The last two posts are a perfect example of the scientific process at work.
My efforts to determine the confidence in our data has many potential flaws and biases…but I had to start somewhere! Much of science is trial and error, then repeat until you find an approach that works!
After last week’s post, Victoria Coles and I had an extremely productive and insightful “brainstorming” on how to combat this issue.
As a recap, I have been analyzing the historical mean and variability trends of the 26 extreme climate indices. I am also in the process of assigning confidence to these trends. This confidence is based on the premise: how many of our 20 data sets display a statistically significant trend for each index?
My initial approach was to apply a 21-year rolling function (mean or coefficient of variation) and to use a regression analysis to determine if the trend was linear. I displayed this approach last week (and give an example in Figure 1).
The Major Problem
Each time series we are investigating has a different length. More specifically, all of these weather data sets start at a different time ranging from 1892 to 1955. Fitting a line through data sets of various lengths can pose some huge problems, especially when we are trying to compare trend directionality (positive or negative slope) and significance.
Here is what I mean: In Figure 1, we show the 21-year rolling mean of the growing season length. The HadEx2 is from 1901-2010 (110 years) while the GHCNdex is shorter, starting in 1951. It is easy to see by the best fit lines how greatly the slope changes because of the length. Thus, if we are analyzing 50 year data sets with 100 year data sets, we may be inaccurately “seeing” huge changes in the shorter time series.
The New Approach
Obviously, we need to account for the start time differences in order to assess if a trend is truly significant. The first, and now seemingly most obvious solution, is to plot the 21-year rolling mean for all 20 time series on the same plot. It may seem busy, or even overwhelming, but this allows a viewer to see the trends and lengths of each data set all together (Figure 3).
Let me walk you through this Figure 3, which shows the Growing Season Length. In black and gray are the two gridded data sets, HadEX2 and GHCNdex, respectively. Next we have the 18 individual weather stations (all situated around the Chesapeake Bay and NERRS sites). We grouped these weather stations as North (red) and South (blue) where the 38.3° latitudinal line separates north and south.
From this plot, we can visually analyze a few important details! First, we can see that most of our data sets have a positive trend, suggesting that the growing season length is increasing at many of our sites. Secondly, we can also see that the gridded products display lower trends, thus are a very conservative measure for this particulate index. (The gridded data sets are area weighted averages, thus it makes sense that they could have a “dampened” signal.). Lastly, we can also see the latitudinal difference in our data. The southern sites have a longer growing season, which makes perfect sense!
The New Confidence Analysis
Now how do we determine if the pretty lines in Figure 3 mean anything? As already mentioned, just determining if the linear regression is significant will be biased to the start date. So, we can use a statistical test called the difference of the means, more commonly known as the T-test.
Here is what I did: I found the mean and variance from 1981-2010 and used a T-test to see if that climate normal was statistically different than the mean and variance from 1951-1980. If significant, then we can say that the most recent 30 years of the growing season length was different than the previous 30 years. This now removes the bias of different lengths.
(For those of you very interest in the tiny details, I used a Student’s T-test if the variance between the two time periods was not different and a Welch T-test if the variance was different. I also repeated this test for the time periods 1951-1970 and 1971-2000.)
So now we have a revised table of our confidence in our trends!