Last updated: 2020-08-12

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Rmd	1ce10e7	jens-daniel-mueller	2020-07-23	read full GLODAP Cant data set rather than joining again
Rmd	0cb3db2	jens-daniel-mueller	2020-07-23	started MLR fitting
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Rmd	6416150	jens-daniel-mueller	2020-07-22	cut gamma into slabs
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Rmd	48cf01f	jens-daniel-mueller	2020-07-22	defined isoneutral slabs
Rmd	32ed280	jens-daniel-mueller	2020-07-22	sign in Cstar delta plot
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Rmd	c398496	jens-daniel-mueller	2020-07-22	plot update
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Rmd	77c9642	jens-daniel-mueller	2020-07-22	formatted plots
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Rmd	8a49adf	jens-daniel-mueller	2020-07-22	adjustment to reference year implemented
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Rmd	d2ed0f8	jens-daniel-mueller	2020-07-21	harmonied lat lon labeling
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Rmd	e688d6e	jens-daniel-mueller	2020-07-19	formating
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Rmd	0992256	jens-daniel-mueller	2020-07-19	plotted individual Cstar terms
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Rmd	e03016e	jens-daniel-mueller	2020-07-14	split read in per data set
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Rmd	dc1c56e	jens-daniel-mueller	2020-07-14	tref calculated
html	b1ece68	jens-daniel-mueller	2020-07-13	Build site.
Rmd	8eb1b22	jens-daniel-mueller	2020-07-13	cleaned data base file
Rmd	9e8f7f1	jens-daniel-mueller	2020-07-13	untracked changes
html	79312b2	jens-daniel-mueller	2020-07-13	Build site.
Rmd	ffbc2a1	jens-daniel-mueller	2020-07-13	added Cstar calculation
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Rmd	e6a2ade	jens-daniel-mueller	2020-07-13	added Cstar calculation

library(tidyverse)
library(lubridate)
library(patchwork)
library(broom)
library(GGally)
library(olsrr)
library(knitr)
library(kableExtra)
library(broom)
library(corrr)

1 Required data

Required are:

GLODAPv2.2020
- cleaned data file
- horizontal grid of sampling coordinates
Cant from GLODAPv2_2016b_MappedClimatologies
annual mean atmospheric pCO₂

GLODAP <- read_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
                              "GLODAPv2.2020_clean.csv"))

GLODAP_obs_grid <- read_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
                                           "GLODAPv2.2020_clean_obs_grid.csv"))

Cant_clim <- read_csv(here::here("data/GLODAPv2_2016b_MappedClimatologies/_summarized_files",
                                 "Cant.csv"))

co2_atm <- read_csv(here::here("data/pCO2_atmosphere/_summarized_data_files",
                               "co2_atm.csv"))

2 C*

C* serves as a conservative tracer of anthropogenic CO₂ uptake. It is derived from measured DIC by removing the impact of

organic matter formation and respiration
calcification and calcium carbonate dissolution

Contributions of those processes are estimated from phosphate and alkalinity concentrations.

2.1 Stoichiometric ratios

rCP <- 117
rNP <- 16

The stoichiometric nutrient ratios for the production and mineralization of organic matter were set to:

C/P: 117
N/P: 16

2.2 Calculation

C* is calculated as:

print("Cstar = tco2  + rCP_phosphate  + talk_05  + rNP_phosphate_05")

[1] "Cstar = tco2  + rCP_phosphate  + talk_05  + rNP_phosphate_05"

GLODAP <- GLODAP %>% 
  mutate(rCP_phosphate = -rCP * phosphate,
         talk_05 = -0.5 * talk,
         rNP_phosphate_05 = -0.5 * rNP * phosphate,
         Cstar = tco2  + rCP_phosphate  + talk_05  + rNP_phosphate_05)

rm(rCP, rNP)

3 PO₄* calculation

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

GLODAP <- GLODAP %>% 
  mutate(phosphate_star = phosphate + (oxygen / 170)  - 1.95)

GLODAP <- GLODAP %>% 
  mutate(phosphate_star = phosphate - 16*nitrate  + 2.9)

4 Reference year adjustment

The reference year adjustment relies on an apriori estimate of Cant at a given location and depth, which is used as a scaling factor for the concurrent change in atmospheric CO₂. The underlying assumption is a transient steady state for the oceanic Cant uptake. Here, Cant from the GLODAP mapped Climatology was used.

Note that eq. 6 in Clement and Gruber (2018) misses pCO₂ pre-industrial in the denominator. Here we use the equation published in Gruber et al. (2019).

4.1 Merge data sets

4.1.1 GLODAP + Cant

Cant_clim <- Cant_clim %>% 
  drop_na()

Cant_clim_obs <- left_join(GLODAP_obs_grid, Cant_clim) %>% 
  select(-n)

rm(Cant_clim, GLODAP_obs_grid)

GLODAP_Cant_obs <- full_join(GLODAP, Cant_clim_obs)

rm(Cant_clim_obs, GLODAP)

The mapped Cant product was merged with GLODAP observation by:

using an identical 1x1° horizontal grid
linear interpolation of Cant from standard to sampling depth

GLODAP_Cant_obs <- GLODAP_Cant_obs %>% 
  group_by(lat, lon) %>% 
  arrange(depth) %>% 
  mutate(Cant_int = approxfun(depth, Cant, rule = 2)(depth)) %>% 
  ungroup()

ggplot() +
    geom_path(data = GLODAP_Cant_obs %>% 
              filter(lat == 48.5, lon == 165.5, !is.na(Cant)) %>% 
              arrange(depth),
            aes(Cant, depth, col = "mapped")) +
  geom_point(data = GLODAP_Cant_obs %>% 
              filter(lat == 48.5, lon == 165.5, !is.na(Cant)) %>% 
              arrange(depth),
            aes(Cant, depth, col = "mapped")) +
  geom_point(data = GLODAP_Cant_obs %>% 
              filter(lat == 48.5, lon == 165.5, date == ymd("2018-06-27")),
            aes(Cant_int, depth, col = "interpolated")) +
  scale_y_reverse() +
  scale_color_brewer(palette = "Dark2", name = "") +
  labs(title = "Cant interpolation to sampling depth - example profile")

GLODAP <- GLODAP_Cant_obs %>% 
  filter(!is.na(Cstar)) %>% 
  mutate(Cant = Cant_int) %>% 
  select(-Cant_int)

rm(GLODAP_Cant_obs)

4.1.2 GLODAP + atm. pCO₂

GLODAP observations were merged with mean annual atmospheric pCO₂ levels by year.

GLODAP <- left_join(GLODAP, co2_atm)

4.2 Calculate adjustment

GLODAP <- GLODAP %>% 
  group_by(era) %>% 
  mutate(tref = median(year)) %>% 
  ungroup()

tref <- GLODAP %>% 
  group_by(era) %>% 
  summarise(year = median(year)) %>% 
  ungroup()

co2_atm_tref <- right_join(co2_atm, tref) %>% 
  select(-year) %>% 
  rename(pCO2_tref = pCO2)

GLODAP <- full_join(GLODAP, co2_atm_tref)

rm(co2_atm, co2_atm_tref, tref)

GLODAP <- GLODAP %>% 
  mutate(Cstar_tref_delta = 
           ((pCO2 - pCO2_tref) / (pCO2_tref - 280)) * Cant,
         Cstar_tref = Cstar - Cstar_tref_delta)

4.3 Control plots

4.3.1 Histogram

GLODAP %>% 
  ggplot(aes(Cstar_tref_delta)) +
  geom_histogram()

4.3.2 Time series

GLODAP %>% 
  sample_n(1e4) %>% 
  ggplot(aes(year, Cstar_tref_delta, col = Cant)) +
  geom_point() +
  scale_color_viridis_c() +
  labs(title = "random subsample 1e4")

5 Selected section plots

A selected section is plotted to demonstrate the magnitude of various parameters and corrections relevant to C*.

cruises_meridional <- c("1041")

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

landmask <- read_csv(here::here("data/World_Ocean_Atlas_2018/_summarized_files",
                                 "land_mask_WOA18.csv"))

GLODAP_cruise %>%
  arrange(date) %>% 
  ggplot(aes(lon, lat)) +
  geom_raster(data = landmask %>% filter(region == "land"),
              aes(lon, lat), fill = "grey80") +
  geom_path() +
  geom_point(aes(col = date)) +
  coord_quickmap(expand = 0) +
  scale_color_viridis_c(trans = "date") +
  labs(title = paste("Cruise year:", mean(GLODAP_cruise$year))) +
  theme(legend.position = "bottom")

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 = tco2))

lat_section +
  geom_point(aes(col = talk))

lat_section +
  geom_point(aes(col = phosphate))

lat_section +
  geom_point(aes(col = rCP_phosphate))

lat_section +
  geom_point(aes(col = talk_05))

lat_section +
  geom_point(aes(col = rNP_phosphate_05))

lat_section +
  geom_point(aes(col = Cstar))

lat_section +
  geom_point(aes(col = Cant))

lat_section +
  geom_point(aes(col = -Cstar_tref_delta))

rm(lat_section, GLODAP_cruise)

6 MLR

6.1 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.

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

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

GLODAP <- bind_rows(GLODAP_Atl, GLODAP_Ind_Pac)

rm(GLODAP_Atl, GLODAP_Ind_Pac, slabs_Atl, slabs_Ind_Pac)

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

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

lat_section +
  geom_point(aes(col = gamma)) +
  scale_color_viridis_c()

lat_section +
  geom_point(aes(col = gamma_slab)) +
  scale_color_viridis_d()

rm(lat_section, GLODAP_cruise, cruises_meridional)

GLODAP %>% 
  ggplot(aes(lat, fill = era)) +
  geom_histogram() +
  facet_grid(gamma_slab~basin)

6.2 Predictor correlation

The correlation between:

pairs of seven potential predictor variables and
C* and seven potential predictor variables

were investigated based on:

property-property plots and
calculated correlation coeffcients.

6.2.1 Correlation plots

For an overview, a random subset of data from all eras was plotted separately for both basins, with color indicating neutral density slabs (high density = dark-purple color).

GLODAP %>% 
  filter(basin == "Atlantic") %>% 
  sample_frac(0.05) %>% 
  ggpairs(columns = c("Cstar",
                      "sal",
                      "tem",
                      "aou",
                      "oxygen",
                      "silicate",
                      "phosphate",
                      "phosphate_star"),
          upper = "blank",
          ggplot2::aes(col = gamma_slab, fill = gamma_slab, alpha = 0.01)) +
      scale_fill_viridis_d(direction = -1) +
      scale_color_viridis_d(direction = -1) +
      labs(title = paste("Basin: Atlantic | era: all | subsample size: 5 % of",
                         nrow(GLODAP %>% filter(basin == "Atlantic"))))

GLODAP %>% 
  filter(basin == "Indo-Pacific") %>% 
  sample_frac(0.05) %>% 
  ggpairs(columns = c("Cstar",
                      "sal",
                      "tem",
                      "aou",
                      "oxygen",
                      "silicate",
                      "phosphate",
                      "phosphate_star"),
          upper = "blank",
          ggplot2::aes(col = gamma_slab, fill = gamma_slab, alpha = 0.01)) +
      scale_fill_viridis_d(direction = -1) +
      scale_color_viridis_d(direction = -1) +
      labs(title = paste("Basin: Indo-Pacific | era: all | subsample size: 5 % of",
                         nrow(GLODAP %>% filter(basin == "Indo-Pacific") )))

Individual correlation plots for each basin, era and neutral density (gamma) slab are available here.

for (i_basin in unique(GLODAP$basin)) {
  for (i_era in unique(GLODAP$era)) {

# i_basin <- unique(GLODAP$basin)[1]
# i_era   <- unique(GLODAP$era)[1]

print(i_basin)
print(i_era)

GLODAP_basin_era <- GLODAP %>% 
  filter(basin == i_basin,
         era == i_era)

for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
  
  # i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[5]
  print(i_gamma_slab)
  
  GLODAP_highlight <- GLODAP_basin_era %>% 
  mutate(gamma_highlight = if_else(gamma_slab == i_gamma_slab,
                                   "in", "out")) %>%
    arrange(desc(gamma_highlight))
  
p <- GLODAP_highlight %>% 
  ggpairs(columns = c("Cstar",
                      "sal",
                      "tem",
                      "aou",
                      "oxygen",
                      "silicate",
                      "phosphate",
                      "phosphate_star"),
          ggplot2::aes(col = gamma_highlight, fill = gamma_highlight, alpha = 0.01)) +
      scale_fill_manual( values = c("red", "grey")) +
      scale_color_manual(values = c("red", "grey")) +
      labs(title = paste(i_basin,
                         "|", i_era,
                         "| Gamma slab", i_gamma_slab,
                         "| # obs total", nrow(GLODAP_basin_era),
                         "| # obs slab", nrow(GLODAP_highlight %>% 
                                             filter(gamma_highlight == "in"))))
  

png(here::here("output/figure/eMLR/predictor_correlation",
               paste("predictor_correlation", i_basin, i_era, i_gamma_slab, ".png", sep = "_")),
    width = 12, height = 12, units = "in", res = 300)

print(p)

dev.off()
  
    }
  }
}

6.2.2 Correlation assesment

6.2.2.1 Calculation of correlation coeffcients

Correlation coefficients were calculated indivdually within each slabs, era and basin.

for (i_basin in unique(GLODAP$basin)) {
  for (i_era in unique(GLODAP$era)) {

# i_basin <- unique(GLODAP$basin)[1]
# i_era   <- unique(GLODAP$era)[1]
print(i_basin)
print(i_era)

GLODAP_basin_era <- GLODAP %>% 
  filter(basin == i_basin,
         era == i_era) %>% 
  select(basin,
         era,
         gamma_slab,
         Cstar,
         sal,
         tem,
         aou,
         oxygen,
         silicate,
         phosphate,
         phosphate_star)

for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
  
  # i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[5]
  print(i_gamma_slab)
  
  GLODAP_basin_era_slab <- GLODAP_basin_era %>%
    filter(gamma_slab == i_gamma_slab)

  cor_Cstar_predictor_temp <- GLODAP_basin_era_slab %>% 
    select(-c(basin, era, gamma_slab)) %>% 
    correlate() %>% 
    focus(Cstar) %>% 
    mutate(basin = i_basin,
       era = i_era,
       gamma_slab = i_gamma_slab)
  
  if (exists("cor_Cstar_predictor")) {
        cor_Cstar_predictor <- bind_rows(cor_Cstar_predictor, cor_Cstar_predictor_temp)
      }
      
    if (!exists("cor_Cstar_predictor")) {
        cor_Cstar_predictor <- cor_Cstar_predictor_temp
    }
  
  
  cor_predictors_temp <- GLODAP_basin_era_slab %>% 
    select(-c(basin, era, gamma_slab)) %>% 
    correlate() %>% 
    shave %>% 
    stretch() %>% 
    filter(!is.na(r),
           x != "Cstar",
           y != "Cstar") %>% 
    mutate(pair = paste(x, y, sep = " + ")) %>% 
    select(-c(x, y)) %>% 
    mutate(basin = i_basin,
       era = i_era,
       gamma_slab = i_gamma_slab)
  
    if (exists("cor_predictors")) {
        cor_predictors <- bind_rows(cor_predictors, cor_predictors_temp)
      }
      
    if (!exists("cor_predictors")) {
        cor_predictors <- cor_predictors_temp
    }
  
  
  
    }
  }
}


cor_predictors %>%
  write_csv(here::here("data/eMLR",
                       "cor_predictors.csv"))

cor_Cstar_predictor %>%
  write_csv(here::here("data/eMLR",
                       "cor_Cstar_predictor.csv"))

rm(cor_predictors_temp, cor_Cstar_predictor_temp,
   i_gamma_slab, i_era, i_basin,
   GLODAP_basin_era, GLODAP_basin_era_slab)

6.2.2.2 Predictor pairs

Below, the range of correlations coefficients for each predictor pair is plotted per basin (facet) and density slab (color). Note that the range indicates the min and max values of in total 3 calculated coefficients (one per era).

