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)
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)
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)
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)
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)
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)
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)
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)
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
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.
The Science of Doom 
Nice post. Unfortunately, averaging over the whole global can obscure important patterns.
You quote Sun et al: “The water vapor in the region right above the tropical convective boundary layer has the weakest dependence on the local temperature.”
We wouldn’t be surprised by this if we account for the circulation pattern in the Hadley cells. In subsiding regions (which cover more than half of the tropics), the air immediately above the boundary layer was last part of the boundary layer further in the past than any other part of the troposphere. A large fraction of the water vapor it contained when it left the boundary layer precipitated (>99% if it rose high enough). Some of the air may have been at the tropical tropopause. Isn’t this the coldest and possibly the driest place in the troposphere?
Why does increasing water vapor in any climate model below the tropopause cause an increase in surface temperature? Isn’t convection plus latent heat supposed to increase to compensate for loss of radiative cooling? Did the authors comment on the ability of the models they used to handle this problems?
Frank,
The problem with GCM’s is the coarse resolution which doesn’t allow detailed modeling within the 10,000 km2 area of the grid cell. Convective adjustments are therefore done for the whole grid cell at once. Deep convection (Sun and Lindzen 1993 Figure 1and Held and Soden Figure 10 above) isn’t modeled directly at all. There may be some effort at parameterization of deep convection, I don’t know. This may explain in part why the upper tropical troposphere hasn’t been warming as fast as the models predicted. See also Pielke Sr.’s comment on his new paper with Christy, et.al.
Hope all these HTML links work.
Frank:
This is true but a more important point to consider is that even in the “ascending” branch of the large-scale circulation a majority of the surface area is slowly subsiding air.
This is why the correlation, which is done on a geographical basis, is weak for specific humidity between surface and upper layers of the atmosphere. This is fig. 8, the last in the article.
There are competing effects, but first of all the key point (which probably you already see) is that if we reduce radiative cooling to space then it doesn’t matter how much more heat we cycle between the surface and the troposphere (or move permanently from the surface to the troposphere).
So the competing effects are:
1. the increased radiation to space when the upper atmosphere is hotter (the lapse rate feedback)
2. the reduced radiation to space when the atmosphere is optically thicker from more water vapor
Most (all?) calculations by models have the second effect stronger than the first.
They weren’t using a model, they were analyzing data.
SoD and Dewitt: In regions where convection controls dT/dH, I currently postulate that any decrease in radiative cooling caused by increasing water vapor is immediately compensated for by an increase in convection/latent heat. If I were peer-reviewing these papers (ha), I would reject them unless the authors admitted that their models were incapable of reproducing the expected increase in convection and that their results therefore were only reliable at and above the tropopause.
Since several such papers have been published, is my “postulate” about compensation too strict?
Dewitt is probably correct in pointing to the large size of grid cells compared with convecting regions, but that isn’t my point. Why doesn’t everyone who looks at Figure 2 say: “The model is wrong.”
Frank:
If I’m understanding you correctly then I think you misunderstand the point of these particular models.
It’s a simple question – all other things being equal, if we change one parameter by so much and keep all other factors constant, what happens to the result?
This is normal for any field of study.
In fact, if first of all you ran some model where everything else moved to “equilibrium” then after you had the results people would be asking – what happens if you only change x, if you only change y, if you only change z.
All other things being equal, how much impact does more water vapor, as a function of height, have on heating rates or OLR? Nothing wrong with the question.
Science of Doom – I think you are making things far too complicated here, and getting yourself and others confused in the process.
Yes, increases in water vapor in the upper troposphere would cause larger increases in surface temperature than comparable increases lower down. That’s simply because there’s much less water higher up, (a) due to the lower temperatures, and (b) due to the atmospheric circulation structure that Lindzen et al like to talk about.
So if upper troposphere water vapor did increase substantially, that would be a large positive feedback on greenhouse forcing.
But do the estimates of water vapor feedback in climate models depend on the increase happening in the upper troposphere? Or is an increase in the lower troposphere sufficient? The Spencer and Braswell graph you quote, for instance, shows quite clearly that the increase expected (remembering the exponential nature of the partial pressure dependence on temperature) in the lower troposphere should have a substantial effect, regardless of whether there’s any increase at all above the trade inversion.
