I’d originally set out to figure out how many Watts / square meter were being moved by a hurricane. I may still make that posting some day (it’s an interesting thing…) but along the way reached a different interesting point.
It all hinges on how much heat is moved by precipitation, and to what degree of precision is the global precipitation known?
Can we really say anything at all about “forcing functions” and “heat gain” and “global warming” from CO2 if we are assuming static something that is very much non-static? And what if it has a magnitude that is significantly larger than the CO2 “contribution”? Could not, then, minor variations in precipitation completely erase any “CO2 signature”? (Not to mention completely mitigate any CO2 impact via a minor change of precipitation levels).
Precision, Units, and Such
So first, some nice to know numbers and a couple of comments about precision.
First off, I’m going to do a lot of this in calories, then turn it into Joules. Largely because the values in calories are more ’round’ and more convenient. Partly as that’s the way I learned to do it years back. Partly because I’m just not fond of the whole notion of units named to laud dead people instead of being clear and self explanatory. (Yes, I like “cps” or “cycles-per-second” much more than Hz, as it ‘self explains’ and makes it more obvious if you have a ‘units error’ in your problem set-up…)
I am, mostly, going to be rounding things off to the 1 or 2 decimal points. Sometimes to integers. I’m going to be a bit “sloppy” about the precision for the simple reason that anything beyond the first decimal point is a fiction in our global measurements anyway, so it’s really rather a moot point. So ought I to use the “International Steam Table calorie” or the “thermochemical calorie”? ( 4.1868 vs 4.184 joules respectively). Frankly, it just does not matter. Toward the end I do a ‘calories to joules to Watts” conversion and you could use any of: 4.2, 4.18, 4.185, or the two standards and not change the conclusions on Watts/m^2 enough to care. Anyone who really cares can go do it themselves and find out how much time they waste… For most things, I use 4.185 joules / calorie, but for many things I use the “close enough” calorie numbers I learned in high school chem. 540 calories / gram for the heat of vaporization of water. 80 calories per gram for the heat of fusion of ice. 1 calorie / gram for the specific heat of water. (Close enough to the 539.xx where xx can range both sides of the round up/down divide depending on who’s calorie and what all else you assume).
Into The Numbers Game
OK, how much rain / snow / whatever falls, globally, each year?
Conveniently, there’s a Wiki that has that number so I don’t need to calculate it:
Precipitation is a major component of the water cycle, and is responsible for depositing the fresh water on the planet. Approximately 505,000 cubic kilometres (121,000 cu mi) of water falls as precipitation each year; 398,000 cubic kilometres (95,000 cu mi) of it over the oceans. Given the Earth’s surface area, that means the globally averaged annual precipitation is 990 millimetres (39 in). Climate classification systems such as the Köppen climate classification system use average annual rainfall to help differentiate between differing climate regimes. The urban heat island effect may lead to increased rainfall, both in amounts and intensity, downwind of cities. Global warming is also causing changes in the precipitation pattern globally. Precipitation may occur on other celestial bodies, e.g. when it gets cold, Mars has precipitation which most likely takes the form of ice needles, rather than rain or snow.
OK, so it’s 99 cm or just a touch under 1 meter of rain globally. I’ll work out the heat content / flow for 1 M of rain, then adjust by 0.99 later.
So, just for fun, we’ll take a detour through the land of inches as that’s how rain is reported in much of the civilized world ;-) and come back to the cm and meters used in those places that are “fraction challenged” 8-)
Besides, it would be far less interesting to just calculate the total heat of vaporization of a cubic meter of water, and the heat of cooling it 40 C, and pointing out that much got dumped at altitude when it condensed and rained back down… 1000 kg x 40 calories/gram + (1000 kg x 540 calories / gram) = 40,000,000 + 540,000,000 = 580,000,000 calories = (at 4.18 joules or watt-seconds per calorie) 2,424,400,000 Watt-seconds or 2,424,400 kW-seconds, with about 31,536,000 seconds in a year (using a simplified 365 day year…) you get 76.88, or about 77 W/m^2-year of power put into that cubic meter of water, evaporated, condensed at 40 C cooler, and precipitated out. That makes CO2 about 1.5/77 or about 2% of the impact of precipitation (IFF the CO2 impact exists at all as hypothesized…)
(I note in passing that the IPCC chart lacks any “time” dimension, so who knows what they were thinking… IFF they are talking about a 24 hour day instead of a year, the irrelevance of CO2 goes even higher, as a foot of rain really swamps 2 Watts)
Or put another way, we would need to know the global precipitation numbers and their changes (deltas or anomalies) to within 2% in order to say anything about CO2 causing temperature changes. If we don’t have those numbers to that precision AND accuracy, we don’t know squat about what is causing a 2% change in any measured heat flow.
