Redefining Physics

Dexter Wright re-defined the radiative transfer equations in his American Thinker article “Global Warming on Trial” with these immortal words:

Clearly, H2O absorbs more than ten times the amount of energy in the IR spectrum as does CO2. Furthermore, H2O is more than one hundred times more abundant in the atmosphere than CO2. The conclusion is that H2O is more than one thousand times as potent a greenhouse gas (GHG) as CO2.With such immutable facts facing the EPA, how will they explain their stance that CO2 is a greater danger to the public than water vapor?

So far, neither Dexter, nor his enthusiastic supporters at American Thinker have got around to updating the now defunct Wikipedia article on the Radiative Transfer Equations which describe the “old school” mathematics and are slightly more complicated.. (See also CO2- An Insignificant Trace Gas? Part Three.)

But in wondering why they hadn’t, it did occur to me that non-linearity is something that most people struggle with. Or don’t struggle with because they’ve never heard of it.

I think that the non-linear world we live in is not really understood because of the grocery factor..

(And it would be impolite of me to point out that Dexter didn’t know how to interpret the transmittance graphs he showed).

Groceries and Linearities

Dexter is in the supermarket. His car has broken down so he walked a mile to get here. He has collected a few groceries but his main buy is a lot of potatoes. He has a zucchini in his hand. He picks up a potato in the other hand and it weighs three times as much. He needs 100 potatoes – big cooking plan ahead – clearly 100 potatoes will weigh 300 times as much as one zucchini.

Carrying them home will be impossible, unless the shopping trolley can help him negotiate the trip..

Perhaps this is how most people are thinking of atmospheric physics.

In a book on Non-linear Differential Equations the author commented (my memory of what he stated):

The term “non-linear differential equations” is a strange one. In fact, books about linear differential equations should be called “linear differential equations” and books about everything else should just be called “differential equations” – after all, this subject describes almost all of the real-world problems

What is the author talking about?

Perhaps I can dive into some simple maths to explain. I usually try and avoid maths, knowing that it isn’t a crowd-puller. Stay with me..

If we had the weight of a zucchini = M z , and the weight of a potato = M p , then the weight of our shopping expedition would be:

Weight = M z x 1 + M p x 100, or more generally

Weight = M z N z + M p N p , where N z = number of zucchinis and N p = number of potatoes. (Maths convention is that AB means the same as AxB to make it easier to read equations)

Not so hard? This is a linear problem. If you change the weight (or number) of potatoes the change in total is easy to calculate because we can ignore the number and weight of zucchinis to calculate the change.

Suppose instead the equation was:

Weight = (M z N z ) N p 2 + (M p N p ) N z 3

What happens when we halve the number of potatoes? It’s much harder to work out because the term on the left depends on the number of zucchinis and the number of potatoes (squared) and the term on the right depends on the number of potatoes and the number of zucchinis (cubed).

So the final result from a change in one variable could not be calculated without knowing the actual values of the other variables.

This is most real-world science/engineering problems in a nutshell. When we have a linear equation – like groceries but not engineering problems – we can nicely separate it into multiple parts and consider each one in turn. When we have a non-linear equation – real world engineering and not like groceries – we can’t do this.

It’s the grocery fallacy. Science and engineering does not usually work like groceries.

Stratospheric Water Vapor

In many blogs, the role of water vapor in the atmosphere (usually the troposphere) is “promoted” and CO2 is “diminished” because of the grocery effect. Doing the radiative transfer equations in your head is pretty difficult, no one can disagree. But that doesn’t mean we can just randomly multiply two numbers together and claim the result is reality.

A recent (2010) paper, Contributions of Stratospheric Water Vapor to Decadal Changes in the Rate of Global Warming by Solomon and her co-workers has already attracted quite a bit of attention.

This is mainly because they attribute a significant proportion of late 20th century warming to increased stratospheric water vapor, and the last decade of cooling/warming/pause in warming/statistically significant “stuff” (delete according to preferences as appropriate) to reduced water vapor in the stratosphere.

(If you are new to the subject of the stratosphere, there is more about it at Stratospheric Cooling and useful background at Tropospheric Basics ).

There is much that is interesting in this paper.

Firstly, take a look at the basic physics. The graph on the left is the effect of 1ppmv change in water vapor in 1km “layers” at different altitudes (from solving the radiative transfer equations).

Notice the very non-linear effect of “radiative forcing” of stratospheric water vapor vs height. This is a tiny 1ppmv of water vapor. Higher up in the stratosphere, 1 ppmv change doesn’t have much effect, but in the lower stratosphere it does have a significant effect. Very non-grocery-like behavior..

Unfortunately, historical stratospheric water vapor measurements are very limited, and prior to 1990 are limited to one site above Boulder, Colorado. After 1990, especially the mid-1990’s, much better quality satellite data is available. Here is the Boulder data with the later satellite data for that latitude “grafted on”:

And the global changes from post-2000 less pre-2000 from satellite data:

It looks as though the major (recent) changes have occurred in the most sensitive region – the lower stratosphere.

