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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)

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

GLODAP_cruise %>%
  arrange(date) %>% 
  ggplot(aes(lon, lat)) +
  mapWorld +
  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(mapWorld, 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)

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",
                      "salinity",
                      "temperature",
                      "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",
                      "salinity",
                      "temperature",
                      "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",
                      "salinity",
                      "temperature",
                      "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,
                         "| total nr", nrow(GLODAP_basin_era),
                         "| slab nr", nrow(GLODAP_highlight %>% 
                                             filter(gamma_highlight == "slab"))))
  

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,
         salinity,
         temperature,
         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]	-0.9199892	-0.9636779	-0.8894647
aou + oxygen	Indo-Pacific	(26,26.5]	-0.9803426	-0.9845577	-0.9728250
aou + oxygen	Indo-Pacific	(26.5,26.75]	-0.9850881	-0.9877960	-0.9817863
aou + oxygen	Indo-Pacific	(26.75,27]	-0.9836727	-0.9846370	-0.9829894
aou + oxygen	Indo-Pacific	(27,27.25]	-0.9886504	-0.9929829	-0.9800836
aou + oxygen	Indo-Pacific	(27.25,27.5]	-0.9913226	-0.9954821	-0.9836315
aou + oxygen	Indo-Pacific	(27.5,27.75]	-0.9926744	-0.9967320	-0.9852991
aou + oxygen	Indo-Pacific	(27.75,27.85]	-0.9961082	-0.9989585	-0.9921026
aou + oxygen	Indo-Pacific	(27.85,27.95]	-0.9968241	-0.9990057	-0.9946008
aou + oxygen	Indo-Pacific	(27.95,28.05]	-0.9951951	-0.9964353	-0.9934380
aou + oxygen	Indo-Pacific	(28.05,28.1]	-0.9956157	-0.9966147	-0.9946222
aou + oxygen	Indo-Pacific	(28.1, Inf]	-0.9908663	-0.9923555	-0.9887596
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]	0.9403499	0.9073617	0.9670963
aou + phosphate	Indo-Pacific	(26,26.5]	0.9545261	0.9481344	0.9627786
aou + phosphate	Indo-Pacific	(26.5,26.75]	0.9511342	0.9393080	0.9626975
aou + phosphate	Indo-Pacific	(26.75,27]	0.9500133	0.9461165	0.9539790
aou + phosphate	Indo-Pacific	(27,27.25]	0.9666580	0.9484321	0.9806798
aou + phosphate	Indo-Pacific	(27.25,27.5]	0.9711209	0.9521979	0.9808396
aou + phosphate	Indo-Pacific	(27.5,27.75]	0.9751403	0.9605167	0.9825862
aou + phosphate	Indo-Pacific	(27.75,27.85]	0.9823398	0.9735339	0.9883639
aou + phosphate	Indo-Pacific	(27.85,27.95]	0.9801186	0.9705015	0.9891580
aou + phosphate	Indo-Pacific	(27.95,28.05]	0.9674872	0.9566842	0.9761508
aou + phosphate	Indo-Pacific	(28.05,28.1]	0.9574105	0.9442222	0.9715225
aou + phosphate	Indo-Pacific	(28.1, Inf]	0.7800593	0.7279375	0.8296450
aou + phosphate_star	Atlantic	(-Inf,26]	0.0751886	-0.4341508	0.3482348
aou + phosphate_star	Atlantic	(26,26.5]	0.3475250	0.0643405	0.6175442
aou + phosphate_star	Atlantic	(26.5,26.75]	0.4741260	0.3723426	0.6411307
aou + phosphate_star	Atlantic	(26.75,27]	0.2753734	0.2256466	0.3240950
aou + phosphate_star	Atlantic	(27,27.25]	0.1490537	-0.0321727	0.3056935
aou + phosphate_star	Atlantic	(27.25,27.5]	0.1729314	0.0440112	0.3213433
aou + phosphate_star	Atlantic	(27.5,27.75]	0.5455524	0.4836519	0.5929938
aou + phosphate_star	Atlantic	(27.75,27.85]	0.7638965	0.7433138	0.7962242
aou + phosphate_star	Atlantic	(27.85,27.95]	0.7180275	0.6537077	0.7855705
aou + phosphate_star	Atlantic	(27.95,28.05]	0.8229635	0.7423182	0.9319089
aou + phosphate_star	Atlantic	(28.05,28.1]	0.8861871	0.8392220	0.9523375
aou + phosphate_star	Atlantic	(28.1,28.15]	0.9253933	0.9114497	0.9418630
aou + phosphate_star	Atlantic	(28.15,28.2]	0.9755588	0.9625218	0.9834872
aou + phosphate_star	Atlantic	(28.2, Inf]	0.4783872	0.3898943	0.6414743
aou + phosphate_star	Indo-Pacific	(-Inf,26]	0.6620179	0.5215468	0.7430101
aou + phosphate_star	Indo-Pacific	(26,26.5]	0.5812512	0.5202906	0.6206208
aou + phosphate_star	Indo-Pacific	(26.5,26.75]	0.4265043	0.1669141	0.5829578
aou + phosphate_star	Indo-Pacific	(26.75,27]	0.3870938	0.3240540	0.4860624
aou + phosphate_star	Indo-Pacific	(27,27.25]	0.1607629	0.0764660	0.2290589
aou + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.4139314	-0.4787101	-0.3597691
aou + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.6003363	-0.6957268	-0.4920225
aou + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.4758166	-0.6105114	-0.3557962
aou + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.0689547	-0.1201820	0.0056397
aou + phosphate_star	Indo-Pacific	(27.95,28.05]	0.2346827	0.1165401	0.3284777
aou + phosphate_star	Indo-Pacific	(28.05,28.1]	0.4091718	0.3650681	0.4643695
aou + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.6155817	-0.6499367	-0.5641977
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]	0.7213888	0.6365610	0.7899518
aou + silicate	Indo-Pacific	(26,26.5]	0.6505259	0.5381656	0.7487756
aou + silicate	Indo-Pacific	(26.5,26.75]	0.6121560	0.4093259	0.7315507
aou + silicate	Indo-Pacific	(26.75,27]	0.7488040	0.6938246	0.7813525
aou + silicate	Indo-Pacific	(27,27.25]	0.8648235	0.8075377	0.9105990
aou + silicate	Indo-Pacific	(27.25,27.5]	0.8993870	0.8537286	0.9387602
aou + silicate	Indo-Pacific	(27.5,27.75]	0.9194243	0.8681200	0.9540944
aou + silicate	Indo-Pacific	(27.75,27.85]	0.9671074	0.9511809	0.9761360
aou + silicate	Indo-Pacific	(27.85,27.95]	0.9644635	0.9545940	0.9707377
aou + silicate	Indo-Pacific	(27.95,28.05]	0.9493197	0.9417607	0.9533539
aou + silicate	Indo-Pacific	(28.05,28.1]	0.9487765	0.9460695	0.9532193
aou + silicate	Indo-Pacific	(28.1, Inf]	0.6256825	0.5387657	0.6694329
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]	-0.7839570	-0.9067335	-0.6823081
oxygen + phosphate	Indo-Pacific	(26,26.5]	-0.8838199	-0.9048178	-0.8555408
oxygen + phosphate	Indo-Pacific	(26.5,26.75]	-0.8889792	-0.9140662	-0.8726298
oxygen + phosphate	Indo-Pacific	(26.75,27]	-0.8827241	-0.8880642	-0.8745155
oxygen + phosphate	Indo-Pacific	(27,27.25]	-0.9238446	-0.9561043	-0.8755487
oxygen + phosphate	Indo-Pacific	(27.25,27.5]	-0.9427922	-0.9674903	-0.8953701
oxygen + phosphate	Indo-Pacific	(27.5,27.75]	-0.9585959	-0.9797089	-0.9229040
oxygen + phosphate	Indo-Pacific	(27.75,27.85]	-0.9755911	-0.9887694	-0.9587606
oxygen + phosphate	Indo-Pacific	(27.85,27.95]	-0.9722513	-0.9878715	-0.9581609
oxygen + phosphate	Indo-Pacific	(27.95,28.05]	-0.9466635	-0.9591235	-0.9304693
oxygen + phosphate	Indo-Pacific	(28.05,28.1]	-0.9340143	-0.9526139	-0.9221487
oxygen + phosphate	Indo-Pacific	(28.1, Inf]	-0.7014531	-0.7608328	-0.6356990
oxygen + phosphate_star	Atlantic	(-Inf,26]	0.1893903	-0.1230309	0.6411888
oxygen + phosphate_star	Atlantic	(26,26.5]	0.0228416	-0.3412350	0.3696066
oxygen + phosphate_star	Atlantic	(26.5,26.75]	-0.2360841	-0.4598066	-0.1076626
oxygen + phosphate_star	Atlantic	(26.75,27]	-0.0749306	-0.1287144	0.0167700
oxygen + phosphate_star	Atlantic	(27,27.25]	0.0693905	-0.0997210	0.2947309
oxygen + phosphate_star	Atlantic	(27.25,27.5]	0.1276161	-0.0503131	0.2955341
oxygen + phosphate_star	Atlantic	(27.5,27.75]	-0.2177089	-0.3157434	-0.0747768
oxygen + phosphate_star	Atlantic	(27.75,27.85]	-0.6170288	-0.6556548	-0.5972095
oxygen + phosphate_star	Atlantic	(27.85,27.95]	-0.6181154	-0.7085527	-0.5422986
oxygen + phosphate_star	Atlantic	(27.95,28.05]	-0.7502733	-0.8930381	-0.6783013
oxygen + phosphate_star	Atlantic	(28.05,28.1]	-0.8239907	-0.9270406	-0.7284906
oxygen + phosphate_star	Atlantic	(28.1,28.15]	-0.8866594	-0.9116651	-0.8736184
oxygen + phosphate_star	Atlantic	(28.15,28.2]	-0.9682666	-0.9801919	-0.9467860
oxygen + phosphate_star	Atlantic	(28.2, Inf]	-0.3117873	-0.4938331	-0.2050104
oxygen + phosphate_star	Indo-Pacific	(-Inf,26]	-0.3698447	-0.5847842	-0.1280827
oxygen + phosphate_star	Indo-Pacific	(26,26.5]	-0.4202618	-0.4584822	-0.3719583
oxygen + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.2761827	-0.4243091	-0.0048738
oxygen + phosphate_star	Indo-Pacific	(26.75,27]	-0.2217661	-0.3227939	-0.1608680
oxygen + phosphate_star	Indo-Pacific	(27,27.25]	-0.0265311	-0.1236776	0.1115391
oxygen + phosphate_star	Indo-Pacific	(27.25,27.5]	0.5064386	0.4721050	0.5407410
oxygen + phosphate_star	Indo-Pacific	(27.5,27.75]	0.6614212	0.6066151	0.7182471
oxygen + phosphate_star	Indo-Pacific	(27.75,27.85]	0.5145704	0.4301678	0.6144466
oxygen + phosphate_star	Indo-Pacific	(27.85,27.95]	0.1122673	0.0557543	0.1740921
oxygen + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.1584253	-0.2445424	-0.0445188
oxygen + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.3379210	-0.4043857	-0.2788553
oxygen + phosphate_star	Indo-Pacific	(28.1, Inf]	0.7065238	0.6675602	0.7338818
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]	-0.4884062	-0.6825358	-0.3169944
oxygen + silicate	Indo-Pacific	(26,26.5]	-0.5302245	-0.6549671	-0.4175494
oxygen + silicate	Indo-Pacific	(26.5,26.75]	-0.4928426	-0.6371103	-0.2746742
oxygen + silicate	Indo-Pacific	(26.75,27]	-0.6349982	-0.6716084	-0.5683559
oxygen + silicate	Indo-Pacific	(27,27.25]	-0.7945613	-0.8639831	-0.6962955
oxygen + silicate	Indo-Pacific	(27.25,27.5]	-0.8492028	-0.9092098	-0.7707499
