Earth systems models of intermediate complexity (EMICs) form an important class of climate models, primarily used to investigate the earth's systems on long timescales or at reduced computational cost. This is mostly achieved through operation at lower temporal and spatial resolution than more comprehensive general circulation models (GCMs). Due to the nonlinear relationship between spatial resolution and model run-speed, modest reductions in resolution can lead to large improvements in model run-speed. This has historically allowed the inclusion of previously unincorporated earth-systems such as ice sheets and carbon cycle feedbacks. These benefits are conventionally understood to come at the cost of some model accuracy. However, the degree to which higher resolution models improve accuracy rather than simply precision is contested.Jakob, C. (2014). Going back to basics. Nature Climate Change, 4:1042–1045.Lovejoy, S. (2015). A voyage through scales, a missing quadrillion and why the climate is not what you expect. Climate Dynamics, 44(11):3187–3210.

History

Computing power had become sufficiently powerful by the middle of the 20th century to allow mass and energy flow models on a vertical and horizontally resolved grid.Lynch, P. (2008). The origins of computer weather prediction and climate modeling. Journal of Computational Physics, 227(7):3431–3444 By 1955 these advances had produced what is recognisable now as a primitive GCM (Phillips prototype Phillips, N. A. (1956). The general circulation of the atmosphere: A numerical experiment. Quarterly Journal of the Royal Meteorological Society, 82(352):123–164). Even at this early stage, a lack of computing power formed a significant barrier to entry and limitation on model-time.

The next half century saw rapid improvement and exponentially increasing computational demands.McGuffie, K. and Henderson-Sellers, A. (2001). Forty years of numerical climate modelling. International Journal of Climatology, 21(9):1067–1109. Modelling on ever smaller length scales required smaller time steps due to the Courant–Friedrichs–Lewy condition.Courant, R., Friedrichs, K., and Lewy, H. (1967). On the partial difference equations of mathematical physics. IBM journal of Research and Development, 11(2):215–234. For example, doubling the spatial resolution increases the computational cost by a factor of 16 (factors of 2 for each spatial dimension and time).Flato, G. M. (2011). Earth system models: an overview. Wiley Interdisciplinary Reviews: Climate Change, 2(6):783– 800. As well as working on smaller scales, GCMs began to solve more accurate versions of the Navier–Stokes equations.White, A. A. and Bromley, R. A. (1995). Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the coriolis force. Quarterly Journal of the Royal Meteorological Society, 121(522):399– 418. GCMs also began to incorporate more earth systems and feedback mechanisms, transforming themselves into coupled Earth Systems Models. The inclusion of elements from the cryosphere, carbon cycle and cloud feedbacks was both facilitated and constrained by growth in computing power.

The powerful computers and high cost required to run these "comprehensive" models limited accessibility to many university research groups. This helped drive the development of EMICs. Through judicious parametrisation of key variables, researchers could run climate simulations on less powerful computers, or alternatively much faster on comparable computers. A modern example of this difference in speed can be seen between the EMIC JUMP-LCM and the GCM MIROC4h; the former runs 63,000 times faster than the latter.Hajima, T., Kawamiya, M., Watanabe, M., Kato, E., Tachiiri, K., Sugiyama, M., Watanabe, S., Okajima, H., and Ito, A. (2014). Modeling in earth system science up to and beyond ipcc ar5. Progress in Earth and Planetary Science, 1(1):29. The decrease in required computing power allowed EMICs to run over longer model times, and thus include earth systems occupying the "slow domain".

Petoukhov's 1980 statistical dynamical modelPetoukhov, V. (1980). A zonal climate model of heat and moisture exchange in the atmosphere over the underlying layers of ocean and land in: Golitsyn gs, yaglom am (eds) physics of the atmosphere and the problem of climate. has been cited as the first modern EMIC, but despite development throughout the 1980s, their specific value only achieved wider recognition in the late 1990s with inclusion in IPCC AR2 under the moniker of "Simple Climate Models". It was shortly afterwards at the IGBP congress in Shonnan Village, Japan, in May 1999, where the acronym EMICs was publicly coined by Claussen. The first simplified model to adopt the nomenclature of "intermediate complexity" is now one of the best known: CLIMBER 2. The Potsdam conference under the guidance of Claussen identified 10 EMICs, a list updated to 13 in 2005. Eight models contributed to IPCC AR4, and 15 to AR5.Randall, D. A., Wood, R. A., Bony, S., Colman, R., Fichefet, T., Fyfe, J., Kattsov, V., Pitman, A., Shukla, J., Srinivasan, J., et al. (2007). Climate models and their evaluation. In Climate change 2007: The physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the IPCC (FAR), pages 589–662. Cambridge University Press.Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S., Collins, W., Cox, P., Driouech, F., Emori, S., Eyring, V., Forest, C., Gleckler, P., Guilyardi, E., Jakob, C., Kattsov, V., Reason, C., and Rummukainen, M. (2013). Evaluation of Climate Models, book section 9, page 741866. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

