Assigning Confidence

It’s no secret, climate change research is a hot topic.

Figure 1: Annual mean increase of the maximum temperature in Maryland and Virginia.

Figure 1: Annual mean increase of the maximum temperature in Maryland and Virginia.

As we know, climate change does not just mean “warming”. While global, and Chesapeake Bay, temperatures have  increased over the past century (Figure 1), there are other changes we need to understand in order to plan for the future.

For example, climate change in Chesapeake Bay has manifested as an extension of the growing season, an increase is precipitation intensity, and a decrease in frost events.

These changes are associated with the potential for earlier tree budding, more runoff, and overwintering pests. Each of these potential situations can have cascading effects on Chesapeake Bay ecosystems and communities!

But when you talk about climate change research, there is one question you will certainly get asked: How confident are you?

How we determine confidence

We assign different levels of confidence to our 26 extreme climate indices using statistics. For each and every extreme climate index, we conducted three measures of statistical confidence.

1) Simple Linear Regression

Figure 2: A n example of a line with a strong linear relationship (blue) and a set of data with no relationship (red).

Figure 2: An example of a data set with a strong linear relationship (blue) and a data set with no relationship (red).

A simple linear regression measures the relationship between a dependent variable (our climate index) and an independent variable (year). The correlation coefficient (R) measures the strength of that relationship.

With our time series, we can apply a hypothesis test using a p-value. A p-value tests the validity of your null hypothesis (that there is no linear relationship). If that p-value is <0.05, you can reject the null hypothesis…in other words, there is a significant relationship between the climate index and date.

2) Smoothed Simple Linear Regression

This statistical test is the same as the simple linear regression, but we first smoothed the time series using a 21-year moving mean. Smoothing reduces the magnitude of the year-to-year variability, allowing for a trend to be more pronounced (if it is there!).

A 21-year moving mean, for example, calculates the mean from 1900 to 1921, then the mean from 1901 to 1922….and so on. If the p-value is <0.05, we denote climate index as having a significant trend.

images3) Mann-Kendall Test

Mann-Kendall is a non-parametric test for the significant of a monotonic trend (single direction). This test determines the tau which measures the strength between two variables, similar to the correlation coefficient (R). In other words, how straight is the line and what is its direction (increase or decrease)?

Again, if the p-value is <0.05, we can say that the index has a significant trend.

Summarizing the Statistics with Pizzazz

Table 1: Definitions of confidence.

Table 1: Definitions of confidence.

Now that the statistical tests are done, how do we convey confidence in each extreme climate time series?

We created 5 difference “levels” of confidence based on the agreement of the three statistical tests completed above (Table 1). For example, if all three tests had p-values <0.05, that index would have a strong confidence . Oppositely, if none of the tests had significant trends, we could say we are confidence that there is no trend.

Table 2: Our assigned confidence in the annual-based indices.

Table 2: Our assigned confidence in the annual-based indices.

There were a few occasions when 2 out of the 3 tests were significant (high confidence) or only 1 of the test were significant (low confidence). In only three cases, the direction of the trends differed between the Mann-Kendall and linear regression (unclear confidence). These head-scratching results occurred in the seasonal Diurnal Temperature Range index, which had a unique pattern.

Now, we can assign confidence in our extreme climate analysis! For example, we have a strong confidence that Frost Days have decreased, high confidence that the amount of days with >20mm of precipitation has increased in North Chesapeake, and we are confidence that there has been no change in consecutive dry days in South Chesapeake.

So now when we are asked: how confident are you?, we can answer that question with, well, confidence!

Kari Pohl

About Kari Pohl

I am a post-doctoral researcher at NOAA and the University of Maryland (Center for Environmental Science at Horn Point Laboratory). My work investigates how climate variability and extremes affect the diverse ecosystems in Chesapeake Bay. I received a Ph.D. in oceanography from the University of Rhode Island (2014) and received a B.S. in Environmental Science and a B.A. in Chemistry from Roger Williams University (2009). When I am not busy being a scientist, my hobbies include running, watching (and often yelling at) the Boston Bruins, and taking photos of my cat.
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