Non-calendar-day observations of 24-h minimum and maximum air temperatures can be considerably different from calendar-day or midnight observations. This paper examines the influence of time-of-observation on 24-h temperature observations. Diurnal minimum and maximum temperatures measured at common observation times (0700 and 1700 LST) are compared with minimum and maximum temperatures measured at midnight. The principal methods make use of hourly temperature observations, sampled over 24-h moving windows, to approximate once-daily observations. Surprisingly, non-calendar-day observations are similar to calendar-day observations on a majority of days. When differences do occur, however, they can be large and of either sign. Differences between 1700 LST observations and midnight observations are typically smaller than those arising from 0700 LST observations. Daily differences can be grouped by temperature extrema recorded on the incorrect day (a bookkeeping problem) or temperature extrema recorded on two successive days (bias). Bias scenarios arise when very cold mornings or very warm afternoons influence the temperature measured on successive days. Locations or seasons with the least day-to-day temperature variability often display the least time-of-daily-observation influence on temperature. Determining those days on which large departures and biases are likely to occur is possible by measuring day-to-day temperature persistence. First-order differences of daily time series may be used explicitly in adjustment procedures for morning observations of maximum temperature. Otherwise, first-order differences may be used to determine those days on which large observation-time differences are likely or those days on which observation-time dependencies are trivial.
Compilations of historical daily average temperature in the United States are primarily derived from the Cooperative Station Network of the National Weather Service (Easterling et al. 1999; Reek et al. 1992). Because of the volunteer nature of their observers, cooperative weather stations generally record maximum and minimum air temperatures once daily over a 24-h “observational” day rather than a calendar day. An observational day is a 24-h period ending at any time other than midnight and is usually the time most convenient for the volunteer. Different daily observation times may introduce bias in daily temperature statistics, such as extremes, averages, and ranges of air temperature. This condition, called time-of-observation bias (TOB), is defined as the difference between observational-day temperatures and calendar-day temperatures. Temperature differences due to non-calendar-day observations can be further separated into bookkeeping problems (extrema recorded on the wrong day) and biases.
Problems associated with daily observation times have been well documented for monthly minimum, maximum, and mean temperatures (Mitchell 1958; Baker 1975; Schaal and Dale 1977; Blackburn 1983). The sensitivity of derived climatic parameters and measures to daily observation times has also been recognized. For example, Winkler et al. (1981) found monthly urban–rural temperature differences in Minneapolis–St. Paul, Minnesota, were influenced by observation time differences. Schaal and Dale (1977) reported monthly growing degree-days, heating degree-days, and cooling degree-days were biased by observation time differences. DeGaetano and Knapp (1993) adjusted weekly growing degree-days to account for observation-time differences. Methods for adjusting monthly maximum and minimum temperatures have been developed and employed as standard corrections to historical records such as the U.S. Historical Climatology Network (Karl et al. 1986; DeGaetano 2000).
Similar adjustments, however, are not yet available for the Daily Historical Climatology Network (Easterling et al. 1999). Moreover, comprehensive analyses of the magnitudes, seasonal variability, and regional patterns of time-of-observation bias for daily temperature data are not currently available. In this study, differences between non-calendar-day observations of minimum and maximum temperatures and calendar-day observation are examined. Differences are classified as observation-time (OT)-dependent departures or biases. Departures are bookkeeping problems that arise from recording diurnal temperature extrema on the incorrect day. Biases occur when the observational day overlaps portions of extrema periods from two diurnal cycles. This scenario can lead to recording very cold or warm temperatures on multiple days. A first-order difference method is developed for examining the occurrence of large observation-time-dependent differences. Estimates of OT departures and biases can be used as reference points for applied research and climatic studies concerning daily temperature data.
