Tuesday, December 2, 2014

Intra-Annual Climate Variability

If you don't like the weather in New England, just wait a few minutes – Mark Twain

What parts of the U.S. have the most temperature and precipitation variability? This question is actually not so difficult to answer. What is more difficult is the definition of variability. Many maps exist displaying temperature ranges and annual precipitation – but very little has been done to assess overall intra-annual climate variability. This post attempts to remedy the situation.

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 stations. (April 17th note: the NCDC is now the NCEI - National Centers for Environmental Information). These data are the basis for my climate variability analysis.

Figure 1. Location of 9,708 stations that NCDC (now NCEI) 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.

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

The largest values of temperature variability are in interior Alaska north of the Alaska Range. Umiat, Alaska, wins 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 an average daily standard deviation of 1.5°F. In the Contiguous U.S., the lowest values are along the west coast and southern Florida. A number of stations have average daily standard deviations under 4.0°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. Probably 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 3 shows the month-to-month variability in precipitation values across the year. 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 against a uniform distribution. 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 3. 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.

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. On the flip side, the stations with the least precipitation variability are in eastern New England and the North Carolina Piedmont.

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 here.

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) on a scale of 0 to 100 and similarly scaled all precipitation variability values on a scale of 0 to 100 too. In both cases, the scaling was done on a percentile basis. This makes the average score exactly 50. We then combined the score for each station by simple addition (temperature variability percentile + precipitation variability percentile). Finally, the new composite number was transformed to a scale of 0 to 100. A score of 0 means that a station's summed temperature variability percentile and precipitation variability percentile was lower than all other stations. A score of 100 means that a station's summed temperature variability percentile and precipitation variability percentile was higher than all other stations. Since there are many thousands of stations and the values are rounded to one decimal point, multiple stations have a value of 0.0 and 100.0. Figure 4 shows the final variability score for the entire U.S.

Figure 4. Precipitation-climatology combined variability score. Values are scaled up to 100.

At the large scale, most of Alaska and 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 Prudhoe Bay, Alaska. Their value is 100. Prudhoe Bay is along the North Slope of Alaska at the shore of the Arctic Ocean. In the Contiguous U.S., Cut Bank, Montana, has the highest climate variability. The station with the lowest value is East Harwich, Massachusettes, on Cape Cod. Their combined value was 0.002.

Variability of 50 Most Populous Cities

Earlier we noted which stations had the greatest and lowest values. However, the stations at the top and bottom of the list have very small populations. If we look at just "big" cities – the 50 most populous cities in the U.S. according to the 2010 Census – we get a better idea about how places compare to one another. Figure 5 shows the location of the 50 most populous cities and a ranking, from 1 to 50, identifying which cities have the greatest inter-annual climate variability. The names of the cities and the values are shown in Table 1.

Colorado Springs, CO, barely edges out Omaha, NE, on the list for the top spot. Both cities have a variability score (percentile) between 74 and 75 (note: if the list were expanded to include the top 100 cities, Lincoln, NE, would be at the top of he list). At the bottom of the list is Atlanta, Georgia. Atlanta has a very low average daily temperature variability and a nearly perfect distribution of precipitation throughout the year.

A couple of things stand out right away on the map and table. First, how can the California cities have such large variability rankings? Remember, this is a combined index of temperature variability and precipitation variability. The California cities have low to moderate temperature variability but they are all in the 95th to 100th percentile for precipitation variability. In some cases, 60% of annual precipitation falls in only three months and 15% falls in five other months.

On the flip side, how does New England score so low? The have the same issue as California but in reverse. Their temperature variability is in the moderate range but they have nearly uniform precipitation throughout the course of the year. A number of stations have less than a 5% difference between their wettest month and their driest month.

Figure 5. Precipitation-climatology combined variability score. Values are scaled up to 100. The 50 most populated cities (2010 Census) are overlaid and their relative rankings is shown.

CityStatePopulationVariability ScoreVariability Rank
Colorado SpringsCO416,42774.81
Kansas CityMO459,78766.64
Los AngelesCA3,792,62158.89
San JoseCA945,94257.810
Long BeachCA462,25757.611
San FranciscoCA805,23557.012
San DiegoCA1,307,40256.913
El PasoTX649,12156.615
Oklahoma CityOK579,99951.918
Las VegasNV583,75633.327
Fort WorthTX741,20630.528
Virginia BeachVA437,99418.038
San AntonioTX1,327,40714.041
New YorkNY8,175,1334.847

Table 1. Ranking of variability score for 50 most populated cities (2010 Census).


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?

***** Footnote on April 2, 2014  *****

Last December 4th, a post at fivethirtyeight.com identified the cities with the "most unpredictable weather" in the U.S. Ironically, two days earlier (12/2/2014) is when this analysis was published. There is a large difference between predictability and variability. In terms of predictability, their temperature index is fairly close to mine. However, for precipitation, predictability is related to the frequency of rainfall, while variability looks at the distribution throughout the year. Predictability is therefore closely related to precipitation amount and is therefore biased toward dry areas. In general, the fivethirtyeight.com index is essentially the same as a persistence forecast.

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