def calc_revelle_factor(TA, DIC, BT, TP, TSi, TS, TF, Ks):
"""
Calculate Revelle Factor
(dpCO2 / dDIC)
"""
dDIC = 1e-6 # (1 umol kg-1)
pH = TA_DIC(TA=TA, DIC=DIC, BT=BT, TP=TP, TSi=TSi, TS=TS, TF=TF, Ks=Ks)
fCO2 = cCO2(ch(pH), DIC, Ks) / Ks.K0
# Calculate new fCO2 above and below given value
pH_hi = TA_DIC(TA=TA,
DIC=DIC + dDIC,
BT=BT,
TP=TP,
TSi=TSi,
TS=TS,
TF=TF,
Ks=Ks)
fCO2_hi = cCO2(ch(pH_hi), DIC, Ks) / Ks.K0
pH_lo = TA_DIC(TA=TA,
DIC=DIC - dDIC,
BT=BT,
TP=TP,
TSi=TSi,
TS=TS,
TF=TF,
Ks=Ks)
fCO2_lo = cCO2(ch(pH_lo), DIC, Ks) / Ks.K0
return (fCO2_hi - fCO2_lo) * DIC / (fCO2 * 2 * dDIC)
def calc_B_species(pHtot=None, BT=None, BO3=None, BO4=None, Ks=None):
# B system calculations
if pHtot is not None and BT is not None:
H = ch(pHtot)
elif BT is not None and BO3 is not None:
H = BT_BO3(BT, BO3, Ks)
elif BT is not None and BO4 is not None:
H = BT_BO4(BT, BO4, Ks)
elif BO3 is not None and BO4 is not None:
BT = BO3 + BO3
H = BT_BO3(BT, BO3, Ks)
elif pHtot is not None and BO3 is not None:
H = ch(pHtot)
BT = pH_BO3(pHtot, BO3, Ks)
elif pHtot is not None and BO4 is not None:
H = ch(pHtot)
BT = pH_BO4(pHtot, BO4, Ks)
# The above makes sure that BT and H are known,
# this next bit calculates all the missing species
# from BT and H.
if BO3 is None:
BO3 = cBO3(BT, H, Ks)
if BO4 is None:
BO4 = cBO4(BT, H, Ks)
if pHtot is None:
pHtot = np.array(cp(H), ndmin=1)
return Bunch({'pHtot': pHtot, 'H': H, 'BT': BT, 'BO3': BO3, 'BO4': BO4})
def pH_ABO4(pH, ABO4, Ks, alphaB):
"""
Returns ABT
"""
H = ch(pH)
chiB = chiB_calc(H, Ks)
return (ABO4 * (-ABO4 * alphaB * chiB + ABO4 * alphaB + ABO4 * chiB -
ABO4 + alphaB * chiB - chiB + 1) /
(ABO4 * alphaB - ABO4 + 1))
def pH_ABO3(pH, ABO3, Ks, alphaB):
"""
Returns ABT
"""
H = ch(pH)
chiB = chiB_calc(H, Ks)
return (ABO3 *
(-ABO3 * alphaB * chiB + ABO3 * chiB + alphaB * chiB - chiB + 1) /
(-ABO3 * alphaB + ABO3 + alphaB))
def pH_BO4(pH, BO4, Ks):
"""
Returns BT
"""
H = ch(pH)
return BO4 * (1 + H / Ks.KB)
def pH_BO3(pH, BO3, Ks):
"""
Returns BT
"""
H = ch(pH)
return BO3 * (1 + Ks.KB / H)
def CO2_pH(CO2, pH, Ks):
"""
Returns DIC
"""
h = ch(pH)
return CO2 * (1 + Ks.K1 / h + Ks.K1 * Ks.K2 / h**2)
def pH_DIC(pH, DIC, Ks):
"""
Returns CO2
"""
h = ch(pH)
return DIC / (1 + Ks.K1 / h + Ks.K1 * Ks.K2 / h**2)
def pH_CO3(pH, CO3, Ks):
"""
Returns DIC
"""
h = ch(pH)
return CO3 * (1 + h / Ks.K2 + h**2 / (Ks.K1 * Ks.K2))
def pH_HCO3(pH, HCO3, Ks):
"""
Returns DIC
"""
h = ch(pH)
return HCO3 * (1 + h / Ks.K1 + Ks.K2 / h)
def calc_C_species(pHtot=None,
DIC=None,
CO2=None,
HCO3=None,
CO3=None,
TA=None,
fCO2=None,
pCO2=None,
T_in=None,
BT=None,
TP=0,
TSi=0,
TS=0,
TF=0,
Ks=None):
"""
Calculate all carbon species from minimal input.
"""
# if fCO2 is given but CO2 is not, calculate CO2
if CO2 is None:
if fCO2 is not None:
CO2 = fCO2_to_CO2(fCO2, Ks)
elif pCO2 is not None:
CO2 = fCO2_to_CO2(pCO2_to_fCO2(pCO2, T_in), Ks)
# Carbon System Calculations (from Zeebe & Wolf-Gladrow, Appendix B)
# 1. CO2 and pH
if CO2 is not None and pHtot is not None:
H = ch(pHtot)
DIC = CO2_pH(CO2, pHtot, Ks)
# 2. CO2 and HCO3
elif CO2 is not None and HCO3 is not None:
H = CO2_HCO3(CO2, HCO3, Ks)
DIC = CO2_pH(CO2, cp(H), Ks)
# 3. CO2 and CO3
elif CO2 is not None and CO3 is not None:
H = CO2_CO3(CO2, CO3, Ks)
DIC = CO2_pH(CO2, cp(H), Ks)
# 4. CO2 and TA
elif CO2 is not None and TA is not None:
# unit conversion because OH and H wrapped
# up in TA fns - all need to be in same units.
pHtot = CO2_TA(CO2=CO2,
TA=TA,
BT=BT,
TP=TP,
TSi=TSi,
TS=TS,
TF=TF,
Ks=Ks)
H = ch(pHtot)
DIC = CO2_pH(CO2, pHtot, Ks)
# 5. CO2 and DIC
elif CO2 is not None and DIC is not None:
H = CO2_DIC(CO2, DIC, Ks)
# 6. pHtot and HCO3
elif pHtot is not None and HCO3 is not None:
H = ch(pHtot)
DIC = pH_HCO3(pHtot, HCO3, Ks)
# 7. pHtot and CO3
elif pHtot is not None and CO3 is not None:
H = ch(pHtot)
DIC = pH_CO3(pHtot, CO3, Ks)
# 8. pHtot and TA
elif pHtot is not None and TA is not None:
H = ch(pHtot)
DIC = pH_TA(pH=pHtot,
TA=TA,
BT=BT,
TP=TP,
TSi=TSi,
TS=TS,
TF=TF,
Ks=Ks)
# 9. pHtot and DIC
elif pHtot is not None and DIC is not None:
H = ch(pHtot)
# 10. HCO3 and CO3
elif HCO3 is not None and CO3 is not None:
H = HCO3_CO3(HCO3, CO3, Ks)
DIC = pH_CO3(cp(H), CO3, Ks)
# 11. HCO3 and TA
elif HCO3 is not None and TA is not None:
Warning(
'Nutrient alkalinity not implemented for this input combination.\nCalculations use only C and B alkalinity.'
)
H = HCO3_TA(HCO3, TA, BT, Ks)
DIC = pH_HCO3(cp(H), HCO3, Ks)
# 12. HCO3 amd DIC
elif HCO3 is not None and DIC is not None:
H = HCO3_DIC(HCO3, DIC, Ks)
# 13. CO3 and TA
elif CO3 is not None and TA is not None:
Warning(
'Nutrient alkalinity not implemented for this input combination.\nCalculations use only C and B alkalinity.'
)
H = CO3_TA(CO3, TA, BT, Ks)
DIC = pH_CO3(cp(H), CO3, Ks)
# 14. CO3 and DIC
elif CO3 is not None and DIC is not None:
H = CO3_DIC(CO3, DIC, Ks)
# 15. TA and DIC
elif TA is not None and DIC is not None:
pHtot = TA_DIC(TA=TA,
DIC=DIC,
BT=BT,
TP=TP,
TSi=TSi,
TS=TS,
TF=TF,
Ks=Ks)
H = ch(pHtot)
# The above makes sure that DIC and H are known,
# this next bit calculates all the missing species
# from DIC and H.
if CO2 is None:
CO2 = cCO2(H, DIC, Ks)
if fCO2 is None:
fCO2 = CO2_to_fCO2(CO2, Ks)
if pCO2 is None:
pCO2 = fCO2_to_pCO2(fCO2, T_in)
if HCO3 is None:
HCO3 = cHCO3(H, DIC, Ks)
if CO3 is None:
CO3 = cCO3(H, DIC, Ks)
# Calculate all elements of Alkalinity
(TA, CAlk, BAlk, PAlk, SiAlk, OH, Hfree, HSO4, HF) = cTA(H=H,
DIC=DIC,
BT=BT,
TP=TP,
TSi=TSi,
TS=TS,
TF=TF,
Ks=Ks,
mode='multi')
# if pH not calced yet, calculate on all scales.
if pHtot is None:
pHtot = np.array(cp(H), ndmin=1)
return Bunch({
'pHtot': pHtot,
'TA': TA,
'DIC': DIC,
'CO2': CO2,
'H': H,
'HCO3': HCO3,
'fCO2': fCO2,
'pCO2': pCO2,
'CO3': CO3,
'CAlk': CAlk,
'BAlk': BAlk,
'PAlk': PAlk,
'SiAlk': SiAlk,
'OH': OH,
'Hfree': Hfree,
'HSO4': HSO4,
'HF': HF
})
def CBsys(
pHtot=None,
DIC=None,
CO2=None,
HCO3=None,
CO3=None,
TA=None,
fCO2=None,
pCO2=None,
BT=None,
BO3=None,
BO4=None,
ABT=None,
ABO3=None,
ABO4=None,
dBT=None,
dBO3=None,
dBO4=None,
alphaB=None,
T_in=25.0,
S_in=35.0,
P_in=None,
T_out=None,
S_out=None,
P_out=None,
Ca=None,
Mg=None,
TP=0.0,
TSi=0.0,
TS=None,
TF=None,
pHsws=None,
pHfree=None,
pHNBS=None,
Ks=None,
pdict=None,
unit="umol",
):
"""
Calculate carbon, boron and boron isotope chemistry of seawater from a minimal parameter set.
Constants calculated by MyAMI model (Hain et al, 2015; doi:10.1002/2014GB004986).
Speciation calculations from Zeebe & Wolf-Gladrow (2001; ISBN:9780444509468) Appendix B
pH is Total scale.
Inputs must either be single values, arrays of equal length or a mixture of both.
If you use arrays of unequal length, it won't work.
