Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis

Bocquet, Marc

doi:10.5194/npg-15-127-2008

Cited by 24 publications

(19 citation statements)

References 24 publications

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“…7, one learns that the diagnosed errors depend strongly on most measurements in France and Benelux: a change in a measurement results in an increase of the errors, rather than a new piece of information on the source. This contrasts with the analogue result for ETEX-I (Bocquet, 2008). Nor is it the case for ETEX-II data coming from Central and Eastern Europe.…”

Section: Marginal Gain Of Information Provided By Each Observationcontrasting

confidence: 49%

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Probing ETEX-II data set with inverse modelling

2008

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Abstract.We give here an account on the results of source inversion of the ETEX-II experiment. Inversion has been performed with the maximum entropy method on the basis of non-zero measurements and in conjunction with a transport model POLAIR3D. The discrepancy scaling factor between the reconstructed and the true mass has been estimated to be equal to 7. The results contrast with the method's performance on the ETEX-I source. In the latter case its mass has been reconstructed with an accuracy exceeding 80%. The large value of the discrepancy factor for ETEX-II could be ascribed to modelling difficulties, possibly linked not to the transport model itself but rather to the quality of the measurements.

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Section: Marginal Gain Of Information Provided By Each Observationcontrasting

confidence: 49%

“…That is why one investigates the marginal contribution ∂ µ i K σ of an observation µ i , for all the observations. In (Bocquet, 2008), it was shown how to compute such a marginal contribution. These contributions have also been computed for ETEX-II and are plotted in Fig.…”

Section: Marginal Gain Of Information Provided By Each Observationmentioning

confidence: 99%

Probing ETEX-II data set with inverse modelling

2008

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“…It is known from previous studies that non-Gaussian statistics change the way observations are used in data assimilation (e.g. Bocquet, 2008). This paper presents analytical results to explain this change in observation impact.…”

Section: Introductionmentioning

confidence: 92%

Observation impact in data assimilation: the effect of non-Gaussian observation error

Fowler

Leeuwen

2013

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.

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“…When the prior is non-Gaussian, the additional structure in the prior will be shown to be important for calculating the impact of the observations. A study performed by Bocquet (2008) compared the information content of observations when the prior is assumed to be Gaussian and Bernoulli for the inverse modelling of a pollutant source. For this case study, a tracer gas was released from a point source over Northern France; observations of the gas were then made at locations across Europe.…”

Section: Observation Impact In Non-gaussian Data Assimilationmentioning

confidence: 99%

Measures of observation impact in non-Gaussian data assimilation

Fowler

Leeuwen

2012

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz '63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

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Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis

Cited by 24 publications

References 24 publications

Probing ETEX-II data set with inverse modelling

Probing ETEX-II data set with inverse modelling

Observation impact in data assimilation: the effect of non-Gaussian observation error

Measures of observation impact in non-Gaussian data assimilation

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