Guest Post by Willis Eschenbach
In my last post I investigated the mathematical relationship between the amount of total precipitable water vapor (TPW) in the atmosphere, and the clear-sky greenhouse effect. Here is the main figure from that post showing the relationship:
Figure 1. Scatterplot, TPW (horizontal scale) versus Atmospheric Absorption (vertical scale). Dashed yellow line shows theoretical value based on TPW. Dashed vertical line shows area-weighted global average value. Dotted vertical lines show the range of the global average value over the period. The slope of the curve at any point is 62.8/TPW (W/m2 per degree)
In this post I’m looking at the other half of the relationship. The other half is the relationship between the ocean surface temperature and the total precipitable water. The good news is that unlike the CERES data which is only about 15 years, we have TPW records since 1988 and sea surface temperature for the period as well. Figure 2 shows the relationship between the two:
Figure 2. Scatterplot, RSS total precipitable water (TPW) versus the ReynoldsOI surface temperature data. See end notes for data sources
As you can see, the relationship is regular but not simple. I first thought that the relationship was logarithmic, but it turns out not to be so. It is also very poorly represented by a power function. After unsuccessfully investigating a variety of curves, I found it could be approximated by an inverse sigmoid function (shown in yellow above). Now, given the number of very smart folks here, I suspect someone will be able to give a physical reason complete with the right equation, but this one suffices for my purposes.
Now, the relationship between water vapor and atmospheric absorption is clearly logarithmic, as is predicted by theory. On the other hand, I don’t know of any simple theory relating SST to total precipitable water. For example, the curve doesn’t match the Clausius-Clapeyron increase in water vapor. And clearly, my method is purely heuristic and brute-force … but that’s OK because I’m not claiming that it is explanatory. My purpose in doing it is quite different—I want to figure out how much change there is in the precipitable water per degree of change in the sea surface temperature (SST). And for that, the main quality is that the function needs to be differentiable.
So let me recap where we stand. In the last post I derived a mathematical relationship between the two variables shown in Figure 1. Those are clear-sky atmospheric absorption of upwelling longwave radiation from the surface, and the total precipitable water content (TPW) of the atmosphere.
And above in this post, I’ve derived a mathematical relationship between the two variables shown in Figure 2. Those are the total precipitable water content (TPW) of the atmosphere, and the sea surface temperature (SST).
That means that by substituting the latter into the former, I can derive a mathematical relationship between the SST and the atmospheric absorption.
Of course I wanted to ground-test my formula that converts from sea surface temperature to atmospheric absorption. I only have the CERES data for the absorption, so this covers a shorter period than that shown in Figure 2. Since the overall relationship was established using the Reynolds sea surface temperature data, I used that for the comparison.
Figure 3. Atmospheric absorption of upwelling longwave radiation versus sea-surface temperature. See end notes for mathematical derivation.
Dang, I’m pretty satisfied with that as a comparison of theoretical and observed atmospheric absorption. A few comments. First, the difference below 0°C is because CERES and Reynolds are measuring slightly different things below freezing, when there is ice in the picture. CERES is measuring the average temperature of the ice and the water, and Reynolds is measuring water temperature alone.
Next, the slight bend in the black line from 0°C to 25°C is not completely captured by the red line. This is because I’ve included the data below freezing, which has slightly distorted the results. Probably should have left it out, but I figured for completeness …
Next, the slight bend in the black line from 0°C to 25°C is due to the fact that surface radiation is proportional to the fourth power of the temperature. If absorption were calculated against surface upwelling radiation rather than temperature, it would plot as a straight line … go figure. I’ve done it this way because there is much discussion about the value of the “water vapor radiative feedback” which is measured per degree C. I could get a slightly closer fit by including the T^4 relationship, but my conclusion was that the gain wasn’t worth the pain … if I need greater accuracy I can redo the figure, but it is more than adequate for the present purposes.
The amount of the feedback is calculated as the slope of the red line in Figure 3. The slope is the change in the absorption for a 1°C change in the sea surface temperature. Figure 4 shows the amplitude of the water vapor radiative feedback across the range of ocean temperatures:
Figure 4. Water vapor radiative feedback, calculated as the change in atmospheric absorption of upwelling longwave radiation per 1°C change in surface temperature.
That is a very interesting shape. Now, given the general shapes of Figure 1 and Figure 2, I might have expected the shape … but it came as a surprise anyhow. Over much of the world, the two tendencies cancel each other out and the clear-sky water vapor radiative feedback is about 3-4 W/m2 per degree C. But in the tropics, where the water is warm, the water vapor feedback goes through the roof.
DISCUSSION
So … with such a large radiative feedback from water vapor, three to four watts per square metre per degree and much higher in the tropics, why is there not runaway feedback? I mean, the so-called “climate sensitivity” claimed by the IPCC says that 2-3 W/m2 of additional radiation will cause one degree of warming. And according to observations above, when it warms one degree, we get additional downwelling radiation from water vapor of 3-4 W/m2. And that amount is claimed to be sufficient to warm it more than one additional degree … a recipe for runaway positive feedback if I ever saw one. So … with that large a radiative feedback, why isn’t there runaway feedback?
Well, you might start by perusing Dr. Roy Spencer’s discussion of the subject, yclept Five Reasons Why Water Vapor Feedback Might Not Be Positive. The TL;DR version is that as the amount of water vapor in the air increases, downwelling radiation does indeed increase … but there are plenty of other things that change as well.
To expand a bit on one of the things Dr. Roy mentioned, in his discussion of evaporation versus precipitation he said:
While we know that evaporation increases with temperature, we don’t know very much about how the efficiency of precipitation systems changes with temperature.
The latter process is much more complex than surface evaporation (see Renno et al., 1994), and it is not at all clear that climate models behave realistically in this regard.
Let me add a bit to that. Rainfall goes up with increasing atmospheric water as shown in Figure 5:
Figure 5. Scatterplot, rainfall evaporative cooling versus total precipitable water. TRMM data only covers latitudes 40°N to 40°S.
Note the size of the cooling involved … not watts per square metre, but hundreds of watts per square metre. As precipitable water goes from about forty to fifty-five kg per square metre, evaporative cooling goes from fifty to two hundred fifty watts per square metre or more … that’s a serious amount of cooling, about ten watts of additional cooling per additional kg of precipitable water.
