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.