A comparison of climatological observing windows and their impact on detecting daily temperature extrema

Original Paper

Abstract

Climatological observing window (COW) is defined as a time frame over which continuous or extreme air temperature measurements are collected. A 24-h time interval, ending at 00UTC or shifted to end at 06UTC, has been associated with difficulties in characterizing daily temperature extrema. A fixed 24-h COW used to obtain the temperature minima leads to potential misidentification due to fragmentation of “nighttime” into two subsequent nighttime periods due to the time discretization interval. The correct identification of air temperature extrema is achievable using a COW that identifies daily minimum over a single nighttime period and maximum over a single daytime period, as determined by sunrise and sunset. Due to a common absence of hourly air temperature observations, the accuracy of the mean temperature estimation is dependent on the accuracy of determination of diurnal air temperature extrema. Qualitative and quantitative criteria were used to examine the impact of the COW on detecting daily air temperature extrema. The timing of the 24-h observing window occasionally affects the determination of daily extrema through a mischaracterization of the diurnal minima and by extension can lead to errors in determining daily mean temperature. Hourly air temperature data for the time period from year 1987 to 2014, obtained from Toronto Buttonville Municipal Airport weather station, were used in analysis of COW impacts on detection of daily temperature extrema and calculation of annual temperature averages based on such extrema.

1 Introduction

The determination of daily minimum and maximum temperatures, often used in calculating the daily mean temperature, has been surprisingly difficult. On 1st July 1961, the climatological day was redefined in Canada to end at 06UTC instead at 00UTC in order to correct for the potential mischaracterization of air temperature minima. This change to the new climatological observing window (COW), however, introduced a cold bias to the observations by increasing the potential for recording minimal temperatures on two consecutive days from the same diurnal minimum, in effective double counting particularly cold days. Between 15 and 38% of days in Canada at different stations has been affected by this cold bias annually (Vincent et al. 2009, 2012). At the same time, it was found that the change in COW did not significantly affect the recording of daily maximum temperature. Unlike night time, day time with the new COW was not fragmented and the maximum temperature was unambiguously determined.

Non-climatic variations, such as somewhat arbitrarily defined COWs, affect proper assessment of climate trends and a number of techniques to date have been developed to detect inhomogeneities in data records. Homogenization was applied to the original temperature data recorded at 120 synoptic stations throughout Canada to correct for the bias in minimum temperature due to the change of COW. The temperature adjustment on individual days varied from 0.5 °C to as much as 12.5 °C (Vincent et al. 2012). It is clear that the COW affects the determination of daily air temperature extrema. This draws attention to the importance of developing a COW that corresponds better to the physical time frame of daily air temperature extrema.

Due to the common lack of continuous temperature observations (i.e., hourly), knowledge of daily air temperature extrema is crucial for the calculation of daily mean temperatures and in turn all other larger time periods such as monthly, seasonal, annual, and decadal. Daily mean temperature is the key variable in the field of climate observations, modeling, and climate change impacts. Climatological studies typically use mean temperature obtained from 24 observations at intervals of 1 h (true mean), derived from daily extrema (mean of daily extrema), (Tmax + Tmin) / 2, or fixed sampling at coarser than hourly temporal resolution. As a result of scarcity of hourly data records in general, many algorithms for the calculation of daily mean temperature have been developed (Hartzell 1919; Collison and Tabony 1984; Reicosky et al. 1989; Weber 1993; Harris and Pedersen 1995; Zeng and Wang 2012; Trewin 2004; Weiss and Hays 2005; Bonacci et al. 2013; Gough and He 2015).

Correct identification of daily air temperature extrema, i.e., minima and maxima measurements, is climatologically a vitally important, but surprisingly complex, task. Daily air temperature extrema are the points, on the temperature-time curve, in which the trend of daily air temperature cycle changes its sign. Temperature trend changes happens at least two times per solar day, with maximum air temperature typically occurring during the daytime, and the minimum air temperature during the nighttime as one expects from radiative considerations. The complications associated with local and regional geography, season, and with atmospheric circulation modify this picture enabling a wider range of times for the minimum and maximum temperature of the day to occur. For example, winds associated with midlatitude cyclones can cause the maximum temperature to occur at night and the minimum to occur during the daytime. As a general practice, the discrete determination of daily extreme values when performed on a continuous temperature data set searches for both minima and maxima over a 24-h time period time frame, fixed at a starting point regardless of the season or geographic location. The objective of this study is to assess the applicability of different climatological observing windows in addressing the problem of finding the true (mathematical) daily extrema.

