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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
Rmd	1a4d1a8	jens-daniel-mueller	2020-08-18	parameters included in mapping
html	453e077	jens-daniel-mueller	2020-08-18	Build site.
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]	-0.8649592	-0.9534952	-0.7550657
aou + oxygen	Atlantic	(26,26.5]	-0.8926537	-0.9107476	-0.8626230
aou + oxygen	Atlantic	(26.5,26.75]	-0.9715136	-0.9853712	-0.9536791
aou + oxygen	Atlantic	(26.75,27]	-0.9810944	-0.9922152	-0.9718314
aou + oxygen	Atlantic	(27,27.25]	-0.9770245	-0.9875749	-0.9659895
aou + oxygen	Atlantic	(27.25,27.5]	-0.9575743	-0.9707979	-0.9410822
aou + oxygen	Atlantic	(27.5,27.75]	-0.9433656	-0.9784925	-0.9036579
aou + oxygen	Atlantic	(27.75,27.85]	-0.9811625	-0.9898826	-0.9759298
aou + oxygen	Atlantic	(27.85,27.95]	-0.9902785	-0.9945578	-0.9874310
aou + oxygen	Atlantic	(27.95,28.05]	-0.9891231	-0.9921957	-0.9834418
aou + oxygen	Atlantic	(28.05,28.1]	-0.9899171	-0.9952334	-0.9821174
aou + oxygen	Atlantic	(28.1,28.15]	-0.9937494	-0.9945629	-0.9925700
aou + oxygen	Atlantic	(28.15,28.2]	-0.9983276	-0.9988974	-0.9974572
aou + oxygen	Atlantic	(28.2, Inf]	-0.9865746	-0.9901176	-0.9831004
aou + oxygen	Indo-Pacific	(-Inf,26]	-0.9236200	-0.9667488	-0.8972692
aou + oxygen	Indo-Pacific	(26,26.5]	-0.9809220	-0.9846582	-0.9738150
aou + oxygen	Indo-Pacific	(26.5,26.75]	-0.9853216	-0.9882411	-0.9820145
aou + oxygen	Indo-Pacific	(26.75,27]	-0.9839547	-0.9853368	-0.9830976
aou + oxygen	Indo-Pacific	(27,27.25]	-0.9886682	-0.9928848	-0.9803680
aou + oxygen	Indo-Pacific	(27.25,27.5]	-0.9912564	-0.9952681	-0.9836197
aou + oxygen	Indo-Pacific	(27.5,27.75]	-0.9906898	-0.9938939	-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]	0.4734826	0.3638387	0.6886229
aou + phosphate	Atlantic	(26,26.5]	0.7653975	0.6261582	0.9141044
aou + phosphate	Atlantic	(26.5,26.75]	0.8900471	0.8461375	0.9294296
aou + phosphate	Atlantic	(26.75,27]	0.8795523	0.8327046	0.9238679
aou + phosphate	Atlantic	(27,27.25]	0.8131734	0.7311669	0.8599479
aou + phosphate	Atlantic	(27.25,27.5]	0.7107692	0.6507924	0.8023489
aou + phosphate	Atlantic	(27.5,27.75]	0.8619240	0.7979749	0.9188449
aou + phosphate	Atlantic	(27.75,27.85]	0.9516507	0.9423379	0.9684618
aou + phosphate	Atlantic	(27.85,27.95]	0.9583522	0.9518099	0.9679321
aou + phosphate	Atlantic	(27.95,28.05]	0.9644631	0.9541793	0.9836725
aou + phosphate	Atlantic	(28.05,28.1]	0.9720019	0.9561714	0.9907812
aou + phosphate	Atlantic	(28.1,28.15]	0.9800003	0.9782494	0.9823565
aou + phosphate	Atlantic	(28.15,28.2]	0.9926726	0.9890888	0.9944703
aou + phosphate	Atlantic	(28.2, Inf]	0.9008667	0.8698418	0.9476150
aou + phosphate	Indo-Pacific	(-Inf,26]	0.9430427	0.9128374	0.9696641
aou + phosphate	Indo-Pacific	(26,26.5]	0.9553712	0.9492126	0.9640881
aou + phosphate	Indo-Pacific	(26.5,26.75]	0.9515874	0.9392975	0.9638471
aou + phosphate	Indo-Pacific	(26.75,27]	0.9504577	0.9459297	0.9537914
aou + phosphate	Indo-Pacific	(27,27.25]	0.9660082	0.9484998	0.9794664
aou + phosphate	Indo-Pacific	(27.25,27.5]	0.9665270	0.9520615	0.9786942
aou + phosphate	Indo-Pacific	(27.5,27.75]	0.9572593	0.9503456	0.9610480
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]	-0.0046708	-0.3912141	0.3114819
aou + phosphate_star	Atlantic	(26,26.5]	0.4300772	0.1321752	0.7973664
aou + phosphate_star	Atlantic	(26.5,26.75]	0.4796013	0.3786756	0.6411307
aou + phosphate_star	Atlantic	(26.75,27]	0.2222188	0.0842917	0.3240950
aou + phosphate_star	Atlantic	(27,27.25]	0.1079916	-0.0375423	0.3056935
aou + phosphate_star	Atlantic	(27.25,27.5]	0.1051856	-0.0808192	0.3213433
aou + phosphate_star	Atlantic	(27.5,27.75]	0.5876151	0.4954788	0.6735107
aou + phosphate_star	Atlantic	(27.75,27.85]	0.7792143	0.7509359	0.8345555
aou + phosphate_star	Atlantic	(27.85,27.95]	0.7164088	0.6541662	0.7614266
aou + phosphate_star	Atlantic	(27.95,28.05]	0.8225135	0.7423182	0.9224381
aou + phosphate_star	Atlantic	(28.05,28.1]	0.8913122	0.8404144	0.9665203
aou + phosphate_star	Atlantic	(28.1,28.15]	0.9222166	0.9102596	0.9326315
aou + phosphate_star	Atlantic	(28.15,28.2]	0.9766519	0.9624803	0.9848581
aou + phosphate_star	Atlantic	(28.2, Inf]	0.7171355	0.6490846	0.8429139
aou + phosphate_star	Indo-Pacific	(-Inf,26]	0.6693175	0.5307313	0.7555587
aou + phosphate_star	Indo-Pacific	(26,26.5]	0.5837717	0.5240940	0.6188757
aou + phosphate_star	Indo-Pacific	(26.5,26.75]	0.4266782	0.1688017	0.5786039
aou + phosphate_star	Indo-Pacific	(26.75,27]	0.3818999	0.3175560	0.4745062
aou + phosphate_star	Indo-Pacific	(27,27.25]	0.1504071	0.0554197	0.2370912
aou + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.3701667	-0.3896454	-0.3512955
aou + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.2957834	-0.4968851	0.0532720
