Last updated: 2020-08-05

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Rmd	1443a30	jens-daniel-mueller	2020-08-04	Included gamma values from Clement based on WOA13
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library(tidyverse)
library(lubridate)
library(oce)
library(marelac)
library(metR)

1 Required data

Currently we use following data sets for mapping:

GLODAPv2_2016b_MappedClimatologies
- Salinity
- Temperature
- Phosphate
- Nitrate
- Silicate
- oxygen
World Ocean Atlas 2013
- Neutral densities calculated by D Clement
World Ocean Atlas 2018
- basin mask
eMLR model coefficients

We aim to use WOA18 instead of WOA13, but still need to implement neutral density calculation.

variables <- c("salinity", "temperature", "NO3", "oxygen", "PO4", "silicate")

for (i_variable in variables) {
  
  # i_variable <- variables[2]
  # print(i_variable)
  temp <- read_csv(
    here::here("data/GLODAPv2_2016b_MappedClimatologies/_summarized_files",
               paste(i_variable,".csv", sep = "")))
  
  if (exists("GLODAP_predictors")) {
     GLODAP_predictors <- full_join(GLODAP_predictors, temp)
  }
  
  if (!exists("GLODAP_predictors")) {
    GLODAP_predictors <- temp
  }

}

rm(temp, i_variable, variables)

# GLODAP_depths <- unique(GLODAP_predictors$depth)
# GLODAP_lon <- unique(GLODAP_predictors$lon)
# min(GLODAP_lon)
# max(GLODAP_lon)

WOA18_predictors <-
  read_csv(here::here("data/World_Ocean_Atlas_2018/_summarized_files",
                       "WOA18_predictors.csv"))

WOA18_predictors <- WOA18_predictors %>% 
  rename(salinity = s_an, temperature = t_an)

# WOA18_depths <- unique(WOA18_predictors$depth)

WOA13 <-
  read_csv(here::here("data/World_Ocean_Atlas_2018/_summarized_files",
                       "WOA13_mask_gamma.csv"))

WOA13_gamma <- WOA13 %>% 
  select(-mask)

WOA13_gamma <- WOA13_gamma %>% 
  rename(lat = latitude, lon = longitude) %>% 
  mutate(lon = if_else(lon > 180, lon - 360, lon))

rm(WOA13)

# WOA13_depths <- unique(WOA13_gamma$depth)
# GLODAP_depths - WOA13_depths

basinmask <- read_csv(here::here("data/World_Ocean_Atlas_2018/_summarized_files",
                                 "basin_mask_WOA18.csv"))

all_lm <- read_csv(here::here("data/eMLR",
                              "all_lm.csv"))

2 Join predictor climatologies

CAVEAT: Coverage of GLODAP climatologies differs slightly for parameters (some are NA in some regions)

2.1 Control plots

Maps of number of observations per horizontal grid cell.

2.1.1 GLODAP climatology

GLODAP_n <- GLODAP_predictors %>% 
  drop_na() %>% 
  group_by(lat, lon) %>% 
  summarise(n = n()) %>% 
  ungroup()

GLODAP_n %>%
  ggplot(aes(lon, lat, fill = n)) +
  geom_raster() +
  scale_fill_viridis_c(direction = -1) +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom")

rm(GLODAP_n)

2.1.2 WOA13 climatology

WOA13_gamma_n <- WOA13_gamma %>% 
  drop_na() %>% 
  group_by(lat, lon) %>% 
  summarise(n = n()) %>% 
  ungroup()

WOA13_gamma_n %>%
  ggplot(aes(lon, lat, fill = n)) +
  geom_raster() +
  scale_fill_viridis_c(direction = -1) +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom")

rm(WOA13_gamma_n)

