The 'Greenhouse Effect' On A Rotating Water Planet



Ventura Photonics Climate Post 001.1 Sept. 7 2021



Roy Clark





SUMMARY



The basic concept underlying the so called ‘greenhouse effect’ is that the earth’s surface is warmer than it would be without the presence of IR absorbing and emitting gases in the atmosphere. Unfortunately, the energy transfer processes involved have been oversimplified by assuming an equilibrium average climate. Physical reality has been abandoned in favor of mathematical simplicity. The downward long wave IR (LWIR) flux from the lower troposphere to the surface produces a time dependent exchange energy that ‘blocks’ a large fraction of the upward LWIR flux emitted by the surface. Photons are exchanged without a net transfer of heat. In order to dissipate the heat generated by the absorbed solar flux, the surface must warm up until the excess heat is removed by moist convection (evapotranspiration). This is a non-equilibrium process in which heat is stored in the surface thermal reservoir and then released as the rates of heating and cooling change during the diurnal and seasonal cycles.


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.


The surface temperature is determined by the interaction of four main flux terms with the surface thermal reservoir. These are the absorbed solar flux, the net LWIR emission, the moist convection (evapotranspiration) and the subsurface transport. The four terms are coupled together and should not be separated and analyzed independently of each other. There are significant diurnal and seasonal time delays or phase shifts between the peak solar flux and the surface temperature response. These are clear evidence of non-equilibrium thermal transfer. This is not a new discovery. Such phase shifts for the subsurface land temperatures were described by Fourier in 1824. At mid latitudes the seasonal phase shift can be 4 to 8 weeks or more. These have been measured as part of the weather station record for over 100 years.


The energy transfer processes at the land-air and ocean-air interfaces are different and have to be considered separately. Over land, the solar flux is absorbed by a thin surface layer. The heating is localized and almost all of the stored heat is dissipated within the same diurnal cycle by a combination of net LWIR emission and moist convection as the surface warms and cools during the day. In the evening, 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 surface is almost transparent to the incident solar flux. Approximately 90% of the solar flux is absorbed within the first 10 m ocean layer. In order to dissipate the absorbed heat, the bulk ocean temperature increases until the excess heat is removed by wind driven evaporation. 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. Any small increase in downward LWIR flux to the surface produced by an increases in atmospheric CO2 concentration cannot couple below the ocean surface and produce a measurable change in ocean surface temperature. In addition, part of the absorbed solar heat may be transported over long distances by the wind driven ocean gyre currents.


The fundamental error that has led to a basic misunderstanding of the greenhouse effect is the assumption of an equilibrium average climate. Climate stability only requires that there is an approximate long term planetary energy balance between the absorbed solar flux and the LWIR flux returned to space. This simply has to maintain the surface temperature within the relatively narrow bounds needed to sustain life. There is no requirement for an exact short term flux balance and there is no equilibrium. The rate of heating does not equal the rate of cooling. The earth’s planetary energy balance for a rotating sphere illuminated by a collimated disk of short wave radiation from the sun requires that the long term average of the long wave IR (LWIR) flux returned to space at the top of the atmosphere (TOA) should be near 240 W m-2. However, satellite radiometer measurements show that the short term variation is approximately ±100 W m-2. Furthermore, the spectral distribution of the LWIR flux emitted by the earth at TOA is not that of a blackbody. There is no ‘shell’ of gas surrounding the earth with a temperature near 255 K. The use of the planetary average LWIR intensity to determine an ‘effective emission temperature’ from Stefan’s Law is invalid. The 33 K ‘greenhouse effect temperature’ is a just a mathematical construct. The LWIR flux at TOA is simply the cumulative cooling flux produced by the emission from many different levels of the atmosphere at different temperatures. The upward emission from each level is modified by the LWIR absorption and emission of the layers above.


The atmospheric LWIR flux is produced by the 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. 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. 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 LWIR flux from the stratosphere and the upper troposphere cannot couple to the surface and influence the surface temperature.



