Dee DP, Gaspari G, Redder C, et al., 1999b. Maximum-likelihood estimation of forecast and observation error covariance parameters. Part II: Applications, Mon Weather Rev127 (8), 1835-1849.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the random vector z 1;0 ( is given in Appendix A.1. To use the methods here, a small set of the most important and relatively unaliased free parameters (here ; must be isolated and the models tuned appropriately. Maximum likelihood estimates of certain parameters may also be considered, see Dee, Gaspari, Redder, Rukhovets daSilva (1998). However, we believe that that our present conclusions are relatively robust to reasonable changes in the model used here. 6.2 Three space dimensions A vertical coordinate may be included, which may be discrete or continuous, depending on the application. Santer et al. 1996) Tett et al. ....

Dee, D., Gaspari, G., Redder, C., Rukhovets, L. & daSilva, A. (1998), `Maximum-likelihood estimation of forecast and observation error covariance parameters. part ii: Applications', Monthly Weather Review in press, xx{xx.

....subject of future articles. Covariance functions developed in this article have been successfully tuned to observed data using the maximum likelihood estimation procedure developed by Dee (1995) and the generalized cross validation technique of Wahba (1990, Ch. 4) These results are reported in Dee and da Silva (1998) and Dee et al. 1998) 2 Background Material The purpose of this section is to summarize notation, definitions, and a variety of known results pertinent to correlation function modeling on R 3 and subsets of R 3 . The general context of this summary is the correlation theory of real valued ....

....Covariance functions developed in this article have been successfully tuned to observed data using the maximum likelihood estimation procedure developed by Dee (1995) and the generalized cross validation technique of Wahba (1990, Ch. 4) These results are reported in Dee and da Silva (1998) and Dee et al. 1998). 2 Background Material The purpose of this section is to summarize notation, definitions, and a variety of known results pertinent to correlation function modeling on R 3 and subsets of R 3 . The general context of this summary is the correlation theory of real valued (that is, scalar) ....

Dee, D. P., and da Silva, A. M., 1998, Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I: Methodology: Submitted to Mon. Wea.

....We remark that both the GCV and GML estimate can be defined when K is nonlinear. In either the linear or nonlinear case the trace of A may be estimated by the randomized trace method without having A explicitly, given a black box which produces Kx given y, see Wahba, Johnson, Gao Gong (1995) Dee daSilva (1998) and Dee, Gaspari, Redder, Rukhovets daSilva (1998) have used maximum likelihood methods to estimate parameters in forecast error covariances in several practical examples, and have compared some of the results with GCV estimates, obtaining generally similar results in the examples tried. It may ....

....and GML estimate can be defined when K is nonlinear. In either the linear or nonlinear case the trace of A may be estimated by the randomized trace method without having A explicitly, given a black box which produces Kx given y, see Wahba, Johnson, Gao Gong (1995) Dee daSilva (1998) and Dee, Gaspari, Redder, Rukhovets daSilva (1998) have used maximum likelihood methods to estimate parameters in forecast error covariances in several practical examples, and have compared some of the results with GCV estimates, obtaining generally similar results in the examples tried. It may be possible to combine the strengths of both methods ....

Dee, D., Gaspari, G., Redder, C., Rukhovets, L. & daSilva, A. (1998), `Maximum-likelihood estimation of forecast and observation error covariance parameters. part ii: Applications', Monthly Weather Review in press, xx--xx.

....; 32. The analysis system operates under the null hypothesis v N (0; S) 22) with S ij = 1; for i = j, 1 2 e 0:2(i j) 2 ; otherwise. 23) This simple model represents residuals with a spatially uncorrelated observation error component and a correlated forecast error component; see Dee and da Silva 1999. The actual residuals, however, are distributed according to v N b; 2 S ; 24) with b j = 2 sin j 32 ; 25) 2: 26) Here b represents a bias in the residual, and is a noise ampli cation factor. Both b and are unknown to the algorithm. This type of situation can easily ....

....for the SQC consists of observed minus forecast residuals and a preliminary estimate of their variances, derived from prescribed error statistics for the global analysis system. Observation error standard deviations for most GEOS DAS data types were estimated using maximum likelihood techniques (Dee and da Silva 1999; Dee et al. 1999) Forecast error standard deviations currently used in GEOS DAS are global, spatially variable estimates based on monthly statistics of rawinsonde and TOVS observed minus forecast height residuals (DAO 1996) 3.1 The background check The SQC rst performs a simple background ....

