Climate model

From Wikipedia, the free encyclopedia

 

Climate models are systems of differential equations based on the basic laws of physics, fluid motion, and chemistry. To “run” a model, scientists divide the planet into a 3-dimensional grid, apply the basic equations, and evaluate the results. Atmospheric models calculate winds, heat transfer, radiation, relative humidity, and surface hydrology within each grid and evaluate interactions with neighboring points.

Climate models use quantitative methods to simulate the interactions of the important drivers of climate, including atmosphere, oceans, land surface and ice. They are used for a variety of purposes from study of the dynamics of the climate system to projections of future climate.

All climate models take account of incoming energy from the sun as short wave electromagnetic radiation, chiefly visible and short-wave (near) infrared, as well as outgoing long wave (far) infrared electromagnetic. Any imbalance results in a change in temperature.

Models vary in complexity:

• A simple radiant heat transfer model treats the earth as a single point and averages outgoing energy
• This can be expanded vertically (radiative-convective models) and/or horizontally
• Finally, (coupled) atmosphere–ocean–sea ice global climate models solve the full equations for mass and energy transfer and radiant exchange.
• Box models can treat flows across and within ocean basins.
• Other types of modelling can be interlinked, such as land use, allowing researchers to predict the interaction between climate and ecosystems.

Box models

Box models are simplified versions of complex systems, reducing them to boxes (or reservoirs) linked by fluxes. The boxes are assumed to be mixed homogeneously. Within a given box, the concentration of any chemical species is therefore uniform. However, the abundance of a species within a given box may vary as a function of time due to the input to (or loss from) the box or due to the production, consumption or decay of this species within the box.
Simple box models, i.e. box model with a small number of boxes whose properties (e.g. their volume) do not change with time, are often useful to derive analytical formulas describing the dynamics and steady-state abundance of a species. More complex box models are usually solved using numerical techniques.

Box models are used extensively to model environmental systems or ecosystems and in studies of ocean circulation and the carbon cycle.^[1]

Zero-dimensional models

A very simple model of the radiative equilibrium of the Earth is

${\displaystyle (1-a)S\pi r^{2}=4\pi r^{2}\epsilon \sigma T^{4}}$

where

• the left hand side represents the incoming energy from the Sun
• the right hand side represents the outgoing energy from the Earth, calculated from the Stefan-Boltzmann law assuming a model-fictive temperature, T, sometimes called the 'equilibrium temperature of the Earth', that is to be found,

and

• S is the solar constant – the incoming solar radiation per unit area—about 1367 W·m⁻²
• ${\displaystyle a}$ is the Earth's average albedo, measured to be 0.3.^[2][3]
• r is Earth's radius—approximately 6.371×10⁶m
• π is the mathematical constant (3.141...)
• ${\displaystyle \sigma }$ is the Stefan-Boltzmann constant—approximately 5.67×10⁻⁸ J·K⁻⁴·m⁻²·s⁻¹
• ${\displaystyle \epsilon }$ is the effective emissivity of earth, about 0.612

The constant πr² can be factored out, giving

${\displaystyle (1-a)S=4\epsilon \sigma T^{4}}$

Solving for the temperature,

${\displaystyle T={\sqrt[{4}]{\frac {(1-a)S}{4\epsilon \sigma }}}}$

This yields an apparent effective average earth temperature of 288 K (15 °C; 59 °F).^[4] This is because the above equation represents the effective radiative temperature of the Earth (including the clouds and atmosphere). The use of effective emissivity and albedo account for the greenhouse effect.

This very simple model is quite instructive, and the only model that could fit on a page. For example, it easily determines the effect on average earth temperature of changes in solar constant or change of albedo or effective earth emissivity.