aou + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.4758260	-0.6105114	-0.3604524
aou + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.0706109	-0.1217541	0.0022432
aou + phosphate_star	Indo-Pacific	(27.95,28.05]	0.2334948	0.1165401	0.3272652
aou + phosphate_star	Indo-Pacific	(28.05,28.1]	0.4075649	0.3611234	0.4634936
aou + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.6157020	-0.6504537	-0.5640415
aou + silicate	Atlantic	(-Inf,26]	0.2483086	0.0999433	0.4145649
aou + silicate	Atlantic	(26,26.5]	0.6752140	0.5721489	0.7731182
aou + silicate	Atlantic	(26.5,26.75]	0.8898595	0.8630962	0.9291670
aou + silicate	Atlantic	(26.75,27]	0.8813735	0.8604505	0.8978525
aou + silicate	Atlantic	(27,27.25]	0.7485513	0.7001785	0.8355002
aou + silicate	Atlantic	(27.25,27.5]	0.4386835	0.1974552	0.6853791
aou + silicate	Atlantic	(27.5,27.75]	0.6463627	0.5686096	0.6986785
aou + silicate	Atlantic	(27.75,27.85]	0.8599027	0.8457486	0.8725979
aou + silicate	Atlantic	(27.85,27.95]	0.8991805	0.8894100	0.9097791
aou + silicate	Atlantic	(27.95,28.05]	0.9463989	0.9389015	0.9587778
aou + silicate	Atlantic	(28.05,28.1]	0.9726957	0.9622239	0.9871131
aou + silicate	Atlantic	(28.1,28.15]	0.9753232	0.9722655	0.9793741
aou + silicate	Atlantic	(28.15,28.2]	0.9914205	0.9861528	0.9949392
aou + silicate	Atlantic	(28.2, Inf]	0.9091296	0.8734476	0.9335909
aou + silicate	Indo-Pacific	(-Inf,26]	0.7342122	0.6585781	0.8063089
aou + silicate	Indo-Pacific	(26,26.5]	0.6572498	0.5417991	0.7585899
aou + silicate	Indo-Pacific	(26.5,26.75]	0.6158987	0.4104356	0.7404216
aou + silicate	Indo-Pacific	(26.75,27]	0.7501441	0.6944079	0.7795344
aou + silicate	Indo-Pacific	(27,27.25]	0.8633912	0.8054567	0.9080614
aou + silicate	Indo-Pacific	(27.25,27.5]	0.8991978	0.8521049	0.9374566
aou + silicate	Indo-Pacific	(27.5,27.75]	0.9199124	0.8664890	0.9511857
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]	-0.1674162	-0.4104103	0.0641100
oxygen + phosphate	Atlantic	(26,26.5]	-0.4406083	-0.6340318	-0.2503399
oxygen + phosphate	Atlantic	(26.5,26.75]	-0.7647928	-0.8281720	-0.6498762
oxygen + phosphate	Atlantic	(26.75,27]	-0.7743550	-0.8714102	-0.6807798
oxygen + phosphate	Atlantic	(27,27.25]	-0.6748693	-0.7574642	-0.5326930
oxygen + phosphate	Atlantic	(27.25,27.5]	-0.4878919	-0.6095132	-0.3610448
oxygen + phosphate	Atlantic	(27.5,27.75]	-0.6639666	-0.8346478	-0.4787250
oxygen + phosphate	Atlantic	(27.75,27.85]	-0.8808883	-0.9296785	-0.8562542
oxygen + phosphate	Atlantic	(27.85,27.95]	-0.9158667	-0.9438711	-0.8972977
oxygen + phosphate	Atlantic	(27.95,28.05]	-0.9287904	-0.9647496	-0.8937457
oxygen + phosphate	Atlantic	(28.05,28.1]	-0.9393797	-0.9822157	-0.8922176
oxygen + phosphate	Atlantic	(28.1,28.15]	-0.9584996	-0.9641119	-0.9526257
oxygen + phosphate	Atlantic	(28.15,28.2]	-0.9893669	-0.9941651	-0.9808489
oxygen + phosphate	Atlantic	(28.2, Inf]	-0.8387832	-0.9065604	-0.7960997
oxygen + phosphate	Indo-Pacific	(-Inf,26]	-0.7930285	-0.9142219	-0.7019392
oxygen + phosphate	Indo-Pacific	(26,26.5]	-0.8864940	-0.9082971	-0.8594038
oxygen + phosphate	Indo-Pacific	(26.5,26.75]	-0.8902712	-0.9168553	-0.8728122
oxygen + phosphate	Indo-Pacific	(26.75,27]	-0.8842393	-0.8898956	-0.8744815
oxygen + phosphate	Indo-Pacific	(27,27.25]	-0.9233286	-0.9555708	-0.8761859
oxygen + phosphate	Indo-Pacific	(27.25,27.5]	-0.9395039	-0.9631710	-0.8950246
oxygen + phosphate	Indo-Pacific	(27.5,27.75]	-0.9521420	-0.9704333	-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]	0.3528865	0.0500131	0.5970716
oxygen + phosphate_star	Atlantic	(26,26.5]	-0.0319199	-0.4264965	0.2905837
oxygen + phosphate_star	Atlantic	(26.5,26.75]	-0.2731943	-0.4598066	-0.1296881
oxygen + phosphate_star	Atlantic	(26.75,27]	-0.0391704	-0.1287144	0.0366768
oxygen + phosphate_star	Atlantic	(27,27.25]	0.0975925	-0.0997210	0.2017008
oxygen + phosphate_star	Atlantic	(27.25,27.5]	0.1736420	-0.0503131	0.3089785
oxygen + phosphate_star	Atlantic	(27.5,27.75]	-0.3120462	-0.5272656	-0.0896321
oxygen + phosphate_star	Atlantic	(27.75,27.85]	-0.6523957	-0.7566859	-0.5982221
oxygen + phosphate_star	Atlantic	(27.85,27.95]	-0.6234716	-0.7023252	-0.5429232
oxygen + phosphate_star	Atlantic	(27.95,28.05]	-0.7512223	-0.8819436	-0.6783013
oxygen + phosphate_star	Atlantic	(28.05,28.1]	-0.8327954	-0.9487435	-0.7332019
oxygen + phosphate_star	Atlantic	(28.1,28.15]	-0.8825460	-0.8983426	-0.8725450
oxygen + phosphate_star	Atlantic	(28.15,28.2]	-0.9700198	-0.9835994	-0.9472213
oxygen + phosphate_star	Atlantic	(28.2, Inf]	-0.6201236	-0.7758158	-0.5387402
oxygen + phosphate_star	Indo-Pacific	(-Inf,26]	-0.3861119	-0.6074860	-0.1539277
oxygen + phosphate_star	Indo-Pacific	(26,26.5]	-0.4255621	-0.4676614	-0.3769321
