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
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
There seem to be many and varied confused views here. And as usual many are dressed up in the phoney mathematics of radiative imbalance caused by ‘greenhouse gases’, a misnomer if ever there was one.
The first major confusion seems to be with regard to how actual (real) heat behaves on the planet.
It should be obvious to anyone (other than a Warmist Climate ‘scientist’) and by ‘obvious’ I mean clearly apparent from the observation of real time data…that ocean currents are the dominant form of heat transference on the planet and that water vapour is the dominant medium of heat transference in the atmosphere.
But don’t take my silly old word for it!
Get on the satellite viewers and look at the ocean currents check out that Gulf Stream…literally a river of warm water cutting northwards from the mid atlantic towards the Arctic… The ocean currents transport heat to the POLES.
Now whilst you’re on the satellite viewers, go check out the excellent University of Wisconsin Tropical Cyclones page…there you will be able to see (in actual real time) rapid convective cooling of equatorial oceans and land areas…
30˚C at the surface and MINUS 50˚C or colder at the tops of the clouds. (which are trailing off eastwards and southwards/northwards, heading to guess where? That’s right the POLES.
Now before any smart alec points out that the latent heat of evaporation is equal to the latent heat of condensation (yawn) let ME point out that the cooling process very much depends on WHERE the two take place.
The heat being collected by the water vapour is at the surface…the heat being rejected by the water vapour is at 30 or 40 thousand feet…where it is permanently and eternally COLD.
The day some clever Warmist, shows me evidence that the earth’s atmosphere is warming rapidly at 30,000 feet is the day I will start getting mildly alarmed.
Tell you what would alarm me though, be an announcement that the Earth’s tilt angle had shifted.
That would scare me.
“There seem to be many and varied confused views here. And as usual many are dressed up in the phoney mathematics of radiative imbalance caused by ‘greenhouse gases’, a misnomer if ever there was one.”
Thank you, I thought I was going insane.
All these calculations of radiative forcing and evap are useless if you cant show how winds are interacting with sufficient resolution.
Feeding Intellectualism little more.
As Lindzen says, these “are all thing being” equal base calculations and they are entirely misleading.
Too many are jumping down the rabbit hole
but it looks good on paper for sure ROFL
I’ve noticed the weather station near me on weatherunderground.com also shows sun intensity in wats/m2. It’s been interesting to see how it changes from day to day and within the day because of cloud cover.
Willis, thank you for your analysis and thought-provoking points. Many good comments too, e.g. Don V, Dr. Spencer, ristvan, etc.
I would like to offer something to deal with the no-net-cooling-from-precipitation idea. Sure, the outward emission of LWIR is the only final flux which rejects absorbed heat from the earth/atmosphere system. But the system is equipped with a variable-geometry, variable-altitude, variable-composition, variable-temperature upper “emitter” which does most of this work. This emitter is supplied with heat energy and IR-active substances (water, CO2, etc) from below, at variable velocities and rates. Absorption of outward/upward emitted LWIR by the overlying atmosphere diminishes with altitude, so getting the mass and heat to higher altitude, with favorable geometry and emission physics, is what it’s all about for best emitter performance.
Mechanically, buoyancy drives heat and mass upward based on the influence of temperature and water vapor on CAPE, and gravity is kind enough to return it all for free, much of the water having changed phase perhaps numerous times. So convection and precipitation dynamics must have a huge influence on the “emitter” output. An example: imagine an isolated cumulonimbus cloud reaching to 50,000 feet. The geometry of LWIR emission from the cloud is not just upward but outward, and the low-absorption path to space opens up dramatically.
Please keep up the good work about water vapor, the idea of a governed system, and the power of emergent phenomena.
Elegantly put…and essentially correct.
If the system is “circular”, might it be possibly better to think of it as “recursive”, like a fractal?
Nick Stokes,
Yes there is no net cooling from evaporation if you look at the entire atmosphere. But there is a large transport of heat from low altitude to high, where it is far easier for that heat to escape to space. There most certainly is net evaporative cooling at the surface, which is where most solar short wave energy is absorbed, and where rain falls to replace what has evaporated. You can, of course, focus on the ” whole atmosphere”, but the whole atmosphere is not where warming is measured by surface thermometers, and, we should remember, is where people live. Willis raises a perfectly legitimate question: is the net feedback from increasing water vapor in the atmosphere positive or negative with respect to surface temperatures? Seems to me Willis presents data which support a likely net negative feedback, at least over the oceans, when everything is considered, including clouds. Land may be somewhat different since available water is usually not unlimited as in the ocean.
Steve,
Yes, I agreed that more evap/rain transports more heat. But the statement of Willis that I was commenting on was quite quantitative:
” that’s a serious amount of cooling, about ten watts of additional cooling per additional kg of precipitable water”
And my query was, where does that come from? It’s a lot. Willis gives average PW value at 29kg/m2. Average wv transport is 80 W/m2 (Trenberth). So it would be a little surprising if 1 kg increased transport by 10 W/m2. But he doesn’t say transport – he says cooling, which is something else again. He has cited just TRMM data for rainfall, along with the SST data and PW. It looks a lot to me as if he has just multiplied mass of rain increment by specific heat. That is also where Trenberth’s 80 W/m2 figure comes from. But Willis then treats that not as a local transport (most condensation occurs at relatively low levels of the troposphere) but as a feedback to be offset against forcings. For that, it would have to be heat taken in total from the atmosphere, not just moved.
Amazing that everyone understands why the desert gets cold at night, but seem to be stuck on why the upper atmosphere should be so cold!
Nick Stokes,
The increase in PW is only important to the extent that it relates to the rate of rainfall. PW over deserts is non-zero, but rainfall is near zero. Over the tropical ocean, a 1kg/m^2 increase in PW does appear to strongly influence rainfall, and net evaporative cooling at the surface (considered globally) is just proportional to the total rate of rainfall. This is a not-trivial issue for sure. The net positive feedback for GCM’s is in part due to their prediction that PW will increase globally, restricting heat loss to space, without a large increase in rainfall (and its associated surface cooling). When Mears et al suggested that *measured* rainfall did in fact appear to increase with temperature in proportion (roughly) to the increase in water vapor pressure with temperature, the modelers were, shall we say, less than very happy. Much like they are less than very happy with balloon and satellite measurements of tropospheric temperatures. There is a repeating pattern here that you might notice…. and it seems to me related to political motivations.
I believe I partially agree with your general point here – however, doesn’t it have to be true that at any given point in the atmosphere, *on average* doesn’t more heat have to move upwards than downwards. OTW, could not effectively cool. IOW, if we increase evaporation by 10W/m2, doesn’t that have to cool the surface by at 5W/m2?
Furthermore, for the portion of the 10 W/m2 that does, in fact, return to warm the surface, wouldn’t that have to show up as “backradiation” which amount is already accounted for in the positive side of the WV feedback?
