Willis Eschenbach has a new post on Watts Up With That (WUWT) called forcing the ocean to confess. In this post Willis calculates the global forcing associated with increases in the ocean heat content. I’m not quite sure that this is strictly speaking a forcing, but it has the same units, so I’ll forgive him this misuse of terminology (if this is the case).
So what did Willis do? He downloaded ocean heat content data from NOAA. He then calculated the annual change in heat content, divided this by the number of seconds in a year, and then by the surface area of the Earth. This essentially gives the yearly average flux associated with energy going into the oceans. He then produces the following figure which shows the variation in this flux, and shows the mean, trend and associated errors.
So, what does Willis go on to say
The first one is how small the average value of the forcing actually is. On average, little energy is going into the ocean, only two-tenths of a watt per square metre. In a world where the 24/7 average downwelling energy is about half a kilowatt per square metre, that’s tiny, lost in the noise. Nor does it portend much heating “in the pipeline”, whatever that may mean.
Well this is a rather odd thing to say. The increase in ocean heat content is due to an energy imbalance at the top of the atmosphere. This is measured to be between 0.5 and 1 Wm-2. That’s fairly close to what he gets (0.2 Wm-2) and is all his calculation was ever going to give. So, what if the downwelling energy is 0.5kWm-2, that’s the steady flux. He was only calculating the flux associated with the increase in ocean heat content (i.e., the difference between the expected steady flux and the actual flux).
Willis then goes on to say
The second is that neither the average forcing, nor the trend in that forcing, are significantly different from zero. It’s somewhat of a surprise.
Roy Spencer in the comments agrees with this and claims that Bob Spencer has come to the same conclusion. This all seems a little odd as it seems that scientists are convinced that the ocean heat content has risen dramatically in the last few decades. If so, how can the average flux be consistent with zero. That would surely suggest that the change in ocean heat content is also consistent with zero.
Below is a figure from Balmaseda et al., 2013, GRL, 40, 1754-1759 showing the change in ocean heat content since 1955. The changes shown are for the upper 300m, the upper 700m and for the full depth of 2000m. It also includes an estimate of the uncertainties (although not all uncertainties).
Balmaseda also include estimates of the linear trends (Wm-2) with errors for various time intervals. This is shown in the table below. It’s clear that the estimated linear trends are consistent with the measured energy imbalance and for most periods (especially the period 1975 – 2009) are not statistically consistent with zero, which should be obvious from the ocean heat content figure above.
So, what has Willis actually done? Well, I know what he’s done. He’s calculated the trend on an annual basis. He’s then calculated the error by summing the error in the two ocean heat content measurements in quadrature. This isn’t the right way to calculate the error in this case. What he is trying to determine is the gradient (linear trend) in the ocean heat content data. The error is therefore the range of possible gradients (i.e., the min and max trend).
Furthermore, what he’s doing is analogous to calculating the trend in the temperature anomaly data. If you’ve read some of my earlier posts you’ll have read me commenting on how the error in the trend is larger if the time interval considered is smaller. The longer the time interval, the smaller the error (relative to the trend). What Willis has done is essentially calculate the trend and error on an annual basis and then averaged these over the full time interval. Even if he was calculating the error correctly, he will end up averaging a set of very large errors. What he should do (as is done by Balmaseda et al.) is consider the full time interval of interest when determining the error. The error will then be much smaller than the value he gets. One could do this yourself just from the figure above, but for the time interval 1975-2009, Balmaseda et al. get 0.47 +- 0.03Wm-2, clearly not consistent with zero.
What I find amazing about this is that Willis Eschenbach, Roy Spencer and – apparently – Bob Tisdale all do not realise that this calculation is essentially determining the fraction of the energy imbalance that is associated with heating the ocean. That the result is a few tenths of a Watt per square metre is essentially what would be expected. Furthermore, they’re surprised by the size of the error and the result that the flux is consistent with zero. Well there’s a good reason for this. It’s because the error analysis is complete nonsense.
If I can give them some advice, it is this. If something seems surprising it’s worth checking that you didn’t completely mess-up your calculation. The difference between good scientists and bad scientists is not that good scientists get all their calculations right first time, it’s that they check their calculations when the results don’t seem quite right (in fact, they normally check them anyway, just to be sure).