Case studies with seacarb

Requirements

R - https://cran.r-project.org/

Rstudio - https://www.rstudio.com/products/rstudio/download/#download

Start R or Rstudio

Install packages seacarb, ggplot2 and dplyr

Download the datasets: https://drive.google.com/open?id=1inOpVRuOAhOVrjRR8ej7_0l5Gco0niat&authuser=fgazeau%40gmail.com&usp=drive_fs

Set the working directory where the datasets are: setwd(“my path”)

Case study #1

Exercise

We are conducting an experiment in our lab during 7 days, and we have recorded pH and total alkalinity during Day 1, 3 and 7. This experiment is focused on evaluating the effect of ocean acidification on the physiological traits of the copepod Acartia tonsa and was conducted at a temperature of 25 \(^\circ\)C. We have considered two different levels of pCO2, 400 and 1200 \(\mu\)atm. We need to check if obtained pCO2 levels are in agreement with our experimental setup. Our lab assistant measured pHT and AT (in \(\mu\)mol kg-1). Please, consider the following data (Dataset#1.txt) and compare the pCO2 calculated with the theoretical level we considered in our experimental setup.

Day Sal pHT AT Sal pHT AT
1 34.2 8.06 2376.33 34.2 7.66 2376.21
2 34.1 8.05 2326.24 34.1 7.65 2325.14
3 32.0 7.95 1800.34 32.0 7.55 1799.21

Answer

cs1 <- read.table("./Dataset#1.txt", header=TRUE)
cc_cs1 <- carb(8, cs1$pH, cs1$ALK/1000000, S=cs1$S, T=25, Patm=1, P=0, Pt=0, Sit=0,
        k1k2="x", kf="x", ks="d", pHscale="T", b="u74", gas="potential", 
        warn="y", eos="eos80", long=1.e20, lat=1.e20)
Results_cs1 <- cbind(cs1$Day, cs1$Treatment, cs1$S, cs1$T, cs1$pH, cs1$ALK, cc_cs1$pCO2)
kable(Results_cs1, col.names = c("Day", "Treatment", "S", "T", "pH~T~", "*A*~T~", "*p*CO~2~"), align=c('l','c', 'c', 'c','c', 'c', 'c')) %>%
kable_styling("striped")
Day Treatment S T pHT AT pCO2
1 Ambient 34.2 25 8.06 2376.33 397.553603821651
3 Ambient 34.1 25 8.05 2326.24 400.348675364518
7 Ambient 32 25 7.95 1800.34 412.899814809415
1 LowpH 34.2 25 7.66 2376.21 1158.47285558744
3 LowpH 34.1 25 7.65 2325.14 1163.00622542091
7 LowpH 32 25 7.55 1799.21 1167.79080379562

Case study #2

Exercise

We run an experiment in Monaco on coccolithophorids with two treatments in closed batch bottles that we have enriched with HCl and NaHCO3 (to acidify but to keep AT constant). Everyday during the experiment, we sacrifice a bottle and measure AT and CT as well as salinity and temperature. We report the results in a table with AT and CT being expressed in \(\mu\)mol L^-1, this table is named Dataset#2.txt.

  • What was the average pCO2 for both treatments? Use the function subset() to separate your treatments.

Answer

cs2 <- read.table("./Dataset#2.txt", header=TRUE)
cc_cs2 <- carb(15, cs2$ALK/1000000/(rho(cs2$S, cs2$T, P=0)/1000), cs2$DIC/1000000/(rho(cs2$S, cs2$T, P=0)/1000), S=cs2$S, T=cs2$T, Patm=1, P=0, Pt=0, Sit=0,
        k1k2="x", kf="x", ks="d", pHscale="T", b="u74", gas="potential", warn="y", eos="eos80", long=1.e20, lat=1.e20)
Results_cs2 <- data.frame(cbind(cs2$Day, cs2$Treatment, cs2$S, cs2$T, cs2$DIC, cs2$ALK, cc_cs2$pCO2))
colnames(Results_cs2) = c("Day", "Treatment", "S", "T", "CT", "AT", "pCO2")

T1_cs2 <- subset(Results_cs2, Treatment == "A")
T1_mean_pCO2 <- mean(as.numeric(T1_cs2$pCO2))
T1_std_pCO2 <- sd(as.numeric(T1_cs2$pCO2))

