Climate model parameterization

Why must a climate model invent clouds that it is far too coarse to see?

A global climate model divides the atmosphere into boxes. In the generation of models used for the recent assessment reports, those boxes are typically some tens of kilometres across. A fair-weather cumulus is a few hundred metres wide. Even a vigorous thunderstorm updraught is only a kilometre or two.

So the model cannot see clouds. Not "sees them poorly" — there is no variable in the grid that could hold one. And yet every such model contains elaborate machinery producing cloud cover, cloud water, precipitation and the heating that goes with them. That looks, at first glance, like making things up: filling a gap in the data with a plausible invention.

The question is whether it is. Could a model not simply leave out what it cannot resolve, and be honest about the omission?

Take that last suggestion seriously first, because rejecting it is what motivates everything else. What would a model with no clouds do? Sunlight would reach the surface unimpeded, since low cloud is the single largest reflector in the system. Water vapour would condense nowhere, so latent heat would never be released aloft, and the tropical atmosphere — whose vertical heat transport is carried almost entirely by convective towers occupying a tiny fraction of the area — would have no way to move energy upward. The result would not be a slightly imperfect climate. It would not be a climate at all.

So omission is not on offer. The unresolved processes are not a small correction to the resolved ones; in places they dominate. That reframes the problem: the model does not have the option of ignoring what it cannot see, so it must represent it somehow.

Now ask what "represent" can honestly mean here. The model knows, for each box, the average temperature, humidity, pressure and winds. It does not know how those quantities are distributed inside the box — and that distribution is precisely what determines whether convection fires. So the question becomes: given only the box averages, what can be said about the collective effect of whatever is happening inside?

That is a statistical question rather than a fabrication, and it has a real answer in many cases. A grid box whose lower air is warm and moist and whose upper air is cool and dry is convectively unstable; we cannot say where the towers will be, but we can say a great deal about how much heat and moisture they will carry, because the ensemble behaviour is far more predictable than any individual cloud. A parameterization is a closure: a rule mapping the resolved state onto the aggregate effect of the unresolved state.

Notice what has and has not been invented. The model is not inventing a cloud at a location. It is asserting a relationship between a grid-mean condition and a grid-mean consequence — and that assertion is testable against field campaigns, satellite retrievals, and against high-resolution simulations of small domains, which serve as the reference the scheme is built to reproduce.

Then where does the real weakness lie? In the form of the rule, not in its existence. Every scheme contains parameters with no direct observational counterpart — an entrainment rate, a critical relative humidity, an autoconversion threshold — because they describe a fictitious ensemble rather than a measurable object. Those must be set by tuning against observed climate. And different, defensible choices of scheme give different answers to exactly the question we most want settled: how cloud cover changes as the planet warms. Cloud feedback has remained the largest single contributor to the spread in estimated climate sensitivity across models, and that is a direct inheritance of the fact that clouds are represented rather than resolved.

Three refinements.

The first is that "parameterization" is not confined to clouds. Turbulence in the boundary layer, drag from mountains too small to appear in the topography, gravity waves, radiative transfer through a partly cloudy box, sea-ice ridging, and everything the land surface does are all sub-grid. Clouds are simply the case where the stakes are highest.

The second is that tuning is a narrower activity than its reputation suggests. It is not adjusting the model until it produces a desired warming. It is choosing values for the free parameters — most often to close the top-of-atmosphere energy budget — within ranges the process knowledge allows, and it is now documented rather than hidden. That said, the practice deserves scrutiny: a model tuned to reproduce the historical record has, to that extent, less independent authority when it reproduces the historical record.

The third is that the boundary moves but does not vanish, and this is the point most often missed. Global storm-resolving models running at grid spacings of a few kilometres do resolve deep convective systems explicitly, which removes the single most troublesome scheme. But at that resolution, shallow clouds, turbulence and the microphysics of droplet and ice formation are all still sub-grid — and microphysics is unresolvable in principle, since droplets are microns across. Every model at every resolution has a smallest represented scale, and something always lives below it.

• How cloud feedback is decomposed into low, high and mixed-phase components, and why the low clouds are the hard part.
• Superparameterization, where a small cloud-resolving model is embedded inside each grid column.
• Machine-learned parameterizations trained on high-resolution simulations, and the stability problems they run into.

Every term the collection defines is gathered in the glossary.