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CO2System.jl
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1970 lines (1858 loc) · 84.8 KB
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module CO2System
export CO2SYS
function CO2SYS(PAR1,PAR2,PAR1TYPE,PAR2TYPE,SAL,TEMPIN,TEMPOUT,PRESIN,PRESOUT,
SI,PO4,pHSCALEIN,K1K2CONSTANTS,KSO4CONSTANTS)
#**************************************************************************
#
# First CO2SYS.m version: 1.1 (Sep 2011)
# Current CO2SYS.m version: 2.0 (20 Dec 2016)
# Current CO2SYS.jl version: 2.0.5-jl1 (2019)
#
# For Julia version updates, bug reports and support:
# https://github.com/mvdh7/CO2SYS.jl
#
# CO2SYS is Julia port of the MATLAB version of the original CO2SYS for DOS.
# CO2SYS calculates and returns the state of the carbonate system of
# oceanographic water samples, if supplied with enough input.
#
# Please note that this software is intended to be exactly identical to the
# DOS and Excel versions that have been released previously, meaning that
# results obtained should be very nearly indentical for identical input.
# Additionally, several of the dissociation constants K1 and K2 that have
# been published since the original DOS version was written are implemented.
# For a complete list of changes since version 1.0, see below.
#
# For much more info please have a look at:
# Lewis, E., and D. W. R. Wallace. 1998. Program Developed for
# CO2 System Calculations. ORNL/CDIAC-105. Carbon Dioxide Information
# Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy,
# Oak Ridge, Tennessee.
# http://cdiac.ornl.gov/oceans/co2rprt.html
#
#**************************************************************************
#
# **** SYNTAX:
# [RESULT,HEADERS,NICEHEADERS] = CO2SYS(PAR1,PAR2,PAR1TYPE,PAR2TYPE,
# SAL,TEMPIN,TEMPOUT,PRESIN,PRESOUT,SI,PO4,pHSCALEIN,
# K1K2CONSTANTS,KSO4CONSTANTS)
#
# **** SYNTAX EXAMPLES:
# [Result] = CO2SYS(2400,2200,1,2,35,0,25,4200,0,15,1,1,4,1)
# [Result,Headers] = CO2SYS(2400, 8,1,3,35,0,25,4200,0,15,1,1,4,1)
# [Result,Headers,Niceheaders] = CO2SYS( 500, 8,5,3,35,0,25,4200,0,15,1,1,4,1)
# [A] = CO2SYS(2400,2000:10:2400,1,2,35,0,25,4200,0,15,1,1,4,1)
# [A] = CO2SYS(2400,2200,1,2,0:1:35,0,25,4200,0,15,1,1,4,1)
# [A] = CO2SYS(2400,2200,1,2,35,0,25,0:100:4200,0,15,1,1,4,1)
#
# **** APPLICATION EXAMPLE (copy and paste this into command window):
# tmps=0:40; sals=0:40; [X,Y]=meshgrid(tmps,sals);
# A = CO2SYS(2300,2100,1,2,Y[:],X[:],nan,0,nan,1,1,1,9,1);
# Z=nan(size(X)); Z[:]=A(:,4); figure; contourf(X,Y,Z,20); caxis([0 1200]); colorbar;
# ylabel('Salinity [psu]'); xlabel('Temperature [degC]'); title('Dependence of pCO2 [uatm] on T and S')
#
#**************************************************************************
#
# INPUT:
#
# PAR1 (some unit) : scalar or vector of size n
# PAR2 (some unit) : scalar or vector of size n
# PAR1TYPE () : scalar or vector of size n (*)
# PAR2TYPE () : scalar or vector of size n (*)
# SAL () : scalar or vector of size n
# TEMPIN (degr. C) : scalar or vector of size n
# TEMPOUT (degr. C) : scalar or vector of size n
# PRESIN (dbar) : scalar or vector of size n
# PRESOUT (dbar) : scalar or vector of size n
# SI (umol/kgSW) : scalar or vector of size n
# PO4 (umol/kgSW) : scalar or vector of size n
# pHSCALEIN : scalar or vector of size n (**)
# K1K2CONSTANTS : scalar or vector of size n (***)
# KSO4CONSTANTS : scalar or vector of size n (****)
#
# (*) Each element must be an integer,
# indicating that PAR1 (or PAR2) is of type:
# 1 = Total Alkalinity
# 2 = DIC
# 3 = pH
# 4 = pCO2
# 5 = fCO2
#
# (**) Each element must be an integer,
# indicating that the pH-input (PAR1 or PAR2, if any) is at:
# 1 = Total scale
# 2 = Seawater scale
# 3 = Free scale
# 4 = NBS scale
#
# (***) Each element must be an integer,
# indicating the K1 K2 dissociation constants that are to be used:
# 1 = Roy, 1993 T: 0-45 S: 5-45. Total scale. Artificial seawater.
# 2 = Goyet & Poisson T: -1-40 S: 10-50. Seaw. scale. Artificial seawater.
# 3 = HANSSON refit BY DICKSON AND MILLERO T: 2-35 S: 20-40. Seaw. scale. Artificial seawater.
# 4 = MEHRBACH refit BY DICKSON AND MILLERO T: 2-35 S: 20-40. Seaw. scale. Artificial seawater.
# 5 = HANSSON and MEHRBACH refit BY DICKSON AND MILLERO T: 2-35 S: 20-40. Seaw. scale. Artificial seawater.
# 6 = GEOSECS (i.e., original Mehrbach) T: 2-35 S: 19-43. NBS scale. Real seawater.
# 7 = Peng (i.e., originam Mehrbach but without XXX) T: 2-35 S: 19-43. NBS scale. Real seawater.
# 8 = Millero, 1979, FOR PURE WATER ONLY (i.e., Sal=0) T: 0-50 S: 0.
# 9 = Cai and Wang, 1998 T: 2-35 S: 0-49. NBS scale. Real and artificial seawater.
# 10 = Lueker et al, 2000 T: 2-35 S: 19-43. Total scale. Real seawater.
