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Last updated: 2020-08-18

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Knit directory: Cant_eMLR/

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File	Version	Author	Date	Message
html	42925f1	jens-daniel-mueller	2020-08-18	Build site.
html	29a537a	jens-daniel-mueller	2020-08-18	Build site.
Rmd	7fb61d5	jens-daniel-mueller	2020-08-18	rerun with all parameters in one file
html	80c1a52	jens-daniel-mueller	2020-08-18	Build site.
Rmd	2016e10	jens-daniel-mueller	2020-08-18	coefficient selection based on rmse sum per two (not all) eras
html	923a88f	jens-daniel-mueller	2020-08-14	Build site.
Rmd	a614044	jens-daniel-mueller	2020-08-14	checked gamma calculation and sabine cant
html	2c0a2c2	jens-daniel-mueller	2020-08-14	Build site.
Rmd	f6a3179	jens-daniel-mueller	2020-08-14	checked gamma calculation and sabine cant
html	a3b6b68	jens-daniel-mueller	2020-08-13	Build site.
html	00c2120	jens-daniel-mueller	2020-08-13	Build site.
Rmd	a279558	jens-daniel-mueller	2020-08-13	rebuild with extended basin mask
html	bf69270	jens-daniel-mueller	2020-08-13	Build site.
html	d69fbad	jens-daniel-mueller	2020-08-12	Build site.
Rmd	1be0bc4	jens-daniel-mueller	2020-08-12	gamma slab coverage visualised
html	bc8f3c1	jens-daniel-mueller	2020-08-12	Build site.
Rmd	cc3a876	jens-daniel-mueller	2020-08-12	gamma_slab histogram added
html	1176c9a	jens-daniel-mueller	2020-08-12	Build site.
Rmd	e58d075	jens-daniel-mueller	2020-08-12	harmonized variable names, added analysis file
html	f143b2d	jens-daniel-mueller	2020-08-12	Build site.
html	2d179e7	jens-daniel-mueller	2020-08-12	Build site.
html	5d33341	jens-daniel-mueller	2020-08-11	Build site.
html	8a010ca	jens-daniel-mueller	2020-08-11	Build site.
html	a01041a	jens-daniel-mueller	2020-08-11	Build site.
html	e18e59a	jens-daniel-mueller	2020-08-10	Build site.
html	7d7900a	jens-daniel-mueller	2020-08-07	Build site.
Rmd	ceb438a	jens-daniel-mueller	2020-08-07	rebuild with Gruber Cant
html	846ab5e	jens-daniel-mueller	2020-08-04	Build site.
Rmd	bafc589	jens-daniel-mueller	2020-08-04	tested identical rmse output, which seems correct
html	15fb263	jens-daniel-mueller	2020-08-03	Build site.
Rmd	f8f8b17	jens-daniel-mueller	2020-08-03	corrections to eMLR fit and cleaning
html	6b95e62	jens-daniel-mueller	2020-07-31	Build site.
Rmd	2b887d4	jens-daniel-mueller	2020-07-31	separate basin corr plots
html	a469d3a	jens-daniel-mueller	2020-07-31	Build site.
Rmd	1692f11	jens-daniel-mueller	2020-07-31	link to individual corr plots, one example individual plot shown
html	e9a52c5	jens-daniel-mueller	2020-07-31	Build site.
Rmd	5ee70b2	jens-daniel-mueller	2020-07-31	formatting
html	d28701c	jens-daniel-mueller	2020-07-30	Build site.
Rmd	3938c9c	jens-daniel-mueller	2020-07-30	chunk labels changed
html	f22eed2	jens-daniel-mueller	2020-07-30	Build site.
Rmd	2bc1628	jens-daniel-mueller	2020-07-30	correlation table and plot update
html	e1e81fc	jens-daniel-mueller	2020-07-30	Build site.
Rmd	85c758f	jens-daniel-mueller	2020-07-30	PO4* calculation based on oxygen, correlation tables added, formating
html	7fc7fd4	jens-daniel-mueller	2020-07-30	Build site.
Rmd	48e1767	jens-daniel-mueller	2020-07-30	correlation coeffcients plots added
html	9dc5d7f	jens-daniel-mueller	2020-07-29	Build site.
Rmd	bf5ea88	jens-daniel-mueller	2020-07-29	rebuild, site definition in index.Rmd, without colinear plots
html	21524b4	jens-daniel-mueller	2020-07-29	Build site.
Rmd	3ad6a3c	jens-daniel-mueller	2020-07-29	rebuild all with new navbar labels, colinear plots updated
html	ff17968	jens-daniel-mueller	2020-07-29	Build site.
Rmd	cb5074e	jens-daniel-mueller	2020-07-29	subset Cant to GLODAP before merging
html	44502a9	jens-daniel-mueller	2020-07-28	Build site.
Rmd	5dce915	jens-daniel-mueller	2020-07-28	fit top 10 models
html	35f1cd4	jens-daniel-mueller	2020-07-28	Build site.
Rmd	da498d0	jens-daniel-mueller	2020-07-28	formatted table, loaded kableExtra
html	e5fc772	jens-daniel-mueller	2020-07-28	Build site.
Rmd	7fe0338	jens-daniel-mueller	2020-07-28	rmse output, 10 best models selected
html	4eebe14	jens-daniel-mueller	2020-07-24	Build site.
Rmd	12f9ef2	jens-daniel-mueller	2020-07-24	started neutral density calculation
html	2e08795	jens-daniel-mueller	2020-07-24	Build site.
html	61a1a48	jens-daniel-mueller	2020-07-24	Build site.
Rmd	864a6e3	jens-daniel-mueller	2020-07-24	merged predictor data sets
html	7f51d57	jens-daniel-mueller	2020-07-24	Build site.
Rmd	4a8deb2	jens-daniel-mueller	2020-07-24	corrected false to FALSE
html	2df2065	jens-daniel-mueller	2020-07-23	Build site.
Rmd	fa350cf	jens-daniel-mueller	2020-07-23	predictor correlation plots, bin2d map plots
html	9d1d67d	jens-daniel-mueller	2020-07-23	Build site.
Rmd	3b6658b	jens-daniel-mueller	2020-07-23	predictor correlation plots, bin2d map plots
html	2e3691a	jens-daniel-mueller	2020-07-23	Build site.
Rmd	26bdc0a	jens-daniel-mueller	2020-07-23	new era label, predictor correlation check started
html	556e6cc	jens-daniel-mueller	2020-07-23	Build site.
Rmd	1ce10e7	jens-daniel-mueller	2020-07-23	read full GLODAP Cant data set rather than joining again
Rmd	0cb3db2	jens-daniel-mueller	2020-07-23	started MLR fitting
Rmd	cf8bc74	jens-daniel-mueller	2020-07-23	started MLR fitting
Rmd	0252675	jens-daniel-mueller	2020-07-23	modeling started
html	fdfa7b9	jens-daniel-mueller	2020-07-22	Build site.
Rmd	6416150	jens-daniel-mueller	2020-07-22	cut gamma into slabs
html	0cecfbf	jens-daniel-mueller	2020-07-22	Build site.
Rmd	48cf01f	jens-daniel-mueller	2020-07-22	defined isoneutral slabs
Rmd	32ed280	jens-daniel-mueller	2020-07-22	sign in Cstar delta plot
html	44334f8	jens-daniel-mueller	2020-07-22	Build site.
Rmd	c398496	jens-daniel-mueller	2020-07-22	plot update
html	0ff656b	jens-daniel-mueller	2020-07-22	Build site.
Rmd	4b81f16	jens-daniel-mueller	2020-07-22	plot update
html	23038c8	jens-daniel-mueller	2020-07-22	Build site.
Rmd	09b3ca8	jens-daniel-mueller	2020-07-22	eding plain text, restructuring some code
html	ac6308d	jens-daniel-mueller	2020-07-22	Build site.
Rmd	77c9642	jens-daniel-mueller	2020-07-22	formatted plots
html	40b99cb	jens-daniel-mueller	2020-07-22	Build site.
Rmd	8a49adf	jens-daniel-mueller	2020-07-22	adjustment to reference year implemented
html	bb9c002	jens-daniel-mueller	2020-07-21	Build site.
Rmd	d2ed0f8	jens-daniel-mueller	2020-07-21	harmonied lat lon labeling
html	e1488e6	jens-daniel-mueller	2020-07-19	Build site.
Rmd	e688d6e	jens-daniel-mueller	2020-07-19	formating
html	f7ea007	jens-daniel-mueller	2020-07-19	Build site.
Rmd	0992256	jens-daniel-mueller	2020-07-19	plotted individual Cstar terms
html	22b588c	jens-daniel-mueller	2020-07-18	Build site.
html	fdfe5a0	jens-daniel-mueller	2020-07-17	Build site.
Rmd	f7485c6	jens-daniel-mueller	2020-07-17	re run als emlr
html	56c3ed9	jens-daniel-mueller	2020-07-14	Build site.
html	74d4abd	jens-daniel-mueller	2020-07-14	Build site.
html	1c511ce	jens-daniel-mueller	2020-07-14	Build site.
Rmd	e03016e	jens-daniel-mueller	2020-07-14	split read in per data set
html	45ed0ea	jens-daniel-mueller	2020-07-14	Build site.
Rmd	dc1c56e	jens-daniel-mueller	2020-07-14	tref calculated
html	b1ece68	jens-daniel-mueller	2020-07-13	Build site.
Rmd	8eb1b22	jens-daniel-mueller	2020-07-13	cleaned data base file
Rmd	9e8f7f1	jens-daniel-mueller	2020-07-13	untracked changes
html	79312b2	jens-daniel-mueller	2020-07-13	Build site.
Rmd	ffbc2a1	jens-daniel-mueller	2020-07-13	added Cstar calculation
html	090cfeb	jens-daniel-mueller	2020-07-13	Build site.
Rmd	e6a2ade	jens-daniel-mueller	2020-07-13	added Cstar calculation

---

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

1 Required data

Required are:

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

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

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

# Cant_clim <-
#   read_csv(here::here("data/GLODAPv1_1/_summarized_files",
#                       "Cant_94.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"
  ))

Cant_clim <- Cant_clim %>%
  rename(cant = Cant)

2 C*

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

• organic matter formation and respiration
• calcification and calcium carbonate dissolution

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

2.1 Stoichiometric ratios

rCP <- 117
rNP <- 16

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

• C/P: 117
• N/P: 16

2.2 Calculation

C* is calculated as:

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

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

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

rm(rCP, rNP)

3 PO₄* calculation

Currently, the predictor PO₄* is calculated according to Clement and Gruber (2018), ie based on oxygen rather than nitrate, as claimed in Gruber et al (2019).

