R/rconstants.r
In manfredo89/ED2io: Manages Input/Output for Ecosystem Demography 2 Model
#------------------------------------------------------------------------------------------#
# Trigonometric constants #
#------------------------------------------------------------------------------------------#
pii = 1./pi # 1/Pi [ ---]
halfpi = pi/2 # Pi/2 [ ---]
sqrtpii = 0.564189583547756 # 1/(pi**0.5) [ ---]
twopi = pi* 2. # 2 Pi [ ---]
pio180 = pi/ 180. # Pi/180 (deg -> rad) [ ---]
onerad = 180. / pi # 180/pi (rad -> deg) [ ---]
pi4 = pi * 4. # 4 Pi [ ---]
pio4 = pi / 4. # Pi/4 [ ---]
pio6 = pi / 6. # Pi/6 [ ---]
pio6i = 6. / pi # 6/Pi [ ---]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Algebraic shortcuts #
#------------------------------------------------------------------------------------------#
srtwo = sqrt(2.) # Square root of 2. [ ---]
srthree = sqrt(3.) # Square root of 3. [ ---]
sqrt2o2 = srtwo / 2. # Half of srtwo [ ---]
sqrt2o4 = srtwo / 4. # Quarter of srtwo [ ---]
sqrt2o6 = srtwo / 6. # One-sixth of srtwo [ ---]
srtwoi = 1./srtwo # 1./ Square root of 2. [ ---]
srthreei = 1./srthree # 1./ Square root of 3. [ ---]
onethird = 1./3. # 1/3 [ ---]
twothirds = 2./3. # 2/3 [ ---]
onesixth = 1./6. # 1/6 [ ---]
golden = 0.5*(1+sqrt(5.)) # Golden ratio [ ---]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Universal constants #
#------------------------------------------------------------------------------------------#
stefan = 5.6696e-8 # Stefan-Boltzmann constant [ W/m2/K4]
boltzmann = 1.3806503e-23 # Boltzmann constant [m2 kg/s2/K]
t00 = 273.15 # 0 degC [ degC]
rmol = 8.314510 # Molar gas constant [ J/mol/K]
volmol = 0.022710980 # Molar volume at STP [ m3]
volmoll = volmol*1.e3 # Molar volume at STP [ L]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Molar masses and derived variables #
#------------------------------------------------------------------------------------------#
mmdry = 0.02897 # Mean dry air molar mass [ kg/mol]
mmo2 = 0.03199880 # Mean water molar mass [ kg/mol]
mmh2o = 0.01801505 # Mean water molar mass [ kg/mol]
mmco2 = 0.0440095 # Mean CO2 molar mass [ kg/mol]
mmdoc = mmdry/mmco2 # mmdry/mmco2 [ ----]
mmcod = mmco2/mmdry # mmco2/mmdry [ ----]
mmdry1000 = 1000.*mmdry # Mean dry air molar mass [ kg/mol]
mmcod1em6 = mmcod * 1.e-6 # Convert ppm to kgCO2/kgair [ ----]
mmdryi = 1./mmdry # 1./mmdry [ mol/kg]
mmco2i = 1./mmco2 # 1./mmco2 [ mol/kg]
mmh2oi = 1./mmh2o # 1./mmh2o [ mol/kg]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Time conversion units #
#------------------------------------------------------------------------------------------#
yr.day = 365.2425 # # of days in a year [ day/yr]
yr.ftnight = 26 # # of fornights in a year [ftnight/yr]
yr.mon = 12 # # of months in a year [ mon/yr]
day.sec = 86400. # # of seconds in a day [ s/day]
day.sec2 = day.sec^2 # # Square of day.sec [ s2/day2]
day.mon = yr.day/yr.mon # # of days in a month [ day/mon]
day.min = 1440. # # of minutes in a day [ min/day]
day.hr = 24. # # of hours in a day [ hr/day]
hr.sec = 3600. # # of seconds in an hour [ s/hr]
hr.min = 60. # # of minutes in an hour [ min/hr]
min.sec = 60. # # of seconds in a minute [ s/min]
yr.sec = yr.day * day.sec # # of seconds in a year [ s/yr]
kg2g = 1000. # # of grams in a kilogram [ g/kg]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# General Earth properties #
#------------------------------------------------------------------------------------------#