Examination of the observation-time metadata for stations in the Daily Historical Climatology Network (HCN/D) found the most common observation times from 1948 to 1997 are 0700 or 0800 local standard time (LST) and 1700 or 1800 LST (Fig. 1). Preferential daily observation schedules for stations in the HCN/D have not been static through time. Morning schedules, for example, accounted for more than 45% of all observation times in the 1990s, but only slightly more than 20% of observation times in the 1950s. Nearly 55% of the 1950s observation times were in the evening; by the 1990s evening schedules accounted for only 30% of observation times. Midnight schedules account for less than 10% of the observation times throughout the study period. It is somewhat apparent that over time the preferential observation times have become less homogeneous across the network and have shifted, in time, away from “calendar” day observation times (i.e., from evening to morning). Problems associated with changing observation times on daily minimum and maximum temperatures will be quantified in the following sections.
To estimate departures or biases associated with non-calendar-day observation times, a daily cycle of hourly temperatures is needed. Hourly air temperatures are derived from the Solar and Meteorological Surface Observation Network (SAMSON) 1961–1990 (NCDC 1993) and Hourly United States Weather Observations 1990–1995 (NCDC 1997). Here, these products are combined to create a network of 209 stations with continuous records over the period 1961–95 [hereinafter referred to as SAMSON; Fig. 2]. SAMSON, primarily composed of National Weather Service first-order stations, provides a readily accessible, quality assured, dataset for high-temporal-resolution climatic analyses. Observation-time-dependent measures derived from SAMSON, albeit at lower spatial resolution, can be used to estimate differences at nearby HCN/D locations. Six locations were chosen, a posteriori, to display typical patterns of departures and biases (Table 1). These locations were chosen pseudorandomly based on their representativeness over large areas (e.g., Columbia) or based on their unique signatures (e.g., Seattle). No grouping or spatial aggregation of station data was performed in these analyses. Although these six locations represent much of the spatial component of observation-time departures and biases, for any other location measures should be examined specifically.
Daily observation-time-dependent temperature differences
Using hourly air temperature measurements from a subset of SAMSON stations, observation time differences are estimated from 24-h moving-window calculations of diurnal temperature extrema (i.e., minimum and maximum temperatures). For each calendar day, differences are calculated between the midnight observations and each of the 23 hourly observations. Although differences can be computed for all observation times, two non-midnight observation times, 0700 and 1700 LST (hereinafter morning and evening), are more common than all other observation times in the U.S. HCN/D (see Fig. 1). Results presented for these observation times may be extended to other morning or evening observation times.
Monthly distributions of observation-time-dependent temperature differences
For each day over the 35-yr time period, temperature differences from midnight observations are calculated for morning and evening observations of minimum and maximum temperatures. For morning observations of minimum temperature and evening observations of maximum temperature, differences are separated into departures or biases. For other observations, differences are defined only as departures. Temperature biases arise for those observation times that record, on two consecutive days, extreme minimum or maximum temperatures that occur on a single morning or afternoon. For example, a 0700 LST observation schedule will measure, depending on latitude and time of year, minimum temperatures from the calendar day as well as the previous day. Air temperatures during an extremely cold morning on the previous day may be recorded on consecutive days. Similar arguments can be made for evening observations of daily maximum temperature. In this analysis, biases are identified when morning (afternoon) temperatures on the previous day are cooler (warmer) than those on the calendar day and observation-time differences are exclusively negative for minimum temperature bias or positive for maximum temperature bias.
Daily differences are aggregated by month and plotted as a time series of box plots (Figs. 3–10). Daily differences were computed for 35 years and approximately 31 days (i.e., N ≤ 1085). Monthly distributions were composed of either departures or biases, thus, reducing N for most plots (see Table 2 for frequency of bias events). Values plotted are the distribution quartiles, the inner fences, and the differences falling outside of the inner fences (plotted as circles). The inner fences are defined as less than or greater than the 25th or 75th percentiles by 1½ times the interquartile range (Wilks 1995). With the exception of morning observations of maximum temperature and the two bias scenarios, the interquartile range is often “collapsed” at zero (plotted as long dashes) indicating that at least 50% of the differences are zero for those observation times.