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

GLODAP <- GLODAP %>% 
  mutate(phosphate_star_nit = phosphate - nitrate/16  + 2.9)

GLODAP %>% 
  ggplot(aes(phosphate_star_oxy, phosphate_star_nit)) +
  geom_bin2d() +
  scale_fill_viridis_c() +
  facet_wrap(~basin)

GLODAP <- GLODAP %>% 
  select(-phosphate_star_nit) %>% 
  rename(phosphate_star = phosphate_star_oxy)

4 Reference year adjustment

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

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

4.1 Merge data sets

4.1.1 GLODAP + Cant

Cant_clim <- Cant_clim %>% 
  drop_na()

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

# Cant_clim_obs_nr <- Cant_clim_obs %>%
#   group_by(lon, lat) %>%
#   summarise(n_cant = n()) %>%
#   ungroup()

# Cant_clim_obs %>% 
#   filter(n < 1) %>% 
#   ggplot(aes(lon,lat)) +
#   geom_point(data = GLODAP_obs_grid, aes(lon, lat)) +
#   geom_point(col = "red")

rm(Cant_clim, GLODAP_obs_grid)

GLODAP_Cant_obs <- full_join(GLODAP, Cant_clim_obs)

rm(GLODAP, Cant_clim_obs)

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 <- full_join(GLODAP_Cant_obs, Cant_clim_obs_nr)

GLODAP_Cant_obs <- GLODAP_Cant_obs %>%
  # filter(n_cant > 1) %>% 
  group_by(lat, lon) %>%
  arrange(depth) %>%
  mutate(cant_int = approxfun(depth, cant, rule = 2)(depth)) %>%
  ungroup()

# GLODAP_Cant_obs_set <- GLODAP_Cant_obs %>%
#   filter(n_cant == 1) %>% 
#   group_by(lat, lon) %>%
#   arrange(depth) %>%
#   mutate(cant_int = mean(cant, na.rm = TRUE)) %>%
#   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")

# remove cant data at grid cells without observations

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

rm(GLODAP_Cant_obs)

4.1.2 GLODAP + atm. pCO₂

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

GLODAP <- left_join(GLODAP, co2_atm)

4.2 Calculate adjustment

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

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

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

GLODAP <- full_join(GLODAP, co2_atm_tref)

rm(co2_atm, co2_atm_tref, tref)

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

4.3 Control plots

4.3.1 Histogram

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

4.3.2 Time series

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

5 Selected section plots

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

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

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

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

lat_section +
  geom_point(aes(col = tco2))

lat_section +
  geom_point(aes(col = talk))

lat_section +
  geom_point(aes(col = phosphate))

lat_section +
  geom_point(aes(col = rCP_phosphate))

lat_section +
  geom_point(aes(col = talk_05))

lat_section +
  geom_point(aes(col = rNP_phosphate_05))

lat_section +
  geom_point(aes(col = Cstar))

lat_section +
  geom_point(aes(col = cant))

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

rm(lat_section, GLODAP_cruise)

6 MLR

6.1 Isoneutral slabs

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,

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

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

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

GLODAP <- bind_rows(GLODAP_Atl, GLODAP_Ind_Pac)

rm(GLODAP_Atl, GLODAP_Ind_Pac)

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

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

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

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

rm(lat_section, GLODAP_cruise)

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

library(oce)
GLODAP_cruise <- GLODAP_cruise %>% 
  mutate(THETA = swTheta(salinity = sal,
                         temperature = tem,
                         pressure = depth,
                         referencePressure = 0,
                         longitude = lon-180,
                         latitude = lat))

GLODAP_cruise <- GLODAP_cruise %>% 
  rename(LATITUDE = lat,
         LONGITUDE = lon,
         SALNTY = sal,
         CTDPRS = depth,
         gamma_provided = gamma)

library(reticulate)
source_python(here::here("code/python_scripts",
                         "Gamma_GLODAP_python.py"))

GLODAP_cruise <- calculate_gamma(GLODAP_cruise)

GLODAP_cruise <- GLODAP_cruise %>% 
  mutate(gamma_delta = gamma_provided - GAMMA)

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

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

GLODAP_cruise %>% 
  ggplot(aes(gamma_delta))+
  geom_histogram()

rm(lat_section, GLODAP_cruise, cruises_meridional)

6.1.1 Observations coverage

GLODAP <- GLODAP %>% 
  mutate(era = factor(era, c("JGOFS_WOCE", "GO_SHIP", "new_era"))) %>%
  mutate(gamma_slab = factor(gamma_slab), 
         gamma_slab = factor(gamma_slab, levels = rev(levels(gamma_slab))))

GLODAP %>% 
  filter(basin == "Atlantic") %>% 
  ggplot(aes(lat, gamma_slab)) +
  geom_bin2d(binwidth = 5) +
  scale_fill_viridis_c(option = "magma", direction = -1, trans = "log10",
                       name = "log10(n)") +
  scale_x_continuous(breaks = seq(-100,100,20)) +
  facet_grid(era~basin)

GLODAP %>% 
  filter(basin == "Indo-Pacific") %>% 
  ggplot(aes(lat, gamma_slab)) +
  geom_bin2d(binwidth = 5) +
  scale_fill_viridis_c(option = "magma", direction = -1, trans = "log10",
                       name = "log10(n)") +
  scale_x_continuous(breaks = seq(-100,100,20)) +
  facet_grid(era~basin)

6.2 Predictor correlation

The correlation between:

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

were investigated based on:

• property-property plots and
• calculated correlation coeffcients.

6.2.1 Correlation plots

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

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

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

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

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

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

print(i_basin)
print(i_era)

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

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

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

print(p)

dev.off()
  
    }
  }
}

6.2.2 Correlation assesment

6.2.2.1 Calculation of correlation coeffcients

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

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

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

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

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

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


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

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

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

6.2.2.2 Predictor pairs

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

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

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

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

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

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

rm(cor_predictors, cor_predictors_stats)

6.2.2.3 C* vs individual predictors

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

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

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

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

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

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

rm(cor_Cstar_predictor, cor_Cstar_predictor_stats)

6.3 Model fitting

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

6.3.1 Predictor selection

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

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

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

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

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

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

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

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

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

all_lm_stats <- all_lm_stats %>% 
  filter(n >= parameters$predictors_min,
         n <= parameters$predictors_max)

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

AIC is an alternative criterion to RMSE to judge model quality, but not (yet) taken into account.

all_lm_stats %>% 
  ggplot(aes(rmse, aic, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(era~basin)

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

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

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

all_lm_stats_wide <- all_lm_stats_wide %>%
  mutate(
    rmse_sum_JGOFS_GO = rmse_JGOFS_WOCE + rmse_GO_SHIP,
    rmse_sum_GO_new = rmse_GO_SHIP + rmse_new_era
  )

all_lm_stats <- all_lm_stats_wide %>%
  pivot_longer(
    c(rmse_sum_JGOFS_GO, rmse_sum_GO_new),
    names_to = "eras",
    values_to = "rmse_sum",
    names_prefix = "rmse_sum_"
  )

lm_best <- all_lm_stats %>%
  group_by(basin, gamma_slab, eras) %>%
  slice_min(order_by = rmse_sum,
            with_ties = FALSE,
            n = parameters$MLR_number) %>%
  ungroup() %>% 
  arrange(basin, gamma_slab, eras, predictors)

