Analysis of cant estimates

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Last updated: 2020-12-21

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Knit directory: emlr_mod_v_XXX/

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1 Data sources

Cant estimates from this sensitivity case:

• Mean and SD per grid cell (lat, lon, depth)
• Zonal mean and SD (basin, lat, depth)
• Inventories (lat, lon)

cant_3d <-
  read_csv(paste(path_version_data,
                 "cant_3d.csv",
                 sep = ""))

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

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

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

Target variable (cstar_tref) estimates from this sensitivity case:

• Mean and SD per grid cell (lat, lon, depth)
• Zonal mean and SD (basin, lat, depth)

target_3d <-
  read_csv(paste(path_version_data,
                 "target_3d.csv",
                 sep = ""))

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

Cleaned GLODAPv2_2020 file as used in this sensitivity case

GLODAP <-
  read_csv(paste(
    path_version_data,
    "GLODAPv2.2020_MLR_fitting_ready.csv",
    sep = ""
  ))

2 Cant budgets

Global Cant inventories were estimated in units of Pg C. Please note that here we added Cant (all vs postitive only) values and do not apply additional corrections for areas not covered.

cant_inv_budget <- cant_inv %>% 
  mutate(surface_area = earth_surf(lat, lon),
         cant_inv_grid = cant_inv*surface_area,
         cant_pos_inv_grid = cant_pos_inv*surface_area) %>% 
  group_by(basin_AIP, eras, inv_depth) %>% 
  summarise(cant_total = sum(cant_inv_grid)*12*1e-15,
            cant_total = round(cant_total,1),
            cant_pos_total = sum(cant_pos_inv_grid)*12*1e-15,
            cant_pos_total = round(cant_pos_total,1)) %>% 
  ungroup()

2.1 Standard depth

Results integrated over the upper 3000 m

cant_inv_budget %>%
  filter(inv_depth == params_global$inventory_depth_standard) %>% 
  gt(rowname_col = "basin_AIP",
     groupname_col = c("eras", "inv_depth"),
     row_group.sep = " | Depth: ") %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )

	cant_total	cant_pos_total
1982-1999 --> 2000-2012 | Depth: 3000
Atlantic	6.6	7.0
Indian	7.2	8.0
Pacific	9.5	12.0
total	23.30	27.00
2000-2012 --> 2013-2019 | Depth: 3000
Atlantic	4.1	4.6
Indian	4.3	5.6
Pacific	14.7	15.3
total	23.10	25.50

2.2 Other depths

Results integrated over the upper 100, 500, 1000, 3000, 10^{4} m

cant_inv_budget %>%
  filter(inv_depth != params_global$inventory_depth_standard) %>% 
  gt(rowname_col = "basin_AIP",
     groupname_col = c("eras", "inv_depth"),
     row_group.sep = " | Depth: ") %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )

	cant_total	cant_pos_total
1982-1999 --> 2000-2012 | Depth: 100
Atlantic	1.3	1.3
Indian	1.1	1.2
Pacific	2.4	2.4
total	4.80	4.90
1982-1999 --> 2000-2012 | Depth: 500
Atlantic	4.2	4.2
Indian	4.2	4.3
Pacific	7.8	7.8
total	16.20	16.30
1982-1999 --> 2000-2012 | Depth: 1000
Atlantic	5.1	5.4
Indian	6.5	6.5
Pacific	9.7	10.1
total	21.30	22.00
1982-1999 --> 2000-2012 | Depth: 10000
Atlantic	6.5	7.4
Indian	6.8	8.0
Pacific	9.0	12.3
total	22.30	27.70
2000-2012 --> 2013-2019 | Depth: 100
Atlantic	0.8	0.8
Indian	0.6	0.6
Pacific	1.6	1.7
total	3.00	3.10
2000-2012 --> 2013-2019 | Depth: 500
Atlantic	2.7	2.8
Indian	2.6	2.7
Pacific	5.2	5.3
total	10.50	10.80
2000-2012 --> 2013-2019 | Depth: 1000
Atlantic	3.6	3.7
Indian	4.0	4.2
Pacific	7.3	7.6
total	14.90	15.50
2000-2012 --> 2013-2019 | Depth: 10000
Atlantic	4.3	5.2
Indian	3.8	5.8
Pacific	19.4	20.1
total	27.50	31.10

rm(cant_inv_budget)

The following analysis is restricted to the standard inventory depth of 3000 m.

cant_inv <- cant_inv %>%
  filter(inv_depth == params_global$inventory_depth_standard)

3 Cant - positive

In a first series of plots we explore the distribution of Cant, taking only positive estimates into account (positive here refers to the mean cant estimate across MLR model predictions available for each grid cell). Negative values were set to zero before calculating mean sections and inventories.

