In this article in the series we will look an interesting paper:

*An analysis of the dependence of clear-sky top-of-atmosphere outgoing longwave radiation on atmospheric temperature and water vapor*, by Dessler, Yang, Lee, Solbrig, Zhang and Minschwaner, JGR (2008).

This paper can be downloaded for free.

I used some results of this paper in Theory and Experiment – Atmospheric Radiation, but only for comparing calculated top of atmosphere radiative fluxes vs measurement.

I think that the “basic physics” of radiative transfer and atmospheric convection is challenging enough, and the question of feedback even harder.

There are hundreds of papers (thousands really) on this confusing subject and so, for me, drawing conclusions requires a lot of research. Luckily, most people interested in the climate debate already know the answer to the question of feedback from water vapor, so this article won’t be so interesting to them.

In fact, the paper under review doesn’t claim any real answers in the subject of water vapor feedback with climate change:

We are looking at regional variations in lapse rate in a fixed climate, rather than variations in the average lapse rate as the climate changes. This result demonstrates the unsuitability of using variations in different regions in our present climate as a proxy for climate change.

But even with the guarded comments of a published paper, the results are very interesting – and help, at the very least, to **illuminate **some aspects of how water vapor and atmospheric temperature interact to change the radiative cooling from the planet.

So for people looking for a quick answer, it’s not here. For people wanting to understand the interaction between surface temperature, atmospheric temperature, water vapor and outgoing longwave radiation (OLR) – this might provide a few insights on their journey.

### Background

In trying to understand feedback we want to know what happens to the outgoing longwave radiation (OLR) from the climate as surface temperature changes.

Some basic (but hard to calculate) radiative physics – already covered in many places including CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers (and the preceding parts of the series) – tells us that, all other things being equal, a doubling of CO2 in the atmosphere from pre-industrial levels will lead to a surface temperature change of about 1°C.

Apart from other variability – how will the climate respond to this increase in surface temperature?

*It is only by isolating different causes and effects that we can hope to understand the complexity of the climate. It’s slow but there is more chance of getting the correct answer.*

The main miscreant identified as possibly causing a much higher than 1°C increase is water vapor feedback. Water vapor is the dominant “greenhouse” gas, but is variable in space and time as it responds to climate conditions. See, for example, Clouds and Water Vapor – Part Two.

When we think about feedback, one of the most important considerations is how OLR responds to a change in surface temperature.

Let’s consider the change in surface radiation when the temperature increases by 1°C. Most of the earth’s surface has an emissivity very close to 1. At 15°C the increase in surface radiation for this 1°C increase, ΔR = 5.5 W/m². So if the OLR **also increased **by 5.5 W/m² then the **feedback** from the climate would be zero. (*See comment below for why this is not quite correct*).

Why? Because all of the increase in surface radiation has also been emitted from the climate system into space. Picture the scene if instead 10 W/m² was emitted into space after this 1°C increase in surface temperature – this would be negative feedback.

And if the OLR change was 1 W/m² ? This would be positive feedback. Because the increase in radiation from the surface wasn’t matched by radiation from the climate system.

If this doesn’t make sense, ask a question. It’s hard to make progress without grasping this point.

### Measurements and “Model”

Dessler compares the results of over 100,000 measurements of top of atmosphere (TOA) fluxes from the CERES satellite with two band models which provide computational efficiency (see note 1).

*Figure 1 – Comparison of a band model with measured results*

This is simply to demonstrate that **the model** for calculating TOA fluxes is reliable and accurate. The results are used for later calculations. Other graphs in the paper compare the results against surface temperature and latitude to confirm that no bias exists in the results.

Atmospheric temperature and water vapor are measured using **AIRS** – Atmospheric Infrared Sounder flying on the NASA Aqua satellite. **CERES **= “Clouds and the Earth Radiant Energy System”, which is also flying on the Aqua satellite.

The measurements taken by AIRS and CERES are “virtually simultaneous”.

These measurements were all taken in March 2005 between 70°N and 70°S over the ocean under clear skies.

The measurements were selected from nighttime measurements. Why? To eliminate any contribution around the 4μm wavelength from solar radiation.