Cheers, 🙂
Just some general comments about the energy balance and radiation fluxes. I refer to my energy balance figure (aveollila at 1:40). The energy balance must be calculated separately for the surface, for the atmosphere, and for the TOA. As in all energy balance calculations the incoming and outgoing energy fluxes must be the same; that is why it is called a balance. The energy balance values for these three places are for all-sky conditions (W/m2): TOA 237.8, atmosphere 511.5, and surface 554.2.
As always, the downward LW radiation flux (Ed = 344.7 W/m2) from the atmosphere at the surface, creates comments that it is not possible. It is simply true therefore that 1) it can be measured, and 2) it can be calculated by spectral analysis methods as I have done. Also the radiation flux (Es = 395.6 W/m2) emitted by the surface can be calculated and can be measured. Theory and the practice are so close to each other that there is no conflict.
One more comment about the absorption caused by the GH gases in the atmosphere. In my figure it is marked by the acronym Ag. It is in in clear sky conditions 310.9 W/m2 and in this case it is based on the spectral analysis calculations. There is a kind of confusion about this absorption, because Willis has used the term “The atmospheric absorption” being about 155 W/m2 (estimated by from Figure 1) in the normal atmosphere. In my energy balance presentation this figure is the difference between the surface emitted flux 395.6 and the OLR flux at TOA 237.8 making 157.8 W/2.
I include also a figure below showing how quickly the absorption by GH happens in the atmosphere: 95 % below 2 km altitude. Therefore it does not make sense to talk about how much there are GH gases above the troposphere because 98 % of GH absorption happens below 11 km. And this absorption is the key in GH phenomenon.
Here is also a simplified presentation about the energy balance showing only the all-sky values. They very close to the values of NASA. The only big difference is in a LW radiation flux going through the so called “atmospheric window” without any absorption directly into the space.
More slideshow presentations at my website http://www.climatexam.com
“Here is also a simplified presentation about the energy balance showing only the all-sky values.”
I think that’s where you start going wrong in your thinking…I mean the ‘all-sky’ bit.
It may be mathematically calculable but from an engineering point of view it’s completely meaningless.
Charles. If you say that the energy balance is meaningless, you have to to specify it more accurately. My basic university training is in engineering concerning chemical processes, mechanical processes, energy and mass transfer processes, and process dynamic et automation. The basis tool of engineering is to find out the mass and energy balance for every new process under design. If you do not know these elements of the process, you are are lost.
aveollila: that diagram shows where climate went off the rails. Applying steady-state theories that are reasonable in fast kinetic systems, to clear sky conditions in order to look at climate might have been reasonable in the 80s to look at crude effects of GHGs, but the earth on a daily basis is *never* in equilibrium thermally at the surface, nor anywhere else. That’s why you have a daytime max and a daytime min temp and those extremes don’t usually coincide with solar noon and solar midnight. Averaging might fool some people into thinking they have equilibrium, but they don’t, and for the question of whether CO2 is important in decadal climate, that matters. A lot.
Dixon. When we talk about the climate change, the minimum period to detect the global temperature change is the solar cycle, in average 11.2 years. The warming effects of GHGs for shorter period or even for cosmic forces does not work. The changes are so small that they are impossible to measure. You may calculate the warming effects of GHGs or sun irradiation changes or cloudiness changes, but it does not lead to anywhere.
That is why the energy balance values are based on the yearly averages concerning flux values. In many cases the measured flux values are averaged even for a decade. It is possible to use shorter time periods but they are not useful in the case of climate change.
Roy Spencer July 29, 2016 at 4:26 am
Dr. Roy, always good to hear from you. A couple of comments.
First, a thousand metres below where I’m standing it’s about 30°C warmer than where I am. And three thousand metres straight up it is freezing. When I’m sailing comfortably on the tropical ocean, a thousand metres down it’s quite cold.
So what?
The issue is and always has been the temperatures and conditions here on the surface where we live. And as a result, it doesn’t matter if the cooling of the surface is “exactly balanced” by things happening where we don’t live. The dangers hyped by the alarmists are about temperatures on the surface. And unless a change makes something happen here on the surface, we’ll not even notice it.
Next, it’s not true that “There is no net cooling of the climate system” due to “evaporation and convective rainfall activity”. I can think of several ways that those phenomena actively cool the whole climate system.
To start with, the clouds associated with “convective rainfall activity” push the albedo much higher than it would be otherwise. This reduces the amount of incoming solar energy, so the whole system cools.
Next, the overall temperature of the planet depends in part on how fast the excess energy in the tropics can be moved to the poles and rejected into space. If it cannot be moved quickly, the energy builds up and the temperature rises. But the speed of the tropics-poles transport depends on the strength of the convective rainfall activity in the Inter Tropical Convergence Zone … so that’s the second way increased convective rainfall activity brings net cooling to the climate system.
Third, as I showed above, increased evaporation increases absolute humidity, which increases the absorption of the downwelling sunlight before it reaches the surface. Obviously, this will cool the surface, but it will also in turn leave the entire system cooler than it would have been if that sunlight had reached the surface.
Fourth, the thunderstorm towers serve as “heat pipes” which move immense amounts of warm air from the surface up to the upper troposphere … and they do it without allowing the moving air to interact with the surrounding troposphere. On the way from the surface up to the bottom of the cloud the energy is moved as latent heat, which doesn’t increase radiation. Once the moist warm air enters the bottom of the thunderstorm cloud it condenses, and the latent heat is released as sensible heat. But within the cloud the radiation of the air is immediately absorbed by the water droplets that make up the cloud, so the rising column of air inside the thunderstorm tower is not interacting radiatively with the air surrounding the cloud. It’s a neat trick, the heat is kept hidden away from interacting with the surrounding GHGS all the way from the surface to high in the troposphere.
When the rising air inside the pipe finally emerges at the top of the thunderstorm towers, is is above the majority of the greenhouse gases. In particular it is above virtually all of the water vapor, but at an altitude of 15 km in the tropics, for example, it’s also above 80% of the CO2. As a result, this movement of heat will increase the rate of heat loss for the entire system.
Fifth, the winds created by and surrounding the convective rainfall activity roughen up the surface of the ocean. This increases the surface albedo of the ocean by about 10%. Since on average about 170 W/m2 of sunlight strike the surface, that would be a change of about 17 W/m2, and again this cools the entire system.
Sixth, the air descending in between the thunderstorm towers is very dry. This lack of the main GHG, water vapor, allows the more efficient loss of energy to space.
So while the most important activity from our viewpoint is the cooling of the surface, there are also a number of ways in which evaporation and convective rainfall activity cool the entire climate system.
Best regards,
w.
There IS a net cooling of the climate system.
As the man said, I can explain it to you…but I can’t understand it for you!
