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  • View in gallery
    Fig. 1.

    Schematic representation of physics–dynamics coupling. (a) Two models: an ocean model and an atmosphere model. Both of these have spatial scales (here indicated by the plane with red lines) and temporal scales (indicated by the blue axis). These are coupled (thick lines); that means one domain in the spatial plane maps into the spatial plane of the other model (thick red line) and similarly in the temporal axis (thick blue line). In the spatial plane, aspects such as grid type, fixed vs variable resolution, one-dimensional vs three-dimensional, and fine vs coarse are shown as some of the aspects of the spatial resolution that can vary between models and do not necessarily have a straightforward mapping. Then, each of these models has its ecosystem of parameterizations (an arbitrary set of processes was chosen here for illustration only), which interact with the model and themselves via coupling. These parameterizations also occupy potentially—or almost certainly—different areas on the spatial plane and temporal axis. All of this exists in front of a background problem of thermodynamics, which ultimately governs them all (or ought to, anyhow). (b) Four-tier scheme of investigation, ranging from (by necessity) abstract analysis via reduced equation sets (with less necessity for abstraction) to simplified physics tests and finally full model runs. The complexity of the analysis increases from one to the other. The manner in which the results and conclusions from the experimentation can inform the production runs ranges from “difficult” (results are expected in the form of guidance or informing a choice that needs to be made in the design phase) to “direct” (a benefit can be demonstrated straightaway by producing an improved forecast).

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    Fig. 2.

    Global-mean surface temperature change (K) resulting from a doubling of CO2 in simulations conducted with the ECHAM5 atmosphere model (Roeckner et al. 2003, 2006) coupled with a slab ocean. Red and blue markers indicate high- and low-sensitivity models, which differ only in a few uncertain parameters in the physics parameterizations (Klocke et al. 2011). For each time step size listed on the x axis, the global-mean surface temperature change is computed as the difference between a 10-yr present-day simulation and the last 10 years of a 50-yr simulation with doubled CO2. The spatial resolution of the atmosphere model is T31 with 19 layers. Error bars indicate interannual variability of global- and annual-mean surface temperature.

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    Fig. 3.

    (a) Scatterplots of cloudy mass flux against large-scale mass flux and (b) minus dry mass flux against cloudy updraft mass flux. The mass fluxes have been converted to velocities in units of m s−1 by normalization with density. The data are taken from a height of 3195 m and are averaged in the horizontal to scale of 24 km. Met Office Unified Model.

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    Fig. 4.

    Convergence to circulation required to maintain Ekman balance of the vertical slice primitive equation simulations (Beare and Cullen 2016) for different time-stepping schemes: implicit, K-update, and Wood et al. (2007). Ro1.7 is shown in gray for reference of the slope (y-axis intercept is arbitrary).

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    Fig. 5.

    Snapshots of instantaneous (left) 850-hPa vertical pressure velocities and (right) precipitation rates in MITC simulations. (a),(e) CAM-FV; (b),(f) CAM-EUL; and (c),(d),(g),(h) CAM-SE dynamical cores. (c),(g) se_ftype = 1 denotes a physics–dynamics coupling with the long physics time step; (d),(h) se_ftype = 0 couples with a subcycled, short dynamics time step. The physics time steps are 1800 (FV, SE) and 600 s (EUL); the dynamics time steps are 180 (FV), 600 (EUL), and 300 s (SE). In the case of SE with se_ftype=0, the forcing was gradually applied every 300 s. The EUL dynamical core is coupled to the physics in a process split (parallel) way; the SE and FV physics–dynamics coupling is time split.

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    Fig. 6.

    The 2-yr-mean zonal-mean precipitation rate in four aquaplanet simulations with the CAM5 dynamical cores SE (111 km), FV (111 km), EUL (T85), SLD (T85), and the default CAM5 physics package.

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    Fig. 7.

    Aquaplanet simulations with the alternative CLUBB PBL, macrophysics, and shallow convection schemes in CAM5. Latitude–pressure cross section of the 1-yr-mean zonal-mean vertical pressure velocity in the tropics for the dynamical cores (a) SE with diffusion (hyperviscosity) coefficient m4 s−1, (b) SE with diffusion coefficient m4 s−1, and (c) SLD without explicit horizontal diffusion. (d)–(f) The 1-yr-mean zonal-mean precipitation rates of the three runs, split into total (red), large-scale (green), and convective (blue) precipitation.

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    Fig. 8.

    Schematic view of the coupling between the computational domains of the atmosphere model and ocean model , with time advancing to the right. The function represents the parameterization of air–sea fluxes with (), the oceanic (atmospheric) state vector. Term is a given time averaging operator, and , the dynamical time step of the models such that .

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    Fig. 9.

    Operational ECMWF forecast with a spectral truncation T1279 (a) 16- and (b) 9-km reduced Gaussian grid. Three-day accumulated surface large-scale precipitation for forecasts starting at 0000 UTC 20 May 2015 valid at 0000 UTC 23 May 2015. (c) Study area marked with red square.

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    Fig. 10.

    Element polynomials in one dimension. The figure shows three elements. The edges of the elements are marked with blue arrows. The red curves are the degree 3 polynomials in each element, and, following the CAM-SE algorithm, the polynomial values from each side of an element boundary are averaged. The filled green circles show the GLL quadrature point values, and the red filled circles are the locations of the GLL quadrature points in each element for . The histogram bar shows the cell-averaged values on an physics grid (each element has been divided into three equal-sized control volumes) obtained by integrating the Lagrange basis functions over the control volumes.

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    Fig. 11.

