Abstract. State-of-the-art Earth System models typically employ grid spacings of O(100 km), 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 already now (i) be run coupled globally on seasonal time scales with a grid spacing of 5 km and on monthly time scales with a grid spacing of 2.5 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 a finest grid spacing of 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 to observations of these various configurations reveals no obvious pitfall. 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.
We analyze the generalized k-variations for the solution to the wave equation driven by an additive Gaussian noise which behaves as a fractional Brownian with Hurst parameter H > 1 2 in time and which is white in space. The k-variations are defined along filters of any order p ≥ 1 and of any length. We show that the sequence of generalized k-variation satisfies a Central Limit Theorem when p > H + 1 4 and we estimate the rate of convergence for it via the Stein-Malliavin calculus. The results are applied to the estimation of the Hurst index. We construct several consistent estimators for H and these estimators are analyzed theoretically and numerically.2010 AMS Classification Numbers: 60G15, 60H05, 60G18.
We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the quadratic variations of the solution, defined via higher order increments. Then we apply our results to construct and study estimators for the Hurst index.2010 AMS Classification Numbers: 60G15, 60H05, 60G18.
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