“When the rising air inside the pipe finally emerges at the top of the thunderstorm towers, is is above the majority of the greenhouse gases. In particular it is above virtually all of the water vapor, but at an altitude of 15 km in the tropics, for example, it’s also above 80% of the CO2. As a result, this movement of heat will increase the rate of heat loss for the entire system.”
Willis, aveollila July 29, 2016 at 10:31 pm posted a figure which shows that 95% of the Greenhouse Effect happens below 2 km altitude. I cannot control that number, but I like to know at what height (for every latitude) heat transport by clouds effectively ‘pass the greenhouse blanket’, so to say. I suppose spaceward emission by molecules will become exponentionally effective at rising altitudes.
I think it is important to know. The evaporation minus precipitation figure as posted by lgl July 29, 2016 at 9:09 am shows a precipitation surplus near the poles, in the area where we normally find low pressure area’s. Those low pressure area’s are impressive upward heat transport systems as well. For an image about the extent: https://earth.nullschool.net/#current/wind/surface/level/overlay=mean_sea_level_pressure/orthographic=-46.86,-82.28,587/loc=109.193,-61.962
What I would like to know is what role those depressions play in ‘cooling the earth’. I suppose that besides thunderstorms and hurricanes they are the third upward ‘heatpipe’ system that can be activated at warming. Activated by pressure differences which arise when temperature gradients rise, resulting in more wind, more evaporation and more upward energy transport.
There is a big transport of energy poleward, by oceans and wind. That energy has to disappear spaceward. And there is a big blanket of clouds near the poles. http://www.esa.int/Our_Activities/Observing_the_Earth/Space_for_our_climate/Highlights/Cloud_cover
So, how does the poleward transported energy reaches space?
So, how does the poleward transported energy reaches space?
I find it very bizarre that people who drone on endlessly about radiative imbalances and down welling IR etc etc…STILL haven’t figured out that there’s not much down welling anything over the Winter Poles!!!
It’s DARK and it’s COLD…any energy contained in water vapour reaching these areas…or any energy being carried there by ocean currents to these regions is lost to space because the surface temperature…minus 20˚C is not much different from the temperature at 30,000 feet i.e. minus 50˚C…the winter poles are like a direct conduit for heat loss.
Have you ever tried looking at Nullschol Earth?
Wim Röst July 30, 2016 at 3:52 am
Good question, Wim. If you go to MODTRAN and click on the “Submit the calculation” button, on the lower right of the page you can see how each of the major GHGs varies with altitude.
Regards,
w.
charles nelson July 30, 2016 at 4:10 am
I find it very bizarre that people make claims without running the numbers. According to MODTRAN the midwinter subarctic downwelling longwave, with the ground temperature at zero degrees, is still 163 W/m2.
And since 163 W/m2 is about the amount of sunlight striking the surface on a 24/7 basis, I would hardly call it “not much downwelling”.
w.
My apologies Willis, two very interesting posts, as always when you talk of water vapour, clouds and rain, it’s enlightening. I know you have said you like the way you fit your science around your paid work, I just hope you get the formal recognition you deserve one day. Many an academic would have retired having contributed far less than you have to the advancement of a field.
On your 4th point, could someone clever than I build a relatively simple model to look at the transport side of a tropical cumulonimbus system? We need to know how much energy is transported upwards and in what time, while considering how long it would take that equivalent amount of energy to radiate back down through a clear sky atmosphere (or even a wet cloudy one which will be even slower). The ‘345’ in aveollila’s model is (I think) a much slower process than the convection upwards that got it there (which isn’t shown).
QUESTION- Why is it global temperatures warm during an El Nino which supports more convection in the tropics, given what you just said which I agree with? Why is that so? Thanks.
Willis, thanks for an again innovative post and clarifying comments. Please keep enlightening us.
https://wattsupwiththat.com/2016/07/28/precipitable-water-redux/#comment-2267291
>>>
In this comment you get to an evaporative cooling power of 80 W/m2 based on precipitation of 1 cubic metre per year. Is this 80 W/m2 a rounded figure, or else what specific evaporative heat (J/kg, cal/g) are you calculating with and where can I find it?
https://wattsupwiththat.com/2016/07/28/precipitable-water-redux/#comment-2268115
“Fourth, the thunderstorm towers serve as “heat pipes” which move immense amounts of warm air from the surface up to the upper troposphere … and they do it without allowing the moving air to interact with the surrounding troposphere. On the way from the surface up to the bottom of the cloud the energy is moved as latent heat, which doesn’t increase radiation. Once the moist warm air enters the bottom of the thunderstorm cloud it condenses, and the latent heat is released as sensible heat. But within the cloud the radiation of the air is immediately absorbed by the water droplets that make up the cloud, so the rising column of air inside the thunderstorm tower is not interacting radiatively with the air surrounding the cloud. It’s a neat trick, the heat is kept hidden away from interacting with the surrounding GHGS all the way from the surface to high in the troposphere.
When the rising air inside the pipe finally emerges at the top of the thunderstorm towers, is is above the majority of the greenhouse gases.”
>>>
This is a truly interesting mechanism. Is this your own reasoning, or did you find support for it in literature or elsewhere?
If I understand correctly, the latent heat released at condensing, which occurs from cloud bottom to top, stays within the cloud as warmed up rising air and water droplets. When this warmed up air and water mass reaches the cloud top, what exactly happens to the formerly latent heat it contains? Bearing in mind the low density of the air at cloud top altitude, is the heat mainly passed as sensible heat to the surrounding thin air, or is it rapidly shed as IR radiation with about half of it passing directly to space without heating the atmosphere?
Greg July 29, 2016 at 5:21 am
I fear you’ve misunderstood the caption. Yes, the slope of the graph varies. It varies as 63.8 / TPW. When you put in different values for TPW you get different values for the slope. That’s the whole point. Differentiating the underlying equation allows us to specify the slope at any point.
w.
Willis….you need to use the correct nomenclature in your equations. LOG is log10…Ln is LOGe. The equation should read. 62.8xLn(tpw)-60
Jamie July 30, 2016 at 4:47 am
Thanks Jamie, and sorry for the confusion, but obviously we move in different circles. On my planet “Log” always means the natural log to the base “e”, with the others distinguished as Log2 or Log10 .
Well, except when I’m using Excel, which uses its own peculiar terminology for many things …
All the best,
w.
Jamie:
In all the programming languages and math libraries I use on a professional basis, “log” by itself means the natural log.