At that point, the posting would be done… So, rather than that, lets wander off through the land of inches (and the odd compound of inches of rain per square meter of surface area) as a kind of “cross check”. It also gives us some nice ‘rules of thumb’ for measuring specific amounts of heat being moved by specific amounts of precipitation in particular places as well. Oh, and I’ll be adding in a bit for the Heat Of Fusion for those cases where the water turns to snow or hail before it starts falling back toward earth.
Why? Well, even if the snow or hail does not reach the surface, the HEAT of fusion was dumped up at the tops of those stratospheric thunderheads and hurricanes, so if the melting happens at, oh, 1000 feet above ground level, it still moved a heck of a lot of heat up into the upper air to be dumped to space.
Into The Land Of Inches
OK, a small table of numbers. The top row is a set of headings as “delta Degrees C”. So “20C” means that column is for taking water at 20C evaporating it, and condensing it back out at 0C without freezing (or from 30 C condensing at 10 C), in either case, you get the heat of vaporization of 540 c/gm and the 1 c/gm of specific heat x (delta degrees). For 20C, that’s 540 + 20 = 560. Columns with “+fus” in them include the 80 calories/gm of the heat of fusion which would happen if snow or hail forms at the tops of the clouds.
But to get joules we need to multiply it by whichever “standard” you like. I used 4.185 for this chart as it is about in between the Steam Table calorie and the thermochemical calorie. As noted above, it doesn’t really matter as the 3rd decimal place is not really relevant. So 560 x 4.185 is 2473.3 kj for a kg of water (or one liter). (or 2473.3 j/gm). That’s the second line. How many kj is represented by a liter of water that is evaporated, taken up into the clouds, and condensed at a lower temperature (and perhaps also frozen).
As a joule is one Watt for a second, those numbers are also the Watt-seconds needed to heat the water that much. 2.473 kW for a second will warm a gram of water from 0C to 40C and evaporate it (if I’ve not buggered the math somewhere). Oh, and realize that in the real world it will be somewhat more complicated than this as the specific heat of steam is different from the specific heat of water, so the actual values will depend on when it evaporates vs when it heats and when it condenses vs when it cools. As liquid or vapor. But as a first approximation, this gets us close to what’s happening, on an order of magnitude basis at least. We can reasonably presume that if the water was at 40C in the tropical ocean, and was at 0C in the cloud tops as condensed rain, the heat flow was the same as that of the specific heat of that much water, even if it traveled as water vapor in between. We also know the heat of vaporization was taken at the surface, and released somewhere in the cloud as water condensed and rose. (Then transported on up to the tops). Oh, and two ‘nice to know’ numbers are that there are 86400 seconds in a day and 31536000 in a year (more or less, modulo an occasional leap year ;-)
I then take the “plug number” of 25.4 liters of water per “inch” of rainfall per meter squared, and find the number of joules in that many liters of water as being the “joules / inch of rain”. (100 cm on a side is 10000 cc. 2.54 cm / inch, 25400 cc or 25.4 l)
I do the same thing for kW-seconds / m^2 for 10 cm of rain (about 4 inches) so the fraction challenged folks can have a decimalized system for reference ;-)
20C 40C 20C+fus 30C+fus 40C+fus 2343.6 2427.3 2678.4 2720.25 2762.1 kj/liter 59527 61653 68031 69094 70157 kW-seconds/m^2 per inch of rain 234360 242730 267840 272025 276210 kW-seconds/m*2 per 10 cm of rain
OK, that’s a lot of joules, but most folks don’t really have a good handle on what a joule is, and a Watt Second is kind of unfamiliar in normal day to day life, so lets turn it into how many Watts that would take, spread steadily over a whole day, and over the whole year. Just using those ‘seconds / day’ and ‘seconds / year’ numbers to look at the total impact, rather than just ‘what if it all happened in seconds?’
689 714 787 800 812 W/m^2 in one day per inch 2713 2809 3100 3148 3197 W/m^2 in one day per 10 cm 1.89 1.96 2.16 2.19 2.22 W/m^2 in one YEAR per inch 7.43 7.70 8.49 8.63 8.76 W/m^2 in one YEAR per 10 cm
Hmmm… Starting to be interesting. We’ve got about 689 W to 812 W needed over the whole day to evaporate an inch of rain. As the typical tropical earth surface gets a bit over a kW for about 1/3 of the day, we’re looking a each inch of rain representing at least a couple of days of total sunshine if it all reached the surface.
