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A new comprehensive space-time model for the characterization of point rainfall rate is presented. A detailed assessment of four key rain characteristics (probability of rain/no rain condition, first and second order lognormal statistics and, space and time correlation functions) with consideration of the impact of varying spatial-temporal integration lengths are discussed. A set of empirical equations have been developed and the results show that they provide estimates of probability of rain/no rain with root mean square errors of less than 1.3 in space and 0.04 in time. They provide good estimates of the parameters at any space-time scales, particularly at higher resolutions that are of great importance to the design and planning of networks operating at frequencies above 10 GHz. In particular, the authors have created databases of rain characteristic parameters spanning North West Europe from which rain rate at any location of interest at different space-time scales can be conveniently obtained. These have been validated by comparing the rain rate exceedance distribution, R0.01, from the model estimates at different space-time scales across the British Isles with values calculated from measured data. It has been found that the proposed model gives highly accurate estimates of R0.01 for the continental area with error percentages (E) generally less than 2.5 but the error percentage increases at the edges of the radar scans and in the oceanic area due to low data availability.

Typhoon Bolaven caused significant damage with severe rainfall all over South Korea, including Cheju Island, which received more than 250 mm in 2 days in August 2012. It was regarded as the most powerful storm to strike the Korean Peninsula in nearly a decade. The rainfall-rate datasets were obtained from S-band radar operated by the Korea Meteorological Administration to be analyzed and compared with the mesoscale Cloud Resolving Storm Simulator (CReSS) model simulation. Multifractal analysis was conducted to understand the structure of the rainfall rate with height in the typhoon system. The radar rainfall data presented with strong intermittency across scales at lower altitudes (1 and 2 km) and a more homogeneous rainfall field at high altitude (5 km) with two parameters (fractal codimension and multifractality index). The statistical scaling moment function and maximal singularities show clear significant differences between radar and the CReSS model.

Rain gauge measurement represents only point rainfall and considered as the “Ground truth” for rainfall rate, but it is associated with different errors and exposed to outliers. On the other hand radar does not directly measure rainfall rates, but it estimates rainfall rate, R (mm/h) by an empirical relationship with the radar reflectivity factor, Z (mm6/m3). Reflectivity is converted into a rainfall rate by the Z-R relationship using the formula: Z = aRb and we determine both of the coefficients (with 95% confidence bounds) , and For Bahir Dar station- I, Bahir Dar station-II and the overall station respectively.

This contribution describes a realistic rain model that considers a cluster of axis-symmetric but flattened raindrops with a specified shape–size relation, a raindrop size distribution, and a distribution of orientation angle of the symmetry axis. The backscattering cross section and specific attenuation due to the rain medium are determined by the extended boundary condition method. The model is applied to data from two X-band radars to estimate reflectivity and rainfall rate, considering attenuation effects during the two-way propagation between the radar and each sampled rain volume. The results are then compared with corresponding ones from well-established attenuation-correction methods. One of these methods, which relies on unattenuated reflectivities measured by an S-band radar, has been carefully validated by a previous study. The reasonable agreement between the two methods indicates that the proposed model may be a suitable option to estimate reflectivity and rainfall rate fields based on X-band radar data, particularly when no such references are available.