Note: Special Case! If pH is not known, you must provide either:
- Two of [DIC, CO2, HCO3, CO3], and one of [BT, BO3, BO4]
- One of [DIC, CO2, HCO3, CO3], and TA and BT
- Two of [BT, BO3, BO4] and one of [DIC, CO2, HCO3, CO3]
Isotopes will only be calculated if one of [ABT, ABO3, ABO4, dBT, dBO3, dBO4]
is provided.
Error propagation:
If inputs are ufloat or uarray (from uncertainties package) errors will
be propagated through all calculations, but:
**WARNING** Error propagation NOT IMPLEMENTED for carbon system calculations
with zero-finders (i.e. when pH is not given; cases 2-5 and 10-15).
Concentration Units
+++++++++++++++++++
* Ca and Mg must be in molar units.
* All other units must be the same, and can be specified in the 'unit' variable. Defaults to umolar.
* Isotopes can be in A (11B / BT) or d (delta). Either specified, both returned.
Parameters
----------
pH, DIC, CO2, HCO3, CO3, TA : array-like
Carbon system parameters. Two of these must be provided.
If TA is specified, a B species must also be specified.
pH, BT, BO3, BO4 : array-like
Boron system parameters. Two of these must be provided.
pH, ABT, ABO3, ABO4, dBT, dBO3, dBO4 : array-like
Boron isotope system parameters. pH and one other
parameter must be provided.
alphaB : array-like
Alpha value describing B fractionation (1.0XXX).
If missing, it's calculated using the temperature
sensitive formulation of Honisch et al (2008)
T, S : array-like
Temperature in Celcius and Salinity in PSU.
Used in calculating MyAMI constants.
P : array-like
Pressure in Bar.
Used in calculating MyAMI constants.
unit : str
Concentration units of C and B parameters (all must be in
the same units).
Can be 'mol', 'mmol', 'umol', 'nmol', 'pmol' or 'fmol'.
Used in calculating Alkalinity. Default is 'umol'.
Ca, Mg : arra-like
The [Ca] and [Mg] of the seawater, * in mol / kg *.
Used in calculating MyAMI constants.
Ks : dict
A dictionary of constants. Must contain keys
'K1', 'K2', 'KB' and 'KW'.
If None, Ks are calculated using MyAMI model.
pdict : dict
Optionally, you can provide some or all parameters as a dict,
with keys the same as the parameter names above. Any parameters
included in the dict will overwrite manually specified
parameters. This is particularly useful if you're including
this in other code.
Returns
-------
dict(/Bunch) containing all calculated parameters.
"""
# Bunch inputs
ps = Bunch(locals())
if isinstance(pdict, dict):
ps.update(pdict)
# convert unit to multiplier
udict = {
"mol": 1.0,
"mmol": 1.0e3,
"umol": 1.0e6,
"nmol": 1.0e9,
"pmol": 1.0e12,
"fmol": 1.0e15,
}
if isinstance(ps.unit, str):
ps.unit = udict[ps.unit]
elif isinstance(ps.unit, (int, float)):
ps.unit = unit
upar = [
"DIC",
"CO2",
"HCO3",
"CO3",
"TA",
"fCO2",
"pCO2",
"BT",
"BO3",
"BO4",
"TP",
"TSi",
]
for p in upar:
if ps[p] is not None:
ps[p] = np.divide(ps[p], ps.unit) # convert to molar
# reassign unit, convert back at end
orig_unit = ps.unit
ps.unit = 1.0
# Conserved seawater chemistry
if ps.TS is None:
ps.TS = calc_TS(ps.S_in)
if ps.TF is None:
ps.TF = calc_TF(ps.S_in)
# Calculate Ks
ps.Ks = calc_Ks(ps.T_in, ps.S_in, ps.P_in, ps.Mg, ps.Ca, ps.TS, ps.TF,
ps.Ks)
# Calculate pH scales (does nothing if none pH given)
ps.update(
calc_pH_scales(
ps.pHtot,
ps.pHfree,
ps.pHsws,
ps.pHNBS,
ps.TS,
ps.TF,
ps.T_in + 273.15,
ps.S_in,
ps.Ks,
))
# if fCO2 is given but CO2 is not, calculate CO2
if ps.CO2 is None:
if ps.fCO2 is not None:
ps.CO2 = fCO2_to_CO2(ps.fCO2, ps.Ks)
elif ps.pCO2 is not None:
ps.CO2 = fCO2_to_CO2(pCO2_to_fCO2(ps.pCO2, ps.T_in), ps.Ks)
# if no B info provided, assume modern conc.
nBspec = NnotNone(ps.BT, ps.BO3, ps.BO4)
if nBspec == 0:
ps.BT = calc_TB(ps.S_in)
elif isinstance(BT, (int, float)):
ps.BT = ps.BT * ps.S_in / 35.0
# count number of not None C parameters
nCspec = NnotNone(ps.DIC, ps.CO2, ps.HCO3, ps.CO3) # used below
# if pH is given, it's easy
if ps.pHtot is not None or nBspec == 2:
ps.update(
calc_B_species(pHtot=ps.pHtot,
BT=ps.BT,
BO3=ps.BO3,
BO4=ps.BO4,
Ks=ps.Ks))
ps.update(
calc_C_species(
pHtot=ps.pHtot,
DIC=ps.DIC,
CO2=ps.CO2,
HCO3=ps.HCO3,
CO3=ps.CO3,
TA=ps.TA,
fCO2=ps.fCO2,
pCO2=ps.pCO2,
T_in=ps.T_in,
BT=ps.BT,
TP=ps.TP,
TSi=ps.TSi,
TS=ps.TS,
TF=ps.TF,
Ks=ps.Ks,
))
