Construction of a random signal with a specific Psd and a uniform Pdf

The performance of a dynamic element matching (DEM) flash digital to analog converter (DAC) can be improved by controlling the DEM DAC\u27s interconnection network with a random signal that has a specific power spectral density (PSD) and a uniform probability distribution function (PDF). Many algorithms exist for generating a random signal with a white PSD and a uniform PDF, but there exists only one algorithm for generating a random signal with a specific PSD and a particular PDF. For DEM DAC applications, the random signal must be generated at the speed of the DEM DAC. However, a real time implementation of this existing algorithm is too computation intensive for a typical DEM DAC. In this thesis, an algorithm that constructs a uniformly distributed random signal with a specific PSD is developed. This uniformly distributed colored random signal is implemented using a finite state machine (FSM) and Linear Feedback Shift Registers (LFSRs)

Microwave radiative transfer studies of precipitation

Since the deployment of the DMSP SSM/I microwave imagers in 1987, increased utilization of passive microwave radiometry throughout the 10 - 100 GHz spectrum has occurred for measurement of atmospheric constituents and terrestrial surfaces. Our efforts have focused on observations and analysis of the microwave radiative transfer behavior of precipitating clouds. We have focused particular attention on combining both aircraft and SSM/I radiometer imagery with ground-based multiparameter radar observations. As part of this and the past NASA contract, we have developed a multi-stream, polarized radiative transfer model which incorporates scattering. The model has the capability to be initialized with cloud model output or multiparameter radar products. This model provides the necessary 'link' between the passive microwave radiometer and active microwave radar observations. This unique arrangement has allowed the brightness temperatures (TB) to be compared against quantities such as rainfall, liquid/ice water paths, and the vertical structure of the cloud. Quantification of the amounts of ice and water in precipitating clouds is required for understanding of the global energy balance

Optimal area approach to intercomparing polarimetric radar rain-rate algorithms with gauge data, An

Includes bibliographical references (page 623).An optimal area method is described that is used as a basis for comparing KDP-, (KDP, ZDR)-, and Zh-based estimates of rain rates with gauge-measured rain rates. The location and dimensions of an elliptically shaped optimal area within the radar scan area surrounding the gauge are determined objectively via an rms error minimization of the difference between the KDP-based radar estimate and gauge data and via use of the spatial structure of the rms difference field itself. Four convective events were analyzed with rain rates in the range of 20-120 mm h-1, with two of the events containing marble-sized hail. The analysis shows that excellent results could be achieved using KDP-based rain-rate estimators

Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation

Includes bibliographical references (pages 75-76).The potential use of differential reflectivity measurements at orthogonal polarizations to determine rainfall rate is examined. The method involves measurements of ZH and ZV, the radar reflectivity factors due to horizontally and vertically polarized incident waves respectively. The differential reflectivity, ZDR= 10 log (ZH/ZV), which should be precisely determinate, occurs as a result of the distortion of raindrops as they fall at terminal velocity. The approximate theory of Gans for electromagnetic scattering by spheroids is applied to the distorted raindrops. Assuming a general exponential form for the raindrop size distribution, equation sare derived relating the distribution parameters to the measurements. The determination of rainfall rate follows directly. Finally, the sensitivity of the distribution parameters to radar inaccuracies is examined, and several methods of implementing the measurements are suggested. It is concluded that good estimates of rainfall rate using a single non-attenuating wavelength radar are possible under ideal conditions

Specular null polarization theory: applications to radar meteorology

Includes bibliographical references.Specular null polarization theory (SNPT) has been recently introduced for the case of coherent scattering where a 2 x 2 scattering matrix is sufficient to describe the scattering process. In this paper, SNPT is extended to the case of incoherent scattering. Optimum polarization states are derived and the results are discussed in relation to the classic radar optimum polarizations. In traditional radar polarimetry, modeling of the radar receive/transmit network is included in the radar voltage equation and consequently this affects the optimum polarizations and polarization responses of scatterers. SNPT eliminates this effect and therefore allows for a more direct analysis of scatterers. Modeling of ensembles of precipitation particles is used to illustrate the results of the analysis.This work was supported by the National Science Foundation under Grants ATM-8915141 and ATM-9214864