oxygen + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.2775835	-0.4205419	-0.0071261
oxygen + phosphate_star	Indo-Pacific	(26.75,27]	-0.2179551	-0.3107928	-0.1579429
oxygen + phosphate_star	Indo-Pacific	(27,27.25]	-0.0170436	-0.1348686	0.1312766
oxygen + phosphate_star	Indo-Pacific	(27.25,27.5]	0.4571403	0.3974966	0.5157307
oxygen + phosphate_star	Indo-Pacific	(27.5,27.75]	0.3199847	-0.1091433	0.6122944
oxygen + phosphate_star	Indo-Pacific	(27.75,27.85]	0.5158211	0.4360726	0.6144466
oxygen + phosphate_star	Indo-Pacific	(27.85,27.95]	0.1146866	0.0598608	0.1772438
oxygen + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.1571118	-0.2433196	-0.0445188
oxygen + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.3362079	-0.4034532	-0.2746486
oxygen + phosphate_star	Indo-Pacific	(28.1, Inf]	0.7065573	0.6673037	0.7342386
oxygen + silicate	Atlantic	(-Inf,26]	0.0740460	-0.1715993	0.2547323
oxygen + silicate	Atlantic	(26,26.5]	-0.3515704	-0.4412467	-0.2235934
oxygen + silicate	Atlantic	(26.5,26.75]	-0.7836869	-0.8436954	-0.7158471
oxygen + silicate	Atlantic	(26.75,27]	-0.7944084	-0.8525194	-0.7406337
oxygen + silicate	Atlantic	(27,27.25]	-0.6127201	-0.7169366	-0.5261458
oxygen + silicate	Atlantic	(27.25,27.5]	-0.1942779	-0.4764353	0.0213081
oxygen + silicate	Atlantic	(27.5,27.75]	-0.4015912	-0.5576857	-0.2067138
oxygen + silicate	Atlantic	(27.75,27.85]	-0.7635908	-0.8042959	-0.7344798
oxygen + silicate	Atlantic	(27.85,27.95]	-0.8380938	-0.8686412	-0.8205418
oxygen + silicate	Atlantic	(27.95,28.05]	-0.8959268	-0.9213483	-0.8675450
oxygen + silicate	Atlantic	(28.05,28.1]	-0.9353880	-0.9704777	-0.8998925
oxygen + silicate	Atlantic	(28.1,28.15]	-0.9499802	-0.9535507	-0.9460925
oxygen + silicate	Atlantic	(28.15,28.2]	-0.9877779	-0.9917614	-0.9805963
oxygen + silicate	Atlantic	(28.2, Inf]	-0.8490122	-0.8881395	-0.8031895
oxygen + silicate	Indo-Pacific	(-Inf,26]	-0.5099508	-0.7068590	-0.3570615
oxygen + silicate	Indo-Pacific	(26,26.5]	-0.5398888	-0.6683985	-0.4221230
oxygen + silicate	Indo-Pacific	(26.5,26.75]	-0.4981957	-0.6493148	-0.2760317
oxygen + silicate	Indo-Pacific	(26.75,27]	-0.6376236	-0.6739034	-0.5692528
oxygen + silicate	Indo-Pacific	(27,27.25]	-0.7926824	-0.8597978	-0.6943939
oxygen + silicate	Indo-Pacific	(27.25,27.5]	-0.8486711	-0.9067036	-0.7684755
oxygen + silicate	Indo-Pacific	(27.5,27.75]	-0.8755877	-0.9227396	-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]	0.8417941	0.6992611	0.9358873
phosphate + phosphate_star	Atlantic	(26,26.5]	0.9014826	0.8536369	0.9698602
phosphate + phosphate_star	Atlantic	(26.5,26.75]	0.8221100	0.7499166	0.8785106
phosphate + phosphate_star	Atlantic	(26.75,27]	0.6462558	0.4582646	0.7495924
phosphate + phosphate_star	Atlantic	(27,27.25]	0.6554500	0.4963605	0.7485194
phosphate + phosphate_star	Atlantic	(27.25,27.5]	0.7675629	0.6750316	0.8224384
phosphate + phosphate_star	Atlantic	(27.5,27.75]	0.9127247	0.9080826	0.9173402
phosphate + phosphate_star	Atlantic	(27.75,27.85]	0.9327288	0.9261612	0.9443083
phosphate + phosphate_star	Atlantic	(27.85,27.95]	0.8834459	0.8468075	0.9054896
phosphate + phosphate_star	Atlantic	(27.95,28.05]	0.9404093	0.9033721	0.9749010
phosphate + phosphate_star	Atlantic	(28.05,28.1]	0.9713228	0.9612726	0.9912106
phosphate + phosphate_star	Atlantic	(28.1,28.15]	0.9798787	0.9754099	0.9827341
phosphate + phosphate_star	Atlantic	(28.15,28.2]	0.9950335	0.9915205	0.9973162
phosphate + phosphate_star	Atlantic	(28.2, Inf]	0.9465203	0.9311984	0.9696368
phosphate + phosphate_star	Indo-Pacific	(-Inf,26]	0.8617496	0.8117964	0.8962017
phosphate + phosphate_star	Indo-Pacific	(26,26.5]	0.7940721	0.7552344	0.8324453
phosphate + phosphate_star	Indo-Pacific	(26.5,26.75]	0.6767405	0.4942636	0.7995575
phosphate + phosphate_star	Indo-Pacific	(26.75,27]	0.6465057	0.5909912	0.7328202
phosphate + phosphate_star	Indo-Pacific	(27,27.25]	0.3913168	0.3627796	0.4209450
phosphate + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.1358574	-0.2023155	-0.0794665
phosphate + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.0387328	-0.2587534	0.3458440
phosphate + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.3193581	-0.4896367	-0.1615271
phosphate + phosphate_star	Indo-Pacific	(27.85,27.95]	0.1145057	0.0487248	0.2281269
phosphate + phosphate_star	Indo-Pacific	(27.95,28.05]	0.4623862	0.3254063	0.5807686
phosphate + phosphate_star	Indo-Pacific	(28.05,28.1]	0.6478739	0.6019465	0.7257729
phosphate + phosphate_star	Indo-Pacific	(28.1, Inf]	0.0044632	-0.0947674	0.1490954
sal + aou	Atlantic	(-Inf,26]	-0.1432646	-0.4515416	0.3475255
sal + aou	Atlantic	(26,26.5]	-0.3201926	-0.7540350	-0.0089766
sal + aou	Atlantic	(26.5,26.75]	-0.3104417	-0.5297627	-0.0916656