Perhaps more importantly, secondly, I still fail to see any mechanism under which, when surface temperatures increase, any portion of the atmosphere would expect a *reduced* level of water vapor. For that to happen, you would need some process that took parcels of air to a region of *colder* temperature than they previously went through, so more of their water would precipitate out. Where is this expected to happen? I don’t see it, but maybe I’m still just missing something! It certainly doesn’t seem to be a question directly addressed by the Sun, Lindzen etc. papers you’ve been looking at.
Frank,
I don’t see how you can get an increase in convective heat transfer unless the surface temperature also increases permanently. But a higher surface temperature, which is necessary to increase the specific humidity, means higher LW emission from the surface. That leaves less room for an increase in convective heat transfer. 100% compensation seems impossible to me.
Frank,
Not to belabor a point, but to take things from another perspective, when you say,
“I currently postulate that any decrease in radiative cooling caused by increasing water vapor is immediately compensated for by an increase in convection/latent heat.”
a) Theoretical argument
So, convection works up to the tropopause. The tropopause varies by season and latitude, but has a height somewhere between 10 and 15 km for the most part. The mean radiating altitude of the atmosphere is somewhere around 6-7 km if I remember correctly. If there is a decrease in radiative cooling, convection will carry more water to higher altitudes, above the current mean radiating altitude. More water vapor higher means that the whatever decrease in radiative cooling there was before, there will be more of a decrease with more water vapor higher up.
b) Empirical argument
If an increase in convection were 100% efficient in compensating for a decrease in radiative cooling, then I’m not sure how events like the PETM would have been possible.
For that matter, I’m not sure how the end of an ice age would have been possible. The initial forcing of a Milankovitch cycle is too small to cause the transition to an interglacial state without positive feedbacks, and I think it still considered the case that there is a lag between the initial warming and increase in CO2. That leaves H2O as the best candidate for positive feedback at the start of an interglacial.
Arthur Smith,
Check out this paper in the latest issue of E&E The Thermodynamic Relationship between Surface Temperature and Water Vapor Concentration in the Troposphere (on page 263).
I believe this lends support to Frank and may help answer the questions posed by Chris G. and DeWitt Payne.
William,
I skimmed the issue you pointed to; so, I may have missed some things, but I did note a few problems:
There was a misrepresentation that the hypothesis that CO2 induced warming predicts it throughout the atmospheric column. My understanding is that what is predicted is lower troposphere warming and stratospheric cooling (at least until a new equilibrium is reached).
There was an argument which had the basic theme that correlation is not causation, which is true enough, but it seemed to altogether ignore that there exists sound theory in addition to the measured correlations. I did not see that it offered an alternative explanation to the observed warming.
There was a repeat of arguments made by Lindzen which have already been refuted in the literature.
If there was something in particular you wanted to point out, please identify it.
Chris G,
The paper I was referring to is on page 263 (“The Thermodynamic Relationship between Surface Temperature and Water Vapor Concentration in the Troposphere”). I do not have a link to the individual paper. This paper explores the question that Arthur raised about how any decrease in water vapor concentration could occur with an increase in surface temperature. This also touches on the “theoretical” question that you raised and the convection behavior that Frank discussed. The abstract of the paper reads:
”The theoretical and empirical thermodynamics discussed in this paper explain the physics behind the observed reduction in relative humidity in the upper troposphere as surface temperature and surface humidity increase. This contradicts the physics embedded in current GCM models commonly used by the climate science community. The key to the physics discussed in this paper is the understanding of the relationship between water vapor condensation and the resulting PV work energy distribution under the influence of a gravitational field. New analyses of empirical, observational radiosonde data are presented which show the relationship between thermal energy and PV work energy resulting from this water vapor condensation process.”
The rate of convection and the resulting upper tropospheric water vapor concentration are linked to the PV work/thermal energy distribution generated from water vapor condensation. The higher the water vapor concentration at the surface the greater the PV work/thermal energy ratio generated from the latent heat release. This in turn leads to a more efficient condensation process leading to a lower water vapor concentration in the upper troposphere.
There are several other papers in this issue, some are very good and some are not so good. Miskolczi’s latest paper is also in this issue – I’ll leave it to others to decide which category it falls in.
Arthur Smith:
I wish I could see the simple side.
It’s something that Lindzen puts forward as a possibility in his 1990 paper. He proposes that higher temperatures could cause “deeper” (higher) convection with consequently more drying out of these convective towers.
I’m still trying to understand the Sun and Lindzen (1993) paper.
Sun and Oort show that water vapor response has been somewhere between constant relative humidity and constant specific humidity.
I believe that GCMs are quite close to constant relative humidity, but I’m not certain about that.
