FORCING THE CLIMATE FRAUD

Ventura Photonics Climate Post 004.1a Feb. 24 2022

Roy Clark

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The issue therefore is not the value of the change in atmospheric LWIR flux produced by an increase in atmospheric CO₂ concentration, but the effect of this change on the earth’s climate, starting with the calculation of the increase in surface temperature. Here there is complete disagreement between the conventional thermal engineering approach and the equilibrium radiative forcing techniques used in the climate models [Poyet, 2020, Gerlich and Tscheuschner, 2009]. The engineering calculation involves the determination of the change in residual heat content or enthalpy in the surface thermal reservoir after a solar thermal cycle with increased downward LWIR flux from CO₂. All four of the main time dependent heat flux terms, the absorbed solar flux, the net LWIR emission, the evapotranspiration (moist convection) and the subsurface thermal transport have to be included in this calculation. (This discussion only includes these four main flux terms. It does not include rainfall or freeze/thaw effects). The change in temperature is determined by dividing the change in heat content by the local heat capacity of the thermal reservoir. There are two parts to this analysis. First, the change in temperature from the small increase in downward LWIR flux from CO₂ has to be evaluated. Second, the effect of other processes such as changes in local weather conditions have to be evaluated to determine if the CO₂ induced changes are even measurable. In signal processing terms, this is the determination of the signal to noise ratio. The results of such calculations show that the increase in surface temperature produced by the increase in downward LWIR flux from CO₂ is too small to measure.

The climate models start from the invalid concept of an equilibrium average climate. It is assumed that there is an exact long term planetary energy balance between the average absorbed solar flux and the average outgoing LWIR radiation (OLR) returned to space. An increase in the atmospheric CO₂ concentration produces a slight reduction the LWIR flux at TOA. This is considered to be a perturbation to the equilibrium state and the climate is then presumed to ‘adjust’ so that there is an increase in ‘equilibrium surface temperature’ that restores the flux balance at TOA [Knutti, and Hegerl, 2008]. The change in flux at TOA is called a radiative forcing, RF. It is further assumed that there is a linear relationship between the ‘radiative forcing’ and the surface temperature response

[Harde, 2017, 2013 IPCC, 2013 Chap. 8]. Climate sensitivity is defined in terms of the temperature change produced by doubling of the CO₂ concentration from a ‘preindustrial’ level of 280 ppm to 560 ppm. It is assumed a-priori that all of the recent changes in temperature record must be attributable to the increase in ‘radiative forcing’. An elaborate modeling ritual has been developed that describes the equilibrium climate response to a single step doubling of the CO₂ concentration [Hansen et al, 2005 1981]. The initial warming produced by a ‘radiative forcing’ is also assumed to be amplified by a ‘water vapor feedback’. As the surface warms, the water vapor pressure is assumed to increase which adds to the ‘forcing’. A set of ‘radiative forcings’ has been constructed that includes changes in flux attributed to wide range of ‘greenhouse gases’, various types of aerosols, changes in land use and other factors. The climate sensitivity is determined by comparing the radiative forcings to the average climate temperature anomaly and changes in the earth’s ‘heat content’ which is dominated by ocean warming [Otto et al, 2013]. All of this is a pseudoscientific facade. In reality, the dominant contribution to the climate record has been the Atlantic Multi-decadal Oscillation (AMO) [NOAA, AMO, 2019]. This is coupled into the weather station record as the weather systems that form over the N. Atlantic Ocean move over land. The influence of the AMO extends over a large area including parts of N. America, Europe and Africa. Radiative forcing has no relationship to the energy transfer processes that occur in the real atmosphere. However, the climate sensitivity is the pseudoscientific foundation of the 2 C temperature limit incorporated into the Paris Climate Accord.

The engineering calculation of the surface temperature and the pseudoscience of radiative forcing will now be considered in more detail. Since both of these topics include various aspects of atmospheric energy transfer, this will be considered first. Further details of the atmospheric energy transfer are given in the ‘Greenhouse Effect’ post (see Research Page 1).

The earth is an isolated planet that is heated by the absorbed short wave radiation from the sun and cooled by the emission of LWIR radiation back to space. While there is an approximate long term planetary energy balance, this only has to maintain the surface temperature within the relatively narrow bounds needed to sustain life. There is no requirement for an exact short term local flux balance. The surface temperature is determined by the operation of the Second Law of Thermodynamics, not the First [Gerlich and Tscheuschner, 2009]. In order to dissipate the absorbed solar heat from the surface there must be a thermal gradient or temperature difference. For evaporation, there must be a humidity gradient. This usually includes a thermal gradient.

