Functions to initialize and expand a ring of tracheids to simulate secondary growth.

```
woodformation_initRing()
woodformation_temperatureEffect(
Tc,
Y_T = 5,
DHa = 87500,
DSd = 1090,
DHd = 333000
)
woodformation_relativeExpansionRate(psi, Tc, pi, phi, Y_P, Y_T)
woodformation_growRing(
ring,
psi,
Tc,
Nc = 8.85,
phi0 = 0.13,
pi0 = -0.8,
CRD0 = 8.3,
Y_P = 0.05,
Y_T = 5,
h = 0.043 * 1.8,
s = 1.8
)
woodformation_relativeGrowthRate(dbh1, dbh2, yeardiff, lower = -2, upper = 8)
```

- Tc
Temperature in Celsius.

- Y_T
Temperature yield threshold (in Celsius)

- DHa, DSd, DHd
Enthalpy of activation, enthalpy difference and entropy difference between the catalytically active and inactive states of the enzymatic system (Parent et al. 2010).

- psi
Water potential (in MPa).

- pi
Osmotic potential (in MPa)

- phi
Cell extensibility (in MPa-1 day-1)

- Y_P
Turgor pressure yield threshold (in MPa)

- ring
An object of class

`ring`

returned by function`woodformation_initRing`

.- Nc
Number of active cells in the cambium.

- phi0
Initial value of cell extensibility (in MPa-1 day-1)

- pi0
Initial value of cell osmotic potential (in MPa)

- CRD0
Initial value of cell radial diameter

- h
Cell wall hardening coefficient (in day-1)

- s
Cell wall softening coefficient (unitless)

- dbh1, dbh2
Initial and final diameter at breast height.

- yeardiff
Interval between dbh measurements, in years.

- lower, upper
Lower and upper bounds for root finding.

Function `woodformation_initRing()`

returns a list of class 'ring',
that is a list containing a data frame `cells`

and two vectors: `P`

and `SA`

.
Dataframe `cells`

contains the columns "formation_date", "phi", "pi" and "CRD" and as many rows as dates processed.
Vectors `P`

and `SA`

contain, respectively, the number of cells produced and the sapwood area
corresponding to the ring of cells (assuming a tangencial radius of 20 micrometers).

Function `woodformation_growRing()`

modifies the input 'ring' object according to the environmental conditions given as input.

Function `woodformation_relativeExpansionRate()`

returns a numeric scalar with the relative expansion rate.

Function `woodformation_temperatureEffect()`

returns a scalar between 0 and 1 reflecting the temperature effect on tissue formation rate.

Function `woodformation_relativeGrowthRate`

returns the annual growth rate, relative to cambium perimeter, estimated from initial and final diameter values.

Code modified from package xylomod by Antoine Cabon, available at GitHub

Cabon A, Fernández-de-Uña L, Gea-Izquierdo G, Meinzer FC, Woodruff DR, Martínez-Vilalta J, De Cáceres M. 2020a. Water potential control of turgor-driven tracheid enlargement in Scots pine at its xeric distribution edge. New Phytologist 225: 209–221.

Cabon A, Peters RL, Fonti P, Martínez-Vilalta J, De Cáceres M. 2020b. Temperature and water potential co-limit stem cambial activity along a steep elevational gradient. New Phytologist: nph.16456.

Parent, B., O. Turc, Y. Gibon, M. Stitt, and F. Tardieu. 2010. Modelling temperature-compensated physiological rates, based on the co-ordination of responses to temperature of developmental processes. Journal of Experimental Botany 61:2057–2069.