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License: OTHER
Kernel: SageMath 7.3

Table of symbolic variables used in other worksheets

Below, we import variables and their definitions and units from other worksheets and display them in a sorted table. We also generate latex code for inclusion in manuscript.

%%capture storage
# The above redirects all output of the below commands to the variable 'storage' instead of displaying it.
# It can be viewed by typing: 'storage()'
# Setting up worksheet and importing equations for explicit leaf energy balance
load('temp/Worksheet_setup.sage')

# List all .ipynb files
list_files = os.listdir('.')
for fname in list_files:
    if fname[-5:] == 'ipynb':
        print fname
Tables_of_variables.ipynb Worksheet_update.ipynb Worksheet_setup.ipynb stomatal_cond_eqs.ipynb leaf_chamber_eqs.ipynb leaf_chamber_data.ipynb leaf_enbalance_eqs.ipynb E_PM_eqs.ipynb 
# From leaf_enbalance_eqs, E_PM_eqs and stomatal_cond_eqs

load_session('temp/leaf_enbalance_eqs.sobj')
dict_vars1 = dict_vars.copy()

load_session('temp/stomatal_cond_eqs.sobj')
dict_vars1.update(dict_vars)

load_session('temp/E_PM_eqs.sobj')
dict_vars1.update(dict_vars)

dict_vars = dict_vars1.copy()
fun_loadvars(vardict=dict_vars)   # re-loading variable definitions
udict = {}
for key1 in dict_vars.keys():
    udict[key1] = dict_vars[key1]['units']     # exporting units information from dict_vars to udict, which will be used below.

# Creating dictionary to substitute names of units with shorter forms
var('m s J Pa K kg mol')
subsdict = {meter: m, second: s, joule: J, pascal: Pa, kelvin: K, kilogram: kg, mole: mol}
var('N_Re_L N_Re_c N_Le N_Nu_L N_Gr_L N_Sh_L')
dict_varnew = {Re: N_Re_L, Re_c: N_Re_c, Le: N_Le, Nu: N_Nu_L, Gr: N_Gr_L, Sh: N_Sh_L}
dict_varold = {v: k for k, v in dict_varnew.iteritems()}
variables = sorted([str(variable.subs(dict_varnew)) for variable in udict.keys()],key=str.lower)
tableheader = [('Variable', 'Description (value)', 'Units')]
tabledata = [('Variable', 'Description (value)', 'Units')]
for variable1 in variables:
    variable2 = eval(variable1).subs(dict_varold)
    variable = str(variable2)
    tabledata.append((eval(variable),docdict[eval(variable)],fun_units_formatted(variable)))