The Global Precipitation Measurement mission is a major U.S.–Japan joint mission to understand the physics of the Earth’s global precipitation as a key component of its weather, climate, and hydrological systems. The core satellite carries a dual-precipitation radar and an advanced microwave imager which provide measurements to retrieve the drop size distribution (DSD) and rain rates using a Combined Radar-Radiometer Algorithm (CORRA). Our objective is to validate key assumptions and parameterizations in CORRA and enable improved estimation of precipitation products, especially in the middle-to-higher latitudes in both hemispheres. The DSD parameters and statistical relationships between DSD parameters and radar measurements are a central part of the rainfall retrieval algorithm, which is complicated by regimes where DSD measurements are abysmally sparse (over the open ocean). In view of this, we have assembled optical disdrometer datasets gathered by research vessels, ground stations, and aircrafts to simulate radar observables and validate the scattering lookup tables used in CORRA. The joint use of all DSD datasets spans a large range of drop concentrations and characteristic drop diameters. The scaling normalization of DSDs defines an intercept parameter NW, which normalizes the concentrations, and a scaling diameter Dm, which compresses or stretches the diameter coordinate axis. A major finding of this study is that a single relationship between NW and Dm, on average, unifies all datasets included, from stratocumulus to heavier rainfall regimes. A comparison with the NW–Dm relation used as a constraint in versions 6 and 7 of CORRA highlights the scope for improvement of rainfall retrievals for small drops (Dm < 1 mm) and large drops (Dm > 2 mm). The normalized specific attenuation–reflectivity relationships used in the combined algorithm are also found to match well the equivalent relationships derived using DSDs from the three datasets, suggesting that the currently assumed lookup tables are not a major source of uncertainty in the combined algorithm rainfall estimates.

In radar observations of hydrometeors, the 0°C isotherm in the atmosphere (i.e., the freezing level) usually appears as a region of enhanced reflectivity. This region is known as the bright band (BB). In this study, observations over 12 months from a vertically pointing 35-GHz radar and a collocated disdrometer at the Natural Environment Research Council (NERC) Facility for Atmospheric and Radio Research (NFARR) are used to identify and compare microphysical differences between BB and non-brightband (NBB) periods. From these observations, the relationship between radar reflectivity Z and rainfall intensity R is found to be Z = 772R0.57 for BB periods and Z = 108R0.99 for NBB periods. Additionally, the brightband strength (BBS) was calculated using a novel method derived from the Michelson contrast equation in an attempt to explain the observed variability in BB precipitation. A series of Z–R relationships are computed with respect to BBS. The coefficients increase with increasing BBS from 227 to 926, while the exponents decrease with increasing BBS from 0.85 to 0.38. The results also indicate that NBB periods identified in the presence of a 0°C isotherm in other studies may be misclassified due to their inability to identify weak brightband periods. As such, it is hypothesized that NBB periods are solely due to warm rain processes.

Method for rainfall rate estimation with satellite based microwave radiometer data is proposed. A method to consider the geometric relationship of the observed ice particles and microwave radiometer in the estimation of precipitation is shown, and its validity is shown by comparing it with precipitation radar data on the ground. Observations at high altitudes, such as ice particles, differ greatly in the location of the observation point projected on the ground surface and in the upper troposphere where the observations exist. This effect was insignificant when the precipitation was small because ice particles were often absent, but it was found that the effect was large when the precipitation was large. In other words, the proposed method is effective and effective for Advanced Microwave Scanning Radiometer (AMSR) data in Houston, which was shown as an example of a highly developed convective rain cloud with an In the case of Kwajalein, the effect is insignificant. In addition, the proposed method requires an assumption of ice particle height, and it is necessary to make assumptions based on climatic values. In addition, microwaves in the 89 GHz band, which are considered to be sensitive to ice particles, are not only sensitive to ice particles, so it must be taken into account that they are also affected by the presence of non-ice particles.

187 p. Due to the need for an understanding of the rain structure and the effect of rainfall on the high frequency wireless communication links, several issues related to the characters of rainfall rates and rain attenuation in Singapore are studied. This will enable the development of a comprehensive rain attenuation model. MASTER OF ENGINEERING (EEE)

