About a week ago, I looked at the apparent interannual divergence in satellite temperature records. Lucia also blogged about why the UAH vs RSS temperature differences might have energy at 1 year. There was also a good discussion in the blog comments about energy being observed at 1 year when the current UAH data is subtracted from the UAH data from late last year.

Last time when I looked at the difference between the difference between the anomalies, there was a jump that occured in 1992. This was attributed by many to the differences in splicing the different satelittes together between the two groups. After the 1992 jump, there was a very obvious ~1 year periodic cycle. In the comments at Lucia’s blog, Spence_UK noted that the period was not exactly 1 year, but slightly less. Robb commented that the periodicity may be from the diurnal and hot target temperature corrections.

Limited Time Period Trends

To better understand the ~1 year periodicity, I decided to use find the linear trends over very short time ranges to act as a sort of filter to the data. 9-month trends were calculated for every month of the data record, except for the 4 months at the ends of the records. Below they are plotted versus the mean year of the trend.

(Click for much larger version)

As when comparing the 2 temperature time series qualitiatively, the 2 temperature trend time series are very similar. There is a large peak in the temperature trend to over 1C per year during the 1998 El Nino. But there are differences as well. The largest negative trend for RSS occured immediately after the 1998 El Nino, as global temperatures were returning to normal. There was also a large negative trend in UAH, but not the largest, which occured in 2004.

Trends in Frequency Space

Even without looking at the bottom panel (the difference plot), there is an apparent 1-year periodicity in the UAH data (top panel). This is most evident after 2002. When each of the above time series is decomposed using a Fourier transform the difference in periodicities stands out.

(Click for much larger version)

The vertical red line represents periods of 1 year. The UAH temperature trend time series has power of ~1E-3 C^2 at 1 year, while RSS only has power ~1E-4 C^2. This factor of 10 difference is the largest difference between the UAH and RSS data, as is clearly seen in the bottom panel. The peak power in the difference time serier is at 1 year, with a power ~1E-3 C^2, which is clearly due to the UAH data. The power quickly falls off on both sides to a factor of 10 less than the peak power.

It should be noted that just because the peak of the difference series is due to UAH, that does not necessarily mean that the UAH data is flawed. Other temperature trend time series (e.g. GISS, Hadley) show similar power at 1 year as UAH. RSS has less power at 1 year than the other temperature trends. (Not shown.)

Wavelet Analysis of Difference Series

When looking at the bottom panel in the first figure, there is an apparent decrease in the 1-year periodicity from 1992-1995. A cool tool to quantify this is the use of wavelet analysis. This technique basically finds the power at all periods for each time step. So when the temperature trend difference time series is fed through the wavelet black box, it spits out the following.

(Click for larger version)

It’s clear that most of the power of the difference time series is at 1 year. But during the 1992-1995 time period, there is no significant power at any period. And for years before 1992, there is significant power at 2-3 year periods. I won’t speculate about the 2-3 year periods, but I will discuss the years after 1995 time.

In the comments at Lucia’s blog, she notes that it appeared that the 1-year cycle in the temperature difference time series was increasing. I too noted that it qualitiatively appeared that way. This wavelet analysis of the short term temperature trends shows that the 1-year periodicity has indeed been increasing from 1995 through the present. The darker shades of red indicate that there is more power in that particular period. For instance, 2005 has a very dark red for 1-year periods indicating that almost all the power is located there.

Conclusions

From the above discussion, it is easy to see that the UAH and RSS temperature trend time series have similarities and differences. When the difference time series was looked at in frequency space, the difference in the 1-year periods stands out. The UAH data have much more power at 1 year than RSS. The Fourier analysis of the difference time series showed that most of the difference between the two occurs at 1 year. This was confirmed by the wavelet analysis.

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