The average emissivity of the earth is readily estimated from available data. The emissivities of terrestrial surfaces are all in the range of 0.96 to 0.99^[5][6] (except for some small desert areas which may be as low as 0.7). Clouds, however, which cover about half of the earth’s surface, have an average emissivity of about 0.5^[7] (which must be reduced by the fourth power of the ratio of cloud absolute temperature to average earth absolute temperature) and an average cloud temperature of about 258 K (−15 °C; 5 °F).^[8] Taking all this properly into account results in an effective earth emissivity of about 0.64 (earth average temperature 285 K (12 °C; 53 °F)).

This simple model readily determines the effect of changes in solar output or change of earth albedo or effective earth emissivity on average earth temperature. It says nothing, however about what might cause these things to change. Zero-dimensional models do not address the temperature distribution on the earth or the factors that move energy about the earth.

Radiative-convective models

The zero-dimensional model above, using the solar constant and given average earth temperature, determines the effective earth emissivity of long wave radiation emitted to space. This can be refined in the vertical to a one-dimensional radiative-convective model, which considers two processes of energy transport:

• upwelling and downwelling radiative transfer through atmospheric layers that both absorb and emit infrared radiation
• upward transport of heat by convection (especially important in the lower troposphere).

The radiative-convective models have advantages over the simple model: they can determine the effects of varying greenhouse gas concentrations on effective emissivity and therefore the surface temperature. But added parameters are needed to determine local emissivity and albedo and address the factors that move energy about the earth.

Effect of ice-albedo feedback on global sensitivity in a one-dimensional radiative-convective climate model.^[9][10][11]

Higher-dimension models

The zero-dimensional model may be expanded to consider the energy transported horizontally in the atmosphere. This kind of model may well be zonally averaged. This model has the advantage of allowing a rational dependence of local albedo and emissivity on temperature – the poles can be allowed to be icy and the equator warm – but the lack of true dynamics means that horizontal transports have to be specified.^[12]

EMICs (Earth-system models of intermediate complexity)

Depending on the nature of questions asked and the pertinent time scales, there are, on the one extreme, conceptual, more inductive models, and, on the other extreme, general circulation models operating at the highest spatial and temporal resolution currently feasible. Models of intermediate complexity bridge the gap. One example is the Climber-3 model. Its atmosphere is a 2.5-dimensional statistical-dynamical model with 7.5° × 22.5° resolution and time step of half a day; the ocean is MOM-3 (Modular Ocean Model) with a 3.75° × 3.75° grid and 24 vertical levels.^[13]

GCMs (global climate models or general circulation models)

General Circulation Models (GCMs) discretise the equations for fluid motion and energy transfer and integrate these over time. Unlike simpler models, GCMs divide the atmosphere and/or oceans into grids of discrete "cells", which represent computational units. Unlike simpler models which make mixing assumptions, processes internal to a cell—such as convection—that occur on scales too small to be resolved directly are parameterised at the cell level, while other functions govern the interface between cells.
Atmospheric GCMs (AGCMs) model the atmosphere and impose sea surface temperatures as boundary conditions. Coupled atmosphere-ocean GCMs (AOGCMs, e.g. HadCM3, EdGCM, GFDL CM2.X, ARPEGE-Climat)^[14] combine the two models. The first general circulation climate model that combined both oceanic and atmospheric processes was developed in the late 1960s at the NOAA Geophysical Fluid Dynamics Laboratory^[15] AOGCMs represent the pinnacle of complexity in climate models and internalise as many processes as possible. However, they are still under development and uncertainties remain. They may be coupled to models of other processes, such as the carbon cycle, so as to better model feedback effects. Such integrated multi-system models are sometimes referred to as either "earth system models" or "global climate models."

Research and development

There are three major types of institution where climate models are developed, implemented and used:

• National meteorological services. Most national weather services have a climatology section.
• Universities. Relevant departments include atmospheric sciences, meteorology, climatology, and geography.
• National and international research laboratories. Examples include the National Center for Atmospheric Research (NCAR, in Boulder, Colorado, USA), the Geophysical Fluid Dynamics Laboratory (GFDL, in Princeton, New Jersey, USA), the Hadley Centre for Climate Prediction and Research (in Exeter, UK), the Max Planck Institute for Meteorology in Hamburg, Germany, or the Laboratoire des Sciences du Climat et de l'Environnement (LSCE), France, to name but a few.