# 11 = Mojica Prieto and Millero, 2002. T: 0-45 S: 5-42. Seaw. scale. Real seawater
# 12 = Millero et al, 2002 T: -1.6-35 S: 34-37. Seaw. scale. Field measurements.
# 13 = Millero et al, 2006 T: 0-50 S: 1-50. Seaw. scale. Real seawater.
# 14 = Millero 2010 T: 0-50 S: 1-50. Seaw. scale. Real seawater.
# 15 = Waters, Millero, & Woosley 2014 T: 0-50 S: 1-50. Seaw. scale. Real seawater.
#
# (****) Each element must be an integer that
# indicates the KSO4 dissociation constants that are to be used,
# in combination with the formulation of the borate-to-salinity ratio to be used.
# Having both these choices in a single argument is somewhat awkward,
# but it maintains syntax compatibility with the previous version.
# 1 = KSO4 of Dickson 1990a & TB of Uppstrom 1974 (PREFERRED)
# 2 = KSO4 of Khoo et al 1977 & TB of Uppstrom 1974
# 3 = KSO4 of Dickson 1990a & TB of Lee 2010
# 4 = KSO4 of Khoo et al 1977 & TB of Lee 2010
#
#**************************************************************************#
#
# OUTPUT: * an array containing the following parameter values (one row per sample):
# * a cell-array containing crudely formatted headers
# * a cell-array containing nicely formatted headers
#
# POS PARAMETER UNIT
#
# 01 - TAlk (umol/kgSW)
# 02 - TCO2 (umol/kgSW)
# 03 - pHin ()
# 04 - pCO2 input (uatm)
# 05 - fCO2 input (uatm)
# 06 - HCO3 input (umol/kgSW)
# 07 - CO3 input (umol/kgSW)
# 08 - CO2 input (umol/kgSW)
# 09 - BAlk input (umol/kgSW)
# 10 - OH input (umol/kgSW)
# 11 - PAlk input (umol/kgSW)
# 12 - SiAlk input (umol/kgSW)
# 13 - Hfree input (umol/kgSW)
# 14 - RevelleFactor input ()
# 15 - OmegaCa input ()
# 16 - OmegaAr input ()
# 17 - xCO2 input (ppm)
# 18 - pH output ()
# 19 - pCO2 output (uatm)
# 20 - fCO2 output (uatm)
# 21 - HCO3 output (umol/kgSW)
# 22 - CO3 output (umol/kgSW)
# 23 - CO2 output (umol/kgSW)
# 24 - BAlk output (umol/kgSW)
# 25 - OH output (umol/kgSW)
# 26 - PAlk output (umol/kgSW)
# 27 - SiAlk output (umol/kgSW)
# 28 - Hfree output (umol/kgSW)
# 29 - RevelleFactor output ()
# 30 - OmegaCa output ()
# 31 - OmegaAr output ()
# 32 - xCO2 output (ppm)
# 33 - pH input (Total) ()
# 34 - pH input (SWS) ()
# 35 - pH input (Free) ()
# 36 - pH input (NBS) ()
# 37 - pH output (Total) ()
# 38 - pH output (SWS) ()
# 39 - pH output (Free) ()
# 40 - pH output (NBS) ()
# 41 - TEMP input (deg C) ***
# 42 - TEMPOUT (deg C) ***
# 43 - PRES input (dbar or m) ***
# 44 - PRESOUT (dbar or m) ***
# 45 - PAR1TYPE (integer) ***
# 46 - PAR2TYPE (integer) ***
# 47 - K1K2CONSTANTS (integer) ***
# 48 - KSO4CONSTANTS (integer) ***
# 49 - pHSCALE of input (integer) ***
# 50 - SAL (psu) ***
# 51 - PO4 (umol/kgSW) ***
# 52 - SI (umol/kgSW) ***
# 53 - K0 input ()
# 54 - K1 input ()
# 55 - K2 input ()
# 56 - pK1 input ()
# 57 - pK2 input ()
# 58 - KW input ()
# 59 - KB input ()
# 60 - KF input ()
# 61 - KS input ()
# 62 - KP1 input ()
# 63 - KP2 input ()
# 64 - KP3 input ()
# 65 - KSi input ()
# 66 - K0 output ()
# 67 - K1 output ()
# 68 - K2 output ()
# 69 - pK1 output ()
# 70 - pK2 output ()
# 71 - KW output ()
# 72 - KB output ()
# 73 - KF output ()
# 74 - KS output ()
# 75 - KP1 output ()
# 76 - KP2 output ()
# 77 - KP3 output ()
# 78 - KSi output ()
# 79 - TB (umol/kgSW)
# 80 - TF (umol/kgSW)
# 81 - TS (umol/kgSW)
# 82 - TP (umol/kgSW)
# 83 - TSi (umol/kgSW)
#
# *** SIMPLY RESTATES THE INPUT BY USER
#
# In all the above, the terms "input" and "output" may be understood
# to refer to the 2 scenarios for which CO2SYS performs calculations,
# each defined by its own combination of temperature and pressure.
# For instance, one may use CO2SYS to calculate, from measured DIC and TAlk,
# the pH that that sample will have in the lab (e.g., T=25 degC, P=0 dbar),
# and what the in situ pH would have been (e.g., at T=1 degC, P=4500).
# A = CO2SYS(2400,2200,1,2,35,25,1,0,4200,1,1,1,4,1)
# pH_lab = A(3); # 7.84
# pH_sea = A(18); # 8.05
#
#**************************************************************************
#
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# Ported for Julia v1.1.0 by Matthew P. Humphreys, University of East Anglia
#
# MATLAB code forked from https://github.com/jamesorr/CO2SYS-MATLAB
# on 27th Feb 2019
#
# Original MATLAB version history follows
#
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# This is version 2.0 (uploaded to CDIAC at SEP XXth, 2011):
#
# **** Changes since 2.0
# - slight changes to allow error propagation
# - new option to choose K1 & K2 from Waters et al. (2014): fixes inconsistencies with Millero (2010) identified by Orr et al. (2015)
#
# **** Changes since 1.01 (uploaded to CDIAC at June 11th, 2009):
# - Function cleans up its global variables when done (if you loose variables, this may be the cause -- see around line 570)
