Currently in operational numerical weather prediction (NWP) the density of high-resolution observations, such as Doppler radar radial winds (DRWs), is severely reduced in part to avoid violating the assumption of uncorrelated observation errors. To improve the quantity of observations used and the impact that they have on the forecast requires an accurate specification of the observation uncertainties. Observation uncertainties can be estimated using a simple diagnostic that utilizes the statistical averages of observation-minus-background and observation-minus-analysis residuals. We are the first to use a modified form of the diagnostic to estimate spatial correlations for observations used in an operational ensemble data assimilation system. The uncertainties for DRW superobservations assimilated into the Deutscher Wetterdienst convection-permitting NWP model are estimated and compared to previous uncertainty estimates for DRWs. The new results show that most diagnosed standard deviations are smaller than those used in the assimilation, hence, it may be feasible to assimilate DRWs using reduced error standard deviations. However, some of the estimated standard deviations are considerably larger than those used in the assimilation; these large errors highlight areas where the observation processing system may be improved. The error correlation length scales are larger than the observation separation distance and influenced by both the superobbing procedure and observation operator. This is supported by comparing these results to our previous study using Met Office data. Our results suggest that DRW error correlations may be reduced by improving the superobbing procedure and observation operator; however, any remaining correlations should be accounted for in the assimilation.

We consider a left-transient random walk in a random environment on Z that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.

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We establish recurrence and transience criteria for critical branching processes in random environments with immigration. These results are then applied to the recurrence and transience of a recurrent random walk in a random environment on ℤ disturbed by cookies inducing a drift to the right of strength 1.

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 to assimilate and for assignment of the OE covariance matrix that can be diagonal or full and correlated.

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.

Near-surface temperature and humidity observations over Germany, coming on the one hand from the citizen weather station's network Netatmo and on the other hand from synoptic weather stations, were assimilated into the limited are mode of the Icosahedral Nonhydrostatic Model with 2-km resolution (ICON-D2). For that we use the Kilometre-Scale Ensemble Data Assimilation (KENDA) system and a bias-correction approach that improves the assimilation of the observations by taking into account the diurnal cycle of temperature and humidity variables. Our results show that the assimilation of bias-corrected observations from Netatmo stations reduces the forecast error considerably; meanwhile, the assimilation of Netatmo observations without bias correction leads to a strong warm bias with a negative impact on forecast performance.In contrast, for the assimilation of synoptic observations the usage of our bias-correction approach does not lead to any significant decrease in the forecast error, yet reduces the bias for the diurnal cycle of synoptic stations. Overall, it can be concluded that the forecast quality can gain from assimilating Netatmo data, provided an effective bias-correction approach is applied.

he first Joint World Climate Research Programme (WCRP)-World Weather Research Programme (WWRP) Symposium on Data Assimilation and Reanalysis took place on 13-17 September 2021, and it was organized in conjunction with the ECMWF Annual Seminar on Observations. The last WCRP-WWRP-organized meetings were held separately for data assimilation and reanalysis in 2017 (Buizza et al. 2018;Cardinali et al. 2019). Since then, common challenges and new emerging topics have increased the need to bring these communities together to exchange new ideas and findings. Thus, a symposium involving the aforementioned communities was jointly organized by the German Meteorological Service (DWD), Hans-Ertel-Centre for Weather Research (HErZ), WCRP, WWRP, and the ECMWF Annual Seminar. Major goals were to increase diversity, provide early career scientists with opportunities to present their work and extend their professional network, and bridge gaps between the various communities.The online format allowed more than 500 participants from over 50 countries to meet in a virtual setting, using the Gather platform (www.gather.town) as the central tool to access the meeting. A virtual conference center was created where people could freely move around and talk to other close-by participants. A lobby served as the main hub, and it connected the poster halls and the conference rooms for the oral presentations and the ECMWF seminar talks. The feedback from the participants was overwhelmingly positive.Scientifically, the meeting offered opportunities to bring together the communities of Earth system data assimilation, reanalysis, and observations to identify current challenges, seek opportunities for collaboration, and discuss strategic planning on more integrated systems for the longer term. The contributions totaled 140 oral and over 150 poster presentations covering a large variety of topics with increased interest in Earth system approaches, machine learning, and increased spatial resolutions. Key findings of the symposium and the ECMWF Annual Seminar are summarized in the next section. The "Conclusions and remarks" section highlights the common and emerging challenges of these communities. TopicsOperational data assimilation and infrastructure. Many participants were affiliated with operational numerical weather prediction centers and thus a significant portion of the program focused on related updates. One common theme was moving beyond medium-range