Statistical Significance in Satellite Data

If you’ve been following along here you probably suspected the difference between UAH and RSS are substantial enough to reach 95% significance. In this short post, you can see you were right. Significance is a measure of likelihood that the short term noise is creating the slope we see. Now since we’re looking at a difference between two series measuring the same thing, a simple reasonable method is to take the difference between the two series and look at the residuals for significance.

Global RSS and UAH temperature anomalies look like this.

By taking the difference between the two anomalies, the graph below is calculated. You can see that if 95 significance in trend is 0.0104 the trend of 0.027 is almost 3 times outside of what is created by noise in the data. Much of this was created by a well known and still contested step at 1992 which was a particularly difficult satellite transition point.

Now recently UAH and RSS started using different datasets for the first time. RSS continued using the old NOAA style satellites which decay in orbit over time while UAH switched to the AQUA station keeping satellite. The obital decay of NOAA-15 causes the instruments to measure different parts of earth at different times of day, gradually shifting over years. Imagine the difficulty in correcting temperature for all locations on earth based on time of day. You would need to quantify how the land, mountains, oceans, forests and even ice react over a day of heating. Each day being different over a year. RSS solved the problem with computer modeling of each grid square while UAH did it by measurement employing other satellites measuring at different times in the same day. I vastly prefer measurement to modeling in this case but that doesn’t mean RSS is wrong, just that there’s another black box step which is exceptionally difficult to verify.

The new AQUA satellite used in UAH has a station keeping thruster which keeps the measurement time of each gridcell constant for years at a time. The thing I think some miss about this is that the huge massive corrections which must be implemented over a day are suddenly the same correction value from day to day – no change. Therefore errors in corrections no longer create artificial trends. We’ve got our first high accuracy global trend measurement –ever. The record only extends from June 2002 though and RSS is already experiencing a large divergence over that time.

The last figure is UAH minus RSS for June 2002 until present. The data was re-anomalized after subtracting but the trend difference between the correct trend UAH and the old style calculation RSS is just past 95% significance.

RSS is showing too low of a trend over this timeframe. Dr. Christy mentioned that it’s a result of overcorrection for diurnal shift of the old style satellites orbit. Either way the UAH with the better quality trend since 2002 is below.

UAH negative trend nearly reached 95% significance. So of course we have to look at RSS.

RSS is cooling outside of 95% significance for the past 8ish years. That’s the first statistically significant cooling I’ve seen so far. A short check of RSS on an annual basis shows that in 1978 over an 8 year window the trend is significantly negative. This means that by RSS there is a 95% certainty that cooling is occurring outside of weather variation since 2002. Not that it’s that big of a big deal, but cooling is cooling right?

My opinion is that UAH is the superior metric still, remember though I’m just an aeronautical engineer and not an expert. As a side note I’ve got a beauty of a quote in a private email from a specialist saying that nobody outside of Alabama prefers UAH. I wonder if the fickle tides of science will be turning.

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Addendum: Dr. Steig left this quote on another blog. It was ironically sent to me by email just today (what are the odds). I do actually agree with his comment but the wording is funny. Rather than saying ‘warming (has/has not) stopped’ we can say cooling has occurred, however it’s not outside the statistical limits of significance of the higher frequency weather noise.

21. At 9:42pm on 09 Nov 2009, Eric Steig wrote:Paul,

It is well known this “warming has stopped” idea is a complete red herring, as we have patiently explained here:

http://www.realclimate.org/index.php/archives/2008/11/mind-the-gap

and here:

http://www.realclimate.org/index.php/archives/2009/10/a-warming-pause

Your article merely promotes further confusion and misinformation by adding the mark of credibility that “BBC meterologist” provides. The preceding comment by “timjenvey” is a typical example characteristic of the misuse of the data that is the result. (Why does he choose October only, for example?)

