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The potential of rainfall-rate assignment using Meteosat Second Generation (MSG) Spinning Enhanced Visible and Infrared Instrument (SEVIRI) data is investigated. For this purpose, a new conceptual model for precipitation processes in connection with midlatitude cyclones is developed, based on the assumption that high rainfall rates are linked to a high optical thickness and a large effective particle radius, whereas low rainfall rates are linked to a low optical thickness and a small effective particle radius. Reflection values in the 0.56-0.71-[micro]m ([VIS.sub.0.6]) and 1.5-1.78-[micro]m ([NIR.sub.1.6]) channels, which provide information about the optical thickness and the effective radius, are considered in lieu of the optical and microphysical cloud properties. An analysis of the relationship between [VIS.sub.0.6] and [NIR.sub.1.6] reflection and the ground-based rainfall rate revealed a high correlation between the sensor signal and the rainfall rate. Based on these findings, a method for rainfall-rate assignment as a function of [VIS.sub.0.6] and [NIR.sub.1.6] reflection is proposed. The validation of the proposed technique showed encouraging results, especially for temporal resolutions of 6 and 12 h. This is a significant improvement compared to existing IR retrievals, which obtain comparable results for monthly resolution. The existing relationship between the [VIS.sub.0.6] and [NIR.sub.1.6] reflection values and the ground-based rainfall rate is corroborated with the new conceptual model. The good validation results indicate the high potential for rainfall retrieval in the midlatitudes with the high spatial and temporal resolution provided by MSG SEVIRI. DOI: 10.1175/2010JAMC2284.1

Rainfall-rate statistics are frequently derived on the basis of rain gauge recordings with effective integration times of 10 min or longer. The conversion of such data to equivalent statistics for an effective integration time of 1 min is very important to predict rainfall attenuation at a location accurately. Because of the limited availability of 1-min rainfall-rate data, conversion of available rainfall-rate distributions with longer integration times to the desired 1-min distributions is needed. Several methods for converting 60-min rainfall rates to l-rain rainfall rates are tested against measured rainfall rates from tropical, high-rainfall-rate regions. Segal's method was found to perform the best overall when compared with other conversion methods.

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 [Z.sub.dr] and differential phase shift [[phi].sub.dp] and iteratively refining the coefficient a in the relationship Z = a[R.sup.b] 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 [Z.sub.dr] of up to 1 dB and in [[phi].sub.dp] of up to 5[degrees]. 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 [Z.sub.dr] and chap 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 [Z.sub.dr] and [[phi].sub.dp] 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.

Power law relationships of the form R = a[A.sup.b] are derived, where R is the rainfall rate, and A is the 35-GHz specific attenuation [A.sub.h] or specific differential attenuation [DELTA] A = [A.sub.h] - [A.sub.v], where the subscripts h and v indicate horizontal and vertical polarizations. The effects of raindrop size distribution, canting, and oscillation on these relationships are evaluated quantitatively. The drop size distributions (DSDs) are obtained from ground-based disdrometer measurements from three different geographical locations around the world. The R-[A.sub.h] relationship is negligibly affected by raindrop canting and oscillation. It is affected to some extent by DSD variations, with less than 15% fractional standard error (FSE) in the estimated rainfall rate [R.sub.Ah]. On the other hand, the R-[DELTA] A relationship is most sensitive to raindrop oscillation, up to about 35% difference in [R.sub.[DELTA]A] compared to the no-oscillation case, and the effect of canting is about 9% for a standard deviation of 10[degrees] of the polar canting angle compared with no canting. The FSE due to variations in the DSD for R < 5 mm [h.sup.-1] is greater than 30% and increases with decreasing R. However, for R > 20 mm [h.sup.-1], the FSE in [R.sub.[DELTA]A] is comparable (and even lower for R > 30 mm [h.sup.-1]) to that of [R.sub.Ah]. The exceptions to this are rainfall rates with DSDs dominated by smaller raindrops (diameters less than 2.4 mm). It is also emphasized that because oscillation and canting affect [DELTA]A but not [A.sub.h], they could be used in combination for determining the presence of drop oscillation and canting and for estimating an effective raindrop shape model (axial ratio versus size). Index Terms--Attenuation, differential attenuation, dual polarization, microwave propagation, millimeter-wave propagation, rain, rain drop size distribution.

In this paper, the delta function is introduced to describe the observed rainfall-rate distribution including the mixture of discrete and continuous parts. Thus the observed rainfall-rate distribution can be expressed as a simple mathematical formula. Also the probability density function (pdf) of frontal rainfall in the region of the United Kingdom is investigated. It is found that the pdf during the period of 26 January-25 February 1990 can be fitted well by the lognormal distribution, and there is a linear correlation between the mean and the standard deviation of rainfall-rate pdf during this period. The GARP Atlantic Tropical Experiment (GATE) data for pixel sizes of 4.0 and 40.0 km are also analyzed in this paper. It is also found that both mean and standard deviation decrease with the increment of the observing pixel size. Based on the rainfall-rate distribution formula; the research results of Kedem et al. regarding modeling the rain-rate pdf as lognormal, gamma, and inverse Gaussian; the correlation between the mean and variance of rainfall-rate pdf; and the specified values of mean and variance, some conclusions on the threshold method (or area-time integral method) are presented that do not require the assumption that rain rate is homogeneous in time and space. The results show that the area-average rain rate and fractional area are nonlinearly related at low rain-rate thresholds and that there is variation of the regression slope with rainfall-rate threshold, observing pixel size, and rain type, and so on. From these results, it can be concluded that the rainfall-rate threshold, precipitation type, and the observing pixel size are three major factors for the threshold method (or area-time integral method). The three elements have to be considered if the threshold method (or area-time integral method) is applied. Also, it is known that the reasons that the threshold method (or area-time integral method) works well arise from the observed precipitation properties such as the lognormal rainfall-rate pdf, the correlation between the mean and variance, and the specified values of the mean and variance. Such observed precipitation properties originate from the mesoscale dynamics and cloud physics. At the same time, such observed precipitation properties should be constrained by mesoscale dynamics and cloud physics.

