Technical Note: Trend estimation from irregularly sampled, correlated data Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Karlsruhe, Germany
Received: 16 November 2009 – Published in Atmos. Chem. Phys. Discuss.: 21 December 2009 Abstract. Estimation of a trend of an atmospheric state variable is usually performed by
fitting a linear regression line to a set of data of this variable sampled at
different times. Often these data are irregularly sampled in space and time
and clustered in a sense that error correlations among data points cause a
similar error of data points sampled at similar times. Since this can affect
the estimated trend, we suggest to take the full error covariance matrix of
the data into account. Superimposed periodic variations can be jointly
fitted in a straightforward manner, even if the shape of the periodic
function is not known. Global data sets, particularly satellite data, can
form the basis to estimate the error correlations.
State-dependent amplitudes of superimposed periodic corrections result in
a non-linear optimization problem which is solved iteratively.
Revised: 12 July 2010 – Accepted: 12 July 2010 – Published: 22 July 2010
Citation: von Clarmann, T., Stiller, G., Grabowski, U., Eckert, E., and Orphal, J.: Technical Note: Trend estimation from irregularly sampled, correlated data, Atmos. Chem. Phys., 10, 6737-6747, doi:10.5194/acp-10-6737-2010, 2010.