THE SEVEN SINS OF THE EQUILIBRIUM CLIMATE MODELS



Ventura Photonics Climate Post 005.1 Sept. 7 2021


Roy Clark





SUMMARY



The climate models have failed. The model results do not agree with the measurements. There is no need to look at a single line of computer code to find out why. The models must fail because the assumptions used to simplify the climate energy transfer processes created climate warming as a mathematical artifact by definition, before any code was written. In particular, there is no such entity as an equilibrium average climate state that can be perturbed by an increase in the atmospheric CO2 concentration. The equilibrium climate and related assumptions incorporated into just two of the early climate models have created seven fundamental scientific errors. Unfortunately, the increase in atmospheric CO2 concentration has coincided with a natural climate warming related mainly to the positive or warming phase of the Atlantic Multi-decadal Oscillation (AMO). An elaborate scheme of pseudoscientific ‘radiative forcings’ and ‘climate sensitivities’ has been created to hide the model errors. The climate models have no predictive capabilities and have simply been ‘tuned’ to match the temperature record. Correlation has been used instead of validation. Physical reality has been abandoned in favor of mathematical simplicity. The 2 C temperature limit incorporated into the Paris Climate Accord has no basis in physical reality. There is no ‘climate crisis’. Eisenhower’s warning about the corruption of science by government funding has come true.



1.0 INTRODUCTION



Simple comparison of climate model results with the measured climate record shows that the two do not agree and that the climate models have failed [Christy, 2019 Rawls, 2012 Spencer, 2021 2013]. This is illustrated in Figure 1.




Figure 1: Mid tropospheric temperatures, models (pink) compared to observations, five year averages 1979 to 2017 [Data from Christy, 2019]



However, in order to understand the reasons for the failure it is necessary to delve quite deeply into the underlying modeling assumptions and compare them to the basic physics of the climate energy transfer. When this is done, it is found that seven fundamental scientific errors are created using the assumptions described in just two of the earlier modeling papers:

1) Manabe, S. and R. T. Wetherald, J. Atmos. Sci., 24 241-249 (1967), ‘Thermal equilibrium of the atmosphere with a given distribution of relative humidity’ http://www.gfdl.noaa.gov/bibliography/related_files/sm6701.pdf

2) Hansen, J. D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind and G. Russell Science 213 957-956 (1981), ‘Climate impact of increasing carbon dioxide’ https://pubs.giss.nasa.gov/docs/1981/1981_Hansen_ha04600x.pdf

The 1967 paper by Manabe and Wetherald (M&W) described the first generally accepted radiative-convective equilibrium climate model and provided the foundation for later [fraudulent] equilibrium climate model development. The concept of climate equilibrium follows from a misunderstanding of the earth’s energy balance. The earth is an isolated planet that is heated by the absorption of shortwave electromagnetic radiation from the sun and cools by the emission of longwave IR (LWIR) radiation back to space. For several billion years, the surface temperature has stayed within the relatively narrow bounds needed to sustain the evolution of life into its present forms. However, this only requires an approximate long term planetary energy balance. Different parts of the earth will always be heating and cooling at different rates. Satellite measurements show that the intensity of the LWIR flux returned to space is approximately 240 ±100 W m-2 [CERES 2011]. This in agreement with a simple planetary average energy balance calculation of about 240 W m-2 [Taylor, 2006]. At the surface, the local solar flux changes on both a daily and a seasonal time scale. The peak flux with the sun overhead is near 1000 W m-2. At night and during polar winter it is zero. The absorbed solar heat is stored and released over a wide range of time scales. There is no equilibrium. The short term local rate of heating rate does not equal the rate of cooling.


As soon as the equilibrium assumption is made, physical reality is abandoned and the models no longer describe planet earth. The M&W model was just a mathematical platform for the development and evaluation of radiative transfer and related algorithms. This is illustrated in Figure 2. The model consisted of a static column of air divided into 9 or 18 layers. This was illuminated by a ‘24 hour average’ sun with a fixed intensity. The surface at the bottom of the model was a blackbody surface with zero heat capacity. It just absorbed all of the downward flux and re-radiated it as heat. The various air layers contained water, carbon dioxide and ozone modeled using the spectroscopic constants that were available at the time. The relative humidity of each layer was fixed so that the water vapor concentration changed with the layer temperature. The model was run iteratively until the layer temperatures stabilized and the LWIR flux emitted by the top layer matched the absorbed solar flux. In terms of model time (number of steps times the step time) the model took over a year to reach equilibrium. The computational time was much less. When the CO2 concentration was increased, the LWIR flux emitted by the top layer was reduced and the surface and layer temperatures were increased until the LWIR flux emitted by the top layer again matched the absorbed solar flux. This created global warming by definition as a result of model input assumptions. Furthermore, since the relative humidity was fixed, there was an additional amplification or ‘feedback’ caused by the increase in water vapor concentration as the temperature increased. Again, this is a mathematical artifact of the model assumptions. The original M&W model was recently re-evaluated using an updated code [Kluft, 2020]. All of the original M&W assumptions were still accepted without question. The new code produced similar mathematical artifacts to the original one.





Figure 2: The 9 or 18 layer M&W model. Three separate model runs to steady state were required to generate the three temperature distributions with different CO2 concentrations.



The M&W model assumptions lead to four fundamental scientific errors:


1) There is no equilibrium climate on any time or spatial scale.

2) There is no such entity as a blackbody surface with zero heat capacity.