Realistic estimate of background field and observation errors and horizontal correlation of these errors with distance are necessary for correct analysis of rainfall rate. Information from satellites and results of a numerical prediction model are used for objective analysis, done using a method of statistical interpolation. Results show that such an objective analysis is possible as the quality of short-term precipitation forecasts, used as background field, is good.

A best-fit curve relating measured voltage to drop size is compared to a linear interpolation between calibration points of a disdrometer. Both are used in the calculation of drop size distributions in an experiment of the Malaysian Meteorologial Service and the University of Toronto in Penang, Malyasia. Results showed that raindrop spectra were affected by the best-fit curve of the calibration data. Rain rate and radar reflectivity were unaffected.

The performance (stability and accuracy) of a new range profiling algorithm (kZS), using the measurement of surface echo as a constraint on total path integrated attenuation, for rainfall retrieval from a spaceborne radar was presented and discussed in a previous paper (1). Omitting other causes of errors previously examined, the present paper focuses specifically on possible bias due to non uniform beam filling effects. This problem is studied analytically for identifying the physical origin of the biasing terms. In addition, bias in rainfall profile estimate are quantified through simulations of Ku-band spaceborne radar data processing, featuring the intercept of a raincell model by the downward looking radar beam.

A study of the spatial correlation of rainfall between earth stations showed a joint event probability still prevails at distances of less than 800 kilometers. The analysis of ten years of hourly data from 50 sites in Italy was done with a view for the design of on-board processing systems of advance satellites linked to numerous earth stations. Besides the joint probability approach, which is the fundamental parameter for the design of on-board systems, a statistical dependance index explained the spatial large scale structure of the rain independently of the site climatic characteristics.

Abstract: Attenuation due to rain is a primary cause of communication impairment on satellite-earth paths, especially above 10GHz. Rainfall is a serious source of attenuation at such a frequency. This [...]

The Tropical Rainfall Measuring Mission Global Validation Program provides a unique opportunity to compare radar datasets from different sites, because they are analyzed in a relatively uniform procedure. Monthly observed radar reflectivity-rainfall rate ([Z.sub.e]-R) relations for four different sites that are surrounded by tipping bucket gauge networks (Melbourne, Florida; Houston, Texas; Darwin, Australia; and Kwajalein Atoll, Republic of Marshall Islands) were derived. The radar and gauge data from all sites are controlled for quality using the same algorithms, which also include an automated procedure to filter unreliable rain gauge data upon comparison with radar data. The relations are generated by two different methods. The first method is based on using a power law [Z.sub.e]-R with a fixed exponent of 1.4, and the second is based on matching unconditional probabilities of rain rates as measured by the gauge to radar-observed reflectivities and is known as the window probability matching method (WPMM). Both methods tune the radar observations to a network of quality-controlled gauges to adjust the total monthly rainfall to match the gauges. Separate relations are generated for convective and stratiform rain, as classified by the horizontal reflectivity structure. In the WPMM-based [Z.sub.e]-R relations, a given [Z.sub.e] was matched to a much lower R in convective rainfall than in stratiform rainfall. These relations were found to be curved lines in log--log space rather than a straight-line power law. The WPMM-based [Z.sub.e]-R curves demonstrated systematic variation between the convective and stratiform rain, but the power law--based [Z.sub.e]-R curves showed no systematic trend. The systematic variation in the relations shown here contradicts previous findings in which the classification is based only on the existence or nonexistence of brightband signature. The latter indicates a higher reflectivity in stratiform rain as compared with that in convective rain, for a given rain rate. Recent studies, based on disdrometer data, suggest that during a typical event there are three principal types of rain (convective, transition, and stratiform), each characterized by a different type of Z-R relation. The current study suggests that to distinguish each type, both the horizontal and the vertical reflectivity field structure should be analyzed.

Precipitation characteristics of trade wind clouds over the Atlantic Ocean near Barbuda are derived from radar and aircraft data and are compared with satellite-observed cloud fields collected during the Rain in Cumulus over the Ocean (RICO) field campaign. S-band reflectivity measurements Z were converted to rainfall rates R using a Z-R relationship derived from aircraft measurements. Daily rainfall rates varied from 0 to 22 mm [day.sup.-1]. The area-averaged rainfall rate for the 62-day period was 2.37 mm [day.sup.-1]. If corrected for evaporation below cloud base, this value is reduced to 2.23 mm [day.sup.-1], which translates to a latent heat flux to the atmosphere of 63 W [m.sup.-2]. When compared with the wintertime ocean-surface latent heat flux from this region, the average return of water to the ocean through precipitation processes within the trade wind layer during RICO was 31%-39%. A weak diurnal cycle was observed in the area-averaged rainfall rate. The magnitude of the rainfall and the frequency of its occurrence had a maximum in the predawn hours and a minimum in the midmorning to early afternoon on 64% of the days. Radar data were collocated with data from the Multiangle Imaging Spectroradiometer (MISR) to develop relationships between cloud-top height, cloud fraction, 866-nm bidirectional reflectance factor (BRF), and radar-derived precipitation. The collocation took place at the overpass time of ~1045 local time. These relationships revealed that between 5.5% and 10.5% of the cloudy area had rainfall rates that were > 0.1 mm [h.sup.-1], and between 1.5% and 3.5% of the cloudy area had rainfall rates that were >1 mm [h.sup.-1]. Cloud-top heights between ~3 and 4 km and BRFs between 0.4 and 1.0 contributed ~50% of the total rainfall. For cloudy pixels having detectable rain, average rainfall rates increased from ~1 to 4 mm [h.sup.-1] as cloud-top heights increased from ~1 to 4 km. Rainfall rates were closely tied to the type of mesoscale organization, with much of the rainfall originating from shallow (

