Open Mind

Highs and Lows

May 4, 2008 · 7 Comments

A reader recently suggested that daily or even hourly temperature measurements were more relevant to the human experience of global warming, than monthly or annual averages. I’m not sure whether I agree or not. Daily values, especially extreme ones, are the most visible and unavoidable aspect of weather, but monthly, annual, or even decadal averages of climate parameters can, in some cases, be more relevant.

A hot day isn’t likely to cause massive melting of glaciers or ice sheets, while an entire hot season, year, or decade is. A severe chilling frost may not be sufficient to check the survival of pine bark beetles and thereby protect pine forests from those parasites when a cold season may be more than sufficient. Precipitation is a case where longer-term averages seem to dominate the human impact of the weather. A day without rain is a normal event, but a year without rain is a disaster for human societies; likewise, a day of heavy rain may bring problems, but a week of heavy rain is likely to lead to the kind of flooding that can disrupt the conduct of life.

But it can’t be denied that individual days (or even hours!) can also have a notable impact. If the rain is heavy enough, then a single day can lead to flooding. And if the temperature, even for a day, is hot enough or cold enough, it can not only disrupt society, it can threaten human health.


An excellent source of daily weather data is the European Climate Assessment & Dataset Project, or ECA. While looking around the site, I came across Moberg et al. 2006 (J. Geoph. Res. 111, D22106), which is a study of how weather extremes have changed over the 20th century in European locations. Many such studies examine the number of days in a given season with, say, high temperature in the top 2% of all days from all years for that season, or the top 5%, or 10%. Or they may study cold extremes by examining the number of days in a given season with low temperature in the bottom 2% of all days, or 5% or 10%. Moberg et al. take a different approach, determining the temperature of the top (or bottom) 2% (or 5% or 10%) mark for that season alone. For example, a given season (say, summer 1990) could conceivably have every day in the top 10% for summers in general, but Moberg et al. don’t study that measure, instead they determine the temperature of the top 10% for that season alone, i.e., the 10% mark for summer 1990. They wanted to see whether the temperatures corresponding to percentile ranks of individual seasons showed any secular change. The results are well summarized in the abstract:


We analyze century-long daily temperature and precipitation records for stations in Europe west of 60E. A set of climatic indices derived from the daily series, mainly focusing on extremes, is defined. Linear trends in these indices are assessed over the period 1901–2000. Average trends, for 75 stations mostly representing Europe west of 20E, show a warming for all temperature indices. Winter has, on average, warmed more (~1.0C/100 yr) than summer (~0.8C), both for daily maximum (TX) and minimum (TN) temperatures. Overall, the warming of TX in winter was stronger in the warm tail than in the cold tail (1.6 and 1.5C for 98th and 95th, but ~1.0C for 2nd, 5th and 10th percentiles). There are, however, large regional differences in temperature trend patterns. For summer, there is a tendency for stronger warming, both for TX and TN, in the warm than in the cold tail only in parts of central Europe. Winter precipitation totals, averaged over 121 European stations north of 40N, have increased significantly by ~12% per 100 years. Trends in 90th, 95th and 98th percentiles of daily winter precipitation have been similar. No overall long-term trend occurred in summer precipitation totals, but there is an overall weak (statistically insignificant and regionally dependent) tendency for summer precipitation to have become slightly more intense but less common. Data inhomogeneities and relative sparseness of station density in many parts of Europe preclude more robust conclusions. It is of importance that new methods are developed for homogenizing daily data.

For temperature extremes, they mainly study two variables, TX (the daily high temperature) and TN (the daily low temperature). They determine the temperature defining certain percentile ranks for both of these variables, for the winter season (Dec-Jan-Feb) and for the summer season (Jun-Jul-Aug). The looked for trends in the 2%, 5%, 10%, M (median), 90%, 95%, and 98% levels; the average 20th-century trend over a large number of European stations was warming, at all percentiles, for both measures (TX and TN) and for both winter and summer (click the graph for a much clearer view):

There’s greater change in the “warm tail” of the distribution, i.e., the warmest of all days/nights, and the largest trend is in TX (daily high) in winter, at the 98th percentile (the hottest winter days). In other words, the daily high temperature of the hottest winter days has increased more rapidly than any other variable, averaging 1.6 deg.C/century for the 72 stations studied. The smallest trend is in TN (overnight low) in summer at the 2% level (the coldest summer nights). The overnight low of the coldest summer nights has increased less than any other variable, but is still significant at just over 0.5 deg.C/century.

