Climate-sensitive radial increment model of Norway spruce in Tyrol based on a distributed lag model with penalized splines for year-ring time series

Abstract

A novel methodological framework is presented for climate-sensitive modeling of annual radial stem increment using year-ring width time series. The approach is based on a generalized additive model with penalized regression splines together with a distributed time lag model taking into account smooth nonlinear effects of a series of monthly temperature and precipitation values, as well as their interactions. Climate effects are also assumed to vary smoothly with time lag. The model framework enables both the detrending of the individual time series and the regression modeling to be performed simultaneously in a single model step. The approach is applied to year-ring width time series of Norway spruce (Picea abies (L.) H. Karst.) trees in Tyrol, Austria. The marginal response curves show that tree growth is mainly promoted by high temperatures in late spring and early summer and by precipitation in fall and winter. Summer drought does not have a negative influence on the current year’s radial increment; however, when it is associated with high temperatures, it lowers the increment in the subsequent growth period. Higher winter precipitation in conjunction with lower temperatures has a positive effect. A significant non-climate related long-term growth trend is demonstrated, probably reflecting NOx and SO2 emission trends in Austria.

Size‐, species‐, and site‐specific tree growth responses to climate variability in old‐growth subalpine forests

“…Our study demonstrated highly diverse subalpine tree growth responses to interannual climate variable fluctuations. This finding adds to a growing body of tree-ring research providing novel insights about the complexity of tree growth responses to climate variability (Girardin et al 2016, Buechling et al 2017, D'Orangeville et al 2018, Housset et al 2018, Klesse et al 2018, Marchand et al 2018, Millar et al 2018, Nothdurft and Vospernik 2018, Babst et al 2019, Büntgen et al 2019, Cailleret et al 2019, Correa-Díaz et al 2019, Hararuk et al 2019, Sáenz-Romero et al 2019. Interactions among ecological factors -tree size and life stage, species traits, and site conditions-and interannual fluctuations in temperature and precipitation, as well as decadal/multidecadal climate variability, can influence tree growth responses, sometimes in unexpected ways (Linderholm 2002, Millar et al 2018.…”

“…The relatively weak relationships we found between growth increment and PAS imply other factors play a more important role. Some studies reporting negative relationships between winter temperature and annual growth suggest the rapid consumption of stored carbohydrates needed for early reactivation of cambial growth may be a limiting factor (Sala et al 2012, Locosselli and Buckeridge 2017, Hartmann et al 2018, Nothdurft and Vospernik 2018).…”

“…There are several ways the function f ijk could be formulated to extract size, age, and competition trends from times series of annual basal area increment. After comparing the nearly identical outcomes of four options (see Appendix ), we selected a parametric function because of its transparency and to avoid poorly supported tree‐specific decisions about frequency cutoff points for the extraction of non‐parametric time series trends (Fritts 1976, Cook and Kairiukstis 1990, Magnussen and Alfaro 2012, Schofield et al 2016, Nothdurft and Vospernik 2018). The selected parametric detrending function iswhere the parameters α 0 to α 7 were estimated by nonlinear least squares (Gallant 1987) with the observed basal area increments as the dependent variable.…”

“…The outcomes of growth–climate analyses may be dependent upon the detrending method used to first remove non‐climate influences on growth (i.e., size/age trends, or competition effects) (Esper et al 2003, McShane and Wyner 2010, Peters et al 2015, Schofield et al 2016, Wood et al 2016, Lee et al 2017, Dietrich and Anand 2019). Traditional analytical approaches that estimate climate‐related effects on tree growth from a “site‐level” time series (obtained by averaging individual‐tree times series of standardized values of annual growth) ignore statistical problems associated with averaging time series of individual trees that exhibit variance heteroscedasticity and different covariance structures (Esper et al 2003, McShane and Wyner 2010, Schofield et al 2016, Nothdurft and Vospernik 2018). These traditional approaches to modeling growth–climate relationships using tree rings have also rested on the assumption that tree growth remains sensitive to the same aspects of climate over time (Babst et al 2019, Wilmking et al 2020).…”

Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations

“…We chose the distance-dependent covariance function for an isotropic weakly stationary fractional Gaussian noise process (FNG, Baillie 1996). FNG's have been used to characterize 'long-term' memory processes (Johannesson et al 2007;Nothdurft and Vospernik 2018). Accordingly, the covariance between observations from two units or two points separated by a distance h is…”