Morning observations of minimum temperature
For Columbia, daily departures for morning observations of minimum temperature are as large as ±20°C during winter and less than ±10°C during summer (Fig. 3a). Less than 50% of wintertime departures of minimum temperature are identically zero while more than 70% of summertime departures are zero (cf. interquartile range). Monthly distributions of OT biases for morning observations of minimum temperature in Columbia also follow a seasonal cycle with the largest extreme biases (−15° to −20°C) and the largest mean biases (−4°C) occurring during the winter (Fig. 4a). Relative to Columbia, wintertime biases are smaller for Brownsville but larger for Caribou (not shown—mean bias >|−5°C|, maximum bias >|−20°C|, and interquartile range >5°C). However, the frequency of bias events during the winter is similar (20%–29%) for these locations (Table 2). Summertime biases are typically small (<|−5°C|) and infrequent (≤5%) for all locations.
Daily departures and biases for morning observations of minimum temperature in San Diego are typically less than ±5°C regardless of season (Figs. 5a, 6a). Fewer than 10% of days are biased for all months (Table 2). Wintertime departures and biases greater than 5°C are observed for Seattle (Figs. 7a, 8a) while differences as large as ±10°C are observed for Miami (Figs. 9a, 10a). The frequency of bias events in months November through March is between 14% and 20% for Seattle and 14% and 26% for Miami. For both Seattle and Miami, average biases for morning observations of minimum temperature are approximately −1°C from May through September. Minimum temperature departures for the same period may be as large as ±5°C.
Morning observations of maximum temperature
Morning observations of daily maximum temperature are different from calendar-day observations by as much as ±15°C in Seattle, San Diego, and Miami (Figs. 5b, 7b, 9b). In Seattle differences are greater during the summer when day-to-day temperature variability is greater. For Miami, differences are greater during the winter. For locations such as Columbia, Brownsville, and Caribou (Fig. 3b), extreme OT differences for morning observations of maximum temperature are larger than ±20°C during the winter but may be less than ±10°C during the summer (especially for southern locations such as Brownsville—not shown). For all locations, differences for morning observations of maximum temperature are nonzero on more than 50% of the days and the interquartile range is greater than zero for all months. Differences for morning observations of maximum temperature illustrate the bookkeeping problem associated with non-calendar-day observations.
Evening observations of minimum temperature
Departures for evening observations of minimum temperature at Seattle are ±5°C during the winter but are one-half that range during the summer (Fig. 7c). For Miami and Brownsville, departures are between −5° and +15°C during winter months but less than ±5°C during summer months (Fig. 9c). For San Diego, daily departures are generally less than 5°C year round (Fig. 5d). In general, Columbia and Caribou display larger departures during the winter than during the summer, with more than 50% of the minimum temperature departures greater than 0°C during the winter (Fig. 3c).
Evening observations of maximum temperature
Seattle has larger positive departures for evening observation of maximum temperature during the summer (+10°C) than during the winter (±5°C, Fig. 7d). During the summer, when the potential for daytime heating is larger, the potential for large differences for evening observations of maximum temperature is also larger but depends on the day-to-day cloud cover variability. Biases of evening observations of maximum temperature follow a cycle of more frequent (25% vs 9%, Table 2) and larger extreme differences during the summer than during winter (Fig. 8b). For San Diego, departures for evening observations of maximum temperature are generally less than 5°C (Fig. 5d). Zero departures account for more than 50% of the days for any month. Biases for evening observations of maximum temperature in San Diego are less than 5°C, average only 1°C (Fig. 6b), and account for fewer than 10% of days for any month.
For evening observations of maximum temperature in Miami and Brownsville, departures are rarely negative but may be as large as 15°C during winter (Fig. 9d). Seasonal differences are not as extreme in Miami as in Brownsville and the percentage of zero departures during July and August may as large as 97% in Miami. Biases for these locations are similar to departures in seasonal cycle and magnitude (Fig. 10b), but occur on fewer than 5% of days from April through November (Table 2). For Columbia and Caribou, maximum temperature bias is, on average, greater than 2°C for all months but may be as large as 10°C (Fig. 4b). For these locations, the frequency of bias events for evening observations of maximum temperature is greater than 10% for all months.
