## Toward a variational assimilation of polarimetric radar observations in a convective-scale numerical weather prediction (NWP) model

#### Thomas, Guillaume ; Mahfouf, Jean-François ; Montmerle, Thibaut

Année de publication

2020

Résumé

<p align=justify>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 (<span class="inline-formula"><i>Z</i><sub>HH</sub></span> and <span class="inline-formula"><i>Z</i><sub>VV</sub></span>), the differential reflectivity <span class="inline-formula"><i>Z</i><sub>DR</sub></span>, the specific differential phase <span class="inline-formula"><i>K</i><sub>DP</sub></span> and the co-polar correlation coefficient <span class="inline-formula"><i>ρ</i><sub>HV</sub></span>. To assess the uncertainty of such simulations, perturbations have been applied to input parameters of the operator, such as dielectric constant, shape and orientation of the scatterers. Statistics of innovations, defined by the difference between simulated and observed values, are then performed. After some specific filtering procedures, shapes close to a Gaussian distribution have been found for both reflectivities and for <span class="inline-formula"><i>Z</i><sub>DR</sub></span>, contrary to <span class="inline-formula"><i>K</i><sub>DP</sub></span> and <span class="inline-formula"><i>ρ</i><sub>HV</sub></span>. A linearized version of this observation operator has been obtained by its Jacobian matrix estimated with the finite difference method. This step allows us to study the sensitivity of polarimetric variables to hydrometeor content perturbations, in the model geometry as well as in the radar one. The polarimetric variables <span class="inline-formula"><i>Z</i><sub>HH</sub></span> and <span class="inline-formula"><i>Z</i><sub>DR</sub></span> appear to be good candidates for hydrometeor initialization, while <span class="inline-formula"><i>K</i><sub>DP</sub></span> seems to be useful only for rain contents. Due to the weak sensitivity of <span class="inline-formula"><i>ρ</i><sub>HV</sub></span>, its use in data assimilation is expected to be very challenging.</p>

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