SURFACE TEMPERATURE AND THE PSEUDOSCIENTIFIC 2 C TEMPERATURE LIMIT IN THE PARIS CLIMATE ACCORD



Ventura Photonics Climate Post 003.1 Sept. 7 2021


Roy Clark





SUMMARY



The surface temperature is determined at the earth’s surface by the interaction of four main time dependent flux terms with the surface thermal reservoir. These are the absorbed solar flux, net LWIR flux, the moist convection or evapotranspiration and the subsurface transport. 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 downward LWIR flux from the lower troposphere interacts with the upward LWIR flux from the surface to produce a partial LWIR exchange energy. Within the main absorption and emission bands when the surface and air temperatures are similar, photons are exchanged with minimal transfer of thermal energy. This is real source of the so called ‘greenhouse effect’. In order to dissipate the absorbed solar flux, the surface warms up until the excess solar heat is removed by moist convection. The surface heat is stored and released over a wide range of time scales. The four flux terms are interactive and should not be separated and analyzed independently of each other.


Because of molecular line broadening effects, 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. 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 ‘greenhouse effect’ is an integral part of the energy transfer processes that determine the earth’s weather patterns. 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 greenhouse effect is produced by the time dependent surface LWIR exchange energy on a rotating water planet (See Research Page 1 for more on the Greenhouse Effect).


There are three important parameters that have been neglected in conventional equilibrium climate modeling. These are the time delay or phase shift between the peak solar flux and the peak temperature flux, the diurnal convection transition temperature and the sensitivity of the ocean evaporation to the wind speed. The phase shift is clear evidence of a non-equilibrium thermal response related to heat storage in the thermal reservoirs. In particular, at mid latitudes there is a seasonal time delay of 4 to 8 weeks. This is not new science. This phase shift has been recorded as part of the weather station record for over 100 years. The subsurface phase shift was described by Fourier in 1824 and 1827. The energy transfer processes at the land-air and ocean-air interfaces are different. The underlying reason is related to the definition of a blackbody surface. This has two parts. First, a blackbody surface should absorb electromagnetic radiation at all wavelengths. Second, the surface should emit electromagnetic radiation based on Planck’s law according to the absolute temperature of the surface. Water is almost transparent to the solar incident radiation, so the ocean-air interface is not a blackbody absorber for the solar flux.


Over land, almost all of the absorbed solar heat is dissipated within the same diurnal cycle. As the surface warms during the day, the excess heat is removed by moist convection. Some of the heat is conducted below the surface, stored and returned to the surface later in the day. In the evening, the surface cools and the convection essentially stops as the surface and air temperatures equalize. The surface then cools more slowly over night by net LWIR emission. The equalization or convection transition temperature is reset each day by the local weather system passing through. Over the oceans, the water surface is almost transparent to the solar flux. Approximately 90% of the solar flux is absorbed within the first 10 m layer of the ocean. The diurnal temperature rise is small and the bulk ocean temperature increases until the excess solar heat is dissipated by wind driven evaporation. The cooler surface water sinks and is replaced by warmer water from below. This allows the evaporation to continue at night. Within the ±30° latitude bands the sensitivity of the evaporation to the wind speed is approximately 15 W m-2/m s-1. The latent heat flux increases by 15 W m-2 for an increase in wind speed of 1 m s-1. The penetration depth of the LWIR flux into the ocean surface is 100 micron or less. Here the LWIR flux is fully coupled to the wind driven cooling flux. The two should not be separated and analyzed separately


The effect of an increase in atmospheric CO2 concentration on the surface temperature has to be determined from the increase in enthalpy of the surface thermal reservoir after a thermal cycle with increased CO2 concentration. The increase in downward LWIR flux from CO2 has to be added to the rest of the surface flux terms. Over land, the day to day variations in the convection transition temperature are much larger than any change in surface temperature from CO2. Over the ocean, the observed 120 ppm increase in atmospheric CO2 concentration since the start of the industrial revolution has produced an increase in downward LWIR flux of approximately 2 W m-2. Within the ±30° latitude bands, this flux is dissipated by an increase in wind speed of approximately 13 cm s-1. At present, the increase in CO2 concentration is approximately 2.4 ppm per year which produces an increase in downward LWIR flux to the surface near 0.034 W m-2 per year. The magnitude and variation in the wind driven evaporation is sufficiently large that any change in LWIR flux from CO2 is too small to have any measurable effect on the ocean surface temperature.


There is no requirement that the wind driven ocean evaporation exactly balance the absorbed solar flux on any time scale. The interaction of the solar heating and wind driven cooling within the ocean gyre circulation produces characteristic quasi-periodic ocean oscillations that have a major impact on the earth’s climate. These include the El Nino Southern Oscillation (ENSO) with a period between 3 and 7 years and the Pacific Decadal Oscillation (PDO) and Atlantic Multi-decadal oscillation (AMO) with longer term periods in the 60 to 70 year range. In many regions of the world, the prevailing weather systems form over the oceans. As they move overland they still retain the ocean surface temperature from the ocean path, including the phase shift. These are coupled to the weather station temperature record through the convection transition temperature. Because of the area weighted averaging process used, the ‘global average temperature anomaly’ is dominated by the AMO. This has been used to create the fraudulent pseudoscientific ‘climate sensitivity’ to CO2.


Normally, the lapse rate or temperature profile in the troposphere is negative. The warm air cools as it rises from the surface. However, under certain conditions involving downslope winds and blocking high pressure systems there is a downward flow of dry air. This is warmed as it is compressed during the descent. Temperatures can easily rise 10 C over a period of a few days or less. In some regions, such as parts of California and Australia, these conditions are associated with a high risk of brushfires. These temperature changes are a normal part of the regional weather systems and are not connected in any way to increases in the atmospheric CO2 concentration. Similarly, climate changes related to ocean oscillations have been ‘attributed’ to an increase in the CO2 concentration using pseudoscientific arguments based on ‘radiative forcings’, ‘feedbacks’ and a ‘climate sensitivity’ to CO2. Once the evidence related to phase shifts, the convection transition temperature and the sensitivity of the ocean evaporation to the wind speed are understood, the pseudoscience used in the equilibrium climate models is revealed for all to see. The 2 C (or 1.5 C) temperature limit in the Paris Climate Accord is pseudoscientific nonsense.



1.0 INTRODUCTION



Since the start of the industrial revolution in about 1800, the atmospheric concentration of CO2 has increased by approximately 120 parts per million (ppm) from 280 to 400 ppm [Keeling, 2020]. This has produced a slight decrease near 2 W m-2 in the long wave IR (LWIR) flux emitted by the CO2 band at the top of the atmosphere and a similar increase in downward flux from the lower troposphere to the surface [Harde, 2017]. The change in LWIR flux in the atmosphere can be calculated to high accuracy using radiative transfer algorithms and the HITRAN spectral database [HITRAN, 2021, Wijngaarden, and Happer 2020]. The increase in CO2 concentration is shown in Figure 1a and the changes in LWIR flux as the CO2 concentration is increased from 35 to 760 ppm are shown in Figure 1b. At present, the average CO2 concentration is increasing by about 2.4 ppm per which corresponds to a change in LWIR flux near 0.034 W m-2 per year.





Figure 1: a) The increase in atmospheric CO2 concentration from 1800 and b) calculated changes in atmospheric LWIR flux produced by an increase in atmospheric CO2 concentration from 35 to 760 ppm. Data from Harde, 2017 Clark, 2013 Hansen, 2005.