Based on the greater percentage of zero departures and smaller overall magnitude of departures, evening observations are better suited for approximating calendar-day temperatures. Evening observations and midnight observations contain roughly 75% commensurate hours and both daily maximum and minimum temperatures typically occur before evening observations. For evening observation times, departures decrease as the length of overlap between observational and calendar days increase. Though the total number of days affected by non-calendar-day observation times may be small, these findings suggest daily recording stations should practice evening observations as a secondary standard to midnight observations.
Substitution of non-calendar-day minimum and maximum temperatures
Since daily observation-time-dependent temperature differences are zero for many scenarios, substituting morning or evening observations for midnight observations may be more appropriate than applying complicated corrections (i.e., simply using the daily data as published without standardization for observation time). The root-mean-square error (rmse) between calendar-day and non-calendar-day temperature extrema is computed to illustrate the substitution problem (Willmott 1981). For morning observations of minimum temperature and evening observations of maximum temperature, days were classified as either bias scenarios or departure scenarios. For other scenarios, days were classified as departure days. Root-mean-square differences are calculated when non-calendar-day observations are used to approximate calendar-day observations, placing the observation-time problem in the context of model validation. This does not imply that non-calendar-day observations are themselves erroneous, but illustrates the potential problems due to nonstandard observation times.
The seasonal variation of rmse at Columbia, Caribou, and Brownsville is approximately 1°C for evening departure scenarios but nearly 3°C for morning departure scenarios with larger rmse usually occurring during the winter (Fig. 11). San Diego consistently displays the lowest rmse of all locations and displays the smallest seasonal variation. Seasonal differences in rmse are more pronounced for bias scenarios of minimum temperature (Fig. 12a). From April to August, rmse for morning and evening observations of minimum temperature is less than 2°C for all locations (Figs. 11a,c). Unlike most other locations, rmse for maximum temperature in Seattle is larger during summer than during winter (Figs. 11b,d, 12b). Evening observations generally lead to lower rmse than morning observations when substituting for midnight observations, especially when considering differences caused by bias scenarios [for minimum temperature compare Figs. 11a and 12a (morning) with Fig. 11c (evening); for maximum temperature compare Fig. 11b (morning) with Figs. 11d and 12b (evening)].
Non-calendar-day temperature extrema overestimate or underestimate calendar-day temperature extrema under most scenarios (see Figs. 3–10). Thus, unsystematic differences account for a majority of rmse departure scenarios (greater than 75% for maximum temperature and greater than 80% for minimum temperature, Fig. 13). Unsystematic mean-square-error (MSEu) is the component of total error that cannot be accounted for by linear regression. Therefore, (MSEu/MSE) × 100 is the percent of random differences in the relationship between non-calendar-day observations and calendar-day observations. Less than 50% of the bias scenarios for minimum and maximum temperature are unsystematic or random (Fig. 14). It may be possible to model the relationship between non-calendar-day observations for the more extreme bias cases. With few exceptions, geographically unique relationships were not uncovered in the “substitution” analyses.
A comparative examination of monthly TOB for the same data agrees with the findings of Schaal and Dale (1977) and Karl et al. (1986). Monthly averages of maximum and minimum temperature are computed from midnight observations and from non-calendar-day observations (i.e., 0700 and 1700 LST). Average monthly TOB is less than daily differences (≤|1°C|—not shown). Rmse plots of monthly TOB show that systematic error dominates the rmse for evening observations at Columbia, for example, while TOB for morning observations is somewhat more random (Fig. 15). Monthly TOB displays different error components than daily departures and daily biases (i.e., lower random error). Since there is much less potential for introducing error by adjustment of monthly data, a priori TOB adjustments should be performed on monthly temperatures (e.g., Karl et al. 1986).
Though exceptionally large daily time-of-observation differences are observed (±20°C), performing unnecessary (and inaccurate) adjustments for a majority of days with negligible observation-time-dependent temperature differences may be avoided. Adjustments may be applied with a priori knowledge of those days on which large differences are likely to occur without modifying those daily temperatures that are relatively accurate with respect to calendar-day observations. The ability to make such adjustments relies on the day-to-day variability of maximum and minimum temperatures as well as accurate observation-time metadata (DeGaetano 1999, 2000). The following section presents a method for identifying those days on which large differences are likely to occur.