3) The concept of an ‘equilibrium atmosphere’ with a fixed relative humidity distribution is incorrect.

4) The upward and downward LWIR fluxes through the atmosphere are not equivalent. Instead, they are decoupled by molecular linewidth effects. This leads to the formation of two independent tropospheric thermal reservoirs.


The first three errors follow directly from the assumptions listed on the second page of the M&W paper. The fourth error requires a more detailed analysis of the atmospheric radiative transfer [Clark, 2013]. Variants of the M&W model were used to create the global warming artifacts found in the 1979 Charney Report [Charney et al, 1979, Manabe and Wetherald, 1975]. This gave a warming estimate of 3 ±1.5 C for a doubling of the atmospheric CO2 concentration from about 300 to 600 ppm. Later climate modeling work failed to address the errors in the underlying M&W assumptions. Instead ‘improvements’ were introduced that added three more fundamental scientific errors. These may be found in the 1981 paper by Hansen et al.


5) A ‘slab’ ocean model was used instead of the M&W blackbody surface. However, there was no consideration of surface energy transfer effects. In particular, wind driven evaporation was ignored and the LWIR flux was assumed to heat the ocean even though the penetration depth was only 100 micron.

6) A prescribed mathematical ritual of ‘radiative forcing’ was introduced. No thermal engineering calculation of the change in surface temperature was performed to validate the models.

7) There was a ‘bait and switch’ change from surface temperature to the weather station temperature record. The various flux terms interact with the surface, not the weather station thermometer located in a ventilated enclosure at eye level above the ground.


However, before these errors are considered in more detail it is necessary to understand how the earth’s climate energy transfer really works [Clark, 2013]. This is discussed in more detail in the related ‘Greenhouse Effect’ and ‘Surface Temperature’ posts (see Research Pages 1 and 3).



1.1 Climate Energy Transfer



At the local surface, the solar flux changes on both a daily and a seasonal time scale. The peak solar flux with the sun overhead is approximately 1000 W m-2. This corresponds to a blackbody emission temperature near 94 C. The downward LWIR flux from the lower troposphere establishes a partial exchange energy with the upward LWIR flux from the surface. This limits the rate of cooling of the surface from net LWIR emission. The surface warms up until the excess absorbed solar heat is dissipated by moist convection. Heat is also stored below the surface and released over a range of time scales. In order to dissipate the heat from the surface there must be a (time dependent) thermal gradient. This of course follows from the Second Law of Thermodynamics [Gerlich and Tscheuschner, 2009]. For evaporation, a humidity gradient is required, which usually includes a thermal gradient [Yu et al, 2008].


The land and ocean surfaces behave differently and must be considered separately. Over land, the incident solar flux, the net LWIR flux, the evapotranspiration (convection or sensible heat flux and the latent heat flux) interact with a thin surface layer. The net LWIR cooling flux is insufficient to dissipate the absorbed solar flux. The surface heating produces a thermal gradient both with the cooler air layer above and the subsurface layers below. The surface-air gradient drives the convection or sensible heat flux. The subsurface thermal gradient conducts heat into the first 0.5 to 2 meter layer of the ground. Later in the day this thermal gradient reverses and the stored heat is released back into the troposphere. The thermal gradients are reduced by evaporation if the land surface is moist. Almost all of the absorbed solar heat is dissipated within the same diurnal cycle. An important consideration in setting the land surface temperature is the night time convection transition temperature at which the surface and surface air temperatures equalize. Convection then essentially stops and the surface continues to cool more slowly by net LWIR emission. This convection transition temperature is reset each day by the local weather conditions.


The ocean surface is almost transparent to the solar flux. Approximately 90% of the solar flux is absorbed within the first 10 m layer. The ocean surface-air temperature gradient is quite small, usually less than 2 K. The excess absorbed solar heat is removed through a combination of net LWIR flux emission and wind driven evaporation with a small contribution from the sensible heat flux. The penetration depth of the LWIR flux into the ocean surface is 100 µm or less and the evaporation removes water molecules from a thin surface layer. These two processes combine to produce cooler water at the surface. This then sinks and is replaced by warmer water from below. The subsurface ocean heat transfer is a Rayleigh-Benard convection process, not simple diffusion. The upwelling warm water allows the wind driven ocean evaporation to continue at night. As the cooler water sinks, it carries with it the surface momentum or linear motion produced by the wind coupling at the surface. This establishes the subsurface ocean gyre currents. The magnitude and variation in the wind driven evaporation or latent heat flux are so large that any small increases in LWIR flux from an increase in atmospheric CO2 concentration cannot produce a measurable change in ocean surface temperature.


The surface energy transfer processes are also part of the tropospheric heat engine. This removes heat from the surface and transfers it to higher altitudes by convection. From here it is radiated back to space. This heat engine has some unusual properties. It operates at low temperatures and pressures. This means that the LWIR flux cannot be described simply in terms of blackbody radiation. Instead, a high resolution spectral and spatial radiative transfer analysis is required. Convection is a mass transport process that is coupled both to the earth’s gravitational field and the earth’s axial rotation or angular momentum. As a warm air parcel ascends from the surface it must expand and cool as it performs mechanical work to overcome the gravitational potential. This establishes the tropospheric temperature profile or lapse rate. If the air is moist, water may condense to form clouds and release its latent heat of evaporation. This reduces the magnitude of the local lapse rate. The cooling produced by the convective ascent is usually much larger than that produced by the net LWIR emission. The LWIR flux cannot be separated from the convection and analyzed independently. The local LWIR flux is emitted at the local air temperature. The coupling of the ascending air parcel to the rotation of the earth establishes the basic Hadley, Ferrel and Polar convective cell structure which in turn drives the trade winds and the ocean gyre circulation. The earth’s weather patterns are determined mainly by the thermodynamic and fluid dynamic properties of the tropospheric heat engine, not the LWIR flux. The earth’s climate is usually defined as the long term (30 year) average of these weather patterns.