sal + aou	Atlantic	(26.75,27]	-0.1615592	-0.2786631	0.0067566
sal + aou	Atlantic	(27,27.25]	-0.1165768	-0.3548045	0.0723922
sal + aou	Atlantic	(27.25,27.5]	-0.0813213	-0.3370859	0.1745205
sal + aou	Atlantic	(27.5,27.75]	-0.5179065	-0.6268218	-0.4303694
sal + aou	Atlantic	(27.75,27.85]	-0.5789004	-0.6947863	-0.4959685
sal + aou	Atlantic	(27.85,27.95]	-0.3629963	-0.4900203	-0.1651523
sal + aou	Atlantic	(27.95,28.05]	-0.5444372	-0.7817031	-0.2117975
sal + aou	Atlantic	(28.05,28.1]	-0.7522458	-0.8748602	-0.6651277
sal + aou	Atlantic	(28.1,28.15]	-0.8192995	-0.8471379	-0.7855980
sal + aou	Atlantic	(28.15,28.2]	-0.9570206	-0.9830836	-0.9258731
sal + aou	Atlantic	(28.2, Inf]	-0.7460679	-0.8727438	-0.6675143
sal + aou	Indo-Pacific	(-Inf,26]	-0.1009165	-0.1352064	-0.0327037
sal + aou	Indo-Pacific	(26,26.5]	-0.0454146	-0.2481356	0.1363007
sal + aou	Indo-Pacific	(26.5,26.75]	-0.0497733	-0.3658215	0.2665079
sal + aou	Indo-Pacific	(26.75,27]	-0.1459755	-0.3473383	0.0457714
sal + aou	Indo-Pacific	(27,27.25]	-0.0649881	-0.1830167	0.1660639
sal + aou	Indo-Pacific	(27.25,27.5]	0.1377868	0.0643601	0.2796906
sal + aou	Indo-Pacific	(27.5,27.75]	0.2886377	0.1342531	0.4871885
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]	-0.3068160	-0.6018367	-0.0830958
sal + oxygen	Atlantic	(26,26.5]	-0.0940830	-0.4081977	0.3368707
sal + oxygen	Atlantic	(26.5,26.75]	0.0922200	-0.0688608	0.3329757
sal + oxygen	Atlantic	(26.75,27]	-0.0209838	-0.1260055	0.0825327
sal + oxygen	Atlantic	(27,27.25]	-0.0855749	-0.2229050	0.1542667
sal + oxygen	Atlantic	(27.25,27.5]	-0.1912696	-0.3922490	0.0699327
sal + oxygen	Atlantic	(27.5,27.75]	0.2325269	0.0201987	0.4689222
sal + oxygen	Atlantic	(27.75,27.85]	0.4185409	0.2998878	0.5925420
sal + oxygen	Atlantic	(27.85,27.95]	0.2436699	0.0265106	0.4082932
sal + oxygen	Atlantic	(27.95,28.05]	0.4447584	0.1139659	0.7153856
sal + oxygen	Atlantic	(28.05,28.1]	0.6624337	0.5789025	0.8292691
sal + oxygen	Atlantic	(28.1,28.15]	0.7534079	0.7203871	0.7787160
sal + oxygen	Atlantic	(28.15,28.2]	0.9410378	0.8997154	0.9747515
sal + oxygen	Atlantic	(28.2, Inf]	0.6530541	0.5554187	0.8087762
sal + oxygen	Indo-Pacific	(-Inf,26]	-0.2049084	-0.3225624	-0.0853819
sal + oxygen	Indo-Pacific	(26,26.5]	-0.1337941	-0.2895367	0.0329220
sal + oxygen	Indo-Pacific	(26.5,26.75]	-0.1107593	-0.4189775	0.1870082
sal + oxygen	Indo-Pacific	(26.75,27]	-0.0259236	-0.2113746	0.1739144
sal + oxygen	Indo-Pacific	(27,27.25]	-0.0719179	-0.3515906	0.0715461
sal + oxygen	Indo-Pacific	(27.25,27.5]	-0.2467897	-0.4392475	-0.1477670
sal + oxygen	Indo-Pacific	(27.5,27.75]	-0.3947749	-0.5708843	-0.2210226
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]	-0.6674974	-0.7820996	-0.5430745
sal + phosphate	Atlantic	(26,26.5]	-0.8108444	-0.9106026	-0.7555726
sal + phosphate	Atlantic	(26.5,26.75]	-0.6648296	-0.7958907	-0.4410535
sal + phosphate	Atlantic	(26.75,27]	-0.5830817	-0.7103664	-0.3527974
sal + phosphate	Atlantic	(27,27.25]	-0.6473049	-0.7748703	-0.4488195
sal + phosphate	Atlantic	(27.25,27.5]	-0.7277690	-0.8205324	-0.5666448
sal + phosphate	Atlantic	(27.5,27.75]	-0.8381648	-0.8500802	-0.8286912
sal + phosphate	Atlantic	(27.75,27.85]	-0.7676593	-0.8124161	-0.7242229
sal + phosphate	Atlantic	(27.85,27.95]	-0.5753866	-0.6558290	-0.4163852
sal + phosphate	Atlantic	(27.95,28.05]	-0.6925713	-0.8394380	-0.4308056
sal + phosphate	Atlantic	(28.05,28.1]	-0.8424815	-0.8975681	-0.7678284
sal + phosphate	Atlantic	(28.1,28.15]	-0.8850963	-0.9173239	-0.8539576
sal + phosphate	Atlantic	(28.15,28.2]	-0.9626776	-0.9794588	-0.9536888
sal + phosphate	Atlantic	(28.2, Inf]	-0.9500395	-0.9784209	-0.9210421
sal + phosphate	Indo-Pacific	(-Inf,26]	-0.2199671	-0.2522199	-0.1978531
sal + phosphate	Indo-Pacific	(26,26.5]	-0.2773404	-0.4960600	-0.0980940
sal + phosphate	Indo-Pacific	(26.5,26.75]	-0.3020486	-0.6021266	-0.0358526
sal + phosphate	Indo-Pacific	(26.75,27]	-0.4004903	-0.6011400	-0.2166537
sal + phosphate	Indo-Pacific	(27,27.25]	-0.2470692	-0.3543849	-0.0875812
sal + phosphate	Indo-Pacific	(27.25,27.5]	0.0385895	-0.0184517	0.0674829
sal + phosphate	Indo-Pacific	(27.5,27.75]	0.3251282	0.1069794	0.6706634
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]	-0.8254683	-0.8980924	-0.7017069
sal + phosphate_star	Atlantic	(26,26.5]	-0.9626072	-0.9663574	-0.9589304
sal + phosphate_star	Atlantic	(26.5,26.75]	-0.9261629	-0.9792901	-0.8219973
sal + phosphate_star	Atlantic	(26.75,27]	-0.9712580	-0.9870860	-0.9469998
sal + phosphate_star	Atlantic	(27,27.25]	-0.9805519	-0.9853382	-0.9712125
sal + phosphate_star	Atlantic	(27.25,27.5]	-0.9731320	-0.9837478	-0.9521275
sal + phosphate_star	Atlantic	(27.5,27.75]	-0.9470258	-0.9551832	-0.9327318
