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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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Alain Protat and Isztar Zawadzki

Abstract

Recently, Protat and Zawadzki described an analysis method to retrieve the three wind components and their temporal derivatives from measurements collected by a bistatic multiple-Doppler radar network deployed around Montreal for nowcasting and research purposes. In the present paper, an extension of this method to retrieve the corresponding pressure and potential temperature perturbations is presented. The method consists of adding the three projections of the momentum equations as weak constraints to the minimization procedure, as is classically done. An evaluation of the performance of this basic constraining model indicates that, after minimization, the residuals of the horizontal momentum equations are of the same order of magnitude as the dominant terms of these equations. It is then shown that including the vorticity equation as an additional constraint substantially improves the perturbation pressure and temperature solutions, leading to negligible residuals of the horizontal momentum equations. This is due to the fact that the vorticity equation is equivalent to the condition that pressure derives from a potential (the second-order horizontal cross-derivatives of pressure are equal), which ensures that the problem has a mathematical solution.

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Marc Berenguer and Isztar Zawadzki

Abstract

The contribution of various physical sources of uncertainty affecting radar rainfall estimates at the ground has been recently quantified at a resolution typically used in schemes assimilating rainfall at the ground onto mesoscale models. Here, the contribution of the two most important sources of uncertainty at nonattenuating wavelengths (the range-dependent error and the uncertainty due to the ZR transformation) and their interaction are studied as a function of the resolution of radar observations.

The analysis is carried out using a large dataset of collocated reflectivity profiles from the McGill S-band radar and disdrometric measurements obtained in stratiform rainfall at resolutions of 1 × 1, 5 × 5, and 15 × 15 km2. Results show that the errors affecting radar quantitative precipitation estimation (QPE) have a strong dependence with range, and that their structure is scale dependent. At the analyzed resolutions, QPE errors are significantly correlated in time and over several grid points.

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Dominik Jacques and Isztar Zawadzki

Abstract

In data assimilation, analyses are generally obtained by combining a “background,” taken from a previously initiated model forecast, with observations from different instruments. For optimal analyses, the error covariance of all information sources must be properly represented. In the case of radar data assimilation, such representation is of particular importance since measurements are often available at spatial resolutions comparable to that of the model grid. Unfortunately, misrepresenting the covariance of radar errors is unavoidable as their true structure is unknown. This two-part study investigates the impacts of misrepresenting the covariance of errors when dense observations, such as radar data, are available. Experiments are performed in an idealized context. In Part I, analyses were obtained by using artificially simulated background and observation estimates. For the second part presented here, background estimates from a convection-resolving model were used. As before, analyses were generated with the same input data but with different misrepresentation of errors. The impacts of these misrepresentations can be quantified by comparing the two sets of analyses. It was found that the correlation of both the background and observation errors had to be represented to improve the quality of analyses. Of course, the concept of “errors” depends on how the “truth” is considered. When the truth was considered as an unknown constant, as opposed to an unknown random variable, background errors were found to be biased. Correcting these biases was found to significantly improve the quality of analyses.

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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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Wanda Szyrmer and Isztar Zawadzki

Abstract

Based on the theory developed in Part III, this paper introduces a new method to retrieve snow microphysics from ground-based collocated X- and W-band vertically pointing Doppler radars. To take into account the variety of microphysical relations observed in natural precipitating snow and to quantify the uncertainty in the retrieval results caused by this variety, the retrieval is formulated using the ensemble-based method. The ensemble is determined by the spread of uncertainties in the microphysical descriptions applied to map the same radar observables to the retrieved quantities.

The model descriptors use diverse assumptions concerning functional forms of particle size distribution and mass–velocity relations, all taken from previous observational studies. The mean of each ensemble is assumed to be the best estimate of the retrieval while its spread is defined by the standard deviation that characterizes its uncertainty. The main retrieved products are the characteristic size, the snow mass content, and the density parameter, as well as the vertical air motion. Four observables used in the retrieval are the difference in reflectivities and in Doppler velocities at two wavelengths, together with the equivalent reflectivity factor and Doppler velocity at X band. The solutions that are not consistent with all four observables after taking into account their estimated measurement errors are eliminated from the ensembles. The application of the retrieval algorithm to the real data yields a snow microphysical description that agrees with the snow characteristics seen in the vertical profile of the observed Doppler spectrum.