### A Basic Equation

Equations aren’t fun for a lot of people and that’s understandable. Stay with me, I will try and explain it in plain English.

What we want to know is how OLR (radiation from the climate to space) changes as surface temperature changes. If we can establish this, we can understand how the climate currently responds to surface temperatures – and what feedbacks are **currently **in place, at least for the time under consideration:

*Figure 2 – The equation*

The red term is the main value we want to know – the “rate of change” of OLR with surface temperature

Or, how much does the outgoing longwave radiation change as surface temperature changes?

The orange term = the sum (vertically through the atmosphere) of all the changes in OLR as surface temperature changes, **due** to the change in **atmospheric **temperature

The green term = the sum (vertically through the atmosphere) of all the changes in OLR as surface temperature changes, **due** to the change in **water vapor**

And before we “dive in”, the basic concepts are, in simple terms:

- if the atmosphere gets warmer it radiates more to space – and this
**cools**the climate - if water vapor increases it reduces the OLR (because it is a “greenhouse” gas) – and this
**heats**the climate (because less radiation to space takes place) - if water vapor increases it reduces the “lapse rate” (note 2), making the atmosphere warmer higher up, increasing radiation to space – and this
**cools**the climate

Now let’s take a look at the graphical picture of how atmospheric temperature and humidity vary with surface temperature and height. Think of surface temperature as a proxy for latitude.

Here is how the air temperature vs height, and humidity vs height, vary with surface temperature:

*Figure 3 – Measurements*

For those new to humidity measurements in the atmosphere, note the strong dependency on surface temperature and on height in the atmosphere (1000hPa is the surface and 200hPa is around 12km above the surface).

Now we want to plot two of the terms in the equation (figure 2). *The colors are matched up with the highlighted terms in the original equation*.

*Figure 4 – Calculated – Color text added*

These values are **calculated **by using the model. (We have already seen that this band model accurately calculates the OLR from surface temperature, air temperature and humidity).

As you would expect, when air temperature increases by 1K the OLR increases – because a **hotter** atmosphere radiates at a higher intensity. This is with all other conditions held the same.

And as you might expect, when the humidity is increased by 10% the OLR decreases – because a more **opaque** atmosphere has a lower transmittance to surface radiation. This is with all other conditions held the same.

We have been calculating these terms from figure 2:

Now, find how OLR changes due to **surface temperature changes **we need to also find out these terms:

Or, in English:

- the change in air temperature due to surface temperature changes
- the change in humidity due to surface temperature changes.

*Figure 5 – Measured – Color text added*

So, to give an example of what these graphs show, we can see that at around 293-294K, an increase in surface temperature has little or no effect on humidity. Around 300K an increase in surface temperature has a large effect on humidity.

Now we are going to multiply the terms together to find:

- the change in OLR with surface temperature – due to atmospheric temperature changes
- the change in OLR with surface temperature – due to humidity changes

*Figure 6 – Results – Color text added*

The advantage of this method is that when we look at the summary and say, for example:

Oh that’s interesting, the strongest positive feedback effects are around 302 K, what causes that? The strongest negative feedback effects are around 290 – 295 K, what causes that?

- we can review the terms that created the result and see which dominates – *and why*.

Looking at the total, we can see that between 298 – 303 K the **OLR decreases as surface temperature increases** (note that the plot is of the change in OLR as Ts increases versus Ts). And below 298 K the OLR increases as surface temperature increases.

This is in agreement with Raval & Ramanathan’s work based on ERBE data shown in Part One where the positive feedback comes from the tropics, and is reduced by the negative feedback from the sub-tropics and mid-latitudes.

The decrease of OLR as surface temperature increases became known as the **super-greenhouse effect**. Remember that any effect below an increase of 5.5W/m².K (at 15°C) is a positive feedback. (And at 30°C, this threshold value is 6.3W/m².K). An actual decrease of OLR as surface temperature increases is, therefore, a very strong positive feedback effect.