T2_cs2 <- subset(Results_cs2, Treatment == "B")
T2_mean_pCO2 <- mean(as.numeric(T2_cs2$pCO2))
T2_std_pCO2 <- sd(as.numeric(T2_cs2$pCO2))

print(T1_mean_pCO2)
## [1] 457.3336
print(T1_std_pCO2)
## [1] 26.55828
print(T2_mean_pCO2)
## [1] 1782.073
print(T2_std_pCO2)
## [1] 322.0461

Case study #3

Exercise

We conducted an experiment in an open-flow system with mussels. The system comprises two tanks, one non-acidified and one acidified. In these two tanks, we have continuous (every 1 h) data of voltage using a glass electrode that was calibrated at the salinity and temperature of the experiment with TRIS buffer (ETRIS = -72.4 mV). We assumed AT to be constant during the experiment and equal to 2500 \(\mu\)mol kg-1. Data are stored in the file Dataset#3.txt.

  • Plot these continuous pH data as a function of time for both tanks on the total scale (red line for the acidified and blue line for the non-acidified)

Answer

cs3 <- read.table("./Dataset#3.txt", header=TRUE)
pHT_NA <- pH(Ex=cs3$mVNA,Etris=-72.4,S=cs3$S,T=cs3$T)
pHT_A <- pH(Ex=cs3$mVA,Etris=-72.4,S=cs3$S,T=cs3$T)

ggplot() +
  geom_line(data = cs3, aes(x=cs3$Hour, y=pHT_NA), color="blue") +
  geom_line(data = cs3, aes(x=cs3$Hour, y=pHT_A), color="red") +
  xlab("Time") +
  ylab("pH")

Case study #4

Exercise

During the same experiment, we sampled three times and measured pH using a spectrophotometric method at 25 \(^\circ\)C. Temperature and salinity of the tanks were recorded when samples were taken. Data are stored in the file Dataset#4.txt.

  • Compare these discrete values to the continuous records on the previous plot (blue dots for the non acidified, red dots for the acidified).

Answer

cs4 <- read.table("./Dataset#4.txt", header=TRUE)
pHspec_NA <- pHinsi(pH=cs4$pHspec25NA,ALK=2500/1000000,Tinsi=cs4$T,Tlab=25,Pinsi=0,S=cs4$S,Pt=0,Sit=0)
pHspec_A <- pHinsi(pH=cs4$pHspec25A,ALK=2500/1000000,Tinsi=cs4$T,Tlab=25,Pinsi=0,S=cs4$S,Pt=0,Sit=0)

ggplot() +
  geom_line(data = cs3, aes(x=cs3$Hour, y=pHT_NA), color="blue") +
  geom_line(data = cs3, aes(x=cs3$Hour, y=pHT_A), color="red") +
  geom_point(data = cs4, aes(x=cs4$Hour, y=pHspec_NA), color="blue", size=4) +
  geom_point(data = cs4, aes(x=cs4$Hour, y=pHspec_A), color="red", size=4) +
  xlab("Time") +
  ylab("pH")

Case study #5

Exercise

For an experiment, we want to acidify a closed bottle of 1 L, initially at a pCO2 of 430 \(\mu\)atm, to reach a pHT of 7.78 and keep AT constant at 2340 \(\mu\)mol kg-1. We do not have pure CO2 to acidify and we only have access to HCl 0.1 N. Salinity is 34.5 and the bottle is kept at 22 \(^\circ\)C.

  • How much HCl 0.1 N do we need to add to this 1 L bottle?
  • How much did AT change?
  • How much NaHCO3 should we add to compensate and increase AT to its initial level (in g)?

