# Estimating daily mean temperature

There are different ways to calculate daily mean temperature (DMT) at a station from data collected at different times of the day. In many countries, including the US, the approach is to average the minimum and maximum temperature observed, although this may be the minimum and maximum hourly readings or the actual minimum and maximum obtained from minimum and maximum thermometers or other devices (see WMO, 2008, for details about temperature measurements). In other countries a linear combination of measurements taken at different times of the day is used, sometimes including the minimum and maximum as well. For example, the Nordic countries each have a different linear combination of data, depending on the frequency of recorded observations (Nordli et al., 1996, Appendix II), while Germany employs yet another linear combination of data. When using temperature data for climatological purposes, such as calculating the uncertainty of estimates of global mean temperature, it is important to take into account the bias and variability of the method used to calculate DMT.

In order to assess the bias and variability of various approaches to estimating DMT, we can look at data collected at different frequencies. The finest resolution available is minute data, which we have available for a station in Sweden (although not collected at the standard 2m altitude above ground) and for several North American stations. Data sets will be made available at the course page.

Questions of interest include
• How well does the average of daily min and daily max approximate the daily mean temperature?
• What is the effect on bias and variability of different observational schemes (such as hourly, 3-hourly, 6-hourly etc.)
• Does daily min and daily max add value to measures of daily mean temperature, taken several times a day (such as the Swedish Ekholm-Modén formula as described in Nordli et al, 1996, Appendix II)
• Does it matter much when using the average of min and max whether you use actual min and max or min and max of hourly readings?
• If daily temperatures were described by a sine curve, the average daily temperature would indeed be the average of min and max. How well is daily temperature described by a sine curve?
The groups need to decide on one or two questions to answer, develop a strategy for answering them, and give a 30 minute oral presentation of their results to the class. The 30 minutes include questions, so you need to leave enough time for that. You can use any presentation software you like (including the white boards). The due date depends to some extent on class progress, but I am aiming at finishing this project no later than 23 September.

Visby minute data for January (column 14 is surface temperature)
Visby minute data for July

Minute data from Red Oak, TN

NCDC five minute temperature data page

Here are the Ekholm-Modén coefficients.