2 Data and methods

We define three different climatological observing windows (COWs) over a 24-h period (Table 1). The first observing window starts from midnight in local standard time (LST) and is labeled as COW0–24, referred to as “0 to 24 h observing window.” The second is the “06 to 06 h observing window”, selected to begin at 6:00 am LSTand is denoted as COW6–6. These two observing frames identify both minimum and maximum temperatures over an undifferentiated 24-h period staring at a fixed time. In contrast to these, an observing window that begins at floating time of a daily sunrise (plus 1 h,1 LST) to identify daily maximum extrema over daytime (sunrise to sunset period) and minimum extrema over nighttime (sunset to next sunrise period) is proposed. This window will be referred to as “Night and Day Climatological Observing Window” denoted as COWND. Table 1 lists these observing windows and specifies the diurnal time frame for selection of their corresponding air temperature extrema.
Table 1

Characteristics of three climatological observing windows and their related time frame for determination of diurnal air temperature extrema

COW

Beginning at

Ending at

Method of identifying Tmax

Method of identifying Tmin

COW0–24

0:00 LST

23:00 LST

\( {T}_{\max }=\underset{0\le h\le 23}{ \max }{T}_h \)

\( {T}_{\min }=\underset{0\le h\le 23}{ \min }{T}_h \)

COW6–6

06:00 LST

05:00 LST (next day)

\( {T}_{\max }=\underset{6\le h\le 5}{ \max }{T}_h \)

\( {T}_{\min }=\underset{6\le h\le 5}{ \min }{T}_h \)

COWND

trise + 1 h LST

trise + 1 h LST (next day)

\( {T}_{\max }=\underset{t_{\mathrm{rise}}\le h\le {t}_{\mathrm{set}}}{ \max }{T}_h \)

\( {T}_{\min }=\underset{t_{\mathrm{set}}\le h\le {t}_{\mathrm{rise}}}{ \max }{T}_h \)

Sunrise and sunset times required for determination of daily temperature extrema using COWND are calculated using the following formulae:
$$ \begin{array}{c}\hfill {t}_{\mathrm{rise}}={12}^h-{ \cos}^{-1}\left(- \tan \varphi \ast \tan {\delta}_o\right)\hfill \\ {}\hfill {t}_{\mathrm{set}}={12}^h+{ \cos}^{-1}\left(- \tan \varphi \ast \tan {\delta}_o\right)\hfill \end{array} $$
with trise representing diurnal time of sunrise, tset diurnal time of sunset, φ geographic latitude, and δo solar declination.2
Determination of the daily period over which maxima and minima are calculated is given by the following:
$$ \begin{array}{l}{P}_{\mathrm{DayTime}}={t}_{\mathrm{rise}}-{t}_{\mathrm{set}}\hfill \\ {}{P}_{\mathrm{NightTime}}={t}_{\mathrm{set}}-{t}_{\mathrm{next}\ \mathrm{rise}}\hfill \end{array} $$
with P representing the diurnal length of local daylight and nighttime segments specific for the location and season. Definition of a climatological observing window over a night-and-day period seems logical based on radiative arguments that air temperature maxima is more likely to occur during daytime due to solar heating and minima during nighttime due to solar radiation absence and infrared heat loss. There are of course exceptions to these resulting from advection of warm or cool air into the region which could cause the maximum temperature to occur during the nighttime or the minimum temperature to occur during the daytime.
For illustrative purposes, we present Fig. 1 which depicts the COW0–24, COW6–6, and COWND observing windows applied on a random 4-day period.
Fig. 1

Diurnal air temperature extrema search using three different climatological observing windows. Shaded regions indicate nighttime (sunset to sunrise), and dashed lines indicate midnight while solid yellow lines indicate noon time (LST). Black solid line represents measured hourly temperatures. Tn corresponds to daily minimum temperatures and Tx to daily maximum temperatures with 0–24, 6–6, and ND subscripts representing COW0–24, COW6–6, and COWND methods

