Four-dimensional ensemble Kalman filtering

Hunt, Brian R.; Kalnay, Eugenia; Kostelich, Eric J.; Ott, Edward; Patil, D. J.; Sauer, Tim; Szunyogh, Istvan; Yorke, James A.; Zimin, Aleksey V.

doi:10.3402/tellusa.v56i4.14424

Cited by 144 publications

(134 citation statements)

References 19 publications

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“…While this approach to assimilating asynchronous observations is suitable for any ensemble Kalman filter [23], it is particularly simple to implement in the LETKF framework. We call this extension 4D-LETKF; see [19] for an alternate derivation of this algorithm.…”

Section: Asynchronous Observations: 4d-letkfmentioning

confidence: 99%

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Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Hunt

Kostelich

Szunyogh

2007

Physica D: Nonlinear Phenomena

1,297

1,754

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Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to "forecast" the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, we describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of "ensemble Kalman filter", in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. We discuss both the mathematical basis of this approach and its implementation; our primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble 1 Kalman filtering. We include some numerical results demonstrating the efficiency and accuracy of our implementation for assimilating real atmospheric data with the global forecast model used by the U.S. National Weather Service.

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Section: Asynchronous Observations: 4d-letkfmentioning

confidence: 99%

“…ThenP a = (k − 1) −1 W a (W a ) T , and (13) follows from (23). The use of the symmetric square root to determine W a fromP a (as compared to, for example, a Cholesky factorization, or the choice described in [4]), is important for two main reasons.…”

Section: Letkf: a Local Ensemble Transform Kalman Filtermentioning

confidence: 99%

Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Hunt

Kostelich

Szunyogh

2007

Physica D: Nonlinear Phenomena

1,297

1,754

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“…In this framework, methods to obtain accurate background model error covariance by adding random perturbation to the analysis ensemble perturbation, or applying covariance inflation, are developed. The other approach involves assimilation of observations at times that are different from the assimilation time (Cohn et al, 1994;Evensen and van Leeuwen, 2000;Huang et al, 2002;Hunt et al, 2004). Many researchers working with this framework expect that with the use of future data, in addition to current and past data, the effective amount of data available for each analysis will be doubled, and analysis errors will be reduced.…”

Section: Introductionmentioning

confidence: 99%

“…One approach is to obtain an accurate background error covariance matrix estimated using ensemble spread within the EnKF framework, e.g. Gaussian probability distribution function (pdf) assumptions with linear dynamics (Burgers et al, 1998;Anderson and Anderson, 1999;Evensen, 2003;Hunt et al, 2004). In this framework, methods to obtain accurate background model error covariance by adding random perturbation to the analysis ensemble perturbation, or applying covariance inflation, are developed.…”

Section: Introductionmentioning

confidence: 99%

“…After their initial attempts, Evensen and van Leeuwen (2000) extended the Kalman smoother to ensemble-based initialization referred to as the Ensemble Kalman Smoother (EnKS), and they proved that in a simple Lorenz system, the analysis quality of the EnKS is superior to that of the EnKF. Hunt et al (2004) developed a four-dimensional ensemble Kalman filtering algorithm to unify the Kalman Filter and the four-dimensional variational method (4D-Var). Their key idea was that the analysis value is a linear combination of the ensemble forecasts which best fits the observations within the assimilation window, and the analysis equation was modified to find the weighting coefficients for each forecast ensemble.…”

Section: Introductionmentioning

confidence: 99%

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Growing‐error correction of ensemble Kalman filter using empirical singular vectors

Ham

Kang

2010

Quart J Royal Meteoro Soc

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In this study, a new Ensemble Kalman Filter (EnKF) algorithm called EnKF with growing-error correction (EnKF-GEC) is developed for minimizing the growing component of the forecast error; for this purpose, prospective observations are assimilated using empirical singular vectors (ESVs). Unlike the Ensemble Kalman Smoother (EnKS) or four-dimensional EnKF (4DEnKF), the EnKF-GEC is designed to reduce the analysis error at the last analysis time (errors of initial condition for prediction). By performing assimilation experiments using the CZ-SPEEDY coupled model within a perfect model framework, it is shown that the analysis errors obtained using the EnKF-GEC are significantly reduced as compared to those obtained using the conventional EnKF until the last analysis time as well as during the middle of analysis time. This indicates that the new algorithm is beneficial for prediction. Seasonal prediction results show that the prediction skill when initial conditions are generated by the EnKF-GEC is superior to when initial conditions are generated by the conventional EnKF or EnKS, particularly during the early forecast lead month. For example, correlation skill improvement with 16 ensemble members is about 0.1 for a 3-month lead forecast. In addition, it is shown that the new EnKF algorithm is more effective for unpredictable regions, where the value of the unstable singular vector is robust.

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Observation system simulation experiments using water vapor isotope information

Yoshimura

Miyoshi

Kanamitsu

2014

J. Geophys. Res. Atmos.

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Measurements of water vapor isotopes (δ 18 O and δD) have dramatically increased in recent years with the availability of new spectroscopic technology. To utilize these data more efficiently, this study first developed a new data assimilation system using a local transform ensemble Kalman filter (LETKF) and the Isotope-incorporated Global Spectral Model (IsoGSM). An observation system simulation experiment (OSSE) was then conducted. The OSSE used a synthetic data set of vapor isotope measurements, mimicking Tropospheric Emission Spectrometer (TES)-retrieved δD from the mid-troposphere, SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY)-retrieved δD from the water vapor column, and the virtual Global Network of Isotopes in Precipitation (GNIP)-like surface vapor isotope (both δD and δ 18 O) monitoring network. For TES and SCIAMACHY, we assumed a similar spatiotemporal coverage as that of the real data sets. For the virtual GNIP-like network, we assumed~200 sites worldwide and 6-hourly measurements. An OSSE with 20 ensemble members was then conducted for January 2006. The results showed a significant improvement in not only the vapor isotopic field but also meteorological fields, such as wind speed, temperature, surface pressure, and humidity, when compared with a test with no observations. For surface air temperature, the global root mean square error has dropped by 10%, with 40-60% of the decrease occurring in the east-southeast Asia where the concentration of observations is relatively higher. When there is a conventional radiosonde network, the improvement gained by adding isotopic measurements was small but positive for all variables.

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Four-dimensional ensemble Kalman filtering

Cited by 144 publications

References 19 publications

Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Growing‐error correction of ensemble Kalman filter using empirical singular vectors

Observation system simulation experiments using water vapor isotope information

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