Improbable Maximum Precipitation

Guest post by Willis Eschenbach

There’s a new study out from NOAA called “Probable maximum precipitation (PMP) and climate change”, paywalled of course, which claims that global warming will lead to a 20%-30% increase in “probable maximum precipitation”. The abstract says:

Probable Maximum Precipitation (PMP) is the greatest accumulation of precipitation for a given duration meteorologically possible for an area. Climate change effects on PMP are analyzed, in particular, maximization of moisture and persistent upward motion, using both climate model simulations and conceptual models of relevant meteorological systems. Climate model simulations indicate a substantial future increase in mean and maximum water vapor concentrations. For the RCP8.5 scenario, the changes in maximum values for the continental United States are approximately 20–30% by 2071–2100. The magnitudes of the maximum water vapor changes follow temperature changes with an approximate Clausius-Clapeyron relationship. Model-simulated changes in maximum vertical and horizontal winds are too small to offset water vapor changes. Thus, our conclusion is that the most scientifically sound projection is that PMP values will increase in the future due to higher levels of atmospheric moisture content and consequent higher levels of moisture transport into storms.

When I heard that number, a 20%-30% increase in maximum rainfalls, my urban legend detector starting ringing like crazy.

maximum daily precipitation differenceFigure 1. The authors’ guess at how much more rain will be falling by the end of the century.

So … why did my urban legend detector go off from this claim? It has to do with energy.

The press release quotes the authors as saying:

“We have high confidence that the most extreme rainfalls will become even more intense, as it is virtually certain that the atmosphere will provide more water to fuel these events,” said Kenneth Kunkel, Ph.D., senior research professor at CICS-NC and lead author of the paper.

Now, the increase in maximum rainfall is said by the authors to be due to the increase in water vapor in the air. It’s unclear if the 30% increase in maximum rainfall will be matched by a corresponding overall increase in rainfall. However, it is highly unlikely that an increase in water vapor will only increase maximum rainfall events. The authors themselves say that their projections show “a substantial future increase in mean and maximum water vapor concentrations”. 

So to be conservative, let’s cut the 30% increase in maximum water vapor down to a 20% increase in mean water vapor, and see what that looks like.

I want to determine how much energy we’re talking about here. Suppose the rainfall were to go up (on average) by about 20% globally. Right now, the globally averaged rainfall is on the order of a metre of rain over the entire surface per year, a bit more or less depending on who is measuring. Twenty percent of that is 200 mm. So we need to evaporate an additional 200 mm over every square metre of surface to produce the stated increase in rain.

It takes 2260 joules of energy to evaporate a gram of water. For each square metre we need to evaporate 200 mm, or 200 kg of water. To evaporate that much water takes 4.52e+8 (452,000,000) joules of energy.

Now, a joule is a watt-second. We need 4.52e+8 joules of energy every year to evaporate the additional water, which is 4.52e+8 watt-seconds per year. Dividing that by the number of seconds in a year (3.16e+7) gives us the change in constant 24/7 watts needed to evaporate that much water. Remember, this is an increase in the constant watts of energy striking every square metre of the planet.

And that number, dear friends, the amount of additional energy needed to increase global evaporation and thus rainfall) by 20%, turns out to be 14.3 W/m2. That’s about the amount of energy increase from three doublings of CO2. Yes, CO2 would have to go from the current ~400 ppmv to about 3,200 ppmv to provide that much extra forcing …

So my urban legend detector is still working fine. There’s nowhere near enough energy available to power that claimed jump in rainfall.

Now, I could leave it there, since the energy necessary to make their claims possible doesn’t exist. But in order to confirm that finding, my plan of further inquiry was to see whether either the intensity of rainfall events or the mean rainfall has changed over the last century. People are always claiming that we don’t have any controls for our experiments when we study nature. But nature provides its own experiments. To start with, we have the warming since 1900. On land, according the Berkeley Earth Surface Temperature data, the temperature has gone up about a degree over that time … but did the rainfall go up as well?

Figure 2. Global precipitation over the land, in mm/day. Data Source 1901-2009: CRU TS 3.10.01 (land)

OK … no increase at all in global rainfall, neither in the monthly means nor in the maximums. So no support for their claims there.

So how about local maximum rainfall events? Are those going up?

