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In press, Geophysical Research Letters
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The relative increase of record high
maximum temperatures compared to record
low minimum temperatures in the U.S.
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Gerald A. Meehl1*, Claudia Tebaldi2, Guy Walton3, David Easterling4,
and Larry McDaniel1
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National Center for Atmospheric Research+, Boulder, CO, U.S.A.
Climate Central, Princeton, N.J., U.S.A.
The Weather Channel, Atlanta, GA, U.S.A.
National Climate Data Center, Asheville, NC, U.S.A.
October 19, 2009
Index terms: 1616, 1626, 1630, 1637, 3305
* Corresponding author: meehl@ncar.ucar.edu 303-497-1331
(+) The National Center for Atmospheric Research is sponsored by the National Science
Foundation
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Abstract
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The current observed value of the ratio of daily record high maximum temperatures to record
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low minimum temperatures averaged across the U.S. is about two to one. This is because
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records that were declining uniformly earlier in the 20th century following a decay
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proportional to 1/n (n being the number of years since the beginning of record keeping) have
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been declining less slowly for record highs than record lows since the late 1970s. Model
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simulations of U.S. 20th century climate show a greater ratio of about four to one due to more
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uniform warming across the U.S. than in observations. Following an A1B emission scenario
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for the 21st century, the U.S. ratio of record high maximum to record low minimum
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temperatures is projected to continue to increase, with ratios of about 20 to 1 by mid-century,
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and roughly 50 to 1 by the end of the century.
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1.
Introduction
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As of the end of September, 2009, inspection of the National Climatic Data Center web site that
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archives observed annual record high maximum and record low minimum daily temperatures
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from weather stations across the U.S. (
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http://www.ncdc.noaa.gov/oa/climate/research/records/)
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showed that since January 1, 2000, there had been 291,237 record high maximum daily
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temperatures set, and 142,420 record low minimum daily temperatures, or a ratio of roughly two
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to one. Since January 1, 2009 (also compiled to the end of September, 2009), there had been
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11,711 record highs and 7,449 record lows, with a ratio of just less than two to one. Though
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this simple summation does not take into account station record length or any autocorrelation
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effects, it is not unexpected that there would be more record high maximum temperatures being
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set than record low minima simply because the annual U.S. average surface temperatures have
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been increasing since the 1970s (Karl et al., 2006; Trenberth et al., 2007, Hegerl et al. 2007). A
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simple shift of the statistical distribution of temperatures at a given station would dictate that
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there would be more record high temperatures than record lows (see Box TS.5, Fig. 1 in
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Solomon et al., 2007). However, we would not expect a two to one ratio of record highs to
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record lows to persist for a long time in a steadily warming climate, and we attempt in this paper
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to put this particular value of the ratio in context, as we look at observations over the last 50-plus
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years and, in particular, to model simulations that allow us to study the effects of future
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warming.
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We use a subset of quality controlled NCDC US COOP network station observations of daily
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maximum and minimum temperatures, retaining only those stations with less than 10% missing
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data (in fact the median number of missing records over all stations is 2.6%, the mean number is
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1.2%) . All stations record span the same period, from 1950 to 2006, to avoid any effect that
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would be introduced by a mix of shorter and longer records. The missing data are filled in by
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simple averages from neighboring days with reported values when there are no more than two
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consecutive days missing, or otherwise by interpolating values at the closest surrounding
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stations. Thus we do not expect extreme values to be introduced by this essentially smoothing
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procedure. In addition our results are always presented as totals over the entire continental U.S.
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region or its East and West portions, with hundreds of stations summed up. It is likely that
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record low minima for some stations are somewhat skewed to a cool bias (e.g. more record lows
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than should have occurred) due to changes of observing time (see discussion in Easterling, 2002,
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and discussion in auxiliary material), though this effect is considered to be minor and should not
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qualitatively change the results. Additionally, at some stations two types of thermometers were
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used to record maximum and minimum temperatures. The switch to the Max/Min Temperature
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System (MMTS) in the 1980s at about half the stations means that thermistor measurements are
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made for maximum and minimum. This has been documented by Quayle et al. (1991), and the
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effect is also considered to be small. To address this issue, an analysis of records within
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temperature minima and within temperature maxima shows that the record minimum
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temperatures are providing most of the signal of the increasing ratio of record highs to record
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lows (see further discussion in auxiliary material).