HITRAN was initially developed by the US Air Force independent of climate science, so the results are reliable and have been thoroughly validated. The issue is not the change in the atmospheric LWIR flux. Instead it is the determination of the change in surface temperature produced by the change in the LWIR flux. In the real engineering world, a change in surface temperature is determined by a change in heat content or enthalpy of the surface thermal reservoir divided by the heat capacity. In the fantasy land created by the computer climate models, it is determined using an approach known as ‘radiative forcing’ [IPCC 2013, Chap. 8]. First, it is assumed, without any justification or validation that the time dependent energy transfer processes that determine the surface temperature can be replaced by an ‘equilibrium average climate’. In this mathematical construct there is an exact energy balance between an ‘average absorbed solar flux’ and the ‘average LWIR flux’ returned to space at the top of the atmosphere (TOA). An increase in the atmospheric concentration of CO2, or any other ‘greenhouse gas’ perturbs this ‘equilibrium state’ by absorbing more of the LWIR flux in the atmosphere and decreasing the LWIR flux at TOA. The climate system is then supposed to respond by increasing the ‘equilibrium surface temperature’ until the ‘equilibrium flux balance’ is restored at TOA [Knutti and Hegerl, 2008]. It is also assumed that there is a linear response between the change in temperature and the change in LWIR flux at TOA. This change in flux is called a ‘radiative forcing’, RF [Ramaswamy et al, 2019].





Instead of comparing the climate model results to the measured surface temperature using the time dependent surface flux balance and a realistic error analysis, 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 2. Two pseudoscientific ‘climate sensitivities’ have been created. 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. The ECS and TCS have been determined using correlation between the increase in CO2 concentration and a ‘global average’ climate record created using an area weighted average of the ‘surface temperature anomaly’. This is the average of weather station data after it has been ‘homogenized’ to remove ‘bias’ and the mean has been subtracted. It has been assumed a-priori that all of the observed increase in this ‘temperature anomaly’ can be attributed to CO2 [Otto et al, 2013].





Figure 2: 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.



In reality, the weather station temperature increases have been caused by an increase in ocean surface temperature related mainly to the Atlantic Multi-decadal Oscillation (AMO) (see Figure 32a, below) and a lot of ‘adjustments’ to the raw weather station temperature data [Andrews, 2017a, 2017b, 2017c D’Aleo, 2010]. Using this 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 Inter-comparison Project Phase 5). In the US, this modeling effort is coordinated by the climate group at Lawrence Livermore National Laboratories (LLNL). They also maintain a ‘library’ of climate model results. 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]. This is the pseudoscientific basis of the 2 C temperature limit incorporated into the Paris Climate Accord [Luning and Vahrenholt, 2017]. For the upcoming AR6 IPCC report, the CMIP6 climate model ECS is given as 1.8 to 5.6 K [Hausfather, 2019]. TheCMIP5 and CMIP6 equilibrium climate sensitivities are shown in Figure 3. Radiative forcing is considered in more detail in the separate ‘Forcing’ post (see Research Page 4).





Figure 3: Equilibrium climate sensitivities (ECS) for CMIP5 and CMIP6 climate models.



The engineering calculation of the sensitivity of the surface temperature to a change in the CO2 flux requires the determination of the change in the residual amount of heat stored in the surface reservoir after a solar thermal cycle. There are two parts to this analysis. First, the change in temperature produced by the small change LWIR flux from CO2 has to be evaluated using the time dependent surface flux terms. Second, the effect of other energy transfer processes has 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 energy transfer processes for the land and ocean surfaces are different and need to be analyzed separately.


However, in order to understand the climate energy transfer processes and the errors incorporated into the climate models it is necessary to start with the planetary energy balance and the so called ‘greenhouse effect’. Then the effects of molecular line broadening on the LWIR flux and the tropospheric heat engine have to be considered.



1.1 The Planetary Energy Balance and the Greenhouse Effect



The concept of an equilibrium average climate is based on a fundamental misunderstanding of the difference between thermal equilibrium and a planetary energy balance. Thermal equilibrium means that the rate of heating equals the rate of cooling. There is almost no time delay between a change in the rate of heating and the temperature response. This is the case for the lunar surface under solar illumination [Vasavada et al, 2012]. Unlike the moon, the earth is a water planet that has both an atmosphere and oceans. Part of the solar flux is absorbed, stored as heat, and released over a wide range of time scales. Since the earth is an isolated planet with a stable climate, there is an approximate long term planetary energy balance between the absorbed solar flux and the LWIR flux returned to space. This has been sufficient to maintain the surface temperature remain within the relatively narrow bounds needed to sustain life on earth. There is no thermal equilibrium and no requirement for an exact short term flux balance.


The use of the equilibrium assumption has also led to confusion over the so called ‘greenhouse effect’. The surface temperature of the earth is warmer that it should be based on simple conservation of energy arguments. This can be understood quite easily when the time dependent flux terms are considered. The downward LWIR flux from the lower troposphere to the surface limits the net LWIR cooling flux that can be emitted by the surface. In order to dissipate the absorbed solar flux, the surface must warm up until the excess heat is removed by moist convection (evapotranspiration). The greenhouse effect is simply the time dependent LWIR surface exchange energy. It can be defined as either the net LWIR cooling flux or as an opacity factor. This is the ratio between the downward and the upward LWIR flux at the surface. The peak solar flux at the surface is near 1000 W m-2. This corresponds to a blackbody emission temperature near 94 C (367 K). In simple terms, the Second Law of Thermodynamics requires a thermal gradient for heat transfer to occur [Gerlich and Tscheuschner, 2009]. In order to dissipate the excess solar heat, the surface must be warmer than the air above. In addition, for evaporation there has to be a humidity gradient.


Conservation of energy arguments indicate that the planetary average of the outgoing LWIR radiation (OLR) returned to space should be near 240 W m-2. Satellite radiometry measurements give a value of approximately 240 ±100 W m-2 [CERES, 2011]. Unfortunately, the intensity of the OLR flux has been used incorrectly to define an ‘effective emission temperature’ near 255 K based on Stefan’s law. This has then been combined with an average surface temperature of 288 K to give a ‘greenhouse effect temperature’ of 33 K. [Taylor, 2006]. However, the spectral distribution of the OLR is not that of a blackbody near 255 K. Instead the OLR is the cumulative LWIR emission from many different levels in the atmosphere. The emission from each level is modified by the absorption and emission of the intervening layers up through the atmosphere. The OLR is simply a cooling flux. There is no ‘shell’ of ‘greenhouse gases’ in the atmosphere emitting LWIR radiation at a temperature near 255 K. This is discussed in more detail in the ‘Greenhouse Effect’ post (see Research Page 1).



