Guest Post by Willis Eschenbach
I’ve been looking again into the satellite rainfall measurements from the Tropical Rainfall Measurement Mission (TRMM). I discussed my first look at this rainfall data in a post called Cooling and Warming, Clouds and Thunderstorms. There I showed that the cooling from thunderstorm-driven evaporation is a major heat-regulating mechanism in the tropics. This is another piece of evidence for my hypothesis that the global temperature is regulated by emergent phenomena, including tropical thunderstorms. This regulation keeps the temperature within a very narrow range (e.g. ± 0.3°C over the entire 20th century).
In that post, I looked at averages over the period of record. For this post, instead of averages over time I’ve looked at the changes in rainfall amounts over time. To begin the temporal investigation, Figure 1 shows the month-by-month variations in the average rainfall.
Figure 1. Movie loop of the monthly averages of the tropical rainfall, Dec 1997 – Mar 2015. The coverage of the mission only extends from 40°N to 40°S. Note that this covers about two-thirds of the surface of the planet. Units are mm/month.
Note how the rainfall amounts clearly delineate the Inter-Tropical Convergence Zone (ITCZ) that runs along and generally just above the Equator. As the name implies, the winds of both the northern and southern tropics converge near the equator. Where the winds meet there is intense rainfall, along with the deep thunderstorm convection that drives the global atmospheric circulation.
It is interesting to see the waves of precipitation wash over places like India. It’s like the earth breathing—in the summer when India gets hot, the hot air rises. When the air rises, it draws in the moist air from off of the Indian Ocean, which pours down as the monsoon rain.
Brazil, on the other hand, was a surprise in that I never knew that all of Brazil but the far north has a long dry period from July to January or so. And when it rains, the rain comes down from the north. Always more to learn.
Now, when I look at a timeseries record, I want to be able to separate out the regular seasonal changes from the rest of the data. Figure 2 shows the month-by-month rainfall averages for the area 40°N to 40°S, decomposed into the seasonal and residual components.
Figure 2. Decomposition of the monthly rainfall record (red line, top panel) into two components—a repeating seasonal component (blue line, middle panel) and a residual component (bottom panel) which is the data minus the seasonal component. The p-value is adjusted for autocorrelation by using the Hurst exponent to calculate the effective degrees of freedom. See here for details of the adjustment.
The main thing that stands out for me in this record are the two biggest El Nino/La Nina episodes, one in 1997-1998, and one in 2009-2010. We can see that during these episodes the tropical rainfall went up. There is also an overall trend, but it is not statistically significant.
Now, we can convert the rainfall data into evaporative cooling data. To do so, we utilize the rule that what comes down must go up. So if a half meter of rain falls in a month, a half meter of water must have been evaporated during the month.
And we know that it takes about 75 watt-years of energy to evaporate one cubic meter of seawater. This lets us convert the rainfall data to evaporative cooling data. Figure 3 shows that result. Of course it is identical in shape to the rainfall data, only the units are changed.
Figure 3. As in Figure 2, showing the decomposition of the monthly evaporative cooling record (red line, top panel) into two components—a repeating seasonal component (blue line, middle panel) and a residual component (bottom panel) which is the data minus the seasonal component.
As mentioned above, I’ve shown that as the temperature goes up, so does the thunderstorm-driven evaporative cooling. In other words, the variations in thunderstorm evaporative cooling are a response to the temperature variations.
Note the size of the variations in cooling, which can change by up to eight watts per square metre in a single month. This can be compared with the estimated changes in CO2 which are expected to be about four watts per square metre in a century …
This dependence of thunderstorm evaporative cooling on temperature be seen more clearly by looking at the deep tropics, what are sometimes called the “wet tropics”. The graph below shows the area from 10°N to 10°S. You can see in the bottom panel that the evaporative cooling was high during the 1997/8, the 2002/3, the 2006/7, and the 2009/10 El Nino/La Nina episodes, and decreased during the subsequent La Nina episodes
Figure 4. As in Figure 1, but for the deep tropics from 10°N to 10°S. This shows the decomposition of the monthly thunderstorm evaporative cooling record (red line, top panel) into two components—a repeating seasonal component (blue line, middle panel) and a residual component (bottom panel) which is the data minus the seasonal component.
The first thing that caught my eye is that at 120 watts per square metre, the evaporative cooling in the deep tropics is about 50% stronger than in the full TRMM 40°N/S dataset.
You can also see the El Nino/La Nina pump in operation. The “La Nina” portion of the El Nino/La Nina pump is much clearer in this deep tropical data. We can also see the smaller El Ninos of 2002/3 and 2007/8 along with the subsequent La Ninas.
Now, here is the interesting part. I wanted to compare the evaporation with the surface temperature. To start with, I used the HadCRUT4 surface temperature for the deep tropics. Figure 5 shows the two datasets, one of temperature, and the other of evaporative cooling.
Figure 5. Temperature and evaporation in the deep tropics 10°N to 10°S latitude. The upper panel shows the HadCRUT4 surface temperature data. The lower panel shows the evaporative cooling calculated from the TRMM rainfall data.
