Modelling the true monthly mean temperature from continuous measurements over global land

The true monthly mean temperature is defined as the integral of the continuous temperature measurements in a month (Td0), which is apparently different from the average (Td1) of the monthly averaged maximum (Tmax) and minimum (Tmin) temperatures. Unfortunately, Td1 instead of Td0 has been widely used as the monthly mean temperature, not only as an input parameter for various models in ecology, climatology and hydrology but also as an effective factor for climate change studies. It has already been demonstrated in previous researches that the bias between Td0 and Td1 (Tbias = Td1 − Td0) cannot be ignored; in some places, it could even be very large. Therefore, it is with great urgency that Td0 should replace Td1 to eliminate the impact of the imperfect monthly mean temperature on related researches. However, Td0 cannot be obtained directly due to the lack of the historical observations of land surface air temperature (Ta) at a higher temporal resolution, e.g. hourly observations. In this study, a multiple linear regression (MLR)-based method is created to calculate Td0 with the predictors of daylength, diurnal temperature range (DTR = Tmax − Tmin) and Td1. The MLR method performs very well, with a mean R2 of 0.61 over global land and 0.76 in arid or semi-arid areas. It can be used to improve studies on regional climate change and evaluations of climate model simulations.