Discrete Inverse and State Estimation Problems

Wunsch,

doi:10.1017/cbo9780511535949

Cited by 143 publications

(139 citation statements)

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“…In practice, the salt and heat conservations are formulated relative to a reference tracer value (taken here as the estimated average of the tracer over the considered layer volume, see Table C.5). As explained by (Wunsch, 2006), this formulation reduces the impact of possible mass imbalance on the tracer imbalance. In (C.1) the tracer divergence in the bottom friction layer is ignored.…”

Section: Water Massmentioning

confidence: 99%

“…The conservation constraints being applied simultaneously to several layers/tracers, after discretizing the tracer fluxes across the boundaries, a system of linear equations is solved for the model unknowns (see Appendix C.1 215 for more details). The number of constraints being usually smaller than the number of unknowns, we used the Gauss-Markov method which is adapted to find the best unbiased estimation of underdetermined systems of linear equations (see Wunsch, 2006).…”

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confidence: 99%

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Circulation and water mass transports on the East Antarctic shelf in the Mertz Glacier region

Martin¹,

Houssais²,

Goff³

et al. 2017

Deep Sea Research Part I: Oceanographic Research Papers

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The East Antarctic shelf off Adélie-George V Land is known to be an important region for Dense Shelf Water (DSW) formation as a result of intense sea ice production in the Mertz Glacier Polynya during the winter season. It is also a region where the warm modified Circumpolar Deep Water (mCDW) penetrates onto the shelf during the summer. Using hydrographic observations from a summer survey in 2008 we implement a box inverse model to propose a comprehensive view of the steady state circulation on this shelf in summer. Additional information from mooring observations collected on the depression slope is used to provide context to the retrieved circulation scheme. Over the depression slope, the summer baroclinic structure of the currents is found to contrast with the almost barotropic structure in winter.The summer circulation is strongly constrained by the DSW distribution and forms a clockwise circulation primarily transporting the fresh surface waters and the warm mCDW around the dome of DSW. Over the upper flank of the Mertz Bank, the inflow branch transports the mCDW towards the Mertz Glacier, while, over the lower part of the slope, the outflow branch returns to the sill a diluted mode of the same water mass. A total of 0.19 Sv of mCDW inflows at the sill and two-third reach the Mertz Glacier and recirculate in front of it, allowing the mCDW to penetrate into the deeper part of the depression. Possible scenarios of interaction between the mCDW and the DSW with the glacier are examined. It is shown that, despite the water mass pathways and transports suggest possible ice-ocean interaction, both lateral and basal melting were likely small in summer 2008. Finally, our results suggest that, in addition to bathymetric features, the distribution of the residual DSW which is left from the preceding winter sets up regional pressure gradients which provide a seasonal control on the shelf circulation. In particular, the spring collapse of the convective patch would contribute to setting up a deep pycnocline which strongly impacts the shelf circulation in the following summer, with possible feedback of the mCDW transports on the polynya activity and water mass formation.

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Section: Water Massmentioning

confidence: 99%

mentioning

confidence: 99%

Circulation and water mass transports on the East Antarctic shelf in the Mertz Glacier region

Martin¹,

Houssais²,

Goff³

et al. 2017

Deep Sea Research Part I: Oceanographic Research Papers

View full text Add to dashboard Cite

show abstract

“…147], and connects to almost everything in the computational mathematics of PDEs. To mention some examples of relevance to the computational physicist, adjoints are central to a priori and a posteriori error estimation [18,19,20,21,17], sensitivity studies [22,23], PDE-constrained optimisation [24,25,26,27,28], non-normal stability analysis [29,30,31], and PDE-constrained Bayesian inference [32].…”

Section: Adjoint Modelsmentioning

confidence: 99%

Rapid development and adjoining of transient finite element models

Maddison

Farrell

2014

Computer Methods in Applied Mechanics and Engineering

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Recent advances in high level finite element systems have allowed for the symbolic representation of discretisations and their efficient automated implementation as model source code. This allows for the extremely compact implementation of complex non-linear models in a handful of lines of high level code. In this work we extend the high level finite element FEniCS system to introduce an abstract representation of the temporal discretisation: this enables the similarly rapid development of transient finite element models. Efficiency is achieved via aggressive optimisations that exploit the temporal structure, such as automated pre-assembly and caching of forms, and the robust re-use of matrix factorisations and preconditioner data. The resulting models are as fast or faster than hand-optimised finite element codes. The high level representation of the system remains extremely compact and easily manipulated. This structure is exploited to derive the associated discrete adjoint model automatically, with the adjoint model inheriting the performance advantages of the forward model. Combined, this provides a system for the rapid development of efficient transient models, together with their discrete adjoints.

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“…Data assimilation synthesizes observed data and modeled physics based on statistical theories. This is an effective approach to fill the gap between observation and modeling studies (Wunsch, 2006;Blayo et al, 2015). Generally, data assimilation minimizes a modeldata misfit with an assessment of errors; the autocorrelation function and the decorrelation scale are necessary for these error assessments (Carton et al, 2000;Forget and Wunsch, 2007).…”

Section: Introductionmentioning

confidence: 99%

Decorrelation scales for Arctic Ocean hydrography – Part I: Amerasian Basin

et al. 2018

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Abstract. Any use of observational data for data assimilation requires adequate information of their representativeness in space and time. This is particularly important for sparse, non-synoptic data, which comprise the bulk of oceanic in situ observations in the Arctic. To quantify spatial and temporal scales of temperature and salinity variations, we estimate the autocorrelation function and associated decorrelation scales for the Amerasian Basin of the Arctic Ocean. For this purpose, we compile historical measurements from 1980 to 2015. Assuming spatial and temporal homogeneity of the decorrelation scale in the basin interior (abyssal plain area), we calculate autocorrelations as a function of spatial distance and temporal lag. The examination of the functional form of autocorrelation in each depth range reveals that the autocorrelation is well described by a Gaussian function in space and time. We derive decorrelation scales of 150-200 km in space and 100-300 days in time. These scales are directly applicable to quantify the representation error, which is essential for use of ocean in situ measurements in data assimilation. We also describe how the estimated autocorrelation function and decorrelation scale should be applied for cost function calculation in a data assimilation system.

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Discrete Inverse and State Estimation Problems

Cited by 143 publications

References 0 publications

Circulation and water mass transports on the East Antarctic shelf in the Mertz Glacier region

Circulation and water mass transports on the East Antarctic shelf in the Mertz Glacier region

Rapid development and adjoining of transient finite element models

Decorrelation scales for Arctic Ocean hydrography – Part I: Amerasian Basin

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