2.2 WOA13 + GLODAP

predictors <- full_join(GLODAP_predictors, WOA13_gamma)
rm(GLODAP_predictors, WOA13_gamma)

predictors <- predictors %>% 
  group_by(lat, lon) %>% 
  mutate(n_NO3 = sum(!is.na(NO3)),
         n_oxygen = sum(!is.na(oxygen)),
         n_PO4 = sum(!is.na(PO4)),
         n_silicate = sum(!is.na(silicate)),
         n_salinity = sum(!is.na(salinity)),
         n_temperature = sum(!is.na(temperature)),
         n_gamma = sum(!is.na(gamma))) %>% 
  ungroup()

predictors <- predictors %>% 
  filter(n_NO3 > 0,
         n_oxygen > 0,
         n_PO4 > 0,
         n_silicate > 0, 
         n_salinity > 0, 
         n_temperature > 0, 
         n_gamma > 0) %>% 
  select(-c(n_NO3, 
            n_oxygen, 
            n_PO4, 
            n_silicate, 
            n_salinity, 
            n_temperature,
            n_gamma))


predictors <- predictors %>% 
  drop_na()

2.2.1 Spatial boundaries

min_depth <- 150
min_bottomdepth <- 500
max_lat <- 65

Only mapped variables were taken into consideration with:

minimum depth: 150m
minimum bottom depth: 500m
maximum latitude: 65°N

predictors <- predictors %>% 
  filter(depth >= min_depth)

predictors <- predictors %>% 
  filter(lat <= max_lat)

predictors <- predictors %>% 
  group_by(lat, lon) %>% 
  mutate(bottomdepth = max(depth)) %>% 
  ungroup()

predictors <- predictors %>% 
  filter(bottomdepth >= min_bottomdepth) %>% 
  select(-bottomdepth)

rm(min_depth, max_lat, min_bottomdepth)

2.2.2 Basin mask

Please note that some predictor variables are available outside the WOA18 basin mask and will be removed for further analysis.

predictors <- inner_join(predictors, basinmask)
rm(basinmask)

2.2.3 Maps

predictors %>%
  ggplot(aes(lon, lat)) +
  geom_bin2d(binwidth = c(1,1)) +
  scale_fill_viridis_c(direction = -1) +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom")

predictors %>%
  filter(depth == 150) %>% 
  ggplot(aes(lon, lat, fill = PO4)) +
  geom_raster() +
  scale_fill_viridis_c() +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom") +
  labs(title = "150m values")

predictors %>%
  filter(depth == 150) %>% 
  ggplot(aes(lon, lat, fill = gamma)) +
  geom_raster() +
  scale_fill_viridis_c() +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom") +
  labs(title = "150m values")

2.2.4 Predictor profiles

N_Atl <- predictors %>% 
  filter(lat == 40.5, lon == -20.5)

N_Atl <- N_Atl %>% 
  pivot_longer(salinity:gamma, names_to = "parameter", values_to = "value")

N_Atl %>% 
  ggplot(aes(value, depth)) +
  geom_path() +
  geom_point() +
  scale_y_reverse() +
  facet_wrap(~parameter,
             scales = "free_x",
             ncol = 2)

rm(N_Atl)

2.3 WOA18 + GLODAP

WOA18 data are currently not used. Code chunks in this section are not executed.

predictors <- full_join(GLODAP_predictors, WOA18_predictors)
rm(GLODAP_predictors, WOA18_predictors)

predictors <- predictors %>% 
  group_by(lat, lon) %>% 
  mutate(n_NO3 = sum(!is.na(NO3)),
         n_oxygen = sum(!is.na(oxygen)),
         n_PO4 = sum(!is.na(PO4)),
         n_silicate = sum(!is.na(silicate)),
         n_salinity = sum(!is.na(salinity)),
         n_temperature = sum(!is.na(temperature))) %>% 
  ungroup()

predictors <- predictors %>% 
  filter(n_NO3 > 1,
         n_oxygen > 1,
         n_PO4 > 1,
         n_silicate > 1, 
         n_salinity > 1, 
         n_temperature > 1) %>% 
  select(-c(n_NO3 , n_oxygen , n_PO4 , n_silicate , n_salinity , n_temperature))

predictors %>%
  ggplot(aes(lon, lat)) +
  geom_bin2d(binwidth = c(1,1)) +
  scale_fill_viridis_c(direction = -1) +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom")