The troposphere functions as an open cycle heat engine that transports part of the absorbed solar heat from the surface to the middle and upper troposphere by moist convection. From here it is radiated back to space, mainly by LWIR emission from water vapor. This heat engine has some unusual properties. The heat source is the solar flux that is changing on both a daily and a seasonal time scale. The peak solar flux incident at the surface with the sun overhead is near 1000 W m^-2 and at night and during polar winter it is zero. The solar heat is stored by the surface layer over land and especially by the oceans. It is released over a wide range of time scales. There are characteristic time delays or phase shifts between the peak solar flux and the temperature response. The heat transfer from the surface to the troposphere occurs by both moist convection and net LWIR emission. These two are interactive and should not be separated and analyzed independently of each other. The heat engine operates at low temperatures and pressures. This means that the LWIR flux has to be calculated using high resolution radiative transfer techniques. A simple blackbody description is inadequate. Since convection is a mass transport process, it is coupled to both the gravitational field and the angular momentum or rotation of the earth. This coupling produces the Hadley, Ferrel, polar convective cell structure, the trade winds and the ocean gyre circulation that give rise to the earth’s basic weather patterns.

The LWIR absorption and emission in the atmosphere consists of thousands of overlapping lines each involving transitions between specific molecular rotation-vibration states [Clark, 2013]. The dominant species are H₂O and CO₂. Through the troposphere and most of the stratosphere the molecular linewidth is determined by pressure broadening. This is the result of molecular collisions. Near the surface, within the main absorption bands the individual lines merge to form a quasi-continuous blackbody. The absorption and the molecular linewidths decrease as the pressure, temperature and the species concentration decrease with altitude. The upward and downward LWIR fluxes through the atmosphere are not equivalent. Some of the upward flux from the wings of the broader lines below can pass through the gaps between the lines above. Conversely the downward flux from the narrower lines above is fully absorbed by the wider lines below. The change in linewidth with altitude is illustrated in Figure 2. Almost all of the downward flux reaching the surface from the main absorption bands is emitted within the first 2 km layer above the surface. Approximately half of this flux is emitted by the first 100 m layer above the surface. It is this downward flux that provides the photons for the surface exchange energy. The cumulative downward flux from H₂O and CO₂ vs. altitude is shown in Figure 3. Four cases are plotted for surface temperatures of 272 and 300 K each with relative humidities of 20 and 70%. The downward flux near the surface increases with temperature and humidity. Even for the lowest flux case, 272 K and 20% RH, 95% of the surface flux originates from within the first 2 km layer. The downward flux to the surface is decoupled from the LWIR emission to space. The troposphere divides naturally into two thermal reservoirs. The lower reservoir extends from the surface to 2 km and the upper reservoir extends from 2 km to the tropopause. The concept of radiative forcing is invalid [Ramaswamy, et al, 2019]. There is no equilibrium flux that can be perturbed by an increase in ‘greenhouse gas’ concentration.

Figure 2: Transition from absorption-emission to free photon flux as the linewidth decreases with altitude. Single H₂O line near 231 cm^-1

Figure 3: 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 lower tropospheric reservoir.

2.1 The OLR Emitted to Space

Conservation of energy requires that the planetary average OLR returned to space be approximately 240 W m^-2. The is based on an average incident solar flux at the top of the atmosphere (TOA) near 1368 W m^-2, an albedo or reflectivity of 0.3 and a geometric factor of 4, the area ratio of a sphere to a circular illumination disk [1368*(1-0.3)/4 ≈ 240]. Satellite radiometer measurements give 240 ±100 W m^-2 [CERES, 2012]. However, the spectral distribution of the OLR flux is not that of a blackbody radiator near 255 K. Instead, the LWIR emission to space is produced by the cumulative effect of the LWIR emission from many different levels in the atmosphere. It is simply a cooling flux that cannot be associated with any single temperature. The emission from each level is modified by the absorption and emission of the levels above. The intensity of the LWIR flux at TOA cannot be used to define an ‘effective emission temperature’ of 255 K using Stefan’s Law. This means that there is no ‘greenhouse effect temperature’ of 33 K [Taylor, 2006]. Nor is there any kind of thermal equilibrium. The solar insolation for any location at TOA changes on a daily and a seasonal time scale. The LWIR flux at TOA does not show similar changes in intensity. There are significant time delays between the absorption of the solar flux by the climate system and the subsequent LWIR emission to space. The absorbed solar heat is stored both as heat in various climate thermal reservoirs and as gravitational potential energy in the atmosphere.

