## Thursday, December 11, 2014

### Intra-Annual Climate Variability

If you don't like the weather, just wait 15 minutes – unknown

What parts of the U.S. have the most temperature and precipitation variability? This question is actually not so difficult to answer. The National Climate Data Center (NCDC) publishes temperature and precipitation values for nearly 10,000 stations across the country. Figure 1 shows the location of those station.

Figure 1. Location of 9,708 stations that NCDC publishes daily normal temperatures and/or daily normal precipitation. 5,869 stations have temperature data and 8,533 stations have precipitation data.

Temperature variability

There are a myriad of methods for computing the variability of temperatures at a location. For temperatures, the NCDC does all of the heavy lifting for us. One of the temperature variables that they compute in addition to the daily normal temperature is a daily normal standard deviation. For the statistically uninitiated, standard deviation is a measure of dispersion from the mean (average). In theory, 68% of daily temperatures at a station will be within 1 standard deviation from the daily mean. For example, is a station's normal temperature on October 1st is 60°F and the daily standard deviation is 8°F on that date, we expect that the temperature on October 1st will fall between 52°F and 68°F on 68% of years. We also expect temperatures to fall within 2 standard deviations approximately 95% of the time. Therefore, mapping the average daily standard deviation (of all 365 days) for all stations is a direct measure of temperature variability. Figure 2 shows the average published NCDC standard deviation for 5,869 stations and Figure 3 shows only stations in Alaska.

Figure 2. Average daily standard deviation for 5,869 stations based on NCDC published values.

Figure 3. Average daily standard deviation forAlaska stations based on NCDC published values.

The largest values of temperature variability are in interior Alaska north of the Alaska Range. Umiat, Alaska, wind the variability contest. On average, Umiat has a daily temperature standard deviation of 12.2°F. In the Contiguous U.S., the largest values are in Montana and North Dakota. Powers Lake , North Dakota has that largest value in the Contiguous U.S. (10.8°F). Stations with the largest values are subject to the widest variations of temperature whereas stations with the lowest values have very constant temperatures. The 44 lowest variability stations are all in Hawaii. The Ohe'O 256 station in Hawaii has a standard deviation of 1.5°F. In the Contiguous U.S., the lowest values are right around San Franciso, California. Several station there have standard deviations under 3.5°F. In Alaska, Shemya has the lowest average annual standard deviation of 2.7°F.

Precipitation variability

Unlike temperature variability, precipitation variability is much more difficult to measure. Since precipitation does not fall on every day, the distribution of precipitation events has a skewed distribution. If a station averages 30" of precipitation a year that falls on 100 days a year, that works out to a daily average of  0.08" per day. What that also means is that on 265 days, when no precipitation fell, they are below normal in terms of precipitation. Probable 30 or 40 of the other days had under 0.08" so those days were below normal too. This is why the NCDC does not compute a precipitation daily standard deviation.

A much better method is to look at monthly precipitation values and see how much they change over the course of the year. In many cases there are substantial difference between wet and dry months. Some stations in California and Alaska receive 60% of their annual precipitation in a three-month window. On the flip-side, many stations in the Northeast and mid-Atlantic have precipitation evenly distributed across all months.

Figure 4 shows the month-to-month variability in precipitation values across the year for the entire U.S. and Figure 5 shows Alaska only.. To make this map we calculated the difference between the NCDC normal precipitation for each month and compared it to the value that would occur if each month received 1/12th of the annual precipitation. For example, image two stations that each average 24" of precipitation per year. One station averages 2" for each of the 12 months. The other station receives 80% of their annual precipitation between May and August. In this hypothetical, the first station has very low monthly precipitation variability while the second station has very large precipitation variability. This type of assessment is called a goodness-of-fit test. In this case we used the chi square goodness-of-fit-test. The values produced by this test are unitless and are evaluated against a table of significance values. To avoid confusion, the values are left off the map and substituted with "high" to "low" labels.

Figure 4. Intra-annual precipitation variability based on monthly totals of 8,533 stations. Stations with consistent precipitation values throughout the year are shown in green and stations with large month-to-month variation (e.g., distinct wet and dry seasons) are shown in red.

Figure 5. Intra-annual precipitation variability based on monthly totals of Alaska stations. Stations with consistent precipitation values throughout the year are shown in green and stations with large month-to-month variation (e.g., distinct wet and dry seasons) are shown in red.

As you can see, some areas have low month-to-month variability and others have quite a bit. The precipitation variability winners are mostly in California. Of the 188 stations with the most variability, 185 are in California. This is due to the strong seasonal concentration of precipitation during just a few winter months. The highest variability a non-California station is Kuparuk. The second highest non-California station is Northway. On the flip side, the stations with the least precipitation variability are in eastern New England and the North Carolina Piedmont. In Alaska Kodiak and Kitoi Bay have the lowest monthly precipitation variability.