sal + phosphate_star	Atlantic	(27.75,27.85]	-0.9134508	-0.9232617	-0.9045425
sal + phosphate_star	Atlantic	(27.85,27.95]	-0.8452080	-0.8714906	-0.7945287
sal + phosphate_star	Atlantic	(27.95,28.05]	-0.8461318	-0.9222741	-0.7178387
sal + phosphate_star	Atlantic	(28.05,28.1]	-0.9101646	-0.9446164	-0.8593220
sal + phosphate_star	Atlantic	(28.1,28.15]	-0.9339203	-0.9602568	-0.9092295
sal + phosphate_star	Atlantic	(28.15,28.2]	-0.9655413	-0.9761462	-0.9510508
sal + phosphate_star	Atlantic	(28.2, Inf]	-0.9859854	-0.9940342	-0.9793382
sal + phosphate_star	Indo-Pacific	(-Inf,26]	-0.5171328	-0.5389392	-0.4999915
sal + phosphate_star	Indo-Pacific	(26,26.5]	-0.7240844	-0.8392745	-0.6202371
sal + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.8405565	-0.9178041	-0.7841366
sal + phosphate_star	Indo-Pacific	(26.75,27]	-0.8890168	-0.9339791	-0.8427789
sal + phosphate_star	Indo-Pacific	(27,27.25]	-0.8325452	-0.8599267	-0.7857501
sal + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.5923856	-0.8520808	-0.3259006
sal + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.1234873	-0.7611786	0.5427391
sal + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.2722999	-0.5935319	0.2022713
sal + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.3835630	-0.5877746	-0.0749978
sal + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.7494771	-0.7923241	-0.6991280
sal + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.8194795	-0.8746502	-0.7474471
sal + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.8277533	-0.8552088	-0.8111767
sal + silicate	Atlantic	(-Inf,26]	-0.7261494	-0.7525608	-0.6740976
sal + silicate	Atlantic	(26,26.5]	-0.7796266	-0.9153686	-0.7102851
sal + silicate	Atlantic	(26.5,26.75]	-0.5866197	-0.7294011	-0.3798612
sal + silicate	Atlantic	(26.75,27]	-0.4743076	-0.5946755	-0.2657279
sal + silicate	Atlantic	(27,27.25]	-0.6265728	-0.7124112	-0.5266697
sal + silicate	Atlantic	(27.25,27.5]	-0.7804214	-0.8072218	-0.7380133
sal + silicate	Atlantic	(27.5,27.75]	-0.8335519	-0.8724894	-0.8104220
sal + silicate	Atlantic	(27.75,27.85]	-0.8068261	-0.8711408	-0.7518060
sal + silicate	Atlantic	(27.85,27.95]	-0.6645767	-0.7424304	-0.5233429
sal + silicate	Atlantic	(27.95,28.05]	-0.7297796	-0.8813418	-0.4777178
sal + silicate	Atlantic	(28.05,28.1]	-0.8586566	-0.9215330	-0.7987466
sal + silicate	Atlantic	(28.1,28.15]	-0.8986062	-0.9139383	-0.8712317
sal + silicate	Atlantic	(28.15,28.2]	-0.9600948	-0.9814279	-0.9324982
sal + silicate	Atlantic	(28.2, Inf]	-0.9288831	-0.9859207	-0.8845923
sal + silicate	Indo-Pacific	(-Inf,26]	-0.5270930	-0.5734450	-0.4408109
sal + silicate	Indo-Pacific	(26,26.5]	-0.5594750	-0.6826305	-0.4549151
sal + silicate	Indo-Pacific	(26.5,26.75]	-0.6672722	-0.8095833	-0.5567328
sal + silicate	Indo-Pacific	(26.75,27]	-0.6555953	-0.7628181	-0.4768095
sal + silicate	Indo-Pacific	(27,27.25]	-0.4558834	-0.5432176	-0.3205614
sal + silicate	Indo-Pacific	(27.25,27.5]	-0.1485818	-0.1965007	-0.0874834
sal + silicate	Indo-Pacific	(27.5,27.75]	0.1190636	-0.0579965	0.3812169
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]	0.9243866	0.8381654	0.9836628
sal + tem	Atlantic	(26,26.5]	0.9689040	0.9614255	0.9743585
sal + tem	Atlantic	(26.5,26.75]	0.9689940	0.9283729	0.9899580
sal + tem	Atlantic	(26.75,27]	0.9731618	0.9560699	0.9835156
sal + tem	Atlantic	(27,27.25]	0.9739276	0.9655494	0.9804064
sal + tem	Atlantic	(27.25,27.5]	0.9651866	0.9459424	0.9754742
sal + tem	Atlantic	(27.5,27.75]	0.9511977	0.9293291	0.9632293
sal + tem	Atlantic	(27.75,27.85]	0.9721381	0.9542083	0.9813340
sal + tem	Atlantic	(27.85,27.95]	0.9291113	0.8991159	0.9512567
sal + tem	Atlantic	(27.95,28.05]	0.8732041	0.8069203	0.9305324
sal + tem	Atlantic	(28.05,28.1]	0.9499251	0.9127320	0.9696202
sal + tem	Atlantic	(28.1,28.15]	0.9418760	0.9168693	0.9692410
sal + tem	Atlantic	(28.15,28.2]	0.8792869	0.8448086	0.9065752
sal + tem	Atlantic	(28.2, Inf]	0.1242844	0.0276649	0.1790116
sal + tem	Indo-Pacific	(-Inf,26]	0.7709446	0.7412215	0.8182287
sal + tem	Indo-Pacific	(26,26.5]	0.9286350	0.8849934	0.9530410
sal + tem	Indo-Pacific	(26.5,26.75]	0.9782777	0.9690853	0.9832743
sal + tem	Indo-Pacific	(26.75,27]	0.9768624	0.9720412	0.9799282
sal + tem	Indo-Pacific	(27,27.25]	0.9501887	0.9326527	0.9710015
sal + tem	Indo-Pacific	(27.25,27.5]	0.8810593	0.8280724	0.9585099
sal + tem	Indo-Pacific	(27.5,27.75]	0.8641666	0.7977158	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]	0.6416577	0.6151173	0.6703874
silicate + phosphate	Atlantic	(26,26.5]	0.9168791	0.9020743	0.9253733
silicate + phosphate	Atlantic	(26.5,26.75]	0.9668808	0.9622374	0.9712821
silicate + phosphate	Atlantic	(26.75,27]	0.9507435	0.9407716	0.9610085
silicate + phosphate	Atlantic	(27,27.25]	0.9377999	0.9185888	0.9556204