# if not, this section works out the order that things should be calculated in.
# Special case: if pH is missing, must have:
# a) two C or one C and both TA and BT
# b) two B (above)
# c) one pH-dependent B, one pH-dependent C... But that's cray...
# (c not implemented!)
elif (nCspec == 2) | ((nCspec == 1) &
(NnotNone(ps.TA, ps.BT) == 2)): # case A
ps.update(
calc_C_species(
pHtot=ps.pHtot,
DIC=ps.DIC,
CO2=ps.CO2,
HCO3=ps.HCO3,
CO3=ps.CO3,
TA=ps.TA,
fCO2=ps.fCO2,
pCO2=ps.pCO2,
T_in=ps.T_in,
BT=ps.BT,
TP=ps.TP,
TSi=ps.TSi,
TS=ps.TS,
TF=ps.TF,
Ks=ps.Ks,
))
ps.update(
calc_B_species(pHtot=ps.pHtot,
BT=ps.BT,
BO3=ps.BO3,
BO4=ps.BO4,
Ks=ps.Ks))
# elif nBspec == 2: # case B -- moved up
# ps.update(calc_B_species(pHtot=ps.pHtot, BT=ps.BT, BO3=ps.BO3, BO4=ps.BO4, Ks=ps.Ks))
# ps.update(calc_C_species(pHtot=ps.pHtot, DIC=ps.DIC, CO2=ps.CO2,
# HCO3=ps.HCO3, CO3=ps.CO3, TA=ps.TA,
# fCO2=ps.fCO2, pCO2=ps.pCO2,
# T_in=ps.T_in, BT=ps.BT, TP=ps.TP, TSi=ps.TSi,
# TS=ps.TS, TF=ps.TF, Ks=ps.Ks)) # then C
else: # if neither condition is met, throw an error
raise ValueError(
("Impossible! You haven't provided enough parameters.\n" +
"If you don't know pH, you must provide either:\n" +
" - Two of [DIC, CO2, HCO3, CO3], and one of [BT, BO3, BO4]\n" +
" - One of [DIC, CO2, HCO3, CO3], and TA and BT\n" +
" - Two of [BT, BO3, BO4] and one of [DIC, CO2, HCO3, CO3]"))
ps["revelle_factor"] = calc_revelle_factor(
TA=ps.TA,
DIC=ps.DIC,
BT=ps.BT,
TP=ps.TP,
TSi=ps.TSi,
TS=ps.TS,
TF=ps.TF,
Ks=ps.Ks,
)
# If any isotope parameter specified, calculate the isotope systen.
if NnotNone(ps.ABT, ps.ABO3, ps.ABO4, ps.dBT, ps.dBO3, ps.dBO4) != 0:
ps.update(ABsys(pdict=ps))
# Calculate Isotopes
if ps.dBT is None and ps.dBO3 is None and ps.dBO4 is None:
ps.dBT = 0
# if deltas provided, calculate corresponding As
if ps.dBT is not None:
ps.ABT = d11_2_A11(ps.dBT)
if ps.dBO3 is not None:
ps.ABO3 = d11_2_A11(ps.dBO3)
if ps.dBO4 is not None:
ps.ABO4 = d11_2_A11(ps.dBO4)
# calculate alpha
ps.alphaB = alphaB_calc(ps.T_in)
if ps.pHtot is not None and ps.ABT is not None:
ps.H = ch(ps.pHtot)
elif ps.pHtot is not None and ps.ABO3 is not None:
ps.ABT = pH_ABO3(ps.pHtot, ps.ABO3, ps.Ks, ps.alphaB)
elif ps.pHtot is not None and ps.ABO4 is not None:
ps.ABT = pH_ABO3(ps.pHtot, ps.ABO4, ps.Ks, ps.alphaB)
else:
raise ValueError("pH must be determined to calculate isotopes.")
if ps.ABO3 is None:
ps.ABO3 = cABO3(ps.H, ps.ABT, ps.Ks, ps.alphaB)
if ps.ABO4 is None:
ps.ABO4 = cABO4(ps.H, ps.ABT, ps.Ks, ps.alphaB)
if ps.dBT is None:
ps.dBT = A11_2_d11(ps.ABT)
if ps.dBO3 is None:
ps.dBO3 = A11_2_d11(ps.ABO3)
if ps.dBO4 is None:
ps.dBO4 = A11_2_d11(ps.ABO4)
# clean up output
outputs = [
"BAlk",
"BT",
"CAlk",
"CO2",
"CO3",
"DIC",
"H",
"HCO3",
"HF",
"HSO4",
"Hfree",
"Ks",
"OH",
"PAlk",
"SiAlk",
"TA",
"TF",
"TP",
"TS",
"TSi",
"fCO2",
"pCO2",
"pHfree",
"pHsws",
"pHtot",
"pHNBS",
"BO3",
"BO4",
"ABO3",
"ABO4",
"dBO3",
"dBO4",
]
for k in outputs:
if not isinstance(ps[k], np.ndarray):
# convert all outputs to (min) 1D numpy arrays.
ps[k] = np.array(ps[k], ndmin=1)
# Handle Units
for p in upar + [
"CAlk", "BAlk", "PAlk", "SiAlk", "OH", "HSO4", "HF", "Hfree"
]:
