, N. S. Sivakumaran, & R. Todling, 1994: A fixed-lag Kalman smoother for retrospective data assimilation. Mon. Wea. Rev., 122, 2838--2867.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....estimate at the final time will be identical for the smoother and the filter, as one would expect. At all previous times it will be suboptimal since future observations have not been used to define the estimate. 2. 3 A Lagged Smoother It is also possible to define a lagged smoother (see e.g. Cohn et al. 1994). This is an approach which is normally used for reducing the CPU requirements and it is based on the assumption that the observations at time t k will only influence the estimate in an interval t 2 [t k Gamma t lag ; t k ] In practical applications t lag would typically be a few times the ....

Cohn, S. E., N. S. Sivakumaran, and R. Todling, A fixed-lag Kalman smoother for retrospective data assimilation, Mon. Weather Rev., 122, 2838--2867, 1994.

.... Talagrand and Vasiljevic (1993) Zou, Navon and Sela (1993) Under some assumptions the solution of the 4D Var problem with the model as a weak strong constraint can be shown to be equivalent to a Kalman smoother with model error without model error, see Thepaut, Hoffman and Courtier (1993) Cohn, Sivakumaran and Todling (1994). We include terms which govern the fit of the analysis to the data and to the forecast, and a smoothness (read balance ) penalty term. In the weak constraint case we also include a penalty term which governs the closeness of the analysis to the model. The strong constraint case here forces the ....

.... Recently several authors have GONG, WAHBA, JOHNSON and TRIBBIA July 22, 1996 proposed simplified versions of the forecast error covariance prescribed by KF theory, and then have derived or estimated a small number of coefficients in this covariance, see for example Cohn (1993) Todling and Cohn (1994) and references there. Model error covariances are in theory part of the KF equations but are not easy to specify realistically. Recent work in the development of model error covariances includes Daley (1992) Mitchell and Daley (1995a,b) In particular Mitchell and Daley (1995b) note that ....

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Cohn, S., Sivakumaran, N. & Todling, R. (1994), `A fixed-lag Kalman smoother for retrospective data assimilation', Mon. Wea. Rev. 122, 2838--2867.

....a Linear Shallow Water Model Let us now examine the results of the fixed lag Kalman smoother applied to the linear shallow water model of the previous section. The interest here is to improve up on previously calculated filter analysis by using data past the analysis time. Following Cohn et al. [35], we consider the case of the A network introduced above, but to show the more stringent results from that work we consider the case in which only the western half of the radiosondes are used in the assimilation experiments. Figure 9.5 displays the time evolution of the domain averaged ....

, N. S. Sivakumaran, & R. Todling, 1994: A fixed-lag Kalman smoother for retrospective data assimilation. Mon. Wea. Rev., 122, 2838--2867.

....weather forecast and climate studies. For this purpose, a delay in the production of the analysis is permitted, then one could conceive of more observations becoming available during the delay interval and being used in producing the analysis. Thus the so called retrospective analysis proposed by Cohn et al. 1994), which incorporates future observation data, as well as current and past observation data, would serve the purpose. Because more observations are used in producing the retrospective analysis, it is expected to be more accurate and complete than the filter solution. The problem using both future ....

....model dynamics is termed smoothing problem in estimation theory. Presently, several algorithms have been proposed and tested for the smoothing problems, among which the fixed lag Kalman smoother (FLKS) 4D VAR and 4D PSAS have attracted more and more attention. The FLKS algorithm was proposed by Cohn et al. 1994) as a means to perform the retrospective analysis, and numerical experiments using a two dimensional linear shallow water model were carried out to demonstrate the ability of the FLKS in improving the analysis quality. Further numerical experiments with suboptimal schemes were done by Todling et ....

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Cohn, S.E., N.S. Sivakumaran, and R. Todling, 1994: A fixed-lag Kalman smoother for retrospective data assimilation. Mon. Wea. Rev., 122, 2838--2867.

....Selection with PSAS, 4 2 97 5. To enable flexibility for future developments in data assimilation methodology. The PSAS system was envisioned from the outset to provide a computational framework for the development of techniques for approximate fixed lag Kalman smoothing (Todling et al. 1996, Cohn et al. 1994), approximate Kalman filtering (e.g. Cohn and Todling 1996) forecast bias estimation (Dee and da Silva 1997) and other topics known from the estimation theory literature but not yet implemented in operational data assimilation systems. Solution of the innovation covariance equation, a key ....

Cohn, S. E., N. S. Sivakumaran, and R. Todling, 1994: A fixed-lag Kalman smoother for retrospective data assimilation. Mon. Wea. Rev., 122, 2838--2867.

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