Willis
Well on my planet called earth we have standard notations in accordance with the ISO standard
http://physics.nist.gov/cuu/pdf/sp811.pdf Page 33 for logarithms
The reason we have something like this is because someone like me who has to write calculations all the time so other engineers can review and understand them. But someone who has like a psychology degree wouldn’t understand this
Jamie July 30, 2016 at 3:41 pm
I fear you are reading something that is not there. On the page you listed there was no definition of what is meant by “log(x)”. Instead, your reference says (emphasis mine):
So the question becomes, when is it “required”? And that is a judgement call. I judged it wasn’t required, but obviously YMMV …
I do find this:
But as you say, “someone who has not progressed to much more advanced mathematics wouldn’t understand this” … sorry, I couldn’t resist the karmic response. Someone once described “karma” as hitting a golf ball in a tiled bathroom … and making nasty comments about my education is definitely bathroom golf.
Look, Jamie, I have no time for grammar Nazis, even in science. Lots and lots of scientists and programmers on this planet use “log” to mean the natural log, see e.g. Ed Bo’s comment just above. Me, I speak math the way that it is actually spoken by scientists and programmers, not the way some pundit claims it should be spoken. And with the exception of Excel Visual Basic, which is like programming for dummies, the programming languages I have used for the past fifty years (mainly R, Mathematica, MatLab, Fortran, and C) ALL use “log(x)” for the natural log.
So, are you gonna call the NIST swat team to teach the programmers of the world the error of their ways? For sixty years now the makers of Fortran have spread their evil lies about “log(x)” being the natural log … are you going to sit still for this insidious weakening of our mathematical moral fiber? Are you going to send nasty comments to the mathematical giant Steven Wolfram, insulting his education because Mathematica uses “log(x)” for the natural log?
What’s next? Well, there are still plenty of opportunities, lots of things you could grouse about. The NIST document you referred to says:
So … are gonna complain that I didn’t use italic boldface for vector quantities? … seriously, Jamie, you strike me as nobody’s fool, aren’t there better uses of your fine mind?
w.
Willis…
Sorry. It was page 41…..
It states that people in the physical sciences and technologies should use these terms
Of which either LOGeX or Ln x is acceptable
This is not computer programming. This is physical sciences.
And again my point your education level has everything to do with this. You don’t work the the physical sciences or have the degree…. The warmists basic assessment of you is correct.
I’ll ignore the harpies whose only ability is to cut and paste, this is for climate scientists, I’ve seen their work, and while they might annotate logN correctly, some of them are clueless as scientists and would be better served by wearing a dress and shaking pom poms.
Jamie July 31, 2016 at 6:39 am
Sorry, but Page 41 doesn’t contain the word “Log” or “Ln” on it anywhere … you sure you understand this “reading” lark? The page number is the little number down at the bottom of th… aw, never mind.
Dear heavens, you are indeed a grammar Nazi. What’s next, you gonna put up some fences to keep the riff-raff and the computer programmers out?
Here’s the thing, Jamie. Most of the texts and the studies that I read use “Log” to mean the natural log, and “log10 to mean log to the base ten.
And obviously, most of the texts and the studies that you read use “Log” to mean log to the base 10, and “Ln” to mean log to the base e. And that’s just fine.
But the language is what it is, not what you say it is. The NIST document you attempted to reference said that one should subscript the word log “as required”. In the studies I read it’s not required, because most everyone uses “log” to mean the natural log.
The warmists’ basic assessment of me is that like you, they can find little to attack in my scientific work, so they are reduced to making meaningless ad hominem attacks on my habits, my ancestry, my use of the word “log”, my education, my history … any and every puerile meaningless thing, but not my science.
And in the middle of all of this ankle-biting from twerps and grammar Nazis like yourself, I continue to publish in the scientific journals, where fortunately the editors sometimes still care about my science and don’t care about my education, as science should be. The Editors of Nature magazine didn’t ask me about my education before publishing my small contribution to moving science forwards … call me crazy, but I’ll take their opinion over yours.
As I said before, you are wasting your obvious talents on this meaningless attack. And you are harming your own reputation in the process. I know, for example, that when I next see your name on a comment, I’ll pay less attention to whatever it is you’re saying … and I doubt I’m the only one.
Is this what you want?
How about if you apply your obvious gifts to DISCUSSING THE INTERESTING SCIENTIFIC QUESTIONS that abound in climate like everyone else is doing, and give up this obsession with shooting yourself in the foot? You’ve succeeded. Move on.
Sincerely,
w.
Well on the planet where I come from, the logarithmic function is taught in classes in Pure Mathematics, not in classes on computer programming.
And on that planet, the term Ln or ln is used exclusively in reference to the NATURAL or NAPERIAN logarithm where the base is (e = 2.71828…)
Just Log would refer to the function usually found printed in books to four or five or even seven digits which are logarithms to the base 10, which is what is the common base system of the real human inhabited world.
I would think that computer programmers, would use base (2) or even base (16).
Now I can’t vouch for any ” science ” discipline which uses invented terms like ” forcings ” and such.
Now one of the advantages of the Rod / Stone / Fortnight system of units, is that we use almost any number as a base, so you will find , 2, 5, 10, 12, 14, 20, 22 and so on as counting bases for various things and many more.
G
Yes, apologies, I did misunderstand what you meant there.
What is the effect on emission spaceward from a thunderstorm that rises above 80% of the CO2?
I suppose a calculation can be done (by someone who knows better than I how to do so) but I will do a simple attempt.
We must keep in mind a system with ‘rounds’ like in the Bill Illis’
July 29, 2016 at 6:53 am figure. (the blue one: “Initial Temperature Increase from CO2 and then how Feedbacks Lead to 3,0C of Warming”)
In this simple thought experiment energy can only be emitted upward and downward, so 50% each way. The energy of the thunderstorm is brought upwards to a level where most of the greenhouse gases are below.
1st Round. In the first round nearly all the upward emitted energy (50%) reaches space. Let’s say that all of the downward emission is captured by greenhouse gases below and is re-emitted in round 2 half upwards and half downwards.
2nd Round. Half of the below catched 50% (=25%) is emitted to space and a bit less than this 25% reaches space. The other 25% goes downwards and will be captured by greenhouse gases.
3rd Round. From the remaining 25% half goes upwards direction space etc.
Of course this is far too simple, but it must be, that by far most of the energy that is brought ‘above the greenhouse blanket’ will be emitted to space. And so effectively will cool the Earth. I am sure someone can make nice calculations on this.
Ah, Willis…I think we’ve finally got to the source of your confusion.
Quote:
“I find it very bizarre that people make claims without running the numbers. According to MODTRAN the midwinter subarctic downwelling longwave, with the ground temperature at zero degrees, is still 163 W/m2.
And since 163 W/m2 is about the amount of sunlight striking the surface on a 24/7 basis, I would hardly call it “not much downwelling”.
You see diddling round with meaningless numbers/averages they can get themselves in an awful muddle when confronted by actual reality.
Right now the surface temperature in Antarctica is MINUS 55˚C…the temperature at 250 hPa is?
MINUS 60˚C.
There a appears to be a ‘hole in your greenhouse’ mate!
Charles, look up the word “subarctic”. You will find it does NOT refer to Antarctica as you seem to think.