Moberg et al. also divided the 72 stations studied into six regions, and estimated results separately for each region. Dots indicate rates which are significant at 95% confidence, points without dots those that aren’t (click the graph for a clearer view):

Of course I wanted to look at some data myself, in a similar (but not identical) way, extending further back in time than just 1900. This requires not only having access to daily data, but to daily highs and overnight lows. The longest set of daily temperature estimates in the ECA database is for Stockholm, Sweden, but that record includes only the daily mean (Tmean), not high (TX) and low (TN) temperatures. The longest record in the ECA database which includes both TX and TN is for Praha in the Czech republic, including daily high temperature (TX) for the complete summer seasons from 1775 to 2004. I’ll emphasize that the Moberg et al. study is regional rather than global, studying only stations in Europe, and that what I’m about to present is even more limited in its geographic scope, examining only one station. But let’s have a little fun and see what’s there.

Praha is at latitude 50.1 N, longitude 14.4 E, so it’s definitely in the northern part of our hemisphere. Instead of determining percentile temperatures for each individual season in isolation, I counted the number of days in the summer season for which the daily high temperature was above the 90th, 95th, and 98th percentile for all summer days for all years, as well as the number of days in the summer season for which the daily high temperature was below the 10th, 5th, and 2nd percentile for all summer days for all years.

First let’s look at the number of days per year, in the summer season, for which the daily high did not exceed the 10th percentile of all summer daily high for all years. I can call these “cool summer days”:

Visually the number of cool summer days seems to have declined, but the linear fit indicates a trend which is not statistically significant. However, “change point analysis” (looking for times which separate the data into two sub-spans with significantly different averages) indicates that yes, indeed the average has declined; from 1775 to 1926 Praha had an average of 10.2 cool summer days per year, from 1927 through 2004 the average was only 6.7.

Looking at the 5th percentile data for summertime daily high, we have a count of what I’ll call “cold summer days”:

Again there’s a visual impression of a decrease in the number of cold summer days, but a linear regression is not statistically significant. Yet again, change point analysis indicates that there has indeed been a decrease, but not a linear one. From 1775 to 1923 Praha averaged 5.2 cold summer days per season, from 1924 to 2004 the average was only 3.0.

The 2nd percentile indicates the number of “coldest summer days” per season in Praha:

The situation is again the same. Linear regression gives no significant result, but change point analysis indicates a decrease which is statistically significant. From 1775 to 1923 Praha had an average of 2.2 cold summer days per season, from 1924 to 2004 only 1.1.

On the high end, the 90th percentile enables us to count the number of “warm summer days” per year:

Both the visual impression, and the linear regression, indicate an increase which is stronger than the decrease indicated for the cool, cold, or coldest days. The linear regression is, this time, statistically significant, as is change point analysis. From 1775 to 1926 Praha averaged 7.7 warm summer days per year, from 1927 to 2004 it averaged nearly twice as many, 13.8 per year.

The 95th percentile identifies the “hot summer days”:

Again both linear regression and change point analysis are statistically significant. From 1775 to 1927 the average number of hot summer days was 3.5 per year, from 1928 to 2004 the average was more than twice as high, 7.6 per year.

Finally, the 98th percentile indicates the “hottest summer days”:

Just as before, both linear regression and change point analysis are statistically significant. From 1775 to 1927 Praha saw only 1.3 hottest summer days per year, but from 1928 to 2004 it experienced 3.5. During the deadly European heat wave of 2003, Praha had fully 17 days for which the daily high was in the top 2% of all summer days since records began in 1775.

The record of daily high temperature in Praha clearly and strongly indicates an increase in the number of hot days and a decrease in the number of cold days in summer. There’s a great deal more information in the Praha data, including the daily low temperatures, and the record for the winter season. And of course there are many other data sets to be explored. Furthermore, the use of change point analysis does a much better job than linear regression at detecting trends which are strongly nonlinear, and should be applied to the data analyzed by Moberg et al. 2006 (who restrict their trend analysis to linear regression). This exploration of Praha data has been more an exercise in example than any indication of regional, let alone global, patterns. Clearly there’s much yet to be done in understanding how daily highs and lows have changed over the centuries, and over the globe.

