Climate Data Homogenization Using Edge Detection Algorithms

Abstract:

The problem of climate data homogenization has predominantly been addressed by testing the likelihood of one or more breaks inserted into a given time series and modeling the mean to be stationary in between the breaks. We recast the same problem in a slightly different form: that of detecting step-like changes in noisy data, and observe that this problem has spawned a large number of approaches to its solution as the “edge detection” problem in image processing. With respect to climate data, we ask the question: How can we optimally separate step-like from smoothly-varying low-frequency signals?

We study the hypothesis that the edge-detection approach makes better use of all information contained in the time series than the "traditional" approach (e.g. Caussinus and Mestre, 2004), which we base on several observations. 1) The traditional formulation of the problem reduces the available information from the outset to that contained in the test statistic. 2) The criterion of local steepness of the low-frequency variability, while at least hypothetically useful, is ignored. 3) The practice of using monthly data corresponds, mathematically, to applying a moving average filter (to reduce noise) and subsequent subsampling of the result; this subsampling reduces the amount of available information beyond what is necessary for noise reduction.

Most importantly, the tradeoff between noise reduction (better with filters with wide support in the time domain) and localization of detected changes (better with filters with narrow support) is expressed in the well-known uncertainty principle and can be addressed optimally within a time-frequency framework. Unsurprisingly, a large number of edge-detection algorithms have been proposed that make use of wavelet decompositions and similar techniques.

We are developing this framework in part to be applied to a particular set of climate data from Greenland; we will present results from this application as well as from tests with “benchmark” and synthetic data.