# - Added the outputting of K values
# - Implementation of constants of Cai and Wang, 1998
# - Implementation of constants of Lueker et al., 2000
# - Implementation of constants of Mojica-Prieto and Millero, 2002
# - Implementation of constants of Millero et al., 2002 (only their eqs. 19, 20, no TCO2 dependency)
# - Implementation of constants of Millero et al., 2006
# - Implementation of constants of Millero et al., 2010
# - Properly listed Sal and Temp limits for the available constants
# - added switch for using the new Lee et al., (2010) formulation of Total Borate (see KSO4CONSTANTS above)
# - Minor corrections to the GEOSECS constants (gave NaN for some output in earlier version)
# - Fixed decimal point error on [H+] (did not get converted to umol/kgSW from mol/kgSW).
# - Changed 'Hfreein' to 'Hfreeout' in the 'NICEHEADERS'-output (typo)
#
# **** Changes since 1.00 (uploaded to CDIAC at May 29th, 2009):
# - added a note explaining that all known bugs were removed before release of 1.00
#
#**************************************************************************
#
# CO2SYS originally by Lewis and Wallace 1998
# Converted to MATLAB by Denis Pierrot at
# CIMAS, University of Miami, Miami, Florida
# Vectorization, internal refinements and speed improvements by
# Steven van Heuven, University of Groningen, The Netherlands.
# Questions, bug reports et cetera: svheuven@gmail.com
#
#**************************************************************************
#**************************************************************************
# NOTHING BELOW THIS SHOULD REQUIRE EDITING BY USER!
#**************************************************************************
# Declare global variables
global pHScale, WhichKs, WhoseKSO4, Pbar
global Sal, sqrSal, TempK, logTempK, TempCi, TempCo, Pdbari, Pdbaro
global FugFac, VPFac, PengCorrection, ntps, RGasConstant
global fH, RT
global K0, K1, K2, KW, KB, KF, KS, KP1, KP2, KP3, KSi
global TB, TF, TS, TP, TSi, F
# # Added by JM Epitalon
# # For computing derivative with respect to Ks, one has to call CO2sys with a perturbed K
# # Requested perturbation is passed through the following global variables
# global PertK # Id of perturbed K
# global Perturb # perturbation
# Input conditioning
# Convert scalars to arrays [Julia only]
function scalar2array(argin)
if size(argin) == ()
argin = [argin]
end
return argin
end
PAR1 = scalar2array(PAR1)
PAR2 = scalar2array(PAR2)
PAR1TYPE = scalar2array(PAR1TYPE)
PAR2TYPE = scalar2array(PAR2TYPE)
SAL = scalar2array(SAL)
TEMPIN = scalar2array(TEMPIN)
TEMPOUT = scalar2array(TEMPOUT)
PRESIN = scalar2array(PRESIN)
PRESOUT = scalar2array(PRESOUT)
SI = scalar2array(SI)
PO4 = scalar2array(PO4)
pHSCALEIN = scalar2array(pHSCALEIN)
K1K2CONSTANTS = scalar2array(K1K2CONSTANTS)
KSO4CONSTANTS = scalar2array(KSO4CONSTANTS)
# Get list of all vectors [Julia only]
allvecs = [PAR1, PAR2, PAR1TYPE, PAR2TYPE, SAL, TEMPIN, TEMPOUT,
PRESIN, PRESOUT, SI, PO4, pHSCALEIN, K1K2CONSTANTS, KSO4CONSTANTS]
# Determine lengths of input vectors
veclengths = [max(size(vec)...) for vec in allvecs]
if max(size(unique(veclengths))...) > 2
println(" ")
println("*** INPUT ERROR: Input vectors must all be of same length, or of length 1. ***")
println(" ")
return
end
# Make column vectors of all input vectors
PAR1 = Float64.(PAR1[:])
PAR2 = Float64.(PAR2[:])
PAR1TYPE = PAR1TYPE[:]
PAR2TYPE = PAR2TYPE[:]
SAL = Float64.(SAL[:])
TEMPIN = Float64.(TEMPIN[:])
TEMPOUT = Float64.(TEMPOUT[:])
PRESIN = Float64.(PRESIN[:])
PRESOUT = Float64.(PRESOUT[:])
SI = Float64.(SI[:])
PO4 = Float64.(PO4[:])
pHSCALEIN = pHSCALEIN[:]
K1K2CONSTANTS = K1K2CONSTANTS[:]
KSO4CONSTANTS = KSO4CONSTANTS[:]
# Find the longest column vector:
ntps = max(veclengths...)
# Populate column vectors
function popvecs(vec,ntps)
if size(vec)[1] == 1
vec = fill(vec[1],ntps)
end # if
return vec
end # function popvecs
PAR1 = popvecs(PAR1,ntps)
PAR2 = popvecs(PAR2,ntps)
PAR1TYPE = popvecs(PAR1TYPE,ntps)
PAR2TYPE = popvecs(PAR2TYPE,ntps)
SAL = popvecs(SAL,ntps)
TEMPIN = popvecs(TEMPIN,ntps)
TEMPOUT = popvecs(TEMPOUT,ntps)
PRESIN = popvecs(PRESIN,ntps)
PRESOUT = popvecs(PRESOUT,ntps)
SI = popvecs(SI,ntps)
PO4 = popvecs(PO4,ntps)
pHSCALEIN = popvecs(pHSCALEIN,ntps)
K1K2CONSTANTS = popvecs(K1K2CONSTANTS,ntps)
KSO4CONSTANTS = popvecs(KSO4CONSTANTS,ntps)
# Assign input to the 'historical' variable names.
pHScale = pHSCALEIN
WhichKs = K1K2CONSTANTS
WhoseKSO4 = KSO4CONSTANTS
p1 = PAR1TYPE
p2 = PAR2TYPE
TempCi = TEMPIN
TempCo = TEMPOUT
Pdbari = PRESIN
Pdbaro = PRESOUT
Sal = SAL
sqrSal = sqrt.(SAL)
TP = PO4
TSi = SI
RGasConstant = 83.1451 # ml bar-1 K-1 mol-1, DOEv2
#RGasConstant = 83.14472 # ml bar-1 K-1 mol-1, DOEv3
# Generate empty vectors for
TA = fill(NaN,ntps) # Talk
TC = fill(NaN,ntps) # DIC
PH = fill(NaN,ntps) # pH
PC = fill(NaN,ntps) # pCO2
FC = fill(NaN,ntps) # fCO2
# Assign values to empty vectors.
F = p1 .== 1; TA[F] = PAR1[F] / 1e6 # Convert from micromol/kg to mol/kg
F = p1 .== 2; TC[F] = PAR1[F] / 1e6 # Convert from micromol/kg to mol/kg
F = p1 .== 3; PH[F] = PAR1[F]
F = p1 .== 4; PC[F] = PAR1[F] / 1e6 # Convert from microatm. to atm.
