Tables_of_variables.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table of symbolic variables used in other worksheets\n",
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%capture storage\n",
    "# The above redirects all output of the below commands to the variable 'storage' instead of displaying it.\n",
    "# It can be viewed by typing: 'storage()'\n",
    "# Setting up worksheet and importing equations for explicit leaf energy balance\n",
    "load('temp/Worksheet_setup.sage')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tables_of_variables.ipynb\n",
      "perforated_foils_data.ipynb\n",
      "Worksheet_update.ipynb\n",
      "leaf_enbalance2s_eqs.ipynb\n",
      "Worksheet_setup.ipynb\n",
      "stomatal_cond_eqs.ipynb\n",
      "leaf_chamber_eqs.ipynb\n",
      "leaf_chamber_data.ipynb\n",
      "leaf_enbalance_eqs.ipynb\n",
      "E_PM_eqs.ipynb\n"
     ]
    }
   ],
   "source": [
    "# List all .ipynb files\n",
    "list_files = os.listdir('.')\n",
    "for fname in list_files:\n",
    "    if fname[-5:] == 'ipynb':\n",
    "        print fname"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# From leaf_chamber_eqs, Leaf_enbalance2s_eqs and stomatal_cond_eqs\n",
    "\n",
    "load_session('temp/leaf_enbalance2s_eqs.sobj')\n",
    "dict_vars1 = dict_vars.copy()\n",
    "\n",
    "load_session('temp/stomatal_cond_eqs.sobj')\n",
    "dict_vars1.update(dict_vars)\n",
    "\n",
    "load_session('temp/leaf_chamber_eqs.sobj')\n",
    "dict_vars1.update(dict_vars)\n",
    "\n",
    "dict_vars = dict_vars1.copy()\n",
    "fun_loadvars(vardict=dict_vars)   # re-loading variable definitions\n",
    "udict = {}\n",
    "for key1 in dict_vars.keys():\n",
    "    udict[key1] = dict_vars[key1]['units']     # exporting units information from dict_vars to udict, which will be used below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"notruncate\">\n",
       "<table  class=\"table_form\">\n",
       "<tbody>\n",
       "<tr>\n",
       "<th>Variable</th>\n",
       "<th>Description (value)</th>\n",
       "<th>Units</th>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">A_{p}</script></td>\n",
       "<td>Cross-sectional pore area</td>\n",
       "<td> m<script type=\"math/tex\">^{2}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">a_{s}</script></td>\n",
       "<td>Fraction of one-sided leaf area covered by stomata (1 if stomata are on one side only, 2 if they are on both sides)</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{a_{sh}}</script></td>\n",
       "<td>Fraction of projected area exchanging sensible heat with the air (2)</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">\\alpha_{a}</script></td>\n",
       "<td>Thermal diffusivity of dry air</td>\n",
       "<td> m<script type=\"math/tex\">^{2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">B_{l}</script></td>\n",
       "<td>Boundary layer thickness</td>\n",
       "<td>m </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{c_{pa}}</script></td>\n",
       "<td>Specific heat of dry air (1010) </td>\n",
       "<td>J  K<script type=\"math/tex\">^{-1}</script>  kg<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{C_{wa}}</script></td>\n",
       "<td>Concentration of water in the free air </td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-3}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{C_{wl}}</script></td>\n",
       "<td>Concentration of water in the leaf air space </td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-3}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">d_{p}</script></td>\n",
       "<td>Pore depth</td>\n",
       "<td>m </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{D_{va}}</script></td>\n",
       "<td>Binary diffusion coefficient of water vapour in air</td>\n",
       "<td> m<script type=\"math/tex\">^{2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">E_{l}</script></td>\n",
       "<td>Latent heat flux from leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{E_{l_l}}</script></td>\n",
       "<td>Latent heat flux from lower side of leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{E_{l,mol}}</script></td>\n",
       "<td>Transpiration rate in molar units</td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{E_{l_u}}</script></td>\n",
       "<td>Latent heat flux from upper side of leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">\\epsilon_{l}</script></td>\n",
       "<td>Longwave emmissivity of the leaf surface (1.0)</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">F_{p}</script></td>\n",
