Daniel Shapero Research Scientist/Engineer - Senior shapero@apl.washington.edu Phone 206-543-1348 |
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 |
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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 ![]() |
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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. |
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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 ![]() |
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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. |
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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 ![]() |
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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. |
In The News
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Edge of Pine Island Glacier’s ice shelf is ripping apart, causing key Antarctic glacier to gain speed UW News, Hannah Hickey For decades, the ice shelf helping to hold back one of the fastest-moving glaciers in Antarctica has gradually thinned. Analysis of satellite images reveals a more dramatic process in recent years: From 2017 to 2020, large icebergs at the ice shelf’s edge broke off, and the glacier sped up. |
11 Jun 2021
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