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

cor_predictors_stats <- cor_predictors %>% 
  group_by(pair, basin, gamma_slab) %>% 
  summarise(mean_r = mean(r),
            min_r = min(r),
            max_r = max(r)) %>% 
  ungroup()

cor_predictors_stats %>% 
  mutate(pair = reorder(pair, mean_r)) %>%
  ggplot() +
  geom_vline(xintercept = c(-0.9, 0.9), col = "red") +
  geom_vline(xintercept = 0) +
  geom_linerange(
    aes(y = pair, xmin = min_r, xmax = max_r, col = gamma_slab),
    position = position_dodge(width = 0.6)) +
  facet_wrap(~basin) +
  scale_color_viridis_d(direction = -1) +
  labs(x = "correlation coefficient", y = "") +
  theme(legend.position = "top")

kable(cor_predictors_stats) %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

pair	basin	gamma_slab	mean_r	min_r	max_r
aou + oxygen	Atlantic	(-Inf,26]	-0.9181612	-0.9566141	-0.8863166
aou + oxygen	Atlantic	(26,26.5]	-0.9168222	-0.9409620	-0.8987570
aou + oxygen	Atlantic	(26.5,26.75]	-0.9652673	-0.9754904	-0.9501770
aou + oxygen	Atlantic	(26.75,27]	-0.9782180	-0.9856810	-0.9697365
aou + oxygen	Atlantic	(27,27.25]	-0.9744293	-0.9820587	-0.9637201
aou + oxygen	Atlantic	(27.25,27.5]	-0.9522776	-0.9608428	-0.9397143
aou + oxygen	Atlantic	(27.5,27.75]	-0.9303794	-0.9470832	-0.9028461
aou + oxygen	Atlantic	(27.75,27.85]	-0.9772131	-0.9786507	-0.9759298
aou + oxygen	Atlantic	(27.85,27.95]	-0.9893344	-0.9918342	-0.9873376
aou + oxygen	Atlantic	(27.95,28.05]	-0.9889256	-0.9926695	-0.9823756
aou + oxygen	Atlantic	(28.05,28.1]	-0.9893533	-0.9942939	-0.9813655
aou + oxygen	Atlantic	(28.1,28.15]	-0.9938055	-0.9945634	-0.9923620
aou + oxygen	Atlantic	(28.15,28.2]	-0.9981383	-0.9986039	-0.9974366
aou + oxygen	Atlantic	(28.2, Inf]	-0.9785520	-0.9837852	-0.9737943
aou + oxygen	Indo-Pacific	(-Inf,26]	-0.9236143	-0.9667488	-0.8972692
aou + oxygen	Indo-Pacific	(26,26.5]	-0.9808894	-0.9845577	-0.9738178
aou + oxygen	Indo-Pacific	(26.5,26.75]	-0.9853155	-0.9882411	-0.9820234
aou + oxygen	Indo-Pacific	(26.75,27]	-0.9839420	-0.9853368	-0.9830976
aou + oxygen	Indo-Pacific	(27,27.25]	-0.9886685	-0.9928849	-0.9803680
aou + oxygen	Indo-Pacific	(27.25,27.5]	-0.9912493	-0.9952739	-0.9836197
aou + oxygen	Indo-Pacific	(27.5,27.75]	-0.9925089	-0.9967320	-0.9850839
aou + oxygen	Indo-Pacific	(27.75,27.85]	-0.9959869	-0.9989585	-0.9919032
aou + oxygen	Indo-Pacific	(27.85,27.95]	-0.9967344	-0.9990057	-0.9944556
aou + oxygen	Indo-Pacific	(27.95,28.05]	-0.9951746	-0.9964353	-0.9934051
aou + oxygen	Indo-Pacific	(28.05,28.1]	-0.9956092	-0.9966147	-0.9946069
aou + oxygen	Indo-Pacific	(28.1, Inf]	-0.9908817	-0.9923555	-0.9887883
aou + phosphate	Atlantic	(-Inf,26]	0.6488368	0.5161554	0.7417322
aou + phosphate	Atlantic	(26,26.5]	0.7509904	0.5753655	0.9216757
aou + phosphate	Atlantic	(26.5,26.75]	0.8799344	0.8385999	0.9294296
aou + phosphate	Atlantic	(26.75,27]	0.8653866	0.8170427	0.8970329
aou + phosphate	Atlantic	(27,27.25]	0.7961680	0.6776659	0.8599479
aou + phosphate	Atlantic	(27.25,27.5]	0.7214986	0.6277934	0.8023489
aou + phosphate	Atlantic	(27.5,27.75]	0.8384476	0.7895234	0.8678536
aou + phosphate	Atlantic	(27.75,27.85]	0.9466782	0.9405605	0.9553219
aou + phosphate	Atlantic	(27.85,27.95]	0.9573251	0.9478591	0.9688590
aou + phosphate	Atlantic	(27.95,28.05]	0.9643270	0.9511925	0.9862507
aou + phosphate	Atlantic	(28.05,28.1]	0.9705710	0.9555563	0.9871036
aou + phosphate	Atlantic	(28.1,28.15]	0.9805780	0.9784785	0.9841974
aou + phosphate	Atlantic	(28.15,28.2]	0.9922852	0.9889823	0.9946912
aou + phosphate	Atlantic	(28.2, Inf]	0.8184560	0.7760113	0.8773826
aou + phosphate	Indo-Pacific	(-Inf,26]	0.9430311	0.9128374	0.9696641
aou + phosphate	Indo-Pacific	(26,26.5]	0.9553162	0.9491949	0.9640881
aou + phosphate	Indo-Pacific	(26.5,26.75]	0.9515877	0.9393080	0.9638471
aou + phosphate	Indo-Pacific	(26.75,27]	0.9505203	0.9459297	0.9539790
aou + phosphate	Indo-Pacific	(27,27.25]	0.9664795	0.9484998	0.9806798
aou + phosphate	Indo-Pacific	(27.25,27.5]	0.9709204	0.9520615	0.9803746
aou + phosphate	Indo-Pacific	(27.5,27.75]	0.9749164	0.9603843	0.9823181
aou + phosphate	Indo-Pacific	(27.75,27.85]	0.9822762	0.9736000	0.9883639
aou + phosphate	Indo-Pacific	(27.85,27.95]	0.9801007	0.9706154	0.9891580
aou + phosphate	Indo-Pacific	(27.95,28.05]	0.9675386	0.9569900	0.9761508
aou + phosphate	Indo-Pacific	(28.05,28.1]	0.9573078	0.9443355	0.9715225
aou + phosphate	Indo-Pacific	(28.1, Inf]	0.7805310	0.7289653	0.8296450
aou + phosphate_star	Atlantic	(-Inf,26]	-0.8923905	-0.9183924	-0.8772572
aou + phosphate_star	Atlantic	(26,26.5]	-0.8933367	-0.9384669	-0.8343264
aou + phosphate_star	Atlantic	(26.5,26.75]	-0.9492546	-0.9748982	-0.9362400
aou + phosphate_star	Atlantic	(26.75,27]	-0.9315267	-0.9493338	-0.9014717
aou + phosphate_star	Atlantic	(27,27.25]	-0.8647670	-0.9128106	-0.7698567
aou + phosphate_star	Atlantic	(27.25,27.5]	-0.7824957	-0.8505337	-0.6946999
aou + phosphate_star	Atlantic	(27.5,27.75]	-0.8623106	-0.8929301	-0.8168445
aou + phosphate_star	Atlantic	(27.75,27.85]	-0.9559132	-0.9597149	-0.9518413
aou + phosphate_star	Atlantic	(27.85,27.95]	-0.9618303	-0.9712720	-0.9520253
aou + phosphate_star	Atlantic	(27.95,28.05]	-0.9658849	-0.9857587	-0.9533034
aou + phosphate_star	Atlantic	(28.05,28.1]	-0.9737469	-0.9844808	-0.9608342
aou + phosphate_star	Atlantic	(28.1,28.15]	-0.9852890	-0.9886459	-0.9811148
aou + phosphate_star	Atlantic	(28.15,28.2]	-0.9920551	-0.9960114	-0.9883376
aou + phosphate_star	Atlantic	(28.2, Inf]	-0.8179057	-0.8785730	-0.7796276
aou + phosphate_star	Indo-Pacific	(-Inf,26]	-0.9215305	-0.9609277	-0.8846722
aou + phosphate_star	Indo-Pacific	(26,26.5]	-0.9062277	-0.9170201	-0.8982568
aou + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.9168439	-0.9322594	-0.8962566
aou + phosphate_star	Indo-Pacific	(26.75,27]	-0.9396358	-0.9428877	-0.9350229
aou + phosphate_star	Indo-Pacific	(27,27.25]	-0.9461166	-0.9705723	-0.9005201
aou + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.9421992	-0.9742031	-0.8784340
aou + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.9495700	-0.9817387	-0.8930001
aou + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.9702798	-0.9908660	-0.9392251
aou + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.9751755	-0.9916509	-0.9564150
aou + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.9618317	-0.9786594	-0.9435386
aou + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.9526787	-0.9739551	-0.9313490
aou + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.7844217	-0.8642836	-0.7212390
aou + silicate	Atlantic	(-Inf,26]	0.2654543	0.0884202	0.4145649
aou + silicate	Atlantic	(26,26.5]	0.6747329	0.5172910	0.8265329
aou + silicate	Atlantic	(26.5,26.75]	0.8953646	0.8608648	0.9291670
aou + silicate	Atlantic	(26.75,27]	0.8767545	0.8429220	0.9015240
aou + silicate	Atlantic	(27,27.25]	0.7587540	0.6532535	0.8355002
aou + silicate	Atlantic	(27.25,27.5]	0.5181865	0.4038500	0.6853791
aou + silicate	Atlantic	(27.5,27.75]	0.6086402	0.5720276	0.6699890
aou + silicate	Atlantic	(27.75,27.85]	0.8515955	0.8448051	0.8642328
aou + silicate	Atlantic	(27.85,27.95]	0.8977712	0.8893889	0.9121609
aou + silicate	Atlantic	(27.95,28.05]	0.9473367	0.9366867	0.9638062
aou + silicate	Atlantic	(28.05,28.1]	0.9710848	0.9618608	0.9826435
aou + silicate	Atlantic	(28.1,28.15]	0.9768582	0.9752126	0.9792466
aou + silicate	Atlantic	(28.15,28.2]	0.9911038	0.9862753	0.9955321
aou + silicate	Atlantic	(28.2, Inf]	0.8287733	0.7792842	0.8681030
aou + silicate	Indo-Pacific	(-Inf,26]	0.7341802	0.6585781	0.8063089
aou + silicate	Indo-Pacific	(26,26.5]	0.6560246	0.5381656	0.7585899
aou + silicate	Indo-Pacific	(26.5,26.75]	0.6155266	0.4093259	0.7404216
aou + silicate	Indo-Pacific	(26.75,27]	0.7499497	0.6938246	0.7795344
aou + silicate	Indo-Pacific	(27,27.25]	0.8632804	0.8054567	0.9080507
aou + silicate	Indo-Pacific	(27.25,27.5]	0.8983801	0.8521049	0.9373634
aou + silicate	Indo-Pacific	(27.5,27.75]	0.9184567	0.8664890	0.9528226
aou + silicate	Indo-Pacific	(27.75,27.85]	0.9668533	0.9508782	0.9761360
aou + silicate	Indo-Pacific	(27.85,27.95]	0.9642729	0.9543989	0.9707377
aou + silicate	Indo-Pacific	(27.95,28.05]	0.9491873	0.9415492	0.9533539
aou + silicate	Indo-Pacific	(28.05,28.1]	0.9486127	0.9459875	0.9528102
aou + silicate	Indo-Pacific	(28.1, Inf]	0.6263672	0.5401927	0.6694759
oxygen + phosphate	Atlantic	(-Inf,26]	-0.4412587	-0.6061311	-0.3072346
oxygen + phosphate	Atlantic	(26,26.5]	-0.4575598	-0.7627491	-0.1724774
oxygen + phosphate	Atlantic	(26.5,26.75]	-0.7300061	-0.8281720	-0.6306966
oxygen + phosphate	Atlantic	(26.75,27]	-0.7453860	-0.8115376	-0.6537454
oxygen + phosphate	Atlantic	(27,27.25]	-0.6443769	-0.7382896	-0.4603906
oxygen + phosphate	Atlantic	(27.25,27.5]	-0.4827029	-0.6095132	-0.3297344
oxygen + phosphate	Atlantic	(27.5,27.75]	-0.5966809	-0.6749872	-0.4653694
oxygen + phosphate	Atlantic	(27.75,27.85]	-0.8629912	-0.8760309	-0.8562542
oxygen + phosphate	Atlantic	(27.85,27.95]	-0.9109015	-0.9348224	-0.8915953
oxygen + phosphate	Atlantic	(27.95,28.05]	-0.9275300	-0.9680297	-0.8866843
oxygen + phosphate	Atlantic	(28.05,28.1]	-0.9356801	-0.9742818	-0.8890527
oxygen + phosphate	Atlantic	(28.1,28.15]	-0.9594641	-0.9679879	-0.9515113
oxygen + phosphate	Atlantic	(28.15,28.2]	-0.9886288	-0.9933712	-0.9803690
oxygen + phosphate	Atlantic	(28.2, Inf]	-0.7033246	-0.7805874	-0.6632504
oxygen + phosphate	Indo-Pacific	(-Inf,26]	-0.7929968	-0.9142219	-0.7019392
oxygen + phosphate	Indo-Pacific	(26,26.5]	-0.8862491	-0.9082971	-0.8593493
oxygen + phosphate	Indo-Pacific	(26.5,26.75]	-0.8901984	-0.9168553	-0.8726298
oxygen + phosphate	Indo-Pacific	(26.75,27]	-0.8841471	-0.8898956	-0.8744815
oxygen + phosphate	Indo-Pacific	(27,27.25]	-0.9235393	-0.9561043	-0.8761859
oxygen + phosphate	Indo-Pacific	(27.25,27.5]	-0.9422463	-0.9674903	-0.8950246
oxygen + phosphate	Indo-Pacific	(27.5,27.75]	-0.9578123	-0.9797089	-0.9221370
oxygen + phosphate	Indo-Pacific	(27.75,27.85]	-0.9752401	-0.9887694	-0.9585316
oxygen + phosphate	Indo-Pacific	(27.85,27.95]	-0.9720875	-0.9878715	-0.9582296
oxygen + phosphate	Indo-Pacific	(27.95,28.05]	-0.9467136	-0.9591235	-0.9309152
oxygen + phosphate	Indo-Pacific	(28.05,28.1]	-0.9338575	-0.9526139	-0.9222755
oxygen + phosphate	Indo-Pacific	(28.1, Inf]	-0.7020610	-0.7608328	-0.6369693
oxygen + phosphate_star	Atlantic	(-Inf,26]	0.7865517	0.7327100	0.8180245
oxygen + phosphate_star	Atlantic	(26,26.5]	0.6681961	0.5374254	0.7834098
oxygen + phosphate_star	Atlantic	(26.5,26.75]	0.8415472	0.7883927	0.9061182
oxygen + phosphate_star	Atlantic	(26.75,27]	0.8386104	0.7712405	0.8848335
oxygen + phosphate_star	Atlantic	(27,27.25]	0.7343223	0.5760302	0.8197204
oxygen + phosphate_star	Atlantic	(27.25,27.5]	0.5628038	0.4135220	0.6758859
oxygen + phosphate_star	Atlantic	(27.5,27.75]	0.6349337	0.5085658	0.7151415
oxygen + phosphate_star	Atlantic	(27.75,27.85]	0.8786350	0.8750420	0.8839863
oxygen + phosphate_star	Atlantic	(27.85,27.95]	0.9183379	0.8980476	0.9397390
oxygen + phosphate_star	Atlantic	(27.95,28.05]	0.9312940	0.8914315	0.9693612
oxygen + phosphate_star	Atlantic	(28.05,28.1]	0.9410425	0.8985993	0.9724058
oxygen + phosphate_star	Atlantic	(28.1,28.15]	0.9675592	0.9564225	0.9760167
oxygen + phosphate_star	Atlantic	(28.15,28.2]	0.9887973	0.9809134	0.9939642
oxygen + phosphate_star	Atlantic	(28.2, Inf]	0.7046203	0.6583356	0.7831452
oxygen + phosphate_star	Indo-Pacific	(-Inf,26]	0.7330805	0.6222680	0.8846818
oxygen + phosphate_star	Indo-Pacific	(26,26.5]	0.8225764	0.7896305	0.8506652
oxygen + phosphate_star	Indo-Pacific	(26.5,26.75]	0.8486576	0.8253500	0.8776107
oxygen + phosphate_star	Indo-Pacific	(26.75,27]	0.8723411	0.8687001	0.8750640
oxygen + phosphate_star	Indo-Pacific	(27,27.25]	0.8964122	0.8102509	0.9435023
oxygen + phosphate_star	Indo-Pacific	(27.25,27.5]	0.9016707	0.7909855	0.9583043
oxygen + phosphate_star	Indo-Pacific	(27.5,27.75]	0.9176698	0.8195438	0.9751664
oxygen + phosphate_star	Indo-Pacific	(27.75,27.85]	0.9538054	0.9019055	0.9889471
oxygen + phosphate_star	Indo-Pacific	(27.85,27.95]	0.9621937	0.9323389	0.9896092
oxygen + phosphate_star	Indo-Pacific	(27.95,28.05]	0.9384194	0.9108558	0.9621106
oxygen + phosphate_star	Indo-Pacific	(28.05,28.1]	0.9266754	0.9040632	0.9550349
oxygen + phosphate_star	Indo-Pacific	(28.1, Inf]	0.7061323	0.6301705	0.7991590
oxygen + silicate	Atlantic	(-Inf,26]	-0.0202925	-0.1715993	0.1534811
oxygen + silicate	Atlantic	(26,26.5]	-0.3941576	-0.6443663	-0.1482352
oxygen + silicate	Atlantic	(26.5,26.75]	-0.7701318	-0.8436954	-0.6846121
oxygen + silicate	Atlantic	(26.75,27]	-0.7780682	-0.8302180	-0.7139144
oxygen + silicate	Atlantic	(27,27.25]	-0.6142032	-0.7169366	-0.4522280
oxygen + silicate	Atlantic	(27.25,27.5]	-0.2596380	-0.4764353	-0.0923371
oxygen + silicate	Atlantic	(27.5,27.75]	-0.3185453	-0.4360723	-0.2092809
oxygen + silicate	Atlantic	(27.75,27.85]	-0.7407622	-0.7579846	-0.7298223
oxygen + silicate	Atlantic	(27.85,27.95]	-0.8322018	-0.8599509	-0.8161961
oxygen + silicate	Atlantic	(27.95,28.05]	-0.8965103	-0.9290503	-0.8615934
oxygen + silicate	Atlantic	(28.05,28.1]	-0.9316667	-0.9616389	-0.8975675
oxygen + silicate	Atlantic	(28.1,28.15]	-0.9522411	-0.9528684	-0.9511337
oxygen + silicate	Atlantic	(28.15,28.2]	-0.9869917	-0.9916129	-0.9808054
oxygen + silicate	Atlantic	(28.2, Inf]	-0.7163708	-0.7458716	-0.6760719
oxygen + silicate	Indo-Pacific	(-Inf,26]	-0.5098696	-0.7068590	-0.3570615
oxygen + silicate	Indo-Pacific	(26,26.5]	-0.5383409	-0.6683985	-0.4175494
oxygen + silicate	Indo-Pacific	(26.5,26.75]	-0.4977414	-0.6493148	-0.2746742
