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Jianxin Wang and David B. Wolff

Abstract

Given the decade-long and highly successful Tropical Rainfall Measuring Mission (TRMM), it is now possible to provide quantitative comparisons between ground-based radars (GRs) and the spaceborne TRMM precipitation radar (PR) with greater certainty over longer time scales in various tropical climatological regions. This study develops an automated methodology to match and compare simultaneous TRMM PR and GR reflectivities at four primary TRMM Ground Validation (GV) sites: Houston, Texas (HSTN); Melbourne, Florida (MELB); Kwajalein, Republic of the Marshall Islands (KWAJ); and Darwin, Australia (DARW). Data from each instrument are resampled into a three-dimensional Cartesian coordinate system. The horizontal displacement during the PR data resampling is corrected. Comparisons suggest that the PR suffers significant attenuation at lower levels, especially in convective rain. The attenuation correction performs quite well for convective rain but appears to slightly overcorrect in stratiform rain. The PR and GR observations at HSTN, MELB, and KWAJ agree to about ±1 dB on average with a few exceptions, whereas the GR at DARW requires +1 to −5 dB calibration corrections. One of the important findings of this study is that the GR calibration offset is dependent on the reflectivity magnitude. Hence, it is proposed that the calibration should be carried out by using a regression correction rather than by simply adding an offset value to all GR reflectivities.

This methodology is developed to assist TRMM GV efforts to improve the accuracy of tropical rain estimates, but can also be applied to the proposed Global Precipitation Measurement and other related activities over the globe.

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Jianxin Wang and David B. Wolff

Abstract

Ground-validation (GV) radar-rain products are often utilized for validation of the Tropical Rainfall Measuring Mission (TRMM) space-based rain estimates, and, hence, quantitative evaluation of the GV radar-rain product error characteristics is vital. This study uses quality-controlled gauge data to compare with TRMM GV radar rain rates in an effort to provide such error characteristics. The results show that significant differences of concurrent radar–gauge rain rates exist at various time scales ranging from 5 min to 1 day, despite lower overall long-term bias. However, the differences between the radar area-averaged rain rates and gauge point rain rates cannot be explained as due to radar error only. The error variance separation method is adapted to partition the variance of radar–gauge differences into the gauge area–point error variance and radar-rain estimation error variance. The results provide relatively reliable quantitative uncertainty evaluation of TRMM GV radar-rain estimates at various time scales and are helpful to understand better the differences between measured radar and gauge rain rates. It is envisaged that this study will contribute to better utilization of GV radar-rain products to validate versatile space-based rain estimates from TRMM, as well as the proposed Global Precipitation Measurement satellite and other satellites.

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Brad Fisher and David B. Wolff

Abstract

Passive and active microwave rain sensors on board Earth-orbiting satellites estimate monthly rainfall from the instantaneous rain statistics collected during satellite overpasses. It is well known that climate-scale rain estimates from meteorological satellites incur sampling errors resulting from the process of discrete temporal sampling and statistical averaging. Sampling and retrieval errors ultimately become entangled in the estimation of the mean monthly rain rate. The sampling component of the error budget effectively introduces statistical noise into climate-scale rain estimates that obscures the error component associated with the instantaneous rain retrieval. Estimating the accuracy of the retrievals on monthly scales therefore necessitates a decomposition of the total error budget into sampling and retrieval error quantities. This paper presents results from a statistical evaluation of the sampling and retrieval errors for five different spaceborne rain sensors on board nine orbiting satellites. Using an error decomposition methodology developed by one of the authors, sampling and retrieval errors were estimated at 0.25° resolution within 150 km of ground-based weather radars located at Kwajalein, Marshall Islands, and Melbourne, Florida. Error and bias statistics were calculated according to the land, ocean, and coast classifications of the surface terrain mask developed for the Goddard Profiling (GPROF) rain algorithm. Variations in the comparative error statistics are attributed to various factors related to differences in the swath geometry of each rain sensor, the orbital and instrument characteristics of the satellite, and the regional climatology. The most significant result from this study found that each of the satellites incurred negative long-term oceanic retrieval biases of 10%–30%.

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Jianxin Wang and David B. Wolff

Abstract

This study evaluates space-based rain estimates from the Tropical Rainfall Measuring Mission (TRMM) satellite using ground-based measurements from the radar (GR) and tipping-bucket rain gauges (TG) over the TRMM Ground Validation (GV) site at Melbourne, Florida. The satellite rain products are derived from the TRMM Microwave Imager (TMI), precipitation radar (PR), and combined (COM) rain algorithms using observations from both instruments. The TRMM satellite and GV rain products are spatiotemporally matched and are intercompared at multiple time scales over the 12-yr period from 1998 to 2009. On monthly and yearly scales, the TG agree excellently with the GR because the GR rain rates are generated using the TG data as a constraint on a monthly basis. However, large disagreements exist between the GR and TG at shorter time scales because of their significantly different spatial and temporal sampling modes. The yearly biases relative to the GR for the PR and TMI are generally negative, with a few exceptions. The COM bias fluctuates from year to year over the 12-yr period. The PR, TMI, and COM are in good overall agreement with the GR in the lower range of rain rates, but the agreement is notably worse at higher rain rates. The diurnal cycle of rainfall is captured well by all products, but the peak satellite-derived rainfall (PR, TMI, and COM) lags the peak from the ground measurements (GR and TG) by ~1 h.