Correcting C-band radar reflectivity and differential reflectivity data for rain attenuation: a self-consistent method with constraints

Includes bibliographical references.Quantitative use of C-band radar measurements of reflectivity (Zh) and differential reflectivity (Zdr) demands the use of accurate attenuation-correction procedures, especially in convective rain events. With the availability of differential phase measurements (Φdp) with a dual-polarized radar, it is now possible to improve and stabilize attenuation-correction schemes over earlier schemes which did not use Φdp. The recent introduction of constraint-based correction schemes using Φdp constitute an important advance [8], [9]. In this paper, a self-consistent, constraint-based algorithm is proposed and evaluated which extends the previous approaches in several important respects. Radar data collected by the C-POL radar during the South China Sea Monsoon Experiment (SCSMEX) are used to illustrate the correction scheme. The corrected radar data are then compared against disdrometer-based scattering simulations, the disdrometer data being acquired during SCSMEX. A new algorithm is used to retrieve the median volume diameter from the corrected Zh, corrected Zdr, and Kdp radar measurements which is relatively immune to the precise drop axis ratio versus drop diameter relation. Histograms of the radar-retrieved Do compared against Do from disdrometer data are in remarkable good agreement lending further validity to the proposed attenuation-correction scheme, as well as to confidence in the use of C-band radar for the remote measurement of rain microphysics.The work of V. N. Bringi and V. Chandrasekar was supported by the NASA/TRMM Grant NAG5-7717 and -7876

Comparisons of precipitation measurements by the Advanced Microwave Precipitation Radiometer and multiparameter radar

Includes bibliographical references.Multiparameter microwave radar measurements are based on dual-polarization and dual-frequency techniques and are well suited for microphysical inferences of complex precipitating clouds, since they depend upon the size, shape, composition, and orientation of a collection of discrete random scatterers. Passive microwave radiometer observations represent path integrated scattering and absorption phenomena of the same scatterers. The response of the upwelling brightness temperatures TB to the precipitation structure depends on the vertical distribution of the various hydrometeors and gases, and the surface features. As a result, combinations of both active and passive techniques contain great potential to markedly improve the longstanding issue of precipitation measurement from space. The NASA airborne Advanced Microwave Precipitation Radiometer (AMPR) and the National Center for Atmospheric Research (NCAR) CP-2 multiparameter radar were jointly operated during the 1991 Convection and Precipitation/Electrification experiment (CaPE) in central Florida. The AMPR is a four channel, high resolution, across-track scanning total power radiometer system using the identical multifrequency feedhorn as the widely utilized Special Sensor Microwave/Imager (SSM/I) satellite system. Surface and precipitation features are separable based on the TB behavior as a function of the AMPR channels. The radar observations are presented in a remapped format suitable for comparison with the multifrequency AMPR imagery. Striking resemblances are noted between the AMPR imagery and the radar reflectivity at successive heights, while vertical profiles of the CP-2 products along the nadir trace suggest a storm structure consistent with the viewed AMPR TB. Directly over the storm cores, the difference between the 37 and 85 GHz TB was noted to approach (and in some cases fall below) zero. Microwave radiative transfer computations show that this is theoretically possible for hail regions suspended aloft in the core of strong convective storms.This work was supported by the NASA Earth Science and Applications Division under Grant NAG8-890. The National Center for Atmospheric Research is sponsored by the National Science Foundation