       "<td>Fractional pore area (pore area per unit leaf area)</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">g</script></td>\n",
       "<td>Gravitational acceleration (9.81)</td>\n",
       "<td>m  s<script type=\"math/tex\">^{-2}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{g_{bw}}</script></td>\n",
       "<td>Boundary layer conductance to water vapour </td>\n",
       "<td>m  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{g_{bw,mol}}</script></td>\n",
       "<td>Boundary layer conductance to water vapour </td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">g_{\\mathit{sp}}</script></td>\n",
       "<td>Diffusive conductance of a stomatal pore</td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{g_{sw}}</script></td>\n",
       "<td>Stomatal conductance to water vapour</td>\n",
       "<td>m  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{g_{sw_l}}</script></td>\n",
       "<td>Stomatal conductance to water vapour on lower side</td>\n",
       "<td>m  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{g_{sw,mol}}</script></td>\n",
       "<td>Stomatal conductance to water vapour</td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{g_{sw_u}}</script></td>\n",
       "<td>Stomatal conductance to water vapour on upper side</td>\n",
       "<td>m  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{g_{tw}}</script></td>\n",
       "<td>Total leaf conductance to water vapour</td>\n",
       "<td>m  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{g_{tw,mol}}</script></td>\n",
       "<td>Total leaf layer conductance to water vapour</td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">h_{c}</script></td>\n",
       "<td>Average 1-sided convective transfer coefficient</td>\n",
       "<td>J  K<script type=\"math/tex\">^{-1}</script>  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{h_{c_l}}</script></td>\n",
       "<td>Sensible heat flux coefficient on lower leaf side</td>\n",
       "<td>J  K<script type=\"math/tex\">^{-1}</script>  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{h_{c_u}}</script></td>\n",
       "<td>Sensible heat flux coefficient on upper leaf side</td>\n",
       "<td>J  K<script type=\"math/tex\">^{-1}</script>  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">H_{l}</script></td>\n",
       "<td>Sensible heat flux from leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{H_{l_l}}</script></td>\n",
       "<td>Sensible heat flux from lower side of leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{H_{l_u}}</script></td>\n",
       "<td>Sensible heat flux from upper side of leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">k_{a}</script></td>\n",
       "<td>Thermal conductivity of dry air</td>\n",
       "<td>J  K<script type=\"math/tex\">^{-1}</script>  m<script type=\"math/tex\">^{-1}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{k_{dv}}</script></td>\n",
       "<td>Ratio <script type=\"math/tex\">D_{va}/V_m</script></td>\n",
       "<td>mol  m<script type=\"math/tex\">^{-1}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">k_{l}</script></td>\n",
       "<td>Thermal conductivity of a fresh leaf</td>\n",
       "<td>J  K<script type=\"math/tex\">^{-1}</script>  m<script type=\"math/tex\">^{-1}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">L_{l}</script></td>\n",
       "<td>Characteristic length scale for convection (size of leaf)</td>\n",
       "<td>m </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">l_{p}</script></td>\n",
       "<td>Pore length</td>\n",
       "<td>m </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">\\lambda_{E}</script></td>\n",
       "<td>Latent heat of evaporation (2.45e6)</td>\n",
       "<td>J  kg<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">M_{N_{2}}</script></td>\n",
       "<td>Molar mass of nitrogen (0.028)</td>\n",
       "<td>kg  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">M_{O_{2}}</script></td>\n",
       "<td>Molar mass of oxygen (0.032)</td>\n",
       "<td>kg  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">M_{w}</script></td>\n",
       "<td>Molar mass of water (0.018)</td>\n",
       "<td>kg  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{N_{Gr_L}}</script></td>\n",
       "<td>Grashof number</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{N_{Le}}</script></td>\n",
       "<td>Lewis number</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{N_{Nu_L}}</script></td>\n",
       "<td>Nusselt number</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">n_{p}</script></td>\n",
       "<td>Pore density</td>\n",
