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Rmd	e6a2ade	jens-daniel-mueller	2020-07-13	added Cstar calculation

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

1 Required data

Required are:

clean version of GLODAPGLODAPv2.2020
observations grid of clean version of GLODAPGLODAPv2.2020
C_ant 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)

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 scaling factor for the reference year adjustment is an apriori estiamte of Cant at a given location and depth. 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_Cant_full %>% write_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
#                                           "GLODAP_Cant_full.csv"))
# 
# GLODAP_Cant_full <- read_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
#                                           "GLODAP_Cant_full.csv"))

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 <- 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(10000) %>% 
  ggplot(aes(year, Cstar_tref_delta, col = Cant)) +
  geom_point() +
  scale_color_viridis_c() +
  labs(title = "random subsample 1e4")

5 Selected section plots

Selected sections are 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)

bbox <- c(
  "xmin" = min(GLODAP_cruise$lat),
  "ymin" = min(GLODAP_cruise$depth),
  "xmax" = max(GLODAP_cruise$lat),
  "ymax" = max(GLODAP_cruise$depth)
)

grd_template <- expand.grid(
  lat = seq(from = bbox["xmin"], to = bbox["xmax"], by = 1),
  depth = seq(from = bbox["ymin"], to = bbox["ymax"], by = 50) # 20 m resolution
)

crs_raster_format <- " +proj=utm  +zone=33  +ellps=GRS80  +towgs84=0,0,0,0,0,0,0  +units=m  +no_defs"

grd_template_raster <- grd_template %>% 
  dplyr::mutate(Z = 0) %>% 
  raster::rasterFromXYZ( 
    crs = crs_raster_format)


# Generalized Additive Model
fit_GAM <- mgcv::gam( # using {mgcv}
  gamma ~ s(lat, depth),      # here come our X/Y/Z data - straightforward enough
  data = GLODAP_cruise      # specify in which object the data is stored
)

# Generalized Additive Model
interp_GAM <- grd_template %>% 
  mutate(Z = predict(fit_GAM, .)) %>% 
  raster::rasterFromXYZ(crs = crs_raster_format)

df <- raster::rasterToPoints(interp_GAM) %>% as_tibble()
colnames(df) <- c("X", "Y", "Z")
  
ggplot(df, aes(x = X, y = Y, fill = Z, z = Z))  +
  geom_raster()  +
  geom_contour(col="white")  +
  ggtitle(label = "interp GAM")  +
  scale_fill_viridis_c()  +
  scale_y_reverse() +
  coord_cartesian(expand = 0)

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,

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)

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()

6.2 Predictor correlation

6.2.1 Overview

GLODAP %>% 
  sample_frac(0.01) %>% 
  ggpairs(columns = c("Cstar",
                      "salinity",
                      "temperature",
                      "aou",
                      "oxygen",
                      "silicate",
                      "phosphate",
                      "phosphate_star"),
          ggplot2::aes(col = gamma_slab, fill = gamma_slab, alpha = 0.01)) +
      scale_fill_viridis_d() +
      scale_color_viridis_d() +
      labs(title = paste("Basin: all | era: all | subsample size: 1 % of", nrow(GLODAP)))

6.2.2 Grouped for basin, era, slab

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

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()
  
    }
  }
}

6.2.3 Correlation assesment

6.2.3.1 Calculation of correlation coeffcients

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)

6.2.3.2 Predictor pairs

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)

6.2.3.3 C* vs individual predictors

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

# gamma_slab_max <- GLODAP %>%
#   filter(basin == "Atlantic", era == "new_era") %>% 
#   group_by(gamma_slab) %>% 
#   count() %>% 
#   ungroup() %>% 
#   filter(n == max(n)) %>% 
#   pull(1)


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"))

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


# all_lm_stats <- all_lm_stats %>% 
#   rename(sigma = rmse)

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")

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

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

# all_lm_stats %>% 
#   ggplot(aes(rmse, predictors, col = gamma_slab)) +
#   geom_point(shape = 21) +
#   facet_grid(.~basin)