The spatial variability of raindrop size distributions (DSDs) and precipitation fields is investigated utilizing disdrometric measurements from the four Precipitation Occurrence Sensor Systems (POSS) and radar reflectivity fields from S-band dual-polarization radar and vertically pointing X-band radar. The spatial cross correlation of the moments of DSDs, their ratio, error in rainfall estimate, and normalization parameters are quantified using a 'noncentered' correlation function. The time-averaged spatial autocorrelation function of observed radar reflectivity factor ([Z.sub.e]) is smaller than that of estimated rainfall rate from [Z.sub.e] because of power-law R-Z transformation with its exponent larger than unity. The important spatial variability of DSDs and rain integral fields is revealed by the significant differences among average DSDs and leads to an average fractional error of 25% in estimating rainfall accumulation during an event. The spatial correlation of the reflectivity from POSS is larger than that of [Z.sub.e] because of larger measurement noise in [Z.sub.e]. The higher moments of DSDs are less correlated in space than lower moments. The correlation of rainfall estimate error is higher than that of estimated rainfall rate and of rainfall rate calculated from DSDs. The correlation of the characteristic number density is low (0.87 at 1.3-km distance), suggesting that the assumed homogeneity of the characteristic number density in space could result in larger errors in the retrieval of DSDs and rainrelated parameters. However, the characteristic diameter is highly correlated in space.

This paper discusses the basis for a new rainfall estimation method using geostationary infrared and visible data. The precipitation radar on board the Tropical Rainfall Measuring Mission satellite is used to train the algorithm presented (which is the basis of the estimation method) and the further intercomparison. The algorithm uses daily Geostationary Operational Environmental Satellite infrared-visible (IR-VIS) cloud classifications together with radiative and evolution properties of clouds over the life cycle of mesoscale convective systems (MCSs) in different brightness temperature ([T.sub.b]) ranges. Despite recognition of the importance of the relationship between the life cycle of MCSs and the rainfall rate they produce, this relationship has not previously been quantified precisely. An empirical relationship is found between the characteristics that describe the MCSs' life cycle and the magnitude of rainfall rate they produce. Numerous earlier studies focus on this subject using cloud-patch or pixel-based techniques: this work combines the two techniques. The algorithm performs reasonably well in the case of convective systems and also for stratiform clouds, although it tends to overestimate rainfall rates. Despite only using satellite information to initialize the algorithm, satisfactory results were obtained relative to the hydroestimator technique, which in addition to the IR information uses extra satellite data such as moisture and orographic corrections. This shows that the use of IR-VIS cloud classification and MCS properties provides a robust basis for creating a future estimation method incorporating humidity Eta field outputs for a moisture correction, digital elevation models combined with low-level moisture advection for an orographic correction, and a nighttime cloud classification.

The spatial variability and temporal variability of precipitation are widely recognized. In particular, rainfall rates can fluctuate widely in regions where the raindrops are clustered and where mean conditions are changing (statistical heterogeneity). Indeed, at times, the ambiguity associated with an estimated average rainfall rate may become very large. Therefore, in quantitative measurements of precipitation, it would be useful to identify where this occurs. In this work a technique is proposed and applied to quantify the variability in rainfall rates introduced by statistical heterogeneity and raindrop clustering using deviations from Rayleigh statistics of intensity fluctuations. This technique separates the Rayleigh contributions to the observed relative dispersion from those arising from clustering and statistical heterogeneities. Applications to conventional meteorological radar measurements are illustrated using two scans. Often, but not always, the greatest ambiguities in estimates of the average rainfall rate occur just where the rainfall rates are the largest and presumably where accurate estimates are most important. This ambiguity is not statistical; rather, it indicates the presence of important sub-beam-scale fluctuations. As a consequence, no single average value can be applied uniformly to the entire domain. The examples provided here also demonstrate that the appropriate observations are feasible using current conventional meteorological radars with adequate processing capabilities. However, changes in radar technology that improve and increase pulse-to-pulse statistical independence will permit such observations to be gathered more routinely at finer spatial resolution and with enhanced precision.

In a recent study, the authors performed numerical simulations of moist nearly neutral flows over a ridge using the Weather Research and Forecasting (WRF) Model in a regime where the Coriolis force can be neglected and with the simple Kessler (warm rain) microphysical scheme. In the present work, further numerical solutions using more general and realistic experimental conditions are discussed. The upstream-propagating disturbance, which was found in the author's previous study to desaturate the initially saturated sounding for intermediate mountain heights, is present for all the simulations with taller mountains considered in the present work. The inclusion of the Coriolis force however suppresses the upwind propagation of the dry region and weakens the downstream development of convective cells. The sensitivity to different microphysical schemes has also been investigated. The simple Kessler scheme was compared with a more complete scheme, by Lin et al., which includes ice species. Some differences between the warm-rain-only and ice-microphysics simulations emerge mainly as a consequence of the different distributions of initial cloud water needed to produce a steady-state environmental flow. The effects of the different microphysical schemes on the rainfall rate have also been analyzed, with significant differences between them emerging in the case of narrower mountains. Finally, the sensitivity of the rainfall to the surface temperature has been studied, showing that for higher surface temperatures, the rainfall rate can be smaller although the available water content is larger, as a consequence of the differing microphysical processes activated in the different temperature regimes.

We present annual/seasonal rainfall rate statistics derived from a 29-month data bank of 1 sample/min, measured by a disdrometer located inside the National Technical University of Athens Campus. We discuss both the inaccuracy and the unavailability of the measuring equipment, as well as the statistical reliability of the rainfall rate sample. Additionally, after applying the Synthetic Storm Technique on the measured rainfall rate time series, we present the first long term simulated annual/seasonal and diurnal rain attenuation statistics, at 12 GHz for a hypothetical downlink from Hellas Sat 2 to Athens. According to the results, we predict that communication downlinks working in the afternoon and early evening hours must be given an extra power margin, to compensate for high rain attenuation. Index Terms--Annual/seasonal and diurnal statistics, Hellas Sat 2, microwave propagation, rain attenuation, synthetic storm technique.