We can compare that to the slope of increasing water vapor radiative feedback in Figure 1. The slope in Figure 1 is 62.8 W/m2 divided by TPW, so at a TPW of 50 kg/m2 that would be about 1.2 W/m2 of additional radiative warming per additional kg/m2 of water … versus 10 W/m2 of rainfall evaporative cooling per additional kg/m2 of water.
But wait … there’s more. Figure 6 shows the rainfall evaporative cooling versus sea surface temperature (SST). Since SST and precipitable water are closely related, Figure 6 is quite similar to Figure 5.
Figure 6. Scatterplot, rainfall evaporative cooling versus Reynolds sea surface temperature.
As in Figure 5, at the hot (right hand) end of the scale, the rainfall evaporative cooling goes from about 50 to about 200 W/m2 very quickly. However, in this case it makes that change as the SST goes from about 27° to 30°. And that gives us a net cooling of about 50 W/m2 per degree … kinda dwarfs the 3-4 W/m2 per degree of water vapor based warming …
There is another interesting aspect of Figure 6 … the empty area at the lower right. I have long stated that the thermoregulatory phenomena like thunderstorms are based on temperature thresholds. The blank area in the lower right corner of Figure 6 shows that above a certain sea surface temperature … it’s gonna rain and cool it down. And not only will it rain, but the hotter it gets, the greater the rainfall evaporative cooling overall, and the greater the minimum evaporative cooling as well.
Nor do the cooling effects of water vapor end there. Increasing water vapor also increases the amount of solar energy absorbed as it comes through the atmosphere. As with the absorption of the upwelling longwave, the relationship is logarithmic. Figure 7 shows that relationship.
Figure 7. Scatterplot, atmospheric absorption of downwelling solar radiation (vertical axis) versus total precipitable water (horizontal axis)
Logarithmic relationships of the form “m log(x) + b” have a simple slope, which is m / x. The slope of the equation shown in Figure 7 is 31.6/TPW (W/m2 per degree). Now, earlier we saw that the slope of the warming from increasing water was 62.8/TPW (W/m2 per degree). This means that at any point, half of the warming due to water vapor radiative feed back is cancelled out by the loss in downwelling sunlight due to increased water vapor.
Nor is this the end of the related phenomena … Figure 8 shows the correlation between total precipitable water and cloud albedo:
Figure 8. Correlation of total precipitable water (TPW) and cloud albedo.
As you can see, over much of the tropics, as precipitable water increases so does the cloud albedo (red-yellow). Makes sense, more water in the air means more clouds. Again, this has a cooling effect.
Nor is this an exhaustive list, I haven’t discussed changes in downwelling longwave radiation due to clouds … the relationships go on.
FINAL THOUGHTS
The center of climate action is the tropics. Half of the available sunlight strikes the earth between 23° north and south. The main phenomena regulating the amount of incoming solar energy occur in the tropics. And as the graphs above show, the amount of water in the atmosphere is at the heart of those phenomena.
So … is the feedback of water vapor positive or negative? Overall, I’d have to say it is well negative, for two reasons. The first is the long-term stability of the global climate system (e.g. global surface temperature only changed ± 0.3° over the entire 20th century). This implies negative rather than positive feedback.
The second reason I’d say it’s negative is the relative sizes of the various feedbacks above. These are dominated by the evaporative cooling due to rainfall and by the changes in reflected sunlight due to albedo, both of which are much larger than the 3-4 W/m2 in increased water vapor radiative warming.
However, there is a very large difficulty in isolating the so-called “water vapor feedback” from the myriad of other phenomena. This difficulty is embodied in what I refer to as my “First Rule Of Climate”, which states:
In the climate system, everything is connected to everything else … which is turn is connected to everything else … except when it isn’t.
For example, the temperature affects the water vapor – when the temperature goes up, the water vapor goes up. When the water vapor goes up, clouds and rain go up. When clouds and rain go up, temperatures go down. When temperatures go down, water vapor goes down … you can see the problem. Rather than having things which are clearly cause and clearly effect, the whole system is what I describe as a “circular chain of effects”, wherein there is no clear cause and no clear boundaries.
Anyhow, those are the insights that I got from examining the total precipitable water dataset … like I said, no telling where a new dataset will take me.
And speaking of precipitable water, it is sunset here on our hillside. As I look out the kitchen window towards the ocean I see the fog washing in from the Pacific. It is pouring in waves over the far hills, swallowing redwood trees as it rolls on toward our house … it came and visited last night as well.
I love that sea fog. It reeks of my beloved ocean, with the smell of fishing boats and slumbering clams, of hidden coves and youthful dreams. And when the fog comes in, it brings with it the sound of the foghorn at the mouth of Bodega Bay. It’s about seven miles (ten kilometres) from my house to the bay, but the sound seems to get trapped in the fog layer, and when the fog comes I hear that foghorn calling to me in the far distance, a mournful midnight wail. I took frequent breaks from my scientific research and writing last night to sit outside on a bench, where I let the fog wreathe around my head and bear me away. I breathe in the precipitated water, and I emerged refreshed …
My best to everyone, and for each of you, I wish for whatever fog it is that carries you away in reverie and washes off the mask of socialization …
w.
REQUESTS
My Usual Request: Misunderstandings suck, but we can avoid them by being specific about our disagreements. If you disagree with me or anyone, please quote the exact words you disagree with, so we can all understand the exact nature of your objections. I can defend my own words. I cannot defend someone else’s interpretation of some unidentified words of mine.
My Other Request: If you believe that e.g. I’m using the wrong method or the wrong dataset, please educate me and others by demonstrating the proper use of the right method or identifying the right dataset. Simply claiming I’m wrong about methods or data doesn’t advance the discussion unless you can point us to the right way to do it.