Categories: Global Warming

7 responses so far ↓

  • TCO // May 4, 2008 at 9:16 pm

    A practical example where extremes generally are more important than overalls is plant hardiness: what allows growth of palms, citrus, etc. in Marseilles but not in New York.

    The USDA plant hardiness is based on averaging 5 succeeding annual EXTREMES. In a lot of cases the prescense or absences of the coldest days is what changes what plants can live where…NOT the overall coldness of the season OR the warmness of the YEAR.

    http://www.usna.usda.gov/Hardzone/ushzmap.html

    http://en.wikipedia.org/wiki/Hardiness_zone

  • John Mashey // May 4, 2008 at 11:35 pm

    We ski in British Columbia, hence have become more familiar with pine beetles, and they illustrate how complicated effects can get. For those unfamiliar with these beetles, as winter approaches, they generate internal antifreeze (ethylene glycol) for a while, which protects them in the winter and then dissipates. Also, they are protected by bark, and if there is snow, by its further insulation.

    So if they get “surprised” by a quick -18C cold spell in Fall/Spring, many die, but in Winter you want to get some sustained (to penetrate bark+snow) -34C to kill them off for sure.

    So, in this case:

    - it’s the extreme that matters, not the average
    - however, the extreme has to last “long” enough
    - and the necessary extreme value is different at different times
    - and (I think) the length of time required at at extreme changes during the year as well.

    http://www.geog.ubc.ca/courses/klink/g470/class03/schan/background.html

  • Ben Lankamp // May 4, 2008 at 11:45 pm

    Another excellent post, Tamino. Being Dutch, it is nice to see some analysis on European climate on your blog. Thanks for that :-). One small correction though: Praha (Prague) is definitely located east of the prime meridian, so the longitude 14.4 W should be 14.4 E.

    [Response: Thanks for the correction. It's now fixed.

    There's probably more European station analysis to come, since the ECA provides such a wealth of data in such easily accessible form.]

  • Hank Roberts // May 4, 2008 at 11:53 pm

    http://fruitsandnuts.ucdavis.edu/weather/aboutgdh.shtml

    ” Growing Degreee Hours (GDH) are the result of a calculation which combines the passage of time with the temperature experienced during that time period. It is similar to a degree-day calculation in describing plant development because growth and development of peaches, plums, and nectarines are strongly influenced by temperature and time….”

    http://fruitsandnuts.ucdavis.edu/weather/aboutchilling.html

    “About Chilling Units

    “Stone and pome fruit trees rely on enough chill hours for flowers and leaf buds to develop normally. If the buds do not receive sufficient chilling temperatures during winter to completely release dormancy, trees may develop physiological symptoms such as delayed and extended bloom, delayed foliation, reduced fruit set and reduced fruit quality. Growers and industry keep track of chilling hours beginning in November to get a sense of the orchard management practices needed and comparison of past year’s weather and crop load. The approximate number of hours needed for normal development varies ….”

  • Aaron Lewis // May 5, 2008 at 3:45 pm

    Hank,
    Fruit chillhours are above freezing. Hours below freezing do not count. In 2000, we had more frost and less chill hours. This year we had more chill hours and no frost.

    I thought fruit trees actually needed actual frost for proper dormancy. Apparently not.

  • Hank Roberts // May 5, 2008 at 5:44 pm

    Aaron, I think each cultivar is different; I know some apples require a period of below-freezing temps; others can’t take that. I looked at various state Ag dep’t pages and each has somewhat different local requirements and tracking.

  • Hank Roberts // May 10, 2008 at 3:33 pm

    Relevant to the topic:
    http://www.agu.org/pubs/crossref/2008/2008GL034145.shtml

    “Previous studies of the long-term climate effects of irrigation have focused on average monthly temperatures. Given the importance of temperature (T) extremes to agriculture and human health, we evaluated irrigation induced changes in various metrics of T extremes using daily observations in California and Nebraska. In addition, simulations from a regional climate model were used to evaluate irrigation effects on T and heat index (HI; also known as the discomfort index) extremes in California, with the latter representing a combined measure of T and humidity….”

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