vonk = 0.40 # Von Karman constant [ ---]
grav = 9.80665 # Gravity acceleration [ m/s2]
gg = .5 * grav # Half of grav [ m/s2]
erad = 6370997. # Earth radius [ m]
spcon = pio180*erad # One degree of latitude [ m]
spconkm = spcon*0.001 # One degree of latitude [ km]
eradi = 1./erad # Inverse of Earth radius [ 1/m]
erad2 = erad*2 # Earth diameter [ m]
ss60 = 1.8663 # Polar stereo conversion to 60 deg [ ]
omega = 7.292e-5 # Earth's rotation speed [ rad/s]
viscos = .15e-4 # Viscosity coefficient [ ]
solar = 1.3533e3 # Solar constant [ W/m2]
p00 = 1.e5 # Reference pressure [ Pa]
prefsea = 101325. # Reference sea level pressure [ Pa]
p00i = 1. / p00 # 1/p00 [ 1/Pa]
o2.ref = 0.209 # Nominal O2 concentration [ mol/mol]
capri = -23.44 * pio180 # Tropic of Capricornium latitude [ rad]
shsummer = -10 # Day of year of S.Hemisphere summer solstice [ day]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Reference for this block: #
# MU08 - Monteith, J. L., M. H. Unsworth, 2008. Principles of Environmental Physics, #
# third edition, Academic Press, Amsterdam, 418pp. (Chapters 3 and 10). #
# #
# Air diffusion properties. These properties are temperature-dependent in reality, #
# but for simplicity we assume them constants, using the value at 20C. #
# #
# Thermal diffusivity - Computed from equation on page 32 of MU08; #
# Kinematic viscosity - Computed from equation on page 32 of MU08; #
# Thermal expansion coefficient - determined by inverting the coefficient at equation #
# 10.11 (MU08). #
# These terms could be easily made function of temperature in the future if needed be. #
#------------------------------------------------------------------------------------------#
th.diff.0 = 1.890e-5 # Air thermal diffusivity [ m2/s]
dth.diff = 0.007 # Temperature dependency slop [ 1/K]
kin.visc.0 = 1.330e-5 # Kinematic viscosity [ m2/s]
dkin.visc = 0.007 # Temperature dependency slop [ 1/K]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Dry air properties #
#------------------------------------------------------------------------------------------#
rdry = rmol/mmdry # Gas constant for dry air (Ra) [ J/kg/K]
rdryi = mmdry/rmol # 1./Gas constant for dry air (Ra) [ kg K/J]
cpdry = 1004. # Specific heat at constant pressure [ J/kg/K]
cvdry = 717. # Specific heat at constant volume [ J/kg/K]
cpog = cpdry /grav # cp/g [ m/K]
rocp = rdry / cpdry # Ra/cp [ ----]
cpor = cpdry / rdry # Cp/Ra [ ----]
rocv = rdry / cvdry # Ra/Cv [ ----]
gocp = grav / cpdry # g/Cp, dry adiabatic lapse rate [ K/m]
gordry = grav / rdry # g/Ra [ K/m]
cpdryi = 1. / cpdry # 1/Cp [ kg K/J]
cpdryi4 = 4. * cpdryi # 4/Cp [ kg K/J]
p00k = p00^(rdry/cpdry) # p0 ** (Ra/Cp) [ Pa^0.286]
p00ki = 1. / p00k # p0 ** (-Ra/Cp) [Pa^-0.286]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Typical lapse rates for tropics and temperate zone. #
# The value for tropics came from: #
# Gaffen, D. J.; B. D. Santer, J. S. Boyle, J. R. Christy, N. E. Graham, R. J. Ross, #
# 2000: Multidecadal changes in the vertical temperature structure of the #
# tropical troposphere. Science, 287, 1242-1245. #
#------------------------------------------------------------------------------------------#
lapse.trop = 5.5e-3 # g/Cp, dry adiabatic lapse rate [ K/m]
lapse.temp = 6.5e-3 # g/Cp, dry adiabatic lapse rate [ K/m]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Water vapour properties #