    Zonal–time average (top left) surface pressure, (top right) total precipitation rate, (bottom left) total cloud fraction, and (bottom right) albedo as a function of latitude (from the equator to 80°N) for the different configurations of CAM-SE. Temporal averaging over a period of 24 months and mapping to a 1.5° × 1.5° regular latitude–longitude grid was applied for analysis.

  • View in gallery
    Fig. 12.

    Influence of on the resolution sensitivity of the CAM4 physics (precipitation) to QU and VRs using MPAS-A. (a) Sensitivity of equatorial (±2° latitude) precipitation to gridcell size (x axis) in different values of R as represented by three arrows. (b) Fraction of convective precipitation as a function of R (x axis) and gridcell size (240 vs 120 km). (c) Zonal anomaly of precipitation in a VR simulation with . (d) As in (c), but a VR simulation with . (e) Zonal anomaly of velocity potential (shading) and divergent component of wind (arrows) with . (f) As in (e), but for . The solid and dashed circles in (c)–(f) represent the boundaries enclosing the domain with 30-km grid and the transition to 240-km grid domain, respectively.

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    Fig. 13.

    Illustration of the Ma et al. (2014) and Fowler et al. (2016) approaches for scale-aware convection using the Zhang–McFarlane closure. (a) Term τ from Ma et al. (2014) as a function of grid spacing. (b) The fractional convective cloud cover (σ; red line) and scaling factor for cloud-base mass flux used in Fowler et al. (2016). (c) The cloud-base mass flux (inside y axis) based on the Zhang–McFarlane closure with J kg−1 and J m2 kg−2 and different modifications. Dashed line is the default with s (Default); blue line is τ following Ma et al. (2014); red line is s (Grell and Freitas–Fowler); and green line is combined. The outside y axis in (c) shows the mass increment through the cloud base for s (i.e., multiply each curve by 600). (d) Mass increment through the cloud base is shown for the same cases in (c), using .

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Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress

Markus Gross Departamento de Oceanografía Física, Centro de Investigación Científica y Educación Superior de Ensenada, Ensenada, Baja California, México

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Hui Wan Pacific Northwest National Laboratory, Richland, Washington

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Philip J. Rasch Pacific Northwest National Laboratory, Richland, Washington

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Peter M. Caldwell Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California

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David L. Williamson National Center for Atmospheric Research, Boulder, Colorado

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Daniel Klocke Hans Ertel Center for Weather Research, Deutscher Wetterdienst, Offenbach, Germany

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Christiane Jablonowski Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, Michigan

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Diana R. Thatcher Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, Michigan

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Nigel Wood Met Office, Exeter, United Kingdom

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Mike Cullen Met Office, Exeter, United Kingdom

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Bob Beare CEMPS, Exeter University, Exeter, United Kingdom

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Martin Willett Met Office, Exeter, United Kingdom

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Florian Lemarié INRIA, University of Grenoble–Alpes, LJK, CNRS, Grenoble, France

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Eric Blayo INRIA, University of Grenoble–Alpes, LJK, CNRS, Grenoble, France

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Sylvie Malardel ECMWF, Shinfield Park, Reading, United Kingdom

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Piet Termonia Royal Meteorological Institute of Belgium, Brussels, Belgium
Department of Physics and Astronomy, Ghent University, Ghent, Belgium

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Almut Gassmann IAP Kühlungsborn, Leibniz–Institut für Atmosphärenphysik e.V. an der Universität Rostock, Kühlungsborn, Germany

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Peter H. Lauritzen National Center for Atmospheric Research, Boulder, Colorado

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Hans Johansen Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, Berkeley, California

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Open access

Abstract

Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Markus Gross, mgross@cicese.mx

Abstract

Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Markus Gross, mgross@cicese.mx

1. Introduction

Weather, climate, and Earth system models approximate the solutions to sets of equations that describe the relevant physics and chemistry. These equations represent, for example, balances of momentum, energy, and mass of the appropriate system. Discrete approximations in space and time to these continuous equations are necessary to solve these equations numerically. Creating a single, coherent, and consistent discretization of an entire system of equations covering the entire range of spatial and temporal scales, even for one component such as the atmosphere, is indeed challenging, if not an impossible task. Even if it is possible, the numerical solution of such a system (spanning all possible scales) is currently beyond the reach of even the most powerful computers. Therefore, the system is separated into components that are discretized mostly independently of each other and then coupled together in some manner. These components can broadly be classified as comprising the resolved fluid dynamical aspects of the atmosphere or the ocean, unresolved fluid dynamical aspects (e.g., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical elements such as radiation and microphysical processes.

The challenges associated with bringing together all the various discretized components to create a coherent model will be referred to here as physics–dynamics coupling. The term physics–dynamics coupling has evolved from the fact that the resolved fluid dynamics components are commonly known as the dynamical cores or simply “dynamics,” and the physical parameterizations that represent the unresolved and underresolved processes and the nonfluid dynamical processes are collectively referred to as “physics.” The weather, climate, and Earth system modeling communities have relatively recently started to make focused efforts on addressing physics–dynamics coupling in the broader sense as a topic by itself (Gross et al. 2016a).

Figure 1a schematically shows the variety of model components and the different aspects of discretizing them in both space and time, as well as the coupling between them. For simplicity, Fig. 1a includes only two component models: the atmosphere and the ocean. However, modeling systems often include a large number of other components, such as land, glacier, sea ice, atmospheric chemistry, and ocean biogeochemistry models. These components are inherently coupled to each other through the momentum, mass, and energy exchanges at their interfaces.

Fig. 1.