       "<td> m<script type=\"math/tex\">^{-2}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{N_{Re_c}}</script></td>\n",
       "<td>Critical Reynolds number for the onset of turbulence</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{N_{Re_L}}</script></td>\n",
       "<td>Reynolds number</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{N_{Sh_L}}</script></td>\n",
       "<td>Sherwood number</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">\\nu_{a}</script></td>\n",
       "<td>Kinematic viscosity of dry air</td>\n",
       "<td> m<script type=\"math/tex\">^{2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">P_{a}</script></td>\n",
       "<td>Air pressure</td>\n",
       "<td>Pa </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{P_{N2}}</script></td>\n",
       "<td>Partial pressure of nitrogen in the atmosphere</td>\n",
       "<td>Pa </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{P_{O2}}</script></td>\n",
       "<td>Partial pressure of oxygen in the atmosphere</td>\n",
       "<td>Pa </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{P_{wa}}</script></td>\n",
       "<td>Vapour pressure in the atmosphere</td>\n",
       "<td>Pa </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{P_{was}}</script></td>\n",
       "<td>Saturation vapour pressure at air temperature</td>\n",
       "<td>Pa </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{P_{wl}}</script></td>\n",
       "<td>Vapour pressure inside the leaf</td>\n",
       "<td>Pa </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{N_{Pr}}</script></td>\n",
       "<td>Prandtl number (0.71)</td>\n",
       "<td>1 </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">Q_{l}</script></td>\n",
       "<td>Conductive heat flux from upper to lower side of leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{r_{bw}}</script></td>\n",
       "<td>Boundary layer resistance to water vapour, inverse of <script type=\"math/tex\">g_{bw}</script></td>\n",
       "<td>s  m<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{r_{bw,mol}}</script></td>\n",
       "<td>Leaf BL resistance in molar units</td>\n",
       "<td>s  m<script type=\"math/tex\">^{2}</script>  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">r_{\\mathit{end}}</script></td>\n",
       "<td>End correction, representing resistance between evaporating sites and pores</td>\n",
       "<td>s  m<script type=\"math/tex\">^{2}</script>  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{R_{ll}}</script></td>\n",
       "<td>Longwave radiation away from leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{R_{ll_l}}</script></td>\n",
       "<td>Longwave heat flux from lower side of leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{R_{ll_u}}</script></td>\n",
       "<td>Longwave heat flux from upper side of leaf</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{R_{mol}}</script></td>\n",
       "<td>Molar gas constant (8.314472)</td>\n",
       "<td>J  K<script type=\"math/tex\">^{-1}</script>  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">r_{p}</script></td>\n",
       "<td>Pore radius (for ellipsoidal pores, half the pore width)</td>\n",
       "<td>m </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">R_{s}</script></td>\n",
       "<td>Solar shortwave flux</td>\n",
       "<td>J  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">r_{\\mathit{sp}}</script></td>\n",
       "<td>Diffusive resistance of a stomatal pore</td>\n",
       "<td>s  m<script type=\"math/tex\">^{2}</script>  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{r_{sw}}</script></td>\n",
       "<td>Stomatal resistance to water vapour, inverse of <script type=\"math/tex\">g_{sw}</script></td>\n",
       "<td>s  m<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{r_{tw}}</script></td>\n",
       "<td>Total leaf resistance to water vapour, <script type=\"math/tex\">r_{bv} + r_{sv}</script></td>\n",
       "<td>s  m<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">r_{\\mathit{vs}}</script></td>\n",
       "<td>Diffusive resistance of a stomatal vapour shell</td>\n",
       "<td>s  m<script type=\"math/tex\">^{2}</script>  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">\\rho_{a}</script></td>\n",
       "<td>Density of dry air</td>\n",
       "<td>kg  m<script type=\"math/tex\">^{-3}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">\\rho_{\\mathit{al}}</script></td>\n",
       "<td>Density of air at the leaf surface</td>\n",
       "<td>kg  m<script type=\"math/tex\">^{-3}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">s_{p}</script></td>\n",
       "<td>Spacing between stomata</td>\n",