oxygen + silicate	Indo-Pacific	(27.5,27.75]	-0.8794456	-0.9316797	-0.7938492
oxygen + silicate	Indo-Pacific	(27.75,27.85]	-0.9519542	-0.9721552	-0.9212389
oxygen + silicate	Indo-Pacific	(27.85,27.95]	-0.9504681	-0.9648651	-0.9328229
oxygen + silicate	Indo-Pacific	(27.95,28.05]	-0.9245872	-0.9323370	-0.9110657
oxygen + silicate	Indo-Pacific	(28.05,28.1]	-0.9256529	-0.9269820	-0.9237752
oxygen + silicate	Indo-Pacific	(28.1, Inf]	-0.5366149	-0.5919324	-0.4282915
phosphate + phosphate_star	Atlantic	(-Inf,26]	0.7624671	0.5332725	0.8902339
phosphate + phosphate_star	Atlantic	(26,26.5]	0.8668735	0.8515142	0.8809509
phosphate + phosphate_star	Atlantic	(26.5,26.75]	0.8320960	0.7783560	0.8785106
phosphate + phosphate_star	Atlantic	(26.75,27]	0.7162345	0.6721479	0.7456449
phosphate + phosphate_star	Atlantic	(27,27.25]	0.7086069	0.6647082	0.7485194
phosphate + phosphate_star	Atlantic	(27.25,27.5]	0.8031728	0.7826237	0.8224384
phosphate + phosphate_star	Atlantic	(27.5,27.75]	0.9115930	0.9041334	0.9174374
phosphate + phosphate_star	Atlantic	(27.75,27.85]	0.9300108	0.9253656	0.9385056
phosphate + phosphate_star	Atlantic	(27.85,27.95]	0.8862340	0.8465936	0.9129611
phosphate + phosphate_star	Atlantic	(27.95,28.05]	0.9408191	0.9033721	0.9773587
phosphate + phosphate_star	Atlantic	(28.05,28.1]	0.9701545	0.9612884	0.9876899
phosphate + phosphate_star	Atlantic	(28.1,28.15]	0.9809299	0.9757912	0.9856240
phosphate + phosphate_star	Atlantic	(28.15,28.2]	0.9948207	0.9916620	0.9964604
phosphate + phosphate_star	Atlantic	(28.2, Inf]	0.8932301	0.8684747	0.9289934
phosphate + phosphate_star	Indo-Pacific	(-Inf,26]	0.8603014	0.8124352	0.8961438
phosphate + phosphate_star	Indo-Pacific	(26,26.5]	0.7938226	0.7526968	0.8355190
phosphate + phosphate_star	Indo-Pacific	(26.5,26.75]	0.6775601	0.4926295	0.8031857
phosphate + phosphate_star	Indo-Pacific	(26.75,27]	0.6518593	0.6008772	0.7413236
phosphate + phosphate_star	Indo-Pacific	(27,27.25]	0.3985357	0.3824574	0.4090257
phosphate + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.2020783	-0.3104182	-0.0694949
phosphate + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.4289067	-0.5642191	-0.2537503
phosphate + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.3195294	-0.4896367	-0.1558532
phosphate + phosphate_star	Indo-Pacific	(27.85,27.95]	0.1162110	0.0487248	0.2323633
phosphate + phosphate_star	Indo-Pacific	(27.95,28.05]	0.4635889	0.3254063	0.5827854
phosphate + phosphate_star	Indo-Pacific	(28.05,28.1]	0.6489135	0.6019465	0.7266992
phosphate + phosphate_star	Indo-Pacific	(28.1, Inf]	0.0053285	-0.0947674	0.1503829
salinity + aou	Atlantic	(-Inf,26]	-0.0452495	-0.3257778	0.3355069
salinity + aou	Atlantic	(26,26.5]	-0.1316899	-0.2309276	0.0334238
salinity + aou	Atlantic	(26.5,26.75]	-0.3436234	-0.5297627	-0.1936560
salinity + aou	Atlantic	(26.75,27]	-0.2274688	-0.2786631	-0.1798969
salinity + aou	Atlantic	(27,27.25]	-0.1722725	-0.3548045	0.0243317
salinity + aou	Atlantic	(27.25,27.5]	-0.1716808	-0.3370859	-0.0600930
salinity + aou	Atlantic	(27.5,27.75]	-0.4656439	-0.4956237	-0.4140142
salinity + aou	Atlantic	(27.75,27.85]	-0.5438494	-0.6028770	-0.4959685
salinity + aou	Atlantic	(27.85,27.95]	-0.3566450	-0.5027073	-0.1656048
salinity + aou	Atlantic	(27.95,28.05]	-0.5444684	-0.7924660	-0.2117975
salinity + aou	Atlantic	(28.05,28.1]	-0.7479505	-0.8681681	-0.6651277
salinity + aou	Atlantic	(28.1,28.15]	-0.8326742	-0.8705770	-0.7857761
salinity + aou	Atlantic	(28.15,28.2]	-0.9536576	-0.9757986	-0.9232777
salinity + aou	Atlantic	(28.2, Inf]	-0.5299343	-0.7118279	-0.4183440
salinity + aou	Indo-Pacific	(-Inf,26]	-0.0976234	-0.1346395	-0.0319685
salinity + aou	Indo-Pacific	(26,26.5]	-0.0501848	-0.2595400	0.1341664
salinity + aou	Indo-Pacific	(26.5,26.75]	-0.0552989	-0.3767854	0.2662912
salinity + aou	Indo-Pacific	(26.75,27]	-0.1605742	-0.3700368	0.0263806
salinity + aou	Indo-Pacific	(27,27.25]	-0.0833167	-0.2071071	0.1440841
salinity + aou	Indo-Pacific	(27.25,27.5]	0.1152309	0.0311502	0.2680199
salinity + aou	Indo-Pacific	(27.5,27.75]	0.0468967	-0.0757758	0.2344463
salinity + aou	Indo-Pacific	(27.75,27.85]	-0.1678875	-0.4051461	0.0905928
salinity + aou	Indo-Pacific	(27.85,27.95]	-0.3774176	-0.6902419	-0.1322621
salinity + aou	Indo-Pacific	(27.95,28.05]	-0.3780087	-0.4619637	-0.2601785
salinity + aou	Indo-Pacific	(28.05,28.1]	-0.4597512	-0.5848017	-0.3719058
salinity + aou	Indo-Pacific	(28.1, Inf]	0.3997470	0.2765693	0.4833991
salinity + oxygen	Atlantic	(-Inf,26]	-0.3109640	-0.5824114	-0.0830958
salinity + oxygen	Atlantic	(26,26.5]	-0.2558098	-0.4586109	-0.0978965
salinity + oxygen	Atlantic	(26.5,26.75]	0.0954246	-0.0452345	0.3329757
salinity + oxygen	Atlantic	(26.75,27]	0.0271900	-0.0618028	0.0825327
salinity + oxygen	Atlantic	(27,27.25]	-0.0428928	-0.2848910	0.1542667
salinity + oxygen	Atlantic	(27.25,27.5]	-0.1247762	-0.2755115	0.0699327
salinity + oxygen	Atlantic	(27.5,27.75]	0.1285747	0.0007210	0.2049111
salinity + oxygen	Atlantic	(27.75,27.85]	0.3596203	0.2998878	0.4260460
salinity + oxygen	Atlantic	(27.85,27.95]	0.2285522	0.0268688	0.3965104
salinity + oxygen	Atlantic	(27.95,28.05]	0.4435389	0.1139659	0.7289259
salinity + oxygen	Atlantic	(28.05,28.1]	0.6554291	0.5677434	0.8196414
salinity + oxygen	Atlantic	(28.1,28.15]	0.7693824	0.7201298	0.8169252
salinity + oxygen	Atlantic	(28.15,28.2]	0.9361833	0.8965298	0.9637406
salinity + oxygen	Atlantic	(28.2, Inf]	0.3650789	0.2179548	0.5646201
salinity + oxygen	Indo-Pacific	(-Inf,26]	-0.2157463	-0.3359558	-0.1039456
salinity + oxygen	Indo-Pacific	(26,26.5]	-0.1316348	-0.2879960	0.0406246
salinity + oxygen	Indo-Pacific	(26.5,26.75]	-0.1064139	-0.4189153	0.1974485
salinity + oxygen	Indo-Pacific	(26.75,27]	-0.0126002	-0.1962625	0.1972547
salinity + oxygen	Indo-Pacific	(27,27.25]	-0.0535173	-0.3319775	0.0959141
salinity + oxygen	Indo-Pacific	(27.25,27.5]	-0.2236543	-0.4282238	-0.1152695
salinity + oxygen	Indo-Pacific	(27.5,27.75]	-0.1310450	-0.3816878	0.0324730
salinity + oxygen	Indo-Pacific	(27.75,27.85]	0.0993157	-0.2068707	0.3778925
salinity + oxygen	Indo-Pacific	(27.85,27.95]	0.3221359	0.0409348	0.6777124
salinity + oxygen	Indo-Pacific	(27.95,28.05]	0.3031510	0.1635871	0.4038045
salinity + oxygen	Indo-Pacific	(28.05,28.1]	0.3840285	0.2817047	0.5276693
salinity + oxygen	Indo-Pacific	(28.1, Inf]	-0.4956548	-0.5910869	-0.3703990
salinity + phosphate	Atlantic	(-Inf,26]	-0.5368678	-0.7820996	-0.3151151
salinity + phosphate	Atlantic	(26,26.5]	-0.6861720	-0.7694493	-0.5227085
salinity + phosphate	Atlantic	(26.5,26.75]	-0.7286769	-0.7958907	-0.6260673
salinity + phosphate	Atlantic	(26.75,27]	-0.6705112	-0.7056194	-0.6198328
salinity + phosphate	Atlantic	(27,27.25]	-0.7145275	-0.7748703	-0.6639096
salinity + phosphate	Atlantic	(27.25,27.5]	-0.7876444	-0.8205324	-0.7418126
salinity + phosphate	Atlantic	(27.5,27.75]	-0.8352052	-0.8445523	-0.8291386
salinity + phosphate	Atlantic	(27.75,27.85]	-0.7551779	-0.7831275	-0.7242229
salinity + phosphate	Atlantic	(27.85,27.95]	-0.5751115	-0.6726756	-0.4171452
salinity + phosphate	Atlantic	(27.95,28.05]	-0.6954715	-0.8503110	-0.4308056
salinity + phosphate	Atlantic	(28.05,28.1]	-0.8442799	-0.9056577	-0.7678284
salinity + phosphate	Atlantic	(28.1,28.15]	-0.8938608	-0.9149390	-0.8537034
salinity + phosphate	Atlantic	(28.15,28.2]	-0.9592330	-0.9685939	-0.9542868
salinity + phosphate	Atlantic	(28.2, Inf]	-0.8964793	-0.9415770	-0.8474669
salinity + phosphate	Indo-Pacific	(-Inf,26]	-0.2194966	-0.2517569	-0.2020443
salinity + phosphate	Indo-Pacific	(26,26.5]	-0.2842714	-0.5082835	-0.1021091
salinity + phosphate	Indo-Pacific	(26.5,26.75]	-0.3083614	-0.6118401	-0.0366340
salinity + phosphate	Indo-Pacific	(26.75,27]	-0.4155439	-0.6195949	-0.2396882
salinity + phosphate	Indo-Pacific	(27,27.25]	-0.2652062	-0.3794062	-0.1086066
salinity + phosphate	Indo-Pacific	(27.25,27.5]	0.0061186	-0.0358510	0.0567469
salinity + phosphate	Indo-Pacific	(27.5,27.75]	-0.0111189	-0.0732762	0.0984362
salinity + phosphate	Indo-Pacific	(27.75,27.85]	-0.1895421	-0.3793168	0.0420360
salinity + phosphate	Indo-Pacific	(27.85,27.95]	-0.4214157	-0.6925250	-0.1799031
salinity + phosphate	Indo-Pacific	(27.95,28.05]	-0.5186201	-0.5966346	-0.4036067
salinity + phosphate	Indo-Pacific	(28.05,28.1]	-0.6204174	-0.7160040	-0.5713107
salinity + phosphate	Indo-Pacific	(28.1, Inf]	-0.1349102	-0.2265805	-0.0763846
salinity + phosphate_star	Atlantic	(-Inf,26]	-0.7974374	-0.9317164	-0.5625034
salinity + phosphate_star	Atlantic	(26,26.5]	-0.9224630	-0.9699638	-0.8348915
salinity + phosphate_star	Atlantic	(26.5,26.75]	-0.9690939	-0.9798972	-0.9501833
salinity + phosphate_star	Atlantic	(26.75,27]	-0.9811322	-0.9867684	-0.9769403
salinity + phosphate_star	Atlantic	(27,27.25]	-0.9837524	-0.9853382	-0.9820819
salinity + phosphate_star	Atlantic	(27.25,27.5]	-0.9808522	-0.9835208	-0.9755483
salinity + phosphate_star	Atlantic	(27.5,27.75]	-0.9529986	-0.9547226	-0.9511752
salinity + phosphate_star	Atlantic	(27.75,27.85]	-0.9150719	-0.9211116	-0.9045425
salinity + phosphate_star	Atlantic	(27.85,27.95]	-0.8473387	-0.8810768	-0.7953825
salinity + phosphate_star	Atlantic	(27.95,28.05]	-0.8504594	-0.9230189	-0.7178387
salinity + phosphate_star	Atlantic	(28.05,28.1]	-0.9138634	-0.9442163	-0.8593220
salinity + phosphate_star	Atlantic	(28.1,28.15]	-0.9379116	-0.9600247	-0.9089368
