Evaluation of methods for the combination of phenological time series and outlier detection

There are several applications of combined phenological time series; e.g., trend analysis with long continuous time series, obtaining a compound and representative time series around weather stations for model fitting, data gap filling and outlier detection. Various methods to combine phenological time series have been proposed. We show that all of these methods can be analyzed within the theory of linear models. This has the advantage that the underlying assumptions for each model become transparent providing a theoretical basis for selecting a model for a particular situation. Moreover, the common theoretical background provides a means of comparing methods by Monte-Carlo simulation and with real data. Additionally, we explored the influences of two outlier detection methods. We show that the error called the month-mistake, whose origin is known and which is one of the few mistakes that can be detected in phenological data because of its large deviation, is best detected by the distribution-free 30-day residual rule in combination with a robust estimation procedure based on the minimization of the sum of absolute residuals (L1-norm).