I had assumed that all cold regions would have low winter precipitation values due to the moisture capacity of the air being greatly reduced. However, that is only the case in the Northern Great Plains and Alaska – not in New England. The other quite surprising finding is the low month-to-month variability in the Great Basin. Perhaps this is an artifact of multiple synoptic-scale parameters in other regions that all converge in this region.

Overall variability

So which regions have the overall highest variability? To combine the maps, we need to make a few assumptions and do a few calculations. First we need to arbitrarily declare that 50% of a station's variability is based on the precipitation variability and 50% is based on the temperature variability. On the calculation side of the equation, we have a problem combining datasets with different units – especially since the precipitation variability calculation is unitless! Therefore, we scaled all temperature variability values (standard deviations) to a maximum score of 50 and scaled all temperature variability values to a maximum score of 50. We then added the two together and rescaled the results on a scale from that maxes out at 100 (8 to 100). Figure 6 shows the final variability score for the entire U.S. and Figure 7 shows the score for Alaska only.

Figure 6. Precipitation-climatology combined variability score. Values are scaled up to 100.

Figure 7. Precipitation-climatology combined variability score for Alaska only. Values are scaled up to 100.

At the large scale, much of California, most of Alaska, and a large part of the northern Great Plains have high values of variability. The very highest values are in northern Alaska. The lowest values of climate variability are found across all of Hawaii, the western Aleutian Islands of Alaska, and the northern coast of the Gulf of Mexico.

The station with the highest annual climate variability is the U.S. is Kuparuk – their value is 100. They have the 34th largest temperature variability (of 5,869 stations) and the 57th largest precipitation variability (of 8,533 station). Their precipitation variability is the largest of any non-California station. In the Contiguous U.S., Sandberg, California, has the highest climate variability. They are located at 4,000' in the high desert east of Los Angeles. Sandberg has a pronounced winter precipitation concentration and due to their elevation, they have a surprisingly large annual temperature variation.

The station with the lowest value is Ohe'O 256 on the island of Maui. Their combined value was 8.3. All of Hawaii has uniform temperatures and this portion of Hawaii has very consistent precipitation. Outside of Hawaii and the Aleutian Islands in Alaska, the station with the lowest value is Dauphin Island, Alabama. Their combined value is 26.5.

Greatest and Least Variability by State

Earlier we noted which stations had the greatest and lowest values. However, if we limit the analysis to cities with at least 25,000 people, it becomes a little easier for people to relate to. Table 1 below shows the station with the largest variability score (max =100) for each state. Santa Clarita, California, has the largest value of any city in the nation. At the bottom of the list is Hilo, Hawaii. Their variability score is less than half that of the second lowest statewide value.

Table 1. Largest variability score for each state when looking at cities with at least 25,000 people.

Table 2. Smallest variability score for each state when looking at cities with at least 25,000 people.

That analysis was limited to cities with over 30,000 people. However, Alaska has only three such cities. Therefore, a proper analysis of Alaska needs to drop the threshold substantially. In this case, we decided on a value of 100. Table 3 shows the list of the 25 cities with the larges values (left side) and the 25 cities with the smallest values (right side).

Table 3. Largest (left) and smallest (right) variability scores for Alaska cities with at least 100 people. These are "cities" as defined by the U.S. Census Bureau. We make no distinction between a city, Census defined place (CDC), a village, or a Native village.

The maps in Figures 6 and 7 clearly show maximum variability along the North Slope and the eastern interior. Why is there so much variability in these locations? The answer is twofold. First, interior areas have an extreme continental climate. This results in very large temperature differences between summer and winter. Also, winter temperatures can vary by 100°F or more from one year to the next on the same calendar date. This is reflected in the very large temperature standard deviation values (see Figures 2 and 3). On the precipitation side of the equation, the extreme cold of winter dramatically reduces precipitation in areas with monthly temperatures below 0°F. Most of these areas receive 60% to 80% of their total annual precipitation in 3 to 4 months. The extreme concentration of precipitation in a small number of months gives those places large precipitation variability scores.

Conclusion

Some stations live up to the "just wait 15 minutes" saying and others don't. The variability in the northern Great Plains is not surprising but the variability in much of Alaska and especially California was somewhat unexpected. At the other end of the scale, the low measures of variability in the Great Basin was entirely unexpected. This region has nearly even precipitation throughout the entire year. The very low precipitation variability overwhelmed the modest temperature variability. Was there anything here that surprised you?