Package 'tealeaves' reference manual

Title:	Solve for Leaf Temperature Using Energy Balance
Description:	Implements models of leaf temperature using energy balance. It uses units to ensure that parameters are properly specified and transformed before calculations. It allows separate lower and upper surface conductances to heat and water vapour, so sensible and latent heat loss are calculated for each surface separately as in Foster and Smith (1986) <doi:10.1111/j.1365-3040.1986.tb02108.x>. It's straightforward to model leaf temperature over environmental gradients such as light, air temperature, humidity, and wind. It can also model leaf temperature over trait gradients such as leaf size or stomatal conductance. Other references are Monteith and Unsworth (2013, ISBN:9780123869104), Nobel (2009, ISBN:9780123741431), and Okajima et al. (2012) <doi:10.1007/s11284-011-0905-5>.
Authors:	Chris Muir [aut, cre]
Maintainer:	Chris Muir <[email protected]>
License:	MIT + file LICENSE
Version:	1.0.6
Built:	2025-02-19 03:44:27 UTC
Source:	https://github.com/cdmuir/tealeaves

d_wv: water vapour gradient (mol / m ^ 3)

Description

d_wv: water vapour gradient (mol / m ^ 3)

Usage

.get_dwv(T_leaf, pars, unitless)
.get_dwv(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

Water vapour gradient: The water vapour pressure differential from inside to outside of the leaf is the saturation water vapor pressure inside the leaf (p_leaf) minus the water vapor pressure of the air (p_air):

$d_\mathrm{wv} = p_\mathrm{leaf} / (R T_\mathrm{leaf}) - RH p_\mathrm{air} / (R T_\mathrm{air})$

Note that water vapor pressure is converted from kPa to mol / m^3 using ideal gas law.

Symbol	R	Description	Units	Default
$p_\mathrm{air}$	`p_air`	saturation water vapour pressure of air	kPa	calculated
$p_\mathrm{leaf}$	`p_leaf`	saturation water vapour pressure inside the leaf	kPa	calculated
$R$	`R`	ideal gas constant	J / (mol K)	8.3144598
$\mathrm{RH}$	`RH`	relative humidity	%	0.50
$T_\mathrm{air}$	`T_air`	air temperature	K	298.15
$T_\mathrm{leaf}$	`T_leaf`	leaf temperature	K	input

Value

Value in mol / m^3 of class units

Examples


# Water vapour gradient: 

leaf_par <- make_leafpar()
enviro_par <- make_enviropar()
constants <- make_constants()
pars <- c(leaf_par, enviro_par, constants)
T_leaf <- set_units(300, K)
T_air <- set_units(298.15, K)
p_leaf <- set_units(35.31683, kPa)
p_air <- set_units(31.65367, kPa)

d_wv <- p_leaf / (pars$R * T_leaf) - pars$RH * p_air / (pars$R * T_air)

# Water vapour gradient: 

leaf_par <- make_leafpar()
enviro_par <- make_enviropar()
constants <- make_constants()
pars <- c(leaf_par, enviro_par, constants)
T_leaf <- set_units(300, K)
T_air <- set_units(298.15, K)
p_leaf <- set_units(35.31683, kPa)
p_air <- set_units(31.65367, kPa)

d_wv <- p_leaf / (pars$R * T_leaf) - pars$RH * p_air / (pars$R * T_air)

D_x: Calculate diffusion coefficient for a given temperature and pressure

Description

D_x: Calculate diffusion coefficient for a given temperature and pressure

Usage

.get_Dx(D_0, Temp, eT, P, unitless)
.get_Dx(D_0, Temp, eT, P, unitless)

Arguments

`D_0`	Diffusion coefficient at 273.15 K (0 °C) and 101.3246 kPa
`Temp`	Temperature in Kelvin
`eT`	Exponent for temperature dependence of diffusion
`P`	Atmospheric pressure in kPa
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$D = D_\mathrm{0} (T / 273.15) ^ {eT} (101.3246 / P)$

According to Montieth & Unger (2013), eT is generally between 1.5 and 2. Their data in Appendix 3 indicate $eT = 1.75$ is reasonable for environmental physics.

Value

Value in m $^2$ /s of class units

References

Monteith JL, Unsworth MH. 2013. Principles of Environmental Physics. 4th edition. Academic Press, London.

Examples


tealeaves:::.get_Dx(
  D_0 = set_units(2.12e-05, m^2/s),
  Temp = set_units(298.15, K),
  eT = set_units(1.75),
  P = set_units(101.3246, kPa),
  unitless = FALSE
)

tealeaves:::.get_Dx(
  D_0 = set_units(2.12e-05, m^2/s),
  Temp = set_units(298.15, K),
  eT = set_units(1.75),
  P = set_units(101.3246, kPa),
  unitless = FALSE
)

g_bw: Boundary layer conductance to water vapour (m / s)

Description

g_bw: Boundary layer conductance to water vapour (m / s)

Usage

.get_gbw(T_leaf, surface, pars, unitless)
.get_gbw(T_leaf, surface, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`surface`	Leaf surface (lower or upper)
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$g_\mathrm{bw} = D_\mathrm{w} Sh / d$

