# Buffer capacities of the seawater carbonate system from Egleston et al. (2010), corrected and enhanced Returns the six buffer factors of the seawater carbonate system as defined by Egleston, Sabine and Morel (2010), denoted here as ESM. Also returns the classic Revelle factor (relative change in pCO2 over that for DIC). In ESM, there are errors in the equations in Table 1 for $S$, $\Omega_{DIC}$, and $\Omega_{Alk}$. These errors have been corrected here. The results of this routine have been validated: when input concentrations of Pt and Sit are set to zero, they produce results that are identical to those shown in ESM's Fig. 2. But when Pt and Sit are nonzero, contributions from phosphoric and silicic acid systems are taken into account, an improvement to the Egleston et al. (2010) approach. This routine was inspired and adapted from seacarb's ``buffer'' function. Its input arguments are indentical to those in the ``buffer'' and ``carb'' functions of seacarb. latin1 ```r buffesm(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", warn = "y", eos = "eos80", long = 1e+20, lat = 1e+20) ``` ## 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`: enter value of the first variable in mol/kg, except for pH and for pCO2 in $\mu$atm - `var2`: enter 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 1 atm - `P`: Hydrostatic pressure in bar (surface = 0) - `Pt`: Concentration of total phosphate in mol/kg; set to 0 if NA; when nonzero, account for phosphoric acid system, unlike in Egleston et al. (2010). - `Sit`: Concentration of total silicate in mol/kg; set to 0 if NA; when nonzero, account for silicic acid system, unlike in Egleston et al. (2010). - `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 Dickon (1990), "k" for using Ks from Khoo et al. (1977), default is "d" - `pHscale`: choice of pH scale: "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" - `warn`: "y" to show warnings when T or S go beyond the valid range for constants; "n" to supress warnings. The default is "y". - `eos`: "teos10" to specify T and S according to Thermodynamic Equation Of Seawater - 2010 (TEOS-10); "eos80" to specify T and S according to EOS-80. - `long`: longitude of data point, used when eos parameter is "teos10" as a conversion parameter from absolute to practical salinity. - `lat`: latitude of data point, used when eos parameter is "teos10". ## 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 K0:** * 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 and Ksi, 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). long and lat are used as conversion parameters from absolute to practical salinity: when seawater is not of standard composition, practical salinity alone is not sufficient to compute absolute salinity and vice-versa. One needs to know the density. When long and lat are given, density is inferred from WOA silicate concentration at given location. When they are not, an arbitrary geographic point is chosen: mid equatorial Atlantic. Note that this implies an error on computed salinity up to 0.02 g/kg. ## Returns The function returns a data frame containing the following columns: - **gammaDIC**: $\gamma_{DIC}$, ocean's capacity to buffer changes in [CO2] due to accumulation of CO2 from the atmosphere $(\partial ln[CO_2]/\partial DIC)^{-1}$ (units = mol/kg; multiply by 1000 to get mmol/kg, i.e., the units presented in Egleston et al., 2010) - **betaDIC**: $\beta_{DIC}$, ocean's capacity to buffer changes in [H+] due to accumulation of CO2 from the atmosphere $(\partial ln[H^+]/\partial DIC)^{-1}$ (units = mol/kg) - **omegaDIC**: $\Omega_{DIC}$, ocean's capacity to buffer changes in $[CO_3^{2-}]$ due to accumulation of CO2 from the atmosphere $(\partial ln[CO_3^{2-}]/\partial DIC)^{-1}$; same as $(\partial ln \Omega_A / \partial DIC)^{-1}$ and $(\partial ln \Omega_C / \partial DIC)^{-1}$ (units= mol/kg) - **gammaALK**: $\gamma_{Alk}$, ocean's capacity to buffer changes in [CO2] due to changes in alkalinity $(\partial ln[CO_2]/\partial ALK)^-1$ (units = mol/kg) - **betaALK**: $\beta_{Alk}$, ocean's capacity to buffer changes in [H+] due to changes in alkalinity $(\partial ln[H^+]/\partial ALK)^{-1}$ (units = mol/kg) - **omegaALK**: $\Omega_{Alk}$, ocean's capacity to buffer changes in $[CO_3^{2-}]$ due to changes