predictors %>%
  filter(depth == 0) %>% 
  ggplot(aes(lon, lat, fill = PO4)) +
  geom_raster() +
  scale_fill_viridis_c() +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom") +
  labs(title = "Surface values")

predictors %>%
  filter(depth == 0) %>% 
  ggplot(aes(lon, lat, fill = temperature)) +
  geom_raster() +
  scale_fill_viridis_c() +
  coord_quickmap(expand = 0) +
  theme(legend.position = "bottom") +
  labs(title = "Surface values")

predictors <- predictors %>% 
  group_by(lat, lon) %>% 
  arrange(depth) %>% 
  mutate(temperature = approxfun(depth, temperature, rule = 2)(depth),
         salinity = approxfun(depth, salinity, rule = 2)(depth)) %>% 
  ungroup()


predictors <- predictors %>% 
  filter(depth %in% GLODAP_depths)

3 Map Cant

3.1 PO₄* calculation

Currently, the predictor PO₄* is calculated according to Clement and Gruber (2018), ie based on oxygen rather than nitrate.

predictors <- predictors %>% 
  rename(phosphate = PO4) %>% 
  mutate(phosphate_star = phosphate + (oxygen / 170)  - 1.95)

3.2 AOU climatology

3.2.1 Calculation

predictors <- predictors %>% 
  mutate(oxygen_sat = gas_satconc(S = salinity,
                                  t = temperature,
                                  P = 1.013253,
                                  species = "O2"),
         aou = oxygen_sat - oxygen) %>% 
  select(-oxygen_sat)

3.2.2 Atlantic section

Atl_lon <- 335.5 - 360

predictors %>% 
  filter(lon == Atl_lon) %>% 
  ggplot(aes(lat, depth, z = aou)) +
  geom_contour_filled() +
  scale_y_reverse() +
  coord_cartesian(expand = 0) +
  theme(legend.position = "top")

rm(Atl_lon)

3.3 Isoneutral slabs

slabs_Atl <- c(
-Inf,
26.00,
26.50,
26.75,
27.00,
27.25,
27.50,
27.75,
27.85,
27.95,
28.05,
28.10,
28.15,
28.20,
Inf)

slabs_Ind_Pac <- c(
-Inf,
26.00,
26.50,
26.75,
27.00,
27.25,
27.50,
27.75,
27.85,
27.95,
28.05,
28.10,
Inf)

The following boundaries for isoneutral slabs were defined:

Atlantic: -, 26, 26.5, 26.75, 27, 27.25, 27.5, 27.75, 27.85, 27.95, 28.05, 28.1, 28.15, 28.2,
Indo-Pacific: -, 26, 26.5, 26.75, 27, 27.25, 27.5, 27.75, 27.85, 27.95, 28.05, 28.1,

Continous neutral densities (gamma) values from GLODAP are grouped into isoneutral slabs.

predictors_Atl <- predictors %>% 
  filter(basin == "Atlantic") %>% 
  mutate(gamma_slab = cut(gamma, slabs_Atl))

predictors_Ind_Pac <- predictors %>% 
  filter(basin == "Indo-Pacific") %>% 
  mutate(gamma_slab = cut(gamma, slabs_Ind_Pac))

predictors <- bind_rows(predictors_Atl, predictors_Ind_Pac)

rm(predictors_Atl, predictors_Ind_Pac, slabs_Atl, slabs_Ind_Pac)

3.4 Prepare model coefficients

all_lm <- all_lm %>% 
  select(term, estimate, basin, era, gamma_slab, model)

all_lm <- all_lm %>% 
  mutate(estimate = if_else(is.na(estimate), 0, estimate))

all_lm_wide <- all_lm %>% 
  pivot_wider(names_from = era, values_from = estimate,
              names_prefix = "coeff_")

all_lm_wide <- all_lm_wide %>% 
  mutate(JGOFS_GO = coeff_GO_SHIP - coeff_JGOFS_WOCE,
         GO_new = coeff_new_era - coeff_GO_SHIP) %>% 
  select(-c(coeff_JGOFS_WOCE,
            coeff_GO_SHIP,
            coeff_new_era))

all_lm_long <- all_lm_wide %>% 
  pivot_longer(JGOFS_GO:GO_new, names_to = "eras", values_to = "delta_coeff")

all_lm_wide <- all_lm_long %>% 
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

rm(all_lm_long, all_lm)