Symbol	R	Description	Units	Default
$d$	`leafsize`	Leaf characteristic dimension in meters	m	0.1
$D_\mathrm{w}$	`D_w`	diffusion coefficient for water vapour	m $^2$ / s	calculated
$Sh$	`Sh`	Sherwood number	none	calculated

Value

Value in m / s of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_gbw(T_leaf, "lower", c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_gbw(T_leaf, "lower", c(cs, ep, lp), FALSE)

g_h: boundary layer conductance to heat (m / s)

Description

g_h: boundary layer conductance to heat (m / s)

Usage

.get_gh(T_leaf, surface, pars, unitless)
.get_gh(T_leaf, surface, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`surface`	Leaf surface (lower or upper)
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$g_\mathrm{h} = D_\mathrm{h} Nu / d$

Symbol	R	Description	Units	Default
$d$	`leafsize`	Leaf characteristic dimension in meters	m	0.1
$D_\mathrm{h}$	`D_h`	diffusion coefficient for heat in air	m $^2$ / s	calculated
$Nu$	`Nu`	Nusselt number	none	calculated

Value

Value in m/s of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_gh(T_leaf, "lower", c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_gh(T_leaf, "lower", c(cs, ep, lp), FALSE)

Gr: Grashof number

Description

Gr: Grashof number

Usage

.get_gr(T_leaf, pars, unitless)
.get_gr(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$Gr = t_\mathrm{air} G d ^ 3 |T_\mathrm{v,leaf} - T_\mathrm{v,air}| / D_\mathrm{m} ^ 2$

Symbol	R	Description	Units	Default
$d$	`leafsize`	Leaf characteristic dimension in meters	m	0.1
$D_\mathrm{m}$	`D_m`	diffusion coefficient of momentum in air	m $^2$ / s	calculated
$G$	`G`	gravitational acceleration	m / s $^2$	9.8
$t_\mathrm{air}$	`t_air`	coefficient of thermal expansion of air	1 / K	1 / Temp
$T_\mathrm{v,air}$	`Tv_air`	virtual air temperature	K	calculated
$T_\mathrm{v,leaf}$	`Tv_leaf`	virtual leaf temperature	K	calculated

Value

A unitless number of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_gr(T_leaf, c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_gr(T_leaf, c(cs, ep, lp), FALSE)

g_tw: total conductance to water vapour (m/s)

Description

g_tw: total conductance to water vapour (m/s)

Usage

.get_gtw(T_leaf, pars, unitless)
.get_gtw(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

Total conductance to water vapor: The total conductance to water vapor ( $g_\mathrm{tw}$ ) is the sum of the parallel lower (abaxial) and upper (adaxial) conductances:

$g_\mathrm{tw} = g_\mathrm{w,lower} + g_\mathrm{w,upper}$

The conductance to water vapor on each surface is a function of parallel stomatal ( $g_\mathrm{sw}$ ) and cuticular ( $g_\mathrm{uw}$ ) conductances in series with the boundary layer conductance ( $g_\mathrm{bw}$ ). The stomatal, cuticular, and boundary layer conductance on the lower surface are:

$g_\mathrm{sw,lower} = g_\mathrm{sw} (1 - sr) R (T_\mathrm{leaf} + T_\mathrm{air}) / 2$

$g_\mathrm{uw,lower} = g_\mathrm{uw} / 2 R (T_\mathrm{leaf} + T_\mathrm{air}) / 2$

See .get_gbw for details on calculating boundary layer conductance. The equations for the upper surface are:

$g_\mathrm{sw,upper} = g_\mathrm{sw} sr R (T_\mathrm{leaf} + T_\mathrm{air}) / 2$

$g_\mathrm{uw,upper} = g_\mathrm{uw} / 2 R (T_\mathrm{leaf} + T_\mathrm{air}) / 2$

Note that the stomatal and cuticular conductances are given in units of ( $\mu$ mol H2O) / (m $^2$ s Pa) (see make_leafpar) and converted to m/s using the ideal gas law. The total leaf stomatal ( $g_\mathrm{sw}$ ) and cuticular ( $g_\mathrm{uw}$ ) conductances are partitioned across lower and upper surfaces. The stomatal conductance on each surface depends on stomatal ratio (sr); the cuticular conductance is assumed identical on both surfaces.

Symbol	R	Description	Units	Default
$g_\mathrm{sw}$	`g_sw`	stomatal conductance to H2O	( $\mu$ mol H2O) / (m $^2$ s Pa)	5
$g_\mathrm{uw}$	`g_uw`	cuticular conductance to H2O	( $\mu$ mol H2O) / (m $^2$ s Pa)	0.1
$R$	`R`	ideal gas constant	J / (mol K)	8.3144598
$\mathrm{logit}(sr)$	`logit_sr`	stomatal ratio (logit transformed)	none	0 = logit(0.5)
$T_\mathrm{air}$	`T_air`	air temperature	K	298.15
$T_\mathrm{leaf}$	`T_leaf`	leaf temperature	K	input

Value

Value in m/s of class units

Examples


# Total conductance to water vapor

## Hypostomatous leaf; default parameters
leaf_par <- make_leafpar(replace = list(logit_sr = set_units(-Inf)))
enviro_par <- make_enviropar()
constants <- make_constants()
pars <- c(leaf_par, enviro_par, constants)
T_leaf <- set_units(300, K)

