A stochastic framework for inequality constrained estimation

Roese-Koerner, Lutz; Devaraju, Balaji; Sneeuw, Nico; Schuh, Wolf-Dieter

doi:10.1007/s00190-012-0560-9

Cited by 16 publications

(5 citation statements)

References 12 publications

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“…For our setting, DALECv2 site-based experiment, the complexity is relatively small and a MCMC approach is affordable. Used in Bloom and Williams (2015), the MCMC approach for DALEC is studied in detail in Safta et al (2015), and the resulting parameter distributions suggest that 4DVAR and the inherent Gaussian approximation provide a reasonable posterior distribution.…”

Section: Discussionmentioning

confidence: 99%

“…Such information is crucial for model design, inverse modelling and reduction of complex non-linear models. A global sensitivity analysis for DALEC was recently performed in Safta et al (2015). Here we consider a local approach where first-order derivatives are used to build sensitivity indices that help us understand the influence of input variables on the output.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Here our focus is on the mean of the time series of DALEC fluxes (LAI, NEE) over a 12-year period. Finer analysis could be carried out by looking at seasonal aspects of the carbon cycle, identifying what variables are the most sensitive at certain times of the year, for example as studied in Safta et al (2015).…”

Section: Sensitivity Analysismentioning

confidence: 99%

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Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

2017

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Abstract. We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2 (Data Assimilation Linked Ecosystem Carbon). Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. Here we recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their advantage through a linear analysis. Using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matrices to diagnose the nature of the ill-posedness and evaluate regularisation strategies. We then study the non-linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach.

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Section: Discussionmentioning

confidence: 99%

Section: Sensitivity Analysismentioning

confidence: 99%

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Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

2017

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“…where g is the nonlinear operator defining the EDCs described in Section 2.2, and l and u are the lower and upper bounds defined in Table 2.1. This approach provides an efficient, robust and quick strategy to find an acceptable solution; however, stability properties are not easily determined, see Roese-Koerner et al (2012).…”

Section: Edcs and 4dvarmentioning

confidence: 99%

Constraining DALEC v2 using multiple data streams and ecological constraints: analysis and application

Delahaies

Roulstone

Nichols

2017

Preprint

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Abstract. We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2. Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. Here we recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their benefit through a linear analysis. Using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matrices to diagnose the nature of the ill-posedness and evaluate regularisation strategies. We then study the non linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach.

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“…The quality description including the covariance matrix of the parameter estimates is given based on the aggregate function proposed by Li (1991), which was used in Peng et al (2006) and Zeng et al (2015). Note that the aggregate function based method only provides an approximate quality description, because Roese-Koerner et al (2012) explained that in an inequality constrained estimate it is not possible to represent the complete stochastic information in form of a variance-covariance matrix as the description of the first two moments of the PDF is no longer sufficient.…”

Section: Introductionmentioning

confidence: 99%

On the errors-in-variables model with equality and inequality constraints for selected numerical examples

Fang

2015

Acta Geod Geophys

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It is well known that the errors-in-variables (EIV) model has been treated as a special case of the traditional geodetic model, the nonlinear Gauss-Helmert model (GHM), for more than a century. In this contribution, an adjustment of the EIV model with equality and inequality constraints is investigated based on the nonlinear GHM. In each iteration, the constrained EIV model is linearized to form a quadratic program. Furthermore, the precision description is investigated for the mixed constrained problem. The demonstrated results from the numerical examples show that this approach avoids the large computational expenses of the existing combinatorial solution that normally accompany the number of inequality constraints.

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A stochastic framework for inequality constrained estimation

Cited by 16 publications

References 12 publications

Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

Constraining DALEC v2 using multiple data streams and ecological constraints: analysis and application

On the errors-in-variables model with equality and inequality constraints for selected numerical examples

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