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Archive for the ‘Feedback’ Category

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:

from Dessler (2008)

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.

From Dessler (2008)

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.

From Dessler (2008)

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):

Σi(∂OLR/∂Ti)(∂Ti/∂Ts) + Σi(∂OLR/∂qi)(∂qi/∂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.

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In Part One we had a look at Ramanathan’s work (actually Raval and Ramanathan) attempting to measure the changes in outgoing longwave radiation vs surface temperature.

In Part Two (Part Zero perhaps) we looked at some basics on water vapor as well as some measurements. The subject of the non-linear effects of water vapor was raised.

Part One Responses attempted a fuller answer to various questions and objections about Part One

Water vapor feedback isn’t a simple subject.

First, a little more background.

Effectiveness of Water Vapor at Different Heights

Here are some model results of change in surface temperature for changes in specific humidity at different heights:

From Shine & Sinha (1991)

From Shine & Sinha (1991)

For newcomers, 200mbar is the top of the troposphere (lower atmosphere), and 1000mbar is the surface.

You can see that for a given increase in the mixing ratio of water vapor the most significant effect comes at the top of the troposphere.

The three temperatures: cool = 277K (4°C); average = 287K (14°C); and warm = 298K (23°C).

Now a similar calculation using changes in relative humidity:

From Shine & Sinha (1991)

From Shine & Sinha (1991)

The average no continuum shows the effect without the continuum absorption portion of the water vapor absorption. This is the frequency range between 800-1200 cm-1, (wavelength range 12-8μm) – often known as the “atmospheric window”. This portion of the spectral range is important in studies of increasing water vapor, something we will return to in later articles.

Here we can see that in warmer climates the lower troposphere has more effect for changes in relative humidity. And for average and cooler climates, changes in relative humidity are still more important in the lower troposphere, but the upper troposphere does become more significant.

(This paper, by Shine & Sinha, appears to have been inspired by Lindzen’s 1990 paper where he talked about the importance of upper tropospheric water vapor among other subjects).

So clearly the total water vapor in a vertical section through the atmosphere isn’t going to tell us enough (see note 1). We also need to know the vertical distribution of water vapor.

Here is a slightly different perspective from Spencer and Braswell (1997):

Spencer and Braswell (1997)

Spencer and Braswell (1997)

This paper took a slightly different approach.

  • Shine & Sinha looked at a 10% change in relative humidity – so for example, from 20% to 22% (20% x 110%)
  • Spencer & Braswell said, let’s take a 10% change as 20% to 30% (20% + 10%)

This isn’t an argument about how to evaluate the effect of water vapor – just how to illustrate a point. Spencer & Braswell are highlighting the solid line in the right hand graph, and showing Shine & Sinha’s approach as the dashed line.

In the end, both will get the same result if the water vapor changes from 20% to 30% (for example).

Boundary Layers and Deep Convection

Here’s a conceptual schematic from Sun and Lindzen 1993:

The bottom layer is the boundary layer. Over the ocean the source of water vapor in this boundary layer is the ocean itself. Therefore, we would assume that the relative humidity would be high and the specific humidity (the amount of water vapor) would be strongly dependent on temperature (see Part Two).

Higher temperatures drive stronger convection which creates high cloud levels. This is often called “deep convection” in the literature. These convective towers are generally only a small percentage of the surface area. So over most of the tropics, air is subsiding.

Here is a handy visualization from Held & Soden (2000):

Held and Soden (2000)

Held and Soden (2000)

The concept to be clear about is within the well-mixed boundary layer there is a strong connection between the surface temperature and the water vapor content. But above the boundary layer there is a disconnect. Why?

Because most of the air (by area) is subsiding (see note 2). This air has at one stage been convected high up in the atmosphere, has dried out and now is returning back to the surface.

Subsiding air in some parts of the tropics is extremely dry with a very low relative humidity. Remember the graphs in Part Two – air high up in the atmosphere can only hold 1/1,000th of the water vapor that can be held close to the surface. So air which is saturated when it is at the tropopause is – in relative terms – very dry when it returns to the surface.

Therefore, the theoretical connection between surface temperature and specific humidity becomes a challenging one above the boundary layer.

And the idea that relative humidity is conserved is also challenged.

Relationship between Specific Humidity and Local Temperature

Sun and Oort (1995) analyzed the humidity and temperature in the tropics (30°S to 30°N) at a number of heights over a long time period:

Sun and Oort (1995)

Sun and Oort (1995)

Note that the four graphs represent four different heights (pressures) in the atmosphere. And note as well that the temperatures plotted are the temperatures at that relevant height.

Their approach was to average the complete tropical domain (but not the complete globe) and, therefore, average out the ascending and descending portions of the atmosphere:

Through horizontal averaging, variations of water vapor and temperature that are related to the horizontal transport by the large-scale circulation will be largely removed, and thus the water vapor and temperature relationship obtained is more indicative of the property of moist convection, and is thus more relevant to the issue of water vapor feedback in global warming.

In analyzing the results, they said:

Overall, the variations of specific humidity correlate positively at all levels with the temperature variations at the same level. However, the strength of the correlation between specific humidity variations and the temperature variations at the same level appears to be strongly height dependent.

Sun & Oort (1995)

Sun & Oort (1995)

Early in the paper they explained that pre-1973 values of water vapor were more problematic than post-1973 and therefore much of the analysis would be presented with and without the earlier period. Hence, the two plots in the graph above.

Now they do something even more interesting and plot the results of changes in specific humidity (q) with temperature and compare with the curve for constant relative humidity:

Sun & Oort (1995)

Sun & Oort (1995)

The dashed line to the right is the curve of constant relative humidity. (For those still trying to keep up, if specific humidity was constant, the measured values would be a straight vertical line going through the zero).

The largest changes of water vapor with temperature occur in the boundary layer and the upper troposphere.

They note:

The water vapor in the region right above the tropical convective boundary layer has the weakest dependence on the local temperature.