Sun and Oorts findings would mean a positive feedback, as water vapor would need to be at constant specific humidity for zero feedback (well – ignoring the complexity of non-linear response from height & latitude).
You write “[Lindzen] proposes that higher temperatures could cause “deeper” (higher) convection with consequently more drying out of these convective towers.”
What does “more drying” refer to? The final quantity of water vapor per unit mass of air depends only on the lowest temperature it passes through. If convection goes “higher” due to higher temperatures, does that explicitly mean it goes to points of lower temperatures than before the warming? Higher temperatures leading to lower temperature processes seems a very odd consequence.
I.e. temperatures increase throughout the tropopause, to first order by a uniform amount DT. There is also the lapse rate by which temperatures decline with height at a rate L: T(z+dz) = T(z) – L dz.
So for the change in convection to cause a *lower* minimum temperature for a given process you would need a change in that process so that the height increased by a value dz > DT/L. For a 1 K temperature increase, that means at least 100 meters higher.
But I didn’t find such an analysis in the Lindzen papers I looked at – have you?
Chris G,
The best candidate for positive feedback is albedo not water vapor.
Yes, my mind was tunneled into atmospheric components when I wrote that.
Or, I may have been thinking that the change in albedo as an effect of changing the tilt with respect to perihelion and hence a change in the amount and distribution of ice was a direct influence and others were feedbacks.
But, of course, a change in albedo as a result of ice loss is its own positive feedback. I don’t think it matters; soon enough, albedo and water vapor feedbacks are reinforcing each other.
SoD, DeWitt, Chris: Thank you for your comments. I’m currently struggling with two problems.
One problem relates to the type of models used in the above studies, which appear to be based on purely radiative changes in OLR leaving the atmosphere and DLR reaching the surface. (Presumably DLR translates to surface temperature by oT^4.) I don’t see how other such models could include responses such as increasing convection.
The second problem relates to misconceptions I have developed created by thinking of increased GHGs as a blockage of OLR. (Thank you, CAGWers.) A blockage can be overcome by increased convection. GHG’s both absorb and emit and are incompatible with “blockage”. “Diversion” seems to be a much better concept. Increased GHGs lead to increased diversion of upward energy flux into DLR. Increased DLR can only be overcome by increased convection only after surface temperature have risen, but convection may limit that rise.
So I’m forced withdraw my working “postulate” that increasing GHG’s below the tropopause will be negated by convection and simply say that part of the effect will be negated. It isn’t clear to me whether model limitations bias the conclusions about the importance of altitude in WV feedback.
Reply to Arthur Smith’s comment 9/20 6:24 am. Arthur said:
“Perhaps more importantly, secondly, I still fail to see any mechanism under which, when surface temperatures increase, any portion of the atmosphere would expect a *reduced* level of water vapor. For that to happen, you would need some process that took parcels of air to a region of *colder* temperature than they previously went through, so more of their water would precipitate out. ”
In general, the warmer the surface, the colder the tropopause. (www-das.uwyo.edu/~geerts/cwx/notes/chap01/tropo.html). Convection is responsible for this counter-intuitive phenomenon. If CO2 warms the surface of the earth and increases convection, we logically could expect the tropopause to get cooler and therefore drier. In subsiding regions, the temperature of the tropopause has much more influence over water vapor than the temperature of the surface or boundary layer.
Observations indicate that the upper tropical tropopause has warmed only about as much as the surface, results that are inconsistent with troposphere cooling AND with the expectation that relative humidity has remained constant. Even though the upper tropical troposphere has warmed on average, the lack of the expected hotspot suggests that this drying mechanism may operate locally.
I misspoke in my earlier comment, saying tropopause instead of troposphere. Nevertheless, the reason the tropopause gets colder is because it increases in altitude. I’m not sure what convection has to do with that, I thought it was a consequence of the combination of tropospheric warming, and stratospheric cooling, both of which are greenhouse gas impacts.
Given that the lapse rate doesn’t change, or in fact decreases, under warming conditions, the temperature at any given height in the troposphere *must* be warmer than it was before, by an amount at least equal to the increase in surface temperature. So the problem is exactly as I stated – for Lindzen’s claim to be true, convection must change in such a way that it increases the maximum height of any given parcel of air by over 100 m for every 1 K surface temperature increase. Has that been proved?
