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In this paper, we use the co-located brightness temperature measurements collected by three different radiometers to estimate the radar reflectivities for the particular flight leg.
In writing the integral equations for the median mass diameter and number concentration, or comparable parameters of the raindrop size distribution, it is apparent that the forms of the equations for dual-polarization and dual-wavelength radar data are identical when attenuation effects are included. The differential backscattering and extinction coefficients appear in both sets of equations: for the dual-polarization equations, the differences are taken with respect to polarization at a fixed frequency while for the dual-wavelength equations, the differences are taken with respect to frequency at a fixed polarization. An alternative to the integral equation formulation is that based on the k-Z (attenuation coefficient-radar reflectivity factor) parameterization. This-technique was originally developed for attenuating single-wavelength radars, a variation of which has been applied to the TRMM Precipitation Radar data (PR). Extensions of this method have also been applied to dual-polarization data. In fact, it is not difficult to show that nearly identical equations are applicable as well to dualwavelength radar data. In this case, the equations for median mass diameter and number concentration take the form of coupled, but non-integral equations. Differences between this and the integral equation formulation are a consequence of the different ways in which attenuation correction is performed under the two formulations. For both techniques, the equations can be solved either forward from the radar outward or backward from the final range gate toward the radar. Although the forward-going solutions tend to be unstable as the attenuation out to the range of interest becomes large in some sense, an independent estimate of path attenuation is not required. This is analogous to the case of an attenuating single-wavelength radar where the forward solution to the Hitschfeld-Bordan equation becomes unstable as the attenuation increases. To circumvent this problem, the equations can be expressed in the form of a final-value problem so that the recursion begins at the far range gate and proceeds inward towards the radar. Solving the problem in this way traditionally requires estimates of path attenuation to the final gate: in the case of orthogonal linear polarizations, the attenuations at horizontal and vertical polarizations (same frequency) are required while in the dual-wavelength case, attenuations at the two frequencies (same polarization) are required.
Multi-sensor measurements of total lightning (in-cloud plus cloud-to-ground) from the Lightning Imaging Sensor (LIS) aboard the TRMM satellite has been combined with passive microwave ice scattering and precipitation radar reflectivity profile information previously cataloged for precipitation features observed by TRMM. These precipitation features are defined by their surface rainfall or ice scattering signatures, with horizontal scales approx. 100 - 10000 sq km. Additionally, convective scale (approx. 100 sq km) storms are defined by the lightning data. Over the U.S. the national cloud-to-ground lightning observations are used to also determine the ratio of in-cloud to cloud-to-ground lightning, where it is hypothesized these ratios are related to the vertical profile of reflectivity and concentration of precipitation-sized ice. Combining the LIS, TRMM Microwave Imager (TMI), and Precipitation Radar (PR) for these storms allows investigation of the convective structures and convective regimes leading to observed lightning, scattering, and reflectivity signatures. Application of this approach to a global, multi-year data set (1998-2000) furthers our understanding of convective processes in different climatological regimes. The figure shows the distribution of high flash rate storms.
Assimilating high-resolution radar reflectivity and radial velocity into convection-permitting numerical weather prediction models has proven to be an important tool for improving forecast skill of convection. The use of satellite data for the application is much less well understood, only recently receiving significant attention. Since both radar and satellite data provide independent information, combing these two sources of data in a robust manner potentially represents the future of high-resolution data assimilation. This research combines Geostationary Operational Environmental Satellite 13 (GOES-13) cloud water path (CWP) retrievals with Weather Surveillance Radar-1988 Doppler (WSR-88D) reflectivity and radial velocity to examine the impacts of assimilating each for a severe weather event occurring in Oklahoma on 24 May 2011. Data are assimilated into a 3-km model using an ensemble adjustment Kalman filter approach with 36 members over a 2-h assimilation window between 1800 and 2000 UTC. Forecasts are then generated for 90 min at 5-min intervals starting at 1930 and 2000 UTC. Results show that both satellite and radar data are able to initiate convection, but that assimilating both spins up a storm much faster. Assimilating CWP also performs well at suppressing spurious precipitation and cloud cover in the model as well as capturing the anvil characteristics of developed storms. Radar data are most effective at resolving the 3D characteristics of the core convection. Assimilating both satellite and radar data generally resulted in the best model analysis and most skillful forecast for this event.