And as for your pathetic attempt at sniping, where after foolishly thinking that Antarctica is in the subarctic you say:
May I suggest that you take a lesson from the humble rooster, and before you start crowing you make sure it is actually dawn?
Best regards,
w.
I’ve recently started using Mathematica (with mixed results, and mixed feelings). But it has a built in function called FindFormula[data]. It takes the data list, and finds the best kind of formula to approximate the data. There are, in fact, extensions of it. The most interesting is FindFormula[data,x,n,prop], where x is, of course the independent variable, but “n” is the number of different formulas it will find, not their order. Finally “prop” is a specified property for the formula, and includes “complexity,” “mean square error”, and “score” (an internal score). It’re really quite a remarkable feature.
Well the aim of contriving ANY formula to match to measured data is multifold.
The first aim would be to describe any measured set of numbers with a formula that has fewer independent variables than the number of measured data points.
That is always good, as otherwise the set of observed data points is the best expression of the results.
A second aim, when trying to fit a set of measured data values to a mathematical formula, is to do so with a mathematical form that describes the mathematical behavior of a proposed model of the actual physical system.
For example, I believe that the Planck Formula for the black body radiation function was concocted in just such a fashion. As far as I know, a theoretical derivation of the BB radiation law was developed somewhat later by Bose.
Planck basically made up his formula out of whole cloth, using the failed Wiens and Raleigh-Jeans formulas as a starting point.
I think it was either Bose or Einstein, or both collaboratively who eventually derived the Planck formula including the exact physically based first and second radiation constants C1 and C2.
I can’t find much reason to force fit measured data into a formula, unless that derived formula actually describes the behavior or a model of the real physical system.
The Planck formula for BB radiation, which is a totally fictitious non real physical object, is made up entirely of well known fundamental physical constants, that are extremely accurately know from painstaking experimental measurements. And yes real practical approximations to an ideal Black Body do match the Planck theoretical formula with remarkable accuracy.
That blows my mind, that something completely fictitious, which cannot possibly exist, can be approximated quite accurately so that its fictional theory can be used as a useful tool for study and research.
G
For those still following this article, you may find the material at the following link to be of interest: https://younghs.com/2016/07/09/the-mystery-of-evaporation/
Willis: You may be able to fit many functions to a plot of some observable variable vs absorption (or some fraction of such a plot), but such as a mathematical relationship doesn’t tell you anything you didn’t already know. Purely mathematical relationships have no limited value in science. Understanding is gained when that mathematical relationship arise from a theory about the fundamental behavior of water vapor and/or radiation. The greenhouse effect (aka atmospheric absorption) is a complicated phenomena involving absorption, emission, the lapse rate, and competing GHGs. Radiative transfer is calculated by numerically integrating a differential equation (the Schwarzschild eqn) that applies to radiation traveling through a non-scattering atmosphere (and other materials). There is no analytical formula that describes the GHE.
The behavior of water vapor is somewhat simpler. The C-C eqn tell us how saturated water vapor pressure changes temperature. If convection didn’t exists, you might expect diffusion to eventually saturate all of the atmosphere – based on Ts near the surface and decreasing with altitude due to the lapse rate. That would be the simplest possible model. In the real world, convection carries some air upwards above the point where it precipitates and dries. After radiatively cooling, that dry air returns to the surface. This overturning make the relative humidity in the boundary layer over oceans about 80%, not 100%. Since convection is difficult to model, that means the relationship between Ts and TPW is unlikely to be a simple one.
If you plotted the expectations of the C-C equation for various relative humidities on the same graph as your TPW vs Ts data, I think you would find that TPW decreases with surface temperature faster than saturation vapor pressure. We also know that the amount of convection decreases with lower surface temperature and relative humidity falls at higher altitudes.
My guess is that the relationship you found between G (atmospheric absorption) and log2(TPW) is an emergent property of a complicated climate system, not something that will eventually have a simple explanation.
Frank July 30, 2016 at 7:34 pm
Yeah, that damn mathematics nonsense is useless, I don’t know why they even teach it to kids these days … wait, what?
In fact, the mathematical relationships allowed me to differentiate the function and thereby calculate the water vapor radiative feedback, but don’t let that get in the way of your aversion to math …
Bad guess. The logarithmic relationship is predicted by the physics of the situation. That is why it applies equally to water vapor and to CO2.
w.
Willis wrote: “In fact, the mathematical relationships allowed me to differentiate the function and thereby calculate the water vapor radiative feedback, but don’t let that get in the way of your aversion to math …”
Frank replies: FWIW, I love math. However, you don’t need a to fit a function to data to calculate a derivative. The derivative at any point is merely the slope. The same information is present whether I present the relationship between two variables as a table of values, a scatter plot, or as an equation. One can say the same thing about a table of differences/derivatives or sums/integrals.
The problem with fitting data to arbitrary mathematical functions was brought home to my by attempts to teach one of my children “how science is done” after they brought home data from a math class showing how the maximum load a “bridge” made out of dry spaghetti strands could carry (measured in pennies) varied with the number of strands of spaghetti and the gap the bridge spanned. The goal of the math class was to illustrate a function dependent on two variables, but I thought could learn something about the physics of forces on bridges. The functional relationship between the load and the span was the tricky part. A negative exponential, Inverse, inverse-square were about equally good, the power law with an exponent of around -1.6 was marginally better, and a second degree polynomial was reasonable too. We discussed the practicality of doing experiments using shorter an longer spans to distinguish between these functions, but the length spaghetti strands (and climate data) limit the dynamic range of the independent variable. Common sense allowed us to eliminate the second degree polynomial because it predicted that after a minimum, a longer could carry more load. (You may be able to eliminate some functional relationships by asking what predictions they make outside the current range of data. I sure didn’t want to look up the answer, but fitting functions wasn’t providing one. It wasn’t until I cheated and looked up the answer that I realized what I had been missing: a hypothesis. A bridge span that is about to break under a load is like two cantilevers touching in the middle: each half the span is the lever arm with half the load on one end.
Or consider the height vs time data you might get from a ping pong ball (where air resistance is important) dropping off a roof before and after injecting water to change its weight. One could fit a lot of functions to that data without ever stumbling on the right principles: 0.5gt^2 for part and air resistance that varies with the square of the velocity.
Or consider Kennan’s criticism of fitting warming data with a linear AR1 model. He has gotten the Met Office admitting that pure statistics (mathematical fitting) can’t even say for certain that it has been warming over the past century, because we can’t be sure what kind of noise (unforced variability) is present in the data. The Met Office has admitted that climate models (hypotheses) are needed.
Unfortunately, the physics of the GHE (which we do understand) and of evaporation (which we marginally understand) and convection and condensation (which we don’t) suggests to me that the mathematical functions used to fit your data above are unlikely to be lead to a better understand of why these phenomena behave as they do. However, your linear relationship between G and log(TPW) may very well represent an IMPORTANT EMERGENT PROPERTY of our climate system that can’t be derived from fundamental physics.
