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.
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.
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