A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation

Kalmikov, Alexander; Heimbach, Patrick

doi:10.1137/130925311

Cited by 49 publications

(43 citation statements)

References 40 publications

(86 reference statements)

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“…Thus we are unable to provide accurate confidence intervals on ice loss based on observational uncertainty. Estimation of a posteriori uncertainties based on observational uncertainties may be possible e.g., through methods that infer the Hessian of the cost function (Kalmikov and Heimbach, 2014;Isaac et al, 2014). Enabling such calculations within our estimation framework is a future research goal.…”

Section: Uncertainty Of Sea Level Contribution Projectionmentioning

confidence: 99%

Committed retreat of Smith, Pope, and Kohler Glaciers over the next 30 years inferred by transient model calibration

et al. 2015

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Abstract. A glacial flow model of Smith, Pope and KohlerGlaciers is calibrated by means of control methods against time varying, annually resolved observations of ice height and velocities, covering the period 2002 to 2011. The inversion -termed "transient calibration" -produces an optimal set of time-mean, spatially varying parameters together with a time-evolving state that accounts for the transient nature of observations and the model dynamics. Serving as an optimal initial condition, the estimated state for 2011 is used, with no additional forcing, for predicting grounded ice volume loss and grounding line retreat over the ensuing 30 years. The transiently calibrated model predicts a near-steady loss of grounded ice volume of approximately 21 km 3 a −1 over this period, as well as loss of 33 km 2 a −1 grounded area. We contrast this prediction with one obtained following a commonly used "snapshot" or steady-state inversion, which does not consider time dependence and assumes all observations to be contemporaneous. Transient calibration is shown to achieve a better fit with observations of thinning and grounding line retreat histories, and yields a quantitatively different projection with respect to ice volume loss and ungrounding. Sensitivity studies suggest large near-future levels of unforced, i.e., committed sea level contribution from these ice streams under reasonable assumptions regarding uncertainties of the unknown parameters.

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Section: Uncertainty Of Sea Level Contribution Projectionmentioning

confidence: 99%

Committed retreat of Smith, Pope, and Kohler Glaciers over the next 30 years inferred by transient model calibration

et al. 2015

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“…As is the case with forward models, not all state estimates are equally credible. Because of the computational load, necessary full uncertainty estimates are not yet available, and efforts to obtain them are ongoing (e.g., Kalmikov & Heimbach 2014). Surely the future lies that way.…”

Section: Synthesesmentioning

confidence: 99%

Global Ocean Integrals and Means, with Trend Implications

Wunsch

2016

Annu. Rev. Mar. Sci.

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Understanding the ocean requires determining and explaining global integrals and equivalent average values of temperature (heat), salinity (freshwater and salt content), sea level, energy, and other properties. Attempts to determine means, integrals, and climatologies have been hindered by thinly and poorly distributed historical observations in a system in which both signals and background noise are spatially very inhomogeneous, leading to potentially large temporal bias errors that must be corrected at the 1% level or better. With the exception of the upper ocean in the current altimetric-Argo era, no clear documentation exists on the best methods for estimating means and their changes for quantities such as heat and freshwater at the levels required for anthropogenic signals. Underestimates of trends are as likely as overestimates; for example, recent inferences that multidecadal oceanic heat uptake has been greatly underestimated are plausible. For new or augmented observing systems, calculating the accuracies and precisions of global, multidecadal sampling densities for the full water column is necessary to avoid the irrecoverable loss of scientifically essential information.

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“…There is currently no straightforward means to determine comprehensive uncertainties in ocean state estimates derived using the method of Lagrange multipliers. Developing tools for uncertainty quantification is an important and ongoing effort in ocean state estimation (Kalmikov and Heimbach 2014). Contrasting results in DW14, KN17, and this study suggest a sensitivity to prior choices of model controls and covariances and point to difficulties in constraining the deep ocean circulation at the LGM from available observations (e.g., LeGrand and Wunsch 1995;Huybers et al 2007;Marchal and Curry 2008;Burke et al 2011;KurahashiNakamura et al 2014;Gebbie et al 2016).…”

Section: Discussionmentioning

confidence: 67%

A Global Glacial Ocean State Estimate Constrained by Upper-Ocean Temperature Proxies

et al. 2018

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We use the method of least squares with Lagrange multipliers to fit an ocean general circulation model to the Multiproxy Approach for the Reconstruction of the Glacial Ocean Surface (MARGO) estimate of near sea surface temperature (NSST) at the Last Glacial Maximum (LGM; circa 23-19 thousand years ago). Compared to a modern simulation, the resulting global, last-glacial ocean state estimate, which fits the MARGO data within uncertainties in a free-running coupled ocean-sea ice simulation, has global-mean NSSTs that are 28C lower and greater sea ice extent in all seasons in both the Northern and Southern Hemispheres. Increased brine rejection by sea ice formation in the Southern Ocean contributes to a stronger abyssal stratification set principally by salinity, qualitatively consistent with pore fluid measurements. The upper cell of the glacial Atlantic overturning circulation is deeper and stronger. Dye release experiments show similar distributions of Southern Ocean source waters in the glacial and modern western Atlantic, suggesting that LGM NSST data do not require a major reorganization of abyssal water masses. Outstanding challenges in reconstructing LGM ocean conditions include reducing effects from model biases and finding computationally efficient ways to incorporate abyssal tracers in global circulation inversions. Progress will be aided by the development of coupled oceanatmosphere-ice inverse models, by improving high-latitude model processes that connect the upper and abyssal oceans, and by the collection of additional paleoclimate observations.

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A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation

Cited by 49 publications

References 40 publications

Committed retreat of Smith, Pope, and Kohler Glaciers over the next 30 years inferred by transient model calibration

Committed retreat of Smith, Pope, and Kohler Glaciers over the next 30 years inferred by transient model calibration

Global Ocean Integrals and Means, with Trend Implications

A Global Glacial Ocean State Estimate Constrained by Upper-Ocean Temperature Proxies

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