As you can see, the two datasets follow each other very closely. To demonstrate that, Figure 6 below shows the evaporation, along with the linear estimate of the evaporation based solely on the surface temperature:
Note that this covers the entire deep tropics from 10°N to 10°S. This is not just the El Nino region in the Pacific, but also the other oceans and the land as well. And as you can see, in the deep tropics the temperature and the evaporative cooling are quite intimately related around the globe.
Now this correlation of temperature and evaporation should be no surprise. Common experience tells us that the warmer a wet object is, the quicker it dries by evaporation. So we’d expect evaporation to increase and decrease in parallel with temperature.
The surprising part of this analysis from my perspective was the size of the variation in evaporative cooling. We get a very large variation in evaporative cooling given a small change in temperature. Evaporative cooling rises by 27 W/m2 of increased cooling for each one degree C of surface warming.
I wasn’t all that convinced that big a number was correct, so I decided to check it against the CERES surface temperature data. It turns out that the CERES data gives us about the same answer. CERES data for the deep tropics says there’s an average of a 23 W/m2 increase in evaporative cooling per degree of surface warming for the deep tropics (10°N/S). Here’s the larger picture from the CERES data:
As noted above, the TRMM data covers about two-thirds of the surface area of the Earth. From appearances, unlike in the tropics, the correlation of evaporation and temperature is negative in the unsurveyed areas of both the northern and southern extratropics. The grey line at about 30°N/S shows where the relationship goes negative. This is no surprise. In the extratropics, rain is associated with cold fronts instead of being associated with thermally driven tropical thunderstorms. As a result, although the overall average change in cooling shown in Fig. 6 is 11.7 W/m2 per degree of warming, I suspect this be largely offset once we have precipitation data for the currently unsurveyed areas.
Regardless of the unknown global average, however, in the tropics (and particularly the deep tropics) evaporative cooling generally goes up, and sometimes very rapidly, with increasing temperature. To take another look at it, Figure 8 shows deep tropical evaporation as a function of the CERES temperature data (note that the CERES data doesn’t cover the end of the 1997/8 El Nino-La Nina episode.
So I got to thinking … if there were no thunderstorms, how large would we expect the change in evaporation to be for a one degree change in temperature? We expect the evaporation to go up with increasing temperature … but how fast?
To answer this, I turned to the literature. Evaporation can only be approximated, and there is more than one way to do it. I used the formula given here (Equation 5) for evaporation over the ocean, as well as the formula in the R package EcoHydRology. The two methods gave somewhat different answers for the change in evaporative cooling per degree of warming (see “Math Notes” below). One says that assuming tropical conditions gives us about 4 W/m2 per degree warming in the deep tropics. The other says about 6-7 W/m2 per degree. And no matter how I play with the variables of wind and temperature and relative humidity, I can’t fit the data with anything more than about 7-9 W/m2 increase in evaporative cooling per degree of surface warming.
On the other hand, the answer that we’ve gotten from a couple of sets of observations (HadCRUT4 and CERES) gives a value of around 25 W/m2 of increased evaporative cooling per degree of warming for the deep tropics. And the trends of individual gridcells in Figure 6 shows evaporative cooling of more than three times that per degree of warming.
To put the contrast starkly, at the average temperature of the deep tropics (~27°C), from theoretical considerations we’d expect a 1°C rise in temperature to increase evaporation by somewhat less than ten W/m2 depending on your assumptions … but the observed average increase is 23-27 W/m2, much more than the theoretical increase in evaporation from temperature alone. I hold that this is because of the thermally controlled nature of thunderstorms.
I think that the causative chain runs as follows:
Increased surface temperature ==> earlier and more daily thunderstorms ==> increased evaporation ==> increased cooling
However, I’m happy to entertain alternative hypotheses.
To recap: the unexpected finding is NOT that evaporation increases with temperature. We’d expect that. The unexpected part is that the evaporation increases by 27 W/m2 per degree C of warming, while the theoretical increase in evaporation per degree of warming is much less than that, under ten W/m2 per degree C.
How is this increase in evaporation accomplished? Well, therein lies the story of one of the under-appreciated abilities of the thunderstorm. A thunderstorm is a dual-fuel heat engine. It runs on either temperature or water vapor. And beyond that, it can create its own fuel as it runs.
Thunderstorms run off of low-density air. The low-density air rises, bearing water vapor upwards to the level where the water vapor condenses. The heat of condensation then powers the deep convection up the tower of the thunderstorm.
Now, there are two ways to get low-density air. One way is to heat the air, so it expands and rises. The other way is to increase the relative humidity of the air, because counterintuitively, water vapor is lighter than the air. So when evaporation increases, the air gets lighter and rises.
And here’s the beauty part. The thunderstorm doesn’t just depend on the existing evaporation. Instead, it generates its own increased evaporation (and thus increased evaporative cooling) in several ways.