3.1 Zonal mean sections

# i_basin_AIP <- unique(cant_zonal$basin_AIP)[2]
# i_eras <- unique(cant_zonal$eras)[1]

for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
  for (i_eras in unique(cant_zonal$eras)) {
   
     print(
      p_section_zonal(
        df = cant_zonal %>%
          filter(basin_AIP == i_basin_AIP,
                 eras == i_eras),
        var = "cant_pos_mean",
        subtitle_text =
          paste("Basin:", i_basin_AIP, "| eras:", i_eras))
    )
    
  }
}

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3.2 Isoneutral slab distribution

Mean of positive cant within each horizontal grid cell (lon x lat) per isoneutral slab.

Please note that:

• density slabs covering values >28.1 occur by definition only either in the Atlantic or Indo-Pacific basin
• gaps in the maps represent areas where (thin) density layers fit between discrete depth levels used for mapping

cant_gamma_maps <- m_cant_slab(cant_3d)

cant_gamma_maps <- cant_gamma_maps %>% 
  arrange(gamma_slab, eras)

# i_eras <- unique(cant_gamma_maps$eras)[1]
# i_gamma_slab <- unique(cant_gamma_maps$gamma_slab)[1]

for (i_eras in unique(cant_gamma_maps$eras)) {
  for (i_gamma_slab in unique(cant_gamma_maps$gamma_slab)) {
    print(
      p_map_cant_slab(
        df = cant_gamma_maps %>%
          filter(eras == i_eras,
                 gamma_slab == i_gamma_slab),
        subtitle_text = paste(
          "Eras:", i_eras,
          "| Neutral density:", i_gamma_slab)
        )
    )
    
  }
}

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3.3 Inventory map

Column inventory of positive cant between the surface and m water depth per horizontal grid cell (lat x lon).

# i_eras <- unique(cant_inv$eras)[1]

for (i_eras in unique(cant_inv$eras)) {
  
  print(
    p_map_cant_inv(
      df = cant_inv %>% filter(eras == i_eras),
      var = "cant_pos_inv",
      subtitle_text = paste("Eras:", i_eras))
  )
  
}

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3.4 Global sections

for (i_eras in unique(cant_3d$eras)) {
  print(
    p_section_global(
      df = cant_3d %>% filter(eras == i_eras),
      var = "cant_pos",
      subtitle_text = paste("Eras:", i_eras)
    )
  )
  
}

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4 Cant - all

In a second series of plots we explore the distribution of all Cant, taking positive and negative estimates into account.

4.1 Zonal mean sections

# i_eras <- unique(cant_zonal$eras)[1]
# i_basin_AIP <- unique(cant_zonal$basin_AIP)[1]

for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
  for (i_eras in unique(cant_zonal$eras)) {
    print(
      p_section_zonal(
        df = cant_zonal %>%
          filter(basin_AIP == i_basin_AIP,
                 eras == i_eras),
        var = "cant_mean",
        gamma = "gamma_mean",
        breaks = params_global$breaks_cant,
        col = "divergent",
        subtitle_text =
          paste("Basin:", i_basin_AIP, "| eras:", i_eras))
    )
    
  }
}

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4.2 Isoneutral slab distribution

Mean of all Cant within each horizontal grid cell (lon x lat) per isoneutral slab.

Please note that:

• density slabs covering values >28.1 occur by definition only either in the Atlantic or Indo-Pacific basin
• gaps in the maps represent areas where (thin) density layers fit between discrete depth levels used for mapping

# i_eras <- unique(cant_gamma_maps$eras)[1]
# i_gamma_slab <- unique(cant_gamma_maps$gamma_slab)[5]

for (i_eras in unique(cant_gamma_maps$eras)) {
  for (i_gamma_slab in unique(cant_gamma_maps$gamma_slab)) {
    print(
      p_map_cant_slab(
        df = cant_gamma_maps %>%
          filter(eras == i_eras,
                 gamma_slab == i_gamma_slab),
        var = "cant",
        col = "divergent",
        subtitle_text = paste(
          "Eras:", i_eras,
          "| Neutral density:", i_gamma_slab))
    )
    
  }
}

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4.3 Inventory map

Column inventory of all Cant between the surface and 3000m water depth per horizontal grid cell (lat x lon).

