Guest Post by Willis Eschenbach
In my recent post “Put it in reverse“I discussed the relationship between temperature and total surface radiation absorbed. By “total absorbed surface radiation”, I mean the total long-wave radiation from the clouds and atmosphere, plus sunlight falling at the surface, minus sunlight reflected from above.
Here is an image from that post. If you haven’t read it yet, you can do so as an introduction to this post. However, it is not necessary as this one stands on its own.
Original Notes: Figure 1: Gridcell by correlation between surface absorbed radiation (short wave + long wave) and surface temperature. Gridcells are 1° latitude x 1° longitude.
In this post, I focused on the radiation balance at the surface — the amount of radiation absorbed versus the amount emitted. I did this because it is a very simple and transparent part of the whole. There is no intermediate step – the surface absorbs radiation, it warms up and emits radiation.
According to CERES satellite data, according to a 24/7 global average, the heat radiation from homes (directed into space) from the surface is just under 400 watts per square meter (W/m2). The thermal radiation from the clouds/atmosphere absorbed by the surface is about 345 W/m2. And net solar (lighting down to the surface is less surface reflective) the energy absorbed by the surface is just under 165 W/m2.
This gives a global 24/7 average of just over 500 W/m2, about half a kilowatt/m2, radiation absorbed by the surface.
But only about 400 W/m2 is radiated away. What about the other 100 W/m2 of absorbed energy?
First, something on the order of 3/4 of that energy is used to vaporize water from the surface. It is called “latent heat”. This, of course, leaves the surface cooler than it would otherwise have been for the potential heat loss.
The remaining quarter is lost through conduction into the atmosphere and subsequent convection away from the surface. It’s called “reasonable heat”. This also makes the surface cooler than usual without losing heat.
Below is a scatter plot showing the relationship and trend of the surface radiation emitted from the upper stratum to the absorbed lower layer radiation.
Figure 2. Scatterplot, where each dot is a month. For each month, the bottom “X” scale indicates the radiation absorbed in that month, and the vertical “Y” scale indicates the radiation emitted in that same month. Seasonal variation was removed from the data in all graphics.
Figure 2 shows that for every watt per square meter absorbed, only 3/4 of the watt per square meter is emitted as cascade radiation from the surface. The rest goes to a state of reasonable and latent heat loss. (Yes, there is a very small residual, less than 1/2%, of energy from/to storage, mainly in the ocean. However, because it is so small, it is often ignored in this type of analysis. this top.)
So… why does this matter?
Well, around 1880, some very clever people named Joseph Stefan and Ludwig Boltzmann discovered that there was a mathematical relationship between the temperature of an object and its thermal radiation. The relationship is given by the “Stefan-Boltzmann Law”. Using that law, if you know the radiation you can calculate the temperature and vice versa. Figure 3 shows the same data as in Figure 2, but this time I used Stefan-Boltzmann’s Law to convert the raised surface radiation in Figure 2 into temperature. So, in Figure 3, the “Y” axis is vertical in degrees Celsius.
Figure 3. Scatterplot, where each dot represents a month. For each month, the bottom “X” scale shows the radiation absorbed for that month, and the vertical “Y” scale shows the temperature for that same month.
This is because since only part of the absorbed radiation converts to longwave emission at the surface (AKA temperature), almost 7 watts per square meter of energy is needed to raise the left surface temperature. soil add 1°C.
And that’s a lot. A doubling of CO2 levels in the atmosphere is thought to increase laminar radiation by 3.7 W/m2. So if that extra energy to raise the temperature by 1°C came only from the increased CO2, it would be almost double our current 410 ppmv CO2. The CO2 level would have to be ~1,500 ppmv for a 1°C increase from the current temperature.
Here is a graph showing how closely the surface temperature and the absorbed radiation on the surface are.
Figure 4. Total radiation absorbed at the surface (blue scale, right) compared to temperature (red, left scale). Total irradiance is the sum of longwave radiation (heat) from the atmosphere, plus shortwave radiation (solar). Also shown is the theoretical forced increase in CO2 over time (yellow/black line), and the trend of total radiation absorbed (cyan/black dashed line). Horizontal black dashed line, showing what would happen without an increase in surface absorbed radiation.
Obviously, more CO2 is happening… I will leave all of this here for further reflection and discussion.
Evening now, dinner here on the hillside. Three generations live here in a ramshackle house built by myself. We eat together every night. Mine gorgeous ex-fiancée and I make our dinner. Our daughter made dinner for her husband and two children, a 3 year old girl and a 10 month old boy. Works perfectly, we can all eat together and I will starve what they eat…
This is my ex-fiancée at the moment as seen from my window, tending to her beloved garden…
With the hope that your life contains true joy, laughter, family, friends and loved ones, I still,
Yr. Obt. Svt.,
w.
Note Math 01: As usual in the field, I used an emissivity of 1.0 to convert the radiation to temperature. I could fine-tune that, but a) Earth’s emissivity is quite high, on the order of 0.95 or more, and b) changing emissivity changes the absolute values, but it produces very very little difference to the trends of interest.
Problem 02: Since there is uncertainty in the “X” (total absorbed radiation) axis values in Figures 2 and 3, I used Deming Regression to determine the exact trend, instead of Least Squares Regression It is common to underestimate trends when there is uncertainty. And if you don’t know what Deming regression is, don’t worry — most people don’t, including most climate scientists.
My Note: When you comment, please quote the exact words you are responding to. This avoids many misunderstandings. It’s also the only way to refute someone’s idea.
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