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 57

climatic influence on tree growth, and on the other hand, improves our understand-
ing of the tree growth-climate relationship. There are several examples and issues
that illustrate the advance in tree growth-climate relationships resulting from the
use of the model as a research tool.

3.7 Process Model Description

The Vaganov-Shashkin model makes use of a limited number of equations relat-
ing daily temperature, precipitation, and sunlight to the kinetics of secondary xylem
development (Vaganov et al. 2006 ) in order to model tree-ring growth and the inter-
nal characteristics (density, cell sizes) of annual rings. The model consists of two
primary modules, or blocks. The Growth (or Environmental) Block calculates a
daily external growth rate based on climatic variability, including temperature, soil
moisture balance, and solar irradiance. The Cambial Block uses this external growth
rate to simulate the rate and timing of growth and division of cells in the cambium
following the hierarchical model described above. In this way, the kinetics of xylem
formation are explicitly modeled as a function of climate variability modified by
parameterized environmental and cambial processes.

3.7.1 Growth (Environmental) Block

Relative growth rate calculations made by the model are used to determine the rate
of the growth and division of cells during xylogenesis, as well as the timing of the
transition between stages. Daily growth rates themselves are determined by compar-
ing daily temperature and soil moisture (calculated from precipitation, transpiration,
and soil drainage) to piecewise linear approximations of parabolic growth func-
tions (Fig. 3.2 , inset). Four parameters define the shape of the trapezoidal growth
functions—a minimum (g( t ) = 0), lower and upper optimal bounds (g( t ) = 1),

and a maximum (g( t ) 0). Between the minimum (or maximum) and the lower

(or upper) bounds of the optimal values for the climate parameter (temperature,
sunlight, or soil moisture), growth rates will be between 0 and 1. Relative growth
rates are calculated for precipitation (g W ( t )), temperature (g T ( t )), and sunlight
(g E ( t )). The determination of the overall growth rate G ( t ) for any given day t is
calculated as

=

G ( t ) = g E ( t ) · min[ g T ( t ), g W ( t )] (3.4)

Water balance is computed daily by the model as a function of precipitation (as
well as snowmelt), evaporation (which is a function of temperature), and runoff
(Thornthwaite and Mather 1955 ) . Solar irradiance is determined by the model from
the latitude of the meteorological station from which the input data are taken.
Because of the minimization term in the calculation of the growth rate, and the