Interpreting estimated observation error statistics of weather radar measurements using the ICON-LAM-KENDA system

Abstract

Abstract. Assimilation of weather radar measurements including radar reflectivity and radial wind data has been operational at the Deutscher Wetterdienst, with a diagonal observation error (OE) covariance matrix. For an implementation of a full OE covariance matrix, the statistics of the OE have to be a priori estimated, for which the Desroziers method has been often used. However, the resulted statistics consists of contributions from different error sources and are difficult to interpret. In this work, we use an approach that is based on samples for truncation error in radar observation space to approximate the representation error due to unresolved scales and processes (RE) and compare its statistics with the OE statistics estimated by the Desroziers method. It is found that the statistics of the RE help the understanding of several important features in the variances and correlation length scales of the OE for both reflectivity and radial wind data and the other error sources from the microphysical scheme, radar observation operator and the superobbing technique may also contribute, for instance, to differences among different elevations and observation types. The statistics presented here can serve as a guideline for selecting which observations are assimilated and for assignment of the OE covariance matrix that can be diagonal or full and correlated.

Evaluating Latent-Heat-Nudging Schemes and Radar forward Operator Settings for a Convective Summer Period over Germany Using the ICON-KENDA System

“…For each elevation, the samples are binned every 5 km in the separation distance. As in Zeng et al [5,26], Waller et al [33], the correlation length scale is the distance where the correlation coefficient becomes not longer than 0.2.…”

“…For data assimilation experiments, we use the ICON-LAM-KENDA system with the the LETKF and choose the convective period 10-15 June in 2020 (part of the specific period for hindcasts). As in previous studies [5,26], the assimilation window is one hour. The ensemble size is 40 and additionally a deterministic run is carried on.…”

“…For the observation error covariance, a diagonal R is used. R = 10 • 10 • I [dBZ 2 ] for reflectivity, and R = 2.5 • 2.5 • γ • I [m 2 /s 2 ] for radial wind, where γ is a scaling factor that inflates errors if onsite reflectivities are too small (more about this in [26]). A horizontal localization radius of 16 km and a height-depending vertical localization radius (0.0075 to 0.5 in logarithm of pressure) are applied to radar data.…”

“…In contrast to DA_mie1, DA_ray uses the Rayleigh scattering scheme, whereas DA_mie2 uses the Mie scattering scheme with new parameters to reduce the brightband effect. As in Zeng et al [5,26], Waller et al [33], for the Desroziers method, samples of d o−a d T o−b of the deterministic run are used to calculate the statistics of the OE. For each elevation, standard deviations and horizontal correlations are averaged over all samples from all times and stations.…”

“…are background and analysis departures, and y o is the observation vector. Theoretically, the Desroziers method is an iterative process; however, in practice, the estimation of one iteration is often used due to its sufficient accuracy and low computational expense [23][24][25][26]), as in this work.…”