Predictive methods for rain attenuation using radar and in-situ measurements tested against the 28-GHz Comstar beacon signal

A program to measure the rain attenuation of the Comstar beacon signal at 28.56 GHz has been in continuous operation since March of 1977 at Wallops Island, VA. During the summer of 1977 simultaneous radar and disdrometer measurements at the site were also made and used for predicting path attenuation. The best-fit values ofaandbof the relationk = aZ^{b}were deduced for each rain period from the raindrop size measurements, wherekis the attenuation coefficient [dB/km] andZis the reflectivity factor [mm⁶/m³]. The measuredk-Zrelations and the simultaneous radar reflectivity measurements along the beacon path were injected into a computer program for estimating the path attenuation. Predicted attenuations, when compared with the directly measured ones, show generally good correlation on a case-by-case basis and very good agreement statistically after an empirical calibration adjustment is applied to the radar data. A method was also tested for predicting fade statistics at another frequency (e.g., 19 GHz) using simultaneous rain rate and fade distributions (28 GHz) in conjunction with disdrometer data. The predicted distributions showed good agreement with radar-predicted levels. The results demonstrate the utility of using radar in conjunction with disdrometer and rain gauge measurements for predicting fade events, long-term fade distributions, and establishing predictive criteria associated with earth-satellite telecommunications.     

Rain-induced attenuation effects on C-banddual-polarization meteorological radars

An attenuation correction procedure is proposed and evaluated by simulations using raindrop size distribution obtained from ground-based disdrometer measurements. The results show that under certain conditions it is possible to retrieve C-band reflectivity factor (Z _H) and differential reflectivity (Z_DR) radar observables affected by attenuation along rain-filled propagation paths. Rainfall rates estimated from Z _H and Z_DR with and without attenuation correction are compared to determine the effects of attenuation and the capability of the correction procedure to account for it     

Retrieval of Snow and Rain From Combined X- and W-Band Airborne Radar Measurements

Two independent airborne dual-wavelength techniques, based on nadir measurements of radar reflectivity factors and Doppler velocities, respectively, are investigated with respect to their capability of estimating microphysical properties of hydrometeors. The data used to investigate the methods are taken from the ER-2 Doppler radar (X-band) and cloud radar system (W-band) airborne Doppler radars during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment campaign in 2002. Validity is assessed by the degree to which the methods produce consistent retrievals of the microphysics. For deriving snow parameters, the reflectivity-based technique has a clear advantage over the Doppler-velocity-based approach because of the large dynamic range in the dual- frequency ratio (DFR) with respect to the median diameter D₀ and the fact that the difference in mean Doppler velocity at the two frequencies, i.e., the differential Doppler velocity (DDV), in snow is small relative to the measurement errors and is often not uniquely related to D₀. The DFR and DDV can also be used to independently derive D₀ in rain. At W-band, the DFR-based algorithms are highly sensitive to attenuation from rain, cloud water, and water vapor. Thus, the retrieval algorithms depend on various assumptions regarding these components, whereas the DDV-based approach is unaffected by attenuation. In view of the difficulties and ambiguities associated with the attenuation correction at W-band, the DDV approach in rain is more straightforward and potentially more accurate than the DFR method.     

A method for estimating rain rate and drop size distribution frompolarimetric radar measurements

Polarimetric radar measurements are sensitive to the size, shape and orientation of raindrops and provide information about drop size distribution (DSD), canting angle distribution and rain rate. The authors propose and demonstrate a method for retrieving DSD parameters for calculating rain rate and the characteristic particle size. The DSD is assumed to be a gamma distribution and the governing parameters are retrieved from radar measurements: reflectivity (Z_HH), differential reflectivity (ZDR), and a constrained relation between the shape (CL) and slope (Λ) parameters derived from video disdrometer observations. The estimated rain rate is compared with that obtained from more traditional methods and the calculated characteristic size is compared with the measured values. The calculated K_DP based on the retrieved Gamma DSD is also compared with measurements. The proposed method shows improvement over the existing models and techniques because it can retrieve all three parameters of the gamma distribution. For maintaining the continuity of earlier published results, raindrop shape is assumed to be equilibrium     

A dual-polarization rain profiling algorithm

A new attenuation correction algorithm based on profiles of reflectivity, differential reflectivity, and differential propagation phase shift is presented. A solution for specific attenuation retrieval in rain medium is proposed, which solves the integral equations for reflectivity and differential reflectivity with cumulative differential propagation phase shift constraint. The conventional rain profiling algorithms that connect reflectivity and specific attenuation can retrieve specific attenuation values along the radar path assuming a constant intercept parameter of the normalized drop size distribution. However, in convective storms, the drop size distribution parameters can have significant variation along the path. This paper presents a dual-polarization rain profiling algorithm for horizontal looking radars incorporating reflectivity as well as differential reflectivity profiles. The dual-polarization rain profiling algorithm has been evaluated with X-band radar observations simulated from drop size distribution derived from high-resolution S-band measurements collected by the Colorado Statue University CHILL radar. The analysis shows that the retrieved specific attenuation, differential attenuation, reflectivity, and differential reflectivity from the dual-polarization rain profiling algorithm provide significant improvement over the current algorithms.     