And also that the results are consistent with the conceptual picture put forward by Sun and Lindzen (1993). Well, it is the same De-Zheng Sun..

Vertical Structure of Water Vapor Variations

How well can we correlate what happens at the surface with what happens in the “free troposphere” (the atmosphere above the boundary layer)?

If we want to understand temperature vertically through the atmosphere it correlates very well with the surface temperature. Probably not a surprise to anyone.

If we want to understand variations of specific humidity in the upper troposphere, we find (Sun & Oort find) that it doesn’t correlate very well with specific humidity in the boundary layer.

Sun & Oort (1995)

Sun & Oort (1995)

Take a look at (b) – this is the correlation of local temperature at any height with the surface temperature below. There is a strong correlation and no surprise.

Then look at (a) – this is the correlation of specific humidity at any height with the surface specific humidity. We can see that the correlation reduces the higher up we go.

This demonstrates that the vertical movement of water vapor is not an easy subject to understand.

Sun and Oort also comment on Raval and Ramanathan (1989), the source of the bulk of Clouds and Water Vapor – Part One:

Raval and Ramanathan (1989) were probably the first to use observational data to determine the nature of water vapor feedback in global warming. They examined the relationship between sea surface temperature and the infrared flux at the top of the atmosphere for clear sky conditions. They derived the relationship from the geographical variations..

However, whether the tropospheric water vapor content at all levels is positively correlated with the sea surface temperature is not clear. More importantly, the air must be subsiding in clear-sky regions. When there is a large-scale subsidence, the influence from the sea is restricted to a shallow boundary layer and the free tropospheric water vapor content and temperature are physically decoupled from the sea surface temperature underneath.

Thus, it may be questionable to attribute the relationships obtained in such a way to the properties of moist convection.

Conclusion

The subject of water vapor feedback is not a simple one.

In their analysis of long-term data, Sun and Oort found that water vapor variations with temperature in the tropical domain did not match constant relative humidity.

They also, like most papers, caution drawing too much from their results. They note problems in radiosonde data, and also that statistical relationships observed from inter-annual variability may not be the same as those due to global warming from increased “greenhouse” gases.

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 Four – discussion and results of a paper by Dessler et al using the latest AIRS and CERES data to calculate current atmospheric and water vapor feedback vs height and surface temperature

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

References

How Dry is the Tropical Free Troposphere? Implications for Global Warming Theory,
Spencer & Braswell, Bulletin of the American Meteorological Society (1997)

Humidity-Temperature Relationships in the Tropical Troposphere, Sun & Oort, Journal of Climate (1995)

Distribution of Tropical Tropospheric Water Vapor, Sun & Lindzen, Journal of Atmospheric Sciences (1993)

Sensitivity of the Earth’s Climate to height-dependent changes in the water vapor mixing ratio, Shine & Sinha, Nature (1991)

Some Coolness concerning Global Warming, Lindzen,Bulletin of the American Meteorological Society (1990)

Notes

Note 1 – The total amount of water vapor, TPW ( total precipitable water), is obviously something we want to know, but we don’t have enough information if we don’t know the distribution of this water vapor with height. It’s a shame, because TPW is the easiest value to measure via satellite.

Note 2 – Obviously the total mass of air is conserved. If small areas have rapidly rising air, larger areas will have have slower subsiding air.

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After posting Part Two on water vapor, some people were unhappy that questions from Part One were not addressed.

I have re-read through the many comments and questions and attempt to answer them here. I ignore the questions unrelated to the feedbacks of water vapor and clouds – like the many questions about the moon, answered in Lunar Madness and Physics Basics. I also ignore the personal attacks from a commenter that my article(s) was/were deceptive.

The Definition

The major point from the perspective of a few commenters (including critics of Part Two) was about the radiometric definition of the “greenhouse” effect.

Ramanathan analyzed the following equation:

F = σT4 – G

where F is outgoing longwave radiation (OLR) at top of atmosphere (TOA), T is surface temperature, and G is the “greenhouse” effect.

For newcomers, F averages around 240 W/m² (and higher in clear sky conditions).

The first term on the right, σT4, is the Stefan-Boltzmann equation which calculates radiation from a surface from its temperature, e.g., for a 288K surface (15°C) the surface radiation = 390 W/m².

If the atmosphere had no radiative absorbers (no “greenhouse” effect) then F= σT4, which means G=0. See The Hoover Incident.

The approach Ramanathan took was to find out the actual climate response over 1988-89 from ERBE scanner data. What happens to the parameters F and G when temperature increases?

Why is it important?

If increasing CO2 warms the planet, will there be positive, negative or no feedback from water vapor? Apparently, Ramanathan thought that analyzing the terms in the equation under changing conditions could shed some light on the subject.

However, the equation itself was brought into question, mainly by Colin Davidson, in a number of comments including:

..In the section “Greenhouse Effect and Water Vapour”, he introduces an equation:

F = σTs^4 – G

I didn’t understand what this equation was trying to say. How are the Surface Radiation and the Outgoing Long Range Radiation linked, noting that there are other fluxes from the Surface into the Atmosphere? And one of these (evaporation) is stronger than the NET Surface radiation, while direct Conduction is also a significant flux?
The sentence “So the radiation from the earth’s surface less the “greenhouse” effect is the amount of radiation that escapes to space.” is not accurate.

Missing from this sentence are the following:
Incoming Solar Radiation Absorbed by the Atmosphere(A);
Evaporated Water from the Surface(E);
Direct Conduction from Surface to Atmosphere(C)
Back-Radiation from Atmosphere to Surface (B)

Writing down the fluxes for the atmosphere as a black box:
F= A+(S-B)+E+C (where S=Stephan-Boltzmann Surface Radiation),
Making G = S-F = B-A-E-C

So G doesn’t appear to me to make much PHYSICAL sense, and is certainly NOT the “Greenhouse Effect”, as the evaporative and conductive species are not greenhouse animals, but B and A certainly belong in the zoo..

