## Ground vs Sat Covariance Plot

Posted by Jeff Id on January 24, 2009

From my last post on temperature trend, I showed that there is a short term signal in the satellite data which has a higher rate of change than the ground data while the ground data 30 year trend is higher than the satellite data. Both are substantially different in trend yet models predict the UAH satellite trend should be 1.2 time GISS. Dr. Christy hypothesized that long term temperature trend has a negative feedback mechanism not accounted for in the models. If that were the case we should be able to look at various frequencies and their relative magnitude to see that UAH is higher than GISS at 2 years and as we approach the longer annual frequencies, GISS would trend higher than UAH.

My last post on this was

### Bifurcated Temperature Trend

The crux of the matter is this.

1 – short term 5 yr trends on sats are greater than GISS

2 – longer term trends 30 year from sats are less than GISS

3 – models predict both trends MUST be greater than GISS

4 – All data sets have problems which have supposedly been corrected for. **Which is correct, uah, giss or model. Somebody has a serious problem.**

Dr Christy is looking to the models.

For this graph I used detrended data. It is the ratio between UAH and GISS with various degrees of filtering.

The graph is GISS/UAH covariance at various filter levels. It has meaning in that if the data is filtered by a gaussian function 3 years in width the data achieves a maximum variance of UAH ~ 1.15 to Giss ~ 1. After that the data trends back downward. This is expected if the models are in error and there is a missing longer term feedback in the model projections. I can extend the graph but it has no meaning since I detrended the 30 year data so it is forced to drop to a level of 1:1.

What’s interesting is first that high frequency data near 0 tends towards the zero level indicating a random process which in this case is GISS monthly noise as the Sat data is more smoothed. The second thing I notice is that the data peaks at 3 years and trends back downward to the 30 year trend of 1.

I have some FFT plots as well but they will need to wait until tomorrow.

## Chris H said

I may be out of my depth (I guessed at the technical meaning of “covariance”), but do not see why a model problem is needed to explain the above graph of measurement data. Surely you would EXPECT that shape given the following conditions:

1. Frequencies are shared by both GISS & UAH, except that GISS’s absolute values are about 1.2 times higher than UAH for some unknown reason (but nothing to do with models). With this alone we would expect a horizontal line at a value of 1.2 .

2. Additional GISS-only noise at frequencies (with a period of) up to approximately 1.5 years. (Of course, rather than just stop suddenly at some point, the noise is likely to reduce gradually, and perhaps not reach a minimum until perhaps 3 years). i.e. The covariance tends to zero for frequencies near zero, as you stated yourself.

3. Both data sets have “detrended the 30 year data so it is forced to drop to a level of 1:1″. Presumably this means that as frequencies come closer to 30 years they both come closer to having zero amplitude, and thus covariance drops to 1.0 . This then gives the gradual down slope after 3 years.

So guess I’m just wondering if this is another “hockey stick algorithm” that produces one shape for any reasonably realistic range of input data (e.g. red noise for condition 1, additional GISS-only white noise for condition 2, and detrended data for condition 3).

## Layman Lurker said

“Which is correct, uah, giss or model. Somebody has a serious problem.”

The existence of a problem in one of the above does not exlude possible problems in each of the others.

## Jeff Id said

Chris, you are basically right. I plotted the graph here because I think there was some potential for a sharper drop off to 1:1. What this shows is what I have by calculation of the variance at individual points. I did make some comments about it, so I wanted to show people that it was true.

## Jeff Id said

#2, You bet. It could be all of the above, which is my belief. One or two of the three may be close though.