salinity + phosphate_star	Atlantic	(28.15,28.2]	-0.9621816	-0.9727023	-0.9506763
salinity + phosphate_star	Atlantic	(28.2, Inf]	-0.9717163	-0.9756048	-0.9639516
salinity + phosphate_star	Indo-Pacific	(-Inf,26]	-0.5186648	-0.5420309	-0.4997099
salinity + phosphate_star	Indo-Pacific	(26,26.5]	-0.7288970	-0.8430713	-0.6266783
salinity + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.8431342	-0.9196684	-0.7882671
salinity + phosphate_star	Indo-Pacific	(26.75,27]	-0.8928260	-0.9361704	-0.8471015
salinity + phosphate_star	Indo-Pacific	(27,27.25]	-0.8387976	-0.8582931	-0.8065417
salinity + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.6298080	-0.8494018	-0.4417094
salinity + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.4110256	-0.7556259	-0.0693757
salinity + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.2591739	-0.5854542	0.2022713
salinity + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.3802058	-0.5771706	-0.0749978
salinity + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.7514025	-0.7918821	-0.7053462
salinity + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.8195662	-0.8740056	-0.7483517
salinity + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.8277035	-0.8551669	-0.8111767
salinity + silicate	Atlantic	(-Inf,26]	-0.7139001	-0.7950883	-0.6725144
salinity + silicate	Atlantic	(26,26.5]	-0.6824066	-0.7243435	-0.6125911
salinity + silicate	Atlantic	(26.5,26.75]	-0.6350098	-0.7294011	-0.5055632
salinity + silicate	Atlantic	(26.75,27]	-0.5545102	-0.5946755	-0.5155890
salinity + silicate	Atlantic	(27,27.25]	-0.6607943	-0.7124112	-0.6219032
salinity + silicate	Atlantic	(27.25,27.5]	-0.7972274	-0.8097390	-0.7859144
salinity + silicate	Atlantic	(27.5,27.75]	-0.8197880	-0.8386444	-0.8101704
salinity + silicate	Atlantic	(27.75,27.85]	-0.7884695	-0.8228682	-0.7518060
salinity + silicate	Atlantic	(27.85,27.95]	-0.6617053	-0.7465839	-0.5237283
salinity + silicate	Atlantic	(27.95,28.05]	-0.7307836	-0.8883221	-0.4777178
salinity + silicate	Atlantic	(28.05,28.1]	-0.8591589	-0.9274773	-0.7987466
salinity + silicate	Atlantic	(28.1,28.15]	-0.9053625	-0.9385148	-0.8708267
salinity + silicate	Atlantic	(28.15,28.2]	-0.9565403	-0.9729301	-0.9307135
salinity + silicate	Atlantic	(28.2, Inf]	-0.8546034	-0.9653379	-0.7751529
salinity + silicate	Indo-Pacific	(-Inf,26]	-0.5327640	-0.5805799	-0.4445816
salinity + silicate	Indo-Pacific	(26,26.5]	-0.5678803	-0.6927174	-0.4641915
salinity + silicate	Indo-Pacific	(26.5,26.75]	-0.6741637	-0.8161866	-0.5696984
salinity + silicate	Indo-Pacific	(26.75,27]	-0.6672540	-0.7747210	-0.4979258
salinity + silicate	Indo-Pacific	(27,27.25]	-0.4685733	-0.5470162	-0.3358847
salinity + silicate	Indo-Pacific	(27.25,27.5]	-0.1679460	-0.2354897	-0.0950205
salinity + silicate	Indo-Pacific	(27.5,27.75]	-0.0843286	-0.1062914	-0.0648291
salinity + silicate	Indo-Pacific	(27.75,27.85]	-0.2171798	-0.3571247	-0.0574093
salinity + silicate	Indo-Pacific	(27.85,27.95]	-0.3985178	-0.6239515	-0.2184840
salinity + silicate	Indo-Pacific	(27.95,28.05]	-0.4391131	-0.4910533	-0.3621739
salinity + silicate	Indo-Pacific	(28.05,28.1]	-0.5463477	-0.6170559	-0.4790016
salinity + silicate	Indo-Pacific	(28.1, Inf]	-0.0742257	-0.1716903	0.0723564
salinity + temperature	Atlantic	(-Inf,26]	0.9207161	0.8381654	0.9786562
salinity + temperature	Atlantic	(26,26.5]	0.9600524	0.9470189	0.9717127
salinity + temperature	Atlantic	(26.5,26.75]	0.9866701	0.9811261	0.9902331
salinity + temperature	Atlantic	(26.75,27]	0.9794774	0.9741859	0.9843463
salinity + temperature	Atlantic	(27,27.25]	0.9773384	0.9758270	0.9794429
salinity + temperature	Atlantic	(27.25,27.5]	0.9728298	0.9698213	0.9754742
salinity + temperature	Atlantic	(27.5,27.75]	0.9596412	0.9556522	0.9622929
salinity + temperature	Atlantic	(27.75,27.85]	0.9789351	0.9753679	0.9808720
salinity + temperature	Atlantic	(27.85,27.95]	0.9441199	0.9369742	0.9480091
salinity + temperature	Atlantic	(27.95,28.05]	0.8823423	0.8069203	0.9317987
salinity + temperature	Atlantic	(28.05,28.1]	0.9497597	0.9127320	0.9685717
salinity + temperature	Atlantic	(28.1,28.15]	0.9486238	0.9195421	0.9706795
salinity + temperature	Atlantic	(28.15,28.2]	0.8825453	0.8477644	0.9035039
salinity + temperature	Atlantic	(28.2, Inf]	0.4658301	0.3653252	0.6272068
salinity + temperature	Indo-Pacific	(-Inf,26]	0.7708602	0.7410815	0.8179872
salinity + temperature	Indo-Pacific	(26,26.5]	0.9289978	0.8853113	0.9536617
salinity + temperature	Indo-Pacific	(26.5,26.75]	0.9783761	0.9690919	0.9833196
salinity + temperature	Indo-Pacific	(26.75,27]	0.9769327	0.9720313	0.9799861
salinity + temperature	Indo-Pacific	(27,27.25]	0.9494681	0.9326539	0.9706486
salinity + temperature	Indo-Pacific	(27.25,27.5]	0.8759716	0.8219365	0.9581021
salinity + temperature	Indo-Pacific	(27.5,27.75]	0.7034281	0.5144167	0.9146415
salinity + temperature	Indo-Pacific	(27.75,27.85]	0.8099353	0.6545628	0.9380027
salinity + temperature	Indo-Pacific	(27.85,27.95]	0.6993368	0.4548127	0.8692827
salinity + temperature	Indo-Pacific	(27.95,28.05]	0.7212254	0.6298824	0.8192591
salinity + temperature	Indo-Pacific	(28.05,28.1]	0.6984918	0.5756878	0.7976297
salinity + temperature	Indo-Pacific	(28.1, Inf]	0.7137388	0.5996297	0.8277495
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]	0.7876839	0.7391622	0.8126822
silicate + phosphate	Indo-Pacific	(26,26.5]	0.7574193	0.6608833	0.8319689
silicate + phosphate	Indo-Pacific	(26.5,26.75]	0.7499238	0.5908688	0.8379373
silicate + phosphate	Indo-Pacific	(26.75,27]	0.8528399	0.8041063	0.8787578
silicate + phosphate	Indo-Pacific	(27,27.25]	0.8991939	0.8740174	0.9339553
silicate + phosphate	Indo-Pacific	(27.25,27.5]	0.8886196	0.8594089	0.9287864
silicate + phosphate	Indo-Pacific	(27.5,27.75]	0.8903745	0.8465955	0.9317081
silicate + phosphate	Indo-Pacific	(27.75,27.85]	0.9511429	0.9310040	0.9641457
silicate + phosphate	Indo-Pacific	(27.85,27.95]	0.9644519	0.9518321	0.9716657
silicate + phosphate	Indo-Pacific	(27.95,28.05]	0.9593524	0.9507325	0.9638756
silicate + phosphate	Indo-Pacific	(28.05,28.1]	0.9558313	0.9482752	0.9622640
silicate + phosphate	Indo-Pacific	(28.1, Inf]	0.7938885	0.7638105	0.8300839
silicate + phosphate_star	Atlantic	(-Inf,26]	0.6657357	0.5879842	0.7603159
silicate + phosphate_star	Atlantic	(26,26.5]	0.8170619	0.7939173	0.8600889
silicate + phosphate_star	Atlantic	(26.5,26.75]	0.7520637	0.6827585	0.8197783
silicate + phosphate_star	Atlantic	(26.75,27]	0.6116921	0.5791991	0.6496392
silicate + phosphate_star	Atlantic	(27,27.25]	0.6681878	0.6433144	0.7005654
silicate + phosphate_star	Atlantic	(27.25,27.5]	0.8415873	0.8273388	0.8515505
silicate + phosphate_star	Atlantic	(27.5,27.75]	0.9216818	0.9165649	0.9291800
silicate + phosphate_star	Atlantic	(27.75,27.85]	0.9440820	0.9353454	0.9528566
silicate + phosphate_star	Atlantic	(27.85,27.95]	0.9202164	0.8884566	0.9395646
silicate + phosphate_star	Atlantic	(27.95,28.05]	0.9338785	0.8893533	0.9735236
silicate + phosphate_star	Atlantic	(28.05,28.1]	0.9553651	0.9419911	0.9811098
silicate + phosphate_star	Atlantic	(28.1,28.15]	0.9750655	0.9683713	0.9863218
silicate + phosphate_star	Atlantic	(28.15,28.2]	0.9862398	0.9747826	0.9943196
silicate + phosphate_star	Atlantic	(28.2, Inf]	0.8433934	0.7614150	0.9449404
silicate + phosphate_star	Indo-Pacific	(-Inf,26]	0.7846398	0.7499336	0.8320484
silicate + phosphate_star	Indo-Pacific	(26,26.5]	0.7849543	0.7460552	0.8089737
silicate + phosphate_star	Indo-Pacific	(26.5,26.75]	0.8025628	0.7203978	0.8551129
silicate + phosphate_star	Indo-Pacific	(26.75,27]	0.7486277	0.7228274	0.7794527
silicate + phosphate_star	Indo-Pacific	(27,27.25]	0.4430103	0.4144601	0.4661379
silicate + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.2204614	-0.3420444	-0.0625492
silicate + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.4798617	-0.6607115	-0.2462836
silicate + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.4151131	-0.6129553	-0.2445990
silicate + phosphate_star	Indo-Pacific	(27.85,27.95]	0.0587229	0.0037064	0.1504415
silicate + phosphate_star	Indo-Pacific	(27.95,28.05]	0.4020673	0.2858781	0.4954316
silicate + phosphate_star	Indo-Pacific	(28.05,28.1]	0.5537216	0.5219203	0.6015185
silicate + phosphate_star	Indo-Pacific	(28.1, Inf]	0.0313625	-0.0797758	0.1882002
temperature + aou	Atlantic	(-Inf,26]	-0.0687693	-0.3518914	0.3120683
temperature + aou	Atlantic	(26,26.5]	-0.2026044	-0.3782715	-0.0257882
temperature + aou	Atlantic	(26.5,26.75]	-0.3626266	-0.5394586	-0.2278605
temperature + aou	Atlantic	(26.75,27]	-0.2258924	-0.2684537	-0.1748759
temperature + aou	Atlantic	(27,27.25]	-0.1116539	-0.2812963	0.0747144
temperature + aou	Atlantic	(27.25,27.5]	-0.1280238	-0.2994314	-0.0069762
temperature + aou	Atlantic	(27.5,27.75]	-0.4163606	-0.4606483	-0.3507414
temperature + aou	Atlantic	(27.75,27.85]	-0.5228423	-0.5682867	-0.4812475
temperature + aou	Atlantic	(27.85,27.95]	-0.3044515	-0.4569619	-0.0804600
temperature + aou	Atlantic	(27.95,28.05]	-0.5202876	-0.7151551	-0.3144163
temperature + aou	Atlantic	(28.05,28.1]	-0.6062227	-0.8064307	-0.4385820
temperature + aou	Atlantic	(28.1,28.15]	-0.6597060	-0.7330619	-0.5223213
temperature + aou	Atlantic	(28.15,28.2]	-0.7563883	-0.8202708	-0.7093370
temperature + aou	Atlantic	(28.2, Inf]	0.3523127	0.2491837	0.4736749