F = p1 .== 5; FC[F] = PAR1[F] / 1e6 # Convert from microatm. to atm.
F = p2 .== 1; TA[F] = PAR2[F] / 1e6 # Convert from micromol/kg to mol/kg
F = p2 .== 2; TC[F] = PAR2[F] / 1e6 # Convert from micromol/kg to mol/kg
F = p2 .== 3; PH[F] = PAR2[F]
F = p2 .== 4; PC[F] = PAR2[F] / 1e6 # Convert from microatm. to atm.
F = p2 .== 5; FC[F] = PAR2[F] / 1e6 # Convert from microatm. to atm.
# Generate the columns holding Si, Phos and Sal.
# Pure Water case:
F = WhichKs .== 8
Sal[F] .= 0.0
# GEOSECS and Pure Water:
F = @. (WhichKs == 8) | (WhichKs == 6)
TP[F] .= 0.0
TSi[F] .= 0.0
# All other cases
F = .!F
TP[F] /= 1e6
TSi[F] /= 1e6
# The vector 'PengCorrection' is used to modify the value of TA, for those
# cases where WhichKs==7, since PAlk(Peng) = PAlk(Dickson) + TP.
# Thus, PengCorrection is 0 for all cases where WhichKs is not 7
PengCorrection = zeros(ntps)
F = WhichKs .== 7; PengCorrection[F] = TP[F]
# Calculate the constants for all samples at input conditions
# The constants calculated for each sample will be on the appropriate pH scale!
Constants(TempCi,Pdbari)
# # Added by JM Epitalon
# # For computing derivative with respect to Ks, one has to perturb the value of one K
# # Requested perturbation is passed through global variables PertK and Perturb
# if (~ isempty(PertK))
# switch PertK
# case {'K0'}
# K0 = K0 + Perturb;
# case {'K1'}
# K1 = K1 + Perturb;
# case {'K2'}
# K2 = K2 + Perturb;
# case {'KB'}
# KB = KB + Perturb;
# case {'KW'}
# KW = KW + Perturb;
# case {'BOR'}
# TB = TB + Perturb;
# end
# end
# Make sure fCO2 is available for each sample that has pCO2.
F = @. (p1 == 4) | (p2==4)
FC[F] = PC[F] .* FugFac[F]
# Generate vector for results, and copy the raw input values into them. This
# copies ~60# NaNs, which will be replaced for calculated values later on.
TAc = deepcopy(TA)
TCc = deepcopy(TC)
PHic = deepcopy(PH)
PCic = deepcopy(PC)
FCic = deepcopy(FC)
# Generate vector describing the combination of input parameters
# So, the valid ones are: 12,13,15,23,25,35
Icase = 10*min(p1,p2) + max(p1,p2)
# Calculate missing values for AT,CT,PH,FC:
# pCO2 will be calculated later on, routines work with fCO2.
F = @. (Icase == 12) # input TA, TC
if any(F)
PHic[F], FCic[F] = CalculatepHfCO2fromTATC(TAc[F] .- PengCorrection[F], TCc[F])
end
F = @. (Icase == 13) # input TA, pH
if any(F)
TCc[F] = CalculateTCfromTApH(TAc[F] .- PengCorrection[F], PHic[F])
FCic[F] = CalculatefCO2fromTCpH(TCc[F], PHic[F])
end
F = @. (Icase == 14) | (Icase == 15) # input TA, (pCO2 or fCO2)
if any(F)
PHic[F] = CalculatepHfromTAfCO2(TAc[F] .- PengCorrection[F], FCic[F])
TCc[F] = CalculateTCfromTApH(TAc[F] .- PengCorrection[F], PHic[F])
end
F = @. (Icase == 23) # input TC, pH
if any(F)
TAc[F] = CalculateTAfromTCpH(TCc[F], PHic[F]) .+ PengCorrection[F]
FCic[F] = CalculatefCO2fromTCpH(TCc[F], PHic[F])
end
F = @. (Icase == 24) | (Icase == 25) # input TC, (pCO2 or fCO2)
if any(F)
PHic[F] = CalculatepHfromTCfCO2(TCc[F], FCic[F])
TAc[F] = CalculateTAfromTCpH(TCc[F], PHic[F]) .+ PengCorrection[F]
end
F = @. (Icase == 34) | (Icase == 35) # input pH, (pCO2 or fCO2)
if any(F)
TCc[F] = CalculateTCfrompHfCO2(PHic[F], FCic[F])
TAc[F] = CalculateTAfromTCpH(TCc[F], PHic[F]) .+ PengCorrection[F]
end
# By now, an fCO2 value is available for each sample.
# Generate the associated pCO2 value:
PCic = FCic ./ FugFac
# CalculateOtherParamsAtInputConditions:
HCO3inp, CO3inp, BAlkinp,
OHinp, PAlkinp,
SiAlkinp, Hfreeinp,
HSO4inp, HFinp = CalculateAlkParts(PHic, TCc)
PAlkinp += PengCorrection
CO2inp = @. TCc - CO3inp - HCO3inp
F = fill(true,ntps) # i.e., do for all samples:
Revelleinp = RevelleFactor(TAc .- PengCorrection, TCc)
OmegaCainp, OmegaArinp = CaSolubility(Sal, TempCi, Pdbari, TCc, PHic)
xCO2dryinp = PCic ./ VPFac # ' this assumes pTot = 1 atm
# Just for reference, convert pH at input conditions to the other scales, too.
pHicT, pHicS, pHicF, pHicN = FindpHOnAllScales(PHic)