This small sample shows the effects of the observing window selection on the identification of daily minimum temperature. Values of daily maximum extrema obtained through three different observing windows are identical for all for days presented in Fig. 1 while two out of the 4 days have different minimum extrema as a result of the COW chosen. Method COWND detects all four minima within the appropriate nighttime periods. Also, COWND is the only method that detects the nighttime minimum during the third night in this example. All methods coincide in the minimum value for nights two and four but double counting of minimum value occurs for COW6–6 method on the second night and for both COW0–24 and COW6–6 methods on the fourth night. To illustrate these points, we walk sequentially through the 4 days. The sequence begins at night with the temperature falling with a minimum just before sunrise. Both COWND and COW0–24 identify this as a minimum (TnND and Tn respectively). However, since the COW6–6 begins after this minimum, the first minimum for this window is the second night. This illustrates how the COW6–6 and COW0–24 typically identify minima from different night time periods. However, the third night introduces another wrinkle. All three methods capture the minimum temperature occurring before sunrise. However since the fourth night is substantially warmer than the third night, only the COWND identifies that minimum. For COW6–6, the temperature at sunrise after the second night is the “third night” minimum, whereas for COW0–24 the minimum occurs at midnight of the fourth night. In both cases, a cold bias is introduced as these two temperatures are colder than the temperature actually experienced (and detected by COWND) on the third night.

The obvious reason for this incorrect representation of minima is the definition of climatological observing window associated with the determination of these extrema. Recording of daily minima using current observing practices involves searching for the daily minimum value using fragments of two different climatological events, i.e., two different nights. To avoid this fragmentation of nights and inconsistent association of minima to the incorrect nighttime segment, a nighttime-daytime discretization of time is proposed for the determination of daily extrema. Two qualitative and two quantitative criteria are used to objectively assess the ability of different COWs to correctly identify extrema in large temperature data sets. We first visually compare air temperature extrema and times of their occurrences obtained by different COWs to indicate the apparent magnitude and frequency of discrepancies between the methods. These observations are discussed in section 3.1. Section 3.2 illustrates how linear interpolation function, in conjunction with two different COW methods, tracks measured air temperature data. The first quantitative comparison focuses on the first two statistical moments of the distributions of differences between measured hourly temperatures and corresponding temperatures calculated by linear interpolation between consecutive extrema as obtained by two COWs. Distributions of differences are in fact error distributions of the associated COW methods. Comparison of mean and standard deviation is performed to determine the conformity of the COWs with observed temperature variation and presented in section 3.3. The second quantitative comparison focuses on the overall differences between minima, maxima, daily mean, and daily temperature range derived by COW selection of climatological parameters on annual basis. Results and observations of these comparisons are presented in section 3.4.

We now apply these COWs to a climatological data set. This data set includes hourly temperatures so that identification of true minimum and maximum temperature is unambiguous. Hourly air temperature data set was obtained from the Environment Canada Historical Climate Data Service for Buttonville A weather station for the period from June 1986 to December 2014.

Buttonville A Municipal Airport weather station is located in Greater Toronto Area, Ontario, Canada (Fig. 2).
Fig. 2

Location of Toronto Buttonville Municipal Airport weather station in Ontario, Canada

The weather station is located at elevation of 198.1 masl and latitude and longitude of φ = 43°51′44″ N, λ = 79°22′12″ W respectively. The weather station is located in a suburban environment with humid continental climate characterized by severe winters, warm summers, and strong seasonality. The air temperature is measured at 1.25–2 m above the ground. In addition to hourly air temperature data, solar declination data at 18:00 UTC (corresponding to13:00 LST) were downloaded from ssd.jpl.nasa.gov website for the purpose of calculation of sunrise and sunset times for the 1986- to 2014-year time period.

3 Results

3.1 A comparison of climatological observing windows

Hourly air temperature data set was utilized for identification of daily temperature extrema with the three different climatological observing windows, COW0–24, COW6–6, and COWND. In addition to the respective air temperatures extrema, occurrence times of extrema were also recorded. Further, true mean daily temperature associated with each of the climatological observing windows was calculated as arithmetic mean of 24 hourly temperatures as well as those derived as the average of the minimum and maximum temperatures derived by each of the COWs.