# i_eras <- unique(cant_inv$eras)[1]

for (i_eras in unique(cant_inv$eras)) {
  
  print(
    p_map_cant_inv(
      df = cant_inv %>% filter(eras == i_eras),
      var = "cant_inv",
      col = "divergent",
      subtitle_text = paste("Eras:", i_eras))
  )
  
}

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5 Cant variability

5.1 Across models

Standard deviation across Cant from all MLR models was calculate for each grid cell (XYZ). The zonal mean of this standard deviation should reflect the uncertainty associated to the predictor selection within each slab and era.

# i_eras <- unique(cant_zonal$eras)[1]
# i_basin_AIP <- unique(cant_zonal$basin_AIP)[2]

for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
  for (i_eras in unique(cant_zonal$eras)) {
    print(
      p_section_zonal(
        df = cant_zonal %>%
          filter(basin_AIP == i_basin_AIP,
                 eras == i_eras),
        var = "cant_sd_mean",
        gamma = "gamma_mean",
        legend_title = "sd",
        title_text = "Zonal mean section of SD across models",
        subtitle_text =
          paste("Basin:", i_basin_AIP, "| eras:", i_eras))
    )
    
  }
}

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

5.2 Across basins

Standard deviation of mean cant values was calculate across all longitudes. This standard deviation should reflect the zonal variability of cant within the basin and era.

# i_eras <- unique(cant_zonal$eras)[1]
# i_basin_AIP <- unique(cant_zonal$basin_AIP)[2]

for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
  for (i_eras in unique(cant_zonal$eras)) {
    print(
      p_section_zonal(
        df = cant_zonal %>%
          filter(basin_AIP == i_basin_AIP,
                 eras == i_eras),
        var = "cant_sd",
        gamma = "gamma_mean",
        legend_title = "sd",
        title_text = "Zonal mean section of Cant SD",
        subtitle_text =
          paste("Basin:", i_basin_AIP, "| eras:", i_eras))
    )
    
  }
}

Past versions of cant_sections_sd_cant-1.png

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

5.3 Correlation

5.3.1 Cant vs model SD

5.3.1.1 Era vs basin

cant_3d %>% 
  ggplot(aes(cant, cant_sd)) +
  geom_vline(xintercept = 0) +
  geom_hline(yintercept = 10) +
  geom_bin2d() +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10",
                       name = "log10(n)") +
  facet_grid(basin_AIP ~ eras)

Past versions of cant_vs_sd_by_basin_era-1.png

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

5.3.1.2 Basin vs gamma

cant_3d %>% 
  ggplot(aes(cant, cant_sd)) +
  geom_vline(xintercept = 0) +
  geom_hline(yintercept = 10) +
  geom_bin2d() +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10",
                       name = "log10(n)") +
  facet_grid(gamma_slab ~ basin_AIP)

Past versions of cant_vs_sd_by_basin_gamma-1.png

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

5.3.2 Cant vs regional SD

5.3.2.1 Era vs basin

cant_zonal %>% 
  ggplot(aes(cant_mean, cant_sd)) +
  geom_vline(xintercept = 0) +
  geom_hline(yintercept = 10) +
  geom_bin2d() +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10",
                       name = "log10(n)") +
  facet_grid(basin_AIP ~ eras)

Past versions of cant_vs_sd_by_basin_era_zonal-1.png

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

5.3.2.2 Era vs basin

cant_zonal %>% 
  ggplot(aes(cant_mean, cant_sd)) +
  geom_vline(xintercept = 0) +
  geom_hline(yintercept = 10) +
  geom_bin2d() +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10",
                       name = "log10(n)") +
  facet_grid(gamma_slab ~ basin_AIP)

Past versions of cant_vs_sd_by_basin_gamma_zonal-1.png

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

6 Cant - predictor contribution

for (i_var in paste("cant",
                    c("intercept", params_local$MLR_predictors),
                    sep = "_")) {

  print(
    p_section_zonal_divergent_gamma_eras_basin(df = cant_predictor_zonal,
                                               var = i_var,
                                               gamma = "gamma")
  )
  
}

Past versions of cant_section_predictor_contribution-1.png

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

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c8b76b3	jens-daniel-mueller	2020-12-19

rm(i_var)

7 Neutral density

7.1 Slab depth

The plot below shows the depths of individual gamma slabs (color) together with the observations available in the respective slab.