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Dee, D. P., and A. M. da Silva, 1999: Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I: Methodology. Mon. Wea. Rev., 124, 1822-1834.

.... Omega v k v T k ff = H k P f k H T k H k P b k H T k R k ; 17) where we used (A.3,A.5,A. 6) This relation between the data and the covariance models provides the basis for estimating parameters of P f k , P b k , and R k by, for example, maximum likelihood techniques (Dee 1995; Dee and da Silva 1999). Parameters of forecast and bias estimation error covariances are probably not separately identifiable, so that a model such as (7) will still be needed to close the problem. 4 Implementation in GEOS As a first test of on line forecast bias estimation and correction in an operational data ....

....errors are assumed uncorrelated in space and time, while forecast error correlations are represented by a separable function of horizontal distance and pressure. The variances and correlation parameters have been estimated from observed minus forecast residuals by maximum likelihood techniques (Dee et al. 1999). Clearly, these exceedingly simple models leave ample room for improvement. 4.2 Description of GEOS UNB The experimental system GEOS UNB is identical to GEOS 2.8 in all respects, except that the two step algorithm (3,4) replaces the moisture analysis equation (1) Both steps are solved with ....

Dee, D. P., and A. M. da Silva, 1999: Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I: Methodology.

....constant in operational data assimilation systems in fact vary significantly with time. This may well reflect the use of overly simplistic covariance models that cannot adequately describe state dependent error components such as representativeness error. The Corresponding author: Dr. Dick P. Dee, NASA GSFC Data Assimilation Office, Mail Code 910.3, Greenbelt, MD 20771, USA (dee dao.gsfc.nasa.gov) y Monthly Weather Review, in press. sensitivity of the parameter estimates to the treatment of bias, and to the choice of the model representing spatial correlations, is examined in detail. Several experiments emulate an on line covariance ....

Dee, D. P., and A. M. da Silva, 1998b: Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I: Methodology.

....concerns the estimation of unknown forecast and observation error covariance parameters for an atmospheric data assimilation system from observational residuals. The method we present is based on maximum likelihood covariance parameter estimation as described by Dee (1995) In a companion paper (Dee et al. 1998, hereafter referred to as Part II) we describe three different applications, involving univariate as well as multivariate covariance models, and data from both stationary and moving observing systems. The simplest example of a covariance parameter which is required for atmospheric data ....

....hv k i b o k Gamma H k b f k ; 17) Omega (v k Gamma hv k i) v k Gamma hv k i) T ff R k Gamma X k H T k Gamma H k X T k H k P f k H T k : 18) We used the additional approximation hH k Delta i H k h Delta i; both (17) and (18) are exact for linear observation operators. Dee and da Silva (1998) show how the mean equation (17) can be used to estimate forecast bias in a statistical data assimilation system, using unbiased (or bias corrected) observations. They also discuss, in general terms, the implications of using biased forecasts and or biased observations in an analysis system. For ....

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Dee, D. P., G. Gaspari, C. Redder, L. Rukhovets, and A. M. da Silva, 1998: Maximum-likelihood estimation of forecast and observation error covariance parameters. Part II: Applications. Mon. Wea. Rev., this issue.

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Dee DP, Gaspari G, Redder C, et al., 1999b. Maximum-likelihood estimation of forecast and observation error covariance parameters. Part II: Applications, Mon Weather Rev127 (8), 1835-1849.

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Dee DP, da Silva AM , 1999a. Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I: Methodology, Mon Weather Rev,127 (8), 1822-1834.

No context found.

Dee DP, Gaspari G, Redder C, et al., 1999b: Maximum-likelihood estimation of forecast and observation error covariance parameters. Part II: Applications, Mon Weather Rev127 (8), 1835-1849.

No context found.

Dee DP, da Silva AM , 1999a: Maximum-likelihood estimation of forecast and observation error covariance parameters. Part I: Methodology, Mon Weather Rev,127 (8), 1822-1834.

No context found.

Soc. 123, 2449--2461. Dee, D. & daSilva, A. (1998), `Maximum-likelihood estimation of forecast and observation error covariance parameters. part i: Methodology', Monthly Weather Review in press, xx--xx.

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