# Merge the Ks at input into an array. Ks at output will be glued to this later.
KIVEC = hcat(K0, K1, K2, -log10.(K1), -log10.(K2), KW, KB, KF, KS, KP1, KP2, KP3, KSi)
# Calculate the constants for all samples at output conditions
Constants(TempCo,Pdbaro)
# # Added by JM Epitalon
# # For computing derivative with respect to Ks, one has to perturb the value of one K
# # Requested perturbation is passed through global variables PertK and Perturb
# if (~ isempty(PertK))
# switch PertK
# case {'K0'}
# K0 = K0 + Perturb;
# case {'K1'}
# K1 = K1 + Perturb;
# case {'K2'}
# K2 = K2 + Perturb;
# case {'KB'}
# KB = KB + Perturb;
# case {'KW'}
# KW = KW + Perturb;
# case {'KW'}
# TB = TB + Perturb;
# end
# end
# Calculate, for output conditions, using conservative TA and TC, pH, fCO2 and pCO2
F = fill(true,ntps) # i.e., do for all samples:
PHoc, FCoc = CalculatepHfCO2fromTATC(TAc .- PengCorrection, TCc)
PCoc = FCoc ./ FugFac
# Calculate Other Stuff At Output Conditions:
HCO3out, CO3out, BAlkout,
OHout, PAlkout,
SiAlkout, Hfreeout,
HSO4out, HFout = CalculateAlkParts(PHoc, TCc)
PAlkout += PengCorrection
CO2out = @. TCc - CO3out - HCO3out
Revelleout = RevelleFactor(TAc, TCc)
OmegaCaout, OmegaArout = CaSolubility(Sal, TempCo, Pdbaro, TCc, PHoc)
xCO2dryout = PCoc ./ VPFac # ' this assumes pTot = 1 atm
# Just for reference, convert pH at output conditions to the other scales, too.
pHocT, pHocS, pHocF, pHocN = FindpHOnAllScales(PHoc)
KOVEC = hcat(K0, K1, K2, -log10.(K1), -log10.(K2), KW, KB, KF, KS, KP1, KP2, KP3, KSi)
TVEC = hcat(TB, TF, TS)
# Saving data in array, 81 columns, as many rows as samples input
DATA= hcat(
TAc*1e6 , TCc*1e6 , PHic , PCic*1e6 , FCic*1e6 ,
HCO3inp*1e6 , CO3inp*1e6 , CO2inp*1e6 , BAlkinp*1e6 , OHinp*1e6 ,
PAlkinp*1e6 , SiAlkinp*1e6 , Hfreeinp*1e6 , Revelleinp , OmegaCainp , ### Multiplied Hfreeinp *1e6, svh20100827
OmegaArinp , xCO2dryinp*1e6 , PHoc , PCoc*1e6 , FCoc*1e6 ,
HCO3out*1e6 , CO3out*1e6 , CO2out*1e6 , BAlkout*1e6 , OHout*1e6 ,
PAlkout*1e6 , SiAlkout*1e6 , Hfreeout*1e6 , Revelleout , OmegaCaout , ### Multiplied Hfreeout *1e6, svh20100827
OmegaArout , xCO2dryout*1e6 , pHicT , pHicS , pHicF ,
pHicN , pHocT , pHocS , pHocF , pHocN ,
TEMPIN , TEMPOUT , PRESIN , PRESOUT , PAR1TYPE ,
PAR2TYPE , K1K2CONSTANTS , KSO4CONSTANTS , pHSCALEIN , SAL ,
PO4 , SI , KIVEC , KOVEC , TVEC*1e6 )
HEADERS = ["TAlk","TCO2","pHin","pCO2in","fCO2in","HCO3in","CO3in",
"CO2in","BAlkin","OHin","PAlkin","SiAlkin","Hfreein","RFin",
"OmegaCAin","OmegaARin","xCO2in","pHout","pCO2out","fCO2out",
"HCO3out","CO3out","CO2out","BAlkout","OHout","PAlkout",
"SiAlkout","Hfreeout","RFout","OmegaCAout","OmegaARout","xCO2out",
"pHinTOTAL","pHinSWS","pHinFREE","pHinNBS",
"pHoutTOTAL","pHoutSWS","pHoutFREE","pHoutNBS","TEMPIN","TEMPOUT",
"PRESIN","PRESOUT","PAR1TYPE","PAR2TYPE","K1K2CONSTANTS","KSO4CONSTANTS",
"pHSCALEIN","SAL","PO4","SI","K0input","K1input","K2input","pK1input",
"pK2input","KWinput","KBinput","KFinput","KSinput","KP1input","KP2input",
"KP3input","KSiinput","K0output","K1output","K2output","pK1output",
"pK2output","KWoutput","KBoutput","KFoutput","KSoutput","KP1output",
"KP2output","KP3output","KSioutput","TB","TF","TS"]
NICEHEADERS = [
"01 - TAlk (umol/kgSW) ",
"02 - TCO2 (umol/kgSW) ",
"03 - pHin () ",
"04 - pCO2in (uatm) ",
"05 - fCO2in (uatm) ",
"06 - HCO3in (umol/kgSW) ",
"07 - CO3in (umol/kgSW) ",
"08 - CO2in (umol/kgSW) ",
"09 - BAlkin (umol/kgSW) ",
"10 - OHin (umol/kgSW) ",
"11 - PAlkin (umol/kgSW) ",
"12 - SiAlkin (umol/kgSW) ",
"13 - Hfreein (umol/kgSW) ",
"14 - RevelleFactorin () ",
"15 - OmegaCain () ",
"16 - OmegaArin () ",
"17 - xCO2in (ppm) ",
"18 - pHout () ",
"19 - pCO2out (uatm) ",
"20 - fCO2out (uatm) ",
"21 - HCO3out (umol/kgSW) ",
"22 - CO3out (umol/kgSW) ",
"23 - CO2out (umol/kgSW) ",
"24 - BAlkout (umol/kgSW) ",
"25 - OHout (umol/kgSW) ",
"26 - PAlkout (umol/kgSW) ",
"27 - SiAlkout (umol/kgSW) ",
"28 - Hfreeout (umol/kgSW) ", ### Changed "Hfreein" to "Hfreeout", svh20100827
"29 - RevelleFactorout () ",
"30 - OmegaCaout () ",
"31 - OmegaArout () ",
"32 - xCO2out (ppm) ",
"33 - pHin (Total) () ",
"34 - pHin (SWS) () ",
"35 - pHin (Free) () ",
"36 - pHin (NBS ) () ",
"37 - pHout(Total) () ",
"38 - pHout(SWS) () ",
"39 - pHout(Free) () ",
"40 - pHout(NBS ) () ",
"41 - TEMPIN (Deg C) ",
"42 - TEMPOUT (Deg C) ",
"43 - PRESIN (dbar) ",
"44 - PRESOUT (dbar) ",
"45 - PAR1TYPE () ",
"46 - PAR2TYPE () ",
"47 - K1K2CONSTANTS () ",
"48 - KSO4CONSTANTS () ",
"49 - pHSCALEIN () ",
"50 - SAL (umol/kgSW) ",
"51 - PO4 (umol/kgSW) ",
"52 - SI (umol/kgSW) ",
"53 - K0input () ",
"54 - K1input () ",
"55 - K2input () ",
"56 - pK1input () ",
"57 - pK2input () ",
"58 - KWinput () ",
"59 - KBinput () ",
"60 - KFinput () ",
"61 - KSinput () ",
"62 - KP1input () ",
"63 - KP2input () ",
"64 - KP3input () ",
"65 - KSiinput () ",
"66 - K0output () ",
"67 - K1output () ",
"68 - K2output () ",
"69 - pK1output () ",
"70 - pK2output () ",
"71 - KWoutput () ",
"72 - KBoutput () ",
"73 - KFoutput () ",
"74 - KSoutput () ",
"75 - KP1output () ",
"76 - KP2output () ",
"77 - KP3output () ",
"78 - KSioutput () ",
"79 - TB (umol/kgSW) ",
"80 - TF (umol/kgSW) ",
"81 - TS (umol/kgSW) "]
return DATA, HEADERS, NICEHEADERS
end # end main function
#**************************************************************************
# Subroutines:
#**************************************************************************
function Constants(TempC,Pdbar)