oxygen + silicate	Indo-Pacific	(26.75,27]	-0.6373246	-0.6739034	-0.5683559
oxygen + silicate	Indo-Pacific	(27,27.25]	-0.7925279	-0.8597847	-0.6943939
oxygen + silicate	Indo-Pacific	(27.25,27.5]	-0.8475756	-0.9066026	-0.7684755
oxygen + silicate	Indo-Pacific	(27.5,27.75]	-0.8776475	-0.9290188	-0.7911157
oxygen + silicate	Indo-Pacific	(27.75,27.85]	-0.9512889	-0.9721552	-0.9203932
oxygen + silicate	Indo-Pacific	(27.85,27.95]	-0.9499935	-0.9648651	-0.9322933
oxygen + silicate	Indo-Pacific	(27.95,28.05]	-0.9243300	-0.9323370	-0.9106410
oxygen + silicate	Indo-Pacific	(28.05,28.1]	-0.9254025	-0.9263804	-0.9236258
oxygen + silicate	Indo-Pacific	(28.1, Inf]	-0.5374285	-0.5927076	-0.4299572
phosphate + phosphate_star	Atlantic	(-Inf,26]	-0.7246652	-0.7603510	-0.7003933
phosphate + phosphate_star	Atlantic	(26,26.5]	-0.9255695	-0.9886250	-0.8893376
phosphate + phosphate_star	Atlantic	(26.5,26.75]	-0.9766255	-0.9818145	-0.9666308
phosphate + phosphate_star	Atlantic	(26.75,27]	-0.9825627	-0.9850995	-0.9801916
phosphate + phosphate_star	Atlantic	(27,27.25]	-0.9875967	-0.9903419	-0.9843432
phosphate + phosphate_star	Atlantic	(27.25,27.5]	-0.9921676	-0.9935190	-0.9909282
phosphate + phosphate_star	Atlantic	(27.5,27.75]	-0.9959024	-0.9964220	-0.9956397
phosphate + phosphate_star	Atlantic	(27.75,27.85]	-0.9968701	-0.9977268	-0.9963606
phosphate + phosphate_star	Atlantic	(27.85,27.95]	-0.9949163	-0.9958776	-0.9940222
phosphate + phosphate_star	Atlantic	(27.95,28.05]	-0.9938602	-0.9953857	-0.9913353
phosphate + phosphate_star	Atlantic	(28.05,28.1]	-0.9928625	-0.9940815	-0.9905919
phosphate + phosphate_star	Atlantic	(28.1,28.15]	-0.9952762	-0.9964594	-0.9932125
phosphate + phosphate_star	Atlantic	(28.15,28.2]	-0.9969649	-0.9977864	-0.9963027
phosphate + phosphate_star	Atlantic	(28.2, Inf]	-0.9889567	-0.9949464	-0.9786039
phosphate + phosphate_star	Indo-Pacific	(-Inf,26]	-0.9698752	-0.9769677	-0.9611886
phosphate + phosphate_star	Indo-Pacific	(26,26.5]	-0.9526861	-0.9600135	-0.9469746
phosphate + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.9596354	-0.9701601	-0.9479436
phosphate + phosphate_star	Indo-Pacific	(26.75,27]	-0.9834628	-0.9895121	-0.9802433
phosphate + phosphate_star	Indo-Pacific	(27,27.25]	-0.9820325	-0.9919428	-0.9671313
phosphate + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.9817667	-0.9925823	-0.9619816
phosphate + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.9784779	-0.9935614	-0.9500403
phosphate + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.9787389	-0.9939804	-0.9514364
phosphate + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.9823503	-0.9951048	-0.9615154
phosphate + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.9818528	-0.9931431	-0.9678949
phosphate + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.9776019	-0.9880526	-0.9620262
phosphate + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.9350647	-0.9730936	-0.8781849
sal + aou	Atlantic	(-Inf,26]	-0.0452495	-0.3257778	0.3355069
sal + aou	Atlantic	(26,26.5]	-0.1316899	-0.2309276	0.0334238
sal + aou	Atlantic	(26.5,26.75]	-0.3436234	-0.5297627	-0.1936560
sal + aou	Atlantic	(26.75,27]	-0.2274688	-0.2786631	-0.1798969
sal + aou	Atlantic	(27,27.25]	-0.1722725	-0.3548045	0.0243317
sal + aou	Atlantic	(27.25,27.5]	-0.1716808	-0.3370859	-0.0600930
sal + aou	Atlantic	(27.5,27.75]	-0.4656439	-0.4956237	-0.4140142
sal + aou	Atlantic	(27.75,27.85]	-0.5438494	-0.6028770	-0.4959685
sal + aou	Atlantic	(27.85,27.95]	-0.3566450	-0.5027073	-0.1656048
sal + aou	Atlantic	(27.95,28.05]	-0.5444684	-0.7924660	-0.2117975
sal + aou	Atlantic	(28.05,28.1]	-0.7479505	-0.8681681	-0.6651277
sal + aou	Atlantic	(28.1,28.15]	-0.8326742	-0.8705770	-0.7857761
sal + aou	Atlantic	(28.15,28.2]	-0.9536576	-0.9757986	-0.9232777
sal + aou	Atlantic	(28.2, Inf]	-0.5299343	-0.7118279	-0.4183440
sal + aou	Indo-Pacific	(-Inf,26]	-0.1007275	-0.1348394	-0.0327037
sal + aou	Indo-Pacific	(26,26.5]	-0.0462443	-0.2484904	0.1341664
sal + aou	Indo-Pacific	(26.5,26.75]	-0.0499808	-0.3662272	0.2662912
sal + aou	Indo-Pacific	(26.75,27]	-0.1465444	-0.3473383	0.0457714
sal + aou	Indo-Pacific	(27,27.25]	-0.0664612	-0.1869272	0.1660639
sal + aou	Indo-Pacific	(27.25,27.5]	0.1235788	0.0311502	0.2796906
sal + aou	Indo-Pacific	(27.5,27.75]	0.0539318	-0.0757758	0.2444715
sal + aou	Indo-Pacific	(27.75,27.85]	-0.1591760	-0.4051461	0.1020511
sal + aou	Indo-Pacific	(27.85,27.95]	-0.3664921	-0.6902419	-0.1163589
sal + aou	Indo-Pacific	(27.95,28.05]	-0.3710596	-0.4619637	-0.2457736
sal + aou	Indo-Pacific	(28.05,28.1]	-0.4568953	-0.5848017	-0.3673960
sal + aou	Indo-Pacific	(28.1, Inf]	0.4000127	0.2765693	0.4836507
sal + oxygen	Atlantic	(-Inf,26]	-0.3109640	-0.5824114	-0.0830958
sal + oxygen	Atlantic	(26,26.5]	-0.2558098	-0.4586109	-0.0978965
sal + oxygen	Atlantic	(26.5,26.75]	0.0954246	-0.0452345	0.3329757
sal + oxygen	Atlantic	(26.75,27]	0.0271900	-0.0618028	0.0825327
sal + oxygen	Atlantic	(27,27.25]	-0.0428928	-0.2848910	0.1542667
sal + oxygen	Atlantic	(27.25,27.5]	-0.1247762	-0.2755115	0.0699327
sal + oxygen	Atlantic	(27.5,27.75]	0.1285747	0.0007210	0.2049111
sal + oxygen	Atlantic	(27.75,27.85]	0.3596203	0.2998878	0.4260460
sal + oxygen	Atlantic	(27.85,27.95]	0.2285522	0.0268688	0.3965104
sal + oxygen	Atlantic	(27.95,28.05]	0.4435389	0.1139659	0.7289259
sal + oxygen	Atlantic	(28.05,28.1]	0.6554291	0.5677434	0.8196414
sal + oxygen	Atlantic	(28.1,28.15]	0.7693824	0.7201298	0.8169252
sal + oxygen	Atlantic	(28.15,28.2]	0.9361833	0.8965298	0.9637406
sal + oxygen	Atlantic	(28.2, Inf]	0.3650789	0.2179548	0.5646201
sal + oxygen	Indo-Pacific	(-Inf,26]	-0.2050939	-0.3225624	-0.0853819
sal + oxygen	Indo-Pacific	(26,26.5]	-0.1331539	-0.2879960	0.0333019
sal + oxygen	Indo-Pacific	(26.5,26.75]	-0.1105800	-0.4189153	0.1874838
sal + oxygen	Indo-Pacific	(26.75,27]	-0.0254177	-0.2113746	0.1739144
sal + oxygen	Indo-Pacific	(27,27.25]	-0.0704212	-0.3515906	0.0755114
sal + oxygen	Indo-Pacific	(27.25,27.5]	-0.2325910	-0.4392475	-0.1152695
sal + oxygen	Indo-Pacific	(27.5,27.75]	-0.1397071	-0.3924178	0.0324730
sal + oxygen	Indo-Pacific	(27.75,27.85]	0.0892654	-0.2197215	0.3778925
sal + oxygen	Indo-Pacific	(27.85,27.95]	0.3099987	0.0234029	0.6777124
sal + oxygen	Indo-Pacific	(27.95,28.05]	0.2958454	0.1485588	0.4038045
sal + oxygen	Indo-Pacific	(28.05,28.1]	0.3810227	0.2769292	0.5276693
sal + oxygen	Indo-Pacific	(28.1, Inf]	-0.4958183	-0.5911751	-0.3703990
sal + phosphate	Atlantic	(-Inf,26]	-0.5368678	-0.7820996	-0.3151151
sal + phosphate	Atlantic	(26,26.5]	-0.6861720	-0.7694493	-0.5227085
sal + phosphate	Atlantic	(26.5,26.75]	-0.7286769	-0.7958907	-0.6260673
sal + phosphate	Atlantic	(26.75,27]	-0.6705112	-0.7056194	-0.6198328
sal + phosphate	Atlantic	(27,27.25]	-0.7145275	-0.7748703	-0.6639096
sal + phosphate	Atlantic	(27.25,27.5]	-0.7876444	-0.8205324	-0.7418126
sal + phosphate	Atlantic	(27.5,27.75]	-0.8352052	-0.8445523	-0.8291386
sal + phosphate	Atlantic	(27.75,27.85]	-0.7551779	-0.7831275	-0.7242229
sal + phosphate	Atlantic	(27.85,27.95]	-0.5751115	-0.6726756	-0.4171452
sal + phosphate	Atlantic	(27.95,28.05]	-0.6954715	-0.8503110	-0.4308056
sal + phosphate	Atlantic	(28.05,28.1]	-0.8442799	-0.9056577	-0.7678284
sal + phosphate	Atlantic	(28.1,28.15]	-0.8938608	-0.9149390	-0.8537034
sal + phosphate	Atlantic	(28.15,28.2]	-0.9592330	-0.9685939	-0.9542868
sal + phosphate	Atlantic	(28.2, Inf]	-0.8964793	-0.9415770	-0.8474669
sal + phosphate	Indo-Pacific	(-Inf,26]	-0.2198128	-0.2517569	-0.1978531
sal + phosphate	Indo-Pacific	(26,26.5]	-0.2788263	-0.4965027	-0.1021091
sal + phosphate	Indo-Pacific	(26.5,26.75]	-0.3024912	-0.6026729	-0.0366340
sal + phosphate	Indo-Pacific	(26.75,27]	-0.4017141	-0.6011400	-0.2166537
sal + phosphate	Indo-Pacific	(27,27.25]	-0.2502806	-0.3556547	-0.0875812
sal + phosphate	Indo-Pacific	(27.25,27.5]	0.0124007	-0.0277407	0.0674829
sal + phosphate	Indo-Pacific	(27.5,27.75]	-0.0070455	-0.0695993	0.1069794
sal + phosphate	Indo-Pacific	(27.75,27.85]	-0.1826353	-0.3793168	0.0529917
sal + phosphate	Indo-Pacific	(27.85,27.95]	-0.4106655	-0.6925250	-0.1626217
sal + phosphate	Indo-Pacific	(27.95,28.05]	-0.5116451	-0.5966346	-0.3879426
sal + phosphate	Indo-Pacific	(28.05,28.1]	-0.6183353	-0.7160040	-0.5687749
sal + phosphate	Indo-Pacific	(28.1, Inf]	-0.1340679	-0.2265805	-0.0753210
sal + phosphate_star	Atlantic	(-Inf,26]	0.1998114	-0.0441654	0.3224651
sal + phosphate_star	Atlantic	(26,26.5]	0.4669722	0.4252582	0.4991462
sal + phosphate_star	Atlantic	(26.5,26.75]	0.5841224	0.4822478	0.6822662
sal + phosphate_star	Atlantic	(26.75,27]	0.5408556	0.4969719	0.5683795
sal + phosphate_star	Atlantic	(27,27.25]	0.6152328	0.5573508	0.6941158
sal + phosphate_star	Atlantic	(27.25,27.5]	0.7265547	0.6672941	0.7688312
sal + phosphate_star	Atlantic	(27.5,27.75]	0.8094865	0.7999244	0.8184019
sal + phosphate_star	Atlantic	(27.75,27.85]	0.7335917	0.6948847	0.7727746
sal + phosphate_star	Atlantic	(27.85,27.95]	0.5573448	0.3908420	0.6585912
sal + phosphate_star	Atlantic	(27.95,28.05]	0.6864666	0.4188034	0.8436039
sal + phosphate_star	Atlantic	(28.05,28.1]	0.8332615	0.7550822	0.8997839
sal + phosphate_star	Atlantic	(28.1,28.15]	0.8799648	0.8373786	0.9045802
sal + phosphate_star	Atlantic	(28.15,28.2]	0.9568581	0.9479875	0.9635437
sal + phosphate_star	Atlantic	(28.2, Inf]	0.8918222	0.8425701	0.9411809
sal + phosphate_star	Indo-Pacific	(-Inf,26]	0.3534643	0.3127014	0.3794176
sal + phosphate_star	Indo-Pacific	(26,26.5]	0.3606897	0.1968814	0.5708911
sal + phosphate_star	Indo-Pacific	(26.5,26.75]	0.3483125	0.0794106	0.6374159
sal + phosphate_star	Indo-Pacific	(26.75,27]	0.4109705	0.2625066	0.5868281
sal + phosphate_star	Indo-Pacific	(27,27.25]	0.2892141	0.2085420	0.3456438
sal + phosphate_star	Indo-Pacific	(27.25,27.5]	0.0672090	0.0209922	0.1333828
sal + phosphate_star	Indo-Pacific	(27.5,27.75]	0.1147146	0.0936756	0.1255064
sal + phosphate_star	Indo-Pacific	(27.75,27.85]	0.2840688	0.1511085	0.4227808
sal + phosphate_star	Indo-Pacific	(27.85,27.95]	0.4744299	0.3011865	0.7065521
sal + phosphate_star	Indo-Pacific	(27.95,28.05]	0.5405203	0.4647126	0.5871297
sal + phosphate_star	Indo-Pacific	(28.05,28.1]	0.6419724	0.5867936	0.7125517
sal + phosphate_star	Indo-Pacific	(28.1, Inf]	0.1268535	0.1031580	0.1682807
sal + silicate	Atlantic	(-Inf,26]	-0.7139001	-0.7950883	-0.6725144
sal + silicate	Atlantic	(26,26.5]	-0.6824066	-0.7243435	-0.6125911
sal + silicate	Atlantic	(26.5,26.75]	-0.6350098	-0.7294011	-0.5055632
sal + silicate	Atlantic	(26.75,27]	-0.5545102	-0.5946755	-0.5155890
sal + silicate	Atlantic	(27,27.25]	-0.6607943	-0.7124112	-0.6219032
sal + silicate	Atlantic	(27.25,27.5]	-0.7972274	-0.8097390	-0.7859144
sal + silicate	Atlantic	(27.5,27.75]	-0.8197880	-0.8386444	-0.8101704
sal + silicate	Atlantic	(27.75,27.85]	-0.7884695	-0.8228682	-0.7518060
sal + silicate	Atlantic	(27.85,27.95]	-0.6617053	-0.7465839	-0.5237283
sal + silicate	Atlantic	(27.95,28.05]	-0.7307836	-0.8883221	-0.4777178
sal + silicate	Atlantic	(28.05,28.1]	-0.8591589	-0.9274773	-0.7987466
sal + silicate	Atlantic	(28.1,28.15]	-0.9053625	-0.9385148	-0.8708267
sal + silicate	Atlantic	(28.15,28.2]	-0.9565403	-0.9729301	-0.9307135
sal + silicate	Atlantic	(28.2, Inf]	-0.8546034	-0.9653379	-0.7751529
sal + silicate	Indo-Pacific	(-Inf,26]	-0.5269882	-0.5731307	-0.4408109
sal + silicate	Indo-Pacific	(26,26.5]	-0.5615187	-0.6829091	-0.4549151
sal + silicate	Indo-Pacific	(26.5,26.75]	-0.6677445	-0.8098948	-0.5567328
sal + silicate	Indo-Pacific	(26.75,27]	-0.6562476	-0.7628181	-0.4768095
sal + silicate	Indo-Pacific	(27,27.25]	-0.4573032	-0.5470162	-0.3205614
sal + silicate	Indo-Pacific	(27.25,27.5]	-0.1630008	-0.2354897	-0.0874834
sal + silicate	Indo-Pacific	(27.5,27.75]	-0.0820400	-0.1062914	-0.0579965
sal + silicate	Indo-Pacific	(27.75,27.85]	-0.2108744	-0.3571247	-0.0466023
sal + silicate	Indo-Pacific	(27.85,27.95]	-0.3894004	-0.6239515	-0.2031514
sal + silicate	Indo-Pacific	(27.95,28.05]	-0.4335087	-0.4910533	-0.3501070
sal + silicate	Indo-Pacific	(28.05,28.1]	-0.5445378	-0.6170559	-0.4767160
sal + silicate	Indo-Pacific	(28.1, Inf]	-0.0734950	-0.1703735	0.0732319
sal + tem	Atlantic	(-Inf,26]	0.9207161	0.8381654	0.9786562
sal + tem	Atlantic	(26,26.5]	0.9600524	0.9470189	0.9717127
sal + tem	Atlantic	(26.5,26.75]	0.9866701	0.9811261	0.9902331
sal + tem	Atlantic	(26.75,27]	0.9794774	0.9741859	0.9843463
sal + tem	Atlantic	(27,27.25]	0.9773384	0.9758270	0.9794429
sal + tem	Atlantic	(27.25,27.5]	0.9728298	0.9698213	0.9754742
sal + tem	Atlantic	(27.5,27.75]	0.9596412	0.9556522	0.9622929
sal + tem	Atlantic	(27.75,27.85]	0.9789351	0.9753679	0.9808720
sal + tem	Atlantic	(27.85,27.95]	0.9441199	0.9369742	0.9480091
sal + tem	Atlantic	(27.95,28.05]	0.8823423	0.8069203	0.9317987
sal + tem	Atlantic	(28.05,28.1]	0.9497597	0.9127320	0.9685717
sal + tem	Atlantic	(28.1,28.15]	0.9486238	0.9195421	0.9706795
sal + tem	Atlantic	(28.15,28.2]	0.8825453	0.8477644	0.9035039
sal + tem	Atlantic	(28.2, Inf]	0.4658301	0.3653252	0.6272068
sal + tem	Indo-Pacific	(-Inf,26]	0.7708979	0.7410815	0.8182287
sal + tem	Indo-Pacific	(26,26.5]	0.9287394	0.8853113	0.9530410
sal + tem	Indo-Pacific	(26.5,26.75]	0.9782800	0.9690919	0.9832747
sal + tem	Indo-Pacific	(26.75,27]	0.9768591	0.9720313	0.9799282
sal + tem	Indo-Pacific	(27,27.25]	0.9501819	0.9326539	0.9710015
sal + tem	Indo-Pacific	(27.25,27.5]	0.8788236	0.8219365	0.9585099
sal + tem	Indo-Pacific	(27.5,27.75]	0.7118918	0.5144167	0.9159312
sal + tem	Indo-Pacific	(27.75,27.85]	0.8138537	0.6545628	0.9395278
sal + tem	Indo-Pacific	(27.85,27.95]	0.7036211	0.4548127	0.8728347
