Reblog: Roy Clark on climate models, 14 March 2021, from WUWT

Reblog: Roy Clark on climate models, 14 March 2021, from WUWT

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Roy Clark

March 14, 2021 9:54 pm

How many people have taken the trouble to go back and look in detail at the original Manabe and Wetherald (M&W) model and their underlying assumptions? [M&W, 1967] They started by ASSUMING an equilibrium average climate. This idea goes back to Pouillet in 1836 and comes from a fundamental misunderstanding of climate energy transfer [Pouillet 1836]. Conservation of energy for a stable climate on planet earth requires an approximate long term planetary energy balance between the absorbed solar flux and the long wave IR flux returned to space. Using an average solar flux of 1368 W m^-2, an albedo (reflectivity) of 0.3 and an illumination area ratio (sphere to disk) of 4, the average LWIR flux is about 240 W m^-2. (The exact number depends on satellite calibration). Simple inspection of the CERES IR images gives a value of about 240 ±100 W m^-2 [CERES, 2011]. There is NO exact short term energy balance.

Furthermore, the spectral distribution of the outgoing longwave radiation (OLR) at the top of the atmosphere (TOA) is not that of a blackbody near 255 K. The OLR consists of the upward emission of the LWIR flux from many different levels in the atmosphere. The emission from each level is modified by the absorption and emission of the levels above. The OLR does not define an ‘effective emission temperature’. It is just a cooling flux. There is no 255 K temperature that can be subtracted from an ‘average’ surface temperature of 288 K to give a ‘greenhouse effect’ temperature of 33 K [Taylor, 2006].

Thermal equilibrium means that the rate of heating equals the rate of cooling. The lunar surface under solar illumination is in thermal equilibrium so that the absorbed solar flux is re-radiated back to space as LWIR radiation as it is received. There is almost no time delay. The earth is very different from the moon. It has an atmosphere with IR active species (‘greenhouse gases’), mainly H₂O and CO₂. It also has oceans that cover about three quarters of the surface. In addition, the period of rotation is also faster, 24 hours instead of 27.3 days. On the real planet earth there are significant time delays between the absorption of the solar flux and the emission of the LWIR flux. This is irrefutable evidence of non-equilibrium energy transfer. Diurnal time delays or phase shifts between the peak solar flux at local noon and the surface temperature response can easily reach 2 hours and the seasonal phase shift at mid latitudes for the ocean surface temperature may reach 8 weeks. This is not new physics. The phase shift for the subsurface ground temperature was described by Fourier in 1824 [Fourier, 1824]. It has been ignored for almost 200 years. Similar non-equilibrium phase shifts are also found in other energy storage devices such as capacitors in AC electronic circuits.

The surface temperature is determined at the surface by the interaction of four main time dependent flux terms with the surface thermal reservoir. These are the absorbed solar flux, the net LWIR emission, the moist convection and the subsurface transport. (This does not include rainfall or freeze/thaw effects). The fluxes are interactive and should not be separated and analyzed independently of each other. A change in surface temperature requires the calculation of the change in heat content or enthalpy of the surface reservoir divide by the local heat capacity [Clark, 2013]. The (time dependent) downward LWIR flux from the lower troposphere to the surface limits the surface cooling by net LWIR emission. In order to dissipate the excess solar heat, the surface warms up until the excess heat is removed by moist convection. This is real source of the so called greenhouse effect. The ocean-air and land-air interfaces have different energy transfer properties and have to be analyzed separately. In addition, for the oceans, long range transport by ocean currents is important.

The M&W ‘model’ has nothing to do with planet earth. It was simply a mathematical platform for the development and evaluation of atmospheric radiative transfer algorithms. M&W left physical reality behind as soon as they made their first assumption of an exact flux balance between an average absorbed solar flux and the LWIR flux returned to space. They started with a static air column divided into 9 or 18 layers. The IR species were CO₂, H₂O and O₃ simulated using the spectroscopic constants available in 1967. The surface was a blackbody surface with zero heat capacity. This absorbed all of the incident radiation and converted it to blackbody LWIR emission. To simulate the atmospheric temperature profile they fixed the relative humidity in each air layer. The water vapor concentration therefore changed with temperature as the surface and layer temperatures changed. The model was run iteratively until the absorbed solar flux matched the outgoing LWIR flux. It took about a year of model time (step time multiplied by the number of steps) to reach equilibrium. Actual computation time was of course much less. In 1967, getting such a model to run at all and then reach equilibrium was a major achievement. However, the effects of surface heat capacity, ocean evaporation and convection were ignored. When the CO₂ concentration in the M&W model was increased, there was a decrease in the LWIR flux emitted at the top of the atmosphere. In order to reach a new ‘equilibrium state’ the surface temperature and the tropospheric temperatures had to increase. As the temperature increased, the water vapor concentration also increased. This then ‘amplified’ the surface warming produced by the CO₂. All of this was a mathematical artifact of the input modeling assumptions. There is no equilibrium climate on planet earth.

