Correct Temporal and Spatial Averaging of Atmospheric and Surface Variables for Weather and Climate Studies

Most weather and climate studies include the temporal and/or spatial averaging of atmospheric and surface variables from observations, reanalysis, and numerical models. While the correct temporal averaging rules for several atmospheric variables (temperature, mixing ratio, and wind vector) are well recognized, the use of incorrect temporal and spatial averaging of some variables remains widespread in the literature and at data and modeling centers. Here, we overview and expand the rules for the correct averaging of near-surface atmospheric variables (e.g., air temperature, dewpoint temperature, web-bulb temperature, specific humidity, relatively humidity) and surface variables (e.g., skin temperature, surface albedo). Using hourly 0.25° gridded data from fifth generation European Centre for Medium-Range Weather Forecasts atmospheric reanalysis (ERA5), we find that the correct averaging can have a large effect on some monthly and regional mean quantities (e.g., 5.73 K difference between correct and default averages of dewpoint temperatures over global land for July 2024). This effect remains large for seasonal differences, but it becomes smaller for the trends.