First-order differences related to observation-time-dependent temperature differences
First-order differences calculated from observational-day time series reveal whether cold days preceding warm days or vice versa leads to large observation-time-dependent temperature differences. First-order differences are calculated by subtracting the observational-day (i + 1) temperature extrema from the observational-day (i) temperature extrema. Observational-day time series, used in these analyses, mimic the information a researcher might have when faced with a time series of non-calendar-day minimum and maximum temperatures that require standardization, that is, how to extract observation-time-dependent information from a series of first-order differences calculated from observational-day time series. Since adjacent observational-day time periods span the calendar-day time period they often provide limits for extremes of diurnal temperature. For morning observations of minimum temperature and evening observations of maximum temperature, first-order differences are calculated based on whether calendar-day temperature differences are classified as biases or departures.
Geographic variation in the association between first-order differences and observation-time-dependent differences is caused by regional variation in the persistence of diurnal temperature extrema. First-order differences and OT differences can be as large as ±20°C in Caribou (Fig. 16) but are typically less than ±10°C in San Diego (Fig. 17). Larger first-order differences, however, are not always associated with larger OT differences. Despite regional differences in the magnitude of diurnal persistence, some generalizations can be drawn from the correlation between first-order differences and OT differences. Since these correlations display broad regionality, two locations, Caribou and San Diego, illustrate the range of relationships.
Morning observations of minimum temperature
When cooler days precede warmer days (i.e., ODi < ODi+1), observational-day minimum temperatures are often cooler than calendar-day minimum temperatures and OT differences are often less than zero (Figs. 16a, 17a). Differences are always less than or equal to zero when warmer minimum temperatures precede cooler minimum temperatures. Correlations between negative first-order differences and departures for morning (0700 LST) observations of minimum temperature are weak for most locations (r2 ≤ 0.37, Table 3). Yet, when the observational-day (i) minimum temperature is less than the observational-day (i + 1) minimum temperature by more than 10°C, the first-order difference provide a good approximation for departures of morning observations. Biases for morning observations of minimum temperature are, by definition, associated with negative OT differences (Figs. 18, 19). Correlations between first-order differences and bias events are strong (0.70 ≤ r2 ≤ 0.82) at most locations except San Diego (r2 = 0.53, Fig. 19), suggesting some potential for use in temperature adjustments.
When warmer days precede cooler days (i.e., ODi > ODi+1), non-calendar-day minimum temperature recordings often overestimate calendar-day minimum temperatures. Differences for morning observations of minimum temperature are bound by first-order differences (i.e., ≤mini − mini+1,). The correlation between positive first-order differences and departures for morning (0700 LST) observations of minimum temperature are slightly stronger than correlations for negative and for combined first-order differences (0.59 ≤ r2 ≤ 0.86, Table 3).
Morning observations of maximum temperature
Morning observations of maximum temperature may record the maximum temperature from the previous calendar day, providing a good illustration of the bookkeeping problem for both Caribou (Fig. 16b) and San Diego (Fig. 17b). Cooler days preceding warmer days leads to negative observation-time departures but warmer days preceding cooler days, leads to positive departures. In either case, the difference between maximum temperature measured on day i and that measured on day i + 1 is approximately the magnitude of the difference between maximum temperature measured on day i and the unknown calendar-day observation of maximum temperature. For morning (0700 LST) observations of maximum temperature, combined first-order differences are strongly related to temperature departures (0.97 ≤ r2, Table 3). A first-order difference series may provide a reasonable basis for adjustment of morning observations of maximum temperature by adding the first-order difference to the observation or by creating a regression equation from nearby hourly weather stations.