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David Atlas, Daniel Rosenfeld, and David B. Wolff

Abstract

The probability matching method (PMM) is used as a basis for estimating attenuation in tropical rains near Darwin, Australia. PMM provides a climatological relationship between measured radar reflectivity and rain rate, which includes the effects of rain and cloud attenuation. When the radar sample is representative, PMM estimates the rainfall without bias. When the data are stratified for greater than average rates, the method no longer compensates for the higher attenuation and the radar rainfall estimates are biased low. The uncompensated attenuation is used to estimate the climatological attenuation coefficient. The method is applicable to any wavelength. The two-way attenuation coefficient was found to be 0.0085 dB km−1 (mm h−1)−1.08 for the tropical rains and associated clouds in Darwin for the first 2 months of the year for horizontally polarized radiation at 5.63 GHz. This unusually large value is discussed. The risks of making real-time corrections for attenuation are also treated.

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David Atlas, Daniel Rosenfeld, and David B. Wolff

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Relations between either the point- or beam-averaged effective reflectivity, Ze, and surface rain rate, R, are determined by a probability matching method similar to that of Calheiros and Zawadzki, and Rosenfeld. The cumulative density functions (CDF) of reflectivity and rain rate are matched at pairs of Ri, Zi, which give the same percentile contribution. One obtains range dependent ZeR relations by stratifying the Ze data by range. Truncation of the Ze distribution by too large a threshold causes the threshold rain rate retrieved from the radar data to exceed that in the matching gage distribution. Forcing a match between the mean rate measured by the gages and those retrieved by use of a set of trial ZeR equations provides for the adjustment of the final ZeR relation and compensates for the truncation. The radar retrieved CDFs of rain rate then replicate the CDF of gage measured rates nicely. In the case of GATE the probability matching scheme produces a ZeR relation that agrees with the bias adjusted relation of Hudlow et al. when one accounts for the approximate inverse relation between the effective reflectivity and beamwidth. The range dependence of ZeR manifests the slope of the vertical reflectivity profile with height and the usual decrease in beamfilling with range, and therefore depends upon storm type. Ale method also implicitly includes climatological variations of drop size distribution and rain rate with height due to a variety of physical factors. Because of the sensitivity of the ZeR relation to beamwidth and viewing angle, it can not be transferred either to airborne or spaceborne radars. It is notable that the climatologically tuned ZeR may be applied to smaller space-time domains than those for which they were developed as long as the PDF of Ze closely approximates that for which the relation was developed. This occurs in tropical regimes and elsewhere when the day-to-day storms resemble the climatically typical storm. This is the reason for the success of the area-lime integral methods of Doneaud and Rosenfeld et al.

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Daniel Rosenfeld, David B. Wolff, and David Atlas

Abstract

A method of deriving the relation between radar-observed reflectivities Ze and gauge-measured rain intensity, R is presented. It is based on matching the probabilities of the two variables. The observed reflectivity is often very different from the true reflectivity near the surface due to the averaging of the real reflectivity field aloft by the beam, path attenuation, and variations in the drop-size distribution (DSD) between the pulse volume and the surface. The probability-matching method (PMM) inherently accounts for all of these differences on average. The formulation of the ZeR functions is constrained such that 1) the radar-retrieved probability density function (PDF) of R is identical to the gauge-measured PDF, and 2) the traction of the time that it is raining is identical for both the radar and for simultaneous, collocated gauge measurements. This ensures that the rain measured by the radar is equal to that observed at the gauges. The resultant ZeR functions are not constrained to be power laws.

The method was applied to data obtained by a 1.65° beamwidth C-band radar and 22 gauges located near Darwin, Australia. The data were stratified by range and also by rainfall type. The resultant ZeR functions manifest the nature of the PDF of R and the manner in which the beam effects the PDF of Ze through beam averaging and the average effects of C-band attenuation. In this regard, the ZeR functions reflect the nature of the precipitation. This provides the hope for greatly improved rainfall measurements, especially for climatic purposes and for sufficiently large space-time domains. In those climates where the storms closely resemble one another, the relations may be used for individual storms over their lifetime or for a few storms at any one moment. The time-space domain in this study was sufficient for the instability driven convective storm in Darwin but too small for the synoptic-scale systems.

The functions show a particularly strong range dependence for rain types characterized by large reflectivity gradients; that is, those in which the beam-average Ze differs most from the actual reflectivity Z. Because of the dominance of the beam effects relative to those due to variations in DSD, the use of radar polarimetry will improve the accuracy of rainfall retrievals, based on specification of the DSD alone, only with narrow beams or at short ranges and for small-scale, short-term purposes when the probability based relations may not be representative. Polarimetry is also valuable for smaller space-time domains than those for which the probability matched ZeR relations may be valid.