NOTES
The math … I start with the equation for relationship between absorption (A) and total precipitable water (TPW) shown in Figure 1:
A = 62.8 Log(TPW) – 60
To this I add the inverse sinusoidal relationship between TPW and sea surface temperature, as shown in Figure 2:
TPW = – 13.5 Log[-1 + 1/(0.00368 SST + .887)] -19.1
Combining the two gives us:
A = 62.8 Log[-19.1 – 13.5 Log[-1 + 1/(0.887 + 0.00368 SST)]] – 60
Differentiating with respect to sea surface temperature gives the result as shown in Figure 3:
dA/dT = 3.13/((-1 + 1/(0.887 + 0.00368 SST)) (0.887 + 0.00368 SST)^2 (-19.1 – 13.5 Log[-1 + 1/(0.887 + 0.00368 SST)]))
Further Reading: NASA says water vapor feedback is only 1.1 W/m2 per degree C …
DATA
Reynolds SST data, NetCDF file at the bottom of the page
TRMM data, NetCDF file at the bottom of the page
Willis: “Here is the main figure from that post showing the relationship:”
Not quite, this is the same as your earlier graph but this time with a linear scale, not log scale. This is useful as a second way to visualise the data.
The caption to fig. 1 says: ” The slope of the curve at any point is 62.8/TPW (W/m2 per degree)”
This is clearly not correct. The slope of that graph varies notably. It is the slope of the log graph which is constant.
This ties in with a comment I made in the previous thread about the change in slope as TPW increases.
As TWP increases the slope decreases. This means that the magnitude of the positive feedback decreases. While remaining positive and finite it is reducing in magnitude.
At 12 kg/m^2 the slope looks to be about 5 W/kg. At your ‘average’ point it is less then half that.
So this is positive feedback which is itself subject to a negative feedback. The negative f/b being the masking effect as the density of water molecules rises. They become masked by others and the net effect of a give increase is less and less. This is the classic log relationship of absorption.
This shows that the positive w.v. feedback will be stronger in cooler, higher latitudes than in the warm and humid tropics.
Willis, your previous thread said:
ie about 2.2 W/kg at 29 kg/m^2
This is consistent with my eyeball slope estimate at that point above. It is about 5W/kg at TPW=12kg/m^2
The figure of 62.8/TPW has changed in the fitted log expression. Your last post had the constant as 43.5 . It seems that you are now using natural logs instead of log2. Natural logs are abbreviated ln , log on it’s own usually denotes log10. That is going to cause some confusion if anyone uses the value of 43.5 given as log instead of ln.
For us visually oriented learners, a diagram showing all the effects would be most helpful.
Your math appears incorrect on figure 1. First of all…I’m not really sure where you got this….figure or the calculation for this. You’re showing the y intercept at around 40 for the dashed yellow line yet your equation shows A y intercept at -60. . But you explain that this is the portion of the olr due to water vapor. Intrinsically you’d expect the water absorption would be 0 at 0 Tpw. There is clearly some inflection point at around 9 tpw. Also the slope calculation of 62.8/tpw is incorrect. …what is the R function…..also the equation doesn’t make sense. R is just a constant.
See my comments above about the base of the logs used and note that you do not see the *zero* intercept on that graph. Also R is the correlation coeff. of the data and the fitted fn ( I presume ). It has a single value, ie constant. If you don’t know what something is you really need to hold back of saying it does not make sense.
he showing the dashed yellow line as the plot of the equation 62.8 log tpw – 60….at tpw = 1 the value should be around y value should be around 2.8. there is no value for log (0). ….the relationship between aa and tpw is probably more linear between 0 and 9. the R is not defined…and you assumed something…that’s incorrect. it’s not clear how it’s even applied. the slope of the equation is the first derivative of the equation.
which would be slope = 62.8/(tpw ln (2))
so at tpw = 29.5 the slope is 3.07 w/m^2
Willis, with respect to figure 8 you wrote:
“As you can see, over much of the tropics, as precipitable water increases so does the cloud albedo”
Years ago I would occasionally fly small planes from the Mississippi gulf coast westward towards New Orleans in the afternoon. The first time I neared the end of the relatively cool waters of the Mississippi Sound and approached the much warmer swamps, marshes, and lakes of Louisiana I was alarmed by the panorama before me. The air was obviously hazy and moist, but in this case it was also dark, almost an “Edge of Night” effect, 1950s black-and-white style.
I had flown in the shadow of clouds before but this was different. After some thought I attributed it to many miles of tall cumulus rejecting the slanting afternoon sunlight and the moisture and scattered rain in the air below the clouds. While I prepared for instrument conditions, once I was under the cloud deck my eyes adjusted and I was able to continue in marginal daylight VFR. Over time I understood that this was a typical condition for this locale for much of the year.
Willis, you have done more science in these last two posts that the entire field has done in the last 35 years.
I’ve spent some time looking at these issues so I can provide some input.
First, you have provided real data that can be used to test the most important assumptions contained in the global warming theory – the feedbacks.
The feedbacks provide most of the warming that eventually arises from doubled CO2.
—> water vapor increase +2.0 W/m2 per 1.0C;
—> cloud albedo decrease +0.7 W/m2 per 1.0C;
—> others -0.3 W/m2 (these have changed some in the last IPCC report but the theory is still around this value.
—> TOTAL +2.4 W/m2 per 1.0C
The +2.4 W/m2 per 1.0C is an important value because this provides for just enough feedback so that one gets a feedback on feedback on feedback loop that takes doubled CO2 from its initial 1.1C increase to 3.0C eventually. The first round of water vapor and cloud feedbacks provide for another 0.71C temperature increase. That 0.71C then produces another round of water vapor increases and cloud albedo reductions leading to another 0.45C. That 0.45C provides another … and so on. After 11 rounds of feedback on feedback we get to 3.0C and there is basically no extra lift after that.
The +2.4 W/m2 per 1.0C is, thus, a VERY important number. It is “everything”. If, in reality, the feedbacks are only half of predicted, global warming would fall to 1.6C per doubling. If it were one-quarter, warming falls to 1.3C per doubling. If it were twice as big, well, global warming would then +47.0C per doubling and there would be a runaway greenhouse effect.
That is how finely tuned the chosen feedbacks are. It is the difference between benign-nothing warming and a runaway greenhouse effect.
You have a lot of data here that can test those assumptions in real life (something climate science does not seem to be able to do).
Water vapor. (Just an aside, but I think there is some inconsistency in your graphs. global average water vapor 29 kg/m2 – Reynolds SST at 29 kg/m2 is 24C or so. The most often quoted global average TPW is 24.5 kg/m2 and global average SST is about 18.0C. So I think there is an issue here).