Communication via satellite is still one of the most important choices in telecommunication especially for areas which are not covered by optical fiber networks. However, the radio frequency used in communication satellites is affected by rain attenuation, which is called as rain attenuation. The rain attenuation increases with increasing rainfall rate and operating frequency. Therefore, accurate estimation of 1-min rainfall rate is important for modelling rain attenuation. However, in the tropics such as Indonesia, precipitation varies in several time scales. Furthermore, climate change has increased the frequency of occurrence of extreme rain and this condition may also affect the communication system. The ITU-R model which is widely used to estimate rain attenuation assumes a stationary climate. This research analysed rainfall pattern in Indonesia. In addition, the variation in melting layer height was also investigated. The rain gauge observation in some locations in Indonesia, i.e., Kototabang, Pontianak, Manado and Biak, were analyzed. The rainfall pattern was analysed using wavelet transforms. In addition, the percentage of time exceeded of several rainfall rate which are commonly used in modeling and design of telecommunication systems was also discussed. For melting layer height, 17 years of the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) data particularly TRMM PR 2A25 version 7 data were used. A 128–256 days scale band oscillation (seasonal) is observed at Kototabang, Pontianak and Biak, but it is not observed at Manado. This seasonal oscillation is an interval-independent characteristic, indicating a stationary dynamic of this signal. Intrasesonal oscillation is an interval-dependent characteristic in which the period of oscillation is not constant indicating a nonstationary dynamic of this signal. At Manado, Pontianak and Kototabang, 256–512 days scale band oscillation is also observed, but it is not clearly observed at Biak. It was also found that there is an increase of rainfall rate for small percentage of time exceeded. Furthermore, there is a slight increase of melting layer height at Kototabang, Pontianak and Biak. In Manado, linear regression shows a decrease of melting layer height with the increase of year.

The prediction of rainfall rate characteristics at small space-time scales is currently an important topic, particularly within the context of the planning and design of satellite network systems. A new comprehensive interpolation approach is presented in this paper to deal with such an issue. There are three novelties in the proposed approach: (1) the proposed interpolation approach is not directly applied to measured rain precipitation (either radar or raingauge-derived data) but focuses on the coefficients of the fitted statistical distributions and/or computed rain characteristics at each location; (2) the parameter databases are provided and the contour maps of coefficients spanning Western Europe have been created. It conveniently and efficiently provides the rain parameter for any location within the studied map; (3) more speculatively, the 3D space-time interpolation approach can extrapolate to rain parameters at space-time resolutions shorter than those in the NIMROD databases.

During the intensive observation period of the Watershed Allied Telemetry Experimental Research (WATER), a total of 1074 raindrop size distribution were measured by the Parsivel disdrometer, the latest state-of-the-art optical laser instrument. Because of the limited observation data in Qinghai-Tibet Plateau, the modelling behaviour was not well done. We used raindrop size distributions to improve the rain rate estimator of meteorological radar in order to obtain many accurate rain rate data in this area. We got the relationship between the terminal velocity of the raindrop and the diameter (mm) of a raindrop: v(D) = 4.67D0.53. Then four types of estimators for X-band polarimetric radar are examined. The simulation results show that the classical estimator R (ZH) is most sensitive to variations in DSD and the estimator R (KDP, ZH, ZDR) is the best estimator for estimating the rain rate. An X-band polarimetric radar (714XDP) is used for verifying these estimators. The lowest sensitivity of the rain rate estimator R (KDP, ZH, ZDR) 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 KDP, is proportional to the 3rd power of the drop diameter. On the other hand, the exponent of the backscatter cross-section, which contributes to ZH, is proportional to the 6th power of the drop diameter. Because the rain rate R is proportional to the 3.57th power of the drop diameter, KDP is less sensitive to DSD variations than ZH.