#------------------------------------------------------------------------------------------#
rh2o = rmol/mmh2o # Gas const. for water vapour (Rv) [ J/kg/K]
cph2o = 1859. # Heat capacity at const. pres. [ J/kg/K]
cph2oi = 1. / cph2o # Inverse of heat capacity [ kg K/J]
cvh2o = cph2o-rh2o # Heat capacity at const. volume [ J/kg/K]
gorh2o = grav / rh2o # g/Rv [ K/m]
ep = mmh2o/mmdry # or Ra/Rv, epsilon [ kg/kg]
epi = mmdry/mmh2o # or Rv/Ra, 1/epsilon [ kg/kg]
epim1 = epi-1. # that 0.61 term of virtual temp. [ kg/kg]
rh2oocp = rh2o / cpdry # Rv/cp [ ----]
toodry = 1.e-8 # Minimum acceptable mixing ratio. [ kg/kg]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Liquid water properties #
#------------------------------------------------------------------------------------------#
wdns = 1.000e3 # Liquid water density [ kg/m3]
wdnsi = 1./wdns # Inverse of liquid water density [ m3/kg]
cliq = 4.186e3 # Liquid water specific heat (Cl) [ J/kg/K]
cliqi = 1./cliq # Inverse of water heat capacity [ kg K/J]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Ice properties #
#------------------------------------------------------------------------------------------#
idns = 9.167e2 # "Hard" ice density [ kg/m3]
idnsi = 1./idns # Inverse of ice density [ m3/kg]
cice = 2.093e3 # Ice specific heat (Ci) [ J/kg/K]
cicei = 1. / cice # Inverse of ice heat capacity [ kg K/J]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Phase change properties #
#------------------------------------------------------------------------------------------#
t3ple = 273.16 # Water triple point temp. (T3) [ K]
t3plei = 1./t3ple # 1./T3 [ 1/K]
es3ple = 611.65685464 # Vapour pressure at T3 (es3) [ Pa]
es3plei = 1./es3ple # 1./es3 [ 1/Pa]
epes3ple = ep * es3ple # epsilon * es3 [ Pa kg/kg]
rh2ot3ple = rh2o * t3ple # Rv * T3 [ J/kg]
alli = 3.34e5 # Lat. heat - fusion (Lf) [ J/kg]
alvl3 = 2.50e6 # Lat. heat - vaporisation (Lv) at T = T3 [ J/kg]
alvi3 = alli + alvl3 # Lat. heat - sublimation (Ls) at T = T3 [ J/kg]
allii = 1. / alli # 1./Lf [ kg/J]
aklv = alvl3 / cpdry # Lv/Cp [ K]
akiv = alvi3 / cpdry # Ls/Cp [ K]
lvordry = alvl3 / rdry # Lv/Ra [ K]
lvorvap = alvl3 / rh2o # Lv/Rv [ K]
lsorvap = alvi3 / rh2o # Ls/Rv [ K]
lvt3ple = alvl3 * t3ple # Lv * T3 [ K J/kg]
lst3ple = alvi3 * t3ple # Ls * T3 [ K J/kg]
uiicet3 = cice * t3ple # internal energy at triple point, only ice [ J/kg]
uiliqt3 = uiicet3 + alli # internal energy at triple point, only liq. [ J/kg]
dcpvl = cph2o - cliq # Difference of sp. heat [ J/kg/K]
dcpvi = cph2o - cice # Difference of sp. heat [ J/kg/K]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# The following variables are useful when defining the derivatives of theta_il. They #
# correspond to L?(T) - L?' T. #
#------------------------------------------------------------------------------------------#
del.alvl3 = alvl3 - dcpvl * t3ple
del.alvi3 = alvi3 - dcpvi * t3ple
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Tsupercool are defined as temperatures of supercooled liquid water (water vapour) #