3.5 Merge model + climatology

Cant <- full_join(predictors, all_lm_wide)

rm(predictors, all_lm_wide)

3.6 Calculate Cant

Cant <- Cant %>% 
  mutate(Cant = `delta_coeff_(Intercept)` +
           delta_coeff_aou * aou +
           delta_coeff_oxygen * oxygen +
           delta_coeff_phosphate * phosphate +
           delta_coeff_phosphate_star * phosphate_star +
           delta_coeff_silicate * silicate +
           delta_coeff_salinity * salinity + 
           delta_coeff_temperature * temperature)

Cant_model_average <- Cant %>% 
  mutate(Cant_pos = if_else(Cant < 0, 0, Cant)) %>% 
  group_by(lon, lat, depth, eras, basin) %>% 
  summarise(Cant_mean = mean(Cant),
            Cant_sd = sd(Cant),
            Cant_pos_mean = mean(Cant_pos),
            Cant_pos_sd = sd(Cant_pos),
            gamma_mean = mean(gamma)) %>% 
  ungroup()

Cant_model_average_zonal <- Cant_model_average %>% 
  group_by(lat, depth, eras, basin) %>% 
  summarise(Cant_mean_sd = sd(Cant_mean, na.rm = TRUE),
            Cant_mean = mean(Cant_mean, na.rm = TRUE),
            Cant_sd_mean = mean(Cant_sd, na.rm = TRUE),
            Cant_pos_mean_sd = sd(Cant_pos_mean, na.rm = TRUE),
            Cant_pos_mean = mean(Cant_pos_mean, na.rm = TRUE),
            Cant_pos_sd_mean = mean(Cant_pos_sd, na.rm = TRUE),
            gamma_mean = mean(gamma_mean)) %>% 
  ungroup()

4 Neutral density section

4.1 Mean values

The mean zonal distribution of neutral densities was calculated. CAVEAT: The binning here does not reflect the isoneutral density slabs used for MLR fitting.

Cant_model_average_zonal %>% 
  filter(depth <= 4500,
         lat > -60) %>% 
  ggplot(aes(lat, depth, z = gamma_mean)) +
  geom_contour_filled(binwidth = 0.25) +
  scale_fill_viridis_d(name = "Gamma",
                       direction = -1) +
  scale_y_reverse() +
  coord_cartesian(expand = 0) +
  guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
  facet_grid(basin~eras)

5 Cant sections

5.1 Mean values

Cant_model_average_zonal %>% 
  filter(depth <= 4500,
         lat > -60) %>% 
  ggplot(aes(lat, depth, z = Cant_mean)) +
  geom_contour_fill(breaks = MakeBreaks(5),
                    na.fill = TRUE) +
  scale_fill_divergent(guide = "colorstrip",
                       breaks = MakeBreaks(5),
                       name = "Cant") +
  scale_y_reverse() +
  coord_cartesian(expand = 0) +
  guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
  facet_grid(basin~eras)

5.2 Mean zonal standard deviation across MLR 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.

Cant_model_average_zonal %>% 
  filter(depth <= 4500,
         lat > -60) %>% 
  ggplot(aes(lat, depth, z = Cant_sd_mean)) +
  geom_contour_filled() +
  scale_fill_viridis_d(name = "Cant") +
  scale_y_reverse() +
  coord_cartesian(expand = 0) +
  guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
  facet_grid(basin~eras)

5.3 Zonal standard deviation of mean Cant estimates

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.