Unfortunately the ‘global warming apocalypse’ predicted by the M&W model became a lucrative source of research funds that was too good given up. Two early climate ‘bandwagons’ were created. First, the radiative transfer algorithms could be improved with better spectroscopic constants and more IR species. Second, a large number of M&W ‘unit’ models could be incorporated into a global circulation model. In addition, everyone one needed the biggest and fastest computer available. No one tried to calculate the change surface temperature from first principles or otherwise independently validate the M&W model. Global warming had been created by model definition. Do not kill the goose that lays the golden eggs. By 1975, M&W had created a ‘highly simplified’ global circulation model that still produced ‘global warming’ and by 1978, eleven more (minor) IR species had been added to the M&W model [M&W, 1975; Ramanathan and Coakley, 1978].

Instead of correcting the equilibrium assumption, three additional invalid assumptions were added to the M&W model by Hansen and his group in 1981 [Hansen et al, 1981]. First, the ‘blackbody surface’ was replaced by a 2 layer ‘slab’ ocean. This was used to add heat capacity and a delayed time response but little else to the ‘model’. The ocean surface energy transfer, particularly the wind driven evaporation (latent heat flux) was ignored. Second, the effect of a ‘doubling’ of the atmospheric CO₂ concentration on an ‘equilibrium average climate’ was discussed as though it applied to planet earth. The mathematical warming artifacts created by the equilibrium model were presented as though they were real. On planet earth, the changes in LWIR are far too small to have any effect on surface temperature. Third, the weather station temperature was substituted for the surface or skin temperature. The flux terms interact with the surface. The weather or meteorological surface air temperature (MSAT) is measured in a ventilated enclosure located 1.5 to 2 m above the ground. This was a fundamental ‘bait and switch’ change made to the observables that were ‘predicted’ by the ‘model’ without any change to the model calculations. How did the ‘blackbody surface’ turn into a weather station? Furthermore, one of the real causes of climate change, the Atlantic Multi-decadal Oscillation (AMO) was clearly visible in the temperature plots shown by Hansen et al, but they chose to ignore reality and called these temperature variations ‘noise’. The only change that has been made to the basic equilibrium climate ‘model’ since 1981 was the addition of ‘efficacies’ to the radiative forcing terms by Hansen et al in 2005 [Hansen et al, 2005].

Since the start of the industrial revolution around 1800, the atmospheric concentration of CO₂ has increased from about 280 to 400 ppm. This has produced a decrease in the LWIR flux at TOA of approximately 2 W m^-2 with a similar increase in the downward LWIR flux to the surface [Harde, 2017]. At present, the average CO₂ concentration is increasing by about 2.4 ppm per year, which corresponds to a change in LWIR flux near 0.034 W m^-2 per year. The effect of an increase in CO₂ concentration on surface temperature has to be determined by calculating the effect of the increase in LWIR flux on the change in heat content of the surface thermal reservoir after a thermal cycle with and without the change in flux. This is simply too small to measure.

