What is monthly mean land surface air temperature?

Land surface air temperature is one of the fundamental variables in weather and climate observations, modeling, and applications. Its monthly mean has been computed as the average of daily maximum and minimum temperatures [Jones et al., 1999]. This is different from the true monthly mean temperature, which is defined as the integral of the continuous temperature measurements in a month divided by the integration period and can be very accurately represented using hourly data, as has long been recognized [e.g., Brooks, 1921]. We argue, from scientific, technological, and historical perspectives, that it is time to compute the true monthly mean using hourly data for the national and international climate data record.