## Fixing boundary layer conductance rather than calculating
gbw_lower <- set_units(0.1, m / s)
gbw_upper <- set_units(0.1, m / s)

# Lower surface ----
## Note that pars$logit_sr is logit-transformed! Use stats::plogis() to convert to proportion.
gsw_lower <- set_units(pars$g_sw * (set_units(1) - stats::plogis(pars$logit_sr)) * pars$R * 
                         ((T_leaf + pars$T_air) / 2), "m / s")
guw_lower <- set_units(pars$g_uw * 0.5 * pars$R * ((T_leaf + pars$T_air) / 2), m / s)
gtw_lower <- 1 / (1 / (gsw_lower + guw_lower) + 1 / gbw_lower)

# Upper surface ----
gsw_upper <- set_units(pars$g_sw * stats::plogis(pars$logit_sr) * pars$R * 
                         ((T_leaf + pars$T_air) / 2), m / s)
guw_upper <- set_units(pars$g_uw * 0.5 * pars$R * ((T_leaf + pars$T_air) / 2), m / s)
gtw_upper <- 1 / (1 / (gsw_upper + guw_upper) + 1 / gbw_upper)

## Lower and upper surface are in parallel
g_tw <- gtw_lower + gtw_upper

# Total conductance to water vapor

## Hypostomatous leaf; default parameters
leaf_par <- make_leafpar(replace = list(logit_sr = set_units(-Inf)))
enviro_par <- make_enviropar()
constants <- make_constants()
pars <- c(leaf_par, enviro_par, constants)
T_leaf <- set_units(300, K)

## Fixing boundary layer conductance rather than calculating
gbw_lower <- set_units(0.1, m / s)
gbw_upper <- set_units(0.1, m / s)

# Lower surface ----
## Note that pars$logit_sr is logit-transformed! Use stats::plogis() to convert to proportion.
gsw_lower <- set_units(pars$g_sw * (set_units(1) - stats::plogis(pars$logit_sr)) * pars$R * 
                         ((T_leaf + pars$T_air) / 2), "m / s")
guw_lower <- set_units(pars$g_uw * 0.5 * pars$R * ((T_leaf + pars$T_air) / 2), m / s)
gtw_lower <- 1 / (1 / (gsw_lower + guw_lower) + 1 / gbw_lower)

# Upper surface ----
gsw_upper <- set_units(pars$g_sw * stats::plogis(pars$logit_sr) * pars$R * 
                         ((T_leaf + pars$T_air) / 2), m / s)
guw_upper <- set_units(pars$g_uw * 0.5 * pars$R * ((T_leaf + pars$T_air) / 2), m / s)
gtw_upper <- 1 / (1 / (gsw_upper + guw_upper) + 1 / gbw_upper)

## Lower and upper surface are in parallel
g_tw <- gtw_lower + gtw_upper

H: sensible heat flux density (W / m^2)

Description

H: sensible heat flux density (W / m^2)

Usage

.get_H(T_leaf, pars, unitless)
.get_H(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$H = P_\mathrm{a} c_p g_\mathrm{h} (T_\mathrm{leaf} - T_\mathrm{air})$

Symbol	R	Description	Units	Default
$c_p$	`c_p`	heat capacity of air	J / (g K)	1.01
$g_\mathrm{h}$	`g_h`	boundary layer conductance to heat	m / s	calculated
$P_\mathrm{a}$	`P_a`	density of dry air	g / m^3	calculated
$T_\mathrm{air}$	`T_air`	air temperature	K	298.15
$T_\mathrm{leaf}$	`T_leaf`	leaf temperature	K	input

Value

Value in W / m $^2$ of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_H(T_leaf, c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_H(T_leaf, c(cs, ep, lp), FALSE)

h_vap: heat of vaporization (J / mol)

Description

h_vap: heat of vaporization (J / mol)

Usage

.get_hvap(T_leaf, unitless)
.get_hvap(T_leaf, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

Heat of vaporization: The heat of vaporization ( $h_\mathrm{vap}$ ) is a function of temperature. I used data from on temperature and $h_\mathrm{vap}$ from Nobel (2009, Appendix 1) to estimate a linear regression. See Examples.

Value

Value in J/mol of class units

References

Nobel PS. 2009. Physicochemical and Environmental Plant Physiology. 4th Edition. Academic Press.

Examples


# Heat of vaporization and temperature
## data from Nobel (2009)

T_K <- 273.15 + c(0, 10, 20, 25, 30, 40, 50, 60)
h_vap <- 1e3 * c(45.06, 44.63, 44.21, 44.00, 
                 43.78, 43.35, 42.91, 42.47) # (in J / mol)
                 
fit <- lm(h_vap ~ T_K)

## coefficients are 56847.68250 J / mol and 43.12514 J / (mol K)

coef(fit) 

T_leaf <- 298.15
h_vap <- set_units(56847.68250, J / mol) - 
           set_units(43.12514, J / mol / K) * set_units(T_leaf, K)

## h_vap at 298.15 K is 43989.92 [J/mol]

set_units(h_vap, J / mol)

tealeaves:::.get_hvap(set_units(298.15, K), FALSE)

# Heat of vaporization and temperature
## data from Nobel (2009)

T_K <- 273.15 + c(0, 10, 20, 25, 30, 40, 50, 60)
h_vap <- 1e3 * c(45.06, 44.63, 44.21, 44.00, 
                 43.78, 43.35, 42.91, 42.47) # (in J / mol)
                 
fit <- lm(h_vap ~ T_K)