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	eras	rmse_sum
Atlantic	(-Inf,26]	sal aou oxygen silicate phosphate	7.367183	6.669551	2.819161	GO_new	9.488712
Atlantic	(-Inf,26]	sal aou oxygen silicate phosphate_star	7.367183	6.669551	2.819161	GO_new	9.488712
Atlantic	(-Inf,26]	sal aou silicate phosphate phosphate_star	7.367183	6.669551	2.819161	GO_new	9.488712
Atlantic	(-Inf,26]	sal tem aou oxygen phosphate	7.173663	6.639387	2.699587	GO_new	9.338974
Atlantic	(-Inf,26]	sal tem aou oxygen phosphate_star	7.173663	6.639387	2.699587	GO_new	9.338974
Atlantic	(-Inf,26]	sal tem aou phosphate phosphate_star	7.173663	6.639387	2.699587	GO_new	9.338974
Atlantic	(-Inf,26]	sal tem aou silicate phosphate	7.278011	6.732505	2.786012	GO_new	9.518517
Atlantic	(-Inf,26]	sal tem aou silicate phosphate_star	7.258007	6.738390	2.781099	GO_new	9.519489
Atlantic	(-Inf,26]	sal tem oxygen silicate phosphate_star	7.248967	6.745194	2.784042	GO_new	9.529236
Atlantic	(-Inf,26]	sal tem silicate phosphate phosphate_star	7.248967	6.745194	2.784042	GO_new	9.529236
Atlantic	(-Inf,26]	sal aou oxygen silicate phosphate	7.367183	6.669551	2.819161	JGOFS_GO	14.036734
Atlantic	(-Inf,26]	sal aou oxygen silicate phosphate_star	7.367183	6.669551	2.819161	JGOFS_GO	14.036734
Atlantic	(-Inf,26]	sal tem aou oxygen phosphate	7.173663	6.639387	2.699587	JGOFS_GO	13.813050
Atlantic	(-Inf,26]	sal tem aou oxygen phosphate_star	7.173663	6.639387	2.699587	JGOFS_GO	13.813050
Atlantic	(-Inf,26]	sal tem aou phosphate phosphate_star	7.173663	6.639387	2.699587	JGOFS_GO	13.813050
Atlantic	(-Inf,26]	sal tem aou silicate phosphate	7.278011	6.732505	2.786012	JGOFS_GO	14.010516
Atlantic	(-Inf,26]	sal tem aou silicate phosphate_star	7.258007	6.738390	2.781099	JGOFS_GO	13.996398
Atlantic	(-Inf,26]	sal tem oxygen silicate phosphate	7.248967	6.745194	2.784042	JGOFS_GO	13.994160
Atlantic	(-Inf,26]	sal tem oxygen silicate phosphate_star	7.248967	6.745194	2.784042	JGOFS_GO	13.994160
Atlantic	(-Inf,26]	sal tem silicate phosphate phosphate_star	7.248967	6.745194	2.784042	JGOFS_GO	13.994160
Atlantic	(26,26.5]	sal aou oxygen silicate phosphate	5.434466	7.405553	3.069029	GO_new	10.474582
Atlantic	(26,26.5]	sal aou oxygen silicate phosphate_star	5.434466	7.405553	3.069029	GO_new	10.474582
Atlantic	(26,26.5]	sal aou silicate phosphate phosphate_star	5.434466	7.405553	3.069029	GO_new	10.474582
Atlantic	(26,26.5]	sal tem aou oxygen phosphate	5.477425	7.346736	3.118023	GO_new	10.464759
Atlantic	(26,26.5]	sal tem aou oxygen phosphate_star	5.477425	7.346736	3.118023	GO_new	10.464759
Atlantic	(26,26.5]	sal tem aou phosphate phosphate_star	5.477425	7.346736	3.118023	GO_new	10.464759
Atlantic	(26,26.5]	sal tem aou silicate phosphate	5.461410	7.412711	3.074943	GO_new	10.487654
Atlantic	(26,26.5]	tem aou oxygen silicate phosphate	5.363554	7.360474	3.065512	GO_new	10.425986
Atlantic	(26,26.5]	tem aou oxygen silicate phosphate_star	5.363554	7.360474	3.065512	GO_new	10.425986
Atlantic	(26,26.5]	tem aou silicate phosphate phosphate_star	5.363554	7.360474	3.065512	GO_new	10.425986
Atlantic	(26,26.5]	sal aou oxygen silicate phosphate	5.434466	7.405553	3.069029	JGOFS_GO	12.840019
Atlantic	(26,26.5]	sal aou oxygen silicate phosphate_star	5.434466	7.405553	3.069029	JGOFS_GO	12.840019
Atlantic	(26,26.5]	sal aou silicate phosphate phosphate_star	5.434466	7.405553	3.069029	JGOFS_GO	12.840019
Atlantic	(26,26.5]	sal tem aou oxygen phosphate	5.477425	7.346736	3.118023	JGOFS_GO	12.824162
Atlantic	(26,26.5]	sal tem aou oxygen phosphate_star	5.477425	7.346736	3.118023	JGOFS_GO	12.824162
Atlantic	(26,26.5]	sal tem aou phosphate phosphate_star	5.477425	7.346736	3.118023	JGOFS_GO	12.824162
Atlantic	(26,26.5]	tem aou oxygen silicate phosphate	5.363554	7.360474	3.065512	JGOFS_GO	12.724027
Atlantic	(26,26.5]	tem aou oxygen silicate phosphate_star	5.363554	7.360474	3.065512	JGOFS_GO	12.724027
Atlantic	(26,26.5]	tem aou phosphate phosphate_star	5.478784	7.362490	3.142747	JGOFS_GO	12.841274
Atlantic	(26,26.5]	tem aou silicate phosphate phosphate_star	5.363554	7.360474	3.065512	JGOFS_GO	12.724027
Atlantic	(26.5,26.75]	sal tem aou oxygen phosphate	5.318827	6.182233	3.188366	GO_new	9.370599
Atlantic	(26.5,26.75]	sal tem aou oxygen phosphate_star	5.318827	6.182233	3.188366	GO_new	9.370599
Atlantic	(26.5,26.75]	sal tem aou phosphate phosphate_star	5.318827	6.182233	3.188366	GO_new	9.370599
Atlantic	(26.5,26.75]	sal tem aou silicate phosphate	5.080928	6.189493	3.157471	GO_new	9.346963
Atlantic	(26.5,26.75]	sal tem aou silicate phosphate_star	5.074249	6.162444	3.151326	GO_new	9.313769
Atlantic	(26.5,26.75]	sal tem oxygen silicate phosphate	5.073639	6.161326	3.152137	GO_new	9.313462
Atlantic	(26.5,26.75]	sal tem oxygen silicate phosphate_star	5.073639	6.161326	3.152137	GO_new	9.313462
Atlantic	(26.5,26.75]	sal tem silicate phosphate phosphate_star	5.073639	6.161326	3.152137	GO_new	9.313462
Atlantic	(26.5,26.75]	tem aou oxygen silicate phosphate	5.153695	6.171505	3.261512	GO_new	9.433017
Atlantic	(26.5,26.75]	tem aou oxygen silicate phosphate_star	5.153695	6.171505	3.261512	GO_new	9.433017
Atlantic	(26.5,26.75]	sal aou oxygen silicate phosphate	5.121400	6.278369	3.156785	JGOFS_GO	11.399769
Atlantic	(26.5,26.75]	sal aou oxygen silicate phosphate_star	5.121400	6.278369	3.156785	JGOFS_GO	11.399769
Atlantic	(26.5,26.75]	sal tem aou silicate phosphate	5.080928	6.189493	3.157471	JGOFS_GO	11.270421
Atlantic	(26.5,26.75]	sal tem aou silicate phosphate_star	5.074249	6.162444	3.151326	JGOFS_GO	11.236693
Atlantic	(26.5,26.75]	sal tem oxygen silicate phosphate	5.073639	6.161326	3.152137	JGOFS_GO	11.234964
Atlantic	(26.5,26.75]	sal tem oxygen silicate phosphate_star	5.073639	6.161326	3.152137	JGOFS_GO	11.234964
Atlantic	(26.5,26.75]	sal tem silicate phosphate phosphate_star	5.073639	6.161326	3.152137	JGOFS_GO	11.234964
Atlantic	(26.5,26.75]	tem aou oxygen silicate phosphate	5.153695	6.171505	3.261512	JGOFS_GO	11.325200
Atlantic	(26.5,26.75]	tem aou oxygen silicate phosphate_star	5.153695	6.171505	3.261512	JGOFS_GO	11.325200
Atlantic	(26.5,26.75]	tem aou silicate phosphate phosphate_star	5.153695	6.171505	3.261512	JGOFS_GO	11.325200
Atlantic	(26.75,27]	sal tem aou silicate phosphate	4.708472	5.279945	3.666486	GO_new	8.946431
Atlantic	(26.75,27]	sal tem aou silicate phosphate_star	4.688937	5.253248	3.665075	GO_new	8.918323
Atlantic	(26.75,27]	sal tem oxygen silicate phosphate	4.689137	5.255316	3.664798	GO_new	8.920113
Atlantic	(26.75,27]	sal tem oxygen silicate phosphate_star	4.689137	5.255316	3.664798	GO_new	8.920113
Atlantic	(26.75,27]	sal tem silicate phosphate phosphate_star	4.689137	5.255316	3.664798	GO_new	8.920113
Atlantic	(26.75,27]	tem aou oxygen silicate phosphate	4.802227	5.348802	3.665657	GO_new	9.014459
Atlantic	(26.75,27]	tem aou oxygen silicate phosphate_star	4.802227	5.348802	3.665657	GO_new	9.014459
Atlantic	(26.75,27]	tem aou silicate phosphate phosphate_star	4.802227	5.348802	3.665657	GO_new	9.014459
Atlantic	(26.75,27]	tem aou silicate phosphate_star	4.803550	5.355648	3.666312	GO_new	9.021960
Atlantic	(26.75,27]	tem oxygen silicate phosphate	4.803963	5.356851	3.666006	GO_new	9.022858
Atlantic	(26.75,27]	sal aou silicate phosphate phosphate_star	4.810239	5.344351	3.679790	JGOFS_GO	10.154590
Atlantic	(26.75,27]	sal tem aou silicate phosphate	4.708472	5.279945	3.666486	JGOFS_GO	9.988417
Atlantic	(26.75,27]	sal tem aou silicate phosphate_star	4.688937	5.253248	3.665075	JGOFS_GO	9.942185
Atlantic	(26.75,27]	sal tem oxygen silicate phosphate	4.689137	5.255316	3.664798	JGOFS_GO	9.944452
Atlantic	(26.75,27]	sal tem oxygen silicate phosphate_star	4.689137	5.255316	3.664798	JGOFS_GO	9.944452
Atlantic	(26.75,27]	sal tem silicate phosphate phosphate_star	4.689137	5.255316	3.664798	JGOFS_GO	9.944452
Atlantic	(26.75,27]	sal tem silicate phosphate_star	4.697648	5.324409	3.937664	JGOFS_GO	10.022058
Atlantic	(26.75,27]	tem aou oxygen silicate phosphate	4.802227	5.348802	3.665657	JGOFS_GO	10.151029
Atlantic	(26.75,27]	tem aou oxygen silicate phosphate_star	4.802227	5.348802	3.665657	JGOFS_GO	10.151029
Atlantic	(26.75,27]	tem aou silicate phosphate phosphate_star	4.802227	5.348802	3.665657	JGOFS_GO	10.151029
Atlantic	(27,27.25]	sal aou silicate phosphate phosphate_star	5.272709	5.715880	5.031411	GO_new	10.747292
Atlantic	(27,27.25]	sal tem aou silicate phosphate	5.078648	5.623468	5.051530	GO_new	10.674998
Atlantic	(27,27.25]	sal tem aou silicate phosphate_star	5.013740	5.583407	5.085420	GO_new	10.668827
Atlantic	(27,27.25]	sal tem oxygen silicate phosphate	5.018688	5.589122	5.077798	GO_new	10.666920
Atlantic	(27,27.25]	sal tem oxygen silicate phosphate_star	5.018688	5.589122	5.077798	GO_new	10.666920
Atlantic	(27,27.25]	sal tem silicate phosphate phosphate_star	5.018688	5.589122	5.077798	GO_new	10.666920
Atlantic	(27,27.25]	tem aou oxygen silicate phosphate	5.132734	5.610171	5.007417	GO_new	10.617588
Atlantic	(27,27.25]	tem aou oxygen silicate phosphate_star	5.132734	5.610171	5.007417	GO_new	10.617588
Atlantic	(27,27.25]	tem aou silicate phosphate	5.199454	5.645126	5.100418	GO_new	10.745543
Atlantic	(27,27.25]	tem aou silicate phosphate phosphate_star	5.132734	5.610171	5.007417	GO_new	10.617588
Atlantic	(27,27.25]	sal tem aou silicate phosphate	5.078648	5.623468	5.051530	JGOFS_GO	10.702117
