Statistical uncertainty of 1967-2005 thermospheric density trends derived from orbital drag

Estimation of trend uncertainties is an essential element of long-term climate change study. Standard error analysis assumes independent (i.e., uncorrelated) random deviations of the data around the trend, a requirement that is rarely fulfilled by upper atmospheric time series; consequently, uncertainty estimates are typically unrealistically small. To obtain internally consistent estimates of linear trends and trend uncertainties in thermospheric density data, we account for correlated noise by incorporating autoregressive (AR) models of varying order into our error analysis. We apply our method to daily, monthly, and yearly averages of thermospheric mass density data derived from orbital drag, after subtracting out solar and seasonal effects. The resulting trend uncertainty estimates are mutually congruent among the three temporal cadences; in contrast, assuming independent random error produces uncertainty estimates that differ considerably among the daily, monthly, and yearly cases. At 400 km, we estimate the 1967-2005 density trend to be -1.94% per decade, with a 95% confidence interval of [-3.30, -0.59] % per decade. The AR model residuals are consistent with the assumption of independent, normally distributed random errors with uniform variance. Our methodology permits realistic analytical estimates of trend uncertainties for AR processes of arbitrary order, superseding the use of Monte Carlo simulations, and the approach is applicable to trend analysis of other upper atmospheric parameters.