# that will cause the internal energy (enthalpy) to be the same as ice at 0K. It can be #
# used as an offset for temperature when defining internal energy (enthalpy). The next #
# two methods of defining the internal energy for the liquid part: #
# #
# Uliq = Mliq [ Cice T3 + Cliq (T - T3) + Lf] #
# Uliq = Mliq Cliq (T - Tsupercool_liq) #
# #
# H = Mliq [ Cice T3 + Cliq (Ts - T3) + Lv3 + (Cpv - Cliq) (Ts-T3) + Cpv (T-T3) ] #
# H = Mliq Cpv (T - Tsupercool_vap) ] #
# #
# You may be asking yourself why would we have the ice term in the internal energy #
# definition. The reason is that we can think that internal energy is the amount of energy #
# a parcel received to leave the 0K state to reach the current state (or if you prefer the #
# inverse way, Uliq is the amount of energy the parcel would need to lose to become solid #
# at 0K.) #
#------------------------------------------------------------------------------------------#
tsupercool.liq = t3ple - (uiicet3+alli) * cliqi
tsupercool.vap = cph2oi * ( (cph2o - cice) * t3ple - alvi3 )
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Minimum temperature for computing the condensation effect of temperature on #
# theta_il, thetae_iv, and associates. Below this temperature, assuming the latent #
# heats as constants becomes a really bad assumption. See : #
# #
# Tripoli, J. T.; and Cotton, W.R., 1981: The use of ice-liquid water potential temper- #
# ature as a thermodynamic variable in deep atmospheric models. Mon. Wea. Rev., #
# v. 109, 1094-1102. #
#------------------------------------------------------------------------------------------#
ttripoli = 253. # "Tripoli-Cotton" temp. (Ttr) [ K]
htripoli = cpdry*ttripoli # Sensible enthalpy at T=Ttr [ J/kg]
htripolii = 1./htripoli # 1./htripoli [ kg/J]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Unit conversion, it must be defined locally even for coupled runs. #
#------------------------------------------------------------------------------------------#
mol.2.umol = 1.e6 # mol => umol
umol.2.mol = 1.e-6 # umol => mol
umol.2.kgC = 1.20107e-8 # umol(CO2) => kg(C)
Watts.2.Ein = 4.6e-6 # W/m2 => mol/m2/s
Ein.2.Watts = 1./Watts.2.Ein # mol/m2/s => W/m2
kgC.2.umol = 1. / umol.2.kgC # kg(C) => umol(CO2)
kgom2.2.tonoha = 10. # kg(C)/m2 => ton(C)/ha
tonoha.2.kgom2 = 0.1 # ton(C)/ha => kg(C)/m2
umols.2.kgCyr = umol.2.kgC * yr.sec # umol(CO2)/s => kg(C)/yr
kgCyr.2.umols = 1. / umols.2.kgCyr # kg(C)/yr => umol(CO2)/s
kgCday.2.umols = kgC.2.umol / day.sec # kg(C)/day => umol(CO2)/s
Torr.2.Pa = prefsea / 760. # Torr => Pa
Pa.2.Torr = 1. / Torr.2.Pa # Pa => Torr
kt.2.mos = 1852 / hr.sec # knots => m/s
mos.2.kt = 1. / kt.2.mos # m/s => knots
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Guess for ET from : #
# Malhi, Y., et al. 2009: Exploring the likelihood and mechanism of a climate-change- #
# -induced dieback of the Amazon rainforest. Proc. Natl. Ac. Sci., 106, 20610--20615. #
#------------------------------------------------------------------------------------------#
et.malhi = 100 # [mm/month]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Mean global wood density, from: #
# #
# Kraft, N. J. B., M. R. Metz, R. S. Condit, and J. Chave. The relationship between wood #
# density and mortality in a global tropical forest data set. New Phytol., #
# 188(4):1124-1136, Dec 2010. doi:10.1111/j.1469-8137.2010.03444.x #
# #
#------------------------------------------------------------------------------------------#
mean.wood.dens.global = 0.58
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# These are the lower and upper bounds in which we compute exponentials. This is to #
# avoid overflows and/or underflows when we compute exponentials. #
#------------------------------------------------------------------------------------------#
lnexp.min = -38.
lnexp.max = 38.