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The model data are from the NCAR Community Climate System Model version 3 (CCSM3) that
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was run for simulations of 20th century and 21st century climate (Meehl et al., 2006), where for
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20th century, both natural (volcanoes and solar) and anthropogenic (GHGs, ozone and direct
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effect of sulfate aerosols) forcings are included. In the model, warming over the U.S. at the end
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of the 20th century is somewhat greater than observed (Meehl et al., 2006), and mostly attributed
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to human activity (Meehl et al., 2007, Hegerl et al., 2007).
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20th century
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Probability theory states that, in the case of an independent sequence of random variables
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identically distributed, the number of records should decrease as 1/n, where n is the number of
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realizations of the independent variable accumulating as we observe it. In our case n is time, in
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particular it is the year for which we observe the value of a calendar day maximum and
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minimum temperature and we compare it to the standing record highs and lows. As years (and
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records) accumulate it becomes increasingly difficult for a stationary process to break a record,
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asymptotically as difficult as an event with probability 1/n. (e.g. Arnold et al., 1998). Thus, the
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number of years a station has been operating is an important aspect of accounting for numbers of
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records. Analysis of observed station data for the U.S. has shown that starting a 1/n calculation
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by taking all stations available in mid-20th century produces a credible accounting of records with
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distinct seasonal and geographical features (Portman et al., 2009a). They also show that two
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factors influence changes in the numbers of records that deviate from the theoretical 1/n
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relationship, involving 1) different natural variability translating into a wider or narrower
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variance of the climatological distribution of temperature and 2) changes in temperature trends.
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It has been shown that regional changes of temperatures and precipitation are related to regional
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changes of extreme temperatures in some areas and seasons (Portmann et al., 2009b).
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Fig. 1a shows the decay of observed annual record high maximum temperatures (red dots)
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compared to annual record low minimum temperatures (blue dots) averaged over the U.S. since
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1950. The smooth line is the theoretical or expected rate of decay corresponding to 1/n times the
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number of stations over which the records are summed. The expected rate of decay is a good
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explanation for the time series of annual number of records (both highs and lows) up to about
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1980, whereas after 1980 there are clearly more red dots falling above the line and more blue
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dots below the line, making the theoretical behavior under a stationary process a poorer fit than
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in the first part of the record. In particular the position of the dots relative to the theoretical line
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seems to suggest that the number of observed record lows has been declining more rapidly than
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expected, while record highs stay closer to their expected behavior even in the later part of the
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period. The ratios of record high maxima to record low minima are shown in Fig. 1b, with a
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non-linear curve fit to the values. The expected ratio in a stationary climate would be 1.0, but it
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can be seen that in the 1950s this ratio was somewhat above 1.0, it dropped to a bit below 1.0 in
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the 1960s and 1970s, and then has been rising ever since such that in the most recent decade the
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ratio is roughly 2 to 1 as noted earlier. The time evolution of this ratio reflects the rate of change
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of U.S. average temperatures, with greater rates of warming in the 1950s, almost no warming in
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the late 1950s and 1960s, and warming since the 1970s (Karl et al., 2006; Trenberth et al.,
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2007). From the results in Fig.1a we can also infer that the larger than expected values of the
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ratio seem to be due to less than expected record lows rather than more than expected record
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highs. It is also seen that the recent period when the ratio has been 2 to 1 is just the latest value
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characteristic of a warming climate, while the ratio was less than that in the previous several
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decades. In order to characterize the significance of these “larger values” of the ratio (i.e. values
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greater than 1.0), we perform a bootstrap analysis by resampling the sequence of 55 years in the
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observed records using blocks of three consecutive years to account for the possible presence of
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time correlation. We produce one hundred new time sequences and we apply them uniformly
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across the set of stations and for maximum and minimum temperature. We repeat the
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computation of records for the new artificial sequences of observations, sum the annual numbers
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of records over space and recompute the 55 values of the ratio for each of the 100 bootstrap
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samples.
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By applying the smooth fit to each, we determine an envelope of possible results where the
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presence of a trend in the measurement of minimum and maximum temperature would be
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eliminated by the random resampling of (blocks of) years. This envelope of results is shown as
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grey lines, against which the observed is plotted as a thick black line (Auxiliary material, Fig.
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A1). Only one other trajectory of the ratio is higher than the observed after the late-1990s, out of
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the 100 bootstrapped trajectories, indicating that the large recent values of the ratio as observed
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are statistically significant.