       "<td>m </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{\\sigma}</script></td>\n",
       "<td>Stefan-Boltzmann constant (5.67e-8)</td>\n",
       "<td>J  K<script type=\"math/tex\">^{-4}</script>  m<script type=\"math/tex\">^{-2}</script>  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">T_{a}</script></td>\n",
       "<td>Air temperature</td>\n",
       "<td>K </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">T_{l}</script></td>\n",
       "<td>Leaf temperature</td>\n",
       "<td>K </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">{T_{l_l}}</script></td>\n",
       "<td>Leaf surface temperature of lower side</td>\n",
       "<td>K </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">{T_{l_u}}</script></td>\n",
       "<td>Leaf surface temperature of upper side</td>\n",
       "<td>K </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">T_{w}</script></td>\n",
       "<td>Radiative temperature of objects surrounding the leaf</td>\n",
       "<td>K </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">V_{m}</script></td>\n",
       "<td>Molar volume of air</td>\n",
       "<td> m<script type=\"math/tex\">^{3}</script>  mol<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td><script type=\"math/tex\">v_{w}</script></td>\n",
       "<td>Wind velocity</td>\n",
       "<td>m  s<script type=\"math/tex\">^{-1}</script> </td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td><script type=\"math/tex\">z_{l}</script></td>\n",
       "<td>Leaf thickness (m)</td>\n",
       "<td>m </td>\n",
       "</tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Variable    Description (value)                                                                                                   Units\n",
       "+-----------+---------------------------------------------------------------------------------------------------------------------+----------------------------------+\n",
       "  A_p         Cross-sectional pore area                                                                                              m$^{2}$\n",
       "  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\n",
       "  a_sh        Fraction of projected area exchanging sensible heat with the air (2)                                                  1\n",
       "  alpha_a     Thermal diffusivity of dry air                                                                                         m$^{2}$  s$^{-1}$\n",
       "  B_l         Boundary layer thickness                                                                                              m\n",
       "  c_pa        Specific heat of dry air (1010)                                                                                       J  K$^{-1}$  kg$^{-1}$\n",
       "  C_wa        Concentration of water in the free air                                                                                mol  m$^{-3}$\n",
       "  C_wl        Concentration of water in the leaf air space                                                                          mol  m$^{-3}$\n",
       "  d_p         Pore depth                                                                                                            m\n",
       "  D_va        Binary diffusion coefficient of water vapour in air                                                                    m$^{2}$  s$^{-1}$\n",
       "  E_l         Latent heat flux from leaf                                                                                            J  m$^{-2}$  s$^{-1}$\n",
       "  E_ll        Latent heat flux from lower side of leaf                                                                              J  m$^{-2}$  s$^{-1}$\n",
       "  E_lmol      Transpiration rate in molar units                                                                                     mol  m$^{-2}$  s$^{-1}$\n",
       "  E_lu        Latent heat flux from upper side of leaf                                                                              J  m$^{-2}$  s$^{-1}$\n",
       "  epsilon_l   Longwave emmissivity of the leaf surface (1.0)                                                                        1\n",
       "  F_p         Fractional pore area (pore area per unit leaf area)                                                                   1\n",
       "  g           Gravitational acceleration (9.81)                                                                                     m  s$^{-2}$\n",
       "  g_bw        Boundary layer conductance to water vapour                                                                            m  s$^{-1}$\n",