Doppler lidar and multiple Doppler radar data were obtained in a convectively mixed planetary boundary layer. The lidar measurements were possible due to scattering from existing aerosols; radar reflecting chaff was released in the atmosphere to make it visible to the multiple Doppler radar network. The data were analyzed to obtain detailed horizontal wind structures. The divergence of the horizontal wind was calculated and the anelastic continuity equation integrated to obtain vertical air motions. Differences between the areally averaged quantities and the grid point values provided a measure of the fluctuations in the wind components or the turbulent wind fluctuations. Vertical profiles of the mean winds and quantities related to the turbulent kinetic energy components and the turbulent momentum transfers were also calculated.
The applications of satellite and aircraft sensors to precipitation estimation are discussed. The advanced microwave moisture sensor and imagery and the PPI photographs and digital radar data are described. The aircraft microwave sensor and radar imagery representing the relationships between patterns and gradients of brightness temperature, T(B), and echo intensities for three cases (evolution of an oceanic squall line, convection over land, and intense thunderstorms over land) are examined and compared. The observed T(B)s are also compared with the theoretical calculations of Wu and Weinman (1984) and Szejwach et al. (1986). The observations of convective precipitation from an aircraft microwave radiometer operating at 92 and 183 GHz reveal that the areas of T(B) much colder than atmospheric temperature are positively correlated with regions of higher radar reflectivity, and the patterns and gradients of T(B) are similar in appearance to the radar echoes.
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 two-way attenuation coefficient was found to be 0.0085 dB/km ( mm/h) exp -1.08 for the tropical rains and associated clouds in Darwin for the first two 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.
An aircraft experiment has been conducted with a dual-frequency (X/Ka-bands) radar to test various rainfall retrieval methods from space. The authors test a method to derive raindrop size distribution (DSD) parameters from the combination of a radar reflectivity profile and a path-integrated attenuation derived from surface return, which may be available from most spaceborne radars. The estimated DSD parameters are reasonable in that the values generally fall within the range of commonly measured ones and that shifts in DSD parameters appear to be correlated with changes in storm type. The validity of the estimation result is also demonstrated by a consistency check using the Ka-band reflectivity profile which is independent of the DSD estimation process. Although errors may occur in the cases of nonuniform beam filling, these test results indicate the feasibility of the dual-parameter radar measurement from space in achieving a better accuracy in quantitative rainfall remote measurements.
Corrected Moments in Antenna Coordinates (CMAC) calculates quantitative precipitation estimates (QPE) from empirical relationships based on equivalent radar reflectivity factor, specific differ- ential phase, and specific attenuation. To evaluate these empirical relationships, the Extracted Radar Columns and In-Situ Sensors (RADclss) product was developed. Utilizing Py-ART, RAD- clss extracts CMAC radar columns above various ARM and partner locations. These columns are then spatiotemporally synced with in-situ observations at the surface utilizing the Atmospheric data Community Toolkit (ACT; Theisen et al. 2025), allowing direct comparison of radar parameters with rain gauges and laser disdrometers for further investigation.
It is pointed out that the importance of digital terrain models in the processing, analysis, and interpretation of remote sensing data is increasing. In investigations related to the study of radar images, digital terrain models can have a particular significance, because radar reflection is a function of the terrain characteristics. A procedure for the analysis and interpretation of radar images is discussed. The procedure is based on a utilization of computer simulation which makes it possible to produce simulated radar images on the basis of a digital terrain model. The simulated radar images are used for the geometric and radiometric rectification of real radar images. A description of the employed procedures is provided, and the obtained results are discussed, taking into account a test area in Northern California.
