Technical Note: Trend estimation from irregularly sampled, correlated data

Estimation of a trend of an atmospheric state variable is often 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
5 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 straight forward manner, even if the shape of the periodic function is
not known. Global data sets, particularly satellite data, can form the basis to estimate
10 the error correlations.