Error covariance sensitivity and impact estimation with adjoint 4D‐Var: theoretical aspects and first applications to NAVDAS‐AR

Daescu, Dacian N.; Langland, Rolf H.

doi:10.1002/qj.1943

Cited by 23 publications

(23 citation statements)

References 69 publications

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“…The above function can be used for GPS-RO error variance retuning. The suggestion that observations should be given more weight where they are known to have a large positive impact is in line with the findings of Daescu and Langland (2013a). However, the present results are more stringent because they imply correlations between the mean FER and mean FSR in the vertical interval between 10 and 20 km.…”

Section: Resultssupporting

confidence: 89%

“…Recently, Daescu (2008), Daescu and Todling (2010) and Daescu and Langland (2013a, 2013b) have derived and computed the sensitivity of the forecast error to the observation error variance. This measure depends on the forecast error, K T , the residuals ( y − H x a ) and the observations number.…”

Section: Data Assimilation Diagnostic Toolsmentioning

confidence: 99%

“…In particular, the sensitivity with respect to the observation error variance offers guidance for tuning the variances. Recently, Daescu and Todling (2010) and Daescu and Langland (2013a, 2013b) have shown how the forecast sensitivity to the observation error variance can be computed and variances accordingly tuned.…”

Section: Introductionmentioning

confidence: 99%

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Impact of GPS radio occultation measurements in the ECMWF system using adjoint‐based diagnostics

Cardinali

Healy

2014

Quart J Royal Meteoro Soc

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In this article, a comprehensive assessment of the impact of radio occultation (RO) observations in the operational ECMWF assimilation and forecast system is presented using different diagnostic tools. In particular, the observations' influence in the assimilation process and the related contribution to the short‐range forecast error of radio occultation observations is evaluated with recently developed diagnostic tools based on the adjoint version of the assimilation and forecast model. The sensitivity with respect to observation error variances is also evaluated for the assimilated observations. GPS‐RO is found to have the largest mean influence among satellite observations in the analysis. It is the fourth best satellite system for analysis information content and the second largest satellite contributor together with IASI and AIRS to decreasing the 24 h forecast error. For the whole observing system, with the exception of radiosondes and polar atmospheric motion vectors, the forecast error sensitivity to the observation error variance indicates that a deflation of the assumed observation errors would improve the forecast skill. For RO observations at all vertical levels, but predominantly between 10 and 20 km, a deflation of the observation error variance is suggested. Interestingly, the sensitivity computation recommends reducing the assumed errors mostly in layers where the weight given to GPS‐RO data is quite large.

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Section: Resultssupporting

confidence: 89%

Section: Data Assimilation Diagnostic Toolsmentioning

confidence: 99%

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Impact of GPS radio occultation measurements in the ECMWF system using adjoint‐based diagnostics

Cardinali

Healy

2014

Quart J Royal Meteoro Soc

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“…We also note that the covariance diagnostics (1) and (2) are used for online estimation of observation and model error variances in ensemble Kalman filters (EnKF) (Li et al, 2009) and to scale the background-error covariance in EnKF (Desroziers et al, 2009b). The diagnostics in observation space are also used in the analysis sensitivity by calculating the degree of freedom of the signal (Fisher, 2003;Lupu et al, 2011;Chapnik et al, 2006), as well as in forecast sensitivity to observation and background errors by Daescu and Langland (2013).…”

Section: Introductionmentioning

confidence: 99%

Error covariance estimation methods based on analysis residuals: theoretical foundation and convergence properties derived from simplified observation networks

Ménard

2015

Quart J Royal Meteoro Soc

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We examine the theoretical foundation of the method to estimate error covariances based on analysis residuals in observation space, also known as the Desroziers method. Our analysis also includes a method based on a posteriori diagnostics of variational analysis schemes. A mathematical analysis of convergence is carried out with a simplified regular observation network, where we identify stable and unstable fixed‐point solutions, examine their rate of convergence and the conditions for convergence to the truth and compare it with maximum‐likelihood estimation. It is shown that the estimation of variance parameters converges to the truth if the error correlation is specified correctly. The convergence is much faster with the analysis increment method than with the method designed for variational analysis schemes. We also propose a combination of the Desroziers scheme and the maximum‐likelihood estimation method that could be used to estimate the spatial correlation length‐scale of observation errors. The estimation of both full observation and background‐error covariances matrices derived entirely from observation‐based residuals does not change the gain matrix, but the estimation of either one matrices is well‐defined. An analysis of the estimation of the full observation error covariance matrix using a regular observation network reveals that if all eigenvalues of the prescribed background‐error covariance are smaller than their corresponding innovation covariance eigenvalue, then the estimated error covariance converges to the truth but only if the prescribed background error is correctly specified. In the case where some eigenvalues of the background‐error covariance greatly exceed those of the innovation covariance, the convergent observation‐error matrix may become rank‐deficient. Its inverse does not exist.

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“…In some cases the input is an observation, an entire class of observations, or the specification of background errors in data assimilation, whose effect is of interest. Approaches based on adjoints, and ensembles, or both have been proposed for performing SA (Ancell and Hakim 2007;Daescu and Langland 2013;Davis and Emanuel 1991;Gombos and Hansen 2008;Hacker et al 2011;Torn and Hakim 2008).…”

Section: Introductionmentioning

confidence: 99%

Variance-Based Sensitivity Analysis: Preliminary Results in COAMPS

Marzban

Sandgathe

Doyle

et al. 2014

Monthly Weather Review

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Numerical weather prediction models have a number of parameters whose values are either estimated from empirical data or theoretical calculations. These values are usually then optimized according to some criterion (e.g., minimizing a cost function) in order to obtain superior prediction. To that end, it is useful to know which parameters have an effect on a given forecast quantity, and which do not. Here the authors demonstrate a variance-based sensitivity analysis involving 11 parameters in the Coupled Ocean-Atmosphere Mesoscale Prediction System (COAMPS). Several forecast quantities are examined: 24-h accumulated 1) convective precipitation, 2) stable precipitation, 3) total precipitation, and 4) snow. The analysis is based on 36 days of 24-h forecasts between 1 January and 4 July 2009. Regarding convective precipitation, not surprisingly, the most influential parameter is found to be the fraction of available precipitation in the Kain-Fritsch cumulus parameterization fed back to the grid scale. Stable and total precipitation are most affected by a linear factor that multiplies the surface fluxes; and the parameter that most affects accumulated snow is the microphysics slope intercept parameter for snow. Furthermore, all of the interactions between the parameters are found to be either exceedingly small, or have too much variability (across days and/or parameter values) to be of primary concern AU1.

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Error covariance sensitivity and impact estimation with adjoint 4D‐Var: theoretical aspects and first applications to NAVDAS‐AR

Cited by 23 publications

References 69 publications

Impact of GPS radio occultation measurements in the ECMWF system using adjoint‐based diagnostics

Impact of GPS radio occultation measurements in the ECMWF system using adjoint‐based diagnostics

Error covariance estimation methods based on analysis residuals: theoretical foundation and convergence properties derived from simplified observation networks

Variance-Based Sensitivity Analysis: Preliminary Results in COAMPS

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