def A_trans(p, trans, Ci, Tleaf=None, inf_gb=False):
"""
Calculates the assimilation rate given the supply function, gc.
Arguments:
----------
p: recarray object or pandas series or class containing the data
time step's met data & params
trans: array
transpiration [mol m-2 s-1], an array of values depending on
the possible leaf water potentials (P) and the Weibull
parameters b, c
Ci: float
intercellular CO2 concentration [Pa], corresponding to a leaf
water potential (P) for which the transpiration cost is minimal
and the C assimilation gain is maximal
Tleaf: float
leaf temperature [degC]
inf_gb: bool
if True, gb is prescrived and very large
Returns:
--------
Calculates the photosynthetic gain A [umol m-2 s-1] for a given
Ci(P) and over an array of Gc(P) values.
"""
try: # is Tleaf one of the input fields?
Tleaf = p.Tleaf
except (IndexError, AttributeError, ValueError): # calc. Tleaf
pass
# get CO2 diffusive conduct.
gc, __, __, __ = leaf_energy_balance(p, trans, Tleaf=Tleaf, inf_gb=inf_gb)
A_P = conv.MILI * gc * (p.CO2 - Ci) / p.Patm
try:
A_P[np.isclose(np.squeeze(gc), cst.zero, rtol=cst.zero,
atol=cst.zero)] = cst.zero
except TypeError:
pass
return A_P
def profit_psi(p, photo='Farquhar', res='low', inf_gb=False, deriv=False):
"""
Finds the instateneous profit maximization, following the
optmization criterion for which, at each instant in time, the
stomata regulate canopy gas exchange and pressure to achieve the
maximum profit, which is the maximum difference between the
normalized photosynthetic gain (gain) and the hydraulic cost
function (cost). That is when d(gain)/dP = d(cost)/dP.
Arguments:
----------
p: recarray object or pandas series or class containing the data
time step's met data & params
photo: string
either the Farquhar model for photosynthesis, or the Collatz
model
res: string
either 'low' (default), 'med', or 'high' to run the optimising
solver
onopt: boolean
if True, the optimisation is performed. If Fall, fall back on
previously performed optimisation for the value of the maximum
profit.
inf_gb: bool
if True, gb is prescrived and very large
Returns:
--------
E_can: float
transpiration [mmol m-2 s-1] at maximum profit across leaves
gs_can: float
stomatal conductance [mol m-2 s-1] at maximum profit across
leaves
An_can: float
net photosynthetic assimilation rate [umol m-2 s-1] at maximum
profit across leaves
Ci_can: float
intercellular CO2 concentration [Pa] at maximum profit across
leaves
rublim_can: string
'True' if the C assimilation is rubisco limited, 'False'
otherwise
"""
# hydraulics
P, trans = hydraulics(p, res=res)
cost, __ = hydraulic_cost(p, P)
# look for the most net profit
gain, Ci, mask = photo_gain(p, trans, photo, res, inf_gb=inf_gb)
expr = gain - cost[mask]
if deriv:
expr = np.abs(np.gradient(expr, P[mask]))
# deal with edge cases by rebounding the solution
gc, gs, gb, __ = leaf_energy_balance(p, trans[mask], inf_gb=inf_gb)
try:
if inf_gb: # check on valid range
check = expr[gc > cst.zero]
else: # further constrain the realm of possible gs
check = expr[np.logical_and(gc > cst.zero, gs < 1.5 * gb)]
idx = np.isclose(expr, max(check))
if deriv:
idx = np.isclose(expr, min(check))
idx = [list(idx).index(e) for e in idx if e]
if inf_gb: # check for algo. "overshooting" due to inf. gb
while Ci[idx[0]] < 2. * p.gamstar25:
idx[0] -= 1
if idx[0] < 3:
break
# optimized where Ci for both photo models are close
Ci = Ci[idx[0]]
trans = trans[mask][idx[0]] # mol.m-2.s-1
gs = gs[idx[0]]
Pleaf = P[mask][idx[0]]
# rubisco- or electron transport-limitation?
An, Aj, Ac = calc_photosynthesis(p, trans, Ci, photo, inf_gb=inf_gb)
rublim = rubisco_limit(Aj, Ac)
# leaf temperature?
Tleaf, __ = leaf_temperature(p, trans, inf_gb=inf_gb)
if (np.isclose(trans, cst.zero, rtol=cst.zero, atol=cst.zero) and
(An > 0.)) or (idx[0] == len(P) - 1) or any(
np.isnan([An, Ci, trans, gs, Tleaf, Pleaf])):
An, Ci, trans, gs, gb, Tleaf, Pleaf = (9999., ) * 7
elif not np.isclose(trans, cst.zero, rtol=cst.zero, atol=cst.zero):
trans *= conv.MILI # mmol.m-2.s-1
return An, Ci, rublim, trans, gs, gb, Tleaf, Pleaf
except ValueError: # no opt
return (9999., ) * 8
def Cmax_gs(p, photo='Farquhar', res='low', inf_gb=False):
"""
Finds the instantaneous optimal C gain for a given C cost.
