Research Page 14 - Ventura Photonics

SUMMARY

In order to move beyond the acrimonious arguments over climate change and the 1.5 or 2 °C temperature limits contained in the Paris Climate Accord it is necessary to step back and look more carefully into the underlying climate science and the assumptions used in the climate models.

Since the start of the industrial revolution about 200 years ago, the atmospheric concentration of CO₂ has increased by approximately 140 parts per million (ppm). Radiative transfer analysis allows the changes in atmospheric longwave IR flux produced by this increase in atmospheric CO₂ concentration to be calculated. These LWIR flux changes can then be used in a thermal engineering analysis to determine the change in surface temperature. The results of such calculations show that any changes in temperature are ‘too small to measure’. However, a more careful investigation shows that the climate models use the pseudoscientific concepts of radiative forcing, feedbacks and a climate sensitivity to CO₂ in an equilibrium average climate. It is assumed that the observed increase the global average temperature record can be explained using a contrived set of radiative forcings. The climate models are simply ‘tuned’ to match the average temperature record. Physical reality has been abandoned in favor of mathematical simplicity.

INTRODUCTION

There are three parts to the climate fraud. First there is the technical fraud that started in the nineteenth century with the oversimplification of climate energy transfer using the equilibrium assumption. This provided the foundation for the later development of climate models based on the pseudoscience of radiative forcing, feedbacks and climate sensitivity. Second, there was ‘mission creep’. As funding was reduced for NASA space exploration and for DOE nuclear programs, climate modeling became an alternative source of revenue. Third, there was a deliberate decision by various outside interests, including environmentalists and politicians to exploit the fictional climate apocalypse to further their own causes. Here we focus on the development of the climate models and radiative forcing. A more detailed discussion of the climate fraud is provided in the related post VPCP21 ‘What Part of Too Small to measure Don’t You Understand?’ on Research Page 12.

The basic climate facts related to CO₂ that need to be addressed are as follows: Since the start of the Industrial Revolution about 200 years ago, the atmospheric concentration of CO₂ has increased by approximately 140 parts per million (ppm) from 280 to 420 ppm [Keeling, 2023]. This is shown in Figure 1a. Radiative transfer calculations show that the observed increase of 140 ppm in CO₂ concentration has produced a decrease of approximately 2 Watts per square meter (W m^-2) in the longwave infrared (LWIR) emission to space at the top of the atmosphere (TOA) within the spectral region of the CO₂ emission bands. There is a similar increase in the downward LWIR flux from the lower troposphere to the surface. For a doubling of the atmospheric CO₂ concentration from 280 to 560 ppm, the LWIR flux changes by approximately 4 W m^-2. The changes in LWIR flux vs CO₂ concentration are shown in Figure 1b [Harde, 2017]. At present the average atmospheric CO₂ concentration is increasing by approximately 2.4 ppm per year. This produces a change in LWIR flux near 0.034 W m^-2 per year.

There are two basic questions that need to be answered:

1) How have these changes in LWIR flux caused the ‘global average surface temperature’ of the earth to increase?

2) What damage, if any, has this caused?

We get two different answers.

1) If we follow the scientific path, thermal engineering calculations show that any increase in the surface temperature of the earth is ‘too small to measure’. There is no damage. These engineering calculations are described in detail in the recent book ‘Finding Simplicity in a Complex World - The Role of the Diurnal Temperature Cycle in Climate Energy Transfer and Climate Change’ (C&R23) [Clark and Rörsch, 2023]. There is also major benefit - increased plant growth - since CO₂ is a good fertilizer [CO₂ Science, 2023].

2) If we read the climate assessment reports published by the UN Intergovernmental Panel on Climate Change (UN IPCC), we are told that there is unprecedented warming and that we must take action to control the atmospheric concentration of CO₂ so that the temperature rise is less than 2 or even 1.5 °C [IPCC, 2021, 2013]. There are all kinds of damages including melting polar ice, sea level rise and increases in ‘extreme weather events’ such as floods, fires, heat waves and hurricanes.

At present, US policy and that of many other countries is based on the second answer. If we look a little deeper into the IPCC reports we find that their conclusions are based on the comparison between climate model results and a global average temperature. The climate model results used for the IPCC Sixth Climate Assessment Report, (AR6), are based on the Coupled Model Intercomparison Project Phase 6 (CMIP6) model ensemble. The IPCC itself is a political organization that does not conduct climate research or modeling. In general, the science is selected to match the political objectives [Crok and May, 2023]. A detailed discussion of the climate modeling approach is given in Chapter 7 of the Working Group 1 AR6 Report ‘The Earth’s energy budget, climate feedbacks, and climate sensitivity’ [IPCC 2021]. The introduction starts:

This chapter assesses the present state of knowledge of Earth’s energy budget, that is, the main flows of energy into and out of the Earth system, and how these energy flows govern the climate response to a radiative forcing. Changes in atmospheric composition and land use, like those caused by anthropogenic greenhouse gas emissions and emissions of aerosols and their precursors, affect climate through perturbations to Earth’s top-of-atmosphere energy budget. The effective radiative forcings (ERFs) quantify these perturbations, including any consequent adjustment to the climate system (but excluding surface temperature response). How the climate system responds to a given forcing is determined by climate feedbacks associated with physical, biogeophysical and biogeochemical processes. These feedback processes are assessed, as are useful measures of global climate response, namely equilibrium climate sensitivity (ECS) and the transient climate response (TCR).

A more concise summary was provided by Knutti and Hegerl [2008]:

When the radiation balance of the Earth is perturbed, the global surface temperature will warm and adjust to a new equilibrium state.

To evaluate the IPCC arguments, we must therefore understand the basic concepts of radiative forcing, feedbacks and climate sensitivity. We must also understand the process used to convert the raw weather station data into a global temperature average.