temperature + aou	Indo-Pacific	(-Inf,26]	-0.2687307	-0.4106364	-0.1750756
temperature + aou	Indo-Pacific	(26,26.5]	-0.1238013	-0.3087069	-0.0170725
temperature + aou	Indo-Pacific	(26.5,26.75]	-0.0458774	-0.3460052	0.2570151
temperature + aou	Indo-Pacific	(26.75,27]	-0.1772755	-0.3633119	-0.0314426
temperature + aou	Indo-Pacific	(27,27.25]	-0.1612950	-0.2850675	0.0541017
temperature + aou	Indo-Pacific	(27.25,27.5]	0.0851221	-0.0155813	0.2506184
temperature + aou	Indo-Pacific	(27.5,27.75]	0.1057566	0.0131166	0.2585448
temperature + aou	Indo-Pacific	(27.75,27.85]	-0.0078459	-0.1982387	0.1848164
temperature + aou	Indo-Pacific	(27.85,27.95]	-0.0752691	-0.2789347	0.0530825
temperature + aou	Indo-Pacific	(27.95,28.05]	0.0868853	0.0687610	0.1173523
temperature + aou	Indo-Pacific	(28.05,28.1]	0.1568685	0.0330026	0.2601188
temperature + aou	Indo-Pacific	(28.1, Inf]	0.8409642	0.8007045	0.8667850
temperature + oxygen	Atlantic	(-Inf,26]	-0.3163713	-0.5749811	-0.1206498
temperature + oxygen	Atlantic	(26,26.5]	-0.1968196	-0.4148047	0.0427067
temperature + oxygen	Atlantic	(26.5,26.75]	0.1118365	-0.0150026	0.3410353
temperature + oxygen	Atlantic	(26.75,27]	0.0214474	-0.0706434	0.0678025
temperature + oxygen	Atlantic	(27,27.25]	-0.1086535	-0.3379192	0.0727534
temperature + oxygen	Atlantic	(27.25,27.5]	-0.1762577	-0.3351416	0.0234851
temperature + oxygen	Atlantic	(27.5,27.75]	0.0584126	-0.0852544	0.1518829
temperature + oxygen	Atlantic	(27.75,27.85]	0.3304151	0.2786541	0.3801715
temperature + oxygen	Atlantic	(27.85,27.95]	0.1653514	-0.0686148	0.3399528
temperature + oxygen	Atlantic	(27.95,28.05]	0.3933041	0.1904284	0.6256963
temperature + oxygen	Atlantic	(28.05,28.1]	0.4917184	0.3267804	0.7418371
temperature + oxygen	Atlantic	(28.1,28.15]	0.5766872	0.4345949	0.6498435
temperature + oxygen	Atlantic	(28.15,28.2]	0.7180076	0.6732370	0.7888052
temperature + oxygen	Atlantic	(28.2, Inf]	-0.5293353	-0.6164468	-0.4358133
temperature + oxygen	Indo-Pacific	(-Inf,26]	-0.1162531	-0.2916973	-0.0104878
temperature + oxygen	Indo-Pacific	(26,26.5]	-0.0707788	-0.1580104	0.0803955
temperature + oxygen	Indo-Pacific	(26.5,26.75]	-0.1205630	-0.4160528	0.1616372
temperature + oxygen	Indo-Pacific	(26.75,27]	-0.0005306	-0.1431829	0.1863308
temperature + oxygen	Indo-Pacific	(27,27.25]	0.0182729	-0.2509850	0.1689748
temperature + oxygen	Indo-Pacific	(27.25,27.5]	-0.2071617	-0.4206513	-0.0793657
temperature + oxygen	Indo-Pacific	(27.5,27.75]	-0.2160274	-0.4195962	-0.0938038
temperature + oxygen	Indo-Pacific	(27.75,27.85]	-0.0722622	-0.3064867	0.1534029
temperature + oxygen	Indo-Pacific	(27.85,27.95]	0.0003896	-0.1561502	0.2362149
temperature + oxygen	Indo-Pacific	(27.95,28.05]	-0.1821228	-0.1995946	-0.1652786
temperature + oxygen	Indo-Pacific	(28.05,28.1]	-0.2391831	-0.3522109	-0.1209645
temperature + oxygen	Indo-Pacific	(28.1, Inf]	-0.9013842	-0.9172228	-0.8763236
temperature + phosphate	Atlantic	(-Inf,26]	-0.4465037	-0.6217540	-0.2872539
temperature + phosphate	Atlantic	(26,26.5]	-0.7252611	-0.7977219	-0.6318815
temperature + phosphate	Atlantic	(26.5,26.75]	-0.7441481	-0.8013726	-0.6584993
temperature + phosphate	Atlantic	(26.75,27]	-0.6690712	-0.7005508	-0.6280295
temperature + phosphate	Atlantic	(27,27.25]	-0.6703935	-0.7235873	-0.6197743
temperature + phosphate	Atlantic	(27.25,27.5]	-0.7580177	-0.7945460	-0.7146478
temperature + phosphate	Atlantic	(27.5,27.75]	-0.7998618	-0.8089097	-0.7910859
temperature + phosphate	Atlantic	(27.75,27.85]	-0.7425998	-0.7630549	-0.7137399
temperature + phosphate	Atlantic	(27.85,27.95]	-0.5252112	-0.6256550	-0.3343713
temperature + phosphate	Atlantic	(27.95,28.05]	-0.6492760	-0.7702004	-0.4548313
temperature + phosphate	Atlantic	(28.05,28.1]	-0.7213138	-0.8442823	-0.5630099
temperature + phosphate	Atlantic	(28.1,28.15]	-0.7416721	-0.8216944	-0.6194000
temperature + phosphate	Atlantic	(28.15,28.2]	-0.7549808	-0.7961936	-0.6943424
temperature + phosphate	Atlantic	(28.2, Inf]	-0.1112661	-0.1984830	-0.0519485
temperature + phosphate	Indo-Pacific	(-Inf,26]	-0.4319706	-0.5907832	-0.2930051
temperature + phosphate	Indo-Pacific	(26,26.5]	-0.3748471	-0.5663897	-0.2747163
temperature + phosphate	Indo-Pacific	(26.5,26.75]	-0.3119225	-0.5942870	-0.0615034
temperature + phosphate	Indo-Pacific	(26.75,27]	-0.4475683	-0.6253158	-0.3132553
temperature + phosphate	Indo-Pacific	(27,27.25]	-0.3618353	-0.4445069	-0.2190449
temperature + phosphate	Indo-Pacific	(27.25,27.5]	-0.0569980	-0.1307047	0.0170352
temperature + phosphate	Indo-Pacific	(27.5,27.75]	0.0397540	-0.0165849	0.1160272
temperature + phosphate	Indo-Pacific	(27.75,27.85]	-0.0313387	-0.1669361	0.1257444
temperature + phosphate	Indo-Pacific	(27.85,27.95]	-0.1248251	-0.2780650	-0.0132564
temperature + phosphate	Indo-Pacific	(27.95,28.05]	-0.0750418	-0.1054087	-0.0398646
temperature + phosphate	Indo-Pacific	(28.05,28.1]	-0.0300473	-0.1526343	0.0485644
temperature + phosphate	Indo-Pacific	(28.1, Inf]	0.3939452	0.2669475	0.4779643
temperature + phosphate_star	Atlantic	(-Inf,26]	-0.7061483	-0.8582740	-0.5189364
temperature + phosphate_star	Atlantic	(26,26.5]	-0.9343385	-0.9733157	-0.8856727
temperature + phosphate_star	Atlantic	(26.5,26.75]	-0.9771888	-0.9831216	-0.9694274
temperature + phosphate_star	Atlantic	(26.75,27]	-0.9848572	-0.9878559	-0.9828411
temperature + phosphate_star	Atlantic	(27,27.25]	-0.9872929	-0.9897957	-0.9859356
temperature + phosphate_star	Atlantic	(27.25,27.5]	-0.9827437	-0.9848519	-0.9792676
temperature + phosphate_star	Atlantic	(27.5,27.75]	-0.9457047	-0.9496670	-0.9430617
temperature + phosphate_star	Atlantic	(27.75,27.85]	-0.9165933	-0.9234699	-0.9037825
temperature + phosphate_star	Atlantic	(27.85,27.95]	-0.8235049	-0.8668068	-0.7510793
temperature + phosphate_star	Atlantic	(27.95,28.05]	-0.8044664	-0.8822707	-0.6772425
temperature + phosphate_star	Atlantic	(28.05,28.1]	-0.8295893	-0.8899325	-0.7112782
temperature + phosphate_star	Atlantic	(28.1,28.15]	-0.8215634	-0.8914645	-0.7272136
temperature + phosphate_star	Atlantic	(28.15,28.2]	-0.7699644	-0.8118849	-0.7039532
temperature + phosphate_star	Atlantic	(28.2, Inf]	-0.4817703	-0.6144520	-0.3740281
temperature + phosphate_star	Indo-Pacific	(-Inf,26]	-0.7517559	-0.8459188	-0.6176220
temperature + phosphate_star	Indo-Pacific	(26,26.5]	-0.8257311	-0.9021705	-0.7660248
temperature + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.8700434	-0.9311307	-0.8117115
temperature + phosphate_star	Indo-Pacific	(26.75,27]	-0.9386195	-0.9624515	-0.9120804
temperature + phosphate_star	Indo-Pacific	(27,27.25]	-0.9218151	-0.9321647	-0.9027204
temperature + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.7653579	-0.9093303	-0.6472260
temperature + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.5678149	-0.8145377	-0.3176058
temperature + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.3921300	-0.6657844	0.0137202
temperature + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.5021655	-0.6685866	-0.2610595
temperature + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.7356150	-0.8076554	-0.6815412
temperature + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.5963326	-0.6150003	-0.5756832
temperature + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.8757538	-0.8944860	-0.8648381
temperature + silicate	Atlantic	(-Inf,26]	-0.6058851	-0.7356100	-0.5118555
temperature + silicate	Atlantic	(26,26.5]	-0.6940228	-0.7324635	-0.6713966
temperature + silicate	Atlantic	(26.5,26.75]	-0.6575854	-0.7401620	-0.5514632
temperature + silicate	Atlantic	(26.75,27]	-0.5731056	-0.6058513	-0.5474068
temperature + silicate	Atlantic	(27,27.25]	-0.6439136	-0.6895759	-0.6139537
temperature + silicate	Atlantic	(27.25,27.5]	-0.8337342	-0.8392335	-0.8288195
temperature + silicate	Atlantic	(27.5,27.75]	-0.8573527	-0.8796812	-0.8389417
temperature + silicate	Atlantic	(27.75,27.85]	-0.8042016	-0.8434315	-0.7626576
temperature + silicate	Atlantic	(27.85,27.95]	-0.6354677	-0.7301266	-0.4645337
temperature + silicate	Atlantic	(27.95,28.05]	-0.7256101	-0.8518541	-0.5596467
temperature + silicate	Atlantic	(28.05,28.1]	-0.7473424	-0.8802581	-0.6125043
temperature + silicate	Atlantic	(28.1,28.15]	-0.7610483	-0.8231982	-0.6456801
temperature + silicate	Atlantic	(28.15,28.2]	-0.7570242	-0.8073258	-0.7273218
temperature + silicate	Atlantic	(28.2, Inf]	-0.0842811	-0.1558594	0.0039567
temperature + silicate	Indo-Pacific	(-Inf,26]	-0.5999219	-0.7261407	-0.4490039
temperature + silicate	Indo-Pacific	(26,26.5]	-0.6176997	-0.7251983	-0.4810773
temperature + silicate	Indo-Pacific	(26.5,26.75]	-0.6733967	-0.8085773	-0.5740942
temperature + silicate	Indo-Pacific	(26.75,27]	-0.6780530	-0.7655022	-0.5519163
temperature + silicate	Indo-Pacific	(27,27.25]	-0.5369362	-0.6256717	-0.4284266
temperature + silicate	Indo-Pacific	(27.25,27.5]	-0.2491110	-0.3118250	-0.1549767
temperature + silicate	Indo-Pacific	(27.5,27.75]	-0.1764726	-0.2391804	-0.1254418
temperature + silicate	Indo-Pacific	(27.75,27.85]	-0.1261121	-0.2532228	0.0014025
temperature + silicate	Indo-Pacific	(27.85,27.95]	-0.1986039	-0.3604705	-0.1009276
temperature + silicate	Indo-Pacific	(27.95,28.05]	-0.1028996	-0.1330721	-0.0704056
temperature + silicate	Indo-Pacific	(28.05,28.1]	0.0329346	-0.1020876	0.1151647
temperature + silicate	Indo-Pacific	(28.1, Inf]	0.2405551	0.0668675	0.3358980