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Stéphane Laroche and Isztar Zawadzki

Abstract

Four methods for retrieval of the horizontal wind field are described and compared using single-Doppler observations of a sea-breeze front measured during the Convective and Precipitation/Electrification Experiment. The first method examined is the TREC (tracking radar echoes by correlation) technique similar to the one proposed by Tuttle and Foote. Two other methods, similar to TREC, in which wind vectors are estimated by minimizing the difference between successive patterns of reflectivity, are then examined. These methods conceptually link the TREC method and the velocity volume processing (VVP) approach to the variational wind retrieval method described here. The variational formulation uses the conservation of reflectivity and the radial momentum equation as physical constraints and in this way it incorporates the concepts on which TREC and VVP are based. The performance of the methods is compared using the dual-Doppler wind analysis as ground truth. Results show that the variational method can retrieve the wind field with higher resolution than the TREC method.

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Aitor Atencia and Isztar Zawadzki

Abstract

Lagrangian extrapolation of recent radar observations is a widely used deterministic nowcasting technique in operational and research centers. However, this technique does not account for errors due to changes in precipitation motion and to growth and decay, thus limiting forecasting skill. In this work these uncertainties have been introduced in the Lagrangian forecasts to generate different realistic future realizations (ensembles). The developed technique benefits from the well-known predictable large scales (low pass) and introduces stochastic noise in the small scales (high pass). The existence of observed predictable properties in the small scales is introduced in the generation of the stochastic noise. These properties provide realistic ensembles of different meteorological situations, narrowing the spread among members. Finally, some statistical spatial and temporal properties of the final set of ensembles have been verified to determine if the technique developed introduced enough uncertainty while keeping the properties of the original field.

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Wanda Szyrmer and Isztar Zawadzki

Abstract

To obtain the full description of the dynamical and microphysical finescale structures required for the computation of the radar-derived brightband parameters, a numerical model has been developed. A bulk microphysics module was introduced into a nonhydrostatic, fully compressible dynamic framework. A microphysical parameterization scheme, with five water categories (vapor, cloud water, snow, melting snow, and rain), describes the interactions related to the evolution of the melting layer (melting and diffusional exchanges of mass of each hydrometeor category). Dynamic, thermodynamic, and microphysical processes are fully coupled. The main characteristics of the bulk parameterization scheme for melting of snow are the following: 1) wet snow is described by its water content and by an additional prognostic variable, namely, the diameter of the smallest snowflake not yet completely melted; 2) the fall velocity of the melting snowflakes is based on the laboratory observations; and 3) a size-dependent ventilation coefficient of the melting particles is used. With this new formulation of the melting process some approximate analytical relations between variables that characterize the melting layer are obtained. The results of simulations show that the nonuniformity of the snow content causes horizontal variability of various atmospheric properties within the melting layer, which leads to the generation of convective cells. The impact of the induced finescale dynamics on the microphysical structure within the melting zone is analyzed.

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Urs Germann and Isztar Zawadzki

Abstract

The lifetime of precipitation patterns in Eulerian and Lagrangian space derived from continental-scale radar images is used as a measure of predictability. A three-step procedure is proposed. First, the motion field of precipitation is determined by variational radar echo tracking. Second, radar reflectivity is advected by means of a modified semi-Lagrangian advection scheme assuming stationary motion. Third, the Eulerian and Lagrangian persistence forecasts are compared to observations to calculate the lifetime and other measures of predictability. The procedure is repeated with images that have been decomposed according to scales to describe the scale-dependence of predictability.

The analysis has a threefold application: (i) determine the scale-dependence of predictability, (ii) set a standard against which the skill for quantitative precipitation forecasting by numerical modeling can be evaluated, and (iii) extend nowcasting by optimal extrapolation of radar precipitation patterns. The methodology can be applied to other field variables such as brightness temperatures of weather satellites imagery.

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