This paper presents the potential of nonlinear and linear versions of an observation operator for simulating polarimetric variables observed by weather radars. These variables, deduced from the horizontally and vertically polarized backscattered radiations, give information about the shape, the phase and the distributions of hydrometeors. Different studies in observation space are presented as a first step toward their inclusion in a variational data assimilation context, which is not treated here.
Input variables are prognostic variables forecasted by the AROME-France numerical weather prediction (NWP) model at convective scale, including liquid and solid hydrometeor contents. A nonlinear observation operator, based on the T-matrix method, allows us to simulate the horizontal and the vertical reflectivities (

For a couple of decades, convective-scale numerical weather prediction (NWP) models have been developed to forecast mesoscale meteorological phenomena such as storms, wind gusts and fog, which can represent important socioeconomic threats. Nowadays, most of operational convective-scale NWP models have fine, kilometer-scale, horizontal resolutions (see review by

The dual-polarization radar technology allows us to go further in the description of precipitating systems.

Nowadays, however, only the horizontal reflectivity and the Doppler wind are operationally exploited in the retrieval of initial conditions of NWP models. From a data assimilation (hereafter DA) point of view, the challenge is to extract useful information about the main control variables from

In this paper, preliminary work is presented in order to prepare the assimilation of DPOL variables in a convective-scale variational DA system. Such a system is based on the minimization of a cost function, which is composed of two terms defining distances (i) between the model state and a background and (ii) between the model state in the observation space and the observations. The second term requires nonlinear (hereafter NL) observation operators in order to retrieve the model equivalent of every observation at their locations. Statistics between observed and simulated values (called innovations) are used at this stage to quantify the performance of the model in this particular space and to perform quality controls in order to produce innovation distributions that are close to a Gaussian shape, such conditions leading to optimal variational DA results. In this study, the NL observation operator described by

When error Gaussianity and operator linearity are respected, the cost function of a variational DA system is close to a quadratic function for which the minimum can be easily obtained by, e.g., the method of least squares. The estimation of its gradient, which needs linearized versions of the observation operators, is then required. For operators related to precipitation, this is not straightforward as cloud microphysical processes are often highly nonlinear due to the presence of on–off switches

The main goal of this paper is to study an observation operator of DPOL variables in order to determine its properties and suitability for DA, especially for hydrometeor contents initialization in the variational context of the AROME-France convective-scale NWP model. No assimilations are thus performed yet, and only results in the observation space are discussed at this point. The behavior of the operators presented in this paper in a variational DA system will be the focus of a future paper. Section 2 first describes the NL observation operator, a quantification of its errors and examples of DPOL variables simulation for different meteorological situations simulated by AROME-France. In Sect. 3, innovation statistics are discussed and used to perform quality controls on polarimetric observations. Finally, Sect. 4 focuses on the DPOL observation operator Jacobians to determine the validity of the linearity hypothesis and to quantify the sensitivity of DPOL variables to the various simulated hydrometeor contents. Conclusions and perspectives from this study are given in Sect. 5.

The

Two other parameters are required for the backscattering coefficient computation: the hydrometeor shape and the dielectric constant. The latter, which describes how a material reacts to the application of electrical field, is simulated by the Debye model for raindrops

Once the hydrometeors characteristics are defined, the T-matrix method is used to compute the backscattering coefficients for different values of particle diameters, radar elevations, temperatures and water contents (as listed in Table 1 of

The reader should note that “horizontal reflectivity” (

The specific differential phase

To assess qualitatively the ability of

Observed

Figure

Hydrometeor mixing ratios from a 1h AROME-France forecast valid the 10 October 2018 at 14:00 UTC for

The

In agreement with areas of large

The observed and simulated specific differential phase

In Fig.

Considering all case studies (Table

In order to describe the uncertainties associated with the simulation of DPOL variables, the impact of changes to three

Simulated meteorological cases used to assess simulation uncertainties. The two radars of interest operate in S-band. Times are expressed in UTC.

Parameters modified to study uncertainties in the

Simulation uncertainty for

The results are displayed in Fig.

The results of these sensitivity tests show that

A similar study to the one presented here with S-band radars has been conducted with 11 different meteorological cases, but with C-band radars (not shown). Comparable results have been obtained, the spread being nevertheless slightly larger for

Nevertheless, despite choices made in

As explained previously, the optimality of variational DA requires Gaussianity of errors. For that purpose, innovation statistics (differences between observation and model counterparts) are examined. An ad hoc quality control could then be defined in order to improve Gaussianity. In this study, such statistics have been computed for 12 contrasted meteorological cases, encompassing convective and stratiform precipitation. Among those cases, only the Collobrières case has been observed by an S-band radar, while the others have been sampled by C-band radars (see Table

Meteorological cases selected to study the innovation statistics of DPOL variables. Times are expressed in UTC.