When the atmospheric concentration of CO₂ is increased, there is a slight decrease in LWIR flux emitted to space at TOA within the spectral regions of the CO₂ emission bands. An increase in the atmospheric concentration of other greenhouse gases also produces a decrease in LWIR flux in a spectral emission region specific to each gas (see Figure 8 below) [Wijngaarden and Happer, 2022]. A change in flux at TOA is called radiative forcing. It is claimed that such forcings change the energy balance of the earth. For greenhouse gas forcings it is then claimed that the surface temperature increases in response to the forcing until the energy balance at TOA is restored. Other ‘forcing agents’ such as aerosols of various kinds have the opposite effect. They increase the reflected solar flux returned to space and produce cooling. The IPCC claims that a set of contrived radiative forcings explains the changes in the global temperature record.

It is then assumed that these forcings are modified by feedbacks of various kinds. In particular, the increase in surface temperature that is supposed to be produced by a greenhouse gas forcing leads to a presumed increase in water vaper pressure. This in turn increases the downward LWIR flux to the surface that amplifies the initial warming from CO₂. Such an increase in temperature called a positive feedback.

The equilibrium climate sensitivity, ECS, is the hypothetical increase in global average surface temperature produced by a doubling of the atmospheric CO₂ concentration after the oceans have reached a new ‘equilibrium state’. This is often used as a benchmark for model inter-comparison. There is also a transient climate response, TCR which is the initial response as the CO₂ concentration is increased, before equilibrium is reached.

It is assumed that the global surface air temperature (GSAT) responds linearly to the radiative forcing:

ΔN = ΔF + αΔT ........................................................................................... Eqn. (1)

Here N is the change in flux in TOA, ΔF is the ERF and α is a feedback parameter (W m^-2 °C^-1). This functions to restore the radiation balance as the surface temperature ‘adjusts’. [IPCC 2021, AR6 WG1 Chap. 7]

The use of radiative forcings, feedbacks and climate sensitivity is pseudoscientific nonsense. A radiative forcing is a change in flux which has to be interpreted as a change in the rate of heating or cooling when coupled to a thermal reservoir. A radiative forcing does not directly produce a change in temperature. In the troposphere a ‘CO₂ doubling’ produces a maximum warming rate (decrease in cooling rate) of + 0.08 K per day [Iacono et al, 2008]. At a lapse rate of -6.5 K km^-1 an increase in temperature of +0.08 K is produced by a decrease in altitude of 12 meters. This is equivalent to riding an elevator down four floors. The small amount of heat released in the troposphere is reradiated back to space by wideband LWIR emission. It does not change the energy balance of the earth. At the surface, any temperature change produced by the increase in downward LWIR flux from the lower troposphere is too small to measure in the normal diurnal and seasonal changes in temperature.

The global temperature change record is an area weighted average of the weather station data after it has been extensively processed or ‘homogenized’ and the mean has been subtracted. The observed temperature increases in the global average temperature record can be explained as a combination of ocean influences, mainly related to the Atlantic Multi-decadal Oscillation, (AMO), urban heat island effects, and various biases introduced in the calculation of the average temperature. These include changes to the urban/rural mix of weather stations in the raw temperature data and data processing practices known as ‘homogenization’ that have added warming to the raw station temperature data. There can be no ‘CO₂ signature’ in the global average temperature record. A characteristic feature of this record is a peak near 1940 that is related to the warming phase of the AMO [AMO, 2022].

The contrived set of forcings used in IPCC AR6, the energy transfer and averaging procedures that contribute the global climate record, atmospheric and surface energy transfer and the history of radiative forcing will now be considered in more detail.

THE RADIATIVE FORCINGS, TEMPERATURES AND CLIMATE SENSITIVITIES FROM IPCC WG1 AR6

The IPCC claims that the global temperature record can be explained using a contrived set of radiative forcings as shown in Figure 2. Figures 2a and 2b shows the cumulative radiative forcings (W m^-2) and estimated temperature changes from 1750 to 2019. Increases in ‘greenhouse gas’ concentrations produce a decrease in the LWIR flux at TOA. This is supposed to produce an increase in surface temperature and is called a positive forcing. Other forcings, such as an increase in various aerosol concentrations reflect sunlight and produce cooling. Figures 2c and 2d show the time series of the forcings and the estimated time dependent temperatures from 1750 to 2019. Figure 2e shows the estimated increase in the ‘global mean temperature anomaly’. Figure 2f shows the attribution of the temperature to ‘natural’ and ‘human’ causes. The models are run twice. The first run has all of the forcings and the second run has the ‘human’ forcings, mainly greenhouse gases removed. Figures 2a through 2f are from the IPCC WG1 AR6 Report (figures 7.7, 7.6, 2.10, 7.8, 4.4b and FAQ 3.1 fig.1) [IPCC, 2021]. Figure 3 shows the estimated equilibrium climate sensitivities for the CMIP5 and CMIP5 climate models from AR6 WG1 table 7.SM.5. The climate models have simply been ‘tuned’ to match the global average temperature record. The correct thermal engineering value of the climate sensitivity is ‘too small to measure’.

Figure 2: a) Changes in radiative forcings since 1750, b) simulated temperature increases from 1750 to 2019, based on a), c) time dependence of the radiative forcings and d) time dependence of the temperature changes derived from c), e) ‘tuned’ temperature record using a contrived set of radiative forcings that appear to simulate the global mean temperature record and f) the separation of the contrived forcings to create fraudulent ‘human’ and ‘natural’ temperature records, (IPCC AR6, WG1, figures 7.6, 7.7, 2.10, 7.8, 3.4b and FAQ 3.1 Fig. 1). The 1940 AMO peak in the temperature record is indicated in e) and f).

Figure 4 illustrates the fraudulent attribution of the observed warming in the global average temperature record to ‘human caused’ radiative forcings in more detail. Figure 4a shows the time series of the forcings divided into the contributions from greenhouse gases (ghg), natural and ‘other’ anthropogenic sources, mainly aerosol effects. This is adapted from AR6 WG1 cross chapter box 1.2 fig.1. As described in more detail below, the ghg forcings cannot produce a measurable change in surface temperature. This also means that the presumed cooling effects of the aerosol forcings are overestimated. They are really just ‘tuning knobs’ used to reduce the ghg warming effects and make the model results appear to fit the temperature record.