First, the C gain equation is derived for gs, beta, Ci unknown.
Then, the derived form of the equation is solved for Ci over a range of
possible betas, gs, all of which are directly or indirectly leaf
water potential P dependent.
A check (check_solve) is performed to verify that the optimization satisfies
the zero equality criteria and, finally, results are bound via a range of
physically possible Ci values.
N.B.: there can be several possible optimizations
Arguments:
----------
p: recarray object or pandas series or class containing the data
time step's met data & params
photo: string
either the Farquhar model for photosynthesis, or the Collatz model
inf_gb: bool
if True, gb is prescrived and very large
Returns:
--------
gsOPT: float
stomatal conductance [mol.m-2.s-1] for which the A(gs) is maximized
AnOPT: float
maximum C assimilation rate [μmol.m-2.s-1] given by the diffusive supply
of CO2
transOPT: float
transpiration rate [mmol.m-2.s-1] for which the A(gs) is maximized
CiOPT: float
intercellular CO2 concentration [Pa] for which the A(gs) is maximized
"""
# energy balance
P, trans = hydraulics(p, res=res, kmax=p.kmaxCM)
# expression of optimization
Ci, mask = Ci_sup_dem(p, trans, photo=photo, res=res, inf_gb=inf_gb)
gc, gs, gb, __ = leaf_energy_balance(p, trans[mask], inf_gb=inf_gb)
expr = np.abs(
np.gradient(A_trans(p, trans[mask], Ci, inf_gb=inf_gb), P[mask]) -
dcost_dpsi(p, P[mask], gs))
try:
if inf_gb: # check on valid range
check = expr[gc > cst.zero]
else: # further constrain the realm of possible gs
check = expr[np.logical_and(gc > cst.zero, gs < 1.5 * gb)]
idx = np.isclose(expr, min(check))
idx = [list(idx).index(e) for e in idx if e]
if inf_gb: # check for algo. "overshooting" due to inf. gb
while Ci[idx[0]] < 2. * p.gamstar25:
idx[0] -= 1
if idx[0] < 3:
break
# optimized where Ci for both photo models are close
Ci = Ci[idx[0]]
trans = trans[mask][idx[0]] # mol.m-2.s-1
gs = gs[idx[0]]
Pleaf = P[mask][idx[0]]
# rubisco limitation or electron transport-limitation?
An, Aj, Ac = calc_photosynthesis(p,
trans,
Ci,
photo=photo,
inf_gb=inf_gb)
rublim = rubisco_limit(Aj, Ac)
# leaf temperature?
Tleaf, __ = leaf_temperature(p, trans, inf_gb=inf_gb)
if (np.isclose(trans, cst.zero, rtol=cst.zero, atol=cst.zero) and
(An > 0.)) or (idx[0] == len(P) - 1) or any(
np.isnan([An, Ci, trans, gs, Tleaf, Pleaf])):
An, Ci, trans, gs, gb, Tleaf, Pleaf = (9999., ) * 7
elif not np.isclose(trans, cst.zero, rtol=cst.zero, atol=cst.zero):
trans *= conv.MILI # mmol.m-2.s-1
return An, Ci, rublim, trans, gs, gb, Tleaf, Pleaf
except ValueError: # no opt
return (9999., ) * 8
def fmtx(p, model, photo='Farquhar', inf_gb=True):
# hydraulics
if (model == 'CAP') or (model == 'MES'):
if model == 'CAP':
P, trans = hydraulics(p, kmax=p.krlC, Pcrit=p.PcritC)
else:
P, trans = hydraulics(p, kmax=p.krlM, Pcrit=p.PcritM)
elif model == 'LeastCost':
P, trans = hydraulics(p, kmax=p.kmaxLC)
else:
P, trans = hydraulics(p)
# expressions of optimisation
if model == 'ProfitMax': # look for the most net profit
cost, __ = hydraulic_cost(p, P)
gain, Ci, mask = photo_gain(p, trans, photo, 'low', inf_gb=inf_gb)
expr = gain - cost[mask]
elif (model != 'CAP') and (model != 'MES'):
Ci, mask = Ci_sup_dem(p, trans, photo=photo, inf_gb=inf_gb)
if model == 'ProfitMax2':
expr = A_trans(p, trans[mask], Ci,
inf_gb=inf_gb) * (1. - trans[mask] / trans[-1])
if model == 'CGain':