For this, we can turn to the temperature and precipitation records of England. For the Central England region, we have daily temperatures and daily precipitation records since 1931. Since 1931, the average Central England Temperature (CET) record has gone up by just under one full degree.  So we should see any thermal effect on the maximum rainfall. With that 1°C temperature rise as the backdrop, here’s the maximum central England daily rainfalls, month by month, for the last eighty years.

maximum daily rainfall by month central englandFigure 3. Maximum daily rainfall, 1931-2012, Central England. Data Source Photo Source

Here, we find the same thing. There is no evidence of any increase in maximum rainfall events, despite a 1° temperature rise.

Hmmm …

The part I really don’t like in all of this is that once again, all of their claims are built on computer models. But what I don’t find is any serious testing of their whiz-bang models against things like the global or the CET temperature and rainfall records. In fact, I don’t see any indication in any venue that any computer models are worth a bucket of warm spit when it comes to rainfall. Computer models are known to perform horribly at hindcasting rainfall, they do no better than chance.

So once again, we’re back in the land of Models All The Way Down. I gotta confess, this kind of thing is getting old. NOAA and NASA appear to be falling further and further behind reality, still churning out useless studies based on useless models.

Just one more waste of taxpayers money.

w.

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They can’t let go, Willis, it’s all they’ve got.

Gil Russell

Willis, I have a problem with the research being paywalled. I take it that the study was financed by taxpayer dollars supporting NOAA – it should be free access. Is money, in the form of paywall fees, owed the U.S. Treasury?…,

Oh, no, it’s ….you know the rest. But weren’t we told, at least here in Oz by ‘Climate Commissioner’ Tim Flannery that we had entered the era of ‘permanent drought’? Instead we have record rains.

Willis, if you were a real climate scientist you would have used a proxy (manipulated) for daily rainfall instead of using actual data.

Curious George

“It takes 2260 joules of energy to evaporate a gram of water.” Willis, you have fallen in a modeler’s trap – that is the number models use. It is correct only at a freezing point (0C, 32F). It changes by about 1% for every 10 degrees C.

Latitude

Willis, shouldn’t one of these be different?…..or did I eat too much chocolate again!
“It’s unclear if the 30% increase in maximum rainfall will be matched by a corresponding overall increase in rainfall.”
…who would have thought that temperatures staying the same, or slightly decreasing…….would be so dangerous

John Mason

Once again, conclusions by models contradicting historical evidence. Whatever happened to the idea of empiricism in science?

Willis Eschenbach

Gil Russell says:
April 6, 2013 at 5:09 pm

Willis, I have a problem with the research being paywalled. I take it that the study was financed by taxpayer dollars supporting NOAA – it should be free access. Is money, in the form of paywall fees, owed the U.S. Treasury?…,

At least it’s getting better. The US just announced that all federally funded research must be made available one year after it is published.
Not ideal, but better …
Thanks,
w.

Other_Andy

We are having a record draught here in New Zealand.
Where is our 20%-30% increase in “probable maximum precipitation”?
The UK is still waiting for milder winters, dry summers and the disappearance of snow.
I am now convinced they make it up as they go….

Richard M

Good analysis, Willis. Even using conservative numbers they come out looking like idiots. And, you didn’t even mention that the temperature differential problem. If there’s a decrease in uplift the storms won’t be as intense.

Curious George

Correction: Models use the value of 2500 for 0 degrees C. 2260 is correct for 100 degrees C. So your numbers actually underestimate the energy needed. Apologies.

Mike McMillan

So each cubic centimeter of raindrops represents 2260 joules hauled up and dumped high in the atmosphere and unable to contribute to global warming down here where we live. More heat, more rain, less warming.

Steve Keohane

Thanks Willis. Wouldn’t all that extra evaporation transfer heat to where some would be lost causing a negative feedback or self-limiting system? I am probably influenced by your writing about the same. Your elegant-as-usual dissection is complete without further foray.

Bill_W

The part I really don’t like about this Willis is they use “high confidence” to describe their projection based on a computer model that is predicting a fairly extreme change over a fairly short time span.

Scott Scarborough

If there were enough energy in our addition of CO2 to the atmosphere to just evaporate all of the water they refer to, wouldn’t that mean that there would be no energy left over to warm the atmosphere (no global warming)?

Peter

Doesn’t most of the energy come back when the water vapor condenses?

