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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

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.

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., EOR, doi:10.1007/s00211-024-01405-y, 2024.

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30 Apr 2024

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.

Ocean-induced melt volume directly paces ice loss from Pine Island Glacier

Joughin, I., D. Shapero, P. Dutrieux, and B. Smith, "Ocean-induced melt volume directly paces ice loss from Pine Island Glacier," Sci. Adv., 7, doi:10.1126/sciadv.abi5738, 2021.

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22 Oct 2021

The spatial distribution of ocean-induced melting beneath buttressing ice shelves is often cited as an important factor controlling Antarctica’s sea-level contribution. Using numerical simulations, we investigate the relative sensitivity of grounded-ice loss to the spatial distribution and overall volume of ice-shelf melt over two centuries. Contrary to earlier work, we find only minor sensitivity to melt distribution (<6%), with a linear dependence of ice loss on the total melt. Thus, less complex models that need not reproduce the detailed melt distribution may simplify the projection of future sea level. The linear sensitivity suggests a contribution of up to 5.1 cm from Pine Island Glacier over the next two centuries given anticipated levels of ocean warming, provided its ice shelf does not collapse because of other causes.

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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