The World Climate Research Programme (WCRP), hosted by the World Meteorological Organization (WMO), coordinates research activities on climate modelling worldwide.

A 2012 U.S. National Research Council report discussed how the large and diverse U.S. climate modeling enterprise could evolve to become more unified.^[16] Efficiencies could be gained by developing a common software infrastructure shared by all U.S. climate researchers, and holding an annual climate modeling forum, the report found.^[17]

Best of the greenhouse

Posted on December 2, 2010 by Judith Curry
Original link:  https://judithcurry.com/2010/12/02/best-of-the-greenhouse/

On this thread, I try to synthesize the main issues and arguments that were made and pull some of what I regard to be the highlights from the comments.

The problem with explaining the atmospheric greenhouse effect is eloquently described by Nullius in Verba:

A great deal of confusion is caused in this debate by the fact that there are two distinct explanations for the greenhouse effect: one based on that developed by Fourier, Tyndall, etc. which works for purely radiative atmospheres (i.e. no convection), and the radiative-convective explanation developed by Manabe and Wetherald around the 1970s, I think. (It may be earlier, but I don’t know of any other references.)

Climate scientists do know how the basic greenhouse physics works, and they model it using the Manabe and Wetherald approach. But almost universally, when they try to explain it, they all use the purely radiative approach, which is incorrect, misleading, contrary to observation, and results in a variety of inconsistencies when people try to plug real atmospheric physics into a bad model. It is actually internally consistent, and it would happen like that if convection could somehow be prevented, but it isn’t how the real atmosphere works.

This leads to a tremendous amount of wasted effort and confusion. The G&T paper in particular got led down the garden path by picking up several ‘popular’ explanations of the greenhouse effect and pursuing them ad absurdam. A tremendous amount of debate is expended on questions of the second law of thermodynamics, and whether back radiation from a cold sky can warm the surface.

The Tyndall gas effect

John Nielsen-Gammon focuses in on the radiative explanation, which he refers to as the “Tyndall gas effect,” in a concurrent post on his blog Climate Abyss.

Vaughan Pratt succintly describes the Tyndall gas effect:

The proof of infrared absorption by CO2 was found by John Tyndall in the 1860s and measured at 972 times the absorptivity of air. Since then we have learned how to measure not only the strength of its absorption but also how the strength depends on the absorbed wavelength. The physics of infrared absorption by CO2 is understood in great detail, certainly enough to predict what will happen to thermal radiation passed through any given quantity of CO2, regardless of whether that quantity is in a lab or overhead in the atmosphere.

In a second post, John Nielsen-Gammon describes the Tyndall gas effect from the perspective of weather satellites that measure infrared radiation at different wavelengths.

In a slightly more technical treatment, Chris Colose explains the physics behind what the weather satellites are seeing in terms of infrared radiative transfer:

An interesting question to ask is to take a beam of energy going from the surface to space, and ask how much of it is received by a sensor in space. The answer is obviously the intensity of the upwelling beam multiplied by that fractional portion of the beam which is transmitted to space, where the transmissivity is given as 1-absorptivity (neglecting scattering) or exp(-τ), where τ is the optical depth. This relation is known as Beer’s Law, and works for wavelengths where the medium itself (the atmosphere) is not emitting (such as in the visble wavelengths). In the real atmosphere of course, you have longwave contribution from the outgoing flux not only from the surface, but integrated over the depth of the atmosphere, with various contributions from different layers, which in turn radiate locally in accord with the Planck function for a given temperature. The combination of these terms gives the so-called Schwartzchild equation of radiative transfer.