Answer

ppH(flag=24, sys=0, var1=430, var2=2340e-6, pCO2a=384, vol=seq(-10e-3, 0, 0.5e-3), N=0.1, S=34.5, T=22, P=0, pHscale="T", kf="pf", k1k2="l", ks="d")
##               comment flag    S  T Patm P       pH          CO2       fCO2
## 1  ppH-closed-initial   24 34.5 22    1 0 8.027174 1.318900e-05   428.5765
## 2    ppH-closed-final   15 34.5 22    1 0 6.132145 7.315797e-04 23772.6836
## 3    ppH-closed-final   15 34.5 22    1 0 6.177986 6.828989e-04 22190.7998
## 4    ppH-closed-final   15 34.5 22    1 0 6.225448 6.342322e-04 20609.3762
## 5    ppH-closed-final   15 34.5 22    1 0 6.274901 5.855968e-04 19028.9682
## 6    ppH-closed-final   15 34.5 22    1 0 6.326793 5.370154e-04 17450.3176
## 7    ppH-closed-final   15 34.5 22    1 0 6.381675 4.885195e-04 15874.4407
## 8    ppH-closed-final   15 34.5 22    1 0 6.440239 4.401529e-04 14302.7702
## 9    ppH-closed-final   15 34.5 22    1 0 6.503377 3.919800e-04 12737.3897
## 10   ppH-closed-final   15 34.5 22    1 0 6.572260 3.440972e-04 11181.4391
## 11   ppH-closed-final   15 34.5 22    1 0 6.648459 2.966562e-04  9639.8441
## 12   ppH-closed-final   15 34.5 22    1 0 6.734112 2.499057e-04  8120.6854
## 13   ppH-closed-final   15 34.5 22    1 0 6.832125 2.042732e-04  6637.8587
## 14   ppH-closed-final   15 34.5 22    1 0 6.946268 1.605245e-04  5216.2448
## 15   ppH-closed-final   15 34.5 22    1 0 7.080518 1.200393e-04  3900.6785
## 16   ppH-closed-final   15 34.5 22    1 0 7.235908 8.506670e-05  2764.2427
## 17   ppH-closed-final   15 34.5 22    1 0 7.404050 5.812711e-05  1888.8406
## 18   ppH-closed-final   15 34.5 22    1 0 7.566930 3.990046e-05  1296.5654
## 19   ppH-closed-final   15 34.5 22    1 0 7.710766 2.844632e-05   924.3631
## 20   ppH-closed-final   15 34.5 22    1 0 7.833107 2.122571e-05   689.7296
## 21   ppH-closed-final   15 34.5 22    1 0 7.937228 1.647497e-05   535.3543
## 22   ppH-closed-final   15 34.5 22    1 0 8.027174 1.318900e-05   428.5765
##          pCO2    fCO2pot    pCO2pot fCO2insitu pCO2insitu        HCO3
## 1    430.0000   428.5765   430.0000   428.5765   430.0000 0.001872607
## 2  23853.7204 23772.6836 23853.7204 23772.6836 23853.7275 0.001322716
## 3  22266.3143 22190.7998 22266.3143 22190.7998 22266.3205 0.001372153
## 4  20679.3882 20609.3762 20679.3882 20609.3762 20679.3936 0.001421531
## 5  19093.4997 19028.9682 19093.4997 19028.9682 19093.5043 0.001470822
## 6  17509.3930 17450.3176 17509.3930 17450.3176 17509.3968 0.001519989
## 7  15928.0880 15874.4407 15928.0880 15874.4407 15928.0912 0.001568978
## 8  14351.0221 14302.7702 14351.0221 14302.7702 14351.0247 0.001617718
## 9  12780.2861 12737.3897 12780.2861 12737.3897 12780.2881 0.001666100
## 10 11219.0303 11181.4391 11219.0303 11181.4391 11219.0319 0.001713964
## 11  9672.1968  9639.8441  9672.1968  9639.8441  9672.1980 0.001761056
## 12  8147.8932  8120.6854  8147.8932  8120.6854  8147.8941 0.001806960
## 13  6660.0615  6637.8587  6660.0615  6637.8587  6660.0620 0.001850962
## 14  5233.6645  5216.2448  5233.6645  5216.2448  5233.6648 0.001891777
## 15  3913.6854  3900.6785  3913.6854  3900.6785  3913.6856 0.001927091
## 16  2773.4483  2764.2427  2773.4483  2764.2427  2773.4484 0.001953118
## 17  1895.1246  1888.8406  1895.1246  1888.8406  1895.1247 0.001965575
## 18  