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]	-0.4996104	-0.6193266	-0.4220052
aou	Indo-Pacific	(26,26.5]	-0.8377855	-0.8483028	-0.8184451
aou	Indo-Pacific	(26.5,26.75]	-0.8398693	-0.8584880	-0.8156240
aou	Indo-Pacific	(26.75,27]	-0.8457455	-0.8923007	-0.8147475
aou	Indo-Pacific	(27,27.25]	-0.6293704	-0.6922140	-0.5706964
aou	Indo-Pacific	(27.25,27.5]	0.0762664	0.0183026	0.1150447
aou	Indo-Pacific	(27.5,27.75]	0.4224227	0.2950276	0.5018787
aou	Indo-Pacific	(27.75,27.85]	0.4569819	0.2840598	0.5841937
aou	Indo-Pacific	(27.85,27.95]	0.2879750	0.1623772	0.4147307
aou	Indo-Pacific	(27.95,28.05]	-0.1200218	-0.2021546	0.0217023
aou	Indo-Pacific	(28.05,28.1]	-0.2536276	-0.3866125	-0.1783939
aou	Indo-Pacific	(28.1, Inf]	0.1307578	-0.0382601	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]	0.5040644	0.4248754	0.6262807
oxygen	Indo-Pacific	(26,26.5]	0.7496681	0.6998708	0.7792208
oxygen	Indo-Pacific	(26.5,26.75]	0.7564835	0.7280525	0.7937860
oxygen	Indo-Pacific	(26.75,27]	0.7673178	0.7374483	0.8254535
oxygen	Indo-Pacific	(27,27.25]	0.6155390	0.5409389	0.7060918
oxygen	Indo-Pacific	(27.25,27.5]	-0.0352779	-0.0838439	0.0205076
oxygen	Indo-Pacific	(27.5,27.75]	-0.3653738	-0.4647683	-0.2077907
oxygen	Indo-Pacific	(27.75,27.85]	-0.4188507	-0.5629082	-0.2167310
oxygen	Indo-Pacific	(27.85,27.95]	-0.2653503	-0.4000667	-0.1233800
oxygen	Indo-Pacific	(27.95,28.05]	0.1139176	-0.0268951	0.1906271
oxygen	Indo-Pacific	(28.05,28.1]	0.2336410	0.1646883	0.3569015
oxygen	Indo-Pacific	(28.1, Inf]	-0.1811320	-0.4177864	-0.0123509
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]	-0.5638239	-0.6878116	-0.4972373
phosphate	Indo-Pacific	(26,26.5]	-0.9321381	-0.9444061	-0.9206850
phosphate	Indo-Pacific	(26.5,26.75]	-0.9479832	-0.9544130	-0.9445690
phosphate	Indo-Pacific	(26.75,27]	-0.9431337	-0.9637762	-0.9182553
phosphate	Indo-Pacific	(27,27.25]	-0.7095520	-0.7337122	-0.6694928
phosphate	Indo-Pacific	(27.25,27.5]	-0.0313802	-0.1047596	0.0186200
phosphate	Indo-Pacific	(27.5,27.75]	0.3083326	0.1797954	0.3997344
phosphate	Indo-Pacific	(27.75,27.85]	0.3466687	0.1603515	0.4817711
phosphate	Indo-Pacific	(27.85,27.95]	0.1586467	0.0061840	0.3154189
phosphate	Indo-Pacific	(27.95,28.05]	-0.2708156	-0.3647272	-0.0880230
phosphate	Indo-Pacific	(28.05,28.1]	-0.4197660	-0.5487571	-0.3012822
phosphate	Indo-Pacific	(28.1, Inf]	-0.2895288	-0.4373891	-0.0213370
phosphate_star	Atlantic	(-Inf,26]	-0.5935735	-0.8157792	-0.4771581
phosphate_star	Atlantic	(26,26.5]	-0.8718047	-0.9201545	-0.8427446
phosphate_star	Atlantic	(26.5,26.75]	-0.9255284	-0.9349912	-0.9207291
phosphate_star	Atlantic	(26.75,27]	-0.9328314	-0.9400878	-0.9199980
phosphate_star	Atlantic	(27,27.25]	-0.9262818	-0.9387045	-0.9125823
phosphate_star	Atlantic	(27.25,27.5]	-0.9298303	-0.9479061	-0.9206732
phosphate_star	Atlantic	(27.5,27.75]	-0.9304176	-0.9426621	-0.9161227
phosphate_star	Atlantic	(27.75,27.85]	-0.9060442	-0.9148401	-0.8969919
phosphate_star	Atlantic	(27.85,27.95]	-0.8181430	-0.8415868	-0.7867834
phosphate_star	Atlantic	(27.95,28.05]	-0.8787212	-0.9070702	-0.8355508
phosphate_star	Atlantic	(28.05,28.1]	-0.9181583	-0.9313194	-0.9010139
phosphate_star	Atlantic	(28.1,28.15]	-0.9415685	-0.9519313	-0.9220626
phosphate_star	Atlantic	(28.15,28.2]	-0.9802308	-0.9841552	-0.9727547
phosphate_star	Atlantic	(28.2, Inf]	-0.9281786	-0.9386588	-0.9144437
phosphate_star	Indo-Pacific	(-Inf,26]	-0.4450676	-0.5969589	-0.3356988
phosphate_star	Indo-Pacific	(26,26.5]	-0.8343674	-0.8809910	-0.8073142
phosphate_star	Indo-Pacific	(26.5,26.75]	-0.7774699	-0.8827000	-0.6367511
phosphate_star	Indo-Pacific	(26.75,27]	-0.7172191	-0.8260731	-0.6434565
phosphate_star	Indo-Pacific	(27,27.25]	-0.3806223	-0.5134801	-0.2858245
phosphate_star	Indo-Pacific	(27.25,27.5]	-0.1979648	-0.2506467	-0.1569013
phosphate_star	Indo-Pacific	(27.5,27.75]	-0.3915037	-0.5454948	-0.1507756
phosphate_star	Indo-Pacific	(27.75,27.85]	-0.5061099	-0.7408345	-0.2439190
phosphate_star	Indo-Pacific	(27.85,27.95]	-0.4836665	-0.5537441	-0.3976820
phosphate_star	Indo-Pacific	(27.95,28.05]	-0.5243472	-0.6153159	-0.4006077
phosphate_star	Indo-Pacific	(28.05,28.1]	-0.5991372	-0.6751435	-0.4640165
phosphate_star	Indo-Pacific	(28.1, Inf]	-0.5474076	-0.6637739	-0.4380748
salinity	Atlantic	(-Inf,26]	0.2893199	0.2228703	0.3269860
salinity	Atlantic	(26,26.5]	0.7307163	0.5226450	0.8666493
salinity	Atlantic	(26.5,26.75]	0.8567660	0.8063865	0.8880440
salinity	Atlantic	(26.75,27]	0.8973845	0.8699793	0.9146719
salinity	Atlantic	(27,27.25]	0.9172249	0.8999376	0.9429090
salinity	Atlantic	(27.25,27.5]	0.9109993	0.8814810	0.9378890
salinity	Atlantic	(27.5,27.75]	0.8557359	0.8418518	0.8667822
salinity	Atlantic	(27.75,27.85]	0.7298170	0.7081495	0.7436290
salinity	Atlantic	(27.85,27.95]	0.4577464	0.3090975	0.5387157
salinity	Atlantic	(27.95,28.05]	0.5549736	0.2690369	0.7159448
salinity	Atlantic	(28.05,28.1]	0.7234078	0.6613456	0.7730548
salinity	Atlantic	(28.1,28.15]	0.7974262	0.7724322	0.8443428
salinity	Atlantic	(28.15,28.2]	0.9099105	0.8925141	0.9326793
salinity	Atlantic	(28.2, Inf]	0.9028001	0.8621840	0.9295343
salinity	Indo-Pacific	(-Inf,26]	0.1424162	0.1302355	0.1490515
salinity	Indo-Pacific	(26,26.5]	0.4116612	0.2672732	0.6357848
salinity	Indo-Pacific	(26.5,26.75]	0.4397660	0.2122471	0.7191236
salinity	Indo-Pacific	(26.75,27]	0.4597281	0.3190997	0.6789589
salinity	Indo-Pacific	(27,27.25]	0.0123945	-0.1171006	0.2012728
salinity	Indo-Pacific	(27.25,27.5]	-0.4118120	-0.6169920	-0.2106017
salinity	Indo-Pacific	(27.5,27.75]	-0.3507712	-0.4420790	-0.2781870
salinity	Indo-Pacific	(27.75,27.85]	-0.4422701	-0.5218193	-0.3402807
salinity	Indo-Pacific	(27.85,27.95]	-0.2650744	-0.3579383	-0.1096441
salinity	Indo-Pacific	(27.95,28.05]	0.1894492	0.0558813	0.3305911
salinity	Indo-Pacific	(28.05,28.1]	0.2948295	0.2278978	0.4117443
salinity	Indo-Pacific	(28.1, Inf]	0.3146967	0.2545246	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]	-0.5042313	-0.6084832	-0.4353253
silicate	Indo-Pacific	(26,26.5]	-0.7720302	-0.8099400	-0.7136697
silicate	Indo-Pacific	(26.5,26.75]	-0.7649857	-0.8394297	-0.6332848
silicate	Indo-Pacific	(26.75,27]	-0.7688679	-0.7989565	-0.7199367
silicate	Indo-Pacific	(27,27.25]	-0.4288905	-0.5067920	-0.3808500
silicate	Indo-Pacific	(27.25,27.5]	0.3487353	0.2863804	0.4238548
silicate	Indo-Pacific	(27.5,27.75]	0.6207373	0.5432704	0.6742328
silicate	Indo-Pacific	(27.75,27.85]	0.5180889	0.3788004	0.6335329
silicate	Indo-Pacific	(27.85,27.95]	0.2837091	0.1630961	0.4182219
silicate	Indo-Pacific	(27.95,28.05]	-0.1466626	-0.2390264	0.0164143
silicate	Indo-Pacific	(28.05,28.1]	-0.3088625	-0.4332697	-0.2382106
silicate	Indo-Pacific	(28.1, Inf]	-0.2082541	-0.3356880	-0.0587563
temperature	Atlantic	(-Inf,26]	0.0655155	-0.0827931	0.1465154
temperature	Atlantic	(26,26.5]	0.7223412	0.5595250	0.8169447
temperature	Atlantic	(26.5,26.75]	0.8562581	0.8275488	0.8735358
temperature	Atlantic	(26.75,27]	0.8850341	0.8656686	0.9019147
temperature	Atlantic	(27,27.25]	0.8879506	0.8729674	0.9066721
temperature	Atlantic	(27.25,27.5]	0.8839156	0.8608731	0.9128891
temperature	Atlantic	(27.5,27.75]	0.8129182	0.7950602	0.8219969
temperature	Atlantic	(27.75,27.85]	0.7102829	0.6959796	0.7246136
temperature	Atlantic	(27.85,27.95]	0.4251724	0.2476208	0.5283781
temperature	Atlantic	(27.95,28.05]	0.5337535	0.3266584	0.6577087
temperature	Atlantic	(28.05,28.1]	0.6005779	0.4727863	0.6745071
temperature	Atlantic	(28.1,28.15]	0.6225691	0.5370767	0.7289768
temperature	Atlantic	(28.15,28.2]	0.6648944	0.6118608	0.7276289
temperature	Atlantic	(28.2, Inf]	0.1867555	0.0586055	0.3122400
temperature	Indo-Pacific	(-Inf,26]	-0.0095803	-0.0853838	0.0630388
temperature	Indo-Pacific	(26,26.5]	0.4530371	0.3284862	0.6438857
temperature	Indo-Pacific	(26.5,26.75]	0.4357882	0.2238553	0.6994812
temperature	Indo-Pacific	(26.75,27]	0.5017951	0.3992145	0.6959193
temperature	Indo-Pacific	(27,27.25]	0.1560749	0.0539126	0.3437092
temperature	Indo-Pacific	(27.25,27.5]	-0.3384487	-0.5112289	-0.1887612
temperature	Indo-Pacific	(27.5,27.75]	-0.4346242	-0.5502807	-0.3667787
temperature	Indo-Pacific	(27.75,27.85]	-0.4515418	-0.5549833	-0.3402104
temperature	Indo-Pacific	(27.85,27.95]	-0.3311004	-0.4395518	-0.1852648
temperature	Indo-Pacific	(27.95,28.05]	0.0334726	-0.0145886	0.0670336
temperature	Indo-Pacific	(28.05,28.1]	0.1142159	0.1022677	0.1252990
temperature	Indo-Pacific	(28.1, Inf]	0.2929595	0.1220996	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 ~ 
                salinity  + 
                temperature  + 
                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]	salinity temperature aou oxygen phosphate_star	7.173663	6.319107	2.765130	16.257900
Atlantic	(-Inf,26]	salinity temperature aou oxygen phosphate	7.173663	6.319107	2.765130	16.257900
Atlantic	(-Inf,26]	salinity temperature aou phosphate phosphate_star	7.173663	6.319107	2.765130	16.257900
Atlantic	(-Inf,26]	salinity temperature silicate phosphate phosphate_star	7.248967	6.204419	2.852778	16.306164
Atlantic	(-Inf,26]	salinity temperature oxygen silicate phosphate_star	7.248967	6.204419	2.852778	16.306164
Atlantic	(-Inf,26]	salinity temperature oxygen silicate phosphate	7.248967	6.204419	2.852778	16.306164
Atlantic	(-Inf,26]	salinity temperature aou silicate phosphate	7.278011	6.171501	2.857798	16.307310
Atlantic	(-Inf,26]	salinity temperature aou silicate phosphate_star	7.258007	6.200249	2.851674	16.309930
Atlantic	(-Inf,26]	salinity aou oxygen silicate phosphate_star	7.367183	6.069229	2.875347	16.311759
Atlantic	(-Inf,26]	salinity aou oxygen silicate phosphate	7.367183	6.069229	2.875347	16.311759
Atlantic	(26,26.5]	temperature aou silicate phosphate phosphate_star	5.363554	6.815718	3.120245	15.299516
Atlantic	(26,26.5]	temperature aou oxygen silicate phosphate	5.363554	6.815718	3.120245	15.299516
Atlantic	(26,26.5]	temperature aou oxygen silicate phosphate_star	5.363554	6.815718	3.120245	15.299516
Atlantic	(26,26.5]	salinity temperature aou phosphate phosphate_star	5.477425	6.872313	3.164633	15.514372
Atlantic	(26,26.5]	salinity temperature aou oxygen phosphate	5.477425	6.872313	3.164633	15.514372
Atlantic	(26,26.5]	salinity temperature aou oxygen phosphate_star	5.477425	6.872313	3.164633	15.514372
Atlantic	(26,26.5]	temperature aou phosphate phosphate_star	5.478784	6.872333	3.181060	15.532177
Atlantic	(26,26.5]	temperature aou oxygen phosphate	5.478784	6.872333	3.181060	15.532177
Atlantic	(26,26.5]	temperature aou oxygen phosphate phosphate_star	5.478784	6.872333	3.181060	15.532177
Atlantic	(26,26.5]	temperature aou oxygen phosphate_star	5.478784	6.872333	3.181060	15.532177
Atlantic	(26.5,26.75]	temperature aou oxygen silicate phosphate_star	5.153695	5.620094	3.704869	14.478657
Atlantic	(26.5,26.75]	temperature aou silicate phosphate phosphate_star	5.153695	5.620094	3.704869	14.478657
Atlantic	(26.5,26.75]	temperature aou oxygen silicate phosphate	5.153695	5.620094	3.704869	14.478657
Atlantic	(26.5,26.75]	salinity temperature aou silicate phosphate	5.080928	5.614607	3.805535	14.501071
Atlantic	(26.5,26.75]	salinity temperature silicate phosphate phosphate_star	5.073639	5.596750	3.838208	14.508597
Atlantic	(26.5,26.75]	salinity temperature oxygen silicate phosphate_star	5.073639	5.596750	3.838208	14.508597
Atlantic	(26.5,26.75]	salinity temperature oxygen silicate phosphate	5.073639	5.596750	3.838208	14.508597
Atlantic	(26.5,26.75]	salinity temperature aou silicate phosphate_star	5.074249	5.596367	3.847880	14.518496
Atlantic	(26.5,26.75]	salinity aou oxygen silicate phosphate_star	5.121400	5.673332	3.769774	14.564506
Atlantic	(26.5,26.75]	salinity aou oxygen silicate phosphate	5.121400	5.673332	3.769774	14.564506
Atlantic	(26.75,27]	salinity temperature aou silicate phosphate_star	4.688937	4.955801	3.438819	13.083557
Atlantic	(26.75,27]	salinity temperature oxygen silicate phosphate	4.689137	4.956845	3.438851	13.084832
Atlantic	(26.75,27]	salinity temperature silicate phosphate phosphate_star	4.689137	4.956845	3.438851	13.084832