n_predictors_max <- 5
n_predictors_min <- 2

all_lm_stats <- all_lm_stats %>% 
  filter(n >= n_predictors_min,
         n <= n_predictors_max) %>% 
  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(rmse_sum, n = 10) %>% 
  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	7.233104	6.424028	2.765130	16.422262
Atlantic	(-Inf,26]	temperature aou oxygen phosphate phosphate_star	7.238731	6.515207	2.671672	16.425610
Atlantic	(-Inf,26]	temperature oxygen silicate phosphate phosphate_star	7.342865	6.367196	2.734672	16.444733
Atlantic	(-Inf,26]	salinity aou oxygen silicate phosphate	7.363174	6.256378	2.875347	16.494899
Atlantic	(-Inf,26]	salinity temperature oxygen silicate phosphate	7.246124	6.404483	2.852778	16.503385
Atlantic	(-Inf,26]	salinity temperature aou silicate phosphate	7.276259	6.370141	2.857798	16.504198
Atlantic	(-Inf,26]	temperature aou silicate phosphate phosphate_star	7.399728	6.385907	2.744721	16.530356
Atlantic	(-Inf,26]	temperature aou oxygen silicate phosphate	7.055656	6.789733	2.766765	16.612154
Atlantic	(-Inf,26]	salinity temperature oxygen phosphate phosphate_star	7.594469	6.323889	2.711688	16.630046
Atlantic	(-Inf,26]	salinity temperature aou phosphate phosphate_star	7.637863	6.281897	2.717708	16.637469
Atlantic	(26,26.5]	temperature aou oxygen silicate phosphate	5.363576	6.786906	3.120245	15.270727
Atlantic	(26,26.5]	temperature aou oxygen phosphate phosphate_star	5.437464	6.819617	3.180828	15.437908
Atlantic	(26,26.5]	salinity temperature aou oxygen phosphate	5.453636	6.837398	3.164633	15.455668
Atlantic	(26,26.5]	aou oxygen silicate phosphate phosphate_star	5.394684	6.892097	3.178032	15.464813
Atlantic	(26,26.5]	temperature aou oxygen phosphate	5.456491	6.837548	3.181060	15.475099
Atlantic	(26,26.5]	temperature aou silicate phosphate phosphate_star	5.430921	6.955271	3.193715	15.579907
Atlantic	(26,26.5]	salinity aou oxygen phosphate phosphate_star	5.443918	6.941283	3.196238	15.581438
Atlantic	(26,26.5]	salinity aou oxygen silicate phosphate	5.432267	6.973621	3.182424	15.588312
Atlantic	(26,26.5]	aou oxygen phosphate phosphate_star	5.467333	6.943299	3.206234	15.616865
Atlantic	(26,26.5]	aou oxygen silicate phosphate	5.439014	7.001567	3.184956	15.625537
Atlantic	(26.5,26.75]	temperature aou oxygen silicate phosphate	5.219837	5.589322	3.704869	14.514028
Atlantic	(26.5,26.75]	salinity temperature aou silicate phosphate	5.156094	5.583682	3.805535	14.545311
Atlantic	(26.5,26.75]	salinity temperature oxygen silicate phosphate	5.145692	5.566412	3.838208	14.550311
Atlantic	(26.5,26.75]	temperature oxygen silicate phosphate phosphate_star	5.211439	5.585131	3.758446	14.555017
Atlantic	(26.5,26.75]	temperature aou silicate phosphate phosphate_star	5.228077	5.603867	3.730283	14.562227
Atlantic	(26.5,26.75]	aou oxygen silicate phosphate phosphate_star	5.263529	5.643834	3.699733	14.607095
Atlantic	(26.5,26.75]	salinity aou oxygen silicate phosphate	5.201822	5.640533	3.769774	14.612130
Atlantic	(26.5,26.75]	salinity temperature aou oxygen phosphate	5.359083	5.561143	3.703778	14.624004
Atlantic	(26.5,26.75]	temperature aou oxygen phosphate phosphate_star	5.397508	5.580509	3.646853	14.624871
Atlantic	(26.5,26.75]	salinity temperature oxygen phosphate phosphate_star	5.369848	5.574805	3.734403	14.679057
Atlantic	(26.75,27]	salinity temperature oxygen silicate phosphate	4.683879	5.085526	3.618918	13.388323
Atlantic	(26.75,27]	salinity temperature aou silicate phosphate	4.703334	5.094493	3.629813	13.427639
Atlantic	(26.75,27]	salinity temperature oxygen phosphate phosphate_star	4.729705	5.146821	3.618566	13.495093
Atlantic	(26.75,27]	temperature oxygen silicate phosphate phosphate_star	4.734490	5.134443	3.633381	13.502314
Atlantic	(26.75,27]	salinity temperature aou phosphate phosphate_star	4.749608	5.152628	3.629477	13.531713
Atlantic	(26.75,27]	salinity temperature aou oxygen phosphate	4.742004	5.170997	3.622653	13.535654
Atlantic	(26.75,27]	salinity temperature oxygen phosphate	4.742309	5.171062	3.623176	13.536547
Atlantic	(26.75,27]	temperature aou silicate phosphate phosphate_star	4.761655	5.140782	3.647651	13.550089
Atlantic	(26.75,27]	temperature aou oxygen phosphate phosphate_star	4.757625	5.161932	3.641829	13.561385
Atlantic	(26.75,27]	salinity temperature aou phosphate	4.758055	5.173299	3.634027	13.565381
Atlantic	(27,27.25]	temperature oxygen silicate phosphate phosphate_star	5.150199	4.920376	4.425074	14.495649
Atlantic	(27,27.25]	temperature aou oxygen phosphate phosphate_star	5.155952	4.955575	4.485850	14.597377
