Global Temperature – A Comparative Analysis, GISS versus NCDC
Posted by The Diatribe Guy on June 2, 2008
Well, now that just rolls right off the tongue, doesn’t it? Welcome to statistical geekdom.
Due to my interest in looking at temperature trends, and now that I have models put together both for GISS and NCDC data, I decided to take a look at how well they correspopnd to one another, and to see if that correlation has changed over time, and in what direction. Ah… if only I put this much effort into things that could earn me money…
So, let’s explain the various things I took a look at:
(1) The Correlation coefficient between GISS and NCDC temperature anomalies for all periods 1880 – end of period. A correlation coefficient of 1.00 means that for every 1 point move in the anomaly for GISS, there is a 1 point move in the same direction on NCDC. This is perfect correlation. A coefficient of -1.00 means that for every 1 point move in the GISS anomaly, there is a 1 point move in the opposite direction on NCDC. This is referred to as perfect negative correlation. So, the higher the positive number, the more of a tendency that both measures will move in the same direction at the same time. We will see that, overall, the two sets of data exhibit very high correlation, that this corellation has improved over time, that it fluctuates, but has fluctuated less in recent decades than earlier on.
This first chart shows how the correlation of the entire data set from January 1880 to each point has evolved. It did not take long for correlation between the two sets to become evident. By 1886, it is already in the 75% range. This has continued to increase over the course of the entire data set to the overall value of 0.9609. So, the GISS and NCDC are indeed highly correlated, and this means that, on average, the values are expected to go in the same direction at nearly the same magnitude.
Next, we take a look at rolling five year correlation values between the two sets of data. There are some interesting results here. First, we see the much lower correlation in the late 1800s. This tells us that the results are much more uncertain between the two sets of data. It does not indicate which set is more accurate without further study. By the 1900s, the correlation was above 0.800 and fluctated to levels above 0.900, until a period during the 1940s where we see a few years of relatively poor correlation. This again improved to varying levels, but has really steadied itself out starting around 1970. Since that time, there has been less variation in the correlation measure and it has been consistently above 0.800. The two data sets are much more in concert on a consistent basis than before that time.
Conclusion: GISS and NCDC are well correlated in recent decades. Their system of measurement is similar and this is to be expected. Of more concern the correlation during the 1940s and the correlation prior to 1900. Further study is required to determine which data set better reflects actual temperature trends during these periods.
2) I evaluated the differences between the GISS and the NCDC anomalies. NCDC was subtracted from GISS, so a negative difference represents a higher NCDC temperature reading than GISS and vice-versa. The raw chart of differences follows:
Conclusions: Paying particular attention to the periods of low correlation, GISS recorded much lower anomalies prior to 1900 than NCDC did. The effect of this is to increase the slope of the overall period trend line from the NCDC data, when a trend is fitted to the entire period. You can see the difference in that trend line in previous posts. However, the poor correlation in the 1940s appears to be driven by higher GISS anomalies than NCDC. The largest positive difference occurs during that period, with three other significant differences within close proximity in the same period.
3) I decided to round the differences to a 0.01 Celsius anomaly range and plot the distribution of differences, GISS – NCDC:
The chart above does seem to approximate a normal curve. Assuming it is normally distributed, the mean is a difference of -2.89 and the standard deviation is 7.34 (we’ll look at these measures more in a bit). Another way to take a look at some of the outliers is to understand that 99% of the values should be within 2.33 standard deviations from the mean. This is the range -19.99 to 14.21. There have been a few outliers in recent years. We can see how far outside the bound the 1940s were. But the most problematic area of the chart is the pre-1900 period. There are far too many outliers for this to properly fit the normal curve. This has to be attributed to insufficient coverage between the two measures, or misestimation in one measure versus another.
4) The mean differential was observed to see if it has changed over time. This was evaluated in total from 1880 – end point and in 5-year rolling periods.
The first chart is the cumulative observed mean:
This chart shows the early means being much larger than the overall observed sample mean of -2.89. We see how the rolling 60-month means changed over time:
Conclusion: The early periods drive much of the negative difference for GISS minus NCDC. However, there is a tendency for GISS to hover below the NCDC anomaly, though the most recent 60-month average is near zero (0.04). Based on simple observation, the -2.89 difference may be a bit too large in magnitude, but it is reasonable to select an average difference between -2.00 and -1.50.
5) Standard Deviation is an expression for the dispersion of values about the mean. The higher the standard deviation, the more inconsistent the value of differences is. This was looked at, again, on the cumulative Standard Deviation as it grew from 1880 and out, and also in rolling 60-month periods.
The cumulative chart is here:
It took a while for the Standard Deviation to settle into a consistent level. This result is similar to the look at the correlation measure. In fact, you can see the blip back up in the 1940s after a long, steep downward trend.
Looking at the rolling Standard Deviation:
This graph confirms the uncertainty of the pre-1900 data and the data in the 1940s. However, it is interesting to note that, despite some relatively high and stable correlation in the last 50 years, the Standard Deviation still fluctuates. Now, scale is important here, and all in all the measure is fairly stable. But the Standard Deviation has been a little higher during the period from the 1970s to 2000, and since then has been a little tighter.
It is difficult to determine which measure is less reliable in the periods of large differences. Overall, the two measures give similar answers, so perhaps it is not of vital importance in our understanding of the larger trends. But it is worth questioning. A good way to look at this is to test each set against other measures. I’ll plan on getting to that some day. One step at a time, my friends. After all, I have a day job…