Atlantic	(27,27.25]	sal tem aou silicate phosphate_star	5.013740	5.583407	5.085420	JGOFS_GO	10.597147
Atlantic	(27,27.25]	sal tem oxygen silicate phosphate	5.018688	5.589122	5.077798	JGOFS_GO	10.607810
Atlantic	(27,27.25]	sal tem oxygen silicate phosphate_star	5.018688	5.589122	5.077798	JGOFS_GO	10.607810
Atlantic	(27,27.25]	sal tem silicate phosphate phosphate_star	5.018688	5.589122	5.077798	JGOFS_GO	10.607810
Atlantic	(27,27.25]	tem aou oxygen silicate phosphate	5.132734	5.610171	5.007417	JGOFS_GO	10.742905
Atlantic	(27,27.25]	tem aou oxygen silicate phosphate_star	5.132734	5.610171	5.007417	JGOFS_GO	10.742905
Atlantic	(27,27.25]	tem aou silicate phosphate phosphate_star	5.132734	5.610171	5.007417	JGOFS_GO	10.742905
Atlantic	(27,27.25]	tem aou silicate phosphate_star	5.153233	5.614185	5.142494	JGOFS_GO	10.767419
Atlantic	(27,27.25]	tem oxygen silicate phosphate	5.156878	5.617843	5.133226	JGOFS_GO	10.774722
Atlantic	(27.25,27.5]	sal tem aou oxygen phosphate	4.685854	4.506963	3.523918	GO_new	8.030880
Atlantic	(27.25,27.5]	sal tem aou oxygen phosphate_star	4.685854	4.506963	3.523918	GO_new	8.030880
Atlantic	(27.25,27.5]	sal tem aou phosphate phosphate_star	4.685854	4.506963	3.523918	GO_new	8.030880
Atlantic	(27.25,27.5]	tem aou oxygen phosphate	4.776702	4.554342	3.528315	GO_new	8.082657
Atlantic	(27.25,27.5]	tem aou oxygen phosphate phosphate_star	4.776702	4.554342	3.528315	GO_new	8.082657
Atlantic	(27.25,27.5]	tem aou oxygen phosphate_star	4.776702	4.554342	3.528315	GO_new	8.082657
Atlantic	(27.25,27.5]	tem aou oxygen silicate phosphate	4.708352	4.554250	3.467433	GO_new	8.021683
Atlantic	(27.25,27.5]	tem aou oxygen silicate phosphate_star	4.708352	4.554250	3.467433	GO_new	8.021683
Atlantic	(27.25,27.5]	tem aou phosphate phosphate_star	4.776702	4.554342	3.528315	GO_new	8.082657
Atlantic	(27.25,27.5]	tem aou silicate phosphate phosphate_star	4.708352	4.554250	3.467433	GO_new	8.021683
Atlantic	(27.25,27.5]	sal tem aou oxygen phosphate	4.685854	4.506963	3.523918	JGOFS_GO	9.192816
Atlantic	(27.25,27.5]	sal tem aou oxygen phosphate_star	4.685854	4.506963	3.523918	JGOFS_GO	9.192816
Atlantic	(27.25,27.5]	sal tem aou phosphate phosphate_star	4.685854	4.506963	3.523918	JGOFS_GO	9.192816
Atlantic	(27.25,27.5]	sal tem aou silicate phosphate_star	4.761998	4.518766	3.948074	JGOFS_GO	9.280765
Atlantic	(27.25,27.5]	sal tem oxygen silicate phosphate	4.779166	4.504624	3.915107	JGOFS_GO	9.283789
Atlantic	(27.25,27.5]	sal tem oxygen silicate phosphate_star	4.779166	4.504624	3.915107	JGOFS_GO	9.283789
Atlantic	(27.25,27.5]	sal tem silicate phosphate phosphate_star	4.779166	4.504624	3.915107	JGOFS_GO	9.283789
Atlantic	(27.25,27.5]	tem aou oxygen silicate phosphate	4.708352	4.554250	3.467433	JGOFS_GO	9.262602
Atlantic	(27.25,27.5]	tem aou oxygen silicate phosphate_star	4.708352	4.554250	3.467433	JGOFS_GO	9.262602
Atlantic	(27.25,27.5]	tem aou silicate phosphate phosphate_star	4.708352	4.554250	3.467433	JGOFS_GO	9.262602
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate	4.181349	4.384925	4.678199	GO_new	9.063125
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate phosphate_star	4.181349	4.384925	4.678199	GO_new	9.063125
Atlantic	(27.5,27.75]	aou silicate phosphate phosphate_star	4.181349	4.384925	4.678199	GO_new	9.063125
Atlantic	(27.5,27.75]	sal aou oxygen silicate phosphate	4.170632	4.369707	4.676151	GO_new	9.045858
Atlantic	(27.5,27.75]	sal aou oxygen silicate phosphate_star	4.170632	4.369707	4.676151	GO_new	9.045858
Atlantic	(27.5,27.75]	sal aou silicate phosphate phosphate_star	4.170632	4.369707	4.676151	GO_new	9.045858
Atlantic	(27.5,27.75]	sal tem aou silicate phosphate	4.157749	4.384594	4.678127	GO_new	9.062721
Atlantic	(27.5,27.75]	tem aou oxygen silicate phosphate	4.148689	4.355735	4.666207	GO_new	9.021941
Atlantic	(27.5,27.75]	tem aou oxygen silicate phosphate_star	4.148689	4.355735	4.666207	GO_new	9.021941
Atlantic	(27.5,27.75]	tem aou silicate phosphate phosphate_star	4.148689	4.355735	4.666207	GO_new	9.021941
Atlantic	(27.5,27.75]	sal aou oxygen silicate phosphate	4.170632	4.369707	4.676151	JGOFS_GO	8.540339
Atlantic	(27.5,27.75]	sal aou oxygen silicate phosphate_star	4.170632	4.369707	4.676151	JGOFS_GO	8.540339
Atlantic	(27.5,27.75]	sal aou silicate phosphate phosphate_star	4.170632	4.369707	4.676151	JGOFS_GO	8.540339
Atlantic	(27.5,27.75]	sal tem aou silicate phosphate	4.157749	4.384594	4.678127	JGOFS_GO	8.542343
Atlantic	(27.5,27.75]	sal tem oxygen silicate phosphate	4.148971	4.399401	4.683535	JGOFS_GO	8.548373
Atlantic	(27.5,27.75]	sal tem oxygen silicate phosphate_star	4.148971	4.399401	4.683535	JGOFS_GO	8.548373
Atlantic	(27.5,27.75]	sal tem silicate phosphate phosphate_star	4.148971	4.399401	4.683535	JGOFS_GO	8.548373
Atlantic	(27.5,27.75]	tem aou oxygen silicate phosphate	4.148689	4.355735	4.666207	JGOFS_GO	8.504424
Atlantic	(27.5,27.75]	tem aou oxygen silicate phosphate_star	4.148689	4.355735	4.666207	JGOFS_GO	8.504424
Atlantic	(27.5,27.75]	tem aou silicate phosphate phosphate_star	4.148689	4.355735	4.666207	JGOFS_GO	8.504424
Atlantic	(27.75,27.85]	sal aou oxygen silicate phosphate	4.113685	4.285353	7.686739	GO_new	11.972092
Atlantic	(27.75,27.85]	sal aou oxygen silicate phosphate_star	4.113685	4.285353	7.686739	GO_new	11.972092
Atlantic	(27.75,27.85]	sal aou silicate phosphate phosphate_star	4.113685	4.285353	7.686739	GO_new	11.972092
Atlantic	(27.75,27.85]	sal oxygen silicate phosphate_star	4.121204	4.285377	7.689071	GO_new	11.974448
Atlantic	(27.75,27.85]	sal silicate phosphate phosphate_star	4.121204	4.285377	7.689071	GO_new	11.974448
Atlantic	(27.75,27.85]	sal tem aou silicate phosphate	4.114571	4.284915	7.687911	GO_new	11.972827
Atlantic	(27.75,27.85]	sal tem aou silicate phosphate_star	4.111828	4.289070	7.684140	GO_new	11.973210
Atlantic	(27.75,27.85]	sal tem oxygen silicate phosphate	4.112834	4.285301	7.687608	GO_new	11.972910
Atlantic	(27.75,27.85]	sal tem oxygen silicate phosphate_star	4.112834	4.285301	7.687608	GO_new	11.972910
Atlantic	(27.75,27.85]	sal tem silicate phosphate phosphate_star	4.112834	4.285301	7.687608	GO_new	11.972910
Atlantic	(27.75,27.85]	sal aou oxygen silicate phosphate	4.113685	4.285353	7.686739	JGOFS_GO	8.399038
Atlantic	(27.75,27.85]	sal aou oxygen silicate phosphate_star	4.113685	4.285353	7.686739	JGOFS_GO	8.399038
Atlantic	(27.75,27.85]	sal aou silicate phosphate phosphate_star	4.113685	4.285353	7.686739	JGOFS_GO	8.399038
Atlantic	(27.75,27.85]	sal oxygen silicate phosphate_star	4.121204	4.285377	7.689071	JGOFS_GO	8.406581
Atlantic	(27.75,27.85]	sal silicate phosphate phosphate_star	4.121204	4.285377	7.689071	JGOFS_GO	8.406581
Atlantic	(27.75,27.85]	sal tem aou silicate phosphate	4.114571	4.284915	7.687911	JGOFS_GO	8.399486
Atlantic	(27.75,27.85]	sal tem aou silicate phosphate_star	4.111828	4.289070	7.684140	JGOFS_GO	8.400899
Atlantic	(27.75,27.85]	sal tem oxygen silicate phosphate	4.112834	4.285301	7.687608	JGOFS_GO	8.398135
Atlantic	(27.75,27.85]	sal tem oxygen silicate phosphate_star	4.112834	4.285301	7.687608	JGOFS_GO	8.398135
Atlantic	(27.75,27.85]	sal tem silicate phosphate phosphate_star	4.112834	4.285301	7.687608	JGOFS_GO	8.398135
Atlantic	(27.85,27.95]	sal aou oxygen silicate phosphate	3.733203	4.162374	5.126559	GO_new	9.288933
Atlantic	(27.85,27.95]	sal aou oxygen silicate phosphate_star	3.733203	4.162374	5.126559	GO_new	9.288933
Atlantic	(27.85,27.95]	sal aou silicate phosphate phosphate_star	3.733203	4.162374	5.126559	GO_new	9.288933
Atlantic	(27.85,27.95]	sal aou silicate phosphate_star	3.733249	4.210578	5.172242	GO_new	9.382820
Atlantic	(27.85,27.95]	sal tem aou silicate phosphate	3.755350	4.186637	5.158031	GO_new	9.344668
Atlantic	(27.85,27.95]	sal tem aou silicate phosphate_star	3.732711	4.163977	5.135340	GO_new	9.299317
Atlantic	(27.85,27.95]	sal tem oxygen silicate phosphate	3.744962	4.180818	5.155292	GO_new	9.336111
Atlantic	(27.85,27.95]	sal tem oxygen silicate phosphate_star	3.744962	4.180818	5.155292	GO_new	9.336111
Atlantic	(27.85,27.95]	sal tem silicate phosphate	3.981432	4.271866	5.181192	GO_new	9.453058
Atlantic	(27.85,27.95]	sal tem silicate phosphate phosphate_star	3.744962	4.180818	5.155292	GO_new	9.336111
Atlantic	(27.85,27.95]	sal aou oxygen silicate phosphate	3.733203	4.162374	5.126559	JGOFS_GO	7.895576
Atlantic	(27.85,27.95]	sal aou oxygen silicate phosphate_star	3.733203	4.162374	5.126559	JGOFS_GO	7.895576
Atlantic	(27.85,27.95]	sal aou silicate phosphate phosphate_star	3.733203	4.162374	5.126559	JGOFS_GO	7.895576
Atlantic	(27.85,27.95]	sal aou silicate phosphate_star	3.733249	4.210578	5.172242	JGOFS_GO	7.943827
Atlantic	(27.85,27.95]	sal tem aou silicate phosphate	3.755350	4.186637	5.158031	JGOFS_GO	7.941987
Atlantic	(27.85,27.95]	sal tem aou silicate phosphate_star	3.732711	4.163977	5.135340	JGOFS_GO	7.896689
Atlantic	(27.85,27.95]	sal tem oxygen silicate phosphate	3.744962	4.180818	5.155292	JGOFS_GO	7.925780
Atlantic	(27.85,27.95]	sal tem oxygen silicate phosphate_star	3.744962	4.180818	5.155292	JGOFS_GO	7.925780
Atlantic	(27.85,27.95]	sal tem silicate phosphate	3.981432	4.271866	5.181192	JGOFS_GO	8.253298
Atlantic	(27.85,27.95]	sal tem silicate phosphate phosphate_star	3.744962	4.180818	5.155292	JGOFS_GO	7.925780
