Tables_of_variables.ipynb

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)

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}