sal + tem	Indo-Pacific	(27.95,28.05]	0.7224713	0.6298824	0.8210732
sal + tem	Indo-Pacific	(28.05,28.1]	0.6987818	0.5756878	0.7977441
sal + tem	Indo-Pacific	(28.1, Inf]	0.7138260	0.5996297	0.8278324
silicate + phosphate	Atlantic	(-Inf,26]	0.6435212	0.5417703	0.7736760
silicate + phosphate	Atlantic	(26,26.5]	0.9197612	0.9020743	0.9319463
silicate + phosphate	Atlantic	(26.5,26.75]	0.9667453	0.9625265	0.9712821
silicate + phosphate	Atlantic	(26.75,27]	0.9516208	0.9345927	0.9610085
silicate + phosphate	Atlantic	(27,27.25]	0.9447014	0.9296485	0.9556204
silicate + phosphate	Atlantic	(27.25,27.5]	0.8978592	0.8721677	0.9280920
silicate + phosphate	Atlantic	(27.5,27.75]	0.8895426	0.8694482	0.9021325
silicate + phosphate	Atlantic	(27.75,27.85]	0.9520945	0.9423096	0.9653637
silicate + phosphate	Atlantic	(27.85,27.95]	0.9714709	0.9666891	0.9776300
silicate + phosphate	Atlantic	(27.95,28.05]	0.9807086	0.9759663	0.9866261
silicate + phosphate	Atlantic	(28.05,28.1]	0.9890124	0.9850664	0.9911994
silicate + phosphate	Atlantic	(28.1,28.15]	0.9933245	0.9921857	0.9941494
silicate + phosphate	Atlantic	(28.15,28.2]	0.9941483	0.9898345	0.9973286
silicate + phosphate	Atlantic	(28.2, Inf]	0.9695668	0.9599850	0.9887272
silicate + phosphate	Indo-Pacific	(-Inf,26]	0.7970365	0.7532736	0.8266286
silicate + phosphate	Indo-Pacific	(26,26.5]	0.7607970	0.6608833	0.8380775
silicate + phosphate	Indo-Pacific	(26.5,26.75]	0.7518371	0.5908688	0.8429329
silicate + phosphate	Indo-Pacific	(26.75,27]	0.8535440	0.8041063	0.8812693
silicate + phosphate	Indo-Pacific	(27,27.25]	0.8988752	0.8736363	0.9333806
silicate + phosphate	Indo-Pacific	(27.25,27.5]	0.8884682	0.8592060	0.9285349
silicate + phosphate	Indo-Pacific	(27.5,27.75]	0.8900713	0.8459587	0.9314354
silicate + phosphate	Indo-Pacific	(27.75,27.85]	0.9510737	0.9308561	0.9640862
silicate + phosphate	Indo-Pacific	(27.85,27.95]	0.9643449	0.9516445	0.9715323
silicate + phosphate	Indo-Pacific	(27.95,28.05]	0.9592635	0.9505559	0.9637854
silicate + phosphate	Indo-Pacific	(28.05,28.1]	0.9558185	0.9482961	0.9622048
silicate + phosphate	Indo-Pacific	(28.1, Inf]	0.7942203	0.7644862	0.8300839
silicate + phosphate_star	Atlantic	(-Inf,26]	-0.4597412	-0.5262541	-0.3528730
silicate + phosphate_star	Atlantic	(26,26.5]	-0.8574505	-0.9335528	-0.8130364
silicate + phosphate_star	Atlantic	(26.5,26.75]	-0.9685756	-0.9766017	-0.9601052
silicate + phosphate_star	Atlantic	(26.75,27]	-0.9519782	-0.9612813	-0.9358391
silicate + phosphate_star	Atlantic	(27,27.25]	-0.9294604	-0.9493202	-0.9137595
silicate + phosphate_star	Atlantic	(27.25,27.5]	-0.8663259	-0.9105063	-0.8263441
silicate + phosphate_star	Atlantic	(27.5,27.75]	-0.8716164	-0.8856450	-0.8506583
silicate + phosphate_star	Atlantic	(27.75,27.85]	-0.9466740	-0.9588018	-0.9372276
silicate + phosphate_star	Atlantic	(27.85,27.95]	-0.9682789	-0.9748126	-0.9643712
silicate + phosphate_star	Atlantic	(27.95,28.05]	-0.9787977	-0.9851869	-0.9750396
silicate + phosphate_star	Atlantic	(28.05,28.1]	-0.9883932	-0.9908217	-0.9862850
silicate + phosphate_star	Atlantic	(28.1,28.15]	-0.9911087	-0.9920310	-0.9900185
silicate + phosphate_star	Atlantic	(28.15,28.2]	-0.9948277	-0.9971700	-0.9910553
silicate + phosphate_star	Atlantic	(28.2, Inf]	-0.9684514	-0.9898211	-0.9538790
silicate + phosphate_star	Indo-Pacific	(-Inf,26]	-0.8810392	-0.8928076	-0.8633550
silicate + phosphate_star	Indo-Pacific	(26,26.5]	-0.8193160	-0.8792221	-0.7409978
silicate + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.7815493	-0.8711187	-0.6272799
silicate + phosphate_star	Indo-Pacific	(26.75,27]	-0.8465096	-0.8733674	-0.8017950
silicate + phosphate_star	Indo-Pacific	(27,27.25]	-0.8921453	-0.9255978	-0.8656112
silicate + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.8819789	-0.9229355	-0.8463770
silicate + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.8910168	-0.9291147	-0.8443627
silicate + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.9449097	-0.9600448	-0.9163417
silicate + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.9580159	-0.9685465	-0.9409673
silicate + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.9491689	-0.9665294	-0.9335964
silicate + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.9549649	-0.9610554	-0.9484612
silicate + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.8057462	-0.8556006	-0.7743155
tem + aou	Atlantic	(-Inf,26]	-0.0687693	-0.3518914	0.3120683
tem + aou	Atlantic	(26,26.5]	-0.2026044	-0.3782715	-0.0257882
tem + aou	Atlantic	(26.5,26.75]	-0.3626266	-0.5394586	-0.2278605
tem + aou	Atlantic	(26.75,27]	-0.2258924	-0.2684537	-0.1748759
tem + aou	Atlantic	(27,27.25]	-0.1116539	-0.2812963	0.0747144
tem + aou	Atlantic	(27.25,27.5]	-0.1280238	-0.2994314	-0.0069762
tem + aou	Atlantic	(27.5,27.75]	-0.4163606	-0.4606483	-0.3507414
tem + aou	Atlantic	(27.75,27.85]	-0.5228423	-0.5682867	-0.4812475
tem + aou	Atlantic	(27.85,27.95]	-0.3044515	-0.4569619	-0.0804600
tem + aou	Atlantic	(27.95,28.05]	-0.5202876	-0.7151551	-0.3144163
tem + aou	Atlantic	(28.05,28.1]	-0.6062227	-0.8064307	-0.4385820
tem + aou	Atlantic	(28.1,28.15]	-0.6597060	-0.7330619	-0.5223213
tem + aou	Atlantic	(28.15,28.2]	-0.7563883	-0.8202708	-0.7093370
tem + aou	Atlantic	(28.2, Inf]	0.3523127	0.2491837	0.4736749
tem + aou	Indo-Pacific	(-Inf,26]	-0.2722316	-0.4106364	-0.1756575
tem + aou	Indo-Pacific	(26,26.5]	-0.1194041	-0.2979562	-0.0170725
tem + aou	Indo-Pacific	(26.5,26.75]	-0.0403527	-0.3355578	0.2570151
tem + aou	Indo-Pacific	(26.75,27]	-0.1647195	-0.3441368	-0.0129495
tem + aou	Indo-Pacific	(27,27.25]	-0.1447080	-0.2850675	0.0782669
tem + aou	Indo-Pacific	(27.25,27.5]	0.0937411	-0.0020667	0.2629607
tem + aou	Indo-Pacific	(27.5,27.75]	0.1113591	0.0131166	0.2677859
tem + aou	Indo-Pacific	(27.75,27.85]	-0.0032064	-0.1982387	0.1936379
tem + aou	Indo-Pacific	(27.85,27.95]	-0.0703416	-0.2789347	0.0637697
tem + aou	Indo-Pacific	(27.95,28.05]	0.0906200	0.0763459	0.1173523
tem + aou	Indo-Pacific	(28.05,28.1]	0.1582755	0.0357532	0.2615890
tem + aou	Indo-Pacific	(28.1, Inf]	0.8408267	0.8004585	0.8667850
tem + oxygen	Atlantic	(-Inf,26]	-0.3163713	-0.5749811	-0.1206498
tem + oxygen	Atlantic	(26,26.5]	-0.1968196	-0.4148047	0.0427067
tem + oxygen	Atlantic	(26.5,26.75]	0.1118365	-0.0150026	0.3410353
tem + oxygen	Atlantic	(26.75,27]	0.0214474	-0.0706434	0.0678025
tem + oxygen	Atlantic	(27,27.25]	-0.1086535	-0.3379192	0.0727534
tem + oxygen	Atlantic	(27.25,27.5]	-0.1762577	-0.3351416	0.0234851
tem + oxygen	Atlantic	(27.5,27.75]	0.0584126	-0.0852544	0.1518829
tem + oxygen	Atlantic	(27.75,27.85]	0.3304151	0.2786541	0.3801715
tem + oxygen	Atlantic	(27.85,27.95]	0.1653514	-0.0686148	0.3399528
tem + oxygen	Atlantic	(27.95,28.05]	0.3933041	0.1904284	0.6256963
tem + oxygen	Atlantic	(28.05,28.1]	0.4917184	0.3267804	0.7418371
tem + oxygen	Atlantic	(28.1,28.15]	0.5766872	0.4345949	0.6498435
tem + oxygen	Atlantic	(28.15,28.2]	0.7180076	0.6732370	0.7888052
tem + oxygen	Atlantic	(28.2, Inf]	-0.5293353	-0.6164468	-0.4358133
tem + oxygen	Indo-Pacific	(-Inf,26]	-0.1032603	-0.2745694	-0.0104878
tem + oxygen	Indo-Pacific	(26,26.5]	-0.0727019	-0.1580104	0.0734543
tem + oxygen	Indo-Pacific	(26.5,26.75]	-0.1248874	-0.4160528	0.1518972
tem + oxygen	Indo-Pacific	(26.75,27]	-0.0118269	-0.1574711	0.1667299
tem + oxygen	Indo-Pacific	(27,27.25]	0.0015818	-0.2729761	0.1689748
tem + oxygen	Indo-Pacific	(27.25,27.5]	-0.2162391	-0.4322640	-0.0949851
tem + oxygen	Indo-Pacific	(27.5,27.75]	-0.2228174	-0.4294064	-0.0938038
tem + oxygen	Indo-Pacific	(27.75,27.85]	-0.0780331	-0.3165264	0.1534029
tem + oxygen	Indo-Pacific	(27.85,27.95]	-0.0054680	-0.1680901	0.2362149
tem + oxygen	Indo-Pacific	(27.95,28.05]	-0.1860042	-0.1995946	-0.1673701
tem + oxygen	Indo-Pacific	(28.05,28.1]	-0.2406214	-0.3537611	-0.1237291
tem + oxygen	Indo-Pacific	(28.1, Inf]	-0.9012284	-0.9172228	-0.8760409
tem + phosphate	Atlantic	(-Inf,26]	-0.4465037	-0.6217540	-0.2872539
tem + phosphate	Atlantic	(26,26.5]	-0.7252611	-0.7977219	-0.6318815
tem + phosphate	Atlantic	(26.5,26.75]	-0.7441481	-0.8013726	-0.6584993
tem + phosphate	Atlantic	(26.75,27]	-0.6690712	-0.7005508	-0.6280295
tem + phosphate	Atlantic	(27,27.25]	-0.6703935	-0.7235873	-0.6197743
tem + phosphate	Atlantic	(27.25,27.5]	-0.7580177	-0.7945460	-0.7146478
tem + phosphate	Atlantic	(27.5,27.75]	-0.7998618	-0.8089097	-0.7910859
tem + phosphate	Atlantic	(27.75,27.85]	-0.7425998	-0.7630549	-0.7137399
tem + phosphate	Atlantic	(27.85,27.95]	-0.5252112	-0.6256550	-0.3343713
tem + phosphate	Atlantic	(27.95,28.05]	-0.6492760	-0.7702004	-0.4548313
tem + phosphate	Atlantic	(28.05,28.1]	-0.7213138	-0.8442823	-0.5630099
tem + phosphate	Atlantic	(28.1,28.15]	-0.7416721	-0.8216944	-0.6194000
tem + phosphate	Atlantic	(28.15,28.2]	-0.7549808	-0.7961936	-0.6943424
tem + phosphate	Atlantic	(28.2, Inf]	-0.1112661	-0.1984830	-0.0519485
tem + phosphate	Indo-Pacific	(-Inf,26]	-0.4323561	-0.5907832	-0.2998380
tem + phosphate	Indo-Pacific	(26,26.5]	-0.3689015	-0.5549061	-0.2683633
tem + phosphate	Indo-Pacific	(26.5,26.75]	-0.3057328	-0.5850451	-0.0615034
tem + phosphate	Indo-Pacific	(26.75,27]	-0.4350420	-0.6099013	-0.2910911
tem + phosphate	Indo-Pacific	(27,27.25]	-0.3471856	-0.4234578	-0.1961448
tem + phosphate	Indo-Pacific	(27.25,27.5]	-0.0500689	-0.1213691	0.0284870
tem + phosphate	Indo-Pacific	(27.5,27.75]	0.0426798	-0.0155293	0.1237490
tem + phosphate	Indo-Pacific	(27.75,27.85]	-0.0281936	-0.1669361	0.1343332
tem + phosphate	Indo-Pacific	(27.85,27.95]	-0.1200123	-0.2780650	-0.0010696
tem + phosphate	Indo-Pacific	(27.95,28.05]	-0.0710536	-0.0944506	-0.0398646
tem + phosphate	Indo-Pacific	(28.05,28.1]	-0.0289602	-0.1498496	0.0490411
tem + phosphate	Indo-Pacific	(28.1, Inf]	0.3944451	0.2679137	0.4779643
tem + phosphate_star	Atlantic	(-Inf,26]	0.1519132	-0.0653365	0.3096019
tem + phosphate_star	Atlantic	(26,26.5]	0.5529396	0.5079708	0.6251879
tem + phosphate_star	Atlantic	(26.5,26.75]	0.6108935	0.5279889	0.6975139
tem + phosphate_star	Atlantic	(26.75,27]	0.5487442	0.5154852	0.5714517
tem + phosphate_star	Atlantic	(27,27.25]	0.5717025	0.5126821	0.6424344
tem + phosphate_star	Atlantic	(27.25,27.5]	0.6922955	0.6336130	0.7397797
tem + phosphate_star	Atlantic	(27.5,27.75]	0.7695790	0.7645013	0.7779957
tem + phosphate_star	Atlantic	(27.75,27.85]	0.7207069	0.6838512	0.7517880
tem + phosphate_star	Atlantic	(27.85,27.95]	0.5069296	0.3076263	0.6091582
tem + phosphate_star	Atlantic	(27.95,28.05]	0.6369114	0.4399580	0.7593713
tem + phosphate_star	Atlantic	(28.05,28.1]	0.7094623	0.5514256	0.8374482
tem + phosphate_star	Atlantic	(28.1,28.15]	0.7212057	0.5931143	0.8075016
tem + phosphate_star	Atlantic	(28.15,28.2]	0.7529396	0.7100942	0.7864352
tem + phosphate_star	Atlantic	(28.2, Inf]	0.1012601	0.0295041	0.1975806
tem + phosphate_star	Indo-Pacific	(-Inf,26]	0.5273644	0.3799723	0.6777656
tem + phosphate_star	Indo-Pacific	(26,26.5]	0.4429074	0.3337122	0.6245983
tem + phosphate_star	Indo-Pacific	(26.5,26.75]	0.3503523	0.1038031	0.6211509
tem + phosphate_star	Indo-Pacific	(26.75,27]	0.4443595	0.3256567	0.6016652
tem + phosphate_star	Indo-Pacific	(27,27.25]	0.3884500	0.3035589	0.4398328
tem + phosphate_star	Indo-Pacific	(27.25,27.5]	0.1320934	0.0860420	0.1640058
tem + phosphate_star	Indo-Pacific	(27.5,27.75]	0.0671267	0.0292266	0.0984471
tem + phosphate_star	Indo-Pacific	(27.75,27.85]	0.1238721	0.0502088	0.2175226
tem + phosphate_star	Indo-Pacific	(27.85,27.95]	0.1766033	0.1145829	0.2972145
tem + phosphate_star	Indo-Pacific	(27.95,28.05]	0.0951229	0.0319698	0.1546229
tem + phosphate_star	Indo-Pacific	(28.05,28.1]	0.0498790	-0.0248495	0.1965124
tem + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.3998708	-0.5302868	-0.2681462
tem + silicate	Atlantic	(-Inf,26]	-0.6058851	-0.7356100	-0.5118555
tem + silicate	Atlantic	(26,26.5]	-0.6940228	-0.7324635	-0.6713966
tem + silicate	Atlantic	(26.5,26.75]	-0.6575854	-0.7401620	-0.5514632
tem + silicate	Atlantic	(26.75,27]	-0.5731056	-0.6058513	-0.5474068
tem + silicate	Atlantic	(27,27.25]	-0.6439136	-0.6895759	-0.6139537
tem + silicate	Atlantic	(27.25,27.5]	-0.8337342	-0.8392335	-0.8288195
tem + silicate	Atlantic	(27.5,27.75]	-0.8573527	-0.8796812	-0.8389417
tem + silicate	Atlantic	(27.75,27.85]	-0.8042016	-0.8434315	-0.7626576
tem + silicate	Atlantic	(27.85,27.95]	-0.6354677	-0.7301266	-0.4645337
tem + silicate	Atlantic	(27.95,28.05]	-0.7256101	-0.8518541	-0.5596467
tem + silicate	Atlantic	(28.05,28.1]	-0.7473424	-0.8802581	-0.6125043
tem + silicate	Atlantic	(28.1,28.15]	-0.7610483	-0.8231982	-0.6456801
tem + silicate	Atlantic	(28.15,28.2]	-0.7570242	-0.8073258	-0.7273218
tem + silicate	Atlantic	(28.2, Inf]	-0.0842811	-0.1558594	0.0039567
tem + silicate	Indo-Pacific	(-Inf,26]	-0.5967725	-0.7261407	-0.4499679
tem + silicate	Indo-Pacific	(26,26.5]	-0.6110836	-0.7160420	-0.4703853
tem + silicate	Indo-Pacific	(26.5,26.75]	-0.6666527	-0.8021744	-0.5602649
tem + silicate	Indo-Pacific	(26.75,27]	-0.6684323	-0.7561768	-0.5323795
tem + silicate	Indo-Pacific	(27,27.25]	-0.5265025	-0.6256717	-0.4123352
tem + silicate	Indo-Pacific	(27.25,27.5]	-0.2437907	-0.3118250	-0.1471327
tem + silicate	Indo-Pacific	(27.5,27.75]	-0.1739307	-0.2391804	-0.1198311
tem + silicate	Indo-Pacific	(27.75,27.85]	-0.1230091	-0.2532228	0.0094038
tem + silicate	Indo-Pacific	(27.85,27.95]	-0.1946195	-0.3604705	-0.0905682
tem + silicate	Indo-Pacific	(27.95,28.05]	-0.1000350	-0.1253313	-0.0704056
tem + silicate	Indo-Pacific	(28.05,28.1]	0.0336616	-0.1001331	0.1153910
tem + silicate	Indo-Pacific	(28.1, Inf]	0.2411614	0.0680485	0.3365357

