Boundary Conditions for Limited-Area Ensemble Kalman Filters

Ryan D. Torn University of Washington, Seattle, Washington

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Gregory J. Hakim University of Washington, Seattle, Washington

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Chris Snyder National Center for Atmospheric Research,* Boulder, Colorado

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Abstract

One aspect of implementing a limited-area ensemble Kalman filter (EnKF) involves the specification of a suitable ensemble of lateral boundary conditions. Two classes of methods to populate a boundary condition ensemble are proposed. In the first class, the ensemble of boundary conditions is provided by an EnKF on a larger domain and is approximately a random draw from the probability distribution function for the forecast (or analysis) on the limited-area domain boundary. The second class perturbs around a deterministic estimate of the state using assumed spatial and temporal covariance relationships. Methods in the second class are relatively flexible and easy to implement. Experiments that test the utility of these methods are performed for both an idealized low-dimensional model and limited-area simulations using the Weather Research and Forecasting (WRF) model; all experiments employ simulated observations under the perfect model assumption. The performance of the ensemble boundary condition methods is assessed by comparing the results of each experiment against a control “global” EnKF that extends beyond the limited-area domain. For all methods tested, results show that errors for the limited-area EnKF are larger near the lateral boundaries than those from a control EnKF, but decay inside the limited-area domain so that errors there are comparable to the control case. The relatively larger errors near the boundaries in the limited-area EnKF originate from not assimilating observations outside the limited-area domain and, in the second class of methods, from deficiencies in boundary spatial and temporal covariances. Overall, these experiments suggest that for observation densities typical in numerical weather prediction models, ensemble boundary conditions can be specified in the absence of a global ensemble without significant penalty in the domain interior by perturbing around an ensemble mean.

Corresponding author address: Ryan D. Torn, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640. Email: torn@atmos.washington.edu

Abstract

One aspect of implementing a limited-area ensemble Kalman filter (EnKF) involves the specification of a suitable ensemble of lateral boundary conditions. Two classes of methods to populate a boundary condition ensemble are proposed. In the first class, the ensemble of boundary conditions is provided by an EnKF on a larger domain and is approximately a random draw from the probability distribution function for the forecast (or analysis) on the limited-area domain boundary. The second class perturbs around a deterministic estimate of the state using assumed spatial and temporal covariance relationships. Methods in the second class are relatively flexible and easy to implement. Experiments that test the utility of these methods are performed for both an idealized low-dimensional model and limited-area simulations using the Weather Research and Forecasting (WRF) model; all experiments employ simulated observations under the perfect model assumption. The performance of the ensemble boundary condition methods is assessed by comparing the results of each experiment against a control “global” EnKF that extends beyond the limited-area domain. For all methods tested, results show that errors for the limited-area EnKF are larger near the lateral boundaries than those from a control EnKF, but decay inside the limited-area domain so that errors there are comparable to the control case. The relatively larger errors near the boundaries in the limited-area EnKF originate from not assimilating observations outside the limited-area domain and, in the second class of methods, from deficiencies in boundary spatial and temporal covariances. Overall, these experiments suggest that for observation densities typical in numerical weather prediction models, ensemble boundary conditions can be specified in the absence of a global ensemble without significant penalty in the domain interior by perturbing around an ensemble mean.

Corresponding author address: Ryan D. Torn, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640. Email: torn@atmos.washington.edu

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