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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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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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Wanda Szyrmer and Isztar Zawadzki

Abstract

As a first step toward retrieval of snow microphysics from two vertically pointing radars operating at X band and W band, a theoretical model of snow microphysics is formulated in which the number of unknown parameters is reduced to snow particle density and to two bulk quantities controlling the particle size distribution. This reduction of parameters is achieved by normalizing not only the size distribution but also the snow particle mass in the mass–size relationship as well as by using a relationship between snow density and snow terminal fall velocity. However, no single snow microphysical model could describe the observed variability in the radar measurements. The uncertainty in the developed deterministic relations that map the microphysical parameters to the observables is shown to be mainly associated with the assumed dependence of particle velocity on its mass and on the particle size distribution (PSD) representation. Hence, various mass–velocity relationships together with different generic functional forms of the PSD reported in literature are described in this paper and then used in the retrieval. The derived relations provide a reasonable range of uncertainty associated with the microphysics when used for the actual retrieval of snow properties from observations in Part IV. The uncertainty in the backscattering computations of an individual particle, performed using Mie theory assuming spherical form with nonuniform density, is not taken into account in this study.

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Alain Protat and Isztar Zawadzki

Abstract

A variational method for the retrieval of the 3D wind field from bistatic multiple-Doppler radar network data is developed, and its performance is evaluated. This bistatic network consists of one S-band weather radar and two passive low-gain receivers at remote sites. To allow for measurement error, the method uses the Doppler velocities of the three receivers as weak constraints and uses the continuity equation as a strong constraint in a cost function in which the two horizontal wind components are the control variables. Improvements are brought to the classical upward integration of the continuity equation, using a weighted combination of upward and downward integrations and its adjoint. A unique characteristic of a bistatic network is that all Doppler velocity measurements from individual resolution volumes are collected simultaneously, which minimizes the errors on the vertical wind component arising from the local evolution of the airflow. However, the time required to sample a complete weather volume with a Doppler radar (typically 5 min) represents another source of error that must be accounted for. Consequently, linear time interpolation of the measurements to a single reference time is used.

Finally, evaluation of the volume scanning strategy for aviation weather services shows that two retrieval modes can be processed in parallel, using the McGill University radar scanning strategy: a “fast” mode that provides the 3D wind field below 3-km height every 2.5 min and a “standard” mode that provides the 3D wind field for the full volume every 5 min.

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Wanda Szyrmer and Isztar Zawadzki

Abstract

This study uses a dataset of low-density snow aggregates measurements collected by a ground-based optical disdrometer that provides particle size and terminal fall speed for each size interval from which the velocity–size and area ratio–size relationships can be derived. From these relationships and relations between the Best and Reynolds numbers proposed in the literature, the mass power-law coefficients are obtained. Then, an approximate average relation between the coefficients in the experimentally determined velocity–size power law (with exponent fixed at 0.18) and the coefficients in the estimated mass power law (with exponent fixed at 2) is obtained. The validation of the retrieved relation is made by comparing, for each snowfall event, the time series of the reflectivity factor calculated from the derived mass–size relationship for a snowflake and from the size distribution measured by the optical disdrometer, with the reflectivity obtained from measurements. Using the measured snow size distribution and the retrieved mass–velocity relationship, a few useful relations between the bulk quantities of snow are derived. This study considers relations suitable for the microphysical modeling consistent with radar measurements of precipitating snow composed of unrimed or lightly rimed aggregate snowflakes.

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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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Marielle Gosset and Isztar Zawadzki

Abstract

Most attenuation correction algorithms are based on the assumption of an average, range-independent power-law relationship, k = aZ b, between attenuation k and reflectivity Z. This paper analyzes how nonuniform beam filling (NUBF) of the radar beam can modify the value of the coefficients a and b with distance.

This analytical study shows that there are two mechanisms in which NUBF affects the apparent attenuation. One is the global averaging performed by the radar beam within the sampling volume itself. This tends to increase the apparent attenuation. The other mechanism is the gradual building of an angular weighting function due to the accumulated attenuation by a nonuniform rain field between the radar and the sampling volume. This can cause a serious decrease in the apparent specific and path-integrated attenuations.

The practical consequences of these analytical results and their quantitative effects on rain retrieval with an X-band ground-based radar are then analyzed by simulations. A radar simulator “scanning” on a real, high-resolution reflectivity field is used to study the scatter in the relationship between the specific attenuation and Z. It is shown that in a typical horizontal rain structure, the two mechanisms responsible for overestimation or underestimation of the specific attenuation tend to compensate each other with distance. The resulting effect of NUBF from the point of view of ground-based radar is quite neutral.

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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

Nowcasting is the short-range forecast obtained from the latest observed state. Currently, heuristic techniques, such as Lagrangian extrapolation, are the most commonly used for rainfall forecasting. However, the Lagrangian extrapolation technique does not account for changes in the motion field or growth and decay of precipitation. These errors are difficult to analytically model and are normally introduced by stochastic processes. According to the chaos theory, similar states, also called analogs, evolve in a similar way plus an error related with the predictability of the situation. Consequently, finding these states in a historical dataset provides a way of forecasting that includes all the physical processes such as growth and decay, among others.

The difficulty of this approach lies in finding these analogs. In this study, recent radar observations are compared with a 15-yr radar dataset. Similar states within the dataset are selected according to their spatial rainfall patterns, temporal storm evolution, and synoptic patterns to generate ensembles. This ensemble of analog states is verified against observations for four different events. In addition, it is compared with the previously mentioned Lagrangian stochastic ensemble by means of different scores. This comparison shows the weaknesses and strengths of each technique. This could provide critical information for a future hybrid analog–stochastic nowcasting technique.

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Aitor Atencia and Isztar Zawadzki

Abstract

Intrinsic predictability is defined as the uncertainty in a forecast due to small errors in the initial conditions. In fact, not only the amplitude but also the structure of these initial errors plays a key role in the evolution of the forecast. Several methodologies have been developed to create an ensemble of forecasts from a feasible set of initial conditions, such as bred vectors or singular vectors. However, these methodologies consider only the fastest growth direction globally, which is represented by the Lyapunov vector.

In this paper, the simple Lorenz 63 model is used to compare bred vectors, random perturbations, and normal modes against analogs. The concept of analogs is based on the ergodicity theory to select compatible states for a given initial condition. These analogs have a complex structure in the phase space of the Lorenz attractor that is compatible with the properties of the nonlinear chaotic system.

It is shown that the initial averaged growth rate of errors of the analogs is similar to the one obtained with bred vectors or normal modes (fastest growth), but they do not share other properties or statistics, such as the spread of these growth rates. An in-depth study of different properties of the analogs and the previous existing perturbation methodologies is carried out to shed light on the consequences of forecasting the choice of the perturbations.

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