Atlantic	(27,27.25]	temperature aou silicate phosphate phosphate_star	5.201088	4.956303	4.448113	14.605505
Atlantic	(27,27.25]	salinity temperature oxygen phosphate phosphate_star	5.205096	4.944247	4.501528	14.650871
Atlantic	(27,27.25]	temperature oxygen phosphate phosphate_star	5.243274	4.975377	4.507371	14.726023
Atlantic	(27,27.25]	salinity temperature oxygen silicate phosphate	5.025839	5.042443	4.665827	14.734108
Atlantic	(27,27.25]	salinity temperature aou phosphate phosphate_star	5.259815	4.977166	4.519119	14.756100
Atlantic	(27,27.25]	salinity temperature aou silicate phosphate	5.086705	5.064103	4.676695	14.827503
Atlantic	(27,27.25]	temperature aou phosphate phosphate_star	5.294046	5.010556	4.526341	14.830943
Atlantic	(27,27.25]	aou oxygen silicate phosphate phosphate_star	5.340125	5.046883	4.477069	14.864077
Atlantic	(27.25,27.5]	salinity temperature oxygen phosphate phosphate_star	4.784084	4.325538	3.661619	12.771241
Atlantic	(27.25,27.5]	salinity temperature aou phosphate phosphate_star	4.831010	4.335440	3.672001	12.838450
Atlantic	(27.25,27.5]	temperature aou oxygen phosphate phosphate_star	4.778594	4.486817	3.662943	12.928355
Atlantic	(27.25,27.5]	temperature oxygen silicate phosphate phosphate_star	4.815587	4.464644	3.651525	12.931757
Atlantic	(27.25,27.5]	salinity aou oxygen phosphate phosphate_star	4.909921	4.380487	3.693874	12.984282
Atlantic	(27.25,27.5]	temperature aou silicate phosphate phosphate_star	4.864184	4.466131	3.654361	12.984677
Atlantic	(27.25,27.5]	temperature oxygen phosphate phosphate_star	4.836475	4.492731	3.663888	12.993095
Atlantic	(27.25,27.5]	salinity temperature aou oxygen phosphate	4.690176	4.375626	3.957693	13.023495
Atlantic	(27.25,27.5]	temperature aou phosphate phosphate_star	4.877589	4.486869	3.672726	13.037184
Atlantic	(27.25,27.5]	salinity temperature oxygen silicate phosphate	4.785817	4.370284	3.888408	13.044510
Atlantic	(27.5,27.75]	temperature aou silicate phosphate phosphate_star	4.178798	4.405750	4.230958	12.815506
Atlantic	(27.5,27.75]	temperature oxygen silicate phosphate phosphate_star	4.171250	4.419163	4.233864	12.824277
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate phosphate_star	4.197885	4.399525	4.230411	12.827821
Atlantic	(27.5,27.75]	salinity temperature oxygen silicate phosphate	4.179766	4.394406	4.324356	12.898528
Atlantic	(27.5,27.75]	salinity temperature aou silicate phosphate	4.191718	4.383035	4.326416	12.901169
Atlantic	(27.5,27.75]	salinity aou oxygen silicate phosphate	4.210252	4.376137	4.327749	12.914138
Atlantic	(27.5,27.75]	temperature aou oxygen silicate phosphate	4.183773	4.409376	4.344048	12.937196
Atlantic	(27.5,27.75]	temperature aou silicate phosphate	4.197530	4.418293	4.345437	12.961259
Atlantic	(27.5,27.75]	temperature oxygen silicate phosphate	4.186794	4.431777	4.344048	12.962619
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate	4.219326	4.412680	4.348932	12.980938
Atlantic	(27.75,27.85]	salinity aou oxygen silicate phosphate	4.155188	4.343314	6.006423	14.504925
Atlantic	(27.75,27.85]	salinity temperature oxygen silicate phosphate	4.152518	4.345415	6.018195	14.516128
Atlantic	(27.75,27.85]	salinity oxygen silicate phosphate phosphate_star	4.148845	4.341301	6.027563	14.517708
Atlantic	(27.75,27.85]	salinity temperature aou silicate phosphate	4.156656	4.348980	6.020016	14.525652
Atlantic	(27.75,27.85]	salinity aou silicate phosphate phosphate_star	4.141199	4.359680	6.036728	14.537608
Atlantic	(27.75,27.85]	salinity oxygen silicate phosphate	4.165017	4.346978	6.027909	14.539904
Atlantic	(27.75,27.85]	temperature aou oxygen silicate phosphate	4.221683	4.350846	5.972594	14.545123
Atlantic	(27.75,27.85]	salinity aou silicate phosphate	4.158893	4.364303	6.036854	14.560050
Atlantic	(27.75,27.85]	temperature oxygen silicate phosphate phosphate_star	4.213737	4.380967	6.023641	14.618345
Atlantic	(27.75,27.85]	temperature aou silicate phosphate phosphate_star	4.216149	4.387433	6.025514	14.629095
Atlantic	(27.85,27.95]	salinity aou oxygen silicate phosphate	3.727889	4.172888	4.843709	12.744486
Atlantic	(27.85,27.95]	salinity temperature oxygen silicate phosphate	3.739892	4.187911	4.879615	12.807418
Atlantic	(27.85,27.95]	salinity temperature aou silicate phosphate	3.750570	4.193737	4.879217	12.823524
Atlantic	(27.85,27.95]	salinity temperature silicate phosphate phosphate_star	3.882773	4.290264	4.849271	13.022309
Atlantic	(27.85,27.95]	salinity temperature silicate phosphate	3.980800	4.290271	4.879951	13.151023