And:

..I have shown that both those claims are incorrect. G does not represent the “Greenhouse” effect of an IR active atmosphere, as it contains terms (Evaporation and Conduction) which are plainly IR insensitive, nor does it represent the upward surface flux less the amount of longwave radiation leaving the planet.

What G represents is anyone’s guess, but it is not an easily identifiable physical quantity.

Hence my problem with the equation F=S-G as a starting point for any analysis – it doesn’t seem to represent anything coherent. Why not start with the TOA balance, the Surface balance, or the Atmospheric balance?

I am concerned about this. Is the whole theorem of climate sensitivity based on the incorrect notion that the factor G represents the Greenhouse Effect?

As well as:

In this post I summarise some of my concerns.

1. F= Sunlight – Reflected sunlight. Unless the earth’s short-wave albedo changes, the Outgoing Long-Wave Radiation(F) is constant, whatever the state of the Greenhouse. So dF/dTs does not represent the Greenhouse Effect, but is a representation of the change of surface temperature with cloudiness.

2. F= S(urface Radiation) + G, but G= E(vaporation) +C(onduction) + A(bsorbed Solar Radiation) – B(ack Radiation). Of these terms, only A and B are Greenhouse dependent. C and E are Greenhouse independent. dG/dTs is therefore not a measure of the Greenhouse Effect.

3. It is unclear if the amount of radiation from the surface escaping “through the window” direct to space is constant. If CO2 concentration increases we expect some tightening of the window, but not much. On the other hand any increase in surface temperature will increase the amount of radiation, so the two processes may balance. Kiehl and Trenberth keep this constant at 40W/m^2 despite raising the surface temperature over time by 1DegC, suggesting that it may be close to constant.

Assuming that is so, the fluxes warming the atmosphere from the Surface are constant, the (B)ack radiation increasing by roughly the same as the sum of the increases in Radiation from the Surface(S) and (E)vaporation. Basically when the surface temperature increases, the increase in Evaporation is balanced by a
decrease in Net Surface Radiation Absorbed by the Atmosphere.
As the heat entering the lower atmosphere is unchanged (though the amounts entering at each height will change), the overall Lapse Rate to the tropopause will be unchanged. So the temperature at the Tropopause will always be the Surface Temperature minus a Constant. The sensitivity of the Tropopause temperature is therefore the same as (and driven by) the sensitivity of the Surface temperature to changes in “forcing” (either solar or back-radiation).

This sensitivity is between 0.095 and 0.15 DegC/W/m^2.

And a search in that post will highlight all the other comments.

My attempts at explaining the concept did not appear successful. I don’t think I will have any more success this time, but clearly others think it is important.

I find Colin’s comments confused, but I’ll start with the main point of Ramanathan (paraphrased by me):

What happens if the climate warms from CO2 (or solar or any other cause) – will water vapor in the climate increase, causing a larger “greenhouse” effect?

That’s the question that many people have asked. These people include well-known figures like Richard Lindzen and Roy Spencer, who believe that negative feedbacks dominate.

Scenarios to Demonstrate the Usefulness of the Definition

If the surface temperature in one location goes from 288K (15°C) to 289K (16°C) the surface radiation will increase by 5.4 W/m². (The Stefan-Boltzmann law). How can we determine whether positive or negative feedbacks exist?

Condition 1. Suppose under clear skies when the temperature was 288K we measured OLR = 265 W/m² and when the temperature increased to 289K we measured OLR = 275 W/m². That means OLR has increased by 10 W/m² for a surface radiation increase of 5.4 W/m². Let’s call this condition Good.

Condition 2. Suppose instead that when the temperature increased to 289K we measured OLR = 265W/m². That means OLR has not changed when surface radiation increased by 5.4 W/m². Let’s call this condition Bad.

  • In condition Good we have negative feedback, where the atmospheric “greenhouse” response to higher temperatures is to reduce its absorption of longwave radiation
  • In condition Bad we have positive feedback – the situation where more heat has been trapped by the atmosphere – the atmosphere has increased its absorption of longwave radiation

Whether or not more heat also leaves the surface by evaporation or conduction doesn’t really matter for this analysis. It doesn’t tell us what we need to know.

In fact, it’s quite likely that if evaporation increases we might find that positive feedback exists. However, that depends on exactly where the water vapor ends up in the atmosphere (as the absorption of longwave radiation by water vapor is non-linear with height) and how this also changes the lapse rate (as the moist lapse rate is less than the dry lapse rate).

It’s possible that if convective heat fluxes from the surface increase we might find that negative feedback exists – this is because heat moved from the surface to higher levels in the atmosphere increases the ability of the atmosphere to radiate out heat. This is also part of the lapse rate feedback.

But all of these different effects are wrapped up in the ultimate question of how much heat leaves the top of atmosphere as a function of changes in the surface temperature. This is what feedback is about.

So for feedback we really want to know – does the absorptance of the atmosphere increase as surface temperature increases? (see note 3).

That’s as much as I can explain as to why this measure is the useful one for understanding feedback. This is why everyone that deals with the subject reviews the same fundamental equation. This includes those who believe that negative feedbacks dominate.

See Note 2 and Note 3.

Colin Davidson’s points

Colin often makes very sensible statements and points but many of the statements and claims cited earlier suffer from irrelevance, inaccuracy or a lack of any proof.

Missing the point – as I described above – was the main problem. In the interests of completeness we will consider some of his statements.

The third comment cited above indicates one of the main problems with his approach:

..Unless the earth’s short-wave albedo changes, the Outgoing Long-Wave Radiation(F) is constant, whatever the state of the Greenhouse. So dF/dTs does not represent the Greenhouse Effect..