The decrease in LWIR flux at TOA has been turned into a ‘radiative forcing’ and an elaborate climate modeling ritual has been developed to describe the effect of a hypothetical ‘CO₂ doubling’ on a fictional equilibrium average climate [Ramaswamy et al, 2019; IPCC, 2013; Hansen, 2005]. In order to understand what really happens on planet earth, the ‘radiative forcing’ has to be converted back into a change in the rate of heating at different levels in atmosphere [Feldman et al. 2008]. For CO₂, the ‘radiative forcing’ is a wavelength specific decrease in the LWIR flux in the P and R branches of the main CO₂ emission band at TOA, produced by absorption at lower levels in the atmosphere. This results in a slight warming in the troposphere and a cooling in the stratosphere. (There is also a smaller effect for the CO₂ overtone bands). For a ‘CO₂ doubling’, the maximum warming rate in the troposphere is less than 0.1 K per day [Iacono et al, 2008]. This is simply dissipated by the normal convective motion in the troposphere. There is a very small increase in emission from the H₂O band and a small increase in the gravitational potential energy. The lapse rate is not a mathematical function, it is a real vertical motion of the air in the troposphere – upwards and downwards. At an average lapse rate of -6.5 K km^-1 a temperature increase of 0.1 K is produced by a descent of 15 m. This is equivalent to riding an elevator down about 4 floors. The dissipation of the radiative forcing is illustrated schematically in Figure 1 (attached). The slight heating effect is illustrated in Figure 2 (attached).

In addition, the LWIR flux in the atmosphere is produced by many thousands of overlapping molecular lines. In the lower troposphere, these are pressure broadened and overlap to produce a quasi-continuum within the main H₂O and CO₂ absorption emission bands. About half of the downward LWIR flux reaching the surface from the troposphere originates from within the first 100 m layer above the surface and almost all of the downward LWIR flux originates from within the first 2 km layer. Any ‘radiative forcing’ at TOA from a decrease in LWIR flux cannot couple to the surface and cause any kind of temperature change [Clark, 2013].

The global warming in the climate models has been created by ‘tuning’ the models to match the ‘global average temperature anomaly’ such as the HadCRUT4 temperature series from the UK Met. Office [HadCRUT4, 2019]. The climate warming has been produced by a combination of the warming phase of the Atlantic Multi-decadal Oscillation (AMO) and various ‘adjustments’ to the temperature record [Andrews, 2017a; 2017b; 2017c; D’Aleo, 2010; NOAA, AMO, 2019,]. The HadCRUT4 climate series was used by Otto et al [2013] to create a pseudoscientific equilibrium climate sensitivity (ECR) and transient climate response (TCR) using the correlation between HadCRUT4 and a set of contrived ‘radiative forcings’. In reality, the downward LWIR component of the forcings from the lower troposphere to the surface cannot couple below the ocean surface. They are absorbed within the first 100 micron layer and fully mixed with the much larger and more variable wind driven evaporation. The two cannot be separated and analyzed independently of each other. Figure 3a (attached) shows the HadCRUT4 data used by Otto et al and Figure 3b shows the radiative forcings. Figure 3c shows the HadCRut4 data set from Figure 3a overlapped with the AMO. From 1850 to 1970, there is a good match between the two, including both the nominal 60 year oscillation and the short term ‘fingerprint’ variations. After 1970 there is an offset of approximately 0.3 C. This requires further investigation, but is probably related to ‘adjustments’ during the climate averaging process. The correlation coefficient between the two data sets is 0.8. The linear slope is the temperature recovery from the Little Ice Age. Figure 3d shows the tree ring reconstruction of the AMO from 1567 by Gray et al [Gray et al, 2004; Gray.NOAA, 2021]. The instrument record from 1850 is also shown. The variations in the AMO have no relationship to changes in the atmospheric CO₂ concentration.

The increase in the surface temperature of the N. Atlantic Ocean is transported over land by the prevailing weather systems and coupled to the weather station record through the diurnal convection transition temperature. The land surface temperature is reset each day by the local temperature at which the land and air temperatures equalize. Changes in this transition temperature are larger than any possible changes that can be produced by the observed increase in atmospheric CO₂ concentration. Temperature changes produced by downslope winds and ‘blocking’ high pressure systems can easily reach 10 C over course of a few days.

The forcings, feedbacks and climate sensitivities found in the climate models can be traced back to the mathematical artifacts created by the original M&W model. There is no equilibrium average climate that can be perturbed by an increase in atmospheric CO₂ concentration.