It has long been known that an increase in surface temperature produces an increase in the OLR emitted to space and that the (cloud free) OLR response is approximately linear in temperature. This temperature response is shown in Figure 4 [Koll and Cronin, 2018]. However, this is not a reversible process. A change in atmospheric LWIR flux at TOA produced by an increase in ‘greenhouse gas concentration’ is decoupled from the surface by molecular linewidth effects. This is discussed in more detail in Section 4.1.

Figure 4: Linear dependence of OLR emission on near surface temperature

Figure 5 shows the spectral distribution for the ‘clear sky’ OLR flux for a surface and surface air temperature of 288 K at 70% surface relative humidity (RH). The spectral range is from 100 to 1500 cm^-1 at a resolution of 2 cm^-1. These spectra are from MODTRAN calculations using the default tropical atmosphere with a CO₂ concentration of 400 ppm [MODTRAN, 2020]. Starting from left to right, the main spectral features are the rotational H₂O band from 100 to 600 cm^-1, the CO₂ v₂ vibration band from 600 to 750 cm^-1 and the H₂O v₂ vibration band above 1300 cm^-1 [Herzberg, 1991]. P and R denote the CO₂ band structure associated with the P (delta J = -1) and R (delta J = +1) rotational transitions. Between 750 and 1250 cm^-1 there is a spectral transmission window that consists of weak H₂O lines and two CO₂ overtone bands near 950 and 1050 cm^-1. This allows some of the blackbody emission from the surface to be transmitted directly to space. There is also an absorption feature from stratospheric ozone, O₃ that occurs near 1050 cm^-1 in the OLR emission. The OLR is for 70 km looking down. For reference, blackbody emission curves for 300 to 220 K in 20 K intervals are also plotted. The calculated MODTRAN 288 K blackbody emission from the surface and the 255 K blackbody emission curve are also shown. There is no relationship between the OLR (orange line) and the 255 K blackbody emission curve (black dotted line).

Figure 5: Spectral distribution of the OLR flux to surface for a 288 K surface temperature. The principal spectral features are indicated (MODTRAN calculation).

Figure 6 shows the OLR flux from Figure 5 divided into the separate atmospheric and surface emission contributions. Assuming a lapse rate near -6.5 K km^-1, each 20 K decrease in temperature corresponds approximately to a 3 km increase in altitude. In the 500 to 600 cm^-1 region, the H₂O emission is from an altitude of ~4.5 km at a temperature of ~270 K. Near 300 cm^-1 the H₂O emission temperature has decreased to ~240 K at an altitude of ~9 km. However, the emission temperature of the main CO₂ P and R bands is ~220 K indicating that the absorption and emission process continues through the troposphere and into the stratosphere (see Figure 7).

Within the main H₂O and CO₂ absorption bands, the OLR emission does not change significantly with surface temperature. The absorption and emission process continues with increasing altitude until the molecular linewidths narrow sufficiently to allow the transition to a free photon flux to space. For H₂O, this transition occurs near a temperature of 253 K (-20 C). The H₂O emission is a rate limited process. It depends mainly on the air local temperature. Heat is stored as gravitational potential energy. As the surface temperature changes, the altitude of the H₂O emission band changes. For CO₂ the free photon transition occurs at a lower temperature near 220 K. Most of the CO₂ band emission occurs in the stratosphere. The calculated spectral band cooling rates vs altitude for a tropical atmosphere are shown in Figure 7 [Feldman et al, 2008]. The linear temperature dependence comes from the flux in the spectral transmission window.

Figure 6: OLR to space, 288 K surface temperature showing the separate atmospheric and surface contributions to the 70 km level emission (MODTRAN calculation).

Figure 7: Total and band-averaged IR cooling rate profiles for the Tropical Model Atmosphere on a log-pressure scale [Data from Feldman et al, 2008]