Atlantic	(27.85,27.95]	salinity oxygen silicate phosphate phosphate_star	3.771723	4.412669	5.319665	13.504056
Atlantic	(27.85,27.95]	salinity oxygen silicate phosphate	3.788228	4.442442	5.332826	13.563495
Atlantic	(27.85,27.95]	salinity aou silicate phosphate phosphate_star	3.896036	4.600259	5.378794	13.875090
Atlantic	(27.85,27.95]	salinity aou silicate phosphate	3.924500	4.616418	5.383425	13.924343
Atlantic	(27.85,27.95]	temperature aou oxygen silicate phosphate	4.214755	4.849638	5.263138	14.327531
Atlantic	(27.95,28.05]	salinity aou oxygen silicate phosphate	3.487770	4.416875	4.820087	12.724732
Atlantic	(27.95,28.05]	salinity temperature oxygen silicate phosphate	3.498901	4.435697	4.910557	12.845155
Atlantic	(27.95,28.05]	salinity oxygen silicate phosphate phosphate_star	3.570396	4.433626	4.875191	12.879213
Atlantic	(27.95,28.05]	salinity temperature aou silicate phosphate	3.508118	4.459459	4.931814	12.899391
Atlantic	(27.95,28.05]	salinity temperature aou oxygen phosphate	3.755336	4.422690	4.799080	12.977106
Atlantic	(27.95,28.05]	salinity oxygen silicate phosphate	3.570686	4.452825	5.020607	13.044118
Atlantic	(27.95,28.05]	salinity temperature silicate phosphate phosphate_star	3.755808	4.829486	4.861915	13.447209
Atlantic	(27.95,28.05]	salinity aou silicate phosphate phosphate_star	3.750648	4.607306	5.100329	13.458284
Atlantic	(27.95,28.05]	salinity aou silicate phosphate	3.757788	4.616897	5.190912	13.565597
Atlantic	(27.95,28.05]	salinity temperature silicate phosphate	3.758011	4.835232	4.988962	13.582204
Atlantic	(28.05,28.1]	salinity temperature aou oxygen phosphate	3.539499	4.427871	4.144983	12.112354
Atlantic	(28.05,28.1]	temperature aou oxygen silicate phosphate	3.643192	4.386906	4.117142	12.147240
Atlantic	(28.05,28.1]	temperature aou oxygen phosphate phosphate_star	3.737328	4.517341	4.186888	12.441557
Atlantic	(28.05,28.1]	temperature aou oxygen phosphate	3.737933	4.520827	4.228193	12.486953
Atlantic	(28.05,28.1]	salinity temperature oxygen silicate phosphate	3.531111	4.629803	4.415293	12.576206
Atlantic	(28.05,28.1]	salinity temperature oxygen phosphate phosphate_star	3.554312	4.684188	4.356252	12.594752
Atlantic	(28.05,28.1]	salinity oxygen silicate phosphate phosphate_star	3.548422	4.631248	4.447473	12.627143
Atlantic	(28.05,28.1]	salinity temperature oxygen phosphate	3.557078	4.688580	4.416199	12.661857
Atlantic	(28.05,28.1]	salinity aou oxygen silicate phosphate	3.554108	4.635135	4.529410	12.718653
Atlantic	(28.05,28.1]	salinity oxygen silicate phosphate	3.555467	4.648734	4.534233	12.738434
Atlantic	(28.1,28.15]	salinity temperature oxygen silicate phosphate	3.349308	4.010613	4.254217	11.614139
Atlantic	(28.1,28.15]	salinity temperature aou oxygen phosphate	3.440411	4.008819	4.211635	11.660865
Atlantic	(28.1,28.15]	temperature aou oxygen silicate phosphate	3.436793	4.025910	4.216057	11.678759
Atlantic	(28.1,28.15]	temperature oxygen silicate phosphate phosphate_star	3.430280	4.041063	4.243363	11.714706
Atlantic	(28.1,28.15]	salinity temperature oxygen phosphate phosphate_star	3.448754	4.022449	4.243864	11.715066
Atlantic	(28.1,28.15]	salinity temperature oxygen phosphate	3.449525	4.022451	4.254795	11.726772
Atlantic	(28.1,28.15]	temperature oxygen silicate phosphate	3.437071	4.041093	4.255279	11.733443
Atlantic	(28.1,28.15]	salinity temperature aou silicate phosphate	3.390856	4.077688	4.319062	11.787606
Atlantic	(28.1,28.15]	temperature aou oxygen phosphate phosphate_star	3.542289	4.045605	4.211446	11.799340
Atlantic	(28.1,28.15]	temperature aou oxygen phosphate	3.542305	4.046629	4.220084	11.809018
Atlantic	(28.15,28.2]	salinity temperature aou oxygen phosphate	3.719163	3.681081	2.836143	10.236388
Atlantic	(28.15,28.2]	salinity temperature aou silicate phosphate	3.739761	3.698785	2.835064	10.273611
Atlantic	(28.15,28.2]	salinity temperature aou phosphate phosphate_star	3.727244	3.710071	2.837066	10.274381
Atlantic	(28.15,28.2]	salinity temperature aou phosphate	3.740143	3.711047	2.837785	10.288975
Atlantic	(28.15,28.2]	salinity aou oxygen silicate phosphate	3.713912	3.687702	2.914045	10.315659
Atlantic	(28.15,28.2]	salinity temperature oxygen silicate phosphate	3.775192	3.734735	2.836415	10.346342
Atlantic	(28.15,28.2]	salinity aou oxygen phosphate phosphate_star	3.705570	3.688287	2.955392	10.349249
Atlantic	(28.15,28.2]	salinity aou oxygen phosphate	3.719217	3.688379	2.956477	10.364073
Atlantic	(28.15,28.2]	salinity temperature oxygen phosphate phosphate_star	3.777038	3.755312	2.835243	10.367592
