In most ways, David Evans’ alternative model is exactly the same as the conventional model. But a reconnection of one forcing, and an additional factor, can make all the difference. Finally, climate model architecture is getting analyzed and discussed — the conventional structure has been in place for over 40 years.
In the conventional basic model the radiation imbalance caused by CO2 is treated like extra sunlight, amplified by the same feedback processes that amplify warming caused by the sun. But as we explained, the effects of CO2 are not just confined to the surface of Earth, but spread through the atmosphere. In the alternative model the warming caused by CO2 is allowed to have its own unique response. Only after the separate “warmings” of the Sun and CO2 are calculated can they be added together. The conventional model adds them too soon, while they are still radiation imbalances, and assumes the Earth’s climate responds to both in the same way — it’s too simplistic.
David’s model also allows for other factors to change cloud cover, with the addition of an input for externally driven albedo (EDA). In conventional models, clouds are just a feedback to surface warming, but we already know that anything that affects the particles that “seed” clouds can dramatically change the amount of sunlight arriving on Earth’s surface. These factors include cosmic rays and aerosols, and although we don’t know exactly what these are, we have data on how much energy arrives on Earth’s surface so we can still allow for the effects of whatever it is that changes the Earth’s albedo (reflectiveness). — Jo
13. The Sum-of-Warmings Model
The sum-of-warmings model is the expression of the organizing theme of the alternative model, namely that each climate driver has its own specific sensitivity and feedbacks (“response”), and that the small surface warmings due to the various drivers are independently calculated then added.
The assumed linearity of the climate system for small perturbations means that small temperature perturbations due to the various climate drivers do not significantly affect one another — so the effects of the various climate drivers superpose.
The solar response describes how the surface temperature responds to changes in absorbed solar radiation (ASR).
From the previous post, for moves between steady states the relationship between the ASR A and the radiating temperature TR is just
How do we then get from ΔTR to “the surface warming due to an increase in ASR”, ΔTS,A? The dependence of TS,A on TR is complicated because TR depends on the temperatures of the various layers that emit OLR, one of which is the surface, and the rest of which are somewhere in the atmosphere. The relationship between TR and TS,A is thus mainly mediated by the atmosphere. The atmosphere is complicated and has many feedbacks. However it acts and reacts quickly — usually within days, always within weeks — which allows a great simplification: on timescales of a year or more (such as moves between steady states, as the CO2 concentration rises) and for small perturbations, ΔTS,A is (presumably) proportional to ΔTR. Accordingly we model ΔTS,A as
where M is the ARTS (Amplification of Radiating Temperature to Surface) multiplier. M therefore describes the effects of all the feedbacks in response to surface warming except those influencing albedo, and is thus the open-loop form of the non-albedo feedbacks in response to surface warming (see the feedbacks diagram in Fig. 1 of post 3).
This is the same form as the solar response in the conventional model, so by comparison with Fig. 2 of post 9 when all inputs are zeroed except ΔANF,
Although M reflects all the complexity of the atmosphere and its feedbacks, it has effectively already been estimated for us in AR5. The climate establishment has researched the solar response pretty thoroughly. All we’ve done here is some minor repackaging — putting the non-albedo feedbacks in line, and replacing the Planck sensitivity (with its problematic reliance on holding all else constant) with the Stefan Boltzmann sensitivity (which always applies).
The CO2 response describes how the surface temperature responds to changes in CO2 forcing — which in turn responds logarithmically to changes in the CO2 concentration, as per the conventional model (no change in that aspect).
The conventional model applies the solar response to the CO2 forcing (Fig. 2 of post 3 and Fig. 2 of post 9), which leads to various unrealistic physical features. So, as noted in the remarks in post 9, the CO2 forcing should not be added to the input of the Planck or Stefan-Boltzmann sensitivities. Also, the CO2 forcing should not affect ΔTR (and thus OLR, because TR is a proxy for OLR) except via surface warming and albedo feedbacks — because by linearity the various climate drivers do not significantly interfere with each other and ΔTR is part of the solar response, and because increasing CO2 merely redistributes OLR between the various pipes without changing to the total amount of OLR or TR (ignoring albedo feedbacks).
There being no existing appropriate modeling structure, we create one. The surface warming due to increased CO2 is presumably proportional to the resulting radiation imbalance DR,2XΔL, where L is the base-2 logarithm of the CO2 concentration (see post 2). So for small temperature perturbations let us define the CO2 sensitivity λC by
where ΔTS,C is the surface warming due to the increase in CO2. λC includes the effect of the rerouting feedback and any other CO2-specific feedbacks. λC is positive (we estimate its value later in this series, and find it is likely less than 0.15 °C per W/m2).
The complete sum-of-warmings model is shown in Fig. 1. Its essence is the adder (or summation node) shown as a big red circle, which sums the temperature perturbations caused by the various climate drivers. It also shows EDA as a separate input, along with TSI, contributing to the no-feedbacks ASR ΔANF.
This is not an energy balance model, except that it is parenthetically noted in the diagram that the increase in ASR is equal to the increase in OLR (this is where we will later bolt on the OLR model, to form the alternative model).
Figure 1: The sum-of-warmings model of the climate system, for changes from one steady state to another. It adds the surface warmings due to each climate driver, calculated independently of each other.
Consider the situation where there are only solar and CO2 inputs (n=2).
The sum-of-warmings model in Fig. 1 is the same as the conventional model in Fig. 2 of post 9, except that the CO2 forcing is applied to its own specific CO2 response instead of added to the input of the solar response. That is, in the sum-of-warmings model, if the output of the “CO2 Influence” box (namely the forcing DR,2XΔL) were added to the summation node where the increase in no-feedbacks ASR ΔANF is added to the albedo feedbacks fαΔTS to form the increase in ASR ΔA, instead of going to the “CO2 Response” box, then the sum-of-warmings model would be identical to the conventional basic climate model. This conventionally-architected counterpart of Fig. 1 is shown in Fig. 2, below.
Hence the sum-of-warmings model is just one reconnection away from the conventional model, and it is not obvious that they are different architectures rather than just differing by a mistaken connection!
The essential difference is that in the sum-of-warmings model the solar and CO2 influences are separate all the way to the surface warming, rather than entangled at the radiative stage as in the conventional model.
One can regard the conventional model as the alternative model but with the CO2 sensitivity λC set equal to the solar sensitivity λSBM (which is equal to about 0.54 °C per W/m2).
Figure 2: The conventionally-architected version of Figure 2, illustrating that the essential difference between the alternative architecture and the conventional architecture is just one connection — what to do with the radiation imbalance due to increasing CO2.