Those total year numbers are also interesting. An inch of rain is about the same as the total CO2 “forcing” (one presumes they really mean “forcing function” and just don’t know how to use the language properly…) attributed to CO2. The flip side of this is that it implies we MUST know the global rainfall to less than one inch of both accuracy and precision to be able to say anything at all about the heat flow in the size scale of the implied CO2 function. IF we don’t know the precipitation that accurately, we don’t have a clue if things are warming, or being taken to space by thunderstorms… OR if any measured warming is just from a bit less rain this decade… Which is the cause and which is the effect is opaque if you lack that data. In short, you must be guessing and calling it a theory or calling it science. But it’s still a guess if that data is not available.
OK, time for our “cross foot”. We’ll figure the Watts / m^2 for 100 inches of rain, for 1 m of rain, and then adjust that to 99 cm as that’s the actual global average.
189 196 216 219 222 100 inches 74.3 77.0 84.9 86.3 87.6 100 cm (or 1 M) of rain 73.6 76.2 84.1 85.4 86.7 99 cm (earth average) 2.0% 2.0% 1.8% 1.8% 1.7% CO2 at 1.5W as % of precipitation
OK, so we’ve got to know the global precipitation and it’s deltas (anomalies) to within less than 2% to know if CO2 is doing anything. Otherwise, it could just be rainfall variation. It is NOT enough to just “assume it doesn’t change”. CO2 might well increase heat gain at the surface, only to have a 1.8% increase in total precipitation wipe out any change of temperature. (Or a slight change in stratospheric temperatures offset it).
I also note that the 77.0 number for 40C non-fusion for a meter of rain is in close agreement with our first cubic meter estimate, so there is some hope I’ve not messed up the math anywhere ;-)
OK, one last little interesting number. Take the two values for ‘with fusion’ vs without at 40C and subtract them. 87.6 vs 77.0 is roughly 11 Watts. That means that a 14% change in how much of the water that falls as precipitation has a “freeze” happen at altitude (regardless of if it reaches the ground frozen or not) can account for the same 1.5% of heat flow as all CO2.
Do we even know what percentage of global precipitation has a freeze event at altitude? If it freezes at 40,000 ft, and melts at 2000 picking up heat down low, how do we even know?
One other complication: Water can cycle high to low to high to low again and never reach the ground. How much variation in that ‘inside the thunderstorm’ heat flow is even known?
It looks to me like the error band on precipitation makes it completely impossible to know what CO2 might or might not be doing. It can only be an article of faith. Since we have no clue, really, how precipitation changes happen over the PDO / AMO cycles to 2% of variation, how can we say if any warming or cooling is CO2 induced or precipitation dependent?
Finally, for those who stuck it out through the text and tables, some ‘eye candy’. A few graphs and pictures that give some supportive evidence for some of the numbers I’ve used here and some of the conclusions I’ve reached.
First off, here is what a cyclone looks like from space in infra-red. Notice just how much heat is being dumped at altitude at the top of that thing? It is just a monster cooling pump dumping heat to the stratosphere. So, any guesses as to how many hurricane strengths are known to within 2%?
(This picture was featured in the Wiki on “Tropical Storms” here: http://en.wikipedia.org/wiki/Tropical_cyclone )
Original image with attributions.
The use of 1.5 Watts as the “CO2 Forcing” is based on this graph:
As found in the wiki on “global warming”. Oh, and they have one on total sunshine here: http://en.wikipedia.org/wiki/Insolation
(Yes, I’m not bothering to make those ‘live links’. If they want to play games with what gets found by their search engine to favor global warming agendas, I can reduce their ‘link count’ metrics by one… What goes around, comes around… )
For what it’s worth, the wiki on heat capacity and enthalpy are fairly decent, even noting many things about heat that I’ve noted before (such as the tendency for averages of temperatures to be a bit daft…) though they persist in the notion that any science using terms or units from less than the last international party, er conference, buggering them, er ‘revamping’ them is “archaic”… Well, I happen to like my science old, musty, archaic, and very well worn. It’s more likely to be right that way. Units are not fashion statements, and it makes not one whit of difference if one uses BTUs, calories, joules, or any other unit.