But are you getting 7.0% increase in TPW per 1.0C (Clausius Clapeyron). Well, your data (Figure 2.) is pretty close on the Clausius Clapeyron at something around 6.5% per 1.0C. Change the formula to a simple TPW = X + (1 + CC%) * SST.
Are you getting +2.0 W/m2 per 1.0C increase. Well you data (Figure 3) is more like 3.75 W/m2 per 1.0C. If water vapor feedback produced 3.75 W/m2 per 1.0C, global warming would be 15.7C per doubling.
Cloud Albedo (Figure 7 – might be different than Cloud Albedo which I know you had shown before, but perhaps Atmospheric Absorption of downwelling Solar is close enough). Well here you clearly have and “Increased Absorption per warmer SST” – completely opposite to the theory that cloud albedo declines as warming occurs. Your data is in the range of -2.4 W/m2 per 1.0C .
Can we add them together to get a Water Vapor/Cloud Albedo feedback value ?? Well that would be +1.35 W/m2 versus global warming theory of +2.7 W/m2. Exactly Half. That would reduce global warming to 1.47C per doubling.
Really good work here. Really good.
Just noting that I think we “should” add these together. The cloud feedback is not really cloud albedo by itself but the combination of the change in solar reflected (albedo) and the change in long-wave downwelling of clouds. When low cloud cover declines in the theory, Albedo declines by more than the downwelling declines so it is a combination of both impacts. The measured cloud feedback is in both Figure 3 and Figure 7 of Willis’ graphs so they should be added together.
Note that Nic Lewis calculated observational energy budget ECS using Bjorn Stevens new estimate of aerosols as ~1.5, essentially the same as your 1.47. Cross check.
Re: Clausius – Clapeyron equation & saturation vapor pressure.
For those delving deeper, the most accurate Clausius Clapeyron equation I have found is by Koutsoyiannis. See:
Koutsoyiannis, Demetris. “Clausius–Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice.” European Journal of Physics 33, No. 2 (2012): 295-314. http://dx.doi.org/10.1088/0143-0807/33/2/295 ITIA preprint, postprint, history
Koutsoyiannis, Demetris, (2012) Corrigendum on “Clausius-Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice” European Journal of Physics 33, No. 4 (2012):1021. http://iopscience.iop.org/0143-0807/33/4/1021
Thanks Willis for yet another very interesting article. I’m interested in Bill Illis’ comment “your data (Figure 2.) is pretty close on the Clausius Clapeyron …“: Eyeballing the graph, I thought the same. My understanding is that precipitation also follows the C-C pretty well (eg. work by Weiffels et al which I now can’t locate). It looks to me like the work that Willis has done would be sufficient to resolve one of the outstanding climate disagreements – the IPCC and the climate models show precipitation at a much lower rate than C-C, namely only 2-3% per deg C instead of the C-C 7%. Willis’ Figure 5 shows precipitation (rainfall) vs precipitatable water, and Figure 2 shows SST vs precipitatable water. Putting the two together should give us a very good indication of whether the models’ precipitation is reasonable. Eyeballing the graphs, I would say that dprecipitation per deg C in the real world is way higher than in the models, but I would like to see the calc done formally. Willis – please can we have just one more calc ….. precipitation vs SST. TIA.
Wijfells, not Weiffels, no wonder I didn’t find it. There are several papers, here’s one :
https://www.researchgate.net/publication/252330096_Fifty_Years_of_Water_Cycle_Change_expressed_in_Ocean_Salinity
It seems self-contradicting …
“ While we confirm that global mean precipitation only weakly change with surface warming (2-3% K-1), the pattern amplification rate in both the freshwater flux and ocean salinity fields indicate larger responses. Our new observed salinity estimates suggest a change of between 8-16% K-1, close to, or greater than, the theoretical response described by the Clausius-Clapeyron relation.”
… but Willis’ data might resolve the issue.
Incidentally, Trenberth et al appear to contradict the IPCC/models too:
http://adsabs.harvard.edu/abs/2007JGRD..11223106T
“The environmental changes related to human influences on climate since 1970 have increased SSTs and water vapor, and the results suggest how this may have altered hurricanes and increased associated storm rainfalls, with the latter quantified to date to be of order 6 to 8%.“.
Mike Jonas July 30, 2016 at 12:18 am
and he quotes Wijfells:
Here you go …
Since evaporative cooling is directly proportional to rainfall, the shape of this is the same as that of Figure 6.
You can see why there is contradiction in the field … this highlights a couple of issues. The first is the attempted representation of a complex situation by means of a simple trendline of some kind (linear, exponential, etc.).
The second is the pernicious nature of averages. It is true that ON AVERAGE there is a slight increase in rainfall with temperature … but that average conceals a period of neutral or a slightly declining relationship at temperatures below 25°, and a strong positive correlation at temperatures above 25° …
Thanks for the request, Mike.
w.
The Feedback Issue:
The CO2 increase alone only causes a small temperature increase per doubling, so the main disagreement between alarmists and skeptics is about the feedback.
In real physical systems, the feedback generally tends to limit increases. Otherwise any small perturbation would tend to lead to instability, and extreme conditions. this is best covered by Le Châtelier’s principle: When a system at equilibrium is subjected to change in concentration, temperature, volume, or pressure, then the system readjusts itself to (partially) counteract the effect of the applied change and a new equilibrium is established.
Leonard Winsteind: “In real physical systems, the feedback generally tends to limit increases. Otherwise any small perturbation would tend to lead to instability, and extreme conditions.”
WR: “the feedback GENERALLY tends to limit increases”. Very important remark!
We know an exception, climate modelling, but indeed, that’s not in the real world.
Sorry typo: Leonard Weinstein. Sorry!
Wim: The cases where the negative feedback does not apply are cases where forcing exceeds boundaries and there is a shift of modes, e.g., a “tipping point”. There can be long period cases of out-of equilibrium response, or a case where external factors cause temporal or spatial shifts, e.g., ocean/ice sinks and currents storing/releasing or moving energy. I do not know of a type of case where there is simple positive feedback amplification as claimed for climate modeling.
Negative feedback creates a condition of equilibrium (balance). Positive feedback creates a condition of hysteresis (the tendency to “latch” in one of two extreme states).
