Some of the IPCC's Many Errors 1) The definition of forcing as a change in net flux at TOT/TOA. - The definition of forcing used by the feedback amplifier model, upon which the climate feedback model depends, refers to all of the input. For the Earth, this is all of the solar energy affecting the planet and not just the instantaneous W/m^2 difference at TOT/TOA. Each of the average incident Joules must contribute equally to the average Joules emitted by the surface, so there's no legitimate reason to distinguish the next Joule of forcing from any other. - Consider the equation, Pi(t) = Po(t) + dE(t)/dt, where Pi(t) is the forcing power arriving from the Sun, Po(t) is the power emitted and reflected into space and the instantaneous difference, dE(t)/dt, is what the IPCC calls forcing, where E(t) is the energy stored by the planet. The steady state is defined when the average dE(t)/dt == 0 or when average Pi == average Po. Note that the proper form for incremental forcing is dPi/dt and not d(Pi-Po)/dt. - While the stored energy, E, is linear to the temperature, T, dE/dt is not linearly proportional to dT/dt. The reason is that the LWIR component of Po originates from E, thus E and T are concurrently decreasing at a rate proportional to T^4. - The dependence of Po on T (and E) establishes a differential equation whose well known solutions are real and complex exponentials. This is nearly identical to the differential equation quantifying the response of an RC circuit to time varying forcing, whose equivalent time constant would be the amount of time it takes to emit all of the stored energy, E, at a rate given by Po. 2) The IPCC's definition of forcing assumes that an instantaneous 1 W/m^2 increase in solar input has the same warming influence on the surface as an instantaneous 1 W/m^2 decrease in outgoing flux at TOT/TOA arising from an increase in surface emissions absorbed by the atmosphere. - Since the amplifier feedback model defines all of the input to be the forcing, best practices consider a change to the system, for example changing CO2 concentrations, to be equivalently represented as having the same effect as a change in forcing, keeping the system constant. - All of the incremental solar input affects the surface temperature, while about half of the energy absorbed by atmospheric GHG's and clouds is ultimately emitted into space and does not contribute towards replenishing any surface emissions beyond the forcing power. - While albedo variability can be considered equivalent to incremental solar forcing at TOT/TOA, incremental absorption by the atmosphere can not, moreover; variable absorption is the physical manifestation of changing GHG concentrations. - As best as I can tell, the 3.7 W/m^2 of forcing said to arise from doubling CO2 is the incremental surface emissions absorbed upon instantly doubling CO2 from pre-industrial levels and is not the equivalent solar forcing that would have the same result while keeping CO2 concentrations constant. 3) Mapping the Bode feedback amplifier model to the climate. - All of the papers related to climate feedback refer to Bode's book, "Network Analysis and Feedback Amplifier Design" as the theory behind the climate feedback model. No other reference is cited as the origin of feedback analysis, thus Bode's preconditions must be honored in order to apply it, starting with those stated in the first 2 paragraphs on page 1 of his book which can be found at this link. https://archive.org/details/NetworkAnalysisFeedbackAmplifierDesign - An important precondition is the existence of an implicit, infinite source of Joules to power the gain. This simplifying assumption avoids having to conserve energy between the input and output of the gain block. Many consider the Sun to be the power supply in which case it's the explicit forcing input and not the implicit power supply, thus COE between the input and output of the amplifier must be accounted for and the Bode model explicitly doesn't do this. - Another precondition is strict linearity, which means that if I is the input and O is the output, constant_gain = O/I = delta_O/delta_I must be true for all I and O. Assuming constant gain and a stateless system is what makes Bode's analysis possible. The climate feedback model with its input expressed as a change in W/m^2, an output expressed as a change in temperature, where the temperature is the state, clearly doesn't conform to Bode's amplifier model. - Some consider the incremental gain to be the AC gain, or the small signal gain and the absolute gain to be the DC gain or even the operating point. In modern integrated amplifiers, the AC and DC gains are the same. The DC gain is often zero in the tube amplifiers Bode used as examples because the extra circuitry required to establish a neutral operating point is cost prohibitive. - Bode's analysis applies to the small signal gain, where the small signal would be the diurnal and seasonal variability in the solar input at each point across the surface. The small signal attribute has nothing to do with the magnitude of a signal change relative to the size of the signal, but refers to any signal up to the maximum value where strict linearity remains valid. 