Willis: In fact, the mathematical relationships allowed me to differentiate the function and thereby calculate the water vapor radiative feedback, but don’t let that get in the way of your aversion to math …
I spent a great deal of time trying to understand exactly what you had and hadn’t proven about water vapor feedback in your last post and am still working on the problem. The fundament problem is that you are analyzing the effect of a change in surface temperature on the GHE (atmospheric absorption, oT^4 – TOA FLUX) by moving to different locations on the planet, not warming all locations on the planet or not raising the concentration of a GHG while holding everything else constant). You have brilliantly (IMO) put together some observational data that points to weaknesses in the expectation that climate sensitivity is high – but I’m not sure that your analysis proves it must be low. If you are interested in climate sensitivity, the variation in TOA OLR (not oT^4 – TOA OLR) with Ts appears to be the critical parameter.
micro6500 July 29, 2016 at 3:12 pm
Interesting. Minimum SW is 524 W-hr/m2/day / 24 hours/day = 22 W/m2, max is 6304 / 24 = 263 W/m2. This is compared to a global 24/7 average of about 170 W/m2 … makes sense.
Is your dataset online? Can mere fools like myself access it? And finally, what is the GSoD when it is at home? The Great State of Denmark? The Galactic Society of Drunkards?
All the best,
w.
GSoD, Global Summary of Days data set from NCDC.
https://micro6500blog.wordpress.com/2015/11/18/evidence-against-warming-from-carbon-dioxide/
On this url above there’s a link to source forge, code and all of the data I generate. I’ve been working on enthalpy and climate sensitivity, and I haven’t uploaded those latest reports, but all of the solar forcing is there.
There is a lot of data, feel free to ask questions.
Clyde Spencer July 29, 2016 at 12:44 pm
My bad, I sometimes forget to define my terms. You are right that clouds are not included. From the Glossary of the American Meteorological Society (emphasis mine):
Regards,
w.
I don’t see where your GAMS definition specifically excludes clouds. After all, the vapor has to be condensed and poured into a bucket to get the thickness of the water layer.
Now I don’t doubt that the GAMS definition is exactly as you cited here. That doesn’t mean that is what they had in mind when whoever wrote it. I usually expect that anything that is not specifically controlled will invariably run amok, and be uncontrolled.
So if I was writing their definition (I’m not going to); I would add the words (after ….. water vapor ….)
” excluding water in all other phases such as liquid or solid , as might be found in clouds. ”
G
I think this has been a great post. The one thing that it illustrated perfectly was how inadequate mathematics is when called upon to explain observable phenomenon.
Dear heavens, miss the point much? To misquote Shakespeare, “The fault, dear Brutus, is not in our mathematics but in ourselves” …
w.
http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/print_5.htm#page_1.3.0
I’ve always wondered why so much climate science is focused on temperature when it is energy that matters. Temperature is, after all, just a proxy for an average energy measurement and it is especially worthless in a gas where energy levels of the constituents obey a distribution.
At the surface, water vapor represents a (relatively) high energy component of a parcel of air. If I magically take that parcel up to, say, 9 km in the uptake of a massive thunderstorm, I haven’t changed the energy content at all, on the way up. The temperature goes down because it is now in a lower pressure regime but the energy is, for all intents and purposes, the same is it was when it left the surface, isn’t it?
When it gets to the top, that water vapor can radiate half of its energy to space without interference. When it does it’s energy level can drop to below that of the nitrogen and oxygen that came up with it. Conduction now moves energy from oxygen and nitrogen to the water vapor which then becomes a radiating proxy for those two gases. The whole parcel loses energy to space; all the constituents, not just water vapor.
For me, this excellent paper and the ensuing comments suggest dozens of focused experiments that could get at the basics that drive climate. I’d like to know the energy radiated away at the top of a tropical thunderstorm, maybe subtropical ones and temperate ones too. I’d like to know the energy radiated away in the dry air down-welling outside the storms. I’d like to know the energy transfers of nitrogen and oxygen to the water vapor in that storm.
I actually could care less what the temperature is. That’s a bit like tasting the smoke coming off your filet on the barbecue.
Not much radiation from thunderstorm cloud tops.
http://science.nasa.gov/media/medialibrary/1998/12/03/essd15jan99_1_resources/NAST-I.gif
http://3.bp.blogspot.com/-lmPcm4WLOq4/Usb_CsHnz8I/AAAAAAAAAuA/lpUiPJl-nU4/s1600/IR_spectrum_anvil_head&clear.jpg
Frans Franken July 31, 2016 at 1:59 am
It is both my pleasure and my curse, and you are welcome.
It is assuredly a rounded figure, and I should have been more specific.
For these kinds of questions I use the Gibbs Seawater (gsw) package in R, which describes itself as:
Before I used the gsw package I used the MIT seawater tables linked to from here.
According to Gibbs, the important values are:
Heat of evaporation, 15°C, salinity of 35 PSU = 2,409 joules per gram, or as I always think of it, 2409 megajoules per tonne.
Sea water density, 15°C, salinity of 35 PSU = 1.022 tonnes per cubic metre
So the equation to evaporate one cubic metre of seawater per year assuming one square metre of surface area looks like this:
1 m3 / year / square metre divided by 1.022 tonnes per cubic metre is 0.978 tonnes/ square metre / year
0.978 tonnes / square metre / year times 2409 MJ / tonne is 2357 MJ / square metre / year
Now, there are 31.56E+6 seconds in a year, so …
2357E+6 J / square metre / year times 1 year / 31.56E+6 seconds, conveniently the E+6 cancels out and we are left with 76.4 joules / second / square metre.
But a joule per second is a watt, so that is 76.4 watts /square metre. I probably should have calculated and used the more accurate figure, but I was running fast.
I developed the idea myself, although I’m sure I’m not the first person to do so. However, I haven’t seen it mentioned in the literature. But then I’m the wrong guy to ask, as I tend to spend my time doing new research rather than looking at previous research … I tend to do the work first and then look at previous work second. Yes, I know it is the wrong way round to do things, but it’s served me well. And in a field with so many peer-reviewed papers that are not only incorrect but point in the wrong direction, you’re as likely to get steered wrong as right … I prefer to start without preconceptions and then read up on the previous work once I’m done. Sadly, the new never-done research is the fascinating part, so I tend to neglect the other … only so many hours in a day.
Mmmm … first, you say “… condensing, which occurs from cloud bottom to top, …”. Actually, most of the condensation takes place at the cloud base, at what is called the “lifting condensation level” or LCL. As air rises it cools, and when it reaches the LCL, it condenses. That’s why a field of thermal cumulus clouds all have their undersides at the same altitude, because that altitude is the LCL. There, the latent heat is converted to sensible heat, warming the air.