1.2 The Tropospheric Heat Engine and Molecular Line Broadening



The troposphere functions as an open cycle heat engine that transports part of the absorbed solar heat from the surface to the middle to upper troposphere by moist convection. From here it is radiated to back space, mainly by the water bands. This emission is a rate limited process. The rate of emission depends largely on the local air temperature that determines the water vapor pressure. The emission band shifts to higher altitude as the surface temperature increases. The LWIR flux consists of absorption and emission by a very large number of molecular lines. In the lower troposphere, these lines are pressure broadened and overlap within the main absorption emission bands to form a quasi-continuum. Part of the upward LWIR flux is transmitted through the gaps between the lines above. The downward flux is absorbed by the broader lines below. Almost all of the downward LWIR flux from the troposphere to the surface originates from within the first 2 km layer above the surface and approximately half of this flux originates from within the first 100 m layer. These line broadening effects are illustrated in Figure 4 [Clark, 2013]. This means that the troposphere divides naturally into two independent thermal reservoirs. The lower tropospheric reservoir extends from the surface to 2 km and the upper tropospheric reservoir extends from 2 km to the tropopause. The downward LIWR flux from the stratosphere and the upper troposphere cannot couple to the surface and influence the surface temperature. The energy transfer processes related to the tropospheric heat engine and for an air parcel in the troposphere are illustrated schematically in Figure 5.





Figure 4: a) Molecular line broadening (schematic) and b) cumulative downward flux to the surface vs. altitude.





Figure 5: a) The tropospheric heat engine and b) energy transfer processes for a local tropospheric air parcel (in a plane-parallel atmosphere).



Convection is a mass transport process. As the warm air ascends from the surface it must interact with both the gravitational field and the rotation or angular momentum of the earth. The rising air expands and cools as it uses internal energy to overcome the gravitational potential. This establishes the lapse rate or temperature profile through the troposphere. If the air is moist, water may condense to form clouds. This releases latent heat that adds to the convection and reduces the magnitude of the lapse rate. For dry air, the adiabatic lapse rate is -9.8 K km-1 and the average moist lapse rate used in the US Standard Atmosphere is -6.5 K km-1. The heat (internal energy) lost to expansion during the convective ascent is stored as gravitational potential energy. As heat is radiated to space by LWIR emission, the air cools and sinks. This converts the gravitational potential energy back to heat as the descending air is compressed. The convection and the net LWIR emission in the troposphere should not be separated and analyzed independently of each other. An air parcel in the troposphere absorbs part of the upward LWIR flux from below and the downward flux from above. In addition, the IR active species in the air parcel are emitting LWIR flux at the local temperature of the air parcel. As the atmospheric concentration of a ‘greenhouse gas’ is increased, any small increase in tropospheric heating produced by the small increase in LWIR absorption is dissipated by the normal convective motion in the troposphere. In addition, as the warm air rises through the troposphere, the moment of inertia increases and the angular velocity decreases. This establishes the trade winds that drive the ocean gyre circulation. The greenhouse effect is an integral part of the energy transfer processes that set the earth’s weather patterns.



1.3 The Surface Temperature



The term ‘surface temperature’ has a variety of meanings. Logically, it should refer to the temperature at the earth’s air-surface interface. This is sometimes called the skin temperature. Any realistic calculation of the surface temperature has to include the interaction of the time dependent flux terms at this interface. However, ‘surface temperature’ is often taken to mean the weather station temperature. This is not a surface temperature. Instead, it is the meteorological surface air temperature (MSAT). This is the temperature measured by a thermometer installed in a ventilated enclosure located for convenience near eye level, 1.5 to 2 m above the ground [Oke, 2016]. Historically in the US, the daily minimum and maximum MSATs were recorded using Six’s thermometer. The min and max readings are often averaged to give an ‘average daily temperature’.

The climate record is not simply the long term average of the weather station data [Andrews, 2017a, 2017b, 2017c, D’Aleo, 2010]. First, the raw data is processed using ‘homogenization’ to remove measurement ‘bias’ and ‘infilling’ to create values for missing data. Area weighted averages within given latitude and longitude ‘bins’ are then determined. To compare the weather station record to computer model predictions, the ‘temperature anomaly’ is often used. This is the long term temperature record with the mean subtracted to highlight the trends. The mean is usually taken over a 30 year reference period. The apparent trends can depend on how the reference period is selected. The end result may bear little resemblance to the raw data. These climate data sets are then analyzed using advanced mathematical techniques to find trends that may or may not be real. To the analyst, the data set is often just a number series, completely disconnected from the original temperature measurements and devoid of any physical meaning.

The surface temperature or skin temperature at the surface-air interface is determined by the interaction of four main time dependent flux terms, the solar flux, the net LWIR flux, the evapotranspiration (moist convection) and the subsurface thermal transport with the surface thermal reservoir. These four flux terms are interactive and should not be separated and analyzed independently of each other. (Other effects such as rainfall and the freeze-thaw cycle are not considered here). The change in temperature is then given by the change in heat content or enthalpy of the thermal reservoir divided by the local heat capacity. In addition, there is a time delay or phase shift between the peak solar flux and the surface temperature response. The diurnal phase shift can reach 2 hours or more and the seasonal phase shift at mid latitudes can reach 6 to 8 weeks. These phase shifts are not new physics. They were described by Fourier in 1824 and 1827 based on his earlier work on the theory of heat [Fourier, 1827, 1824, 1822]. They are clear evidence of a non-equilibrium thermal response. Similar energy storage phase shifts are observed in electronics for example with capacitors in AC circuits and in optics with passive resonant optical cavities (cavity ringdown). In addition, over the oceans, some of the absorbed solar heat may be transported over long distances by wind driven ocean currents.

Over land, almost all of the absorbed solar flux is dissipated within the same diurnal cycle. As the surface warms and cools during the day, heat is removed by a combination of net LWIR emission and evapotranspiration. Some of the absorbed heat is also conducted below the surface and returned later in the day as the subsurface thermal gradient reverses. Over the oceans, the surface is almost transparent to the solar flux. Approximately half of the flux is absorbed within the first meter layer and 90% is absorbed within the first 10 m layer [Clark, 2013]. The diurnal temperature rise at the surface is quite small, typically 2 C or less. The dominant cooling term is the wind driven evaporation or latent heat flux. The LWIR flux is absorbed within the first 100 micron layer [Hale and Querry, 1973]. Here it is fully coupled to the wind driven evaporation or latent heat flux. The sensible heat flux term is usually small, less than 10 W m-2. The cooling terms are fully coupled at the surface and should not be separated and analyzed independently of each other. The cooler water produced at the surface then sinks and is replaced by warmer water from below. This is a Rayleigh-Benard type of convective flow with columns of warmer and cooler water moving in opposite directions. It is not a simple diffusion process. The convective flow and therefore the evaporative cooling continue over the full 24 hour diurnal cycle. In addition, the ocean gyres form a flow system that has to be analyzed separately from the bulk ocean thermal reservoirs. The energy transfer processes at the land- air and ocean-air interfaces are illustrated schematically in Figure 6.





Figure 6: a) Surface energy transfer with the flux terms coupled to a thermal reservoir and b) the time delay or phase shift between the peak solar flux and the temperature response (schematic).



2.0 THE LAND SURFACE TEMPERATURE



The energy transfer processes at the land-air interface are shown schematically in Figure 7. Over land, the four main flux terms, the solar flux, the net LWIR cooling, the evapotranspiration and the subsurface conduction interact with a thin surface layer. Usually, almost all of the absorbed solar flux is dissipated within the same diurnal cycle. The net LWR cooling flux is determined by the LWIR surface exchange energy. During the day, the surface is heated by the absorbed solar flux. As the surface temperature increases, a thermal gradient is established with both the air above and the subsurface ground layers below. The temperature difference at the land-air interface drives the evapotranspiration. Heat is also conducted below the surface by the subsurface gradient. Later in the day, as the surface cools, the subsurface gradient reverses and the stored heat is returned to the surface. The evapotranspiration continues until the surface and surface air temperatures approach each other as the surface cools in the evening. The surface then continues to cool more slowly through the night mainly by net LWIR emission. A temperature inversion layer may form near the surface and water condensation may lead to dew formation. An important parameter is the evening convection transition temperature at which the evapotranspiration essentially stops. This is reset each day by the local weather conditions.