In the case of RSS, it appears that the trend has become at least temporarily significant.
The code for the post is here. In R, functions and libraries stay constant so you don’t know if everything is turnkey. Let me know if you have any problems with it.

ssq=function(x) {sum(x^2)}

plt.avg=function(dat, st=1957, en=c(2009, 12), y.pos=NA, x.pos=NA, main.t=”Untitled”) {

### Get trend
fm=lm(window(dat, st, en)~I(time(window(dat, st, en))))

### Initialize variables
N=length(window(dat, st, en))
I=seq(1:N)/frequency(dat)
rmI=ssq(I-mean(I))

### Calculate sum of squared errors
SSE=ssq(fm[[2]])/(N-2)

### Calculate OLS standard errors
seOLS=sqrt(SSE/rmI)*10

### Calculate two-tailed 95% CI
ci95=seOLS*1.964

### Get lag-1 ACF
resids=residuals(lm(window(dat, st, en)~seq(1:N)))
r1=acf(resids, lag.max=1, plot=FALSE)$acf[[2]]

### Calculate CIs with Quenouille (Santer) adjustment for autocorrelation
Q=(1-r1)/(1+r1)
ciQ=ci95/sqrt(Q)

### Plot data
plot(window(dat, st, en), main=main.t, ylab=”Anomaly (Deg C)”)

### Add trendline and x-axis
abline(h=0, col=2); abline(fm, col=4, lwd=2)

### Annotate text
text(x=ifelse(is.na(x.pos), st, x.pos), y=ifelse(is.na(y.pos), max(dat,na.rm=TRUE)-0.2*max(dat,na.rm=TRUE), y.pos), paste(“Slope: “, round(fm$coef[2]*10, 4), “+/-“, round(ciQ, 4), “Deg C/Decade\n(corrected for AR(1) serial correlation)\nLag-1 value:”, round(r1, 3)), cex=.8, col=4, pos=4)
}

###################################RSS
loc=”ftp://ftp.ssmi.com/msu/monthly_time_series/rss_monthly_msu_amsu_channel_tlt_anomalies_land_and_ocean_v03_2.txt”
wd=c(10,9,9,9,9,9,9,9)
RSSa=read.fwf(loc,skip=3,widths=wd)
RSS=ts(as.numeric(as.vector(unlist(RSSa[,2]))),start=1979,deltat=1/12)

###################################UAH
loc=”http://vortex.nsstc.uah.edu/public/msu/t2lt/tltglhmam_5.2″
wd=c(13,8,8,8,8)
UAHa=read.fwf(loc,skip=5,widths=wd)

UAHa=UAHa[-(372:372),]
UAH=ts(as.numeric(as.vector(unlist(UAHa[,2]))),start=c(1978,12),deltat=1/12)

plt.avg(UAH,st=1978,main.t=”UAH Temperature Anomaly”)
#savePlot(paste(“C:/agw/UAH full.jpg”),type=”jpg”)

plt.avg(RSS,st=1978,main.t=”RSS Temperature Anomaly”)
#savePlot(paste(“C:/agw/RSS full.jpg”),type=”jpg”)

tw=calc.anom(window((UAH-RSS),start=c(1978,6)))
plt.avg(tw,st=1978,main.t=”UAH-RSS Since 2002″)
#savePlot(paste(“C:/agw/UAH-RSS full.jpg”),type=”jpg”)

tw=calc.anom(window((UAH-RSS),start=c(2002,6)))
plt.avg(tw,st=2002,main.t=”UAH-RSS Since June 2002″)
#savePlot(paste(“C:/agw/UAH-RSS after 2002.jpg”),type=”jpg”)

tw=calc.anom(window((UAH),start=c(2002,6)))
plt.avg(tw,st=c(2002,6),main.t=”UAH Since June 2002″)
#savePlot(paste(“C:/agw/UAH after 2002.jpg”),type=”jpg”)

tw=calc.anom(window((RSS),start=c(2002,6)))
plt.avg(tw,st=c(2002,6),main.t=”RSS Since June 2002″)
#savePlot(paste(“C:/agw/RSS after 2002.jpg”),type=”jpg”)