rm(cor_predictors, cor_predictors_stats)

6.2.2.3 C* vs individual predictors

Below, the range of correlations coefficients for C* with each predictor is plotted per basin (facet) and density slab (color). Note that the range indicates the min and max values of in total 3 calculated coefficients (one per era).

cor_Cstar_predictor <-
  read_csv(here::here("data/eMLR",
                       "cor_Cstar_predictor.csv")) %>% 
  rename(predictor = rowname)

cor_Cstar_predictor_stats <- cor_Cstar_predictor %>% 
  group_by(predictor, basin, gamma_slab) %>% 
  summarise(mean_r = mean(Cstar),
            min_r = min(Cstar),
            max_r = max(Cstar)) %>% 
  ungroup()

cor_Cstar_predictor_stats %>% 
  mutate(predictor = reorder(predictor, mean_r)) %>%
  ggplot() +
  geom_vline(xintercept = c(-0.9, 0.9), col = "red") +
  geom_vline(xintercept = 0) +
  geom_linerange(
    aes(y = predictor, xmin = min_r, xmax = max_r, col = gamma_slab),
    position = position_dodge(width = 0.6)) +
  facet_wrap(~basin) +
  scale_color_viridis_d(direction = -1) +
  labs(x = "correlation coefficient", y = "C* correlation with...") +
  theme(legend.position = "top")

kable(cor_Cstar_predictor_stats) %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

predictor	basin	gamma_slab	mean_r	min_r	max_r
aou	Atlantic	(-Inf,26]	0.0948744	-0.3711871	0.5332243
aou	Atlantic	(26,26.5]	-0.3140197	-0.6933099	0.0545390
aou	Atlantic	(26.5,26.75]	-0.5996279	-0.6700148	-0.5064340
aou	Atlantic	(26.75,27]	-0.5053251	-0.5703139	-0.4583983
aou	Atlantic	(27,27.25]	-0.4571842	-0.5506422	-0.2911704
aou	Atlantic	(27.25,27.5]	-0.4924236	-0.5716618	-0.4010756
aou	Atlantic	(27.5,27.75]	-0.7856120	-0.8211551	-0.7382048
aou	Atlantic	(27.75,27.85]	-0.9354504	-0.9470128	-0.9249823
aou	Atlantic	(27.85,27.95]	-0.9469077	-0.9628294	-0.9359087
aou	Atlantic	(27.95,28.05]	-0.9189538	-0.9271593	-0.9128789
aou	Atlantic	(28.05,28.1]	-0.9002490	-0.9131254	-0.8806348
aou	Atlantic	(28.1,28.15]	-0.9281787	-0.9396740	-0.9162489
aou	Atlantic	(28.15,28.2]	-0.9620568	-0.9692194	-0.9510549
aou	Atlantic	(28.2, Inf]	-0.6922519	-0.8195458	-0.6205950
aou	Indo-Pacific	(-Inf,26]	-0.5149130	-0.6400200	-0.4472197
aou	Indo-Pacific	(26,26.5]	-0.8403968	-0.8517341	-0.8211536
aou	Indo-Pacific	(26.5,26.75]	-0.8411200	-0.8622968	-0.8156240
aou	Indo-Pacific	(26.75,27]	-0.8469647	-0.8923007	-0.8202075
aou	Indo-Pacific	(27,27.25]	-0.6301663	-0.6922140	-0.5758841
aou	Indo-Pacific	(27.25,27.5]	0.0751200	0.0133650	0.1165430
aou	Indo-Pacific	(27.5,27.75]	0.4206555	0.2894476	0.5021573
aou	Indo-Pacific	(27.75,27.85]	0.4546896	0.2770580	0.5841937
aou	Indo-Pacific	(27.85,27.95]	0.2854072	0.1545060	0.4147307
aou	Indo-Pacific	(27.95,28.05]	-0.1214957	-0.1998843	0.0217023
aou	Indo-Pacific	(28.05,28.1]	-0.2517368	-0.3794373	-0.1798966
aou	Indo-Pacific	(28.1, Inf]	0.1316069	-0.0348118	0.3660777
oxygen	Atlantic	(-Inf,26]	-0.1061722	-0.5051495	0.2983873
oxygen	Atlantic	(26,26.5]	0.0339248	-0.3966024	0.5419770
oxygen	Atlantic	(26.5,26.75]	0.4001245	0.2477960	0.5192255
oxygen	Atlantic	(26.75,27]	0.3308273	0.2401203	0.4345322
oxygen	Atlantic	(27,27.25]	0.2586414	0.0372186	0.3720205
oxygen	Atlantic	(27.25,27.5]	0.2170106	0.0774325	0.3328796
oxygen	Atlantic	(27.5,27.75]	0.5333498	0.4050772	0.6073790
oxygen	Atlantic	(27.75,27.85]	0.8590177	0.8398607	0.8807056
oxygen	Atlantic	(27.85,27.95]	0.9150818	0.8995165	0.9460879
oxygen	Atlantic	(27.95,28.05]	0.8963245	0.8577963	0.9269719
oxygen	Atlantic	(28.05,28.1]	0.8777149	0.8516523	0.9197717
oxygen	Atlantic	(28.1,28.15]	0.9181816	0.9012301	0.9322195
oxygen	Atlantic	(28.15,28.2]	0.9637201	0.9592676	0.9686129
oxygen	Atlantic	(28.2, Inf]	0.5704957	0.4729743	0.7272496
oxygen	Indo-Pacific	(-Inf,26]	0.5187760	0.4489442	0.6463468
oxygen	Indo-Pacific	(26,26.5]	0.7541153	0.7056275	0.7868059
oxygen	Indo-Pacific	(26.5,26.75]	0.7586165	0.7280525	0.7996299
oxygen	Indo-Pacific	(26.75,27]	0.7693725	0.7368726	0.8254535
oxygen	Indo-Pacific	(27,27.25]	0.6159865	0.5465735	0.7060918
oxygen	Indo-Pacific	(27.25,27.5]	-0.0341996	-0.0859565	0.0258549
oxygen	Indo-Pacific	(27.5,27.75]	-0.3632628	-0.4653161	-0.2009100
oxygen	Indo-Pacific	(27.75,27.85]	-0.4160886	-0.5629082	-0.2079738
oxygen	Indo-Pacific	(27.85,27.95]	-0.2623530	-0.4000667	-0.1137397
oxygen	Indo-Pacific	(27.95,28.05]	0.1155996	-0.0268951	0.1878919
oxygen	Indo-Pacific	(28.05,28.1]	0.2316176	0.1663804	0.3491391
oxygen	Indo-Pacific	(28.1, Inf]	-0.1818398	-0.4177864	-0.0154040
phosphate	Atlantic	(-Inf,26]	-0.4126614	-0.8052489	-0.0480374
phosphate	Atlantic	(26,26.5]	-0.7844496	-0.8659538	-0.6799348
phosphate	Atlantic	(26.5,26.75]	-0.8776544	-0.9092614	-0.8542561
phosphate	Atlantic	(26.75,27]	-0.8525408	-0.8702323	-0.8225758
phosphate	Atlantic	(27,27.25]	-0.8889143	-0.8895507	-0.8881820
phosphate	Atlantic	(27.25,27.5]	-0.9505560	-0.9579696	-0.9420302
phosphate	Atlantic	(27.5,27.75]	-0.9884561	-0.9907126	-0.9853712
phosphate	Atlantic	(27.75,27.85]	-0.9827512	-0.9876438	-0.9756229
phosphate	Atlantic	(27.85,27.95]	-0.9667140	-0.9716584	-0.9627816
phosphate	Atlantic	(27.95,28.05]	-0.9502178	-0.9649152	-0.9339718
phosphate	Atlantic	(28.05,28.1]	-0.9425539	-0.9587959	-0.9251717
phosphate	Atlantic	(28.1,28.15]	-0.9583747	-0.9684832	-0.9464709
phosphate	Atlantic	(28.15,28.2]	-0.9810583	-0.9883310	-0.9724947
phosphate	Atlantic	(28.2, Inf]	-0.9620339	-0.9790526	-0.9387764
phosphate	Indo-Pacific	(-Inf,26]	-0.5757197	-0.7038862	-0.5064227
phosphate	Indo-Pacific	(26,26.5]	-0.9332592	-0.9444061	-0.9231474
phosphate	Indo-Pacific	(26.5,26.75]	-0.9484042	-0.9543277	-0.9445690
phosphate	Indo-Pacific	(26.75,27]	-0.9436843	-0.9637762	-0.9204828
phosphate	Indo-Pacific	(27,27.25]	-0.7103496	-0.7337122	-0.6729956
phosphate	Indo-Pacific	(27.25,27.5]	-0.0322365	-0.1080636	0.0193553
phosphate	Indo-Pacific	(27.5,27.75]	0.3069690	0.1761650	0.3992740
phosphate	Indo-Pacific	(27.75,27.85]	0.3446414	0.1547443	0.4817711
phosphate	Indo-Pacific	(27.85,27.95]	0.1562262	-0.0006677	0.3154189
phosphate	Indo-Pacific	(27.95,28.05]	-0.2719782	-0.3645910	-0.0880230
phosphate	Indo-Pacific	(28.05,28.1]	-0.4185162	-0.5442209	-0.3012822
phosphate	Indo-Pacific	(28.1, Inf]	-0.2882605	-0.4338247	-0.0213370
phosphate_star	Atlantic	(-Inf,26]	0.0852110	-0.3107099	0.4679325
phosphate_star	Atlantic	(26,26.5]	0.5953132	0.4056159	0.8207026
phosphate_star	Atlantic	(26.5,26.75]	0.7837150	0.7341827	0.8316432
phosphate_star	Atlantic	(26.75,27]	0.7557814	0.7184803	0.7776726
phosphate_star	Atlantic	(27,27.25]	0.8173721	0.8104400	0.8256805
phosphate_star	Atlantic	(27.25,27.5]	0.9140649	0.9080173	0.9253392
phosphate_star	Atlantic	(27.5,27.75]	0.9796202	0.9739620	0.9833678
phosphate_star	Atlantic	(27.75,27.85]	0.9785808	0.9743759	0.9834257
phosphate_star	Atlantic	(27.85,27.95]	0.9600672	0.9536722	0.9656760
phosphate_star	Atlantic	(27.95,28.05]	0.9419644	0.9326019	0.9573361
phosphate_star	Atlantic	(28.05,28.1]	0.9314569	0.9217391	0.9505445
phosphate_star	Atlantic	(28.1,28.15]	0.9514635	0.9445157	0.9638225
phosphate_star	Atlantic	(28.15,28.2]	0.9768003	0.9722670	0.9848328
phosphate_star	Atlantic	(28.2, Inf]	0.9465581	0.9097462	0.9702612
phosphate_star	Indo-Pacific	(-Inf,26]	0.5713195	0.5135592	0.6860143
phosphate_star	Indo-Pacific	(26,26.5]	0.8997899	0.8775949	0.9120232
phosphate_star	Indo-Pacific	(26.5,26.75]	0.9163360	0.9060975	0.9331184
phosphate_star	Indo-Pacific	(26.75,27]	0.9286735	0.9016496	0.9488903
phosphate_star	Indo-Pacific	(27,27.25]	0.6811982	0.6279505	0.7078588
phosphate_star	Indo-Pacific	(27.25,27.5]	0.0003180	-0.0355198	0.0544422
phosphate_star	Indo-Pacific	(27.5,27.75]	-0.3714883	-0.4286810	-0.2992500
phosphate_star	Indo-Pacific	(27.75,27.85]	-0.4310357	-0.5307686	-0.3172332
phosphate_star	Indo-Pacific	(27.85,27.95]	-0.2398445	-0.3579772	-0.1570786
phosphate_star	Indo-Pacific	(27.95,28.05]	0.1992997	0.0370836	0.3055968
phosphate_star	Indo-Pacific	(28.05,28.1]	0.3354716	0.2318912	0.4700224
phosphate_star	Indo-Pacific	(28.1, Inf]	0.1380383	-0.0859155	0.3038694
sal	Atlantic	(-Inf,26]	0.2893199	0.2228703	0.3269860
sal	Atlantic	(26,26.5]	0.7307163	0.5226450	0.8666493
sal	Atlantic	(26.5,26.75]	0.8567660	0.8063865	0.8880440
sal	Atlantic	(26.75,27]	0.8973845	0.8699793	0.9146719
sal	Atlantic	(27,27.25]	0.9172249	0.8999376	0.9429090
sal	Atlantic	(27.25,27.5]	0.9109993	0.8814810	0.9378890
sal	Atlantic	(27.5,27.75]	0.8557359	0.8418518	0.8667822
sal	Atlantic	(27.75,27.85]	0.7298170	0.7081495	0.7436290
sal	Atlantic	(27.85,27.95]	0.4577464	0.3090975	0.5387157
sal	Atlantic	(27.95,28.05]	0.5549736	0.2690369	0.7159448
sal	Atlantic	(28.05,28.1]	0.7234078	0.6613456	0.7730548
sal	Atlantic	(28.1,28.15]	0.7974262	0.7724322	0.8443428
sal	Atlantic	(28.15,28.2]	0.9099105	0.8925141	0.9326793
sal	Atlantic	(28.2, Inf]	0.9028001	0.8621840	0.9295343
sal	Indo-Pacific	(-Inf,26]	0.1443091	0.1302355	0.1546539
sal	Indo-Pacific	(26,26.5]	0.4066345	0.2672732	0.6262333
sal	Indo-Pacific	(26.5,26.75]	0.4347134	0.2122471	0.7126362
sal	Indo-Pacific	(26.75,27]	0.4486777	0.2980179	0.6668893
sal	Indo-Pacific	(27,27.25]	0.0056159	-0.1171006	0.1952502
sal	Indo-Pacific	(27.25,27.5]	-0.4052340	-0.6169920	-0.2139092
sal	Indo-Pacific	(27.5,27.75]	-0.3436362	-0.4420790	-0.2545677
sal	Indo-Pacific	(27.75,27.85]	-0.4349627	-0.5218193	-0.3141648
sal	Indo-Pacific	(27.85,27.95]	-0.2636138	-0.3691842	-0.0940164
sal	Indo-Pacific	(27.95,28.05]	0.1868750	0.0427199	0.3360299
sal	Indo-Pacific	(28.05,28.1]	0.2957974	0.2258232	0.4167223
sal	Indo-Pacific	(28.1, Inf]	0.3148342	0.2540835	0.4136392
silicate	Atlantic	(-Inf,26]	-0.3229475	-0.5522968	-0.0825164
silicate	Atlantic	(26,26.5]	-0.7356319	-0.8267582	-0.6270016
silicate	Atlantic	(26.5,26.75]	-0.8212687	-0.8391818	-0.7891525
silicate	Atlantic	(26.75,27]	-0.7667031	-0.7871720	-0.7496485
silicate	Atlantic	(27,27.25]	-0.8433176	-0.8716919	-0.8191915
silicate	Atlantic	(27.25,27.5]	-0.8992211	-0.9059750	-0.8945185
silicate	Atlantic	(27.5,27.75]	-0.8829288	-0.9051178	-0.8630863
silicate	Atlantic	(27.75,27.85]	-0.9073224	-0.9314085	-0.8764643
silicate	Atlantic	(27.85,27.95]	-0.9030935	-0.9219478	-0.8890345
silicate	Atlantic	(27.95,28.05]	-0.9003694	-0.9327048	-0.8740608
silicate	Atlantic	(28.05,28.1]	-0.9082445	-0.9356242	-0.8911054
silicate	Atlantic	(28.1,28.15]	-0.9385935	-0.9562571	-0.9230594
silicate	Atlantic	(28.15,28.2]	-0.9704431	-0.9773359	-0.9651271
silicate	Atlantic	(28.2, Inf]	-0.9111351	-0.9642570	-0.8445701
silicate	Indo-Pacific	(-Inf,26]	-0.5181503	-0.6288626	-0.4567030
silicate	Indo-Pacific	(26,26.5]	-0.7752146	-0.8161663	-0.7136697
silicate	Indo-Pacific	(26.5,26.75]	-0.7667013	-0.8437098	-0.6332848
silicate	Indo-Pacific	(26.75,27]	-0.7707259	-0.7995253	-0.7199367
silicate	Indo-Pacific	(27,27.25]	-0.4302448	-0.5067676	-0.3849373
silicate	Indo-Pacific	(27.25,27.5]	0.3475535	0.2829936	0.4238548
silicate	Indo-Pacific	(27.5,27.75]	0.6195443	0.5405623	0.6742328
silicate	Indo-Pacific	(27.75,27.85]	0.5161567	0.3737043	0.6335329
silicate	Indo-Pacific	(27.85,27.95]	0.2814989	0.1568541	0.4182219
silicate	Indo-Pacific	(27.95,28.05]	-0.1474978	-0.2375041	0.0164143
silicate	Indo-Pacific	(28.05,28.1]	-0.3077753	-0.4291197	-0.2382106
silicate	Indo-Pacific	(28.1, Inf]	-0.2072558	-0.3324222	-0.0587563
tem	Atlantic	(-Inf,26]	0.0655155	-0.0827931	0.1465154
tem	Atlantic	(26,26.5]	0.7223412	0.5595250	0.8169447
tem	Atlantic	(26.5,26.75]	0.8562581	0.8275488	0.8735358
tem	Atlantic	(26.75,27]	0.8850341	0.8656686	0.9019147
tem	Atlantic	(27,27.25]	0.8879506	0.8729674	0.9066721
tem	Atlantic	(27.25,27.5]	0.8839156	0.8608731	0.9128891
tem	Atlantic	(27.5,27.75]	0.8129182	0.7950602	0.8219969
tem	Atlantic	(27.75,27.85]	0.7102829	0.6959796	0.7246136
tem	Atlantic	(27.85,27.95]	0.4251724	0.2476208	0.5283781
tem	Atlantic	(27.95,28.05]	0.5337535	0.3266584	0.6577087
tem	Atlantic	(28.05,28.1]	0.6005779	0.4727863	0.6745071
tem	Atlantic	(28.1,28.15]	0.6225691	0.5370767	0.7289768
tem	Atlantic	(28.15,28.2]	0.6648944	0.6118608	0.7276289
tem	Atlantic	(28.2, Inf]	0.1867555	0.0586055	0.3122400
tem	Indo-Pacific	(-Inf,26]	-0.0028411	-0.0794153	0.0630388
tem	Indo-Pacific	(26,26.5]	0.4477372	0.3214697	0.6350025
tem	Indo-Pacific	(26.5,26.75]	0.4303970	0.2238553	0.6928678
tem	Indo-Pacific	(26.75,27]	0.4918282	0.3790500	0.6861830
tem	Indo-Pacific	(27,27.25]	0.1484349	0.0539126	0.3364576
tem	Indo-Pacific	(27.25,27.5]	-0.3341194	-0.5112289	-0.1917468
tem	Indo-Pacific	(27.5,27.75]	-0.4277935	-0.5502807	-0.3446213
tem	Indo-Pacific	(27.75,27.85]	-0.4471220	-0.5549833	-0.3217166
tem	Indo-Pacific	(27.85,27.95]	-0.3308109	-0.4395518	-0.1738875
tem	Indo-Pacific	(27.95,28.05]	0.0310968	-0.0262811	0.0715985
tem	Indo-Pacific	(28.05,28.1]	0.1150922	0.1068726	0.1233232
tem	Indo-Pacific	(28.1, Inf]	0.2932324	0.1233658	0.5486616