Summary Ground clutter and beam blockage caused by complex terrain deteriorates the accuracy of radar quantitative precipitation estimations (QPE). To improve radar QPE, we have developed a technique for radar rainfall estimation, the Kyungpook National University Hybrid Surface Rainfall (KHSR), based on a two-dimensional hybrid surface consisting of the lowest radar bins that are immune to ground clutter, beam blockage, and non-meteorological echoes. The KHSR map is a composite of a ground echo mask, a beam blockage mask, and a rain echo mask, and it was applied to an operational S-band dual-polarimetric radar that scans six PPIs at a low elevation angle every 2.5 min. By using three rainfall estimators, R ( Z H ), R ( Z H , Z DR ), and R ( Z H , ξ DR ), this technique was compared with an operational Constant Altitude Plan Position Indicator (CAPPI) QPE of the Korea Meteorological Administration during a summer season from June–August 2012. In comparison with CAPPI, KHSR shows improved rainfall estimates for three algorithms, and it was more effective with dual-polarimetric rainfall algorithms than with single polarimetric rainfall algorithms. Error increased with increasing range from radar, but this increase was more rapid using CAPPI than using KHSR. KHSR using the R ( Z H , Z DR ) algorithm was the most accurate long range (>100 km from the radar) estimator.

The goal of this paper is to calculate new calibration matrices using Rapid Scan (RSS) Meteosat Second Generation (MSG) measurements and to evaluate their impact on precipitation estimates for a territory of the Czech Republic. The calibration matrices are the most important part of the Convective Rainfall Rate algorithm, which uses the IR 10.8 μm, WV 6.2 μm and VIS 0.6 μm spectral SEVIRI (Spinning Enhanced Visible and Infrared Imager) channels of the MSG to assess satellite precipitation estimates (SPEs). The calibration matrices were calculated using Czech radar data from 21 summer days during which severe convection and heavy precipitation were observed. The resultant matrices were compared with those obtained using conventional 15 min MSG scans. The comparison showed significant differences in the calibration matrices, which resulted in differences in the estimated precipitation. The application of RSS data significantly increased the rain rates and improved the structure of the matrices; however, the matrices were subjectively modified to increase the accuracy of the resulting SPEs. The calibration matrices were also calibrated by shifting the radar data forward 5, 10, 15 and 20 min with respect to the MSG measurement, because some delay between the information obtained by the MSG and the radars was expected. The impact of the matrices was evaluated by verifying the SPEs with the radar-derived precipitation estimates merged with the rain gauge observations as the ground truth. The results showed that the calibration matrices that were based on the RSS data improved the categorical skill scores and reduced the mean error (ME), the mean absolute error (MAE), and root mean square error (RMSE) of SPEs. Subjectively, the estimated precipitation values are more realistic, the estimated maximum is closer to observations and convective cores are more pronounced and easily identifiable. The difference between the matrices calibrated by shifting the radar data in time was quite small, and the impact on the SPEs was not readily apparent. However, the time shifts of 15 and 20 min slightly improved the categorical skill scores and reduced the ME, MAE and RMSE.

This paper describes and comments the results obtained applying a data processing method to a joint set of radar and a rain gauge data for estimating the 2-D rainfall field at ground averaged over a given observation time T and over a radar coverage area that includes a rain gauge network. The estimate of the rainfall field is based on the processing of a data set composed by rain gauge and horizontal reflectivity radar data gathered during a rainfall phenomenon. The procedure has been tested on an experimental data set collected in Tuscany in 1999.

— Various relationships between radar reflectivity Z and rainfall rate R commonly identified as Z-R relationships have been derived in order to provide better accuracy for rainfall rate estimation using weather radar. It is critical for the air traffic management at the airport to accurately detect existence of potential microburst and wind shear. There are numerous factors that can certainly affect the accuracy of Z-R relationships including poor hardware calibration. However, the inaccuracy of Z-R relationships also might be due to the differences between the precipitation at the ground level and the precipitation aloft because radar does not scan all the way down except at close range. Several Z-R relationships had also been proposed in the attempt to achieve better accuracy for rainfall estimates by radar system in the tropical region. Nonetheless, the most accurate Z-R relationship for Malaysia weather radar is yet to be investigated and to be identified within the study period. This paper presents the preliminary analyses of previously proposed Z-R relationships for Malaysia weather using new radar data and ground rainfall rate. Comparisons were made between values obtained from the previously proposed relationships for radar and the ground truth measurements. It was identified that the previously proposed relationships estimations are significantly lower than the rain gauge data.