1.0 INTRODUCTION



The energy transfer processes involved in the ‘greenhouse effect’ have been oversimplified and averaged to create a ‘greenhouse effect temperature’ of 33 K [Poyet, 2020, Gerlich and Tscheuschner, 2009, Taylor, 2006]. This is illustrated in Figure 1. The earth is an isolated planet that is heated by the absorption of electromagnetic radiation from the sun and cools by the emission of long wave IR (LWIR) radiation back to space. The average solar flux at TOA is near 1368 W m-2. The exact value depends on satellite calibration [Wilson, 2014]. Since the earth’s orbit is slightly elliptical, the solar flux varies by ±45 W m-2 over the year, with the peak flux at perihelion in early January. The illumination geometry is that of a collimated disk of light illuminating a rotating sphere. The area of the emitting surface is four times that of the illuminating disk. The albedo or reflectivity of the earth is near 0.3. Conservation of energy (1368 x 0.7/4) gives a planetary average LWIR flux of approximately 240 W m-2. Stefan’s law is then used to derive an ‘effective emission temperature’ of 255 K for the outgoing longwave radiation returned to space. This is subtracted from an ‘average surface temperature’ of 288 K. The 33 K result is a mathematical construct that has no physical meaning. It is based on a fundamental misunderstanding of the underlying energy transfer processes.





Figure 1: The derivation of the ‘greenhouse effect temperature’ of 33 K (schematic)



Simple inspection of IR satellite images of the earth, such as the CERES image shown in Figure 2 indicates that the short term variation in the LWIR flux is approximately ±100 W m-2 [CERES, 2011]. Climate stability and conservation of energy considerations mean that there should be a long term average planetary flux near 240 W m-2. However, there is no justification for an exact short term flux balance. The various heating and cooling rates within the climate system interact to keep the surface temperature within the relatively narrow range needed to sustain the development of life on earth. These rates are always changing on diurnal, seasonal and longer time scales. There is no equilibrium (See Section 5.0 below). Furthermore, the spectral distribution of the LWIR flux emitted by the earth at the top of the atmosphere is not that of a blackbody. There is no ‘shell’ of gas surrounding the earth with a temperature near 255 K. The outgoing LWIR radiation (OLR) at TOA is simply the cumulative cooling flux produced by the emission from many different levels of the atmosphere at different temperatures. The upward emission from each level is modified by the LWIR absorption and emission of the layers above. The OLR under ‘clear sky’ conditions is illustrated in Figure 3. The LWIR flux consists of a mix of atmospheric emission, mainly from the H2O and CO2 bands and surface emission through the LWIR transmission window. Some of the surface emission is absorbed by stratospheric ozone. The main spectral features are labelled. Blackbody emission curves at selected temperatures are also shown. The 255 K blackbody emission curve is shown as the black dotted line. It has no relationship to the TOA flux shown by the orange line.





Figure 2: CERES IR image of the earth, March 8, 2011





Figure 3: The LWIR flux emitted at TOA. The blackbody emission curves at selected temperatures are also shown. This TOA flux cannot be described as LWIR emission near 255 K. MODTRAN calculation, 288 K surface temperature, 80% RH, 400 ppm CO2, 100 to 1500 cm-1 spectral range, 2 cm-1 spectral resolution, mid latitude summer [MODTRAN, 2020].



The OLR at ‘clear sky’ increases linearly with surface temperature as shown in Figure 4 [Koll and Cronin, 2018]. There are two contributions to the OLR flux shown in Figure 3 with different responses to the surface temperature. Within the LWIR transmission window in the 800 to 1200 cm-1 region, the surface emission is only partially absorbed and some is emitted to space. Here, the clear sky OLR increases linearly with surface temperature. Within the main H2O and CO2 absorption bands, the OLR emission does not change significantly with surface temperature. The water band emission profile shifts to higher altitude as the surface temperature increases. More heat is stored as gravitational potential energy. The absorption and emission process continues with increasing altitude until the molecular linewidths narrow sufficiently to allow the transition to a free photon flux to space. For H2O, this transition occurs near a temperature of 253 K (-20 C). For CO2 the free photon transition occurs at a lower temperature near 220 K. Most of the CO2 band emission occurs in the stratosphere.





Figure 4: The increase in clear sky OLR flux with surface temperature



While an increase in surface temperature produces an increase in OLR flux, the converse is not true. A change in OLR within the atmospheric emission bands is decoupled from the surface by molecular linewidth effects. This is considered in more detail in Section 4.0. The concept of radiative forcing in an equilibrium climate is invalid [Ramaswamy et al, 2019]. This is discussed in more detail in the ‘Forcing’ post.