Atlantic	(26.75,27]	salinity temperature oxygen silicate phosphate_star	4.689137	4.956845	3.438851	13.084832
Atlantic	(26.75,27]	salinity temperature aou silicate phosphate	4.708472	4.969119	3.448332	13.125924
Atlantic	(26.75,27]	temperature aou oxygen silicate phosphate	4.802227	5.046591	3.444518	13.293336
Atlantic	(26.75,27]	temperature aou oxygen silicate phosphate_star	4.802227	5.046591	3.444518	13.293336
Atlantic	(26.75,27]	temperature aou silicate phosphate phosphate_star	4.802227	5.046591	3.444518	13.293336
Atlantic	(26.75,27]	temperature aou silicate phosphate_star	4.803550	5.046726	3.444645	13.294920
Atlantic	(26.75,27]	temperature oxygen silicate phosphate	4.803963	5.046602	3.445002	13.295567
Atlantic	(27,27.25]	salinity temperature aou silicate phosphate_star	5.013740	5.040797	4.664774	14.719311
Atlantic	(27,27.25]	salinity temperature oxygen silicate phosphate	5.018688	5.043558	4.665827	14.728072
Atlantic	(27,27.25]	salinity temperature silicate phosphate phosphate_star	5.018688	5.043558	4.665827	14.728072
Atlantic	(27,27.25]	salinity temperature oxygen silicate phosphate_star	5.018688	5.043558	4.665827	14.728072
Atlantic	(27,27.25]	salinity temperature aou silicate phosphate	5.078648	5.067501	4.676695	14.822845
Atlantic	(27,27.25]	temperature aou oxygen silicate phosphate	5.132734	5.053192	4.710145	14.896071
Atlantic	(27,27.25]	temperature aou oxygen silicate phosphate_star	5.132734	5.053192	4.710145	14.896071
Atlantic	(27,27.25]	temperature aou silicate phosphate phosphate_star	5.132734	5.053192	4.710145	14.896071
Atlantic	(27,27.25]	temperature aou silicate phosphate_star	5.153233	5.053345	4.713141	14.919721
Atlantic	(27,27.25]	temperature oxygen silicate phosphate	5.156878	5.054717	4.711437	14.923032
Atlantic	(27.25,27.5]	salinity temperature aou oxygen phosphate	4.685854	4.337938	3.941030	12.964822
Atlantic	(27.25,27.5]	salinity temperature aou oxygen phosphate_star	4.685854	4.337938	3.941030	12.964822
Atlantic	(27.25,27.5]	salinity temperature aou phosphate phosphate_star	4.685854	4.337938	3.941030	12.964822
Atlantic	(27.25,27.5]	temperature aou oxygen silicate phosphate	4.708352	4.417138	3.863306	12.988797
Atlantic	(27.25,27.5]	temperature aou oxygen silicate phosphate_star	4.708352	4.417138	3.863306	12.988797
Atlantic	(27.25,27.5]	temperature aou silicate phosphate phosphate_star	4.708352	4.417138	3.863306	12.988797
Atlantic	(27.25,27.5]	salinity temperature oxygen silicate phosphate_star	4.779166	4.341614	3.878332	12.999112
Atlantic	(27.25,27.5]	salinity temperature oxygen silicate phosphate	4.779166	4.341614	3.878332	12.999112
Atlantic	(27.25,27.5]	salinity temperature silicate phosphate phosphate_star	4.779166	4.341614	3.878332	12.999112
Atlantic	(27.25,27.5]	salinity temperature aou silicate phosphate_star	4.761998	4.355715	3.891948	13.009662
Atlantic	(27.5,27.75]	salinity aou silicate phosphate phosphate_star	4.174741	4.328080	4.306869	12.809689
Atlantic	(27.5,27.75]	salinity aou oxygen silicate phosphate	4.174741	4.328080	4.306869	12.809689
Atlantic	(27.5,27.75]	salinity aou oxygen silicate phosphate_star	4.174741	4.328080	4.306869	12.809689
Atlantic	(27.5,27.75]	salinity temperature aou silicate phosphate	4.161707	4.340464	4.307726	12.809898
Atlantic	(27.5,27.75]	salinity temperature oxygen silicate phosphate	4.152754	4.352114	4.311898	12.816766
Atlantic	(27.5,27.75]	salinity temperature silicate phosphate phosphate_star	4.152754	4.352114	4.311898	12.816766
Atlantic	(27.5,27.75]	salinity temperature oxygen silicate phosphate_star	4.152754	4.352114	4.311898	12.816766
Atlantic	(27.5,27.75]	temperature aou oxygen silicate phosphate_star	4.152046	4.332673	4.334831	12.819550
Atlantic	(27.5,27.75]	temperature aou oxygen silicate phosphate	4.152046	4.332673	4.334831	12.819550
Atlantic	(27.5,27.75]	temperature aou silicate phosphate phosphate_star	4.152046	4.332673	4.334831	12.819550
Atlantic	(27.75,27.85]	salinity temperature aou silicate phosphate_star	4.111828	4.279565	6.017580	14.408973
Atlantic	(27.75,27.85]	salinity aou oxygen silicate phosphate_star	4.113685	4.277923	6.026571	14.418179
Atlantic	(27.75,27.85]	salinity aou silicate phosphate phosphate_star	4.113685	4.277923	6.026571	14.418179
Atlantic	(27.75,27.85]	salinity aou oxygen silicate phosphate	4.113685	4.277923	6.026571	14.418179
Atlantic	(27.75,27.85]	salinity temperature oxygen silicate phosphate_star	4.112834	4.277933	6.034910	14.425676
Atlantic	(27.75,27.85]	salinity temperature oxygen silicate phosphate	4.112834	4.277933	6.034910	14.425676
Atlantic	(27.75,27.85]	salinity temperature silicate phosphate phosphate_star	4.112834	4.277933	6.034910	14.425676
Atlantic	(27.75,27.85]	salinity temperature aou silicate phosphate	4.114571	4.278130	6.036798	14.429498
Atlantic	(27.75,27.85]	salinity oxygen silicate phosphate_star	4.121204	4.278115	6.042167	14.441486
Atlantic	(27.75,27.85]	salinity oxygen silicate phosphate	4.121204	4.278115	6.042167	14.441486
Atlantic	(27.85,27.95]	salinity aou oxygen silicate phosphate	3.728892	4.171368	4.839290	12.739550
Atlantic	(27.85,27.95]	salinity aou oxygen silicate phosphate_star	3.728892	4.171368	4.839290	12.739550
Atlantic	(27.85,27.95]	salinity aou silicate phosphate phosphate_star	3.728892	4.171368	4.839290	12.739550
Atlantic	(27.85,27.95]	salinity temperature aou silicate phosphate_star	3.728345	4.172239	4.852173	12.752757
Atlantic	(27.85,27.95]	salinity temperature oxygen silicate phosphate	3.740886	4.187591	4.873867	12.802345
Atlantic	(27.85,27.95]	salinity temperature silicate phosphate phosphate_star	3.740886	4.187591	4.873867	12.802345
Atlantic	(27.85,27.95]	salinity temperature oxygen silicate phosphate_star	3.740886	4.187591	4.873867	12.802345
Atlantic	(27.85,27.95]	salinity temperature aou silicate phosphate	3.751565	4.193647	4.873647	12.818859
Atlantic	(27.85,27.95]	salinity aou silicate phosphate_star	3.728950	4.208988	4.967537	12.905475
Atlantic	(27.85,27.95]	salinity temperature silicate phosphate	3.981572	4.291511	4.873938	13.147020
Atlantic	(27.95,28.05]	salinity aou oxygen silicate phosphate_star	3.487770	4.363515	4.820087	12.671372
Atlantic	(27.95,28.05]	salinity aou silicate phosphate phosphate_star	3.487770	4.363515	4.820087	12.671372
Atlantic	(27.95,28.05]	salinity aou oxygen silicate phosphate	3.487770	4.363515	4.820087	12.671372
Atlantic	(27.95,28.05]	salinity temperature aou silicate phosphate_star	3.487662	4.352096	4.850243	12.690002
Atlantic	(27.95,28.05]	salinity aou silicate phosphate_star	3.487779	4.373834	4.864433	12.726046
Atlantic	(27.95,28.05]	salinity temperature oxygen silicate phosphate_star	3.498901	4.381935	4.910557	12.791393
Atlantic	(27.95,28.05]	salinity temperature silicate phosphate phosphate_star	3.498901	4.381935	4.910557	12.791393
Atlantic	(27.95,28.05]	salinity temperature oxygen silicate phosphate	3.498901	4.381935	4.910557	12.791393
Atlantic	(27.95,28.05]	salinity temperature aou silicate phosphate	3.508118	4.406907	4.931814	12.846839
Atlantic	(27.95,28.05]	salinity temperature aou phosphate phosphate_star	3.755336	4.367751	4.799080	12.922167
Atlantic	(28.05,28.1]	salinity temperature aou phosphate phosphate_star	3.539499	4.360234	4.144983	12.044717
Atlantic	(28.05,28.1]	salinity temperature aou oxygen phosphate_star	3.539499	4.360234	4.144983	12.044717
Atlantic	(28.05,28.1]	salinity temperature aou oxygen phosphate	3.539499	4.360234	4.144983	12.044717
Atlantic	(28.05,28.1]	temperature aou silicate phosphate phosphate_star	3.643192	4.334898	4.117142	12.095232
Atlantic	(28.05,28.1]	temperature aou oxygen silicate phosphate_star	3.643192	4.334898	4.117142	12.095232
Atlantic	(28.05,28.1]	temperature aou oxygen silicate phosphate	3.643192	4.334898	4.117142	12.095232
Atlantic	(28.05,28.1]	salinity temperature aou silicate phosphate_star	3.518913	4.525800	4.352501	12.397215
Atlantic	(28.05,28.1]	temperature aou phosphate phosphate_star	3.737933	4.455027	4.228193	12.421153
Atlantic	(28.05,28.1]	temperature aou oxygen phosphate_star	3.737933	4.455027	4.228193	12.421153
Atlantic	(28.05,28.1]	temperature aou oxygen phosphate	3.737933	4.455027	4.228193	12.421153
Atlantic	(28.1,28.15]	salinity temperature aou silicate phosphate_star	3.342361	3.940015	4.245324	11.527700
Atlantic	(28.1,28.15]	salinity temperature oxygen silicate phosphate_star	3.349308	3.947860	4.254217	11.551386
Atlantic	(28.1,28.15]	salinity temperature silicate phosphate phosphate_star	3.349308	3.947860	4.254217	11.551386
Atlantic	(28.1,28.15]	salinity temperature oxygen silicate phosphate	3.349308	3.947860	4.254217	11.551386
Atlantic	(28.1,28.15]	salinity temperature aou oxygen phosphate_star	3.440411	3.952540	4.211635	11.604587
Atlantic	(28.1,28.15]	salinity temperature aou phosphate phosphate_star	3.440411	3.952540	4.211635	11.604587
Atlantic	(28.1,28.15]	salinity temperature aou oxygen phosphate	3.440411	3.952540	4.211635	11.604587
Atlantic	(28.1,28.15]	temperature aou oxygen silicate phosphate_star	3.436793	3.969257	4.216057	11.622107
Atlantic	(28.1,28.15]	temperature aou silicate phosphate phosphate_star	3.436793	3.969257	4.216057	11.622107
Atlantic	(28.1,28.15]	temperature aou oxygen silicate phosphate	3.436793	3.969257	4.216057	11.622107
Atlantic	(28.15,28.2]	salinity temperature aou oxygen phosphate	3.719163	3.607541	2.836143	10.162847
Atlantic	(28.15,28.2]	salinity temperature aou phosphate phosphate_star	3.719163	3.607541	2.836143	10.162847
Atlantic	(28.15,28.2]	salinity temperature aou oxygen phosphate_star	3.719163	3.607541	2.836143	10.162847
Atlantic	(28.15,28.2]	salinity aou silicate phosphate phosphate_star	3.713912	3.607352	2.914045	10.235310
Atlantic	(28.15,28.2]	salinity aou oxygen silicate phosphate	3.713912	3.607352	2.914045	10.235310
Atlantic	(28.15,28.2]	salinity aou oxygen silicate phosphate_star	3.713912	3.607352	2.914045	10.235310
Atlantic	(28.15,28.2]	salinity temperature aou silicate phosphate	3.739761	3.662219	2.835064	10.237044
Atlantic	(28.15,28.2]	salinity temperature aou phosphate	3.740143	3.669008	2.837785	10.246936
Atlantic	(28.15,28.2]	salinity aou phosphate phosphate_star	3.719217	3.607575	2.956477	10.283268
Atlantic	(28.15,28.2]	salinity aou oxygen phosphate	3.719217	3.607575	2.956477	10.283268
Atlantic	(28.2, Inf]	salinity temperature aou phosphate phosphate_star	3.337999	3.057466	2.685083	9.080549
Atlantic	(28.2, Inf]	salinity temperature aou oxygen phosphate	3.337999	3.057466	2.685083	9.080549
Atlantic	(28.2, Inf]	salinity temperature aou oxygen phosphate_star	3.337999	3.057466	2.685083	9.080549
Atlantic	(28.2, Inf]	salinity temperature aou silicate phosphate	3.425561	3.059270	2.696506	9.181337
Atlantic	(28.2, Inf]	salinity aou oxygen silicate phosphate_star	3.358320	3.057387	2.767527	9.183233
Atlantic	(28.2, Inf]	salinity aou oxygen silicate phosphate	3.358320	3.057387	2.767527	9.183233
Atlantic	(28.2, Inf]	salinity aou silicate phosphate phosphate_star	3.358320	3.057387	2.767527	9.183233
Atlantic	(28.2, Inf]	salinity aou phosphate phosphate_star	3.378104	3.057832	2.767543	9.203479
Atlantic	(28.2, Inf]	salinity aou oxygen phosphate_star	3.378104	3.057832	2.767543	9.203479
Atlantic	(28.2, Inf]	salinity aou oxygen phosphate	3.378104	3.057832	2.767543	9.203479
Indo-Pacific	(-Inf,26]	salinity aou silicate phosphate phosphate_star	11.623462	7.157989	5.647250	24.428701
Indo-Pacific	(-Inf,26]	salinity aou oxygen silicate phosphate	11.623462	7.157989	5.647250	24.428701
Indo-Pacific	(-Inf,26]	salinity aou oxygen silicate phosphate_star	11.623462	7.157989	5.647250	24.428701
Indo-Pacific	(-Inf,26]	salinity temperature aou silicate phosphate	11.694737	7.232705	5.850663	24.778105
Indo-Pacific	(-Inf,26]	salinity temperature aou silicate phosphate_star	11.734104	7.275988	5.931195	24.941287
Indo-Pacific	(-Inf,26]	salinity temperature oxygen silicate phosphate	11.733531	7.281349	5.951189	24.966069
Indo-Pacific	(-Inf,26]	salinity temperature oxygen silicate phosphate_star	11.733531	7.281349	5.951189	24.966069
Indo-Pacific	(-Inf,26]	salinity temperature silicate phosphate phosphate_star	11.733531	7.281349	5.951189	24.966069