The use of vertical-incidence Doppler velocity in addition to radar reflectivity may yield information on drop size distribution and therefore result in better rainrate estimates. Doppler velocity can provide useful information on the raindrop size distribution. Doppler velocities from a zenith-pointing radar represent the sum of the mean reflectivity-weighted hydrometeor fallspeed and the vertical air motion. Dual-parameter rain estimation methods using the Doppler velocity, require that the latter can be removed, or is negligible. Atlas et al. (1972) derived relations between Doppler velocity, reflectivity, and rain rate assuming an exponential size distribution for rain. Ulbrich (1994) expanded on this work by deriving the relation between the Doppler velocity and the reflectivity assuming a Gamma size distribution. This distribution provides a more realistic representation of the small rain drops. To get accurate information on raindrop size distributions with the above method, the air motions must be removed from the observed Doppler velocities
The nature of the Venusian surface was revealed by Pioneer-Venus (PV) observations to be diverse at scales from tens to hundreds of kilometers. Spatial correlations of elevation, surface roughness, and radar reflectivity were investigated as a means of assessing the degree of homogeneity of surface radar properties within topographic provinces and develop a map of possible geologic boundaries. Correlations were performed in a supervised fashion whereby unit boundaries were selected on the basis of statistical and empirical studies of the individual data sets. Interpretations of these units in terms of geologic characteristics are based on the determination of physical units which are model dependent.
Synthetic aperture radar (SAR) imagery of the Wind River Range area in Wyoming is compared with visible and near-infrared imagery of the same area. Data from the Seasat L-Band SAR and an aircraft X-Band SAR are compared with Landsat Return Beam Vidicon (RBV) visible data and near-infrared aerial photography and topographic maps of the same area. It is noted that visible and near-infrared data provide more information than the SAR data when conditions are the most favorable. The SAR penetrates clouds and snow, however, and data can be acquired day or night. Drainage density detail is good on SAR imagery because individual streams show up well owing to riparian vegetation; this causes higher radar reflections which result from the 'rough' surface which vegetation creates. In the winter image, the X-Band radar data show high returns because of cracks on the lake ice surfaces. High returns can also be seen in the L-Band SAR imagery of the lakes due to ripples on the surface induced by wind. It is concluded that the use of multispectral data would optimize analysis of hydrologic features.
A variety of different radars have been used to observe the sea surface. The instruments include scatterometers to measure wind velocity, altimeters to measure wind speed and wave height, synthetic aperture radars (SAR) to map the radar reflectivity of the surface in order to see ocean surface waves and other phenomena, and two-frequency radars to measure ocean wavelength. The present investigation is concerned with the accuracy of the measurements of particular oceanic variables, improved means of calculating these variables, and a comparison of the relative similarities and differences among the various radars. Wind speed can be measured to useful accuracy from space using scatterometers such as that on Seasat. Significant wave heights can be measured to useful accuracy from space using altimeters, the present accuracy being + or - 10% for altimeters such as that on Seasat.
During a period spanning more than 5 years, a series of low elevation rain radar measurements encompassing 17 rain days were systematically executed in the mid-Atlantic coast of the United States. Drop size distribution measurements with a nearby disdrometer were also acquired during the same rain days. The drop size data were utilized to convert the radar reflectivity factors to estimated rain rates for the respective rain days of operation. Applying developed algorithms to the radar and disdrometer data, 'core' values of rain intensities and nested families of rain rate isopleths enveloping them were identified and their equi-circle diameters were statistically analyzed.
Earth-based radar data remain an important part of the information set used to select and certify spacecraft landing sites on Mars. Constraints on robotic landings on Mars include: terrain elevation, radar reflectivity. regional and local slopes, rock distribution and coverage, and surface roughness, all of which are addressed by radar data. Indeed, the usefulness of radar data for Mars exploration has been demonstrated in the past. Radar data were critical in assessing the Viking Lander I site, and more recently, the Mars Pathfinder landing site.
Earth-based radar data remain an important part of the information set used to select and certify spacecraft landing sites on Mars. Constraints on robotic landings on Mars include: terrain elevation, radar reflectivity, regional and local slopes, rock distribution and coverage, and surface roughness, all of which are addressed by radar data. Indeed, the usefulness of radar data for Mars exploration has been demonstrated in the past. Radar data were critical in assessing the Viking Lander, and more recently, the Mars Pathfinder landing.
Earth-based radar data remain an important part of the information set used to select and certify spacecraft landing sites on Mars. Constraints on robotic landings on Mars include: terrain elevation, radar reflectivity, regional and local slopes, rock distribution and coverage, and surface roughness, all of which are addressed by radar data. Indeed, the usefulness of radar data for Mars exploration has been demonstrated in the past. Radar data were critical in assessing the Viking Lander 1 site, and more recently, the Mars Pathfinder landing site.