The OLR emission to space is not part of any ‘greenhouse effect’. Instead, the OLR flux defines an overall cooling rate. This consists of the emission from many levels of the atmosphere, each attenuated by the absorption of the intervening atmosphere above. In order to understand the cooling of the troposphere it is necessary to convert the local LWIR cooling flux to a temperature cooling rate by dividing by the local heat capacity of the air parcel. The spectral band cooling rates vs altitude for a tropical atmosphere are shown in Figure 5 [Feldman et al, 2008]. Here the cooling rate for most of the troposphere is near 2 K per day or 0.1 K per hour. The local lapse rate is reset each day by the local weather conditions. The average lapse rate used in the US standard atmosphere is -6.5 K km-1. For a convective ascent rate of 1 km per hour, this gives a cooling rate of 6.5 K per hour.





Figure 5: Total and band-averaged IR cooling rate profiles for the Tropical Model Atmosphere on a log-pressure scale [Feldman et al, 2008]



2.0 THE LWIR EXCHANGE ENERGY AND THE SURFACE TEMPERATURE



The IR active molecules in the atmosphere are emitting IR radiation in all directions. Within the plane parallel atmosphere approximation, the absorbed and emitted horizontal fluxes are assumed to be equal and only the vertical flux needs to be considered. Therefore, in addition to the upward flux to space, there is also a downward flux to the surface. This is the real source of the ‘greenhouse effect’. The downward LWIR flux to the surface establishes a partial exchange energy with the upward LWIR flux emitted by the surface. When the surface and surface air temperatures are similar, this limits the net LWIR cooling flux that can be emitted by the surface to the atmospheric LWIR emission through the LWIR transmission window. This is illustrated in Figure 6 for clear sky conditions at 288 K surface temperature. The transmission through the LWIR atmospheric window depends on the humidity, the temperature and the cloud cover [Clark, 2013]. The transmission increases with decreasing humidity and decreases with increasing cloud cover. The downward LWIR emission from the cloud base ‘fills in’ the transmission window.





Figure 6: Downward LWIR flux to the surface. The surface cooling flux is limited to the transmission through the LWIR transmission window. MODTRAN calculation, 288 K surface temperature, same conditions as for Figure 3.



In order to dissipate the absorbed solar flux, the surface warms up until the excess heat is dissipated by moist convection. Also, some of the solar heat is stored below the surface and can be transported over long distances by ocean currents. This leads to a basic description of the surface temperature in terms of the interaction of four flux terms with the surface thermal reservoir. (Rainfall and freeze/thaw effects are not considered here). A change in surface temperature is produced by a change in the heat content or enthalpy of the local thermal reservoir divided by the local heat capacity. The four flux terms, the absorbed solar flux, the net LWIR emission, the moist convection (evapotranspiration) and the subsurface transport are interactive and should not be separated and analyzed independently of each other. The energy transfer processes at the land-air and ocean-air interfaces are different and have to be considered separately.



2.1 The Temperature at the Land-Air Interface



Over land, the four flux terms interact with a thin surface layer. 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 thermal 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. It is necessary to introduce two important parameters to describe the surface energy transfer. First, there is the evening convection transition temperature at which the evapotranspiration essentially stops. This is reset each day by the local weather system passing through. Second, there is a time delay or phase shift that may reach 2 hours or more between the peak solar flux and the surface temperature response [Clark, 2013]. The time delays for the subsurface temperature responses are longer. This is not a new concept. The subsurface phase shift was described by Fourier in 1824 and has been largely neglected in ‘equilibrium’ climate science for almost 200 years [Fourier, 1824 1827]. It is also important to note that the surface temperature here is the actual surface or skin temperature. The weather station temperature is the meteorological surface air temperature (MSAT) measured in a ventilated enclosure at eye level, 1.5 to 2 m above the ground [Oke, 2006]. The MSAT also shows a similar diurnal phase shift effect. At most weather stations, only the maximum and minimum MSAT temperatures are recorded so the diurnal phase shift data are not generally available. There may also be a seasonal phase shift produced by weather systems that are formed over the ocean and move overland. The energy transfer processes at the land-air interface and the phase shift are shown schematically in Figure 7.