Reply to Arthur Smith 9/23 3:37 am. In your first paragraph, you ask what convection has to do with the fact that the tropopause is higher and therefore colder in the tropics than elsewhere on the planet. Convection (including transfer of latent heat) occurs when net vertical transport of energy by radiation can not remove energy from the sun fast enough. Regions where convection is important are characterized by a relatively fixed lapse rate. The precise altitude of the tropopause is complicated by a variety of phenomena occurring in the stratosphere, but many graphs of temperature vs. height show a fairly sharp transition from a fixed lapse rate to a negligible lapse rate. In most locations, therefore, the temperature at the end of the fixed lapse rate determines the temperature at the tropopause itself. This transition point is obviously the location where convection is no longer needed to take heat away from the surface of the earth and lower atmosphere. Therefore I believe that convection has has everything to do with the fact that the tropopause is higher, colder, and logically drier over the tropics than elsewhere on the planet.
The observation that a warmer, moister surface is associated with a colder, drier tropopause is a phenomena that can’t be explained by radiative transfer and must be due to convection. When GHG’s increase, you assume that the tropopause will warm, be moister, and therefore warm further by feedback. However, if increasing GHG’s cause convection to reach another 1 kilometer higher, the temperature of the tropopause will drop by 6.5 degK, not rise. Without a theory explaining how high convection extends the fixed lapse rate, DO YOU HAVE A RELIABLE REASON FOR ASSUMING THAT THE TEMPERATURE AT THE TROPOPAUSE WILL RISE? (Sorry for the “shouting” capitals. In a long post, there is no other way to draw attention to the key question.)
You may be assuming that the temperature at the tropopause will rise because this is what is predicted by GCMs. However, we know that GCMs have limited capability to model convection and that the “hot spot” predicted to occur near the tropical tropopause has not be observed. (With all of the emphasis on the difference in temperature trends, I’m not sure how the absolute temperature at the end of the fixed lapse rate and at the tropopause itself have changed.)
In your second paragraph you say:
“… convection must change in such a way that it increases the maximum height of any given parcel of air by over 100 m for every 1 K surface temperature increase. Has that been proved?”
Lindzen’s scenario is certainly reasonable. The height of the tropopause (or the end of the fixed lapse rate and therefore convection) varies by almost 10 km, while surface temperature underneath varies by roughly 30? degK. The change you think is dubious is much smaller than this.
SOD says,
Arthur Smith says,
Frank says,
Arthur Smith says,
The specific humidity in the upper troposphere in the tropics is primarily a function of the rate of convective cooling, which is determined by the rate of upward convection, of the lower tropospheric air masses. The rate of upward convection is a function of the rate of condensation of water vapor. The rate of condensation is, in turn, a function of the water vapor content of the lower troposphere. (This is explained in my E&E paper which I referenced in my post of 12/21/10 @ 12:18 AM).
When water vapor condenses, part of that latent heat is converted to thermal energy in the surroundings but part of that latent heat energy is also converted to PV work energy. Since this PV work represents a change in volume and density, buoyancy occurs and incremental convection results. The faster the rate of condensation the more latent heat energy is converted to PV work and the more rapid the resulting convection.
The empirical data shows that upward convecting air with a mixing ratio of 20 g/kg (at the surface) will deliver up to approximately 80% of the latent heat energy that is released in the form of PV work at the maximum condensation altitude. This drops to about 40% for a less humid surface mixing ratio of 18 g/kg. This exponential generation of PV work energy with increasing humidity is what causes the high convection towers. In turn, the rapid cooling rates generated by this rapid latent heat/PV expansion as water vapor concentration increases, also increases the efficiency in condensing out available water vapor (super cooling may even occur). Thus a higher humidity level at the surface should result in a corresponding lower humidity level in the upper troposphere.
The height of the tropopause increases as PV work content in the lower troposphere increases. Volume expansion of the troposphere results with increased convection. That is why the tropopause is at a maximum in the tropics where deep convection is greatest. That is also why you see a marked decrease in the tropopause altitude as you approach the subtropics where the subsiding convection is resulting in atmospheric mass compression (Hadley cell circulation).
Frank says,
If you read the Noor van Andel paper in the reference link I provided, you will see that he shows (based on the Miskolczi empirical data whose paper is also in this issue) that the various layers of the troposphere are close enough to LTE that net radiative heat transfer through the troposphere is basically zero. He states that virtually all heat transfer through the troposphere from the surface to the upper troposphere is via convection. There is nothing to negate.
Can anyone provide links to the Lindzen and other papers that are being mentioned? (Or point me to the posts where they may be found. I may have missed them).
williamcg,
Who ever said that the troposphere wasn’t at LTE? All van Andel did was restate the common knowledge that LTE means that collisional energy transfer dominates radiative transfer. This is required for Kirchhoff’s Law, absorptivity = emissivity, to be valid. That has precisely nothing to do with the fraction of vertical heat transmission due to radiation.