1300.8761  1296.5654  1300.8761  1296.5654  1300.8761 0.001963216
## 19   927.4350   924.3631   927.4350   924.3631   927.4350 0.001949181
## 20   692.0212   689.7296   692.0212   689.7296   692.0212 0.001927657
## 21   537.1327   535.3543   537.1327   535.3543   537.1327 0.001901572
## 22   430.0000   428.5765   430.0000   428.5765   430.0000 0.001872607
##             CO3         DIC         ALK OmegaAragonite OmegaCalcite
## 1  1.907764e-04 0.002076572 0.002340000     2.99785361   4.59174957
## 2  1.715992e-06 0.002056012 0.001326733     0.02696503   0.04130176
## 3  1.978300e-06 0.002057030 0.001376919     0.03108693   0.04761520
## 4  2.286167e-06 0.002058049 0.001427156     0.03592474   0.05502517
## 5  2.650728e-06 0.002059070 0.001477442     0.04165345   0.06379971
## 6  3.087006e-06 0.002060091 0.001527778     0.04850909   0.07430036
## 7  3.615726e-06 0.002061114 0.001578164     0.05681738   0.08702600
## 8  4.266241e-06 0.002062137 0.001628600     0.06703955   0.10268308
## 9  5.081381e-06 0.002063161 0.001679086     0.07984863   0.12230247
## 10 6.125839e-06 0.002064187 0.001729622     0.09626121   0.14744128
## 11 7.501295e-06 0.002065213 0.001780209     0.11787506   0.18054677
## 12 9.374854e-06 0.002066241 0.001830846     0.14731611   0.22564099
## 13 1.203447e-05 0.002067269 0.001881533     0.18910914   0.28965451
## 14 1.599713e-05 0.002068299 0.001932271     0.25137825   0.38503080
## 15 2.219855e-05 0.002069329 0.001983059     0.34882710   0.53429116
## 16 3.217663e-05 0.002070361 0.002033898     0.50562242   0.77445127
## 17 4.769181e-05 0.002071393 0.002084788     0.74942723   1.14788198
## 18 6.931092e-05 0.002072427 0.002135729     1.08914912   1.66822689
## 19 9.583447e-05 0.002073462 0.002186720     1.50593927   2.30661563
## 20 1.256148e-04 0.002074497 0.002237762     1.97390559   3.02338983
## 21 1.574869e-04 0.002075534 0.002288856     2.47474304   3.79051207
## 22 1.907764e-04 0.002076572 0.002340000     2.99785361   4.59174957
ppH(flag=24, sys=0, var1=430, var2=2340e-6, pCO2a=384, vol=seq(-1.5e-3, -1e-3, 0.05e-3), N=0.1, S=34.5, T=22, P=0, pHscale="T", kf="pf", k1k2="l", ks="d")
##               comment flag    S  T Patm P       pH          CO2     fCO2
## 1  ppH-closed-initial   24 34.5 22    1 0 8.027174 1.318900e-05 428.5765
## 2    ppH-closed-final   15 34.5 22    1 0 7.710766 2.844632e-05 924.3631
## 3    ppH-closed-final   15 34.5 22    1 0 7.723934 2.757015e-05 895.8920
## 4    ppH-closed-final   15 34.5 22    1 0 7.736887 2.673332e-05 868.6992
## 5    ppH-closed-final   15 34.5 22    1 0 7.749625 2.593374e-05 842.7170
## 6    ppH-closed-final   15 34.5 22    1 0 7.762152 2.516944e-05 817.8810
## 7    ppH-closed-final   15 34.5 22    1 0 7.774473 2.443853e-05 794.1301
## 8    ppH-closed-final   15 34.5 22    1 0 7.786590 2.373923e-05 771.4062
## 9    ppH-closed-final   15 34.5 22    1 0 7.798508 2.306984e-05 749.6546
## 10   ppH-closed-final   15 34.5 22    1 0 7.810231 2.242879e-05 728.8234
## 11   ppH-closed-final   15 34.5 22    1 0 7.821762 2.181455e-05 708.8638
## 12   ppH-closed-final   15 34.5 22    1 0 7.833107 2.122571e-05 689.7296
##        pCO2  fCO2pot  pCO2pot fCO2insitu pCO2insitu        HCO3          CO3
## 1  430.0000 428.5765 430.0000   428.5765   430.0000 