global pHScale, WhichKs, WhoseKSO4, sqrSal, Pbar, RT
global K0, fH, FugFac, VPFac, ntps, TempK, logTempK
global K1, K2, KW, KB, KF, KS, KP1, KP2, KP3, KSi
global TB, TF, TS, TP, TSi, RGasConstant, Sal
# SUB Constants, version 04.01, 10-13-97, written by Ernie Lewis.
# Inputs: pHScale#, WhichKs#, WhoseKSO4#, Sali, TempCi, Pdbar
# Outputs: K0, K(), T(), fH, FugFac, VPFac
# This finds the Constants of the CO2 system in seawater or freshwater,
# corrects them for pressure, and reports them on the chosen pH scale.
# The process is as follows: the Constants (except KS, KF which stay on the
# free scale - these are only corrected for pressure) are
# 1) evaluated as they are given in the literature
# 2) converted to the SWS scale in mol/kg-SW or to the NBS scale
# 3) corrected for pressure
# 4) converted to the SWS pH scale in mol/kg-SW
# 5) converted to the chosen pH scale
#
# PROGRAMMER'S NOTE: all logs are log base e
# PROGRAMMER'S NOTE: all Constants are converted to the pH scale
# pHScale# (the chosen one) in units of mol/kg-SW
# except KS and KF are on the free scale
# and KW is in units of (mol/kg-SW)^2
TempK = TempC .+ 273.15
RT = RGasConstant * TempK
logTempK = log.(TempK)
Pbar = Pdbar / 10
# Generate empty vectors for holding results
TB = fill(NaN,ntps)
TF = fill(NaN,ntps)
TS = fill(NaN,ntps)
# CalculateTB - Total Borate:
F = WhichKs .== 8 # Pure water case.
if any(F)
TB[F] .= 0.0
end
F = @. (WhichKs == 6) | (WhichKs == 7)
if any(F)
TB[F] = 0.0004106 * Sal[F] / 35 # in mol/kg-SW
# this is .00001173.*Sali
# this is about 1# lower than Uppstrom's value
# Culkin, F., in Chemical Oceanography,
# ed. Riley and Skirrow, 1965:
# GEOSECS references this, but this value is not explicitly
# given here
end
F = @. (WhichKs != 6) & (WhichKs != 7) & (WhichKs != 8) # All other cases
if any(F)
FF = @. F & ((WhoseKSO4 == 1) | (WhoseKSO4 == 2)) # If user opted for Uppstrom's values:
if any(FF)
# Uppstrom, L., Deep-Sea Research 21:161-162, 1974:
# this is .000416.*Sali./35. = .0000119.*Sali
# TB[FF] = (0.000232./10.811).*(Sal[FF]./1.80655); # in mol/kg-SW
TB[FF] = 0.0004157 * Sal[FF] / 35 # in mol/kg-SW
end
FF = @. F & ((WhoseKSO4 == 3) | (WhoseKSO4 == 4)) # If user opted for the new Lee values:
if any(FF)
# Lee, Kim, Byrne, Millero, Feely, Yong-Ming Liu. 2010.
# Geochimica Et Cosmochimica Acta 74 (6): 1801–1811.
TB[FF] = 0.0004326 * Sal[FF] / 35 # in mol/kg-SW
end
end
# CalculateTF;
# Riley, J. P., Deep-Sea Research 12:219-220, 1965:
# this is .000068.*Sali./35. = .00000195.*Sali
TF = (0.000067 / 18.998) * Sal / 1.80655 # in mol/kg-SW
# CalculateTS ;
# Morris, A. W., and Riley, J. P., Deep-Sea Research 13:699-705, 1966:
# this is .02824.*Sali./35. = .0008067.*Sali
TS = (0.14 / 96.062) * Sal / 1.80655 # in mol/kg-SW
# CalculateK0:
# Weiss, R. F., Marine Chemistry 2:203-215, 1974.
TempK100 = TempK / 100
lnK0 = @. -60.2409 + 93.4517 / TempK100 + 23.3585 * log(TempK100) + Sal *
(0.023517 - 0.023656TempK100 + 0.0047036TempK100^2);
K0 = exp.(lnK0) # this is in mol/kg-SW/atm
# CalculateIonS:
# This is from the DOE handbook, Chapter 5, p. 13/22, eq. 7.2.4:
IonS = @. 19.924Sal / (1000 - 1.005Sal)
# CalculateKS:
lnKS = fill(NaN,ntps); pKS = fill(NaN,ntps); KS = fill(NaN,ntps)
F = @. (WhoseKSO4 == 1) | (WhoseKSO4 == 3)
if any(F)
