def stomatal_conductance(self,
g0,
g1,
gb,
m,
A_net,
CO2,
RH,
drb,
gamma=U(10, 'umol/mol')):
Cs = CO2 - (drb * A_net / gb) # surface CO2 in mole fraction
Cs = clip(Cs, lower=gamma)
a = m * g1 * A_net / Cs
b = g0 + gb - a
c = (-RH * gb) - g0
#hs = max(np.roots([a, b, c]))
#hs = scipy.optimize.brentq(lambda x: np.polyval([a, b, c], x), 0, 1)
#hs = scipy.optimize.fsolve(lambda x: np.polyval([a, b, c], x), 0)
hs = quadratic_solve_upper(a, b, c)
#hs = clip(hs, 0.1, 1.0) # preventing bifurcation: used to be (0.3, 1.0) for C4 maize
#FIXME unused?
#T_leaf = l.temperature
#es = w.vp.saturation(T_leaf)
#Ds = (1 - hs) * es # VPD at leaf surface
#Ds = w.vp.deficit(T_leaf, hs)
gs = g0 + (g1 * m * (A_net * hs / Cs))
gs = clip(gs, lower=g0)
return gs
def temperature_dependence_rate(self, Ea, T, Tb=U(25, 'degC')):
R = U(8.314, 'J/K/mol') # universal gas constant (J K-1 mol-1)
#HACK handle too low temperature values during optimization
Tk = clip(T, lower=0, unit='degK')
Tbk = clip(Tb, lower=0, unit='degK')
try:
return np.exp(Ea * (T - Tb) / (Tbk * R * Tk))
except ZeroDivisionError:
return 0
def Vp(self, Vpmax, Cm, Kp):
# PEP carboxylation rate, that is the rate of C4 acid generation
Vp = (Cm * Vpmax) / (Cm + Kp / U(1, 'atm'))
Vpr = U(80, 'umol/m^2/s CO2'
) # PEP regeneration limited Vp, value adopted from vC book
Vp = clip(Vp, 0, Vpr)
return Vp
def optical_air_mass_number(self, elevation_angle):
t_s = clip(elevation_angle, lower=0, unit='rad')
#FIXME need to do max(0.0001, sin(t_s))?
try:
#FIXME check 101.3 is indeed in kPa
return self.atmospheric_pressure / (U(101.3, 'kPa') * sin(t_s))
except:
return 0
def evapotranspiration(self, vp='weather.vp'):
gv = self.stomata.total_conductance_h2o
ea = vp.ambient(self.weather.T_air, self.weather.RH)
es_leaf = vp.saturation(self.temperature)
ET = gv * ((es_leaf - ea) /
self.weather.P_air) / (1 -
(es_leaf + ea) / self.weather.P_air)
return clip(
ET,
lower=0) # 04/27/2011 dt took out the 1000 everything is moles now
def _temperature_effect(self, T_grow, T_peak, T_base):
# T_peak is the optimal growth temperature at which the potential leaf size determined in calc_mophology achieved.
# Similar concept to fig 3 of Fournier and Andreiu (1998)
# phyllochron corresponds to PHY in Lizaso (2003)
# phyllochron needed for next leaf appearance in degree days (GDD8) - 08/16/11, SK.
#phyllochron = (dv->get_T_Opt()- Tb)/(dv->get_Rmax_LTAR());
T_ratio = (T_grow - T_base) / (T_peak - T_base)
# final leaf size is adjusted by growth temperature determining cell size during elongation
return clip(T_ratio * exp(1 - T_ratio), lower=0)
def _water_potential_effect(self, psi_predawn, threshold):
#psi_predawn = self.p.soil.WP_leaf_predawn
psi_th = threshold # threshold wp below which stress effect shows up
# DT Oct 10, 2012 changed this so it was not as sensitive to stress near -0.5 lwp
# SK Sept 16, 2014 recalibrated/rescaled parameter estimates in Yang's paper. The scale of Boyer data wasn't set correctly
# sensitivity = 1.92, LeafWPhalf = -1.86, the sensitivity parameter may be raised by 0.3 to 0.5 to make it less sensitivy at high LWP, SK
s_f = 0.4258 # 0.5
psi_f = -1.4251 # -1.0
e = (1 + exp(s_f * psi_f)) / (1 + exp(s_f * (psi_f -
(psi_predawn - psi_th))))
return clip(e, upper=1.0)
def senescence_ratio(self):
# for MAIZSIM
# t = self.senescence_age
# t_e = self.senescence_duration
# if t >= t_e:
# return 1
# else:
# t_m = t_e / 2
# r = (1 + (t_e - t) / (t_e - t_m)) * (t / t_e)**(t_e / (t_e - t_m))
# return clip(r, 0., 1.)
# for garlic
#HACK prevents nan
if self.length == 0:
r = 0.
else:
r = self.aging_rate * self.senescence_age / self.length
return clip(r, 0., 1.)
def potential_expansion_rate(self):
t = self.elongation_age
t_e = self.growth_duration # 1.5 * w_max / c_m
t = clip(t, upper=t_e)
#FIXME can we introduce new w_max here when w_max in t_e (growth duration) supposed to be potential length?