The issue of correct identification of daily temperature extrema, discussed in methodology section, is examined using seasonally representative air temperature graphs for the time period between 1987 and 2005. Week long samples of air temperature distribution and corresponding daily temperature extrema, determined by the three COWs, are presented in Figs. 3, 4, 5, and 6, each representing a different season beginning with winter. Each figure contains two plots representing the same season of an earlier year (1988/1989) and of a later year (2005/2006) in the data set. Each of the graphs consists of a network of connected air temperature extrema obtained by means of three different observing windows superimposed over the temperature curve obtained from hourly temperature measurements. Some general observations can be readily made from these selected plots:
  1. 1.

    Differences among the observing windows are not apparent for the air temperature maxima as it is for the minima. Maxima are generally identified correctly by all three observing windows.

     
  2. 2.

    Minima are frequently visibly mischaracterized. In such cases, differences between the minima obtained by COWND and other two methods are commonly substantial.

     
  3. 3.

    Regular small variations between identified minima demonstrate the larger difference between COWND and other two observing windows method, COW0–24 and COW6–6, than between the COW0–24 and COW6–6 methods.

     
  4. 4.

    Minima identified by COWND method are generally higher than the minima identified by the other two observing windows.

     
  5. 5.

    On days when daily air temperature cycle does not conform to the solar heating-cooling patterns, it is likely that the local weather pattern is influenced by external factors, such as the passage of midlatitude cyclone. These situations are typically characterized by prolonged increasing or decreasing temperature patterns. In such situations, determination of daily extrema within the COWND framework yields out-of-place extrema with identical or very close daily minimum and maximum values due to loss of the radiatively induced sinusoidal pattern of the temperature diurnality. Figure 7 presents two examples of misidentification of COWND method’s inability to correctly determine daily extrema on days with prolonged increasing or decreasing temperature patterns.

     
  6. 6.

    Observations 1 to 5 appear to be independent of season or year

     
Fig. 3

Winter—diurnal air temperature and daily extrema obtained using different observing windows. Shading indicates nighttime while no shading indicates daytime. Black solid line represents measured hourly temperatures. Solid colored lines connect consecutive minimum or consecutive maximum daily temperature extrema determined by COW0–24, COW6–6, and COWND methods

Fig. 4

Spring—diurnal air temperature and daily extrema obtained using different observing windows. Shading indicates nighttime while no shading indicates daytime. Black solid line represents measured hourly temperatures. Solid colored lines connect consecutive minimum or consecutive maximum daily temperature extrema determined by COW0–24, COW6–6, and COWND methods

Fig. 5

Summer—diurnal air temperature and daily extrema obtained using different observing windows. Shading indicates nighttime while no shading indicates daytime. Black solid line represents measured hourly temperatures. Solid colored lines connect consecutive minimum or consecutive maximum daily temperature extrema determined by COW0–24, COW6–6, and COWND methods

Fig. 6

Fall—diurnal air temperature and daily extrema obtained using different observing windows. Shading indicates nighttime while no shading indicates daytime. Black solid line represents measured hourly temperatures. Solid colored lines connect consecutive minimum or consecutive maximum daily temperature extrema determined by COW0–24, COW6–6, and COWND methods

Fig. 7

Misidentification of extrema by COWND method for days characterized by a non-oscillatory pattern in temperature. Coinciding of minimum and maximum extreme values (magenta and purple markers) is caused by the prolonged decreasing temperature trend

3.2 Linear tracking of air temperature data based on COW0–24 and COWND determined extrema

Figure 8 presents a 6-day summer air temperature variation sample taken from year 2007 of the Buttonville data set. Daily extrema obtained by two contrasting COW methods are linearly connected and superimposed for the comparison of their conformity with measured daily temperatures. Red line represents linear function connecting consecutive extrema obtained by the COW0–24 method while the blue line linearly connects consecutive extrema obtained using COWND method. Shaded areas in the graph represent nighttime periods while dashed black, yellow, and dark blue line represent midnight, sunrise, and sunset time respectively. Examples of incorrect representation of minima are evident on second and fifth day of the temperature sample due to the COW0–24 method association of minima to the second nighttime segment.
Fig. 8

Effects of COW selection on air temperature interpolating function. Black solid line denoted T(t) represents measured hourly temperature while red temperature curve denoted T(t)LIN(0–24) and blue temperature curve denoted T(t)LIN(ND) correspond to linearly interpolated temperatures based on extrema obtained using COW0–24 and COWND methods. Dashed black line indicates midnight, and dashed yellow line indicates sunrise while dashed blue line indicates sunset

At the same time, minima and maxima detected by the COWND method coincide with true mathematical extrema, and consequently, linear function connecting extrema points tracks the temperature trend correctly.

