Uncertainty quantification of ocean driven melting under the Pine Island ice shelf
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Along the Antarctic coastline, ice shelves extend over the ocean, forming where glacial ice streams flow from the land to the sea. Ice shelves are important structures for the climate system, as they hold back land ice from reaching the ocean and contributing to sea level rise. In the Amundsen Sea region of Antarctica, ice shelves are in contact with warm, subsurface ocean waters, which is likely a key driver of high meltrates, thinning, and glacial mass loss. Numerical models of the ocean circulation in the Amundsen Sea have been essential for building our understanding of the mechanisms responsible for heat delivery and meltrate response. However, these computational models are subject to a host of uncertainties stemming from the representation of external forcing and unresolved physical processes. The primary goal of this work is to address this issue. We develop a numerical model of the ocean circulation in the cavity formed by the Pine Island ice shelf, which is fed by one of the fastest flowing glaciers in Antarctica. We then formulate a two-stage Bayesian inverse problem in which we constrain the open boundary conditions of the model to the sparsely available observations of the ocean state in Pine Island Bay. In the inference problem we specify our prior uncertainty according to Gaussian statistics. We build off of previous work to develop a general covariance model that is appropriate for applications with complex boundaries, multivariate control parameters, and highly anisotropic length scales - a common scenario in oceanography. In the first stage of the inference problem we solve an optimal interpolation problem to inform an initial estimate of the mean and posterior uncertainty of the open boundary conditions. We use this initial estimate to refine the nonlinear forward model configuration. We evaluate the sub ice shelf cavity circulation and meltrate response to parameterizations of (1) subgrid-scale ocean turbulence and (2) ice-ocean interactions. We find that a recently developed parameterization scheme based on quasi-geostrophic dynamics together with a velocity dependent meltwater flux provides a reasonable representation of the circulation, and serves as our baseline numerical model. In the second stage of the inverse problem, we condition the open boundary conditions on mooring data, subject to the dynamics of this numerical model. We then use an adjoint-based method to propagate uncertainty onto the simulated sub ice shelf meltrate. We find that most of the information gained in the temperature and salinity fields is achieved during the optimal interpolation problem. In the second stage of the inverse problem, however, we further reduce our uncertainty stemming from the velocity field. We emphasize that no direct observations of the velocity field are considered during this stage, highlighting the success of the numerical model in transferring information from observed to unobserved quantities.