w_max = self.potential_area
# c_m from Eq. 9, r (= dw/dt / c_m) from Eq. 7 of Yin (2003)
#HACK can be more simplified
#c_m = 1.5 / t_e * w_max
#r = 4 * t * (t_e - t) / t_e**2
t_m = t_e / 2
c_m = (2 * t_e -
t_m) / (t_e * (t_e - t_m)) * (t_m / t_e)**(t_m /
(t_e - t_m)) * w_max
r = (t_e - t) / (t_e - t_m) * (t / t_m)**(t_m / (t_e - t_m))
#FIXME dt here is physiological time, whereas timestep multiplied in potential_area_increase is chronological time
return c_m * r # dw/dt
def maximum_electron_transport_rate(self,
T,
T_dep,
N_dep,
Jm25=U(300, 'umol/m^2/s Electron'),
Eaj=U(32800, 'J/mol'),
Sj=U(702.6, 'J/mol/degK'),
Hj=U(220000, 'J/mol')):
R = U(8.314, 'J/K/mol')
Tb = U(25, 'degC')
Tk = T.to('degK')
Tbk = Tb.to('degK')
r = Jm25 * N_dep \
* T_dep(Eaj) \
* (1 + np.exp((Sj*Tbk - Hj) / (R*Tbk))) \
/ (1 + np.exp((Sj*Tk - Hj) / (R*Tk)))
return clip(r, lower=0)
def boundary_layer_conductance(self,
lw='leaf.width',
ww='leaf.weather.wind'):
# maize is an amphistomatous species, assume 1:1 (adaxial:abaxial) ratio.
#sr = 1.0
# switchgrass adaxial : abaxial (Awada 2002)
# https://doi.org/10.4141/P01-031
sr = 1.28
ratio = (sr + 1)**2 / (sr**2 + 1)
# characteristic dimension of a leaf, leaf width in m
d = lw * 0.72
#return 1.42 # total BLC (both sides) for LI6400 leaf chamber
gb = 1.4 * 0.147 * (clip(ww, lower=0.1) / d)**0.5 * ratio
#gb = (1.4 * 1.1 * 6.62 * (wind / d)**0.5 * (P_air / (R * (273.15 + T_air)))) # this is an alternative form including a multiplier for conversion from mm s-1 to mol m-2 s-1
# 1.1 is the factor to convert from heat conductance to water vapor conductance, an avarage between still air and laminar flow (see Table 3.2, HG Jones 2014)
# 6.62 is for laminar forced convection of air over flat plates on projected area basis
# when all conversion is done for each surface it becomes close to 0.147 as given in Norman and Campbell
# multiply by 1.4 for outdoor condition, Campbell and Norman (1998), p109, also see Jones 2014, pg 59 which suggest using 1.5 as this factor.
# multiply by ratio to get the effective blc (per projected area basis), licor 6400 manual p 1-9
return gb
def senescence_duration(self):
# end of growth period, time to maturity
return clip(self.growth_duration -
self.senescence_water_stress_duration,
lower=0)
def stay_green_duration(self):
# SK 8/20/10: as in Sinclair and Horie, 1989 Crop sciences, N availability index scaled between 0 and 1 based on
#nitrogen_index = max(0, (2 / (1 + exp(-2.9 * (self.g_content - 0.25))) - 1))
return clip(self.stay_green * self.growth_duration -
self.stay_green_water_stress_duration,
lower=0)
def light(self):
I2 = self.leaf.light
return clip(I2, lower=0)
def gross_photosynthesis(self):
return clip(
self.A_net + self.Rd, lower=0
) # gets negative when PFD = 0, Rd needs to be examined, 10/25/04, SK
def co2_mesophyll(self):
Cm = self.leaf.co2_mesophyll
return clip(Cm, lower=0)
def co2_mesophyll(self, A_net, w='weather', rvc='stomata.rvc'):
P = w.P_air / U(100, 'kPa')
Ca = w.CO2 * P # conversion to partial pressure
Cm = Ca - A_net * rvc * P
#print(f"+ Cm = {Cm}, Ca = {Ca}, A_net = {A_net}, gs = {self.stomata.gs}, gb = {self.stomata.gb}, rvc = {rvc}, P = {P}")
return clip(Cm, 0, 2 * Ca)
def leaf_number_effect(self, potential_leaves):
# Fig 4 of Birch et al. (1998)
return clip(exp(-1.17 + 0.047 * potential_leaves), 0.5, 1.0)
def solar_radiation(self, elevation_angle, day, SC):
t_s = clip(elevation_angle, lower=0, unit='rad')
g = 2 * pi * (day - 10) / 365
return SC * sin(t_s) * (1 + 0.033 * cos(g))
def phase1_delay(self, rank):
# not used in MAIZSIM because LTAR is used to initiate leaf growth.
# Fournier's value : -5.16+1.94*rank;equa 11 Fournier and Andrieu(1998) YY, This is in plastochron unit
return clip(-5.16 + 1.94 * rank, lower=0)