The local temperature profile of the troposphere is set by the local lapse rate, which depends on the surface temperature, the relative humidity and the convection. The stratosphere is an independent thermal reservoir that is heated mainly by the absorption of UV solar flux by ozone and cools by LWIR emission from CO₂ and ozone. The local solar heating changes on a daily and a seasonal time scale. The downward flux from the LWIR emission in the stratosphere and upper troposphere is absorbed in the lower troposphere and does not reach the surface. The local temperature of an air parcel in the troposphere depends on the local flux balance. Within the plane parallel atmosphere approximation there are four contributing flux terms. The air parcel absorbs part of the LWIR flux from above and below. It is also emitting LWIR radiation upwards and downwards. This emission depends on the local temperature and IR species concentrations. As the air parcel changes altitude, particularly during convective ascent, the temperature change from expansion/compression is generally much larger than the LWIR cooling rate. For an ascent rate of 1 km per hour at a lapse rate of -6.5 K km^-1, the cooling rate is 6.5 K per hour. From Figure 7, the tropospheric cooling rate from LWIR emission is near 2 K per day or 0.08 K per hour. There is no ‘equilibrium state’ that can be perturbed by a change in CO₂ concentration. Any change in the LWIR flux from a change in atmospheric CO₂ concentration defines a change in cooling rates that has to be integrated over time to determine the change in enthalpy and then the temperature of the local air parcels in the atmosphere. The energy transfer processes related to the tropospheric heat engine and for an air parcel in the troposphere are illustrated schematically in Figure 8.

Figure 8: a) The tropospheric heat engine and b) energy transfer processes for a local tropospheric air parcel (in a plane-parallel atmosphere).

2.2 The Downward LWIR Flux to the Surface

The local surface temperature is determined at the surface by the interaction of the various flux terms with the local surface reservoir. The downward LWIR flux from the lower troposphere interacts with the upward LWIR flux from the surface to form a partial exchange energy that limits the surface cooling by net LWIR emission. This is illustrated in Figure 9. When the surface and air temperatures are similar, the net LWIR cooling flux is limited to the emission through the LWIR transmission window. In order to dissipate the absorbed solar flux, the surface warms up until the excess heat is dissipated by moist convection. This is the real source of the so called ‘greenhouse effect’. The downward LWIR flux increases with increasing cloud cover and decreases with decreasing humidity. The local surface air temperature may also change because of the effects of downward air compression related to downslope winds and blocking high pressure systems [Black et al, 2004, Math, 1934]. This is considered in more detail in the ‘Surface Temperature’ post (see Research Page 3).

Figure 9: The net LWIR surface cooling flux is limited by the surface exchange energy. The downward LWIR flux from the lower troposphere (orange) ‘blocks’ the upward flux from the surface. MODTRAN calculation, 288 K surface temperature, 70% RH, 400 ppm CO₂.

3.0 THE ENGINEERING DETERMINATION OF THE SURFACE TEMPERATURE

The energy transfer processes at the land-air and ocean-air interface are different and have to be considered separately. 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 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. The penetration depth of the LWIR flux into the ocean surface is 100 µm or less and the evaporation involves the removal of 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. This 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.

Over land, the incident solar flux, the net LWIR flux, the 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 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 as the surface cools 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. The convection transition temperature is reset each day by the local weather conditions. This is discussed in more detail in the ‘Surface Temperature’ post (see Research Page 3).

There are both diurnal and seasonal phase shifts in the land and ocean temperature response to the solar flux. Over the ocean, there is diurnal phase shift that may reach several hours. This also depends in part on the wind speed. There is also a seasonal phase shift that may reach eight weeks or more at mid latitudes. Near the equator, the timing of the phase shift changes as the peak solar flux transitions from the summer solstice to the equinox points. Over land, the diurnal phase shift may reach two hours or more. However, the heat capacity of the land thermal reservoir is too small to produces a seasonal phase shift at the surface. Instead, the seasonal phase shift comes from the influence of the ocean surface temperature as the weather systems move over land and couple to the local convection transition temperature. The energy transfer processes at the land and ocean surfaces and the phase shift are illustrated schematically in Figure 10.

Figure 10: Surface energy transfer for a) the land surface and b) the ocean surface and c) the time delay or phase shift between the peak solar flux and the temperature response (schematic).

3.1 The Effect of an Increase in Atmospheric CO₂ Concentration on the Ocean Surface Temperature

A small increase in the downward LWIR flux to the ocean surface from an increase in the atmospheric CO₂ concentration is absorbed within the first 100 micron layer at the surface [Hale and Querry, 1973]. Here the increase in LWIR flux is fully coupled to the wind driven evaporation. The two cannot be separated and analyzed independently of each other. If there are no other changes in the heat transfer, there is a small increase in surface temperature and a small increase in the water vapor pressure at the ocean surface. The water vapor is coupled into the humidity gradient and removed by the wind flow. This produces a cooling at the surface through an increase in the latent heat flux. The net heating is reduced below that calculated from coupling the LWIR flux to a blackbody surface. There is no ‘feedback’ or amplification of the surface warming by any increase in LWIR flux from the increase in water vapor pressure. Using long term zonal averages from Yu et al [2008], the sensitivity of the ocean latent heat flux to the wind speed in the ±30° latitude bands is near 15 W m^-2/m s^-1. The 2 W m^-2 increase in downward LWIR flux to the surface from an increase of 120 ppm in the atmospheric CO₂ concentration is dissipated by an increase in wind speed of approximately 13 cm s^-1. Any heating effects from this increase in CO₂ flux are simply overwhelmed by the magnitude and variation in the ocean wind speed. The LWIR component of the radiative forcing used in the climate models cannot couple into the ocean and produce any heating effect. This is considered in more detail in the ‘Surface Temperature’ post (see Research Page 3, Section 3).

