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Observation Bias Correction with an Ensemble Kalman Filter
, 2007
"... This paper considers the use of an ensemble Kalman filter to correct satellite radiance observations for state dependent biases relative to the observation operator in use. Our approach is to use statespace augmentation to estimate satellite biases as part of the ensemble data assimilation procedu ..."
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This paper considers the use of an ensemble Kalman filter to correct satellite radiance observations for state dependent biases relative to the observation operator in use. Our approach is to use statespace augmentation to estimate satellite biases as part of the ensemble data assimilation procedure. We illustrate our approach by applying it to a particular ensemble scheme, the Local Ensemble Transform Kalman Filter (LETKF), to assimilate simulated biased AIRS brightness temperature observations on the Simplified Parameterizations, primitivEEquation DYnamics (SPEEDY) model. The bias parameters estimated by LETKF successfully reduce both the observation bias and analysis error. 1
8 Approximating optimal state estimation
, 2006
"... Minimising forecast error requires accurately specifying the initial state from which the forecast is made by optimally using available observing resources to obtain the most accurate possible analysis. The Kalman filter accomplishes this for linear systems and experience shows that the extended Kal ..."
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Minimising forecast error requires accurately specifying the initial state from which the forecast is made by optimally using available observing resources to obtain the most accurate possible analysis. The Kalman filter accomplishes this for linear systems and experience shows that the extended Kalman filter also performs well in nonlinear systems. Unfortunately, the Kalman filter and the extended Kalman filter require computation of the time dependent error covariance matrix which presents a daunting computational burden. However, the dynamically relevant dimension of the forecast error system is generally far smaller than the full state dimension of the forecast model which suggests the use of reduced order error models to obtain near optimal state estimators. A method is described and illustrated for implementing a Kalman filter on a reduced order approximation of the forecast error system. This reduced order system is obtained by balanced truncation of the Hankel operator representation of the full error system. As an example application a reduced order Kalman filter is constructed for a timedependent quasigeostrophic storm track model. The accuracy of the state identification by the reduced order Kalman filter is assessed and comparison made with the state estimate obtained by the full Kalman filter and with the estimate obtained using an approximation to 4DVar. The accuracy assessment is facilitated by formulating the state estimation methods as observer systems. A practical approximation to the reduced order Kalman filter that utilises 4DVar algorithms is examined.
Dust Storm Ensemble Forecast Experiments in East Asia
, 2008
"... The ensemble Kalman filter (EnKF), as a unified approach to both data assimilation and ensemble forecasting problems, is used to investigate the performance of dust storm ensemble forecasting targeting a dust episode in the East Asia during 23–30 May 2007. The errors in the input wind field, dust em ..."
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The ensemble Kalman filter (EnKF), as a unified approach to both data assimilation and ensemble forecasting problems, is used to investigate the performance of dust storm ensemble forecasting targeting a dust episode in the East Asia during 23–30 May 2007. The errors in the input wind field, dust emission intensity, and dry deposition velocity are among important model uncertainties and are considered in the model error perturbations. These model errors are not assumed to have zeromeans. The model error means representing the model bias are estimated as part of the data assimilation process. Observations from a LIDAR network are assimilated to generate the initial ensembles and correct the model biases. The ensemble forecast skills are evaluated against the observations and a benchmark/control forecast, which is a simple model run without assimilation of any observations. Another ensemble forecast experiment is also performed without the model bias correction in order to examine the impact of the bias correction. Results show that the ensemblemean, as deterministic forecasts have substantial improvement over the control forecasts and correctly captures the major dust arrival and cessation timing at each observation site. However, the forecast skill decreases as the forecast lead time increases. Bias correction further improved the forecasts in down wind areas. The forecasts within 24 hours are most improved and better than those without the bias correction. The examination of the ensemble forecast skills using the Brier scores and the relative operating characteristic curves and areas indicates that the ensemble forecasting system has useful forecast skills.
Application of Generalized Stability Theory to Deterministic and Statistical Prediction
"... Understanding of the stability of deterministic and stochastic dynamical systems has evolved recently from a traditional grounding in the system’s normal modes to a more comprehensive foundation in the system’s propagator and especially in an appreciation for the role of nonnormality of the dynamic ..."
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Understanding of the stability of deterministic and stochastic dynamical systems has evolved recently from a traditional grounding in the system’s normal modes to a more comprehensive foundation in the system’s propagator and especially in an appreciation for the role of nonnormality of the dynamical operator in determining the system’s stability as revealed through the propagator. This set of ideas which approach stability analysis from a nonmodal perspective will be referred to as Generalized Stability Theory (GST). Some applications of GST to deterministic and statistical forecast are discussed in this review. Perhaps the most familiar of these applications is identifying initial perturbations resulting in greatest error in deterministic error systems which is in use for ensemble and targeting applications. But of increasing importance is elucidating the role of temporally distributed forcing along the forecast trajectory and obtaining a more comprehensive understanding of the prediction of statistical quantities beyond the horizon of deterministic prediction. The optimal growth concept can be extended to address error growth in nonautonomous systems in which the fundamental mechanism producing error growth can be identified with the necessary nonnormality of the system. The influence of model error in both the forcing and the system is examined using the methods of stochastic dynamical systems theory. In this review deterministic and statistical prediction, that is forecast and climate prediction, are separately discussed. 1
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, 2015
"... www.atmoschemphys.net/15/8631/2015/ doi:10.5194/acp1586312015 © Author(s) 2015. CC Attribution 3.0 License. Improvement of climate predictions and reduction of their uncertainties using learning algorithms ..."
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www.atmoschemphys.net/15/8631/2015/ doi:10.5194/acp1586312015 © Author(s) 2015. CC Attribution 3.0 License. Improvement of climate predictions and reduction of their uncertainties using learning algorithms