## coefficients are 56847.68250 J / mol and 43.12514 J / (mol K)

coef(fit) 

T_leaf <- 298.15
h_vap <- set_units(56847.68250, J / mol) - 
           set_units(43.12514, J / mol / K) * set_units(T_leaf, K)

## h_vap at 298.15 K is 43989.92 [J/mol]

set_units(h_vap, J / mol)

tealeaves:::.get_hvap(set_units(298.15, K), FALSE)

L: Latent heat flux density (W / m^2)

Description

L: Latent heat flux density (W / m^2)

Usage

.get_L(T_leaf, pars, unitless)
.get_L(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$L = h_\mathrm{vap} g_\mathrm{tw} d_\mathrm{wv}$

Symbol	R	Description	Units	Default
$d_\mathrm{wv}$	`d_wv`	water vapour gradient	mol / m ^ 3	calculated
$h_\mathrm{vap}$	`h_vap`	latent heat of vaporization	J / mol	calculated
$g_\mathrm{tw}$	`g_tw`	total conductance to H2O	( $\mu$ mol H2O) / (m $^2$ s Pa)	calculated

Value

Value in W / m^2 of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_L(T_leaf, c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_L(T_leaf, c(cs, ep, lp), FALSE)

Nu: Nusselt number

Description

Nu: Nusselt number

Usage

.get_nu(T_leaf, surface, pars, unitless)
.get_nu(T_leaf, surface, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`surface`	Leaf surface (lower or upper)
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

The Nusselt number depends on a combination how much free or forced convection predominates. For mixed convection:

$Nu = (a Re ^ b) ^ {3.5} + (c Gr ^ d) ^ {3.5}) ^ {1 / 3.5}$

Symbol	R	Description	Units	Default
$a, b, c, d$	`a, b, c, d`	empirical coefficients	none	calculated
$Gr$	`Gr`	Grashof number	none	calculated
$Re$	`Re`	Reynolds number	none	calculated

Value

A unitless number of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_nu(T_leaf, "lower", c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_nu(T_leaf, "lower", c(cs, ep, lp), FALSE)

P_a: density of dry air (g / m^3)

Description

P_a: density of dry air (g / m^3)

Usage

.get_Pa(T_leaf, pars, unitless)
.get_Pa(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$P_\mathrm{a} = P / (R_\mathrm{air} (T_\mathrm{leaf} - T_\mathrm{air}) / 2)$

Symbol	R	Description	Units	Default
$P$	`P`	atmospheric pressure	kPa	101.3246
$R_\mathrm{air}$	`R_air`	specific gas constant for dry air	J / (kg K)	287.058
$T_\mathrm{air}$	`T_air`	air temperature	K	298.15
$T_\mathrm{leaf}$	`T_leaf`	leaf temperature	K	input

Value

Value in g / m $^3$ of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_Pa(T_leaf, c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_Pa(T_leaf, c(cs, ep, lp), FALSE)

Saturation water vapour pressure (kPa)

Description

Saturation water vapour pressure (kPa)

Usage

.get_ps(Temp, P, unitless)
.get_ps(Temp, P, unitless)

Arguments

`Temp`	Temperature in Kelvin
`P`	Atmospheric pressure in kPa
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

Goff-Gratch equation (see http://cires1.colorado.edu/~voemel/vp.html)

This equation assumes P = 1 atm = 101.3246 kPa, otherwise boiling temperature needs to change

Value

Value in kPa of class units

References

http://cires1.colorado.edu/~voemel/vp.html

Examples


T_leaf <- set_units(298.15, K)
P <- set_units(101.3246, kPa)
tealeaves:::.get_ps(T_leaf, P, FALSE)

T_leaf <- set_units(298.15, K)
P <- set_units(101.3246, kPa)
tealeaves:::.get_ps(T_leaf, P, FALSE)

R_abs: total absorbed radiation (W / m^2)

Description

R_abs: total absorbed radiation (W / m^2)

Usage

.get_Rabs(pars, unitless)
.get_Rabs(pars, unitless)

Arguments

`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

The following treatment follows Okajima et al. (2012):

$R_\mathrm{abs} = \alpha_\mathrm{s} (1 + r) S_\mathrm{sw} + \alpha_\mathrm{l} \sigma (T_\mathrm{sky} ^ 4 + T_\mathrm{air} ^ 4)$

The incident longwave (aka thermal infrared) radiation is modeled from sky and air temperature $\sigma (T_\mathrm{sky} ^ 4 + T_\mathrm{air} ^ 4)$ where $T_\mathrm{sky}$ is function of the air temperature and incoming solar shortwave radiation:

$T_\mathrm{sky} = T_\mathrm{air} - 20 S_\mathrm{sw} / 1000$

Symbol	R	Description	Units	Default
$\alpha_\mathrm{s}$	`abs_s`	absorbtivity of shortwave radiation (0.3 - 4 $\mu$ m)	none	0.80
$\alpha_\mathrm{l}$	`abs_l`	absorbtivity of longwave radiation (4 - 80 $\mu$ m)	none	0.97
$r$	`r`	reflectance for shortwave irradiance (albedo)	none	0.2
$\sigma$	`s`	Stefan-Boltzmann constant	W / (m $^2$ K $^4$ )	5.67e-08
$S_\mathrm{sw}$	`S_sw`	incident short-wave (solar) radiation flux density	W / m $^2$	1000
$S_\mathrm{lw}$	`S_lw`	incident long-wave radiation flux density	W / m $^2$	calculated
$T_\mathrm{air}$	`T_air`	air temperature	K	298.15
$T_\mathrm{sky}$	`T_sky`	sky temperature	K	calculated

Value

Value in W / m $^2$ of class units

References

Okajima Y, H Taneda, K Noguchi, I Terashima. 2012. Optimum leaf size predicted by a novel leaf energy balance model incorporating dependencies of photosynthesis on light and temperature. Ecological Research 27: 333-46.