Nice take-down Willis, and just from their results it is clear where at least part of their model failure must originate. If the speed of the rain-cycle were as sensitive to warming as they estimate the cooling effect of this speed-up would constitute a huge negative climate feedback, greatly moderating the amount of warming. Obviously they still aren’t modeling those “thermostat” effects.

Ducard

I am confused. Wasn’t drought and desertification the scary boogeyman of warmists until a few years ago?

More climate model nonsense. Climate models say global precipitation should have increased since 1979, but precipitation decreased:
http://bobtisdale.files.wordpress.com/2012/12/figure-21.png
From the following post:
http://bobtisdale.wordpress.com/2012/12/27/model-data-precipitation-comparison-cmip5-ipcc-ar5-model-simulations-versus-satellite-era-observations/
Regards

Mark Bofill

Steve Keohane says:
April 6, 2013 at 5:35 pm
Thanks Willis. Wouldn’t all that extra evaporation transfer heat to where some would be lost causing a negative feedback or self-limiting system? I am probably influenced by your writing about the same. Your elegant-as-usual dissection is complete without further foray.
————–
Yeah, that was my first thought too. No free lunches; if the energy is being burned driving more rain, it seems counter intuitive that it should also be available to drive up temperatures.

philincalifornia

Well if Tamino can have his own album (which looks like it has at least 100 tracks by now – see Tamino thread), maybe these guys could have their own album too.
I’ll start with Duran Duran’s “Hold Back the Rain”

(Hope you don’t mind a bit of levity Willis. Great post by the way).

duncan

I thought you mucked about with boats and stuff. What on Earth are you thinking with this stuff? Clinical and undrstandable work. Much appreciated.

Good analysis Willis. I think I commented previously that rainfall appears to be a Poisson distribution (one can not have less than zero rainfall and in my area the SD is very close to the average.) Thus, if a model is using normal probabilities it is out for a start. I find that rainfall in my area is cyclical. Using a five year running average from 1890 to 2013 I find that there was exactly 100 years between the minimum rainfall at 1904 (during the much noted Australian Federation drought) and 2004 during the recently ended (in 2008) drought which all the alarmists blamed on global warming and many predicted (eg T Flannery- Climate Commissioner) that dams would not fill again and desalination plants were required (instead we have had floods and the desalination plants are rusting away not used). Looking at actual peak rainfall, the highest annual rainfalls occurred in 1893 & 1898 and were over 1000mm more than any other annual total since. Peak rainfall seems to occur in cycles of about 11 years. Many older people and farmers know about the11 year cycle. The same cycle appears to occur for bushfires. I lived in another area prone to bushfires. There were bushfires in 1980, 1991 & 2001-2. Twice we fought fires around the house to save it. Unfortunately, 11 years is enough time for people to forget

JC

“We are having a record draught here in New Zealand.
Where is our 20%-30% increase in “probable maximum precipitation”?”
And of course Niwa says that this is climate change and we have to expect that such droughts will become the norm. However there’s a trap here and its recognised by Niwa and other warmers.. how to have extended droughts plus still have all that pesky rain?.. answer, make the rain more intense!
So eventually our monthly climate stats will show 30 brilliant fine and ever warmer days.. with a downpour of six inches of rain in the final hour before midnight on the final day of the month! Mission accomplished 🙂
JC

Frank Kotler

“… assume a spherical raindrop…”
Back when global warming was actually happening, it didn’t cause increased rainfall, but now that it’s not happening it could cause almost anything!
You know how much energy it takes to evaporate all those cats and dogs? 🙂

Nick Stokes

Willis,
“We need 4.52e+8 joules of energy every year to evaporate the additional water,”
Why every year? I don’t get this arithmetic at all. Whatever it took to evaporate the water was released as LH on condensation. It’s not new heat.
The total heat needed is once only, and it’s what is needed to evaporate enough water to increase the humidity. There is only about 100 kg of water vapor in total above every sq m. The heat needed is a once only amount to evaporate maybe 30 kg. Very rough figures, but it’s much less than what you say.

Felix

Of course, since I’m still at the add/subtract/multiply/divide level of mathematics, it would seem to me that a 200mm in increased evaporation would have some effect on sea level rise, no? With more moisture in the atmo at any given time there would be less water in the ocean.
That South Sea Island beachfront investment property is looking better.
Of course, these folks creating one new potential catastrophe appear to be putting paid to their compatriots’ concerns about islands disappearing.
Keeping consistency in the message can be so complicated.

