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Daniel Shapero

Research Scientist/Engineer - Senior

Email

shapero@apl.washington.edu

Phone

206-543-1348

Department Affiliation

Polar Science Center

Education

B.S. Applied Mathematics, McGill University (Montreal, QC, Canada), 2010

Ph.D. Applied Mathematics, University of Washington - Seattle, 2017

Publications

2000-present and while at APL-UW

Numerical simulation of glacier terminus evolution using the dual action principle for momentum balance

Shapero, D.R., and G.G. de Diego, "Numerical simulation of glacier terminus evolution using the dual action principle for momentum balance," J. Glaciol., 71, doi:10.1017/jog.2024.92, 2024.

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18 Nov 2024

The momentum conservation equation for glacier flow can be described through minimization of an action functional. Several software packages for glacier flow modeling use this action principle in the design of numerical solution procedures. We derive here an equivalent dual action principle for the shallow stream approximation and implement this model using the finite element method. The key feature of the dual action is that the flow law and friction law are both inverted, which changes the character of the non-linearities. This altered character makes it possible to implement numerical solvers for the dual form that work even when the ice thickness or strain rate are exactly equal to zero. Solvers for the primal form typically fail on such input data and require regularization of the problem. This robustness makes it possible to implement iceberg calving in a simple way: the modeler sets the ice thickness to zero in the desired area. We provide several demonstrations and a reference implementation.

Consistent point data assimilation in Firedrake and Icepack

Nixon-Hill, R.W., D. Shapero, C.J. Cotter, and D.A. Ham, "Consistent point data assimilation in Firedrake and Icepack," Geosci. Model. Dev., 17, 5369-5386, doi:10.5194/gmd-17-5369-2024, 2024.

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12 Jul 2024

We present a high-level, differentiable, and composable abstraction for the point evaluation of the solution fields of partial differential equation models. The new functionality, embedded in the Firedrake automated finite element system, enables modellers to easily assimilate point data into their models at the point locations, rather than resorting to extrapolation to a computational mesh. We demonstrate the expressiveness and ease with which more mathematically defensible data assimilation can be performed with examples in the fields of groundwater hydrology and glaciology.

In various geoscience disciplines, modellers seek to estimate fields that are challenging to directly observe using measurements of other related fields. These measurements are often sparse, and it is common practice to first extrapolate these measurements to the grid or mesh used for computations. When this estimation procedure is viewed as a deterministic inverse problem, the extrapolation step is undesirable because the choice of extrapolation method introduces an arbitrary algorithmic degree of freedom that can alter the outcomes. When the estimation procedure is instead viewed through the lens of statistical inference, the extrapolation step is undesirable for the additional reason that it obscures the number of statistically independent measurements that are assimilated and thus makes it impossible to apply statistical goodness-of-fit tests or model selection criteria. The introduction of point evaluation into Firedrake, together with its integration into the automatic differentiation features of the system, greatly facilitates the direct assimilation of point data and thus improved methodology for solving both deterministic and statistical inverse problems.

Responses of the Pine Island and Thwaites glaciers to melt and sliding parameterizations

Joughin, I., D. Shapero, and P. Dutrieux, "Responses of the Pine Island and Thwaites glaciers to melt and sliding parameterizations," Cryosphere, 18, 2583-2601, doi:10.5194/tc-18-2583-2024, 2024.

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28 May 2024

The Pine Island and Thwaites glaciers are the two largest contributors to sea level rise from Antarctica. Here we examine the influence of basal friction and ice shelf basal melt in determining projected losses. We examine both Weertman and Coulomb friction laws with explicit weakening as the ice thins to flotation, which many friction laws include implicitly via the effective pressure. We find relatively small differences with the choice of friction law (Weertman or Coulomb) but find losses to be highly sensitive to the rate at which the basal traction is reduced as the area upstream of the grounding line thins. Consistent with earlier work on Pine Island Glacier, we find sea level contributions from both glaciers to vary linearly with the melt volume averaged over time and space, with little influence from the spatial or temporal distribution of melt. Based on recent estimates of melt from other studies, our simulations suggest that the combined melt-driven and sea level rise contribution from both glaciers may not exceed 10 cm by 2200, although the uncertainty in model parameters allows for larger increases. We do not include other factors, such as ice shelf breakup, that might increase loss, or factors such as increased accumulation and isostatic uplift that may mitigate loss.

More Publications

Acoustics Air-Sea Interaction & Remote Sensing Center for Environmental & Information Systems Center for Industrial & Medical Ultrasound Electronic & Photonic Systems Ocean Engineering Ocean Physics Polar Science Center
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