The increase in global average temperature change record adapted from AR6 WG1 fig. 1.12 shows the global average temperature record from 1850 as determined by four similar data sets, Berkeley Earth, HadCRUT5, NOAA Global Temperature and a re-analysis from Kadlow et al [IPCC 2021, WG1 Table 3.SM.1, fig. 3.4]. As shown in Figure 4b, this temperature record can be explained as a combination of the influence of the Atlantic Multi-decadal Oscillation (AMO), a linear temperature recovery from the Little Ice Age (LIA), urban heat island (UHI) effects, changes to the urban/rural mix in the weather stations used in the climate record and various ‘homogenization’ adjustments. The warming phases of the AMO and the recovery from the LIA are shown. The 1940 AMO peak is clearly visible. The influence of the AMO and the more recent warming effects are discussed in more detail below. There should be no ‘attribution’ to human causes [Herring et al, 2022].

THERE CAN BE NO CO₂ SIGNATURE IN THE GLOBAL AVERAGE TEMPERATURE CHANGE RECORD

The global temperature change record is an area weighted average of the weather station data after it has been extensively processed or ‘homogenized’ and the mean has been subtracted. When the climate anomaly record, such as the HadCRUT4 data set is evaluated, the dominant term is found to be the Atlantic Multi-decadal Oscillation (AMO) [AMO, 2022, HadCRUT4, 2022, Morice et al, 2012]. The correlation coefficient between the two data sets is 0.8. This is illustrated in Figure 5. The AMO consists of a quasi-periodic oscillation superimposed on an underlying linear trend. A least squares fit to the data from 1900 gives a sinusoidal oscillation with an amplitude of 0.2 °C and a period of 61 years with a long term linear trend near 0.3 °C per century. The linear trend is attributed to the temperature recovery from the Maunder minimum or Little Ice Age [Akasofu, 2010]. Both the period and the slope may change with time. There is a 0.3 °C offset between the AMO and the HadCRUT data after 1970. The influence of the AMO extends over large areas of N. America, Western Europe and parts of Africa. The weather systems that form over the oceans and move overland couple the ocean surface temperature to the weather station data through the diurnal convection transition temperature (C&R23 Chapter 7). Figure 6 shows a tree ring construction of the AMO from 1567 [Gray et al, 2004a, 2004b]. The modern instrument record is also indicated in green.

There is still an additional part of the recent HadCRUT4 warming that is not included in the AMO signal. This may be explained as a combination of three factors. First there are urban heat islands related to population growth that were not part of the earlier record. Second, the mix of urban and rural weather stations use to create the global record has changed. Third, there are so called ‘homogenization’ adjustments that have been made to the raw temperature data. These include the ‘infilling’ of missing data and adjustments to correct for ‘bias’ related to changes in weather station location and instrumentation. It has been estimated that half of the warming in the ‘global record’ has been created by such adjustments. This has been considered in more detail by Andrews [2017a, 2017b and 2017c], D’Aleo and Watts [2010] and O’Neill et al [2022]. Adjustments to the Australian temperature record have been discussed by Berger and Sherrington [2022].

The role of the AMO in setting the surface air temperature has been misunderstood or ignored for a long time. The first person to claim a measurable warming from an increase in CO₂ concentration was Callendar in 1938. He used weather station temperatures up to 1935 that included most of the 1910 to 1940 warming phase of the AMO [Callendar, 1938]. The warming that he observed was from the AMO not CO₂. During the 1970s there was a ‘global cooling’ scare that was based on the cooling phase of the AMO from 1940 to 1970 [McFarlane, 2018, Peterson et al, 2008, Douglas, 1975, Bryson and Dittberner, 1976]. In their 1981 paper Hansen et al chose to ignore the 1940 AMO peak in their analysis of the effects of CO₂ on the weather station record [Hansen, 1981]. Similarly Jones et al conveniently overlooked the 1940 AMO peak when they started to ramp up the modern global warming scare in 1986 [Jones et al, 1986]. This is illustrated in Figure 7. The AMO and the periods of record used are shown in Figure 7a. The temperature records used by Callendar, Douglas, Jones et al and Hansen et al are shown in Figures 7b through 7e. The Keeling curve showing the increase in atmospheric CO2 concentration is also shown in Figures 7d and 7e [Keeling, 2022].

A GREENHOUSE AS RADIATIVE FORCING CANNOT CHANGE THE ENERGY BALANCE OF THE EARTH

The infrared radiation field in the atmosphere consists of many thousands of narrow overlapping lines. Each line is produced by the transition between two specific rotation-vibration states of an IR active molecule. The principal molecules of interest are CO₂ and H₂O (water vapor). Other minor species include methane, CH₄, ozone, O₃, and nitrous oxide, N₂O. The line structure is illustrated in Figure 8 [Wijngaarden and Happer, 2022]. The main CO₂ emission band in the 600 to 750 cm^-1 spectral region and the weaker overtone bands near 950 and 1050 cm^-1 are circled.

The lines are broadened by molecular collisions and are wider near the surface. This means that the upward and downward LWIR fluxes through the atmosphere are not equivalent. Some of the upward LWIR flux from the wings of the wider lines below is not absorbed by the narrower lines above. Part of this flux can pass through the gaps between these narrower lines and continue to space without additional absorption/emission. The downward LWIR flux from the wings of the narrower lines above is absorbed by the wider lines below. This is illustrated schematically in Figure 9a for a single line and in Figure 9b for a group of lines in the 590 to 600 cm^-1 region. Almost all of the downward LWIR flux from the lower troposphere to the surface originates from within the 2 km layer next to the surface. Approximately half of this flux originates from within the first 100 m layer above the surface. This is shown in Figure 9c [C&R23, Clark, 2013]. In order to understand the heating of the atmosphere, it is necessary to extend the radiative transfer calculations to include the overall rate of LWIR cooling and the change in the rate of cooling produced by a change in CO₂ concentration at different levels in the atmosphere.

Figure 9: a) Transition from absorption-emission to free photon flux as the linewidth decreases with altitude. Single H₂O line near 231 cm^-1. b) Linewidths for H₂O and CO₂ lines in the 590 to 600 cm^-1 spectral region for altitudes of 0, 5 and 10 km. c) Cumulative fraction of the downward flux at the surface vs. altitude for surface temperatures of 272 and 300 K, each with 20 and 70% relative humidity (RH). Almost all of the downward flux reaching the surface originates from within the first 2 km layer.