References

Andrews, R., 2017a, Energy Matters Sept 14, 2017, ‘Adjusting Measurements to Match the Models – Part 3: Lower Troposphere Satellite Temperatures’. http://euanmearns.com/adjusting-measurements-to-match-the-models-part-3-lower-troposphere-satellite-temperatures/#more-19464
Andrews, R., 2017b, Energy Matters Aug 2, 2017, ‘Making the Measurements Match the Models – Part 2: Sea Surface Temperatures’. http://euanmearns.com/making-the-measurements-match-the-models-part-2-sea-surface-temperatures/
Andrews, R., 2017c, Energy Matters July 27, 2017, ‘Adjusting Measurements to Match the Models – Part 1: Surface Air Temperatures’. http://euanmearns.com/adjusting-measurements-to-match-the-models-part-1-surface-air-temperatures/
CERES 2011, CERES OLR Image, March 8 2011, Aqua Mission (EOS/PM-1), https://earth.esa.int/web/eoportal/satellite-missions/a/aqua
Clark, R., 2013, Energy and Environment 24(3, 4) 319-340 (2013), ‘A dynamic coupled thermal reservoir approach to atmospheric energy transfer Part I: Concepts’.
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D’Aleo, J. ‘Progressive Enhancement of Global Temperature Trends’, Science and Public Policy Institute, July 2010. http://scienceandpublicpolicy.org/science-papers/originals/progressive-enhancement
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Otto, A., F. E. L. Otto, O. Boucher, J. Church, G. Hegerl, P. M. Forster, N. P. Gillett, J. Gregory, G. C. Johnson, R Knutti, N. Lewis, U. Lohmann, J. Marotzke, G. Myhre, D. Shindell, B. Stevens and M. R. Allen, Nature Geoscience, 6 (6). 415 – 416 (2013). ISSN 1752-0894, ‘Energy budget constraints on climate response’. http://eprints.whiterose.ac.uk/76064/7/ngeo1836(1)_with_coversheet.pdf
Otto, A., F. E. L. Otto, O. Boucher, J. Church, G. Hegerl, P. M. Forster, N. P. Gillett, J. Gregory, G. C. Johnson, R Knutti, N. Lewis, U. Lohmann, J. Marotzke, G. Myhre, D. Shindell, B. Stevens and M. R. Allen, Nature Geoscience, 6 (6). 415 – 416 (2013). ISSN 1752-0894, ‘Energy budget constraints on climate response’, Supplementary Material. content.springer.com/esm/art%3A10.1038%2Fngeo1836/MediaObjects/41561_2013_BFngeo1836_MOESM299_ESM.pdf
Pouillet, M., in: Scientific Memoirs selected from the Transactions of Foreign Academies of Science and Learned Societies, edited by Richard Taylor, 4 (1837), pp. 44-90. ‘Memoir on the solar heat, on the radiating and absorbing powers of the atmospheric air and on the temperature of space’
http://nsdl.library.cornell.edu/websites/wiki/index.php/PALE_ClassicArticles/archives/classic_articles/issue1_global_warming/n2-Poulliet_1837corrected.pdf
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Ramaswamy, V.; W. Collins, J. Haywood, J. Lean, N. Mahowald, G. Myhre, V. Naik, K. P. Shine, B. Soden, G. Stenchikov and T. Storelvmo, Meteorological Monographs Volume 59 Chapter 14 (2019), ‘Radiative Forcing of Climate: The Historical Evolution of the Radiative Forcing Concept, the Forcing Agents and their Quantification, and Applications’. https://doi.org/10.1175/AMSMONOGRAPHS-D-19-0001.1
Taylor, F. W., Elementary Climate Physics, Oxford University Press, Oxford, 2006, Chapter 7

The climate debate is a culture war

No good evidence for a “greenhouse gas effect”, GHE, exists. It’s supporters bypass scientific discussion of the GHE by demonising skeptics with labels like “shill” (you work for the fossil fuel industry), and “denier” (you support fascists). They avoid talking about fundamental science at all costs. Avoidance of scientific discussion is a common feature of authoritarian politics and scams. In 2007 - 2009, Gerlich and Tscheuschner (G+T 2009) wrote a scientific monograph explaining why a greenhouse gas effect is not a scientific proposition. Their monograph goes unanswered 12 years later.

Let’s look at what this GHE claims. It says the surface of earth is 33°C warmer due to our atmosphere. In particular due to the greenhouse gases (GHG), especially the 2 main ones: carbon dioxide, CO2, and water vapor in our atmosphere. It says that the CO2 warming part, is about a quarter, and was 8°C when CO2 averaged 280 ppm in the atmosphere. It says only a change in CO2 (and other trace GHG such as methane) 'is forcing'; that water vapor greenhouse effects are not forcing but they 'amplify' the CO2 effect.