Sam the First

“Climate change effects on PMP are analyzed, [ … ] using both climate model simulations and conceptual models of relevant meteorological systems. Climate model simulations indicate …. ”
Yadda yadda yadda – How on earth do they get away with this stuff? Willis, Bob, Steve Mc, Anthony and all the others constantly demonstrate that these GIGA simulations produce false projections, yet those in on the public payroll refuse to do proper observation, physics and math.
It’s… incomprehensible; unless there is an ‘agenda’ – no wonder we are conspiracists!

dp

I haven’t read the publication because I don’t like paying for things twice, but my take on this is they have not suggested the global PMP increase. PMP applies to an area. It would not take that many doublings of CO2 to ramp up the PMP of Peoria, for example. But more importantly this is all just more Chicken Little on their part. I marvel at the number of ways we can be told the sky is going to fall if the climate doesn’t stop doing what the climate has always done which is change. Had these numpties been in charge during the LIA can you imagine what the world would be like as a result of unchecked global warming? Oh wait – we don’t have to imagine.

KevinM

OT: for a quick laugh try
http://www.businessinsider.com/us-city-sea-level-rise-maps-nickolay-lamm-2013-4
All of the standard reasons to create all too real scare pics.

FrankK

More computer model [snip] – If you plot the cumulative deviation from the monthly mean of rainfall here in Oz there is absolutely no relationship between the slight warming and/or CO2 we have seen in the 20th Century and rainfall. There have been major fluctuations over time. It wasn’t long ago that the CSIRO (Commonwealth Scientific and Industrial Research Organization) here in Oz was spouting how rainfall would be decreasing echoed by our illustrious alarmist fossil expert Tim Flannery during the naughties that our dams would not fill again. They have since overflowed.
What a minute! – There you see a confirmation of higher rainfall.
That’s how it works in climate astrology you can confirm any prediction.
What utter bullocks.

OssQss

You know it is truly amazing how dependent we have come to be with respect to computing power and products related to such. Heck, your refrigerator doesn’t work without it.
Think about it, or should I say think less for yourself if you will. The scientific process has changed so much that there are very few individuals who can actually understand and troubleshoot things that produce erroneous or flawed performance/results now days. Climate models being just one of them.
When we place so much in the hands of failed, flawed, or fraudulent code, we are at high risk of wrongdoing and or that which precipitates from such. We currently set policy based upon models that the old game “Gnip Gnop” could emulate to the same level of accuracy, or perhaps better from a binary standpoint.
Technology is great, but at the same time, it has a price. You think I am wrong? Try doing some of your old hard math problems from that textbook you hated. Then do one of those hated problems without a calculator.
Pumping out garbage papers, as exemplified here in this post (nice job Willis), based upon growing and willing technological handicaps/crutches is not only a waste of money, it eats away at the heart of science itself.
Ya know, it used to be an obsession for some. Now it is their income stream.
Considering how dependent we are on technology and energy to live what is considered a normal “taken for granted” life, and to think we could be just one “Carrington Event” from the middle ages, is kinda scary, no?
A musical tribute to those who just can’t live without computers >>>

For reference purposes only 🙂
http://en.wikipedia.org/wiki/Gnip_Gnop

Beyond Willis’ assessment, which is on target, where is the increased water vapor? It’s certainly not in my Texas measurements, where total column water vapor (PW) has declined -1.1 mm/decade since February 1990. Nor is there any obvious up or down global trend in PW in the latest NVAP-M study (see http://wattsupwiththat.com/2012/12/14/another-ipcc-ar5-reviewer-speaks-out-no-trend-in-global-water-vapor/). The missing increase in water vapor predicted by models is as intriguing as the missing temperature increase predicted by models, particularly since both have occurred during a significant increase in the concentration of global carbon dioxide.

Bob Tisdale has shown there is no correlation between global average temperatures and global precipitation. This is damming for the climate models, and for their CO2 sensitivity.
Further, if Bob is correct and precipitation decreased during the period surface temperatures, this indicates a common cause, decreased clouds.
Further evidence the surface warming is caused by factors other greenhouse gases, assuming the surface warming is real and not an artifact of urbanization, etc.

