Detrending ability of several regression equations in tree-ring research: a case study based on tree-ring data of Norway spruce (Picea abies [L.])

The aim of this study was to investigate tree-ring width variability and to distinguish groups of trees with similar growth trends in order to study tree growth responses to various stand and site conditions. The methods of cluster analysis were employed for this purpose. Four distinct groups of trees were identified. For each group, the mean tree-ring curve was calculated in order to look for the main signals that distinguish the groups from one another. The idea behind this was to divide the samples into homogeneous groups with similar growth trends, representing typical examples of variability of the studied Norway spruce population. In the next step, several regression functions were studied and compared for their ability to fit the ring-width-age data applied to the mean ring-width curve of each group. Fischer's F-test was used to test the differences in goodness of fit between the equations in each group. From all examined/applied equations, smoothing spline, polynomial of degree 5, and Šmelko-Burgan functions were found to be the most universal and suitable for detrending of all examined ring width curves. Hugershoff function was found to be suitable for curves with one local maximum only. Exponential and Korf's functions were unsatisfactory for the purposes of tree ring curves detrending.