation from Dual-Radar Measurements Combining Reflectivity Profile and Path-integrated Attenuation

Kozu, Toshiaki; Nakamura, Kenji

doi:10.1175/1520-0426(1991)008<0259:rpefdr>2.0.co;2

Cited by 154 publications

(127 citation statements)

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“…It shows results which do not suffer from the positive feedback of numerical errors. Apart from this, the retrieved values of raindrop parameters are valid, because the values in the look-up tables include the raindrop's ranges that were measured by Kozu and Nakamura (1991). The retrieved diameters in Fig.…”

Section: Observationssupporting

confidence: 55%

“…where D, N T ðrÞ and D m ðrÞ denote the diameter in mm, the number density in number/m 3 and the mean volume diameter in mm at a range r. m is assumed as 3, that is the typical value measured by Kozu and Nakamura (1991) at the same site as our observation site. Symbols and superscripts in the text are described in Tables 2 and 3.…”

Section: Size Distributionmentioning

confidence: 97%

“…Each raindrop profile is assumed to be uniform throughout range gates, and those raindrop size distributions are the same as Table 2 of Kozu and Nakamura (1991). Table 4 summarizes typical values of the rainfalls.…”

Section: Computation For the Model Rainfall:mentioning

confidence: 99%

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Retrieval of Raindrop and Cloud Particle Size Distributions with 14 GHz and 95 GHz Radars

Iwasaki

Okamoto

Hanado

et al. 2005

Journal of the Meteorological Society of Japan

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We have developed a sequential algorithm to retrieve vertical profiles of cloud and rainfall microphysical information from radar reflectivities of a 14 GHz precipitation radar, and a 95 GHz cloudprofiling radar. This sequential algorithm retrieves the number density N T , the mean volume diameter D m and the liquid water content LWC from the nearest to the farthest ranges considering the significant attenuation and Mie scattering. To avoid the accumulation of numerical errors, the retrieval is computed in adjacent ranges assuming N T to be constant in each pair. We demonstrate that our method retrieves N T and D m stably, even if the raindrop size distribution is different from our assumption, or even if some bias errors are appended to the radar constant. The method is applied to collocated ground-based observation by a 14 and a 95 GHz radar, and the retrieved results are evaluated by comparing them against disdrometer-derived size distributions, where the rainfall rate was from 0.1 to 4.6 mm/ hr. The retrieved D m , and the disdrometer-derived D m , agree to within 30%. The retrieved log 10 LWC, and the disdrometer-derived log 10 LWC, also agree to within 30% when the rainfall rate is greater than 0.5 mm/ hr.

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Section: Observationssupporting

confidence: 55%

Section: Size Distributionmentioning

confidence: 97%

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Retrieval of Raindrop and Cloud Particle Size Distributions with 14 GHz and 95 GHz Radars

Iwasaki

Okamoto

Hanado

et al. 2005

Journal of the Meteorological Society of Japan

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“…Because the method of moments, which is simple and has been used by many researchers (e.g., Kozu and Nakamura 1991;Tokay and Short 1996), overestimates the DSD parameters if large-diameter drops of the DSD spectrum are truncated (Ulbrich and Atlas 1998), the present study uses a least square fitting method to estimate the three parameters of gamma DSD. The least square fitting method can allow for truncation of the DSD at not only the large-diameter end, but also the smalldiameter end of the spectrum.…”

Section: Equations For Drop Size Distribution Andmentioning

confidence: 99%

Effect of Natural Variations in Rain Drop Size Distributions on Rain Rate Estimators of 3 cm Wavelength Polarimetric Radar

Maki

Park

Bringi

2005

Journal of the Meteorological Society of Japan

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Statistical errors of rain rate estimators due to natural variations in raindrop size distribution (DSD) are studied for 3-cm wavelength polarimetric radar. Four types of estimators are examined: A classical estimator RðZ H Þ, and three types of polarimetric radar estimators RðK DP Þ, RðZ H ; Z DR Þ, and RðK DP ; Z DR Þ, where R is the rain rate, Z H is the reflectivity factor at horizontal polarization, K DP is the specific differential phase, and Z DR is the differential reflectivity. The T-matrix method is employed for the scattering calculations, and a total of 7,664 one-minute raindrop size spectra, measured with a Joss-Waldvogel type disdrometer are used.According to simulation results, the normalized errors (NEs) of RðZ H Þ, RðK DP Þ, RðK DP ; Z DR Þ, and RðZ H ; Z DR Þ for all DSD samples are 25%, 14%, 9%, and 10%, respectively. The NEs of all estimators, except RðZ H Þ, tend to decrease with increasing rain rate. For rain rates larger than 10 mmh À1 , e.g., the average NEs of RðZ H Þ, RðK DP Þ, RðK DP ; Z DR Þ, and RðZ H ; Z DR Þ are 25%, 9%, 5%, and 7%, respectively. The simulation results show that the classical estimator RðZ H Þ is the most sensitive to variations in DSD and the estimator RðK DP ; Z DR Þ is the least sensitive.The lowest sensitivity of the rain estimator RðK DP ; Z DR Þ to variations in DSD can be explained by the following facts. The difference in the forward-scattering amplitudes at horizontal and vertical polarizations, which contributes K DP , is proportional to the 4.78th power of the drop diameter. On the other hand, the exponent of the backscatter cross section, which contributes to Z H , is proportional to the 6.38th power of the drop diameter. Because the rain rate R is proportional to the 3.67th power of the drop diameter, K DP is less sensitive to DSD variations than Z H . However, DSD spectra with unusually large median volume diameter D 0 can increase the estimation error of RðK DP Þ. The differential reflectivity Z DR reduces the effect of unusual D 0 and is useful for further improvement of the estimator RðK DP Þ. This is due to the fact that Z DR itself is a good measure of D 0 .

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“…This makes it possible to define different methods of moments by choosing several subsets of m moments of a given sample. For the gamma distribution, the free parameters that must be calculated include {N 0 , μ, Λ}, while the most widely used subset of moments are 32] and the frequently applied {M 3 , M 4 , M 6 } [7,25,33]. Applications with seventh moment of beyond are generally not used.…”

Section: Methods Of Momentsmentioning

confidence: 99%

A Maximum Entropy Modelling of the Rain Drop Size Distribution

Checa

Tapiador

2011

Entropy

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This paper presents a maximum entropy approach to Rain Drop Size Distribution (RDSD) modelling. It is shown that this approach allows (1) to use a physically consistent rationale to select a particular probability density function (pdf) (2) to provide an alternative method for parameter estimation based on expectations of the population instead of sample moments and (3) to develop a progressive method of modelling by updating the pdf as new empirical information becomes available. The method is illustrated with both synthetic and real RDSD data, the latest coming from a laser disdrometer network specifically designed to measure the spatial variability of the RDSD.

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Rainfall Parameter Estimation from Dual-Radar Measurements Combining Reflectivity Profile and Path-integrated Attenuation

Cited by 154 publications

References 0 publications

Retrieval of Raindrop and Cloud Particle Size Distributions with 14 GHz and 95 GHz Radars

Retrieval of Raindrop and Cloud Particle Size Distributions with 14 GHz and 95 GHz Radars

Effect of Natural Variations in Rain Drop Size Distributions on Rain Rate Estimators of 3 cm Wavelength Polarimetric Radar

A Maximum Entropy Modelling of the Rain Drop Size Distribution

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