table(tabledata, header_row=True)
Variable Description (value) Units
Cross-sectional pore area m
Fraction of one-sided leaf area covered by stomata (1 if stomata are on one side only, 2 if they are on both sides) 1
Fraction of projected area exchanging sensible heat with the air (2) 1
Thermal diffusivity of dry air m s
Boundary layer thickness m
Bowen ratio (sensible/latent heat flux) 1
Latent heat transfer coefficient J Pa m s
Sensible heat transfer coefficient J K m s
Specific heat of dry air (1010) J K kg
Concentration of water in the free air mol m
Concentration of water in the leaf air space mol m
Pore depth m
Binary diffusion coefficient of water vapour in air m s
Slope of saturation vapour pressure at air temperature Pa K
Latent heat flux from leaf J m s
Transpiration rate in molar units mol m s
Latent heat flux from a wet surface J m s
Water to air molecular weight ratio (0.622) 1
Longwave emmissivity of the leaf surface (1.0) 1
Fractional pore area (pore area per unit leaf area) 1
Wind function in Penman approach, f(u) adapted to energetic units J Pa m s
Gravitational acceleration (9.81) m s
Boundary layer conductance to water vapour m s
Boundary layer conductance to water vapour mol m s
Diffusive conductance of a stomatal pore mol m s
Stomatal conductance to water vapour m s
Stomatal conductance to water vapour mol m s
Total leaf conductance to water vapour m s
Total leaf layer conductance to water vapour mol m s
Psychrometric constant Pa K
Average 1-sided convective transfer coefficient J K m s
Sensible heat flux from leaf J m s
Thermal conductivity of dry air J K m s
Ratio mol m s
Characteristic length scale for convection (size of leaf) m
Pore length m
Latent heat of evaporation (2.45e6) J kg
Molar mass of nitrogen (0.028) kg mol
Molar mass of oxygen (0.032) kg mol
Molar mass of water (0.018) kg mol
Grashof number 1
Lewis number 1
n=2 for hypostomatous, n=1 for amphistomatous leaves 1
Nusselt number 1
Pore density m
Critical Reynolds number for the onset of turbulence 1
Reynolds number 1
Sherwood number 1
Kinematic viscosity of dry air m s
Air pressure Pa
Partial pressure of nitrogen in the atmosphere Pa
Partial pressure of oxygen in the atmosphere Pa
Vapour pressure in the atmosphere Pa
Saturation vapour pressure at air temperature Pa
Vapour pressure inside the leaf Pa
Prandtl number (0.71) 1
One-sided boundary layer resistance to heat transfer ( in \citet[][P. 231]{monteith_principles_2013}) s m
Boundary layer resistance to water vapour, inverse of s m
Leaf BL resistance in molar units s m mol
End correction, representing resistance between evaporating sites and pores s m mol
Longwave radiation away from leaf J m s
Molar gas constant (8.314472) J K mol
Pore radius (for ellipsoidal pores, half the pore width) m
Solar shortwave flux J m s
Stomatal resistance to water vapour \citep[][P. 231]{monteith_principles_2013} s m
Diffusive resistance of a stomatal pore s m mol
Stomatal resistance to water vapour, inverse of s m
Total leaf resistance to water vapour, s m
Leaf BL resistance to water vapour, \citep[][Eq. 13.16]{monteith_principles_2013} s m
Diffusive resistance of a stomatal vapour shell s m mol
Density of dry air kg m
Density of air at the leaf surface kg m
Factor representing stomatal resistance in \citet{penman_physical_1952} 1
Spacing between stomata m
Stefan-Boltzmann constant (5.67e-8) J K m s
Air temperature K
Leaf temperature K
Radiative temperature of objects surrounding the leaf K
Molar volume of air m mol
Wind velocity m s 
latex(table(tabledata))
\begin{tabular}{lll} Variable & Description (value) & Units \\ $A_{p}$ & Cross-sectional pore area & m$^{2}$ \\ $a_{s}$ & Fraction of one-sided leaf area covered by stomata (1 if stomata are on one side only, 2 if they are on both sides) & 1 \\ ${a_{sh}}$ & Fraction of projected area exchanging sensible heat with the air (2) & 1 \\ $\alpha_{a}$ & Thermal diffusivity of dry air & m$^{2}$ s$^{-1}$ \\ $B_{l}$ & Boundary layer thickness & m \\ ${\beta_B}$ & Bowen ratio (sensible/latent heat flux) & 1 \\ $c_{E}$ & Latent heat transfer coefficient & J Pa$^{-1}$ m$^{-2}$ s$^{-1}$ \\ $c_{H}$ & Sensible heat transfer coefficient & J K$^{-1}$ m$^{-2}$ s$^{-1}$ \\ ${c_{pa}}$ & Specific heat of dry air (1010) & J K$^{-1}$ kg$^{-1}$ \\ ${C_{wa}}$ & Concentration of water in the free air & mol m$^{-3}$ \\ ${C_{wl}}$ & Concentration of water in the leaf air space & mol m$^{-3}$ \\ $d_{p}$ & Pore depth & m \\ ${D_{va}}$ & Binary diffusion coefficient of water vapour in air & m$^{2}$ s$^{-1}$ \\ ${\Delta_{eTa}}$ & Slope of