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Steven Sandbach
,
John Thuburn
,
Danail Vassilev
, and
Michael G. Duda

Abstract

An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%–20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

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John Thuburn
,
Hilary Weller
,
Geoffrey K. Vallis
,
Robert J. Beare
, and
Michael Whitall

Abstract

A new theoretical framework is derived for parameterization of subgrid physical processes in atmospheric models; the application to parameterization of convection and boundary layer fluxes is a particular focus. The derivation is based on conditional filtering, which uses a set of quasi-Lagrangian labels to pick out different regions of the fluid, such as convective updrafts and environment, before applying a spatial filter. This results in a set of coupled prognostic equations for the different fluid components, including subfilter-scale flux terms and entrainment/detrainment terms. The framework can accommodate different types of approaches to parameterization, such as local turbulence approaches and mass flux approaches. It provides a natural way to distinguish between local and nonlocal transport processes and makes a clearer conceptual link to schemes based on coherent structures such as convective plumes or thermals than the straightforward application of a filter without the quasi-Lagrangian labels. The framework should facilitate the unification of different approaches to parameterization by highlighting the different approximations made and by helping to ensure that budgets of energy, entropy, and momentum are handled consistently and without double counting. The framework also points to various ways in which traditional parameterizations might be extended, for example, by including additional prognostic variables. One possibility is to allow the large-scale dynamics of all the fluid components to be handled by the dynamical core. This has the potential to improve several aspects of convection–dynamics coupling, such as dynamical memory, the location of compensating subsidence, and the propagation of convection to neighboring grid columns.

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Steven C. Hardiman
,
Ian A. Boutle
,
Andrew C. Bushell
,
Neal Butchart
,
Mike J. P. Cullen
,
Paul R. Field
,
Kalli Furtado
,
James C. Manners
,
Sean F. Milton
,
Cyril Morcrette
,
Fiona M. O’Connor
,
Ben J. Shipway
,
Chris Smith
,
David N. Walters
,
Martin R. Willett
,
Keith D. Williams
,
Nigel Wood
,
N. Luke Abraham
,
James Keeble
,
Amanda C. Maycock
,
John Thuburn
, and
Matthew T. Woodhouse

Abstract

A warm bias in tropical tropopause temperature is found in the Met Office Unified Model (MetUM), in common with most models from phase 5 of CMIP (CMIP5). Key dynamical, microphysical, and radiative processes influencing the tropical tropopause temperature and lower-stratospheric water vapor concentrations in climate models are investigated using the MetUM. A series of sensitivity experiments are run to separate the effects of vertical advection, ice optical and microphysical properties, convection, cirrus clouds, and atmospheric composition on simulated tropopause temperature and lower-stratospheric water vapor concentrations in the tropics. The numerical accuracy of the vertical advection, determined in the MetUM by the choice of interpolation and conservation schemes used, is found to be particularly important. Microphysical and radiative processes are found to influence stratospheric water vapor both through modifying the tropical tropopause temperature and through modifying upper-tropospheric water vapor concentrations, allowing more water vapor to be advected into the stratosphere. The representation of any of the processes discussed can act to significantly reduce biases in tropical tropopause temperature and stratospheric water vapor in a physical way, thereby improving climate simulations.

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