Thursday, September 26, 2013
Exposing the Dodge
The fact is that we can’t account for the lack of warming at the moment and it is a travesty that we can’t.
But in May, 2013, Trenberth, et al seemed to say they have found the missing heat in the deep ocean in this paper. They find "considerable warming occurring below 700 m." How considerable?
First, it is possible that the heating of the surface of the ocean by the sun or warm air would warm the adjacent water but it is difficult to believe that the heat moved from the surface to the deep without being fully detected in the intermediate space.
Second, sun-heated water is less dense than cold water and therefore more buoyant than the cold water so it would take an outside force (downwelling current) to make the warmth go deep down. Why downwelling currents would start just when lower troposphere temperatures stopped getting warmer (and indeed began to decline), nearly two decades ago, was never explained.
Finally, I and a few others began to smell a big, fat Commie rat when the y-axis of the supporting charts for the ocean warming were in Joules rather than degrees C. Behold:
It looks pretty bad doesn't it? Nearly 20 times 10 with 22 zeroes Joules in just 50 years. That's a lot of Joules.
I tried my hand at calculating what the Joules would mean to actual heat in the ocean. I came up with an insignificant, tiny amount of heat, but I have never been good at calculus so I never published my calculations, as far as I remember.
But an actual physicists from the Czech Republic, Luboš Motl, has done the numbers and here is what he gets.
The ocean heat content is defined as
So Argo (not the movie but the oceanographic guys) and Dr. Motl find that in 50 years the deep heat in the ocean has skyrocketed about 1/16th of a degree C. This slight warming is below the ability of the ocean going thermometers to detect because the range of error for the oceanographic thermometers is greater than .1 degrees C. This "considerable" warming is merely fluctuation within the "noise" of a chaotic system.where
H=ρcw∫h1h2T(z)dz ρis the water density, cwis the specific heat capacity, and T(z)is the temperature profile from the top depth h1to the bottom depth h2. The additive shift is a bit ambiguous; we want to talk about the changes of the ocean heat content only.
Now, in the first graph, 0-2000 meters, the change between 1968 and 2013 was the difference between
+17and −9"units" used in the graph. That's 26units. Looking at the y-axis, you see that the unit is 1022joules. So the change of the ocean heat content of this layer during the last 45 years wasThat's nice. How much is it? We want to translate it to the average temperature change of this layer of water. To do so, we have to know the volume of the layer and multiply it by the heat capacity. 2.6×1023J.
The total volume of the world's oceans is about
1.4billion cubic kilometers which iswhere the mass in kilograms was obtained by the multiplication by 1.4×1018m3→1.4×1021kg 1,000kg/m3and one cubic kilometer was translated to one billion cubic meters, OK? The heat capacity of the world's ocean is this number multiplied by 4,200J/(kg⋅K)which isThe same page tells us that the average depth of the ocean is 5.9×1024J/K. 3.8kilometers. The layer we consider is slightly more than one-half of that but this layer will carry more water than one-half of the world oceans' water simply because at many/most places, the restriction that the layers beneath 2 kilometers of depth are omitted is inconsequential. (Or did I get it backwards and the deep places are more relevant for the nonlinearity?) So I estimate the heat capacity of the layer between 0 and 2 kilometers of depth to be aroundPlus minus 20 percent. I am just calculating an estimate. The last step is a simple division. We take the change of the ocean heat content from the NOAA graph, 4×1024J/K. 2.6×1023J, and divide it by the figure above. We obtainplus minus 20 percent. In the last 45 years, the average temperature of that layer of the ocean increased by 2.6×1023J4×1024J/K=0.065K 0.065Celsius degrees only! That would give you 0.14 °C per century, about 20 times smaller temperature difference than the changes of the global mean temperature predicted for the surface.
(Update: Paul Matthews informed me via Twitter about this ARGO page where they confirm that since the 1960s, the warming of that layer was 0.06 °C.)
Changing to Joules rather than degrees is classic misdirection. Don't be fooled. Trenberth's missing heat is still missing (or more likely was never missing because the climate models predicting the heat's very existence are all worthless).