3.2 The Effect of an Increase in Atmospheric CO₂ Concentration on the Land Surface Temperature

4.0 RADIATIVE FORCING

Radiative forcing is based on a fundamental misunderstanding of climate energy transfer. The surface temperature is not controlled by the LWIR flux. Instead, the downward LWIR flux to the surface establishes a partial exchange energy. In order to dissipate the absorbed solar flux, the surface has to warm up until the excess heat is removed by moist convection. This misunderstanding started in the nineteenth century when the concept of an equilibrium average climate was introduced by Pouillet in 1836. Speculation that changes in the atmospheric CO₂ concentration could cycle the earth through an Ice Age began with the work of Tyndall in the 1860s [Pouillet, 1836, Tyndall, 1861, 1863]. This idea was resurrected by Svante Arrhenius in 1896 [Arrhenius, 1896]. He used the equilibrium climate assumption to calculate the change in surface temperature produced by a change in atmospheric CO₂ concentration, including a reduction in concentration by one third.

"All authors agree in the view that there prevails an equilibrium in the temperature of the earth and of its atmosphere. The atmosphere must, therefore, radiate as much heat to space as it gains, partly through the absorption of the sun’s rays, partly through the radiation of the from the hotter surface of the earth and by means or ascending currents of air heated by contact with the ground. On the other hand, the earth loses just as much heat by radiation to space and to the atmosphere as it gains by absorption of the sun’s rays."

Arrhenius, 1896, p. 254

It is also clear from discussion in the same paper that Arrhenius was mainly interested in explaining the cause of an Ice Age.

"From geological researches the fact is well established that in Tertiary times there existed a vegetation and an animal life in the temperate and arctic zones that must have been conditioned by a much higher temperature than the present in the same regions. The temperature in the arctic zones appears to have exceeded the present temperature by about 8 or 9 degrees. To this genial time the ice age succeeded and this was one or more times interrupted by interglacial periods with a climate of or about the same character as the present, sometimes even milder."

Arrhenius, 1896, p 267

The concept of an equilibrium average climate that could be perturbed by CO₂ became accepted scientific dogma as part of a ‘greenhouse effect’ and no-one bothered to do any engineering calculations of the change in surface temperature using the time dependent flux terms, or considered the effects of ocean evaporation. Furthermore, no-one bothered to examine Fourier’s ‘memoires’ on the temperature of the earth from 1824 and 1827 [Fourier, 1824, 1827]. Here he clearly describes the phase shift in the subsurface seasonal ground temperature.

"At a moderate depth, as three or four meters, the temperature observed does not vary during each day, but the change is very perceptible in the course of a year it varies and falls alternately. The extent of these variations, that is, the difference between the maximum and minimum of temperature, is not the same at all depths it is inversely as the distance from the surface. The different points of the same vertical line do not arrive at the same time at the extreme temperatures. The extent of the variations, the times of the year, which correspond to the greatest, to the mean, or to the least temperatures, change with the position of the point in the vertical line. There are the same quantities of heat which fall and rise alternately all these values have a fixed relation between themselves, which are indicated by experiments and expressed distinctly by the analysis. The results observed are in accordance with those furnished by the theory no phenomenon is more completely explained."
Fourier 1824

The evidence for a non-equilibrium thermal response to the solar flux was provided by Fourier, more than a decade before Pouillet introduced the invalid concept of an equilibrium average climate.

The equilibrium assumption was incorporated into the first generally accepted climate model published by Manabe and Wetherald (M&W) in 1967. They were honest and stated their assumptions clearly on the second page of their paper. They began with the equilibrium assumption:

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

Manabe and Wetherald, 1967.