It might look like that is what happens, but that is only one limited case, what it does is either oscillate at ever increasing amplitude to infinity, or until feedback stops the growth, running out of energy to sustain the growth is just one.
That hysteresis is the system transitioning from that limited condition, for instance the loud squeal of microphone speaker feedback loop that is limited by the power supply, back to normal operation when you move the mic.
The albedo due to clouds is significant therefore an increase in cloud coverage especially low cloud coverage is going to increase the albedo and lower the global temperatures. Further an increase in total global cloud coverage does not necessarily mean that the total water vapor in the entire atmosphere must also increase.
I think the dynamics of the atmospheric circulation/temperature structure of the atmosphere from ground level to stratosphere ,along with an increase in galactic cosmic rays (which some disagree with ) are the main factors that govern total global cloud coverage. This if true would allow total global cloud coverage to move independently or at least partially independently of total water vapor in the atmosphere.
And I thought the debate was over!
Great to have someone who actually thinks and does the work!
after reviewing figure 1 more closely….it’s apparent that the equation should read 62.8 ln tpw – 60.
nomenclature is not correct. LOG is assumed log10 whereas Ln is LOGe. in that case the slope would be 62.8/tpw. …but the yellow dashed line is not properly drawn…..if it were properly drawn it would probably more closely match the data…..
If you’re looking for a functional form for equilibrium water vapor pressure as it relates to temperature, here’s what I use:
P = exp(-5375.83585/T+21.2023734)
where T is in K and P is in Torr. This might be a possible starting point as a substitute for your “inverse sigmoid function”.
Thanks, Chris. I tried your expression, but it is a lousy fit to the actual data. As I remarked above, a typical exponential function doesn’t have the kind of “hook” at the right hand end.
Appreciated,
w.
Willis:
“The blank area in the lower right corner of Figure 7 shows that above a certain sea surface temperature … it’s gonna rain and cool it down. ” should be figure 6
Fantastic post. I agree. By taking things one at a time and ignoring evaporation and changes in clouds and absorption of solar, the IPCC has assumed a positive feedback that does not exist.
Thanks, Craig. Always more to learn …
Regards,
w.
Figure 2 looks remarkably like the Vapor Pressure vs Temperature curve for water, which follows a Clausius-Clapeyron equation: https://en.wikipedia.org/wiki/Vapour_pressure_of_water
The Log of the Vapor pressure (or, in this case, the TPW) varies linearly with the reciprocal of the absolute temperature.
Try replotting the log of the TPW (not a problem as it is always positive) against the reciprocal of the absolute temperature and looking for a linear regression…
tadchem July 29, 2016 at 8:50 am
Thanks, tadchem, but I fear you must have missed the part in the head post where I said regarding Figure 2:
The human eye isn’t very good at matching curves unless one is overlaid on the other …
Regards,
w.
Willis, my understanding is that the “runaway” part of GHG-induced global warming is caused by increasing amounts of water vapor in the atmosphere because of evaporation, and since water vapor is a more powerful GHG, we get “dangerous” global warming. From what I can find online, there is no trend in atmospheric water vapor at almost all levels except maybe at the lowest levels where there may be a slight increase. Would appreciate your and other’s thoughts. Thanks.
Because that water vapour doesn’t stay vapour – it condenses and precipitates is my 5c.
It does every night as dew, over most of the planet.
OT, but Willis your graphs evoke the sea, being replete with eddys and waves, currents, mists and even impressions of mysterious sea creatures in motion.
On second thought, your precipitable water function climbs more steeply than the function I wrote (which is the Clausius-Clapeyron equation – duh), especially for T > 20C. So there is something else going on. Perhaps there’s a bit of positive feedback in the sense that as T rises, there is more upward convection, leading to more water in the air column. Of course, this positive feedback could wind up being an overall negative feedback with regards to temperature and heat, given that there must be a huge energy cost to putting that much water in the air, and the heat has to come from cooling the surface of the ocean.
If I’m not mistaken (I often am), the Clausius-Clapeyron equation describes the situation in a closed system at equlilibrium, based on thermo-dynamics.
The trouble with that is that the earth climate system is NOT a closed system, and it is never at equilibrium (the earth rotates).
Once evaporation happens the atmosphere moves stuff around, so that materials are transported away form the region where the equilibrium closed system was supposed to be located.
Ergo, although CC might tell you what happens in a closed iso-thermal vessel; it goes all pear shaped when you let stuff leak out of that closed system.
G
Because every night it clamps down on the absolute amount of water vapor in the air, it has to, and this process of air temps nearing dew temps slows the cooling rate.
A non-linear cooling feedback control, and it’s basically controlled by dew point temps.
And I this is dwarfed by the drop in enthalpy over night, it averages about 9kJ/kg from max temp to min temp over night.
I’m starting to think that the cooling rate of the atm is very high, but ultimately regulated late at night from water vapor condensing out, restricting the path to space..
I was thinking of rain (which in the tropics is the big one), but dew is a very good point, esp for mid-latitiudes.
micro6500 July 29, 2016 at 9:55 am
Thanks for that, Micro. However, you need to be a bit careful there. For a given change in temperature, most of the change in enthalpy is from the change in enthalpy of the dry air. Remember that the enthalpy of dry air is 1.006 times the temperature in C. So if the temperature falls overnight from say 25°C to 15°C, with a dewpoint throughout of say 13°C (the atmosphere doesn’t gain or lose water), the change in dry air enthalpy would be 25 kJ/kg minus 15 kJ/kg equals 10 kj/kg. (Note that this would entail a change in relative humidity from ~ 50% during the day to ~ 90% at night.)
With moist air with a dewpoint of 13°, on the other hand, the entropy at 25°C is 48.8 kJ/kg, and at 15°c it is 38.5 kJ/kg. Note that as expected, the energy at both temperatures is significantly higher because of the latent heat. Note also that the difference between the two is 10.3 kJ/kg … and we know that 10 kJ/kg of that is from dry air.
Even if we get a couple of degrees below the dewpoint, so there is condensation, the numbers are still not impressive. If the temperature drops from 25° to 15° and the dewpoint is 17°, the total change is 14 kJ/kg … but 10 kJ/kg of that is still from the dry-air change.