Indo-Pacific	(-Inf,26]	salinity temperature silicate phosphate_star	11.734464	7.311199	6.085233	25.130896
Indo-Pacific	(-Inf,26]	salinity temperature aou phosphate phosphate_star	11.863091	7.575205	6.002886	25.441182
Indo-Pacific	(26,26.5]	salinity aou silicate phosphate phosphate_star	7.889069	5.196372	3.936596	17.022037
Indo-Pacific	(26,26.5]	salinity aou oxygen silicate phosphate	7.889069	5.196372	3.936596	17.022037
Indo-Pacific	(26,26.5]	salinity aou oxygen silicate phosphate_star	7.889069	5.196372	3.936596	17.022037
Indo-Pacific	(26,26.5]	salinity temperature aou silicate phosphate	7.963424	5.154247	4.013896	17.131567
Indo-Pacific	(26,26.5]	salinity temperature oxygen silicate phosphate	8.000579	5.163590	4.053536	17.217705
Indo-Pacific	(26,26.5]	salinity temperature silicate phosphate phosphate_star	8.000579	5.163590	4.053536	17.217705
Indo-Pacific	(26,26.5]	salinity temperature oxygen silicate phosphate_star	8.000579	5.163590	4.053536	17.217705
Indo-Pacific	(26,26.5]	salinity temperature aou silicate phosphate_star	8.010246	5.166535	4.065867	17.242648
Indo-Pacific	(26,26.5]	salinity temperature aou phosphate phosphate_star	7.992846	5.293950	4.249030	17.535826
Indo-Pacific	(26,26.5]	salinity temperature aou oxygen phosphate	7.992846	5.293950	4.249030	17.535826
Indo-Pacific	(26.5,26.75]	salinity aou oxygen silicate phosphate_star	5.927382	5.693985	4.559978	16.181345
Indo-Pacific	(26.5,26.75]	salinity aou oxygen silicate phosphate	5.927382	5.693985	4.559978	16.181345
Indo-Pacific	(26.5,26.75]	salinity aou silicate phosphate phosphate_star	5.927382	5.693985	4.559978	16.181345
Indo-Pacific	(26.5,26.75]	salinity temperature aou oxygen phosphate_star	6.009325	5.700080	4.616972	16.326376
Indo-Pacific	(26.5,26.75]	salinity temperature aou oxygen phosphate	6.009325	5.700080	4.616972	16.326376
Indo-Pacific	(26.5,26.75]	salinity temperature aou phosphate phosphate_star	6.009325	5.700080	4.616972	16.326376
Indo-Pacific	(26.5,26.75]	salinity aou oxygen phosphate_star	6.011205	5.700094	4.633021	16.344321
Indo-Pacific	(26.5,26.75]	salinity aou oxygen phosphate	6.011205	5.700094	4.633021	16.344321
Indo-Pacific	(26.5,26.75]	salinity aou oxygen phosphate phosphate_star	6.011205	5.700094	4.633021	16.344321
Indo-Pacific	(26.5,26.75]	salinity aou phosphate phosphate_star	6.011205	5.700094	4.633021	16.344321
Indo-Pacific	(26.75,27]	temperature aou oxygen silicate phosphate_star	6.542541	4.987407	4.222006	15.751955
Indo-Pacific	(26.75,27]	temperature aou oxygen silicate phosphate	6.542541	4.987407	4.222006	15.751955
Indo-Pacific	(26.75,27]	temperature aou silicate phosphate phosphate_star	6.542541	4.987407	4.222006	15.751955
Indo-Pacific	(26.75,27]	salinity temperature aou oxygen phosphate	6.566186	5.023804	4.249032	15.839021
Indo-Pacific	(26.75,27]	salinity temperature aou oxygen phosphate_star	6.566186	5.023804	4.249032	15.839021
Indo-Pacific	(26.75,27]	salinity temperature aou phosphate phosphate_star	6.566186	5.023804	4.249032	15.839021
Indo-Pacific	(26.75,27]	temperature aou oxygen phosphate_star	6.569450	5.024563	4.262325	15.856337
Indo-Pacific	(26.75,27]	temperature aou oxygen phosphate	6.569450	5.024563	4.262325	15.856337
Indo-Pacific	(26.75,27]	temperature aou oxygen phosphate phosphate_star	6.569450	5.024563	4.262325	15.856337
Indo-Pacific	(26.75,27]	temperature aou phosphate phosphate_star	6.569450	5.024563	4.262325	15.856337
Indo-Pacific	(27,27.25]	temperature aou oxygen silicate phosphate_star	6.034168	4.532777	4.048207	14.615152
Indo-Pacific	(27,27.25]	temperature aou oxygen silicate phosphate	6.034168	4.532777	4.048207	14.615152
Indo-Pacific	(27,27.25]	temperature aou silicate phosphate phosphate_star	6.034168	4.532777	4.048207	14.615152
Indo-Pacific	(27,27.25]	salinity temperature aou oxygen phosphate_star	6.048680	4.607554	4.166144	14.822378
Indo-Pacific	(27,27.25]	salinity temperature aou oxygen phosphate	6.048680	4.607554	4.166144	14.822378
Indo-Pacific	(27,27.25]	salinity temperature aou phosphate phosphate_star	6.048680	4.607554	4.166144	14.822378
Indo-Pacific	(27,27.25]	salinity aou oxygen silicate phosphate_star	6.432599	4.541415	4.107446	15.081460
Indo-Pacific	(27,27.25]	salinity aou oxygen silicate phosphate	6.432599	4.541415	4.107446	15.081460
Indo-Pacific	(27,27.25]	salinity aou silicate phosphate phosphate_star	6.432599	4.541415	4.107446	15.081460
Indo-Pacific	(27,27.25]	temperature aou phosphate phosphate_star	6.076991	4.747237	4.304603	15.128831
Indo-Pacific	(27.25,27.5]	temperature aou oxygen silicate phosphate_star	4.835968	3.913969	3.527790	12.277728
Indo-Pacific	(27.25,27.5]	temperature aou oxygen silicate phosphate	4.835968	3.913969	3.527790	12.277728
Indo-Pacific	(27.25,27.5]	temperature aou silicate phosphate phosphate_star	4.835968	3.913969	3.527790	12.277728
Indo-Pacific	(27.25,27.5]	salinity aou oxygen silicate phosphate_star	5.251519	3.924282	3.243081	12.418882
Indo-Pacific	(27.25,27.5]	salinity aou oxygen silicate phosphate	5.251519	3.924282	3.243081	12.418882
Indo-Pacific	(27.25,27.5]	salinity aou silicate phosphate phosphate_star	5.251519	3.924282	3.243081	12.418882
Indo-Pacific	(27.25,27.5]	salinity temperature aou phosphate phosphate_star	4.862194	4.131183	3.627177	12.620554
Indo-Pacific	(27.25,27.5]	salinity temperature aou oxygen phosphate	4.862194	4.131183	3.627177	12.620554
Indo-Pacific	(27.25,27.5]	salinity temperature aou oxygen phosphate_star	4.862194	4.131183	3.627177	12.620554
Indo-Pacific	(27.25,27.5]	salinity temperature aou silicate phosphate	5.578168	3.945800	3.247152	12.771119
Indo-Pacific	(27.5,27.75]	salinity aou silicate phosphate phosphate_star	4.688828	3.605057	2.968149	11.262034
Indo-Pacific	(27.5,27.75]	salinity aou oxygen silicate phosphate	4.688828	3.605057	2.968149	11.262034
Indo-Pacific	(27.5,27.75]	salinity aou oxygen silicate phosphate_star	4.688828	3.605057	2.968149	11.262034
Indo-Pacific	(27.5,27.75]	salinity temperature aou silicate phosphate	4.857991	3.606697	2.966581	11.431268
Indo-Pacific	(27.5,27.75]	temperature aou oxygen silicate phosphate_star	4.414022	3.814534	3.290961	11.519517
Indo-Pacific	(27.5,27.75]	temperature aou oxygen silicate phosphate	4.414022	3.814534	3.290961	11.519517
Indo-Pacific	(27.5,27.75]	temperature aou silicate phosphate phosphate_star	4.414022	3.814534	3.290961	11.519517
Indo-Pacific	(27.5,27.75]	salinity temperature oxygen silicate phosphate	4.986342	3.612588	2.965966	11.564897
Indo-Pacific	(27.5,27.75]	salinity temperature oxygen silicate phosphate_star	4.986342	3.612588	2.965966	11.564897
Indo-Pacific	(27.5,27.75]	salinity temperature silicate phosphate phosphate_star	4.986342	3.612588	2.965966	11.564897
Indo-Pacific	(27.75,27.85]	temperature aou silicate phosphate phosphate_star	4.269432	3.237786	2.903747	10.410965
Indo-Pacific	(27.75,27.85]	temperature aou oxygen silicate phosphate_star	4.269432	3.237786	2.903747	10.410965
Indo-Pacific	(27.75,27.85]	temperature aou oxygen silicate phosphate	4.269432	3.237786	2.903747	10.410965
Indo-Pacific	(27.75,27.85]	salinity temperature aou silicate phosphate_star	4.307418	3.255299	2.863161	10.425878
Indo-Pacific	(27.75,27.85]	salinity temperature oxygen silicate phosphate_star	4.308811	3.257267	2.865015	10.431092
Indo-Pacific	(27.75,27.85]	salinity temperature silicate phosphate phosphate_star	4.308811	3.257267	2.865015	10.431092
Indo-Pacific	(27.75,27.85]	salinity temperature oxygen silicate phosphate	4.308811	3.257267	2.865015	10.431092
Indo-Pacific	(27.75,27.85]	salinity temperature aou silicate phosphate	4.285667	3.281087	2.876268	10.443022
Indo-Pacific	(27.75,27.85]	salinity aou oxygen silicate phosphate_star	4.262144	3.319860	2.896917	10.478921
Indo-Pacific	(27.75,27.85]	salinity aou oxygen silicate phosphate	4.262144	3.319860	2.896917	10.478921
Indo-Pacific	(27.85,27.95]	salinity temperature aou silicate phosphate	4.318767	2.976677	2.878296	10.173740
Indo-Pacific	(27.85,27.95]	temperature aou oxygen silicate phosphate	4.309845	2.980375	2.891621	10.181842
Indo-Pacific	(27.85,27.95]	temperature aou oxygen silicate phosphate_star	4.309845	2.980375	2.891621	10.181842
Indo-Pacific	(27.85,27.95]	temperature aou silicate phosphate phosphate_star	4.309845	2.980375	2.891621	10.181842
Indo-Pacific	(27.85,27.95]	salinity aou silicate phosphate phosphate_star	4.301346	2.986208	2.896370	10.183924
Indo-Pacific	(27.85,27.95]	salinity aou oxygen silicate phosphate_star	4.301346	2.986208	2.896370	10.183924
Indo-Pacific	(27.85,27.95]	salinity aou oxygen silicate phosphate	4.301346	2.986208	2.896370	10.183924
Indo-Pacific	(27.85,27.95]	salinity temperature aou silicate phosphate_star	4.338346	2.978896	2.868411	10.185653
Indo-Pacific	(27.85,27.95]	salinity temperature oxygen silicate phosphate_star	4.339785	2.978343	2.869502	10.187630
Indo-Pacific	(27.85,27.95]	salinity temperature silicate phosphate phosphate_star	4.339785	2.978343	2.869502	10.187630
Indo-Pacific	(27.95,28.05]	salinity aou silicate phosphate phosphate_star	4.382078	2.841260	3.075517	10.298855
Indo-Pacific	(27.95,28.05]	salinity aou oxygen silicate phosphate	4.382078	2.841260	3.075517	10.298855
Indo-Pacific	(27.95,28.05]	salinity aou oxygen silicate phosphate_star	4.382078	2.841260	3.075517	10.298855
Indo-Pacific	(27.95,28.05]	salinity temperature aou silicate phosphate	4.400737	2.864704	3.064828	10.330269
Indo-Pacific	(27.95,28.05]	salinity temperature aou phosphate phosphate_star	4.382908	2.860058	3.107381	10.350347
Indo-Pacific	(27.95,28.05]	salinity temperature aou oxygen phosphate	4.382908	2.860058	3.107381	10.350347
Indo-Pacific	(27.95,28.05]	salinity temperature aou oxygen phosphate_star	4.382908	2.860058	3.107381	10.350347
Indo-Pacific	(27.95,28.05]	salinity aou phosphate phosphate_star	4.383109	2.869426	3.107563	10.360098
Indo-Pacific	(27.95,28.05]	salinity aou oxygen phosphate	4.383109	2.869426	3.107563	10.360098
Indo-Pacific	(27.95,28.05]	salinity aou oxygen phosphate phosphate_star	4.383109	2.869426	3.107563	10.360098
Indo-Pacific	(28.05,28.1]	salinity aou oxygen silicate phosphate_star	4.232302	2.825488	2.826261	9.884051
Indo-Pacific	(28.05,28.1]	salinity aou oxygen silicate phosphate	4.232302	2.825488	2.826261	9.884051
Indo-Pacific	(28.05,28.1]	salinity aou silicate phosphate phosphate_star	4.232302	2.825488	2.826261	9.884051
Indo-Pacific	(28.05,28.1]	salinity temperature aou oxygen phosphate_star	4.231424	2.842596	2.817179	9.891199
Indo-Pacific	(28.05,28.1]	salinity temperature aou oxygen phosphate	4.231424	2.842596	2.817179	9.891199
Indo-Pacific	(28.05,28.1]	salinity temperature aou phosphate phosphate_star	4.231424	2.842596	2.817179	9.891199
Indo-Pacific	(28.05,28.1]	salinity aou oxygen phosphate_star	4.234927	2.846401	2.828633	9.909961
Indo-Pacific	(28.05,28.1]	salinity aou oxygen phosphate	4.234927	2.846401	2.828633	9.909961
Indo-Pacific	(28.05,28.1]	salinity aou oxygen phosphate phosphate_star	4.234927	2.846401	2.828633	9.909961
Indo-Pacific	(28.05,28.1]	salinity aou phosphate phosphate_star	4.234927	2.846401	2.828633	9.909961
Indo-Pacific	(28.1, Inf]	salinity aou oxygen silicate phosphate_star	3.568320	3.024739	2.582084	9.175143
Indo-Pacific	(28.1, Inf]	salinity aou oxygen silicate phosphate	3.568320	3.024739	2.582084	9.175143
Indo-Pacific	(28.1, Inf]	salinity aou silicate phosphate phosphate_star	3.568320	3.024739	2.582084	9.175143
Indo-Pacific	(28.1, Inf]	temperature aou oxygen silicate phosphate_star	3.598837	2.980806	2.648408	9.228051
Indo-Pacific	(28.1, Inf]	temperature aou oxygen silicate phosphate	3.598837	2.980806	2.648408	9.228051
Indo-Pacific	(28.1, Inf]	temperature aou silicate phosphate phosphate_star	3.598837	2.980806	2.648408	9.228051
Indo-Pacific	(28.1, Inf]	salinity temperature aou oxygen phosphate_star	3.538004	3.218866	2.586405	9.343275
Indo-Pacific	(28.1, Inf]	salinity temperature aou oxygen phosphate	3.538004	3.218866	2.586405	9.343275
Indo-Pacific	(28.1, Inf]	salinity temperature aou phosphate phosphate_star	3.538004	3.218866	2.586405	9.343275
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate_star	3.638706	3.024739	2.696173	9.359619

