A goal oriented error estimator and mesh adaptivity for sea ice simulations

For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal discretization as well as from the splitting in time of the ice momentum equations from further parts of the coupled system. The novelty of the error estimator lies in the consideration of the splitting error, which turns out to be dominant with increasing mesh resolution. Errors are measured in user specified functional outputs like the total sea ice extent. The error estimator is based on the dual weighted residual method that asks for the solution of an additional dual problem for obtaining sensitivity information. Estimated errors can be used to validate the accuracy of the solution and, more relevant, to reduce the discretization error by guiding an adaptive algorithm that optimally balances the mesh size and the time step size to increase the efficiency of the simulation

The effect of the tracer staggering on sea ice deformation fields

Sea ice models can simulate linear deformation characteristics (linear kinematic features) that are observed from satellite imagery. A recent study based on the viscous-plastic sea ice model highlights the role of the velocity placement on the simulation of linear kinematic features (LKFs) and concluded that the tracer staggering has a minor influence on the amount simulated LKFs. In this work we consider the same finite element discretization and show that on triangular meshes the placement of the sea ice tracers and the associated degrees of freedom (DoFs) have a strong influence on the amount of simulated LKFs. This behaivor can be explained by the change of the total number of DoFs associated with the tracer field. We analyze the effect on a benchmark problem and compare P1-P1, P0-P1, CR-P0 and CR-P1 finite element discretizations for the velocity and the tracers, respectively. The influence of the tracer placement is less strong on quadrilateral meshes as a change of the tracer staggering does not modify the total number of DoFs. Among the low order finite element approximations compared in this study, the CR-P0 finite element discretization resolves the deformation structure in the best way. The CR finite element for velocity in combination with the P0 discretization for tracer produces more LKFs than the P1-P1 finite element pair even on grids with fewer DoFs. This can not be achieved with the CR-P1 setup and therefore highlights the importance of the tracer discretization for the simulation of LKFs on triangular meshes

Robust and efficient primal-dual Newton-Krylov solvers for viscous-plastic sea-ice models

We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material law in the momentum equation, the development of fast, robust and scalable solvers is still a substantial challenge. In this paper, we propose a novel primal-dual Newton linearization for the implicitly-in-time discretized momentum equation. Compared to existing methods, it converges faster and more robustly with respect to mesh refinement, and thus enables numerically converged sea-ice simulations at high resolutions. Combined with an algebraic multigrid-preconditioned Krylov method for the linearized systems, which contain strongly varying coefficients, the resulting solver scales well and can be used in parallel. We present experiments for two challenging test problems and study solver performance for problems with up to 8.4 million spatial unknowns.Comment: 18 pages, 7 figure

Understanding the biases to sepsis surveillance and quality assurance caused by inaccurate coding in administrative health data

Purpose Timely and accurate data on the epidemiology of sepsis are essential to inform policy decisions and research priorities. We aimed to investigate the validity of inpatient administrative health data (IAHD) for surveillance and quality assurance of sepsis care. Methods We conducted a retrospective validation study in a disproportional stratified random sample of 10,334 inpatient cases of age ≥ 15 years treated in 2015–2017 in ten German hospitals. The accuracy of coding of sepsis and risk factors for mortality in IAHD was assessed compared to reference standard diagnoses obtained by a chart review. Hospital-level risk-adjusted mortality of sepsis as calculated from IAHD information was compared to mortality calculated from chart review information. Results ICD-coding of sepsis in IAHD showed high positive predictive value (76.9–85.7% depending on sepsis definition), but low sensitivity (26.8–38%), which led to an underestimation of sepsis incidence (1.4% vs. 3.3% for severe sepsis-1). Not naming sepsis in the chart was strongly associated with under-coding of sepsis. The frequency of correctly naming sepsis and ICD-coding of sepsis varied strongly between hospitals (range of sensitivity of naming: 29–71.7%, of ICD-diagnosis: 10.7–58.5%). Risk-adjusted mortality of sepsis per hospital calculated from coding in IAHD showed no substantial correlation to reference standard risk-adjusted mortality (r = 0.09). Conclusion Due to the under-coding of sepsis in IAHD, previous epidemiological studies underestimated the burden of sepsis in Germany. There is a large variability between hospitals in accuracy of diagnosing and coding of sepsis. Therefore, IAHD alone is not suited to assess quality of sepsis care

On discretizing sea-ice dynamics on triangular meshes using vertex, cell or edge velocities

Discretization of the equations of Viscous Plastic and Elastic Viscous Plastic (EVP) sea ice dynamics on triangular meshes can be done by placing discrete velocities at vertices, cells or edges. Since there are more cells and edges than vertices, the cell- and edge-based discretizations simulate more linear kinematic features at the same mesh than the vertex discretization. However, the discretization based on cell and edge velocities suffer from kernels in the strain rate or stress divergence operators and need either special strain rate computations as proposed here for cell velocities, or stabilization as proposed earlier for edge velocities. An elementary Fourier analysis clarifies how kernels are removed, and also shows that cell and edge velocity placement leads to spurious branches of stress divergence operator with large negative eigenvalues. Although spurious branches correspond to fast decay and are not expected to distort sea ice dynamics, they demand either smaller internal time steps or higher stability parameters in explicit EVP-like methods