In the summary of section two he makes the statement that:
That would only be true if Aa is identical to Ed always. But Figure 3 shows that Aa is greater than Ed. Radiative transfer calculations show that this is always the case except where there’s a temperature inversion like in the polar winter. In that case, Ed is greater than Aa. All the other calculations are based on a single slab toy model with a gray atmosphere. That automatically places an artificial upper limit of Sg + K = 2*Fo for the greenhouse effect. The concept of a single value of tau for the atmosphere of a cloudy planet is nonsense.
In fact, Aa cannot be identical to Ed unless the atmosphere is isothermal. An isothermal atmosphere doesn’t have a greenhouse effect because just as much radiation leaves the top of the atmosphere as enters the bottom.
Miskolczi’s other assertion that Eu/Ed = 0.6 is just that, an assertion. It may be approximately true now, but there is no theoretical reason to believe that it will always be true. In fact, it appears to be an assumption that the enthalpy of the atmosphere and surface is constant. If, for example, the tropics were to expand in a warmer planet, the poles would have to cool to maintain Eu/Ed = 0.6 and vice versa. If that is indeed the case, then obviously the theory predicts no change in temperature with ghg concentration. It’s assumed as part of the specification of the boundary conditions.
And then there is cloud covered sky. For a cloud covered sky, S_T = 0 so OLR = E_U and E_U is then greater than 0.5*S_G. That explains the ‘window problem’ with TFK09. There is no window in a cloud covered sky. So for the planet as a whole Aa is greater than Ed even though it is approximately true at every point for both cloudy and clear sky conditions.
DeWitt Payne,
Thanks for the interesting observations about the Miskolczi theory. I didn’t mean to start a discussion on that very complicated topic on this thread, I was just pointing out another way of looking at the radiation vs. convection heat transfer conundrum. I am still on the fence about the theory, especially the Aa = Ed part of the puzzle. My expertise lies more with his variable K and he does not spend a lot of time on that, unfortunately. But I would like to address a few of your statements, if nothing else but to test my understanding up to this point in time. I will not always differentiate between Miskolczi and van Andel since I am not always sure where one begins and the other ends.
I believe van Andel is infering that Trenberth does not based on the K/T 1997 energy balance diagram. Trenberth has Aa = 350, Eu = 324 and St = 40 W/m2. M theory states that Aa = Eu = 324 and St = 66 W/m2. Van Andel included this statement in a presentation to KNMI in the Netherlands last week:
I would be interested in knowing more about that correspondence.
In that same presentation to KNMI van Andel has this statement under what is Figure 4 in his paper (which is the same data as Figure 3, just a different log scale):
Evidently there is a reflectance correction that should be applied to the surface emmission calculation, but you may understand that better than I do.
My understanding is that his (Miskolczi) calculations are based on measurements from hundreds of radiosonde readings from poles to equator. He then used HARTCODE to generate the thousands of spectra needed to analyze the empirical readings. All of this was then crunched using software of his own design. This does not seem like your typical model. Or are you just referring to the schematic diagram that he uses to show the various energy fluxes? I am not clear on what you are saying.
It is my understanding that tau is not a constant across the whole atmosphere but that it is higher at the equator and lower at the poles. But that averaged across the globe it has been relatively constant over a period of several decades. This is based on thousands of empirical radiosonde readings over that period of time and was done on the actual atmosphere which includes clouds at all times. The fact that he uses actual empirical data and not models to arrive at these conclusions is what keeps me very interested in his work.
One other comment about Aa = Ed. As was explained to me by a close associate of Mislolczi, this does not apply to any given layer of atmosphere (which is what I originally thought). Aa represents the absorption of photons originating from the surface and absorbed by the atmosphere through the entire atmospheric depth. Photons emitted from one parcel of atmosphere and absorbed by another parcel of atmosphere are not included in Aa. Conversely Ed represents photons emitted by the atmosphere throughout the entire atmospheric depth and absorbed by the surface. Thus the atmosphere does not need to be isothermal for Aa = Ed. I’m not sure I have wrapped my mind around this as of yet. Your thoughts would be appreciated.
DeWitt,
OOPS. In my statement:
“Trenberth has Aa = 350, Eu = 324 and St = 40 W/m2. M theory states that Aa = Eu = 324 and St = 66 W/m2.”