# 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 Old script chunks

MLRs <- GLODAP %>%
  nest(data = -c(basin, era, gamma_slab)) %>% 
  mutate(
    fit = map(data, ~ lm(Cstar ~ salinity  + temperature  + aou  + oxygen  + silicate  + phosphate  + phosphate_star,
                         data = .x)),
    tidied = map(fit, tidy),
    glanced = map(fit, glance),
    augmented = map(fit, augment)
  )

MLRs_tidied <- MLRs %>% 
  unnest(tidied)

MLRs_tidied

MLRs_tidied <- MLRs_tidied %>% 
  select(era, basin, gamma_slab, term, estimate, p.value)

MLRs_tidied_wide <- MLRs_tidied %>% 
  select(-p.value) %>% 
  pivot_wider(names_from = era, values_from = estimate, names_prefix = "coeff_")

MLRs_tidied_wide <- MLRs_tidied_wide %>% 
  mutate(delta_coeff_J_G = coeff_GO_SHIP - coeff_JGOFS_WOCE,
         delta_coeff_G_n = coeff_new_era - coeff_GO_SHIP,
         delta_coeff_n_G = coeff_new_era - coeff_JGOFS_WOCE)

MLRs_tidied %>% 
  ggplot(aes(p.value, term, col = gamma_slab)) +
  geom_point() +
  facet_grid(basin~era)

MLRs_tidied %>% 
  filter(p.value < 0.05) %>% 
  ggplot(aes(p.value, term, col = gamma_slab)) +
  geom_point() +
  facet_grid(basin~era)

MLRs_tidied %>% 
  ggplot(aes(p.value, term)) +
  geom_boxplot() +
  facet_grid(basin~era)

MLRs %>% 
  unnest(glanced)

MLRs %>% 
  unnest(augmented)

8 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)

9 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    highr_0.8          dbplyr_1.4.4       maps_3.3.0        
[33] rlang_0.4.7        readxl_1.3.1       rstudioapi_0.11    generics_0.0.2    
[37] farver_2.0.3       jsonlite_1.7.0     zip_2.0.4          car_3.0-8         
[41] magrittr_1.5       Rcpp_1.0.5         munsell_0.5.0      fansi_0.4.1       
[45] abind_1.4-5        lifecycle_0.2.0    stringi_1.4.6      whisker_0.4       
[49] yaml_2.2.1         carData_3.0-4      plyr_1.8.6         grid_4.0.2        
[53] blob_1.2.1         promises_1.1.1     crayon_1.3.4       haven_2.3.1       
[57] hms_0.5.3          pillar_1.4.6       reprex_0.3.0       glue_1.4.1        
[61] evaluate_0.14      data.table_1.13.0  modelr_0.1.8       vctrs_0.3.2       
[65] httpuv_1.5.4       cellranger_1.1.0   gtable_0.3.0       reshape_0.8.8     
[69] assertthat_0.2.1   xfun_0.16          openxlsx_4.1.5     later_1.1.0.1     
[73] viridisLite_0.3.0  ellipsis_0.3.1     here_0.1

Data base

Jens Daniel Müller

04 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 Old script chunks

8 Open tasks

9 Open questions

Data base

Jens Daniel Müller

04 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 Old script chunks

8 Open tasks

9 Open questions

3 PO₄* calculation

4.1.2 GLODAP + atm. pCO₂