in alkalinity $(\partial ln[CO_3^{2-}]/\partial ALK)^{-1}$; same as $(\partial ln \Omega_A / \partial ALK)^{-1}$ and $(\partial ln \Omega_C / \partial ALK)^{-1}$ (units = mol/kg) - **R**: Revelle factor, relative change in $[CO_2]$ or $pCO_2$ over the relative change in DIC $(\partial ln[CO_2]/\partial ln DIC)^{-1}$ (unitless) ## References Cai W. J., and Wang Y., 1998. The chemistry, fluxes, and sources of carbon dioxide in the estuarine waters of the Satilla and Altamaha Rivers, Georgia. **Limnology and Oceanography** 43 , 657-668. Dickson A. G., 1990 Standard potential of the reaction: AgCI(s) + 1/2H2(g) = Ag(s) + HCI(aq), and the standard acidity constant of the ion HSO4 in synthetic sea water from 273.15 to 318.15 K. **Journal of Chemical Thermodynamics** 22 , 113-127. Dickson A. G., Sabine C. L. and Christian J. R., 2007 Guide to best practices for ocean CO2 measurements. **PICES Special Publication** 3 , 1-191. Egleston, E. S., Sabine, C. L. and Morel, F. M. M., 2010 Revelle revisited: Buffer factors that quantify the response of ocean chemistry to changes in DIC and alkalinity, Global Biogeochem. Cycles 24 , GB1002, doi:10.1029/2008GB003407. Khoo H. K., Ramette R. W., Culberson C. H. and Bates R. G., 1977 Determination of hydrogen ion concentration in seawater from 5 to 40oC: standard potentials at salinities from 20 to 45. **Analytical Chemistry** 49 , 29-34. Frankignoulle M., 1994 A complete set of buffer factors for acid/base CO2 system in seawater. **Journal of Marine Systems** 5 , 111-118. Lee K., Tae-Wook K., Byrne R.H., Millero F.J., Feely R.A. and Liu Y-M, 2010 The universal ratio of the boron to chlorinity for the North Pacific and North Atlantoc oceans. **Geochimica et Cosmochimica Acta** 74 1801-1811. Lueker T. J., Dickson A. G. and Keeling C. D., 2000 Ocean pCO2 calculated from dissolved inorganic carbon, alkalinity, and equations for K1 and K2: validation based on laboratory measurements of CO2 in gas and seawater at equilibrium. **Marine Chemistry** 70 105-119. Millero F. J., 2010 Carbonate constant for estuarine waters. **Marine and Freshwater Research** 61 : 139-142. Millero F. J., Graham T. B., Huang F., Bustos-Serrano H. and Pierrot D., 2006 Dissociation constants of carbonic acid in seawateras a function of salinity and temperature. **Marine Chemistry** 100 , 80-84. Perez F. F. and Fraga F., 1987 Association constant of fluoride and hydrogen ions in seawater. **Marine Chemistry** 21 , 161-168. Roy R. N., Roy L. N., Vogel K. M., Porter-Moore C., Pearson T., Good C. E., Millero F. J. and Campbell D. M., 1993. The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45oC. **Marine Chemistry** 44 , 249-267. Schockman, K.M., Byrne, R.H., 2021. Spectrophotometric determination of the bicarbonate dissociation constant in seawater, **Geochimica et Cosmochimica Acta**. Uppstrom L.R., 1974 The boron/chlorinity ratio of the deep-sea water from the Pacific Ocean. **Deep-Sea Research I** 21 161-162. ## Author(s) James Orr James.Orr@lsce.ipsl.fr ## Examples ```r ## Computation with a couple of variables buffesm(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Pt=0, Sit=0, pHscale="T", kf="pf", k1k2="l", b="u74") ## 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") buffesm(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b) ## Test for all flags flag <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25) var1 <- c(8.200000, 7.477544e-06, 7.477544e-06, 7.477544e-06, 7.477544e-06, 8.2, 8.2, 8.2, 8.2, 0.001685024, 0.001685024, 0.001685024, 0.0002888382, 0.0002888382, 0.002391252, 264.2008, 264.2008, 264.2008, 264.2008, 264.2008) var2 <- c(7.477544e-06, 0.001685024, 0.0002888382, 0.002391252, 0.001981340, 0.001685024, 0.0002888382, 0.002391252, 0.001981340, 0.0002888382, 0.002391252, 0.001981340, 0.002391252, 0.001981340, 0.001981340, 8.2, 0.001685024, 0.0002888382, 0.002391252, 0.001981340) buffesm(flag=flag, var1=var1, var2=var2) ## Compute 2 additional factors of interest (ratios of relative changes) be <- buffesm(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b) # Ratio of gammaDIC/betaDIC = d ln [H+] / d ln pCO2 Hfac <- (be$gammaDIC/be$betaDIC) #H+ factor # Ratio of gammaDIC/omegaDIC = d ln [CO32-] / d ln pCO2 Satfac <- (be$gammaDIC/be$omegaDIC) #Saturation factor ```

buffesm function