We can see the result plotted against surface temperature and height – now let’s see the total value against surface temperature, and some comparisons of the actuals vs reference scenarios:

*Figure 7 – Color text and highlighting added*

The first graph shows the change in OLR with surface temperature – due to atmospheric temperature changes. The blue line shows the result **if** the lapse rate was fixed. Remember that a **lower** value of changing OLR with Ts is more towards **positive feedback.**

This is a quantitative estimate of the effect of the changing lapse rate on dOLR/dTs, and it shows that it is negative for almost all values of Ts. In other words, as Ts increases, so does the lapse rate, and the general effect of this is to reduce dOLR/dTs, and therefore OLR, below what they would be if the atmosphere maintained a constant lapse rate.

The second graph shows the change in OLR with surface temperature – due to humidity changes. The purple line shows the result **if** relative humidity was constant. (And see the results from Sun & Oort, shown in Part Three).

In the subtropics, the ‘‘changing RH’’ line is positive, meaning that RH decreases with increasing Ts. This relative dryness contributes to high values of OLR here, providing a key pathway for the climate system to lose energy back to space. As Ts crosses the convective threshold, ≈298 K, the RH of the atmosphere abruptly increases, leading to a strong increase in q and a reduction in OLR and its gradient.

The third graph compares the results by using the data graphed in Figure 1 with the results derived through this article – and they are the same.

We also plot in this panel the right-hand side of equation (1):

Σ

_{i}(∂OLR/∂T_{i})(∂T_{i}/∂Ts) + Σ_{i}(∂OLR/∂q_{i})(∂q_{i}/∂Ts) + ∂OLR/∂Ts,derived from lines plotted in Figures 8a and 8b. As one can clearly see, the agreement is excellent. Note that this is a stringent test as these two lines are derived from completely independent data: one line is derived entirely from CERES data while the other line is derived entirely from AIRS data and a radiative transfer model. The excellent agreement gives us great confidence that, given observations of Ta and q, the clear-sky OLR budget is well understood inthe present atmosphere. We also see no evidence that neglected terms are important, in agreement with previous work..

### Conclusion

The paper gives us an excellent insight into how atmospheric temperature and humidity vary as surface temperature varies – over the ocean. And how this maps into changes in OLR as surface temperature changes.

We see that the results are similar to Ramanathan’s work shown in Part One.

These are valuable insights.

If surface temperature increases from any cause, does this mean that positive feedback from water vapor will amplify this? If surface temperature reduces from any cause, does this mean that positive feedback from water vapor will amplify this?

Surely that depends.

But ask yourself this – if the results had shown the opposite effect, would you find them significant?

### Articles in this Series

Part One – introducing some ideas from Ramanathan from ERBE 1985 – 1989 results

Part One – Responses - answering some questions about Part One

Part Two - some introductory ideas about water vapor including measurements

Part Three - effects of water vapor at different heights (non-linearity issues), problems of the 3d motion of air in the water vapor problem and some calculations over a few decades

Part Five – Back of the envelope calcs from Pierrehumbert - focusing on a 1995 paper by Pierrehumbert to show some basics about circulation within the tropics and how the drier subsiding regions of the circulation contribute to cooling the tropics

Part Six – Nonlinearity and Dry Atmospheres - demonstrating that different distributions of water vapor yet with the same mean can result in different radiation to space, and how this is important for drier regions like the sub-tropics

Part Seven – Upper Tropospheric Models & Measurement - recent measurements from AIRS showing upper tropospheric water vapor increases with surface temperature

### Notes

**Note 1**: See CO2 – An Insignificant Trace Gas? Part Four for more explanation of “band models”. A “model” doesn’t mean “GCM”. In this case it simply means a more efficient way of calculating the TOA flux than using “line by line” calculations in the radiative transfer equations.

The HITRANS database contains 2.7M spectral lines and so “doing it the long way” takes a lot of time. Therefore, over time, many band models have been created – and critically evaluated – against the hard way.

**Note 2**: The lapse rate is the decrease in temperature as you go up through the atmosphere. In a dry atmosphere the temperature reduces at around 10K/km. In a very moist atmosphere the temperature reduces at around 4K/km. And, on average, the lapse rate is 6.5K/km. So the more water vapor there is in the atmosphere, the warmer the atmosphere at any given height.