Figure 7: a) Energy transfer processes at the land-air interface and b) the phase shift between the solar flux and the temperature response (schematic)



2.2 The Temperature at the Ocean-Air Interface



The ocean surface is almost transparent to the incident solar flux. Under ‘pristine’ conditions, approximately 50% of the solar flux is absorbed in the first meter layer of the ocean and 90% is absorbed within the first 10 m layer. The diurnal surface temperature rise is smaller than that over land because of the larger heat capacity of the solar heated ocean thermal reservoir. The bulk ocean temperatures therefore have to warm up until the surface temperature is sufficient for the absorbed solar heat to be dissipated by wind driven evaporation. The concept of an average surface temperature controlled by the LWIR flux is invalid. Water is a fluid, so that the cooler water produced at the surface sinks and drives a Rayleigh-Benard type convection process that cools the bulk ocean reservoir below. This allows the evaporation to continue at night. In addition, the trade winds drive the ocean gyre circulation. The penetration depth of the LWIR flux into water is 100 micron or less. The net LWIR flux and the wind driven evaporation (latent heat flux) are coupled together in a thin surface layer and should not be analyzed separately. There is both a diurnal and a seasonal phase shift. At mid latitudes, the seasonal phase shift may reach 6 to 8 weeks. Only the oceans have sufficient heat capacity to produce a seasonal phase shift. Over land, almost all of the absorbed surface heat is dissipated within the same diurnal cycle. In many parts of the world, the prevailing weather systems form over the oceans and move over land. The ocean surface temperature and the seasonal phase shift are coupled to the land weather stations through the convection transition temperature. The energy transfer processes at the ocean-air interface are illustrated schematically in Figure 8.





Figure 8: Energy transfer processes at the ocean air interface (schematic).



Near the equator, in the eastern Atlantic and Pacific Oceans, the wind driven evaporation is insufficient to remove all of the absorbed solar heat and the ocean water warms as it travels westwards with the equatorial ocean currents. This leads to the formation of the equatorial warm pools in the western Atlantic and Pacific Oceans. An upper limit to the ocean temperatures is reached near 30 C. An approximate energy balance is established between the absorbed solar flux and the combined net LWIR emission, convection and evaporative cooling at an average wind speed near 5 m s-1. If the wind speed drops and the ocean surface temperature increases, strong local thunderstorms are formed that cool the surface [Eschenbach, 2010].

There is no requirement for an exact balance between the wind driven evaporation and the solar heating. In the Pacific Ocean, variations in the wind speed produce the El Nino Southern Oscillation (ENSO) [ENSO, 2020 SOI, 2020]. This is a quasi-periodic variation in surface temperature with a period between 3 to 7 years. As the wind speed slows, the evaporation decreases and the equatorial ocean current velocity decreases. Both of these factors increase the rate of surface heating and the warm pool area increases. The maximum ocean surface temperatures do not change significantly [Yu et al, 2008].


At higher latitudes outside of the equatorial region, the wind speed is insufficient to remove all of the absorbed solar heat during the summer. The ocean subsurface layers below 50 m are not coupled to the surface by convective mixing and a stable thermal gradient structure is established. During the winter, the wind driven evaporation exceeds the solar heating and the surface temperatures cool and establish a uniform temperature layer down to 100 m or lower. Ocean thermal storage is a major factor in stabilizing climate temperatures [Clark 2013].



2.3 The Effect of an Increase in Atmospheric CO2 Concentration on the Surface Temperature.



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. This is discussed in more detail in the ‘Surface Temperature’ post.



3.0 THE COUPLING OF THE MOIST CONVECTION TO THE GRAVITATIONAL POTENTIAL AND ROTATION OF THE EARTH



Convection is a mass transport process. As the moist air rises through the troposphere it must interact with both the gravitational field and the angular momentum or rotation of the earth. As the air rises, it expands and cools. 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. Some of the internal energy of the air molecules is converted to gravitational potential energy. Above the saturation level, water vapor condenses to form clouds with the release of latent heat. This establishes the local lapse rate or vertical temperature profile through the troposphere. As the altitude increases, the moment of inertia of the air parcel also increases. Conservation of angular momentum leads to a decrease in angular velocity. There are also Coriolis forces that act on the rotating cyclone and anticyclone air masses. 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. This is illustrated in Figure 9.