A neural network model for rainfall retrieval over ocean from remotely sensed microwave (MW) brightness temperature (BT) is proposed. BT data are obtained from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). The BT values from different channels of TMI over the Pacific Ocean (163[degrees] tto 177[degrees]W and 18[degrees] to 34[degrees]S) are the input features. The near-surface rainfall rate from the Precipitation Radar (PR) are considered as a target. The proposed model consists of a neural network with online feature selection (FS) and clustering techniques. A K-means clustering algorithm is applied to cluster the selected features. Different networks have been trained to give an instantaneous rainfall rate with all input features as well as with selected features obtained by applying the FS algorithm. It is found that the hybrid network utilizing FS and clustering techniques performs better. The developed network is also validated with two independent datasets on March 14, 2000 over the Atlantic Ocean having stratiform rain and on March 21, 2000 over the Pacific Ocean having both stratiform and convective rain. In both cases, the hybrid network performs well with correlation coefficient improving to 0.78 and 0.81, respectively, in contrast to 0.70 and 0.75 for the network with all features. The rainfall rate retrieved from the hybrid network is also compared with the TMI surface rain rate, and a correlation of 0.84 and 0.75 is found for the two events. The proposed hybrid model is validated with a Doppler Weather Radar, and correlation of 0.52 is observed. Index Terms--Backpropagation, clustering, feature selection, microwave brightness temperature, modeling, neural networks, satellite rainfall estimation.

Radiometric brightness temperatures below about 12 GHz provide accurate estimates of path attenuation through precipitation and cloud water. Multiple brightness temperature measurements at X-band frequencies can be used to estimate rainfall rate and parameters of the drop size distribution once correction for cloud water attenuation is made. Employing a stratiform storm model, calculations of the brightness temperatures at 9.5, 10, and 12 GHz are used to simulate estimates of path-averaged median mass diameter, number concentration, and rainfall rate. The results indicate that reasonably accurate estimates of rainfall rate and information on the drop size distribution can be derived over ocean under low to moderate wind speed conditions. Index Terms--Airborne radiometer, drop size distribution, microwave radiometry, rain rate estimation, spaceborne radiometer.

The paper presents the results of 19.9 GHz radiometric propagation studies conducted over a period of one year at Amritsar, for determining rain-induced zenith path attenuation. The zenith path attenuation has been determined by the measurements of sky noise temperature received by the radiometer. The results obtained from the experiment are presented in the form of annual cumulative distributions of rain rate, sky noise temperature, and zenith path attenuation together with worst-month statistics. The rainfall rate cumulative distribution as predicted by ITU-R for our geographical location is lower than the actually measured rainfall rate cumulative distribution. The cumulative distribution of zenith path attenuation predicted by using ITU-R model overestimates the measured cumulative distribution of zenith path attenuation. Index Terms--Radio wave propagation, rain attenuation, rainfall intensity, satellite communication, sky noise temperature.

The use of millimeter radio communication systems has seen a remarkable increase in recent years. However, there remains a need for validation and improvement of millimeter propagation prediction methods tot safe design and operation of the systems. At this high frequency range, propagation related degradation is primarily caused by rainfall. The goal is an improved method for predicting specific attenuation due to rainfall. A general method for establishing the relationship between rainfall rate and specific attenuation is developed. Drop size distributions (DSDs) measured by a Joss distrometer are analyzed, and the three climate classification parameters rain rate, DSD median, and DSD mode are used in the development of these new methods. These parameters are investigated as candidate classes to categorize drop size distributions. Categories of the classes are then established to improve the long-term DSD estimate. The typical long-term DSD is used to derive new prediction methods that are compared with observed attenuation. The influence of wind on the rainfall measurements is studied, and a corresponding correction is suggested, reducing the prediction error significantly. Testing of the three new methods using measurements at 40 and 60 GHz shows noticeable improvement over the method recommended by the International Telecommunication Union (ITU) using measurements at 60 GHz at deep attenuation. Index Terms--Drop size distributions (DSDs), millimeter wave attenuation, propagation prediction methods, rainfall rate.

Polarization radar techniques essentially rely on detecting the oblateness of raindrops to provide a measure of mean raindrop size and then using this information to give a better estimate of rainfall rate R than is available from radar reflectivity Z alone. To derive rainfall rates from these new parameters such as differential reflectivity [Z.sub.DR] and specific differential phase shift [K.sub.DP] and to gauge their performance, it is necessary to know the range of naturally occurring raindrop size spectra. A three parameter gamma function is in widespread use, with the three variables [N.sub.o] [D.sub.o], and [mu] providing a measure of drop concentration, mean size, and spectral shape, respectively. It has become standard practice to derive the range of these three variables in rain by comparing the 69 published values of the constants a and b in the empirical relationships Z = a[R.sup.b] with the values of a and b obtained when R and Z are derived by integrating the appropriately weighted gamma function. The relationships in common use both for inferring R from Z, [Z.sub.DR], and [K.sub.DP], and for developing attenuation correction routines have been derived from a best fit through the values obtained by cycling over these predicted ranges of [N.sub.o], [D.sub.o], and [mu]. It is pointed out that this derivation of the predicted range of [N.sub.o] [D.sub.o], and [mu] arises using a flawed logic for a particular nonnormalized form of the gamma function, and it is shown that the predicted ranges give rise to some very unrealistic drop spectra, including many with high rainfall and very small drop sizes. It is suggested that attenuation correction routines relying on differential phase may be suspect and the commonly used relationships between rainfall rate and Z, [Z.sub.DR], and [K.sub.DP] need to be reexamined. When more realistic drop shapes are also used, it may be that published relationships for deriving R from Z and [Z.sub.DR] are in error by over a factor of 2; a new equation is proposed that, in the absence of hail and attenuation, should yield values of R accurate to 25%, provided that [Z.sub.DR] can be estimated to 0.2 dB and Z is calibrated to 1 dB. Relationships of the form R = a[K.sup.b.sub.DP], with b = 1.15, are in widespread use, but more realistic drop spectra and drop shapes yield a value of b closer to 1.4, similar to the exponent in Z-R relationships. In accord, although [K.sub.DP] has the advantage of insensitivity to hail, it may have the same sensitivity to variations in drop spectra as Z does. In addition, the higher value of the exponent b implies that the proposed use of the total phase shift to give the path-integrated total rainfall is also questionable. However, the consistency of Z, [Z.sub.DR], and [K.sub.DP] in rain can be used to provide absolute calibration of Z to 0.5 dB (12%), and when it fails it indicates that hail is present, in which case a relationship of the form [K.sub.DP] = a[R.sup.1.4] should be used. The technique should work at S, C, and X band, but, in all cases, paths should be chosen so that the total phase shift is not large enough to introduce significant attenuation of Z and [Z.sub.DR].