This is not the case. Suppose that absorbed solar radiation is constant. This does not mean that OLR (=”F” in Colin’s description) will be constant. From the First Law of Thermodynamics:

Energy in = Energy out + energy added to the system

In long term equilibrium energy in = energy out. However, we want to know what happens if something disturbs the system. For example, if increased CO2 reduces OLR then heat will be added to the climate system until eventually OLR rises to match the old value – but with a higher temperature in the climate. The same is the case with any other forcing. (See The Earth’s Energy Budget – Part Two).

In fact we expect that for a particular location and time OLR won’t equal solar radiation absorbed. We also have the problem that any “out of equilibrium” signal we might try to measure at TOA is very small, and within the error bars of our measuring equipment.

I didn’t understand what this equation was trying to say. How are the Surface Radiation and the Outgoing Long Range Radiation linked, noting that there are other fluxes from the Surface into the Atmosphere? And one of these (evaporation) is stronger than the NET Surface radiation, while direct Conduction is also a significant flux?

This is a very basic point. The surface radiation and outgoing longwave radiation (OLR) are linked by the equations of atmospheric absorption and emission (see note 4). With no absorption, OLR = surface radiation. The more the concentration of absorbers in the atmosphere the greater the difference between surface radiation and OLR. If we want to find out the feedback effect of water vapor this is exactly the relationship we need to study. Surface radiation and OLR are linked by the very effect we want to study.

A similar problem is suggested in the second comment cited:

..Hence my problem with the equation F=S-G as a starting point for any analysis – it doesn’t seem to represent anything coherent. Why not start with the TOA balance, the Surface balance, or the Atmospheric balance?

How is it possible to extract positive or negative feedback from these?

We expect that at TOA and at the surface the long term global annual average will balance to zero. But we can’t easily measure evaporation or sensible heat. Without carefully placed pyrgeometers we can’t measure DLR (downward longwave radiation) and without pyranometers we can’t measure the incident solar radiation at the surface. In any case even if we had all of these terms it doesn’t help us extract the sign or magnitude of the water vapor feedback.

If we had lots of measurement capability at a particular location it might help us to estimate the evaporation. But then we have the problem of where does this water vapor end up? This is a problem that Richard Lindzen has frequently made – and is also made by Held & Soden in their review article (cited in Part Two). Approaching the problem (from the surface energy balance) without knowing the answer to where water vapor ends up we can’t attempt to calculate the sign of water vapor feedback.

Colin also makes a number of other comments of dubious relevance in the last section of text I extracted.

He states that evaporation and conduction are “greenhouse independent” – but I question this. More “greenhouse” gases mean more surface irradiation from the atmosphere, and therefore more evaporation and conduction (and convection).

The amount of radiation escaping through the so-called “atmospheric window” is not constant (perhaps a subject for a later article). The rest of the statement covers the belief in some kind of simplified atmospheric model where everything is in balance – and therefore a positive feedback is defined out of existence:

Basically when the surface temperature increases, the increase in Evaporation is balanced by a decrease in Net Surface Radiation Absorbed by the Atmosphere.
As the heat entering the lower atmosphere is unchanged (though the amounts entering at each height will change), the overall Lapse Rate to the tropopause will be unchanged. So the temperature at the Tropopause will always be the Surface Temperature minus a Constant. The sensitivity of the Tropopause temperature is therefore the same as (and driven by) the sensitivity of the Surface temperature to changes in “forcing” (either solar or back-radiation).

When surface temperature increases, evaporation is not balanced by a decrease in net surface radiation absorbed by the atmosphere. In fact, when surface temperature increases, surface radiation increases and possible atmospheric absorption of this radiation increases (due to humidity increases from more evaporation). Exactly what change this brings in DLR (atmospheric radiation received by the surface) is a question to be answered. By saying everything is in balance means that the solution about positive feedback is already known. If so, this needs to be demonstrated – not claimed.

The rest of the statement above suffers from the same problem. None of it has been demonstrated. If I understand it at all, it’s kind of a claim of climate equilibrium which therefore “proves” (?) that there isn’t water vapor feedback. However, I don’t really understand what it might demonstrate.

Other Comments Needing Response from the Original Article

From Leonard Weinstein:

Since the issue is not resolved that the temperature in the upper troposphere has increased, and the relative humidity has not stayed nearly constant (it has clearly decreased) over the period of greatest lower troposphere temperature increase, the argument seems less than resolved. The lack of increased water vapor in the stratosphere pushes that point even further.

The argument isn’t resolved by this piece of work. This is one attempt to measure the effect over a period of good quality data.

Finely, the data and analysis of Roy Spencer seems to lead to different conclusions even on the data interpretation. Can you point out his errors and respond to those issues?

Roy Spencer’s analysis doesn’t address this period of measurement. His paper is about the period from 2000-2008.

From NicL:

However, I take issue with your statement “It should be clear from these graphics that observed variations in the normalized “greenhouse” effect are largely due to changes in water vapor.” The spatial maps referred to merely indicate a correlation between these two things. It is unscientific to infer causation from correlation. Ramathan himself goes no further than to say the graphics suggest that variations in water vapour rather than lapse rates contribute to regional variations in the greenhouse effect.

It’s unscientific to infer causation from correlation in the absence of a theory that links them together. It’s solidly established that water vapor absorbs longwave radiation from the surface, and it’s solidly established that CO2 and other “greenhouse” gases are well-mixed through the atmosphere, while water vapor is not. Therefore, there is a strong theoretical link.

I think, in common with various other repondants, that changes in lapse rates and in the height of the tropopause are key issues in modelling the greenhouse effect, yet they seem rarely discussed. Ramanathan’s chapter does not really cover them.

What makes you say they are rarely discussed? There are many papers discussing the different processes involved in modeling water vapor feedback. However, Ramanathan’s chapter is primarily about measurements. Of course he refers to the different aspects of feedback in the chapter.

Conclusion

One commenter in part two said:

I want to give him a chance to reflect on whether he wants to defend the Ramanathan analysis in Part 1 or separate himself with dignity, which he can still do..

The primary question seemed to be the approach, and not the results, of Ramanathan.