ps[p] *= orig_unit # convert back to input units
# Recursive approach to calculate output params.
# if output conditions specified, calculate outputs.
if ps.T_out is not None or ps.S_out is not None or ps.P_out is not None:
if ps.T_out is None:
ps.T_out = ps.T_in
if ps.S_out is None:
ps.S_out = ps.S_in
if ps.P_out is None:
ps.P_out = ps.P_in
# assumes conserved alkalinity
out_cond = CBsys(
TA=ps.TA,
DIC=ps.DIC,
BT=ps.BT,
T_in=ps.T_out,
S_in=ps.S_out,
P_in=ps.P_out,
unit=ps.unit,
)
# Calculate pH scales (does nothing if no pH given)
out_cond.update(
calc_pH_scales(
out_cond.pHtot,
out_cond.pHfree,
out_cond.pHsws,
out_cond.pHNBS,
out_cond.TS,
out_cond.TF,
out_cond.T_in + 273.15,
out_cond.S_in,
out_cond.Ks,
))
# rename parameters in output conditions
ps.update({k + "_out": out_cond[k] for k in outputs})
# remove some superfluous outputs
rem = ["pdict", "unit"]
for r in rem:
if r in ps:
del ps[r]
return ps
def ABsys(
pHtot=None,
ABT=None,
ABO3=None,
ABO4=None,
dBT=None,
dBO3=None,
dBO4=None,
alphaB=None,
T_in=25.0,
S_in=35.0,
P_in=None,
Ca=None,
Mg=None,
TS=None,
TF=None,
pHsws=None,
pHfree=None,
pHNBS=None,
Ks=None,
pdict=None,
):
"""
Calculate the boron isotope chemistry of seawater from a minimal parameter set.
Constants calculated by MyAMI model (Hain et al, 2015; doi:10.1002/2014GB004986).
Speciation calculations from Zeebe & Wolf-Gladrow (2001; ISBN:9780444509468).
pH is Total scale.
Inputs must either be single values, arrays of equal length or a mixture of both.
If you use arrays of unequal length, it won't work.
Error propagation:
If inputs are ufloat or uarray (from uncertainties package) errors will
be propagated through all calculations.
Concentration Units
+++++++++++++++++++
* 'A' is fractional abundance (11B / BT)
* 'd' are delta values
Either specified, both returned.
Parameters
----------
pH, ABT, ABO3, ABO4, dBT, dBO3, dBO4 : array-like
Boron isotope system parameters. pH and one other
parameter must be provided.
alphaB : array-like
Alpha value describing B fractionation (1.0XXX).
If missing, it's calculated using the temperature
sensitive formulation of Honisch et al (2008)
T, S : array-like
Temperature in Celcius and Salinity in PSU.
Used in calculating MyAMI constants.
P : array-like
Pressure in Bar.
Used in calculating MyAMI constants.
Ca, Mg : arra-like
The [Ca] and [Mg] of the seawater, in mol / kg.
Used in calculating MyAMI constants.
Ks : dict
A dictionary of constants. Must contain keys
'K1', 'K2', 'KB' and 'KW'.
If None, Ks are calculated using MyAMI model.
pdict : dict
Optionally, you can provide some or all parameters as a dict,
with keys the same as the parameter names above. Any parameters
included in the dict will overwrite manually specified
parameters. This is particularly useful if you're including
this in other code.
Returns
-------
dict(/Bunch) containing all calculated parameters.
"""
# Bunch inputs
ps = Bunch(locals())
if isinstance(pdict, dict):
ps.update(pdict)
# Conserved seawater chemistry
if ps.TS is None:
ps.TS = calc_TS(ps.S_in)
if ps.TF is None:
ps.TF = calc_TF(ps.S_in)
# Calculate Ks
ps.Ks = calc_Ks(ps.T_in, ps.S_in, ps.P_in, ps.Mg, ps.Ca, ps.TS, ps.TF,
ps.Ks)
# Calculate pH scales (does nothing if none pH given)
ps.update(
calc_pH_scales(
ps.pHtot,
ps.pHfree,
ps.pHsws,
ps.pHNBS,
ps.TS,
ps.TF,
ps.T_in + 273.15,
ps.S_in,
ps.Ks,
))
# if deltas provided, calculate corresponding As
if ps.dBT is not None:
ps.ABT = d11_2_A11(ps.dBT)
if ps.dBO3 is not None:
ps.ABO3 = d11_2_A11(ps.dBO3)
if ps.dBO4 is not None:
ps.ABO4 = d11_2_A11(ps.dBO4)
# calculate alpha
ps.alphaB = alphaB_calc(ps.T_in)
if ps.pHtot is not None and ps.ABT is not None:
ps.H = ch(ps.pHtot)
elif ps.pHtot is not None and ps.ABO3 is not None:
ps.ABT = pH_ABO3(ps.pHtot, ps.ABO3, ps.Ks, ps.alphaB)
elif ps.pHtot is not None and ps.ABO4 is not None:
ps.ABT = pH_ABO3(ps.pHtot, ps.ABO4, ps.Ks, ps.alphaB)
else:
raise ValueError("pH must be determined to calculate isotopes.")
