2.4.1 Ring-width indices and basal area increment
Two different growth metrics were derived from each series of tree-ring width increments: detrended ring-width indices (RWIs) and basal area increments (BAIs). RWIs are highly suitable to extract the influence of high frequency climatic variability on tree growth and exclude low-temporal frequency effects (e.g. competition, ontogeny). To produce RWIs, we modelled low-frequency growth variation using a Friedman’s super smoother, with the smoothing span optimized via leave-one-out cross-validation (Friedman, 1984). After dividing the observed ring widths by the respective smoothed values, a first order autoregressive model was applied to remove temporal autocorrelation. Tree-level RWIs of specific years can be averaged over different spatial scales to produce tree growth chronologies for specific spatial domains. Thus, we averaged over RWI series within inventory plots to produce plot-level RWI chronologies and plot chronologies were integrated to produce stand chronologies. Detrending and chronology building was entirely conducted using functions in the R package dplR (Bunn, 2008).
RWIs help disentangle various components of tree-growth variation, but as unitless indicators of relative tree growth, they cannot be interpreted in terms of actual quantities of wood produced per year. BAI provides a more direct representation of net wood synthesis (West, 1980). Because our extensive and representative sampling incorporated different tree sizes and competitive statuses, the BAI chronologies produced in our analysis provide an accurate image of spatial variation in forest-level wood production. BAIs are estimated from radial growth increments, by converting these increments into cross sectional areas and subtracting the cross-sectional areas between adjacent years:
BAIt = π*(Dt/2)2 - π*(Dt-1/2)2
Where Dt is the reconstructed tree diameter in a specified year, and Dt-1 is the diameter of the previous year. Diameters were adjusted by a coefficient to account for any potential asymmetry in ring geometry: Ring widths are divided by the length of the corresponding increment core to produce proportional diameters, which are subsequently multiplied by the measured dbh of the tree. If a given core did not include the pith, but came within 10 mm, then the distance to the missing pith was estimated from the arcs of the inner rings (Duncan 1989). Cores which missed the pith by more than 10mm were excluded from analyses involving BAI.