Uncertainties in estimates of the mean vertical velocity from MST radar observations


  • G. D. Nastrom,

  • K. S. Gage,

  • W. L. Ecklund


Mean values of the vertical velocity based on time series of clear-air Doppler radar observations are subject to uncertainties due to several factors. This paper examines the statistical uncertainties due to estimating the population means using only finite periods of record and the uncertainties that are introduced by systematic gaps in the series of observations. The statistical uncertainty, the standard error of the mean, depends on the variance of the data and on the effective sample size. The largest change in the variance of vertical velocity is about a factor of 3 and is seen between clear and cloudy sky conditions. Very little change in the effective sample size is seen under any conditions. The averaging time required to estimate the mean with a standard error of the mean of 2 cm/s is found to be about 6 hours under typical conditions at Flatland. The uncertainty of the mean due to systematic gaps in the data increases with the length of the gaps, even though the total observation period remains constant. The root-mean-square value of this uncertainty is about 2 cm/s; about the size of the standard error of the mean and about half as large as typical expected subsynoptic scale motions. These results suggest that future sampling programs should be designed to eliminate systematic gaps in the data.