The land and especially the oceans are the hot reservoirs (‘boilers’) of the tropospheric heat engine. The troposphere divides naturally into two independent thermal reservoirs. Almost all of the downward LWIR flux reaching the surface originates from within the first 2 km layer that forms the lower tropospheric reservoir. The LWIR emission to space originates mainly from the upper tropospheric reservoir that extends from 2 km to the tropopause. This acts as the cold reservoir of the heat engine. The heat lost by LWIR emission to space is replaced by convection from below. The heat is stored as gravitational potential energy. Above the tropopause, the stratosphere forms a third independent thermal reservoir. The main heat source here is absorption of the UV solar flux by ozone and the cooling is dominated by LWIR emission from CO2. The downward LWIR flux to the surface and the outgoing LWIR radiation to space are decoupled by the molecular line broadening effects. The energy transfer processes associated with the tropospheric heat engine are illustrated schematically in Figure 3. The ocean-air and land-air interfaces have different energy transfer processes and have to be considered separately. The two are coupled through the diurnal convection transition temperature. Many weather systems are formed over the oceans. As they move over land, the bulk surface air temperature is still related to the ocean surface temperature in the region of formation. This explains the influence of the ocean oscillations, particularly the Atlantic Multi-decadal Oscillation (AMO) on the weather station record. Further details are given in the ‘Web of Lies’, ‘Surface Temperature’ and ‘Forcing’ posts (see Research Pages 2,3 and 4).







Figure 3: The basic energy transfer processes for the tropospheric heat engine (schematic). The energy transfer processes at the ocean-air and ocean-air interfaces are different and have to be considered separately. The two are coupled through the diurnal convection transition temperature related to weather systems that move over land from the oceans. There is no thermal equilibrium.



2.0 THE SEVEN CLIMATE MODELING ERRORS



2.1 The Equilibrium Assumption



At a local TOA reference point, the solar radiation is changing on a daily and a seasonal time scale. The intensity depends on the cosine of the illumination angle. It is zero at night and at high latitudes during polar winter. The net incoming radiation used by M&W is the mathematical construct of a 24 hour average solar flux. In making this assumption, they have thrown out the time dependence of the solar flux and abandoned the Laws of Physics, starting with the Second Law of Thermodynamics [Gerlich and Tscheuschner, 2009]. As soon as the climate equilibrium assumption is made, physical reality is left behind and one enters the realm of computational climate fiction.


M&W stated their assumptions quite clearly and honestly on the second page of their paper. Their first assumption was:


"At the top of the atmosphere, the net incoming radiation should be equal to the net outgoing radiation."


M&W were not the first to use the climate equilibrium assumption. It was used by Arrhenius in his 1896 estimate of global warming from CO2 and he traced the concept back to Pouillet in 1836 [Arrhenius, 1896, Pouillet, 1836]


Later climate models used a less stringent annual planetary climate average. However, this is still a mathematical constraint that is not part of the energy transfer on planet earth. As discussed below, in Section 2.6 the climate models have simply been ‘tuned’ to match the global average temperature anomaly. The dominant climate warming term in this anomaly is the AMO. None of the warming can come from an increase in the atmospheric CO2 concentration.



2.2 A Blackbody Surface with Zero Heat Capacity



This assumption adds another layer of computational climate fiction to the M&W model. The earth’s surface is not a blackbody with zero heat capacity. In reality, the change in surface temperature is determined by the time dependent change in heat content or enthalpy of the surface reservoir. The surface layer heat capacity must be included in the time dependent calculation of the surface temperature. The LWIR flux cannot be separated from the other flux terms and analyzed independently. The net LWIR flux emitted by the surface defines a rate of cooling. The LWIR flux can also be used to measure the local surface temperature at the time of the flux measurement. However, a change in LWIR flux absorbed by the surface has to be added to the heat content of the local thermal reservoir along with the changes produced by the rest of the coupled flux terms. The change in temperature is the change heat content divided by the heat capacity. There is also a phase shift or time delay between the peak solar flux and the temperature response. The time delay in the subsurface temperature response was described by Fourier in his memoires on the temperature of the earth in 1824 and 1827 [Fourier, 1824, 1827]. The phase shift is discussed in more detail in the ‘Surface Temperature’ post (see Research Page 3). It is clear evidence of non-equilibrium energy transfer that has been ignored for almost 200 years.



2.3 Fixed Relative Humidity Distribution



M&W also assumed that the atmosphere maintains the given distribution of relative humidity set by the model. This was a mathematical construct used to set the lapse rate and change the water vapor absorption and emission in the air layers used in the model. Near the surface, the initial water vapor concentration is set by the local weather system. The relative humidity changes during the day with solar heating and evaporation. Diurnal and seasonal temperature variations lead to significant changes in the relative humidity near the surface. Approximately half of the downward LWIR flux emitted by the troposphere to the surface originates in the first 100 m layer above the surface. As the surface cools at night, an inversion layer may form and condensation (dew formation) may also occur. The tropospheric lapse rate or temperature profile is set locally by moist convection. This transfers the absorbed solar heat from the surface to the middle troposphere. Here, the LWIR emission from the water bands forms the cold reservoir of the tropospheric heat engine. The emission to space occurs at a temperature near 260 K. This emission band changes in altitude as the surface temperature and lapse rate change. The heat is stored as gravitational potential energy.