4) Assuming that since delta_T/delta_Forcing is approximately linear over narrow ranges of temperature, Bode's feedback analysis can be applied incrementally. - Approximate linearity is insufficient for applying Bode's feedback amplifier analysis. The requirement is that T/Forcing must be constant and equal to delta_T/delta_Forcing for all T which is obviously not true owing to the T^4 dependence of W/m^2 per the Stefan-Boltzmann Law. - When an amplifier goes non linear and the output starts to clip, the gain becomes dependent on the forcing, the output is no longer a faithful copy of the input, Bode's analysis no longer applies and his quantification's of gain, feedback and sensitivity are no longer meaningful. 5) The definition of the climate sensitivity as the incremental gain. - Bode defines the sensitivity as the relative change in gain as a fraction of a proportional change in some attribute of the system. This may be what Hansen and Schlesinger thought they were modeling, but applying Bode's gain model to amplify the sensitivity is wildly incorrect. Schlesinger may have been an accomplished mathematician, but he didn't understand the practical aspects of Bode's analysis. - Of particular importance is Bode's use of dimensionless gains. The output units can differ from the input units if and only if the output units are linearly proportional to the input units, for example, Volts in and Amps out which are linearly related to each other by Ohms Law. - What is called the sensitivity in the climate feedback model is what Bode refers to as the closed loop gain, moreover; since the gain must be constant, there can be no distinction between the absolute gain and the incremental gain. - Distinguishing the incremental gain, much like distinguishing the incremental forcing, serves a singular purpose, which is to obfuscate the requirements of Conservation of Energy by isolating the effect of the next Joule of forcing from the effects of all the others. 6) Climate feedback papers confuse the feedback factor with the feedback fraction. - The feedback fraction is the dimensionless fraction of the output that's added to the forcing input before being amplified by the open loop gain to produce the output. Note that only feedback in the same units as the forcing can be summed before amplification. - The feedback factor is an archaic quantity given as the feedback fraction times the open loop gain. In modern amplifiers, the open loop gain is high enough to be considered infinite, thus so is the feedback factor. This is equal to the feedback fraction only when the dimensionless open loop gain is unity. See the footnote on page 32 of Bode's book for more details. - Hansen's 1984 paper on climate feedback assumed unit open loop gain with no acknowledgment or explanation other than stating, "it follows that" after referring to Bode and then he confused gain with feedback in the resulting equation. Hansen's concept of amplification with positive feedback quickly gained traction as the holy grail providing the theoretical support for a climate sensitivity large enough to justify the formation of the IPCC and UNFCCC. - Just prior to the formation of the IPCC around 1988, Schlesinger identified Hansen's errors and corrected them with a plausible, yet erroneous derivation of the gain equation. He assumes a gain block with a non unit open loop gain that converts a change in forcing into a change in temperature. He then assumes unit open loop gain in the derivation of the gain equation by conflating the feedback fraction with the feedback factor. This is fatal to the analysis, yet since AR1, the Hansen and Schlesinger papers are cited concurrently as the theoretical foundation for amplification by positive feedback. - A more recent work by Roe (2009) repeated the same derivation error as Schlesinger. The only differences were that some of the variable names were changed. 7) The climate sensitivity feedback model considers the surface temperature to be the state which is changed by the output of the sensitivity model. - The Bode feedback model is stateless and the proper application would use all of the equivalent Stefan-Boltzmann emissions of T as the output of the model. None the less, COE would still need to be applied between the forcing input and the output emissions. - The linear 1.62 ratio between the equivalent black body emissions of the surface and the planet's average emissions which in the steady state is equal to the average solar forcing, is easily testable. I've confirmed this to be the most tightly regulated relationship between any pair of related climate variables based on decades of weather satellite data. Even the monthly averages of 2.5 degree slices of latitude are within a few percent of this ratio and are strongly independent of the average surface temperature of the slice. 