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()
ep$T_sky <- ep$T_sky(ep)

tealeaves:::.get_Rabs(c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()
ep$T_sky <- ep$T_sky(ep)

tealeaves:::.get_Rabs(c(cs, ep, lp), FALSE)

Re: Reynolds number

Description

Re: Reynolds number

Usage

.get_re(T_leaf, pars, unitless)
.get_re(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$Re = u d / D_\mathrm{m}$

Symbol	R	Description	Units	Default
$d$	`leafsize`	Leaf characteristic dimension in meters	m	0.1
$D_\mathrm{m}$	`D_m`	diffusion coefficient of momentum in air	m $^2$ / s	calculated
$u$	`wind`	windspeed	m / s	2

Value

A unitless number of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_re(T_leaf, c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_re(T_leaf, c(cs, ep, lp), FALSE)

Sh: Sherwood number

Description

Sh: Sherwood number

Usage

.get_sh(T_leaf, surface, pars, unitless)
.get_sh(T_leaf, surface, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`surface`	Leaf surface (lower or upper)
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

The Sherwood number depends on a combination how much free or forced convection predominates. For mixed convection:

$Sh = (a Re ^ b) ^ {3.5} + (c Gr ^ d) ^ {3.5}) ^ {1 / 3.5}$

Symbol	R	Description	Units	Default
$a, b, c, d$	`a, b, c, d`	empirical coefficients	none	calculated
$Gr$	`Gr`	Grashof number	none	calculated
$Re$	`Re`	Reynolds number	none	calculated

Value

A unitless number of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_sh(T_leaf, "lower", c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_sh(T_leaf, "lower", c(cs, ep, lp), FALSE)

S_r: longwave re-radiation (W / m^2)

Description

S_r: longwave re-radiation (W / m^2)

Usage

.get_Sr(T_leaf, pars)
.get_Sr(T_leaf, pars)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)

Details

$S_\mathrm{r} = 2 \sigma \alpha_\mathrm{l} T_\mathrm{air} ^ 4$

The factor of 2 accounts for re-radiation from both leaf surfaces (Foster and Smith 1986).

Symbol	R	Description	Units	Default
$\alpha_\mathrm{l}$	`abs_l`	absorbtivity of longwave radiation (4 - 80 $\mu$ m)	none	0.97
$T_\mathrm{air}$	`T_air`	air temperature	K	298.15
$\sigma$	`s`	Stefan-Boltzmann constant	W / (m $^2$ K $^4$ )	5.67e-08

Note that leaf absorbtivity is the same value as leaf emissivity

Value

Value in W / m $^2$ of class units

References

Foster JR, Smith WK. 1986. Influence of stomatal distribution on transpiration in low-wind environments. Plant, Cell & Environment 9: 751-9.

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_Sr(T_leaf, c(cs, ep, lp))

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

tealeaves:::.get_Sr(T_leaf, c(cs, ep, lp))

Calculate virtual temperature

Description

Calculate virtual temperature

Usage

.get_Tv(Temp, p, P, epsilon, unitless)
.get_Tv(Temp, p, P, epsilon, unitless)

Arguments

`Temp`	Temperature in Kelvin
`p`	water vapour pressure in kPa
`P`	Atmospheric pressure in kPa
`epsilon`	ratio of water to air molar masses (unitless)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$T_\mathrm{v} = T / [1 - (1 - \epsilon) (p / P)]$

Eq. 2.35 in Monteith & Unsworth (2013)

Symbol	R	Description	Units	Default
$\epsilon$	`epsilon`	ratio of water to air molar masses	unitless	0.622
$p$	`p`	water vapour pressure	kPa	calculated
$P$	`P`	atmospheric pressure	kPa	101.3246

Value

Value in K of class units

References

Monteith JL, Unsworth MH. 2013. Principles of Environmental Physics. 4th edition. Academic Press, London.

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)
p <- ep$RH * tealeaves:::.get_ps(T_leaf, ep$P, FALSE)
tealeaves:::.get_Tv(T_leaf, p, ep$P, cs$epsilon, FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)
p <- ep$RH * tealeaves:::.get_ps(T_leaf, ep$P, FALSE)
tealeaves:::.get_Tv(T_leaf, p, ep$P, cs$epsilon, FALSE)

Ar: Archimedes number

Description

Ar: Archimedes number

Usage

Ar(T_leaf, pars, unitless = FALSE)
Ar(T_leaf, pars, unitless = FALSE)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

The Archimedes number is a dimensionless number that describes when free or forced convection dominates.

