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New Science 11: An Alternative Modeling Strategy

Posted By David Evans On In Global Warming | Comments Disabled

All pipes lead to Space

Inexorably, energy is headed for the coldest vacuum. It’s just a question of how long and what path it takes to get there. On Earth there are four main “pipes” to space — the CO2, water vapor, cloud tops, and surface pipes (see post 6). The basic establishment model treats “trapped” heat as if it were “adding heat” (see post 9). But partially blocking one exit pipe out of four is not the same as adding energy to the incoming pipe. Adding more energy on the incoming side means the total outflow must be higher. But merely slowing the outflow in one pipe means the total outflow remains the same, it just redistributes itself among the four outflow pipes.

David is proposing a paradigm shift in how a basic climate model is organized. This post is a road-map for building an alternative model.

The current paradigm starts from the assumption that reducing the outflow in one pipe is equivalent to the effect of increasing the inflow on the single incoming pipe — it is a radiation balance, where all imbalances are equivalent regardless of origin. Doubling CO2 is “equal” to 2% more sunlight. (So sayeth Hansen 1984.) The feedbacks all work through this same paradigm — all radiation imbalances are equivalent to more sunlight, the sun heats the surface, and therefore the feedbacks need only respond to surface warming. But if something else warms the atmosphere instead, there are no “feedbacks” in the conventional basic model —  the model is blind. If one of the feedbacks to atmospheric warming by CO2 was to increase the flow through the cloud tops or water vapor pipes, the current climate models could not show that, could not even “think” it.

Getting the language right from the start: Any conversation about climate models pretty much leaps straight into quicksand. The paradigm shift needs to begin with the language, and the establishment mucked up both terms: “forcings” and “feedbacks”. “Forcings” doesn’t refer to any old force that affects the Earth’s climate, rather it refers to things assumed to have the same effect as more sunlight. “Feedbacks” doesn’t mean any feedback, in establishment language it only means things that happen in response to surface warming.  By definition, the limiting language sets everyone up to get stuck in a dead-end, to think only long the lines of the current architecture.

David explains that his alternate model is a shift from adding radiation imbalances due to the various things that influence the climate (which means establishment defined “forcings”), to instead adding temperature perturbations caused by any kind of warming factor. Where the current models adds up forcings and applies the same feedbacks to the bundle, David’s model will treat each force on the climate separately and allow different feedbacks for different forces.
Solving the big-one… climate sensitivity: Any climate model is essentially one big complicated equation. In this case, the sum-of-warmings model ends up with two crucial unknowns in the one equation, so it can’t be solved. But David builds a second model on the outgoing radiation, an OLR model. Now with two equations and two variables, it can be solved, at least enough to put an upper bound on the climate’s sensitivity to CO2.

Below, David lays out the plan for assembling the new basic climate model (the “zero-D” one, not the GCMs). Remember, the point of the basic model is that it is the simple application of basic physics that gives climate scientists implacable confidence that they are basically right. They are so convinced they can’t even imagine how it could be any other way, which is why government funded science is never going to get out of this rut unless someone outside the paradigm shakes them out.

— Jo

 

Energy escaping from Earth, Dam, Four Pipes, Radiation, OLR

“Dunno”, says the Minister of Dams,  “We blocked off part of that pipe, but the dam is hardly getting any fuller?”

 

11. An Alternative Modeling Strategy

Dr David Evans, 14 October 2015, David Evans’ Basic Climate Models Home, Intro, Previous, Next, Nomenclature.

This post discusses the strategy used to develop an alternative model, one which fixes or ameliorates all the aforementioned problems with the conventional basic climate model — namely applying the solar response to non-solar climate influences (post 9), omission of feedbacks that respond to climate drivers directly rather than to surface warming (post 5 and post 7), and heavy reliance on unverifiable partial derivatives (post 4). The improvements come at the cost of requiring more climate data.

A New Organizing Principle

The conventional basic climate model is organized around a radiation balance: it adds the radiation imbalance (“forcing”) caused by each climate driver, to produce a total radiation imbalance. Due to the conventional interchangeability of climate drivers (post 9), this total radiation imbalance is equivalent, before feedbacks, to a net increase in absorbed solar radiation (ASR). The surface warming is then calculated, as that required under the Planck conditions* to eliminate this imbalance with a net increase in outgoing longwave radiation (OLR), after feedbacks are applied. This leads to the architecture shown in Fig. 2 of post 3 or, equivalently, Fig. 2 of post 9 — its nub is the adder (or summation node) shown as a big purple circle in either of those diagrams, which sums the radiation imbalances due to the various climate drivers.

That is, the essence of the conventional model is that it sums the radiation imbalances (forcings) due to the various climate influences.

The alternative model is going to use a different organizing principle:  it instead adds the perturbation in surface temperature (“warming”) due to each climate driver, to produce a total surface warming. Its nub will be a sum of warmings. The climate is widely assumed to be linear for the small temperature perturbations involved in global warming, so the temperature perturbations due to the various climate drivers are independent and superpose — that is, we can work out the warming due to each driver independently of what else is happening, and the total warming is just the sum of the individual warmings. By the assumed linearity, the effects of one climate driver on other drivers are only second order.

That is, the essence of the alternative model is that it sums the temperature perturbations (warmings) due to the various climate influences.

For example, suppose we are considering two climate drivers:  an increase in total solar irradiance (TSI) and/or externally driven albedo (EDA), and an increase in CO2. Quite independently of each other, we compute the two warmings:

The surface warming due to ASR is then added to the surface warming due to CO2, to obtain the total surface warming. (To complete the computation, there is also some extra ASR due to albedo feedbacks to surface warming, etc., in a feedback loop.)