At the surface, the LWIR flux must be included with the other flux terms and coupled to the thermal reservoirs. There can be no water vapor feedback to amplify an increase in temperature from the increase in CO2 flux that is too small to measure. This is considered in more detail in the ‘Surface Temperature’ post (see Research Page 3).



2.4 Molecular Linewidth Effects



Although it was not explicitly stated by M&W, they also assumed that the upward and downward LWIR fluxes were equivalent. The atmospheric LWIR flux consists of IR emission and absorption involving many overlapping lines from specific molecular rotation-vibration transitions. At higher altitudes, these lines become narrower as the temperature and pressure decrease. Some of the upward LWIR flux can pass through the gaps between these narrower lines above and continue to space without additional absorption/emission. The downward flux is absorbed by the broader lines below. This is illustrated schematically in Figure 4. The idea that changes in LWIR flux at higher levels in the atmosphere can couple to the surface is incorrect. Almost all of the downward LWIR flux that reaches the surface originates from within the first 2 km layer of the troposphere. Approximately half of this downward flux originates from the first 100 m layer [Clark, 2013]. The cumulative downward flux vs. altitude is shown in Figure 5. These linewidth effects means that the concept of radiative forcing is invalid.





Figure 4: Transition from absorption-emission to free photon flux as the linewidth decreases with altitude. Single H2O line near 231 cm-1.





Figure 5: Cumulative fraction of the downward flux at the surface vs. altitude for surface temperatures of 272 and 300 K, each with 20 and 70% RH. Almost all of the downward flux reaching the surface originates from within the first 2 km layer. This is the location of the lower tropospheric reservoir.



2.5 The Slab Ocean Model



The first Hansen et al error described an M&W type climate model in which the ‘surface with zero heat capacity’ was replaced by a 2 layer ‘slab’ ocean model. The upper layer was a ‘mixed’ layer, usually 100 m thick and the lower layer included everything below this. The ocean ‘slab’ added heat capacity and a delayed thermal response, but little else. The surface energy transfer was ignored. The penetration depth of the LWIR flux into the ocean is approximately 100 micron. Within this layer, the LWIR flux is fully mixed with the wind driven evaporative flux. A small increase in LWIR flux from CO2 cannot couple below this layer and produce any measurable change in ocean temperature.

In more quantitative terms, the increase in downward LWIR flux at the surface produced by a 120 ppm increase in atmospheric CO2 concentration is approximately 2 W m-2 [Harde, 2017]. Within the ±30° latitude bands, the rate of evaporation per unit wind speed is at least 15 W m-2 /m s-1. [Yu et al, 2008, Clark, 2013]. The 2 W m-2 increase in flux from CO2 is equivalent to a change in wind speed of approximately 13 cm s-1. Ocean wind speeds may easily vary from 0 to 13 m s-1 (0 to 30 mph), with additional short term higher speed wind gusts. This means that the increase in flux from CO2 is simply overwhelmed by the magnitude and variability of the wind driven evaporation. The whole ‘equilibrium climate response’ argument is invalid. The downward LWIR flux components of the ‘radiative forcing’ at the surface cannot produce any measurable ocean heating effect.



2.6 Radiative Forcing



The second Hansen et al error was the introduction of radiative forcing [Ramaswamy et al, 2019, Harde, 2017, IPCC Chap. 8 2013, Knutti and Hegerl, 2008, Hansen et al, 1981, 2005]. This is based on an irrational belief in the a-priori assumption that an increase in atmospheric CO2 concentration must cause any increase in ‘surface temperature’. No engineering calculation of the change in surface temperature is performed. Instead, it assumed that there is an equilibrium average climate state in which there is an exact balance between the average absorbed solar flux and the average outgoing LWIR radiation (OLR) returned to space at TOA. As the CO2 concentration is increased, the climate equilibrium state is perturbed. There is a small decrease in the LIWR flux emitted at the top of the atmosphere. There is also a small increase in the downward LWIR flux that reaches the surface. This perturbed climate state is then supposed to ‘adjust’ and return to equilibrium with an increase in ‘equilibrium surface temperature’ that increases the LWIR flux at TOA and restores the flux balance. It is assumed that the change in surface temperature after the climate system ‘equilibrates’ can be described using a ‘climate sensitivity constant’ and the change in LWIR flux emitted to space. This is called a ‘radiative forcing’, RF [Harde, 2017, IPCC, 2013 Chapter 8].





