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.