Optimality of variational data assimilation and its relationship with the Kalman filter and smoother

Li, Zhijin; Navon, I. M.

doi:10.1002/qj.49712757220

Cited by 100 publications

(69 citation statements)

References 50 publications

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“…Other examples are shown in Rabier et al (1997). The implied B-matrix propagation is believed to hold generally in 4d-VAR, which is connected to the equivalence of 4d-VAR to the Kalman smoother (Ménard and Daley, 1996;Li and Navon, 2001;Fisher, Leutbecher and Kelly, 2005), which holds under special conditions (i.e. linear observation operators, linear forecast model, and the same background error covariance matrix at the start of the assimilation).…”

Section: Note About Background Error Propagation In 4d-varmentioning

confidence: 99%

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

Bannister

2008

Quart J Royal Meteoro Soc

201

172

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This article reviews the characteristics of forecast error statistics in meteorological data assimilation from the substantial literature on this subject. It is shown how forecast error statistics appear in the data assimilation problem through the background error covariance matrix, B. The mathematical and physical properties of the covariances are surveyed in relation to a number of leading systems that are in use for operational weather forecasting. Different studies emphasize different aspects of B, and the known ways that B can impact the assimilation are brought together. Treating B practically in data assimilation is problematic. One such problem is in the numerical measurement of B, and five calibration methods are reviewed, including analysis of innovations, analysis of forecast differences and ensemble methods. Another problem is the prohibitive size of B. This needs special treatment in data assimilation, and is covered in a companion article (Part II). Examples are drawn from the literature that show the univariate and multivariate structure of the B-matrix, in terms of variances and correlations, which are interpreted in terms of the properties of the atmosphere. The need for an accurate quantification of forecast error statistics is emphasized.

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Section: Note About Background Error Propagation In 4d-varmentioning

confidence: 99%

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

Bannister

2008

Quart J Royal Meteoro Soc

201

172

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“…In fact, oceanographic observations are commonly collected at asynchronous times. For this reason, in variational data assimilation, the past asynchronous observations are simultaneously used to minimize the cost function that measures the weighted difference between background states and observations over the time interval, and identify the best estimate of the initial state condition (Drecourt, 2004;Ide et al, 1997;Li and Navon, 2001). In addition to the 3D-Var and 4D-Var methods, Hunt et al (2004) proposed a four-dimensional ensemble Kalman filter (4DEnKF) which adapts EnKF to handle observations that have occurred at non-assimilation times.…”

Section: Introductionmentioning

confidence: 99%

Can assimilation of crowdsourced data in hydrological modelling improve flood prediction?

Mazzoleni

Verlaan

Alfonso

et al. 2017

Hydrol. Earth Syst. Sci.

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Abstract. Monitoring stations have been used for decades to properly measure hydrological variables and better predict floods. To this end, methods to incorporate these observations into mathematical water models have also been developed. Besides, in recent years, the continued technological advances, in combination with the growing inclusion of citizens in participatory processes related to water resources management, have encouraged the increase of citizen science projects around the globe. In turn, this has stimulated the spread of low-cost sensors to allow citizens to participate in the collection of hydrological data in a more distributed way than the classic static physical sensors do. However, two main disadvantages of such crowdsourced data are the irregular availability and variable accuracy from sensor to sensor, which makes them challenging to use in hydrological modelling. This study aims to demonstrate that streamflow data, derived from crowdsourced water level observations, can improve flood prediction if integrated in hydrological models. Two different hydrological models, applied to four case studies, are considered. Realistic (albeit synthetic) time series are used to represent crowdsourced data in all case studies. In this study, it is found that the data accuracies have much more influence on the model results than the irregular frequencies of data availability at which the streamflow data are assimilated. This study demonstrates that data collected by citizens, characterized by being asynchronous and inaccurate, can still complement traditional networks formed by few accurate, static sensors and improve the accuracy of flood forecasts.

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“…In theory, it is possible to fully transfer information from the previous assimilation time window to the next via the background term (Li and Navon(2001) [20]. This allows specification of background error covariance matrix at the beginning of assimilation window.…”

Section: Introductionmentioning

confidence: 99%

The Impact of Background Error on Incomplete Observations for 4D-Var Data Assimilation with the FSU GSM

Navon

Daescu

Liu

2005

Lecture Notes in Computer Science

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In the study of 4D Var data assimilation of atmospheric models, an important issue to address is the case of incomplete observations in either space or time dimensions.To assess the impact of incomplete observations on the 4D Var data assimilation, we carried out assimilation experiments with dynamical core the new FSU GSM consisting of a T126L14 global spectral model in a parallel environment using MPI version of its adjoint model. This was done by reducing the number of observations in both the space and time dimensions respectively. The impact of the J b background error covariance term on the problem of incomplete observations in either time or space direction has been investigated Numerical experiments were carried out as follows: first, a twin experiment with observations available at every model grid point (thereafter referred to complete observations) was carried out to ensure that the assimilation system was well constructed, followed by a reduction in the available observations to every 2, 4 or 8 spatial grid points, respectively. Another set of experiments was carried out with data void areas where observations were missing at all ocean grid points locations.Similar experiments reducing the number of time instants where observations are available in the window of assimilation were also done. * Supported by N.S.F. Grant ATM-0201808 1The results obtained show that spatial incomplete observations lead to a slow down in the cost functional minimization. The impact of incomplete observations was even more pronounced for experiments where no observations were available over the southern oceans, in which case the lack of fit between a control run and the aforementioned could not be reduced.In contrast to above results, experiments involving reduction of the number of time instants where observations are available in the assimilation window allowed a successful retrieval of the initial data.To further investigate the issue of incomplete observations, we carried out another set of experiments by including the background term J b to the cost function. The background error covariance matrix was found to control the way in which information is spread from the observations and to provide statistically consistent increments at neighboring grid points.Impact of various scenarios of incomplete observations on ensuing forecasts, and root mean square error were investigated for 24-72h model forecasts for cases when the cost functional with included and/or excluded the background covariance term.

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Optimality of variational data assimilation and its relationship with the Kalman filter and smoother

Cited by 100 publications

References 50 publications

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

Can assimilation of crowdsourced data in hydrological modelling improve flood prediction?

The Impact of Background Error on Incomplete Observations for 4D-Var Data Assimilation with the FSU GSM

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