This study develops a Gaussian mixture rainfall-rate estimator (GMRE) for polarimetric radar-based rainfall-rate estimation, following a general framework based on the Gaussian mixture model and Bayes least squares estimation for weather radar–based parameter estimations. The advantages of GMRE are 1) it is a minimum variance unbiased estimator; 2) it is a general estimator applicable to different rain regimes in different regions; and 3) it is flexible and may incorporate/exclude different polarimetric radar variables as inputs. This paper also discusses training the GMRE and the sensitivity of performance to mixture number. A large radar and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign is used to evaluate the GMRE approach. Results indicate that the GMRE approach can outperform existing polarimetric rainfall techniques optimized for this JPOLE dataset in terms of bias and root-mean-square error.

A comprehensive system that is used to invert the geophysical products from microwave measurements has recently been developed. This system, known as the Microwave Integrated Retrieval System (MiRS), ensures that the final solution is consistent with the measurements and, when used as input to the forward operator, fits them to within the instrument noise levels. In the presence of precipitation, this variational algorithm retrieves a set of hydrometeor products consisting of cloud liquid water, ice water, and rain water content profiles. This paper presents the development and assessment of the MiRS rainfall rate that is derived based on a predetermined relationship of the rainfall with these hydrometeor products. Since this relationship relies on the geophysical products retrieved by the MiRS as inputs and not on sensor-dependent parameters, the technique is suitable for all microwave sensors to which the MiRS is applied. This precipitation technique has been designed to facilitate its transition from research to operations when applied to current and future satellite-based sensors. Currently, the MiRS rainfall rate technique has been implemented operationally at the U.S. National Oceanic and Atmospheric Administration (NOAA) for the NOAA-18, NOAA-19, Metop-A Advanced Microwave Sounding Unit, and Microwave Humidity Sensor, as well as for the Defense Meteorological Satellite Program (DMSP)-F16 and DMSP-F18 Special Sensor Microwave Imager/Sounder microwave satellite sensors. For the validation of the MiRS rainfall rate technique, extensive comparisons with state-of-the-art precipitation products derived from rain gauge, ground-based radar, and satellite-based microwave observations are presented for different regions and seasons, and over land and ocean. The MiRS rainfall rate technique is shown to estimate precipitation, with a skill comparable to other satellite-based microwave precipitation algorithms, including the MSPPS, 3B40RT, and MWCOMB, while showing no discontinuities at coasts. This is a relevant result, considering that the MiRS is a system not merely designed to retrieve the rainfall rate but to consistently estimate a comprehensive set of atmospheric and surface parameters from microwave measurements.

Attenuation measured on terrestrial links can be used to estimate surface rainfall rates along a link path. There is current interest in the use of inverse methods to estimate rainfall over areas inferred from terrestrial links. A power-law relationship can be used to estimate rainfall rate from attenuation measured by a terrestrial link. However, the inverse method is simplified with a linear relationship between attenuation and rainfall rate when determining path averaged rainfall rates. This paper investigates power-law and linear relationships between rainfall rate and attenuation. It examines their goodness of fit for a range of frequencies and rainfall rates. Six years of disdrometer data from Chilbolton in the U.K. has been used to study both linear and power-law fits to attenuation and quantify the associated errors.