First, once the thunderstorm forms it generates strong surface winds in front of and underneath the storm. Evaporation is a linear function of the wind speed, with a coefficient of about 0.7. So if wind speed increases from say 2 m/sec (4.4 mph) up to 10 m/sec (22 mph), you get about three and a half times the evaporation.
The next way that thunderstorms increase evaporation is that they are surrounded by dry descending air. Thunderstorms condense the water out of the air as it is lifted high into the troposphere. As a result, when the air exits from the top of the thunderstorm, it contains very little water. From there it descends, providing a constant source of dry air to the surface. If there is 120 W/m2 evaporative cooling in the deep tropics and the air dries from a relative humidity of 0.75 to 0.65, the evaporative cooling increases by about a third, to about 160 W/m2. So this provision of dry air is quite a large factor in the increased evaporation.
The final way that thunderstorms increase evaporation is by increasing the evaporating surface area of the water. Over the ocean, which is 83% of the deep tropics, wind-driven waves increase the oceanic surface area. Wind-driven short-period waves of say 1/2 metre height and 30 metre wavelength increase the ocean surface area by about 1%. But when those waves start to break, or when the storm winds blow the water off of the tree leaves and the grass, sending fine spray into the air, surface area increase from the spray droplets can be 5% or more.
So once the thunderstorm gets started, it manufactures low-density air that keeps it going by generating strong winds at the base, by lowering the relative humidity of the surrounding air, and by increasing the evaporating surface area. This lets the thunderstorm cool the surface to a temperature well below the thunderstorm initiation temperature.
I highlight this because it is a crucial and often overlooked fact, one than distinguishes thunderstorms from simple linear feedback. Once the thunderstorm is initiated, it operates in the exact same manner as manmade refrigerators. It uses evaporation to remove heat from the area to be cooled. And because it is generating its own fuel (low density moist air) it can continue to cool the surface to below the temperature at which it started. And this “overshoot” in turn means that it can keep a “steady state” temperature that only varies within a narrow range. When the temperature gets too high, it gets pushed down below the thunderstorm initiation temperature. Then the temperature starts to rise again, and when it does, a new thunderstorm forms, and it pushes the temperature down below initiation temperature. The cycle repeats endlessly, and the temperature of the system varies little.
And this is the reason for the large variation of evaporation with temperature. Tropical thunderstorms are a threshold-based emergent phenomena. This means that they emerge spontaneously once a certain threshold is surpassed. In the case of tropical thunderstorms, the threshold is mainly temperature-based. As a result, the evaporative cooling due to tropical thunderstorms is a function of the surface temperature.
In closing let me add this final movie. It shows the entire history of the TRMM tropical rainfall observations, month by month. To me, there’s nothing as fascinating as observational data.
My best wishes to you all,
My Usual Request: If you disagree with me or anyone, please quote the exact words you disagree with. I can defend my own words. I cannot defend someone’s interpretation of my words.
My New Request: If you think that e.g. I’m using the wrong method on the wrong dataset, please educate me and others by demonstrating the proper use of the right method on the right dataset. Simply claiming I’m wrong doesn’t advance the discussion.
Math Notes: I’ve used the R package EcoHydRology to estimate the evaporative heat flows from a wet surface. Most (83%) of the deep tropics is ocean, and the rest is usually wet, so it is a reasonable approximation. The function I used is called “EvapHeat”. The package documentation says
EvapHeat : Evaporative heat exchange between a wet surface and the surrounding air
Evaporative heat exchange between a surface and the surrounding air [ kJ m-2 d-1 ]. This function is only intended for wet surfaces, i.e., it assumes the vapor density at the surface is the saturation vapor density
EvapHeat(surftemp, airtemp, relativehumidity=NULL, Tn=NULL, wind=2)
surftemp : surface temperature [C]
airtemp : average daily air temperature [C]
relativehumidity : relative humidity, 0-1 [-]
Tn : minimum dailiy air temperature, assumed to be dew point temperature if relativehumidity unknown [C]
wind : average daily windspeed [m/s]
This function gives the answer in curious units, kilojoules/m2 per day. So I convert it to watts continuous by multiplying by 1000 joules per kilojoule and dividing by 86,400 seconds per day. This is joules/second/m2, which is the same as watts/m2. I used this function with reasonable numbers for the variables in the deep tropics (surftemp ≈ 27°C, airtemp ≈ surftemp – 0.5°C, relative humidity ≈ 0.85, wind ≈ 2 m/sec.) The values for the surface and air temperatures are from the TAO buoy data.
The second way that I determined the increase in evaporation with temperature was using the formula shown here at the bottom of page 6. It gives smaller values for the increase in evaporation with a 1°C increase in surface temperature.
After much experimentation I found that regardless of the exact values chosen for the variables (surface temperature, etc.), the change in evaporative cooling per degree of surface warming is far below the ~ 25 W/m2 of evaporative cooling shown by the TRMM data. In all cases I investigated, any combination of values that gave a total evaporative cooling of ~ 120 W/m2 also gave a change in cooling of less than ten W/m2 of additional cooling for a 1° surface temperature change.