Finally, I took a look at ten years of hourly data from Canada, and calculated the moist air and dry-air entropy. The correlation between the moist air entropy and the dry-air entropy (which is temperature times 1.006) is very close, with an R^2 of 0.9952 … so given that, it seems that the claim that enthalpy is a much better metric than temperature doesn’t hold up. According to the data I’ve looked at, entropy can be estimated with great accuracy as a linear function of the temperature, so either one would be equally good as a metric.
My best to you
w.
Thanks Willis.
I’ll have to dig into exactly what I’m doing in my code. The average change between min and max temp is ~18F, which likely is just about the same average as the change in enthalpy of 9,000 that I get, and you quoted as for a 10 C change.
I also took some 5 minute data from my weather station and I did eliminate a “enthalpy barrier” as why cooling slows down.
It’s possible ground and air temps being nearly the same slows cooling even though the radiative surface the ground radiates to is still an equally large temperature differential as when the cooling rate is still high.
Or maybe it is an optical effect, it’s gotten a bit humid the last couple nights and we had fog, optically thick.
Did you find the solar forcing data you were looking for?
I had thought I might have included only the water vapor entropy in my equation, leaving the dry-air entropy out. But I hadn’t, I just got back and took a look. It’s the entropy of both the air and water.
I did make a function that’s moisture entropy only, but it won’t show up until I rebuild all the reports.
But as I mentioned, after looking at 5 minute data all the energy loss is proportional to temperature change, just like you you pointed out (thanks, I saw the term but didn’t realize it’s significance in the results).
But it also shows the high rate of energy loss from the surface when the sun goes down, While we had really high temps this year, the rates of cooling will equally be high.
I was seeking the mathematical origin of the 342 +/- W/m^2 ToA ISR/TSI shown on so many atmospheric “heat” balances esp. Trenberth’s Figure 10 so I ran the numbers. Solar surface temp, S-B BB, radius/spherical surface area, orbital distance, orbital spherical area, etc. Yep, with an emissivity of .95 came up with an “average” 1,368 W/m^2 circular surface, 342 W/m^2 spread across the full atmospheric 100 km ToA spherical surface.
When I entered apehelion and perihelion distances I discovered that the total fluctuation of the solar “constant” from closest, 1,390 W/m^2, to farthest, 1,345 W/m^2, was 45.7 W/m^2, +/- 22.9 W/m^2. Wow, that’s one heck of a swing, especially considering IPCC’s 2.5 to 8.5 RPs. Makes those look pretty insignificant.
From what I can tell orbital eccentricity is dismissed as trivial, but 45.7 W/m^2 is far from trivial, it’s greater than any of IPCCs RCPs. IMHO it’s eccentricity that creates the seasons, axis inclination plays a minor role. Combine this large natural power flux fluctuation of eccentricity with the natural fluctuations in albedo, vegetation, and ocean processes and mankind’s CO2 contribution and RFs seem trivial in comparison.
No, this controls the length of night, as soon as the Sun comes up temps start to rise, and as soon as it sets it starts to cool.
Certainly the rotation modulates the daily swings, but when it comes to seasons I think the 45 W/m^2 eccentricity gorilla runs the show. These power fluxes aren’t real “heat” balances anyway. A 24 hour true heat balance based on dark and night, thick troposphere at equator, thin at poles, oblique angle areas, etc. & Q = U A dT would be more accurate & also extremely complex. How would one determine U, thermal conductivity for the atmosphere w/ clouds, moisture, RH, albedo, etc? And consider how thin the atmosphere is. Earth’s radius if 6,370 km, ToA 100 km, troposphere, 12 km. An onion skin wrapped around a soft ball.
I respectfully disagree.
I calculate SW for every surface station in the GSoD data set, in this case by day. For each day of the year, for each year since 1940, for the average TSI from 1978-2014, so an average about 98,000 station records per day for all of those years for every station, for the latitude band of 40 to 60 N, the minimum SW for a day is 524Whr/m-2, the maximum is 6304Whr/m-2, way more than 45W/m-2
Oh, Average daily rising temp is (NH18.22F to SH18.71F) ~1/2F more in the southern hemisphere as compared the northern hemisphere.
I also get a SW climate sensitivity from about 0.003F/Whr/m-2 to 0.014F/Whr/m-2, in the extra-tropics.
What’s “SW”? And you are mixing units, apples and oranges, Wh and W. Wh is energy, W is power, energy over time. Need to agree on terms and definitions. How is this measured? Horizontal surface or tilted to latitude?
I think I lost my post, so…
SW is short wave, or solar.
I think W is energy and Whr is power. 1W = 1J , 1W for 3,600 seconds is 1 Whr.
And tilted for latitude.
willis,
I like what you’ve done here. seems there’s lots of comments looking at only portions of what’s going on though. keep up the good work.
Salv wrote: “The albedo due to clouds is significant therefore an increase in cloud coverage especially low cloud coverage is going to increase the albedo and lower the global temperatures”
This principle has been described by a number of posters on this site. While it obviously holds a degree of truth I hope to demonstrate that it is ‘not always so”. Clear skies can lead to reduced measured LST in some latitudes. We should not overlook the fact that night follows day. What occurs at night?