silicate + phosphate	Atlantic	(27.25,27.5]	0.8621449	0.7619586	0.9280920
silicate + phosphate	Atlantic	(27.5,27.75]	0.8959625	0.8913960	0.9025059
silicate + phosphate	Atlantic	(27.75,27.85]	0.9536127	0.9486100	0.9622012
silicate + phosphate	Atlantic	(27.85,27.95]	0.9701883	0.9660126	0.9779890
silicate + phosphate	Atlantic	(27.95,28.05]	0.9796016	0.9759663	0.9861861
silicate + phosphate	Atlantic	(28.05,28.1]	0.9891717	0.9850664	0.9915874
silicate + phosphate	Atlantic	(28.1,28.15]	0.9932582	0.9920966	0.9941059
silicate + phosphate	Atlantic	(28.15,28.2]	0.9945504	0.9904101	0.9979614
silicate + phosphate	Atlantic	(28.2, Inf]	0.9863763	0.9807922	0.9966812
silicate + phosphate	Indo-Pacific	(-Inf,26]	0.7970067	0.7532736	0.8266286
silicate + phosphate	Indo-Pacific	(26,26.5]	0.7619353	0.6642843	0.8380775
silicate + phosphate	Indo-Pacific	(26.5,26.75]	0.7521585	0.5918573	0.8429329
silicate + phosphate	Indo-Pacific	(26.75,27]	0.8535242	0.8040469	0.8812693
silicate + phosphate	Indo-Pacific	(27,27.25]	0.8982683	0.8736363	0.9330540
silicate + phosphate	Indo-Pacific	(27.25,27.5]	0.8839535	0.8592060	0.9262076
silicate + phosphate	Indo-Pacific	(27.5,27.75]	0.8684476	0.8459587	0.8983565
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]	0.6366914	0.5879842	0.7021616
silicate + phosphate_star	Atlantic	(26,26.5]	0.8440720	0.7942715	0.9407649
silicate + phosphate_star	Atlantic	(26.5,26.75]	0.7613263	0.7229402	0.8197783
silicate + phosphate_star	Atlantic	(26.75,27]	0.5519551	0.3915525	0.6496392
silicate + phosphate_star	Atlantic	(27,27.25]	0.6489643	0.5898768	0.7005654
silicate + phosphate_star	Atlantic	(27.25,27.5]	0.8415918	0.8273388	0.8510667
silicate + phosphate_star	Atlantic	(27.5,27.75]	0.9306729	0.9174791	0.9551222
silicate + phosphate_star	Atlantic	(27.75,27.85]	0.9493268	0.9353454	0.9676196
silicate + phosphate_star	Atlantic	(27.85,27.95]	0.9164859	0.8884907	0.9359810
silicate + phosphate_star	Atlantic	(27.95,28.05]	0.9331219	0.8893533	0.9698010
silicate + phosphate_star	Atlantic	(28.05,28.1]	0.9567132	0.9419911	0.9853204
silicate + phosphate_star	Atlantic	(28.1,28.15]	0.9748909	0.9683881	0.9855393
silicate + phosphate_star	Atlantic	(28.15,28.2]	0.9870362	0.9759047	0.9955390
silicate + phosphate_star	Atlantic	(28.2, Inf]	0.9205540	0.8771634	0.9753485
silicate + phosphate_star	Indo-Pacific	(-Inf,26]	0.7890529	0.7522686	0.8318447
silicate + phosphate_star	Indo-Pacific	(26,26.5]	0.7857894	0.7483522	0.8083937
silicate + phosphate_star	Indo-Pacific	(26.5,26.75]	0.8015539	0.7209918	0.8535863
silicate + phosphate_star	Indo-Pacific	(26.75,27]	0.7451556	0.7159369	0.7756234
silicate + phosphate_star	Indo-Pacific	(27,27.25]	0.4367303	0.4056670	0.4543556
silicate + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.1848546	-0.2468943	-0.0670824
silicate + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.2136161	-0.3915646	-0.0028587
silicate + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.4132408	-0.6129553	-0.2477974
silicate + phosphate_star	Indo-Pacific	(27.85,27.95]	0.0579413	0.0037064	0.1476500
silicate + phosphate_star	Indo-Pacific	(27.95,28.05]	0.4012843	0.2858781	0.4946502
silicate + phosphate_star	Indo-Pacific	(28.05,28.1]	0.5528485	0.5198432	0.6009765
silicate + phosphate_star	Indo-Pacific	(28.1, Inf]	0.0305801	-0.0810146	0.1870916
tem + aou	Atlantic	(-Inf,26]	-0.1743816	-0.4969123	0.3256589
tem + aou	Atlantic	(26,26.5]	-0.3580329	-0.8053558	-0.0649893
tem + aou	Atlantic	(26.5,26.75]	-0.3722841	-0.5394586	-0.2549241
tem + aou	Atlantic	(26.75,27]	-0.1683674	-0.2684537	-0.0276806
tem + aou	Atlantic	(27,27.25]	-0.0682557	-0.2812963	0.0881961
tem + aou	Atlantic	(27.25,27.5]	-0.0475537	-0.2994314	0.1889626
tem + aou	Atlantic	(27.5,27.75]	-0.4692662	-0.5735174	-0.3726367
tem + aou	Atlantic	(27.75,27.85]	-0.5371895	-0.5972745	-0.4812475
tem + aou	Atlantic	(27.85,27.95]	-0.2871178	-0.4114486	-0.0801036
tem + aou	Atlantic	(27.95,28.05]	-0.5029701	-0.6507725	-0.3144163
tem + aou	Atlantic	(28.05,28.1]	-0.6055560	-0.7966052	-0.4385820
tem + aou	Atlantic	(28.1,28.15]	-0.6251286	-0.7359709	-0.5162407
tem + aou	Atlantic	(28.15,28.2]	-0.7568571	-0.8386287	-0.7053858
tem + aou	Atlantic	(28.2, Inf]	0.3945630	0.3290807	0.4367369
tem + aou	Indo-Pacific	(-Inf,26]	-0.2723472	-0.4109832	-0.1756575
tem + aou	Indo-Pacific	(26,26.5]	-0.1190502	-0.2974707	-0.0164962
tem + aou	Indo-Pacific	(26.5,26.75]	-0.0400474	-0.3350699	0.2574432
tem + aou	Indo-Pacific	(26.75,27]	-0.1641702	-0.3441368	-0.0129495
tem + aou	Indo-Pacific	(27,27.25]	-0.1429234	-0.2802564	0.0782669
tem + aou	Indo-Pacific	(27.25,27.5]	0.1101352	0.0034490	0.2629607
tem + aou	Indo-Pacific	(27.5,27.75]	0.3195645	0.1858558	0.5050516