Figures 9, 10, 11, and 12 represent different seasons of an earlier (1996) and later year (2013) of the Buttonville data set. Numerous departures of COW0–24 minima from the true mathematical extrema are observable in all presented graphs. Mischaracterizations of daily minima by the COW0–24 method are due to the fact that the method searches for daily minimum over segments of two different nights. As a consequence, if the temperature in the second night segment is lower than the temperature in the first night segment, COW0–24 method will reject the lower value of the two minima, even though the lower value minimum is in fact the true mathematical extreme. Overall, these omissions or mischaracterizations of minima influence the calculation of daily mean temperature and cause misbehavior of air temperature approximating functions linked in extrema points.
Fig. 9

Winter–linear interpolation of air temperature using COW0–24 and COWND methods for obtaining daily extrema. Black solid line represents measured hourly temperatures while red and blue temperature curves correspond to linearly interpolated temperatures connected in extrema points determined by COW0–24 and COWND methods

Fig. 10

Spring–linear interpolation of air temperature using COW0–24 and COWND methods for obtaining daily extrema. Black solid line represents measured hourly temperatures while red and blue temperature curves correspond to linearly interpolated temperatures connected in extrema points determined by COW0–24 and COWND methods

Fig. 11

Summer–linear interpolation of air temperature using COW0–24 and COWND methods for obtaining daily extrema. Black solid line represents measured hourly temperatures while red and blue temperature curves correspond to linearly interpolated temperatures connected in extrema points determined by COW0–24 and COWND methods

Fig. 12

Fall—linear interpolation of air temperature using COW0–24 and COWND methods for obtaining daily extrema. Black solid line represents measured hourly temperatures while red and blue temperature curves correspond to linearly interpolated temperatures connected in extrema points determined by COW0–24 and COWND methods

3.3 Error distribution comparison of two contrasting climatological observing windows

In order to contrast the COW0–24 and COWND methods, hourly temperatures were first calculated using linear interpolation between consecutive temperature extrema and their respective occurrence times as identified by COW0–24and COWND. These linearly approximated temperatures are then subtracted from the corresponding measured temperatures in order to form an error distribution for each COW method. Error distributions are presented in Fig. 13 while Table 2 provides a summary of error statistics for the two COW methods.
Fig. 13

Error distribution of hourly differences between measured and interpolated temperatures for COW0–24 and COWND methods. Histograms with red bins represents differences between hourly measured temperatures and linearly interpolated hourly temperatures connected in consecutive extrema obtained by COW0–24 method while histograms with blue bins represents differences between hourly measured temperatures and linearly interpolated hourly temperatures connected in consecutive extrema obtained by COWND method

Table 2

Summary statistics for error distributions of COW0–24 and COWND methods

METHOD

Minimum (°C)

1st quart. (°C)

Median (°C)

Mean (°C)

3rd quart. (°C)

Maximum (°C)

St. Dev. (°C)

COW0–24

-17.93

-1.14

-0.09

-0.30

0.79

10.70

1.98

COWND

-10.96

-0.09

-0.07

-0.12

0.75

10.57

1.53

Mean and standard deviation of COWND error distributions are −0.12 and 1.53 °C respectively while their values for COW0–24 are −0.30 and 1.98 °C. Apparently, error distribution for COWND is centered closer to zero and is slightly narrower than COW0–24 distribution rendering this method better in the sense of the second criterion discussed in section 2. This observation is confirmed by quartiles and distribution bounding values presented in Table 2.