Now, as you know, warm air tends to rise. It is this rewarmed air in a cumulus cloud which, when there is enough of it, provides the power to construct the cumulonimbus (thunderstorm) tower upwards from the lowly cumulus. You might think of a thunderstorm as a fire in the cumulus cloud with a column of smoke and heated air rising from it … except that in place of smoke there is liquid water and ice.
And because there is liquid water turning into ice in the core of the thunderstorm, there is a secondary effect which is also going on. Just as energy is released when a gas condenses into a liquid, energy is also released when a liquid turns into a solid. So a thunderstorm wrings even more energy out of a part of the moisture that left the surface. And that released latent heat of fusion further expands the air and pushes the thunderstorm tower even higher.
Now, of course in nature nothing is ever quite that simple. Actually there is more complexity inside the thunderstorm tower, where the second phase change takes place as liquid water turns to ice. What happens is much like what happens during the first phase change, where water vapor turned to a liquid. What happened was the liquid fell back to earth as rain.
Well, the same thing is going on inside the thunderstorm tower, except what is falling is not water, it is ice. In both cases at a certain point the accumulation of either water or ice is too large to stay aloft, and it starts to fall. So inside the tower we have falling ice, a hidden hailstorm of great ferocity. But the overall point remains—from inside the thunderstorm tower, radiation is not free to escape and interact with the surrounding troposphere.
So in answer to your question about the fate of the latent heat, the best way to answer it is to consider a thunderstorm as a heat engine that runs off of hot moist air.
Now, for a heat engine to work, we need a hot end, a cold end, and a working fluid. Take for example a steam engine. At the hot end, the boiler heats the working fluid, water, until it evaporates. Then the steam is used to do some kind of useful work, after which it passes to the condenser at the cold end. There, the steam is cooled and condensed back into water, which returns to the boiler to complete the cycle.
So … what happens to the energy from the coal used to fire the steam engine boiler? Well, some of that energy is converted to useful work, some is lost to friction, and the rest simply passes through the heat engine and is rejected into the environment.
The same is true of a thunderstorm. Some of the energy is converted into the work of driving a current of air vertically at great speed. Some of it is lost to turbulence. And some is simply passed through the thunderstorm and rejected at the cold end at altitude. I’ve never seen a detailed breakdown of how much goes into each part. Isaac Held over at GFDL might know.
So the answer is that mostly the latent heat is converted to work. The work is performed when the heated air expands, because it has to physically push other air out of the way to expand. That heated parcel of air rises, and of course as it rises it expands further, and as it expands, it cools. At some point, it will have cooled to the temperature of the surrounding air. At that point the air emerges from the thunderstorm tower. If the thunderstorm is strong enough, fine crystals of ice will get caught in the updraft and make a level flat trail behind the thunderstorm, the familiar “anvil top”.
Bear in mind, however, that in fluids at the end of the day it all turns to heat, as the poet-scientist said:
Bigger whorls have smaller whorls that feed on their velocity,
Smaller whorls have smaller yet, and so on to viscosity.
The real difficulty I have with thunderstorms is that as in any field of study, hard numbers are good to come by. But with a subject matter as evanescent as clouds … good numbers are hard to come by …
Best regards,
w.
PS—You might enjoy one of my previous posts on the subject, Air Conditioning Nairobi, Refrigerating The Planet.
Willis Eschenbach July 31, 2016 at 12:37 pm
“Actually, most of the condensation takes place at the cloud base, at what is called the “lifting condensation level” or LCL. As air rises it cools, and when it reaches the LCL, it condenses. That’s why a field of thermal cumulus clouds all have their undersides at the same altitude, because that altitude is the LCL. There, the latent heat is converted to sensible heat, warming the air.”
Not quite true. If you compare the DALR vs the SALR (dry vs saturated adiabatic lapse rate) on a thermodynamic diagram you’ll see that the SALR is lower then the DALR to considerable heights.
Obviously depending on the the temperature the rising air has when it starts its ascent.
With higher temperatures the rising air will contain more water vapour (WV) to condense.
With start temperature eg 30C it is above 12 km height before all WV has condensed out.
Since the rising air does not lose energy to the surrounding air (adiabatic assumption) is why these lapse rates have been called ‘adiabatic” 😉
Ben Wouters says, August 1, 2016 at 8:54 am:
No. That is NOT why these lapse rates are called “adiabatic”, Ben. The rising air specifically DOES lose (internal) energy to the surrounding air, only it doesn’t happen via heat transfer, but rather via so-called PV work being done as the rising air expands against the surrounding pressure. This is why an adiabatic process is defined by saying Q=0 and so dU=-W = PdV. This subject seems to be an eternal source of confusion …
Sorry. = -PdV.
Willis,
Thanks for your elaboration and patience.
A bit about my background: I’m a mechanical engineer, MSc from Technical University of Eindhoven, Netherlands. I’ve been working for about ten years as a steam turbine engineer and product manager of steam turbines licensed from IMO Industries and General Electric, and as such have co-developed Cogen and CCGT power plants.
On the specific evaporative heat: everything clear. Global average precipitation = (1000/365 =) 2.74 mm/day, specific evaporative heat = 2409 kJ/kg, global evaporative cooling power = 76.4 W/m2.
On the destination of the latent heat, I would like to expand. The energy (power) taken from the surface by evaporation is clear: about 76.4 W/m2. To close the hydrological cycle: precipitation normally comes down as rain of lower temperature than the oceans from which it has evaporated. The heat required to warm up this precipitation to ocean temperature is small, ≈1.3 W/m2 based on a temperature difference of 10 K between rainfall and ocean. For completeness, let’s add this to the latent heat and round it up to (74.6 + 1.3 ≈) 76 W/m2 as the total water cycle heat flux at the surface-atmosphere interface.
Conservation of energy, and the fact that the water (vapor) doesn’t escape to space, require that this amount of heat is released in the atmosphere. If the convection process from surface up to cloud top is adiabatic – no heat exchange with the surrounding atmosphere – then all heat must be released around the cloud top. There, it can be shed either as sensible heat (conduction to surrounding air) or as IR radiation (in all directions).
An exception could arise if the water exits the cloud top sideways as ice, and this hail melts on its way down. In that case, a substantial amount of the heat will be passed to the atmosphere outside the cloud between cloud top and the surface. However to avoid complexity let’s forget about this scenario for now, and assume that the full flux of 76 W/m2 is released at cloud top level.
When looking at the global energy budget cartoons of Kiehl-Trenberth and NASA, such as the one below, a flux of about 30 W/m2 is included as “emitted by clouds”. This looks as if it is meant to present upward IR emission from cloud tops which makes it to space:
See also this thread: https://wattsupwiththat.com/2014/01/17/nasa-revises-earths-radiation-budget-diminishing-some-of-trenberths-claims-in-the-process/#more-101465
Time does not allow me to continue momentarily, but I’ll follow up un this shortly.