By definition, steady rain should have a nearly constant rainfall rate. Thus far, however, the criteria for determining when rain is steady remain qualitative and arbitrary. The authors suggest a definition for steadiness that can be used to quantify the elusive notion of natural variability. In particular, the logical criteria for steadiness imply statistical stationarity and lack of correlation between raindrops in neighboring volumes, requirements identical to those for the drops being distributed according to a Poisson process at all scales. Hence, steady rain is Poissonian. Explicit equations for the variance [[sigma].sup.2.sub.R] of the rainfall rates are developed. They show that, in general, raindrop clustering enhances the variance beyond that for Poissonian rain ([[sigma].sup.2.sub.P]). It is also demonstrated by using observations that this enhancement is augmented further when the rain is statistically nonstationary. Identifying steady rain is important. To be specific, because steady rain is statistically stationary, the drop size distributions have physical, deterministic meanings independent of the measurement process. Observables such as the radar reflectivity factor and the rainfall rate are then steady and linearly related also. Techniques for determining when rain is steady are discussed. The ratio [[sigma].sup.2.sub.R]/[[sigma].sup.2.sub.P] is proposed as a useful quantitative measure of the steadiness of the rain. It is also shown that an estimate of the minimum possible standard deviation for steady rain is [bar]R/[square root of k] where [bar]R and [bar]k are the mean rain rate and average number of drops per sample, respectively. Examples using video-disdrometer data are also presented.

Precipitation radar and microwave radiometer data collected by the Tropical Rainfall Measuring Mission (TRMM) satellite are used to study the variability of precipitation profiles and the relationship between precipitation profile and microwave brightness temperature. The variability has been examined using empirical orthogonal function (EOF) analysis and microwave emission and scattering signatures. Precipitation profiles are divided into three groups according to emission signatures at 19.4 GHz and three groups according to scattering signatures at 85.5 GHz. For stratiform rain, the differences of vertical precipitation profiles among these groups are small and are mainly seen in the slope of profiles below the freezing level. However, clear differences in vertical precipitation profiles can be found among the deep-convective rain groups. The maximum rainfall rate occurs at a considerably lower altitude when low liquid-emission or low ice-scattering signatures are observed. When emission or scattering signatures are high, precipitation profiles peak near the freezing level, a feature that is similar to the one in stratiform precipitation profiles. The three patterns of the vertical profiles derived from microwave signatures are very similar to the three patterns derived by EOF analysis. This similarity suggests that the three patterns derived by microwave signatures represent the most significant variability in vertical precipitation profiles. Results also show that, for the same near-surface rainfall rate, the pixel group with anomalously high microwave emission also shows anomalously high microwave scattering, and vice versa, suggesting that the liquid and ice water amounts in tropical rains are correlated over scales the size of a satellite pixel. It is also found that, for a given surface rainfall rate, the brightness-temperature differences among the pixel groups are large, highlighting the importance of vertical precipitation profile in determining upwelling microwave radiation and, therefore, the need to incorporate realistic precipitation profile information in rain retrieval algorithms.

In past work it is argued that rain consists of patches of coherent, physical drop size distributions passing in an unpredictable fashion for an unknown duration over a sensor. This leads to the detection both of correlations among drops and of clustering. While the analyses thus far support this characterization, in this final paper in this series, techniques are developed demonstrating that clustering of drops of a specific size in rain is occurring even on scales as small as a few centimeters. Moreover, using video disdrometer data processed to achieve high temporal resolution, it is shown that drops of different sizes are also cross correlated over times from 0.01 to several seconds. It is then shown that physical patches of drop size distributions (often exponential in form) exist and can be measured even over time periods as small as 2-3 s. Such distributions may be the result of enhanced drop interactions due to clustering or perhaps simply stochastic 'accidents' brought about by some 'clustering' mechanism. Since most drop spectra are measured over considerably longer intervals, however, observed distributions are likely probability mixtures of many short duration spectra. Such mixed distributions exhibit enhanced variance and curvatures reminiscent of gamma spectra often described in the literature. Thus, as measurement intervals increase, the form of the observed drop distributions apparently changes from an exponential-like distribution, to a mixture of distributions, finally returning once again to an exponential when the averaging is over very long intervals and a wide variety of conditions. It is also shown that for these data, much of the variability in rainfall rate arises due to concentration fluctuations rather than to changes in the average drop size. For completeness, it is also shown that the dimensionality of drop counts and rainfall rate are consistent with Euclidean scaling over distances from centimeters to kilometers. Finally, a specific example of drop clustering in wide sense statistically stationary rain is also given. These observations cannot be explained in terms of a nonhomogeneous Poisson process. Consequently, it appears most appropriate to characterize clustering and the structure of rain in terms of correlations and probability ruling discussed here and in previous papers in this series. This approach can be used to simulate rain numerically in order to explore not only the statistical properties of the rain itself, but also to achieve a better understanding of the effect of raindrop clustering and rainfall variability on a variety of topics, such as signal statistics and interpretations of remote sensing measurements.

