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Adjoint Sensitivity of an Ocean General Circulation Model to Bottom Topography

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  • 1 Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven, Germany
  • | 2 Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Bottom topography, or more generally the geometry of the ocean basins, is an important ingredient in numerical ocean modeling. With the help of an adjoint model, it is shown that scalar diagnostics or objective functions in a coarse-resolution model, such as the transport through Drake Passage, the strength of the Atlantic Ocean meridional overturning circulation, the Deacon cell, and the meridional heat transport across 32°S, are sensitive to bottom topography as much as they are to surface boundary conditions. For example, adjoint topography sensitivities of the transport through Drake Passage are large in choke-point areas such as the Crozet–Kerguélen Plateau and south of New Zealand; the Atlantic meridional overturning circulation is sensitive to topography in the western boundary region of the North Atlantic Ocean and along the Scotland–Iceland Ridge. Many sensitivities are connected to steep topography and can be interpreted in terms of bottom form stress, that is, the product of bottom pressure and topography gradient. The adjoint sensitivities are found to agree with direct perturbation methods with deviations smaller than 30% for significant perturbations on time scales of 100 yr, so that the assumption of quasi linearity that is implicit in the adjoint method holds. The horizontal resolution of the numerical model affects the sensitivities to bottom topography, but large-scale patterns and the overall impact of changes in topography appear to be robust. The relative impact of changes in topography and surface boundary conditions on the model circulation is estimated by multiplying the adjoint sensitivities with assumed uncertainties. If the uncertainties are correlated in space, changing the surface boundary conditions has a larger impact on the scalar diagnostics than topography does, but the effects can locally be on the same order of magnitude if uncorrelated uncertainties are assumed. In either case, bottom topography variations within their prior uncertainties affect the solution of an ocean circulation model. To this extent, including topography in the control vector can be expected to compensate for identifiable model errors and, thus, to improve the solutions of estimation problems.

Corresponding author address: M. Losch, Alfred-Wegener-Institut für Polar- und Meeresforschung, Postfach 120161, 27515 Bremerhaven, Germany. Email: martin.losch@awi.de

This article included in the In Honor of Carl Wunsch special collection.

Abstract

Bottom topography, or more generally the geometry of the ocean basins, is an important ingredient in numerical ocean modeling. With the help of an adjoint model, it is shown that scalar diagnostics or objective functions in a coarse-resolution model, such as the transport through Drake Passage, the strength of the Atlantic Ocean meridional overturning circulation, the Deacon cell, and the meridional heat transport across 32°S, are sensitive to bottom topography as much as they are to surface boundary conditions. For example, adjoint topography sensitivities of the transport through Drake Passage are large in choke-point areas such as the Crozet–Kerguélen Plateau and south of New Zealand; the Atlantic meridional overturning circulation is sensitive to topography in the western boundary region of the North Atlantic Ocean and along the Scotland–Iceland Ridge. Many sensitivities are connected to steep topography and can be interpreted in terms of bottom form stress, that is, the product of bottom pressure and topography gradient. The adjoint sensitivities are found to agree with direct perturbation methods with deviations smaller than 30% for significant perturbations on time scales of 100 yr, so that the assumption of quasi linearity that is implicit in the adjoint method holds. The horizontal resolution of the numerical model affects the sensitivities to bottom topography, but large-scale patterns and the overall impact of changes in topography appear to be robust. The relative impact of changes in topography and surface boundary conditions on the model circulation is estimated by multiplying the adjoint sensitivities with assumed uncertainties. If the uncertainties are correlated in space, changing the surface boundary conditions has a larger impact on the scalar diagnostics than topography does, but the effects can locally be on the same order of magnitude if uncorrelated uncertainties are assumed. In either case, bottom topography variations within their prior uncertainties affect the solution of an ocean circulation model. To this extent, including topography in the control vector can be expected to compensate for identifiable model errors and, thus, to improve the solutions of estimation problems.

Corresponding author address: M. Losch, Alfred-Wegener-Institut für Polar- und Meeresforschung, Postfach 120161, 27515 Bremerhaven, Germany. Email: martin.losch@awi.de

This article included in the In Honor of Carl Wunsch special collection.

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