In 2012 the Météo France metropolitan operational radar network consists of 24 radars operating at C and S bands. In addition, a network of four X-band gap-filler radars is being deployed in the French Alps. The network combines polarimetric and nonpolarimetric radars. Consequently, the operational radar rainfall algorithm has been adapted to process both polarimetric and nonpolarimetric data. The polarimetric processing chain is available in two versions. In the first version, now operational, polarimetry is only used to correct for attenuation and filter out clear-air echoes. In the second version there is a more extensive use of polarimetry. In particular, the specific differential phase Kdp is used to estimate rainfall rate in intense rain. The performance of the three versions of radar rainfall algorithms (conventional, polarimetric V1, and polarimetric V2) at different frequency bands (S, C, and X) is evaluated by processing radar data of significant events offline and comparing hourly radar rainfall accumulations with hourly rain gauge data. The results clearly show a superior performance of the polarimetric products with respect to the nonpolarimetric ones at all frequency bands, but particularly at higher frequency. The second version of the polarimetric product, which makes a broader use of polarimetry, provides the best overall results.

Radar measurements are useful for determining rainfall rates because of their ability to cover large areas. Unfortunately, estimating rainfall rates from radar reflectivity data alone is prone to errors resulting from variations in drop size distributions, precipitation types, and other physics that cannot be represented in a simple, one-dimensional Z–R relationship. However, improving estimates is possible by utilizing additional inputs, thereby increasing the dimensionality of the model. The main purpose of this study is to determine the value of surface observations for improving rainfall-rate estimation. This work carefully designed an artificial neural network to fit a model that would relate radar reflectivity, surface temperature, humidity, pressure, and wind to observed rainfall rates. Observations taken over 13 years from the Oklahoma Mesonet and the KTLX WSR-88D radar near Oklahoma City, Oklahoma, were used for the training dataset. While the artificial neural network underestimated rainfall rates for higher reflectivities, it did have an overall better performance than the best-fit Z–R relation. Most importantly, it is shown that the surface data contributed significant value to an unaugmented radar-based rainfall-rate estimation model.

It is well known that rainfall rate is enhanced over mountains due to orographic uplifting. It would be beneficial to rainfall nowcasting if the intensity of the orographic enhancement could be estimated using simple parameters. In the present study, we found a clear relationship between orographic enhancement of the rainfall rate and the movement speed of radar echoes in a case study of rainfall over mountains in the southwestern area of the Kanto District in Japan during Typhoon 0709, by using rainfall data derived from X-band polarimetric radar. The increasing rate of rainfall rate per unit altitude (ΔR/ΔH) showed a positive correlation (r = 0:95) with the movement speed of radar echoes (V) when V > 10 m s-1. Such a correlation suggests that V is an effective parameter for quickly estimating the orographic enhancement of rainfall, however, more case studies are required before it can be used in practical applications.

Seasonal and spatial variation of the vertical gradient of rainfall rate was investigated using global precipitation data observed by the Precipitation Radar (PR) on the Tropical Rainfall Measuring Mission (TRMM) satellite. The vertical gradient was rendered by features of downward decreasing (DD) or downward increasing (DI) rainfall rate in the lower part of the profile. The DD profiles dominated tropical interior landmasses such as Africa and the Brazilian Plateau in summer. The DI profiles were observed over land in winter and over ocean except for regions with very little rainfall. In addition, DI profiles appeared during the height of the wet season even over the tropical landmasses, such as the mature monsoon period over inland India and over the Amazon River basin. Individual precipitation systems were also investigated in terms of their areally averaged DD and DI characteristics mainly over India. Deep (shallow) profiles tended to be DD (DI) for all seasons except the premonsoon season. A...

The effect of quantization on rainfall rate estimation from the Global Precipitation Measurement dual-frequency radar is studied quantitatively through numerical simulations. The error generated by a deterministic quantization or by a dithered quantization on rainfall rate estimation is combined with the errors from statistical fluctuation of the signal and the receiver noise. The preliminary results for the rain-rate range of 1-10 mmh/sup -1/ are presented.