The illustration of ‘CO2 doubling’ in an equilibrium average climate and the calculated increases in ‘equilibrium surface temperature’ produced by various ‘radiative perturbations’, now called ‘radiative forcings’ from Hanson et al [1981] are shown in Figure 6. Somehow, small changes in the LWIR flux cause changes in the ‘equilibrium surface temperature’ even though the solar flux may change from 0 to 1000 W m-2 during a single diurnal cycle. The flux changes produced by a ‘CO2 doubling’ described by Hansen et al in Figure 6a have now become an elaborate climate modeling ritual that is performed to determine the climate ‘equilibration’. This is shown in Figure 7 [Hansen et al, 2005, IPCC, 2013]. The small ‘radiative forcing’ decrease in the OLR is produced by a small increase in the LWIR flux absorbed by the atmosphere. For each ‘greenhouse gas’, the forcing is associated with a wavelength specific absorption. For example, for CO2, this absorption occurs mainly in the P and R branches of the CO2 band near 670 cm-1. In order to determine the effect that this absorption has on the temperature of the atmosphere, it is necessary to convert the absorbed flux at each level to a rate of heating. For a ‘CO2 doubling’, the maximum tropospheric heating rate is less than 0.1 K per day [Iacono et al, 2008]. In the troposphere, the LWIR flux is part of the heat transfer processes related to the tropospheric heat engine. The LWIR flux is fully coupled to the mass transport. A heating rate of 0.1 K per day is equivalent to a change in altitude of 15 meters at a lapse rate of -6.5 K km-1. The wavelength specific changes in radiative forcing at TOA from a small increase in tropospheric absorption are dissipated as broadband spectral emission and changes in the gravitational potential. Line broadening effects mean that they cannot couple to the surface. This is considered in more detail in the ‘Forcing’ post (see Research Page 4). For cloud free conditions, the change in OLR flux with surface temperature is approximately linear [Koll and Cronin, 2018]. However, the converse does not apply. There is no surface heating from a ‘radiative forcing’.







Figure 6: Mathematical artifacts generated by Hansen et al [1981]. a) Changes in ‘equilibrium flux’ and b) changes in ‘equilibrium surface temperature’. None of this has any relationship to planet earth.





Figure 7: The radiative forcing ritual used to determine the change in surface temperature from a ‘radiative forcing’ at TOA or the tropopause

[IPCC, 2013, Chapter 8].



Two pseudoscientific ‘climate sensitivities’ are used to describe the equilibration process. The first is an ‘equilibrium climate sensitivity’ (ECS) and the second is a ‘transient climate response’ (TCR). The ECS is the climate response to a radiative forcing after the oceans have adjusted to a new equilibrium state and the TCR is the response to a gradual increase in the radiative forcing, usually from a 1% per year increase in CO2 concentration before equilibrium is reached [IPCC 2013 Chapter 9].


Otto et al [2013] define these as:





Here, F2x is the radiative forcing produced by a doubling of the atmospheric CO2 concentration, set to 3.44 W m-2 for a doubling from ‘preindustrial levels’, 280 to 560 ppm. The change in temperature is taken from the HadCRUT4 global temperature anomaly [HadCRUT4, 2019] and the radiative forcings are taken from CIMP5 /RCP4.5 climate model ensemble. The change in heat content is dominated by ocean heat uptake, which has nothing to do with changes in the atmospheric concentration of ‘greenhouse gases’. More recent estimates of ECS and TCR are provided by Lewis and Curry [2018].


The main climate modeling program that has generated the results used by the IPCC is known as CMIP (Coupled Model Intercomparison Project). CMIP5 results were used for the Fifth IPCC Climate Assessment Report [IPCC 2013] and CMIP6 results will be used for the upcoming Sixth Assessment. The library of CMIP results in the US is maintained by Lawrence Livermore National Labs [Hausfather, 2019]. The climate sensitivities used in the CMIP5 models were discussed by Andrews et al, and by Gregory et al [Andrews et al, 2012, Gregory et al, 2019]. The CMIP6 sensitivities have been discussed by Zelinka et al [Zelinka et al, 2020]. The ‘equilibrium climate sensitivity’ or surface temperature rise produced by a ‘CO2 doubling’ for the CMIP 5 models varies from 2.1 to 4.7 K and for the CMIP6 models it varies from 1.8 to 5.6 K. This is all based on the assumption of CO2 induced warming in a fictional equilibrium average climate. The climate models have simply been ‘tuned’ to obtain the desired result. About 40% of the increase in the downward LWIR flux coupled to the ocean surface from an increase in atmospheric CO2 concentration is lost to the latent heat flux. The increase in water vapor concentration is coupled to the humidity gradient and does not add to the downward LWIR flux as a ‘feedback’. This is discussed in more detail in the ‘Surface Temperature and ‘Forcing’ posts (see Research Pages 3 and 4).


In addition, the HadCRUT4 global temperature anomaly is dominated by the Atlantic Multi-decadal Oscillation (AMO). This has a period of approximately 60 years and an amplitude near 0.4 C. The oscillation is superimposed on a linear temperature rise that has produced an increase of approximately 0.5 C since 1850. This has been attributed to solar heating related to the recovery from the Maunder minimum [Akasofu, 2010].


The decadal temperature changes from the HadCRUT4 temperature record used by Otto et al [2013] are shown in Figure 8a. The radiative forcings are shown in Figure 8b. To show the effects of the AMO on the temperature record used by Otto et al, the AMO has been overlaid on Figure 8a and plotted in Figure 8c. Changes in the AMO back to the sixteenth century have been determined by Gray et al [2004, 2021] using tree ring proxies. This is shown in Figure 8d. The AMO was changing long before the atmospheric CO2 concentration started to increase. The entire global warming argument is based on nothing more than the influence of the AMO on the global temperature record, along with a lot of weather station temperature ‘adjustments’.





Figure 8: a) Decadal mean temperature estimates derived from the HadCRUT4 global mean temperature series and b) decadal mean forcings with standard errors from the CMIP5 /RCP4.5 ensemble. c) AMO and trends scaled and overlaid on the HadCrut4 plot used by Otto et al in their creation of ‘climate sensitivity’, d) AMO from 1567 based on tree ring analysis.