The local rate of LWIR cooling is the net LWIR emission from an air parcel in the atmosphere divided by the local heat capacity. For an air parcel in the troposphere, the energy transfer processes involved are illustrated in Figure 10. Within the plane parallel atmosphere approximation, the air parcel is emitting LWIR radiation upwards and downwards at the local air temperature. It is also absorbing part of the LWIR flux from above and below. In addition, as the air parcel changes altitude in the troposphere, the temperature changes with the local lapse rate as a result of air expansion or compression. For moist convection, the average lapse rate used in the US Standard Atmosphere is -6.5 K km^-1. For dry air this increases to -9.8 K km^-1. The air parcel may also be heated directly by the absorption of near infrared (NIR) solar radiation by the water band vibrational overtones. The total (10 to 3250 cm^-1) and spectral band average LWIR cooling rates for a tropical atmosphere are shown in Figure 11 [Feldman et al, 2017]. The total LWIR cooling rate for most of the troposphere at low latitudes is in the range 2 to 2.5 K per day. The change in the rate of LWIR cooling in the troposphere produced by a doubling of the CO₂ concentration is shown in Figure 12a [Iacono et al, 2008]. The maximum change is +0.08 K per day. At a lapse rate of -6.5 K km^-1, this daily change in temperature is produced by a decrease in altitude of approximately 12 meters. This is equivalent to riding an elevator down four floors. The change in the rates of cooling for the stratosphere are shown in Figure 12b. Here the ‘CO₂ doubling’ produces an increase in the cooling rate with a maximum near -3 K per day. However this is at a pressure of 1 mbar and an altitude near 50 km. The heat capacity of the air at this altitude is approximately 1.2 J m^-3 so the local net cooling flux is only 3.6 J day^-1 or 42 μW m^-2. This is much smaller than the normal variation in the LWIR emitted to space at TOA produced by the diurnal cycle and cloud top emission [Ellingson et al, 1994].

Based on this discussion, the CO₂ radiative forcing or 2 W m^-2 decrease in flux at TOA produces a slight decrease in the rate of cooling of the troposphere of approximately 0.04 K per day. The 140 ppm increase in concentration is half of the ‘CO₂ doubling’ amount of 280 ppm. The total quantity of heat released in the atmosphere is near 0.17 MJ m^-2 per day. To understand how this heat is dissipated, we need to consider the spectral distribution of the LWIR flux. Figure 13 shows the upward LWIR flux emitted at TOA (70 km) for surface and air temperatures at 288 K. The blue line shows the total flux and the orange and gray lines show the atmospheric and surface contributions to the total flux. The spectral range is from 100 to 1500 cm^-1 at a resolution of 2 cm^-1. These spectra are from MODTRAN calculations with a CO2 concentration of 400 ppm and a surface RH of 70% using the mid latitude summer model [MODTRAN, 2022]. Starting from left to right, the main spectral features are the rotational H2O band from 100 to 600 cm^-1, the CO2 ν₂ vibration band from 600 to 750 cm^-1 and the H₂O ν₂ vibration band above 1300 cm^-1. P and R denote the CO₂ band structure associated with the P (ΔJ = -1) and R (ΔJ = +1) rotational transitions. J is the rotational quantum number. 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. There is also an absorption feature from stratospheric ozone, O₃ that occurs near 1050 cm^-1. For reference, blackbody emission curves for 288 K and 280 to 220 K in 20 K intervals are also plotted. 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 ~3.0 km at a temperature of ~270 K. Near 300 cm-1 the H₂O emission temperature has decreased to ~240 K at an altitude of ~7.5 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.

Using simple conservation of energy arguments, the average planetary LWIR flux emitted at TOA is near 240 W m^-2. Using the Stefan Boltzmann law, this average flux is converted to an ‘effective emission temperature’ near 255 K. Assuming an average surface temperature of 288 K, the temperature difference of 33 K is often called a ‘greenhouse effect temperature’ and it is argued that the earth’s surface is 33 K warmer than it would be without ‘greenhouse gases’ in the atmosphere [Taylor, 2006]. This is pseudoscientific nonsense. The LWIR flux emitted to space is simply a cumulative cooling flux emitted by many different levels in the atmosphere at different temperatures. The upward emission from each level is modified by the absorption and emission of the levels above. The spectral distribution is not that of a blackbody radiator at 255 K. This is illustrated in Figure 13. The LWIR emission to space (blue line) is very different from the 255 K blackbody emission curve (dashed black line).

When the CO₂ concentration is increased, the vibrationally excited CO₂ molecules initially produced by the additional absorption are rapidly quenched by molecular collisions. The photon energy is converted to thermal motion within the local air parcel. In the troposphere this heat is simply reradiated to space as wideband LWIR emission, mainly by the water bands. This is illustrated in Figure 14. If the heating also leads to an in increase in altitude of the absorbing air parcel, the gravitational potential energy will increase. Contrary to the claims made by the IPCC, an infrared radiative forcing produce by an increase in atmospheric greenhouse gas concentration does not change the energy balance of the earth.

A GREENHOUSE GAS RADIATIVE FORCING CANNOT CHANGE THE SURFACE TEMPERATURE OF THE EARTH

The net cooling LWIR flux is one of four main interactive, time dependent flux terms that are coupled to the surface thermal reservoir. The others are the absorbed solar flux, the moist convection or evapotranspiration and the subsurface transport. (This does not include rainfall or freeze/thaw effects). A change in surface temperature is determined by the change in heat content or enthalpy of the thermal reservoir divided by the heat capacity. The net LWIR cooling flux (upward minus downward LWIR flux) at the surface is limited to the emission into the LWIR atmospheric transmission window. This LWIR flux is insufficient to dissipate the absorbed solar insolation. The surface warms up so that the excess solar heat is removed by moist convection. The surface heat is stored and released over a wide range of time scales.

