A hybrid 3-dimensional variational (3D-Var) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfect-model assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by computing a set of parallel data assimilation cycles, with each member of the set receiving unique perturbed observations. The perturbed observations are generated by adding random noise consistent with observation error statistics to the control set of observations. Background error statistics for the data assimilation are estimated from a linear combination of time-invariant 3D-Var covariances and flow-dependent covariances developed from the ensemble of short-range forecasts. The hybrid scheme allows the user to weight the relative contributions of the 3D-Var and ensemble-based background covariances. The analysis scheme was cycled for 90 days, with new observations assimilated every 12 h...

this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a significant improvement in the EnKF results, using the same number of members in the ensemble

This work studies the effect of using Monte Carlo based methods to estimate high-dimensional systems. Recent focus in the geosciences has been on representing the atmospheric state using a probability density function, and, for extremely high-dimensional systems, various sample based Kalman filter techniques have been developed to address the problem of real-time assimilation of system information and observations. As the employed sample sizes are typically several orders of magnitude smaller than the system dimension, such sampling techniques inevitably induces considerable variability into the state estimate, primarily through prior and posterior sample covariance matrices. In this article we quantify this variability with mean squared error measures for two Monte-Carlo based Kalman filter variants, the ensemble Kalman filter and the square-root filter. Under weak assumptions, we derive exact expressions of the error measures. In other cases, we rely on matrix expansions and provide approximations. We show that covariance-shrinking (tapering) based on the Schur product of the prior sample covariance matrix and a positive definite function is a simple, computationally feasible, and very effective technique to reduce sample variability and to address rank-deficient sample covariances. We propose practical rules for obtaining optimally tapered sample covariance matrices. The theoretical results are verified and illustrated with extensive simulations.

[1] Many geophysical problems are characterized by high-dimensional, nonlinear systems and pose difficult challenges for real-time data assimilation (updating) and forecasting. The present work builds on the ensemble Kalman filter (EnsKF), with the goal of producing ensemble filtering techniques applicable to non-Gaussian densities and highdimensional systems. Three filtering algorithms, based on representing the prior density as a Gaussian mixture, are presented. The first, referred to as a mixture ensemble Kalman filter (XEnsF), models local covariance structures adaptively using nearest neighbors. The XEnsF is effective in a three-dimensional system, but the required ensemble grows rapidly with the dimension and, even in a 40-dimensional system, we find the XEnsF to be unstable and inferior to the EnsKF for all computationally feasible ensemble sizes. A second algorithm, the local-local ensemble filter (LLEnsF), combines localizations in physical as well as phase space, allowing the update step in high-dimensional systems to be decomposed into a sequence of lower-dimensional updates tractable by the XEnsF. Given the same prior forecasts in a 40-dimensional system, the LLEnsF update produces more accurate state estimates than the EnsKF if the forecast distributions are sufficiently

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It has been widely realized that Monte Carlo methods (approximation via a sample ensemble) may fail in large scale systems. This work offers some theoretical insight into this phenomenon in the context of the particle filter. We demonstrate that the maximum of the weights associated with the sample ensemble converges to one as both the sample size and the system dimension tends to infinity. Specifically, under fairly weak assumptions, if the ensemble size grows sub-exponentially in the cube root of the system dimension, the convergence holds for a single update step in state-space models with independent and identically distributed kernels. Further, in an important special case, more refined arguments show (and our simulations suggest) that the convergence to unity occurs unless the ensemble grows super-exponentially in the system dimension. The weight singularity is also established in models with more general multivariate like-lihoods, e.g. Gaussian and Cauchy. Although presented in the context of atmospheric data assimilation for numerical weather prediction, our results are generally valid for high-dimensional particle filters. 1 1

This paper describes the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme and its implementa-tion on the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) model at the University of Maryland. Numerical results are shown for both simulated observations and observations of the real atmosphere. The role of flow-dependent information in data assimilation is discussed based on the results of the numerical experiments. Preliminary assimilation results with AMSU-A radiance observations are also presented. 1

We formulate a four dimensional Ensemble Kalman Filter (4D-LETKF) that minimizes a cost function similar to that in a 4D-VAR method. Using per-fect model experiments with the Lorenz-96 model, we compare assimilation of simulated asynchronous observations with 4D-VAR and 4D-LETKF. We find that both schemes have comparable error when 4D-LETKF is performed sufficiently frequently and when 4D-VAR is performed over a sufficiently long analysis time window. We explore how the error depends on the time between analyses for 4D-LETKF and the analysis time window for 4D-VAR. 1

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients which can be approximated from prior measurements of wildfires. An Ensemble Kalman Filter technique is then used to assimilate temperatures measured at selected points into running wildfire simulations. The assimilation technique is able to modify the simulations to track the measurements correctly even if the simulations were started with an erroneous ignition location that is quite far away from the correct one.

Abstract. We report on an ongoing effort to build a Dynamic Data Driven Application System (DDDAS) for short-range forecast of weather and wildfire behavior from real-time weather data, images, and sensor streams. The system changes the forecast as new data is received. We encapsulate the model code and apply an ensemble Kalman filter in time-space with a highly parallel implementation. In this paper, we discuss how we will demonstrate that our system works using a DDDAS testbed approach and data collected from an earlier fire. 1