Mean value splines and their use for climatological time series

A new approach of splines to examine climatological time series is introduced and different applications are shown. Instead of the classical spline-procedure to find polynomials which fit given values at certain points (knots), a variational formulation is used here, where a cost function is minimized to obtain smooth interpolated values at arbitrary points. The innovation of the method consists in the selection of the constraint, namely the conservation of mean values within certain smoothing intervals. The methodology allows a sound derivation of the past and present climate conditions in times of climate change. It allows a refined computation of extreme values and of the probability of certain temperature thresholds. The methodology furthermore allows to detect break points in climatological time series. Finally the method leads to a consistent interpolation of time series, which are only given by mean values. Several applications of the method, using climatological time series of Vienna are shown and discussed.

Automated summary

This article introduces a new approach of splines to examine climatological time series and demonstrates various applications. Instead of the classical spline-procedure, a variational formulation is used which minimizes a cost function to obtain smooth interpolated values at arbitrary points. The method innovatively selects the constraint of conserving mean values within specific smoothing intervals. It enables accurate derivation of past and present climate conditions, refined computation of extreme values and probability of temperature thresholds, detection of break points in climatological time series, and consistent interpolation of mean-only time series. The article presents and discusses several applications of the method using climatological time series of Vienna.