Atlantic	(28.15,28.2]	salinity temperature oxygen phosphate	3.784450	3.757169	2.836701	10.378319
Atlantic	(28.2, Inf]	salinity temperature aou oxygen phosphate	3.337999	3.143686	2.685083	9.166769
Atlantic	(28.2, Inf]	salinity aou oxygen silicate phosphate	3.358320	3.145049	2.767527	9.270896
Atlantic	(28.2, Inf]	salinity temperature aou silicate phosphate	3.425561	3.148993	2.696506	9.271059
Atlantic	(28.2, Inf]	salinity aou oxygen phosphate phosphate_star	3.376522	3.141055	2.763926	9.281502
Atlantic	(28.2, Inf]	salinity aou oxygen phosphate	3.378104	3.145072	2.767543	9.290719
Atlantic	(28.2, Inf]	salinity temperature aou phosphate phosphate_star	3.471029	3.143746	2.692778	9.307553
Atlantic	(28.2, Inf]	salinity temperature aou phosphate	3.472721	3.149181	2.700720	9.322622
Atlantic	(28.2, Inf]	salinity temperature oxygen silicate phosphate	3.502342	3.144268	2.676045	9.322655
Atlantic	(28.2, Inf]	temperature aou oxygen silicate phosphate	3.361576	3.278500	2.736479	9.376555
Atlantic	(28.2, Inf]	temperature aou oxygen phosphate phosphate_star	3.384056	3.283704	2.751414	9.419175
Indo-Pacific	(-Inf,26]	salinity aou oxygen phosphate phosphate_star	11.652593	6.872465	4.747255	23.272313
Indo-Pacific	(-Inf,26]	salinity temperature aou phosphate phosphate_star	11.725349	6.849543	4.968075	23.542968
Indo-Pacific	(-Inf,26]	salinity temperature oxygen phosphate phosphate_star	11.771329	6.883678	5.114532	23.769539
Indo-Pacific	(-Inf,26]	salinity aou oxygen silicate phosphate	11.591824	7.146475	5.644898	24.383197
Indo-Pacific	(-Inf,26]	salinity temperature aou silicate phosphate	11.662658	7.221472	5.848813	24.732943
Indo-Pacific	(-Inf,26]	salinity temperature aou oxygen phosphate_star	12.532453	7.048097	5.305447	24.885997
Indo-Pacific	(-Inf,26]	salinity temperature oxygen silicate phosphate	11.701156	7.270085	5.949523	24.920764
Indo-Pacific	(-Inf,26]	salinity temperature oxygen silicate phosphate_star	12.564249	7.054970	5.319566	24.938785
Indo-Pacific	(-Inf,26]	salinity temperature aou silicate phosphate_star	12.593023	7.092992	5.270621	24.956636
Indo-Pacific	(-Inf,26]	salinity temperature oxygen phosphate_star	12.574223	7.054989	5.382004	25.011216
Indo-Pacific	(26,26.5]	salinity temperature aou phosphate phosphate_star	7.884709	5.129658	3.991869	17.006237
Indo-Pacific	(26,26.5]	salinity aou oxygen phosphate phosphate_star	7.825697	5.232341	3.950876	17.008915
Indo-Pacific	(26,26.5]	salinity aou oxygen silicate phosphate	7.863872	5.215921	3.936596	17.016389
Indo-Pacific	(26,26.5]	salinity temperature oxygen phosphate phosphate_star	7.925778	5.121998	4.024452	17.072228
Indo-Pacific	(26,26.5]	salinity temperature aou silicate phosphate	7.935808	5.171091	4.013896	17.120795
Indo-Pacific	(26,26.5]	salinity temperature oxygen silicate phosphate	7.972957	5.179160	4.053536	17.205653
Indo-Pacific	(26,26.5]	salinity temperature aou oxygen phosphate	7.969753	5.311089	4.249030	17.529872
Indo-Pacific	(26,26.5]	salinity temperature aou phosphate	8.020770	5.323834	4.291014	17.635619
Indo-Pacific	(26,26.5]	salinity aou oxygen phosphate	7.970078	5.414262	4.254610	17.638950
Indo-Pacific	(26,26.5]	salinity temperature oxygen phosphate	8.051221	5.312575	4.311661	17.675457
Indo-Pacific	(26.5,26.75]	salinity aou oxygen phosphate phosphate_star	5.643270	5.441635	4.201758	15.286663
Indo-Pacific	(26.5,26.75]	salinity temperature aou phosphate phosphate_star	5.744701	5.481610	4.285316	15.511626
Indo-Pacific	(26.5,26.75]	salinity temperature oxygen phosphate phosphate_star	5.810017	5.522181	4.347636	15.679835
Indo-Pacific	(26.5,26.75]	salinity aou oxygen silicate phosphate	5.905584	5.702333	4.562541	16.170458
Indo-Pacific	(26.5,26.75]	salinity temperature aou oxygen phosphate	5.986932	5.709024	4.619676	16.315632
Indo-Pacific	(26.5,26.75]	salinity aou oxygen phosphate	5.988940	5.709065	4.635932	16.333936
Indo-Pacific	(26.5,26.75]	salinity temperature aou silicate phosphate	6.048583	5.719303	4.660956	16.428842
Indo-Pacific	(26.5,26.75]	aou oxygen silicate phosphate phosphate_star	6.137998	5.852677	4.450257	16.440932
Indo-Pacific	(26.5,26.75]	salinity temperature aou phosphate	6.075088	5.745923	4.716630	16.537642
Indo-Pacific	(26.5,26.75]	temperature aou oxygen phosphate phosphate_star	6.114876	5.850423	4.573040	16.538338
Indo-Pacific	(26.75,27]	temperature aou oxygen phosphate phosphate_star	6.512153	4.907927	4.030310	15.450390
Indo-Pacific	(26.75,27]	salinity aou oxygen phosphate phosphate_star	6.562262	4.957194	4.045916	15.565373
Indo-Pacific	(26.75,27]	aou oxygen silicate phosphate phosphate_star	6.519772	4.958933	4.154753	15.633458
