Hierarchies of Models

With thanks to Inna Polichtchouk.

General circulation models (GCMs) of varying complexity are used in atmospheric and oceanic sciences to study different atmospheric processes and to simulate response of climate to climate change and other forcings.

However, Held (2005) warned the climate community that the gap between understanding and simulating atmospheric and oceanic processes is becoming wider. He stressed the use of model hierarchies for improved understanding of the atmosphere and oceans (Fig. 1). Often at the bottom of the hierarchy lie the well-understood, idealized, one- or two-layer models.  In the middle of the hierarchy lie multi-layer models, which omit certain processes such as land-ocean-atmosphere interactions or moist physics. And finally, at the top of the hierarchy lie fully coupled atmosphere-ocean general circulation models that are used for climate projections. Such model hierarchies are already well developed in other sciences (Held 2005), such as molecular biology, where studying less complex animals (e.g. mice) infers something about the more complex humans (through evolution).

Figure 1: Model hierarchy of midlatitude atmosphere (as used for studying storm tracks). The simplest models are on the left and the most complex models are on the right. Bottom panels show eddy kinetic energy (EKE, contours) and precipitation (shading) with increase in model hierarchy (left-to-right): No precipitation in a dry core model (left), zonally homogeneous EKE and precipitation in an aquaplanet model (middle), and zonally varying EKE and precipitation in the most complex model (right). Source: Shaw et al. (2016), Fig. B2.

Model hierarchies have now become an important research tool to further our understanding of the climate system [see, e.g., Polvani et al. (2017), Jeevanjee et al. (2017), Vallis et al. (2018)]. This approach allows us to delineate most important processes responsible for circulation response to climate change (e.g., mid-latitude storm track shift, widening of tropical belt etc.), to perform hypothesis testing, and to assess robustness of results in different configurations.

In my PhD, I have extensively used the model hierarchies concept to understand mid-latitude tropospheric dynamics (Fig. 1). One-layer barotropic and two-layer quasi-geostrophic models are often used as a first step to understand large-scale dynamics and to establish the importance of barotropic and baroclinic processes (also discussed in my previous blog post). Subsequently, more realistic “dry” non-linear multi-layer models with simple treatment for boundary layer and radiation [the so-called “Held & Suarez” setup, first introduced in Held and Suarez (1994)] can be used to study zonally homogeneous mid-latitude dynamics without complicating the setup with physical parametrisations (e.g. moist processes), or the full range of ocean-land-ice-atmosphere interactions. For example, I have successfully used the Held & Suarez setup to test the robustness of the annular mode variability (see my previous blog post) to different model climatologies (Boljka et al., 2018). I found that baroclinic annular mode timescale and its link to the barotropic annular mode is sensitive to model climatology. This can have an impact on climate variability in a changing climate.

Additional complexity can be introduced to the multi-layer dry models by adding moist processes and physical parametrisations in the so-called “aquaplanet” setup [e.g. Neale and Hoskins (2000)]. The aquaplanet setup allows us to elucidate the role of moist processes and parametrisations on zonally homogeneous dynamics. For example, mid-latitude cyclones tend to be stronger in moist atmospheres.

To study effects of zonal asymmetries on the mid-latitude dynamics, localized heating or topography can be further introduced to the aquaplanet and Held & Suarez setup to force large-scale stationary waves, reproducing the south-west to north-east tilts in the Northern Hemisphere storm tracks (bottom left panel in Fig. 1). This setup has helped me elucidate the differences between the zonally homogeneous and zonally inhomogeneous atmospheres, where the planetary scale (stationary) waves and their interplay with the synoptic eddies (cyclones) become increasingly important for the mid-latitude storm track dynamics and variability on different temporal and spatial scales.

Even further complexity can be achieved by coupling atmospheric models to the dynamic ocean and/or land and ice models (coupled atmosphere-ocean or atmosphere only GCMs, in Fig. 1), all of which bring the model closer to reality. However, interpreting results from such complex models is very difficult without having first studied the hierarchy of models as too many processes are acting simultaneously in such fully coupled models.  Further insights can also be gained by improving the theoretical (mathematical) understanding of the atmospheric processes by using a similar hierarchical approach [see e.g. Boljka and Shepherd (2018)].


Boljka, L. and T.G. Shepherd, 2018: A multiscale asymptotic theory of extratropical wave–mean flow interaction. J. Atmos. Sci., 75, 1833–1852, https://doi.org/10.1175/JAS-D-17-0307.1 .

Boljka, L., T.G. Shepherd, and M. Blackburn, 2018: On the boupling between barotropic and baroclinic modes of extratropical atmospheric variability. J. Atmos. Sci., 75, 1853–1871, https://doi.org/10.1175/JAS-D-17-0370.1 .

Held, I. M., 2005: The gap between simulation and understanding in climate modeling. Bull. Am. Meteorol. Soc., 86, 1609 – 1614.

Held, I. M. and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75, 1825–1830.

Jeevanjee, N., Hassanzadeh, P., Hill, S., Sheshadri, A., 2017: A perspective on climate model hierarchies. JAMES9, 1760-1771.

Neale, R. B., and B. J. Hoskins, 2000: A standard test for AGCMs including their physical parametrizations: I: the proposal. Atmosph. Sci. Lett., 1, 101–107.

Polvani, L. M., A. C. Clement, B. Medeiros, J. J. Benedict, and I. R. Simpson (2017), When less is more: Opening the door to simpler climate models. EOS, 98.

Shaw, T. A., M. Baldwin, E. A. Barnes, R. Caballero, C. I. Garfinkel, Y-T. Hwang, C. Li, P. A. O’Gorman, G. Riviere, I R. Simpson, and A. Voigt, 2016: Storm track processes and the opposing influences of climate change. Nature Geoscience, 9, 656–664.

Vallis, G. K., Colyer, G., Geen, R., Gerber, E., Jucker, M., Maher, P., Paterson, A., Pietschnig, M., Penn, J., and Thomson, S. I., 2018: Isca, v1.0: a framework for the global modelling of the atmospheres of Earth and other planets at varying levels of complexity. Geosci. Model Dev., 11, 843-859.

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