Cant_model_average_zonal %>% 
  filter(depth <= 4500,
         lat > -60) %>% 
  ggplot(aes(lat, depth, z = Cant_mean_sd)) +
  geom_contour_filled() +
  scale_fill_viridis_d(name = "Cant") +
  scale_y_reverse() +
  coord_cartesian(expand = 0) +
  guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
  facet_grid(basin~eras)

5.4 Mean positive values

Cant_model_average_zonal %>% 
  filter(depth <= 4500,
         lat > -60) %>% 
  ggplot(aes(lat, depth, z = Cant_pos_mean)) +
  geom_contour_filled() +
  scale_fill_viridis_d(name = "Cant") +
  scale_y_reverse() +
  coord_cartesian(expand = 0) +
  guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
  facet_grid(basin~eras)

6 Cant maps

depth_level_volume <- tibble(
  depth = unique(Cant_model_average_zonal$depth))

depth_level_volume <- depth_level_volume %>% 
  mutate(layer_thickness_above = replace_na((depth - lag(depth)) / 2, 0),
         layer_thickness_below = replace_na((lead(depth) - depth) / 2, 0),
         layer_thickness = layer_thickness_above + layer_thickness_below) %>% 
  select(-c(layer_thickness_above,
         layer_thickness_below))

Cant_model_average <- full_join(Cant_model_average, depth_level_volume)

rm(depth_level_volume)

Cant_model_average <- Cant_model_average %>% 
  mutate(Cant_layer = Cant_mean * layer_thickness)

Cant_inventory <- Cant_model_average %>% 
  filter(depth < 3000,
         Cant_layer >= 0) %>% 
  group_by(lon, lat, basin, eras) %>% 
  summarise(Cant_inventory = sum(Cant_layer, na.rm = TRUE) / 1000) %>% 
  ungroup()

6.1 Depth layers

mapWorld <- borders("world", colour = "gray60", fill = "gray60")

Cant_model_average %>%
  filter(depth %in% c(150, 500, 1000, 3000)) %>% 
  ggplot(aes(lon, lat, fill = Cant_mean)) + 
  mapWorld +
  geom_raster() +
  scale_fill_steps2(breaks = seq(-100,100,10)) +
  guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
  coord_quickmap(expand = 0) +
  facet_grid(depth~eras)

6.2 Inventories

Cant_inventory %>% 
  ggplot(aes(lon, lat, fill = Cant_inventory)) + 
  mapWorld +
  geom_raster() +
  scale_fill_viridis_c() +
  coord_quickmap(expand = 0) +
  facet_wrap(~eras, ncol = 1)

7 Neutral density calculation

GLODAP <- read_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
                                "GLODAP_MLR_fitting_ready.csv"))

cruises_meridional <- c("1041")

GLODAP_cruise <- GLODAP %>% 
  filter(cruise %in% cruises_meridional)


GLODAP_cruise <- GLODAP_cruise %>% 
  mutate(gamma_calc = swRho(salinity = salinity,
                            temperature = temperature,
                            pressure = depth,
                            longitude = lon,
                            latitude = lat,
                            eos = "gsw"))


GLODAP_cruise <- GLODAP_cruise %>% 
  mutate(gamma_calc = gamma_calc - 1000,
         delta_gamma = gamma - gamma_calc)


lat_section <- 
GLODAP_cruise %>%
  ggplot(aes(lat, depth)) +
  scale_y_reverse() +
  scale_color_viridis_c() +
  theme(legend.position = "bottom")

lat_section +
  geom_point(aes(col = gamma))

lat_section +
  geom_point(aes(col = gamma_calc))

lat_section +
  geom_point(aes(col = delta_gamma))

sessionInfo()

R version 4.0.2 (2020-06-22)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18363)

Matrix products: default

locale:
[1] LC_COLLATE=English_Germany.1252  LC_CTYPE=English_Germany.1252   
[3] LC_MONETARY=English_Germany.1252 LC_NUMERIC=C                    
[5] LC_TIME=English_Germany.1252    