As illustrated above in Figure 9, almost all of the downward LWIR flux to the surface originates from within the first 2 km layer of the troposphere. This means that the troposphere divides naturally into two independent thermal reservoirs [C&R23, Clark. 2013]. The lower reservoir extends from the surface to 2 km and the upper reservoir extends from 2 km to the tropopause. 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 to back space, mainly by the water bands. Some of the surface heat is stored as gravitational potential energy in the troposphere. Convection is a mass transport process that is coupled to both the gravitational potential and the angular momentum or rotation of the earth. These interactions result in the formation of the Hadley, Ferrell and polar cell convective structure, the trade winds and the ocean gyre circulation. The LWIR flux in the troposphere is part of the tropospheric heat engine and should not be separated and analyzed independently from the mass transport. The ocean-air and the land-air interfaces have different energy transfer properties and have to be analyzed separately.

The Ocean-Air Interface

Over the oceans, the surface is almost transparent to the solar flux. The diurnal temperature rise is small and the bulk ocean temperature increases until the water vapor pressure at the surface is sufficient for the excess absorbed solar heat to be removed by wind driven evaporation. The sensible heat flux is usually small, less than 10 W m^-2. The penetration depth of the LWIR flux into the ocean surface is less than 100 micron. This is illustrated in Figure 15 [Hale and Querry, 1973]. The LWIR flux and the wind driven evaporation are coupled together at the surface and should not be analyzed separately. The cooler water produced at the surface sinks and is replaced by warmer water from the bulk ocean below. This allows the evaporation to continue at night. As the cooler water sinks, it carries the surface momentum (wind driven velocity) with it. This drives the ocean currents at lower depths. Figure 16 shows the long term zonal average sensitivity of the latent heat flux to the wind speed. This is calculated from the long term zonal average ocean latent heat flux and wind speed data given by Yu et al [2008]. Over the ±30° latitude bands, the sensitivity is at least 15 W m^-2/m s^-1. As shown above in Figure 1b, the increase in downward LWIR flux to the surface produced by the observed 140 ppm increase in atmospheric CO₂ concentration is approximately 2 W m^-2. Within the ±30° latitude bands, this is dissipated by an increase in wind speed near 13 cm s^-1. For comparison, the long term 1σ variation in wind speed along the equator, measured by the TRITON buoy network is near 2 m s^-1 [C&R23, Chapter 6]. The average annual increase in atmospheric CO₂ concentration at present is near 2.4 ppm. This corresponds to an annual increase of 0.034 W m^-2 in the downward LWIR flux to the surface which is dissipated by an increase in wind speed near 2 millimeters per second. Any change in ocean temperature produced by the increase in the atmospheric CO₂ concentration is therefore too small to measure. There can be no measurable climate sensitivity to CO₂. Nor can the increase in CO₂ concentration have any effect on the frequency or intensity of ‘extreme weather’ events such as hurricanes [Herring et al, 2022].

The Land-Air Interface

Over land, all of the flux terms are absorbed by a thin surface layer. The surface temperature initially increases after sunrise as the solar flux is absorbed. This establishes a thermal gradient with both the cooler air above and the subsurface ground layers below. The surface-air gradient drives the evapotranspiration and the subsurface gradient conducts heat below the surface. Later in the day, as the surface cools, the subsurface gradient reverses and the stored heat is returned to the surface. As the land and air temperatures equalize in the evening, the convection stops and the surface cools more slowly by net LWIR emission. This convection transition temperature is reset each day by the local weather system passing through. Almost all of the absorbed solar heat is dissipated within the same diurnal cycle. The heat transfer is localized. The diurnal temperature change is limited to a shallow depth, typically 0.5 to 2 m, and the seasonal temperature variations may extend to 5 m below the surface [C&R23, Chapter 5, Clark, 2013]. There are also characteristic phase shifts or time delays between the peak solar flux and the temperature response. These are not a new discovery. The subsurface seasonal phase shift was described by Fourier in 1824 [Fourier, 1824]. Such phase shifts are clear evidence for a non-equilibrium climate.

Energy transfer at the land air interface is discussed in detail in C&R23. A simple thermal engineering model of the surface and air temperatures recorded in 2008 at the ‘Grasslands’ site, an advanced AmeriFlux monitoring station located in Limestone Canyon Regional Park, near Irvine, S. California was used to evaluate the effect of an increase in CO₂ concentration on land temperatures [C&R23, Chapter 5, Clark, 2013]. In this case, for a doubling of the CO₂ concentration from 280 to 560 ppm, the increase in MSAT was approximately 0.1 °C. This is too small to measure in the normal day to day variations in the convection transition temperature. In addition, the diurnal and seasonal phase shifts demonstrate that the surface thermal reservoir is not in thermal equilibrium. The 1.5 or 2 °C temperature limit contained in the Paris Climate Accord is pseudoscientific nonsense.

Air Compression: the Neglected Heat Source

An important source of heat in the lower troposphere is air compression. This has been largely ignored by the IPCC. As dry air descends to lower altitudes, the lapse rate is 9.8 K km^-1. There are two main effects. The first is heating by downslope winds and the second is the heating produced by the down flow of air within a high pressure ‘dome’. These processes can produce temperature changes of 10 °C or more over a few days or less. Downslope winds are well known in many regions or the world and there are many different names for the same effect. In S. California they are Santa Ana Winds. In N. California they are diablo winds. In the Rocky Mountains they are chinook (‘snow eating’) winds. In the Alps they are föhn winds. There is no connection between these downslope wind events and any increase in atmospheric CO₂ concentration. Once the necessary weather pattern is established, the hot, dry winds will finish drying out the vegetation very quickly and any ignition source will start a wildfire. The Santa Ana winds in S. California are a good example of this.

The air circulation within a high pressure system produces a downward air flow because of the Coriolis Effect. This provides a natural heat source for these systems. A stationary or blocking high pressure system can result in significant warming over a period of several days [C&R23, Chapter 5]. For example, a high pressure dome formed over the Pacific NW region in late June, 2021 and stayed there for a week as maximum daily temperatures increased from 83 to 116 °F. When this system moved east, the overnight temperature in Portland OR, June 28 to 29, dropped 52 °F from 116 to 64 °F (29 °C from 47 to 18 °C) [Mass, 2021].

Persistent high pressure domes are often associated with drought conditions. Here there is another source of surface warming. As the soil and vegetation moisture content decrease, the latent heat flux decreases. The flux terms are interactive so a loss of latent heat flux results in an increase in sensible heat flux or dry convection and net LWIR emission. This leads to an increase in surface temperature. None of the heating related to downslope winds or high pressure domes has any relationship to CO₂.

