{ "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", "Worksheet_update.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": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# From leaf_enbalance_eqs, E_PM_eqs and stomatal_cond_eqs\n", "\n", "load_session('temp/leaf_enbalance_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/E_PM_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": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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VariableDescription (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 thicknessm
Bowen ratio (sensible/latent heat flux)1
Latent heat transfer coefficientJ Pa m s
Sensible heat transfer coefficientJ 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 depthm
Binary diffusion coefficient of water vapour in air m s
Slope of saturation vapour pressure at air temperaturePa K
Latent heat flux from leafJ m s
Transpiration rate in molar unitsmol m s
Latent heat flux from a wet surfaceJ 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 unitsJ 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 poremol m s
Stomatal conductance to water vapourm s
Stomatal conductance to water vapourmol m s
Total leaf conductance to water vapourm s
Total leaf layer conductance to water vapourmol m s
Psychrometric constantPa K
Average 1-sided convective transfer coefficientJ K m s
Sensible heat flux from leafJ m s
Thermal conductivity of dry airJ K m s
Ratio mol m s
Characteristic length scale for convection (size of leaf)m
Pore lengthm
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 number1
Lewis number1
n=2 for hypostomatous, n=1 for amphistomatous leaves1
Nusselt number1
Pore density m
Critical Reynolds number for the onset of turbulence1
Reynolds number1
Sherwood number1
Kinematic viscosity of dry air m s
Air pressurePa
Partial pressure of nitrogen in the atmospherePa
Partial pressure of oxygen in the atmospherePa
Vapour pressure in the atmospherePa
Saturation vapour pressure at air temperaturePa
Vapour pressure inside the leafPa
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 unitss m mol
End correction, representing resistance between evaporating sites and poress m mol
Longwave radiation away from leafJ m s
Molar gas constant (8.314472)J K mol
Pore radius (for ellipsoidal pores, half the pore width)m
Solar shortwave fluxJ m s
Stomatal resistance to water vapour \\citep[][P. 231]{monteith_principles_2013}s m
Diffusive resistance of a stomatal pores 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 shells m mol
Density of dry airkg m
Density of air at the leaf surfacekg m
Factor representing stomatal resistance in \\citet{penman_physical_1952}1
Spacing between stomatam
Stefan-Boltzmann constant (5.67e-8)J K m s
Air temperatureK
Leaf temperatureK
Radiative temperature of objects surrounding the leafK
Molar volume of air m mol
Wind velocitym s
\n", "
" ], "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", " beta_B Bowen ratio (sensible/latent heat flux) 1\n", " c_E Latent heat transfer coefficient J Pa$^{-1}$ m$^{-2}$ s$^{-1}$\n", " c_H Sensible heat transfer coefficient J K$^{-1}$ m$^{-2}$ s$^{-1}$\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", " Delta_eTa Slope of saturation vapour pressure at air temperature Pa K$^{-1}$\n", " E_l Latent heat flux from leaf J m$^{-2}$ s$^{-1}$\n", " E_lmol Transpiration rate in molar units mol m$^{-2}$ s$^{-1}$\n", " E_w Latent heat flux from a wet surface J m$^{-2}$ s$^{-1}$\n", " epsilon Water to air molecular weight ratio (0.622) 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", " f_u Wind function in Penman approach, f(u) adapted to energetic units J Pa$^{-1}$ m$^{-2}$ s$^{-1}$\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_swmol Stomatal conductance to water vapour mol m$^{-2}$ 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", " gamma_v Psychrometric constant Pa K$^{-1}$\n", " h_c Average 1-sided convective transfer coefficient J K$^{-1}$ m$^{-2}$ s$^{-1}$\n", " H_l Sensible heat flux from 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", " 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", " n_MU n=2 for hypostomatous, n=1 for amphistomatous leaves 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", " r_a One-sided boundary layer resistance to heat transfer ($r_H$ in \\citet[][P. 231]{monteith_principles_2013}) s m$^{-1}$\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_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_s Stomatal resistance to water vapour \\citep[][P. 231]{monteith_principles_2013} s m$^{-1}$\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_v Leaf BL resistance to water vapour, \\citep[][Eq. 13.16]{monteith_principles_2013} 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 Factor representing stomatal resistance in \\citet{penman_physical_1952} 1\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_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$^{-1}$" ] }, "execution_count": 4, "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": 5, "metadata": { "collapsed": false }, "outputs": [ { "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", "${\\beta_B}$ & Bowen ratio (sensible/latent heat flux) & 1 \\\\\n", "$c_{E}$ & Latent heat transfer coefficient & J Pa$^{-1}$ m$^{-2}$ s$^{-1}$ \\\\\n", "$c_{H}$ & Sensible heat transfer coefficient & J K$^{-1}$ m$^{-2}$ s$^{-1}$ \\\\\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", "${\\Delta_{eTa}}$ & Slope of saturation vapour pressure at air temperature & Pa K$^{-1}$ \\\\\n", "$E_{l}$ & Latent heat flux from leaf & J m$^{-2}$ s$^{-1}$ \\\\\n", "${E_{l,mol}}$ & Transpiration rate in molar units & mol m$^{-2}$ s$^{-1}$ \\\\\n", "$E_{w}$ & Latent heat flux from a wet surface & J m$^{-2}$ s$^{-1}$ \\\\\n", "$\\epsilon$ & Water to air molecular weight ratio (0.622) & 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", "$f_{u}$ & Wind function in Penman approach, f(u) adapted to energetic units & J Pa$^{-1}$ m$^{-2}$ s$^{-1}$ \\\\\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", "${g_{sw,mol}}$ & Stomatal conductance to water vapour & mol m$^{-2}$ 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", "$\\gamma_{v}$ & Psychrometric constant & Pa K$^{-1}$ \\\\\n", "$h_{c}$ & Average 1-sided convective transfer coefficient & J K$^{-1}$ m$^{-2}$ s$^{-1}$ \\\\\n", "$H_{l}$ & Sensible heat flux from 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", "$L_{l}$ & 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", "$n_{\\mathit{MU}}$ & n=2 for hypostomatous, n=1 for amphistomatous leaves & 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", "$r_{a}$ & One-sided boundary layer resistance to heat transfer ($r_H$ in \\citet[][P. 231]{monteith_principles_2013}) & s m$^{-1}$ \\\\\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", "${R_{mol}}$ & 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", "$r_{s}$ & Stomatal resistance to water vapour \\citep[][P. 231]{monteith_principles_2013} & s m$^{-1}$ \\\\\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", "${r_{v}}$ & Leaf BL resistance to water vapour, \\citep[][Eq. 13.16]{monteith_principles_2013} & 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", "$S$ & Factor representing stomatal resistance in \\citet{penman_physical_1952} & 1 \\\\\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", "$T_{w}$ & 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", "\\end{tabular}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "latex(table(tabledata))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.3", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" }, "nav_menu": {}, "toc": { "navigate_menu": true, "number_sections": true, "sideBar": true, "threshold": 6, "toc_cell": false, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 0 }