In the optically thin limit (of low infrared opacity) , a sensor from space will see the bulk of radiation emanating from the relatively warm surface. This is the case in desert regions or Antarctica for example, where opacity from water vapor is feeble. As you gradually add more opacity to the atmosphere, the sensor in space will see less upwelling surface radiation, which will be essentially “replaced” by emission from colder, higher levels of the atmosphere. This is all wavelength dependent in the real world, since some regions in the spectrum are pretty transparent, and some are very strongly absorbing. In the 15 micron band of CO2, an observer looking down is seeing emission from the stratosphere, while outward toward ~10 microns, the emission is from much lower down.

These “lines” that form in the spectrum, as seen from space, require some vertical temperature gradient to exist, otherwise the flux from all levels would be the same, even if you have opacity. The net result is to take a “bite” out of a Earth spectrum (viewed from space), see e.g., this image. This reduces the total area under the curve of the outgoing emission, which means the Earth’s outgoing energy is no longer balancing the absorbed incoming stellar energy. It is therefore mandated to warm up until the whole area under the spectrum is sufficiently increased to allow a restoration of radiative equilibrium. Note that there’s some exotic cases such as on Venus or perhaps ancient Mars where you can get a substantial greenhouse effect from infrared scattering, as opposed to absorption/emission, to which the above lapse rate issues are no longer as relevant…but this physics is not really at play on Modern Earth.

A molecular perspective

Maxwell writes:

As a molecular physicist, I think it’s imperative to make sure that the dynamics of each molecule come through in these mechanistic explanations.   A CO2 molecule absorbs an IR photon giving off by the thermally excited surface of the earth (earthlight). The energy in that photon gets redistributed by non-radiative relaxation processes (collisions with other molecules mostly) and then emits a lower energy IR photon in a random direction. A collection of excited CO2 molecules will act like a point source, emitted IR radiation in all directions. Some of that light is directed back at the surface of the earth where it is absorbed and the whole thing happens over again.

All of this is very well understood, though in the context of the CO2 laser. If you’re interested in these dynamics, there is a great literature on the relaxation processes (radiative and otherwise) that occur in an atmosphere-like gas.

Vaughan Pratt describes the underlying physics of the greenhouse effect from a molecular point of view:

The Sun heats the surface of the Earth with little interference from Earth’s atmosphere except when there are clouds, or when the albedo (reflectivity) is high. In the absence of greenhouse gases like water vapor and CO2, Earth’s atmosphere allows all thermal radiation from the Earth’s surface to escape into the void of outer space.

The greenhouse gases, let’s say CO2 for definiteness, capture the occasional escaping photon. This happens probabilistically: the escaping photons are vibrating, and the shared electrons comprising the bonds of a CO2 molecule are also vibrating. When a passing photon is in close phase with a vibrating bond there is a higher-than-usual chance that the photon will be absorbed by the bond and excite it into a higher energy level.

This extra energy in the bond acts as though it were increasing the spring constant, making for a stronger spring. The energy of the captured photon now turns into vibrational energy in the CO2 molecule, which it registers as an increase in its temperature.

This energy now bounces around between the various degrees of freedom of the CO2 molecule. And when it collides with another atmospheric molecule some transfer of energy takes place there too. In equilibrium all the molecules of the atmosphere share the energy of the photons being captured by the greenhouse gases.

By the same token the greenhouse gases radiate this energy. They do so isotropically, that is, in all directions.

The upshot is that the energy of photons escaping from Earth’s surface is diverted to energy being radiated in all directions from every point of the Earth’s atmosphere.

The higher the cooler, with a lapse rate of 5 °C per km for moist air and 9 °C per km for dry air (the so-called dry adiabatic lapse rate or DALR). (“Adiabatic” means changing temperature in response to a pressure change so quickly that there is no time for the resulting heat to leak elsewhere.)