Eu should be Ed in all cases. Sorry about that.
In your part 2 of this series you wrote the following;
“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.”
Yet from this link, from “Bad Science: Clouds”
http://www.ems.psu.edu/~fraser/Bad/BadClouds.html
we learn:
“The idea that it is the air which determines the amount of water vapor which can be present through some sort of holding capacity is an eighteenth century idea which was shown to be false both empirically and theoretically about two hundred years ago! The fact that it is still taught in our schools and defended by teachers and (gulp) professors, is a testimony to the mindless persistence of myth. A discussion of some of the history of this bankrupt idea is offered by Steven M. Babin .”
The Babin link from that page states clearly “Air does not hold water vapor. Water vapor is not dissolved in air.” and he then demonstrates it.
Of course i have lost count of the number of apparently knowledgable men who claim a water vapor “holding capacity” for air in this climate debate. You certainlt aren’t alone. I take a few things from this:
1. It seems to me that many people involved in climate research, being physicists or mathematicians, just don’t have the basic gounding in meteorology that they need if they are going to be modeling or discussing the nature of the atmosphere.
2. Once again the textbooks are wrong so referring to textbook science is not necessarily a correct thing to do.
3. Some myths seem particularly prevalent in climate science. Just like the “Gulf stream” myth eviscerated by Seager here.
http://www.ldeo.columbia.edu/res/div/ocp/gs/
There’s a great kids program on TV that has the catchphrase “Don’t take somebodys word for it; prove it!”. Nice to see kids are taught to be skeptical. A pity about the adults.
JamesG:
So if I understand correctly I shouldn’t believe the myths taught in physics and chemistry textbooks and in undergraduate university courses.. because someone on a website claims that these are wrong?
Here’s one for you if you believe in the bankrupt idea of gravity:
“The idea that it is mass and distance which determines the force between two bodies through some sort of invisible force is a sixteenth century idea which was shown to be false both empirically and theoretically about three hundred years ago! The fact that it is still taught in our schools and defended by teachers and (gulp) professors, is a testimony to the mindless persistence of myth. A discussion of some of the history of this bankrupt idea is offered by John Q. Doe..”
Why do so many people believe these crazy ideas about gravity?
ScienceOfDoom – JamesG’s link actually has a very good point. What matters for condensation is the vapor pressure of the water, not the H2O fraction of a particular body of air. And it also has a good point that in addition to vapor, any body of air, even not part of a cloud, may contain some quantity of liquid water. So I think my statements here on the subject were wrong – as were some of yours – but I’m not sure what the answer is, except that much larger water fraction levels should be allowable even if a body of air goes through a low-temperature region.
JamesG’s link is absolutely correct. Water vapor pressure does not depend on the pressure of the rest of the atmosphere. It’s a function of the amount of water present and the temperature only. But the rest of the argument is semantics, much like most of G&T’s ‘falsification’. The question, though, is whether the incorrect concept of holding capacity is, in fact, taught in schools. I just searched Rodrigo Caballero’s Lecture Notes in Physical Meteorology and could not find one instance of the occurrence of the phrase ‘holding capacity’ in the entire text. That’s a very good Physical Meteorology reference and I highly recommend it, btw. What I did find in Chapter 3 on Thermodynamics of Moist Air was this sentence: “Ideal gases behave as if each molecule ignored all others.” and also this: “Thus we can state that the saturation vapour pressure of water above a plane surface of pure liquid depends only on temperature, es = es(T).”
That says to me that correct physics is indeed being taught, but that lots of people outside the field or in public conversation use incorrect terminology. An incorrect description doesn’t make the underlying concept that is being described incorrect. There are aspects of quantum mechanics that can only be accurately described by using mathematical expressions. That doesn’t stop people from trying to explain what’s happening in plain language even if it isn’t technically correct.
A side note:
Could you possibly change your layout to make links stand out better? Dark green isn’t really all that different from black. Bold and underlined seems to be a common convention.
williamcg,
The subject probably deserves its own thread. There are bits and pieces around the web, but nothing really satisfying. They seem to be dominated by true believers or are so dismissive details are not adequately discussed.
In the absence of cloud cover and with atmospheric temperature decreasing with altitude, I don’t think it’s possible for Ed to equal Aa because Ed comes from a colder medium than Su,from which Aa is derived. 90% of the radiation (and 90% of the absorption of Su) comprising Ed comes from within 1 km of the surface, so the temperature change isn’t large, which is why Aa is approximately equal to Ed. Clouds are effectively black bodies in the thermal IR so for a cloud covered sky Aa and Ed are nearly identical.
