Last updated: 2020-12-21

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Rmd	00a1322	Donghe-Zhu	2020-12-21	first build after creating model template
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1 Required data

1.1 Predictor fields

Currently, we use following combined predictor fields:

WOA18: S, T, and derived variables
GLODAP16: Oxygen, PO4, NO3, Silicate, and derived variables

predictors <-
  read_csv(paste(path_version_data,
                 "W18_st_G16_opsn.csv",
                 sep = ""))

predictors_surface <-
  read_csv(paste(path_version_data,
                 "W18_st_G16_opsn_surface.csv",
                 sep = ""))

1.2 Atm. pCO2

Required only to estimate the change of Cant in surface water and assuming that the ocean pCO2 trend follows the atmospheric forcing.

co2_atm_tref <-
  read_csv(paste(path_version_data,
                 "co2_atm_tref.csv",
                 sep = ""))

1.3 MLR models

lm_best_cant <-
  read_csv(paste(path_version_data,
                 "lm_best_cant.csv",
                 sep = ""))

2 Join MLRs + climatologies

# remove predictor variable from model
lm_best_cant <- lm_best_cant %>% 
  mutate(model = str_remove(model, "Cstar ~ "))

# join predictors and MLR
cant <- full_join(predictors, lm_best_cant)

rm(predictors, lm_best_cant)

3 Map Cant

3.1 Deep water

3.1.1 Apply MLRs to predictor

cant <- b_cant(cant)

3.1.2 Sections by model

Zonal section plots are produced for every 20° longitude, each era and for all models individually. Plots can be accessed here:

/nfs/kryo/work/jenmueller/emlr_cant/model/v_XXX/figures/Cant_model_sections/

if (params_local$plot_all_figures == "y") {
  for (i_eras in unique(cant$eras)) {
    # i_eras <- unique(cant$eras)[2]
    cant_eras <- cant %>%
      filter(eras == i_eras)
    
    for (i_lon in params_global$longitude_sections_regular) {
      # i_lon <- params_global$longitude_sections_regular[7]
      cant_eras_lon <- cant_eras %>%
        filter(lon == i_lon)
      
      limits = max(abs(cant_eras_lon$cant)) * c(-1, 1)
      
      cant_eras_lon %>%
        ggplot(aes(lat, depth, z = cant)) +
        stat_summary_2d(
          fun = "mean",
          na.rm = TRUE,
          bins = 20,
          col = "grey"
        ) +
        scale_fill_scico(name = "Cant",
                         palette = "vik",
                         limit = limits) +
        scale_y_reverse(limits = c(params_global$plotting_depth, NA)) +
        scale_x_continuous(limits = c(-85, 85)) +
        labs(title = paste(
          "eras:",
          i_eras,
          "| lon:",
          i_lon,
          "|",
          params_local$Version_ID
        )) +
        facet_wrap(~ model, ncol = 5)
      
      ggsave(
        paste(
          path_version_figures,
          "Cant_model_sections/",
          paste("Cant_model",
                i_eras,
                "lon",
                i_lon,
                "section.png",
                sep = "_"),
          sep = ""
        ),
        width = 17,
        height = 9
      )
      
    }
  }
}

3.2 Surface water

As outlined in Gruber et al. (2019), a transient equilibrium approach was applied to estimate Cant in surface waters, assuming that the CO₂ system in these waters has followed the increase in atmospheric CO₂ closely.

Using eq 10.2.16 from OBD, the change in anthropogenic CO₂ in the upper ocean was computed as:

\(\Delta\)_tC_ant,eq(t2 − t1) = 1∕\(\gamma\) ⋅ DIC/pCO₂ ⋅ (pCO_2,atm (t2)− pCO_2,atm(t1))

, where DIC and pCO₂ are the in situ values, where \(\gamma\) is the buffer (Revelle) factor and where we evaluated the right-hand side using seacarb employing the Luecker constants using the climatological values for temperature, salinity, DIC and Alk.

3.2.1 pCO₂ climatology

Plots below show the calculated climatolofical pCO₂ values.

# calculate pCO2 from talk and tco2 climatology
predictors_surface <- predictors_surface %>%
  mutate(
    pCO2 = carb(
      flag = 15,
      var1 = TAlk * 1e-6,
      var2 = TCO2 * 1e-6,
      S = sal,
      T = temp,
      P = depth / 10,
      Pt = phosphate * 1e-6,
      Sit = silicate * 1e-6,
      k1k2 = "l"
    )$pCO2
  )

p_map_climatology(df = predictors_surface,
                  var = "pCO2")

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

p_section_climatology_regular(df = predictors_surface,
                              var = "pCO2",
                              surface = "y")

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

3.2.2 Revelle factor

Plots below show the calculated climatolofical Revelle factor values.

