The error of representation: basic understanding

Hodyss, Daniel; Nichols, Nancy K.

doi:10.3402/tellusa.v67.24822

Cited by 48 publications

(52 citation statements)

References 20 publications

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“…Additionally, this work provides a framework for discussing the potential benefits and pitfalls of mixed resolution ensembles. This paper complements the work in [3] and continues the work in [9]. In [3] a theoretical framework was introduced to explicitly account for representation error by translating observations into the forecast model space.…”

Section: Introductionmentioning

confidence: 60%

“…This paper complements the work in [3] and continues the work in [9]. In [3] a theoretical framework was introduced to explicitly account for representation error by translating observations into the forecast model space. An important aspect of this interpretation of representation error is the translation or mapping between high resolution observational data and low resolution numerical simulations.…”

Section: Introductionmentioning

confidence: 60%

“…Both [3] and [9] take the practice of assuming these spaces are related via a smoothing operator, as in (2.4), a condition which we will now relax. Care must be taken in numerically computing this smoother as it is an illposed inverse problem.…”

Section: Estimation Of Fmentioning

confidence: 99%

“…In [3] the existence of a map between the forecast state space and the state space of the true physical processes was hypothesized. The relation (2.3) is a slight departure from [3] which considered a climatological F. In literature F k is often viewed as an interpolation operator or as a spectral truncation. If there is not a significant change in resolution than these methods are computationally less expensive and perform well.…”

Section: Theoretical Reviewmentioning

confidence: 99%

“…One of the contributions of [3] was the description the forecast observation likelihood that explicitly accounts for the relationship between low resolution forecasts and high resolution observations. A bias is then created when conditioning the low resolution forecast on high resolution observations.…”

Section: Enkf With Representation Errormentioning

confidence: 99%

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The Error of Representation in the Ensemble Kalman Filter

King¹,

Hodyss²

2017

2017 Proceedings of the Conference on Control and Its Applications

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We develop techniques needed to account for representation error in data assimilation. Representation error is a characterization of the mismatch between numerical models and the physical processes they are approximating. This mismatch can occur due to computational constraints or due to limited understanding of certain physical processes.In this paper we study the relationship of low resolution forecasts with unresolved processes to high resolution forecasts with fully resolved processes. We begin with a discussion of representation error and then discuss regularization techniques used to build a map from high resolution forecasts to low resolution forecasts. We conclude with a demonstration of these techniques using the Korteweg-DeVries nonlinear wave model.

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Section: Introductionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 60%

Section: Estimation Of Fmentioning

confidence: 99%

Section: Theoretical Reviewmentioning

confidence: 99%

Section: Enkf With Representation Errormentioning

confidence: 99%

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The Error of Representation in the Ensemble Kalman Filter

King¹,

Hodyss²

2017

2017 Proceedings of the Conference on Control and Its Applications

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Data Assimilation in the Solar Wind: Challenges and First Results

et al. 2017

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Data assimilation (DA) is used extensively in numerical weather prediction (NWP) to improve forecast skill. Indeed, improvements in forecast skill in NWP models over the past 30 years have directly coincided with improvements in DA schemes. At present, due to data availability and technical challenges, DA is underused in space weather applications, particularly for solar wind prediction. This paper investigates the potential of advanced DA methods currently used in operational NWP centers to improve solar wind prediction. To develop the technical capability, as well as quantify the potential benefit, twin experiments are conducted to assess the performance of the Local Ensemble Transform Kalman Filter (LETKF) in the solar wind model ENLIL. Boundary conditions are provided by the Wang‐Sheeley‐Arge coronal model and synthetic observations of density, temperature, and momentum generated every 4.5 h at 0.6 AU. While in situ spacecraft observations are unlikely to be routinely available at 0.6 AU, these techniques can be applied to remote sensing of the solar wind, such as with Heliospheric Imagers or interplanetary scintillation. The LETKF can be seen to improve the state at the observation location and advect that improvement toward the Earth, leading to an improvement in forecast skill in near‐Earth space for both the observed and unobserved variables. However, sharp gradients caused by the analysis of a single observation in space resulted in artificial wavelike structures being advected toward Earth. This paper is the first attempt to apply DA to solar wind prediction and provides the first in‐depth analysis of the challenges and potential solutions.

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Accounting for model error in strong‐constraint 4D‐Var data assimilation

Howes

Fowler

Lawless

2017

Quart J Royal Meteoro Soc

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The strong-constraint formulation of four-dimensional variational data assimilation (4D-Var) assumes that the model used in the process perfectly describes the true dynamics of the system. However, this assumption often does not hold and the use of an erroneous model in strong-constraint 4D-Var can lead to a sub-optimal estimation of the initial conditions. We show how the presence of model error can be correctly accounted for in strong constraint 4D-Var by allowing for errors in both the observations and the model when considering the statistics of the innovation vector. We demonstrate that, when these combined model error and observation-error statistics are used in place of the standard observation error statistics in the strong-constraint formulation of 4D-Var, a statistically more accurate estimate of the initial state is obtained.The calculation of the combined model error and observation-error statistics requires the specification of model error covariances, which in practice are often unknown. We present a method to estimate the combined statistics from innovation data that does not require explicit specification of the model error covariances. Numerical experiments using the linear advection equation and a simple nonlinear coupled model demonstrate the success of the new methods in reducing the error in the estimate of the initial state, even in the case when only the uncorrelated part of the model error is accounted for.

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The error of representation: basic understanding

Cited by 48 publications

References 20 publications

The Error of Representation in the Ensemble Kalman Filter

The Error of Representation in the Ensemble Kalman Filter

Data Assimilation in the Solar Wind: Challenges and First Results

Accounting for model error in strong‐constraint 4D‐Var data assimilation

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