Parameter sensitivity analysis of dynamic ice sheet models – numerical computations

Cheng, Gong; Lötstedt, Per

doi:10.5194/tc-14-673-2020

Cited by 10 publications

(15 citation statements)

References 39 publications

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“…Let us now investigate the effect of time-dependent perturbations in the friction parameter on modelled ice velocities and ice surface elevation. A numerical example, based on the Marine Ice Sheet Model Intercomparison Project (MISMIP) (Pattyn et al, 2012) used also in Cheng and Lötstedt (2020) illustrates the findings presented.…”

Section: Adjoint Equations Based On the Fs Modelmentioning

confidence: 81%

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Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the Full Stokes and Shallow Shelf Approximation frameworks

Cheng

Kirchner

Lötstedt

2020

Preprint

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Abstract. Predictions of future mass loss from ice sheets are afflicted with uncertainty, caused, among others, by insufficient understanding of spatio-temporally variable processes at the inaccessible base of ice sheets for which few direct observations exist and of which basal friction is a prime example. Here, we use an inverse modeling approach and the associated time-dependent adjoint equations, derived in the framework of a Full Stokes model and a Shallow Shelf/Shelfy Stream Approximation model, respectively, to determine the sensitivity of ice sheet surface velocities and elevation to perturbations in basal friction and basal topography. Analytical and numerical examples are presented showing the importance of including the time dependent kinematic free surface equation for the elevation and its adjoint, in particular for observations of the elevation. A closed form of the analytical solutions to the adjoint equations is given for a two dimensional vertical ice in steady state under the Shallow Shelf Approximation. There is a delay in time between a perturbation at the ice base and the observation of the change in elevation. A perturbation at the base in the topography has a direct effect in space at the surface above the perturbation and a perturbation in the friction is propagated directly to the surface in time. Perturbations with long wavelength and low frequency will propagate to the surface while those of short wavelength and high frequency are damped.

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Section: Adjoint Equations Based On the Fs Modelmentioning

confidence: 81%

“…The time dependent adjoint equations are solved numerically, and the sensitivity to perturbations varying in time is investigated and illustrated. The accuracy of the analytical solutions and the adjoint approach has been discussed in a companion paper (Cheng and Lötstedt, 2020), supported by extensive numerical computations.…”

mentioning

confidence: 99%

Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the Full Stokes and Shallow Shelf Approximation frameworks

Cheng

Kirchner

Lötstedt

2020

Preprint

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“…Additional uncertainty at the GL is introduced by the approximation of the bedrock geometry, the friction at the GL, and the modeling of the ice-ocean interaction. It is shown in Cheng and Lötstedt (2020) that the solution at the GL is particularly sensitive to variation in the geometry and friction at the ice base.…”

Section: Discussionmentioning

confidence: 99%

“…A system of linear equations is solved at t +1 for z +1 c . This time discretization and its properties are discussed in Cheng et al (2017) and summarized in Algorithm 2.…”

Section: Discretization Of the Advection Equationsmentioning

confidence: 99%

A full Stokes subgrid scheme in two dimensions for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)

2020

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Abstract. The flow of large ice sheets and glaciers can be simulated by solving the full Stokes equations using a finite element method. The simulation is particularly sensitive to the discretization of the grounding line, which separates ice resting on bedrock and ice floating on water, and is moving with time. The boundary conditions at the ice base are enforced by Nitsche's method and a subgrid treatment of the grounding line element. Simulations with the method in two dimensions for an advancing and a retreating grounding line illustrate the performance of the method. The computed grounding line position is compared to previously published data with a fine mesh, showing that similar accuracy is obtained using subgrid modeling with more than 20-times-coarser meshes. This subgrid scheme is implemented in the two-dimensional version of the open-source code Elmer/ICE.

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“…Kyrke-Smith et al (2018) analysed the effects of basal topography on inversions. The sensitivity of inversions to several ice properties was tested by Zhao et al (2018), and sensitivities at the surface to perturbations in basal conditions from inversions have been investigated by Martin and Monnier (2014) and Cheng and Lötstedt (2020). However, there are not many direct comparisons between inversions from different models.…”

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confidence: 99%

The transferability of adjoint inversion products between different ice flow models

Barnes¹,

Santos²,

Goldberg³

et al. 2020

Preprint

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Abstract. Among the most important challenges faced by ice flow models is how to represent basal and rheological conditions, which are challenging to obtain from direct observations. A common practice is to use numerical inversions to calculate estimates for the unknown properties, but there are many possible methods and not one standardised approach. As such, every ice flow model has a unique initialisation procedure. Here we compare the outputs of inversions from three different ice flow models, each employing a variant of adjoint-based optimisation to calculate basal sliding coefficients and flow rate factors using the same observed surface velocities and ice thickness distribution. The region we focus on is the Amundsen Sea Embayment in West Antarctica, the subject of much investigation due to rapid changes in the area over recent decades. We find that our inversions produce similar distributions of basal sliding across all models, despite using different techniques, implying that the methods used are highly robust and represent the physics without much influence by individual model behaviours. Transferring the products of inversions between models results in time-dependent simulations displaying variability on the order of or lower than existing model intercomparisons and process studies. While the successful transfer of inversion outputs from one model to another requires some extra effort and technical knowledge of the particular models involved, it is certainly possible and could indeed be useful for future intercomparison projects.

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Parameter sensitivity analysis of dynamic ice sheet models – numerical computations

Cited by 10 publications

References 39 publications

Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the Full Stokes and Shallow Shelf Approximation frameworks

Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the Full Stokes and Shallow Shelf Approximation frameworks

A full Stokes subgrid scheme in two dimensions for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)

The transferability of adjoint inversion products between different ice flow models

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