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]	-0.3030869	-0.5951659	-0.1206498
tem + oxygen	Atlantic	(26,26.5]	-0.0631834	-0.3662989	0.3951096
tem + oxygen	Atlantic	(26.5,26.75]	0.1501520	0.0229157	0.3410353
tem + oxygen	Atlantic	(26.75,27]	-0.0187923	-0.0969456	0.0678025
tem + oxygen	Atlantic	(27,27.25]	-0.1392797	-0.2470567	0.0727534
tem + oxygen	Atlantic	(27.25,27.5]	-0.2342907	-0.4189103	0.0234851
tem + oxygen	Atlantic	(27.5,27.75]	0.1626846	-0.0599984	0.3923956
tem + oxygen	Atlantic	(27.75,27.85]	0.3665730	0.2786541	0.4775132
tem + oxygen	Atlantic	(27.85,27.95]	0.1550249	-0.0688684	0.2712348
tem + oxygen	Atlantic	(27.95,28.05]	0.3748894	0.1904284	0.5513913
tem + oxygen	Atlantic	(28.05,28.1]	0.4937831	0.3267804	0.7353029
tem + oxygen	Atlantic	(28.1,28.15]	0.5386124	0.4288408	0.6502208
tem + oxygen	Atlantic	(28.15,28.2]	0.7204515	0.6694534	0.8135067
tem + oxygen	Atlantic	(28.2, Inf]	-0.5323950	-0.5910094	-0.4520965
tem + oxygen	Indo-Pacific	(-Inf,26]	-0.1031201	-0.2745694	-0.0100674
tem + oxygen	Indo-Pacific	(26,26.5]	-0.0728758	-0.1580124	0.0729347
tem + oxygen	Indo-Pacific	(26.5,26.75]	-0.1251586	-0.4163080	0.1513389
tem + oxygen	Indo-Pacific	(26.75,27]	-0.0123104	-0.1574711	0.1667299
tem + oxygen	Indo-Pacific	(27,27.25]	-0.0002536	-0.2729761	0.1640281
tem + oxygen	Indo-Pacific	(27.25,27.5]	-0.2324197	-0.4322640	-0.1005341
tem + oxygen	Indo-Pacific	(27.5,27.75]	-0.4416834	-0.6026866	-0.2929571
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]	-0.5737454	-0.6217540	-0.4813899
tem + phosphate	Atlantic	(26,26.5]	-0.8127119	-0.9137204	-0.7461798
tem + phosphate	Atlantic	(26.5,26.75]	-0.7219494	-0.8013726	-0.5982804
tem + phosphate	Atlantic	(26.75,27]	-0.5908528	-0.7059281	-0.3879969
tem + phosphate	Atlantic	(27,27.25]	-0.6118580	-0.7235873	-0.4335709
tem + phosphate	Atlantic	(27.25,27.5]	-0.7028507	-0.7945460	-0.5507688
tem + phosphate	Atlantic	(27.5,27.75]	-0.7979194	-0.8160782	-0.7785202
tem + phosphate	Atlantic	(27.75,27.85]	-0.7386035	-0.7599320	-0.7137399
tem + phosphate	Atlantic	(27.85,27.95]	-0.4996791	-0.6373654	-0.3337133
tem + phosphate	Atlantic	(27.95,28.05]	-0.6304825	-0.7264179	-0.4548313
tem + phosphate	Atlantic	(28.05,28.1]	-0.7140492	-0.8185893	-0.5630099
tem + phosphate	Atlantic	(28.1,28.15]	-0.7129984	-0.8231463	-0.6151388
tem + phosphate	Atlantic	(28.15,28.2]	-0.7561551	-0.8159999	-0.6922176
tem + phosphate	Atlantic	(28.2, Inf]	0.1149220	0.0701460	0.1430906
tem + phosphate	Indo-Pacific	(-Inf,26]	-0.4324320	-0.5910107	-0.2998380
tem + phosphate	Indo-Pacific	(26,26.5]	-0.3679478	-0.5543036	-0.2683633
tem + phosphate	Indo-Pacific	(26.5,26.75]	-0.3051266	-0.5843808	-0.0603493
tem + phosphate	Indo-Pacific	(26.75,27]	-0.4338290	-0.6099013	-0.2910911
tem + phosphate	Indo-Pacific	(27,27.25]	-0.3433012	-0.4220860	-0.1961448
tem + phosphate	Indo-Pacific	(27.25,27.5]	-0.0184775	-0.1096232	0.0284870
tem + phosphate	Indo-Pacific	(27.5,27.75]	0.3479935	0.1237490	0.6725195
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]	-0.7318945	-0.8216824	-0.6327666
tem + phosphate_star	Atlantic	(26,26.5]	-0.9514893	-0.9662142	-0.9440270
tem + phosphate_star	Atlantic	(26.5,26.75]	-0.9570354	-0.9831278	-0.9089610
tem + phosphate_star	Atlantic	(26.75,27]	-0.9793217	-0.9880366	-0.9660538
tem + phosphate_star	Atlantic	(27,27.25]	-0.9842653	-0.9897957	-0.9757177
tem + phosphate_star	Atlantic	(27.25,27.5]	-0.9755946	-0.9852903	-0.9573820
tem + phosphate_star	Atlantic	(27.5,27.75]	-0.9333588	-0.9529755	-0.9026717
tem + phosphate_star	Atlantic	(27.75,27.85]	-0.9073062	-0.9275607	-0.8905753
tem + phosphate_star	Atlantic	(27.85,27.95]	-0.8004039	-0.8743779	-0.7502663
tem + phosphate_star	Atlantic	(27.95,28.05]	-0.7884896	-0.8826831	-0.6772425
tem + phosphate_star	Atlantic	(28.05,28.1]	-0.8201468	-0.8893416	-0.7112782
tem + phosphate_star	Atlantic	(28.1,28.15]	-0.8007936	-0.8922391	-0.7248093
tem + phosphate_star	Atlantic	(28.15,28.2]	-0.7712762	-0.8122706	-0.7028588
tem + phosphate_star	Atlantic	(28.2, Inf]	-0.1489882	-0.2179165	-0.0480381
tem + phosphate_star	Indo-Pacific	(-Inf,26]	-0.7506745	-0.8459975	-0.6170532
tem + phosphate_star	Indo-Pacific	(26,26.5]	-0.8213438	-0.8986420	-0.7608949
tem + phosphate_star	Indo-Pacific	(26.5,26.75]	-0.8671106	-0.9290601	-0.8071063
tem + phosphate_star	Indo-Pacific	(26.75,27]	-0.9353959	-0.9612253	-0.9085892
tem + phosphate_star	Indo-Pacific	(27,27.25]	-0.9136393	-0.9312277	-0.8790975
tem + phosphate_star	Indo-Pacific	(27.25,27.5]	-0.7134369	-0.9113800	-0.5004017
tem + phosphate_star	Indo-Pacific	(27.5,27.75]	-0.2140148	-0.8192619	0.4267555
tem + phosphate_star	Indo-Pacific	(27.75,27.85]	-0.4011292	-0.6718990	0.0137202
tem + phosphate_star	Indo-Pacific	(27.85,27.95]	-0.5044227	-0.6762457	-0.2610595