Atlantic	(27.95,28.05]	sal aou oxygen silicate phosphate	3.487770	4.308349	5.366509	GO_new	9.674857
Atlantic	(27.95,28.05]	sal aou oxygen silicate phosphate_star	3.487770	4.308349	5.366509	GO_new	9.674857
Atlantic	(27.95,28.05]	sal aou silicate phosphate phosphate_star	3.487770	4.308349	5.366509	GO_new	9.674857
Atlantic	(27.95,28.05]	sal aou silicate phosphate_star	3.487779	4.313489	5.385656	GO_new	9.699144
Atlantic	(27.95,28.05]	sal tem aou oxygen phosphate	3.755336	4.353971	4.677615	GO_new	9.031586
Atlantic	(27.95,28.05]	sal tem aou oxygen phosphate_star	3.755336	4.353971	4.677615	GO_new	9.031586
Atlantic	(27.95,28.05]	sal tem aou phosphate phosphate_star	3.755336	4.353971	4.677615	GO_new	9.031586
Atlantic	(27.95,28.05]	sal tem aou silicate phosphate_star	3.487662	4.299678	5.385502	GO_new	9.685180
Atlantic	(27.95,28.05]	sal tem oxygen silicate phosphate	3.498901	4.330126	5.481394	GO_new	9.811519
Atlantic	(27.95,28.05]	sal tem silicate phosphate phosphate_star	3.498901	4.330126	5.481394	GO_new	9.811519
Atlantic	(27.95,28.05]	sal aou oxygen silicate phosphate	3.487770	4.308349	5.366509	JGOFS_GO	7.796119
Atlantic	(27.95,28.05]	sal aou oxygen silicate phosphate_star	3.487770	4.308349	5.366509	JGOFS_GO	7.796119
Atlantic	(27.95,28.05]	sal aou silicate phosphate phosphate_star	3.487770	4.308349	5.366509	JGOFS_GO	7.796119
Atlantic	(27.95,28.05]	sal aou silicate phosphate_star	3.487779	4.313489	5.385656	JGOFS_GO	7.801268
Atlantic	(27.95,28.05]	sal oxygen silicate phosphate_star	3.570686	4.354920	5.524972	JGOFS_GO	7.925607
Atlantic	(27.95,28.05]	sal tem aou silicate phosphate	3.508118	4.354175	5.504209	JGOFS_GO	7.862294
Atlantic	(27.95,28.05]	sal tem aou silicate phosphate_star	3.487662	4.299678	5.385502	JGOFS_GO	7.787340
Atlantic	(27.95,28.05]	sal tem oxygen silicate phosphate	3.498901	4.330126	5.481394	JGOFS_GO	7.829027
Atlantic	(27.95,28.05]	sal tem oxygen silicate phosphate_star	3.498901	4.330126	5.481394	JGOFS_GO	7.829027
Atlantic	(27.95,28.05]	sal tem silicate phosphate phosphate_star	3.498901	4.330126	5.481394	JGOFS_GO	7.829027
Atlantic	(28.05,28.1]	sal tem aou oxygen phosphate	3.539499	4.204534	4.630652	GO_new	8.835185
Atlantic	(28.05,28.1]	sal tem aou oxygen phosphate_star	3.539499	4.204534	4.630652	GO_new	8.835185
Atlantic	(28.05,28.1]	sal tem aou phosphate phosphate_star	3.539499	4.204534	4.630652	GO_new	8.835185
Atlantic	(28.05,28.1]	tem aou oxygen phosphate	3.737933	4.326767	4.638593	GO_new	8.965360
Atlantic	(28.05,28.1]	tem aou oxygen phosphate phosphate_star	3.737933	4.326767	4.638593	GO_new	8.965360
Atlantic	(28.05,28.1]	tem aou oxygen phosphate_star	3.737933	4.326767	4.638593	GO_new	8.965360
Atlantic	(28.05,28.1]	tem aou oxygen silicate phosphate	3.643192	4.179970	4.630074	GO_new	8.810044
Atlantic	(28.05,28.1]	tem aou oxygen silicate phosphate_star	3.643192	4.179970	4.630074	GO_new	8.810044
Atlantic	(28.05,28.1]	tem aou phosphate phosphate_star	3.737933	4.326767	4.638593	GO_new	8.965360
Atlantic	(28.05,28.1]	tem aou silicate phosphate phosphate_star	3.643192	4.179970	4.630074	GO_new	8.810044
Atlantic	(28.05,28.1]	sal tem aou oxygen phosphate	3.539499	4.204534	4.630652	JGOFS_GO	7.744033
Atlantic	(28.05,28.1]	sal tem aou oxygen phosphate_star	3.539499	4.204534	4.630652	JGOFS_GO	7.744033
Atlantic	(28.05,28.1]	sal tem aou phosphate phosphate_star	3.539499	4.204534	4.630652	JGOFS_GO	7.744033
Atlantic	(28.05,28.1]	sal tem aou silicate phosphate_star	3.518913	4.334649	5.077667	JGOFS_GO	7.853562
Atlantic	(28.05,28.1]	sal tem oxygen silicate phosphate	3.531111	4.393917	5.124357	JGOFS_GO	7.925028
Atlantic	(28.05,28.1]	sal tem oxygen silicate phosphate_star	3.531111	4.393917	5.124357	JGOFS_GO	7.925028
Atlantic	(28.05,28.1]	sal tem silicate phosphate phosphate_star	3.531111	4.393917	5.124357	JGOFS_GO	7.925028
Atlantic	(28.05,28.1]	tem aou oxygen silicate phosphate	3.643192	4.179970	4.630074	JGOFS_GO	7.823162
Atlantic	(28.05,28.1]	tem aou oxygen silicate phosphate_star	3.643192	4.179970	4.630074	JGOFS_GO	7.823162
Atlantic	(28.05,28.1]	tem aou silicate phosphate phosphate_star	3.643192	4.179970	4.630074	JGOFS_GO	7.823162
Atlantic	(28.1,28.15]	sal tem aou oxygen phosphate	3.453382	3.943365	4.691597	GO_new	8.634961
Atlantic	(28.1,28.15]	sal tem aou oxygen phosphate_star	3.453382	3.943365	4.691597	GO_new	8.634961
Atlantic	(28.1,28.15]	sal tem aou phosphate phosphate_star	3.453382	3.943365	4.691597	GO_new	8.634961
Atlantic	(28.1,28.15]	sal tem aou silicate phosphate_star	3.341455	3.923614	4.732891	GO_new	8.656505
Atlantic	(28.1,28.15]	sal tem oxygen silicate phosphate	3.349985	3.934786	4.738195	GO_new	8.672981
Atlantic	(28.1,28.15]	sal tem oxygen silicate phosphate_star	3.349985	3.934786	4.738195	GO_new	8.672981
Atlantic	(28.1,28.15]	sal tem silicate phosphate phosphate_star	3.349985	3.934786	4.738195	GO_new	8.672981
Atlantic	(28.1,28.15]	tem aou oxygen silicate phosphate	3.434468	3.944928	4.715162	GO_new	8.660090
Atlantic	(28.1,28.15]	tem aou oxygen silicate phosphate_star	3.434468	3.944928	4.715162	GO_new	8.660090
Atlantic	(28.1,28.15]	tem aou silicate phosphate phosphate_star	3.434468	3.944928	4.715162	GO_new	8.660090
Atlantic	(28.1,28.15]	sal tem aou oxygen phosphate	3.453382	3.943365	4.691597	JGOFS_GO	7.396747
Atlantic	(28.1,28.15]	sal tem aou phosphate phosphate_star	3.453382	3.943365	4.691597	JGOFS_GO	7.396747
Atlantic	(28.1,28.15]	sal tem aou silicate phosphate_star	3.341455	3.923614	4.732891	JGOFS_GO	7.265069
Atlantic	(28.1,28.15]	sal tem oxygen silicate phosphate	3.349985	3.934786	4.738195	JGOFS_GO	7.284771
Atlantic	(28.1,28.15]	sal tem oxygen silicate phosphate_star	3.349985	3.934786	4.738195	JGOFS_GO	7.284771
Atlantic	(28.1,28.15]	sal tem silicate phosphate phosphate_star	3.349985	3.934786	4.738195	JGOFS_GO	7.284771
Atlantic	(28.1,28.15]	tem aou oxygen silicate phosphate	3.434468	3.944928	4.715162	JGOFS_GO	7.379396
Atlantic	(28.1,28.15]	tem aou oxygen silicate phosphate_star	3.434468	3.944928	4.715162	JGOFS_GO	7.379396
Atlantic	(28.1,28.15]	tem aou silicate phosphate phosphate_star	3.434468	3.944928	4.715162	JGOFS_GO	7.379396
Atlantic	(28.1,28.15]	tem aou silicate phosphate_star	3.436151	3.956434	4.793801	JGOFS_GO	7.392585
Atlantic	(28.15,28.2]	sal aou oxygen silicate phosphate	3.726384	3.637891	3.023471	GO_new	6.661362
Atlantic	(28.15,28.2]	sal aou oxygen silicate phosphate_star	3.726384	3.637891	3.023471	GO_new	6.661362
Atlantic	(28.15,28.2]	sal aou silicate phosphate phosphate_star	3.726384	3.637891	3.023471	GO_new	6.661362
Atlantic	(28.15,28.2]	sal tem aou oxygen phosphate	3.726099	3.629154	3.004142	GO_new	6.633295
Atlantic	(28.15,28.2]	sal tem aou oxygen phosphate_star	3.726099	3.629154	3.004142	GO_new	6.633295
Atlantic	(28.15,28.2]	sal tem aou phosphate	3.741007	3.656291	3.004525	GO_new	6.660816
Atlantic	(28.15,28.2]	sal tem aou phosphate phosphate_star	3.726099	3.629154	3.004142	GO_new	6.633295
Atlantic	(28.15,28.2]	sal tem aou silicate phosphate	3.739605	3.638041	2.989969	GO_new	6.628010
Atlantic	(28.15,28.2]	sal tem oxygen silicate phosphate_star	3.770684	3.671003	2.995966	GO_new	6.666968
Atlantic	(28.15,28.2]	sal tem silicate phosphate phosphate_star	3.770684	3.671003	2.995966	GO_new	6.666968
Atlantic	(28.15,28.2]	sal aou oxygen phosphate	3.727404	3.639684	3.100446	JGOFS_GO	7.367088
Atlantic	(28.15,28.2]	sal aou oxygen phosphate phosphate_star	3.727404	3.639684	3.100446	JGOFS_GO	7.367088
Atlantic	(28.15,28.2]	sal aou oxygen phosphate_star	3.727404	3.639684	3.100446	JGOFS_GO	7.367088
Atlantic	(28.15,28.2]	sal aou oxygen silicate phosphate	3.726384	3.637891	3.023471	JGOFS_GO	7.364276
Atlantic	(28.15,28.2]	sal aou oxygen silicate phosphate_star	3.726384	3.637891	3.023471	JGOFS_GO	7.364276
Atlantic	(28.15,28.2]	sal aou phosphate phosphate_star	3.727404	3.639684	3.100446	JGOFS_GO	7.367088
Atlantic	(28.15,28.2]	sal aou silicate phosphate phosphate_star	3.726384	3.637891	3.023471	JGOFS_GO	7.364276
Atlantic	(28.15,28.2]	sal tem aou oxygen phosphate	3.726099	3.629154	3.004142	JGOFS_GO	7.355253
Atlantic	(28.15,28.2]	sal tem aou oxygen phosphate_star	3.726099	3.629154	3.004142	JGOFS_GO	7.355253
Atlantic	(28.15,28.2]	sal tem aou phosphate phosphate_star	3.726099	3.629154	3.004142	JGOFS_GO	7.355253
Atlantic	(28.2, Inf]	sal tem aou oxygen phosphate	3.522234	3.173511	3.190100	GO_new	6.363611
Atlantic	(28.2, Inf]	sal tem aou oxygen phosphate_star	3.522234	3.173511	3.190100	GO_new	6.363611
Atlantic	(28.2, Inf]	sal tem aou phosphate phosphate_star	3.522234	3.173511	3.190100	GO_new	6.363611
Atlantic	(28.2, Inf]	sal tem aou phosphate_star	3.678022	3.187744	3.267841	GO_new	6.455585
Atlantic	(28.2, Inf]	sal tem aou silicate phosphate_star	3.587315	3.154838	3.266541	GO_new	6.421379
Atlantic	(28.2, Inf]	sal tem oxygen phosphate_star	3.651581	3.173715	3.346153	GO_new	6.519868
Atlantic	(28.2, Inf]	sal tem oxygen silicate phosphate	3.544433	3.152200	3.338683	GO_new	6.490883
Atlantic	(28.2, Inf]	sal tem oxygen silicate phosphate_star	3.544433	3.152200	3.338683	GO_new	6.490883
Atlantic	(28.2, Inf]	sal tem phosphate phosphate_star	3.651581	3.173715	3.346153	GO_new	6.519868
Atlantic	(28.2, Inf]	sal tem silicate phosphate phosphate_star	3.544433	3.152200	3.338683	GO_new	6.490883
Atlantic	(28.2, Inf]	sal aou oxygen silicate phosphate	3.487877	3.158126	3.393186	JGOFS_GO	6.646004