Because of this lapse rate, every point in the atmosphere is receiving slightly more photons from below than from above. There is therefore a net flux of photonic energy from below to above. But because the difference is slight, this flux is less than it would be if there were no greenhouse gases. As a result greenhouse gases have the effect of creating thermal resistance, slowing down the rate at which photons can carry energy from the Earth’s surface to outer space.

This is not the usual explanation of what’s going on in the atmosphere, which instead is described in terms of so-called “back radiation.” While this is equivalent to what I wrote, it is harder to see how it is consistent with the 2nd law of thermodynamics. Not that it isn’t, but when described my way it is obviously thermodynamically sound.

Radiative-convective perspective

In what was arguably the most lauded comment on the two threads, Nullius in Verba provides this eloquent explanation:

The greenhouse effect requires the understanding of two effects: first, the temperature of a heated object in a vacuum, and second, the adiabatic lapse rate in a convective atmosphere.

For the first, you need to know that the hotter the surface of an object is, the faster it radiates heat. This acts as a sort of feedback control, so that if the temperature falls below the equilibrium level it radiates less heat than it absorbs and hence heats up, and if the temperature rises above the equilibrium it radiates more heat than it is absorbing and hence cools down. The average radiative temperature for the Earth is easily calculated to be about -20 C, which is close enough although a proper calculation taking non-uniformities into account would be more complicated.

However, the critical point of the above is the question of what “surface” we are talking about. The surface that radiates heat to space is not the solid surface of the Earth. If you could see in infra-red, the atmosphere would be a fuzzy opaque mist, and the surface you could see would actually be high up in the atmosphere. It is this surface that approaches the equilibrium temperature by radiation to space. Emission occurs from all altitudes from the ground up to about 10 km, but the average is at about 5 km.

The second thing you need to know doesn’t involve radiation or greenhouse gases at all. It is a simply physical property of gases, that if you compress them they get hot, and if you allow them to expand they cool down. As air rises in the atmosphere due to convection the pressure drops and hence so does its temperature. As it descends again it is compressed and its temperature rises. The temperature changes are not due to the flow of heat in to or out of the air; they are due to the conversion of potential energy as air rises and falls in a gravitational field.

This sets up a constant temperature gradient in the atmosphere. The surface is at about 15 C on average, and as you climb the temperature drops at a constant rate until you reach the top of the troposphere where it has dropped to a chilly -54 C. Anyone who flies planes will know this as the standard atmosphere.

Basic properties of gases would mean that dry air would change temperature by about 10 C/km change in altitude. This is modified somewhat by the latent heat of water vapour, which reduces it to about 6 C/km.

And if you multiply 6 C/km by 5 km between the layer at equilibrium temperature and the surface, you get the 30 C greenhouse effect.

It really is that simple, and this really is what the peer-reviewed technical literature actually uses for calculation. (See for example Soden and Held 2000, the discussion just below figure 1.) It’s just that when it comes to explaining what’s going on, this other version with back radiation getting “trapped” gets dragged out again and set up in its place.

If an increase in back radiation tried to exceed this temperature gradient near the surface, convection would simply increase until the constant gradient was achieved again. Back radiation exists, and is very large compared to other heat flows, but it does not control the surface temperature.

Increasing CO2 in the atmosphere makes the fuzzy layer thicker, increases the altitude of the emitting layer, and hence its distance from the ground. The surface temperature is controlled by this height and the gradient, and the gradient (called the adiabatic lapse rate) is affected only by humidity.

I should mention for completeness that there are a couple of complications. One is that if convection stops, as happens on windless nights, and during the polar winters, you can get a temperature inversion and the back radiation can once again become important. The other is that the above calculation uses averages as being representative, and that’s not valid when the physics is non-linear. The heat input varies by latitude and time of day. The water vapour content varies widely. There are clouds. There are great convection cycles in air and ocean that carry heat horizontally. I don’t claim this to be the entire story. But it’s a better place to start from.