Figure 7: Energy transfer at the land-air interface (schematic)



The diurnal flux terms and surface and surface air temperature changes for a dry surface under full summer sun illumination are shown schematically in Figure 8. These are based on measurements recorded at the ‘Grasslands’ site located in Limestone Canyon, near Irvine in S. California [Clark, 2013]. The flux is positive if there is a heat flow into the surface. The peak surface temperature of 50 C and peak surface air temperature of 25 C are reached approximately 2 hours after solar noon. This time delay or phase shift is clear evidence of a non-equilibrium thermal response. The transition temperature is reached in the late evening and the surface then cools more slowly by net LWIR emission. The net LWIR flux decreases to 50 W m-2 at night and increases to a maximum value of 218 W m-2 during the day. This is insufficient to dissipate the absorbed solar heat, so the surface temperature adjusts until the excess heat is removed by convection. Heat is also conducted below the surface during the first part of the day after sunrise. This heat flow reverses during the afternoon and the absorbed heat is returned to the surface. In this example, approximately 60% of the absorbed solar flux is dissipated as convection.





Figure 8: Diurnal variation in a) flux terms and b) surface and air temperatures for a dry surface under full summer sun conditions. Schematic based on ‘Grasslands’ data from UC Irvine [Clark, 2013].



2.1 The Influence of Downslope Winds on the Convection Transition Temperature



The role of the convection transition temperature in setting the temperature of the diurnal cycle can be illustrated by examining the annual daily minimum and maximum MSATs recorded at the Grasslands site for 2008 [Clark 2013]. This is shown in Figure 9 along with the 8 day average maximum and minimum surface (skin) temperatures from satellite data. The minimum air and surface temperatures are similar, but the maximum surface temperature during summer is approximately 15 C higher than the measured maximum air temperature because of the cooling effects of convective mixing at the MSAT monitoring level. At this particular monitoring site, there were also well defined fluctuations in air temperature and humidity that were related to the shift from the ocean to the desert origin of the local weather system. Under ocean influences, temperatures were lower, the humidity was higher, and night and early morning clouds could develop. Under desert influences, the temperatures were higher and the humidity was lower. This site also experienced well known Santa Ana wind conditions when air that originates from the inland high desert regions is compressed and produces hot and dry conditions with very strong local winds. The transition from ocean (on shore winds) to desert (off shore winds) can be seen in the temperature ‘spikes’ in both the minimum and maximum MSATs. Some of these are indicated with the arrows. The minimum MSAT may change by 10 C or more over a period of a few days. This demonstrates the effect of the convection transition temperature. When the air temperature is warmed by the offshore flow, the air remains warmer at night and the transition temperature and surface temperature increase. More heat remains stored in the surface thermal reservoir. Figure 10 shows the transition from ocean to desert influence in more detail for days 76 to 85. The half hour MSAT temperatures (blue) and the surface temperatures estimated from the IR flux data (orange) are plotted. The transition from onshore ocean to offshore desert weather conditions occurred over 2 days from day 80 to 82.





Figure 9: Maximum and minimum daily temperatures for 2008 recorded at the ‘Grasslands’ site. The 8 day average max and min satellite surface or ‘skin’ temperatures are also shown. The arrows indicate temperature spikes produced by the transition from ocean to desert influence in the local weather conditions.





Figure 10: The transition from onshore to offshore flow conditions during days 80 to 82. The surface and MSAT temperatures increased by approximately 10 C.



2.2 The Influence of a ‘Blocking’ High Pressure System on the Transition Temperature



Figure 11a shows the total daily solar insolation (MJ m-2 day-1) and precipitation for Woomera, S. Australia for the 2 year period 2018 to 2019. Figure 11b shows the corresponding minimum and maximum weather station temperatures [BOM 2020]. Figures 11c and 11d show the December temperatures for 2018 and 2019 on an enlarged scale. The minimum temperatures are determined by the weather systems passing through and the daily temperature change from minimum to maximum is determined by a combination of solar heating and air compression effects. The decreases in solar insolation are caused by clouds. Temperatures may change by 10 C or more over a period of 5 to 10 days because of the effects of blocking high pressure systems. Almost all of the absorbed solar heat is generally dissipated within the same diurnal cycle. The night time surface temperature is similar to the minimum MSAT temperature. The dotted lines in Figures 11c and 11d show the temperature rise produced by a ‘blocking’ high pressure system. The minimum and maximum temperatures increase each day as the air is warmed and recirculated by the high pressure system. The 2019 high pressure system was also associated with a record high Indian Ocean Dipole index [BOM, IOD, 2020, IOD, 2020]. The ocean temperatures were lower near Australia and higher in the western Indian Ocean near the coast of Africa. This condition leads to drier conditions and higher temperatures over large parts of Australia. Figure 12 shows the 11 day temperature sets indicated in Figures 11c and 11d overlapped and plotted on an enlarged scale. The 2019 blocking high pressure system also remained over the area for 2 additional days compared to 2018 and this produced record high temperatures.





Figure 11: a) Solar insolation and precipitation and b) minimum and maximum temperatures for Woomera. S. Australia, 2018 and 2019, c) and d) December 2018 and 2019 temperatures on an enlarged scale.





Figure 12: Eleven day temperature data sets for the blocking high events shown in Figures 11c and 11d.



2.3 The Ocean Influence on the Convection Transition Temperature



The ‘Grasslands’ MSAT temperature data plotted in Figure 9 show a pattern of small changes in minimum temperature from one day to the next with larger variations from the onshore-offshore transition superimposed. In addition there is a seasonal phase shift of approximately 60 days from the peak solar flux at summer solstice to the peak recorded temperatures. The seasonal changes may be examined in more detail by using the 30 year daily average MSAT Tmin and Tmax 1981-2010 climate data from Santa Ana, CA, located approximately 15 km NW of the Grasslands site [WRCC, 2020]. This is shown in Figure 13. Tmin varies from 8 to 18 C and Tmax varies from 20 to 30 C. The lines labeled sigma+ and sigma- show the 1 sigma standard deviations. The average deviations were 3.6 and 2.2 C for the max and min temperatures. The delta T difference temperature (Tmax – Tmin) is also shown. The delta T remains in a narrower temperature range from 10 to 13 C. This site also shows a seasonal phase shift of approximately 60 days. The phase shift comes from the ocean surface temperatures that are coupled to the prevailing weather systems. These originate in the Gulf of Alaska and move down the west coast of N. America. Figure 14 shows the 2.5 m depth ocean temperatures for 2017 derived from Argo float data [Argo 2020]. The data are for rectangular areas centered at 35° and 45° N, 127.5° W. The angular block size is 2° latitude and 5° longitude. The Argo data consists of monthly averages. These were fit to 5th order polynomials that were used to generate the daily trends. In addition, the 30 year average MSAT minimum data for Santa Ana from Figure 13 and the MSAT minimum data for the Grasslands site from Figure 9 are shown. The seasonal phase shift and the temperature range are consistent with ocean temperatures near 45° N.





Figure 13: Daily 1981-2010 30 year climate average Tmax and Tmin MSAT data for Santa Ana, CA. The one sigma standard deviations and the delta T (Tmax-Tmin) are also shown. The seasonal phase shift is also indicated.