Radar data collected by the 5-cm MIT radar, which was deployed aboard the R/V Vickers during the intensive observing period of the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment, are partitioned into convective and stratiform Cartesian grid columns. The vertical structure of convective echo is examined through the use of two variables: echo top height and the height of the 30-dBZ reflectivity contour. The first of these variables has traditionally been used to describe the vertical structure characteristics of convection, and the second has recently been linked to internal microphysical properties and lightning. Histograms of the relative frequency of convective-only echo top heights and 30-dBZ contour heights were constructed for the three cruises of the Vickers, with each cruise experiencing different phases of the intraseasonal oscillation (ISO). Cruise 1, which was dominated by the convectively 'inactive' phase of the ISO was characterized by the highest frequency of shallow convection (based on echo top heights), whereas cruise 2, which was dominated by a particularly well-defined passage of the convective phase of the ISO, exhibited the tallest echo top heights. Cruise 3 convection was influenced by moderate westerly surface winds characteristic of postwesterly wind burst conditions, and convection was of intermediate height. When viewed as a function of 'internal' vertical structure (i.e., 30-dBZ contour height), the frequency distributions vary less from cruise to cruise, with cruises 1 and 2 having nearly identical distributions of convective 30-dBZ contour heights. Furthermore, when the contribution to convective rainfall is examined as a function of 30-dBZ contour height, it is seen that relatively more rain fell from vertically 'intense' convection (i.e., convection with tall 30-dBZ contours) during cruises 1 and 3 than during cruise 2. Instantaneous correlations between rainfall rate and radar echo height were highly scattered about a mean value of about 0.55, whereas rainfall rate and 30-dBZ contour height correlations peaked at about 0.8 and exhibited much less scatter.

Radar rainfall measurements over the equatorial western Pacific warm pool were collected by two shipboard Doppler radars as part of the Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment during the intensive observing period (November 1992-February 1993). A comprehensive dataset of gridded rainfall fields, convective/stratiform identification maps, and vertical structure products has been produced, covering an area approximately 400 km (E-W) by 300 km (N-S) within the Intensive Flux Array (IFA), centered near 2 [degrees] S, 156 [degrees] E. The radar rainfall product, which was used as validation for the Third Algorithm Intercomparison Project of the Global Precipitation Climatology Project, indicates an overall average of 4.8 mm [day.sup.-1]; however, correction for range dependence increases the total to 5.4 mm [day.sup.-1]. Rainfall patterns varied considerably during the experiment with isolated convection dominating periods of light winds, while squall lines and organized mesoscale systems were abundant during two westerly wind bursts. An area-average rainfall of 9.9 mm [day.sup.-1] was observed during the active 2-week period at the end of December, while 0.4 mm [day.sup.-1] was observed during the quiescent week of 2-8 February. The eastern portion of the IFA received the most rainfall with localized maxima exceeding 16 mm [day.sup.-1] for the most active 3-week period. Comparison of daily radar rainfall totals with those observed by an optical rain gauge (ORG) on the 2 [degrees] S, 156 [degrees] E buoy shows ORG totals to be systematically higher, by a factor of 2.5. The discrepancy results from a higher average rainfall rate, when raining, as reported by the buoy ORG. However, rainfall rate statistics from the ORGs on the research vessel Xiang Yang Hong #5 and from its radar are in excellent agreement under the following conditions: 1) the ship is drifting, and 2) the radar data are in the near vicinity of the ship (3-7 km).

An analysis of temporal variations in gamma parameters of raindrop spectra is presented utilizing surface-based observations from the Tropical Ocean Global Atmosphere Couple Ocean-Atmosphere Experiment. An observed dramatic change in the [N.sub.0] parameter, found to occur during rainfall events with little change in rainfall rate, is suggestive of a transition from rain of convective origin to rain originating from the stratiform portion of tropical systems. An empirical stratiform - convective classification method based on [N.sub.0] and R (rainfall rate) is presented. Properties of the drop size spectra from the stratiform classification are consistent with micro-physical processes occurring within an aggregation/melting layer aloft, which produces more large raindrops and fewer small to medium size raindrops than rain from the convective classification, at the same rainfall rate. The occurrence of precipitation was found to be 74% (stratiform) and 26% (convective), but total rainfall, on the other hand, was 32% and 68%, respectively. Case studies of the tropical systems studied here indicate that heavy convective showers are generally followed by longer intervals of lighter rain from the stratiform portion of the cloud systems. Differences in the shapes of the frequency distributions of the integral rainfall parameters (i.e., liquid water content, rainfall rate, and radar reflectivity) suggest that the lognormal distribution applies to some, but not all cases. The analysis shows that almost all the precipitation with a radar reflectivity above 40 dBZ falls within the convective classification. Regarding radar reflectivity versus rainfall rate relationships, the exponent is lower and the intercept is higher in the tropical stratiform classification than in the tropical convective classification. Collision and evaporation rates, which are important for cloud-modeling studies, indicate substantial variation at different rainfall rates and between the two types.

Attenuation measurements on an earth space path are presented using a passive microwave radiometer operating at 19.4 GHz in the emission mode. Attenuation measured under clear weather showed variation between 0.2 to 1.1 dB, whereas for cloud conditions attenuation as high as 1.0 dB have been recorded. Attenuation measurements for rain events have been correlated with rainfall rate using a fast-response 10 seconds opto-electronic rain gauge. The values of attenuation versus rainfall rate varied between A (dB)= 0.01 + 0.18 R(mm/h) at the minimum and A (dB) = 0.01 + 0.25 R(mm/h) at the maximum, showing considerable variability in the values of attenuation from year to year. The attenuation statistics for different seasons have also been computed and they show considerable changes from season to season - the largest attenuation in excess of 10 dB recorded in July-August-September, whereas minimum attenuation in excess of 2 dB recorded in December-March for nearly two years of data. Comparison of measurements made over New Delhi with those reported elsewhere show that for 0.02% of time attenuation values lie between those of Slough, England, and Crawford Hill, NJ. The concept of effective path length has been discussed based on the relationship between effective path length and the rain rate.

Natural rainfall rate patterns are highly variable. Existing Hortonian infiltration models are not designed specifically to work with such rainfall rate patterns. Thus, for practical applications the models have to be modified to work with the naturally occurring variable-pattern hyetographs. In this paper, a Hortonian infiltration model, developed specifically to work with the variable rainfall-rate patterns and constant time intervals of naturally occurring hyetographs, is described. The structure of the model is hypothesized based on a physical appreciation of the Hortonian infiltration process. It is then refined through repeated testing to simulate the overland flow data associated with the process. A numerical infiltration model has been used to simulate the overland-flow data used in the testing. A three-parameter conceptual model was able to reasonably simulate the numerically simulated overland-flow data due to 10 observed hyetographs falling on three different topsoils. The most important parameter in the model is the saturated hydraulic conductivity (KS) of a topsoil.