Rain Cell Size Statistics Derived from Radar Observations at Wallops Island, Virginia

Results of an investigation are given describing two-di-two-dimensional rain cell size statistics employing radar and disdrometer data bases spanning more than 5 years and all seasons. Radar data were obtained employing the SPANDAR radar located at the NASA Wallops Flight Facility, Wallops Island, Virginia. These data corresponded to approximately 100 low-elevation azimuthal antenna scans encompassing 17 rain days. For each of these rain days, disdrometer data were also obtained. Analysis of the regression relations relating the rain rates to the disdrometer data enabled the determination of least square fit radar reflectivity factors. The individual disdrometer results along with the radar data were employed with a contouring program. More than 22 000 contours were generated, where each isopleth belonged to predefined rain rate intervals. Computing the areas of each of these contours, statistics were generated relating the equi-circle contour diameters and rain rate categories. Two types of contour have been analyzed. One pertained to the above-described isopleth regardless of the rain rate levels interior to it. Another type corresponded to those isopleths in which the rain rates interior to it were equal or greater than the isopleth values. These isopleths were referred to as "total" and "cell" contours, respectively. An abundance of total and cell contours were observed belonging to all rain rate categories. In particular, a dominant number of smallarea contours were observed belonging to the lower rain rate levels. The results showed that the average and median "equi-circle" cell contour diameters were 2.4 and 1.9 km, respectively.     

Radar and atmospheric electricity measurements associated with microwave attenuation and cross-polarization observed on a slant path

The present paper describes experiments performed near Paris using a C-band radar aimed at estimating rain attenuation and cross-polarization discrimination of the various ots signals received at Gometz-La-Ville. An empirical relationship between the measured reflectivity factor and attenuation is derived, allowing an experimental prediction. Correlation between radar reflectivity and cross-polarization is also investigated for a convective precipitation cell. In addition, electrostatic field measurements show a relation between fade depth and electric field intensity.     

Derivation of parameters of Y-Z power-law relation from raindrop size distribution measurements and its application in the calculation of rain attenuation from radar reflectivity factor measurements

The work reported herein empirically derived the coefficients of the power-law relation between the specific attenuation Y and each of two other quantities: the radar reflectivity factor Z and the rainfall rate R. The derivation was accomplished using raindrop size distributions (DSDs) measured in Montreal and Toronto using the precipitation occurrence sensor system (POSS) and a Joss-Waldvogel disdrometer (JWD). The specific attenuation was calculated for both spherical and oblate spheroidal raindrops. Prior to doing so, the effects of inaccuracies in small drop detection by the two systems on the resulting Y-Z and Y-R relations were examined. In computing the relations, the influence of grouping the DSDs according to the corresponding values of Z was assessed. The results from the two sites were then combined in a regression analysis to determine the coefficients of the power-law expressions. The final expressions were used to calculate the probability distribution of rain attenuation over several path lengths at 30 GHz. Conclusions that can be drawn from this work include that (i) the uncertainties in the measurements of small drops do not appear to be critical to the derived relations for some frequencies considered in this work, (ii) in computing rain attenuation estimates from radar reflectivity factors, different criteria for grouping the reflectivity factor measurements can be adopted without changing the statistics of the corresponding attenuation estimates, (iii) differences, which are the smallest for frequencies around 20-30 GHz, are observed in the coefficients derived from the measured DSDs compared with those recommended by the ITU-R, and (iv) the attenuation statistics at 30 GHz computed by applying the Y-Z power-law expression are resistant to spatial averaging.     