$Ar = Gr / Re ^ 2$

Symbol	R	Description	Units	Default
$Gr$	`Gr`	Grashof number	none	calculated
$Re$	`Re`	Reynolds number	none	calculated

Value

unitless = TRUE: A unitless number of class numeric unitless = FALSE: A unitless number of class units Also returns Reynolds and Grashof numbers

Examples

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()
pars <- c(cs, lp, ep)
T_leaf <- set_units(298.15, "K")

Ar(T_leaf, pars)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()
pars <- c(cs, lp, ep)
T_leaf <- set_units(298.15, "K")

Ar(T_leaf, pars)

S3 class constants

Description

Constructor function for constants class. This function ensures that physical constant inputs are properly formatted.

Usage

constants(.x)
constants(.x)

Arguments

`.x`	A list to be constructed into constants. If units are not provided, they will be set without conversion. If units are provided, they will be checked and converted to units that tealeaves uses.

Convert conductance units

Description

Convert conductance units

Usage

convert_conductance(.g, Temp = NULL, P = NULL)
convert_conductance(.g, Temp = NULL, P = NULL)

Arguments

`.g`	Conductance in class units. Units must convertible to one of "m/s", "umol/m^2/s/Pa", or "mol/m^2/s"
`Temp`	A temperature value of class `units`
`P`	A pressure value of class `units` that is convertible to kPa

Value

A list of three values of clas units with units "m/s", "umol/m^2/s/Pa", and "mol/m^2/s".

Examples


g_sw <- set_units(10, "m/s")
convert_conductance(g_sw, 
                    Temp = set_units(298.15, "K"), 
                    P = set_units(101.3246, "kPa"))

g_sw <- set_units(4, "umol/m^2/s/Pa")
convert_conductance(g_sw, 
                    Temp = set_units(298.15, "K"), 
                    P = set_units(101.3246, "kPa"))

g_sw <- set_units(0.4, "mol/m^2/s")
convert_conductance(g_sw, 
                    Temp = set_units(298.15, "K"), 
                    P = set_units(101.3246, "kPa"))

g_sw <- set_units(10, "m/s")
convert_conductance(g_sw, 
                    Temp = set_units(298.15, "K"), 
                    P = set_units(101.3246, "kPa"))

g_sw <- set_units(4, "umol/m^2/s/Pa")
convert_conductance(g_sw, 
                    Temp = set_units(298.15, "K"), 
                    P = set_units(101.3246, "kPa"))

g_sw <- set_units(0.4, "mol/m^2/s")
convert_conductance(g_sw, 
                    Temp = set_units(298.15, "K"), 
                    P = set_units(101.3246, "kPa"))

Evaporation (mol / (m^2 s))

Description

Evaporation (mol / (m^2 s))

Usage

E(T_leaf, pars, unitless)
E(T_leaf, pars, unitless)

Arguments

`T_leaf`	Leaf temperature in Kelvin
`pars`	Concatenated parameters (`leaf_par`, `enviro_par`, and `constants`)
`unitless`	Logical. Should function use parameters with `units`? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

The leaf evaporation rate is the product of the total conductance to water vapour (m / s) and the water vapour gradient (mol / m^3):

$E = g_\mathrm{tw} D_\mathrm{wv}$

If unitless = TRUE, T_leaf is assumed in degrees K without checking.

Value

unitless = TRUE: A value in units of mol / (m ^ 2 / s) number of class numeric unitless = FALSE: A value in units of mol / (m ^ 2 / s) of class units

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

E(T_leaf, c(cs, ep, lp), FALSE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

T_leaf <- set_units(298.15, K)

E(T_leaf, c(cs, ep, lp), FALSE)

Calculate leaf energy balance

Description

Calculate leaf energy balance

Usage

energy_balance(
  tleaf,
  leaf_par,
  enviro_par,
  constants,
  quiet = FALSE,
  components = FALSE,
  set_units = FALSE
)
energy_balance(
  tleaf,
  leaf_par,
  enviro_par,
  constants,
  quiet = FALSE,
  components = FALSE,
  set_units = FALSE
)

Arguments

`tleaf`	Leaf temperature in Kelvin. If input is numeric, it will be automatically converted to `units`.
`leaf_par`	A list of leaf parameters. This can be generated using the `make_leafpar` function.
`enviro_par`	A list of environmental parameters. This can be generated using the `make_enviropar` function.
`constants`	A list of physical constants. This can be generated using the `make_constants` function.
`quiet`	Logical. Should a message appear about conversion from `numeric` to `units`? Useful for finding leaf temperature that balances heat transfer using `uniroot`.
`components`	Logical. Should leaf energy components be returned? Transpiration (in mol / (m^2 s)) also returned.
`set_units`	Logical. Should `units` be set? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Value

A numeric value in W / m^2. Optionally, a named list of energy balance components in W / m^2 and transpiration in mol / (m^2 s).

Examples


library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()
ep$T_sky <- ep$T_sky(ep)

T_leaf <- set_units(298.15, K)

energy_balance(T_leaf, lp, ep, cs, FALSE, TRUE, TRUE)

library(tealeaves)

cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()
ep$T_sky <- ep$T_sky(ep)

T_leaf <- set_units(298.15, K)

energy_balance(T_leaf, lp, ep, cs, FALSE, TRUE, TRUE)

S3 class enviro_par

Description

Constructor function for enviro_par class. This function ensures that environmental parameter inputs are properly formatted.