# Dickson, A. G., J. Chemical Thermodynamics, 22:113-127, 1990
# The goodness of fit is .021.
# It was given in mol/kg-H2O. I convert it to mol/kg-SW.
# TYPO on p. 121: the constant e9 should be e8.
# This is from eqs 22 and 23 on p. 123, and Table 4 on p 121:
lnKS[F] = @. -4276.1/TempK[F] + 141.328 - 23.093logTempK[F] +
(-13856/TempK[F] + 324.57 - 47.986logTempK[F])*sqrt(IonS[F]) +
(35474/TempK[F] - 771.54 + 114.723logTempK[F])*IonS[F] +
(-2698/TempK[F])*sqrt(IonS[F])*IonS[F] + (1776/TempK[F])*IonS[F]^2
KS[F] = @. exp(lnKS[F]) * # this is on the free pH scale in mol/kg-H2O
(1 - 0.001005 * Sal[F]) # convert to mol/kg-SW
end
F = @. (WhoseKSO4 == 2) | (WhoseKSO4 == 4)
if any(F)
# Khoo, et al, Analytical Chemistry, 49(1):29-34, 1977
# KS was found by titrations with a hydrogen electrode
# of artificial seawater containing sulfate (but without F)
# at 3 salinities from 20 to 45 and artificial seawater NOT
# containing sulfate (nor F) at 16 salinities from 15 to 45,
# both at temperatures from 5 to 40 deg C.
# KS is on the Free pH scale (inherently so).
# It was given in mol/kg-H2O. I convert it to mol/kg-SW.
# He finds log(beta) which = my pKS;
# his beta is an association constant.
# The rms error is .0021 in pKS, or about .5# in KS.
# This is equation 20 on p. 33:
pKS[F] = @. 647.59 / TempK[F] - 6.3451 + 0.019085TempK[F] -
0.5208*sqrt(IonS[F])
KS[F] = @. 10.0^(-pKS[F]) * # this is on the free pH scale in mol/kg-H2O
(1 - 0.001005*Sal[F]) # convert to mol/kg-SW
end
# CalculateKF:
# Dickson, A. G. and Riley, J. P., Marine Chemistry 7:89-99, 1979:
lnKF = @. 1590.2/TempK - 12.641 + 1.525IonS^0.5
KF = @. exp(lnKF) * # this is on the free pH scale in mol/kg-H2O
(1 - 0.001005*Sal) # convert to mol/kg-SW
# Another expression exists for KF: Perez and Fraga 1987. Not used here since ill defined for low salinity. (to be used for S: 10-40, T: 9-33)
# Nonetheless, P&F87 might actually be better than the fit of D&R79 above, which is based on only three salinities: [0 26.7 34.6]
# lnKF = @. 874/TempK - 9.68 + 0.111Sal^0.5
# KF = exp.(lnKF) # this is on the free pH scale in mol/kg-SW
# CalculatepHScaleConversionFactors:
# These are NOT pressure-corrected.
SWStoTOT = @. (1 + TS/KS) / (1 + TS/KS + TF/KF)
FREEtoTOT = @. 1 + TS/KS
# CalculatefH
fH = fill(NaN,ntps)
# Use GEOSECS's value for cases 1,2,3,4,5 (and 6) to convert pH scales.
F = @. (WhichKs == 8)
if any(F)
fH[F] .= 1 # this shouldn't occur in the program for this case
end
F = @. (WhichKs == 7)
if any(F)
fH[F] = @. 1.29 - 0.00204TempK[F] + (0.00046 -
0.00000148TempK[F]) * Sal[F]^2
# Peng et al, Tellus 39B:439-458, 1987:
# They reference the GEOSECS report, but round the value
# given there off so that it is about .008 (1#) lower. It
# doesn't agree with the check value they give on p. 456.
end
F = @. (WhichKs != 7) & (WhichKs != 8)
if any(F)
fH[F] = @. 1.2948 - 0.002036TempK[F] + (0.0004607 -
0.000001475TempK[F]) * Sal[F]^2
# Takahashi et al, Chapter 3 in GEOSECS Pacific Expedition,
# v. 3, 1982 (p. 80);
end
# CalculateKB:
KB = fill(NaN,ntps); logKB = fill(NaN,ntps)
lnKBtop = fill(NaN,ntps); lnKB = fill(NaN,ntps)
F = @. (WhichKs == 8) # Pure water case
if any(F)
KB[F] .= 0
end
F = @. (WhichKs == 6) | (WhichKs == 7)
if any(F)
# This is for GEOSECS and Peng et al.
# Lyman, John, UCLA Thesis, 1957
# fit by Li et al, JGR 74:5507-5525, 1969:
logKB[F] = @. -9.26 + 0.00886Sal[F] + 0.01TempC[F]
KB[F] = @. 10.0^(logKB[F]) / # this is on the NBS scale
fH[F] # convert to the SWS scale
end
F = @. (WhichKs != 6) & (WhichKs != 7) & (WhichKs != 8)
if any(F)
# Dickson, A. G., Deep-Sea Research 37:755-766, 1990:
lnKBtop[F] = @. -8966.9 - 2890.53sqrSal[F] - 77.942Sal[F] +
1.728sqrSal[F]*Sal[F] - 0.0996Sal[F]^2
lnKB[F] = @. lnKBtop[F]/TempK[F] + 148.0248 + 137.1942sqrSal[F] +
1.62142Sal[F] + (-24.4344 - 25.085sqrSal[F] - 0.2474*
Sal[F]) * logTempK[F] + 0.053105sqrSal[F]*TempK[F]
KB[F] = @. exp(lnKB[F]) / # this is on the total pH scale in mol/kg-SW
SWStoTOT[F] # convert to SWS pH scale
end
# CalculateKW:
lnKW = fill(NaN,ntps); KW = fill(NaN,ntps)
F = @. (WhichKs == 7)
if any(F)
# Millero, Geochemica et Cosmochemica Acta 43:1651-1661, 1979
lnKW[F] = @. 148.9802 - 13847.26/TempK[F] - 23.6521logTempK[F] +
(-79.2447 + 3298.72/TempK[F] + 12.0408logTempK[F]) *
sqrSal[F] - 0.019813Sal[F]
end
F = @. (WhichKs == 8)
if any(F)
# Millero, Geochemica et Cosmochemica Acta 43:1651-1661, 1979
# refit data of Harned and Owen, The Physical Chemistry of
# Electrolyte Solutions, 1958
lnKW[F] = @. 148.9802 - 13847.26/TempK[F] - 23.6521logTempK[F]
end
F = @. (WhichKs != 6) & (WhichKs != 7) & (WhichKs != 8)
if any(F)