The components of the radiative forcings from Figure 8b are shown in Figure 9 [IPCC, 2013, Chap. 8]. The greenhouse gas forcings are based on changes in the OLR at TOA. As shown above in Figures 4 and 5, line broadening effects mean that the change in LWIR forcing flux at TOA is not coupled to the surface. Any small tropospheric heating effects are dissipated by a combination of radiative cooling and mass transport within the tropospheric heat engine. The spectrally resolved forcings are converted to a small increase in flux spread over the atmospheric emission band. At the ocean surface, the increase in LWIR downward LWIR flux to the surface related to the ‘forcing’ is fully mixed with the wind driven evaporation and any temperature increase is too small to measure.





Figure 9: Components of the radiative forcings used by Otto et al

[IPCC 2013 Ch. 8, Fig. 18]



2.7 The Switch from Surface to Weather Station Temperature



The third Hansen error was a ‘bait and switch’ tactic. They substituted the weather station temperature for the surface temperature. The weather station temperature is the meteorological surface air temperature measured in a ventilated enclosure 1.5 to 2 m above the ground [Oke, 2006]. Even M&W is quite clear that the flux terms interact with the surface. This is a fundamental change in the model output variable. There was no discussion of the implications of this change. Nor were any changes made to the modeling algorithms to include the additional heat transfer processes involved. The change was concealed in the ‘climate sensitivity constant’. The weather station record that was presented by Hansen et al also included the well-defined AMO peak near 1940. They chose to ignore this and called it ‘noise’. This is shown in Figure 10.





Figure 10: Global mean surface temperature trend from Hansen et al, [1981] showing the 1940 AMO peak. The increase in CO2 atmospheric concentration (Keeling curve) is overlaid. There is no relationship between the temperature trend and the CO2 concentration.



The maximum and minimum MSAT are produced by different energy transfer processes. The minimum MSAT is generally a measure of the surface air temperature of the air mass of the local weather system. It is usually similar to the minimum surface temperature. The maximum MSAT is a measure of the warm air from the solar heated surface that is mixed with the cooler air above at the level of the MSAT thermometer. The maximum surface temperature may be 10 to 20 C warmer than the maximum MSAT. An analysis of the surface energy transfer requires consideration of the minimum MSAT and the delta T or heating produced by the solar heating of the surface. The phase shift should also be addressed. Any averaging requires careful consideration of Nyquist sampling theory applied to two pseudorandom temperature signals, the minimum MSAT and the MSAT Delta T (Tmax – Tmin). The average MSAT (Min+Max)/2 has little useful meaning. The climate models have been fraudulently manipulated using ‘radiative forcing’ and ‘climate sensitivity’ so that they appear to match the temperature anomaly of the area averaged weather station temperature record. The weather station record has also been fraudulently ‘adjusted’ using homogenization techniques to create additional warming that was not in the original station data [Andrews, 2017a, 2017b, 2017c].



3.0 CONCLUSIONS



The equilibrium climate models have failed. They consistently predict higher climate temperatures than those observed. The root cause of the failure can be traced back to the simplifying assumptions used to develop the early climate models. In particular, the assumptions made by M&W in 1967 created four fundamental scientific errors and Hansen et al by 1981 had added another three. These errors mean that the models must fail even before any computer code is written. The early model developers chose mathematical simplicity over physical reality. This created global warming as a mathematical artifact of the modeling assumptions.


Unfortunately, Eisenhower’s warnings on the corruption of science by government funding have come true. Predictions of global warming have become a very lucrative source of research funding. The scientific method in climate science has collapsed. The peer review process has been abandoned in favor of blatant cronyism. Various political and environmental groups are using global warming to further their own agendas. The equilibrium climate hypothesis has degenerated past scientific dogma into an unpleasant quasi-religious cult that supports a multi-trillion dollar fraud. The 2 C temperature limit in the Paris Climate Accord is based on nothing more than the pseudoscience of radiative forcing in a fictional equilibrium average climate. Irrational belief in fraudulent climate models has replaced physical reality. In order to restore the scientific method to climate science, a massive fraud that extends to the highest levels of government must be dismantled.



ACKNOWLEDGEMENT



This work was performed as independent research by the author. It was not supported by any grant awards and none of the work was conducted as a part of employment duties for any employer. The views expressed are those of the author.



REFERENCES



Normally, the references given in an article of this nature would be limited almost exclusively to the peer reviewed literature, with limited references to websites that provide access to climate data. Unfortunately, climate science has been thoroughly corrupted by the global warming fraud. The peer review process has collapsed and been replaced by blatant cronyism. Many of the publications in ‘prestigious’ journals such as Nature, Science, PNAS and others that relate to climate modeling predictions of global warming are fraudulent and should never have been published. Consequently many of the important references given here are to website publications. This should not detract from the integrity of the information provided. Many of these website publications have received a more thorough review that they might have received through the traditional peer review process.



