We derive an implicit-explicit (IMEX) formalism for the three-dimensional (3D) Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud resolving and mesoscale (flow in a 3D Cartesian domain) as well as global regimes (flow in spherical geometries). This general IMEX formalism admits numerous types of methods including single-stage multistep methods (e.g., Adams methods and backward difference formulas) and multistage singlestep methods (e.g., additive Runge-Kutta methods). The significance of this result is that it allows a numerical model to reuse the same machinery for all classes of time-integration methods described in this work. We also derive two classes of IMEX methods, one-dimensional and 3D, and show that they achieve their expected theoretical rates of convergence regardless of the geometry (e.g., 3D box or sphere) and introduce a new second-order IMEX Runge-Kutta method that performs better than the other second-order methods considered. We then compare all the IMEX methods in terms of accuracy and efficiency for two types of geophysical fluid dynamics problems: buoyant convection and inertia-gravity waves. These results show that the high-order time-integration methods yield better efficiency particularly when high levels of accuracy are desired. Introduction.In a previous article [20] we introduced the nonhydrostatic unified model of the atmosphere (NUMA) for use in limited-area modeling (i.e., mesoscale or regional flow), namely, applications in which the flows are in large, three-dimensional (3D) Cartesian domains (imagine flow in a 3D box where the grid resolutions are below 10 km); the emphasis of that paper was on the performance of the model on distributed-memory computers with a large number of processors. In that paper we showed that the explicit RK35 time integrator (also used in this paper) was able to achieve strong linear scaling for processor counts on the order of 10 5 . The emphasis of the present article is on the mathematical framework of the model dynamics (i.e., we are not considering the subgrid-scale parameterization at this point;

We present a computational framework for integrating a state-of-the-art numerical weather prediction (NWP) model in stochastic unit commitment/economic dispatch formulations that account for wind power uncertainty. We first enhance the NWP model with an ensemble-based uncertainty quantification strategy implemented in a distributed-memory parallel computing architecture. We discuss computational issues arising in the implementation of the framework and validate the model using real wind-speed data obtained from a set of meteorological stations. We build a simulated power system to demonstrate the developments.

This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different time-steps to be used in different parts of the spatial domain. The discretization is second order accurate in time and preserves the conservation and stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global time-steps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms.

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: The Alpine Orogen contains in South East Europe, from the Carpathians to the Balkans–Srednogorie, an Upper Cretaceous, ore bearing igneous belt: a narrow elongated body which runs discontinously from the Apuseni Mountains in the North, to the western part of the South Carpathians (Banat) in Romania, and further South to the Carpathians of East Serbia and still further East to Srednogorie (Bulgaria). This results in a belt of 750 km/30–70 km, bending from N‐S in Romania and Serbia, to E‐W in Bulgaria. Using the well established century‐old terminology of this region, we describe it in this paper as the Banatitic Magmatic and Metallogenetic Belt (BMMB). Plate tectonics models of the Alpine evolution of South East Europe involve Mesozoic rifting, spreading and thinning of the continental crust or formation of oceanic crust in the Tethian trench system, followed by Cretaceous‐Tertiary convergence of Africa with Europe and opening of Eastern Mediterranean and Black Sea troughs. The result of successive stages in the collision process is not only the continental growth of Europe from N to S by the docking of several microplates formerly separated from it by Mesozoic palaeo–oceans, but also the rise of mountain belts by overthickening of the crust, followed by orogenic collapse, lateral extrusion, exhumation of metamorphic core complexes and post‐collisional magmatism connected to strike‐slip or normal faulting. The BMMB of the Carpathian‐Balkan fold belt is rich in ore deposits related to plutons and/or volcano‐plutonic complexes. Serbian authors have proposed an Upper Cretaceous Paleorift in Eastern Serbia for the Timok zone and some Bulgarian geologists have furnished geologic, petrological and metallogenetic support for this extensional model along the entire BMMB. The existence and importance of previous westwards directed subductions of Transilvanides (=South Apuseni = Mureş Zone) and Severin‐Krajina palaeo–oceans, popular in Roman ian literature, seems to have little relevance to BMMB generation, but the well documented northwards directed subduction of the Vardar‐Axios palaeo–ocean during Jurassic and Lower Cretaceous is a good pre‐condition for the generation, during the Upper Cretaceous, of banatitic magmas in extensional regime, by mantle delamination due to slab break–off. Four magmatic trends are found: a tholeiitic trend, a calc‐alkaline trend, a calc‐alkaline high–K to shoshonitic trend and, restricted to East Srednogorie, a peralkaline trend. For acid intrusives, the typology is clearly I‐type and magnetite–series, pointing to sources in the deep crust or the mantle; however, some high 87Sr/86Sr ratios recorded in banatites prove important contamination from the upper crust. The calc‐alkaline hydrated magmas, most common for banatitic plutons, can be considered as recording three stages of evolution: more primitive – the monzodioritic, dioritic to granodioritic trend (S Apuseni, S Ba–nat, Timok, C and W Srednogorie); more evolved – the granodioritic‐granitic trend (N Apuseni, N Banat, Ridanj–K...