As soon as the equilibrium assumption is made, physical reality is abandoned and one enters the realm of computational climate fiction. The M&W model created global warming as a mathematical artifact of the input assumptions. The surface was a partially reflective blackbody surface with zero heat capacity and relative humidity (RH) profile was fixed. When the concentration of CO₂ was increased, the surface temperature increased by definition as part of the modeling construct. In addition, the fixed RH created a ‘feedback’. As the temperature increased, the water vapor concentration increased because the RH was fixed and the water vapor pressure increases with temperature. This in turn increased the LWIR absorption and ‘amplified’ the effect of the increase in CO₂. The M&W model was really just a platform for the development of radiative transfer and related algorithms. Although the assumptions used were clearly stated by M&W in their paper, there was no discussion of the limitations that these introduced. Nor were the assumptions and their limitations considered in later papers.

The M&W ‘model’ created two ‘bandwagons’ that could be used to obtain research funding. First, the radiative transfer algorithms could be ‘improved’ with better spectroscopic constants and more greenhouse gases. Second, the M&W model could be incorporated into a general circulation model (GCM) with well over a thousand M&W ‘units’ coupled together within a modified global circulation ‘weather forecasting’ program to make ‘improved’ climate ‘predictions’. None of this required any change to the underlying M&W model. All of the ‘improvements’ in the IR spectroscopy were valid, until they were used to calculate the ‘equilibrium temperature’ in the M&W model. Within a decade, an additional 11 ‘minor’ species had been added to the M&W model. This was described in a review by Ramanathan and Coakley [1978]. Here they were quite clear about the equilibrium assumption:

"For radiative-convective equilibrium the net outgoing longwave radiative flux at the top of the atmosphere, F_n0, must equal the net solar radiative flux S_n0. Likewise, because the stratosphere is in radiative equilibrium, the net longwave radiative flux at the base of the stratosphere, F_n1, must equal the net solar radiative flux into the troposphere, Sn1. For any perturbation the stratosphere and the atmosphere as a whole seek a new state of radiative equilibrium."

Ramanathan and Coakley, 1978

Physical reality had been abandoned in favor of mathematical simplicity.

A ‘primitive’ global circulation model was published by M&W in 1975. They had chosen to ignore the limitations imposed by their own 1967 assumptions and continued to develop their GCM model. The 1967 mathematical artifacts were built into each 'cell' of the GCM model. The 1967 ‘model’ was now described as a ‘global average climate model’ [M&W, 1975]. The M&W approach was officially ‘sanctified’ by the Charney report that was published in 1979 [Charney et al, 1979]. This identified a possible warming of 3±1.5 C from a ‘doubling’ of the atmospheric CO₂ concentration. The mathematics used in the climate ‘models’ appeared reasonable based on the acceptance of the invalid equilibrium assumption, so no further investigation was needed.

In 1981, Hansen et al discussed the temperature changes that could be induced by radiative perturbations to a ‘global equilibrium climate’ and its response to a ‘doubling’ of the CO₂ concentration [Hansen et al, 1981]. Also in this paper, a two layer ‘slab’ ocean model was added to the M&W partially reflective blackbody surface. This was used to add heat capacity and a delayed time response but little else to their model. The ocean surface energy transfer, particularly the wind driven evaporation was ignored. In addition, the weather station temperature was substituted for the ‘equilibrium’ surface or surface air temperature. However, 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 ‘surface with zero heat capacity’ 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.

The concept of radiative forcing gradually emerged from the discussion radiative perturbations to a ‘global equilibrium climate’ and the slab ocean led to the concepts of an ‘equilibrium climate sensitivity’ (ECS) and a transient climate sensitivity (ECS). The pseudoscience of radiative forcing has been used in all of climate assessment reports published by the UN Intergovernmental Panel on Climate Change (IPCC) [Ramaswamy et al. 2019]. Instead of comparing climate model results to the measured surface temperatures, the models have been compared to each other using a hypothetical ‘CO₂ doubling’. This is the calculation of the increase in ‘equilibrium surface temperature’ produced by a doubling of the atmospheric CO₂ concentration from its preindustrial value of 280 ppm to 560 ppm. An elaborate modeling ritual has been created based on the assumed perturbation of a fictional equilibrium climate. This is illustrated in Figure 11. The single step ‘radiative forcing’ at TOA is first used to adjust the stratospheric temperature, followed by the atmospheric and land temperatures. Finally, the ocean temperatures reach a new equilibrium temperature. In reality, the current increase in atmospheric CO₂ concentration is 2.4 ppm per year and the ‘radiative forcing’ is approximately 0.034 W m^-2 per year. When the real time dependent energy transfer processes are considered, there can be no ‘climate sensitivity’ to a ‘CO₂ doubling’. The climate sensitivity has been created by ‘tuning’ the climate models to match the measured changes in weather station temperature related to the most recent warming phase of the AMO.

