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Enrico Torlaschi and Bernard Pettigrew

Abstract

The effect of the propagation medium on the measurements of the radar reflectivity factor for circularly polarized S-band radar is assessed using model storms. The results show that for convective cells, the propagation effects can lead to underestimation of the reflectivity factor by an amount that is of the same order of magnitude as the attenuation at C-band.

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Enrico Torlaschi and Isztar Zawadzki

Abstract

Error propagation analysis is applied to evaluate the effects of correcting horizontal and differential attenuation on the precision of the estimates of reflectivity and differential reflectivity. The analysis shows that the loss of precision on reflectivity and differential reflectivity is of the same order of magnitude as the propagation power losses added, notwithstanding how horizontal and differential attenuation are accounted for. Polarimetric weather radar simultaneously transmitting and receiving horizontally and vertically polarized waves is then considered. Differential propagation phase is used as the predictor variable for attenuation. Calculations for three microwave frequencies corresponding to S, C, and X bands show that the losses in accuracy and in precision of the estimates of reflectivity are about 16 and 68 times worse at C and X bands, respectively, than at S band. The corresponding values for the estimates of differential reflectivity are about 20 and 52 times worse.

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Eva Monteiro and Enrico Torlaschi

Abstract

The concept of virtual temperature is reviewed and extended into the definition of the dynamic virtual temperature, which is the temperature that a parcel of dry air should have in order to experience the same acceleration as a parcel of cloud air. It is obtained from the equations of motion and depends on the water content in the three thermodynamic states: vapor, liquid, and solid. The scale analysis of the equation of the dynamic virtual temperature shows that the terms due to the acceleration and phase transitions of the particles are negligible with respect to the terms depending on gravity. Therefore, even though conceptually more adequate, the approximate mathematical expression of the dynamic virtual temperature is practically identical to the conventional definition of virtual temperature accounting for water loading.

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Enrico Torlaschi and Isztar Zawadzki

Abstract

A format for an optimal post-detection integration is discussed. The measurement cells in the integration scheme have equal down-range and cross-range resolution to conserve more of the variability of the precipitation field. Every measurement cell combines partially dependent data both in range and time to achieve an adequate number of independent samples without losing resolution. Thus, the standard deviation of the average signal intensity level over a cell (σj) is reduced to a more desirable value. The radial and tangential extent of the cells change as a function of range, and are determined by σj. Such data processing is optimized for biases related to reflectivity gradients, space resolution and density of information.

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Enrico Torlaschi and Yves Gingras

Abstract

The perturbation method is used to derive the variance of the zero-lag copolar correlation coefficient,  | ρ HV | , for a radar simultaneously transmitting and receiving both horizontal and vertical polarization. The variance of  | ρ HV |  is a function of its expected value, the number of samples, the normalized Doppler velocity spectrum width, σ υn, and the signal-to-noise ratio in the receivers. Assuming the covariances and cross covariance of the radar signals are represented by zero-mean complex Gaussian processes, the precision of the estimate of  | ρ HV |  for alternate and simultaneous transmission and reception of horizontal and vertical polarization is discussed. Calculations show that variations in the expected value of  | ρ HV |  from 0.7 to 0.98 lead to a decrease in the precision of the estimate of  | ρ HV |  of more than one order of magnitude: for narrow spectra (σ υn < 0.04) the estimates do not depend on the sampling scheme used but on the number of samples taken, and at larger spectrum widths (σ υn > 0.1) the simultaneous scheme can be more than one order of magnitude more precise than the alternate scheme. Furthermore, for good precision the signal-to-noise ratio should exceed 10 dB.

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Enrico Torlaschi and Yves Gingras

Abstract

A polarimetric weather radar with alternate transmission of slant linear +45° and −45° polarization and simultaneous reception of both linear vertical and linear horizontal polarization is considered. The equations of the radar observables for a model medium containing nonspherical hydrometeors are presented. Assuming the hydrometeors to be axially symmetric with a canting angle distribution symmetric about the mean canting angle, a set of equations for separation of propagation and backscattering effects is developed. The mean apparent canting angle, the degree of common orientation of the hydrometeors, and the differential phase shift are obtained. Using empirical relationships, the mean and differential attenuations are estimated by means of the differential phase shift. The intrinsic value of the reflectivity, the differential reflectivity, and the copolar correlation coefficient at zero lag time are then determined. Application of this to a model convective rain cell shows that the use of simultaneous transmission and reception of linear vertical and linear horizontal polarization at S, C, and X bands provides accurate estimates of the intrinsic scattering properties of precipitation. The analysis of the bias on the radar observables due to the assumption of a medium of equioriented hydrometeors shows that all the observables with the exception of reflectivity can be severely affected.

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Enrico Torlaschi and Anthony R. Holt

Abstract

Because precipitation particles are generally nonspherical, not only will microwave radiation be depolarized when reflected by precipitation, but also the polarization state of the transmitted wave will change as the radar beam penetrates the region of precipitation. The intrinsic scattering properties of the hydrometeors are, therefore, coupled with the properties of the propagation medium, and both effects contribute to establish the return signal. In this paper it is shown that these effects can be separated when S-band circular polarized radiation is transmitted and the copolar and cross-polar power, and the magnitude and phase of the copolar and cross-polar signal correlation, is available.

The equations of the radar observables for a model medium containing nonspherical raindrops are presented. This model takes into account the distribution of canting angle but assumes the uniformity of the distribution function along the propagation path. Assuming the raindrops to have the same orientations throughout the region of precipitation and using two empirical relationships relating the mean and the differential attenuation to the differential phase shift, a set of equations for separation of propagation and backscattering effects is developed. Application of this to a model convective cell verifies that the use of the circular polarization technique at S band can also provide very good estimates of the intrinsic scattering properties of precipitation in regions of heavy rain rates. Data from a circularly polarized S-band radar system are used to confirm that this separation may be performed and to illustrate the microphysical information that can now be extracted.

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