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Ali Tokay, David B. Wolff, Katherine R. Wolff, and Paul Bashor

Abstract

Four impact disdrometers and 27 tipping bucket rain gauges were operated at 11 different sites during August and September 2001, as part of the Keys Area Microphysics Project. The rain gauge and disdrometer network was designed to study the range dependency of radar calibration and rainfall verification in tropical storms. The gauges were collocated at eight sites, while three to five gauge clusters were deployed at three sites. Four disdrometers were also collocated with rain gauges. Overall the experiment was quite successful, although some problems did occur including flooding of gauge loggers, vandalism, and excessive noise at disdrometer sites.

Both a south-to-north and east-to-west rainfall gradient was observed, whereby the gauges on the western and northern sides of the Lower Keys recorded more rainfall. Considering the campaign-long rain accumulations, collocated gauges agreed well, with differences generally less than 2%, except for one gauge cluster where the rain accumulation difference was attributed to individual gauge calibration error. The duration of a rain event was sensitive to the definition of a rain event, while this was not a factor in rain intensity. Only 7% of the rain events had significant storm total differences in excess of 2.5 mm. All of these events occurred at storm conditional mean and maximum rain rates higher than 5 and 50 mm h−1, respectively. Nevertheless, there were many other rain events for which the storm total differences were not significant in heavy rainfall. Combining most of the rain events from all collocated gauge sites, the correlation coefficient and mean percent absolute difference between the gauge storm totals were 0.99 and about 9%, respectively, on average. A rain gauge was typically able to measure rainfall within ±1.2 mm. As the storm total increased, the standard deviation of the rain total difference and correlation coefficient increased, while mean percent absolute difference decreased. Considering the gauge that recorded higher overall accumulation as the reference, and ignoring the natural variability of rainfall between collocated gauges, the gauge rainfall error was about 9%. Two disdrometers that were placed away from noise sources performed well and recorded higher rainfall accumulation than their collocated rain gauges.

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Daniel Rosenfeld, Eyal Amitai, and David B. Wolff

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Application of the window probability matching method to radar and rain gauge data that have been objectivelyclassified into different rain types resulted in distinctly different Ze-R relationships for the various classifications.The classification parameters, in addition to the range from the radar, are (a) the horizontal radial reflectivitygradients [dB km-1; (b) the cloud depth, as scaled by the effective efficiency; (c) the brightband fraction withinthe radar field window; and (d) the height of the freezing level. Combining physical parameters to identify thetype of precipitation and statistical relations most appropriate to the precipitation types results in considerableimprovement of both point and areal rainfall measurements. A limiting factor in the assessment ofthe improvedaccuracy is the inherent variance between the true rain intensity at the radar measured volume and the rainintensity at the mouth of the rain gauge. Therefore, a very dense rain gauge network is required to validate mostof the suggested realized improvement.

A rather small sample size is required to achieve a stable Ze-R relationship (standard deviation of 15% of Rfor a given Ze)-about 200 mm of rainfall accumulated in all gauges combined for each classification.

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Daniel Rosenfeld, Eyal Amitai, and David B. Wolff

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An automated scheme to characterize precipitation echoes within small windows in the radar field is presented and applied to previously subjectively classified tropical rain cloud systirns near Darwin, Australia. The classification parameters are (a) Ee, effective efficiency, as determined by cloud-top and cloud-base water vaporsaturation mixing ratios; (b) BBF, brightband fraction, as determined by the fraction of the radar echo area in which the maximal reflectivity occurs within +1.5 km of the 0C isotherm level; and (c) ΔrZ, radial reflectivity gradients (dB km-1).

These classification criteria were applied to tropical rain cloud systems near Darwin, Australia, and to winter convective rain cloud systems in Israel. Both sets of measurements were made with nearly identical networks of C-band radars and rain gauge networks.

The results of the application of these objective classification criteria to several independently predetermined rain regimes in Darwin have shown that better organized rain systems have smaller ΔrZ and larger BBF. Similarly, smaller ΔrZ and larger BBF were also observed from maritime rain cloud systems, as compared to continental rain cloud systems with the same degree of organization. Continental rain cloud systems, regardless of their degree of organization, have larger depths, as expressed by E1.

The results suggest that ΔrZ BBF, and E1 can be used in an automated way over small domains, of the order of 100 km2, for the classification of the rain types into physically meaningful regimes. The classification by E1 is particularly useful for rainfall estimation by area-time integral techniques; ΔrZ is useful in assessing the bias errors of rainfall measurements by remote sensing, which are due to partial beam filling. The classification by BBF is useful for assessing the convective-stratiform partitioning of the rainfall volume. Our calculations suggest that previous estimates of the amount of stratiform rainfall in the Tropics may have been too large, by up to afactor of 2.

The rainfall analyses presented in this study are based exclusively on rain gauge measurements, while radar information was used only to classify the individual gauge measurements.

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