The Solar Series: I Background | II: The notch filter | III: The delay | IV: A new solar force? | V: Modeling the escaping heat (You are here). | VI: The solar climate model | VII — Hindcasting | VIII — Predictions
David Evans has analyzed the black box system that is effectively “Sunlight In, Temperature Out”, and found a notch, a delay, and a low pass filter. The problem then is to work out their order and to fill in any other bits needed by the model. This post then, doesn’t have big blockbuster moments (sorry), but these points need to be said.
Energy leaves Earth through a range of electromagnetic frequencies, but the bulk of them can be grouped into three main “pipes”. Radiation either comes directly off the land, oceans, ice and what-not on the ground, or it leaves via the atmosphere. Up in the air, carbon dioxide and water molecules do most of the work sending emissions of infra red to outer space. In the atmosphere, the radiating “surface” is a virtual concept and is effectively at different heights for different greenhouse gases. This is all non-controversial stuff, but a little difficult to see in your head. The three pipes are from the ground, from CO2 and from H2O.
The next problem is that people have measured surface temperature (which is fair enough), and this is what the solar model is aiming to model. But it’s not the same temperature as the temperature of the complex “surface” that is radiating to space. The two layers are tied together in a sense. If the ground surface warms, the radiating surface will warm but not by quite as much. That means any model needs to understand the relationship between changes in the temperature of the radiating layers and the temperature on the ground (and on the seven seas). I’m sorry for anyone looking for a dog-fight here, but the multiplier in the Solar Model is boringly almost the same as the standard one used by mainstream climate scientists. We call it the RATS multiplier (Radiative Amplification To Surface) and its value is about 2.
Basically if it warms by 1 degree on the surface the RATS multiplier tells us it has warmed by about 0.5 degrees on the radiating “surface”. There were times when we thought it would be different, but it did indeed end up being about the same as the mainstream estimates. This is non-controversial stuff, but it’s important, and we’ll be referring back to the RATS multiplier and more importantly to the Three Pipes. – Jo
Modeling the Atmosphere
This post is the second of the three posts in which we build the solar model. We already assembled a notch filter, a delay filter, and a low pass filter in cascade in part III, and in part IV we took a diversion to physically interpret the notch and the delay.
The output of the low pass filter is the record of changes in the effective temperature at which the Earth radiates to space, the “radiating temperature”. We then consider how the model will compute the changes in surface temperature from the changes in radiating temperature. It turns out to require just a very simple model of the atmosphere.
The output of the low pass filter is the temperature of the surface of the Earth that radiates directly to space. This “radiating surface” is a virtual surface, consisting of different physical surfaces at different electromagnetic frequencies of radiation.
At the electromagnetic frequencies that are absorbed and emitted by carbon dioxide, the surface of the Earth is at the “one optical depth” of the carbon dioxide, where an observer from space is looking through sufficient carbon dioxide that they cannot “see” below that layer, on average. The carbon dioxide emissions layer is about 8 km up in the atmosphere at the tropics. It is effectively where all emissions from Earth direct to space at the carbon dioxide frequencies occur, because, on average, emissions below this layer are absorbed by the carbon dioxide (space cannot see those emitting carbon dioxide molecules, so they cannot see space).
The electromagnetic frequencies of the “atmospheric window” are those that pass through the atmosphere unimpeded. At these frequencies, emissions direct to space come from the surface of the Earth.
At the emissions and absorption frequencies of water vapor (which is the main greenhouse gas), the emissions layer is on average about 10 km up in the atmosphere at the tropics.
There are also other emissions layers for other greenhouse gases, but in this simple analysis we’ll ignore them because their effect is small.
Nearly all the heat lost by Earth goes through one of these three “pipes” to space, a “pipe” being a group of electromagnetic frequencies with the same emissions layer. The amount of energy flowing to space through each pipe increases with the temperature of its emission layer.
The “radiating temperature” of the Earth is the effective temperature of the radiating surface, and is simply the temperature as computed by the Stefan-Boltzmann equation for the emissions given off by the Earth. The temperature changes of the radiating surface are some sort of weighted average of the temperatures changes of the main three emissions layers.
The RATS (Radiative Amplification To Surface) Multiplier
The low pass filter computes the changes in the radiating temperature, that is, the temperature changes that determine how much heat is radiated to space. But the output of the solar model is not this temperature, but the temperature at the surface. So how can the model compute the changes in surface temperature from the changes in radiating temperature?
Changes in the temperature of the radiating surface are basically transmitted down through the atmosphere to the surface. At the frequencies of the atmospheric window the radiating surface is also the surface of the Earth so no transmission is required, but at the carbon dioxide and water vapor frequencies the transmission is literally down through the atmosphere.
As it happens, the solar radiation datasets we are using are all deseasonalized—because they measure the solar radiation at a constant distance from the Sun (of 1 AU, the average distance of the Earth from the Sun). Because our solar model is going to be driven by these datasets, it is oblivious to anything on a time scale of less than a year, such as seasons. The atmosphere acts and reacts relatively quickly—usually within days, always within weeks. So from the point of view of our solar model, the atmosphere acts instantly and therefore it can be modeled simply as a multiplier. So on the one hand our model is limited to timescales of a year or more, but on the other it sidesteps most of the complexity in the atmosphere.
The output of the low pass filter is a record of changes in the temperature of the radiating surface, which is around 255 K. The output of the solar model is a record of changes in the temperature at the surface of the Earth, which is around 288 K. The RATS (Radiative Amplification To Surface) multiplier connects them: the changes in (surface) temperature are equal to the changes in radiating temperature multiplied by the RATS multiplier, on the timescales of our model.
Later, fitting the notch-delay solar model to measured temperatures finds the RATS multiplier is most likely 2.1 (but definitely between 1 and 5). Mainstream climate science reckons the value is about two, so there is agreement there.
(The name “RATS” is coined here. The mainstream value is their value of the feedbacks for the sensitivity of climate to any exogenous forcings (note that this is after a Stefan-Boltzmann conversion from forcing to temperature, and that the value of the low pass filter for the long term (that is, at very low frequencies) is the value given by the Stefan Boltzmann equation). However the RATS multiplier does not apply to any reduction in outgoing heat in the CO2 pipe due to an increase in the CO2 concentration. We shall explain this in detail in a later post, but for now we are just focusing on building the solar model.)
In the next post we will finish off building the “notch-delay solar model”, as this solar model is called. [And then the fun will really begin says Jo]
Notch-delay solar project home page, including links to all the articles on this blog, with summaries.