saturation vapour pressure at air temperature & Pa K$^{-1}$ \\ $E_{l}$ & Latent heat flux from leaf & J m$^{-2}$ s$^{-1}$ \\ ${E_{l,mol}}$ & Transpiration rate in molar units & mol m$^{-2}$ s$^{-1}$ \\ $E_{w}$ & Latent heat flux from a wet surface & J m$^{-2}$ s$^{-1}$ \\ $\epsilon$ & Water to air molecular weight ratio (0.622) & 1 \\ $\epsilon_{l}$ & Longwave emmissivity of the leaf surface (1.0) & 1 \\ $F_{p}$ & Fractional pore area (pore area per unit leaf area) & 1 \\ $f_{u}$ & Wind function in Penman approach, f(u) adapted to energetic units & J Pa$^{-1}$ m$^{-2}$ s$^{-1}$ \\ $g$ & Gravitational acceleration (9.81) & m s$^{-2}$ \\ ${g_{bw}}$ & Boundary layer conductance to water vapour & m s$^{-1}$ \\ ${g_{bw,mol}}$ & Boundary layer conductance to water vapour & mol m$^{-2}$ s$^{-1}$ \\ $g_{\mathit{sp}}$ & Diffusive conductance of a stomatal pore & mol m$^{-2}$ s$^{-1}$ \\ ${g_{sw}}$ & Stomatal conductance to water vapour & m s$^{-1}$ \\ ${g_{sw,mol}}$ & Stomatal conductance to water vapour & mol m$^{-2}$ s$^{-1}$ \\ ${g_{tw}}$ & Total leaf conductance to water vapour & m s$^{-1}$ \\ ${g_{tw,mol}}$ & Total leaf layer conductance to water vapour & mol m$^{-2}$ s$^{-1}$ \\ $\gamma_{v}$ & Psychrometric constant & Pa K$^{-1}$ \\ $h_{c}$ & Average 1-sided convective transfer coefficient & J K$^{-1}$ m$^{-2}$ s$^{-1}$ \\ $H_{l}$ & Sensible heat flux from leaf & J m$^{-2}$ s$^{-1}$ \\ $k_{a}$ & Thermal conductivity of dry air & J K$^{-1}$ m$^{-1}$ s$^{-1}$ \\ ${k_{dv}}$ & Ratio $D_{va}/V_m$ & mol m$^{-1}$ s$^{-1}$ \\ $L_{l}$ & Characteristic length scale for convection (size of leaf) & m \\ $l_{p}$ & Pore length & m \\ $\lambda_{E}$ & Latent heat of evaporation (2.45e6) & J kg$^{-1}$ \\ $M_{N_{2}}$ & Molar mass of nitrogen (0.028) & kg mol$^{-1}$ \\ $M_{O_{2}}$ & Molar mass of oxygen (0.032) & kg mol$^{-1}$ \\ $M_{w}$ & Molar mass of water (0.018) & kg mol$^{-1}$ \\ ${N_{Gr_L}}$ & Grashof number & 1 \\ ${N_{Le}}$ & Lewis number & 1 \\ $n_{\mathit{MU}}$ & n=2 for hypostomatous, n=1 for amphistomatous leaves & 1 \\ ${N_{Nu_L}}$ & Nusselt number & 1 \\ $n_{p}$ & Pore density & m$^{-2}$ \\ ${N_{Re_c}}$ & Critical Reynolds number for the onset of turbulence & 1 \\ ${N_{Re_L}}$ & Reynolds number & 1 \\ ${N_{Sh_L}}$ & Sherwood number & 1 \\ $\nu_{a}$ & Kinematic viscosity of dry air & m$^{2}$ s$^{-1}$ \\ $P_{a}$ & Air pressure & Pa \\ ${P_{N2}}$ & Partial pressure of nitrogen in the atmosphere & Pa \\ ${P_{O2}}$ & Partial pressure of oxygen in the atmosphere & Pa \\ ${P_{wa}}$ & Vapour pressure in the atmosphere & Pa \\ ${P_{was}}$ & Saturation vapour pressure at air temperature & Pa \\ ${P_{wl}}$ & Vapour pressure inside the leaf & Pa \\ ${N_{Pr}}$ & Prandtl number (0.71) & 1 \\ $r_{a}$ & One-sided boundary layer resistance to heat transfer ($r_H$ in \citet[][P. 231]{monteith_principles_2013}) & s m$^{-1}$ \\ ${r_{bw}}$ & Boundary layer resistance to water vapour, inverse of $g_{bw}$ & s m$^{-1}$ \\ ${r_{bw,mol}}$ & Leaf BL resistance in molar units & s m$^{2}$ mol$^{-1}$ \\ $r_{\mathit{end}}$ & End correction, representing resistance between evaporating sites and pores & s m$^{2}$ mol$^{-1}$ \\ ${R_{ll}}$ & Longwave radiation away from leaf & J m$^{-2}$ s$^{-1}$ \\ ${R_{mol}}$ & Molar gas constant (8.314472) & J K$^{-1}$ mol$^{-1}$ \\ $r_{p}$ & Pore radius (for ellipsoidal pores, half the pore width) & m \\ $R_{s}$ & Solar shortwave flux & J m$^{-2}$ s$^{-1}$ \\ $r_{s}$ & Stomatal resistance to water vapour \citep[][P. 231]{monteith_principles_2013} & s m$^{-1}$ \\ $r_{\mathit{sp}}$ & Diffusive resistance of a stomatal pore & s m$^{2}$ mol$^{-1}$ \\ ${r_{sw}}$ & Stomatal resistance to water vapour, inverse of $g_{sw}$ & s m$^{-1}$ \\ ${r_{tw}}$ & Total leaf resistance to water vapour, $r_{bv} + r_{sv}$ & s m$^{-1}$ \\ ${r_{v}}$ & Leaf BL resistance to water vapour, \citep[][Eq. 13.16]{monteith_principles_2013} & s m$^{-1}$ \\ $r_{\mathit{vs}}$ & Diffusive resistance of a stomatal vapour shell & s m$^{2}$ mol$^{-1}$ \\ $\rho_{a}$ & Density of dry air & kg m$^{-3}$ \\ $\rho_{\mathit{al}}$ & Density of air at the leaf surface & kg m$^{-3}$ \\ $S$ & Factor representing stomatal resistance in \citet{penman_physical_1952} & 1 \\ $s_{p}$ & Spacing between stomata & m \\ ${\sigma}$ & Stefan-Boltzmann constant (5.67e-8) & J K$^{-4}$ m$^{-2}$ s$^{-1}$ \\ $T_{a}$ & Air temperature & K \\ $T_{l}$ & Leaf temperature & K \\ $T_{w}$ & Radiative temperature of objects surrounding the leaf & K \\ $V_{m}$ & Molar volume of air & m$^{3}$ mol$^{-1}$ \\ $v_{w}$ & Wind velocity & m s$^{-1}$ \\ \end{tabular}