Ramanathan tested the changes in atmospheric absorptance of longwave radiation with temperature changes. To claim this is inherently wrong is a bold claim and one I can’t understand. Neither can Richard Lindzen or Roy Spencer, at least, not from anything I have read of their work.

There are other possible approaches to Ramanathan’s results. Other researchers may have replicated his work and found different results. Other researchers may have analyzed different periods and found different changes.

There are also theoretical considerations – whether changes in the equilibrium temperature as a result of increased CO2 can be considered as the same conditions under which seasonal changes indicated positive water vapor feedback.

The question for readers to ask is: Did Ramanathan find something important that needs to be considered?

Ramanathan himself said:

However, our results do not necessarily confirm the positive feedback resulting from the fixed relative humidity models for global warming, for the present results are based on annual cycle.
If I someone can point out the theoretical flaw in Ramanathan’s work then I might “separate myself with dignity” otherwise I will be happy to stand by the idea that he has demonstrated something that needs to be considered.
 

Articles in this Series

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

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 Four – discussion and results of a paper by Dessler et al using the latest AIRS and CERES data to calculate current atmospheric and water vapor feedback vs height and surface temperature

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

Note 1.

The actual change in emission of radiation for a 1°C rise in temperature depends on the temperature itself, one of the many non-linearities in science. The example in the article was for the specific temperature of 288K, along with the desire to avoid confusing readers with too many caveats.

Here is the graph of radiation change for a 1°C rise vs temperature:

For the mathematicians it is an easy exercise. For non-mathematicians, the change in radiation = 4σT³ W/m².K (obtained by differentiating the Stefan-Boltzmann equation with respect to T).

Note 2.

This article is about a specific point in Ramanathan’s work queried by some of my readers. His explanation of how to determine feedbacks is much more lengthy and includes some important points, especially the demonstration of the relationships in time between the various changes. These are important for the determination of cause and effect. See the original article and especially the online chapter for more a detailed explanation.

Note 3.

The rate of change of surface radiation with temperature, σdT4/dT = 4σT³ W/m².K (see note 1) is 5.4W/m² per K at 288K. However, the rate of change of OLR, dF/dT, for the no feedback condition is slightly more challenging to determine and not intuitively obvious.

Ramanathan, based on his earlier work from 1981, determined the “no feedback” condition (i.e., without lapse-rate feedback or water vapor feedback) was dF/dT=3.3 W/m².K. And for positive feedback this parameter, dF/dT would be less than 3.3.

Roy Spencer and William Braswell in their just-published work in JGR, On the diagnosis of radiative feedback in the presence of unknown radiative forcing has exactly the same value as the determination of the no feedback condition.

Note 4.

There are many different formulations of the solutions to the radiative transfer equations. This version is from Ramanathan’s chapter in Frontiers of Climate Modeling:

This is just to demonstrate that there is a strong mathematical link between surface radiation and OLR, and one that is very relevant for determining whether positive or negative feedbacks exist.

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In Part One we covered a lot of ground. In this next part we will take a look at some basics about water vapor.

The response of water vapor to a warmer climate is at the heart of concerns about the effect of increasing the inappropriately-named “greenhouse” gases like CO2 and methane. Water vapor is actually the major “greenhouse” gas in the atmosphere. But unlike CO2, methane and NO2, there’s a huge potential supply of water vapor readily available to move into the atmosphere. And all it takes is a little extra heat to convert more of the oceans and waterways into water vapor.

Of course, it’s not so simple.

Before we dive into the subject, it’s worth touching on the subject of non-linearity – something that doesn’t just apply to the study of water vapor. Some people are readily able to appreciate the problem of non-linearity. For others it’s something quite vague. So before we’ve even started we’ll digress into slightly more familiar territory, just to give a little flavor to non-linearity.

A Digression on Non-Linearity

People who know all about this can just skip to the next section. For most people who haven’t studied a science or maths subject, it’s a natural assumption to assume that the world is quite a linear place. What am I talking about?

Here’s an example, familiar to regular readers of this blog and anyone who has tried to understand the basic concept of the “greenhouse” effect.

If the atmosphere did not absorb or emit radiation the surface of the earth would radiate at an average of around 240 W/m² (see The Hoover Incident, CO2 – An Insignificant Trace Gas? and many other articles on this blog).

This would mean a surface temperature of a chilly 255K (-18°C).

With the “greenhouse” effect of a radiating atmosphere, the surface is around 288K (+15°C) and radiates 390 W/m².

As one commenter put it (paraphrasing to save finding the quote):

Clearly you haven’t done your sums right. If 240 W/m² means a temperature of 255K, then 390 W/m² means a temperature of (390/240)x255 which is way more than the actual temperature of 288K (15°C).

Now that commenter spelt out the maths but many more people don’t even do that and yet feel instinctively that something is wrong when results can’t be simply added up, or fitted on a straight line.

In the case of that approach, the actual temperature – assuming a linear relationship between radiation and temperature – would be 414K or 141°C. That approach is wrong. The world is not linear.

How much radiation does it take to raise the equilibrium surface temperature by 10°C (or 10K)? This assumes a simple energy balance where more radiation received heats up the surface until it radiates out the same amount.

The answer might surprise you. It depends. It depends a lot. Here’s a graph:

So if the surface is at 100K ( -173°C), it takes only 2.6 W/m² to lift the temperature by 10K (10°C).

  • At 200K (-73°C), it takes 20 W/m²
  • At 300K (27°C), it takes 65 W/m²
  • At 400K (127°C), it takes 151 W/m²

The equation that links radiation to temperature is the Stefan-Boltzmann equation, and the relationship is j=εσT4,where T is temperature.

If the equation was something like j=kT, then it wouldn’t matter what the current temperature was – the same amount of energy would lift the temperature another 10K. For example, if it took 10 W/m² to lift the temperature from 100K to 110K, then it would take 10W/m² to lift the temperature from 300K to 310K. That would be a linear relationship.

