The total mass of the atmosphere

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Abstract
Accurate but approximate formulae for determining the mass of the atmosphere in terms of the surface pressure ps are derived and applied to globally analyzed data from the European Centre for Medium‐Range Weather Forecasts (ECMWF) for 1985 through 1993. The formulae take into account effects of the shape of the Earth and variations in gravity with latitude and height. Variations in total mass occur because of changes in the water vapor loading of the atmosphere. Independent computations are made of the surface pressure due to water vapor pw, which is proportional to the precipitable water, using the ECMWF analyses of specific humidity. Spurious trends in both the mass of dry air and the atmospheric moisture are found to arise from changes in the analysis system at ECMWF, confounding attempts to seek real trends associated with climate change. For the recent 4‐year period 1990 to 1993 the mean annual ps was 984.76 mbar with a maximum in July of 984.98 mbar and a minimum in December of 984.61 mbar which correspond to a total mean mass of the atmosphere of 5.1441×1018 kg with a range of 1.93×1015 kg throughout the year associated with changes in water vapor in the atmosphere. The global mean pw for 1985–1993 is 2.58 mbar, but values are 5 to 10% lower after mid‐1992. Using the Special Sensor Microwave Imager data to make adjustments, the best estimate of the annual global pw is 2.4 mbar, corresponding to ∼2.5 cm of precipitable water. The total atmospheric moisture as given by pw varies with an annual cycle range of 0.36 mbar, a maximum in July, and a minimum in December. Thus the mean mass of water vapor is 1.25×1016 kg and the dry air mass is 5.132×1018 kg, corresponding to a mean surface pressure of 982.4 mbar. Overall uncertainties are ∼0.1 mbar or 0.5×1015 kg in total mass and about double those values for atmospheric moisture content. As well as the global means, hemispheric mean values and meridional profiles of ps and pw are presented for the mean annual cycle and as latitude‐time series to show the interannual and longer‐term variability.