There is no scientific evidence for any of this. It is a fairy story. Environmentalists, and science activists, basically, made it up. Let us consider what scientific evidence is and ideas are, and what separates a scientific idea from pseudoscience. Richard Feynman and Karl Popper explain it well. Specifically: 1) every idea, conjecture, hypothesis, model and theory in science must be grounded in fact. It must be testable against real world observations and/or experiment. An idea grounded in logic is not scientific unless every aspect of the idea resists falsification. Falsification is a process where we take projections (we look at what the idea predicts), and compare those projections with reality. With falsification, we specifically take a skeptical attitude towards the idea (like I'm doing now), and attempt to invalidate it (like a disproof). Scientists do this all the time. Falsification is part of the lifeblood of science. That's what G+T 2009 is. Rather than embracing falsification attempts as good scientists should, the establishment began a culture war against good science to keep their fake greenhouse gas effect. They call legitimate falsification claims 'denialism'. The effect of the culture was is to avoid scientific discussion at all costs so that the establishment, money interests, behind renewables have no critics; all critics and skeptics are demonized, and sometimes cancelled.

The function of the culture war is to polarize society so far such that an issue becomes extreme politics; which, basically, define a position. Unless one betrays one's party one cannot question its fundamental precepts. Global warming is a fundamental precept of the U.S. Democratic Party. The demonization of skepticism by media is Democrat activists (and their puppets and imitators) in action. To get everyone to toe the line, so that policy is justified. This was not, necessarily a conscious conspiracy. Al Gore began it, and he did everything openly. There are elements of conspricy in it; in particular, promises given in secret (e.g. email) and accepted for money. Yet in the main, it's not secret. So not a conspiracy.

How to tell whether a scientist's contribution to the greenhouse gas debate is legitimate

Simples!, just ask them to cite their attempted falsifications, or support for falsification, of the Greenhouse gas effect.

If they never tried to falsify it, they aren't even scientists, at least: not good scientists.

Notes:

• See Anthony Pagden's explanation of modern skepticism in "The Enlightenment And Why It Still Matters".

Leftism in a Nutshell

I wrote the paragraph (below in red) to explain why the Left support such daft energy policies (like 100% renewables). It was a reply to Dr Jay Lehr's article: "The Real Reason The Left Wants Only Wind And Solar Energy". Dr Lehr implies the Left maliciously want state control of everything. I think he's wrong.

Leftism, of all kinds, is best understood as a massive virtue-signaling exercise. In terms of electricity and energy, those aiming for 100% renewable energy have the highest value in the virtue-signaling utopian stock exchange. Only a small number of leftists understand electricity and energy well and most of them are pro-nukes. The 100% renewable thought leaders do not understand it. They have probably brain-washed themselves by only ever considering ideas and arguments of their fellow loonies. Current energy policies promoted by Democrats are not a plan (in the sense – no one did the numbers), they are an aim, or aspiration to ultimate virtue. Incompetence rules; not maliciousness. So 100% renewables only makes sense as a virtue signal power play.

The paragraph above doesn't make sense until one understands the distinctive character of modern leftist 'virtues'. They certainly aren't virtues I grew up with. Modern leftist virtues are solutions to problems defined by leftists. They see all the following are problems:

• capitalism,
• entrepreneurship (leads to capitalism),
• humanity (cause global warming & over-population),
• white people (oppress people of color),
• biology (oppresses gender-fluidity (biological sex) and causes inequality,
• heterosexuals - oppress LGBTQ
• feminism (oppress trans-people by resisting unisex changing rooms & Transwomen in women's sport),
• liberty, free-speech, equality!.

Wait a minute: liberty, free-speech, equality. Really?!? The new woke arguments are :

• free-speech must be banned for anyone who oppresses another with words. Especially banned for anyone who oppresses an intersectional.
  Q: What is oppression? A: It's what the victim feels it is. If it feels like oppression to an intersectional then it is!
• equality is a con-trick: intersectional minorities require equity instead. Equity means they get special treatment to redress the implicit (or institutional oppression) they 'experience'.
• liberty - this can lead to entrepreneurship, which can lead to capitalism, ...

