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“…The numerical dissipation in this model introduced in section 2.2 (D u , Figure 10i) may be primarily due to the interpolation process in the semi-Lagrangian advection scheme [Jablonowski and Williamson, 2011] by which the dissipation resembles fourth-order hyperdiffusion (−K 4 ∇ 4 u) [Yao and Jablonowski, 2013]. The detailed structure and magnitudes of D u shown in Figure 10i match well with −K 4 4 u∕ z 4 when K 4 = 1.5 × 10 6 m 4 s −1 .…”

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“…The numerical dissipation in this model introduced in section 2.2 (D u , Figure 10i) may be primarily due to the interpolation process in the semi-Lagrangian advection scheme [Jablonowski and Williamson, 2011] by which the dissipation resembles fourth-order hyperdiffusion (−K 4 ∇ 4 u) [Yao and Jablonowski, 2013]. The detailed structure and magnitudes of D u shown in Figure 10i match well with −K 4 4 u∕ z 4 when K 4 = 1.5 × 10 6 m 4 s −1 .…”

“…-Optimization of solver efficiency: even though the use of the KPP has simplified the code maintenance and may result in a higher numerical accuracy of the solution, it also caused a considerable slow-down of the numerical efficiency as compared to the EBI solver, as that solver had been optimized for tropospheric ozone chemistry in C-IFS-CB05. Solutions could be an optimization of the initial chemical time step for the KPP solver, depending on prevailing chemical and physical conditions, and an optimization of the automated solver code, which allows for a more efficient code structure (KP4, Jöckel et al, 2010).…”

“…Controlling the Nonlinear Term. We start from the expression (20) for H m k to obtain estimates on the nonlinear term in (14). By definition of E θ , ( 13), one has…”

“…In this work we present a solution theory of 2-dimensional Primitive Equations in the hyperviscous setting D(∆) = −(−∆) θ , for large enough θ and a suitable stochastic forcing. The regularising effect of hyperviscosity for Navier-Stokes and Primitive Equations is well-understood in the deterministic setting, and it is often used in numerical simulations [20]; we refer to [19,22,23] and, more recently, [18] for a thorough discussion. The main contribution of the present paper is thus to introduce a Gaussian invariant measure in the context of 2-dimensional Primitive Equations, and then to exploit the techniques of [15] to provide a first well-posedness result for this singular SPDE in a hyperviscous setting.…”

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