Atlantic	(28.2, Inf]	sal aou oxygen silicate phosphate_star	3.487877	3.158126	3.393186	JGOFS_GO	6.646004
Atlantic	(28.2, Inf]	sal aou silicate phosphate phosphate_star	3.487877	3.158126	3.393186	JGOFS_GO	6.646004
Atlantic	(28.2, Inf]	sal tem aou oxygen phosphate	3.522234	3.173511	3.190100	JGOFS_GO	6.695745
Atlantic	(28.2, Inf]	sal tem aou oxygen phosphate_star	3.522234	3.173511	3.190100	JGOFS_GO	6.695745
Atlantic	(28.2, Inf]	sal tem aou phosphate phosphate_star	3.522234	3.173511	3.190100	JGOFS_GO	6.695745
Atlantic	(28.2, Inf]	sal tem aou silicate phosphate	3.499887	3.184788	3.462424	JGOFS_GO	6.684675
Atlantic	(28.2, Inf]	sal tem oxygen silicate phosphate	3.544433	3.152200	3.338683	JGOFS_GO	6.696633
Atlantic	(28.2, Inf]	sal tem oxygen silicate phosphate_star	3.544433	3.152200	3.338683	JGOFS_GO	6.696633
Atlantic	(28.2, Inf]	sal tem silicate phosphate phosphate_star	3.544433	3.152200	3.338683	JGOFS_GO	6.696633
Indo-Pacific	(-Inf,26]	sal aou oxygen silicate phosphate	11.589172	7.158929	5.649148	GO_new	12.808077
Indo-Pacific	(-Inf,26]	sal aou oxygen silicate phosphate_star	11.589172	7.158929	5.649148	GO_new	12.808077
Indo-Pacific	(-Inf,26]	sal aou silicate phosphate phosphate_star	11.589172	7.158929	5.649148	GO_new	12.808077
Indo-Pacific	(-Inf,26]	sal tem aou phosphate phosphate_star	11.835399	7.592149	6.001991	GO_new	13.594141
Indo-Pacific	(-Inf,26]	sal tem aou silicate phosphate	11.658578	7.235892	5.852129	GO_new	13.088021
Indo-Pacific	(-Inf,26]	sal tem aou silicate phosphate_star	11.697195	7.279661	5.932601	GO_new	13.212261
Indo-Pacific	(-Inf,26]	sal tem oxygen silicate phosphate	11.696367	7.284738	5.952533	GO_new	13.237271
Indo-Pacific	(-Inf,26]	sal tem oxygen silicate phosphate_star	11.696367	7.284738	5.952533	GO_new	13.237271
Indo-Pacific	(-Inf,26]	sal tem silicate phosphate phosphate_star	11.696367	7.284738	5.952533	GO_new	13.237271
Indo-Pacific	(-Inf,26]	sal tem silicate phosphate_star	11.698153	7.311075	6.086066	GO_new	13.397141
Indo-Pacific	(-Inf,26]	sal aou oxygen silicate phosphate	11.589172	7.158929	5.649148	JGOFS_GO	18.748101
Indo-Pacific	(-Inf,26]	sal aou oxygen silicate phosphate_star	11.589172	7.158929	5.649148	JGOFS_GO	18.748101
Indo-Pacific	(-Inf,26]	sal aou silicate phosphate phosphate_star	11.589172	7.158929	5.649148	JGOFS_GO	18.748101
Indo-Pacific	(-Inf,26]	sal tem aou phosphate phosphate_star	11.835399	7.592149	6.001991	JGOFS_GO	19.427548
Indo-Pacific	(-Inf,26]	sal tem aou silicate phosphate	11.658578	7.235892	5.852129	JGOFS_GO	18.894470
Indo-Pacific	(-Inf,26]	sal tem aou silicate phosphate_star	11.697195	7.279661	5.932601	JGOFS_GO	18.976856
Indo-Pacific	(-Inf,26]	sal tem oxygen silicate phosphate	11.696367	7.284738	5.952533	JGOFS_GO	18.981104
Indo-Pacific	(-Inf,26]	sal tem oxygen silicate phosphate_star	11.696367	7.284738	5.952533	JGOFS_GO	18.981104
Indo-Pacific	(-Inf,26]	sal tem silicate phosphate phosphate_star	11.696367	7.284738	5.952533	JGOFS_GO	18.981104
Indo-Pacific	(-Inf,26]	sal tem silicate phosphate_star	11.698153	7.311075	6.086066	JGOFS_GO	19.009228
Indo-Pacific	(26,26.5]	sal aou oxygen silicate phosphate	7.855393	5.185799	3.976710	GO_new	9.162509
Indo-Pacific	(26,26.5]	sal aou oxygen silicate phosphate_star	7.855393	5.185799	3.976710	GO_new	9.162509
Indo-Pacific	(26,26.5]	sal aou silicate phosphate phosphate_star	7.855393	5.185799	3.976710	GO_new	9.162509
Indo-Pacific	(26,26.5]	sal tem aou oxygen phosphate	7.962543	5.283401	4.258474	GO_new	9.541875
Indo-Pacific	(26,26.5]	sal tem aou oxygen phosphate_star	7.962543	5.283401	4.258474	GO_new	9.541875
Indo-Pacific	(26,26.5]	sal tem aou silicate phosphate	7.929705	5.143958	4.051154	GO_new	9.195112
Indo-Pacific	(26,26.5]	sal tem aou silicate phosphate_star	7.976306	5.156206	4.101030	GO_new	9.257236
Indo-Pacific	(26,26.5]	sal tem oxygen silicate phosphate	7.966619	5.153265	4.088387	GO_new	9.241652
Indo-Pacific	(26,26.5]	sal tem oxygen silicate phosphate_star	7.966619	5.153265	4.088387	GO_new	9.241652
Indo-Pacific	(26,26.5]	sal tem silicate phosphate phosphate_star	7.966619	5.153265	4.088387	GO_new	9.241652
Indo-Pacific	(26,26.5]	sal aou oxygen silicate phosphate	7.855393	5.185799	3.976710	JGOFS_GO	13.041193
Indo-Pacific	(26,26.5]	sal aou oxygen silicate phosphate_star	7.855393	5.185799	3.976710	JGOFS_GO	13.041193
Indo-Pacific	(26,26.5]	sal aou silicate phosphate phosphate_star	7.855393	5.185799	3.976710	JGOFS_GO	13.041193
Indo-Pacific	(26,26.5]	sal tem aou oxygen phosphate	7.962543	5.283401	4.258474	JGOFS_GO	13.245944
Indo-Pacific	(26,26.5]	sal tem aou phosphate phosphate_star	7.962543	5.283401	4.258474	JGOFS_GO	13.245944
Indo-Pacific	(26,26.5]	sal tem aou silicate phosphate	7.929705	5.143958	4.051154	JGOFS_GO	13.073663
Indo-Pacific	(26,26.5]	sal tem aou silicate phosphate_star	7.976306	5.156206	4.101030	JGOFS_GO	13.132512
Indo-Pacific	(26,26.5]	sal tem oxygen silicate phosphate	7.966619	5.153265	4.088387	JGOFS_GO	13.119885
Indo-Pacific	(26,26.5]	sal tem oxygen silicate phosphate_star	7.966619	5.153265	4.088387	JGOFS_GO	13.119885
Indo-Pacific	(26,26.5]	sal tem silicate phosphate phosphate_star	7.966619	5.153265	4.088387	JGOFS_GO	13.119885
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate	5.972964	5.696797	4.631952	GO_new	10.328749
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate phosphate_star	5.972964	5.696797	4.631952	GO_new	10.328749
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate_star	5.972964	5.696797	4.631952	GO_new	10.328749
Indo-Pacific	(26.5,26.75]	sal aou oxygen silicate phosphate	5.889764	5.691859	4.563197	GO_new	10.255056
Indo-Pacific	(26.5,26.75]	sal aou oxygen silicate phosphate_star	5.889764	5.691859	4.563197	GO_new	10.255056
Indo-Pacific	(26.5,26.75]	sal aou phosphate phosphate_star	5.972964	5.696797	4.631952	GO_new	10.328749
Indo-Pacific	(26.5,26.75]	sal aou silicate phosphate phosphate_star	5.889764	5.691859	4.563197	GO_new	10.255056
Indo-Pacific	(26.5,26.75]	sal tem aou oxygen phosphate	5.970854	5.696790	4.615782	GO_new	10.312572
Indo-Pacific	(26.5,26.75]	sal tem aou oxygen phosphate_star	5.970854	5.696790	4.615782	GO_new	10.312572
Indo-Pacific	(26.5,26.75]	sal tem aou phosphate phosphate_star	5.970854	5.696790	4.615782	GO_new	10.312572
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate	5.972964	5.696797	4.631952	JGOFS_GO	11.669761
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate phosphate_star	5.972964	5.696797	4.631952	JGOFS_GO	11.669761
Indo-Pacific	(26.5,26.75]	sal aou oxygen phosphate_star	5.972964	5.696797	4.631952	JGOFS_GO	11.669761
Indo-Pacific	(26.5,26.75]	sal aou oxygen silicate phosphate	5.889764	5.691859	4.563197	JGOFS_GO	11.581623
Indo-Pacific	(26.5,26.75]	sal aou oxygen silicate phosphate_star	5.889764	5.691859	4.563197	JGOFS_GO	11.581623
Indo-Pacific	(26.5,26.75]	sal aou phosphate phosphate_star	5.972964	5.696797	4.631952	JGOFS_GO	11.669761
Indo-Pacific	(26.5,26.75]	sal aou silicate phosphate phosphate_star	5.889764	5.691859	4.563197	JGOFS_GO	11.581623
Indo-Pacific	(26.5,26.75]	sal tem aou oxygen phosphate	5.970854	5.696790	4.615782	JGOFS_GO	11.667644
Indo-Pacific	(26.5,26.75]	sal tem aou oxygen phosphate_star	5.970854	5.696790	4.615782	JGOFS_GO	11.667644
Indo-Pacific	(26.5,26.75]	sal tem aou phosphate phosphate_star	5.970854	5.696790	4.615782	JGOFS_GO	11.667644
Indo-Pacific	(26.75,27]	sal tem aou oxygen phosphate	6.516743	5.021419	4.250318	GO_new	9.271737
Indo-Pacific	(26.75,27]	sal tem aou oxygen phosphate_star	6.516743	5.021419	4.250318	GO_new	9.271737
Indo-Pacific	(26.75,27]	sal tem aou phosphate phosphate_star	6.516743	5.021419	4.250318	GO_new	9.271737
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate	6.520101	5.023021	4.264277	GO_new	9.287298
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate phosphate_star	6.520101	5.023021	4.264277	GO_new	9.287298
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate_star	6.520101	5.023021	4.264277	GO_new	9.287298
Indo-Pacific	(26.75,27]	tem aou oxygen silicate phosphate	6.492756	4.983055	4.235837	GO_new	9.218892
Indo-Pacific	(26.75,27]	tem aou oxygen silicate phosphate_star	6.492756	4.983055	4.235837	GO_new	9.218892
Indo-Pacific	(26.75,27]	tem aou phosphate phosphate_star	6.520101	5.023021	4.264277	GO_new	9.287298
Indo-Pacific	(26.75,27]	tem aou silicate phosphate phosphate_star	6.492756	4.983055	4.235837	GO_new	9.218892
Indo-Pacific	(26.75,27]	sal tem aou oxygen phosphate	6.516743	5.021419	4.250318	JGOFS_GO	11.538162
Indo-Pacific	(26.75,27]	sal tem aou oxygen phosphate_star	6.516743	5.021419	4.250318	JGOFS_GO	11.538162
Indo-Pacific	(26.75,27]	sal tem aou phosphate phosphate_star	6.516743	5.021419	4.250318	JGOFS_GO	11.538162
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate	6.520101	5.023021	4.264277	JGOFS_GO	11.543122
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate phosphate_star	6.520101	5.023021	4.264277	JGOFS_GO	11.543122
Indo-Pacific	(26.75,27]	tem aou oxygen phosphate_star	6.520101	5.023021	4.264277	JGOFS_GO	11.543122
Indo-Pacific	(26.75,27]	tem aou oxygen silicate phosphate	6.492756	4.983055	4.235837	JGOFS_GO	11.475811
Indo-Pacific	(26.75,27]	tem aou oxygen silicate phosphate_star	6.492756	4.983055	4.235837	JGOFS_GO	11.475811
Indo-Pacific	(26.75,27]	tem aou phosphate phosphate_star	6.520101	5.023021	4.264277	JGOFS_GO	11.543122