Daveo

The earth already receives over 200 W/m2. Using you calculations, it only takes 71.5 W/m2 to evaporate the 1 meter of current rain fall.
If it was only about W/m2, we should be getting over 3 meters of rainfall.
Something is missing. What about the moisture holding capacity of warmer air. Where’s your calculations on that?
And if there is no increase in rain fall, how does that fit with your thunderstorm hypothesis? SST’s have risen over this time, so we should have seen an increase in rainfall according to your hypothesis.

atarsinc

John Parsons AKA atarsinc
Willis, You are way beyond me in analysis capabilities, but come on. ““We need 4.52e+8 joules of energy every year to evaporate the additional water…” Where did the “every year” come from?
Then you say, “It takes 2260 joules of energy to evaporate a gram of water.” What? What temperature is your water starting from?
Then you proceed with the “Here where I live…” local weather report that seems such a common refrain amongst the skeptical here. You, the rightfully proud proponent of emperical measurement, use the UK as a MODEL to extrapolate a global phenomenon. You know that doesn’t fly.
I read this paper when it first appeared and thought, man, this is a stretch. But your argument against it seems even weaker.
You’re way smarter than me, but I think you’ve might want to address Nick Stokes point. And maybe point to where I’ve gone astray.
Respectfully, JP

Mike McMillan

Peter says: April 6, 2013 at 5:37 pm
Doesn’t most of the energy come back when the water vapor condenses?

No. We add heat energy to evaporate the water, then as it rises with a parcel of air, it continuously gives up that energy doing the work of expanding, and converting the rest to potential energy of altitude. When it has given up enough energy to drop the temperature down to the dew point, it condenses out, giving up another chunk of energy to its surroundings. When it falls as a raindrop, it is now incompressible and cannot regain any temperature by recompressing. The potential energy it converts to inertial energy by falling doesn’t convert to much temperature when it hits the ground.
Net net, it leaves most of its original energy up in the clouds, a one-way transport of heat away from the surface.

Peter says: “Doesn’t most of the energy come back when the water vapor condenses?”
The evaporation happens at ground level, the condensation in the clouds. I.e. it is a heat transfer mechanism moving heat from here to up there. I.e. it would do that much planetary cooling. I.e. however you slice it, the scare is wrong.

MattN

I swear to God they said years ago it was going to get drier as it got hotter….

KevinM

On topic… Stokes sounds right. You only need the energy once, and it can be added incrementally over time. At the margin, there is always at least one condensed droplet on the edge of becoming vapor, and at least one vapor on the edge of forming a droplet, so the energy needed to evaporate the added water might be less than your direct calculation yields.
Still, the model is not supported by historical data.

i.e. It’s colder in the rain than in the sun. And co2 has no effect on the process that I know about. Silver Iodide cloud seeding, on the other hand… Have you checked out Dr. John von Kampen’s website ? He’s put up stories of late diverging from merely debunking AGW to noting reports of weather warfare; Geoengineering. http://my.opera.com/nepmak2000/blog/2013/03/28/a-co2-apocalypse-and-what-caused-it-an-answer http://my.opera.com/nepmak2000/blog/2013/03/04/geo-engineering-do-we-see-weather-warfare-or-dont-we

Ian W

Peter says:
April 6, 2013 at 5:37 pm
Doesn’t most of the energy come back when the water vapor condenses?

And

Mark Bofill says:
April 6, 2013 at 5:47 pm
Steve Keohane says:
April 6, 2013 at 5:35 pm
Thanks Willis. Wouldn’t all that extra evaporation transfer heat to where some would be lost causing a negative feedback or self-limiting system? I am probably influenced by your writing about the same. Your elegant-as-usual dissection is complete without further foray.
————–
Yeah, that was my first thought too. No free lunches; if the energy is being burned driving more rain, it seems counter intuitive that it should also be available to drive up temperatures.

Yes as the water vapor condenses it gives up latent heat of condensation and as it freezes another burst of latent heat of fusion. This heat release is not governed by Stefan Boltzmann as it is not a radiation based on temperature. Therefore all the curious ideas of ‘effective radiation levels’ are spurious.
You can watch this heat being released in real time just go to
http://www.ssd.noaa.gov/goes/east/natl/flash-rb.html
There you will see the outgoing infrared as seen by the GOES East Satellite. Notice how the weather systems show up.
Mike McMillan says:
April 6, 2013 at 6:54 pm

So not a net-net process as we can see energy departing from the frontal and storm systems

tobias

I think this article about 20-30% PMP is based on the arrival of the comet ISON 🙂

Louis Hooffstetter

The paper says rainfall (liquid water, not water vapor) will increase by 20% to 30%. If one gallon of liquid water makes 1603 gallons of water vapor (steam), then a 30% increase in rainfall (liquid water) would require a 48,000% increase in water vapor. (30% X 1603). Double check my math logic, as it’s not my strongest suit.
Is that even possible? If so, how much cloud cover and associated albedo/cooling would that produce? Instead of turning into a hot-house like Venus, we’d turn into an ice ball like Pluto.