0.001872607 1.907764e-04
## 2  927.4350 924.3631 927.4350   924.3631   927.4350 0.001949181 9.583447e-05
## 3  898.8692 895.8920 898.8692   895.8920   898.8692 0.001947305 9.868985e-05
## 4  871.5860 868.6992 871.5860   868.6992   871.5860 0.001945360 1.015758e-04
## 5  845.5174 842.7170 845.5174   842.7170   845.5174 0.001943348 1.044911e-04
## 6  820.5988 817.8810 820.5988   817.8810   820.5988 0.001941272 1.074343e-04
## 7  796.7688 794.1301 796.7688   794.1301   796.7688 0.001939137 1.104041e-04
## 8  773.9694 771.4062 773.9694   771.4062   773.9694 0.001936944 1.133995e-04
## 9  752.1454 749.6546 752.1454   749.6546   752.1454 0.001934697 1.164193e-04
## 10 731.2450 728.8234 731.2450   728.8234   731.2450 0.001932399 1.194624e-04
## 11 711.2190 708.8638 711.2190   708.8638   711.2190 0.001930051 1.225279e-04
## 12 692.0212 689.7296 692.0212   689.7296   692.0212 0.001927657 1.256148e-04
##            DIC         ALK OmegaAragonite OmegaCalcite
## 1  0.002076572 0.002340000       2.997854     4.591750
## 2  0.002073462 0.002186720       1.505939     2.306616
## 3  0.002073565 0.002191822       1.550809     2.375341
## 4  0.002073669 0.002196924       1.596159     2.444803
## 5  0.002073772 0.002202027       1.641969     2.514969
## 6  0.002073876 0.002207131       1.688218     2.585808
## 7  0.002073979 0.002212235       1.734886     2.657289
## 8  0.002074083 0.002217339       1.781956     2.729384
## 9  0.002074187 0.002222444       1.829408     2.802067
## 10 0.002074290 0.002227550       1.877228     2.875311
## 11 0.002074394 0.002232656       1.925399     2.949093
## 12 0.002074497 0.002237762       1.973906     3.023390
ppH(flag=24, sys=0, var1=430, var2=2340e-6, pCO2a=384, vol=-1.14e-3, N=0.1, S=34.5, T=22, P=0, pHscale="T", kf="pf", k1k2="l", ks="d")
##              comment flag    S  T Patm P       pH          CO2     fCO2
## 1 ppH-closed-initial   24 34.5 22    1 0 8.027174 1.318900e-05 428.5765
## 2   ppH-closed-final   15 34.5 22    1 0 7.800868 2.293941e-05 745.4163
##       pCO2  fCO2pot  pCO2pot fCO2insitu pCO2insitu        HCO3          CO3
## 1 430.0000 428.5765 430.0000   428.5765   430.0000 0.001872607 0.0001907764
## 2 747.8931 745.4163 747.8931   745.4163   747.8931 0.001934242 0.0001170261
##           DIC         ALK OmegaAragonite OmegaCalcite
## 1 0.002076572 0.002340000       2.997854     4.591750
## 2 0.002074207 0.002223465       1.838944     2.816671
pTA(15, sys=0, 0.002223465, 0.002074212, pCO2a, 0, 0.00234-0.002223465, S=34.5, T=22, P=0, Pt=0, Sit=0, k1k2="x", kf="x", ks="d", pHscale="T", b="u74")
##              comment flag    S  T Patm P       pH          CO2     fCO2
## 1 pTA-closed-initial   15 34.5 22    1 0 7.800856 2.294013e-05 745.4396
## 2   pTA-closed-final   15 34.5 22    1 0 7.788789 2.494242e-05 810.5040
##       pCO2  fCO2pot  pCO2pot fCO2insitu pCO2insitu        HCO3          CO3
## 1 747.9164 745.4396 747.9164   745.4396   747.9164 0.001934249 0.0001170232
## 2 813.1972 810.5040 813.1972   810.5040   813.1972 0.002045445 0.0001203595
##           DIC         ALK OmegaAragonite OmegaCalcite
## 1 0.002074212 0.002223465       1.838899     2.816603
## 2 0.002190747 0.002340000       1.891325     2.896903
HCO3 <- 0.00234-0.002223465 # mol/kg
M_HCO3 <- 84.007 # g/mol