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# These are the just default huge and tiny numbers that are not the actual huge or #
# tiny values from Fortran intrinsic functions, so if you do any numerical operations you #
# will still be fine. #
#------------------------------------------------------------------------------------------#
huge.num = 1.e+19
tiny.num = 1.e-19
#------------------------------------------------------------------------------------------#
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#------------------------------------------------------------------------------------------#
# Trigonometric constants #
#------------------------------------------------------------------------------------------#
pii = 1./pi # 1/Pi [ ---]
halfpi = pi/2 # Pi/2 [ ---]
sqrtpii = 0.564189583547756 # 1/(pi**0.5) [ ---]
twopi = pi* 2. # 2 Pi [ ---]
pio180 = pi/ 180. # Pi/180 (deg -> rad) [ ---]
onerad = 180. / pi # 180/pi (rad -> deg) [ ---]
pi4 = pi * 4. # 4 Pi [ ---]
pio4 = pi / 4. # Pi/4 [ ---]
pio6 = pi / 6. # Pi/6 [ ---]
pio6i = 6. / pi # 6/Pi [ ---]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Algebraic shortcuts #
#------------------------------------------------------------------------------------------#
srtwo = sqrt(2.) # Square root of 2. [ ---]
srthree = sqrt(3.) # Square root of 3. [ ---]
sqrt2o2 = srtwo / 2. # Half of srtwo [ ---]
sqrt2o4 = srtwo / 4. # Quarter of srtwo [ ---]
sqrt2o6 = srtwo / 6. # One-sixth of srtwo [ ---]
srtwoi = 1./srtwo # 1./ Square root of 2. [ ---]
srthreei = 1./srthree # 1./ Square root of 3. [ ---]
onethird = 1./3. # 1/3 [ ---]
twothirds = 2./3. # 2/3 [ ---]
onesixth = 1./6. # 1/6 [ ---]
golden = 0.5*(1+sqrt(5.)) # Golden ratio [ ---]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Universal constants #
#------------------------------------------------------------------------------------------#
stefan = 5.6696e-8 # Stefan-Boltzmann constant [ W/m2/K4]
boltzmann = 1.3806503e-23 # Boltzmann constant [m2 kg/s2/K]
t00 = 273.15 # 0 degC [ degC]
rmol = 8.314510 # Molar gas constant [ J/mol/K]
volmol = 0.022710980 # Molar volume at STP [ m3]
volmoll = volmol*1.e3 # Molar volume at STP [ L]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Molar masses and derived variables #
#------------------------------------------------------------------------------------------#
mmdry = 0.02897 # Mean dry air molar mass [ kg/mol]
mmo2 = 0.03199880 # Mean water molar mass [ kg/mol]
mmh2o = 0.01801505 # Mean water molar mass [ kg/mol]
mmco2 = 0.0440095 # Mean CO2 molar mass [ kg/mol]
mmdoc = mmdry/mmco2 # mmdry/mmco2 [ ----]
mmcod = mmco2/mmdry # mmco2/mmdry [ ----]
mmdry1000 = 1000.*mmdry # Mean dry air molar mass [ kg/mol]
mmcod1em6 = mmcod * 1.e-6 # Convert ppm to kgCO2/kgair [ ----]
mmdryi = 1./mmdry # 1./mmdry [ mol/kg]
mmco2i = 1./mmco2 # 1./mmco2 [ mol/kg]
mmh2oi = 1./mmh2o # 1./mmh2o [ mol/kg]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Time conversion units #
#------------------------------------------------------------------------------------------#
yr.day = 365.2425 # # of days in a year [ day/yr]
yr.ftnight = 26 # # of fornights in a year [ftnight/yr]
yr.mon = 12 # # of months in a year [ mon/yr]
day.sec = 86400. # # of seconds in a day [ s/day]
day.sec2 = day.sec^2 # # Square of day.sec [ s2/day2]
day.mon = yr.day/yr.mon # # of days in a month [ day/mon]
day.min = 1440. # # of minutes in a day [ min/day]
day.hr = 24. # # of hours in a day [ hr/day]
hr.sec = 3600. # # of seconds in an hour [ s/hr]
hr.min = 60. # # of minutes in an hour [ min/hr]
min.sec = 60. # # of seconds in a minute [ s/min]
yr.sec = yr.day * day.sec # # of seconds in a year [ s/yr]