predictors_surface <- predictors_surface %>%
  mutate(
    rev_fac = buffer(
      flag = 15,
      var1 = TAlk * 1e-6,
      var2 = TCO2 * 1e-6,
      S = sal,
      T = temp,
      P = depth / 10,
      Pt = phosphate * 1e-6,
      Sit = silicate * 1e-6,
      k1k2 = "l"
    )$BetaD
  )

p_map_climatology(df = predictors_surface,
                  var = "rev_fac")

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

p_section_climatology_regular(df = predictors_surface,
                              var = "rev_fac",
                              surface = "y")

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

3.2.3 Cant calculation

# calculate increase in atm pCO2 between eras
co2_atm_tref <- co2_atm_tref %>%
  arrange(pCO2_tref) %>%
  mutate(d_pCO2_tref = pCO2_tref - lag(pCO2_tref),
         eras = paste(lag(era), era, sep = " --> ")) %>%
  drop_na() %>%
  select(eras, d_pCO2_tref)

cant_surface <- full_join(predictors_surface, co2_atm_tref,
                          by = character())

# calculate cant
cant_surface <- cant_surface %>%
  mutate(cant = (1 / rev_fac) * (TCO2 / pCO2) * d_pCO2_tref)

# calculate positive cant
cant_surface <- cant_surface %>%
  mutate(cant_pos = if_else(cant < 0, 0, cant))

3.2.4 Control plots

# i_eras <- unique(cant_average$eras)[2]

for (i_eras in unique(cant_surface$eras)) {
  print(
    p_map_climatology(df = cant_surface %>% filter(eras == i_eras),
                      var = "cant")  +
      labs(subtitle = paste("era:", i_eras))
  )
  
}

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

# i_eras <- unique(cant_surface$eras)[2]

for (i_eras in unique(cant_surface$eras)) {
  print(
    p_section_climatology_regular(df = cant_surface %>% filter(eras == i_eras),
                                  var = "cant",
                                  surface = "y") +
      labs(subtitle = paste("era:", i_eras))
  )
  
}

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

3.3 Average model Cant

Mean and sd are calculated across 10 models for Cant in each grid cell (XYZ), basin and era combination. Calculations are performed for all cant values vs positive values only.

3.3.1 Deep water averaging

cant_average <- m_cant_model_average(cant)
cant_average <- m_cut_gamma(cant_average, "gamma")

# split data set for individual predictor contributions and total cant
cant_predictor_average <- cant_average %>% 
  select(-c("cant", "cant_pos", ends_with("_sd")))

cant_average <- cant_average %>% 
  select(lon, lat, depth, eras, basin, basin_AIP,
            cant, cant_pos, cant_sd, cant_pos_sd,
            gamma, gamma_sd, gamma_slab)

# i_eras <- unique(cant_average$eras)[2]

for (i_eras in unique(cant_surface$eras)) {
  print(
    p_map_climatology(
      df = cant_average %>% filter(eras == i_eras),
      var = "cant_pos",
      subtitle_text = paste("era:", i_eras)
    )
  )
  
}

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

# i_eras <- unique(cant_surface$eras)[2]

for (i_eras in unique(cant_surface$eras)) {
  print(
    p_section_climatology_regular(
      df = cant_average %>% filter(eras == i_eras),
      var = "cant_pos",
      subtitle_text = paste("era:", i_eras)
    )
  )
}

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

3.3.2 Surface water averaging

The averaging function is also applied to the surface data, although only one value per grid cell was mapped, to ensure consistency with the deep water values.

cant_surface_average <- m_cant_model_average(cant_surface)
cant_surface_average <- m_cut_gamma(cant_surface_average, "gamma")
rm(cant_surface)

3.3.3 Join surface and deep water

cant_average <- full_join(cant_average, cant_surface_average)
rm(cant_surface_average)

3.4 Zonal mean sections

For each basin and era combination, the zonal mean cant is calculated, again for all vs positive only values. Likewise, sd is calculated for the averaging of the mean basin fields.

cant_average_zonal <- m_cant_zonal_mean(cant_average)
cant_average_zonal <- m_cut_gamma(cant_average_zonal, "gamma_mean")

3.5 Mean cant sections by coefficient

For each basin and era combination, the zonal mean is calculated for the term of each predictor.

cant_predictor_average_zonal <-
  m_cant_predictor_zonal_mean(cant_predictor_average)

cant_predictor_average_zonal <-
  m_cut_gamma(cant_predictor_average_zonal, "gamma")

3.6 Inventory calculation

To calculate Cant column inventories, we:

Convert Cant concentrations to volumetric units
Multiply layer thickness with volumentric Cant concentration to get a layer inventory
For each horizontal grid cell and era, sum cant layer inventories for different inventory depths (100, 500, 1000, 3000, 10^{4} m)

Step 2 is performed separately for all Cant and positive Cant values only.

cant_inv <- m_cant_inv(cant_average)

p_map_cant_inv(df = cant_inv,
               var = "cant_pos_inv",
               subtitle_text = "for predefined integration depths") +
  facet_grid(inv_depth ~ eras)