When the right conditions occur I will demonstrate using New Zealand Metservice 4-day forecasts that coldest temperatures in New Zealand occur during clear skies, especially in winter. There are no such conditions at the moment but they will return within a week or two. This result in frosts. The day and night temperatures are commonly 3-4 degrees C lower during clear skies as compared to cloudy skies
The pattern consists of clear skies, warm sunshine, and cool shade – followed by rapid dew fall after dark and freezing. There is a net loss of soil moisture and temperature within days, which stops grass growth. Conversely, as long as there is cloud and rain, soil temperatures are such that some grass growth continues. The energy input during the sunny days is not enough to offset night-time freezing
There is usually little wind during these phases resulting in an inverted atmospheric temperature gradient at night. Frost forms in low-lying areas and one can feel the temperature change (warming) by walking up as little as 100 m in elevation
Studying the effects of water vapour and cloud in the tropics is one thing but we also need to consider the all-important higher latitudes that are instrumental in the cooling of the tropics through energy transfer – and the influence of night when no albedo is occurring
It’s never that simple 🙂
In reading both Willis analyses, seeing this data, and thinking about all the comments I have come away with two thoughts that I haven’t seen talked about. First, I wonder why everyone working in this field always tries to reduce data to a single equation that they hope somehow captures and actually represents the real-world process(es) occuring. What I see when I look at the data in the above scatter plots isn’t one catch-all equation . . . rather it’s what data looks like when a cycle is occurring . . . a cycle that includes at least one factor that causes hysteresis or a hysteresis loop . . . . perhaps caused by the fact that when water is leaving one state and moving to another (and perhaps even a third), that it carries energy with it. And then when it gives up that energy by returning it to space it returns by a different “path”. What I see in all that data are the hallmarks of a sigmoidal multi-phase “cooling” cycle with hysteresis typical of a “governor” process that is “working” to regulate the temperature. In some of that data I can even imagine that I see water -> vapor -> condensate -> freeze upward path with return paths from condensate and freeze back to previous states. And in each case more energy is transported up by convection than by radiation! At the very least, the data shows that the radiative energy reflecting, cooling and active heat transport governed by TPW is much more a factor in modulating our surface temperature than CO2!
My second thought is, I am very intrigued about Dr. Pollard’s theory that each little condensate droplet in clouds sucks up IR in the process of forming their liquid crytal layer and droplet surface charge, and my thoughts are: Has that IR sucking process been captured in any of the climate “models”? and Has anyone used the IR images from space of clouds and the “active transport” of energy UP by water to correct the estimates of how much of the energy balance is actually being carried out by the water cycle? After all the data also has shown that changing CO2 concentration has had an almost immeasurable cause/effect relationship for the last 18 years. Perhaps the “missing heat” has actually been transported off the planet quite effectively by the water cycle “heat-governor”??
I have not read all the comments but I noticed that in some commentators asked for the energy flux values for all-sky and cloudy sky. I have carried out a research work, where I have constructed the energy balance for all-sky, clear sky and cloudy sky conditions. I think it is the only presentation covering all these conditions.
There are some additional features not found in any other presentations: 1) The SW radiation reflected from the atmosphere is divided between the clouds and the air, 2) The absorption of SW radiation is divided between the clouds and the air, 3) The reflect SW radiation is partly absorbed by the clouds (in all other presentations the reflected SW radiation from the surface is capable to transmit through the clouds without losing its intensity). The figures attached to each flux are in order all-sky, clear sky and cloudy sky.
ave, thanks for a very interesting global energy balance plot. I will have to take some time and check it against the CERES data but for what it is, it looks reasonable at first blush.
However, like the canonical Kiehl-Trenberth global energy balance, it suffers from a fatal flaw … it doesn’t balance. In fact, no model of the single-atmospheric-layer type can balance. There’s not enough heat gain in a single-layer greenhouse to match the real earth.
This lack of balance in the K/T global energy balance was one of the things that drew me into climate science.
Here is the K/T model of the globe …
And here is the model I developed over a decade ago.
Note that unlike the K/T model, mine is in balance. By that I mean that each level radiates the same amount upwards and downwards, and the total entering each level is the same as the total leaving it.
I suppose I should write up a post on this … but first I have to study up on your lovely graphic and see if I might be able to include it in my model …
Regards,
w.
“I suppose I should write up a post on this”
Yes, please do! I think all of us will read the post with great interest.
The 321 upwelling/downwelling/”back” radiation is bunk.
Diagrams for average atmospheric energy transfer bookmarked.
Thank you.
Nicholas Schroeder July 30, 2016 at 1:15 pm
Uncited, unsupported, unexplained drive-by comments are bunk.
In fact, you can use a cheap IR thermometer to determine that the temperature straight up is not zero degrees … and how does an IR thermometer measure that?
By measuring the downwelling infrared radiation that you claim doesn’t exist … go figure.
w.
The notion that 15 C, 288 K, upwells 390 W/m^2 is bogus. In Trenberth’s Figure 10 et. al. power flux diagrams all of the W/m^2 are accounted for w/o the upwelling/downwelling/”back” radiation which then has to appear out of nowhere.
The GHGs exist in the mid to upper troposphere where it is cold, -20, -30, -40 C. NASA defines ToA as 100 km and the point where radiation balance occurs. That’s a long way from a 15 C surface measured 1.5 m above land.
Because of their low density gases have extremely low emissivity and together with the temperatures mentioned above are not capable of re-emitting a significant fraction of the hallucinated upwelling amount.
For instance S-B BB W/m^2 at:
C K 1.0 0.1 1.0(25%) 0.1(25%
-20 253 232.31 23.23 58.08 5.81
-30 243 197.70 19.77 49.43 4.94
-40 233 167.11 16.71 41.78 4.18
These amounts radiate in all direction, not just back to earth, say 25%. There is no way the downwelling radiation amounts come close to balancing the upwelling 390 W/m^2 and cannot perpetuate this GHE perpetual heat loop.
This GHE theory of upwelling/downwelling/”back” radiation keeping the surface warm is as bogus as cold fusion, phlogiston, Santa Claus and “reflective” steel/glass domes.
The surface is warm thanks to Q = U * A * dT, just like the insulated walls of a house.
BTW the S-B ideal BB radiation equation applies only in a vacuum. For an object to radiate 100% of its energy there can be no conduction or convection, i.e. no molecules or a vacuum. The upwelling calculation of 15 C, 288 K, 390 W/m^2 only applies/works in vacuum, e.g. ToA.
Nicholas Schroeder July 29, 2016 at 3:01 pm
Nicholas Schroeder July 30, 2016 at 9:49 am
For under a hundred dollars you can buy an “IR Thermometer”. You point it at something and it will tell you the temperature of that thing. And provided it is properly calibrated using the emissivity of the object, it will be very accurate.
Now, these thermometers work by using the Stefan-Boltzmann equation which relates temperature and thermal (IR) radiation. It states the following:
Radiation equals 0.000000567 times emissivity times Temperature to the fourth power
Using that S-B equation, the IR thermometer measures the radiation and converts it to temperature. If you point the thermometer at an object that it is at say 15° C, it measures the IR, converts that to temperature using the S-B equation, and voila! The readout says 15°C
So … care to explain to us all how the S-B equation “applies only in a vacuum”?