kg2g = 1000. # # of grams in a kilogram [ g/kg]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# General Earth properties #
#------------------------------------------------------------------------------------------#
vonk = 0.40 # Von Karman constant [ ---]
grav = 9.80665 # Gravity acceleration [ m/s2]
gg = .5 * grav # Half of grav [ m/s2]
erad = 6370997. # Earth radius [ m]
spcon = pio180*erad # One degree of latitude [ m]
spconkm = spcon*0.001 # One degree of latitude [ km]
eradi = 1./erad # Inverse of Earth radius [ 1/m]
erad2 = erad*2 # Earth diameter [ m]
ss60 = 1.8663 # Polar stereo conversion to 60 deg [ ]
omega = 7.292e-5 # Earth's rotation speed [ rad/s]
viscos = .15e-4 # Viscosity coefficient [ ]
solar = 1.3533e3 # Solar constant [ W/m2]
p00 = 1.e5 # Reference pressure [ Pa]
prefsea = 101325. # Reference sea level pressure [ Pa]
p00i = 1. / p00 # 1/p00 [ 1/Pa]
o2.ref = 0.209 # Nominal O2 concentration [ mol/mol]
capri = -23.44 * pio180 # Tropic of Capricornium latitude [ rad]
shsummer = -10 # Day of year of S.Hemisphere summer solstice [ day]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Reference for this block: #
# MU08 - Monteith, J. L., M. H. Unsworth, 2008. Principles of Environmental Physics, #
# third edition, Academic Press, Amsterdam, 418pp. (Chapters 3 and 10). #
# #
# Air diffusion properties. These properties are temperature-dependent in reality, #
# but for simplicity we assume them constants, using the value at 20C. #
# #
# Thermal diffusivity - Computed from equation on page 32 of MU08; #
# Kinematic viscosity - Computed from equation on page 32 of MU08; #
# Thermal expansion coefficient - determined by inverting the coefficient at equation #
# 10.11 (MU08). #
# These terms could be easily made function of temperature in the future if needed be. #
#------------------------------------------------------------------------------------------#
th.diff.0 = 1.890e-5 # Air thermal diffusivity [ m2/s]
dth.diff = 0.007 # Temperature dependency slop [ 1/K]
kin.visc.0 = 1.330e-5 # Kinematic viscosity [ m2/s]
dkin.visc = 0.007 # Temperature dependency slop [ 1/K]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Dry air properties #
#------------------------------------------------------------------------------------------#
rdry = rmol/mmdry # Gas constant for dry air (Ra) [ J/kg/K]
rdryi = mmdry/rmol # 1./Gas constant for dry air (Ra) [ kg K/J]
cpdry = 1004. # Specific heat at constant pressure [ J/kg/K]
cvdry = 717. # Specific heat at constant volume [ J/kg/K]
cpog = cpdry /grav # cp/g [ m/K]
rocp = rdry / cpdry # Ra/cp [ ----]
cpor = cpdry / rdry # Cp/Ra [ ----]
rocv = rdry / cvdry # Ra/Cv [ ----]
gocp = grav / cpdry # g/Cp, dry adiabatic lapse rate [ K/m]
gordry = grav / rdry # g/Ra [ K/m]
cpdryi = 1. / cpdry # 1/Cp [ kg K/J]
cpdryi4 = 4. * cpdryi # 4/Cp [ kg K/J]
p00k = p00^(rdry/cpdry) # p0 ** (Ra/Cp) [ Pa^0.286]
p00ki = 1. / p00k # p0 ** (-Ra/Cp) [Pa^-0.286]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Typical lapse rates for tropics and temperate zone. #
# The value for tropics came from: #
# Gaffen, D. J.; B. D. Santer, J. S. Boyle, J. R. Christy, N. E. Graham, R. J. Ross, #
# 2000: Multidecadal changes in the vertical temperature structure of the #
# tropical troposphere. Science, 287, 1242-1245. #
#------------------------------------------------------------------------------------------#
lapse.trop = 5.5e-3 # g/Cp, dry adiabatic lapse rate [ K/m]
lapse.temp = 6.5e-3 # g/Cp, dry adiabatic lapse rate [ K/m]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Water vapour properties #
#------------------------------------------------------------------------------------------#
rh2o = rmol/mmh2o # Gas const. for water vapour (Rv) [ J/kg/K]
