## Evidence of Missing Model Feedback

Posted by Jeff Id on January 24, 2009

I have been investigating the differences between satellite and GISS data. There is an unusual effect in the trend in which ground data’s long term trend is substantially less than the satellite lower troposphere data yet the short term trend of LT data is greater than ground. Models predict that the longer term 30 satellite trend should be 1.2 times the GISS data as well. Dr. Christy hypothesized that the difference between these measures is a missing feedback in the climate models.

By looking at the covariance between UAH and GISS two detrended year low pass filter data I found a UAH/GISS ratio of 1.15 times yet the 30 year trend is .127/.183 = 0.693. I emailed Dr. Christy for some clarification he gave permission for the following quote.

The global-mean short term tropospheric amplification factor of 1.2 (it’s 1.3 in the tropics) indicates (a) that the ocean’s thermal inertia (sfc datasets use SSTs) works against large shorter-term changes while the atmosphere is much less massive and can respond to a greater extent and (b) there is a lapse-rate feedback process where the lapse rate tends to move toward the moist adiabat when thermally forced from below. Why we don’t see this amplification factor in the trend metric (which models show also occurs for the trend) likely deals with the feedbacks of the climate system – there appear to be negative feedbacks on longer time scales that models don’t capture. This is a hypothesis we want to test.

If there are feedbacks on longer timescales affecting the 30 year trend but not the short term, we should be able to see that in the data. I have done the following analysis several ways now. Unfortunately I had trouble with R overwriting memory for some reason. I don’t see where it’s happening but it forced me to use a gaussian low pass filter to create my own bandpass as the Chebyshev and Butterworth filters caused R trouble when reapplied thousands of times.

My bandpass filter was a crude but working implementation using the CA gaussian filter. I looked at the covariance of the UAH/GISS data in 1 year width filter windows. Because the filter doesn’t have a hard frequency cutoff, sharp changes in the data get spread over greater wavelengths. Since my plots below use ratio’s between UAH and GISS this change in width is the only effect.

For those who don’t do a lot of math, the theory behind frequency analysis is that any waveform can be created by a summation of sine waves at different frequencies and amplitudes. By performing a band pass filter, I am attempting to look at the addition of those sine waves which have a wavelength in the range being tested. So in my graph below I have a point at 5 years, it looks at data from 5 to 6 years wavelength and determines the ratio of the covariance UAH to GISS at that point.

Ok, heres the graphs.

This first graph was a bit of a surprise to me. The trend peaks at about 4 years (there could be 1/2 year shift in this value by the math. The curve drops sharply to 0.7 at 15 years wavelength. This indicates that the 15 year signal has a substantially lower amplitude ratio to GISS than the 4 year. This is what we would expect if there were feedback mechanisms on a longer timeframe in the Lower Troposphere as Dr. Christy hypothesized. Since my filter isn’t the cleanest design this next plot is important as well. I fit an ARMA model to UAH data using the coefficients to create a trendless data series. I then applied GISS trend and UAH trends to the same set of reconstructed data and looked at how my filter would respond to a simple linear offset of the data if GISS or UAH demonstrated only a linear difference.

There it is. Because the graphs of frequency response to my fake 30 year trend only graph and the UAH/GISS graph are different shape, the difference between GISS and Satellite data is not a simple trend or multiplier but rather a complex relationship. The sharp drop at 7-10 years in the first graph indicates to me that Dr. Christy’s climate feedback hypothesis is certainly reasonable (i.e. short term 10 year sat variance is 1.1 times greater than giss). The disagreement between the datasets is greater than a simple linear trend. In the future I will reproduce this result using a sharper step filter to see if I can better localize the change in the magnification factor.

**Model predictions of lower troposphere short and long term trends being 1.2 times greater than the ground temperature measurement, have a significant disagreement with observation. **

Please understand, this post does not consider the effects of complex errors in the dataset but simply accepts the data as is. There are certainly errors in the data and models which everyone acknowledges.

## David Jay said

everyone? ;)

## Jeff Id said

Even hansen admits there are errors. The question is how big are they :)

## Layman Lurker said

Some layman type questions for you Jeff:

1. Would removing the short term postive amplification from the UAH data give a clearer picture of the other relationships between the 2 data sets?

2. Considering the likelihood that there is error in the linear slopes of the metrics, how would more or less divergence of the linear slopes affect the shape of your graph?

## DeWitt Payne said

Willis Eschenbach has a post on something like this at CA today. He looks at balloon and model data as well as satellite.

## Jeff Id said

#3

Regarding 1 -The amplification graph becomes a transform between one set and another. It simply forces UAH to match whatever graph it is compared against. So unless I’m missing something I don’t see the advantage.

Regarding 2 – I would expect altering the linear slope difference to affect only the y axis.

DeWitt Payne,

I’ve seen it. He seems to have done a very thorough job but I haven’t got my head around the detail of his trend matrix yet and I have to work so no time. I asked him a question though which might clarify it for me.

## Layman Lurker said

Jeff, thinking out loud again. It seems to me that you have shown, based on the two graphs above, that there would have to be at least two mechanisms to account for the shape of the first graph. If one mechanism is represented by your ARMA graph is it possible (or even proper) now to derive what the negative amplification mechanism(s) looks like?

## Jeff Id said

#6 Interesting concept, let me think about it.

## John F. Pittman said

Jeff, doesn’t Willis’s trend also agree with yours in that the slope changes rapidily decrease at about 48 months on his? Eyeballing looks like from about 45 to 52 months depending on data source. Interesting that your’s and Willis’s look like a pulse phenomena.

## Jeff Id said

I think Willis’s analysis is pretty close. It just doesn’t make sense to me that the longer term trends be included in the amplification graph. I don’t think I convinced him though either way we did get similar results.

In my graph above, the trend spikes and drops back to about 0.7 at what looks to me like the maximum rate for my filter at 10 years (how fast can a ten year trend change?). The fact that it drops back to 0.7 which is the difference in long term trend from UAH/GISS, makes me think that there could be a sharp climate feedback after 5-7 years. Of course it could be some other data problem.

I see the tail end of Willis’s graph as more of an artifact than an amplification. I felt the the same about my own first post on this topic.