Indo-Pacific	(26.75,27]	temperature aou oxygen silicate phosphate	6.525639	4.983289	4.221813	15.730741
Indo-Pacific	(26.75,27]	aou oxygen phosphate phosphate_star	6.598292	5.006942	4.154785	15.760018
Indo-Pacific	(26.75,27]	salinity temperature aou oxygen phosphate	6.549695	5.020274	4.249159	15.819127
Indo-Pacific	(26.75,27]	temperature aou oxygen phosphate	6.552943	5.020844	4.262915	15.836701
Indo-Pacific	(26.75,27]	temperature aou silicate phosphate phosphate_star	6.552474	5.026245	4.289949	15.868669
Indo-Pacific	(26.75,27]	temperature oxygen silicate phosphate phosphate_star	6.589732	5.091516	4.384008	16.065256
Indo-Pacific	(26.75,27]	salinity temperature aou phosphate phosphate_star	6.677586	5.136264	4.252461	16.066312
Indo-Pacific	(27,27.25]	temperature aou oxygen silicate phosphate	6.057890	4.532863	4.048207	14.638960
Indo-Pacific	(27,27.25]	salinity temperature aou oxygen phosphate	6.083955	4.607439	4.166144	14.857539
Indo-Pacific	(27,27.25]	temperature aou oxygen phosphate phosphate_star	6.113241	4.648067	4.163487	14.924795
Indo-Pacific	(27,27.25]	salinity aou oxygen silicate phosphate	6.431710	4.541014	4.107446	15.080171
Indo-Pacific	(27,27.25]	temperature aou oxygen phosphate	6.115680	4.747192	4.304603	15.167475
Indo-Pacific	(27,27.25]	salinity aou silicate phosphate phosphate_star	6.509533	4.544592	4.121767	15.175892
Indo-Pacific	(27,27.25]	salinity temperature aou silicate phosphate	6.562627	4.548385	4.119478	15.230490
Indo-Pacific	(27,27.25]	salinity aou silicate phosphate	6.576878	4.548729	4.126122	15.251729
Indo-Pacific	(27,27.25]	salinity aou oxygen phosphate phosphate_star	6.431281	4.709064	4.174627	15.314973
Indo-Pacific	(27,27.25]	salinity temperature oxygen silicate phosphate	6.676758	4.583771	4.146776	15.407305
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]	salinity aou oxygen silicate phosphate	5.251519	3.924282	3.243081	12.418882
Indo-Pacific	(27.25,27.5]	temperature aou oxygen phosphate phosphate_star	4.863065	4.084331	3.647515	12.594911
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 silicate phosphate	5.578168	3.945800	3.247152	12.771119
Indo-Pacific	(27.25,27.5]	temperature aou oxygen phosphate	4.866519	4.177465	3.729263	12.773247
Indo-Pacific	(27.25,27.5]	salinity aou oxygen phosphate phosphate_star	5.202101	4.189161	3.564507	12.955770
Indo-Pacific	(27.25,27.5]	salinity temperature oxygen silicate phosphate	5.801738	3.975890	3.253916	13.031545
Indo-Pacific	(27.25,27.5]	aou oxygen silicate phosphate phosphate_star	5.231115	4.179514	3.679102	13.089731
Indo-Pacific	(27.25,27.5]	salinity aou silicate phosphate phosphate_star	5.925597	3.952449	3.239888	13.117934
Indo-Pacific	(27.5,27.75]	salinity aou oxygen silicate phosphate	4.688828	3.618102	2.968149	11.275080
Indo-Pacific	(27.5,27.75]	salinity temperature aou silicate phosphate	4.857991	3.616196	2.966581	11.440767
Indo-Pacific	(27.5,27.75]	temperature aou oxygen silicate phosphate	4.414022	3.841294	3.290961	11.546277
Indo-Pacific	(27.5,27.75]	salinity temperature oxygen silicate phosphate	4.986342	3.619099	2.965966	11.571407
Indo-Pacific	(27.5,27.75]	salinity temperature aou oxygen phosphate	4.436909	3.849001	3.371011	11.656920
Indo-Pacific	(27.5,27.75]	temperature aou oxygen phosphate phosphate_star	4.435934	3.911470	3.405050	11.752454
Indo-Pacific	(27.5,27.75]	temperature aou oxygen phosphate	4.437170	3.916272	3.429891	11.783332
Indo-Pacific	(27.5,27.75]	salinity aou oxygen phosphate phosphate_star	4.689603	3.835711	3.334569	11.859882
Indo-Pacific	(27.5,27.75]	salinity aou oxygen phosphate	4.689770	3.851583	3.372534	11.913887
Indo-Pacific	(27.5,27.75]	aou oxygen silicate phosphate phosphate_star	4.694510	3.840147	3.409260	11.943917
Indo-Pacific	(27.75,27.85]	temperature aou oxygen silicate phosphate	4.269432	3.241574	2.903747	10.414753
Indo-Pacific	(27.75,27.85]	salinity temperature oxygen silicate phosphate	4.308811	3.258512	2.865015	10.432338
Indo-Pacific	(27.75,27.85]	salinity temperature aou silicate phosphate	4.285667	3.281811	2.876268	10.443746
Indo-Pacific	(27.75,27.85]	salinity aou oxygen silicate phosphate	4.262144	3.320317	2.896917	10.479378
Indo-Pacific	(27.75,27.85]	temperature aou silicate phosphate phosphate_star	4.300544	3.271219	2.918998	10.490761
Indo-Pacific	(27.75,27.85]	temperature oxygen silicate phosphate phosphate_star	4.326772	3.254352	2.911216	10.492339
Indo-Pacific	(27.75,27.85]	aou oxygen silicate phosphate phosphate_star	4.272132	3.304968	2.938537	10.515636
