# Buffer factors of the seawater carbonate system as defined by Hagens and Middelburg (2016) Returns the suite of buffer factors presented in Table 3 of Hagens and Middelburg (2016), as well as the proton concentration buffer factor (beta.H of Hofmann et al, 2010) and the classic Revelle factor. For practical purposes, this function excludes the nitrate and nitrite acid-base systems presented in this paper, as well as the fully protonoted form of sulfate (H2SO4) and fully deprotonated form of sulfide (S2-), as their contributions to total alkalinity under natural seawater conditions are negligible. Its input arguments are identical to those in the carbfull function of seacarb. latin1 ```r buffergen(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, k1k2="x", kf="x", ks="d", pHscale="T", b="u74", gas="potential", NH4t=0, HSt=0) ``` ## Arguments - `flag`: select the couple of variables available. The flags which can be used are: flag = 1 pH and CO2 given flag = 2 CO2 and HCO3 given flag = 3 CO2 and CO3 given flag = 4 CO2 and ALK given flag = 5 CO2 and DIC given flag = 6 pH and HCO3 given flag = 7 pH and CO3 given flag = 8 pH and ALK given flag = 9 pH and DIC given flag = 10 HCO3 and CO3 given flag = 11 HCO3 and ALK given flag = 12 HCO3 and DIC given flag = 13 CO3 and ALK given flag = 14 CO3 and DIC given flag = 15 ALK and DIC given flag = 21 pCO2 and pH given flag = 22 pCO2 and HCO3 given flag = 23 pCO2 and CO3 given flag = 24 pCO2 and ALK given flag = 25 pCO2 and DIC given - `var1`: Value of the first variable in mol/kg, except for pH and for pCO2 in $\mu$atm - `var2`: Value of the second variable in mol/kg, except for pH - `S`: Salinity - `T`: Temperature in degrees Celsius - `Patm`: Surface atmospheric pressure in atm, default is 1 atm - `P`: Hydrostatic pressure in bar (surface = 0) - `Pt`: Concentration of total phosphate in mol/kg; set to 0 if NA - `Sit`: Concentration of total silicate in mol/kg; set to 0 if NA - `k1k2`: "cw" for using K1 and K2 from Cai & Wang (1998), "l" from Lueker et al. (2000), "m02" from Millero et al. (2002), "m06" from Millero et al. (2006), "m10" from Millero (2010), "mp2" from Mojica Prieto et al. (2002), "p18" from Papadimitriou et al. (2018), "r" from Roy et al. (1993), "sb21" from Shockman & Byrne (2021), "s20" from Sulpis et al. (2020), and "w14" from Waters et al. (2014). "x" is the default flag; the default value is then "l", except if T is outside the range 2 to 35oC and/or S is outside the range 19 to 43. In these cases, the default value is "w14". - `kf`: "pf" for using Kf from Perez and Fraga (1987) and "dg" for using Kf from Dickson and Riley (1979 in Dickson and Goyet, 1994). "x" is the default flag; the default value is then "pf", except if T is outside the range 9 to 33oC and/or S is outside the range 10 to 40. In these cases, the default is "dg". - `ks`: "d" for using Ks from Dickson (1990) and "k" for using Ks from Khoo et al. (1977), default is "d" - `pHscale`: "T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale, default is "T" (total scale) - `b`: Concentration of total boron. "l10" for the Lee et al. (2010) formulation or "u74" for the Uppstrom (1974) formulation, default is "u74" - `gas`: used to indicate the convention for INPUT pCO2, i.e., when it is an input variable (flags 21 to 25): "insitu" indicates it is referenced to in situ pressure and in situ temperature; "potential" indicates it is referenced to 1 atm pressure and potential temperature; and "standard" indicates it is referenced to 1 atm pressure and in situ temperature. All three options should give identical results at surface pressure. This option is not used when pCO2 is not an input variable (flags 1 to 15). The default is "potential" and should be a unique value.. - `NH4t`: Concentration of total ammonium in mol/kg; set to 0 if NA - `HSt`: Concentration of total hydrogen sulfide in mol/kg; set to 0 if NA ## Details The Lueker et al. (2000) constants for K1 and K2, the Perez and Fraga (1987) constant for Kf and the Dickson (1990) constant for Ks are recommended by Dickson et al. (2007). It is, however, critical to consider that each formulation is only valid for specific ranges of temperature and salinity: **For K1 and K2:** * Cai and Wang (1998): S ranging between 0 and 40 and T ranging between 0.2 and 30oC. * Lueker et al. (2000): S ranging between 19 and 43 and T ranging between 2 and 35oC. * Millero et al. (2002): S ranging from 34 to 37 and T ranging between -1.6 and 35oC. * Millero et al. (2006): S ranging between 0.1 and 50 and T ranging between 1 and 50oC. * Millero (2010): S ranging between 1 and 50 and T ranging between 0 and 50oC. Millero (2010) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale". * Mojica Prieto et al. (2002): S ranging from 5 to 42 and T ranging between 0 and 45oC. * Papadimitriou et al. (2018): S ranging from 33 to 100 and T ranging between -6 to 25oC. * Roy et al. (1993): S ranging between 5 and 45 and T ranging between 0 and 45oC. * Shockman & Byrne (2021): for K2, S ranging from 19.6 to 41 and T ranging between 15 to 35oC. For K1, formulation is that of Waters et al. * Sulpis et al. (2020): S ranging from 30.7 to 37.6 and T ranging between -1.7 to 31.8oC. * Waters et al.