Figure 11: The radiative forcing modeling ritual used to determine the change in ‘equilibrium surface temperature’ from a ‘radiative forcing’ at TOA or the tropopause [IPCC, 2013, Chapter 8]. a) Instantaneous RF, b) RF with stratospheric adjustment, c) atmospheric response, d) atmospheric and land temperature response and e) full GCM response.

Tyndall’s hypothesis that CO₂ could cause an Ice Age was finally disproved in 1976 when the analysis of ocean sediment cores demonstrated that the Ice Age cycle was related to planetary perturbations of the eccentricity of the earth’s orbit [Hays et al, 1976]. Further details were published by Imbrie and Imbrie in 1979 [Imbrie and Imbrie, 1979]. For convenience, this 1979 publication may be identified as the final step in the transition from failed hypothesis to downright climate modeling fraud. It was completely ignored by the reviewers involved in the Charney report.

As discussed above, the small increase in downward LWIR flux to the surface produced by a 130 ppm increase in the atmospheric CO₂ concentration is too small to produce a measurable increase in surface temperature. Two other aspects of the radiative forcing fraud will now be considered. The first is the dissipation of radiative forcing by the troposphere. The second is the fraudulent use of the AMO to create a ‘climate sensitivity’ to CO₂.

4.1 The Dissipation of Radiative Forcing in the Troposphere

The measured increase in atmospheric CO₂ concentration of 130 ppm has produced a decrease in LWIR flux or a ‘radiative forcing’ at TOA of approximately 2 W m^-2 as shown above in Figure 1b. This decrease is produced by wavelength specific absorptions at various levels in the atmosphere in the P and R branches of the main CO2 band. The P and R notation denoted changes in the rotational quantum number of delta J = -1 (P) and +1 (R). There is also a small increase in absorption in the CO2 overtone bands near 950 and 1050 cm^-1. Within the troposphere, a CO₂ ‘doubling’ produces a small increase in the local layer heating of less than 0.1 C per day [Iacono et al, 2008]. This is dissipated by the normal convective energy transfer processes in the troposphere and produces a small increase in both the broadband LWIR emission and the gravitational potential energy. The changes in absorption and emission are illustrated schematically in Figure 12. They are also decoupled from the surface by molecular line broadening effects [Clark, 2013]. There is no measurable surface warming. In addition, there is a net cooling produced in the stratosphere. This has to be considered as part of the normal diurnal and seasonal stratospheric energy transfer processes. None of the CO₂ induced LWIR flux changes in the stratosphere can couple to the surface because of line broadening effects in the lower troposphere. The changes in daily cooling rates vs. altitude are shown in Figure 13. These are too small to have any effect on surface temperature. For reference, at a lapse rate of -6.5 C km^-1, an increase in temperature of +0.08 C corresponds to a decrease in altitude of 12 meters. This is equivalent to riding an elevator down about four floors.

Figure 12: The dissipation of the ‘radiative forcing’ from a ‘CO₂ doubling’ by the normal tropospheric energy transfer processes (schematic). The wavelength specific increase in absorption in the CO₂ P and R bands is dissipated as small changes in broadband LWIR emission and gravitational potential energy.

Figure 13: a) Tropospheric heating and b) stratospheric cooling rates produced by a CO₂ ‘doubling’.

4.2 The Pseudoscientific Determination of ‘Climate Sensitivity’

In order to create the pseudoscientific ‘climate sensitivity’ to CO₂, the basic logic of cause and effect has been ignored and replaced by correlation. Two pseudoscientific ‘climate sensitivities’ have been used. The first is an ‘equilibrium climate sensitivity’ (ECS) which is the surface temperature change after the climate system has reached a new ‘equilibrium state’ including the ‘ocean response’. The second is a ‘transient climate response’ (TCR). This is the response to a gradual increase in the ‘radiative forcing’ before equilibrium is reached. Typically a 1% per year increase in the atmospheric CO₂ concentration is used. The ECS and TCS have been determined using correlation between the increase in CO₂ concentration and a ‘global average’ climate record that uses an area weighted average of the ‘surface temperature anomaly’ [HadCRUT4, 2019]. This is the average of weather station and ocean surface temperature data after it has been ‘homogenized’ to remove ‘bias’ and the mean has been subtracted. It is assumed a-priori that all of the observed increase in this ‘temperature anomaly’ can be attributed to CO₂ [Otto et al, 2013]. In reality, the weather station temperature increases have been caused by an increase in ocean surface temperature related mainly to the last 30 year warming phase of the Atlantic Multi-decadal Oscillation (AMO). In addition, a lot of ‘adjustments’ are made to the raw weather station temperature data [Andrews, 2017a, 2017b, 2017c D’Aleo, 2010]. The AMO is a long term quasi-periodic oscillation in the surface temperature in the N. Atlantic basin. The current period is about 60 years with an amplitude of ±0.2 C. There is also a longer term warming related to the temperature recovery from the Little Ice Age (LIA) or Maunder minimum. This is an approximately linear increase in temperature of 0.4 C over 150 years [Akasofu, 2010].