Indo-Pacific	(26.75,27]	tem aou silicate phosphate phosphate_star	6.492756	4.983055	4.235837	JGOFS_GO	11.475811
Indo-Pacific	(27,27.25]	sal aou oxygen silicate phosphate	6.377139	4.610352	4.154787	GO_new	8.765140
Indo-Pacific	(27,27.25]	sal aou oxygen silicate phosphate_star	6.377139	4.610352	4.154787	GO_new	8.765140
Indo-Pacific	(27,27.25]	sal aou silicate phosphate phosphate_star	6.377139	4.610352	4.154787	GO_new	8.765140
Indo-Pacific	(27,27.25]	sal tem aou oxygen phosphate	5.996869	4.633139	4.167623	GO_new	8.800762
Indo-Pacific	(27,27.25]	sal tem aou oxygen phosphate_star	5.996869	4.633139	4.167623	GO_new	8.800762
Indo-Pacific	(27,27.25]	sal tem aou phosphate phosphate_star	5.996869	4.633139	4.167623	GO_new	8.800762
Indo-Pacific	(27,27.25]	sal tem aou silicate phosphate	6.492264	4.620740	4.179057	GO_new	8.799797
Indo-Pacific	(27,27.25]	tem aou oxygen silicate phosphate	5.981049	4.537003	4.124776	GO_new	8.661779
Indo-Pacific	(27,27.25]	tem aou oxygen silicate phosphate_star	5.981049	4.537003	4.124776	GO_new	8.661779
Indo-Pacific	(27,27.25]	tem aou silicate phosphate phosphate_star	5.981049	4.537003	4.124776	GO_new	8.661779
Indo-Pacific	(27,27.25]	sal tem aou oxygen phosphate	5.996869	4.633139	4.167623	JGOFS_GO	10.630008
Indo-Pacific	(27,27.25]	sal tem aou oxygen phosphate_star	5.996869	4.633139	4.167623	JGOFS_GO	10.630008
Indo-Pacific	(27,27.25]	sal tem aou phosphate phosphate_star	5.996869	4.633139	4.167623	JGOFS_GO	10.630008
Indo-Pacific	(27,27.25]	tem aou oxygen phosphate	6.024170	4.748844	4.304139	JGOFS_GO	10.773014
Indo-Pacific	(27,27.25]	tem aou oxygen phosphate phosphate_star	6.024170	4.748844	4.304139	JGOFS_GO	10.773014
Indo-Pacific	(27,27.25]	tem aou oxygen phosphate_star	6.024170	4.748844	4.304139	JGOFS_GO	10.773014
Indo-Pacific	(27,27.25]	tem aou oxygen silicate phosphate	5.981049	4.537003	4.124776	JGOFS_GO	10.518052
Indo-Pacific	(27,27.25]	tem aou oxygen silicate phosphate_star	5.981049	4.537003	4.124776	JGOFS_GO	10.518052
Indo-Pacific	(27,27.25]	tem aou phosphate phosphate_star	6.024170	4.748844	4.304139	JGOFS_GO	10.773014
Indo-Pacific	(27,27.25]	tem aou silicate phosphate phosphate_star	5.981049	4.537003	4.124776	JGOFS_GO	10.518052
Indo-Pacific	(27.25,27.5]	sal aou oxygen silicate phosphate	5.216429	4.136611	3.512906	GO_new	7.649517
Indo-Pacific	(27.25,27.5]	sal aou oxygen silicate phosphate_star	5.216429	4.136611	3.512906	GO_new	7.649517
Indo-Pacific	(27.25,27.5]	sal aou silicate phosphate phosphate_star	5.216429	4.136611	3.512906	GO_new	7.649517
Indo-Pacific	(27.25,27.5]	sal tem aou silicate phosphate	5.541110	4.185755	3.535978	GO_new	7.721733
Indo-Pacific	(27.25,27.5]	sal tem oxygen silicate phosphate	5.764252	4.233532	3.556430	GO_new	7.789962
Indo-Pacific	(27.25,27.5]	sal tem oxygen silicate phosphate_star	5.764252	4.233532	3.556430	GO_new	7.789962
Indo-Pacific	(27.25,27.5]	sal tem silicate phosphate phosphate_star	5.764252	4.233532	3.556430	GO_new	7.789962
Indo-Pacific	(27.25,27.5]	tem aou oxygen silicate phosphate	4.804957	3.986913	3.603040	GO_new	7.589953
Indo-Pacific	(27.25,27.5]	tem aou oxygen silicate phosphate_star	4.804957	3.986913	3.603040	GO_new	7.589953
Indo-Pacific	(27.25,27.5]	tem aou silicate phosphate phosphate_star	4.804957	3.986913	3.603040	GO_new	7.589953
Indo-Pacific	(27.25,27.5]	sal tem aou oxygen phosphate	4.831746	4.162230	3.629966	JGOFS_GO	8.993977
Indo-Pacific	(27.25,27.5]	sal tem aou oxygen phosphate_star	4.831746	4.162230	3.629966	JGOFS_GO	8.993977
Indo-Pacific	(27.25,27.5]	sal tem aou phosphate phosphate_star	4.831746	4.162230	3.629966	JGOFS_GO	8.993977
Indo-Pacific	(27.25,27.5]	tem aou oxygen phosphate	4.835593	4.192637	3.734596	JGOFS_GO	9.028231
Indo-Pacific	(27.25,27.5]	tem aou oxygen phosphate phosphate_star	4.835593	4.192637	3.734596	JGOFS_GO	9.028231
Indo-Pacific	(27.25,27.5]	tem aou oxygen phosphate_star	4.835593	4.192637	3.734596	JGOFS_GO	9.028231
Indo-Pacific	(27.25,27.5]	tem aou oxygen silicate phosphate	4.804957	3.986913	3.603040	JGOFS_GO	8.791870
Indo-Pacific	(27.25,27.5]	tem aou oxygen silicate phosphate_star	4.804957	3.986913	3.603040	JGOFS_GO	8.791870
Indo-Pacific	(27.25,27.5]	tem aou phosphate phosphate_star	4.835593	4.192637	3.734596	JGOFS_GO	9.028231
Indo-Pacific	(27.25,27.5]	tem aou silicate phosphate phosphate_star	4.804957	3.986913	3.603040	JGOFS_GO	8.791870
Indo-Pacific	(27.5,27.75]	sal tem aou oxygen phosphate	4.409996	4.005957	3.525039	GO_new	7.530996
Indo-Pacific	(27.5,27.75]	sal tem aou oxygen phosphate_star	4.409996	4.005957	3.525039	GO_new	7.530996
Indo-Pacific	(27.5,27.75]	sal tem aou phosphate phosphate_star	4.409996	4.005957	3.525039	GO_new	7.530996
Indo-Pacific	(27.5,27.75]	sal tem aou silicate phosphate	4.822537	4.035117	3.627796	GO_new	7.662913
Indo-Pacific	(27.5,27.75]	sal tem aou silicate phosphate_star	4.952600	4.089199	3.560809	GO_new	7.650008
Indo-Pacific	(27.5,27.75]	sal tem oxygen phosphate_star	4.957364	4.095366	3.574533	GO_new	7.669899
Indo-Pacific	(27.5,27.75]	sal tem oxygen silicate phosphate	4.949934	4.083693	3.565430	GO_new	7.649123
Indo-Pacific	(27.5,27.75]	sal tem oxygen silicate phosphate_star	4.949934	4.083693	3.565430	GO_new	7.649123
Indo-Pacific	(27.5,27.75]	sal tem phosphate phosphate_star	4.957364	4.095366	3.574533	GO_new	7.669899
Indo-Pacific	(27.5,27.75]	sal tem silicate phosphate phosphate_star	4.949934	4.083693	3.565430	GO_new	7.649123
Indo-Pacific	(27.5,27.75]	sal tem aou oxygen phosphate	4.409996	4.005957	3.525039	JGOFS_GO	8.415953
Indo-Pacific	(27.5,27.75]	sal tem aou oxygen phosphate_star	4.409996	4.005957	3.525039	JGOFS_GO	8.415953
Indo-Pacific	(27.5,27.75]	sal tem aou phosphate phosphate_star	4.409996	4.005957	3.525039	JGOFS_GO	8.415953
Indo-Pacific	(27.5,27.75]	tem aou oxygen phosphate	4.410507	4.074666	3.760424	JGOFS_GO	8.485173
Indo-Pacific	(27.5,27.75]	tem aou oxygen phosphate phosphate_star	4.410507	4.074666	3.760424	JGOFS_GO	8.485173
Indo-Pacific	(27.5,27.75]	tem aou oxygen phosphate_star	4.410507	4.074666	3.760424	JGOFS_GO	8.485173
Indo-Pacific	(27.5,27.75]	tem aou oxygen silicate phosphate	4.386458	4.074656	3.738199	JGOFS_GO	8.461113
Indo-Pacific	(27.5,27.75]	tem aou oxygen silicate phosphate_star	4.386458	4.074656	3.738199	JGOFS_GO	8.461113
Indo-Pacific	(27.5,27.75]	tem aou phosphate phosphate_star	4.410507	4.074666	3.760424	JGOFS_GO	8.485173
Indo-Pacific	(27.5,27.75]	tem aou silicate phosphate phosphate_star	4.386458	4.074656	3.738199	JGOFS_GO	8.461113
Indo-Pacific	(27.75,27.85]	sal tem aou silicate phosphate	4.258533	3.311684	2.876268	GO_new	6.187952
Indo-Pacific	(27.75,27.85]	sal tem aou silicate phosphate_star	4.280170	3.289599	2.863161	GO_new	6.152760
Indo-Pacific	(27.75,27.85]	sal tem oxygen silicate phosphate	4.281560	3.291064	2.865015	GO_new	6.156079
Indo-Pacific	(27.75,27.85]	sal tem oxygen silicate phosphate_star	4.281560	3.291064	2.865015	GO_new	6.156079
Indo-Pacific	(27.75,27.85]	sal tem silicate phosphate phosphate_star	4.281560	3.291064	2.865015	GO_new	6.156079
Indo-Pacific	(27.75,27.85]	tem aou oxygen silicate phosphate	4.242882	3.271777	2.903747	GO_new	6.175523
Indo-Pacific	(27.75,27.85]	tem aou oxygen silicate phosphate_star	4.242882	3.271777	2.903747	GO_new	6.175523
Indo-Pacific	(27.75,27.85]	tem aou silicate phosphate phosphate_star	4.242882	3.271777	2.903747	GO_new	6.175523
Indo-Pacific	(27.75,27.85]	tem aou silicate phosphate_star	4.299581	3.295238	2.915852	GO_new	6.211090
Indo-Pacific	(27.75,27.85]	tem oxygen silicate phosphate_star	4.300570	3.296323	2.916579	GO_new	6.212903
Indo-Pacific	(27.75,27.85]	sal tem aou oxygen phosphate	4.233667	3.327161	3.001071	JGOFS_GO	7.560827
Indo-Pacific	(27.75,27.85]	sal tem aou oxygen phosphate_star	4.233667	3.327161	3.001071	JGOFS_GO	7.560827
Indo-Pacific	(27.75,27.85]	sal tem aou phosphate phosphate_star	4.233667	3.327161	3.001071	JGOFS_GO	7.560827
Indo-Pacific	(27.75,27.85]	sal tem aou silicate phosphate	4.258533	3.311684	2.876268	JGOFS_GO	7.570217
Indo-Pacific	(27.75,27.85]	sal tem aou silicate phosphate_star	4.280170	3.289599	2.863161	JGOFS_GO	7.569769
Indo-Pacific	(27.75,27.85]	tem aou oxygen phosphate	4.242883	3.327650	3.002873	JGOFS_GO	7.570533
Indo-Pacific	(27.75,27.85]	tem aou oxygen phosphate_star	4.242883	3.327650	3.002873	JGOFS_GO	7.570533
Indo-Pacific	(27.75,27.85]	tem aou oxygen silicate phosphate	4.242882	3.271777	2.903747	JGOFS_GO	7.514659
Indo-Pacific	(27.75,27.85]	tem aou oxygen silicate phosphate_star	4.242882	3.271777	2.903747	JGOFS_GO	7.514659
Indo-Pacific	(27.75,27.85]	tem aou silicate phosphate phosphate_star	4.242882	3.271777	2.903747	JGOFS_GO	7.514659
Indo-Pacific	(27.85,27.95]	sal tem aou silicate phosphate	4.290311	3.000580	2.878296	GO_new	5.878876
Indo-Pacific	(27.85,27.95]	sal tem aou silicate phosphate_star	4.309949	3.004973	2.868411	GO_new	5.873384
Indo-Pacific	(27.85,27.95]	sal tem oxygen silicate phosphate	4.311405	3.004330	2.869502	GO_new	5.873832
Indo-Pacific	(27.85,27.95]	sal tem oxygen silicate phosphate_star	4.311405	3.004330	2.869502	GO_new	5.873832
Indo-Pacific	(27.85,27.95]	sal tem silicate phosphate phosphate_star	4.311405	3.004330	2.869502	GO_new	5.873832
Indo-Pacific	(27.85,27.95]	tem aou oxygen silicate phosphate	4.280774	3.000763	2.891621	GO_new	5.892384
Indo-Pacific	(27.85,27.95]	tem aou oxygen silicate phosphate_star	4.280774	3.000763	2.891621	GO_new	5.892384