       "  g_bwmol     Boundary layer conductance to water vapour                                                                            mol  m$^{-2}$  s$^{-1}$\n",
       "  g_sp        Diffusive conductance of a stomatal pore                                                                              mol  m$^{-2}$  s$^{-1}$\n",
       "  g_sw        Stomatal conductance to water vapour                                                                                  m  s$^{-1}$\n",
       "  g_swl       Stomatal conductance to water vapour on lower side                                                                    m  s$^{-1}$\n",
       "  g_swmol     Stomatal conductance to water vapour                                                                                  mol  m$^{-2}$  s$^{-1}$\n",
       "  g_swu       Stomatal conductance to water vapour on upper side                                                                    m  s$^{-1}$\n",
       "  g_tw        Total leaf conductance to water vapour                                                                                m  s$^{-1}$\n",
       "  g_twmol     Total leaf layer conductance to water vapour                                                                          mol  m$^{-2}$  s$^{-1}$\n",
       "  h_c         Average 1-sided convective transfer coefficient                                                                       J  K$^{-1}$  m$^{-2}$  s$^{-1}$\n",
       "  h_cl        Sensible heat flux coefficient on lower leaf side                                                                     J  K$^{-1}$  m$^{-2}$  s$^{-1}$\n",
       "  h_cu        Sensible heat flux coefficient on upper leaf side                                                                     J  K$^{-1}$  m$^{-2}$  s$^{-1}$\n",
       "  H_l         Sensible heat flux from leaf                                                                                          J  m$^{-2}$  s$^{-1}$\n",
       "  H_ll        Sensible heat flux from lower side of leaf                                                                            J  m$^{-2}$  s$^{-1}$\n",
       "  H_lu        Sensible heat flux from upper side of leaf                                                                            J  m$^{-2}$  s$^{-1}$\n",
       "  k_a         Thermal conductivity of dry air                                                                                       J  K$^{-1}$  m$^{-1}$  s$^{-1}$\n",
       "  k_dv        Ratio $D_{va}/V_m$                                                                                                    mol  m$^{-1}$  s$^{-1}$\n",
       "  k_l         Thermal conductivity of a fresh leaf                                                                                  J  K$^{-1}$  m$^{-1}$  s$^{-1}$\n",
       "  L_l         Characteristic length scale for convection (size of leaf)                                                             m\n",
       "  l_p         Pore length                                                                                                           m\n",
       "  lambda_E    Latent heat of evaporation (2.45e6)                                                                                   J  kg$^{-1}$\n",
       "  M_N2        Molar mass of nitrogen (0.028)                                                                                        kg  mol$^{-1}$\n",
       "  M_O2        Molar mass of oxygen (0.032)                                                                                          kg  mol$^{-1}$\n",
       "  M_w         Molar mass of water (0.018)                                                                                           kg  mol$^{-1}$\n",
       "  Gr          Grashof number                                                                                                        1\n",
       "  Le          Lewis number                                                                                                          1\n",
       "  Nu          Nusselt number                                                                                                        1\n",
       "  n_p         Pore density                                                                                                           m$^{-2}$\n",
       "  Re_c        Critical Reynolds number for the onset of turbulence                                                                  1\n",
       "  Re          Reynolds number                                                                                                       1\n",