3.4 Effect of COW selection on climatological parameters

In this section, we present systematic effects of COW selection on annual averages of daily temperature extremes. Figures 14, 15, 16, and 17 present annual averages of daily maxima, minima, mean of extrema and true temperature averages, and temperature range as calculated from data obtained by the three observing windows. Annual averages of maxima obtained by COWND are on average lower by ~0.33 °C than the annual averages of maxima determined by COW0–24 and by ~0.19 °C than COW6–6 (Fig. 14). Minima obtained by COWND are on average higher by ~0.64 °C than the annual averages of minima determined by COW0–24 and by ~1.32 °C than COW6–6 (Fig. 15). Annual averages of means (daily extrema) obtained by COW methods and their corresponding annual true temperature averages are presented in Fig. 16. In terms of annual averages of means, COWND are on average higher by ~0.16 °C than the averages of COW0–24 means and by ~0.56 °C than COW6–6 means. True temperature averages of COW0–24 and COW6–6 annual averages closely match and are on average higher by 0.13 °C than the true temperature averages obtained by COWND. As can be seen from Fig. 16, the highest annual temperature averages are obtained by extrema means of COWND method while the lowest annual temperature averages are obtained by extrema means of COW6–6 method.
Fig. 14

Annual average of daily maxima of COW0–24, COW6–6, and COWND methods for period 1987 to 2014, Buttonville (ON). Tx24A, Tx66A, and TxNDA correspond to annual maximum temperatures obtained using COW0–24, COW6–6, and COWND respectively

Fig. 15

Annual average of minima of COW0–24, COW6–6, and COWND methods for period 1987 to 2014, Buttonville (ON). Tn24A, Tn66A, and TnNDA correspond to annual minimum temperatures obtained using COW0–24, COW6–6, and COWND respectively

Fig. 16

Annual average of daily extrema averages and true temperature averages of COW0–24, COW6–6, and COWND methods for period 1987 to 2014, Buttonville (ON). Txn24A, Txn66A, and TxnNDA correspond to annual averages of extrema obtained using COW0–24, COW6–6, and COWND respectively. Ta24A, Ta66A, and TaNDA correspond to annual true temperature averages obtained using COW0–24, COW6–6, and COWND respectively

Fig. 17

Diurnal temperature range of COW0–24, COW6–6, and COWND methods for period 1987 to 2014, Buttonville (ON). TR24A, TR66A, and TRNDA correspond to annual temperature ranges of COW0–24, COW6–6, and COWND methods respectively

Finally, the annual averages of daily temperature ranges of COWND are on average lower by ~0.97 °C than the annual averages of daily temperature range determined by COW0–24 and by ~1.51 °C in comparison to COW6–6 method (Fig. 17). The systematic nature of the observed differences and their magnitude demonstrate that the observing window selection affects the determination of daily extrema.

4 Conclusions

Position of the observing window affects the determination of daily extrema and thus potentially biases climatological assessments. Incorrect characterization of daily air temperature extrema affects diurnal minima more frequently than the maxima. Annual averages of minima determined by COWND for the location of Buttonville and time period from 1986 to 2014 are warmer approximately 0.64 °C than the annual averages of minima determined by COW0–24 and COW6–6.

The COWND framework is proposed for the improvement of the quantification of diurnal distribution of air temperature extrema. Night and Day (Local Standard Time) Climatological Observing Window COWND detects true daily temperature extrema more reliably than climatological observing window COW0–24 and COW6–6. COWND method errs occasionally in absence of a sinusoidal diurnality in daily temperature cycle. Loss of the oscillatory feature in daily temperature variation seems to be symptomatic of unusual weather variations and as such can be indicative of local scale atmospheric phenomena. Results of this preliminary study provide a cautionary note on the determination of daily extrema when assessing the global warming based on extrema means and its sensitivity to the particular COW used. If climate change assessment is based on means of extrema, annual averages of COW0–24 method are systematically lower than the annual averages obtained by COWND method with the differences ranging between 0.07 and 0.25 °C.

Footnotes

  1. 1.

    This period ends at the time of subsequent sunrise plus 1 h, to account for thermal inertia of the atmosphere.

  2. 2.

    Solar declination varies from −23° 26′ (northern hemisphere summer) to +23° 26′ (northern hemisphere winter).

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Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.Department of Physical and Environmental SciencesUniversity of Toronto ScarboroughScarboroughCanada

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