But he world isn’t linear most of the time. Here are some non-linear examples:

  • radiation from surfaces (and gases) vs temperature
  • absorption of radiation by gases vs pressure
  • absorption of radiation by gases vs wavelength
  • pressure vs height (in the atmosphere)
  • water vapor concentration in the atmosphere vs temperature
  • convective heat flow

It’s important to try and unlearn the idea of linearity. Intuition isn’t a good guide for physics. At best you need a calculator or a graph.

Digression over.

Water Vapor Distribution

Let’s take a look at water vapor distribution in the real world (below).

Both graphs below have latitude along the horizontal axis (x-axis) and pressure along the vertical axis (y-axis). Pressure = 1000 (mbar) is sea level, and pressure = 200 is the top of the troposphere (lower atmosphere).

The left side graph is specific humidity, or how much mass of water vapor exists in grams per kg of dry air.

The right side graph is relative humidity, which will be explained. Both are annual averages.

Water Vapor Observations, Soden - "Frontiers of Climate Modeling", chapter 10

Water Vapor Observations, Soden – “Frontiers of Climate Modeling”, chapter 10

Click for a larger view

As a comparison the two graphs below show the change in specific humidity and relative humidity from June/Jul/August to Dec/Jan/Feb:

Water Vapor Observations, Soden - "Frontiers of Climate Modeling", chapter 10

Water Vapor Observations, Soden – “Frontiers of Climate Modeling”, chapter 10

Click for a larger view

The most important parameter for water vapor is the maximum amount of water vapor that can exist – the saturation amount. Here is the graph for saturation mixing ratio at sea level:

You can see that at 0°C the maximum mixing ratio of water vapor is 4 g/kg, while at 30°C it is 27 g/kg. Warmer air, as most people know, can carry much more water vapor than colder air.

(Note that strictly speaking air can become supersaturated, with relative humidities above 100%. But in practice it’s a reasonable guide to assume the maximum at 100%).

Here’s the graph for temperatures below zero, for water and for ice – they are quite similar:

Relative humidity is the ratio of actual humidity to the saturation value.

Saturation occurs when air is in equilibrium over a surface of water or ice. So air very close to water is usually close to saturation – unless it has just been blown in from colder temperatures.

The Simplified Journey of a Parcel of Moist Air

Let’s consider a parcel of air just over the surface of a tropical ocean where the sea surface temperature is 25°C. The relative humidity will be near to 100% and specific humidity will be close to 20 g/kg. The heating effect of the ocean causes convection and the parcel of air rises.

As air rises it cools via adiabatic expansion (see the lengthy Convection, Venus, Thought Experiments and Tall Rooms Full of Gas – A Discussion).

The cooler air can no longer hold so much water and it condenses out into clouds and precipitation. Eventually this parcel of air subsides back to ground. If the maximum height reached on the journey was more than a few km then the mixing ratio of the air will be a small fraction of its original value.

When the subsiding air reaches the ground – much warmer once again due to adiabatic compression – its relative humidity will now be very low – as the holding capacity of this air is once again very high.

Take a look at the graph shown earlier of relative humidity:

Annual averages don’t quite portray the journey of one little parcel of air, but the main features of the graph might make more sense. In a very broad sense air rises in the tropics and descends into the extra-tropics, which is why the air around 30°N and 30°S has a lower relative humidity than the air at the tropics or the higher latitudes.

Why isn’t the air higher up in the tropics at 100% relative humidity?

Because the air is not just made up of air rising, there is faster moving rising air, and a larger area of slowly subsiding air.

Held & Soden in an excellent review article (reference below), said this:

To model the relative humidity distribution and its response to global warming one requires a model of the atmospheric circulation. The complexity of the circulation makes it difficult to provide compelling intuitive arguments for how the relative humidity will change. As discussed below, computer models that attempt to capture some of this complexity predict that the relative humidity distribution is largely insensitive to changes in climate.
(Emphasis added).

The Complexity

The ability of air to hold water vapor is a very non-linear function of temperature. Water vapor itself has very non-linear effects in the radiative balance in the atmosphere depending on its height and concentration. Upper tropospheric water vapor is especially important, despite the low absolute amount of water vapor in this region.

Many many researchers have proposed different models for water vapor distribution and how it will change in a warmer world – we will have a look at some of them in subsequent articles.

Measurement of water vapor distribution has mostly not been accurate enough to paint a full enough picture.

Measurements

There are two ways that water vapor is measured:

Radiosondes (instruments in weather balloons) provide a twice-daily high resolution vertical profile (resolution of 100m) of temperature, pressure and water vapor. However, in many areas the coverage is low, e.g. over the oceans.

Radiosondes provide the longest unbroken series of data – going back to the 1940’s.

Measurements of humidity from radiosondes are problematic – often over-stating water vapor higher up in the troposphere. Many older sensors were not designed to measure the low levels of water vapor above 500hPa. As countries upgrade their sensors it appears to have introduced a spurious drying trend.

Comparison of measurements of water vapor between adjacent countries using different manufacturers of radiosonde sensors demonstrates that there are many measurement problems.

Here’s a map of radiosonde distribution:

From "Frontiers of Climate Modeling" (2006)

From “Frontiers of Climate Modeling” (2006)

Satellites provide excellent coverage but mostly lack the vertical resolution of water vapor. One method of measurement which gives the best vertical resolution (around 1km) is solar occultation or limb sounding. The satellite views the sun “sideways” through the atmosphere at a water vapor absorption wavelength like 0.94μm, and as the effective height changes the amount of water vapor can be calculated against height.

This method also allows us to measure water vapor in the stratosphere (and in fact it’s best suited for measuring the stratosphere and the highest levels of the troposphere).