rm(cor_Cstar_predictor, cor_Cstar_predictor_stats)

6.3 Model fitting

GLODAP %>% write_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
                                "GLODAP_MLR_fitting_ready.csv"))

6.3.1 Predictor selection

Individual linear regression models were fitted for C* as a function of each predictor combination. Fitting was performed separately within each basin, era, and slab. The root mean squared error (RMSE) was calculated for each fitted model.

for (i_basin in unique(GLODAP$basin)) {
  for (i_era in unique(GLODAP$era)) {
    
    # i_basin <- unique(GLODAP$basin)[1]
    # i_era   <- unique(GLODAP$era)[1]
    
    print(i_basin) 
    print(i_era  )
    
    GLODAP_basin_era <- GLODAP %>%
      filter(basin == i_basin, era == i_era)

    for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {

      # i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
      print(i_gamma_slab)
      
      GLODAP_basin_era_slab <- GLODAP_basin_era %>% 
        filter(gamma_slab == i_gamma_slab)
      
      lm_full <- lm(Cstar ~ 
                sal  + 
                tem  + 
                aou  + 
                oxygen  + 
                silicate  + 
                phosphate  + 
                phosphate_star, 
              data = GLODAP_basin_era_slab)
      
      lm_all <- ols_step_all_possible(lm_full)
      
      temp <- as_tibble(lm_all$result)
      
      temp <- temp %>% 
        mutate(basin = i_basin,
               era = i_era,
               gamma_slab = i_gamma_slab)
      
      if (exists("all_lm_stats")) {
        all_lm_stats <- bind_rows(all_lm_stats, temp)
      }
      
      if (!exists("all_lm_stats")) {
        all_lm_stats <- temp
      }
      
      rm(lm_full, lm_all, temp)
      
    }
    
  }
  
}

all_lm_stats %>%
  write_csv(here::here("data/eMLR",
                       "all_lm_stats.csv"))

rm(i_gamma_slab, i_era, i_basin,
   GLODAP_basin_era, GLODAP_basin_era_slab,
   all_lm_stats)

n_predictors_max <- 5
n_predictors_min <- 2

n_predictors_total <- 10

RMSE was plotted against the number of predictors (limited to 2 - 5).

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

# nrow(all_lm_stats)
# length(unique(all_lm_stats$rmse))
# length(unique(all_lm_stats$adjr))
# length(unique(all_lm_stats$rsquare))
# length(unique(all_lm_stats$cp))
# length(unique(all_lm_stats$aic))
# length(unique(all_lm_stats$mindex))

all_lm_stats <- all_lm_stats %>% 
  filter(n >= n_predictors_min,
         n <= n_predictors_max)

all_lm_stats %>% 
  ggplot(aes(n, rmse, col = basin)) +
  geom_hline(yintercept = 10) + 
  geom_point(shape = 21) +
  facet_grid(gamma_slab~era) +
  scale_color_brewer(palette = "Set1")

Within each basin and slab, the 10 linear regression models with lowest summed RMSE across all eras were selected.

all_lm_stats <- all_lm_stats %>% 
  select(basin, era, gamma_slab, predictors, rmse)

all_lm_stats_wide <- all_lm_stats %>% 
  pivot_wider(names_from = era, values_from = rmse, names_prefix = "rmse_")

all_lm_stats_wide <- all_lm_stats_wide %>% 
  mutate(rmse_sum = rmse_JGOFS_WOCE + rmse_GO_SHIP + rmse_new_era)

lm_best <- all_lm_stats_wide %>% 
  group_by(basin, gamma_slab) %>% 
  slice_min(order_by = rmse_sum,
            with_ties = FALSE,
            n = n_predictors_total) %>% 
  ungroup()