# Millero, Geochemica et Cosmochemica Acta 59:661-677, 1995.
# his check value of 1.6 umol/kg-SW should be 6.2
lnKW[F] = @. 148.9802 - 13847.26/TempK[F] - 23.6521logTempK[F] +
(-5.977 + 118.67/TempK[F] + 1.0495logTempK[F]) *
sqrSal[F] - 0.01615Sal[F]
end
KW = exp.(lnKW) # this is on the SWS pH scale in (mol/kg-SW)^2
F = @. (WhichKs == 6)
if any(F)
KW[F] .= 0 # GEOSECS doesn't include OH effects
end
# CalculateKP1KP2KP3KSi:
KP1 = fill(NaN,ntps); KP2 = fill(NaN,ntps)
KP3 = fill(NaN,ntps); KSi = fill(NaN,ntps)
lnKP1 = fill(NaN,ntps); lnKP2 = fill(NaN,ntps)
lnKP3 = fill(NaN,ntps); lnKSi = fill(NaN,ntps)
F = @. (WhichKs == 7)
if any(F)
KP1[F] .= 0.02
# Peng et al don't include the contribution from this term,
# but it is so small it doesn't contribute. It needs to be
# kept so that the routines work ok.
# KP2, KP3 from Kester, D. R., and Pytkowicz, R. M.,
# Limnology and Oceanography 12:243-252, 1967:
# these are only for sals 33 to 36 and are on the NBS scale
KP2[F] = @. exp(-9.039 - 1450/TempK[F]) / # this is on the NBS scale
fH[F] # convert to SWS scale
KP3[F] = @. exp(4.466 - 7276/TempK[F]) / # this is on the NBS scale
fH[F] # convert to SWS scale
# Sillen, Martell, and Bjerrum, Stability Constants of metal-ion complexes,
# The Chemical Society (London), Special Publ. 17:751, 1964:
KSi[F] = 0.0000000004 ./ # this is on the NBS scale
fH[F] # convert to SWS scale
end
F = @. (WhichKs == 6) | (WhichKs == 8)
if any(F)
KP1[F] .= 0
KP2[F] .= 0
KP3[F] .= 0
KSi[F] .= 0
# Neither the GEOSECS choice nor the freshwater choice
# include contributions from phosphate or silicate.
end
F = @. (WhichKs != 6) & (WhichKs != 7) & (WhichKs != 8)
if any(F)
# Yao and Millero, Aquatic Geochemistry 1:53-88, 1995
# KP1, KP2, KP3 are on the SWS pH scale in mol/kg-SW.
# KSi was given on the SWS pH scale in molal units.
lnKP1[F] = @. -4576.752/TempK[F] + 115.54 - 18.453logTempK[F] + (-106.736/TempK[F] +
0.69171) * sqrSal[F] + (-0.65643/TempK[F] - 0.01844) * Sal[F]
KP1[F] = exp.(lnKP1[F])
lnKP2[F] = @. -8814.715/TempK[F] + 172.1033 - 27.927logTempK[F] + (-160.34/TempK[F] +
1.3566) * sqrSal[F] + (0.37335/TempK[F] - 0.05778) * Sal[F]
KP2[F] = exp.(lnKP2[F])
lnKP3[F] = @. -3070.75/TempK[F] - 18.126 + (17.27039/TempK[F] + 2.81197) * sqrSal[F] +
(-44.99486/TempK[F] - 0.09984) * Sal[F]
KP3[F] = exp.(lnKP3[F])
lnKSi[F] = @. -8904.2/TempK[F] + 117.4 - 19.334logTempK[F] + (-458.79/TempK[F] +
3.5913) * sqrt(IonS[F]) + (188.74/TempK[F] - 1.5998) * IonS[F] +
(-12.1652/TempK[F] + 0.07871) * IonS[F]^2
KSi[F] = @. exp(lnKSi[F]) * # this is on the SWS pH scale in mol/kg-H2O
(1 - 0.001005Sal[F]) # convert to mol/kg-SW
end
# CalculateK1K2:
logK1 = fill(NaN,ntps); lnK1 = fill(NaN,ntps)
pK1 = fill(NaN,ntps); K1 = fill(NaN,ntps)
logK2 = fill(NaN,ntps); lnK2 = fill(NaN,ntps)
pK2 = fill(NaN,ntps); K2 = fill(NaN,ntps)
F = @. (WhichKs == 1)
if any(F)
# ROY et al, Marine Chemistry, 44:249-267, 1993
# (see also: Erratum, Marine Chemistry 45:337, 1994
# and Erratum, Marine Chemistry 52:183, 1996)
# Typo: in the abstract on p. 249: in the eq. for lnK1* the
# last term should have S raised to the power 1.5.
# They claim standard deviations (p. 254) of the fits as
# .0048 for lnK1 (.5# in K1) and .007 in lnK2 (.7# in K2).
# They also claim (p. 258) 2s precisions of .004 in pK1 and
# .006 in pK2. These are consistent, but Andrew Dickson
# (personal communication) obtained an rms deviation of about
# .004 in pK1 and .003 in pK2. This would be a 2s precision
# of about 2# in K1 and 1.5# in K2.
# T: 0-45 S: 5-45. Total Scale. Artificial sewater.
# This is eq. 29 on p. 254 and what they use in their abstract:
lnK1[F] = @. 2.83655 - 2307.1266/TempK[F] - 1.5529413logTempK[F] +
(-0.20760841 - 4.0484/TempK[F])*sqrSal[F] + 0.08468345Sal[F] -
0.00654208sqrSal[F]*Sal[F]
K1[F] = @. exp(lnK1[F]) * # this is on the total pH scale in mol/kg-H2O
(1 - 0.001005Sal[F]) / # convert to mol/kg-SW
SWStoTOT[F] # convert to SWS pH scale
# This is eq. 30 on p. 254 and what they use in their abstract:
lnK2[F] = @. -9.226508 - 3351.6106/TempK[F] - 0.2005743*logTempK[F] +
(-0.106901773 - 23.9722/TempK[F])*sqrSal[F] + 0.1130822Sal[F] -
0.00846934sqrSal[F]*Sal[F]
K2[F] = @. exp(lnK2[F]) * # this is on the total pH scale in mol/kg-H2O
(1 - 0.001005.*Sal[F]) / # convert to mol/kg-SW
SWStoTOT[F] # convert to SWS pH scale