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To compare to a single realization of 20th century climate from the CCSM, Fig. 1d shows that the
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actual measurements diverge from the theoretical 1/n line somewhat earlier in the century for
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record high maxima and record low minima, and in a more symmetric fashion when comparing
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lows and highs. Additionally, the ratio for the most recent decade (Fig. 1d) has climbed to about
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4 to 1. The greater ratio compared to observations suggests a larger base state warming in the
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model as noted earlier, which also manifests itself in a more even change between the behavior
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of minimum and maximum temperatures. Similar bootstrap results to those for the observations
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discussed above confirm the significance of the model simulated large values of the ratio. That
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is, generating time series of another 100 realizations of simulated 20th century climate indicates
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that the larger warming (compared to the observations) and corresponding larger ratio is
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significant (Fig A2, supplementary material). Notably the results from CCSM do not show
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decadal modulation of the ratio but rather indicate a steady increase of the ratio over the course
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of the historical period.
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Part of the reason for this greater ratio in the model compared to observations lies in the spatial
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distribution of annual mean temperature increase, with greater observed warming in the western
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U.S. compared to the eastern U.S. (Trenberth et al., 2007). This is reflected in the eastern vs.
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western U.S. record temperatures in Fig. 2, with less of a divergence from the expected 1/n decay
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for record highs versus record lows in the east (all stations east of 100W, Fig. 2) compared to the
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west (Fig. 2 top half), with a ratio for the eastern U.S. that is somewhat less than 2 to 1 where
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warming has been less, compared to the west where the ratio is over 3 to 1 associated with
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greater base state warming. By applying the spatial disaggregation to the bootstrapped results
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described above, we can test the significance of the large values of these two ratios as well,
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(Auxiliary material Fig. A3). The values in the Eastern part of the United States are
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significantly different from what should be expected in the absence of a trend only at a 10% or
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greater level, while in the West the significance of the results is such that none of the
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bootstrapped sequence of ratio values lies above the observed.
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The model shows some indications of greater average warming in the western U.S. compared to
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the east (e.g. Meehl et al., 2006) as evidenced by a simulation of greater decreases of frost days
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(nighttime minimum temperatures below freezing, Meehl et al., 2004) and greater heat wave
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intensity (Meehl and Tebaldi, 2005; Tebaldi et al., 2006) in the west compared to the east. In
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terms of records, though not as pronounced as in the observations, the model shows a divergence
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from the expected 1/n relationships between record highs and record lows for the two parts of the
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country (Fig. 2 bottom half), with a ratio of less than 4 to 1 for the east compared to a ratio of
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over 5 to 1 for the west. Therefore, the model is capturing some elements of the greater ratio of
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record highs to record lows in the west compared to the east as seen in the observations, but with
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ratios that are higher than observed, and a more symmetric change in the numbers of record
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lows and record highs as they deviate from the expected rate. Bootstrap-based tests have
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confirmed the significance of these large values of the ratios similar to what was found for
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observations (Supplementary material, Fig. A4).
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21st century
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Earlier we posed the question of whether the recently observed 2 to 1 ratio of record high
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maximum temperatures to record low minimum temperatures is somehow a unique characteristic
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of a warming climate. To address that question we plot this ratio from the model for the 20th
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century and 21st centuries (the latter following the mid-range A1B scenario; Meehl et al., 2006)
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in Fig. 3. It can be seen that as the climate continues to warm during the 21st century, the
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number of record highs fall in larger and larger measure above the theoretical expectation line as
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compared to the number of record lows falling below the same line (Fig. 3a). This is reflected in
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the ongoing increase in the ratio (Fig. 3b) such that by mid-century the ratio is about 20 to 1, and
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by late century it is around 50 to 1. Presumably at some point after 2100 there would come a
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time when there would be no more record low minima being set, and only record high maxima
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would be recorded, though the model indicates that this has not yet occurred in the A1B scenario
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over the U.S. by 2100. We conducted a similar analysis on simulations from CCSM under SRES
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B1 (lower forcing than A1B) and A1FI (higher forcing than A1B). For the low scenario B1 the
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values of the ratio are about 8 to one by mid-century, but are in the range of hundreds to one
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for scenario A1FI by mid-century, when computed on the same set of grid points covering the
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continental US (on the order of 80 gridpoints). These specific values for the ratios over the 21st
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century are very likely model-dependent, and thus are only indicative of how these ratios could
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evolve. Rather they are suggestive of the order of magnitude of the changes of the ratios in a
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future warming climate.