Figure 14: Comparison of Argo 2.5 m ocean surface temperatures at 35° and 45° N with the 30 year 1981-2010 daily minimum MSAT from Santa Ana and the Grasslands 2008 minimum MSAT data.



The changes in maximum and minimum MSAT from one day to the next (TDn = Tn - Tn-1) derived from Figure 13 are shown in Figure 15. The Santa Ana data were fit to 6th order polynomials to indicate the trends. Almost all of the absorbed solar flux is dissipated within the same diurnal cycle that it is received, unless there are significant weather related changes in the transition temperature. This means that the changes in TDn are quite small, up to 0.18 C, even though the annual temperature range is 10 C. The seasonal phase shift of approximately 2 months can also be seen as the zero crossing point near day 240. The TDn data derived from the 45° N Argo float data shown in Figure 15 are also plotted.


The maximum and minimum MSAT are produced by different energy transfer processes. The minimum MSAT is generally a measure of the surface air temperature of the air mass of the local weather system. The maximum MSAT is a measure of the warm air from the solar heated surface that is mixed with the cooler air above at the level of the MSAT thermometer. An analysis of the surface energy transfer requires consideration of the minimum MSAT and the delta T or heating produced by the solar heating of the surface. The phase shift should also be addressed. Any averaging requires careful consideration of Nyquist sampling theory applied to two pseudorandom temperature signals. The average MSAT (Min+Max)/2 has little useful meaning.





Figure 15: Changes in Tmax and Tmin from one day to the next (TDn = Tn-Tn-1) from the data for Santa Ana shown in Figure 13. 6th order polynomial fits to the data are also shown to indicate the trends. The maximum temperature change from one day to the next is 0.18 C. The data derived from the 45° N Argo float data given in Figure 14 are also shown.



2.3 The Effect of an Increase in CO2 Concentration on Land Surface Temperatures



As discussed above in Section 3.2, the land surface temperature is reset each day by the convection transition temperature. The surface and surface air temperatures continue to cool through the night by net LWIR emission from the surface. The temperatures then rise and fall during the day in response to the solar insolation. The effect of an increase in CO2 concentration on the diurnal temperature cycle was investigated by using the annual minimum air temperatures from the Grasslands 2008 data set as transition temperatures in a simple thermal model of the diurnal cycle. The various flux terms were coupled into a surface layer 1 cm thick. The surface layer was coupled to a subsurface thermal conduction model with 200 x 1 cm layers constructed following the finite element method described by Billo [2007]. The thermal properties of dry sand were used for all layers. The model is described in more detail in Appendix A. The LWIR window transmission, the convection coefficient and the rate of air heating were adjusted until the model output was similar to the Grasslands temperature data. The initial LWIR window flux was 46 W m-2. The model was re-run with the LWIR window flux decreased by 2, 3.7, 5, 10 and 20 W m-2. This represents an increase in CO2 concentration from 280 to approximately 400, 560, 760, 1500 and 8500 ppm [Hansen et al, 2005]. The model was run for full sun 'clear sky' conditions and latent heat effects were not included. The daily maximum and minimum surface and surface air temperatures were extracted from the model and the annual averages were calculated. The measured and calculated temperatures using 46 W m-2 for the LWIR flux term are shown in Figure 16 and the average annual temperature changes are shown in Figure 17.


The calculated average temperatures are shown in Figure 17a. The changes in temperature as the downward LWIR flux is increased are shown in Figure 17b. In the model, these are decreases in LWIR window flux from 46 W m-2. The changes in temperature vs. CO2 concentration are shown in Figure 17c and the same data plotted with a logarithmic concentration scale are shown in Figure 17d. The maximum observed increase is in the minimum surface temperature. However, for a conventional CO2 ‘doubling’ to 560 ppm, this increase is only 0.3 C. Even at a CO2 concentration of approximately 8500 ppm, the increase in surface temperature is only 1.3 C. The increases in surface air temperature are less, with a maximum increase near 0.4 C. This demonstrates that the radiative forcing temperature estimates used in the Paris accord have no basis in physical reality.





Figure 16: Calculated Grassland temperatures compared to measured data from Figure 9.





Figure 17: Calculated changes in 2008 Grassland annual average temperatures a) temperature vs increase in downward LWIR flux, b) increases in temperature from a) with 280 ppm baseline subtracted, c) data from b) plotted vs. increase in CO2 concentration and d) data from c) plotted with concentration on a logarithmic scale.



The Grasslands surface temperature model was then used to investigate the effects of changes in CO2 concentration on the Woomera temperature data shown in Figure 11. The minimum MSAT data was used as input for the transition temperature. The temperature range from June 22 to June 21 the following year was used to match the N. Hemisphere solar flux calculated by the model. The air heating coefficient was adjusted to provide an approximate match to the measured maximum MSAT data. The model was run to simulate both the 2018-19 and 2019-20 Woomera data. The measured and calculated temperatures are shown in Figure 18 and the changes in temperature as the CO2 concentration was increase are shown in Figure 19. The data for both years are shown on the same plot. The results are similar to the Grasslands data shown in Figure 17b. For an increase in downward LWIR flux of 20 W m-2, the maximum average annual average temperature increase was less than 1.4 C for the minimum surface temperature. The maximum increase in air temperatures was less than 0.6 C. Again, these results contradict the pseudoscientific equilibrium climate temperature limits proposed by the Paris Climate Accord.





Figure 18: Calculated and measured temperatures for Woomera, a) 2018-19 and b) 2019-20. Data are shown from June 22 to June 21 so that the peak solar flux occurs on day 172.





Figure 19: Calculated increases in annual average Woomera temperatures for increases in downward LWIR flux to the surface of 2, 3.7, 5, 10 and 20 W m-2. The corresponding CO2 concentrations are shown on the plot. Data for both 2018-19 and 2019-20 are shown.



3.0 THE OCEAN SURFACE TEMPERATURE



The energy transfer processes at the ocean-air interface are shown schematically in Figure 20. The surface is cooled by a combination of wind driven evaporation, net LWIR emission and convection (sensible heat flux). Usually, the dominant cooling term is the wind driven surface evaporation or latent heat flux. This is determined by the humidity gradient and the wind speed. There is no equilibrium. 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. This is illustrated in Figure 21 [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.





Figure 20: The energy transfer processes at the ocean-air interface (schematic).





Figure 21: Penetration depth (micron) of LWIR radiation into the ocean surface for 99% attenuation, a) 50 to 3300 cm-1 and b) 1200 to 200 cm-1. The approximate locations of the CO2 P and R branches and the overtone bands are indicated [Hale and Querry, 1973].



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.



3.1. The Effect of an Increase in CO2 Concentration on Ocean Surface Temperatures



In order to evaluate the effect of an increase in atmospheric CO2 concentration on ocean temperatures, it is necessary to consider the change the residual amount of heat stored in the thermal reservoir after an annual ocean solar thermal cycle. 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 wind speed have to be evaluated to determine if the CO2 induced changes are even measurable. In addition, the ocean gyres form a flow system that has to be analyzed separately from the bulk ocean thermal reservoirs.