Area-average rainfall rate can be calculated accurately for frontal rainfall systems by computing the rate from a fractional area of rainfall rate using a threshold value of 2 mm, without taking bright band data into consideration. This avoids the misleading effects of radar bright band data in weather predictions. Case studies are presented for demonstrating the efficacy of this method and an alternate objective method for rainfall rate computations in areas contaminated by bright band.

Absolute calibration of a weather radar is critical for quantitative estimation of rainfall. This is a very difficult measurement especially for beam-filled targets like precipitation. In this paper we discuss a method that uses the properties of rain medium itself to obtain accurate system gain calibration. This technique is based on the principle that the rainfall rate measured using absolute reflectivity (Z) and differential reflectivity (ZDR) is the same as that obtained from specific differential phase (KDP). The measurements required for this technique are Z, ZDR, and KDP. We compare the rainfall rate estimates RDR obtained from Z and ZDR with the estimates RDP obtained from KDP. The scatter plot between the two rainfall estimates should lie close to a 1:1 line and any systematic deviation from this line can then be removed by appropriately adjusting the system gain. It is noted here that ZDR can be calibrated accurately because it is a differential power measurement and KDP is obtained from differential phase measurement which is unaffected by system calibration. The sensitivity and accuracy of this technique are studied in this paper. We present theoretical and simulation results evaluating the accuracy of this technique for C-band frequencies. Our analysis indicates that by sampling over few data sets of rain, the calibration can be done to an accuracy of 0.6 dB.

Data from the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) and Kwajalein S-band validation radar (KR) agree well for reflectivity exceeding the sensitivity of the PR threshold (~17 dBZ). For echoes above this intensity threshold, the products derived from reflectivity, particularly maps of rainfall rate and convective/stratiform classification, compare well, even though slightly different convective-stratiform separation techniques and different reflectivity-rainfall rate (Z-R) relations are used for the PR and KR. The KR observations indicate the PR misses only 2.3% of near-surface rainfall but 46% of near-surface rain area ([is greater than or equal to] 0 dBZ) because of its 17-dBZ threshold. The PR senses less than 15% of the echo area observed by the KR above 5-km altitude (i.e., above the 0 [degrees] C level). Thus, the PR highly undersamples weaker echoes associated with stratiform rain near the surface and ice particles aloft but still manages to capture most of the near-surface precipitation accumulation. The temporal sampling of the TRMM PR accurately captures the KR's overall frequency distribution of reflectivity and its subdivision into convective and stratiform components. However, diurnal and latitudinal variations of precipitation in the vicinity of Kwajalein are not well sampled.

Rainfall estimation using specific differential phase ([K.sub.DP]) involves estimation of [K.sub.Dp] over a propagation path. The choice of pathlength plays an important role in the performance of rainfall algorithms using [K.sub.DP]. The pathintegrated nature of [K.sub.DP]-based rainfall estimates may involve inhomogeneous paths, thereby having potential implications on the pathlengths used in algorithms for rainfall estimation and measurement errors. The effect of inhomogeneous rainfall paths (over which [K.sub.DP] is estimated) on the choice of rainfall rate algorithms is studied as a function of rain pathlength. Rainfall estimation is biased when algorithms relating rainfall rate and [K.sub.DP] are used over nonuniform paths. This bias is evaluated and compared for different rainfall algorithms. Radar and rain gauge data collected during the Convection and Precipitation/Electrification Experiment (CaPE) are used to evaluate the performance of [K.sub.DP]-based rainfall algorithms, for different pathlengths.

Recent studies have led to the statistical characterization of the flux of drops of a particular size as a doubly stochastic Poisson process (Poisson mixture). Moreover, previous papers in this series show that the fluxes at different sizes are correlated among each other both temporally and spatially over many different scales. Thus, in general, rather than being distributed evenly, significant clustering or bunching of the rain occurs. That is, regions richer in drops are interspersed with those where drops are scarcer. This work applies these recent findings to explore the statistical characteristics of the rainfall rate itself, a triply stochastic random variable resulting from the summation over all the fluxes at different drop sizes. Among the findings, it is shown that clustering of the drops leads to increased frequencies of both smaller and larger rainfall rates. That is, because of clustering, drop rich regions boost the frequency of large rainfall rates, while the likelihood of light rainfall rates increases because of drop poor regions. These results, derived using detailed, physically based Monte Carlo simulations of clustered rain, agree with video-disdrometer observations. Moreover, it is shown that for a given mean rainfall rate, extensive averaging lengthens the tail of the probability density function (pdf) of the rainfall rate, P(R). While the tail of the P(R) for clustered rain is sometimes reminiscent of that of the oft-used lognormal distribution, it is shown that the lognormal pdf is a poor match to the observations and simulations. It is concluded that the lognormal distribution is inconsistent with the statistical physics of natural, clustered rain. It is also argued that for clustered rain, the relative dispersion of the rainfall rate is proportional to the relative dispersion in the total number of drops in the volumes sampled. While the constant of proportionality depends upon drop diameter, observations demonstrate that the relative dispersion in the rainfall rate is due much more to the variability in the number of drops in the sampled volumes than to variations in drop sizes. The results in this work are likely relevant to such areas of research as remote sensing and hydrology.