Usage

enviro_par(.x)
enviro_par(.x)

Arguments

`.x`	A list to be constructed into enviro_par. If units are not provided, they will be set without conversion. If units are provided, they will be checked and converted to units that tealeaves uses.

S3 class leaf_par

Description

Constructor function for leaf_par class. This function ensures that leaf parameter inputs are properly formatted.

Usage

leaf_par(.x)
leaf_par(.x)

Arguments

`.x`	A list to be constructed into leaf_par. If units are not provided, they will be set without conversion. If units are provided, they will be checked and converted to units that tealeaves uses.

Make lists of parameters of leaf, environmental, or constant parameters

Description

Make lists of parameters of leaf, environmental, or constant parameters

make_leafpar

make_enviropar

make_constants

Usage

make_leafpar(replace = NULL)

make_enviropar(replace = NULL)

make_constants(replace = NULL)
make_leafpar(replace = NULL)

make_enviropar(replace = NULL)

make_constants(replace = NULL)

Arguments

replace

A named list of parameters to replace defaults. If NULL, defaults will be used.

Details

Leaf parameters:

Symbol	R	Description	Units	Default
$d$	`leafsize`	Leaf characteristic dimension	m	0.1
$\alpha_\mathrm{l}$	`abs_l`	absorbtivity of longwave radiation (4 - 80 $\mu$ m)	none	0.97
$\alpha_\mathrm{s}$	`abs_s`	absorbtivity of shortwave radiation (0.3 - 4 $\mu$ m)	none	0.50
$g_\mathrm{sw}$	`g_sw`	stomatal conductance to H2O	( $\mu$ mol H2O) / (m $^2$ s Pa)	5
$g_\mathrm{uw}$	`g_uw`	cuticular conductance to H2O	( $\mu$ mol H2O) / (m $^2$ s Pa)	0.1
$\mathrm{logit}(sr)$	`logit_sr`	stomatal ratio (logit transformed)	none	0 = logit(0.5)

Environment parameters:

Symbol	R	Description	Units	Default
$P$	`P`	atmospheric pressure	kPa	101.3246
$r$	`r`	reflectance for shortwave irradiance (albedo)	none	0.2
$\mathrm{RH}$	`RH`	relative humidity	none	0.50
$S_\mathrm{sw}$	`S_sw`	incident short-wave (solar) radiation flux density	W / m $^2$	1000
$S_\mathrm{lw}$	`S_lw`	incident long-wave radiation flux density	W / m $^2$	calculated
$T_\mathrm{air}$	`T_air`	air temperature	K	298.15
$u$	`wind`	windspeed	m / s	2

Constants:

Symbol	R	Description	Units	Default
$c_p$	`c_p`	heat capacity of air	J / (g K)	1.01
$D_{h,0}$	`D_h0`	diffusion coefficient for heat in air at 0 °C	m $^2$ / s	19.0e-06
$D_{m,0}$	`D_m0`	diffusion coefficient for momentum in air at 0 °C	m $^2$ / s	13.3e-06
$D_{w,0}$	`D_w0`	diffusion coefficient for water vapour in air at 0 C	m $^2$ / s	21.2e-06
$\epsilon$	`epsilon`	ratio of water to air molar masses	none	0.622
$eT$	`eT`	exponent for temperature dependence of diffusion	none	1.75
$G$	`G`	gravitational acceleration	m / s $^2$	9.8
$Nu$	`Nu`	Nusselt number	none	calculated
$R$	`R`	ideal gas constant	J / (mol K)	8.3144598
$R_\mathrm{air}$	`R_air`	specific gas constant for dry air	J / (kg K)	287.058
$\sigma$	`s`	Stefan-Boltzmann constant	W / (m $^2$ K $^4$ )	5.67e-08
$Sh$	`Sh`	Sherwood number	none	calculated

Value

make_leafpar: An object inheriting from class leaf_par
make_enviropar: An object inheriting from class enviro_par
make_constants: An object inheriting from class constants

Examples


library(tealeaves)

# Use defaults
cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

# Replace defaults

ep <- make_enviropar(
  replace = list(
    T_air = set_units(300, K)
  )
)

lp <- make_leafpar(
  replace = list(
    leafsize = set_units(c(0.1, 0.2), m)
  )
)

library(tealeaves)

# Use defaults
cs <- make_constants()
ep <- make_enviropar()
lp <- make_leafpar()

# Replace defaults

ep <- make_enviropar(
  replace = list(
    T_air = set_units(300, K)
  )
)

lp <- make_leafpar(
  replace = list(
    leafsize = set_units(c(0.1, 0.2), m)
  )
)

Get vector of parameter names

Description

Get vector of parameter names

Usage

parameter_names(which)
parameter_names(which)

Arguments

which

A character string indicating which parameter names to retrieve, "constants", "enviro", or "leaf". Partial matching allowed.

Examples

parameter_names("leaf")

parameter_names("leaf")

`tealeaves` package

Description

Solve for Leaf Temperature Using Energy Balance

Details

See the README on GitHub

tealeaves example output 1

Description

An example output from the tealeaves function.