When the atmospheric CO2 concentration is increased, the increase in downward LWIR flux is coupled initially into the first 100 micron layer of the ocean surface. There is a small increase in surface temperature that increases both the net LWIR flux and the latent heat flux. If there are no other changes in the heat transfer, the total increase in cooling flux Qcool should match the increase in the downward LWIR flux. This can be estimated from Eqn. 2. As the ocean surface temperature (SST) increases, the latent heat flux Qlat increases faster than the increase in blackbody radiation and the required change in temperature decreases. Representative changes in temperature and the related changes in blackbody radiation and latent heat flux are shown in Figure 22 for increases in downward CO2 flux to the ocean of 2, 4 and 8 W m-2. These correspond approximately to the observed increase of 120 ppm, a doubling and a quadrupling of the atmospheric CO2 concentration. Here, the air temperature was set 1 C below the surface temperature, the RH was 75%, the wind speed was 6 m s-1 and the coupling coefficient was 2.2. From Figure 22a, the increases in ocean temperature at 15 C SST are 0.23, 0.46 and 0.92 C for flux increases of 2, 4 and 8 W m-2. This is an ideal case in which only the temperature and the temperature dependent vapor pressure terms are changed in Eqn. 2. However, this illustrates the combined role of the net LWIR flux and the latent heat flux in changing the surface temperature. For reference, the increase in temperature for a blackbody surface without any evaporation are shown as the dotted lines in Figure 22a. At 15 C, the latent heat flux reduces the blackbody heating effect by approximately 40%.





Figure 22: a) Increase in ocean surface temperature required to counteract an increase in downward LWIR flux from CO2 of 2, 4 and 8 W m-2. The solid lines show the change in temperature estimated from Eqn. 2. The dashed lines show the temperature increase for a blackbody surface without any evaporation. b) The changes in blackbody emission and latent heat flux produced by the temperature increases from Eqn. 2 shown in a). The air temperature was set 1 C below the surface temperature, the RH was 75%, the wind speed was 6 m s-1 and the coupling coefficient was 2.2.



Figure 23 shows the monthly changes in ocean temperature at 30° N, 20° W in the N. Atlantic Ocean down to depths of 200 m derived from Argo float data for 2018 [Argo, 2020]. Minimum temperatures are reached in February and the ocean layers are uniformly mixed down to 100 m at a temperature of 19 C. The ocean temperatures then start to increase from the surface down and a stratified layer structure develops with a peak surface temperature of 24 C in August. The surface temperature mixing layer is now limited to the first 20 to 30 m. The seasonal phase shift in the surface temperature, delta t is approximately 8 weeks. The ocean then cools from the surface until a uniform mixing layer to 100 m is again established. The ocean warms up when the solar heating exceeds the wind driven evaporative cooling. When the ocean cools down, the reverse occurs and the wind driven evaporative cooling exceeds the solar heating. There is no requirement for an exact annual flux balance between the heating and cooling.


The effect of an increase of 120 ppm in atmospheric CO2 concentration on the thermal cycle shown in Figure 23 may be investigated by considering two hypothetical cases. First, the only change in Eqn. 2 is the surface temperature so that both the water vapor pressure and net LWIR emission increase. Second, the wind speed is increased in Eqn. 2 to remove the heating effect of the additional LWIR flux by evaporation alone and restore the initial temperature. From Figure 1b, the increase in LWIR flux is 2 W m-2. For case 1, the calculated monthly changes in cumulative LWIR flux, and LWIR emission (MJ m-2) are shown in Figure 24a and the cumulative increase temperature for the flux coupled to a 100 m column of water is shown in Figure 24b (blue line). For reference, the hypothetical temperature increase produced by a 2 W m-2 flux coupled directly into a 100 m column of water over a period of 1 year is approximately 0.15 C. When the latent heat effects are included, the temperature rise from the LWIR flux is reduced to 0.09 C. The additional water vapor produced by the increase in ocean surface temperature is removed by coupling to the wind flow. It does not add to the local radiation field and provide the feedback or amplification predicted for an equilibrium average climate [IPCC, 2013]. For case 2, the required increase in wind speed is shown in the upper plot (orange line) in Figure 24b. Here, the maximum required increase in wind speed is approximately 19 cm s-1 at 19 C. This decreases to 14 cm s-1 at 24 C. These values are consistent with the long term zonal averages shown below in Figure 25.





Figure 23: Changes in ocean temperatures. 2.5 to 200 m depth at 30 W 20 N in the N. Atlantic Ocean from Argo float data.





Figure 24: a) Changes in the monthly latent heat and blackbody flux for an increase in downward LWIR flux of 2 W m-2 applied to the monthly surface temperatures in Figure 23, b) cumulative temperature change in a 100 m column of water and increase in wind speed needed to restore the initial surface temperature.



Within the ±30° latitude bands that include approximately half of the earth’s ocean surface area, the average rate of evaporation per unit wind speed is at least 15 W m-2/cm s-1. This is shown in Figure 25 using long term (1958-2006) zonal average data from Yu et al [2008]. The entire increase of 2 W m-2 in LWIR flux from the 120 ppm increase in atmospheric CO2 concentration is dissipated by an increase in wind speed of approximately 13 cm s-1. A typical range for the wind speed is 0 to 13 m s-1 (0 to 30 mph) with higher short term wind gusts, not including local storms. This means that the magnitude and variation in the wind driven evaporation are so large that it is impossible for small changes in the LWIR flux from CO2 to penetrate below the surface and warm the bulk ocean underneath.





Figure 25: The change in ocean latent heat flux per unit wind speed based on zonal averages from Yu et al [2008].



3.2 Ocean Heating Within the Equatorial Gyre Circulation



Air and liquid water are fluids that can transport heat long distances both vertically by convection and horizontally through wind driven transport by advection and ocean currents. The energy transfer processes within the equatorial gyre circulation are different from those in the bulk ocean at higher latitudes so the two regions have to be considered separately. This is illustrated in Figure 26 for the equatorial Pacific Ocean. As the equatorial gyre currents transport the ocean water from east to west, the wind driven evaporation is insufficient to remove all of the absorbed solar flux and heat accumulates below the ocean surface leading to the formation of the equatorial warm pools. If the wind speed decreases, the gyre flow velocity decreases, the transit time across the ocean increases and the latent heat flux decreases. This increases the rate of heating and the size of the warm pool. The upper limit to the warm pool surface temperature is near 30 C with an average wind speed near 5 m s-1. If the surface temperature continues to increase at low wind speeds, strong local thunderstorms form that produce local cooling [Eschenbach, 2010]. If the wind speed increases, the flow velocity increases, the latent heat flux increases, the ocean gyre surface temperatures decrease and the warm pool size is reduced. This variation in wind speed leads to the characteristic El Nino Southern Oscillation (ENSO) in the equatorial Pacific Ocean. Figure 26a shows the annual ENSO index (temperature anomaly or deviation from the mean) and the Southern Oscillation Index (SOI) from 1880. The SOI is the atmospheric surface pressure difference between Tahiti and Darwin, Australia. It is a measure of the wind speed. There is an inverse relationship between the SOI and the ENSO. For clarity, the sign of the SOI is inverted in the plot [ENSO, 2019 SOI, 2018]. This clearly demonstrates the wind driven nature of the ENSO. Figure 26b shows the seasonal variation an Argo float drifting in the S. Pacific Ocean at latitudes and longitudes near 1.5° S and 126° W in the S. Pacific equatorial current. The diurnal mixing layer is shallow and only extends down to the 50 m level about half of the time. The solar heat accumulates at lower depths. The Argo floats are not tethered and the decrease in near-surface temperature with time is caused by an eastward drift.