HCO3v <- HCO3 * (rho(S = 34.5, T=22)/1000)
mHCO3 <- HCO3v * M_HCO3

print(mHCO3*1000) # in mg
## [1] 10.02312
## attr(,"unit")
## [1] "(kg/m3)"

Case study #6

Exercise

We conduct an experiment with two pH levels, ambient and pH 7.4 on the total scale. We can acidify by bubbling the tanks with a mixture of air + CO2 that we can regulate.

  • Initial conditions are:

  • CT = 2230 \(\mu\)mol kg-1

  • AT = 2550 \(\mu\)mol kg-1

  • T = 25 \(^\circ\)C

  • S = 38

  • At which pCO2 should we set our mixture?

Answer

pgas(flag=15, var1=2550e-6, var2=2230e-6, pCO2g=seq(500, 2500, 100), S=38, T=25, P=0, Pt=0, Sit=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")
##         comment flag  S  T Patm P       pH          CO2      fCO2      pCO2
## 1  pgas-initial   15 38 25    1 0 8.005736 1.347573e-05  482.0977  483.6412
## 2    pgas-final   24 38 25    1 0 7.993900 1.393154e-05  498.4043  500.0000
## 3    pgas-final   24 38 25    1 0 7.928220 1.671784e-05  598.0849  600.0000
## 4    pgas-final   24 38 25    1 0 7.871644 1.950414e-05  697.7655  700.0000
## 5    pgas-final   24 38 25    1 0 7.821888 2.229044e-05  797.4460  800.0000
## 6    pgas-final   24 38 25    1 0 7.777446 2.507673e-05  897.1264  900.0000
## 7    pgas-final   24 38 25    1 0 7.737267 2.786303e-05  996.8068 1000.0000
## 8    pgas-final   24 38 25    1 0 7.700589 3.064932e-05 1096.4870 1100.0000
## 9    pgas-final   24 38 25    1 0 7.666839 3.343561e-05 1196.1672 1200.0000
## 10   pgas-final   24 38 25    1 0 7.635577 3.622189e-05 1295.8474 1300.0000
## 11   pgas-final   24 38 25    1 0 7.606456 3.900818e-05 1395.5274 1400.0000
## 12   pgas-final   24 38 25    1 0 7.579198 4.179446e-05 1495.2074 1500.0000
## 13   pgas-final   24 38 25    1 0 7.553575 4.458074e-05 1594.8873 1600.0000
## 14   pgas-final   24 38 25    1 0 7.529401 4.736702e-05 1694.5672 1700.0000
## 15   pgas-final   24 38 25    1 0 7.506518 5.015330e-05 1794.2469 1800.0000
## 16   pgas-final   24 38 25    1 0 7.484794 5.293957e-05 1893.9266 1900.0000
## 17   pgas-final   24 38 25    1 0 7.464116 5.572585e-05 1993.6062 2000.0000
## 18   pgas-final   24 38 25    1 0 7.444388 5.851212e-05 2093.2858 2099.9999
## 19   pgas-final   24 38 25    1 0 7.425525 6.129839e-05 2192.9652 2199.9999
## 20   pgas-final   24 38 25    1 0 7.407454 6.408465e-05 2292.6446 2299.9999
## 21   pgas-final   24 38 25    1 0 7.390111 6.687092e-05 2392.3239 2399.9999
## 22   pgas-final   24 38 25    1 0 7.373438 6.965718e-05 2492.0032 2499.9999
##      fCO2pot   pCO2pot fCO2insitu pCO2insitu        HCO3          CO3
## 1   482.0977  483.6412   482.0977   483.6412 0.001984136 2.323881e-04
## 2   498.4043  500.0000   498.4043   500.0000 0.001996100 2.275039e-04
## 3   