FOLLOW THE YELLOW BRICK ROAD - THE HISTORY OF RADIATIVE FORCING

The concepts of radiative forcing, feedbacks and climate sensitivity to CO₂ are not unique to the CMIP6 models used in the AR6 report. They have been part of the underlying foundation of the climate models since they were first developed [Ramaswamy et al, 2019]. We will now ‘Follow the Yellow Brick Road’ and trace these concepts back through earlier IPCC reports and related documents to the climate magic published by Hansen, ‘The Wizard of Goddard’ in 1976 and 1981 and then back to the creation of the Equilibrium Climate Fantasy land by Manabe and Wetherald in 1967 and 1975. This is illustrated in Figure 17.

We join the yellow brick road at AR6 WG1 in 2021 with figures 2.10 and FAQ 3.1 fig. 1 that show the time series of the radiative forcings, the simulation of the global average temperature record and the ‘attribution’ to human factors. (In all of the global average temperature plots, the 1940 AMO peak is indicated by the red asterisk). Next we go to the 2020 US Geological Survey Report, ‘Using information from global climate models to inform policymaking-The role of the U.S. Geological Survey’ [Terando et al, 2020]. Figure 1 from this report is an earlier version of the attribution used in AR6 that is based on CMIP5 model ensemble results (The temperature scale here is °F not °C). We find almost the same figure in the Fourth Climate Assessment Report, NCA4 published by the US Global Change Research Program (USGCRP) in 2017 [Knutson et al, 2017]. An earlier version was published by the USGCRP in NCA3, figure 14, Appendix 4. [Mellillo et al, 2013]. A similar figure to this was published in IPCC AR5, figure 10.7 and the original is found as figure 7 in a paper by Jones et al [2013]. This shows that little has changed since 2013. The USGCRP has blindly copied the IPCC AR5 report and Terrando et al have blindly copied USGCRP NCA4. There has been no attempt at independent model validation using thermal engineering calculations.

The history of radiative forcing was reviewed by Ramaswamy et al [2019]. This provides a convenient source for the earlier history of climate modeling and radiative forcing. The concept of radiative forcing has been used in the climate models reported by the IPCC since it was established in 1988.

Assessment of RF has been firmly embedded in IPCC assessments from its FAR [First Assessment Report] onward. FAR (Shine et al. 1990) took as its starting point the fact that the climate impact of a range of different climate forcing agents could be compared using RF, in watts per square meter, even though this was only starting to be done routinely in the wider literature at the time. Ramaswamy et al, 2019 p. 14.11

Further down the Yellow Brick Road, an even earlier version of Terando et al figure 1 can be found as figure 19 in a review paper by Hansen et al [1993]. The radiative forcings used are shown in figure 15. This is an earlier version of the forcings shown in AR6 WG1 figure 2.10. Little has changed in almost 30 years. As we continue on down the Yellow Brick Road we come to the Emerald City and find the magical climate model creation of Hansen, The Wizard of Goddard [Hansen, 1981].

The 1981 climate model is a one dimensional radiative convective (1-D RC) model based on earlier work by Wang, Hansen et al [1976] and by Manabe and Wetherald [1967]. There are 9 or 18 atmospheric levels in the radiative transfer calculation. The solar flux has been averaged so that it shines 24 hours a day at a fixed intensity. The LWIR flux returned to space must exactly balance the average absorbed solar flux. When the concentration of CO₂ or other greenhouse gases is increased, there is an initial decrease in the LWIR flux at the top of the model atmosphere (TOMA). The model is configured to adjust to a new equilibrium state so that the surface temperature increases until the LWIR flux is restored to its original value.

The paper begins by introducing the invalid effective emission temperature of 255 K. The spectral distribution of the LWIR flux at TOA had been available at least since 1971 [Hanel, 1971] but this was ignored (see Figure 13 above). Various feedback effects that can be used to amplify the surface temperature response are then discussed. The model used in the calculations had a fixed relative humidity, a moist adiabatic lapse rate and a fixed cloud altitude. This gave a feedback amplification of 1.4 and a climate sensitivity of 2.8 °C for a doubling of the CO₂ concentration. A two layer ‘slab’ ocean was used that had a well-mixed upper layer, 100 m thick and a 1000 m diffuse layer below this. The 100 micron penetration depth of the LWIR flux and the coupling to the wind driven evaporation were ignored (see Figures 15 and 16). The effect on the equilibrium surface temperature of an increase in concentration of various greenhouse gases including CO₂ and changes to other ‘forcing agents’ was then considered. The model calculation also took a year (step time interval times number of steps) to reach equilibrium. Next, the CO₂ doubling ritual or response of the model to a step doubling of the CO₂ concentration was introduced. A contrived set of radiative forcings including CO₂, volcanic aerosols and changes in the solar flux was then used to simulate the global mean temperature record derived from weather station data. The 1940 AMO peak was ignored.

To summarize, in this paper we find the foundation of the modern climate fraud including

• The effective emission temperature

• The equilibrium climate assumption

• Radiative forcing

• Water vapor feedback

• A slab ocean model

• The CO₂ doubling ritual and climate sensitivity

• The ‘attribution’ of warming in the ‘global average temperature record to CO₂.

• The neglect of the 1940 AMO peak in the temperature record

In addition

• The effects of molecular line broadening were ignored (see Figure 9)

• The effects of tropospheric air turbulence was also ignored.

To complete our journey we need to follow the path beyond the Emerald City to the start of the Equilibrium Climate Fantasy Land and the work of Manabe and Wetherald (M&W67 and M&W75) [1967, 1975].

The M&W67 model was an ‘equilibrium air column’ with 9 or 18 air layers. It used the equilibrium assumption with a fixed average solar flux. The surface was a partially reflective blackbody with zero heat capacity. There was also a fixed relative humidity distribution that provided a water vapor feedback. M&W went on to develop a ‘highly simplified’ global circulation model (GCM) that incorporated the 1967 air column into each unit cell of the GCM. Although the M&W GCM did not contain any real climate effects such as ocean transport and the cloud cover was fixed, claims of global warming from a ‘CO₂ doubling’ were still made.

