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Yicun Zhen and Fuqing Zhang

Abstract

This study proposes a variational approach to adaptively determine the optimum radius of influence for ensemble covariance localization when uncorrelated observations are assimilated sequentially. The covariance localization is commonly used by various ensemble Kalman filters to limit the impact of covariance sampling errors when the ensemble size is small relative to the dimension of the state. The probabilistic approach is based on the premise of finding an optimum localization radius that minimizes the distance between the Kalman update using the localized sampling covariance versus using the true covariance, when the sequential ensemble Kalman square root filter method is used. The authors first examine the effectiveness of the proposed method for the cases when the true covariance is known or can be approximated by a sufficiently large ensemble size. Not surprisingly, it is found that the smaller the true covariance distance or the smaller the ensemble, the smaller the localization radius that is needed. The authors further generalize the method to the more usual scenario that the true covariance is unknown but can be represented or estimated probabilistically based on the ensemble sampling covariance. The mathematical formula for this probabilistic and adaptive approach with the use of the Jeffreys prior is derived. Promising results and limitations of this new method are discussed through experiments using the Lorenz-96 system.

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Hailing Zhang and Zhaoxia Pu

Abstract

A series of numerical experiments are conducted to examine the impact of surface observations on the prediction of landfalls of Hurricane Katrina (2005), one of the deadliest disasters in U.S. history. A specific initial time (0000 UTC 25 August 2005), which led to poor prediction of Hurricane Katrina in several previous studies, is selected to begin data assimilation experiments. Quick Scatterometer (QuikSCAT) ocean surface wind vectors and surface mesonet observations are assimilated with the minimum central sea level pressure and conventional observations from NCEP into an Advanced Research version of the Weather Research and Forecasting Model (WRF) using an ensemble Kalman filter method. Impacts of data assimilation on the analyses and forecasts of Katrina’s track, landfalling time and location, intensity, structure, and rainfall are evaluated. It is found that the assimilation of QuikSCAT and mesonet surface observations can improve prediction of the hurricane track and structure through modifying low-level thermal and dynamical fields such as wind, humidity, and temperature and enhancing low-level convergence and vorticity. However, assimilation of single-level surface observations alone does not ensure reasonable intensity forecasts because of the lack of constraint on the mid- to upper troposphere. When surface observations are assimilated with other conventional data, obvious enhancements are found in the forecasts of track and intensity, realistic convection, and surface wind structures. More importantly, surface data assimilation results in significant improvements in quantitative precipitation forecasts (QPFs) during landfalls.

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