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4. Conclusions
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Analysis of observed annual U.S. record high maximum compared to record low minimum daily
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temperatures shows that the recent values of the ratio of about 2 to 1 are the current value of this
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ratio that has been increasing with mean annual mean temperature over the U.S. since the late
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1970s. Trewin and Vermont (2009) have also documented a similar recent ratio of about 2 to 1
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over Australia for monthly temperature records. As noted in other studies (Portman et al., 2009),
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there are geographic and seasonal characteristics to these records, and it is shown that the greater
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values of the ratio for the western U.S. (where mean warming has been greater) compared to
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eastern U.S. are simulated with reduced contrast in the model, with greater values of the ratio
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simulated in the model, likely indicative of the greater mean warming in the model over the U.S.
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compared to observations by the early 21st century. Additionally, while observations seem to
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indicate that record lows have been declining in larger measure than record highs have been
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increasing, the model simulates a more symmetric behavior between minimum and maximum
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record temperatures. For later in the 21st century, the model indicates that as warming continues
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(following the A1B scenario), the ratio of record highs to record lows will continue to increase,
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with values of about 20 to 1 by mid-century, and roughly 50 to 1 by late century.
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Two factors contribute to this increase as noted by Portman et al (2009a): 1) increases in
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temperature variance in a future warmer climate (as noted in the model by Meehl and Tebaldi,
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2004), and 2) a future increasing trend of temperatures over the U.S. (model projections shown
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in Meehl et al., 2006). Since the A1B mid-range scenario is used, a lower forcing scenario (e.g.
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B1) produces reduced values of the ratio in the 21st century, and a higher forcing scenario (e.g.
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A2) produces greater values. The model cannot represent all aspects of unforced variability that
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may have influenced the observed changes of record temperatures to date, and the model over-
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estimates warming over the U.S. in the 20th century. The future projections may also reflect this
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tendency and somewhat over-estimate the future increase in the ratio. Under any future scenario
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that involves increases of anthropogenic greenhouse gases and corresponding increases in
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temperature, the ratio of record high maximum to record low minimum temperatures will
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continue to increase above the current value.
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Acknowledgments
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The authors acknowledge insightful discussions with Bob Portmann, Susan Solomon, Bradley
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Efron, and Tony Broccoli during the preparation of this study, and thank Gabi Hegerl and one
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anonymous reviewer for constructive comments that helped improve the text. The authors are
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also grateful to Claude N. Williams for providing an initial dataset of quality controlled stations,
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whose analysis originated the more comprehensive study of this paper. Portions of this study
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were supported by the Office of Science (BER), U.S. Department of Energy, Cooperative
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Agreement No. DE-FC02-97ER62402, and the National Science Foundation. The National
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Center for Atmospheric Research is sponsored by the National Science Foundation.
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Figure captions
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Figure 1: Comparison of observed and modeled statistics of records, averaged over the entire US
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region, a) annual numbers of record high maximum temperatures (red dots) and record low
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minimum temperatures (blue dots) compared to the theoretical values (black line) under
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stationary conditions, following a decay of 1/n where n is the number of years from the start of
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record counting; b (bottom left) observations of the ratio of record highs to record lows each
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year (dots), solid line is a smoothed curve fit, and the envelope of the 95% CI from the bootstrap
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is marked by grey lines; c) (top right) same as (a) except from a single simulation of the 20th
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century from the model; d) (bottom right) same as (b) except for the model. Note that the
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heteroscedasticity of the sample values (increased variance over time) is to be expected since the
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values are obtained as ratios of increasingly smaller numbers (the overall number of annual
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records decreases with the length of the record). Difference of a few units in large
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numerators/denominators do not cause the same variability in the ratio as difference of a few
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units in ratios of small numbers.
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Figure 2: As Figure 1, but for observations and splitting the stations between Western and
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Eastern regions of the US, along the 100W meridian. Top panels show annual numbers of record
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highs (red dots) and lows (blue dots) and expected behavior (black line). Second from top panels
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show annual values of the ratio of number of record highs to lows and a smooth curve fit, plus
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the 95% CI computed by bootstrap. Third from top panels are same as top panels but for the
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model, and bottom panels are same as second from top panels but for the model.
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Figure 3: Annual numbers of record highs and lows (top panel) and their ratio (bottom)
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computed from the model, using 20th century and and SRES A1B 21st century experiments.
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Plots are similar to Fig1c,d but extend the time horizon to the end of the 21st Century.
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Fig1
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Fig. 2
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Fig 3
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