The differential phase ([[PHI].sub.DP]) measured by polarimetric radars is recognized to be a very good indicator of the path integrated by rain. Moreover, if a linear relationship is assumed between the specific differential phase ([K.sub.DP]) and the specific attenuation ([A.sub.H]) and specific differential attenuation ([A.sub.DP]), then attenuation can easily be corrected. The coefficients of proportionality, [[gamma].sub.H] and [[gamma].sub.DP], are, however, known to be dependent in rain upon drop temperature, drop shapes, drop size distribution, and the presence of large drops causing Mie scattering. In this paper, the authors extensively apply a physically based method, often referred to as the 'Smyth and Illingworth constraint,' which uses the constraint that the value of the differential reflectivity [Z.sub.DR] on the far side of the storm should be low to retrieve the [[gamma].sub.DP] coefficient. More than 30 convective episodes observed by the French operational C-band polarimetric Trappes radar during two summers (2005 and 2006) are used to document the variability of [[gamma].sub.DP] with respect to the intrinsic three-dimensional characteristics of the attenuating cells. The Smyth and Illingworth constraint could be applied to only 20% of all attenuated rays of the 2-yr dataset so it cannot be considered the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of [[gamma].sub.DP] is shown to be extremely large, with minimal, maximal, and mean values being, respectively, equal to 0.01, 0.11, and 0.025 [dB[degrees].sup.-1]. Coefficient [[gamma].sub.DP] appears to be almost linearly correlated with the horizontal reflectivity ([Z.sub.H]), differential reflectivity ([Z.sub.DR]), and specific differential phase ([K.sub.DP]) and correlation coefficient ([[rho].sub.HV]) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of [[gamma].sub.DP], above 0.06 [dB[degrees].sup.-1], often referred to as 'hot spots,' are reported for 15%--a nonnegligible figure--of the rays presenting a significant total differential phase shift ([DELTA][phi].sub.DP] > 30[degrees]). The corresponding strongly attenuating cells are shown to have extremely high [Z.sub.DR] (above 4 dB) and [Z.sub.H] (above 55 dBZ), very low [[rho].sub.HV] (below 0.94), and high [K.sub.DP] (above 4[degrees] [km.sup.-1]). Analysis of 4 yr of observed raindrop spectra does not reproduce such low values of [[rho].sub.HV], suggesting that (wet) ice is likely to be present in the precipitation medium and responsible for the attenuation and high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that [K.sub.DP] may not be uniquely related to rainfall rate but can result from the presence of wet ice. This hypothesis is supported by the analysis of the vertical profiles of horizontal reflectivity and the values of conventional probability of hail indexes. DOI: 10.1175/2009JAMC2039.1

A procedure for the estimation of rainfall rate, capitalizing on a radar-based raindrop size distribution (RSD) parameter retrieval and neural network (NN) inversion techniques, is validated using an extensive and quality-controlled archive. The RSD retrieval algorithm utilizes polarimetric variables measured by the polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) in Norman, Oklahoma (KOUN), through an ad hoc regularized neural network method. Evaluation of rainfall estimation from the NN-based method is accomplished using a large radar data and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign. Point estimates of hourly rainfall accumulations and instantaneous rainfall rates from NN-based and parametric polarimetric rainfall relations are compared with dense surface gauge observations. Rainfall accumulations from RSD retrieval-based methods are shown to be sensitive to the choice of a raindrop fall speed model. To minimize the impact of this choice, a new 'direct' neural network approach is tested. Proposed NN-based approaches exhibit bias and root-mean-square error characteristics comparable with those obtained from parametric relations, specifically optimized for the JPOLE dataset, indicating an appealing generalization capability with respect to the climatological context. All tested polarimetric relations are shown to be sensitive to hail contamination as inferred from the results of automatic polarimetric echo classification and available storm reports. DOI: 10.1175/2009JAMC2172.1

A method to retrieve total vertical amounts of cloud liquid and ice in stratiform precipitating systems is described. The retrievals use measurements from the vertically pointing [K.sub.a]- and W-band cloud radars operated by the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) Program and auxiliary measurements from a scanning National Weather Service radar and a ground-based disdrometer. Separation between the cloud liquid and rain is based on estimations of the total attenuation of millimeterwavelength radar signals in the liquid hydrometeor layer. Disdrometer measurements are used for the retrieval constraints. Because the liquid phase hydrometeor retrievals use only differential measurements, they are immune to the absolute radar calibration uncertainties. Estimates of the ice cloud phase are performed using empirical relations between absolute radar reflectivity and ice water content. Data from the nearby scanning weather-service radar, which operates at a lower frequency, are used to correct cloud radar measurements observed above the freezing level for attenuation caused by the layers of liquid and melting hydrometeors and also by wet radomes of cloud radars. Polarimetric and vertical Doppler measurements from ARM cloud radars provide a distinct separation between regions of liquid and ice phases, and therefore the corresponding retrievals are performed in each region separately. The applicability of the suggested method is illustrated for a stratiform precipitation event observed at the ARM Southern Great Plains facility. Expected uncertainties for retrievals of cloud liquid water path are estimated at about :200-250 g [m.sup.-2] for typical rainfall rates observed in stratiform systems (~3-4 mm [h.sup.-1]). These uncertainties increase as rainfall rate increases. The ice water path retrieval uncertainties can be as high as a factor of 2.

Numerical simulations of conditionally unstable flows impinging on a mesoscale mountain ridge have been performed with an explicitly resolving cloud model to investigate the statistically stationary features of the solution precipitation characteristics. The simulations are performed on a three-dimensional domain and at high resolution (grid spacing: 250 m) to properly resolve cellular-scale features. Although the environmental conditions are specified by a simplified idealized conditionally unstable sounding, there are still quite a few external parameters, so only a limited portion of the parameter space was explored. Numerical solutions were first carried out for different uniform-wind profiles impinging on a bell-shaped ridge 2000 m high. In the experiments with weaker environmental wind speeds (2.5 m [s.sup.-1]), the cold-air outflow, caused by the evaporative cooling of rain from precipitating convective cells, is the main mechanism for cell redevelopment and movement; this outflow produces new convective cells near the head of the up- and downstream density currents, which rapidly propagate far from the ridge so that no rainfall is produced close to the ridge at later times. For larger wind speeds (10 and 20 m [s.sup.-1]), there is less time for upwind, evaporation-induced cold-pool formation before air parcels reach the ridge top and descend downwind. For the intermediate wind speed (10 m [s.sup.-1]), evaporation is effective in generating a cold pool only on the downstream side of the ridge, in a region where the air is unsaturated and slow moving. Further experiments with different ridge heights and half-widths were carried out in order to analyze their effect on the distribution and intensity of precipitation. Dimensional analysis reveals that the maximum (nondimensional) rainfall rate mainly depends on the ratio of mountain height to the level of free convection, the ridge aspect ratio, and a parameter that measures the ratio of advective to convective time scales.