8) Applying a feedback model that amplifies the Planck sensitivity into a much larger Equilibrium Climate Sensitivity. - The climate feedback model incorrectly considers that feedback amplifies a sensitivity expressed in the non linear units of degrees per W/m^2. This is a meaningless application of a model whose purpose is to quantify linearly amplifying a signal input into a faithfully scaled copy at the output. - The linearity restriction precludes amplifying a Planck sensitivity expressed as a change in T per change in forcing, however; this can be equivalently modeled as a linear amplifier if the model has unit open loop gain, the output is expressed in the same units as the forcing, the closed loop gain is independent of the forcing input and COE is properly accounted for among the input, feedback and output. - To consider the Planck sensitivity as being amplified, the open loop gain must be expressed as the 1 W/m^2 of surface emissions per W/m^2 of forcing characteristic of an ideal black body which climate system 'feedback' amplifies to 1.62 W/m^2 of surface emissions per W/m^2 of forcing manifesting about a net 390 W/m^2 of surface emissions at 288K from only 240 W/m^2 of solar forcing. - Per Bode, the open loop gain would be 1, the closed loop gain would be 1.62 and the required positive feedback becomes 38.3%. The feedback power offsetting the 620 mw of additional emissions per W/m^2 of forcing originates from the fraction of surface radiant emissions absorbed by the atmosphere (GHG's and clouds) and returned to the surface to be combined with future solar forcing. This additional power is a feed forward signal and not a feedback signal, owing to the significant delay between absorption and the return to the surface of that absorbed energy. In the idealized model applied to amplify the ECS, Bode assumes zero delay between the output and the feedback and this precondition is also ignored. 9) Conflating the energy transported by photons with the energy transported by matter relative to the radiant balance as illustrated in Trenberth's energy balance diagram. - Latent heat leaves the surface as vapor, cooling the water it evaporated from and is returned as liquid water that's warmer than it would be otherwise. The latent heat not returned to the surface by this mechanism either drives the weather or contributes to the otherwise required emissions by the planet, but doesn't actually effect what those emissions must be. - While water in the atmosphere transports energy throughout, in the steady state, that water must be emitting and radiating the same amount of energy. - Thermals are convective currents and when heat rises in one place, cold will be sinking somewhere else. This is a non radiant transport of energy by matter in a closed loop with the surface and has no relevance on the radiant balance as air (N2/O2) does not emit photons at the energy levels involved. - Subtract the return of latent heat, weather and thermals from the 'back radiation' term and all that's left is the power required to offset the Stefan-Boltzmann emissions of the surface at its average temperature. - The question this raises is what effect do non radiant transports between the atmosphere and surface have on the surface temperature beyond the effect they're already having and accounted for by 620 mw of additional surface emissions per W/m^2 of forcing? 10) The nominal sensitivity of 0.8C +/- 0.4C per W/m^2. - If the next W/m^2 of solar input results in a surface temperature increase of 0.8C, the resulting surface emissions will necessarily increase by about 4.4 W/m^2. Each of the original W/m^2 of solar forcing contributes 1.62 W/m^2 to the surface emissions. There's no physics enabling the planet to tell the difference between the next W/m^2 of solar input and all the others so that it can be amplified with 3.4 W/m^2 of feedback, while all the others are amplified with only 0.62 W/m^2 of feedback. - If each of the 240 W/m^2 from the Sun was amplified with 3.4 W/m^2 of 'feedback' per the nominal sensitivity, the predicted surface emissions correspond to a temperature close to the boiling point of water which falsifies the presumed nominal ECS. - If the atmosphere absorbed 100% of what the surface emits, only half of this is returned to the surface to replace increased emissions, while the rest is emitted into space. This limits the maximum emissions sensitivity to 2 W/m^2 of surface emissions per W/m^2 of forcing. The IPCC's lower limit of 0.4C per W/m^2 requires the surface emissions to increase by 2.2 W/m^2 per W/m^2 of forcing which exceeds the theoretical maximum thus falsifying the entire range of ECS presumed by the IPCC. - Confirming evidence is that the emissions at TOA are always more than half the power of the SB emissions of the surface below, even when the densest clouds are present between the surface and space. 