Figure 9: The greenhouse effect is produced by the time dependent LWIR surface exchange energy. This limits the surface cooling by net LWIR emission. The surface warms up until the excess heat is removed by evapotranspiration. This is a mass transport process that is coupled to both the gravitational potential and the rotation or angular momentum of the earth. The greenhouse effect is part of the energy transfer processes that form the earth’s weather patterns.



4.0 THE TROPOSPHERIC HEAT ENGINE



The troposphere functions as an open cycle heat engine that transports 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 [Koll and Cronin, 2018]. 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 10 [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.





Figure 10: a) Molecular line broadening (schematic) and b) cumulative downward flux to the surface vs. altitude.



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 radiation at the local temperature of the air parcel. As shown above in Figure 5, the rate of tropospheric cooling from net LWIR emission in a tropical atmosphere is near 2 K per day or 0.1 K per hour. [Feldman et al, 2008]. During convective ascent, the cooling rate from the air expansion is typically 100 times faster. The energy transfer processes related to the tropospheric heat engine and for an air parcel in the troposphere are illustrated schematically in Figure 11.





Figure 11: a) The tropospheric heat engine and b) energy transfer processes for a local tropospheric air parcel (in a plane-parallel atmosphere).



This means that the concept of radiative forcing has no basis in physical reality because it ignores the effects of tropospheric convection and molecular line broadening. For example, for an increase in atmospheric CO2 concentration, the ‘radiative forcing’ or reduction in OLR is produced by a wavelength specific absorption, mainly in the P and R branches of the CO2 band. When this forcing is converted into an increase in the rate of heating of different levels in the troposphere, the maximum increase is less than 0.1 K per day. This small increase in absorbed LWIR flux is simply converted to a combination of wide band water emission and gravitational potential energy. The conversion from narrow band absorption to wideband emission is illustrated in Figure 12. A chnage in temperature of 0.1 K is produced by a change in elevation of approximately 15 m at a lapse rate of 6.5 K km-1.





Figure 12: a) The dissipation of the ‘radiative forcing’ from a ‘CO2 doubling’ by the normal tropospheric energy transfer processes (schematic). The wavelength specific increase in absorption in the CO2 P and R bands is dissipated as small changes in broadband LWIR emission and gravitational potential energy. b) Tropospheric heating rates produced by a CO2 ‘doubling’ [Iacono et al, 2008]



5.0 CLIMATE EQUILIBRIUM AND THE SURFACE TEMPERATURE PHASE SHIFT



Thermal equilibrium means that the rate of heating equals the rate of cooling. There are two different types of radiative equilibrium. Thermal radiative equilibrium was described by Kirchoff [1860]. Here, two isolated bodies are in radiative thermal equilibrium at the same temperature when they exchange equal amounts of radiative thermal energy. There is also an energy balance type of equilibrium where electromagnetic radiation is absorbed and an equal amount of energy is re-radiated as blackbody radiation at an absolute temperature T. There is no exchange energy. This describes the heating of the lunar surface during solar illumination.

The lunar surface is illuminated directly by the sun. There is almost no atmosphere. The surface material is a mainly regolith. This is a layer of powdered moonrock with very low thermal conductivity. The rotational period of the moon is 27.3 days. The surface layer heats up until the absorbed solar flux is returned to space as LWIR radiation. There is almost no time delay between the absorption of the solar flux and the LWIR emission. This means that the surface is in approximate thermal equilibrium with the solar flux. Along the lunar equator, the peak daytime temperature reaches 390 K (117 C) and at night, the low temperature is near 93 K (-180 C). The equatorial temperature change during a lunar day is 297 K [Williams et al, 2017 Vasavada et al, 2012]. When the surface is illuminated by the sun, the rate of heating and the rate of cooling are nearly equal. As the surface cools at night, heat is initially removed from the surface layer. The rate of cooling then slows as the surface cools and heat is conducted to the surface from the subsurface layers. The daytime temperature can be calculated reasonably well using simple blackbody theory.

The emitted LWIR flux Eir from the surface is equal to the absorbed solar flux and the surface temperature Ts (K) is calculated from Stefan’s Law.