Put simply, if there is increasing CO2 and increasing ASR, then:

The change from the conventional model to the alternative model might qualify as a paradigm shift (though that terms is much overused).

Sum-of-Warmings Model

The major advantage of the sum-of-warmings approach is that it allows tailored responses to different climate influences — a response specifically for CO2 is applied to the influence of CO2, while the solar response is still applied to the increase in ASR. In contrast, the conventional sum-of-forcings approach problematically applies the solar response to all climate drivers — one size fits all, see post 9.

The sum-of-warmings approach fixes both major flaws with the conventional architecture:

It is important to note that the climate responses to extra ASR and to extra CO2 are fundamentally different:

Radiation Balance

Energy must balance between steady states (Eq. (1) in post 2), so the alternative model also applies a radiation balance constraint.

The radiation in the sum-of-warmings model is balanced simply by setting the increase in ASR in the model equal to the  increase in OLR. (Which is why the alternative basic climate model, like the conventional basic climate model, can only be applied between steady states.)

Solvability

The sum-of-warmings model results in one equation, in which the sum of the warmings due to the individual drivers is equated to the total surface warming.

It is assumed that the surface warming caused by increasing CO2 is proportional to the radiation imbalance caused by the increasing CO2, at least over the range of interest. Let us call that proportionality constant the “CO2 sensitivity” λC, and let it include the effect of CO2-specific feedbacks. The surface warming due to increasing CO2 is thus equal to λC times the radiation imbalance due to that increasing CO2. Thus the sum-of-warmings equation includes a single parameter that expresses the CO2 response.

Suppose the climate drivers in our model include the externally-driven albedo (EDA, post 10). The change in EDA over the last few decades is unknown; therefore the change in ASR is unknown. Happily, the radiation balance constraint equated the increase in ASR to the increase in OLR, so we do not need to know the change in ASR — but we do need to know the change in OLR.

So the single equation from the sum-of-warmings model, over an observed period in the last few decades, contains two unknown quantities:

With two unknowns, the equation is not solvable. We need another equation.

OLR Model

We can estimate the increase  in OLR over an observed period, using an OLR model. The alternative model includes an OLR model that estimates the increase in OLR from changes in the physical emissions layers:

This drags a lot more data into the calculation of the sensitivity to CO2, but it is perhaps the simplest way of determining the actual OLR, or at least bounding it.

Why don’t we use the OLR datasets directly? Basically the data isn’t good enough for our purpose. The first OLR dataset is the one at NOAA, from 1974 to 2013, perhaps most easily viewed at KNMI (set latitude -90 to 90, longitude -180 to 180, press “Make time series”). The data before 1979 is unusual and has a break, so like most satellite data more properly begins in 1979. The absolute values read low, around 232 W/m2, while the true value is probably around 239 W/m2.  The data is gridded and interpolated, and to construct a sufficiently sensitive global mean might require the assistance of the people who originally managed the dataset — to make best use of only the actual data, and knowing the sizes of the grid cells (the Earth is not quite spherical) — but they do not seem to have provided a global mean (KNMI presumably adds the gridded data, giving equal weight to interpolated and observed data, and treating the Earth as a sphere). The second dataset is the CERES global OLR, which starts in 2000 — see here (Fig. 2) and here (Fig.3 ) — so unfortunately the period is too short. We use some short recent observation periods, for which the CERES OLR figures are agreeable. A major advantage to using the OLR model, however, is that it gives a lot of insight into what is going on.

Alternative Model

Combining the sum-of-warmings model with the OLR model gives the alternative model. We join them by plugging the increase in OLR from the OLR model into the sum-of-warmings model, yielding a single equation in which the only unknown over a period of observations is λC. So we can estimate λC, and the model is complete. The model can then be used to estimate surface warming from changes in the climate drivers between steady states, and thus the equilibrium climate sensitivity (ECS).

Unfortunately the climate data is not good enough to form an estimate of the increase in OLR over the last few decades. However it is good enough to bound the increase on OLR, which is enough to put meaningful bounds on the estimated ECS. Essentially the emission-layer data puts a lower bound on the increase in OLR, which by energy balance puts a lower bound on the increase in ASR, which puts a lower bound on the component of surface warming due to the solar response (the ASR drive the solar response), which (given the observed surface warming) puts an upper bound on the surface warming due to extra CO2, which puts an upper bound on the ECS.

(In contrast, the conventional basic climate model attempts to compute the ECS while ignoring the increases in EDA, ASR, and OLR over any observed period. It just applies the solar response to the radiation imbalance caused by a doubling of CO2. Very simple, but what if the CO2 response and the solar response turn out to have quite different strengths?)

Comparison

The conventional model is based solely on a radiation balance. It calculates the ECS via a simplistic and problematic analysis primarily using laboratory physics — the Stefan-Boltzmann law (with minor modification for the difference between the Planck and Stefan-Boltzmann sensitivities), the reduction in OLR from CO2 molecules due to a doubling of CO2 (spectroscopy), and the estimated feedbacks to surface warming (which are mainly from the properties of moist air).

The alternative model is based on a sum-of-warmings model and an OLR model. Radiation balance is used to equate the changes in OLR and ASR, then these two models are combined into a joint model, from which the CO2 response can be estimated over observed periods. The ECS can then be estimated as the CO2 response to a doubling of CO2. Thus it calculates the ECS using a mix of laboratory physics and observed climate data.

Over the next few posts we’ll present the sum-of-warmings model, then the OLR model, then the joint model.

 

*Planck conditions (see post 9): All else besides tropospheric temperatures and OLR are held constant — there are no feedbacks, all tropospheric temperatures (including the surface temperature) change in unison, and stratospheric temperatures are unchanged (Soden & Held, 2006, pp. 3355-56). These are the conditions under which the Planck feedback or sensitivity applies.

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