A new surface boundary forcing dataset for uncoupled simulations with the Community Atmosphere Model is described. It is a merged product based on the monthly mean Hadley Centre sea ice and SST dataset version 1 (HadISST1) and version 2 of the National Oceanic and Atmospheric Administration (NOAA) weekly optimum interpolation (OI) SST analysis. These two source datasets were also used to supply ocean surface information to the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40). The merged product provides monthly mean sea surface temperature and sea ice concentration data from 1870 to the present: it is updated monthly, and it is freely available for community use. The merging procedure was designed to take full advantage of the higher-resolution SST information inherent in the NOAA OI.v2 analysis.
The spectral representations for arbitrary discrete parameter infinitely divisible processes as well as for (centered) continuous parameter infinitely divisible processes, which are separable in probability, are obtained. The main tools used for the proofs are (i) a "polar-factorization" of an arbitrary L6vy measure on a separable Hilbert space, and (ii) the Wiener-type stochastic integrals of non-random functions relative to arbitrary "infinitely divisible noise".
Let X = (X(t):t ≥ 0) be a Lévy process and X∊ the compensated sum of jumps not exceeding ∊ in absolute value, σ2(∊) = var(X∊(1)). In simulation, X - X∊ is easily generated as the sum of a Brownian term and a compound Poisson one, and we investigate here when X∊/σ(∊) can be approximated by another Brownian term. A necessary and sufficient condition in terms of σ(∊) is given, and it is shown that when the condition fails, the behaviour of X∊/σ(∊) can be quite intricate. This condition is also related to the decay of terms in series expansions. We further discuss error rates in terms of Berry-Esseen bounds and Edgeworth approximations.
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