cph2o = 1859. # Heat capacity at const. pres. [ J/kg/K]
cph2oi = 1. / cph2o # Inverse of heat capacity [ kg K/J]
cvh2o = cph2o-rh2o # Heat capacity at const. volume [ J/kg/K]
gorh2o = grav / rh2o # g/Rv [ K/m]
ep = mmh2o/mmdry # or Ra/Rv, epsilon [ kg/kg]
epi = mmdry/mmh2o # or Rv/Ra, 1/epsilon [ kg/kg]
epim1 = epi-1. # that 0.61 term of virtual temp. [ kg/kg]
rh2oocp = rh2o / cpdry # Rv/cp [ ----]
toodry = 1.e-8 # Minimum acceptable mixing ratio. [ kg/kg]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Liquid water properties #
#------------------------------------------------------------------------------------------#
wdns = 1.000e3 # Liquid water density [ kg/m3]
wdnsi = 1./wdns # Inverse of liquid water density [ m3/kg]
cliq = 4.186e3 # Liquid water specific heat (Cl) [ J/kg/K]
cliqi = 1./cliq # Inverse of water heat capacity [ kg K/J]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Ice properties #
#------------------------------------------------------------------------------------------#
idns = 9.167e2 # "Hard" ice density [ kg/m3]
idnsi = 1./idns # Inverse of ice density [ m3/kg]
cice = 2.093e3 # Ice specific heat (Ci) [ J/kg/K]
cicei = 1. / cice # Inverse of ice heat capacity [ kg K/J]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Phase change properties #
#------------------------------------------------------------------------------------------#
t3ple = 273.16 # Water triple point temp. (T3) [ K]
t3plei = 1./t3ple # 1./T3 [ 1/K]
es3ple = 611.65685464 # Vapour pressure at T3 (es3) [ Pa]
es3plei = 1./es3ple # 1./es3 [ 1/Pa]
epes3ple = ep * es3ple # epsilon * es3 [ Pa kg/kg]
rh2ot3ple = rh2o * t3ple # Rv * T3 [ J/kg]
alli = 3.34e5 # Lat. heat - fusion (Lf) [ J/kg]
alvl3 = 2.50e6 # Lat. heat - vaporisation (Lv) at T = T3 [ J/kg]
alvi3 = alli + alvl3 # Lat. heat - sublimation (Ls) at T = T3 [ J/kg]
allii = 1. / alli # 1./Lf [ kg/J]
aklv = alvl3 / cpdry # Lv/Cp [ K]
akiv = alvi3 / cpdry # Ls/Cp [ K]
lvordry = alvl3 / rdry # Lv/Ra [ K]
lvorvap = alvl3 / rh2o # Lv/Rv [ K]
lsorvap = alvi3 / rh2o # Ls/Rv [ K]
lvt3ple = alvl3 * t3ple # Lv * T3 [ K J/kg]
lst3ple = alvi3 * t3ple # Ls * T3 [ K J/kg]
uiicet3 = cice * t3ple # internal energy at triple point, only ice [ J/kg]
uiliqt3 = uiicet3 + alli # internal energy at triple point, only liq. [ J/kg]
dcpvl = cph2o - cliq # Difference of sp. heat [ J/kg/K]
dcpvi = cph2o - cice # Difference of sp. heat [ J/kg/K]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# The following variables are useful when defining the derivatives of theta_il. They #
# correspond to L?(T) - L?' T. #
#------------------------------------------------------------------------------------------#
del.alvl3 = alvl3 - dcpvl * t3ple
del.alvi3 = alvi3 - dcpvi * t3ple
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Tsupercool are defined as temperatures of supercooled liquid water (water vapour) #
# that will cause the internal energy (enthalpy) to be the same as ice at 0K. It can be #
# used as an offset for temperature when defining internal energy (enthalpy). The next #
# two methods of defining the internal energy for the liquid part: #
# #
# Uliq = Mliq [ Cice T3 + Cliq (T - T3) + Lf] #
# Uliq = Mliq Cliq (T - Tsupercool_liq) #
# #
# H = Mliq [ Cice T3 + Cliq (Ts - T3) + Lv3 + (Cpv - Cliq) (Ts-T3) + Cpv (T-T3) ] #
# H = Mliq Cpv (T - Tsupercool_vap) ] #
# #
# You may be asking yourself why would we have the ice term in the internal energy #
# definition. The reason is that we can think that internal energy is the amount of energy #
# a parcel received to leave the 0K state to reach the current state (or if you prefer the #
# inverse way, Uliq is the amount of energy the parcel would need to lose to become solid #
# at 0K.) #
#------------------------------------------------------------------------------------------#