The night time cooling can be calculated iteratively using the blackbody emission coupled to a thermal reservoir with a heat capacity Cq





Where t is the time step interval, set here to 0.1 lunar hours and Cq is the heat capacity of the surface layer coupled to the blackbody emission. The units here are J m-2. The depth of the coupled layer is not defined. Two different values of Cq were used, 3.84E4 J m-2 for the initial surface cooling and 3.73E5 J m-2 for the thermal conduction limited case. The measured (blue/gray) data points and calculated (orange line) surface temperatures are shown in Figure 13. There is good agreement between the measured and calculation data, although the simple model used does not include the details of the energy transfer as the surface cools near sunset at 6 lunar hours. The thermal properties are considered in detail by Vasavada et al [2012]





Figure 13: Measured and calculated lunar temperatures at the equator. For solar illumination from 0 to 6 hours, the temperature was calculated using the estimated blackbody emission produced by the absorbed solar flux. For the night time cooling, the blackbody emission was coupled to a surface thermal reservoir. Two heat capacities were used as shown. Measured data from [Vasavada et al, 2012].



On earth, the LWIR exchange energy limits the net LWIR cooling flux that may be emitted by the surface. In order to dissipate the excess absorbed solar flux, the surface warms up until the heat is dissipated by moist convection. As the surface warms, the thermal storage introduces a time delay or phase shift between the peak solar flux and the temperature response. Such phase shifts are also found in other energy storage devices such as capacitors in AC electronic circuits and passive resonant cavities (cavity ringdown) in optics. The observation of such surface temperature phase shifts is irrefutable evidence of a non-equilibrium thermal response. The seasonal phase shift or time delay between the peak solar flux at summer solstice and the peak temperature response is obvious in the weather station temperature data at mid latitudes. Figure 14 shows the phase shifts for selected weather stations in S. California. These are the 30 year daily average MSAT Tmin and Tmax 1981-2010 climate data for Los Angeles, LA Airport (LAX), Redlands, Riverside, San Bernardino, Blythe, Indio and Mecca [WRCC, 2020]. The phase shifts are shown in Figure 15.





Figure 14: 30 year daily average MSAT Tmin and Tmax 1981-2010 climate data for selected weather stations in S. California. The seasonal phase shifts past summer solstice are clearly visible.





Figure 15: 30 year daily average MSAT Tmin and Tmax 1981-2010 climate data for selected weather stations in S. California. The seasonal phase shifts past summer solstice are clearly visible.



Such phase shifts are also found in ocean temperature data. In fact the seasonal phase shifts are first generated when the weather systems form over the ocean. They are coupled to the weather station measurements through the diurnal convective transition temperature as the systems move over land. Figure 16 shows the 2.5 m to 200 m depth ocean temperature profiles for 2018 for a north-south transect of the N. Atlantic Ocean at 20° W derived from Argo float data [Argo 2020]. The data are for a 5° x 1° (latitude x longitude) strip at 10° intervals from 60° N to the equator, 0° N. A map of the locations is also provided. For latitudes from 20° to 60° N, the data show a winter surface temperature minimum in March or April. Summer solar heating then produces a stable stratified thermal layer structure with a surface temperature peak in August or September. The peak temperatures increase from 10 C at 60° N to 25 C at 20° N. The subsurface thermal layer structure then collapses as the wind driven evaporative cooling in winter exceeds the solar heating. In addition, there is a significant time delay or phase shift between the peak solar flux and the peak surface temperature response. These are indicated on the profile plots.


At low latitudes, 0° and 10° N, there is no obvious summer temperature peak. These locations are influenced by the S. Atlantic Equatorial Current. The cooler water from the Benguela Current that flows northwards along the coast of Africa, changes direction and flows westwards towards S. America. For 0° N, the surface temperature increases from approximately 27 to 29 C for the first five months of the year. It then decreases to approximately 24 C over the next three months and gradually warms up during the rest of the year. The April peak is produced by the summer solar heating in the S. Hemisphere.


These phase shifts are considered in more detail in the ‘Surface Temperature’ post.





Figure 16: The 2.5 m to 200 m depth ocean temperature profiles for 2018 for a north-south transect of the N. Atlantic Ocean at 20° W derived from Argo float data [Argo 2020]. The data are for a 5° x 1° (latitude x longitude) strip at 10° intervals from 60° N to the equator, 0° N. A map of the locations is also shown. The seasonal phase shifts are indicated.



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.



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