11) Conflating the climate of Venus with that of the Earth and claiming that the same feedback mechanisms apply. - The Venusian solid surface has more in common with the solid surface of Earth beneath the oceans than it does with the virtual surface whose temperature we care about and its dense atmosphere has more in common with Earth's oceans, then with its atmosphere. - On Venus, the virtual surface in direct equilibrium with the Sun is comprised of the cloud tops high in its atmosphere. - On Earth, the virtual surface in direct equilibrium with the Sun is the top of the oceans and bits of solid surface that poke through. - In both cases, the virtual surface in direct equilibrium with the Sun heats the rest of the system. - Both the solid surface of Venus and that of Earth below the deep ocean exhibit no diurnal or seasonal temperature variability. - Unlike Venusian clouds, the Earth's clouds are tightly coupled to the surface by the hydro cycle and for averages integrated over more than the length of the water cycle, absorption and emission of incident energy by the water in clouds can be considered a proxy for the absorption and emission of incident energy by surface waters. - Most of the Venusian atmosphere is heated from above and the the surface temperature becomes dictated by the PVT profile of the CO2 'ocean' between the clouds providing heat and the solid surface below as gravity establishes a lapse rate of increasing temperatures from the clouds down to the solid surface below. - On Earth, the atmosphere is heated from below and its PVT profile establishes a lapse rate of decreasing temperatures from the virtual surface in direct equilibrium with the Sun up to TOT. - On Earth, the oceans are heated from above and the temperature at their bottom is dependent on the pressure/density/temperature profile of water under compression. - The runaway positive feedback case requires the infinite, implicit power supply assumed by Bode which doesn't exist on either the Earth or Venus. If Venus is a case of runaway anything, it's runaway cloud coverage. 12) Assuming that the relationship seen in the ice cores between CO2 and temperature indicates that CO2 is the temperature control knob for the climate. - Upon closer inspection, min/max CO2 concentrations occur centuries after min/max temperatures indicating that temperature changes result in changes in CO2 concentrations and not the other way around. To the extent that there's any 'mutual feedback', the effect temperature has on CO2 concentrations clearly dominates. - Ocean CO2 concentration changes related to changes in the CO2 partial pressure would be instantaneous relative to the centuries of observed delay. - The delay is consistent with the amount of time it takes to sequester enough natural CO2 to support additional forest land or for forests to die off as conditions slowly change and that more planetary biomass results in higher steady state CO2 concentration. - The CO2 concentrations in the ice cores are a proxy for the amount of planet wide biomass superimposed on a longer term downward trend arising from biology sequestering CO2 as carbonate rocks and fossil fuels at rate that's faster than what can be replenished naturally. 13) Many seem to assume that all of the surface emissions absorbed by GHG molecules becomes 'thermalized' into the kinetic energy of molecules in motion within milliseconds by collisions. - This is contradicted by the observed spectrum at TOA which has significant emissions in bands where 100% of the surface emissions are absorbed by the atmosphere. The flux at TOA in these bands is about 1/2 of what it would be without any absorption. The only possible source of these photons in cloudless skies are GHG molecules. - This is contradicted by Quantum Mechanics which requires the de-engerization to occur all at once, usually by emitting a photon of the same energy that was absorbed, so while a collision may de-energize a GHG molecule, it will do so by initiating the emission of a photon. - The claim is that all of the vibrational state energy is transferred to rotational states and equalized by collisions. While the fine structure in absorption shows such transfers occur, it occurs on both sides of the vibrational resonances. While energy can be added to a rotational state, emitting a lower frequency photon or by absorbing a higher energy photon, the reverse occurs with equal probability removing energy from rotational states. As a result, there's no net conversion between vibrational and rotational state energy. Note that while state energy can be exchanged and/or equalized between collisions of like GHG molecules, this has little to no effect on their kinetic energy of motion, except potentially at levels of kinetic energy much larger than the state energy and far beyond what the atmosphere supports. - The justification seems to be Equipartition of Energy, but this is a macroscopic property of matter that applies to the kinetic energy of matter in motion and not to state energy or the energy transported by massless photons. State energy is not a degree of freedom relative to a temperature consequential to the kinetic energy of collisions with other molecules. The temperature corresponding to state energy is ordinarily manifested by the emission of photons. - Direct thermalization can occur when an energized H2O molecule condenses upon a drop of liquid water in a cloud or when an energized CO2 molecule is absorbed by cloud water. This is observed in the emitted spectrum of the planet by slightly more than 3db of attenuation in the strongest CO2 and H2O absorption lines, where the missing energy is converted into the broad band Planck emissions of cloud water.