598.0849  600.0000   598.0849   600.0000 0.002059128 2.017483e-04
## 4   697.7655  700.0000   697.7655   700.0000 0.002108891 1.813864e-04
## 5   797.4460  800.0000   797.4460   800.0000 0.002149267 1.648487e-04
## 6   897.1264  900.0000   897.1264   900.0000 0.002182732 1.511309e-04
## 7   996.8068 1000.0000   996.8068  1000.0000 0.002210949 1.395573e-04
## 8  1096.4870 1100.0000  1096.4870  1100.0000 0.002235079 1.296547e-04
## 9  1196.1672 1200.0000  1196.1672  1200.0000 0.002255961 1.210814e-04
## 10 1295.8474 1300.0000  1295.8474  1300.0000 0.002274216 1.135837e-04
## 11 1395.5274 1400.0000  1395.5274  1400.0000 0.002290316 1.069692e-04
## 12 1495.2074 1500.0000  1495.2074  1500.0000 0.002304624 1.010892e-04
## 13 1594.8873 1600.0000  1594.8873  1600.0000 0.002317426 9.582700e-05
## 14 1694.5672 1700.0000  1694.5672  1700.0000 0.002328949 9.108932e-05
## 15 1794.2469 1800.0000  1794.2469  1800.0000 0.002339378 8.680099e-05
## 16 1893.9266 1900.0000  1893.9266  1900.0000 0.002348861 8.290061e-05
## 17 1993.6062 2000.0000  1993.6062  2000.0000 0.002357523 7.933755e-05
## 18 2093.2858 2100.0000  2093.2858  2099.9999 0.002365467 7.606964e-05
## 19 2192.9652 2200.0000  2192.9652  2199.9999 0.002372778 7.306151e-05
## 20 2292.6446 2300.0000  2292.6446  2299.9999 0.002379530 7.028324e-05
## 21 2392.3239 2400.0000  2392.3239  2399.9999 0.002385785 6.770934e-05
## 22 2492.0032 2500.0000  2492.0032  2499.9999 0.002391595 6.531799e-05
##            DIC     ALK OmegaAragonite OmegaCalcite
## 1  0.002230000 0.00255       3.607474     5.454006
## 2  0.002237535 0.00255       3.531653     5.339376
## 3  0.002277594 0.00255       3.131836     4.734908
## 4  0.002309781 0.00255       2.815749     4.257027
## 5  0.002336406 0.00255       2.559026     3.868897
## 6  0.002358940 0.00255       2.346079     3.546950
## 7  0.002378369 0.00255       2.166415     3.275323
## 8  0.002395383 0.00255       2.012693     3.042916
## 9  0.002410478 0.00255       1.879605     2.841705
## 10 0.002424022 0.00255       1.763214     2.665738
## 11 0.002436294 0.00255       1.660534     2.510500
## 12 0.002447508 0.00255       1.569257     2.372502
## 13 0.002457834 0.00255       1.487569     2.249001
## 14 0.002467406 0.00255       1.414024     2.137810
## 15 0.002476332 0.00255       1.347454     2.037166
## 16 0.002484702 0.00255       1.286906     1.945626
## 17 0.002492587 0.00255       1.231595     1.862003
## 18 0.002500049 0.00255       1.180866     1.785308
## 19 0.002507138 0.00255       1.134169     1.714709
## 20 0.002513898 0.00255       1.091041     1.649504
## 21 0.002520365 0.00255       1.051085     1.589096
## 22 0.002526570 0.00255       1.013963     1.532973
print(2300)
## [1] 2300

