Warm, subsurface ocean waters that access ice shelves in the Amundsen Sea are likely to be a key driver of high meltrates and ice shelf thinning. Numerical models of the ocean circulation have been essential for gaining understanding of the mechanisms responsible for heat delivery and meltrate response, but a number of challenges remain for simulations that incorporate this region. Here, we develop a suite of numerical experiments to explore how sub ice shelf cavity circulation and meltrate patterns are impacted by parameterization schemes for (1) subgrid-scale ocean turbulence, and (2) ice-ocean interactions. To provide a realistic context, our experiments are developed to simulate the ocean circulation underneath the Pine Island ice shelf, and validated against mooring observations and satellite derived meltrate estimates. Each experiment is forced with data-informed open boundary conditions that bear the imprint of the gyre in Pine Island Bay. We find that even at a ~600 m grid resolution, flow aware ocean parameterizations for subgrid-scale momentum and tracer transfer are crucial for representing the circulation and meltrate pattern accurately. Our simulations show that enhanced meltwater diffusion near the ice-ocean interface intensifies near wall velocities via thermal wind, which subsequently increases meltrates near the grounding line. Incorporating a velocity dependent ice-ocean transfer coefficient together with a flow aware ocean turbulence parameterization therefore seems to be necessary for modelling the ocean circulation underneath ice shelves in the Amundsen Sea at this resolution.

A description and assessment of the first release of the Arctic Subpolar gyre sTate Estimate (ASTE_R1), a data-constrained ocean-sea ice model-data synthesis is presented. ASTE_R1 has a nominal resolution of 1/3o and spans the period 2002-2017. The fit of the model to an extensive (O(10^9)) set of satellite and in situ observations was achieved through adjoint-based nonlinear least-squares optimization. The improvement of the solution compared to an unconstrained simulation is reflected in misfit reductions of 77% for Argo, 50% for satellite sea surface height, 58% for the Fram Strait mooring, 65% for Ice Tethered Profilers, and 83% for sea ice extent. Exact dynamical and kinematic consistency is a key advantage of ASTE_R1, distinguishing the state estimate from existing ocean reanalyses. Through strict adherence to conservation laws, all sources and sinks within ASTE_R1 can be accounted for, permitting meaningful analysis of closed budgets at the grid-scale, such as contributions of horizontal and vertical convergence to the tendencies of heat and salt. ASTE_R1 thus serves as the biggest effort undertaken to date of producing a specialized Arctic ocean-ice estimate over the 21st century. Transports of volume, heat, and freshwater are consistent with published observation-based estimates across important Arctic Mediterranean gateways. Interannual variability and low frequency trends of freshwater and heat content are well represented in the Barents Sea, western Arctic halocline, and east subpolar North Atlantic. Systematic biases remain in ASTE_R1, including a warm bias in the Atlantic Water layer in the Arctic and deficient freshwater inputs from rivers and Greenland discharge.

Data assimilation (DA) is integrated with machine learning in order to perform entirely data-driven online state estimation. To achieve this, recurrent neural networks (RNNs) are implemented as surrogate models to replace key components of the DA cycle in numerical weather prediction (NWP), including the conventional numerical forecast model, the forecast error covariance matrix, and the tangent linear and adjoint models. It is shown how these RNNs can be initialized using DA methods to directly update the hidden/reservoir state with observations of the target system. The results indicate that these techniques can be applied to estimate the state of a system for the repeated initialization of short-term forecasts, even in the absence of a traditional numerical forecast model. Further, it is demonstrated how these integrated RNN-DA methods can scale to higher dimensions by applying domain localization and parallelization, providing a path for practical applications in NWP.

A key component of data assimilation methods is the specification of univariate spatial correlations, which appear in the background-error covariance. For realistic problems in meteorology and oceanography, correlation length scales are nonstationary (variable in space) and anisotropic (variable in each direction). Variational approaches typically use an operator to enforce correlation length scales, and thus the operator must be designed to capture desired levels of nonstationarity and anisotropy. For systems with complex boundaries, such as the ocean, it is natural to use a filtering approach based on the application of an elliptic, Laplacian-like operator. Here we show how an elliptic operator can be formulated to capture a general Matérn-type correlation structure. We show how nonstationarity and anisotropy can be encoded into the operator via a simple change of variables based on user-defined normalization length scales. The change of variables defines a mapping between the computational domain and a space where the analytical Matérn correlation function applies. In addition to the mapping, two other hyperparameters separately control the correlation length scale (i.e. range) and shape. As a practical use-case, we apply the operator to a global ocean model. We show that when the normalizing length scales correspond to the local grid scale, the range parameter has an intuitive interpretation as the number of neighboring grid cells at which correlation drops to 0.14. Finally, the correlation model is shown to be computationally efficient in two regards. First, the necessary linear solve can be performed with a high tolerance (∼10^{-3}) while still achieving the correct statistics, requiring few iterations to converge. Secondly, the operator’s exponent, which controls the correlation shape, is linearly related to the diagonal elements of its matrix representation. As a result, using an exponent greater than one can improve convergence properties. Thus, the framework provides flexibility in controlling correlation shape.