Uncertainties in mesopause temperature trend over Fort Collins, Colorado (41°N, 105°W), using the bootstrap Monte Carlo method

Abstract

[1] Two methods, based on different assumptions, have been investigated for computing the uncertainty in the trend of 960 mesopause region temperature profiles taken over 20 years. In addition to the trend, the fitting model includes annual and semiannual variations, a solar effect, and an episodic term that can be associated with the Mount Pinatubo volcanic eruption. In our standard procedure we assume that the unknown uncertainties of each measurement, and thus the weights of the observations, are constant with time and are determined by assuming that we have a good model. In addition we investigate including second derivatives along with first derivatives of the Hessian matrix. In the Monte Carlo bootstrap method one resamples the data with replacement to obtain new data sets which are fit to the model and yield a distribution of fitting parameters. The standard deviation of the distribution for a parameter is taken to be the uncertainty in the parameter. A possible assumption to justify this method is that the data are “independent and identically distributed.” Although we have not been able to justify the assumptions of either method, the two methods support each other since they give essentially the same results.