Version	Author	Date
c8b76b3	jens-daniel-mueller	2020-12-19

4 Write csv

cant_average %>%
  write_csv(paste(path_version_data,
                  "cant_3d.csv", sep = ""))

cant_predictor_average %>%
  write_csv(paste(path_version_data,
                  "cant_predictor_3d.csv", sep = ""))

cant_average_zonal %>%
  write_csv(paste(path_version_data,
                  "cant_zonal.csv", sep = ""))

cant_predictor_average_zonal %>%
  write_csv(paste(path_version_data,
                  "cant_predictor_zonal.csv", sep = ""))

cant_inv %>%
  write_csv(paste(path_version_data,
                  "cant_inv.csv", sep = ""))

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.1

Matrix products: default
BLAS:   /usr/local/R-4.0.3/lib64/R/lib/libRblas.so
LAPACK: /usr/local/R-4.0.3/lib64/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] seacarb_3.2.14  oce_1.2-0       gsw_1.0-5       testthat_3.0.1 
 [5] metR_0.8.0      scico_1.2.0     patchwork_1.1.0 collapse_1.4.2 
 [9] forcats_0.5.0   stringr_1.4.0   dplyr_1.0.2     purrr_0.3.4    
[13] readr_1.4.0     tidyr_1.1.2     tibble_3.0.4    ggplot2_3.3.2  
[17] tidyverse_1.3.0 workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] httr_1.4.2               jsonlite_1.7.2           viridisLite_0.3.0       
 [4] here_0.1                 modelr_0.1.8             assertthat_0.2.1        
 [7] blob_1.2.1               cellranger_1.1.0         yaml_2.2.1              
[10] pillar_1.4.7             backports_1.2.1          lattice_0.20-41         
[13] glue_1.4.2               RcppEigen_0.3.3.9.1      digest_0.6.27           
[16] promises_1.1.1           checkmate_2.0.0          rvest_0.3.6             
[19] colorspace_2.0-0         htmltools_0.5.0          httpuv_1.5.4            
[22] Matrix_1.2-18            pkgconfig_2.0.3          broom_0.7.3             
[25] haven_2.3.1              scales_1.1.1             whisker_0.4             
[28] later_1.1.0.1            git2r_0.27.1             farver_2.0.3            
[31] generics_0.1.0           ellipsis_0.3.1           withr_2.3.0             
[34] cli_2.2.0                magrittr_2.0.1           crayon_1.3.4            
[37] readxl_1.3.1             evaluate_0.14            fs_1.5.0                
[40] fansi_0.4.1              xml2_1.3.2               RcppArmadillo_0.10.1.2.0
[43] tools_4.0.3              data.table_1.13.4        hms_0.5.3               
[46] lifecycle_0.2.0          munsell_0.5.0            reprex_0.3.0            
[49] isoband_0.2.3            compiler_4.0.3           rlang_0.4.9             
[52] grid_4.0.3               rstudioapi_0.13          labeling_0.4.2          
[55] rmarkdown_2.5            gtable_0.3.0             DBI_1.1.0               
[58] R6_2.5.0                 lubridate_1.7.9          knitr_1.30              
[61] rprojroot_2.0.2          stringi_1.5.3            parallel_4.0.3          
[64] Rcpp_1.0.5               vctrs_0.3.6              dbplyr_1.4.4            
[67] tidyselect_1.1.0         xfun_0.19

Mapping cant

Jens Daniel Müller

21 December, 2020

1 Required data

1.1 Predictor fields

1.2 Atm. pCO2

1.3 MLR models

2 Join MLRs + climatologies

3 Map Cant

3.1 Deep water

3.1.1 Apply MLRs to predictor

3.1.2 Sections by model

3.2 Surface water

3.2.1 pCO₂ climatology

3.2.2 Revelle factor

3.2.3 Cant calculation

3.2.4 Control plots

3.3 Average model Cant

3.3.1 Deep water averaging

3.3.2 Surface water averaging

3.3.3 Join surface and deep water

3.4 Zonal mean sections

3.5 Mean cant sections by coefficient

3.6 Inventory calculation

4 Write csv

Mapping cant

Jens Daniel Müller

21 December, 2020

1 Required data

1.1 Predictor fields

1.2 Atm. pCO2

1.3 MLR models

2 Join MLRs + climatologies

3 Map Cant

3.1 Deep water

3.1.1 Apply MLRs to predictor

3.1.2 Sections by model

3.2 Surface water

3.2.1 pCO2 climatology

3.2.2 Revelle factor

3.2.3 Cant calculation

3.2.4 Control plots

3.3 Average model Cant

3.3.1 Deep water averaging

3.3.2 Surface water averaging

3.3.3 Join surface and deep water

3.4 Zonal mean sections

3.5 Mean cant sections by coefficient

3.6 Inventory calculation

4 Write csv

3.2.1 pCO₂ climatology