Chuck

Wouldn’t the water give up some of the heat when it condensed?

geran

Another good one, Willis.
I see several here that are confused about the thermodynamics that Willis is using. I would feel like helping them, but they are so self-assured in their confusion I hesitate to step in. Something about when someone wants to make a fool of himself, why stop them?
Also, I remember a great line Willis used in a previous post– “Physics, don’t leave home without it.”

atarsinc

Mike McMillan says:
April 6, 2013 at 6:54 pm
“Net net, it leaves most of its original energy up in the clouds, a one-way transport of heat away from the surface.”
Mike, that seems right, but you’re still dumping the heat into the lower troposphere. You know, that part of the atmosphere where weather happens. JP

bobl

Willis, your calculation is wrong – As well as 2260 KJ per Kg you also need to cycle the water to a height sufficient to make it cold enough to condense. Lets say this is on average 3000 m
So mGh = 1 * 9.8 * 3000 = 29400 or 29.4 Kj per Kg and this effort is returned eventually not as heat but kinetic energy of the rainfall. If you calculate this for all rainfall it constitutes a negative feedback of -1.12 W/m2, which I doubt is built into climate sensitivity estimates

richard verney

Ducard says:
April 6, 2013 at 5:40 pm
/////////////////////////////////
In the UK, the Met Office for years were warning that with global warming, the UK would suffer more drought conditions. It was predicting less rainfall.
I was always surprised by that prediction since one’s gut feeling is that with a warming world there will be more evaporation and hence more rainfall. The UK is a small island surrounded by seas so no matter from which direction the wind blows, the air is always moist and humid since it has come over seas. Without a change in the geography and topography of the country, the moist air will sooner or later meet the mountains be forced up, cool and release its precipitation.
Now that the UK has these past few years experienced quite a bit of flooding, the Met Office now predict increased rainfall in the future and more floods.
As Willis notes whilst CET data as from 1975 onwards shows a very slight increase in rainfall, the trend is not statistically significant. On a centenial basis, there has been no statistically significant change in rainfall.
It would appear that the Met Office’s forecasts of doom have been put out to hide poor water management.
Since the 1970, the population of the UK has grown by about 8 to10 million largely living in the South East. During this time not one single new water reservoir has been built in the South East to meet this increase in demand. Hence there have been many water shortages and hose pipe bans. To hide this poor management, the UK Met Office blamed climate change (global warming) on water shortages and the press never questioned the Met Office’s predictions/claims in the light of the CET precipitation data which shows no significant change in rainfall. Poor water management leading to water shortages was masked under the guise of its the consequence of climate change not government error/failings.
Now these past few years the UK has had much flooding leading to substatial property damage and large insurance claims. Some home owners are finding it difficult to obtain insurance for flood risks. This flooding, is not due to increased rainfall but due to poor managment in this case river management and building regulation. Recent home building has taken place in flood plains and hence these new homes are prone to flooding. Sometimes, developers being alive to this problem have built flood defences nearby. But this has created a different problem. rivers no longer flood in their usual past flood plains 9because of the new flood defence), but instead river flow is backed up causing rivers to flood upstream in places where the river rarely use to flood.
Since this is due to poor government management, it appears that the Met Office with a view to hiding this mismangement now sings the flooding is due to more rain caused by climate change mantra. Once again, the government is let off the hook.

atarsinc

geran says:
April 6, 2013 at 8:09 pm
“I see several here that are confused about the thermodynamics that Willis is using…”
I’m one of those, and I’m not “self-assured” about it. So, by all means, help out. I did some study since I asked about initial temp conditions. That may have been a stupid question. Willis was evidently making his computation based on the latent heat of evaporation, but is that the appropriate basis for an open system?
Nick Stokes’ (and others’) question about energy “per year” is still out there. Want to take a stab at that? JP