Polarization radar offers the promise of much more accurate rainfall-rate R estimates than are possible from radar reflectivity factor Z alone, not only by better characterization of the drop size distribution, but also by more reliable correction for attenuation and the identification of hail. However, practical attempts to implement retrieval algorithms have been hampered by the difficulty in coping with the inherent noise in the polarization parameters. In this paper, a variational retrieval scheme is described that overcomes these problems by employing a forward model for differential reflectivity Zdr and differential phase shift ϕdp and iteratively refining the coefficient a in the relationship Z = aRb such that the difference between the forward model and the measurements is minimized in a least squares sense. Two methods are used to ensure that a varies smoothly in both range and azimuth. In range, a is represented by a set of cubic-spline basis functions; in azimuth, the retrieval at one ray is used as a constraint on the next. The result of this smoothing is that the retrieval is tolerant of random errors in Zdr of up to 1 dB and in ϕdp of up to 5°. Correction for attenuation is achieved simply and effectively by including its effects in the forward model. If hail is present then the forward model is unable to match the observations of Zdr and ϕdp simultaneously. This enables a first pass of the retrieval to be used to identify the radar pixels that contain hail, followed by a second pass in which the fraction of the Z in those gates that is due to hail is retrieved, this time with the scheme being able to forward-model both Zdr and ϕdp accurately. The scheme is tested on S-band radar data from southern England in cases of rain, spherical hail, oblate hail, and mixtures of rain and hail. It is found to be robust and stable, even in the presence of differential phase shift on backscatter.

This paper deals with a new algorithm applicable to rainfall rate profiling with a rain-attenuating-frequency radar for vertical incidence from an air or space platform. The proposed algorithm is independent from external radar calibration which is especially difficult to perform in airborne or space-borne applications. In addition to backscattering data from raindrops, path-integrated rainfall rate is used to estimate a rainfall rate profile. The path-integrated rainfall rate may be estimated from surface echo attenuation or from brightness temperature measured with an auxiliary microwave radiometer. The performance of the proposed algorithm is evaluated by a computer simulation experiment assuming backscattering and attenuation models of the radar wave due to rain. Then, airborne radar data are analysed with the algorithm to demonstrate its validity.

A comparison of the rain rate estimated with the assumptions of Rayleigh and Mie scattering is made. We analyzed the different relationships between the radar reflective factor and rain rate (so-called Z-R relationship) with both scattering models for different DSD (droplet size distribution) and rainfall types as the wavelength is 2.2cm which is in accord with the band of TRMM/PR. Meanwhile we introduced a discrete ordinates method to retrieve the Z-R relationship for Mie scattering assumption. It is found that the retrieval result can be represented as the sum of some simple Z-R relationships. By the analysis of the Z-R relationships estimated from Rayleigh and Mie scattering assumptions in the rain types, we found that the difference of Z-R relationships between Rayleigh and Mie scattering in the thunderstorm that represents the larger raindrop size is larger than that in the drizzle that represent the smaller raindrop size.