In their conclusions, M&W stated:

In evaluating these results, one should recall that the current study is based upon a model with fixed cloudiness. The results may be altered significantly if we use a model with the capability to predict cloudiness. Other major characteristics of the model which can affect the sensitivities of the model climate are idealized geography, swamp ocean and no seasonal variation. Because of the various simplifications of the model, it is advisable not to take too seriously the quantitative aspect of the results obtained in this study.

In order to develop a GCM for climate simulation, the 1967 M&W model had to be incorporated into the fluid dynamics equations used to describe atmospheric and ocean flow. These are a complex set of complex partial differential equations that have to be solved numerically. There is no analytical solution. Lorenz [1963] showed that the solutions for such equations were inherently unstable. In weather forecasting, this means that the GCM solutions can be accurate for projections up to about 12 days ahead [Lorenz, 1973]. The accuracy of a weather forecast is easy to establish by comparison of prediction to measurement. There is no reason to expect a complex GCM climate model to have any predictive capability over the time scales required for climate change because of these instabilities.

CONCLUSIONS

Any temperature changes produced by the observed increase in the atmospheric concentration of CO₂ are too small to measure. The radiative forcing or decrease in LWIR flux at TOA produced by an increase in greenhouse gas concentration does not couple to the surface and change the surface temperature. The upward and downward LWIR fluxes are decoupled by molecular line broadening effects. There is no equilibrium, so the small atmospheric heating effects produced by increases in greenhouse gas concentration have to be analyzed as changes to the rate of LWIR cooling. Any heat generated in the troposphere is simply radiated back to space as wideband LWIR emission, mainly by the water bands. There is no change to the energy balance of the earth. At the surface, any small increase in downward LWIR flux has to be added to the interactive, time dependent flux terms coupled to the surface thermal reservoir. A thermal engineering analysis then shows that any change in surface temperature is ‘too small to measure’. The climate modelers have abandoned physical reality in favor of mathematical simplicity. They are playing expensive computer games in an equilibrium climate fantasy land.

Climate modelers are not scientists. They are no longer capable of logical deduction based on observation and measurement. They have become the prophets of the Imperial Cult of the Global Warming Apocalypse. Instead of a flat earth that have chosen to believe in a flat ocean where wind driven oscillations and non-equilibrium phase shifts do not exist. The climate must be controlled by radiative forcings and feedbacks. The climate modelers have trapped themselves in a web of lies of their own making. Eisenhower’s warning about the corruption of science by government funding has come true.

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 them.

REFERENCES

Normally, the references given in an article of this nature would be 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 than they might have received through the traditional peer review process.

Akasofu, S.-I. (2010), “On the recovery from the Little Ice Age” Natural Science 2(11) pp. 1211-1224. Akasofu

AMO (2022), AMO

Andrews, R. (2017a), “Adjusting Measurements to Match the Models – Part 3: Lower Troposphere Satellite Temperatures” Energy Matters Sept 14. Andrews.2017a

Andrews, R. (2017b), “Making the Measurements Match the Models – Part 2: Sea Surface Temperatures” Energy Matters Aug 2. Andrews,2017b

Andrews, R. (2017c), “Adjusting Measurements to Match the Models – Part 1: Surface Air Temperatures” Energy Matters July 27. Andrews,2017c

Berger, T. and G. Sherrington, (2022), “Uncertainty of Measurement of Routine Temperatures–Part Three” WUWT Oct 14 Berger

Bryson, R. A. and G. J. Dittberner (1976), “A non-equilibrium model of hemispheric mean surface temperature” J. Atmos. Sci. 33(11) pp. 2094-2106. Bryson

Callendar, G. S. (1938), “The artificial production of carbon dioxide and its influence on temperature” J. Roy. Met. Soc. 64 pp. 223-240. Callendar also availabe at: Callendar.a

Clark, R. (2013), “A dynamic, coupled thermal reservoir approach to atmospheric energy transfer Part I: Concepts” Energy and Environment 24(3, 4) pp. 319-340. Clark.PI

“A dynamic, coupled thermal reservoir approach to atmospheric energy transfer Part II: Applications” Energy and Environment 24(3, 4) pp. 341-359. Clark.PII

Clark, R. and A. Rörsch, (2023) Finding Simplicity in a Complex World - The Role of the Diurnal Temperature Cycle in Climate Energy Transfer and Climate Change, Clark Rörsch Publications, Thousand Oaks, CA. Available from Amazon.

Paperback: C&R.1 ebook: C&R.2

CO₂ Science (2023) CO₂

Crok, M and A. May, Eds. (May 2023), The frozen climate views of the IPCC, An analysis of AR6, Clintel Crok.May

D’Aleo, J. and A. Watts (Aug. 27, 2010) “Surface temperature records: policy driven deception? [http://scienceandpublicpolicy.org/images/stories/papers/originals/surface_temp.pdf] (Link not working) Available at: D'Aleo.Watts

Douglas, J. H. (March 1, 1975) “Climate change: chilling possibilities” Science News 107 pp. 138-140. Douglas

Ellingson, R. G., H.-T. Lee, D. Yanuk, and A. Gruber (1994), “Validation of a technique for estimating outgoing longwave radiation from HIRS radiance observations” J. Atmos. Ocean. Technol. 11, pp. 357–365. Ellingson

Feldman D.R., K. N. Liou, R. L. Shia and Y. L. Yung (2008), “On the information content of the thermal IR cooling rate profile from satellite instrument measurements” J. Geophys. Res. 113 D1118 pp. 1-14. Feldman

Fourier, J.-B.-J. (1824), “Remarques générales sur les températures du globe terrestre et des espaces planétaires” Annales de Chimie et de Physique 27, pp. 136–167. Fourier.Fr English translation: Fourier.Eng

Gray, S. T., L. J. Graumlich, J. L. Betancourt and G. T. Pederson (2004) “A tree-ring based reconstruction of the Atlantic Multi-decadal Oscillation since 1567 A.D.” Geophys. Res. Letts, 31 L12205, pp. 1-4. Gray