Usage

tl_example1
tl_example1

Format

A data frame with 150 rows and 20 variables:

`tleaves`: find leaf temperatures for multiple parameter sets

Description

tleaves: find leaf temperatures for multiple parameter sets

tleaf: find leaf temperatures for a single parameter set

Usage

tleaves(
  leaf_par,
  enviro_par,
  constants,
  progress = TRUE,
  quiet = FALSE,
  set_units = TRUE,
  parallel = FALSE
)

tleaf(leaf_par, enviro_par, constants, quiet = FALSE, set_units = TRUE)
tleaves(
  leaf_par,
  enviro_par,
  constants,
  progress = TRUE,
  quiet = FALSE,
  set_units = TRUE,
  parallel = FALSE
)

tleaf(leaf_par, enviro_par, constants, quiet = FALSE, set_units = TRUE)

Arguments

`leaf_par`	A list of leaf parameters. This can be generated using the `make_leafpar` function.
`enviro_par`	A list of environmental parameters. This can be generated using the `make_enviropar` function.
`constants`	A list of physical constants. This can be generated using the `make_constants` function.
`progress`	Logical. Should a progress bar be displayed?
`quiet`	Logical. Should messages be displayed?
`set_units`	Logical. Should `units` be set? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.
`parallel`	Logical. Should parallel processing be used via `future_map`?

Value

tleaves:

A tibble with the following units columns

Input:
`abs_l`	Absorbtivity of longwave radiation (unitless)
`abs_s`	Absorbtivity of shortwave radiation (unitless)
`g_sw`	Stomatal conductance to H2O ( $\mu$ mol H2O / (m^2 s Pa))
`g_uw`	Cuticular conductance to H2O ( $\mu$ mol H2O / (m^2 s Pa))
`leafsize` Leaf characteristic dimension	(m)
`logit_sr`	Stomatal ratio (logit transformed; unitless)
`P`	Atmospheric pressure (kPa)
`RH`	Relative humidity (unitless)
`S_lw`	incident long-wave radiation flux density (W / m^2)
`S_sw`	incident short-wave (solar) radiation flux density (W / m^2)
`T_air`	Air temperature (K)
`wind`	Wind speed (m / s)
Output:
`T_leaf`	Equilibrium leaf tempearture (K)
`value`	Leaf energy balance (W / m^2) at `tleaf`
`convergence`	Convergence code (0 = converged)
`R_abs`	Total absorbed radiation (W / m^2; see `.get_Rabs`)
`S_r`	Thermal infrared radiation loss (W / m^2; see `.get_Sr`)
`H`	Sensible heat flux density (W / m^2; see `.get_H`)
`L`	Latent heat flux density (W / m^2; see `.get_L`)
`E`	Evapotranspiration (mol H2O/ (m^2 s))

tleaf:

A data.frame with the following numeric columns:

`T_leaf`	Equilibrium leaf temperature (K)
`value`	Leaf energy balance (W / m^2) at `tleaf`
`convergence`	Convergence code (0 = converged)
`R_abs`	Total absorbed radiation (W / m^2; see `.get_Rabs`)
`S_r`	Longwave re-radiation (W / m^2; see `.get_Sr`)
`H`	Sensible heat flux density (W / m^2; see `.get_H`)
`L`	Latent heat flux density (W / m^2; see `.get_L`)
`E`	Evapotranspiration (mol H2O/ (m^2 s))

Examples

# tleaf for single parameter set:

leaf_par <- make_leafpar()
enviro_par <- make_enviropar()
constants <- make_constants()
tleaf(leaf_par, enviro_par, constants)

# tleaves for multiple parameter set:

enviro_par <- make_enviropar(
  replace = list(
    T_air = set_units(c(293.15, 298.15), K)
  )
)
tleaves(leaf_par, enviro_par, constants)

# tleaf for single parameter set:

leaf_par <- make_leafpar()
enviro_par <- make_enviropar()
constants <- make_constants()
tleaf(leaf_par, enviro_par, constants)

# tleaves for multiple parameter set:

enviro_par <- make_enviropar(
  replace = list(
    T_air = set_units(c(293.15, 298.15), K)
  )
)
tleaves(leaf_par, enviro_par, constants)

Package 'tealeaves'

Help Index

d_wv: water vapour gradient (mol / m ^ 3)

Description

Usage

Arguments

Details

Value

Examples

D_x: Calculate diffusion coefficient for a given temperature and pressure

Description

Usage

Arguments

Details

Value

References

Examples

g_bw: Boundary layer conductance to water vapour (m / s)

Description

Usage

Arguments

Details

Value

Examples

g_h: boundary layer conductance to heat (m / s)

Description

Usage

Arguments

Details

Value

Examples

Gr: Grashof number

Description

Usage

Arguments

Details

Value

Examples

g_tw: total conductance to water vapour (m/s)

Description

Usage

Arguments

Details

Value

Examples

H: sensible heat flux density (W / m^2)

Description

Usage

Arguments

Details

Value

See Also

Examples

h_vap: heat of vaporization (J / mol)

Description

Usage

Arguments

Details

Value

References

Examples

L: Latent heat flux density (W / m^2)

Description

Usage

Arguments

Details

Value

Examples

Nu: Nusselt number

Description

Usage

Arguments

Details

Value

Examples

P_a: density of dry air (g / m^3)

Description

Usage

Arguments

Details