And just why do you think that it is “bogus” that a blackbody at 15°C radiates 390 W/m2? You can measure it, and it has been measured thousands of times.
Best regards,
w.
340 W/m^2 ISR arrive at the ToA (100 km per NASA), 100 W/m^2 are reflected straight away leaving 240 W/m^2 continuing on to be absorbed by the atmosphere (80 W/m^2) and surface (160 W/m^2). In order to maintain the existing thermal equilibrium and atmospheric temperature (not really required) 240 W/m^2 must leave the ToA. Leaving the surface at 1.5 m (IPCC Glossary) are: thermals, 17 W/m^2; evapotranspiration, 80 W/m^2; LWIR, 63 W/m^2 sub-totaling 160 W/m^2 plus the atmosphere’s 80 W/m^2 making a grand total of 240 W/m^2 OLR at ToA.
When more energy leaves ToA than enters it, the atmosphere will cool down. When less energy leaves the ToA than enters it, the atmosphere will heat up. The GHE theory postulates that GHGs impede/trap/store the flow of heat reducing the amount leaving the ToA and as a consequence the atmosphere will heat up. Actually if the energy moving through to the ToA goes down, say from 240 to 238 W/m^2, the atmosphere will cool per Q/A = U * dT. The same condition could also be due to increased albedo decreasing heat to the atmosphere & surface or ocean absorbing energy.
The S-B BB temperature corresponding to ToA 240 W/m^2 OLR is 255 K or -18 C. This ToA “surface” value is compared to a surface “surface” at 1.5 m temperature of 288 K, 15 C. The 33 C higher 1.5 m temperature is allegedly attributed to/explained by the GHE theory.
Comparing ToA values to 1.5 m values is an incorrect comparison.
The S-B BB ToA “surface” temperature of 255 K should be compared to the ToA observed “surface” temperature of 193 K, -80 C, not the 1.5 m above land “surface” temperature of 288 K, 15 C. The – 62 difference is explained by the earth’s effective emissivity. The ratio of the ToA observed “surface” temperature (^4) at 100 km to the S-B BB temperature (^4) equals an emissivity of .328. Emissivity is not the same as albedo.
Because the +33 C comparison between ToA “surface” 255 K and 1.5 m “surface” 288 K is invalid the perceived need for a GHE theory/explanation results in an invalid non-solution to a non-problem.
References: ACS Toolkit, Trenberth et. al. 2011 “Atmospheric Moisture Transports …….” Figure 10, IPCC AR5 Annex III, http://earthobservatory.nasa.gov/IOTD/view.php?id=7373
So what am I missing here? This went to the ACS authors of the tool kit & received zero response.
“340 W/m^2 ISR arrive at the ToA (100 km per NASA), 100 W/m^2 are reflected straight away”
WR: Strange. at a height of 100 km, 100W/m^2 are reflected straight away? Who found that out? Not 98,9 or 103,6 or 89,7???? Or 101,23478? And exactly 340 W/m^2 ISR arrive at ToA (100km)?
Based on Trenberth’s Figure 10 and typical of power flux graphics. See listed references. Not my idea, I wouldn’t do it that way.
TSI measured perpendicular to solar radiation is about 1,368 W/m^2. That’s spread over a circular cross sectional area. Spread same energy over and perpendicular to sphere, area of sphere is 4 times area of disc. Divide 1,368 by 4 = 342 – Presto magico!
Yeah, there are substantial uncertainties noted on Figure 10, orders of magnitude greater than IPCC AR5’s CO2 RF of 2 W/m^2.
Nicholas Schroeder July 29, 2016 at 6:32 pm
“Yeah, there are substantial uncertainties noted on Figure 10, orders of magnitude greater than IPCC AR5’s CO2 RF of 2 W/m^2”
WR: When those data have that high uncertainties – “orders of magnitude greater than IPCC AR5’s CO2 RF of 2 W/m^2” – why is anyone still using them?
TOA over any one area can not be in equalibrium, for instance in the NH during the summer there’s hours more sun than night, and it changes every day. And you pointed out 45W/m-2 (55?) In the orbit, it is never in equalibrium.
The power fluxes, W/m^2, graphics I was referencing don’t account for day/night, oblique sunlight at poles, etc. The 45 W/m^2 is perpendicular to the entire atmosphere’s surface. As I mentioned if one wants a real heat balance that’s a whole ‘nother and quite complicated discussion.
Had to look back at previous exchange.
“…the minimum SW (Solar Wattage = luminosity?) for a day is 524Whr/m-2, the maximum is 6304Whr/m-2, way more than 45W/m-2.”
So the 524 and 6,304 Wh/m^2 were collected over how many hours? 8? 12? 24? What was the peak W/m^2? Average? Was this a tracking instrument maintaining perpendicularity to ISR? The power flux diagrams everyone uses don’t do any of this.
The power flux diagrams assume about 30% albedo. If your instrument sees clear skies, any comparison goes right out the window.
Those were calculated values for an entire 24hr period. And the only point is that the changes in the length of day cause a far higher change in forcing than 45W/m-2
What you are missing is that TSI (annual orbital average value) is about 1362 w/m^2; it is NOT 342 W/m^2.
As a result, when the sun rises in the morning, the earth system, surface and atmosphere (oceans too) warm rapidly above their overnight Temperatures, before sunrise.
At 34 2 W/m^2 continuous all over the earth, this planet will NEVER reach an average near surface Temperature of 288 K, which is what all respected sources say it is.
I can’t observe an average of anything, so I don’t pay any attention to averages.
Neither does planet earth; it has no idea what the hell you are talking about. It responds immediately to whatever happens, even as fast as 10^-43 seconds. After that, the next think that can happen does happen.
G
Do any of the lofty climatologists participate in any open public forum collaborations like this?
It seems like the most productive type of peer review with the highest potential for advancement and discovery.
Maybe Trenberth, Mann, Schmidt et al do not find the idea team worthy?
There have been a few mainstream climate scientists who have been willing to put their ideas out for public examination, and I commend them for it.
However, such free examination in the bright light of the public forum is anathema to Trenberth, Mann, Schmidt, and many of the other leading lights of climate alarmism. They do their best work in the dark.
w.