## Tropospheric Temperature Trend Amplification

Posted by Jeff Id on January 30, 2009

After some thought, I’ve decided to break this post into several parts. It’s just too big to do all at once and in blog world, the worst thing for your blog is to wait a week between posts. First I will do the surface vs sat data, then I will do the climate model data. It should provide some interesting comparisons between actual measurements and climate models.

I’ve been working on Lower troposphere temperature trend amplification as compared to ground temperatures. Models predict an even amplification factor at various timescales of about 1.3 times in the tropics and 1.2 times globally. Here’s a quote from Dr John Christy which makes this the third time I’ve used it but I think it sets the meaning behind some of the graphs.

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.

So you can see how climatology is thinking. Well I got interested in this because there is a visibly higher signal in the lower troposphere RSS and UAH on the short term than ground data, yet the signal has a lower amplitude for long term data. The difference extends to the the mid troposphere measurements as well. Willis Eschenbach did an interesting article which was carried on Climate Audit here.

He developed a unique method for determination of the amplification factor which as I understand it, doesn’t separate the long term trend covariance from the short term trend covariance. The result is a unique looking plot, which I present here because this post uses the same data and there is a lot to be learned on that thread.

Since, I was looking for feedback mechanisms as described by Dr. Christy, it was important for me to separate the signal at each year as much as possible. I used a unique method to sort the amplification factor by signal length. The steps are as follows.

- Filter the satellite time series using a low pass filter at time N+ offset time.

- Subtract low pass data from original series to create a high pass series.

- Filter the high pass data at N

- save point SN

- Perform the same for ground data with the same values

- save point GN

- When the series are built do a scatter plot with ground data GN values on the X axis and satellite SN data on the Y.

- Take the slope of the scatter plot – This is the amplification at time N.

- Repeat the process for all monthly times in the 30 year satellite record.

I ran this process using an offset time of 1 year and the Climate Audit gaussian filter function which allows enough signal to create a reasonable graph. In using this filter method there is some rounding of the final amplification result due to the bleed through of frequencies below the cutoff. Still the graph is reasonably accurate for visualization of the amplification at each time value. Read it like this, at 2.5 years there is a 2.4 times amplification of the satellite 2.5 year trend in comparison to ground 2.5 year trends.

Wow, a tropical magnification of 2.5 times at 3 years – does this make any sense?

You can see the three year wide variances are much higher in the UAH data than Hadcrut surface temperatures. After looking at this plot, I don’t think 2.5 times is unreasonable. Below is the same graph as the second one with only the global data included so the scale is more visible.

The sharp cutoff in tropical trends after about 6 years seems like pretty strong evidence of a feedback mechanism. If the models don’t predict this cutoff in my later post, Dr. Christy is right that there is a serious missing feedback mechanism which this plot shows has about 7 years length.

## DeWitt Payne said

You should probably post your R script or at least a link to it. I’m not clear on the second filter step. You create a high pass series and then low pass filter it again to create a narrow band pass filter? Surely there are digital filters, probably available as plugins to R, that can do that in one step.

## Layman Lurker said

You have put in a lot of work on this Jeff. Thanks for all the effort.

There has been a lot of talk about models vs. surface data vs. sat data. However by comparing the mid and lower troposphere layers, we see the pattern of negative amplification persists between all layers of the atmosphere – the exact opposite of what models predict. Either this is negative feedback coupled with negative amplification outside of the models, or, there is an issue with the satellite data.

The issue of stratospheric contamination came up on the CA thread. Not sure how the sat metrics take this into account at different altitudes but in order for that to fit your graphs there would have to be increasing contamination as measurement altitude increases. Intuitively, this seems plausible as the measurement swath would include larger contributions from the stratosphere with increasing altitude. This stratospheric correction error would also have to be common with RSS and UAH as inverted amplification with altitude exists in both metrics. I’m not sure why there would be postive amplification on any time scale (let alone up to 10 or 12 years) if there was such contamination.

The other thing I find interesting are the time scales (common to both metrics) where there is some recovery in amplification. Roughly 10-12 years; 21-23 years; 26-27 years. The 10-12 year scale predominates outside of the tropics, while 21-23 and 26-27 are strongest within the tropics.

## WhyNot said

In the past I have contributed with only wise-cracks and weird analogies, however, this time I hope to add something a bit more constructive.

My light bulb went off while looking at graphs #2 and #4 especially #4 with the tropical amplification data removed. It reminded me of when my partner and I were trying to determine if an optical optimization routine was calculating the correct output function. We were able to determine it was, due to the simple fact that output waveforms are additive, much like adding two dissimilar sine waves together. The output is the sum of the underlying signals.

Now this is where I assumed the Global amplification is the sum of say, the Northern Hemisphere, the Lower Hemisphere and the Tropical amplification series. If one were to subtract the Tropical amplification from the Global amplification, could you not determine if there is a negative amplification factor for either one or two of the other underlying signals? Just by looking at the graphs, subtracting the two yields a negative amplification. However, without studying the data series, I am not sure if the Tropical amplification is partially weighted or scaled, obviously skewing my visual interpretation. It would be very interesting to separate each of the underlying amplification signals, if possible.

I am not an expert, and I have not studied the temp information, or types of temp information out there, so I apologize if I am completely of the mark here.

## Jeff Id said

I’ll clean up the code (it needs some comments and formatting) and post it tonight. I ran the same graphs with GISS last night and had different results.

## Jeff Alberts said

Temperature is misspelled in the title ;)

## Jeff Id said

DeWitt Payne,

I also tried several R filters, they seemed to work well until I got to longer filter windows (try to filter 30 year data with a 25 year filter). I’m not sure they handled the endpoints of the data cleanly. R also became unstable, like memory was being overwritten. I haven’t given up on it yet though and I have a couple of other ideas.

## Jeff Id said

#5 I don’t know what you mean?????

THX :)

## DeWitt Payne said

If R uses FFT to implement the filters then the number of points has to be a power of two, I think. Since there are less than 512 data points, that would make the lowest frequency 12/256 or 0.047/year (~21 years). The Nyquist criterion also limits the highest frequency to 6/year. Thinking ‘out loud’ as it were as I’m sure you know all that.

## Jeff Id said

DeWitt,

The filters I tried weren’t fft based. I was considering doing my own FFT filter.

## Layman Lurker said

Another observation, RSS TLT and TMT lines cross over abruptly once you hit the 16 year time scale – an artifact of the 1992 step?

## Jeff Id said

10,

I think you’re right. The two series lay almost on top of each other when the step is removed so looking at the curves in that way, the main difference should be the step.