Akasofu, S-I, Natural Science 2(11) 1211-1224 (2010), ‘On the recovery from the Little Ice Age’

http://dx.doi.org/10.4236/ns.2010.211149 Akasofu

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_a

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_b

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/ Andrews_c

Arrhenius, S., Philos. Trans. 41 237-276 (1896), ‘On the influence of carbonic acid in the air upon the temperature of the ground’.

http://empslocal.ex.ac.uk/people/staff/gv219/classics.d/Arrhenius96.pdf Arrhenius

CERES 2011, CERES OLR Image, March 8 2011, Aqua Mission (EOS/PM-1), Figure 8

https://earth.esa.int/web/eoportal/satellite-missions/a/aqua CERES

Charney, J. G. et al, Carbon Dioxide and Climate: A Scientific Assessment, Report of an ad hoc study group on carbon dioxide and climate, Woods Hole, MA July 23-27 (1979),

https://www.bnl.gov/envsci/schwartz/charney_report1979.pdf Charney

Christy, J. R., GWPF Note 17, 2019, ‘The Tropical Skies, Falsifying Climate Alarm’,

https://www.thegwpf.org/content/uploads/2019/05/JohnChristy-Parliament.pdf Christy

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’.

https://doi.org/10.1260/0958-305X.24.3-4.319 Clark_2013a

and

Energy and Environment 24(3, 4) 341-359 (2013), ‘A dynamic coupled thermal reservoir approach to atmospheric energy transfer Part II: Applications’. https://doi.org/10.1260/0958-305X.24.3-4.341 2013_b

Fourier, B. J. B. Mem. R. Sci. Inst., 7 527-604 (1827), ‘Memoire sur les temperatures du globe terrestre et des espaces planetaires’.

https://www.academie-sciences.fr/pdf/dossiers/Fourier/Fourier_pdf/Mem1827_p569_604.pdf. Fourier_1827_a

English translation:

https://courses.seas.harvard.edu/climate/eli/Courses/EPS281r/Sources/Greenhouse-effect/more/Fourier-1827.pdf Fourier_1827_b

Fourier, B. J. B., Annales de Chimie et de Physique, 27, pp. 136–167 (1824), ‘Remarques générales sur les températures du globe terrestre et des espaces planétaires’.

https://gallica.bnf.fr/ark:/12148/bpt6k65708960/f142.image# Fourier_1824_a

English translation:

http://fourier1824.geologist-1011.mobi/ Fourier_1824_b

Gerlich, G. and R. D. Tscheuschner, Int. J. Mod. Phys. B, 23(3) 274-394 (2009) ‘Falsification of the atmospheric CO2 greenhouse effects within the frame of physics’,

https://doi.org/10.1142/S021797920904984X Gerlich

Gray, S. T.' L. J. Graumlich, J. L. Betancourt and G. T. Pederson, Geophys. Res. Letts, 31 L12205, pp1-4 (2004) doi:10.1029/2004GL019932, ‘A tree-ring based reconstruction of the Atlantic Multi-decadal Oscillation since 1567 A.D.’. http://www.riversimulator.org/Resources/ClimateDocs/GrayAMO2004.pdf Gray

Gray.NOAA, 2021, Gray, S.T., et al. 2004, Atlantic Multi-decadal Oscillation (AMO) Index Reconstruction, IGBP PAGES/World Data, Center for Paleoclimatology, Data Contribution Series #2004-062, NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

https://www.ncei.noaa.gov/pub/data/paleo/treering/reconstructions/amo-gray2004.txt Gray.NOAA

Gregory, J. M., T. Andrews, P. Ceppi, T. Mauritsen and M. J. Webb, Climate Dynamics Oct. 2019, ‘How accurately can the climate sensitivity to CO2 be estimated from historical climate change?’

https://link.springer.com/content/pdf/10.1007%2Fs00382-019-04991-y.pdf Gregory

HadCRUT4, 2019, https://www.metoffice.gov.uk/hadobs/hadcrut4/data/current/time_series/HadCRUT.4.6.0.0.annual_ns_avg.txt HadCRUT4

Hansen, J. et al., (45 authors), J. Geophys Research 110 D18104 pp1-45 (2005), ‘Efficacy of climate forcings’.

https://pubs.giss.nasa.gov/docs/2005/2005_Hansen_ha01110v.pdf Hansen_2005

Hansen, J., D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind and G. Russell Science 213 957-956 (1981), ‘Climate impact of increasing carbon dioxide’. https://pubs.giss.nasa.gov/docs/1981/1981_Hansen_ha04600x.pdf Hansen_1981

Harde, H., Int. J. Atmos. Sci.9251034 (2017), ‘Radiation Transfer Calculations and Assessment of Global Warming by CO2’.

https://doi.org/10.1155/2017/9251034 Harde

Hausfather, Z., ‘CMIP6: The next generation of climate models explained’ Carbon Brief, 2019,

https://www.carbonbrief.org/cmip6-the-next-generation-of-climate-models-explained Hausfather

Hays, J. D. J. Imbrie, N. J. Shackleton, Science, 194 Dec. 10, pp 1121-1132 (1976), ‘Variations in the Earth's Orbit: Pacemaker of the Ice Ages’,

https://www.science.org/doi/abs/10.1126/science.194.4270.1121 Hays

Herzberg, G., Molecular Spectra and Molecular Structure, Volume 2, IR and Raman Spectra of Polyatomic Molecules, Krieger, Malabar, FL, 1991.