       "  Sh          Sherwood number                                                                                                       1\n",
       "  nu_a        Kinematic viscosity of dry air                                                                                         m$^{2}$  s$^{-1}$\n",
       "  P_a         Air pressure                                                                                                          Pa\n",
       "  P_N2        Partial pressure of nitrogen in the atmosphere                                                                        Pa\n",
       "  P_O2        Partial pressure of oxygen in the atmosphere                                                                          Pa\n",
       "  P_wa        Vapour pressure in the atmosphere                                                                                     Pa\n",
       "  P_was       Saturation vapour pressure at air temperature                                                                         Pa\n",
       "  P_wl        Vapour pressure inside the leaf                                                                                       Pa\n",
       "  Pr          Prandtl number (0.71)                                                                                                 1\n",
       "  Q_l         Conductive heat flux from upper to lower side of leaf                                                                 J  m$^{-2}$  s$^{-1}$\n",
       "  r_bw        Boundary layer resistance to water vapour, inverse of $g_{bw}$                                                        s  m$^{-1}$\n",
       "  r_bwmol     Leaf BL resistance in molar units                                                                                     s  m$^{2}$  mol$^{-1}$\n",
       "  r_end       End correction, representing resistance between evaporating sites and pores                                           s  m$^{2}$  mol$^{-1}$\n",
       "  R_ll        Longwave radiation away from leaf                                                                                     J  m$^{-2}$  s$^{-1}$\n",
       "  R_lll       Longwave heat flux from lower side of leaf                                                                            J  m$^{-2}$  s$^{-1}$\n",
       "  R_llu       Longwave heat flux from upper side of leaf                                                                            J  m$^{-2}$  s$^{-1}$\n",
       "  R_mol       Molar gas constant (8.314472)                                                                                         J  K$^{-1}$  mol$^{-1}$\n",
       "  r_p         Pore radius (for ellipsoidal pores, half the pore width)                                                              m\n",
       "  R_s         Solar shortwave flux                                                                                                  J  m$^{-2}$  s$^{-1}$\n",
       "  r_sp        Diffusive resistance of a stomatal pore                                                                               s  m$^{2}$  mol$^{-1}$\n",
       "  r_sw        Stomatal resistance to water vapour, inverse of $g_{sw}$                                                              s  m$^{-1}$\n",
       "  r_tw        Total leaf resistance to water vapour, $r_{bv} + r_{sv}$                                                              s  m$^{-1}$\n",
       "  r_vs        Diffusive resistance of a stomatal vapour shell                                                                       s  m$^{2}$  mol$^{-1}$\n",
       "  rho_a       Density of dry air                                                                                                    kg  m$^{-3}$\n",
       "  rho_al      Density of air at the leaf surface                                                                                    kg  m$^{-3}$\n",
       "  s_p         Spacing between stomata                                                                                               m\n",
       "  sigm        Stefan-Boltzmann constant (5.67e-8)                                                                                   J  K$^{-4}$  m$^{-2}$  s$^{-1}$\n",
       "  T_a         Air temperature                                                                                                       K\n",
       "  T_l         Leaf temperature                                                                                                      K\n",