kable(lm_best) %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

basin	gamma_slab	predictors	rmse_JGOFS_WOCE	rmse_GO_SHIP	rmse_new_era	rmse_sum
Atlantic	(-Inf,26]	tem aou oxygen phosphate phosphate_star	7.150296	6.325439	2.671672	16.147407
Atlantic	(-Inf,26]	tem oxygen silicate phosphate phosphate_star	7.358462	6.126738	2.734672	16.219872
Atlantic	(-Inf,26]	sal tem aou oxygen phosphate	7.173663	6.319107	2.765130	16.257900
Atlantic	(-Inf,26]	sal tem oxygen silicate phosphate	7.248967	6.204419	2.852778	16.306164
Atlantic	(-Inf,26]	tem aou silicate phosphate phosphate_star	7.415798	6.146663	2.744721	16.307181
Atlantic	(-Inf,26]	sal tem aou silicate phosphate	7.278011	6.171501	2.857798	16.307310
Atlantic	(-Inf,26]	sal aou oxygen silicate phosphate	7.367183	6.069229	2.875347	16.311759
Atlantic	(-Inf,26]	tem aou oxygen silicate phosphate	7.054569	6.553880	2.766765	16.375214
Atlantic	(-Inf,26]	sal tem oxygen phosphate phosphate_star	7.547678	6.166720	2.711688	16.426086
Atlantic	(-Inf,26]	sal tem aou phosphate phosphate_star	7.585762	6.128055	2.717708	16.431525
Atlantic	(26,26.5]	tem aou oxygen silicate phosphate	5.363554	6.815718	3.120245	15.299516
Atlantic	(26,26.5]	aou oxygen silicate phosphate phosphate_star	5.391757	6.902167	3.178032	15.471956
Atlantic	(26,26.5]	tem aou oxygen phosphate phosphate_star	5.452186	6.854777	3.180828	15.487791
Atlantic	(26,26.5]	sal tem aou oxygen phosphate	5.477425	6.872313	3.164633	15.514372
Atlantic	(26,26.5]	tem aou oxygen phosphate	5.478784	6.872333	3.181060	15.532177
Atlantic	(26,26.5]	tem aou silicate phosphate phosphate_star	5.429777	6.960158	3.193715	15.583650
Atlantic	(26,26.5]	sal aou oxygen silicate phosphate	5.434466	6.997568	3.182424	15.614458
Atlantic	(26,26.5]	sal aou oxygen phosphate phosphate_star	5.456763	6.970849	3.196238	15.623850
Atlantic	(26,26.5]	aou oxygen silicate phosphate	5.446518	7.022801	3.184956	15.654274
Atlantic	(26,26.5]	aou oxygen phosphate phosphate_star	5.479554	6.973773	3.206234	15.659561
Atlantic	(26.5,26.75]	tem aou oxygen silicate phosphate	5.153695	5.620094	3.704869	14.478657
Atlantic	(26.5,26.75]	sal tem aou silicate phosphate	5.080928	5.614607	3.805535	14.501071
Atlantic	(26.5,26.75]	sal tem oxygen silicate phosphate	5.073639	5.596750	3.838208	14.508597
Atlantic	(26.5,26.75]	tem oxygen silicate phosphate phosphate_star	5.141157	5.617650	3.758446	14.517254
Atlantic	(26.5,26.75]	tem aou silicate phosphate phosphate_star	5.154882	5.637006	3.730283	14.522171
Atlantic	(26.5,26.75]	sal aou oxygen silicate phosphate	5.121400	5.673332	3.769774	14.564506
Atlantic	(26.5,26.75]	aou oxygen silicate phosphate phosphate_star	5.187377	5.677938	3.699733	14.565048
Atlantic	(26.5,26.75]	sal tem aou oxygen phosphate	5.318827	5.588430	3.703778	14.611035
Atlantic	(26.5,26.75]	tem aou oxygen phosphate phosphate_star	5.357372	5.609565	3.646853	14.613791
Atlantic	(26.5,26.75]	tem oxygen silicate phosphate	5.158997	5.644808	3.842072	14.645877
Atlantic	(26.75,27]	sal tem oxygen silicate phosphate	4.689137	4.956845	3.438851	13.084832
Atlantic	(26.75,27]	tem oxygen silicate phosphate phosphate_star	4.739924	4.961115	3.415486	13.116525
Atlantic	(26.75,27]	sal tem aou silicate phosphate	4.708472	4.969119	3.448332	13.125924
Atlantic	(26.75,27]	sal tem oxygen phosphate phosphate_star	4.737133	5.008805	3.405761	13.151699
Atlantic	(26.75,27]	tem aou silicate phosphate phosphate_star	4.767595	4.974144	3.429472	13.171211
Atlantic	(26.75,27]	sal tem aou phosphate phosphate_star	4.759298	5.018815	3.415301	13.193415
Atlantic	(26.75,27]	tem aou oxygen phosphate phosphate_star	4.761392	5.006690	3.456965	13.225046
Atlantic	(26.75,27]	tem oxygen phosphate phosphate_star	4.769503	5.012519	3.460589	13.242610
Atlantic	(26.75,27]	tem aou oxygen silicate phosphate	4.802227	5.046591	3.444518	13.293336
Atlantic	(26.75,27]	tem aou phosphate phosphate_star	4.795872	5.022362	3.476304	13.294537
Atlantic	(27,27.25]	tem oxygen silicate phosphate phosphate_star	5.142108	4.888961	4.425074	14.456143
Atlantic	(27,27.25]	tem aou oxygen phosphate phosphate_star	5.147498	4.914744	4.485850	14.548092
Atlantic	(27,27.25]	tem aou silicate phosphate phosphate_star	5.192439	4.929965	4.448113	14.570517
Atlantic	(27,27.25]	sal tem oxygen phosphate phosphate_star	5.196334	4.924601	4.501528	14.622464
Atlantic	(27,27.25]	tem oxygen phosphate phosphate_star	5.234406	4.949687	4.507371	14.691464
Atlantic	(27,27.25]	sal tem oxygen silicate phosphate	5.018688	5.043558	4.665827	14.728072
Atlantic	(27,27.25]	sal tem aou phosphate phosphate_star	5.250498	4.962351	4.519119	14.731969
Atlantic	(27,27.25]	tem aou phosphate phosphate_star	5.284619	4.989642	4.526341	14.800602
Atlantic	(27,27.25]	sal tem aou silicate phosphate	5.078648	5.067501	4.676695	14.822845
Atlantic	(27,27.25]	aou oxygen silicate phosphate phosphate_star	5.328621	5.017816	4.477069	14.823506
Atlantic	(27.25,27.5]	sal tem oxygen phosphate phosphate_star	4.777170	4.300744	3.649328	12.727242
Atlantic	(27.25,27.5]	sal tem aou phosphate phosphate_star	4.823760	4.301531	3.657423	12.782714
Atlantic	(27.25,27.5]	tem aou oxygen phosphate phosphate_star	4.772737	4.401334	3.650559	12.824629
Atlantic	(27.25,27.5]	tem oxygen silicate phosphate phosphate_star	4.808670	4.407059	3.638511	12.854240
Atlantic	(27.25,27.5]	tem aou silicate phosphate phosphate_star	4.856829	4.394293	3.639306	12.890428
Atlantic	(27.25,27.5]	tem oxygen phosphate phosphate_star	4.829126	4.427319	3.650830	12.907275
Atlantic	(27.25,27.5]	sal aou oxygen phosphate phosphate_star	4.902251	4.329200	3.676427	12.907879
Atlantic	(27.25,27.5]	tem aou phosphate phosphate_star	4.869864	4.406926	3.657707	12.934496
Atlantic	(27.25,27.5]	sal tem aou oxygen phosphate	4.685854	4.337938	3.941030	12.964822
Atlantic	(27.25,27.5]	aou oxygen silicate phosphate phosphate_star	4.915736	4.397225	3.652675	12.965636
Atlantic	(27.5,27.75]	tem aou silicate phosphate phosphate_star	4.152646	4.354761	4.230365	12.737772
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate phosphate_star	4.169785	4.343844	4.225606	12.739234
Atlantic	(27.5,27.75]	tem oxygen silicate phosphate phosphate_star	4.143670	4.370246	4.236112	12.750028
Atlantic	(27.5,27.75]	sal aou oxygen silicate phosphate	4.174741	4.328080	4.306869	12.809689
Atlantic	(27.5,27.75]	sal tem aou silicate phosphate	4.161707	4.340464	4.307726	12.809898
Atlantic	(27.5,27.75]	sal tem oxygen silicate phosphate	4.152754	4.352114	4.311898	12.816766
Atlantic	(27.5,27.75]	tem aou oxygen silicate phosphate	4.152046	4.332673	4.334831	12.819550
Atlantic	(27.5,27.75]	tem aou silicate phosphate	4.168309	4.368467	4.336453	12.873229
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate	4.185459	4.356671	4.334895	12.877025
Atlantic	(27.5,27.75]	tem oxygen silicate phosphate	4.158773	4.386122	4.340037	12.884931
Atlantic	(27.75,27.85]	sal oxygen silicate phosphate phosphate_star	4.109309	4.270082	6.038244	14.417635
Atlantic	(27.75,27.85]	sal aou oxygen silicate phosphate	4.113685	4.277923	6.026571	14.418179
Atlantic	(27.75,27.85]	sal tem oxygen silicate phosphate	4.112834	4.277933	6.034910	14.425676
Atlantic	(27.75,27.85]	sal tem aou silicate phosphate	4.114571	4.278130	6.036798	14.429498
Atlantic	(27.75,27.85]	sal aou silicate phosphate phosphate_star	4.106682	4.277368	6.048439	14.432490
Atlantic	(27.75,27.85]	sal oxygen silicate phosphate	4.121204	4.278115	6.042167	14.441486
Atlantic	(27.75,27.85]	sal aou silicate phosphate	4.120126	4.284911	6.051476	14.456513
Atlantic	(27.75,27.85]	tem aou oxygen silicate phosphate	4.200707	4.299464	5.985892	14.486063
Atlantic	(27.75,27.85]	tem oxygen silicate phosphate phosphate_star	4.188746	4.295924	6.039920	14.524590
Atlantic	(27.75,27.85]	tem aou silicate phosphate phosphate_star	4.191536	4.297340	6.042127	14.531002
Atlantic	(27.85,27.95]	sal aou oxygen silicate phosphate	3.728892	4.171368	4.839290	12.739550
Atlantic	(27.85,27.95]	sal tem oxygen silicate phosphate	3.740886	4.187591	4.873867	12.802345
Atlantic	(27.85,27.95]	sal tem aou silicate phosphate	3.751565	4.193647	4.873647	12.818859
Atlantic	(27.85,27.95]	sal tem silicate phosphate phosphate_star	3.880601	4.291497	4.833368	13.005465
Atlantic	(27.85,27.95]	sal tem silicate phosphate	3.981572	4.291511	4.873938	13.147020
Atlantic	(27.85,27.95]	sal oxygen silicate phosphate phosphate_star	3.771449	4.414214	5.307082	13.492745
Atlantic	(27.85,27.95]	sal oxygen silicate phosphate	3.788985	4.443802	5.328717	13.561504
Atlantic	(27.85,27.95]	sal aou silicate phosphate phosphate_star	3.894236	4.600712	5.375904	13.870852
Atlantic	(27.85,27.95]	sal aou silicate phosphate	3.924663	4.617415	5.383637	13.925714
Atlantic	(27.85,27.95]	tem aou oxygen silicate phosphate	4.212035	4.851104	5.267509	14.330648
Atlantic	(27.95,28.05]	sal aou oxygen silicate phosphate	3.487770	4.363515	4.820087	12.671372
Atlantic	(27.95,28.05]	sal tem oxygen silicate phosphate	3.498901	4.381935	4.910557	12.791393
Atlantic	(27.95,28.05]	sal oxygen silicate phosphate phosphate_star	3.570396	4.378362	4.875191	12.823949
Atlantic	(27.95,28.05]	sal tem aou silicate phosphate	3.508118	4.406907	4.931814	12.846839
Atlantic	(27.95,28.05]	sal tem aou oxygen phosphate	3.755336	4.367751	4.799080	12.922167
Atlantic	(27.95,28.05]	sal oxygen silicate phosphate	3.570686	4.398756	5.020607	12.990049
Atlantic	(27.95,28.05]	sal aou silicate phosphate phosphate_star	3.750648	4.565335	5.100329	13.416313
Atlantic	(27.95,28.05]	sal tem silicate phosphate phosphate_star	3.755808	4.805916	4.861915	13.423639
Atlantic	(27.95,28.05]	sal aou silicate phosphate	3.757788	4.574558	5.190912	13.523258
Atlantic	(27.95,28.05]	sal tem silicate phosphate	3.758011	4.813288	4.988962	13.560260
Atlantic	(28.05,28.1]	sal tem aou oxygen phosphate	3.539499	4.360234	4.144983	12.044717
Atlantic	(28.05,28.1]	tem aou oxygen silicate phosphate	3.643192	4.334898	4.117142	12.095232
Atlantic	(28.05,28.1]	tem aou oxygen phosphate phosphate_star	3.737328	4.451323	4.186888	12.375539
Atlantic	(28.05,28.1]	tem aou oxygen phosphate	3.737933	4.455027	4.228193	12.421153
Atlantic	(28.05,28.1]	sal tem oxygen silicate phosphate	3.531111	4.577761	4.415293	12.524164
Atlantic	(28.05,28.1]	sal tem oxygen phosphate phosphate_star	3.554312	4.623523	4.356252	12.534087
Atlantic	(28.05,28.1]	sal oxygen silicate phosphate phosphate_star	3.548422	4.588242	4.447473	12.584137
Atlantic	(28.05,28.1]	sal tem oxygen phosphate	3.557078	4.627894	4.416199	12.601171
Atlantic	(28.05,28.1]	sal aou oxygen silicate phosphate	3.554108	4.594985	4.529410	12.678503
Atlantic	(28.05,28.1]	sal oxygen silicate phosphate	3.555467	4.604476	4.534233	12.694176
Atlantic	(28.1,28.15]	sal tem oxygen silicate phosphate	3.349308	3.947860	4.254217	11.551386
Atlantic	(28.1,28.15]	sal tem aou oxygen phosphate	3.440411	3.952540	4.211635	11.604587
Atlantic	(28.1,28.15]	tem aou oxygen silicate phosphate	3.436793	3.969257	4.216057	11.622107
Atlantic	(28.1,28.15]	sal tem oxygen phosphate phosphate_star	3.448754	3.962868	4.243864	11.655485
Atlantic	(28.1,28.15]	tem oxygen silicate phosphate phosphate_star	3.430280	3.982169	4.243363	11.655811
Atlantic	(28.1,28.15]	sal tem oxygen phosphate	3.449525	3.962887	4.254795	11.667208
Atlantic	(28.1,28.15]	tem oxygen silicate phosphate	3.437071	3.982172	4.255279	11.674522
Atlantic	(28.1,28.15]	sal tem aou silicate phosphate	3.390856	4.014727	4.319062	11.724645
Atlantic	(28.1,28.15]	tem aou oxygen phosphate phosphate_star	3.542289	3.992478	4.211446	11.746213
Atlantic	(28.1,28.15]	tem aou oxygen phosphate	3.542305	3.993360	4.220084	11.755749
Atlantic	(28.15,28.2]	sal tem aou oxygen phosphate	3.719163	3.607541	2.836143	10.162847
Atlantic	(28.15,28.2]	sal tem aou phosphate phosphate_star	3.727244	3.668400	2.837066	10.232710
Atlantic	(28.15,28.2]	sal aou oxygen silicate phosphate	3.713912	3.607352	2.914045	10.235310
Atlantic	(28.15,28.2]	sal tem aou silicate phosphate	3.739761	3.662219	2.835064	10.237044
Atlantic	(28.15,28.2]	sal tem aou phosphate	3.740143	3.669008	2.837785	10.246936
Atlantic	(28.15,28.2]	sal aou oxygen phosphate phosphate_star	3.705570	3.607523	2.955392	10.268485
Atlantic	(28.15,28.2]	sal aou oxygen phosphate	3.719217	3.607575	2.956477	10.283268
Atlantic	(28.15,28.2]	sal tem oxygen silicate phosphate	3.775192	3.711973	2.836415	10.323580
Atlantic	(28.15,28.2]	sal tem oxygen phosphate phosphate_star	3.777038	3.727122	2.835243	10.339403
Atlantic	(28.15,28.2]	sal tem oxygen phosphate	3.784450	3.728657	2.836701	10.349807
Atlantic	(28.2, Inf]	sal tem aou oxygen phosphate	3.337999	3.057466	2.685083	9.080549
Atlantic	(28.2, Inf]	sal tem aou silicate phosphate	3.425561	3.059270	2.696506	9.181337
Atlantic	(28.2, Inf]	sal aou oxygen silicate phosphate	3.358320	3.057387	2.767527	9.183233
Atlantic	(28.2, Inf]	sal aou oxygen phosphate phosphate_star	3.376522	3.052250	2.763926	9.192697
Atlantic	(28.2, Inf]	sal aou oxygen phosphate	3.378104	3.057832	2.767543	9.203479
Atlantic	(28.2, Inf]	sal tem aou phosphate phosphate_star	3.471029	3.052605	2.692778	9.216412
Atlantic	(28.2, Inf]	sal tem aou phosphate	3.472721	3.059318	2.700720	9.232760
Atlantic	(28.2, Inf]	sal tem oxygen silicate phosphate	3.502342	3.059982	2.676045	9.238369
Atlantic	(28.2, Inf]	tem aou oxygen silicate phosphate	3.361576	3.187744	2.736479	9.285798
Atlantic	(28.2, Inf]	tem aou oxygen phosphate phosphate_star	3.384056	3.199139	2.751414	9.334609
Indo-Pacific	(-Inf,26]	sal aou oxygen phosphate phosphate_star	11.656608	6.900704	4.749102	23.306414
Indo-Pacific	(-Inf,26]	sal tem aou phosphate phosphate_star	11.727854	6.878761	4.969301	23.575916
Indo-Pacific	(-Inf,26]	sal tem oxygen phosphate phosphate_star	11.772722	6.912573	5.115444	23.800739
Indo-Pacific	(-Inf,26]	sal aou oxygen silicate phosphate	11.589172	7.158929	5.647250	24.395350
Indo-Pacific	(-Inf,26]	sal tem aou silicate phosphate	11.658578	7.235892	5.850663	24.745133
Indo-Pacific	(-Inf,26]	sal tem aou oxygen phosphate_star	12.529402	7.077213	5.306486	24.913100
Indo-Pacific	(-Inf,26]	sal tem oxygen silicate phosphate	11.696367	7.284738	5.951189	24.932294
Indo-Pacific	(-Inf,26]	sal tem oxygen silicate phosphate_star	12.560468	7.084183	5.319801	24.964453
Indo-Pacific	(-Inf,26]	sal tem aou silicate phosphate_star	12.589079	7.121562	5.271127	24.981768
Indo-Pacific	(-Inf,26]	sal tem oxygen phosphate_star	12.571709	7.084201	5.382382	25.038292
Indo-Pacific	(26,26.5]	sal aou oxygen silicate phosphate	7.855393	5.186663	3.936596	16.978653
Indo-Pacific	(26,26.5]	sal aou oxygen phosphate phosphate_star	7.817898	5.210436	3.950876	16.979211
Indo-Pacific	(26,26.5]	sal tem aou phosphate phosphate_star	7.880514	5.109471	3.991869	16.981853
Indo-Pacific	(26,26.5]	sal tem oxygen phosphate phosphate_star	7.921449	5.102455	4.024452	17.048356
Indo-Pacific	(26,26.5]	sal tem aou silicate phosphate	7.929705	5.144796	4.013896	17.088397
Indo-Pacific	(26,26.5]	sal tem oxygen silicate phosphate	7.966619	5.154135	4.053536	17.174291
Indo-Pacific	(26,26.5]	sal tem aou oxygen phosphate	7.962543	5.284439	4.249030	17.496012
Indo-Pacific	(26,26.5]	sal aou oxygen phosphate	7.963659	5.385492	4.254610	17.603760
Indo-Pacific	(26,26.5]	sal tem aou phosphate	8.017736	5.296122	4.291014	17.604872
Indo-Pacific	(26,26.5]	sal tem oxygen phosphate	8.048135	5.285536	4.311661	17.645332
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate phosphate_star	5.629568	5.427048	4.202174	15.258790
Indo-Pacific	(26.5,26.75]	sal tem aou phosphate phosphate_star	5.730080	5.467521	4.284679	15.482280
Indo-Pacific	(26.5,26.75]	sal tem oxygen phosphate phosphate_star	5.794994	5.507934	4.346552	15.649481
Indo-Pacific	(26.5,26.75]	sal aou oxygen silicate phosphate	5.889764	5.680903	4.559978	16.130645
Indo-Pacific	(26.5,26.75]	sal tem aou oxygen phosphate	5.970854	5.686979	4.616972	16.274805
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate	5.972964	5.687005	4.633021	16.292990
Indo-Pacific	(26.5,26.75]	sal tem aou silicate phosphate	6.032011	5.697592	4.657965	16.387568
Indo-Pacific	(26.5,26.75]	aou oxygen silicate phosphate phosphate_star	6.122193	5.834373	4.451642	16.408209
Indo-Pacific	(26.5,26.75]	sal tem aou phosphate	6.059163	5.723138	4.713418	16.495719
Indo-Pacific	(26.5,26.75]	tem aou oxygen phosphate phosphate_star	6.099615	5.833885	4.575006	16.508507
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate phosphate_star	6.482046	4.918858	4.030858	15.431763
Indo-Pacific	(26.75,27]	sal aou oxygen phosphate phosphate_star	6.533269	4.972238	4.046389	15.551896
Indo-Pacific	(26.75,27]	aou oxygen silicate phosphate phosphate_star	6.488004	4.974323	4.153212	15.615538
Indo-Pacific	(26.75,27]	tem aou oxygen silicate phosphate	6.492756	4.983055	4.222006	15.697817
Indo-Pacific	(26.75,27]	aou oxygen phosphate phosphate_star	6.567840	5.032576	4.153259	15.753675
Indo-Pacific	(26.75,27]	sal tem aou oxygen phosphate	6.516743	5.021419	4.249032	15.787194
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate	6.520101	5.023021	4.262325	15.805447
Indo-Pacific	(26.75,27]	tem aou silicate phosphate phosphate_star	6.519436	5.038575	4.287497	15.845508
Indo-Pacific	(26.75,27]	sal aou oxygen silicate phosphate	6.552579	5.062787	4.418776	16.034141
Indo-Pacific	(26.75,27]	tem oxygen silicate phosphate phosphate_star	6.555616	5.102646	4.381077	16.039339
Indo-Pacific	(27,27.25]	tem aou oxygen silicate phosphate	5.981049	4.528738	4.048207	14.557994
Indo-Pacific	(27,27.25]	sal tem aou oxygen phosphate	5.996869	4.633491	4.166144	14.796504
Indo-Pacific	(27,27.25]	tem aou oxygen phosphate phosphate_star	6.022258	4.653828	4.163487	14.839572
Indo-Pacific	(27,27.25]	tem aou oxygen phosphate	6.024170	4.749439	4.304603	15.078211
Indo-Pacific	(27,27.25]	sal aou oxygen silicate phosphate	6.377139	4.600567	4.107446	15.085152
Indo-Pacific	(27,27.25]	sal aou silicate phosphate phosphate_star	6.447889	4.602734	4.121767	15.172390
Indo-Pacific	(27,27.25]	sal tem aou silicate phosphate	6.492264	4.606457	4.119478	15.218199
Indo-Pacific	(27,27.25]	sal aou silicate phosphate	6.502600	4.606489	4.126122	15.235212
Indo-Pacific	(27,27.25]	sal aou oxygen phosphate phosphate_star	6.376268	4.788951	4.174627	15.339847
Indo-Pacific	(27,27.25]	sal tem oxygen silicate phosphate	6.598846	4.645770	4.146776	15.391393
Indo-Pacific	(27.25,27.5]	tem aou oxygen silicate phosphate	4.804957	3.917807	3.527790	12.250554
Indo-Pacific	(27.25,27.5]	sal aou oxygen silicate phosphate	5.216429	4.018839	3.243081	12.478348
Indo-Pacific	(27.25,27.5]	tem aou oxygen phosphate phosphate_star	4.832492	4.091347	3.647515	12.571355
Indo-Pacific	(27.25,27.5]	sal tem aou oxygen phosphate	4.831746	4.155836	3.627177	12.614759
Indo-Pacific	(27.25,27.5]	tem aou oxygen phosphate	4.835593	4.187854	3.729263	12.752711
Indo-Pacific	(27.25,27.5]	sal tem aou silicate phosphate	5.541110	4.045015	3.247152	12.833277
Indo-Pacific	(27.25,27.5]	sal aou oxygen phosphate phosphate_star	5.168633	4.254738	3.564507	12.987878
Indo-Pacific	(27.25,27.5]	aou oxygen silicate phosphate phosphate_star	5.196364	4.223141	3.679102	13.098607
Indo-Pacific	(27.25,27.5]	sal tem oxygen silicate phosphate	5.764252	4.080878	3.253916	13.099046
Indo-Pacific	(27.25,27.5]	sal aou silicate phosphate phosphate_star	5.884313	4.057400	3.239888	13.181601
Indo-Pacific	(27.5,27.75]	sal aou oxygen silicate phosphate	4.655491	3.688018	2.968149	11.311657
Indo-Pacific	(27.5,27.75]	sal tem aou silicate phosphate	4.822537	3.696125	2.966581	11.485243
Indo-Pacific	(27.5,27.75]	tem aou oxygen silicate phosphate	4.386458	3.842393	3.290961	11.519812
Indo-Pacific	(27.5,27.75]	sal tem oxygen silicate phosphate	4.949934	3.708516	2.965966	11.624416
Indo-Pacific	(27.5,27.75]	sal tem aou oxygen phosphate	4.409996	3.883718	3.371011	11.664725
Indo-Pacific	(27.5,27.75]	tem aou oxygen phosphate phosphate_star	4.409247	3.912393	3.405050	11.726690
Indo-Pacific	(27.5,27.75]	tem aou oxygen phosphate	4.410507	3.921164	3.429891	11.761562
Indo-Pacific	(27.5,27.75]	sal aou oxygen phosphate phosphate_star	4.656269	3.859073	3.334569	11.849911
Indo-Pacific	(27.5,27.75]	sal aou oxygen phosphate	4.656383	3.885574	3.372534	11.914491
Indo-Pacific	(27.5,27.75]	aou oxygen silicate phosphate phosphate_star	4.660946	3.857583	3.409260	11.927789
Indo-Pacific	(27.75,27.85]	tem aou oxygen silicate phosphate	4.242882	3.271777	2.903747	10.418405
Indo-Pacific	(27.75,27.85]	sal tem oxygen silicate phosphate	4.281560	3.291064	2.865015	10.437639
Indo-Pacific	(27.75,27.85]	sal tem aou silicate phosphate	4.258533	3.311684	2.876268	10.446485
Indo-Pacific	(27.75,27.85]	sal aou oxygen silicate phosphate	4.235175	3.347718	2.896917	10.479810
Indo-Pacific	(27.75,27.85]	tem aou silicate phosphate phosphate_star	4.273516	3.302046	2.918998	10.494560
Indo-Pacific	(27.75,27.85]	tem oxygen silicate phosphate phosphate_star	4.299485	3.286256	2.911216	10.496957
Indo-Pacific	(27.75,27.85]	tem oxygen silicate phosphate	4.300570	3.296323	2.916579	10.513473
Indo-Pacific	(27.75,27.85]	tem aou silicate phosphate	4.275388	3.316085	2.924736	10.516208
Indo-Pacific	(27.75,27.85]	aou oxygen silicate phosphate phosphate_star	4.245475	3.332871	2.938537	10.516883
Indo-Pacific	(27.75,27.85]	aou oxygen silicate phosphate	4.249542	3.356084	2.945707	10.551334
Indo-Pacific	(27.85,27.95]	tem aou silicate phosphate phosphate_star	4.274004	2.989254	2.887257	10.150515
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate phosphate_star	4.256269	2.993750	2.902527	10.152545
Indo-Pacific	(27.85,27.95]	sal tem aou silicate phosphate	4.290311	3.000580	2.878296	10.169187
Indo-Pacific	(27.85,27.95]	tem oxygen silicate phosphate phosphate_star	4.294333	2.994511	2.882504	10.171348
Indo-Pacific	(27.85,27.95]	tem aou oxygen silicate phosphate	4.280774	3.000763	2.891621	10.173158
Indo-Pacific	(27.85,27.95]	sal aou oxygen silicate phosphate	4.272593	3.007732	2.896370	10.176695
Indo-Pacific	(27.85,27.95]	sal tem oxygen silicate phosphate	4.311405	3.004330	2.869502	10.185237
Indo-Pacific	(27.85,27.95]	tem aou silicate phosphate	4.295926	3.000801	2.897066	10.193793
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate	4.280926	3.007769	2.912915	10.201610
Indo-Pacific	(27.85,27.95]	sal aou oxygen phosphate phosphate_star	4.237357	3.016584	2.959140	10.213081
Indo-Pacific	(27.95,28.05]	sal aou oxygen silicate phosphate	4.359139	2.857154	3.075517	10.291810
Indo-Pacific	(27.95,28.05]	sal aou oxygen phosphate phosphate_star	4.359852	2.877276	3.073963	10.311091
Indo-Pacific	(27.95,28.05]	aou oxygen silicate phosphate phosphate_star	4.377427	2.861323	3.076725	10.315475
Indo-Pacific	(27.95,28.05]	tem aou oxygen phosphate phosphate_star	4.378207	2.870660	3.073851	10.322719
Indo-Pacific	(27.95,28.05]	sal tem aou silicate phosphate	4.377696	2.882277	3.064828	10.324801
Indo-Pacific	(27.95,28.05]	aou oxygen phosphate phosphate_star	4.378771	2.877804	3.077571	10.334146
Indo-Pacific	(27.95,28.05]	sal tem aou oxygen phosphate	4.359973	2.871354	3.107381	10.338708
Indo-Pacific	(27.95,28.05]	sal aou oxygen phosphate	4.360181	2.879287	3.107563	10.347031
Indo-Pacific	(27.95,28.05]	tem aou silicate phosphate phosphate_star	4.401881	2.886861	3.065987	10.354728
Indo-Pacific	(27.95,28.05]	tem aou oxygen silicate phosphate	4.381237	2.866160	3.109301	10.356698
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate phosphate_star	4.228217	2.860046	2.799367	9.887630
Indo-Pacific	(28.05,28.1]	sal aou oxygen silicate phosphate	4.225670	2.848200	2.826261	9.900131
Indo-Pacific	(28.05,28.1]	sal tem aou oxygen phosphate	4.225054	2.860776	2.817179	9.903010
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate	4.228221	2.863082	2.828633	9.919937
Indo-Pacific	(28.05,28.1]	aou oxygen silicate phosphate phosphate_star	4.227177	2.874648	2.825582	9.927407
Indo-Pacific	(28.05,28.1]	tem aou oxygen phosphate phosphate_star	4.227073	2.874723	2.843130	9.944926
Indo-Pacific	(28.05,28.1]	aou oxygen phosphate phosphate_star	4.232069	2.875188	2.849672	9.956929
Indo-Pacific	(28.05,28.1]	sal tem aou silicate phosphate	4.264970	2.856439	2.836178	9.957587
Indo-Pacific	(28.05,28.1]	tem aou oxygen silicate phosphate	4.226770	2.880685	2.860748	9.968203
Indo-Pacific	(28.05,28.1]	aou oxygen silicate phosphate	4.228213	2.881751	2.870188	9.980152
Indo-Pacific	(28.1, Inf]	sal aou oxygen silicate phosphate	3.570328	3.028688	2.582084	9.181099
Indo-Pacific	(28.1, Inf]	tem aou oxygen silicate phosphate	3.601769	2.985715	2.648408	9.235892
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate phosphate_star	3.635023	2.938152	2.688069	9.261244
Indo-Pacific	(28.1, Inf]	sal aou oxygen phosphate phosphate_star	3.599599	3.136083	2.593341	9.329023
Indo-Pacific	(28.1, Inf]	sal tem aou oxygen phosphate	3.540683	3.225881	2.586405	9.352969
Indo-Pacific	(28.1, Inf]	sal tem aou phosphate phosphate_star	3.540570	3.173834	2.644631	9.359035
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate	3.640879	3.028695	2.696173	9.365747
Indo-Pacific	(28.1, Inf]	sal aou oxygen phosphate	3.599961	3.230532	2.595467	9.425960
Indo-Pacific	(28.1, Inf]	sal tem aou silicate phosphate	3.542161	3.278460	2.644383	9.465004
Indo-Pacific	(28.1, Inf]	sal tem aou phosphate	3.543402	3.311094	2.655950	9.510446