Classification

As well as "complexity", climate models have been classified by their resolution, parametrisation and "integration".Claussen, M., Mysak, L., Weaver, A., Crucifix, M., Fichefet, T., Loutre, M.-F., Weber, S., Alcamo, J., Alexeev, V., Berger, A., Calov, R., Ganopolski, A., Goosse, H., Lohmann, G., Lunkeit, F., Mokhov, I., Petoukhov, V., Stone, P., and Wang, Z. (2002). Earth system models of intermediate complexity: closing the gap in the spectrum of climate system models. Climate Dynamics, 18(7):579–586. Integration expresses the level of interaction of different components of the earth system. This is influenced by the number of different links in the web (interactivity of coordinates), as well as the frequency of interaction. Because of their speed, EMICs offer the opportunity for highly integrated simulations when compared with more comprehensive ESMs. Four EMIC categorisations have been suggested based on the mode of atmospheric simplification: statistical-dynamical models, energy moisture balance models, quasi-geostrophic models, and primitive equation models. Of the 15 models in the community contribution to the IPCC's fifth assessment report, four were statistical-dynamic, seven energy moisture balance, two quasi-geostrophic and two primitive equations models.Eby, M., Weaver, A. J., Alexander, K., Zickfeld, K., Abe-Ouchi, A., Cimatoribus, A. A., Crespin, E., Drijfhout, S. S., Edwards, N. R., Eliseev, A. V., Feulner, G., Fichefet, T., Forest, C. E., Goosse, H., Holden, P. B., Joos, F., Kawamiya, M., Kicklighter, D., Kienert, H., Matsumoto, K., Mokhov, I. I., Monier, E., Olsen, S. M., Pedersen, J. O. P., Perrette, M., Philippon-Berthier, G., Ridgwell, A., Schlosser, A., Schneider von Deimling, T., Shaffer, G., Smith, R. S., Spahni, R., Sokolov, A. P., Steinacher, M., Tachiiri, K., Tokos, K., Yoshimori, M., Zeng, N., and Zhao, F. (2013). Historical and idealized climate model experiments: an intercomparison of earth system models of intermediate complexity. Climate of the Past, 9(3):1111–1140. To illustrate these categories, a case study for each is given.

Statistical-dynamical models: CLIMBER models

CLIMBER-2 and CLIMBER-3α are successive generations of 2.5 and 3 dimensional statistical dynamical models.Petoukhov, V., Ganopolski, A., Brovkin, V., Claussen, M., Eliseev, A., Kubatzki, C., and Rahmstorf, S. (2000). Climber-2: a climate system model of intermediate complexity. part i: model description and performance for present climate. Climate Dynamics, 16(1):1–17.Montoya, M., Griesel, A., Levermann, A., Mignot, J., Hofmann, M., Ganopolski, A., and Rahmstorf, S. (2005). The earth system model of intermediate complexity climber-3. part i: description and performance for present-day conditions. 25:237–263. Rather than continuous evolution of solutions to the Navier–Stokes or primitive equations, atmospheric dynamics are handled through statistical knowledge of the system (an approach not new to CLIMBER Saltzman, B. (1978). A survey of statistical-dynamical models of the terrestrial climate. volume 20 of Advances in Geophysics, pages 183 – 304. Elsevier.). This approach expresses the dynamics of the atmosphere as large-scale, long term fields of velocity and temperature. Climber-3α's horizontal atmospheric resolution is substantially coarser than a typical atmospheric GCM at 7.5°x 22.5°.

With a characteristic spatial scale of 1000 km, this simplification prohibits resolution of synoptic level features. Climber-3α incorporates comprehensive ocean, sea ice and biogeochemistry models. Despite these full descriptions, simplification of the atmosphere allows it to operate two orders of magnitude faster than comparable GCMs. Both CLIMBER models offer performances comparable to that of contemporary GCMs in simulating present climates. This is clearly of interest due to the significantly lower computational costs. Both models have been principally used to investigate paleoclimates, particularly ice sheet nucleation.Ganopolski, A., Rahmstorf, S., Petoukhov, V., and Claussen, M. (1998). Simulation of modern and glacial climates with a coupled global model of intermediate complexity. Nature, 391(6665):351–356.

Energy and moisture balance models: UVic ESCM

The thermodynamic approach of the UVic model involves simplification of mass transport (with Fickian diffusion) and precipitation conditions.Weaver, A., Eby, M., Wiebe, E., Bitz, C., Duffy, P., Ewen, T., F. Fanning, A., M. Holland, M., MacFadyen, A., Matthews, H. D., J. Meissner, K., Saenko, O., Schmittner, A., X. Wang, H., and Yoshimori, M. (2001). The uvic earth system climate model: Model description, climatology, and applications to past, present and future climates. 39:361–428. This model can be seen as a direct descendant of earlier energy balance models.Budyko, M. I. (1969). The effect of solar radiation variations on the climate of the earth. Tellus, 21(5):611–619.Sellers, W. D. (1969). A global climatic model based on the energy balance of the earth-atmosphere system. Journal of Applied Meteorology, 8(3):392–400.North, G. R. (1975). Theory of energy-balance climate models. Journal of the Atmospheric Sciences, 32(11):2033–2043. These reductions reduce the atmosphere to three state variables, surface air temperature, sea surface temperature and specific humidity.Fanning, A. F. and Weaver, A. J. (1996). An atmospheric energy-moisture balance model: Climatology, interpen- tadal climate change, and coupling to an ocean general circulation model. Journal of Geophysical Research:

Atmospheres, 101(D10):15111–15128. By parametrising heat and moisture transport with diffusion, timescales are limited to greater than annual and length scales to greater than 1000 km. A key result of the thermodynamic rather than fluid dynamic approach is that the simulated climate exhibits no internal variability. Like CLIMBER-3α, it is coupled to a state of the art, 3D ocean model and includes other cutting edge models for sea-ice and land-ice. Unlike CLIMBER, the UVic model does not have significantly coarser resolution than contemporary AOGCMs (3.6°x 1.8°). As such, all computational advantage is from the simplification of atmospheric dynamics.

Quasi-geostrophic models: LOVECLIM