Scaling Factors and Uncertainty

I was going to include this in the last post, Stratospheric Cooling and the Missing Tropical Tropospheric Hot Spot, but my spread sheet was acting up.   The troposphere according to the models should warm at a fast rate than the surface.  The lower troposphere about 10 to 20% faster and the upper to middle troposphere about 30 to 60% faster.  So with the models predicting the tropical middle troposphere to warm 60% faster than the surface, it should be pretty noticeable.  The "polar" amplification which is actually "Arctic" amplification should also be pretty obvious.  The models predict those happenings.  Well, land surface air temperatures, which are in the lower troposphere should also warm faster than the oceans.  All of the amplification of warming should be easily predictable and measurable if atmospheric forcing is as simple as models suggest.

Some won't like my choice of data sets, but this is the scale or amplification ratio of CRUTs3.22 Tmax and Tmin to ERSSTv4 global.  I used a satellite record length linear trend for each in a sliding window to show changes in the amplification factor.  The data starts in 1950 to avoid the 1940 -1976 zero slope which messes things up.  You could take a difference of some reference slope to force the trends to be greater than zero, but this is just a quick and dirty comparison.  If you combine the two CRUTs3,22 sets or use Tave, the average scaling factor is about two.

If you are pretty certain that the relationship holds for longer time frames, you could scale the longer land temperature data set to extend say the SST data back in time.  I have scaled BEST, Sea Level Rise, Ocean Heat Content, Central England Temperature as a bit of a sanity check paleo reconstructions , but there is enough variation that the uncertainty is fairly large so it isn't exactly a recommend method in my opinion.

This is what that scaling exercise looked like with Oppo et al. 2009.  As you can see the uncertainty would be pretty large in climate science world, but it does indicate that Oppo et al, 2009 is probably a pretty good reconstruction.  The Oppo reconstruction has an average resolution of about 50 years versus 27 month moving average for the instrumental so I could smooth more to get the statistical uncertain down, but that doesn't do much but hide the real uncertainty.

The explanation for land amplification with respect to oceans is pretty simple, land has about half the specific heat capacity or the ocean skin layer.  You get about twice the warming per unit energy on the land mass.  It gets a bit more complicated because water availability changes the specific heat capacity of land and not all land is at the same altitude or initial temperature.

If that was the only factor you would have a slam dunk, of course it isn't.

The factor changes with time so you have to be careful.  Extremely long term you get the 1.1 for Tmax and 1.4 for Tmin.  The shorter your time frame the more variable it becomes.

The CMIP5 model means indicate a satellite era scaling factor like above.  Depending on what data sets you use you can get a fair match with models or a complete fail.  BEST Tmax and Tmin have a fair match but BEST Tmax and Tmin correlate better with model Tmin and Tmax.

This compares models with BEST and Hadisst using a Callandar baseline 1935-1944.  You can change your baseline around but that wouldn't impact scaling factors.  You only have a "real" scaling factor when all the slopes are of the same sign and a bit greater than zero which is a good reason to use differencing.  Just eyeballing though you can see there is a lot more noise in the land surface data because it is more easily amplified by whatever influence comes along.

Since the largest amplification should be in the tropical troposphere, there is a lot of focus on that with the RATPAC, UAH sand RSS gang.  The theory behind tropical tropospheric warming is similar but you have to consider the lapse rate.  Perfectly dry air would have a lapse rate close to 9.8C per km and saturate moist air a lapse rate of about half that or 5 C per km.  All things remaining equal more warming over the oceans should increase atmospheric water vapor which would tend to push the lapse rate toward saturation.  The upper troposphere has a much lower specific heat capacity so the increase in latent energy would tend to warm the upper troposphere more than the lower troposphere.  The all things remaining equal part is the catch though.  If convection and/or advection increases more that anticipated, there could be not only no tropospheric hot spot it could even cool.  Cooling there though related to advection would move the warming some place else.

With greater than expected amplification in the Arctic and over portions of the land mass, an increase in poleward advection is indicated.  Science of Doom has a nice discussion on the subject near the end and in comments, but the basic issue is that the hotspot is an amplification and if surface temperatures are not warming there is nothing to amplify.  With changes in advection you get other "warm" spots.

Berkeley Earth Surface Temperature did some comparisons and found that 30N-60N warming was amplified more that predicted.  There are plenty of "other" factors that can be involved, but more moisture in a saturated lapse rate situation would just mean a higher convection which would create a wider path for advection.  With moist air that could mean a wider area of cloud cover which would negatively feedback on the surface producing the warming to begin with.

Surface winds, which would be driven to a point by changes in convection/advection which would be related to tropical surface temperature, tend to both expand the tropical sphere of climate influence into higher latitudes and increase ocean mixing.

This is a bit of a double whammy for the "all things remaining equal" assumption, particularly the ocean mixing part which would increase the rate of ocean heat uptake reducing the amount of atmospheric warming.

Obviously, that is not the only thing going on or wind speed would follow surface temperature more closely.  The big things to me are uncertainty and natural variability.

I have just about given up on surface air temperature because of the noise, so this is an attempt at estimating uncertainty using just the SST data and models.  The uncertainty for the observation I am using is one sigma for a fairly aggressively smoothed data set.  Aggressive being a 5 cascade 13 month moving average.  That is compared with modeled SST +/- 0.25 C which is an eyeball fit.  So if you can expect a +/- 0.25 C uncertainty range for the models and a 1.4 scaling factor you have +/-0.35 C expected variation in the surface temperature and/or troposphere at what ever level blows wind up your skirt.  Since the estimated scaling factor varies from 1.1 to nearly 3, it is possible to have a +/- 0.75 range of uncertainty in the atmospheric data.  Measurement wise, the accuracy on a global scale can approach +/- 0.05C, but that doesn't help much when natural/internal variability can be a couple of orders of magnitude greater.  Whether you decide to smooth observation to some politically correct sigma or expand model uncertainty to include observational transgressions, SST variation combined with lower troposphere amplification is not going to be easily dealt with when it comes to attribution of "causes".

I believe Lorentz pointed this out some time ago.  In any case, zero times any scaling factor is still zero.  The missing tropical troposphere hot spot is just an indication of no significant warming, due to what ever cause.


Update:  I forgot the best graph!

30 to 60 north has the highest regional amplification and the most confounding factors, land use, suburban heat island, black carbon etc. and the amplification doesn't really look like a CO2 forcing curve.  No, this is not dependent on data selection.

All the data sets agree there is a plateau in this region that had been the most rapidly warming.  The "suburban" heat island effect is related to general land use impacts, more impervious surfaces, compaction, water cycle changes due to drainage and crop selection in the region that would be a real impact on temperature stations.  The RSS satellite data, controversial as it may be, tends to agree that it not just an isolate instrumental effect.  However, GISS and Cowtan and Way may be interpolating in a small amount from outside the region, but probably less than a tenth of a degree.