expr = (A_trans(p, trans[mask], Ci, inf_gb=inf_gb) -
p.Kappa * fPLC(p, P[mask]))
if model == 'LeastCost':
expr = ((p.Eta * conv.MILI * trans[mask] +
dVmaxoAdXi(p, trans[mask], Ci, inf_gb=inf_gb)) /
A_trans(p, trans[mask], Ci, inf_gb=inf_gb))
# leaf energy balance
gc, gs, gb, ww = leaf_energy_balance(p, trans, inf_gb=inf_gb)
if model == 'CMax':
try:
expr = np.abs(
np.gradient(A_trans(p, trans[mask], Ci, inf_gb=inf_gb),
P[mask]) - dcost_dpsi(p, P[mask], gs))
except Exception:
return 9999. * 1000. # returning an actual NaN causes trouble
if model == 'WUE-LWP':
expr = (A_trans(p, trans[mask], Ci, inf_gb=inf_gb) -
p.Lambda * conv.MILI * trans[mask])
if model == 'CAP':
cost = phiLWP(P, p.PcritC)
Ci, mask = Ci_sup_dem(p,
trans,
photo=photo,
Vmax25=p.Vmax25 * cost,
inf_gb=inf_gb)
An, __, __ = calc_photosynthesis(p,
trans[mask],
Ci,
photo,
Vmax25=p.Vmax25 * cost[mask],
inf_gb=inf_gb)
try:
expr = An
except Exception:
return 9999. * 1000. # returning an actual NaN causes trouble
if model == 'MES': # Ci is Cc
cost = phiLWP(P, p.PcritM)
Cc, mask = Ci_sup_dem(p, trans, photo=photo, phi=cost, inf_gb=inf_gb)
An, __, __ = calc_photosynthesis(p,
trans[mask],
Cc,
photo,
inf_gb=inf_gb)
try:
expr = An
except Exception:
return 9999. * 1000. # returning an actual NaN causes trouble
if inf_gb: # deal with edge cases by rebounding the solution
check = expr[gc[mask] > cst.zero]
else: # accounting for gb
check = expr[np.logical_and(gc[mask] > cst.zero, gs[mask] < 1.5 * gb)]
try:
if (model == 'LeastCost') or (model == 'CMax'):
idx = np.isclose(expr, min(check))
else:
idx = np.isclose(expr, max(check))
idx = [list(idx).index(e) for e in idx if e]
if len(idx) >= 1: # opt values
return gs[mask][idx[0]] * 1000. # mmol/m2/s
else:
return 9999. * 1000. # returning an actual NaN causes trouble
except ValueError: # expr function is empty
return 9999. * 1000.
def Ci_sup_dem(p,
trans,
photo='Farquhar',
res='low',
Vmax25=None,
phi=None,
inf_gb=False):
# ref. photosynthesis
A_ref, __, __ = calc_photosynthesis(p,
trans,
p.CO2,
photo,
Vmax25=Vmax25,
inf_gb=inf_gb)
# Cs < Ca, used to ensure physical solutions
__, __, gb, __ = leaf_energy_balance(p, trans, inf_gb=inf_gb)
boundary_CO2 = p.Patm * conv.FROM_MILI * A_ref / (gb * conv.GbcvGb)
Cs = np.maximum(cst.zero, np.minimum(p.CO2, p.CO2 - boundary_CO2)) # Pa
# potential Ci values over the full range of transpirations
if res == 'low':
NCis = 500
if res == 'med':
NCis = 2000
if res == 'high':
NCis = 8000
# retrieve the appropriate Cis from the supply-demand
Cis = np.asarray(
[np.linspace(0.1, Cs[e], NCis) for e in range(len(trans))])
if (Vmax25 is None) and (phi is not None): # account for gm
Tref = p.Tref + conv.C_2_K # degk, Tref set to 25 degC
try: # is Tleaf one of the input fields?
Tleaf = p.Tleaf
except (IndexError, AttributeError, ValueError): # calc. Tleaf
Tleaf, __ = leaf_temperature(p, trans, inf_gb=inf_gb)
# CO2 compensation point
gamstar = arrhen(p.gamstar25, p.Egamstar, Tref, Tleaf)
try: # now getting the Cc
Ccs = np.asarray([
phi[e] * (Cis[e] - gamstar[e]) + gamstar[e]
for e in range(len(trans))
])
except IndexError: # only one Tleaf
Ccs = np.asarray([
phi[e] * (Cis[e] - gamstar) + gamstar
for e in range(len(trans))
])
if phi is None:
Ccs = None
Ci = mtx_minimise(p,
trans,
Cis,
photo,
Vmax25=Vmax25,
all_Ccs=Ccs,
inf_gb=inf_gb)
mask = ~Ci.mask
try:
if len(mask) > 0:
pass
except TypeError:
mask = ([False] + [
True,
] * len(Ci))[:-1]
return Ci[mask], mask