Precipitation plays a crucial role to the global water and energy cycle that governs the weather, climate, and ecological systems. Thorough understanding and accurate forecasting of precipitation is essential to the affairs of humans. The Tropical Rainfall Measuring Mission (TRMM), launched in 1997, is a joint space mission between NASA and the Japan Aerospace Exploration Agency (JAXA) designed to monitor and study tropical rainfall. The Precipitation Radar (PR) on board the TRMM satellite is the first space borne instrument, capable of providing high-resolution vertical profile of precipitation on a global scale. TRMM-PR operates at a single frequency of Ku- (13.6 GHz) band. The microphysical retrieval algorithms for TRMM-PR rely on the surface-reference technique (SRT) to estimate path attenuation and correct the measured Ku-band reflectivity. With the attenuation-corrected reflectivities, a modified Hitschfeld-Bordan method [1] is then used to retrieve limited drop size distribution (DSD) information, and the rainfall rate [2]. One disadvantage of single-frequency space borne radar such as TRMM-PR is that it is not easy to retrieve the DSD parameters completely. Therefore, k-Z and Z-R relationships, with their inherent assumptions, are used to estimate rainfall rate which is not sufficient to capture the variability of precipitation and has large uncertainty. Global Precipitation Measurement (GPM) mission is poised to be the next generation observations from space after the TRMM mission. GPM is a science mission with integrated applications goals for advancing the knowledge of the global water/energy cycle variability as well as improving weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of global precipitation. The GPM core satellite will be equipped with a dual-frequency precipitation radar (DPR) operating at Ku- (13.6 GHz) and Ka- (35.5 GHz) band [3]. Taking two independent sets of observation, DPR on aboard the GPM is expected to improve our knowledge of precipitation processes relative to the single-frequency (Ku- band) radar used in TRMM by providing greater dynamic range, more detailed information on microphysics. Two parameters of DSDs can be retrieved from dual-frequency observations and better accuracies in rainfall estimation can be achieved. Theoretically, rainfall rate is a function of rain drop size distribution and rain drop terminal velocity, R=0.67π∗10−3∫ v(D)D3N(D)dD. The most critical component in rainfall rate estimation is the time-space variation of drop size distribution. Le and Chandrasekar (2014) [4] developed a hybrid method to retrieve drop size distribution parameters for GPM-DPR. The hybrid method is a profile-based optimization algorithm with the philosophy to combine the attributes of forward method and linear constraints of DSDs in rain. Two of the gamma distribution parameters [5], Do and Nw, at surface are optimized when the deviation between estimates and observations are minimized. The hybrid method can be used to estimate DSDs at each space and temporal resolution of GPM-DPR observation. In this paper, rainfall rate is calculated using DSDs retrieved through the hybrid method [4] based on assumptions of particle terminal velocity. Data collected by GPM-DPR is capability to cover ±65° latitude of the earth with every 2–4 hours. Thus, a global rainfall map can be generated. In polarimetric radar system, rainfall rate can be estimated through dual-polarized radar parameter such as Zdr [6][7]. Zdr is called differential reflectivity and it is a function of particle characteristics itself. Similar of Zdr to the dual-polarization radar retrieval, there is a parameter called dual-frequency ratio (DFR) that plays an important role in the dual-frequency radar retrievals. DFR is defined as the difference of the radar reflectivity at two frequencies in decibels which carries information of single particle characteristics. In this study, we investigate potential relation between rainfall rate, reflectivity at Ku- band and DFR using theoretical simulation [8] and curve fitting. Figure 1 shows a scattergram of rainfall rate estimation from R(Zh, DFR) versus true rainfall rate. Both Zku and DFR are in linear form in this equation. This provides a direct estimation of rainfall rate without prior knowledge of drop size distribution. Since both reflectivity and dual frequency ratio are intrinsic values, attenuation correction is needed before rain rate can be estimated through R(Zh, DFR) equation. The hybrid method [4] described in previous paragraph could be one of the algorithms to perform attenuation correction. The global rainfall map generated through R(Zh, DFR) approach will be cross-compared with DSD approach described in the previous paragraph, as well as other approaches such as attenuation based rainfall rate. The comprehensive analysis of the three techniques are presented.

This paper proposes a method for estimating rainfall rate from ground-based radar observations in eastern Tibet. Firstly, the radar reflectivity-rain rate (Z-R) relationship is derived by regression analysis using the hourly data of a single rain gauge located near the radar and the corresponding radar reflectivity over a period of more than two months. Two different relationships are obtained for stratiformand convective rain types. Secondly, an automated convective-stratiform rain classification methodis introduced that uses the horizontal radar echo structure to identify convective regions and classifies the remainder as stratiform areas. The classification algorithm is verified against visual inspections of horizontal and vertical radar echo structures. Finally, the rain rate is estimated from the radar reflectivity for the rain gauge site using the derived Z-R relationships and the rain type information produced by the classification algorithm. The comparison of the estimation and the gauge data suggests good accuracy.