Indo-Pacific	(27.85,27.95]	tem aou silicate phosphate phosphate_star	4.280774	3.000763	2.891621	GO_new	5.892384
Indo-Pacific	(27.85,27.95]	tem oxygen silicate phosphate	4.315597	3.005155	2.892410	GO_new	5.897565
Indo-Pacific	(27.85,27.95]	tem oxygen silicate phosphate phosphate_star	4.315597	3.005155	2.892410	GO_new	5.897565
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate	4.280926	3.007769	2.912915	JGOFS_GO	7.288694
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate phosphate_star	4.280926	3.007769	2.912915	JGOFS_GO	7.288694
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate_star	4.280926	3.007769	2.912915	JGOFS_GO	7.288694
Indo-Pacific	(27.85,27.95]	aou silicate phosphate phosphate_star	4.280926	3.007769	2.912915	JGOFS_GO	7.288694
Indo-Pacific	(27.85,27.95]	sal aou oxygen silicate phosphate	4.272593	3.007732	2.896370	JGOFS_GO	7.280326
Indo-Pacific	(27.85,27.95]	sal aou oxygen silicate phosphate_star	4.272593	3.007732	2.896370	JGOFS_GO	7.280326
Indo-Pacific	(27.85,27.95]	sal aou silicate phosphate phosphate_star	4.272593	3.007732	2.896370	JGOFS_GO	7.280326
Indo-Pacific	(27.85,27.95]	tem aou oxygen silicate phosphate	4.280774	3.000763	2.891621	JGOFS_GO	7.281537
Indo-Pacific	(27.85,27.95]	tem aou oxygen silicate phosphate_star	4.280774	3.000763	2.891621	JGOFS_GO	7.281537
Indo-Pacific	(27.85,27.95]	tem aou silicate phosphate phosphate_star	4.280774	3.000763	2.891621	JGOFS_GO	7.281537
Indo-Pacific	(27.95,28.05]	sal aou oxygen silicate phosphate	4.359139	2.857154	3.075517	GO_new	5.932671
Indo-Pacific	(27.95,28.05]	sal aou oxygen silicate phosphate_star	4.359139	2.857154	3.075517	GO_new	5.932671
Indo-Pacific	(27.95,28.05]	sal aou silicate phosphate phosphate_star	4.359139	2.857154	3.075517	GO_new	5.932671
Indo-Pacific	(27.95,28.05]	sal tem aou oxygen phosphate	4.359973	2.871354	3.107381	GO_new	5.978735
Indo-Pacific	(27.95,28.05]	sal tem aou oxygen phosphate_star	4.359973	2.871354	3.107381	GO_new	5.978735
Indo-Pacific	(27.95,28.05]	sal tem aou phosphate phosphate_star	4.359973	2.871354	3.107381	GO_new	5.978735
Indo-Pacific	(27.95,28.05]	sal tem aou silicate phosphate	4.377696	2.882277	3.064828	GO_new	5.947104
Indo-Pacific	(27.95,28.05]	tem aou oxygen silicate phosphate	4.381237	2.866160	3.109301	GO_new	5.975461
Indo-Pacific	(27.95,28.05]	tem aou oxygen silicate phosphate_star	4.381237	2.866160	3.109301	GO_new	5.975461
Indo-Pacific	(27.95,28.05]	tem aou silicate phosphate phosphate_star	4.381237	2.866160	3.109301	GO_new	5.975461
Indo-Pacific	(27.95,28.05]	sal aou oxygen phosphate	4.360181	2.879287	3.107563	JGOFS_GO	7.239469
Indo-Pacific	(27.95,28.05]	sal aou oxygen phosphate phosphate_star	4.360181	2.879287	3.107563	JGOFS_GO	7.239469
Indo-Pacific	(27.95,28.05]	sal aou oxygen phosphate_star	4.360181	2.879287	3.107563	JGOFS_GO	7.239469
Indo-Pacific	(27.95,28.05]	sal aou oxygen silicate phosphate	4.359139	2.857154	3.075517	JGOFS_GO	7.216293
Indo-Pacific	(27.95,28.05]	sal aou oxygen silicate phosphate_star	4.359139	2.857154	3.075517	JGOFS_GO	7.216293
Indo-Pacific	(27.95,28.05]	sal aou phosphate phosphate_star	4.360181	2.879287	3.107563	JGOFS_GO	7.239469
Indo-Pacific	(27.95,28.05]	sal aou silicate phosphate phosphate_star	4.359139	2.857154	3.075517	JGOFS_GO	7.216293
Indo-Pacific	(27.95,28.05]	sal tem aou oxygen phosphate	4.359973	2.871354	3.107381	JGOFS_GO	7.231328
Indo-Pacific	(27.95,28.05]	sal tem aou oxygen phosphate_star	4.359973	2.871354	3.107381	JGOFS_GO	7.231328
Indo-Pacific	(27.95,28.05]	sal tem aou phosphate phosphate_star	4.359973	2.871354	3.107381	JGOFS_GO	7.231328
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate	4.228221	2.863082	2.828633	GO_new	5.691715
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate phosphate_star	4.228221	2.863082	2.828633	GO_new	5.691715
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate_star	4.228221	2.863082	2.828633	GO_new	5.691715
Indo-Pacific	(28.05,28.1]	sal aou oxygen silicate phosphate	4.225670	2.848200	2.826261	GO_new	5.674461
Indo-Pacific	(28.05,28.1]	sal aou oxygen silicate phosphate_star	4.225670	2.848200	2.826261	GO_new	5.674461
Indo-Pacific	(28.05,28.1]	sal aou phosphate phosphate_star	4.228221	2.863082	2.828633	GO_new	5.691715
Indo-Pacific	(28.05,28.1]	sal aou silicate phosphate phosphate_star	4.225670	2.848200	2.826261	GO_new	5.674461
Indo-Pacific	(28.05,28.1]	sal tem aou oxygen phosphate	4.225054	2.860776	2.817179	GO_new	5.677955
Indo-Pacific	(28.05,28.1]	sal tem aou oxygen phosphate_star	4.225054	2.860776	2.817179	GO_new	5.677955
Indo-Pacific	(28.05,28.1]	sal tem aou phosphate phosphate_star	4.225054	2.860776	2.817179	GO_new	5.677955
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate	4.228221	2.863082	2.828633	JGOFS_GO	7.091304
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate phosphate_star	4.228221	2.863082	2.828633	JGOFS_GO	7.091304
Indo-Pacific	(28.05,28.1]	sal aou oxygen phosphate_star	4.228221	2.863082	2.828633	JGOFS_GO	7.091304
Indo-Pacific	(28.05,28.1]	sal aou oxygen silicate phosphate	4.225670	2.848200	2.826261	JGOFS_GO	7.073870
Indo-Pacific	(28.05,28.1]	sal aou oxygen silicate phosphate_star	4.225670	2.848200	2.826261	JGOFS_GO	7.073870
Indo-Pacific	(28.05,28.1]	sal aou phosphate phosphate_star	4.228221	2.863082	2.828633	JGOFS_GO	7.091304
Indo-Pacific	(28.05,28.1]	sal aou silicate phosphate phosphate_star	4.225670	2.848200	2.826261	JGOFS_GO	7.073870
Indo-Pacific	(28.05,28.1]	sal tem aou oxygen phosphate	4.225054	2.860776	2.817179	JGOFS_GO	7.085830
Indo-Pacific	(28.05,28.1]	sal tem aou oxygen phosphate_star	4.225054	2.860776	2.817179	JGOFS_GO	7.085830
Indo-Pacific	(28.05,28.1]	sal tem aou phosphate phosphate_star	4.225054	2.860776	2.817179	JGOFS_GO	7.085830
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate	3.640879	3.028695	2.696173	GO_new	5.724868
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate phosphate_star	3.640879	3.028695	2.696173	GO_new	5.724868
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate_star	3.640879	3.028695	2.696173	GO_new	5.724868
Indo-Pacific	(28.1, Inf]	aou silicate phosphate phosphate_star	3.640879	3.028695	2.696173	GO_new	5.724868
Indo-Pacific	(28.1, Inf]	sal aou oxygen silicate phosphate	3.570328	3.028688	2.582084	GO_new	5.610771
Indo-Pacific	(28.1, Inf]	sal aou oxygen silicate phosphate_star	3.570328	3.028688	2.582084	GO_new	5.610771
Indo-Pacific	(28.1, Inf]	sal aou silicate phosphate phosphate_star	3.570328	3.028688	2.582084	GO_new	5.610771
Indo-Pacific	(28.1, Inf]	tem aou oxygen silicate phosphate	3.601769	2.985715	2.648408	GO_new	5.634123
Indo-Pacific	(28.1, Inf]	tem aou oxygen silicate phosphate_star	3.601769	2.985715	2.648408	GO_new	5.634123
Indo-Pacific	(28.1, Inf]	tem aou silicate phosphate phosphate_star	3.601769	2.985715	2.648408	GO_new	5.634123
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate	3.640879	3.028695	2.696173	JGOFS_GO	6.669574
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate phosphate_star	3.640879	3.028695	2.696173	JGOFS_GO	6.669574
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate_star	3.640879	3.028695	2.696173	JGOFS_GO	6.669574
Indo-Pacific	(28.1, Inf]	aou silicate phosphate phosphate_star	3.640879	3.028695	2.696173	JGOFS_GO	6.669574
Indo-Pacific	(28.1, Inf]	sal aou oxygen silicate phosphate	3.570328	3.028688	2.582084	JGOFS_GO	6.599015
Indo-Pacific	(28.1, Inf]	sal aou oxygen silicate phosphate_star	3.570328	3.028688	2.582084	JGOFS_GO	6.599015
Indo-Pacific	(28.1, Inf]	sal aou silicate phosphate phosphate_star	3.570328	3.028688	2.582084	JGOFS_GO	6.599015
Indo-Pacific	(28.1, Inf]	tem aou oxygen silicate phosphate	3.601769	2.985715	2.648408	JGOFS_GO	6.587484
Indo-Pacific	(28.1, Inf]	tem aou oxygen silicate phosphate_star	3.601769	2.985715	2.648408	JGOFS_GO	6.587484
Indo-Pacific	(28.1, Inf]	tem aou silicate phosphate phosphate_star	3.601769	2.985715	2.648408	JGOFS_GO	6.587484

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

all_lm_stats %>%
  ggplot(aes(rmse_GO_SHIP, rmse_sum - rmse_GO_SHIP, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras ~ basin)

rm(all_lm_stats, all_lm_stats_wide)

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

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

lm_1
lm_2

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

6.3.2 Fitting best models

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

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

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

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

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

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

      }
      
 
      }
    }
    
  }
  
}


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

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

7 Open tasks

• combine correlation, rmse and model calculation into one routine, ideally using the purrr map approach
• select exactly best 10 models, even if same rmse sum appears more than once (currently, selection is set two ten, even if doublicated rmse occur)
• check (phosphate_star) NA’s in coeffcients -> cases of exact colinearity?

8 Open questions

Session information

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

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