Actuaries Climate Index

By Caterina Lindman, FCIA

The Actuaries Climate IndexTM (ACI) is an objective, quarterly, online measure of changes in extreme weather frequency and sea level. The ACI is based on quarterly seasonal data in six different index components from 1961 to winter 2016. Higher index values point to an increase in the probability of extreme climate events by comparison with average frequencies during the reference period 1961 to 1990.

The ACI was developed through the partnership of the American Academy of Actuaries, the Canadian Institute of Actuaries, the Casualty Actuarial Society (CAS), and the Society of Actuaries. The Climate Change Committee appointed by these organizations worked with climate scientists from Solterra Solutions to develop the index. The index measures climate extremes in Canada and the continental United States. The ACI will serve to help educate the public about the increased frequency of climate extremes in recent decades. It will also highlight the actuarial profession.

The index contains a component for high temperatures, low temperatures, high winds, precipitation, drought, and sea level. The index, with the exception of the sea level component, measures extremes rather than averages because the increase in extremes is more relevant to climate risk. Each component is a measurement of the value today compared to the reference period of 1961 to 1990. A 30-year reference period is common in measuring climate, as it is long enough to exclude short-term trends. The difference between the current value and the average for the reference period is then divided by the standard deviation of that quantity during the reference period. This can be expressed in the form of

ACI Component = (x - µ)/σref

This creates a dimensionless quantity referred to as a standardized anomaly. The ACI is the average of the standardized anomalies of the six components.

The sea level component measures monthly average sea levels at 76 tidal stations across Canada and the United States. Sea level is measured relative to the land, and therefore, it is possible that the data from some tidal stations show an increase in sea level due to thermal expansions of the oceans as well as from the melting of land-based ice sheets, while some show a decrease in sea level because the land movements offset any increases in the volume of the ocean. The tidal stations in Alaska show a decrease in sea level due to rising land at those locations.

The remaining components are based on grid-level data, where each grid cell is 2.5 degrees longitude by 2.5 degrees latitude across the land portion of Canada and the continental United States. A grid is 275 km by 275 km at the equator, but the width of the grid cell gets smaller as one moves away from the equator, due to the curvature of the Earth’s surface.

Canada and the United States are divided into 12 regions, and the ACI is calculated for each of those 12 regions, as well as the larger regions of 1) Canada, 2) the contiguous United States, and 3) all 12 regions (i.e., the whole of Canada, Alaska, and the contiguous United States). The 12 smaller regions are shown here:

The high temperature component is based on the 90th percentile temperature from the reference period for each calendar day. Note that at a particular grid cell, one would have 30 values from the reference period for each day of the year. Thirty observations are not enough to get a robust 90th percentile, so a five-day window is used, with a total of 150 observations to calculate the 90th percentile. For example, to calculate the 90th percentile temperature threshold for November 3, the temperatures from November 1, 2, 3, 4, and 5 are used. Once the threshold temperature is calculated for each calendar day, we calculate the frequency of high-temperature days for each month and season in the current period. For example, we may find that the frequency of high temperatures has risen to 30% in the current period from 10% in the reference period. The ACI component for temperature is = (x - µ)/σref, where x is the frequency of high temperatures in the current period, and µ is the frequency of high temperatures in the reference period, and σref is the standard deviation of the frequency of high temperatures in the reference period. If the value of σref in our example was 16%, then the ACI component would be (30% - 10%)/16% = 1.25, which means that the value can be thought of as 1.25 standard deviations from average.

The cool temperatures component is based on the 10th percentile temperature. The increased frequency of high temperatures and the decreased frequency of cool temperatures is an indication that the probability distribution function of temperatures has shifted to the right. For that reason, the decrease in cool temperature extremes is added to the index.

The precipitation component is based on monthly maximum precipitation values over a consecutive five-day period.

The drought component is based on the number of consecutive dry days (defined as less than one mm of precipitation) for each calendar year.

The wind component is based on the frequency of high winds. The threshold value is defined as the mean plus 1.28 standard deviations from the reference period, and captures about 13% of the highest wind speeds from the reference period.

Results: The following are two graphs showing three of the components in each graph, as well as the overall ACI value. These values show the five-year moving average, in order to better discern the emerging trend from the values. The clearest trends are seen in the sea level, high temperatures (T90), and less frequent cool temperatures (-T10). The wind power, precipitation, and drought components are more erratic.



Caterina Lindman, FCIA, is a member of the CIA’s Climate Change and Sustainability Committee and chairs the joint Climate Index Working Group. This article was written for the International Association of Consulting Actuaries, and is used with permission.

Canadian Institute of Actuaries/Institut canadien des actuaires