Calculating average daily temperature

Did you know there are different ways to calculate the average daily temperature? A new PACE Turf update discusses this. In that update, I looked at the daily minimum and maximum method, and compared it to the average of hourly measurements method. I checked that for Maui, Whistler, and Tokyo.

The daily average from hourly measurements is calculated as:

$$ T_{\text{avg}} = \frac{\sum_{h=1}^{24} T_h}{24} $$

where $T_h$ is the temperature at hour $h$.

The common method using daily minimum and maximum temperature is calculated as:

$$ T_{\text{avg}} = \frac{T_{\text{min}} + T_{\text{max}}}{2} $$

The World Meteorological Organization¹ notes that:

There are many methods for calculating an average daily temperature … The best statistical approximation of an average is based on the integration of continuous observations over a period of time; the higher the frequency of observations, the more accurate the average. Practical considerations generally preclude the calculation of a daily average from a large number of observations evenly distributed over a 24-hour period because many observing sites do not measure an element continuously. For comparative purposes, a standard processing methodology is desirable for all stations worldwide, with as many stations as possible.

All ordinary climatological stations observe a daily maximum and minimum temperature. Hence, the recommended methodology for calculating average daily temperature is to take the mean of the daily maximum and minimum temperatures. Even though this method is not the best statistical approximation, its consistent use satisfies the comparative purpose of normals.

When I have checked this, the $\frac{T_{\text{min}} + T_{\text{max}}}{2}$ method on average gives a slightly higher average temperature, but practically it is the same.

Of course, there are individual days for which the methods may differ by more than 1 ˚C, or about 2 ˚F, but the overall relationship is close to 1:1.