       "  T_ll        Leaf surface temperature of lower side                                                                                K\n",
       "  T_lu        Leaf surface temperature of upper side                                                                                K\n",
       "  T_w         Radiative temperature of objects surrounding the leaf                                                                 K\n",
       "  V_m         Molar volume of air                                                                                                    m$^{3}$  mol$^{-1}$\n",
       "  v_w         Wind velocity                                                                                                         m  s$^{-1}$\n",
       "  z_l         Leaf thickness (m)                                                                                                    m"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating dictionary to substitute names of units with shorter forms\n",
    "var('m s J Pa K kg mol')\n",
    "subsdict = {meter: m, second: s, joule: J, pascal: Pa, kelvin: K, kilogram: kg, mole: mol}\n",
    "var('N_Re_L N_Re_c N_Le N_Nu_L N_Gr_L N_Sh_L')\n",
    "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}\n",
    "dict_varold = {v: k for k, v in dict_varnew.iteritems()}\n",
    "variables = sorted([str(variable.subs(dict_varnew)) for variable in udict.keys()],key=str.lower)\n",
    "tableheader = [('Variable', 'Description (value)', 'Units')]\n",
    "tabledata = [('Variable', 'Description (value)', 'Units')]\n",
    "for variable1 in variables:\n",
    "    variable2 = eval(variable1).subs(dict_varold)\n",
    "    variable = str(variable2)\n",
    "    tabledata.append((eval(variable),docdict[eval(variable)],fun_units_formatted(variable)))\n",
    "\n",
    "table(tabledata, header_row=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
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    {
     "data": {
      "text/plain": [
       "\\begin{tabular}{lll}\n",
       "Variable & Description (value) & Units \\\\\n",
       "$A_{p}$ & Cross-sectional pore area &  m$^{2}$  \\\\\n",
       "$a_{s}$ & 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  \\\\\n",
       "${a_{sh}}$ & Fraction of projected area exchanging sensible heat with the air (2) & 1  \\\\\n",
       "$\\alpha_{a}$ & Thermal diffusivity of dry air &  m$^{2}$  s$^{-1}$  \\\\\n",
       "$B_{l}$ & Boundary layer thickness & m  \\\\\n",
       "${c_{pa}}$ & Specific heat of dry air (1010)  & J  K$^{-1}$  kg$^{-1}$  \\\\\n",
       "${C_{wa}}$ & Concentration of water in the free air  & mol  m$^{-3}$  \\\\\n",
       "${C_{wl}}$ & Concentration of water in the leaf air space  & mol  m$^{-3}$  \\\\\n",
       "$d_{p}$ & Pore depth & m  \\\\\n",
       "${D_{va}}$ & Binary diffusion coefficient of water vapour in air &  m$^{2}$  s$^{-1}$  \\\\\n",
       "$E_{l}$ & Latent heat flux from leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${E_{l_l}}$ & Latent heat flux from lower side of leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${E_{l,mol}}$ & Transpiration rate in molar units & mol  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${E_{l_u}}$ & Latent heat flux from upper side of leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "$\\epsilon_{l}$ & Longwave emmissivity of the leaf surface (1.0) & 1  \\\\\n",
       "$F_{p}$ & Fractional pore area (pore area per unit leaf area) & 1  \\\\\n",
       "$g$ & Gravitational acceleration (9.81) & m  s$^{-2}$  \\\\\n",
       "${g_{bw}}$ & Boundary layer conductance to water vapour  & m  s$^{-1}$  \\\\\n",
       "${g_{bw,mol}}$ & Boundary layer conductance to water vapour  & mol  m$^{-2}$  s$^{-1}$  \\\\\n",
       "$g_{\\mathit{sp}}$ & Diffusive conductance of a stomatal pore & mol  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${g_{sw}}$ & Stomatal conductance to water vapour & m  s$^{-1}$  \\\\\n",
       "${g_{sw_l}}$ & Stomatal conductance to water vapour on lower side & m  s$^{-1}$  \\\\\n",
       "${g_{sw,mol}}$ & Stomatal conductance to water vapour & mol  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${g_{sw_u}}$ & Stomatal conductance to water vapour on upper side & m  s$^{-1}$  \\\\\n",
       "${g_{tw}}$ & Total leaf conductance to water vapour & m  s$^{-1}$  \\\\\n",
       "${g_{tw,mol}}$ & Total leaf layer conductance to water vapour & mol  m$^{-2}$  s$^{-1}$  \\\\\n",