# lm_best_n <-lm_best %>% 
#   group_by(basin, gamma_slab) %>% 
#   summarise(n()) %>% 
#   ungroup()

rm(n_predictors_max, n_predictors_min, 
   all_lm_stats, all_lm_stats_wide)

lm_1 <- GLODAP %>% 
  filter(basin == "Atlantic",
         gamma_slab == "(-Inf,26]",
         era == "new_era") %>% 
  lm(Cstar ~ salinity + temperature + aou + oxygen + phosphate_star, data = .)

lm_2 <- GLODAP %>% 
  filter(basin == "Atlantic",
         gamma_slab == "(-Inf,26]",
         era == "new_era") %>% 
  lm(Cstar ~ salinity + temperature + aou + oxygen + phosphate, data = .)

lm_1
lm_2

sqrt(mean(lm_1$residuals^2))
sqrt(mean(lm_2$residuals^2))

6.3.2 Fitting best models

After selecting 10 linear regression models with lowest summed RMSE across all eras, models are fitted again and model coefficients are saved to file.

lm_best <- lm_best %>% 
  mutate(lm_coeff = str_replace_all(predictors, " ", " + "),
         lm_coeff = paste("Cstar ~", lm_coeff))

for (i_basin in unique(GLODAP$basin)) {
  for (i_era in unique(GLODAP$era)) {
    
    # i_basin <- unique(GLODAP$basin)[1]
    # i_era   <- unique(GLODAP$era)[1]
    
    print(i_basin) 
    print(i_era  )
    
    GLODAP_basin_era <- GLODAP %>%
      filter(basin == i_basin, era == i_era)

    lm_best_basin <- lm_best %>%
      filter(basin == i_basin)

    for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {

      # i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
      print(i_gamma_slab)
      
      GLODAP_basin_era_slab <- GLODAP_basin_era %>% 
        filter(gamma_slab == i_gamma_slab)
      
      lm_best_basin_slab <- lm_best_basin %>% 
        filter(gamma_slab == i_gamma_slab)
      
      for (i_predictors in unique(lm_best_basin_slab$predictors)) {
        
        # i_predictors <- unique(lm_best_basin_slab$predictors)[1]
        
        lm_best_single <- lm_best_basin_slab %>%
          filter(predictors == i_predictors) %>%
          select(lm_coeff) %>%
          pull()
        
        i_rmse_sum <- lm_best_basin_slab %>%
          filter(predictors == i_predictors) %>%
          select(rmse_sum) %>%
          pull()
        
        lm_formula <- as.formula(lm_best_single)
        
        model_single <- lm(lm_formula, 
              data = GLODAP_basin_era_slab)
        
        coefficients <- tidy(model_single)
        coefficients <- coefficients %>% 
          mutate(basin = i_basin,
                 era = i_era,
                 gamma_slab = i_gamma_slab,
                 model = lm_best_single,
                 rmse = i_rmse_sum)
        
        print(lm_best_single)
      
      if (exists("all_lm")) {
        all_lm <- bind_rows(all_lm, coefficients)
      }
      
      if (!exists("all_lm")) {
        all_lm <- coefficients
      }
      

      }
      
 
    }
    
  }
  
}


rm(lm_formula, model_single, coefficients, i_rmse_sum,
   GLODAP_basin_era, GLODAP_basin_era_slab,
   lm_best, lm_best_basin, lm_best_basin_slab, lm_best_single,
   i_basin, i_era, i_gamma_slab, i_predictors)

all_lm %>%
  write_csv(here::here("data/eMLR",
                       "all_lm.csv"))

7 Open tasks

combine correlation, rmse and model calculation into one routine, ideally using the purrr map approach
select exactly best 10 models, even if same rmse sum appears more than once (currently, selection is set two ten, even if doublicated rmse occur)

8 Open questions

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] corrr_0.4.2      kableExtra_1.1.0 knitr_1.29       olsrr_0.5.3.9000
 [5] GGally_2.0.0     broom_0.7.0      patchwork_1.0.1  lubridate_1.7.9 
 [9] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.0      purrr_0.3.4     
[13] readr_1.3.1      tidyr_1.1.0      tibble_3.0.3     ggplot2_3.3.2   
[17] tidyverse_1.3.0  workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] fs_1.4.2           webshot_0.5.2      RColorBrewer_1.1-2 httr_1.4.2        
 [5] rprojroot_1.3-2    tools_4.0.2        backports_1.1.8    R6_2.4.1          
 [9] nortest_1.0-4      DBI_1.1.0          colorspace_1.4-1   withr_2.2.0       
[13] tidyselect_1.1.0   gridExtra_2.3      curl_4.3           compiler_4.0.2    
[17] git2r_0.27.1       cli_2.0.2          rvest_0.3.6        xml2_1.3.2        
[21] labeling_0.3       scales_1.1.1       goftest_1.2-2      digest_0.6.25     
[25] foreign_0.8-80     rmarkdown_2.3      rio_0.5.16         pkgconfig_2.0.3   
[29] htmltools_0.5.0    dbplyr_1.4.4       highr_0.8          rlang_0.4.7       
[33] readxl_1.3.1       rstudioapi_0.11    generics_0.0.2     farver_2.0.3      
[37] jsonlite_1.7.0     zip_2.0.4          car_3.0-8          magrittr_1.5      
[41] Rcpp_1.0.5         munsell_0.5.0      fansi_0.4.1        abind_1.4-5       
[45] lifecycle_0.2.0    stringi_1.4.6      whisker_0.4        yaml_2.2.1        
[49] carData_3.0-4      plyr_1.8.6         grid_4.0.2         blob_1.2.1        
[53] promises_1.1.1     crayon_1.3.4       haven_2.3.1        hms_0.5.3         
[57] pillar_1.4.6       reprex_0.3.0       glue_1.4.1         evaluate_0.14     
[61] data.table_1.13.0  modelr_0.1.8       vctrs_0.3.2        httpuv_1.5.4      
[65] cellranger_1.1.0   gtable_0.3.0       reshape_0.8.8      assertthat_0.2.1  
[69] xfun_0.16          openxlsx_4.1.5     later_1.1.0.1      viridisLite_0.3.0 
[73] ellipsis_0.3.1     here_0.1

Data base

Jens Daniel Müller

12 August, 2020

1 Required data

2 C*

2.1 Stoichiometric ratios

2.2 Calculation

3 PO₄* calculation

4 Reference year adjustment

4.1 Merge data sets

4.1.1 GLODAP + Cant

4.1.2 GLODAP + atm. pCO₂

4.2 Calculate adjustment

4.3 Control plots

4.3.1 Histogram

4.3.2 Time series

5 Selected section plots

6 MLR

6.1 Isoneutral slabs

6.2 Predictor correlation

6.2.1 Correlation plots

6.2.2 Correlation assesment

6.2.2.1 Calculation of correlation coeffcients

6.2.2.2 Predictor pairs

6.2.2.3 C* vs individual predictors

6.3 Model fitting

6.3.1 Predictor selection

6.3.2 Fitting best models

7 Open tasks

8 Open questions

Data base

Jens Daniel Müller

12 August, 2020

1 Required data

2 C*

2.1 Stoichiometric ratios

2.2 Calculation

3 PO4* calculation

4 Reference year adjustment

4.1 Merge data sets

4.1.1 GLODAP + Cant

4.1.2 GLODAP + atm. pCO2

4.2 Calculate adjustment

4.3 Control plots

4.3.1 Histogram

4.3.2 Time series

5 Selected section plots

6 MLR

6.1 Isoneutral slabs

6.2 Predictor correlation

6.2.1 Correlation plots

6.2.2 Correlation assesment

6.2.2.1 Calculation of correlation coeffcients

6.2.2.2 Predictor pairs

6.2.2.3 C* vs individual predictors

6.3 Model fitting

6.3.1 Predictor selection

6.3.2 Fitting best models

7 Open tasks

8 Open questions

3 PO₄* calculation

4.1.2 GLODAP + atm. pCO₂