Please note that:

• density slabs covering values >28.1 occur by definition only either in the Atlantic or Indo-Pacific basin

GLODAP_obs_coverage <- GLODAP %>% 
  count(lat, lon, gamma_slab, era)

map +
  geom_raster(data = cant_gamma_maps,
              aes(lon, lat, fill = depth_max)) +
  geom_raster(data = GLODAP_obs_coverage,
              aes(lon, lat), fill = "red") +
  facet_grid(gamma_slab ~ era) +
  scale_fill_viridis_c(direction = -1) +
  theme(axis.ticks = element_blank(),
        axis.text = element_blank(),
        legend.position = "top")

Past versions of gamma_maps-1.png

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

rm(GLODAP_obs_coverage)

8 Target variable

The predicted target variable (cstar_tref in this sensitivity case) is based on fitted MLRs and climatological fields of predictor variables, and calculated for each era.

8.1 Zonal mean sections

slab_breaks <- c(params_local$slabs_Atl[1:12], Inf)

target_zonal %>%
  ggplot(aes(lat, depth,
             z = !!sym(
               paste(params_local$MLR_target, "mean", sep = "_")
             ))) +
  geom_contour_filled(bins = 11) +
  scale_fill_viridis_d(name = params_local$MLR_target) +
  geom_contour(aes(lat, depth, z = gamma_mean),
               breaks = slab_breaks,
               col = "white") +
  geom_text_contour(
    aes(lat, depth, z = gamma_mean),
    breaks = slab_breaks,
    col = "white",
    skip = 1
  ) +
  scale_y_reverse() +
  coord_cartesian(expand = 0,
                  ylim = c(params_global$plotting_depth, 0)) +
  scale_x_continuous(breaks = seq(-100, 100, 20)) +
  guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
  facet_grid(basin_AIP ~ era)

Past versions of target_zonal_mean_era-1.png

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

rm(slab_breaks)

Session information

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] gt_0.2.2         kableExtra_1.3.1 marelac_2.1.10   shape_1.4.5     
 [5] scales_1.1.1     metR_0.8.0       scico_1.2.0      patchwork_1.1.0 
 [9] collapse_1.4.2   forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2     
[13] purrr_0.3.4      readr_1.4.0      tidyr_1.1.2      tibble_3.0.4    
[17] ggplot2_3.3.2    tidyverse_1.3.0  workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] fs_1.5.0                 lubridate_1.7.9          gsw_1.0-5               
 [4] webshot_0.5.2            httr_1.4.2               rprojroot_2.0.2         
 [7] tools_4.0.3              backports_1.2.1          R6_2.5.0                
[10] DBI_1.1.0                colorspace_2.0-0         withr_2.3.0             
[13] tidyselect_1.1.0         compiler_4.0.3           git2r_0.27.1            
[16] cli_2.2.0                rvest_0.3.6              xml2_1.3.2              
[19] isoband_0.2.3            labeling_0.4.2           sass_0.2.0              
[22] checkmate_2.0.0          digest_0.6.27            rmarkdown_2.5           
[25] oce_1.2-0                pkgconfig_2.0.3          htmltools_0.5.0         
[28] dbplyr_1.4.4             rlang_0.4.9              readxl_1.3.1            
[31] rstudioapi_0.13          farver_2.0.3             generics_0.1.0          
[34] jsonlite_1.7.2           magrittr_2.0.1           Matrix_1.2-18           
[37] Rcpp_1.0.5               munsell_0.5.0            fansi_0.4.1             
[40] lifecycle_0.2.0          stringi_1.5.3            whisker_0.4             
[43] yaml_2.2.1               plyr_1.8.6               grid_4.0.3              
[46] blob_1.2.1               parallel_4.0.3           promises_1.1.1          
[49] crayon_1.3.4             lattice_0.20-41          haven_2.3.1             
[52] hms_0.5.3                seacarb_3.2.14           knitr_1.30              
[55] pillar_1.4.7             reprex_0.3.0             glue_1.4.2              
[58] evaluate_0.14            RcppArmadillo_0.10.1.2.0 data.table_1.13.4       
[61] modelr_0.1.8             vctrs_0.3.6              httpuv_1.5.4            
[64] testthat_3.0.1           cellranger_1.1.0         gtable_0.3.0            
[67] assertthat_0.2.1         xfun_0.19                broom_0.7.3             
[70] RcppEigen_0.3.3.9.1      later_1.1.0.1            viridisLite_0.3.0       
[73] memoise_1.1.0            ellipsis_0.3.1           here_0.1