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 |
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. |
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. |
High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities Kirby, R.C., and D. Shapero, "High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities," Numer. Math., 156, 927-947, doi:10.1007/s00211-024-01405-y, 2024. |
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30 Apr 2024 |
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Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala (Comput Methods Appl Mech Eng 320:287–334, 2017) enforce such bounds in finite element methods through the solution of variational inequalities rather than linear variational problems. Here, we provide a theoretical justification for this method, including higher-order discretizations. We prove an abstract best approximation result for the linear variational inequality and estimates showing that bounds-constrained polynomials provide comparable approximation power to standard spaces. For any unconstrained approximation to a function, there exists a constrained approximation which is comparable in the W1,p norm. In practice, one cannot efficiently represent and manipulate the entire family of bounds-constrained polynomials, but applying bounds constraints to the coefficients of a polynomial in the Bernstein basis guarantees those constraints on the polynomial. Although our theoretical results do not guaruntee high accuracy for this subset of bounds-constrained polynomials, numerical results indicate optimal orders of accuracy for smooth solutions and sharp resolution of features in convection–diffusion problems, all subject to bounds constraints. |
In The News
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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