HITRAN, 2020, https://hitran.org/ HITRAN

Iacono, M. J. J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, J. Geophys. Res., 113, D13103pp 1-8, (2008), ‘Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models’. https://doi.org/10.1029/2008JD009944 Iacono

IPCC, 2013: Myhre, G., D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee, B. Mendoza, T. Nakajima, A. Robock, G. Stephens, T. Takemura and H. Zhang, ‘Anthropogenic and Natural Radiative Forcing’. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, Chapter 8, Radiative Forcing1535 pp, doi:10.1017/CBO9781107415324. http://www.climatechange2013.org/report/full-report/ IPCC_AR5_Wgp1

Keeling, 2020, https://scripps.ucsd.edu/programs/keelingcurve/ Keeling

Kluft, L., Reports on Earth System Science / Max Planck Institute for Meteorology 239 (2020), ‘Benchmark Calculations of the Climate Sensitivity of Radiative-Convective Equilibrium’.

https://pure.mpg.de/rest/items/item_3274272/component/file_3274608/content Kluft

Knutti, R. and G. C. Hegerl, Nature Geoscience 1 735-743 (2008), ‘The equilibrium sensitivity of the Earth’s temperature to radiation changes’. https://www.nature.com/articles/ngeo337 Knutti_a

Available at:

https://www.researchgate.net/profile/Reto_Knutti/publication/232797742_Knutti_R_Hegerl_G_C_The_equilibrium_sensitivity_of_the_Earth

%27s_temperature_to_radiation_changes_Nature_Geosci_1_735-743/links/00b4952ed256bd5923000000/Knutti-R-Hegerl-G-C-The-equilibrium-sensitivity-of-the-Earths-temperature-to-radiation-changes-Nature-Geosci-1-735-743.pdf Knutti_b

Lewis, N. and J. Curry, J. Climate 31 6051-6070 (2018) DOI: 10.1175/JCLI-D-17-0667.1, ‘The Impact of Recent Forcing and Ocean Heat Uptake Data on Estimates of Climate Sensitivity’,

https://journals.ametsoc.org/jcli/article/31/15/6051/92230/The-Impact-of-Recent-Forcing-and-Ocean-Heat-Uptake Lewis

Koll, D. D. B and T. W. Cronin., PNAS, (2018), ‘Earth’s outgoing longwave radiation linear due to H2O greenhouse effect’.

https://www.pnas.org/content/115/41/10293 Koll

Manabe, S. and R. T. Wetherald, J. Atmos. Sci. 32(1) 3-15 (1975), ‘The effects of doubling the CO2 concentration in the climate of a general circulation model’. https://journals.ametsoc.org/view/journals/atsc/32/1/1520-0469_1975_032_0003_teodtc_2_0_co_2.xml?tab_body=pdf Manabe_1975

Manabe, S. and R. T. Wetherald, J. Atmos. Sci., 24 241-249 (1967), ‘Thermal equilibrium of the atmosphere with a given distribution of relative humidity’. http://www.gfdl.noaa.gov/bibliography/related_files/sm6701.pdf Manabe

Math, F. A., Monthly Weather Review, Feb. 1934 pp 54-57, ‘Battle of the chinook wind at Havre, Mont.’.

https://journals.ametsoc.org/view/journals/mwre/62/2/1520-0493_1934_62_54_botcwa_2_0_co_2.xml Math

MODTRAN, 2020 http://forecast.uchicago.edu/Projects/modtran.orig.html MODTRAN

NOAA, AMO, 2019 https://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.mean.data NOAA, AMO

Oke T. R., WMO/TD-No. 1250, World Meteorological Association, 2006, ‘Initial guidance to obtain representative meteorological observations at urban sites’. https://www.researchgate.net/publication/265347633_Initial_guidance_to_obtain_representative_meteorological_
observations_at_urban_sites Oke

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

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. https://static-content.springer.com/esm/art%3A10.1038%2Fngeo1836/MediaObjects/41561_2013_BFngeo1836_MOESM299_ESM.pdf Otto_Suppl

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 Pouillet_a

Original publication:

Comptes Rendus des Séances de l'Académie des Sciences. Paris. 7, 24-65 (1836). ‘Mémoire sur la chaleur solaire : sur les pouvoirs rayonnants et absorbants de l'air atmosphérique et sur la température de l'espace’.

https://gallica.bnf.fr/ark:/12148/bpt6k95017r.image Pouillet_b

Poyet, P. The Rational Climate e Book, Malta, 2020 e-ISBN 978-99957-1-929-6, https://www.researchgate.net/publication/347150306_The_Rational_Climate_e-Book/link/5fe21ddb92851c13feb1763d/download Poyet

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 Ramaswamy

Rawls, A., 2012, http://www.stopgreensuicide.com/ Rawls

Spencer, R. 2013, http://www.drroyspencer.com/2013/10/maybe-that-ipcc-95-certainty-was-correct-after-all/ Spencer_2013

Spencer, R. 2021, http://www.drroyspencer.com/2021/04/an-earth-day-reminder-global-warming-is-only-50-of-what-models-predict/ Spencer_2021

https://journals.ametsoc.org/doi/pdf/10.1175/BAMS-D-15-00013.1 Stouffer

Taylor, F. W., Elementary Climate Physics, Oxford University Press, Oxford, 2006, Chapter 7

https://arxiv.org/abs/2006.03098 Wijngaarden

Yu, L., Jin, X. and Weller R. A., OAFlux Project Technical Report (OA-2008-01) Jan 2008, ‘Multidecade Global Flux Datasets from the Objectively Analyzed Air-sea Fluxes (OAFlux) Project: Latent and Sensible Heat Fluxes, Ocean Evaporation, and Related Surface Meteorological Variables’.

https://rda.ucar.edu/datasets/ds260.1/docs/OAFlux_TechReport_3rd_release.pdf Yu

Zelinka, M. D., T. A. Myers, D. T. McCoy, S. Po-Chedley, P. M. Caldwell, P. Ceppi, S. A. Klein and K. E. Taylor, Geophysical Research Letters 47, e2019GL085782 pp1-12 (2020), ‘Causes of Higher Climate Sensitivity in CMIP6 Models’.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2019GL085782 Zelinka