Random trend errors in climate station data due to inhomogeneities

Abstract

Inhomogeneities in station series are a large part of the uncertainty budget of long-term temperature trend estimates. This article introduces two analytical equations for the dependence of the station trend uncertainty on the statistical properties of the inhomogeneities. One equation is for inhomogeneities that act as random deviations from a fixed baseline, where the deviation levels are random and independent. The second equation is for inhomogeneities, which behave like Brownian Motion (BM), where not the levels themselves but the jumps between them are independent. It shows that BM-type breaks introduce much larger trend errors, growing linearly with the number of breaks. Using the information about type, strength, and frequency of the breaks for the United States and Germany, the random trend errors for these two countries are calculated for the period 1901–2000. An alternative and independent estimate is obtained by an empirical approach, exploiting the distance dependence of the trend variability for neighbouring station pairs. Both methods (empirical and analytical) find that the station trend uncertainty is larger in the United States (0.71 and 0.82°C per century, respectively) than in Germany (0.50 and 0.58°C per century, respectively). The good agreement of the analytical and the empirical estimate gives confidence in the methods to assess trend uncertainties, as well as in the method to determine the statistical properties of the break inhomogeneities.