(2014): S ranging between 1 and 50 and T ranging between 0 and 50oC. Waters (2014) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale". **For Kf:** * Perez and Fraga (1987): S ranging between 10 and 40 and T ranging between 9 and 33oC. * Dickson and Riley (1979 in Dickson and Goyet, 1994): S ranging between 0 and 45 and T ranging between 0 and 45oC. **For Ks:** * Dickson (1990): S ranging between 5 and 45 and T ranging between 0 and 45oC. * Khoo et al. (1977): S ranging between 20 and 45 and T ranging between 5 and 40oC. The arguments can be given as a unique number or as vectors. If the lengths of the vectors are different, the longer vector is retained and only the first value of the other vectors is used. It is recommended to use either vectors with the same dimension or one vector for one argument and numbers for the other arguments. **Pressure corrections and pH scale:** * For K0, the pressure correction term of Weiss (1974) is used. * For K1, K2, pK1, pK2, pK3, Kw, Kb, Khs, Ksi and K2si, the pressure correction was applied on the seawater scale. Hence, if needed, values were first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS). * For Kf, the pressure correction was applied on the free scale. The formulation of Dickson and Riley (1979 in Dickson and Goyet, 1994) provides Kf on the free scale but that of Perez and Fraga (1987) provides it on the total scale. Hence, in that case, Kf was first transformed from the total scale to the free scale. With both formulations, the pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS). * For Ks, the pressure correction was applied on the free scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS). * For Kn, the pressure correction was applied on the seawater scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS). ## Returns The function returns a list containing the following matrices: - **Carbfull**: Output of the carbfull function that is used within buffergen - **dALK.dH**: Sensitivity of ALK to a change in proton concentration (dimensionless). Species-specific. - **dtotX.dH**: Sensitivity of an acid-base species to a change in proton concentration (dimensionless). Species-specific. - **dALK.dX**: Sensitivity of ALK to a change in an acid-base species (dimensionless). Species-specific. - **dtotX.dX**: Sensitivity of an acid-base species to a change in its total concentration (dimensionless). Species-specific. - **dALK.dpH**: Sensitivity of ALK to a change in pH (mol/kg-soln). Species-specific. - **dtotX.dpH**: Sensitivity of an acid-species to a change in pH (mol/kg-soln). Species-specific. - **dH.dALK**: Sensitivity of proton concentration to a change in ALK (dimensionless). Values are the same for all species and all acid-base systems, except for the fluoride and sulfate acid-base systems, which slightly deviate due to pH scale conversion effects. - **dH.dtotX**: Sensitivity of an acid-species to a change in its total concentration (dimensionless). Values are the same for all species of a specific acid-base system. - **dX.dALK**: Sensitivity of an acid-species to a change in its total concentration (dimensionless). Species-specific. - **dX.dtotX**: Sensitivity of an acid-species to a change in its total concentration (dimensionless). Species-specific. - **dpH.dALK**: Sensitivity of pH due to a change in ALK ((mol/kg-soln)-1). Values are the same for all species and all acid-base systems, except for the fluoride and sulfate acid-base systems, which slightly deviate due to pH scale conversion effects. - **dpH.dtotX**: Sensitivity of pH due to a change in the total concentration of an acid-base system ((mol/kg-soln)-1). Values are the same for all species of a specific acid-base system. - **beta.H**: proton concentration buffer factor (Eq.4 of Hagens and Middelburg (2016), dimensionless) - **RF**: Revelle factor (dimensionless) If the total concentration of an acid-base system is 0, the values of the buffer factors corresponding to all species of that acid-base system return NA. ## References Hagens M. and Middelburg J. J., 2016 Generalised expressions for the response of pH to changes in ocean chemistry. **Geochimica et Cosmochimica Acta** 187 334-349. ## Author(s) Mathilde Hagens m.hagens@uu.nl ## Examples ```r ## With a couple of variables buffergen(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74", gas="potential", NH4t=0, HSt=0) ## With a couple of variables and non-zero nutrient concentrations buffergen(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=5e-6, Sit=2e-6, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74", gas="potential", NH4t=10e-6, HSt=0.1e-6) ## Using vectors as arguments flag <- c(8, 2, 8) var1 <- c(8.2, 7.477544e-06, 8.2) var2 <- c(0.002343955, 0.001649802, 2400e-6) S <- c(35, 35, 30) T <- c(25, 25, 30) P <- c(0, 0, 0) Pt <- c(0, 0, 0) Sit <- c(0, 0, 0) kf <- c("pf", "pf", "pf") k1k2 <- c("l", "l", "l") pHscale <- c("T", "T", "T") b <- c("l10", "l10", "l10") gas <- c("potential") NH4t <- c(0, 0, 0) HSt <- c(0, 0, 0) buffergen(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b, gas=gas, NH4t=NH4t, HSt=HSt) ## Test with all flags flag <- c((1:15), (21:25)) var1 <- c(8.200000, 7.308171e-06, 7.308171e-06, 7.308171e-06, 7.308171e-06, 8.2, 8.2, 8.2, 8.2, 0.001646857, 0.001646857, 0.001646857, 0.0002822957, 0.0002822957, 0.00234, 258.2164, 258.2164, 258.2164, 258.2164, 258.2164 ) var2 <- c(7.308171e-06, 0.001646857, 0.0002822957, 0.00234, 0.001936461, 0.001646857, 0.0002822957, 0.00234, 0.001936461, 0.0002822957, 0.00234, 0.001936461, 0.00234, 0.001936461, 0.001936461, 8.2, 0.001646857, 0.0002822957, 0.00234, 0.001936461) buffergen(flag=flag, var1=var1, var2=var2) ```

buffergen function