Discretization of Sea Ice Dynamics in the Tangent Plane to the Sphere by a CD‐Grid‐Type Finite Element

We present a new discretization of sea ice dynamics on the sphere. The approach describes sea ice motion in tangent planes to the sphere. On each triangle of the mesh, the ice dynamics are discretized in a local coordinate system using a CD‐grid‐like non‐conforming finite element method. The development allows a straightforward coupling to the C‐grid like ocean model in Icosahedral Non‐hydrostatic‐Ocean model, which uses the same infrastructure as the sea ice module. Using a series of test examples, we demonstrate that the non‐conforming finite element discretization provides a stable realization of large‐scale sea ice dynamics on the sphere. A comparison with observation shows that we can simulate typical drift patterns with the new numerical realization of the sea ice dynamics.Plain Language Summary: Sea ice in polar regions plays an important role in the exchange of heat and freshwater between the atmosphere and the ocean and hence for climate in general. Therefore climate models require a description (a set of equations) to express the large‐scale sea ice motion. We present a mathematical framework for describing sea ice flow in a global three‐dimensional Cartesian system. The idea is to express the sea ice motion in tangent planes. In this reference system, we solve the mathematical equations that describe the sea ice motion. The equations are approximated on a computational grid, that consists of triangles covering the surface of the sphere. On each triangle the sea ice velocity is placed at the edge midpoint. The development is motivated by the infrastructure of the ocean and sea ice model Icosahedral Non‐hydrostatic‐Ocean model. The old representation of sea ice dynamics uses a different design principle. Therefore, the communication between the sea ice and ocean model is computationally expensive. To circumvent this problem we have developed a numerical realization of sea ice dynamics that uses the same infrastructure as the ocean model. We show that the new realization of the sea ice dynamics is capable of capturing the sea ice drift.Key Points: First realization of sea ice dynamics in tangent planes to the sphere. Discretization of the sea ice dynamics in a three‐dimensional Cartesian framework. Realization of the sea ice dynamics in the ocean and sea ice model Icosahedral Non‐hydrostatic‐Ocean model.Max Planck SocietyDFGCollaborative Research Center TRR 181Scientific Steering Committeehttp://dx.doi.org/10.17632/2v5shnnmwxhttps://mpimet.mpg.de/en/science/modeling-with-icon/code-availabilityhttps://thredds.met.no/thredds/osisaf/osisaf_cdrseaiceconc.htmlhttp://dx.doi.org/10.22033/ESGF/input4MIPs.10842http://dx.doi.org/10.5067/INAWUWO7QH7

Sea Ice conditions within the Antarctic Marginal Ice Zone in winter 2017, onboard the SA Agulhas II

Our knowledge of sea ice variability, which contributes to the detection of the Antarctic climate change trends, stems primarily from remotely sensed information. However, sea ice in the Southern Ocean is characterized by large variability that remains unresolved and limits our confidence on the remotely sensed products. Therefore, the in situ sea ice observations presented (according to the ASPeCt protocol) provide a greater understanding of the Antarctic sea ice environment - on a local scale - and allows us to evaluate remotely sensed products

ICON-Sapphire: simulating the components of the Earth system and their interactions at kilometer and subkilometer scales

International audienceState-of-the-art Earth system models typically employ grid spacings of O(100 km), which is too coarse to explicitly resolve main drivers of the flow of energy and matter across the Earth system. In this paper, we present the new ICON-Sapphire model configuration, which targets a representation of the components of the Earth system and their interactions with a grid spacing of 10 km and finer. Through the use of selected simulation examples, we demonstrate that ICON-Sapphire can (i) be run coupled globally on seasonal timescales with a grid spacing of 5 km, on monthly timescales with a grid spacing of 2.5 km, and on daily timescales with a grid spacing of 1.25 km; (ii) resolve large eddies in the atmosphere using hectometer grid spacings on limited-area domains in atmosphere-only simulations; (iii) resolve submesoscale ocean eddies by using a global uniform grid of 1.25 km or a telescoping grid with the finest grid spacing at 530 m, the latter coupled to a uniform atmosphere; and (iv) simulate biogeochemistry in an ocean-only simulation integrated for 4 years at 10 km. Comparison of basic features of the climate system to observations reveals no obvious pitfalls, even though some observed aspects remain difficult to capture. The throughput of the coupled 5 km global simulation is 126 simulated days per day employing 21 % of the latest machine of the German Climate Computing Center. Extrapolating from these results, multi-decadal global simulations including interactive carbon are now possible, and short global simulations resolving large eddies in the atmosphere and submesoscale eddies in the ocean are within reach