if ps.ABO3 is None:
ps.ABO3 = cABO3(ps.H, ps.ABT, ps.Ks, ps.alphaB)
if ps.ABO4 is None:
ps.ABO4 = cABO4(ps.H, ps.ABT, ps.Ks, ps.alphaB)
if ps.dBT is None:
ps.dBT = A11_2_d11(ps.ABT)
if ps.dBO3 is None:
ps.dBO3 = A11_2_d11(ps.ABO3)
if ps.dBO4 is None:
ps.dBO4 = A11_2_d11(ps.ABO4)
for k in [
"ABO3",
"ABO4",
"ABT",
"Ca",
"H",
"Mg",
"S_in",
"T_in",
"alphaB",
"dBO3",
"dBO4",
"dBT",
"pHtot",
]:
if not isinstance(ps[k], np.ndarray):
# convert all outputs to (min) 1D numpy arrays.
ps[k] = np.array(ps[k], ndmin=1)
# remove some superfluous outputs
rem = ["pdict"]
for r in rem:
if r in ps:
del ps[r]
return ps
def Csys(pHtot=None,
DIC=None,
CO2=None,
HCO3=None,
CO3=None,
TA=None,
fCO2=None,
pCO2=None,
BT=None,
Ca=None,
Mg=None,
T=25.,
S=35.,
P=None,
TP=0.,
TSi=0.,
pHsws=None,
pHfree=None,
Ks=None,
pdict=None,
unit='umol'):
"""
Calculate the carbon chemistry of seawater from a minimal parameter set.
Constants calculated by MyAMI model (Hain et al, 2015; doi:10.1002/2014GB004986).
Speciation calculations from Zeebe & Wolf-Gladrow (2001; ISBN:9780444509468) Appendix B
pH is Total scale.
Inputs must either be single values, arrays of equal length or a mixture of both.
If you use arrays of unequal length, it won't work.
Error propagation:
If inputs are ufloat or uarray (from uncertainties package) errors will
be propagated through all calculations, but:
**WARNING** Error propagation NOT IMPLEMENTED for carbon system calculations
with zero-finders (i.e. when pH is not given; cases 2-5 and 10-15).
Concentration Units
+++++++++++++++++++
* Ca and Mg must be in molar units.
* All other units must be the same, and can be specified in the 'unit' variable. Defaults to umolar.
Parameters
----------
pH, DIC, CO2, HCO3, CO3, TA : array-like
Carbon system parameters. Two of these must be provided.
BT : array-like
Total B at Salinity = 35, used in Alkalinity calculations.
Ca, Mg : arra-like
The [Ca] and [Mg] of the seawater, in mol / kg.
Used in calculating MyAMI constants.
T, S : array-like
Temperature in Celcius and Salinity in PSU.
Used in calculating MyAMI constants.
P : array-like
Pressure in Bar.
Used in calculating MyAMI constants.
unit : str
Concentration units of C and B parameters (all must be in
the same units).
Can be 'mol', 'mmol', 'umol', 'nmol', 'pmol' or 'fmol'.
Used in calculating Alkalinity. Default is 'umol'.
Ks : dict
A dictionary of constants. Must contain keys
'K1', 'K2', 'KB' and 'KW'.
If None, Ks are calculated using MyAMI model.
pdict : dict
Optionally, you can provide some or all parameters as a dict,
with keys the same as the parameter names above. Any parameters
included in the dict will overwrite manually specified
parameters. This is particularly useful if you're including
this in other code.
Returns
-------
dict(/Bunch) containing all calculated parameters.
"""
# Bunch inputs
ps = Bunch(locals())
if isinstance(pdict, dict):
ps.update(pdict)
# convert unit to multiplier
udict = {
'mol': 1.,
'mmol': 1.e3,
'umol': 1.e6,
'nmol': 1.e9,
'pmol': 1.e12,
'fmol': 1.e15
}
if isinstance(ps.unit, str):
ps.unit = udict[ps.unit]
# elif isinstance(ps.unit, (int, float)):
# ps.unit = ps.unit
if ps.unit != 1:
upar = [
'DIC', 'TA', 'CO2', 'HCO3', 'CO3', 'BT', 'fCO2', 'pCO2', 'TP',
'TSi'
]
for p in upar:
if ps[p] is not None:
ps[p] = np.divide(ps[p], ps.unit) # convert to molar
# Conserved seawater chemistry
if 'TS' not in ps:
ps.TS = calc_TS(ps.S)
if 'TF' not in ps:
ps.TF = calc_TF(ps.S)
if ps.BT is None:
ps.BT = calc_TB(ps.S)
elif isinstance(BT, (int, float)):
ps.BT = ps.BT * ps.S / 35.
# Calculate Ks
ps.Ks = get_Ks(ps)
# Calculate pH scales (does nothing if no pH given)
ps.update(
calc_pH_scales(ps.pHtot, ps.pHfree, ps.pHsws, ps.TS, ps.TF, ps.Ks))
# if fCO2 is given but CO2 is not, calculate CO2
if ps.CO2 is None:
if ps.fCO2 is not None:
ps.CO2 = fCO2_to_CO2(ps.fCO2, ps.Ks)
elif ps.pCO2 is not None:
ps.CO2 = fCO2_to_CO2(pCO2_to_fCO2(ps.pCO2, ps.T), ps.Ks)
# Carbon System Calculations (from Zeebe & Wolf-Gladrow, Appendix B)
# 1. CO2 and pH
if ps.CO2 is not None and ps.pHtot is not None:
ps.H = ch(ps.pHtot)
ps.DIC = CO2_pH(ps.CO2, ps.pHtot, ps.Ks)
# 2. ps.CO2 and ps.HCO3
elif ps.CO2 is not None and ps.HCO3 is not None:
ps.H = CO2_HCO3(ps.CO2, ps.HCO3, ps.Ks)
ps.DIC = CO2_pH(ps.CO2, cp(ps.H), ps.Ks)
# 3. ps.CO2 and ps.CO3
elif ps.CO2 is not None and ps.CO3 is not None:
ps.H = CO2_CO3(ps.CO2, ps.CO3, ps.Ks)
ps.DIC = CO2_pH(ps.CO2, cp(ps.H), ps.Ks)
# 4. ps.CO2 and ps.TA
elif ps.CO2 is not None and ps.TA is not None:
# unit conversion because OH and H wrapped
# up in TA fns - all need to be in same units.
ps.pHtot = CO2_TA(CO2=ps.CO2,
TA=ps.TA,
BT=ps.BT,
TP=ps.TP,
TSi=ps.TSi,
TS=ps.TS,
TF=ps.TF,
Ks=ps.Ks)
ps.H = ch(ps.pHtot)
ps.DIC = CO2_pH(ps.CO2, ps.pHtot, ps.Ks)
# 5. ps.CO2 and ps.DIC
elif ps.CO2 is not None and ps.DIC is not None:
ps.H = CO2_DIC(ps.CO2, ps.DIC, ps.Ks)
# 6. ps.pHtot and ps.HCO3
elif ps.pHtot is not None and ps.HCO3 is not None:
ps.H = ch(ps.pHtot)
ps.DIC = pH_HCO3(ps.pHtot, ps.HCO3, ps.Ks)
# 7. ps.pHtot and ps.CO3
elif ps.pHtot is not None and ps.CO3 is not None:
ps.H = ch(ps.pHtot)
ps.DIC = pH_CO3(ps.pHtot, ps.CO3, ps.Ks)
# 8. ps.pHtot and ps.TA
elif ps.pHtot is not None and ps.TA is not None:
ps.H = ch(ps.pHtot)
ps.DIC = pH_TA(pH=ps.pHtot,
TA=ps.TA,
BT=ps.BT,
TP=ps.TP,
TSi=ps.TSi,
TS=ps.TS,
TF=ps.TF,
Ks=ps.Ks)
# 9. ps.pHtot and ps.DIC
elif ps.pHtot is not None and ps.DIC is not None:
ps.H = ch(ps.pHtot)
# 10. ps.HCO3 and ps.CO3
elif ps.HCO3 is not None and ps.CO3 is not None:
ps.H = HCO3_CO3(ps.HCO3, ps.CO3, ps.Ks)
ps.DIC = pH_CO3(cp(ps.H), ps.CO3, ps.Ks)
# 11. ps.HCO3 and ps.TA
elif ps.HCO3 is not None and ps.TA is not None:
Warning(
'Nutrient alkalinity not implemented for this input combination.\nCalculations use only C and B alkalinity.'
)
ps.H = HCO3_TA(ps.HCO3, ps.TA, ps.BT, ps.Ks)
ps.DIC = pH_HCO3(cp(ps.H), ps.HCO3, ps.Ks)
# 12. ps.HCO3 amd ps.DIC
elif ps.HCO3 is not None and ps.DIC is not None:
ps.H = HCO3_DIC(ps.HCO3, ps.DIC, ps.Ks)
# 13. ps.CO3 and ps.TA
elif ps.CO3 is not None and ps.TA is not None:
Warning(
'Nutrient alkalinity not implemented for this input combination.\nCalculations use only C and B alkalinity.'
)
ps.H = CO3_TA(ps.CO3, ps.TA, ps.BT, ps.Ks)
ps.DIC = pH_CO3(cp(ps.H), ps.CO3, ps.Ks)
# 14. ps.CO3 and ps.DIC
elif ps.CO3 is not None and ps.DIC is not None:
ps.H = CO3_DIC(ps.CO3, ps.DIC, ps.Ks)
# 15. ps.TA and ps.DIC
elif ps.TA is not None and ps.DIC is not None:
ps.pHtot = TA_DIC(TA=ps.TA,
DIC=ps.DIC,
BT=ps.BT,
TP=ps.TP,
TSi=ps.TSi,
TS=ps.TS,
TF=ps.TF,
Ks=ps.Ks)
ps.H = ch(ps.pHtot)
# The above makes sure that DIC and H are known,
# this next bit calculates all the missing species
# from DIC and H.
if ps.CO2 is None:
ps.CO2 = cCO2(ps.H, ps.DIC, ps.Ks)
if ps.fCO2 is None:
ps.fCO2 = CO2_to_fCO2(ps.CO2, ps.Ks)
if ps.pCO2 is None:
ps.pCO2 = fCO2_to_pCO2(ps.fCO2, ps.T)
if ps.HCO3 is None:
ps.HCO3 = cHCO3(ps.H, ps.DIC, ps.Ks)
if ps.CO3 is None:
ps.CO3 = cCO3(ps.H, ps.DIC, ps.Ks)
# Always calculate elements of alkalinity
try:
# necessary for use with CBsyst in special cases
# where BT is not known before Csys is run.
(ps.TA, ps.CAlk, ps.BAlk, ps.PAlk, ps.SiAlk, ps.OH, ps.Hfree, ps.HSO4,
ps.HF) = cTA(H=ps.H,
DIC=ps.DIC,
BT=ps.BT,
TP=ps.TP,
TSi=ps.TSi,
TS=ps.TS,
TF=ps.TF,
Ks=ps.Ks,
mode='multi')
except TypeError:
pass
if ps.pHtot is None:
ps.pHtot = np.array(cp(ps.H), ndmin=1)
# Calculate other pH scales
ps.update(
calc_pH_scales(ps.pHtot, ps.pHfree, ps.pHsws, ps.TS, ps.TF, ps.Ks))
# clean up for output
for k in [
'BT', 'CO2', 'CO3', 'Ca', 'DIC', 'H', 'HCO3', 'Mg', 'S', 'T', 'TA',
'CAlk', 'PAlk', 'SiAlk', 'OH'
]:
if not isinstance(ps[k], np.ndarray):
# convert all outputs to (min) 1D numpy arrays.
ps[k] = np.array(ps[k], ndmin=1)
if ps.unit != 1:
for p in upar + [
'CAlk', 'BAlk', 'PAlk', 'SiAlk', 'OH', 'HSO4', 'HF', 'Hfree'
]:
ps[p] *= ps.unit # convert back to input units
# remove some superfluous outputs
rem = ['pdict']
for r in rem:
if r in ps:
del ps[r]
return ps
def Bsys(pHtot=None,
BT=None,
BO3=None,
BO4=None,
ABT=None,
ABO3=None,
ABO4=None,
dBT=None,
dBO3=None,
dBO4=None,
alphaB=None,
T=25.,
S=35.,
P=None,
Ca=None,
Mg=None,
pHsws=None,
pHfree=None,
Ks=None,
pdict=None):
"""
Calculate the boron chemistry of seawater from a minimal parameter set.
Constants calculated by MyAMI model (Hain et al, 2015; doi:10.1002/2014GB004986).
Speciation calculations from Zeebe & Wolf-Gladrow (2001; ISBN:9780444509468).
pH is Total scale.
Inputs must either be single values, arrays of equal length or a mixture of both.
If you use arrays of unequal length, it won't work.
Error propagation:
If inputs are ufloat or uarray (from uncertainties package) errors will
be propagated through all calculations.
Concentration Units
+++++++++++++++++++
* All concentrations must be in the same units. Returned in the same units as inputs.
Parameters
----------
pH, BT, BO3, BO4 : array-like
Boron system parameters. Two of these must be provided.
T, S : array-like
Temperature in Celcius and Salinity in PSU.
Used in calculating MyAMI constants.
P : array-like
Pressure in Bar.
Used in calculating MyAMI constants.
Ca, Mg : arra-like
The [Ca] and [Mg] of the seawater, in mol / kg.
Used in calculating MyAMI constants.
Ks : dict
A dictionary of constants. Must contain keys
'K1', 'K2', 'KB' and 'KW'.
If None, Ks are calculated using MyAMI model.
pdict : dict
Optionally, you can provide some or all parameters as a dict,
with keys the same as the parameter names above. Any parameters
included in the dict will overwrite manually specified
parameters. This is particularly useful if you're including
this in other code.
Returns
-------
dict(/Bunch) containing all calculated parameters.
"""
# Bunch inputs
ps = Bunch(locals())
if isinstance(pdict, dict):
ps.update(pdict)
# Conserved seawater chemistry
if 'TS' not in ps:
ps.TS = calc_TS(ps.S)
if 'TF' not in ps:
ps.TF = calc_TF(ps.S)
# if neither Ca nor Mg provided, use default Ks
ps.Ks = get_Ks(ps)
# Calculate pH scales (does nothing if none pH given)
ps.update(
calc_pH_scales(ps.pHtot, ps.pHfree, ps.pHsws, ps.TS, ps.TF, ps.Ks))
# B system calculations
if ps.pHtot is not None and ps.BT is not None:
ps.H = ch(ps.pHtot)
elif ps.BT is not None and ps.BO3 is not None:
ps.H = BT_BO3(ps.BT, ps.BO3, ps.Ks)
elif ps.BT is not None and ps.BO4 is not None:
ps.H = BT_BO4(ps.BT, ps.BO4, ps.Ks)
elif ps.BO3 is not None and ps.BO4 is not None:
ps.BT = ps.BO3 + ps.BO3
ps.H = BT_BO3(ps.BT, ps.BO3, ps.Ks)
elif ps.pHtot is not None and ps.BO3 is not None:
ps.H = ch(ps.pHtot)
ps.BT = pH_BO3(ps.pHtot, ps.BO3, ps.Ks)
elif ps.pHtot is not None and ps.BO4 is not None:
ps.H = ch(ps.pHtot)
ps.BT = pH_BO4(ps.pHtot, ps.BO4, ps.Ks)
# The above makes sure that BT and H are known,
# this next bit calculates all the missing species
# from BT and H.
if ps.BO3 is None:
ps.BO3 = cBO3(ps.BT, ps.H, ps.Ks)
if ps.BO4 is None:
ps.BO4 = cBO4(ps.BT, ps.H, ps.Ks)
if ps.pHtot is None:
ps.pHtot = np.array(cp(ps.H), ndmin=1)
# Calculate other pH scales
ps.update(
calc_pH_scales(ps.pHtot, ps.pHfree, ps.pHsws, ps.TS, ps.TF, ps.Ks))
if NnotNone(ps.ABT, ps.ABO3, ps.ABO4, ps.dBT, ps.dBO3, ps.dBO4) != 0:
ps.update(ABsys(pdict=ps))
for k in ['BT', 'H', 'BO3', 'BO4', 'Ca', 'Mg', 'S', 'T']:
# convert all outputs to (min) 1D numpy arrays.
if not isinstance(ps[k], np.ndarray):
# convert all outputs to (min) 1D numpy arrays.
ps[k] = np.array(ps[k], ndmin=1)
# remove some superfluous outputs
rem = ['pdict']
for r in rem:
if r in ps:
del ps[r]
return ps