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

other attached packages:
 [1] metR_0.7.0      marelac_2.1.10  shape_1.4.4     oce_1.2-0      
 [5] gsw_1.0-5       testthat_2.3.2  lubridate_1.7.9 forcats_0.5.0  
 [9] stringr_1.4.0   dplyr_1.0.0     purrr_0.3.4     readr_1.3.1    
[13] tidyr_1.1.0     tibble_3.0.3    ggplot2_3.3.2   tidyverse_1.3.0
[17] workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] httr_1.4.2        maps_3.3.0        jsonlite_1.7.0    viridisLite_0.3.0
 [5] here_0.1          modelr_0.1.8      assertthat_0.2.1  sp_1.4-2         
 [9] blob_1.2.1        cellranger_1.1.0  yaml_2.2.1        lattice_0.20-41  
[13] pillar_1.4.6      backports_1.1.8   glue_1.4.1        digest_0.6.25    
[17] promises_1.1.1    checkmate_2.0.0   rvest_0.3.6       colorspace_1.4-1 
[21] htmltools_0.5.0   httpuv_1.5.4      plyr_1.8.6        pkgconfig_2.0.3  
[25] broom_0.7.0       seacarb_3.2.13    haven_2.3.1       scales_1.1.1     
[29] whisker_0.4       later_1.1.0.1     git2r_0.27.1      generics_0.0.2   
[33] farver_2.0.3      ellipsis_0.3.1    withr_2.2.0       cli_2.0.2        
[37] magrittr_1.5      crayon_1.3.4      readxl_1.3.1      memoise_1.1.0    
[41] evaluate_0.14     fs_1.4.2          fansi_0.4.1       xml2_1.3.2       
[45] tools_4.0.2       data.table_1.13.0 hms_0.5.3         lifecycle_0.2.0  
[49] munsell_0.5.0     reprex_0.3.0      isoband_0.2.2     compiler_4.0.2   
[53] rlang_0.4.7       grid_4.0.2        rstudioapi_0.11   labeling_0.3     
[57] rmarkdown_2.3     gtable_0.3.0      DBI_1.1.0         R6_2.4.1         
[61] knitr_1.29        rprojroot_1.3-2   stringi_1.4.6     Rcpp_1.0.5       
[65] vctrs_0.3.2       dbplyr_1.4.4      tidyselect_1.1.0  xfun_0.16

Mapping

Jens Daniel Müller

05 August, 2020

1 Required data

2 Join predictor climatologies

2.1 Control plots

2.1.1 GLODAP climatology

2.1.2 WOA13 climatology

2.2 WOA13 + GLODAP

2.2.1 Spatial boundaries

2.2.2 Basin mask

2.2.3 Maps

2.2.4 Predictor profiles

2.3 WOA18 + GLODAP

3 Map Cant

3.1 PO₄* calculation

3.2 AOU climatology

3.2.1 Calculation

3.2.2 Atlantic section

3.3 Isoneutral slabs

3.4 Prepare model coefficients

3.5 Merge model + climatology

3.6 Calculate Cant

4 Neutral density section

4.1 Mean values

5 Cant sections

5.1 Mean values

5.2 Mean zonal standard deviation across MLR models

5.3 Zonal standard deviation of mean Cant estimates

5.4 Mean positive values

6 Cant maps

6.1 Depth layers

6.2 Inventories

7 Neutral density calculation

Mapping

Jens Daniel Müller

05 August, 2020

1 Required data

2 Join predictor climatologies

2.1 Control plots

2.1.1 GLODAP climatology

2.1.2 WOA13 climatology

2.2 WOA13 + GLODAP

2.2.1 Spatial boundaries

2.2.2 Basin mask

2.2.3 Maps

2.2.4 Predictor profiles

2.3 WOA18 + GLODAP

3 Map Cant

3.1 PO4* calculation

3.2 AOU climatology

3.2.1 Calculation

3.2.2 Atlantic section

3.3 Isoneutral slabs

3.4 Prepare model coefficients

3.5 Merge model + climatology

3.6 Calculate Cant

4 Neutral density section

4.1 Mean values

5 Cant sections

5.1 Mean values

5.2 Mean zonal standard deviation across MLR models

5.3 Zonal standard deviation of mean Cant estimates

5.4 Mean positive values

6 Cant maps

6.1 Depth layers

6.2 Inventories

7 Neutral density calculation

3.1 PO₄* calculation