What Did You Get For Number 9?

By: Todd Jones

A common way to check your work in school is to turn to your neighbour and ask, “What did you get for this one?”  With a little extra effort, though, students end up having productive discussions and learning to solve problems they didn’t fully understand or discovering new, clearer routes to the solution.  Even answering broadly defined questions, a group of comparisons could lead to consensus or a narrowing of the possibilities.

Particularly effective teachers encourage and schedule these comparison sessions. Scientists, ever the continual students, bring this technique to their research, aspiring to uncover solutions to challenging problems they have not previously considered by comparing their research with that of others. 

While the methods of solving 23÷1.4 with pen and paper varies little, questions about the motions of the atmosphere are not always so well constrained.  The many sensitive equations that describe these motions can often only be solved approximately, and scientists may reasonably choose from a number of approximations (with varying levels of accuracy) based on practical issues, such as how powerful their computers are.  For example, these calculations are often very large problems that require division of the atmosphere to be divided into a number of points where calculations about temperature, wind, and rain can be performed. Between the points, these parameters must be approximated with something like a “best guess.”  Each of these justifiable choices will lead to differing solutions that can generate years of classroom-style “compare and discuss” activity.

For example, we could compare solutions to simple models of the atmosphere.  One can remove complications of the real world and create close approximations that allow an easier solution.  For instance, picture a non-orbiting, non-rotating world that is entirely warm ocean, where the oscillations of night and day replaced by constant moderate sunshine.  The “world” doesn’t even have to be a sphere!  Modelling the atmosphere of this world, we would see that the atmosphere cools off gradually, radiating energy to space.  As the lower atmosphere warms from the ocean’s heat, moist convective bubbles begin to rise to then cool, forming clouds and rain.  Over time, the heat from condensation of water vapour into clouds and rain balances out the radiative cooling of the air.  We call this energetic balancing “radiative-convective equilibrium,” or RCE.  This model is a close approximation to Earth’s climate, and it can be used as a “toy Earth” to learn how the climate might change in response to parameter changes. 

Figure 1.  A scattered deep convective cloud scene from a simulation of the climate of a simplified world in radiative-convective equilibrium with an ocean constantly at 22°C in the UK Met Office model.  The back left wall shows a slice of relative humidity (hur). The back right wall shows a slice of specific humidity (water vapour concentration, hus).  The bottom surface shows the total amount of water vapour in the column of air above each point (prw).  Cloud surfaces are coloured for various levels of frozen cloud particles (cli), liquid cloud droplets (clw), and rain (plw).  Orange arrows show the velocity of the wind near the model surface.

Playing with these models over the past few decades, scientists have noticed some intriguing behaviour.  Choosing different global temperatures, we can investigate how clouds respond to global warming: will more reflective clouds spread and counter the warming?  Much of the time, the deep convective clouds that are generated in these models appear as one might guess: randomly scatted, sputtering across the little world (Figure 1).  However, when oceans are warm enough or the modeled worlds are sufficiently large, the deep convective clouds can spontaneously cluster into isolated locations, with very dry regions in between (Figure 2).  News of this phenomenon spurred tens of independent studies for comparison [1], and scientists began to uncover that phenomena like interactions between radiation and clouds can lead to this convective clustering.

Figure 2.  A clustered deep convective cloud scene from a simulation of the climate of a simplified world in radiative-convective equilibrium with an ocean constantly at 32°C in the UK Met Office model.  Features are as described in Figure 1.

For a fair test, the parameters used by each model should be the same, so a group of scientists gathered to define a specific set of parameters to test warming in RCE climates in models of many geometries and scales.  These “rules” were codified and shared [2], and volunteers reported their solutions for comparison [3].  Formally, this is an intercomparison of models simulating RCE, known as RCEMIP.  The 30+ representations varied between areas on the scale of 100 km to the full globe and between levels of detail (resolution) from 200 m to 50 km.

Though there were many small differences between the model results, there was broad agreement over the formation of aggregating clusters. Over small areas, only one model (that in Figure 2) developed convective clusters, whereas over large areas, all but a few models developed convective clusters.  The deep clouds in most models showed that, as the world is warmed, anvil tops become warmer, are located higher in the atmosphere, and cover smaller areas.  This means that the effect of high cloud tops on climate would vary little under global warming.  Instead, changes in low cloud properties and the degree of convective clustering can influence this [4].

Compared to high-resolution models, lower resolution global models show a change in clustering with global warming that indicates a smaller amount of warming for a given greenhouse gas forcing.  Because the higher resolution models tend to be more correct, it’s possible that coarser climate models have painted too rosy a picture about future warming. 

Though there is disagreement, there is much to be said for comparing solutions.  Many investigations comparing model patterns are underway, ultimately steering toward a better-understood solution of the climate system problem.


[1] Wing, A. A., K. Emanuel, C. E. Holloway, and C. Muller, 2017: Convective self-aggregation in numerical simulations: A review. Surveys in Geophysics, 38 (6), 1173–1197, doi:10.1007/ s10712-017-9408-4, URL https://doi.org/10.1007/s10712-017-9408-4.

[2] Wing, A. A., K. A. Reed, M. Satoh, B. Stevens, S. Bony, and T. Ohno, 2018: Radiative– convective equilibrium model intercomparison project. Geoscientific Model Development, 11 (2), 793–813, doi:10.5194/gmd-11-793-2018, URL https://gmd.copernicus.org/articles/11/ 793/2018/.

[3] Wing, A. A., and Coauthors, 2020: Clouds and convective self-aggregation in a multimodel ensemble of radiative-convective equilibrium simulations. Journal of Advances in Modeling Earth Systems, 12 (9), e2020MS002138, doi:https://doi.org/10.1029/2020MS002138, URL https://doi.org/10.1029/2020MS002138.

[4] Becker, T., and A. A. Wing, 2020: Understanding the extreme spread in climate sensitivity within the radiative-convective equilibrium model intercomparison project. Journal of Advances in Modeling Earth Systems, 12 (10), e2020MS002 165, doi:https://doi.org/10.1029/2020MS002165, URL https://doi.org/10.1029/2020MS002165.

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