In the stock exchange of leftist debate, the point of talking is to demonstrate ones superior ethics over the rest. On the left this has generally been done by taking an extremist, idealist position. The debate becomes one massive virtue signalling contest. The debate can be won by arguing positively for a better idea. It's far more likely for the debate to be won by negative logic; by projecting evil onto one's opponents. That's a very dangerous game - for oneself, as well. It's especially dangerous because modern leftism opposes free-speech for just about everyone except themselves! Leftists don't even know the arguments of the other side who they project as evil: deniers, shills, fascists, TERFs, MCPs, ... Modern leftist debate is an echo chamber of delusions; a long rant against devils, concocted in their own heads.

In modern leftism: censorship and equity are virtues. Equality and free-speech are problems (AKA evils). Perhaps people now understand what I meant by 'incompetence rules' (2nd paragraph above). The kind of reasoning what led to these modern leftist virtues is broken. It is incompetent reasoning.

Venus - effect of heat capacity

IPCC do not understand basic physics. Greenhouse theory promoters base runaway warming claims for earth on their explanation for how Venus’s surface temperature is very hot only due to the greenhouse gas effect. This contradicts basic physics. At the surface, Venus’ atmosphere is 92 times denser than earth’s. Basic physics says: Venus’ greater atmospheric mass increases the heat capacity of the atmosphere, and so decreases the net radiative cooling. So: creating a relative warming effect.

Source: Chemke and Kapsi, Dynamics of Massive Atmospheres, 2017 ApJ 845 1.

Urban heat

In climate science, the urban heat effect is local warming around populated regions. Globally it is a very minor effect; less than 1% of climate change. But since most climate stations are located near urbanized areas, especially airports. On statistic I saw claimed that 60% of weather stations are at airports!

• Urban Heat Island (UHI) effects can raise city temperatures 6-9°C above the temperatures in surrounding rural areas. These significant biases are not sufficiently removed from instrumental records. So 25% and 45% of warming in the instrument record is due to urban heat. A recent study by Nicola Scafetta, 2021, found “0.36 ± 0.04 °C” of non-climatic warming from roofs, asphalt, machines, vehicles…artificially enhances the post-1950s global temperature trend.

  Comments: NoTricksZone, and WUWT

• Causes of UHI
• Station bias is another issue. The Arctic and Antarctic are the least populated regions, so it follows they will have bad climate station coverage.
  
  Dr Fed Goldberg notes a massive bias was introduced into the climate record when many Soviet Union climate stations in cold Arctic locations closed in the early 1990s.
  

  Here we see very rapid [temperature] increase and this of course is said to be caused by human emissions well what really took place is the following: here you see the global average temperature year by year and here's the amount of weather stations recording the temperatures and they slowly went down and then something dramatic happened they fell down very rapidly at the same time the average global temperatures jumped up quite a bit and what happened here? Well the Soviet Union collapsed and not only Soviet Union but more or less all their weather stations in the Arctic. So suddenly there was a heavy imbalance between cold and warm stations making the warm stations dominate and the global average temperature skyrocketed as we see here.

  Dr Fred Goldberg

Does climate work in an opposite sense to climate models?

CO2 is higher at the Poles than the Equator. When air warms, CO2 goes down and water vapor goes up. The warming effects of CO2 and water vapor do not add; they oppose each other. This is opposite of IPCC claims. It is explained in a recent paper; but is not an empirical claim; nor is the IPCC climate feedback supported by observation!

Scientists find more CO2 causes land surface cooling

Biophysical impacts of Earth greening largely controlled by aerodynamic resistance

Satellite observations show widespread increasing trends of leaf area index (LAI), known as the Earth greening. However, the biophysical impacts of this greening on land surface temperature (LST) remain unclear. Here, we quantify the biophysical impacts of Earth greening on LST from 2000 to 2014 and disentangle the contributions of different factors using a physically based attribution model.

... We find that 93% of the global vegetated area shows negative sensitivity of LST to LAI increase at the annual scale, especially for semiarid woody vegetation. Further considering the LAI trends (P ≤ 0.1), 30% of the global vegetated area is cooled by these trends and 5% is warmed ...

93% of the global vegetated area shows ∂T_s^bio/∂LAI < 0 with an average of −0.36 ± 0.22 K m² m⁻² (mean ± 1 SD, where SD indicates spatial variability). We find that the mean magnitude of ∂T_s^bio/∂LAI is larger in temperate regions (−0.44 K m² m⁻²) than those in high-latitude (−0.34 K m² m⁻²) and tropical regions (−0.29 K m² m⁻²) ...

LAI = leaf area index = a measure of vegetation.
LST = land surface temperature