Otto et al [2013] define ECS and TCS as:

Here, F_2x is the radiative forcing is set to 3.44 W m^-2 for a CO₂ 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 the CMIP5 /RCP4.5 model ensemble. The change in heat content is dominated by ocean heat uptake. The decadal temperature and forcing estimates from data given by Otto et al [2013] are shown in Figure 14. The HadCRUT4 temperature series is plotted in Figure 14a. The AMO cycle minimum near 1910 and the maximum near 1940 are indicated. The increase in the downward LWIR flux related to the ‘radiative forcing’ shown in Figure 14b cannot couple below the ocean surface and cause any measurable change in ocean temperature. The penetration depth is less than 100 micron [Hale and Querry, 1973]. The effect of the AMO may be demonstrated by overlapping annual average AMO anomaly with the HadCrut4 data used by Otto et al [NOAA, AMO, 2019]. This is shown in Figure 14c . Both the 60 year period and the short term ‘fingerprint’ detail can be seen in both plots. The correlation coefficient between the two data sets is 0.8. The AMO and HadCRUT4 series are aligned from 1850 to 1970. From 1970 onwards, the HadCRUT4 series is offset approximately 0.3 C higher than the AMO. This requires further investigation and is probably related to the adjustments made to the HadCRUT4 data set. The influence of the AMO extends over large areas of North America, Europe and parts of Africa through the propagation of the ocean surface temperature by weather systems that are formed over the Atlantic Ocean. The ocean surface temperature is coupled to the weather stations through the convection transition temperature. Using tree ring analysis, the AMO has been reconstructed back to 1567 [Gray et al, 2004, Gray.NOAA, 2021]. This is shown in Figure 14d. None of the observed temperature changes associated with the AMO can be attributed to an increase in atmospheric CO₂ concentration.

Figure 14: a) Decadal mean temperature estimates derived from the HadCRUT4 global mean temperature series b) decadal mean forcing with standard errors from the CMIP5 /RCP4.5 ensemble. Data from Otto et al [2013], c) figure a) with the AMO plot overlay and d) AMO reconstruction from 1567.

Using the radiative forcing approach it is claimed that the ECS is in the range from 2.1 to 4.7 C based on a set of climate models known as CMIP5 (Climate Model Intercomparison Project, Phase 5). In the US, this modeling effort is coordinated by the climate group at Lawrence Livermore National Laboratories (LLNL). They also maintain the ‘library’ of climate model results [Stouffer et al, 2017, Taylor et al, 2012]. The CMIP5 model results were used by the UN Intergovernmental Panel on Climate Change (IPCC) in their fifth Climate Assessment Report (AR5) [IPCC 2013, Chap. 9]. For the AR6 IPCC report, the CMIP6 climate model ECS is given as 1.8 to 5.6 K [Hausfather, 2019]. These sensitivities are illustrated in Figure 15. The median ECS of 3.8 C/280 ppm translates into a temperature sensitivity of about 74 ppm C^-1. A 2 C temperature rise corresponds to a CO₂ concentration of approximately 430 ppm. This is the pseudoscientific basis of the 2 C temperature limit incorporated into the Paris Climate Accord [Luning and Vahrenholt, 2017].

Figure 15: Pseudoscientific equilibrium climate sensitivity (ECS) for a doubling of the CO₂ concentration from 280 to 560 ppm for 23 CMIP5 and 40 CMIP6 climate models.

The concept of radiative forcing has no basis in physical reality. Small changes in LWIR flux at the tropopause cannot couple into the surface thermal reservoirs and cause any measurable change in surface temperature. All of the equilibrium climate modeling results used by the IPCC in their assessment reports are fraudulent, based on the use of radiative forcing and the creation of a 'climate sensitivity' to CO₂ using the temperature changes related to the AMO. It is time to dismantle this massive fraud.

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. he hopes that you will agree with him.

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