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:
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:
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):
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):
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:
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.
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:
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.
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.
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.
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
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)
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.