Ku- and C-band SAR for discriminating agricultural crop and soilconditions

A method is proposed to estimate both green leaf area index (GLAI) and soil moisture (h_v), based on radar measurements at the Ku-band (14.85 GHz) and C-band (5.35 GHz) frequencies. The Ku-band backscatter at large incidence angles was found to be independent of soil moisture conditions and could be used alone to estimate GLAI. Then, the Ku-band estimate of GLAI could be used with a measurement of C-band backscatter in a canopy radiative transfer model to isolate the value of h_v. This concept was demonstrated with a set of Kuand C-band synthetic aperture radar (SAR) backscatter data acquired over agricultural fields in Arizona. The demonstration showed promise for operational application of the method, though several limitations were identified. Since both Ku- and C-band σ_° are sensitive to soil roughness, this approach must be applied only to fields of similar soil roughness or row direction. This limitation may be less serious for farm management applications since crop type and cultivation practices are generally well known and can be taken into consideration. Another limitation of the use of Ku- and C-band σ° is the apparent saturation of the Ku-band signal with increasing GLAI. Operational implementation of this approach will require dual-frequency sensors aboard an aircraft or orbiting satellite     

Attenuation of propagation through rain for an earth--Satellite path correlated with predicted values using radar

During the summer of 1974 and spring of 1975, measurements of attenuation of propagation through rain were made at Wallops Island, VA, using 13 and 18 GHz transmitters operating in the uplink mode toward the ATS-6 satellite. Simultaneously, rain reflectivity levels were measured along the earth-satellite path using a high resolution (0.4degbeamwidth)S-band radar having a scanning antenna. Four raingages and two disdrometers were also located in the vicinity of the transmitters. The radar and disdrometer data were used in a modeling program to predict attentuation levels which were subsequently compared to the directly measured fades over nearly simultaneous time intervals. Predicted attentuation levels were obtained for three drop size distributions; namely, those of Joss et al. for thunderstorm activity, Marshall-Palmer, and the average distribution measured in the vicinity of the transmitter (APL distribution). Comparisons between predicted and measured attenuation levels showed the APL dropsize distribution gave the smallest rms difference of 1.3 dB at 13 and 18 GHz although the rms difference corresponding to Marshall-Palmer was close to this value. Although the sample sizes were relatively small, the good agreement suggests the validity of using radar to model path attenuation to obtain attenuation statistics.     

Prediction of slant path rain propagation statistics usingdual-polarized radar

The authors conducted a year-long experiment in which a dual-polarized S-band radar probed the volume surrounding two 11.45-GHz satellite downlink paths during rain. Accuracy was assessed by comparison to directly measured link attenuation with two 11-GHz beacon receivers 7.3-km apart at an 18.5° elevation angle, one colocated with the radar. Drop size distributions calculated from the radar horizontal reflectivity (Z_H) and differential reflectivity (ZDR) measurements were used to predict 11.45-GHz satellite beacon attenuations. The radar-predicted attenuations and those measured on the radio links agree, both on an event basis and in terms of annual cumulative distributions     

Rainfall parameters from disdrometer dropsize measurements at a tropical station

The rain dropsize distributions measured by a disdrometer in 21 rain events consisting of 1, 640one-minute dropsize spectra have been analyzed for a tropical station, Ile-Ife (geog. lat. 7.5°N, long 4.5°E) in South-Western Nigeria. Empirical power law relations of the form Y = aR^b have been obtained between the rainfall rate R, the radar reflectivity factor Z, liquid water content M, optical extinction σ and the median volume diameter D₀ for three types of rainfall. A power law relationship was also obtained between the median volume diameter D₀ and the liquid water content M. The variability in a and b with rain parameters, rain events and rain types is discussed. The empirical relations have been compared with existing relations for other parts of the world, for their utilization in radar meteorology and radar engineering.     

Melting layer attenuation at 28.6 GHz from simultaneous comstar beacon and polarisation diversity radar data

Attenuation data at 28.6 GHz obtained from measurements of the Comstar beacon show that, for moderate rain, slant path attenuation may significantly exceed that calculated from simultaneous radar reflectivity measurements. Polarisation diversity radar data were used for positive identification of the rain and the melting layer, and for estimating the rain attenuation along the path. These results indicate that the melting layer attenuation is significant.     

New radar studies of slant-path attenuation due to rain

Approximately 40 h of data from the summer of 1976 were employed in a comparison of radar and radiometer estimates of slant-path attenuation due to rain. McGill Radar Weather Observatory is situated 20 km west of Montreal; the radiometers, separated by 18 km at two sites located about 90 km northwest of the radar, had fixed antennas pointed approximately southeast at an elevation of 18.5 deg. Values of radar reflectivity along the two radiometer paths were used to calculate the slant-path attenuation at 13 GHz as a function of time with a 1 min resolution for direct comparison with the radiometer measurements. It was found that the cumulative distribution of attenuation inferred by radar from each site could be made to agree satisfactorily with the radiometer distribution assuming that rain was present everywhere along the path with a Marshall-Palmer distribution and applying a 1 dB correction to the independently-determined radar calibration. This agreement, close to within a fraction of a decibel, gives confidence to the use of radar records in compiling attenuation statistics. An example is presented of a new application of such records, namely the assessment of rain-induced interference over adjacent earth-space paths.     