Several filters are applied to the observations, principally to remove non-meteorological echoes and regions of too low a signal-to-noise ratio (SNR). Non-meteorological echoes are filtered using an echo type determination algorithm developed by

Filtering effects on

Figure

In order to quantify the effect of the filters, innovations have been computed on non-filtered and filtered observations. Figure

Innovations without (blue histograms) and with (green histograms) filters on observations for

In order to study if these conclusions depend on the hydrometeor phase, innovation statistics have been computed for different vertical levels. Figure

Innovation distributions over altitude for

First-guess

To better understand the behavior of innovations, separated distributions of simulated and observed values are examined. Figure

Concerning

Same as Fig.

Figure

These innovation statistics can also be used to define an approximation of observation standard deviations. Indeed,

As explained in the introduction, the adjoint of the linearized observation operator is required in the formulation of the gradient of the cost function.

Then, the Jacobian matrix can be estimated as follows:

First of all, it is important to evaluate the validity of the linear regime, according to the size of the perturbation

Difference between

For each hydrometeor type, a single fraction of hydrometeor content has been determined for all DPOL variables, by selecting the highest optimal fraction size in common between the four DPOL variables. It was found that the optimal fraction size is

The information provided by the DPOL variables depends upon the interaction of the different hydrometeors scanned by the radar beam. A primary step towards understanding DPOL variable Jacobians is to exclude the radar beam effect. In that case, it is proposed to first consider the diagonal elements of the Jacobian matrix computed in model space. The perturbation used at each level in the Jacobian computation is applied as follows:

Figure

The Jacobian study has been done with linear reflectivity units in order to stay closer to a linear regime than would be possible with the use of logarithmic reflectivity units.

It is explained by the fact that reflectivity is proportional to the total hydrometeor cross section (see Eq.Contrary to

For

To conclude this section, it has been found that DPOL variables are more sensitive to rain content perturbations than to other hydrometeors, mainly because of large values of liquid water dielectric constant. Another important information is that the most sensitive DPOL variable appears to be the horizontal reflectivity

As observations are not available on the model grid, the NL observation operator has to compute the model equivalent in the observation space. To do so, after a horizontal interpolation of the model profiles to the observation location,

Figure

An interesting feature is also present on the

Another important parameter to consider when dealing with radar geometry is the distance to the radar. With the radar beam being represented as a cone (see Fig. 3 in

This paper focused on studying operators required for the variational assimilation of polarimetric variables from ground-based weather radars in convective-scale NWP models. For that purpose, a radar observation operator

Even if polarimetric radars are able to detect fine spatial structures, filters need to be applied in order to remove non-meteorological data as well as the possible noise. A positive effect of these filters has been found on innovation statistics for the four DPOL variables computed for 12 different meteorological cases, with reductions in biases and standard deviations. Nevertheless, only

A linearized version of the polarimetric observation operator has been evaluated by computing its Jacobians with the finite difference method. The results show that polarimetric variables are more sensitive to rain content perturbations than to solid hydrometeor ones, especially because of their different dielectric constants. The Jacobian computation also supports the fact that

The present results show that only some DPOL variables appear to be promising for the initialization of hydrometeor contents through variational data assimilation. Among them, the horizontal reflectivity

Despite the difficulties encountered for

The polarimetric observation operator is available in the MESO-NH NWP model. It is a non-hydrostatic research model under the CeCILL-C free licence. For more information, please consult the MESO-NH website (

The Météo France polarimetric radar data are accessible for a license fee only. For more information, please consult the following web page:

All the authors conducted the research and analysis. GT wrote the paper. All the authors contributed to the paper's improvement.

The authors declare that they have no conflict of interest.

This research was conducted during the Guillaume Thomas' PhD, funded by Météo France. The authors would like to thank Sylvain Chaumont for providing polarimetric radar data. In addition, the authors also want to thank Nan Yu and Béatrice Fradon for their advice and their carefulness about those data, and Eric Wattrelot for much advice given during the first year of this PhD. Special acknowledgements are also due to Maud Martet, who helped with the polarimetric data decoding, provided advice on weather radar technology and agreed to provide an internal review of this paper. Finally, the authors would like to thank Isaac Moradi, who agreed to edit this paper, as well as the two anonymous referees, who helped to improve the present paper.

This paper was edited by Isaac Moradi and reviewed by two anonymous referees.