How Well Understood Are the Processes that Create Dendroclimatic Records? A Mechanistic Model of the Climatic Control on Conifer Tree-Ring Growth Dynamics - Dendroclimatology - page 59

piecewise approximation of the nonlinear growth function, the model behaves
stoichiometrically—that is, it is controlled by the most limiting factor (e.g., Fritts
1976 ) —at a daily resolution.
A recent study of intra-annual radial growth rates in trees of different species
located in different sites and environmental conditions reveals that maximum growth
rate of weekly cell production and variations in stem circumference at high-latitude
sites occurred around the time of maximum day length (Rossi et al. 2006 ) . These
data were obtained by smoothing seasonal growth curves by using the Gompertz
equation and transferring the cumulative curves into differential rates of cell divi-
sion, expansion, and maturation. These data in general are in good agreement with
what we assume in equation ( 3.4 ) , although equation ( 3.4 ) has more flexibility
because of the combination of day length and temperature for determining the max-
imum growth rate. Observations at high latitudes indicate that the maximum growth
rate, as well as the beginning of the growing season, may vary greatly, even as late
as the summer solstice (Deslauriers et al. 2003 ; Vaganov et al. 2006 ) . Use of the
Gompertz equation for quantitative description of tree-ring growth is ultimately a
statistical tool and not a biological model, but it is potentially useful for combining
subannual observations of cambial dynamics and diameter growth with mechanistic
modeling at daily to weekly resolutions.
3.7.2 Cambial Block
The Cambial Block uses the output from the Growth Block to determine the rate at
which cambial cells grow and divide (Figs. 3.2 and 3.3 ) . Each cell in the Cambial
Block is characterized by two variables at each daily step—its position ( j )inthe
cellular file and its diameter. The growth rate G ( t ) calculated in the prior block
is used to derive a specific growth rate, V ( j,t ), for each cell based on its position
(Fig. 3.2 ) . For cambial cells, diameter increases in the G 1 phase until a maximum
size when division occurs, or until the cell loses the ability to divide as its growth rate
falls below a minimum threshold V min ( j ) for the cell's position in the radial file. Cells
that lose the ability to divide pass out of the cambium, and complete the cell cycle,
including elongation and cell wall thickening. Daily cellular growth rates below a
critical minimum threshold ( V cr ) send the cambium into dormancy. The cells in the
cambium at the end of one simulated growing season will therefore be those which
first grow and divide in the subsequent year, and therefore influence the cambial
dynamics and tree-ring structure of the following year. Activity in the cambium is
initiated each year when the sum of temperatures above a certain threshold over a
specified period of time (i.e., growing degree days) reaches a critical threshold.
The Vaganov-Shashkin model explicitly integrates the essential features of cam-
bial dynamics as previously described. Annual xylem cell production is related to
the number of cells in the cambial zone, the size of which varies over the course of
the year in response to environmental variability. Specific cellular growth rates are
positional and depend on the distance of the simulated cell from the cambial initial,