Nonglobal Parameter Estimation Using Local Ensemble Kalman Filtering

Bellsky, Thomas; Berwald, Jesse; Mitchell, Lewis

doi:10.1175/mwr-d-13-00200.1

Cited by 14 publications

(14 citation statements)

References 59 publications

(107 reference statements)

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“…Bellsky et al () estimated non‐global parameters in the Lorenz '96 system, and found an important impact of the localization on the analysis quality, in particular some values of the localization radius, produce a significant improvement in the experiments they conducted, compared to the filter without localization. We did some preliminary experiments with our settings and we did not find a significant sensitivity to the localization radius so that we present results only without localization.…”

Section: Methodsmentioning

confidence: 99%

Estimation of the functional form of subgrid‐scale parametrizations using ensemble‐based data assimilation: a simple model experiment

Pulido

Scheffler

Ruiz

et al. 2016

Quart J Royal Meteoro Soc

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Oceanic and atmospheric global numerical models represent explicitly the large‐scale dynamics while the smaller‐scale processes are not resolved, so that their effects in the large‐scale dynamics are included through subgrid‐scale parametrizations. These parametrizations represent small‐scale effects as a function of the resolved variables. In this work, data assimilation principles are used not only to estimate the parameters of subgrid‐scale parametrizations but also to uncover the functional dependencies of subgrid‐scale processes as a function of large‐scale variables. Two data assimilation methods based on the ensemble transform Kalman filter (ETKF) are evaluated in the two‐scale Lorenz '96 system scenario. The first method is an online estimation which uses the ETKF with an augmented space state composed of the model large‐scale variables and a set of unknown global parameters from the parametrization. The second method is an offline estimation which uses the ETKF to estimate an augmented space state composed of the large‐scale variables and by a space‐dependent model error term. Then a polynomial regression is used to fit the estimated model error as a function of the large‐scale model variables in order to develop a parametrization of small‐scale dynamics. The online estimation shows a good performance when the parameter‐state relationship is assumed to be a quadratic polynomial function. The offline estimation captures better some of the highly nonlinear functional dependencies found in the subgrid‐scale processes. The nonlinear and non‐local dependence found in an experiment with shear‐generated small‐scale dynamics is also recovered by the offline estimation method. Therefore, the combination of these two methods could be a useful tool for the estimation of the functional form of subgrid‐scale parametrizations.

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Section: Methodsmentioning

confidence: 99%

Estimation of the functional form of subgrid‐scale parametrizations using ensemble‐based data assimilation: a simple model experiment

Pulido

Scheffler

Ruiz

et al. 2016

Quart J Royal Meteoro Soc

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“…The problem of joint state-parameter estimation has been investigated in many previous studies. To deal with the uncertainty of model parameter in the context of DA, a commonly used DA approach such as an ensemble Kalman filter (EnKF; Evensen 1994;Houtekamer and Mitchell 1998) or local ensemble transform Kalman filter (LETKF) in Ott et al (2004) has been adapted by augmenting the state vector with the uncertain parameters; hence, the augmented method (Aksoy et al 2006;Annan et al 2005;Baek et al 2006;Bellsky et al 2014;Carrassi and Vannitsem 2011;Gillijns and De Moor 2007;Koyama and Watanabe 2010). The standard Kalman update equations are then applied to estimate the combined state-parameter vector.…”

Section: Introductionmentioning

confidence: 99%

“…One approach to avoid this difficulty is the interacting Kalman filter whereby two Kalman filters are designed to estimate states and parameter separately and the two filters interact (Friedland 1969;Koyama and Watanabe 2010;Moradkhani et al 2005). A more recent approach to this problem also successfully deals with the local variability of parameters by using the augmented LETKF (Baek et al 2006;Bellsky et al 2014;Kang et al 2011). This approach computes the Kalman update equations for the subdivided local regions in parallel with a dimensionally reduced state vector.…”

Section: Introductionmentioning

confidence: 99%

Two-Stage Filtering for Joint State-Parameter Estimation

Santitissadeekorn

Jones

2015

Monthly Weather Review

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This paper presents an approach for the simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The state augmentation technique, in which the state vector is augmented by the model parameters, has been investigated in many previous studies and some success with this technique has been reported in the case where model parameters are additive. However, many geophysical or climate models contain nonadditive parameters such as those arising from physical parameterization of subgrid-scale processes, in which case the state augmentation technique may become ineffective. This is due to the fact that the inference of parameters from partially observed states based on the cross covariance between states and parameters is inadequate if states and parameters are not linearly correlated. In this paper, the authors propose a two-stage filtering technique that runs particle filtering (PF) to estimate parameters while updating the state estimate using an ensemble Kalman filter (EnKF). These two ''subfilters'' interact recursively based on the point estimates computed at each stage. The applicability of the proposed method is demonstrated using the Lorenz-96 system, where the forcing is parameterized and the amplitude and phase of the forcing are to be estimated jointly with the state. The proposed method is shown to be capable of estimating these model parameters with a high accuracy as well as reducing uncertainty while the state augmentation technique fails.

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“…strategically targeting observations to reduce state estimation and forecast error; 3-16 2. estimating model parameters [17][18][19][20][21][22] within the targeting observation context to further reduce estimation error.…”

Section: Introductionmentioning

confidence: 99%

“…The main part of our numerical results investigates estimating parameters for the chaotic Lorenz-96 model, where we expand on previous literature by applying recently developed parameter estimation techniques [18][19][20] within the novel context of targeted observations. Model parameters are typically fixed quantities that encode physical information about a dynamical system which are often estimated within large weather and climate models.…”

Section: Introductionmentioning

confidence: 99%

Kalman filter data assimilation: Targeting observations and parameter estimation

Bellsky

Kostelich

Mahalov

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4871916]For chaotic systems like the weather, an accurate forecast requires an accurate representation of the current state. Data assimilation (DA) is a methodology that reinitializes the current state of a system by combining observational data along with an estimated state determined by a forecast model. Within data assimilation schemes, the spatial locations of the observational data can have a significant effect on the accuracy of the analysis (re-initialized) state. In this work, we use a particular strategy for locating observations and show that this targeting strategy is successful in reducing state estimation error for a conceptual chaotic model, as compared to fixed or randomly located observations. An additional facet of weather modeling that we investigate is the estimation of model parameters. Parameter estimation is a technique used within modeling that often seeks to fit parameters with historical data or to characterize subgridscale effects. We show that our utilized observation targeting strategy within a particular parameter estimation scheme is successful in accurately estimating a model parameter for this chaotic model. To motivate our study of this chaotic model, we first establish a theorem which is used to justify the use of targeted observations for a linear data assimilation scheme.

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Nonglobal Parameter Estimation Using Local Ensemble Kalman Filtering

Cited by 14 publications

References 59 publications

Estimation of the functional form of subgrid‐scale parametrizations using ensemble‐based data assimilation: a simple model experiment

Estimation of the functional form of subgrid‐scale parametrizations using ensemble‐based data assimilation: a simple model experiment

Two-Stage Filtering for Joint State-Parameter Estimation

Kalman filter data assimilation: Targeting observations and parameter estimation

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