Correction: total water cycle heat flux = 76.4 + 1.3 ≈ 78 W/m2
The sigmoid function arises in the characterization of time-variant feedback systems when you have a delay in the feadback path. I.e S[s] = 1/(1+e^-s) in bode form gives a feedforward gain of unity and a feedback gain of e^-s. The inverse Laplace Transform of e^-s is a pure unit delay. The inverse sigmond function may indicate you’ve derived an output-to-input relationship.
Haven’t read through all the comments so perhaps this already been pointed out
“Some of the energy is converted into the work of driving a current of air vertically at great speed.”
This is probably a dumb question but I’ve often wondered where in your calculation you account for the energy (work) required to lift all that water. Surely this must dwarf the energy required to move air.
Willis, I just read your Air Conditioning Nairobi, Refrigerating the Planet from March 2013. https://wattsupwiththat.com/2013/03/11/air-conditioning-nairobi-refrigerating-the-planet/ You were very clear about the role thunderstorms have anyway:
“My takeaway message is this:
The surface temperature of our amazing planet is set and maintained by the constant refrigeration of the surface hot spots as they form, not by the forcing, whether from CO2 or anything else.“
I myself would like to know more about the role convection plays in losing the heat from the surface to space. In this post the word ‘convection’ so far is mentioned 32 times and I think I can ad a little discussion I had today about that subject. The discussion is from Roy Spencer’s blog.
Any extra information in respect to the role of convection for radiation to space is welcome.
http://www.drroyspencer.com/2016/07/the-warm-earth-greenhouse-effect-or-atmospheric-pressure/#comment-218619
(….)
Kristian says:
August 1, 2016 at 9:58 AM
“Wim Rost says, August 1, 2016 at 6:39 AM:
Kristian, about H2O: “this wont for the most part have anything to do with its radiative properties.”
First, I would like to know which part.
What do you mean? Which part that does involve the radiative properties? That would be the absorption and emission of IR. But any extra cooling from this would just be an effect of extra prior heating (a warmer troposphere emits more OLR to space). It is very unlikely (if you don’t buy into the whole AGW tripe) that Earth would warm or cool as a direct result of changes in its heat OUTPUT. All we can ever observe in the Earth system points to OLR being a radiative RESPONSE only to warming or cooling. And that warming/cooling would come from changes in Earth’s heat INPUT, from the Sun. Like we have now. Global ASR (absorbed solar radiation, TSI minus albedo) went considerably up between the late 80s and cirka 2000, and after that has pretty much stabilised at a slightly higher level again, although still significantly lower than in the 80s. This is all due to changes in (principally tropical) cloud cover during the 90s. At the same time, OLR went up in step with tropospheric temps, that is, it came as a direct radiative EFFECT of the temperature rise (caused by the increase in solar input).
No one seems to want to touch this simple observational fact, even though it’s clearly evident from the data (ERBE+CERES, ISCCP FD, HIRS):
“I would also like to know whether the energy that is transported upwards, will effect radiation in an indirect (!) way. For example, I read about a recent extension of the Hadley Cells. As the level of the troposphere is higher in the tropics, energy is transported closer to the place where it can be emitted to space: the mesosphere and stratosphere. More upward and in latitude extended Hadley cells might improve the outward emitting. I think.”
Again, the Hadley cells only expand when they warm. And so any extra cooling comes from extra prior heating.
“Secondly, as Roy Spencer states: addition of CO2 to the atmosphere is supposed to warm the surface, but cool the stratosphere and mesosphere. In general this must stimulate convection, the more when the lower layers warmed up also. And stronger convection will transport energy closer to the level where it can/will be emitted.”
And this is why we cannot have an “enhanced greenhouse effect” from the addition of more CO2 to the atmosphere. Well, there is no real thermodynamic connection between the lower troposphere and the stratosphere and mesosphere. But the upper layers of the troposphere itself would also cool more. So adding more IR-active constituents to the atmosphere would simply enhance the absorption at lower tropospheric levels and likewise the emission at higher tropospheric levels. And what is it that connects these two levels and makes sure the lower levels don’t get too hot and the higher levels don’t get too cold? You guessed it. It’s convection. Convection will quash any radiative attempt at making the lower levels of the troposphere warmer, thus forcing the surface itself to be as well. It wouldn’t work. If the heat transfer from the surface up was purely and only radiative, then it might’ve worked somehow. But as we all know, it isn’t. Convection (to a large extent evaporatively driven) reigns supreme. *
* WR: I added some “ “
RSS temperatures:
http://www.climate4you.com/images/MSU%20RSS%20DifferentAltitudesGlobalMonthlyTempSince1979%20With37monthRunningAverage.gif
The temperature rise in the troposphere in 2016 (El Nino) coincides with a lowering lower-stratosphere temperature. At more points in the graph an upward troposphere temperature seems to correspond with a lower stratosphere temperature and reverse. Is there a statistical effect measurable?
(Volcanoes (particles in the stratosphere) make the stratosphere temperature rise and lower the lower troposphere temperature. Their effects need to be taken out)
What would be shown when we couple the part of the grid known for the rising number of thunderstorms to the emissions of that specific part of the grid?
===
General question: what effect would have been measured by RSS going up one extra layer in the stratosphere? An even stronger cooling trend?
===
RSS: The average temperature in the stratosphere is generally lowering as predicted: CO2 content rises, stratosphere cools more.
N.B. https://wattsupwiththat.com/2016/08/01/uah-global-temperature-update-for-july-2016/
. UAH Numerical data for the whole (!) tropical sea area don’t show a trend much different from the world trend. Less cooling even: -0,29 against -0,31. But thunderstorms are concentrated in some parts of the tropics as the rainfall data show and for those area’s it might/will be different.
N.B.2. As UAH numerical data for the stratosphere show, the lowering of the temperature of the stratosphere is strongest at the land part of the south pole: trend -0,43 against -0,31 for the global average. It is another subject, but it would be interesting to know why that effect is just strongest there. More energy transport pole ward from the depressions surrounding the pole is an option. Another one is the special role of the Polar vortex: “an upper level low-pressure area, that lies near the Earth’s pole. (….) The bases of the two polar vortices are located in the middle and upper troposphere and extend into the stratosphere.” Source: https://en.wikipedia.org/wiki/Polar_vortex
An impressing image of the actual polar vortex at Nullschool at 10hPa, 26.500 m, deep in the stratosphere: https://earth.nullschool.net/#current/wind/isobaric/10hPa/orthographic=0.44,-84.85,473/loc=15.476,-52.292
(use keyboard shortcut m to go down a level, use i to go up through the atmosphere – found at https://earth.nullschool.net/about.html )
At the poles the Stratosphere starts at around 10 km, in winter time even lower.