'Warming Interrruptus' – Causes for The Pause

While it is clear that the climate models have failed, the underlying reasons for the failure are not obvious. They are deeply rooted in the underlying concepts used to develop the basic climate model algorithms. The fundamental problem is that there is a complete disconnect between the real physics of the climate energy transfer and the mathematical algorithms used in the models. There are 3 levels of incorrect assumptions that have to be addressed.
First, the averaging assumptions used to simplify some of the complexities of the energy transfer are incorrect and produce erroneous results. The averaging removes the dynamic thermal gradients that are required by the Second Law of Thermodynamics to drive the heat transport through the climate system. The sun does not illuminate the Earth’s surface at night. There is no such thing as an ‘equilibrium average climate’.
Second, the original climate modeling concept of an abstract ‘blackbody surface’ was replaced by ocean heating. In reality, the small increase in downward long wave IR (LWIR) flux from the observed increase in atmospheric CO2 concentration is blocked at the ocean surface and dissipated by wind driven evaporation. There can be no ocean warming from the observed increase in atmospheric CO2 concentration. Sun, wind and water determine the Earth’s climate without any help from CO2.
Third, the substitution of the climate record for the surface temperature is incorrect. There can be no ‘CO2 signature’ in the weather station record.
The global warming fraud is clearly revealed when these assumptions are examined in more detail.
The geometric ratio between the area of a sphere and a circle is 4. This mathematical construct is used to create a fictional ‘average solar flux’ at the top of the atmosphere (TOA) of ~340 W m^-2. An albedo of 0.3 is then used to create a fictional ‘surface average solar surface flux’ of 240 W m^-2. Using Stefan’s law, this corresponds to a blackbody emission temperature of 255 K (-18 C). An ‘average surface temperature’ of 288 K (15 C) is then assumed, using an average of weather station temperature data. Somehow 255 K is supposed to be the Earth’s average surface temperature without any atmospheric ‘greenhouse gases’ and heating by ‘greenhouse gas absorption’ produces the ‘greenhouse effect temperature’ of 33 K that mysteriously raises the average surface temperature to 288 K.
In reality, the peak tropical/summer solar flux is near 1000 W m^-2 which corresponds to a blackbody surface temperature near 364.4 K (91.4 C). There is no ‘equilibrium average climate state’. The climate system consists of a set of dynamically coupled thermal reservoirs. Heat is accumulated by these reservoirs during the day and dissipated through a series of rate limited heat transfer processes. At minimum, there are four coupled thermal reservoirs, the oceans, the land and a lower and upper tropospheric reservoir. Almost all of the downward LWIR flux that reaches the surface originates from the first 2 km layer of the troposphere. Similarly, almost all of the net LWIR flux absorbed by the troposphere is absorbed within this 2 km layer. In fact, a large fraction of the atmospheric LWIR flux, near 75%, is absorbed or emitted within the first 100 m layer or the troposphere.
The land and the oceans act as the hot reservoirs of an open cycle heat engine. The working fluid is moist air. Almost all of the heat that is coupled to the troposphere is converted directly or indirectly to convection. The heat engine operates mainly during the day and the thermal transport is determined by the thermal gradients at the surface. At night, the convection almost stops and the lower troposphere acts as a ‘thermal blanket’ that reduces the night time LWIR emission to space. At night, the surface cooling is limited to the LWIR emission through the atmospheric LWIR transmission window. The upper tropospheric reservoir cools continuously by LWIR emission to space. The dominant cooling process is LWIR emission by the water bands in the middle troposphere near 5 km. The average lapse rate or temperature profile assumed by the US Standard Atmosphere is -6.5 K km^-1. The so called ‘greenhouse effect temperature’ is nothing more than the average cooling produced by the climate heat engine as a convective air parcel ascends from the surface to 5 km.
The maximum ocean surface temperature near 303 K (30 C) is found in the equatorial ocean warm pools. This is produced by the net flux balance between the tropical solar flux and the ocean surface cooling. The dominant cooling term is wind driven evaporation from the ocean surface. The cooler water produced at the surface then sinks and cools the bulk ocean layers below. The minimum ocean surface temperature is near 271.2 K (-1.8 C) which is freezing point of sea water under normal salinity conditions. Over land, maximum surface temperatures for a dry surface under full summer/tropical solar illumination can easily reach or exceed 323 K (50) C. Minimum surface temperatures near the south poles may reach 173 K (-100 C). The concept of an average surface temperature is a mathematical construct that has almost no physical meaning.