tsupercool.liq = t3ple - (uiicet3+alli) * cliqi
tsupercool.vap = cph2oi * ( (cph2o - cice) * t3ple - alvi3 )
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Minimum temperature for computing the condensation effect of temperature on #
# theta_il, thetae_iv, and associates. Below this temperature, assuming the latent #
# heats as constants becomes a really bad assumption. See : #
# #
# Tripoli, J. T.; and Cotton, W.R., 1981: The use of ice-liquid water potential temper- #
# ature as a thermodynamic variable in deep atmospheric models. Mon. Wea. Rev., #
# v. 109, 1094-1102. #
#------------------------------------------------------------------------------------------#
ttripoli = 253. # "Tripoli-Cotton" temp. (Ttr) [ K]
htripoli = cpdry*ttripoli # Sensible enthalpy at T=Ttr [ J/kg]
htripolii = 1./htripoli # 1./htripoli [ kg/J]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Unit conversion, it must be defined locally even for coupled runs. #
#------------------------------------------------------------------------------------------#
mol.2.umol = 1.e6 # mol => umol
umol.2.mol = 1.e-6 # umol => mol
umol.2.kgC = 1.20107e-8 # umol(CO2) => kg(C)
Watts.2.Ein = 4.6e-6 # W/m2 => mol/m2/s
Ein.2.Watts = 1./Watts.2.Ein # mol/m2/s => W/m2
kgC.2.umol = 1. / umol.2.kgC # kg(C) => umol(CO2)
kgom2.2.tonoha = 10. # kg(C)/m2 => ton(C)/ha
tonoha.2.kgom2 = 0.1 # ton(C)/ha => kg(C)/m2
umols.2.kgCyr = umol.2.kgC * yr.sec # umol(CO2)/s => kg(C)/yr
kgCyr.2.umols = 1. / umols.2.kgCyr # kg(C)/yr => umol(CO2)/s
kgCday.2.umols = kgC.2.umol / day.sec # kg(C)/day => umol(CO2)/s
Torr.2.Pa = prefsea / 760. # Torr => Pa
Pa.2.Torr = 1. / Torr.2.Pa # Pa => Torr
kt.2.mos = 1852 / hr.sec # knots => m/s
mos.2.kt = 1. / kt.2.mos # m/s => knots
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Guess for ET from : #
# Malhi, Y., et al. 2009: Exploring the likelihood and mechanism of a climate-change- #
# -induced dieback of the Amazon rainforest. Proc. Natl. Ac. Sci., 106, 20610--20615. #
#------------------------------------------------------------------------------------------#
et.malhi = 100 # [mm/month]
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# Mean global wood density, from: #
# #
# Kraft, N. J. B., M. R. Metz, R. S. Condit, and J. Chave. The relationship between wood #
# density and mortality in a global tropical forest data set. New Phytol., #
# 188(4):1124-1136, Dec 2010. doi:10.1111/j.1469-8137.2010.03444.x #
# #
#------------------------------------------------------------------------------------------#
mean.wood.dens.global = 0.58
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# These are the lower and upper bounds in which we compute exponentials. This is to #
# avoid overflows and/or underflows when we compute exponentials. #
#------------------------------------------------------------------------------------------#
lnexp.min = -38.
lnexp.max = 38.
#------------------------------------------------------------------------------------------#
#------------------------------------------------------------------------------------------#
# These are the just default huge and tiny numbers that are not the actual huge or #
# tiny values from Fortran intrinsic functions, so if you do any numerical operations you #
# will still be fine. #
#------------------------------------------------------------------------------------------#
huge.num = 1.e+19
tiny.num = 1.e-19
#------------------------------------------------------------------------------------------#
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