Miskolczi does indeed use a line-by-line program to calculate spectra for lots of conditions. But in the end, he plugs it all into what amounts to a single slab, one dimensional model for the planet as a whole. As to averaging tau. If you consider the surface of the planet, tau is infinite for a cloud covered sky. No thermal radiation from the surface reaches space directly. Therefore you cannot get a finite value of tau by averaging over the whole surface unless you ignore clouds.
The logic of the KT97 and TFK09 St=40 is that St for clear sky is ~100 W/m2. 60% of the sky is covered with clouds with St = 0 so St for the planet as a whole is then 40 W/m2. The question then becomes, is that accurate for partly cloudy sky or for very thin clouds? Dunno. I think that also applies to the satellite measurement, which could be biased high by not properly correcting for clouds when coverage is not complete. But it’s not really important. The numbers could be adjusted to make Ed approximately equal to Aa, you just lower the amount of upward radiation absorbed and lower the amount emitted upward by the atmosphere to space by the same amount. Everything still balances.
Where I think there is an error in KT97 and TFK09 is the 30 W/m2 transmitted directly to space from cloud tops. That number, IMO, is way too low. But that wouldn’t affect the overall balance either because it would just reduce the amount emitted by the atmosphere to space even further.
But that’s actually not important for the validity of Miskolczi theory. I think now that the identity Eu = 0.5*Sg is a fatal flaw. That simply isn’t true for a cloud covered sky. Eu = 0.5*Sg is also a feature of a single slab model of the atmosphere as a whole, as it’s the minimum possible value for Eu as a function of Sg. There is no reason to believe that it must always be true, Venus being a prime example where Eu is orders of magnitude smaller than Sg.
Off-topic question for williamcg:
I was planning on writing about the article “Politics and the Greenhouse Effect” which you co-authored(?) with Hans Jelbring. (I think it has some flaws, which is why I am planning to write about it).
Is this an article you are happy with and does it represent your current point of view?
If you are happy with it, would you like the opportunity to write a followup comment/article before I publish it on the blog? (The comment/followup article would be published with my article).
If you aren’t happy with it, would you like the opportunity to amend it?
If you would prefer to answer “off blog” you can correspond via scienceofdoom – you know what goes here – gmail.com
None of this is about clouds, though, as they are condensed water not water vapor, right? And their main effect is one of scattering both shortwave and longwave radiation through reflection and refraction, not absorption and re-radiation, right? And whether it is cloudy or sunny is more a matter of relative humidity than specific humidity? I’m pretty sure of all of that, but I want to be sure before I get onto my real questions.
So since the incoming and outgoing radiation of Earth must match, it intuitively seems to me that if in any instant you blanket the entire Earth with a cloud, that should not affect the global average temperature, as the solar radiation reflected away should be roughly equal to the terrestrial radiation reflected back. But it also makes intuitive sense to me that this is not the case for any specific location and time — at night there is no solar radiation to block, only terrestrial radiation to trap, whereas during much of the day incoming radiation may exceed outgoing. In Seattle summer clouds have a cooling effect and winter clouds keep it warm. These all seem obvious to me and easily observable, however everything I read about clouds and climate seems to suggest it is altitude that makes all the difference in what effect they have — why?
Also, why do aerosols not have a similar blanketing effect?
Eric L:
Often ambition exceeds ability.
But take a look at Clouds and Water Vapor – Part One where there was a certain amount about clouds, including answers to some of your questions.
Incoming and outgoing radiation don’t actually have to match. If they don’t then there will be heating or cooling. See The Earth’s Energy Budget – Part Two
And The Earth’s Energy Budget – Part Three.
Solar radiation (shortwave) is centered around 0.5um whereas terrestrial radiation (longwave) is centered around 10um. Surfaces and gases absorb very differently at different wavelengths. For example, snow is highly reflective to shortwave but very absorbing for longwave.
Therefore, you can’t assume that a cloud (or anything) will have equal reflectivity for longwave and shortwave.
This is why the atmosphere warms from the bottom (the earth’s surface) – because it is almost transparent to solar radiation. Yet it is quite opaque to longwave radiation.
This is mostly to do with the longwave radiation (cooling) to space from the cloud tops. The higher the cloud top the colder the cloud top, and therefore the lower the outgoing radiation. Less outgoing radiation means less cooling to space.