Most of the IPCC global warming arguments are based on the concept of radiative forcing. This was introduced in its modern form by Manabe and Wetherald (M&W) in 1967. Starting from the observation that the Earth’s climate was stable, M&W introduced the concept of a ‘radiative-convective equilibrium climate state’ to describe a hypothetical, stable average climate. This is just a mathematical construct that produces a set of simplified steady state flux equations. These can be analyzed relatively easily using perturbation theory. The primary objective here was the development of more advanced radiative transfer algorithms for incorporation into climate models. In the mid 1960s, the available computer capabilities were very limited and the algorithms for atmospheric radiative transfer had to be simplified using band models to simulate the detailed line by line molecular energy transfer. However, even with these limitations, the atmospheric radiative transfer equations could be solved with reasonable accuracy and limited altitude resolution to give the steady state flux terms.
The assumptions made by M&W were clearly stated in their paper. [http://www.gfdl.noaa.gov/bibliography/related_files/sm6701.pdf]
1) At the top of the atmosphere, the net incoming solar radiation should be equal to the net outgoing long wave radiation.
2) No temperature discontinuity should exist
3) Free and forced convection, and mixing by the large scale eddies, prevent the lapse rate from exceeding a critical lapse rate equal to 6.5 C km^-1.
4) Whenever the lapse rate is subcritical, the condition of local radiative equilibrium is satisfied.
5) The heat capacity of the earth’s surface is zero
6) The atmosphere maintains the given vertical distribution of relative humidity (new requirement)
The primary objective of the M&W study of radiative convective equilibrium was the incorporation of radiative transfer into the general circulation model of the atmosphere. In particular they wanted to determine the following:
1) How long does it take to reach a state of thermal equilibrium when the atmosphere maintains a realistic distribution of relative humidity that is invariant with time?
2) What is the influence of various factors such as the solar constant, cloudiness, surface albedo and the distribution of the various atmospheric absorbers on the equilibrium temperature of the atmosphere with a realistic distribution of relative humidity?
3) What is the equilibrium temperature of the earth’s surface corresponding to realistic values of these factors?
It is important to note that the term ‘equilibrium’ is used rather loosely here. Strictly, equilibrium requires that the forward and reverse rates are equal. A more appropriate term is steady state in which the outgoing LWIR flux equals the absorbed solar flux and there is no further change in the outgoing LWIR flux with time as the model calculation time step is iterated.
To begin, M&W ignored the time dependence of the solar flux and the thermal storage effects. Instead they created a mathematical 24 hour average solar flux that must be part of an exact top of atmosphere flux balance. The Earth’s surface is treated as an abstract blackbody surface with zero heat capacity. The lapse rate is used as a mathematical constraint to force model convergence. This provides a suitable mathematical framework to facilitate the development of radiative transfer algorithms. However, they have already left physical reality behind and have entered the realm of computational climate fiction.
There is also another implicit assumption inherent in the exact flux balance requirement. This is that upward and downward LWIR fluxes are equivalent, which is not the case. The linwidths of the individual molecular lines are determined by the collision frequency through the application of the Heisenberg Uncertainty Principle. The upward LWIR emission from the wings of the lines in the lower troposphere is not reabsorbed by the narrower lines at higher altitudes. The downward LWIR emission from the narrower lines at higher altitudes is reabsorbed at lower altitudes and does not couple to the surface. In the M&W model, increases in stratospheric water vapor concentration can cause an increase in the ‘equilibrium surface temperature’. This is just a consequence of the unrealistic equilibrium flux balance modeling assumptions and the neglect of the molecular linewidth effects.
M&W used a fixed distribution of relative humidity in their model. Any temperature increase in the model is accompanied by an increase in the water vapor concentration needed to maintain the relative humidity. This leads to a mathematical feedback artifact that amplifies any CO2 induced surface heating created by the model. In reality, the relative humidity is not fixed, particularly near the surface. During the day, the humidity is determined by the surface evaporation and the convective mixing of the solar heated air from the surface. At night, the cooling of the surface air layer and the related increase in relative humidity is determined mainly by the net LWIR emission through the atmospheric transmission window. Humidity levels also depend on the local weather conditions. An increase of 100 ppm in the atmospheric CO2 concentration increases the downward LWIR flux at the surface by approximately 1.5 W m^-2 or 0.13 MJ m^-2 per day. This is equivalent to the evaporation of a 57 micron thick layer of water from the surface. This is too small to make any measurable difference to the normal diurnal evaporation cycle. The whole concept of water vapor feedback has no basis in the physical reality of the surface energy transfer. It is a consequence of the mathematical averaging and other constraints used in the M&W model.
M&W used a 9 or 18 layer model of the atmosphere. The net LWIR flux absorbed and emitted in each layer was determined during each model time step and used to change the temperature profile. This was also constrained so as not to exceed a lapse rate of 6.5 K km-1. Here, the lapse rate is used as a mathematical model constraint. In reality, the lapse rate is determined locally by solar surface heating and convective mixing. Although the computer calculation time was much less, it required several months of simulated time steps to reach the ‘equilibrium state’. This was nothing more than a mathematical exercise to improve the radiative transfer algorithms used in the model. The small temperature changes over several months needed for the model to converge to ‘equilibrium’ are not measurable or physically meaningful when the normal diurnal and seasonal changes in the atmospheric temperature profile are considered.