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. Gray.Data [https://www.ncei.noaa.gov/pub/data/paleo/treering/reconstructions/amo-gray2004.txt] HadCRUT4 (2022), HadCRUT4

Hale, G. M. and M. R. Querry (1973), “Optical constants of water in the 200 nm to 200 µm wavelength region” Applied Optics 12(3) pp. 555-563. HandQ

Hanel, R. A., B. Schlachman, D. Rogers and D. Vanous (1971) “Nimbus 4 Michelson Interferometer” Applied Optics 10(6) pp. 1376-1382. Hanel

Hansen, J., D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind and G. Russell (1981), “Climate impact of increasing carbon dioxide” Science 213 pp. 957-956. Hansen81

Hansen, J., A. Lacis, R. Ruedy M. Sato and H. Wilson (1993), “How sensitive is the world's climate?” National Geographic Research and Exploration 9(2) pp. 142-158. Hansen93

Harde, H. (2017), “Radiation Transfer Calculations and Assessment of Global Warming by CO2” Int. J. Atmos. Sci. 9251034 pp. 1-30. Harde

Herring, S. C., N. Christidis, A. Hoell and P. A. Stott (2022), “Explaining Extreme Events of 2020 from a Climate Perspective” Bull. Amer. Meteor. Soc. 101 (1), pp. S1–S128. Herring (and prior years in this series)

Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins (2008), “Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models” J. Geophys. Res. 113, D13103 pp. 1-8. Iacono

IPCC, Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. (2021). In Press. doi:10.1017/9781009157896. IPCC21

IPCC, 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, (2014)1535 pp. ISBN 9781107661820. IPCC13

Jones, G. S., P. A. Stott and N. Christidis (2013), “Attribution of observed historical near surface temperature variations to anthropogenic and natural causes using CMIP5 simulations” J. Geophys. Res. Atmos. 118(10) pp. 4001-4024. Jones13

Jones, P. D., T. M. Wigley and P. B Wright (1986), “Global temperature variations between 1861 and 1984” Nature 323(31) pp. 430-434. Jones86

Keeling (2022), The Keeling Curve. Keeling

Knutson, T., J.P. Kossin, C. Mears, J. Perlwitz and M.F. Wehner (2017), “Detection and attribution of climate change” In: Climate Science Special Report: Fourth National Climate Assessment, Volume I, Wuebbles, D.J., D.W. Fahey, K.A. Hibbard, D.J. Dokken, B.C. Stewart, and T.K. Maycock (eds.). U.S. Global Change Research Program, Washington, DC, USA, pp. 114-132. Knutson

Knutti, R. and G. C. Hegerl (2008), “The equilibrium sensitivity of the Earth’s temperature to radiation changes” Nature Geoscience 1 pp. 735-743. Knutti

Lorenz, E. N. (1973), “On the Existence of Extended Range Predictability” J. Applied Meteorology and Climatology 12(3) pp. 543-546. Lorenz73

Lorenz, E.N. (1963), “Deterministic nonperiodic flow” Journal of the Atmospheric Sciences 20(2) pp. 130-141. Lorenz63

Manabe, S. and R. T. Wetherald (1975) “The effects of doubling the CO₂ concentration in the climate of a general circulation model” J. Atmos. Sci. 32(1) pp. 3-15. MW75

Manabe, S. and R. T. Wetherald (1967) “Thermal equilibrium of the atmosphere with a given distribution of relative humidity” J. Atmos. Sci. 24 pp. 241-249. MW67

Mass, C. (2021), “Showtime. Temperatures Are Surging to Unparalleled Highs” Cliff Mass Weather Blog. Mass

McFarlane, F. (2018), “The 1970s Global Cooling Consensus was not a Myth” Watts Up with That, 11.19.2018 McFarlane

Melillo, J. M., T. C. Richmond, and G. W. Yohe, eds., (2014) Climate Change Impacts in the United States: The Third National Climate Assessment. U.S. Global Change Research Program, 841 pp. Melillo.pdf , on line Melillo.online

MODTRAN (2021), Modtran

Morice, C. P., J. J. Kennedy,N. A. Rayner and P. D. Jones (2012) “Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: The HadCRUT4 data set” J. Geophysical Res. Atmospheres 117 D08101 pp. 1-22. Morice

O’Neill, P., R. Connolly, M. Connolly, Willie Soon, B. Chimani, M. Crok, R. de Vos, H. Harde, P. Kajaba, P. Nojarov, R. Przybylak, D. Rasol, O. Skrynyk, O. SkrynykP. Štěpánek, A. Wypych and P. Zahradníček, (2022), “Evaluation of the Homogenization Adjustments Applied to European Temperature Records in the Global Historical Climatology Network Dataset” Atmosphere 13(2) 285 pp. 1-21. O'Neill

Peterson, T. C., W. M. Connolley and J. Fleck, (2008) “The myth of the 1970’s global cooling consensus” Bull. Amer. Meteor. Soc. 86 pp. 1325-1337. Peterson

Ramaswamy, V., W. Collins, J. Haywood, J. Lean, N. Mahowald, G. Myhre, V. Naik, K. P. Shine, B. Soden, G. Stenchikov and T. Storelvmo (2019) “Radiative Forcing of Climate: The Historical Evolution of the Radiative Forcing Concept, the Forcing Agents and their Quantification, and Applications” Meteorological Monographs Volume 59 Chapter 14. Ramaswamy

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

Terando, A. D. Reidmiller, S. W. Hostetler, J. S. Littell, T. D. Beard, Jr., S. R. Weiskopf, J. Belnap, G. S. Plumlee (2020) “Using information from global climate models to inform policymaking—The role of the U.S. Geological Survey” U.S. Geological Survey Open-File Report 2020–1058, 25 pp. Terando

Wang, W. C., Y. L. Yung, A. A. Lacis, T. Mo and J. E. Hansen (1976), “Greenhouse effects due to man-made perturbations of trace gases” Science 194 pp. 685-690. Wang

Wijngaarden, W. A. van and W. Happer (2022), “IR Forcing by Greenhouse Gases” CO₂ Coalition publication 6/10/22, Wijngaarden

Yu, L., X. Jin, and R.A. Weller (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” OAFlux project technical report OA-2008-01. Yu