The paper comments:

Because of a lack of global data, we have considered only the stratospheric changes, but if the drop in water vapor after 2000 were to extend downward by 1 km, Fig. 2 shows that this would significantly increase its effect on surface climate.

The calculations done by Solomon compare the increases in radiative forcing from changes in CO2 with the stratospheric water vapor changes.

Increases in CO2 have caused a radiative forcing change of:

From 1980-1996, about +0.36 W/m 2

From 1996-2005, about +0.26 W/m2

Changes in stratospheric water vapor have caused a radiative forcing change of:

From 1980-1996, between 0 and +0.24 W/m 2

From 1996-2005, about -0.10 W/m2

The range in the 1980-1996 number for stratospheric water vapor reflects the lack of available data. The upper end of the range comes from the assumption that the changes recorded at Boulder are reflected globally. The lower end that there has been no global change.

What Causes Stratospheric Water Vapor Changes?

There are two mechanisms:

methane oxidation

transport of water vapor across the tropopause (i.e., from the troposphere into the stratosphere)

Methane oxidation has a small contribution near the tropopause – the area of greatest effect – and the paper comments that studies which only consider this effect have, therefore, found a smaller radiative forcing than this new study.

Water transport across the tropopause – the coldest point in the lower atmosphere – has of course been studied but is not well-understood.

Is this All New?

Is this effect something just discovered in 2010?

From Stratospheric water vapour changes as a possible contributor to observed stratospheric cooling by Forster and Shine (1999):

This study shows how increases in stratospheric water vapour, inferred from available observations, may be capable of causing as much of the observed cooling as ozone loss does; as the reasons for the stratospheric water vapour increase are neither fully understood nor well characterized, it shows that it remains uncertain whether the cooling of the lower stratosphere can yet be fully attributable to human influences. In addition, the changes in stratospheric water vapour may have contributed, since 1980, a radiative forcing which enhances that due to carbon dioxide alone by 40%.

(Emphasis added)

From Radiative Forcing due to Trends in Stratospheric Water Vapour (2001):

A positive trend in stratospheric H2O was first observed in radiosonde data [Oltmans and Hofmann, 1995] and subsequently in Halogen Occultation Experiment (HALOE) data [Nedoluha et. al., 1998; Evans et. al., 1998; Randel et. al., 1999]. The magnitude of the trend is such that it cannot all be accounted for by the oxidation of methane in the stratosphere which also show increasing trends due to increased emissions in the troposphere. This leads to the hypothesis that the remaining increase in stratospheric H2O must originate from increased injection of tropospheric H2O across the tropical tropopause.

And back in 1967, Manabe and Wetherald said:

It should be useful to evaluate the effect of the variation of stratospheric water vapor upon the thermal equilibrium of the atmosphere, with a given distribution of relative humidity.. The larger the stratospheric mixing ratio, the warmer is the tropospheric temperature.. The larger the water vapor mixing ratio in the stratosphere, the colder is the stratospheric temperature..

Emphasis added – note that this paper was discussed a little in Stratospheric Cooling

Conclusion

The potential role of stratospheric water vapor on climate is not a new understanding – but finally there are some observations which can be used to calculate the effect on the radiative balance in the climate.

The paper does illustrate the non-linear effect of various climate mechanisms. It shows that small, almost unnoticed, influencers can have a large effect on climate.

And it demonstrates that important climate mechanisms are still not understood. The paper comments:

It is therefore not clear whether the stratospheric water vapor changes represent a feedback to global average climate change or a source of decadal variability. Current global climate models suggest that the stratospheric water vapor feedback to global warming due to carbon dioxide increases is weak, but these models do not fully resolve the tropopause or the cold point, nor do they completely represent the QBO, deep convective transport and its linkages to SSTs, or the impact of aerosol heating on water input to the stratosphere. This work highlights the importance of using observations to evaluate the effect of stratospheric water vapor on decadal rates of warming, and it also illuminates the need for further observations and a closer examination of the representation of stratospheric water vapor changes in climate models aimed at interpreting decadal changes and for future projections.

Given that the modeled changes add up to 70% on top of CO2 radiative forcing in an earlier period and then reduce CO2 radiative forcing by 40% in a later period, this is a very significant effect.

I expect that uncovering the mechanisms behind stratospheric water vapor change is an area of focus for the climate science community.

References

Contributions of Stratospheric Water Vapor to Decadal Changes in the Rate of Global Warming, by Solomon et al, Science (2010)

Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity, by Manabe and Wetherald, Journal of Atmospheric Sciences (1967)

Stratospheric water vapour changes as a possible contributor to observed stratospheric cooling, by Forster and Shine, Geophysical Research Letters (1999)

Radiative Forcing due to Trends in Stratospheric Water Vapour, Smith et al, Geophysical Research Letters (2001)