Indo-Pacific	(27.75,27.85]	temperature oxygen silicate phosphate	4.327841	3.271370	2.916579	10.515790
Indo-Pacific	(27.75,27.85]	temperature aou silicate phosphate	4.302407	3.293390	2.924736	10.520533
Indo-Pacific	(27.75,27.85]	temperature aou oxygen phosphate phosphate_star	4.261066	3.299139	3.000201	10.560406
Indo-Pacific	(27.85,27.95]	temperature aou silicate phosphate phosphate_star	4.303730	2.964754	2.889269	10.157754
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate phosphate_star	4.288887	2.967361	2.903249	10.159496
Indo-Pacific	(27.85,27.95]	salinity temperature aou silicate phosphate	4.321113	2.980023	2.878668	10.179804
Indo-Pacific	(27.85,27.95]	temperature oxygen silicate phosphate phosphate_star	4.322979	2.972074	2.886339	10.181392
Indo-Pacific	(27.85,27.95]	salinity aou oxygen silicate phosphate	4.308082	2.987020	2.896438	10.191540
Indo-Pacific	(27.85,27.95]	temperature aou oxygen silicate phosphate	4.314832	2.983036	2.896340	10.194207
Indo-Pacific	(27.85,27.95]	salinity temperature oxygen silicate phosphate	4.340586	2.984254	2.870691	10.195531
Indo-Pacific	(27.85,27.95]	temperature aou silicate phosphate	4.326316	2.983354	2.899097	10.208768
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate	4.314868	2.989308	2.913618	10.217794
Indo-Pacific	(27.85,27.95]	salinity aou oxygen phosphate phosphate_star	4.271402	2.998071	2.959829	10.229302
Indo-Pacific	(27.95,28.05]	salinity aou oxygen silicate phosphate	4.380825	2.852408	3.078449	10.311682
Indo-Pacific	(27.95,28.05]	salinity aou oxygen phosphate phosphate_star	4.381490	2.878636	3.076442	10.336569
Indo-Pacific	(27.95,28.05]	aou oxygen silicate phosphate phosphate_star	4.398487	2.860645	3.079305	10.338437
Indo-Pacific	(27.95,28.05]	salinity temperature aou silicate phosphate	4.399293	2.875842	3.067839	10.342974
Indo-Pacific	(27.95,28.05]	temperature aou oxygen phosphate phosphate_star	4.399165	2.871522	3.076308	10.346995
Indo-Pacific	(27.95,28.05]	aou oxygen phosphate phosphate_star	4.399784	2.878684	3.080077	10.358546
Indo-Pacific	(27.95,28.05]	salinity temperature aou oxygen phosphate	4.381680	2.872244	3.110001	10.363925
Indo-Pacific	(27.95,28.05]	salinity aou oxygen phosphate	4.381858	2.881876	3.110180	10.373914
Indo-Pacific	(27.95,28.05]	temperature aou silicate phosphate phosphate_star	4.422479	2.885926	3.068729	10.377135
Indo-Pacific	(27.95,28.05]	temperature aou oxygen silicate phosphate	4.402331	2.868436	3.112341	10.383108
Indo-Pacific	(28.05,28.1]	salinity aou oxygen phosphate phosphate_star	4.234297	2.857998	2.800839	9.893134
Indo-Pacific	(28.05,28.1]	salinity aou oxygen silicate phosphate	4.231465	2.843034	2.829063	9.903562
Indo-Pacific	(28.05,28.1]	salinity temperature aou oxygen phosphate	4.230598	2.861453	2.819898	9.911949
Indo-Pacific	(28.05,28.1]	salinity aou oxygen phosphate	4.234300	2.864288	2.831678	9.930266
Indo-Pacific	(28.05,28.1]	aou oxygen silicate phosphate phosphate_star	4.232564	2.871417	2.826666	9.930646
Indo-Pacific	(28.05,28.1]	temperature aou oxygen phosphate phosphate_star	4.232111	2.872811	2.844050	9.948973
Indo-Pacific	(28.05,28.1]	salinity temperature aou silicate phosphate	4.271623	2.848117	2.838349	9.958088
Indo-Pacific	(28.05,28.1]	aou oxygen phosphate phosphate_star	4.237606	2.873181	2.851534	9.962321
Indo-Pacific	(28.05,28.1]	temperature aou oxygen silicate phosphate	4.231850	2.881579	2.863461	9.976889
Indo-Pacific	(28.05,28.1]	aou oxygen silicate phosphate	4.233558	2.883351	2.872585	9.989494
Indo-Pacific	(28.1, Inf]	salinity aou oxygen silicate phosphate	3.567664	3.090883	2.618254	9.276801
Indo-Pacific	(28.1, Inf]	temperature aou oxygen silicate phosphate	3.599744	3.042637	2.653758	9.296139
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate phosphate_star	3.633084	2.982321	2.697944	9.313349
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate	3.638971	3.091267	2.706785	9.437024
Indo-Pacific	(28.1, Inf]	salinity aou oxygen phosphate phosphate_star	3.596967	3.202683	2.651638	9.451287
Indo-Pacific	(28.1, Inf]	salinity temperature aou phosphate phosphate_star	3.537341	3.234509	2.701246	9.473096
Indo-Pacific	(28.1, Inf]	salinity temperature aou oxygen phosphate	3.537528	3.314768	2.641163	9.493459
Indo-Pacific	(28.1, Inf]	salinity aou oxygen phosphate	3.597324	3.320281	2.652926	9.570531
Indo-Pacific	(28.1, Inf]	salinity temperature aou silicate phosphate	3.538830	3.348288	2.712252	9.599369
Indo-Pacific	(28.1, Inf]	salinity temperature oxygen phosphate phosphate_star	3.590808	3.275252	2.761419	9.627479