Case study #7

Exercise

We are starting an experiment with pelagic mesocosms. We want to set two levels of pCO2: Ambient, 700, 1200 \(\mu\)atm. To acidify, we want to add CO2-saturated seawater. We measure CT and AT at the start of the experiment, as well as T, S, an concentrations of phosphate and silicate.

  • CT = 2230 \(\mu\)mol kg-1
  • AT = 2550 \(\mu\)mol kg-1
  • T = 25 \(^\circ\)C
  • S = 38
  • Pt = 50 nmol kg-1
  • Si = 20 \(\mu\)mol kg-1

Our mesocosms are all 30 m3 of volume.

  • How much CO2-saturated seawater should I inject to each mesocosm (in liter)?
  • Provide a matrix with the results

Answer

pmix(flag=15, var1=2550e-6, var2=2230e-6, pCO2s=1e6, wf=0.00282, S=38, T=25, P=0, Pt=50e-9, Sit=20e-6, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")
##               comment flag  S  T Patm P       pH          CO2     fCO2     pCO2
## 1 pmix-closed-initial   15 38 25    1 0 8.004518 1.351730e-05 483.5848 485.1330
## 2   pmix-closed-final   15 38 25    1 0 7.871275 1.951844e-05 698.2771 700.5132
##    fCO2pot  pCO2pot fCO2insitu pCO2insitu        HCO3          CO3         DIC
## 1 483.5848 485.1330   483.5848   485.1330 0.001984682 0.0002318010 0.002230000
## 2 698.2771 700.5132   698.2771   700.5132 0.002108647 0.0001812116 0.002309377
##       ALK OmegaAragonite OmegaCalcite
## 1 0.00255       3.598358     5.440225
## 2 0.00255       2.813036     4.252925
pmix(flag=15, var1=2550e-6, var2=2230e-6, pCO2s=1e6, wf=0.0064, S=38, T=25, P=0, Pt=50e-9, Sit=20e-6, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")
##               comment flag  S  T Patm P       pH          CO2      fCO2
## 1 pmix-closed-initial   15 38 25    1 0 8.004518 1.351730e-05  483.5848
## 2   pmix-closed-final   15 38 25    1 0 7.666654 3.344578e-05 1196.5312
##       pCO2   fCO2pot  pCO2pot fCO2insitu pCO2insitu        HCO3         CO3
## 1  485.133  483.5848  485.133   483.5848    485.133 0.001984682 0.000231801
## 2 1200.365 1196.5312 1200.365  1196.5312   1200.365 0.002255686 0.000121015
##           DIC     ALK OmegaAragonite OmegaCalcite
## 1 0.002230000 0.00255       3.598358     5.440225
## 2 0.002410146 0.00255       1.878574     2.840147
print(30 * 0.00282 * 1000)
## [1] 84.6
print(30 * 0.0064 * 1000)
## [1] 192

Case study #8

Exercise

We are starting a monitoring of carbonate chemistry off Villefranche coast. In our laboratory, we can measure pH, total alkalinity, pCO2 and dissolved inorganic carbon.

The values and precisions obtained with the different methods we use for each parameter are:

  • pH: 8.01 ± 0.01
  • AT: 2500 ± 5 \(\mu\)mol kg-1
  • CT: 2204 ± 5 \(\mu\)mol kg-1
  • pCO2: 477 ± 10 \(\mu\)atm

What is the couple allowing the best characterisation of carbonate chemistry in our system (assume a temperature of 25 \(^\circ\)C and a salinity of 35)?

Answer

pH_AT <- errors(8, 8.01, 2500/1000000, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, 
              evar1=0.01, evar2=5/1000000, eS=0.01, eT=0.01, ePt=0, eSit=0, 
              epK=c(0.002, 0.0075, 0.015, 0.01, 0.01, 0.02, 0.02),
              eBt=0.02, method = "ga", r=0.0, runs=10000,
              k1k2='x', kf='x', ks="d", pHscale="T", b="u74", gas="potential", 
              warn="y", eos = "eos80", long = 1e+20, lat = 1e+20)

pH_CT <- errors(9, 8.01, 2204/1000000, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, 
              evar1=0.01, evar2=5/1000000, eS=0.01, eT=0.01, ePt=0, eSit=0, 
              epK=c(0.002, 0.0075, 0.015, 0.01, 0.01, 0.02, 0.02),
              eBt=0.02, method = "ga", r=0.0, runs=10000,
              k1k2='x', kf='x', ks="d", pHscale="T", b="u74", gas="potential", 
              warn="y", eos = "eos80", long = 1e+20, lat = 1e+20)

pH_pCO2 <- errors(21, 477, 8.01, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, 
              evar1=10, evar2=0.01, eS=0.01, eT=0.01, ePt=0, eSit=0, 
              epK=c(0.002, 0.0075, 0.015, 0.01, 0.01, 0.02, 0.02),
              eBt=0.02, method = "ga", r=0.0, runs=10000,
              k1k2='x', kf='x', ks="d", pHscale="T", b="u74", gas="potential", 
              warn="y", eos = "eos80", long = 1e+20, lat = 1e+20)

AT_CT <- errors(15, 2500/1000000, 2204/1000000, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, 
              evar1=5/1000000, evar2=5/1000000, eS=0.01, eT=0.01, ePt=0, eSit=0, 
              epK=c(0.002, 0.0075, 0.015, 0.01, 0.01, 0.02, 0.02),
              eBt=0.02, method = "ga", r=0.0, runs=10000,
              k1k2='x', kf='x', ks="d", pHscale="T", b="u74", gas="potential", 
              warn="y", eos = "eos80", long = 1e+20, lat = 1e+20)