Here are the established satellite systems for measuring water vapor:

From "Frontiers of Climate Modelling" (2006)

From “Frontiers of Climate Modelling” (2006)

Here is a water vapor measurement from Sage II:

From "Frontiers in Climate Modeling" (2006)

From “Frontiers in Climate Modeling” (2006)

There are many disadvantages of solar occultation measurement – large geographic footprint of measurement, knowledge of ozone distribution is required and measurements are limited to sunrise and sunset.

The other methods involve looking down through the atmosphere – so they provide better horizontal resolution but worse vertical resolution. Water vapor absorbs and emits thermal radiation at wavelengths through the infrared spectrum. Different wavelengths with stronger or weaker absorption provide different “weighting” to the water vapor vertical distribution.

The new Earth Observing System, EOS, which began in 1999 has many instruments for improved measurement:

Mostly these provide improvements, rather than revolutions, in accuracy and resolution.

Finally, an interesting picture of upper tropospheric relative humidity from Held & Soden (2000):

Upper tropospheric humidity, Held & Soden (2000)

Upper tropospheric humidity, Held & Soden (2000)

You can see – no surprise – that the relative humidity is highest around the clouds and reduces the further away you move from the clouds.

Conclusion

Understanding water vapor is essential to understanding the climate system and what kind of feedback effect it might have.

However, the subject is not simple, because unlike CO2, water vapor is “heterogeneous” – meaning that its concentration varies across the globe and vertically through the atmosphere. And the response of the climate system to water vapor is non-linear.

Measurements of water vapor are not quite at the level of accuracy and resolution they need to be to confirm any models, but there are many recent advances in measurements.

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 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 Four – discussion and results of a paper by Dessler et al using the latest AIRS and CERES data to calculate current atmospheric and water vapor feedback vs height and surface temperature

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

References

Frontiers of Climate Modeling, ed. J.T. Kiehl & V. Ramanathan, Cambridge University Press (2006)

Water Vapor Feedback and Global Warming, I.M. Held & B.J. Soden, Annual Review of Energy and the Environment (2000)

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In the CO2 series we looked at the effect of CO2 without climate feedbacks. The “answer” to the doubling of CO2 was a “radiative forcing” of 3.7W/m^2 and an increase in surface temperature of about 1°C.

What about feedbacks?

There are many ways to introduce this problem. We’ll start with the great Ramanathan, who is always worth reading. This article discusses the ideas in the chapter The Radiative Forcing due to Clouds and Water Vapor (by Ramanathan and Inamdar) from Frontiers of Climate Modeling by Kiehl and Ramanathan (2006). Note that the link allows you to download the chapter. Well worth reading.

And if you have questions about whether CO2 can influence temperature or whether the inappropriately-named “greenhouse” effect exists, take a look at the CO2 series (and ask questions there).

Preamble

Various papers from the 60’s onwards that attempted to model the change in radiative flux and surface temperature (as a result of changes in CO2 concentrations) usually solved the problem using (at least) two scenarios:

  • constant absolute humidity
  • constant relative humidity

The reason is that absolute humidity is less realistic than relative humidity – and the concept of relative humidity leads to positive feedback. Why positive feedback? Higher concentrations of CO2 lead to increased radiative forcing and so the surface and tropospheric temperature increases. As a result – under constant relative humidity – the amount of water vapor in the troposphere increases. Water vapor is a greenhouse gas and so further increases “radiative forcing”.

One of the questions that come to people’s minds is whether this leads to thermal runaway. The answer, when considering the “extra” effect from water vapor is no, and this is because there are also negative feedbacks in the system, especially the fact that radiation (a negative feedback) increases as the 4th power of absolute temperature.

But enough of trying to think about the complete solution before we have even begun. Let’s take the time to understand the thinking behind the problem.

Cloudy Skies

Clouds are one of the toughest problems in climate science, and as a result, many models and experiments differentiate between cloudy and clear skies.

The ERBE experiments clarified the main effects from clouds.

Here is OLR (outgoing longwave radiation) under clear and cloudy (=all skies) averaged over 1985-1989:

ERBE OLR for clear and cloudy skies, 1985-1989

ERBE OLR for clear and cloudy skies, 1985-1989

Here is the albedo (%), or % of solar radiation reflected:

Albedo, or reflected solar radiation %, from ERBE, 1985-1989

ERBE albedo = reflected solar radiation % for clear and cloud skies, 1985-1989

Clouds reflect solar radiation by 48 W/m2 but reduce the outgoing longwave radiation (OLR) by 30 W/m2, therefore the average net effect of clouds – over this period at least – is to cool the climate by 18 W/m2. Note that these values are the global annual average.

Here are the net shortwave (solar reflection) and net OLR effects from clouds over the whole period:

and the two effects combined:

The “Greenhouse” Effect and Water Vapor

I’ll try and keep any maths to a minimum, but a few definitions are needed.. if you don’t like seeing equations the explanations in the text mean you haven’t missed anything essential.

We will call the “greenhouse” effect of the atmosphere and clouds, G, and the average OLR (outgoing longwave radiation), F:

F = σTs4 – G

The first term on the right-hand side of the equation, σTs4, is just the radiation from the earth’s surface at a temperature of Ts (the Stefan-Boltzmann equation). So the radiation from the earth’s surface less the “greenhouse” effect is the amount of radiation that escapes to space.

G is made up of the clear sky “greenhouse” effect, Gclear, and the (longwave) effect of clouds, Gcloud.

Now as we move from the hotter equator to the colder poles we would expect Gclear to reduce simply because the surface radiation is much reduced – a 30°C surface emits 480 W/m2 and a 0°C surface emits 315 W/m2. A large proportion of the changes in the “greenhouse” effect, Gclear, are simply due to changes in surface temperature.

Therefore, we introduce a normalized “greenhouse” effect, gclear:

gclear = Gclear / σTs4

This parameter simply expresses the ratio between the clear sky “greenhouse” effect and the surface radiation. The variations in this normalized value reflect changes in atmospheric humidity and lapse rates (the temperature profile up through the atmosphere). See especially CO2 – An Insignificant Trace Gas? Part Five for a little more illumination on this.