       "$h_{c}$ & Average 1-sided convective transfer coefficient & J  K$^{-1}$  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${h_{c_l}}$ & Sensible heat flux coefficient on lower leaf side & J  K$^{-1}$  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${h_{c_u}}$ & Sensible heat flux coefficient on upper leaf side & J  K$^{-1}$  m$^{-2}$  s$^{-1}$  \\\\\n",
       "$H_{l}$ & Sensible heat flux from leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${H_{l_l}}$ & Sensible heat flux from lower side of leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${H_{l_u}}$ & Sensible heat flux from upper side of leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "$k_{a}$ & Thermal conductivity of dry air & J  K$^{-1}$  m$^{-1}$  s$^{-1}$  \\\\\n",
       "${k_{dv}}$ & Ratio $D_{va}/V_m$ & mol  m$^{-1}$  s$^{-1}$  \\\\\n",
       "$k_{l}$ & Thermal conductivity of a fresh leaf & J  K$^{-1}$  m$^{-1}$  s$^{-1}$  \\\\\n",
       "$L_{l}$ & Characteristic length scale for convection (size of leaf) & m  \\\\\n",
       "$l_{p}$ & Pore length & m  \\\\\n",
       "$\\lambda_{E}$ & Latent heat of evaporation (2.45e6) & J  kg$^{-1}$  \\\\\n",
       "$M_{N_{2}}$ & Molar mass of nitrogen (0.028) & kg  mol$^{-1}$  \\\\\n",
       "$M_{O_{2}}$ & Molar mass of oxygen (0.032) & kg  mol$^{-1}$  \\\\\n",
       "$M_{w}$ & Molar mass of water (0.018) & kg  mol$^{-1}$  \\\\\n",
       "${N_{Gr_L}}$ & Grashof number & 1  \\\\\n",
       "${N_{Le}}$ & Lewis number & 1  \\\\\n",
       "${N_{Nu_L}}$ & Nusselt number & 1  \\\\\n",
       "$n_{p}$ & Pore density &  m$^{-2}$  \\\\\n",
       "${N_{Re_c}}$ & Critical Reynolds number for the onset of turbulence & 1  \\\\\n",
       "${N_{Re_L}}$ & Reynolds number & 1  \\\\\n",
       "${N_{Sh_L}}$ & Sherwood number & 1  \\\\\n",
       "$\\nu_{a}$ & Kinematic viscosity of dry air &  m$^{2}$  s$^{-1}$  \\\\\n",
       "$P_{a}$ & Air pressure & Pa  \\\\\n",
       "${P_{N2}}$ & Partial pressure of nitrogen in the atmosphere & Pa  \\\\\n",
       "${P_{O2}}$ & Partial pressure of oxygen in the atmosphere & Pa  \\\\\n",
       "${P_{wa}}$ & Vapour pressure in the atmosphere & Pa  \\\\\n",
       "${P_{was}}$ & Saturation vapour pressure at air temperature & Pa  \\\\\n",
       "${P_{wl}}$ & Vapour pressure inside the leaf & Pa  \\\\\n",
       "${N_{Pr}}$ & Prandtl number (0.71) & 1  \\\\\n",
       "$Q_{l}$ & Conductive heat flux from upper to lower side of leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${r_{bw}}$ & Boundary layer resistance to water vapour, inverse of $g_{bw}$ & s  m$^{-1}$  \\\\\n",
       "${r_{bw,mol}}$ & Leaf BL resistance in molar units & s  m$^{2}$  mol$^{-1}$  \\\\\n",
       "$r_{\\mathit{end}}$ & End correction, representing resistance between evaporating sites and pores & s  m$^{2}$  mol$^{-1}$  \\\\\n",
       "${R_{ll}}$ & Longwave radiation away from leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${R_{ll_l}}$ & Longwave heat flux from lower side of leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${R_{ll_u}}$ & Longwave heat flux from upper side of leaf & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "${R_{mol}}$ & Molar gas constant (8.314472) & J  K$^{-1}$  mol$^{-1}$  \\\\\n",
       "$r_{p}$ & Pore radius (for ellipsoidal pores, half the pore width) & m  \\\\\n",
       "$R_{s}$ & Solar shortwave flux & J  m$^{-2}$  s$^{-1}$  \\\\\n",
       "$r_{\\mathit{sp}}$ & Diffusive resistance of a stomatal pore & s  m$^{2}$  mol$^{-1}$  \\\\\n",
       "${r_{sw}}$ & Stomatal resistance to water vapour, inverse of $g_{sw}$ & s  m$^{-1}$  \\\\\n",
       "${r_{tw}}$ & Total leaf resistance to water vapour, $r_{bv} + r_{sv}$ & s  m$^{-1}$  \\\\\n",
       "$r_{\\mathit{vs}}$ & Diffusive resistance of a stomatal vapour shell & s  m$^{2}$  mol$^{-1}$  \\\\\n",
       "$\\rho_{a}$ & Density of dry air & kg  m$^{-3}$  \\\\\n",
       "$\\rho_{\\mathit{al}}$ & Density of air at the leaf surface & kg  m$^{-3}$  \\\\\n",
       "$s_{p}$ & Spacing between stomata & m  \\\\\n",
       "${\\sigma}$ & Stefan-Boltzmann constant (5.67e-8) & J  K$^{-4}$  m$^{-2}$  s$^{-1}$  \\\\\n",
       "$T_{a}$ & Air temperature & K  \\\\\n",
       "$T_{l}$ & Leaf temperature & K  \\\\\n",
       "${T_{l_l}}$ & Leaf surface temperature of lower side & K  \\\\\n",
       "${T_{l_u}}$ & Leaf surface temperature of upper side & K  \\\\\n",
       "$T_{w}$ & Radiative temperature of objects surrounding the leaf & K  \\\\\n",
       "$V_{m}$ & Molar volume of air &  m$^{3}$  mol$^{-1}$  \\\\\n",
       "$v_{w}$ & Wind velocity & m  s$^{-1}$  \\\\\n",
       "$z_{l}$ & Leaf thickness (m) & m  \\\\\n",
       "\\end{tabular}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latex(table(tabledata))"
   ]
  },
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