Figure 26: Ocean gyre circulation (schematic). a) The variation in the ENSO and SOI indices from 1880, b) Argo data at approximately 1.5° S, 126° W in the S. Pacific equatorial gyre circulation.



The 20 year (2000 to 2019) average of daily solar, latent heat, net IR, sensible heat and net heat flux terms derived from TRITON buoy data are shown in Figure 27 for 10 buoys moored along the equator in the S. Pacific Equatorial current [TRITON, 2020]. The averages are based on available data and large blocks of data may be missing because of sensor failure. The buoy sensor configuration may also change with time. The total heat flux coupled into the ocean decreases from approximately 150 W m-2 in the E. equatorial Pacific Ocean to 50 W m-2 in the western warm pool. These changes are produced by an increase the latent heat flux and a decrease in the solar flux. Individual plots of eight flux and related terms are shown in Figure 28. The thin lines are the ±1 sigma standard deviations. The SST increases from approximately 24±2 C in the eastern equatorial current to 30±0.4 C in the Pacific warm pool. The temperature variations in the eastern part of the S. Equatorial Pacific current are produced by the seasonal variations in the Humboldt Current that flows northwards along the west coast of S. America. This turns west near the Galapagos Islands and becomes the S. Pacific equatorial current. The changes in monthly average SST are shown in Figure 29. The temperature variations in the central equatorial Pacific Ocean are part of the ENSO shown in Figure 26a above. The latent heat flux increases from approximately 40±40 W m-2 at longitude 100° W to 100±40 W m-2 in the western warm pool. Similarly, the net LWIR flux increases from approximately 40±14 W m-2 to 50±10 W m-2 and the sensible heat flux generally stays below 10 W m-2. The average wind speed increases from approximately 5±2 m s-1 near 100° W to 6±2 m s-1 in the central equatorial region and then decreases to 4±2 m s-1 in the western warm pool. An increase of 0.034 W m-2 per year in the LWIR flux related to an increase in the atmospheric CO2 concentration near 2.4 ppm per year can have no effect on the SST.





Figure 27: 20 year (2000 to 2019) average flux terms for the TRITON buoys moored along the equator in the S. Pacific equatorial gyre current.





Figure 28: 20 year (2000 to 2019) average flux terms and related data for the TRITON buoys moored along the equator plotted with one sigma error margins.





Figure 29: Monthly SSTs (1.5 m depth) recorded by the TRITON buoy network along the equator from 2000 to 2019.



3.3 The Ocean Diurnal Phase Shift



In addition to the seasonal phase sift, there is also a diurnal phase shift between the solar flux and the ocean surface temperature rise that depends on both the solar flux and the wind speed. Figure 30 shows the effect of wind speed on the diurnal temperature rise recorded at the TRITON buoy located on the equator at a longitude of 165° E in the Pacific warm pool. These data were recorded during July 2010 [TRITON, 2020]. The maximum daily solar flux was near 3 MJ m-2 hr-1 (850 W m-2). During this 4 day period, the wind speed increased from 1 to 8 m s-1. The diurnal change in 1.5 m sea surface temperature (SST) was near 1 C for day 10 and decreased to 0.3 C for day 13. The time delay or phase shift between the peak solar flux and the peak 1.5 m SST was near 5 hours for day 10 and decreased to approximately 3 hours for day 13 as the wind speed increased. The estimated energy balances for the ocean conditions shown in Figures 30 are given in Figure 31. As the wind speed increased, the magnitude of the latent heat flux increased from approximately 36 to 136 W m-2. The amount of heat coupled into the ocean decreased by a similar amount. The cooler water produced at the surface sinks and cools the bulk ocean layers below. It is replaced by upwelling warm water. This is a Rayleigh-Benard type of convection with columns of water moving in opposite directions. It is not a simple diffusion process. This convection cycle continues to provide heat to the surface at night, so the wind driven evaporation continues at night. As the cooler water sinks, it transports the surface momentum or velocity to lower depths. This drives the ocean gyre circulation.


At the present time, the atmospheric CO2 concentration is increasing by approximately 2.4 ppm per year. The corresponding increase in the downward LWIR flux to the surface is 0.034 W m-2. Such a small change in the downward LWIR flux to the ocean surface can have no measurable effect whatsoever on ocean surface temperatures. As shown in Figures 30 and 31, short term variations in wind speed produce changes in the latent heat flux of 100 W m-2 over a few days.





Figure 30: 1.5 m ocean temperature, wind speed and solar flux for 4 days, July 2010 recorded at the TRITON buoy on the equator at 165 E in the Pacific warm pool. The diurnal temperature rise and the magnitude of the phase shift decrease with increasing wind speed.





Figure 31: Estimated daily average flux balance terms from Figure 30.



4.0 CLIMATE SENSITIVITY AND THE AMO



The equilibrium climate sensitivity (ECS) for the more recent climate models has been determined using the method described by Gregory et al [2004]. The CO2 concentration in the model is quadrupled and the increase in surface temperature is plotted against the decrease in radiative forcing at TOA. This produces a straight line from which the ECS may be estimated. Such a response has been programmed into the models. The ECS for CMIP5 and CMIP6 models is shown above in Figure 3. The determination of the ECS and TCR from the climate record is described by Otto et al [2013]. They define ECS and TCS as:





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 are shown in Figures 32a and 32b. The HadCRUT4 temperature anomaly series is plotted in Figure 32a. The AMO cycle minimum near 1910 and the maximum near 1940 are indicated. Since 1975, the AMO has continued its positive warming phase and has now reached its maximum. The penetration depth of the LWIR flux into the oceans is less than 100 micron. Here it is fully coupled to the much larger and more variable wind driven surface evaporation or latent heat flux. This means that the increase in the downward LWIR flux related to the ‘radiative forcing’ shown in Figure 32b cannot couple below the ocean surface and cause any measurable change in ocean temperature.

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 32c. 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 ‘homogenization’ adjustments made to the HadCRUT4 data set. Using tree ring analysis, the AMO has been reconstructed back to 1567 [Gray et al, 2004 Gray.NOAA, 2021]. This is shown in Figure 32d. None of the observed temperature changes associated with the AMO can be attributed to an increase in atmospheric CO2 concentration.





Figure 32: 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.



The HadCRUT4 climate record is not simply the long term average of the weather station record. The raw data have been adjusted or ‘homogenized’ to correct for various ‘biases’ and include the effects of urban heat islands and station changes [Andrews, 2017a, 2017b, 2017c, D’Aleo, 2010]. There is also an underlying linear trend in the HadCRUT4 record. This is the temperature recovery from the Maunder minimum or Little Ice Age (LIA) [Akasofu, 2010]. During the LIA, very few sunspots were observed. Solar activity as measured by sunspots and other parameters then increased as the sun passed through the modern solar maximum. The warming trend observed in the HadCRUT4 climate record may be expected to change now that the modern sunspot cycle maximum has ended and the AMO should transition to its negative or cooling phase.



