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