The global average value for Gclear = 131 W/m2 and for gclear = 0.33 – i.e., the atmosphere reduces the radiation escaping to space by 33%.

Here is how gclear varies around the world (top graphic) compared with water vapor around the world (bottom graphic):

It should be clear from these graphics that observed variations in the normalized “greenhouse” effect are largely due to changes in water vapor. [Note – change of notation from the graphics – ga in the graphic is gclear in my text]

Water vapor decreases from equator to pole due to temperature (lower temperatures mean lower absolute humidity), and increases over ocean compared with land (because of the availability of water to evaporate).

Feedback

If we can see that the “greenhouse” effect is strongly influenced by water vapor, we want to know how water vapor changes in response to surface and tropospheric temperature changes.

To make sense of this section it’s helpful to follow some maths. However, I recognize that many people would rather skip any maths so this is in the last section for reference.

Here are the results from ERBE for: the tropics (30°N – 30°S) with surface temperature; the “greenhouse” effect + the normalized version; and the change in water vapor in different vertical sections of the atmosphere:

Ramanathan says:

For the tropics, Ts peaks in March/April, while for 90°N–90°S, Ts peaks in July. We can qualitatively interpret the phase of the annual cycle as follows. The tropical annual cycle is dominated by the coupled ocean–atmosphere system and as a result, the temperature response lags behind the forcing by a maximum of about three months (π/2); thus, with the solar insolation peaking in December 21, the temperature peaks in late March as shown in Figure 10.

Now the whole globe as a comparison:

Ramanathan again:

The extra-tropical and global annual cycle is most likely dominated by the hemispherical asymmetry in the land fraction. During the northern-hemisphere summer (June, July, and August), the large land masses warm rapidly (with about a one month lag) which dominates the hemispherical and global mean response; however, during the southern-hemisphere summer, the relatively smaller fraction of land prevents a corresponding response. Thus, the globe is warmest during June/July and is coldest during December/January.

What can we make of the correlation? Correlation doesn’t equal causation.

The best fit is a phase lag of less than a month which implies that water vapor and gclear are not driving Ts – because the feedback in that case would require more than one month. The converse, that Ts is driving water vapor and gclear, is much more likely because convective time scales are very short.

Of course, this is a deduction from a limited time period.

One of the key relationships in understanding feedback is the change in Gclear with Ts (mathematically we write this as dGclear/dTs – which means “the rate of change with Gclear as Ts varies “).

For reasons briefly outlined in the maths section, if dGclear / dTs > 2.2 it implies positive feedback from the climate.

When the data is plotted from the ERBE data we can see that in the tropics the value is the highest, much greater than 2.2, and when the whole globe is included the value reduces significantly. However, the value for the whole globe still implies positive feedback.

In this last graph we see the feedback value for progressively wider latitude ranges – so on the left we are only looking at the tropics, while over on the right (90°N to 90°S) we are looking at the entire planet. This helps to see the contribution from the tropics progressively outweighed by the rest of the plant – so the important point is that without the strong effect from the tropics the feedback might well have moved to negative.

The feedback doesn’t change between clear sky and all sky, implying that the cloud feedback doesn’t impact the climate system feedback (on these timescales).

Ramanathan comments:

However, our results do not necessarily confirm the positive feedback resulting from the fixed relative humidity models for global warming, for the present results are based on annual cycle. We need additional tests with decadal time-scale data for a rigorous test. Nevertheless, the analysis confirms that water vapor has a positive feedback effect for global-scale changes on seasonal to inter-annual time scales.

He also comments on other work (including Lindzen) that finds different results for the relative important of water vapor in different vertical sections of the troposphere.

Hopefully, we will get the opportunity to consider these in future articles.

Articles in this Series

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 Four – discussion and results of a paper by Dessler et al using the latest AIRS and CERES data to calculate current atmospheric and water vapor feedback vs height and surface temperature

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

Conclusion

This is a big subject which has lots of different perspectives, and only one is developed here. Therefore, I hope that this is the first of many articles on the subject.

It should be helpful to see the approach and one way of interpreting the data. There is a theoretical framework behind the concepts, which can be seen in Ramanathan’s paper from 1981: The Role of Ocean-Atmosphere Interaction in the CO2 Climate Problem. (You can find a free copy online). It’s quite involved but perhaps some of the concepts from this paper will be in one of the next posts in this series.

Maths

I’ll follow the notations from the chapter reasonably closely. But I think they are confusing so I have changed a few of them.

And if you do want to understand the maths it’s definitely worth taking a look at the more detailed explanations in the chapter to understand this beyond the surface.

F = OLR (outgoing longwave radiation)

F = Fclear (1-f) + f.Fcloudy, where f is the fraction of clouds, and Fclear is the clear sky OLR

F = σTs4 – G                [1], where G is the “greenhouse” effect

and G = Gclear + Gcloud [2]

Now the main feedback parameter is dF/dTs, so:

dF/dTs = 4σTs3 – dG/dTs = 4σTs3 – (dGclear/dTs + dGcloud/dTs)           [3]

Note that 4σTs3 = 5.5 Wm-2K-1 (at T=289K)

Background:  dGclear/dTs is affected by water vapor and lapse rate and dGcloud/dTs is affected by cloud feedback and lapse rate

Now dGclear/dTs = 4σTs3 – dFclear/dTs [4]

now for Ts changing with no lapse rate feedback and no water vapor feedback, dFclear/dTs = 3.3 Wm-2K-1 (from Ramanathan 1981, see ref above in conclusion).

Therefore, if there is positive feedback dFclear/dTs < 3.3 Wm-2K-1 and if negative feedback dFclear/dTs > 3.3 Wm-2K-1 – because a lower value of F (OLR) means a higher value of G (greenhouse effect)

And from [4], if dGclear/dTs > 5.5 – 3.3 = 2.2 then there is positive feedback.

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