rm(n_predictors_max, n_predictors_min)

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

# test_lm <- lm_best %>% 
#   slice_min(rmse_sum) %>% 
#   select(lm_coeff) %>% 
#   pull()
# 
# class(test_lm)
# test_lm_formula <- as.formula(test_lm)
# class(test_lm_formula)

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_rmse_sum in unique(lm_best_basin_slab$rmse_sum)) {
        
        # i_rmse_sum <- unique(lm_best_basin_slab$rmse_sum)[2]
        
        lm_best_single <- lm_best %>%
          filter(rmse_sum == i_rmse_sum) %>%
          select(lm_coeff) %>%
          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)
        
      }
      
 
    }
    
  }
  
}


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

6.3.2 All predictors

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)

7 Open tasks

Check if intercept is modeled

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

30 July, 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 Overview

6.2.2 Grouped for basin, era, slab

6.2.3 Correlation assesment

6.2.3.1 Calculation of correlation coeffcients

6.2.3.2 Predictor pairs

6.2.3.3 C* vs individual predictors

6.3 Model fitting

6.3.1 Predictor selection

6.3.2 All predictors

7 Open tasks

Data base

Jens Daniel Müller

30 July, 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 Overview

6.2.2 Grouped for basin, era, slab

6.2.3 Correlation assesment

6.2.3.1 Calculation of correlation coeffcients

6.2.3.2 Predictor pairs

6.2.3.3 C* vs individual predictors

6.3 Model fitting

6.3.1 Predictor selection

6.3.2 All predictors

7 Open tasks

3 PO₄* calculation

4.1.2 GLODAP + atm. pCO₂