5.0 THE ATTRIBUTION OF ‘EXTREME WEATHER EVENTS’



The mathematical warming artifacts created by the equilibrium climate models have been used to create the illusion that an increase in atmospheric CO2 concentration will create more ‘extreme weather events’. A good example of this is the work of King et al [2017] related to Australian weather conditions. They identified four different forms of ‘extreme weather’: 1) The drought in SE Australia in 2006, 2) Heavy rainfall in NE Australia in December 2010 3) Heatwaves during the so called ‘angry summer’, 2012-2013 and 4) Coral bleaching caused by high temperatures in the Coral Sea in 2016. All of these events are the result of normal variations in weather patterns related mainly to changes in ocean surface temperatures. During drought conditions, soil moisture content decreases and surface temperatures naturally increase because of reduced evaporation. Figure 33 shows the changes in the ENSO and IOD (Indian Ocean Dipole) from 2004 with the ‘extreme weather events’ indicated [IOD, 2020]. The 2019 drought is also included. They are associated with variations in the ocean indices that are coupled into the Australian weather systems. This is an example of the fraudulent claims of CO2 induced warming that have been used to justify the 2 (or 1.5) C temperature limit created by the Paris Climate Accord. The changes in wind speed associated with the 2015/2016 El Nino event will now be considered in more detail.





Figure 33: ENSO and IOD indices from 2005 to 2019. The ‘extreme weather events’ considered by King et al [2017] are indicated. The 2019 drought is also included.



5.1 The 2015/2016 El Nino Event



The influence of changing wind speed on the 2015/2016 El Nino event in the equatorial Pacific Ocean is illustrated in Figure 34. The average monthly wind speeds from 2014 through 2017 as recorded by the TRITON buoys at 155° W, 0°, 2°, 5° and 8° S located in the S. Pacific equatorial current are shown in Figure 34a. There was a decrease in wind speed of approximately 2 m s-1 towards the end of 2015 and in early 2016. The average wind speed over the four years was 5.6 m s-1. The ocean temperatures at 1, 25, 50 75 and 100 m recorded by the buoy at 115° W, 5° S are shown in Figure 34b. The 1 m and 25 m temperatures decreased by 2.5 C as the wind speed recovered after the start of 2016. During this 6 month interval, the CO2 concentration increased by approximately 1.2 ppm and the related downward LWIR flux increased by 0.017 W m-2. The change in enthalpy for a 2.5 C change temperature in a 1 x 1 x 25 m column of water is 105 MJ m-2. The cumulative increase in downward LWIR flux from CO2 over 6 months was 0.26 MJ m-2. This is approximately 400 times less than the change in enthalpy to 25 m depth.





Figure 34: a) Average monthly wind speeds recorded by the TRITON buoys at 155° W, 0°, 2°, 5° and 8° S from 2014 through 2017 and b) Monthly average temperatures recorded by the buoy at 155° W, 5° S for depths to 100 m over the same time period.



The stored ocean heat from an El Nino event is dissipated by evaporation which warms the troposphere as the water vapor condenses during cloud formation. This may be seen in the lower tropospheric air temperatures from satellite measurements reported by the group at the University of Huntsville, Alabama. This is shown in Figure 35. The lower troposphere temperature reported by UAH is plotted with the ENSO data over the same period of record, scaled to match the UAH data [UAH 2019]. The lower troposphere temperature tracks the ENSO with a delay of a few months. The increase in the extent of the Pacific warm pool during an El Nino event significantly increases the amount of water vapor released into the troposphere and this in turn heats the troposphere by condensation. The El Nino peaks of 1998 and 2016 are indicated. The temperature delay of a few months clearly shows the wind/ENSO driven nature of the temperature changes. The increase in evaporation is produced by an increase in the size of the warm pool, not by an increase in warm pool temperature above 30 C.





Figure 35: ENSO (scaled/4) and the UAH global lower troposphere satellite temperature record from 1980.



5.2 The Annual Attribution Ritual



The use of the equilibrium climate models to ‘explain’ presumed ‘extreme weather events’ has now degenerated into an annual ritual. Since 2012, the Bulletin of the American Meteorological Society (BAMS) has published an annual supplement on ‘Explaining Extreme Events of [Year] From a Climate Perspective’. [Herring et al, 2020 2019 2018 2017 2016 2015 2015 Peterson et al, 2013 2012]. Unfortunately, these supplements have implied that there is an underlying climate warming produced by CO2 that is somehow contributing to at least some of these events. This again is nothing more than an artifact of the use of fraudulent radiative forcing techniques in the equilibrium climate models such as the CMIP5/6 ensembles and the HadGEM model series [Andrews et al, 2019, 2012]. As discussed above, the current increase in downward LWIR flux to the surface from the observed increase in atmospheric CO2 concentration is approximately 0.034 W m-2 per year. When a proper thermal engineering analysis of the surface temperature is performed using a dynamic flux balance coupled to the surface reservoirs, there can be no warming effect from CO2. Instead, the natural warming from the AMO has been incorrectly attributed to ‘CO2 forcing’.



APPENDIX A: THE LAND SURFACE TEMPERATURE MODEL



The model used to calculate the land surface temperature is illustrated schematically in Figure A1. It is a simple representation that is intended to capture the basic physics of the surface energy transfer and illustrate the changes in surface temperature produced by increases in the downward LWIR flux from an increase in atmospheric CO2 concentration. The various flux terms were coupled into a surface layer 1 cm thick. The thermal properties of dry sand were used as shown in Table A1. The surface layer was also coupled into a subsurface thermal conduction model constructed following the finite element method described by Billo [2007]. 200 layers 1 cm thick were used in the model and the lowest layer was set to remain at a temperature of 10 C. The numerical values used are given in Table A1. The model time step was 1 minute. The calculation was run for a 1 year simulation (365x24x60 steps). The computer run time was approximately 30 seconds. The data were output at 2 hour intervals. In addition, the full 1 minute step data sets were output for the solstice and equinox points for days 81, 172, 264 and 355. Initial model evaluation showed that the heat capacity of the land subsurface reservoir was not large enough to simulate the observed diurnal and seasonal phase shifts. Additional air heating and cooling terms were added to provide the diurnal phase shift. An offset (time delay) was incorporated into the transition temperature algorithm to simulate the seasonal phase shift.





Figure A1: Land surface temperature model structure (schematic).





Table A1 Numerical Values Used in the Thermal Conduction Model.



The incident solar flux was calculated using the ‘clean air’ solar algorithm from IEEE Standard 738 [IEEE, 1993]. An adjustable solar fraction was incorporated that reduced the solar flux to simulate cloud attenuation effects.





An empirical minimum offset temperature (Toffset) is also set in the model. These were adjusted to provide an approximate match to the daily minimum MSAT profile for the weather station data of interest. For the ‘Grasslands’ analysis, this calculated transition temperature was replaced by the daily measured minimum MSAT. The air temperature Ta was initially calculated using:


Ta = Ttransition + ftr*(Tsurf – Ttransition) (Eqn. A2)


Where ftr is a fraction empirically set in the model. This was set to 0.5.


In order to simulate the diurnal phase shift, the air temperature algorithm was modified to include a heating and a cooling term. The heating term was set as a fraction of the surface convection and the cooling term was set as a fraction of the difference between the air temperature and the transition temperature. The values used were 1/4000 for the heating and 1/40 for the cooling. The air temperature was reset at the start of each day using Eqn. A2. It was then calculated using:


Ta = Ta + Tconv/4000 – (Ta – Ttrans)/40 (Eqn. A3)


This approach gave reasonable values for the air temperature and the diurnal phase shift.





ACKNOWLEDGEMENT



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



REFERENCES



Normally, the references given in an article of this nature would be 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, Natural Science 2(11) 1211-1224 (2010), ‘On the recovery from the Little Ice Age’

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