The modeling results presented by M&W have no basis in physical reality and have no application to the Earth’s climate. The equilibrium flux equations do not apply to Planet Earth.
It is important to understand that once an atmospheric profile of temperature and species concentration has been defined, the LWIR flux can be reliably calculated from the radiative transfer equations. It is the mathematical constraints of a ‘climate equilibrium state’ and their use to determine changes in ‘equilibrium surface temperature’ that are incorrect. Instead of treating the M&W model as a failed hypothesis, subsequent researchers continued to try to improve the model within the framework of the original assumptions. Other IR active species were added to the radiative transfer algorithms and additional atmospheric layers and other features were added as the computer technology improved. The next level of incorrect assumptions was added when the atmospheric model of M&W was coupled to an ocean model.
The basic definition of a blackbody surface is that it absorbs all electromagnetic radiation at all wavelengths and emits radiation according to Planck’s Law. Water however is almost transparent at visible wavelengths. Approximately half of the solar flux is absorbed within the first meter depth of the ocean and 90% is absorbed within the first 10 m. In contrast, the penetration depth of the LWIR flux into the oceans is barely 100 micron. The dominant ocean cooling process is wind driven evaporation and this is also limited to a thin surface layer. The increase in LWIR flux from the 100 ppm increase in atmospheric CO2 concentration is dissipated as a minute part of the evaporative cooling flux. Any changes in ocean surface temperature are simply too small to measure and the additional LWIR flux cannot penetrate below the surface and heat the ocean below. However, the need to create global warming required that the oceans were heated by the increase in LWIR flux from CO2. This approach of course has no basis in physical reality, but mathematically, an ocean heat capacity and a diffusion coefficient were used to create the heating. By 1980, the ocean cycles had entered a natural warming phase that was of course blamed on CO2. Ocean heating also provides a convenient mathematical excuse that can be used to delay the effects of global warming. The high ocean heat capacity requires a long time to reach ‘equilibrium’. There is no equilibrium. The ocean is indeed a large thermal storage reservoir that is always heating or cooling, depending on the flux balance. However, the upper limit to the heat capacity of the surface ‘skin layer’ is approximately 4 kJ K^-1 for a 1 mm x 1 m^2 layer. This layer responds rapidly to any change in LWIR/cooing flux. The solar flux heats the bulk ocean layers underneath.
The third and final level of the incorrect model assumptions is the ‘calibration’ of the so called ‘forcing constants’ using the measured climate record from the weather station data. It was assumed without any physical proof that the calculated increase in downward surface atmospheric LWIR flux of 1.5 W m^-2 caused by a 100 ppm increase in atmospheric CO2 concentration produced an increase of 1 C in the weather station record. In reality, the net flux balance in the surface layer determines the surface temperature. The weather station temperature however, is the meteorological surface air temperature (MSAT). This is the air temperature measured in a ventilated enclosure placed at eye level, 1.5 to 2 m above the ground. At night, the minimum MSAT is an approximate measure of the base temperature of the air mass of the local weather system as it is passing through. During the day, the maximum MSAT is a measure of the convective mixing between the warm air rising from the solar heated surface and the cooler air at the weather station level. There can be no CO2 warming signal in the MSAT. The heat capacity of the weather system is too large. Instead, since most weather systems form over the oceans, long term changes in the minimum MSAT are a measure of changes in the ocean surface temperature in the formation region of the weather system. The climate models were ‘calibrated’ using ocean surface temperatures.
Simple inspection of the climate average weather station data sets such as HADCRUT4 reveals that the dominant climate trend is the Atlantic Multidecadal Oscillation (AMO). This is the result of both the area averaging used to create the climate trend and the natural influence of the AMO over large areas of the Americas, Europe and Africa. Part of the S. Atlantic gyre is also diverted northwards along the coast of Brazil into the Caribbean where it is coupled into the AMO. The Earth has been warming since end of the Little Ice Age. The warming process is the gradual accumulation of solar heat into the oceans. Before the recent solar maximum, the average increase in the top of atmosphere (TOA) solar flux was near 0.4 W m^-2. From 1950 to 2010, the average increased to 0.7 W m^-2. In addition, the AMO was in its warming phase from approximately 1980 to 2010. These are the real sources of the observed ‘global warming’. A cooling phase has now started. The Earth’s climate system still obeys the basic Laws of Physics. The Earth itself has revealed the climate modeling fraud for all to see. The coincidence between the increase in atmospheric CO2 concentration, the warm phase of the ocean cycles and the modern solar maximum has ended. The climate astrologers are now trapped in a web of pseudoscientific lies of their own making.

Trying to explain the “pause” is like trying to explain why there are no fairies.
There is no pause (the most simple explanation) because CO2 is not a climate driver.