Classification of particles in stratiform clouds using the 33 and95 GHz polarimetric cloud profiling radar system (CPRS)

This paper describes the identification of regions of ice, cloud droplets, rain, mixed-phase hydrometers, and insects in stratiform clouds using 33 and 95 GHz radar measurements of reflectivity, linear-depolarization ratio (LDR), dual-wavelength ratio, and velocity from a single-antenna radar system. First, the radar system, experiment, and data products are described. Then, regions are classified using a rule-based classifier derived primarily from LDR, velocity, and altitude. Next, a region-dependent attenuation-correction algorithm is developed to remove attenuation biases in the reflectivity estimate, and histograms of the corrected data are presented for each data product and class. The labeled regions and attenuation-corrected data are then used to train a neural net and maximum likelihood classifier. These agree with the rule-based classifier 96% and 94% of the time, respectively. Finally, the paper evaluates the importance of measuring dual-frequency parameters, velocity, and depolarization ratio     

Calibration of radars using polarimetric techniques

A method that uses the properties of rain medium itself to obtain accurate weather radar system gain calibration is discussed. This technique is based on the principle that the rainfall rate measured using absolute reflectivity (Z) and differential reflectivity ( Z_DR) is the same as that obtained from specific differential phase (K_DP). The measurements required for this technique are Z, Z_DR, and K _DP. The rainfall rate estimates obtained from Z and Z_DR are compared with the estimates obtained from K_DP. The scatter plot between the two rainfall estimates should lie close to a 1:1 line, and any systematic deviation from this line can be removed by appropriately adjusting the system gain. It is noted that Z_DR can be calibrated accurately because it is a differential power measurement, and K_DP is obtained from differential phase measurement, which is unaffected by system calibration. The sensitivity and accuracy of this technique are studied, and theoretical and simulation results for C-band frequencies are presented     

Statistical rainstorm models: Their theoretical and physical foundations

Precipitation has become a serious source of attenuation as higher frequencies are being employed for microwave communications. System performance is strongly influenced by the quantity and character of precipitation that occurs over the links of the system. Rain appears to be the precipitation form that accounts for most of the serious attenuation occurrences. It is also for rain that the Scattering theory is most complete. Rain attenuation can be accurately predicted if the drop-size distribution along the propagation path is known. The drop spectrum determines as well the rainfall rate, radar reflectivity, and microwave emission of rain. Consequently, it is possible to make estimates of rain attenuation through indirect measurements by raingauge, radar, and radiometer. Recent experiments have confirmed that these estimates are sufficiently accurate for practical purposes. From propagation experiments and studies of the fine-scale structure of rain, data are becoming available on the horizontal extent of heavy rain areas and the way this structure influences system performance. These data have been used to formulate statistical raincell models that permit prediction of the performance of single-path and path-diversity systems. The current status of raincell models is reviewed and suggestions for future research are offered.     

QuikSCAT geophysical model function for tropical cyclones andapplication to Hurricane Floyd

The QuikSCAT radar measurements of several tropical cyclones in 1999 have been studied to develop the geophysical model function (GMF) of Ku-band radar σ₀ values (normalized radar cross section) for extreme high wind conditions. To account for the effects of precipitation, the authors analyze the co-located rain rates from the Special Sensor Microwave/Imager (SSM/I) and propose the rain rate as a parameter of the GMF. The analysis indicates the deficiency of the NSCAT2 GMF developed for the NASA scatterometer, which overestimates the ocean σ₀ for tropical cyclones and ignores the influence of rain. It is suggested that the QuikSCAT σ₀ is sensitive to the wind speed of up to about 40-50 m s^-1. The authors introduce modifications to the NSCAT2 GMF and apply the modified GMF to the QuikSCAT observations of Hurricane Floyd. The QuikSCAT wind estimates for Hurricane Floyd in 1999 was improved with the maximum wind speed reaching above 60 m s^-1. The authors perform an error analysis by comparing the QuikSCAT winds with the analyses fields from the National Oceanic and Atmospheric Administration (NOAA) Hurricane Research Division (HRD). The reasonable agreement between the improved QuikSCAT winds and the HRD analyses supports the applications of scatterometer wind retrievals for hurricanes     

Cross-polarized radar reflections from wet snow and ice droplets atweather radar wavelengths

The copolar radar reflection cross sections Q_HH and Q_VV from a collection of spheroid scatterers in the melting layer formed by ice precipitation prior to becoming rain have been analyzed by the authors in a recent work (IEEE Trans. Antennas and Propagation, vol.38, p.1317-25, Sept. 1990). The model is extended to calculate the cross-polarized cross section Q_VH due to reception at an electric-field polarization orthogonal to that of transmission. The authors are specifically interested in the cross-polarized differential reflectivity L_dr=10 log₁₀(Q_VH/Q_HH)