Andy Lacis describes in general terms how this is determined in climate models:

While we speak of the greenhouse effect primarily in radiative transfer terms, the key component is the temperature profile that has to be defined in order to perform the radiative transfer calculations. So, it is the Manabe-Moller concept that is being used. In 1-D model calculations, such as those by Manabe-Moller, the temperature profile is prescribed with the imposition of a “critical” lapse rate that represents convective energy transport in the troposphere when the radiative lapse rate becomes too steep to be stable. In 3-D climate GCMs no such assumption is made. The temperature profile is determined directly as the result of numerically solving the atmospheric hydrodynamic and thermodynamic behavior. Radiative transfer calculations are then performed for each (instantaneous) temperature profile at each grid box.

It is these radiative transfer calculations that give the 33 K (or 150 W/m2) measure of the terrestrial greenhouse effect. If radiative equilibrium was calculated without the convective/advective temperature profile input (radiative energy transport only), the radiative only greenhouse effect would be about 66 K (for the same atmospheric composition), instead of the current climate value of 33 K.

Skeptical perspectives

The  skeptical perspectives on the greenhouse effect that were most widely discussed were papers by Gerlich and Tscheuschner, Claes Johnson, and (particularly) Miskolczi.  The defenses put forward of these papers did not stand up at all to the examinations by the radiative transfer experts that participated in this discussion.  Andy Lacis summarizes the main concerns with the skeptical arguments:

Actually, the Gerlich and Tscheuschner, Claes Johnson, and Miskolczi papers are a good test to evaluate one’s understanding of radiative transfer. If you looked through these papers and did not immediately realize that they were nonsense, then it is very likely that you are simply not up to speed on radiative transfer. You should then go and check the Georgia Tech’s radiative transfer course that was recommended by Judy, or check the discussion of the greenhouse effect on Real Climate or Chris Colose science blogs.

The notion by Gerlich and Tscheuschner that the second law of thermodynamics forbids the operation of a greenhouse effect is nonsense. The notion by Claes Johnson that “backradiation is unphysical because it is unstable and serves no role” is beyond bizarre. A versatile LW spectrometer used at the DoE ARM site in Oklahoma sees downwelling “backradiation” (water vapor lines in emission) when pointed upward. When looking downward from an airplane it sees upwelling thermal radiation (water vapor lines in absorption). When looking horizontally it sees a continuum spectrum since the water vapor and background light source are both at the same temperature. Miskolczi, on the other hand, acknowledges and includes downwelling backradiation in his calculations, but he then goes and imposes an unphysical constraint to maintain a constant atmospheric optical depth such that if CO2 increases water vapor must decrease, a constraint that is not supported by observations.

Summary

While there is much uncertainty about the magnitude of the climate sensitivity to doubling CO2 and the magnitude and nature of the various feedback processes, the fundamental underlying physics of the atmospheric greenhouse effect (radiative plus convective heat transfer) is well understood.

That said, the explanation of the atmospheric greenhouse effect is often confusing, and the terminology “greenhouse effect” is arguably part of the confusion.  We need better ways to communicate this.  I think the basic methods of explaining the greenhouse effect that have emerged from this discussion are right on target; now we need some good visuals/animations, and translations of this for an audience that is less sophisticated in terms of understanding science. Your thoughts on how to proceed with this?

And finally, I want to emphasize again that our basic understanding of the underlying physics of the atmospheric greenhouse effect does not direct translate into quantitative understanding of the sensitivity of the Earth’s energy balance to doubling CO2, which remains a topic of substantial debate and ongoing research.  And it does not say anything about other processes that cause climate change, such as solar and the internal ocean oscillations.

So that is my take home message from all this.  I am curious to hear the reactions from the commenters that were asking questions or others lurking on these threads.  Did the dialogue clarify things for you or confuse you?   Do the explanations that I’ve highlighted make sense to you?   What do you see as the outstanding issues in terms of public understanding of the basic mechanism behind the greenhouse effect?