Measurement of mean raindrop shape from polarimetric radar observations

Includes bibliographical references (page 3413).Interpretation of polarimetric radar measurements in rainfall such as differential reflectivity and specific differential phase shifts depends on the mean raindrop shape-size relationship. Currently, semiempirical relations between the oblateness and the diameter of the drop are being used. This paper presents an algorithm to obtain the mean shape of the rain drops from polarimetric radar measurements, namely, the reflectivity factor, the differential reflectivity and the specific differential phase shift. The accuracy of the estimate mean drop shape depends on the measurement accuracies of polarimetric radar observations. Based on asymptotic error analysis and simulations it is shown that the mean raindrop shape can be estimated to an accuracy of 10%. The raindrop shape estimator algorithm developed in this paper is applied to polarimetric radar data collected by the CSU-CHILL radar during the 28 July 1997 Fort Collins. Colorado, flood

Rainfall estimation from polarimetric radar measurements: composite algorithms immune to variability in raindrop shape-size relation

Includes bibliographical references (pages 1785-1786).Polarization diversity radar measurements such as reflectivity factor, differential reflectivity, and differential propagation phase are extensively used in rainfall estimation. Algorithms to estimate rainfall from polarimetric radar measurements are based on a model for the raindrop shape as a function of drop diameter. Most of the current algorithms use an equilibrium shape-size model for raindrops. Variation of the prevailing mean raindrop shapes from an assumed model has a direct impact on the accuracy of radar rainfall estimates. This paper develops composite algorithms to estimate rainfall from polarimetric radar data without an a priori assumption about the specific form of mean raindrop shape-size model such as equilibrium shape model. The accuracy of rainfall estimates is evaluated in the presence of random measurement errors as well as systematic bias errors. The composite algorithms, independent of a prespecified raindrop shape model, were applied to radar parameters simulated from disdrometer data collected over 3 months, and the corresponding rainfall estimates were found to be in good agreement with disdrometer estimates. The composite algorithms were also tested with Colorado State University CHILL radar observations of the 28 July 1997 Fort Collins (Colorado) flood event. The storm total precipitation estimates based on the composite algorithms developed in this paper were in much better agreement with rain gauge estimates in comparison with conventional algorithms

Drop Axis Ratio Distributions in Stratiform and Convective Rain

A fully calibrated low profile 2D video disdrometer (2DVD) has been recording many different rainfall events in Northern Alabama (USA) since June 2007. An earlier publication reported drop shapes and axis ratio distributions determined for some of the events. For one of the cases examined, a noticeable shift in the 3.5 - 3.75 mm drop axis ratio distribution was noted. In this paper, we extend the earlier work by separating the 2DVD measurements into stratiform and convective rain. The separation is made possible by using the minute-by-minute drop size distribution (DSD) measured by the 2DVD. The 1-minute DSDs are fitted to a gamma distribution, and using a simple indexing technique which involves two of the fitted parameters, periods of convective and stratiform rain are separated for a given event. The output of the DSD indexing technique is qualitatively confirmed by comparing with simultaneous time series observations from a co-located UHF profiler which continuously records height profiles of reflectivity, Doppler mean and spectral width, all of which enable the identification of bright-band periods and, furthermore, periods of moderate and deep convection. Excellent consistency is found between the output of the DSD-based separation method and the profiler observations. Next, we utilize the output of DSD index-based separation method to flag the periods of severe convection for a given event. Drop axis ratios during the flagged periods are derived and compared with those during stratiform rain periods. Five cases have been considered. Axis ratio distributions do not show appreciable differences between stratiform and convective periods for four of the cases. The fifth case (the same case as reported earlier) shows a shift in the 3.5 - 3.75 mm drop axis ratios during a prolonged period of convection. The contoured shapes for these drops determined from the 2DVD camera data indicate the possibility of non-axisymmetric oscillations, compared with the contoured images for other events which fit well to our reference drop shapes. For all of above cases, observations from a C-band polarimetric radar - situated 15 km away are examined. The variations between the co-polar radar reflectivity and the differential reflectivity as well as the specific differential phase are compared with the 2DVD data based scattering calculations for the 5 events. The implications will be discussed