Evening observations of minimum temperature
Departures for evening observations of minimum temperature are also bound by the magnitude of first-order differences (Figs. 16c, 17c). Evening observations usually resolve minimum temperature from the morning of the calendar day. Yet, minimum temperatures occurring on the calendar day, but after the observation time, lead to positive OT departures for the calendar day. If that evening's low temperature maintained to be the minimum temperature for the following calendar day, a bias scenario for the following calendar day would result. Since temperatures typically continue to decrease during the evening and early morning, this scenario is not common. Correlations between positive first-order differences and departures for evening (1700 LST) observations of minimum temperature are modest but stronger than those for negative and combined first-order differences (0.66 ≤ r2 ≤ 0.78, Table 3). Departures for evening observations of minimum temperature, however, are poorly related to negative first-order differences (r2 ≤ 0.16).
Evening observations of maximum temperature
Since evening observations may resolve maximum temperature from either the calendar day (before observation time) or the previous calendar day (after observation time) there are two extrema periods from which maximum temperature may be recorded. When cooler days precede warmer days (i.e., ODi < ODi+1) for maximum temperature, departures are always greater than maxi − maxi+1 but seldom greater than zero, since temperatures do not typically increase after 1700 LST (Figs. 16d, 17d). Correlations between negative first-order differences and departures for evening observations of maximum temperature are weak (r2 ≤ 0.36, Table 3). Although positive first-order differences for maximum temperature are always associated with positive departures, correlations are not strong (0.16 ≤ r2 ≤ 0.51). Biases for evening observations of maximum temperature are associated with positive OT differences (Figs. 17, 18). Correlations with first-order differences (0.40 ≤ r2 ≤ 0.64) are modest but indicate more predictive capacity than correlations between departures and combined first-order differences (0.12 ≤ r2 ≤ 0.46).
Discussion and summary
Morning and evening observations of 24-h minimum and maximum temperatures are estimated from hourly temperatures records and compared with calendar-day (midnight) observations at 209 locations across the contiguous United States. Differences between non-calendar-day temperatures and calendar-day temperatures can be categorized into problems of extrema recorded on the incorrect day (bookkeeping) or problems of extrema recorded twice (bias). Large positive or negative differences may occur on any day depending on seasonal weather patterns. Moreover, near-zero differences may occur on any day and more often than 70% of days for any month. For most locations, observation-time-dependent temperature differences are larger during winter than during summer. Although it appears temperature differences are too variable from day to day for systematic adjustment, knowledge of those days on which large differences are likely to occur may be valuable for cursory adjustment.
Day-to-day temperature differences hold some potential for estimating observation-time-dependent differences. Findings for morning observations of maximum temperature suggest first-order differences may be used explicitly in adjustment procedures to correct a bookkeeping problem. First-order differences may be used to determine those days on which large temperature differences are likely or those days on which differences are minimal. Occurrences of large observation-time differences, however, are not always associated with large first-order differences. For evening observations of minimum temperature in Caribou, for instance, temperature differences are approximately zero while first-order differences are −15°C or greater and the coefficient of determination is 0.14. However, for positive first-order differences, the coefficient of determination is 0.78. By separating the bias scenarios from the bookkeeping scenarios for morning observations of minimum temperature and evening observations of maximum temperature and by identifying whether the previous day was colder or warmer, differences from calendar-day extrema may be more predictable.
Daily maximum and minimum temperatures are often used to derive climatic parameters such as growing-season length, heating and cooling degree-days, and the variability of the annual temperature cycle (Robinson et al. 1995). Though TOB adjustment is primarily a temporal homogeneity issue, it is also an important consideration for spatial analyses. A single station containing an observation time change may display an artificial step change in its historical temperature record. Two adjacent stations with different observation times also may have disparate temperature records simply due to observation time differences. The consequence of such a scenario may include inaccurate interpolation estimates, spatial averages, or other spatially derived measures. The cumulative spatial–temporal effect of daily TOB may substantially degrade fundamental measures of climatic change and variability. Because a posteriori adjustment for daily TOB is difficult, implementing a standard observation time (preferably evening observations) is in the best interest for monitoring climatic change and variability.
The helpful comments of Scott M. Robeson (Indiana University) and two anonymous reviewers are gratefully appreciated.
Corresponding author address: Dr. Michael J. Janis, Southeast Regional Climate Center, South Carolina Department of Natural Resources, 2221 Devine St., Suite 222, Columbia, SC 29205. firstname.lastname@example.org