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.
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.
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:
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.
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.
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:
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:
Here is a water vapor measurement from Sage II:
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):
You can see – no surprise – that the relative humidity is highest around the clouds and reduces the further away you move from the clouds.
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
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)