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.
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).
Citation: Monthly Weather Review 146, 11; 10.1175/MWR-D-17-0345.1
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