Eric L’s claim that clouds “main effect is one of scattering both shortwave and longwave radiation through reflection and refraction, not absorption and re-radiation” is also, I believe wrong. Clouds are strongly absorbing (and radiating) in the infrared (longwave radiation). This is similar to snow and ice which largely reflect or scatter visible light, and water which largely transmits it, vs. long wave radiation for which all are strong absorbers (and emitters).
[…] 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 […]
[…] Now note the caveats around the value for the moist parcel of air rising. I said “..in the tropics near the surface..”, but for the DALR there are no caveats. That’s because once we consider moisture we have to consider how much water vapor and the amount varies hugely depending on temperature (and also on other factors – see Clouds and Water Vapor – Part Three). […]
[…] to absolute humidity at a given temperature for saturated air. Science of Doomcovers this rather well. Pointing out that water vapor is Earth’s dominant greenhouse gas does not minimize the […]
[…] an earlier article on water vapor we saw that changing water vapor in the upper troposphere has a disproportionate effect on outgoing […]
[…] 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 […]
The online version of Modtran allows one to increase the water vapor scale, which I gather simply increases the amount of water vapor at all altitudes by the factor one inputs. In clear tropical skies, a 7% increase in the water vapor scale (inputing 1.07) reduces OLR through clear tropical skies by 1.6 W/m2 and the decrease is less where it is cooler. The global average appears to be about 1.3 W/m2. If one adds clouds in the tropics, the reduction is only 0.8-1.2 W/m2.
If I understand correctly, this data suggests that Modtran is projecting a WV feedback around +1 W/m2/K rather than the IPCC’s central estimate for AOGCMs. Where am I going wrong?
One possibility is that 7%/K is an approximation for the increase in saturation vapor pressure that is accurate near 280 K, but has risen 50% to 10.5%/K near 230 K and 100% to 14%/K near 200 K. So a water vapor scale factor of 1.07 is equivalent to 1 K of warming near the surface and 0.5 K of warming near the tropopause. If lapse rate feedback amplifies warming high in the troposphere compared to the surface, the water vapor scale factor of 1.07 high in the troposphere should be equivalent to less than 0.5 K of surface warming. These adjustment could yield a water vapor feedback near 2 K/m2/K assuming constant relative humidity.
Spencer and Braswell asked how much a 10% change in relative humidity at various altitudes changed OLR. Water vapor feedback is normally quantified in terms of W/m2/K, where K is measured at the surface. Not in terms of W/m2/(10% change in RH). Fundamentally, the change in absolute humidity, not relative humidity, changes OLR. (The density of water vapor is used In the Schwarzschild eqn.) It is unfortunate that these authors didn’t design this experiment to produce water vapor feedback expressed in W/m2/K.
And timing is important to. Another error in models.
“Porporato and first author Jun Yin, a postdoctoral research associate in civil and environmental engineering, found that not accurately capturing the daily cloud cycle has models showing the sun bombarding Earth with an extra one or two watts of energy per square meter. The increased carbon dioxide in the atmosphere since the start of the Industrial Age is estimated to produce an extra 3.7 watts of energy per square meter. “The error here is half of that, so in that sense it becomes substantial,” Porporato said.
Yin and Porporato undertook their study after attending a seminar on cloud coverage and climate sensitivity. “The speaker talked a lot about where the clouds are, but not when,” Yin said. “We thought the timing was just as important and we were surprised to find there were fewer studies on that.”
Clouds change from hour to hour and from day to day. Climate models do a good job of capturing the average cloud coverage, Yin said, but they miss important peaks in actual cloud coverage. These peaks can have a dramatic effect on daily conditions, such as in the early afternoon during the hottest part of the day.
“Climate scientists have the clouds, but they miss the timing,” Porporato said. “There’s a strong sensitivity between the daily cloud cycle and temperature. It’s like a person putting on a blanket at night or using a parasol during the day. If you miss that, it makes a huge difference.””
“The researchers used satellite images from 1986-2005 to calculate the average diurnal cycles of clouds in each season worldwide. Yin analyzed the cloud coverage at three-hour intervals, looking at more than 6,000 points on the globe measuring 175 miles by 175 miles each.
Yin and Porporato compared the averages they came up with to those from nine climate models used by climate scientists. The majority of models have the thickest coverage occurring in the morning over the land, rather than in the early afternoon when clouds shield the Earth from the sun’s most intense heat. “A small difference in timing can have a big radiative impact,” Yin said.”
https://www.princeton.edu/news/2018/01/10/spotty-coverage-climate-models-underestimate-cooling-effect-daily-cloud-cycle