tem + phosphate_star	Indo-Pacific	(27.95,28.05]	-0.7343945	-0.8076554	-0.6766540
tem + phosphate_star	Indo-Pacific	(28.05,28.1]	-0.5964383	-0.6160697	-0.5749309
tem + phosphate_star	Indo-Pacific	(28.1, Inf]	-0.8757873	-0.8944860	-0.8648595
tem + silicate	Atlantic	(-Inf,26]	-0.6224072	-0.6907364	-0.5118555
tem + silicate	Atlantic	(26,26.5]	-0.7607022	-0.8811499	-0.6782082
tem + silicate	Atlantic	(26.5,26.75]	-0.6518273	-0.7401620	-0.5527532
tem + silicate	Atlantic	(26.75,27]	-0.5053257	-0.6058513	-0.3330611
tem + silicate	Atlantic	(27,27.25]	-0.6229851	-0.6895759	-0.5534387
tem + silicate	Atlantic	(27.25,27.5]	-0.8332092	-0.8378258	-0.8288195
tem + silicate	Atlantic	(27.5,27.75]	-0.8642311	-0.8919458	-0.8390068
tem + silicate	Atlantic	(27.75,27.85]	-0.8113282	-0.8564200	-0.7626576
tem + silicate	Atlantic	(27.85,27.95]	-0.6180989	-0.7277576	-0.4641837
tem + silicate	Atlantic	(27.95,28.05]	-0.7134765	-0.8095948	-0.5596467
tem + silicate	Atlantic	(28.05,28.1]	-0.7428275	-0.8611493	-0.6125043
tem + silicate	Atlantic	(28.1,28.15]	-0.7357393	-0.8171544	-0.6424877
tem + silicate	Atlantic	(28.15,28.2]	-0.7582635	-0.8228728	-0.7255889
tem + silicate	Atlantic	(28.2, Inf]	0.1328867	0.1035429	0.1811469
tem + silicate	Indo-Pacific	(-Inf,26]	-0.5967580	-0.7260970	-0.4499679
tem + silicate	Indo-Pacific	(26,26.5]	-0.6097280	-0.7156437	-0.4703853
tem + silicate	Indo-Pacific	(26.5,26.75]	-0.6660606	-0.8017637	-0.5602649
tem + silicate	Indo-Pacific	(26.75,27]	-0.6678028	-0.7561768	-0.5323795
tem + silicate	Indo-Pacific	(27,27.25]	-0.5247966	-0.6210395	-0.4123352
tem + silicate	Indo-Pacific	(27.25,27.5]	-0.2262236	-0.2669660	-0.1471327
tem + silicate	Indo-Pacific	(27.5,27.75]	0.0529397	-0.1198311	0.3062197
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]	0.1962379	-0.0371786	0.5033064
aou	Atlantic	(26,26.5]	-0.3152840	-0.6201297	-0.0224342
aou	Atlantic	(26.5,26.75]	-0.5840182	-0.6700148	-0.5402426
aou	Atlantic	(26.75,27]	-0.4939077	-0.4986205	-0.4872630
aou	Atlantic	(27,27.25]	-0.4424529	-0.5506422	-0.3846990
aou	Atlantic	(27.25,27.5]	-0.4374568	-0.5716618	-0.3101149
aou	Atlantic	(27.5,27.75]	-0.8087856	-0.8823577	-0.7454535
aou	Atlantic	(27.75,27.85]	-0.9368260	-0.9498178	-0.9249823
aou	Atlantic	(27.85,27.95]	-0.9467996	-0.9597906	-0.9359819
aou	Atlantic	(27.95,28.05]	-0.9206054	-0.9307407	-0.9142522
aou	Atlantic	(28.05,28.1]	-0.9040499	-0.9272739	-0.8806348
aou	Atlantic	(28.1,28.15]	-0.9307093	-0.9387451	-0.9164782
aou	Atlantic	(28.15,28.2]	-0.9672658	-0.9682740	-0.9657233
aou	Atlantic	(28.2, Inf]	-0.8359408	-0.9230036	-0.7911054
aou	Indo-Pacific	(-Inf,26]	-0.5149052	-0.6400200	-0.4472197
aou	Indo-Pacific	(26,26.5]	-0.8407364	-0.8517341	-0.8212178
aou	Indo-Pacific	(26.5,26.75]	-0.8411202	-0.8622968	-0.8157234
aou	Indo-Pacific	(26.75,27]	-0.8462493	-0.8901544	-0.8202075
aou	Indo-Pacific	(27,27.25]	-0.6228797	-0.6737912	-0.5758841
aou	Indo-Pacific	(27.25,27.5]	0.0068697	-0.0729025	0.0801465
aou	Indo-Pacific	(27.5,27.75]	-0.0416633	-0.4559617	0.2894476
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]	-0.2635989	-0.4741533	-0.1117546
oxygen	Atlantic	(26,26.5]	-0.0051740	-0.3123412	0.3404195
oxygen	Atlantic	(26.5,26.75]	0.4149548	0.2967826	0.5192255
oxygen	Atlantic	(26.75,27]	0.3365427	0.2898871	0.4019115
oxygen	Atlantic	(27,27.25]	0.2555653	0.1515054	0.3720205
oxygen	Atlantic	(27.25,27.5]	0.1787039	0.0903432	0.3328796
oxygen	Atlantic	(27.5,27.75]	0.5999598	0.4166954	0.7921388
oxygen	Atlantic	(27.75,27.85]	0.8706697	0.8398607	0.9156512
oxygen	Atlantic	(27.85,27.95]	0.9170948	0.8997904	0.9475655
oxygen	Atlantic	(27.95,28.05]	0.8992918	0.8635961	0.9300740
oxygen	Atlantic	(28.05,28.1]	0.8847504	0.8518059	0.9407247
oxygen	Atlantic	(28.1,28.15]	0.9205329	0.9015037	0.9390123
oxygen	Atlantic	(28.15,28.2]	0.9684661	0.9628147	0.9742852
oxygen	Atlantic	(28.2, Inf]	0.7669378	0.7075446	0.8786036
oxygen	Indo-Pacific	(-Inf,26]	0.5187811	0.4489442	0.6463468
oxygen	Indo-Pacific	(26,26.5]	0.7547055	0.7058046	0.7868059
oxygen	Indo-Pacific	(26.5,26.75]	0.7587996	0.7285108	0.7996299
oxygen	Indo-Pacific	(26.75,27]	0.7690282	0.7368726	0.8244207
oxygen	Indo-Pacific	(27,27.25]	0.6094642	0.5465735	0.6892912
oxygen	Indo-Pacific	(27.25,27.5]	0.0337696	-0.0490524	0.1245063
oxygen	Indo-Pacific	(27.5,27.75]	0.1252141	-0.2009100	0.5429088
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]	-0.4327703	-0.7948885	-0.1187246
phosphate	Atlantic	(26,26.5]	-0.7761612	-0.8379815	-0.6830420
phosphate	Atlantic	(26.5,26.75]	-0.8539502	-0.8694455	-0.8322186
phosphate	Atlantic	(26.75,27]	-0.8250796	-0.8759120	-0.7767510
phosphate	Atlantic	(27,27.25]	-0.8649319	-0.9020856	-0.8045281
phosphate	Atlantic	(27.25,27.5]	-0.9336948	-0.9586613	-0.9003928
phosphate	Atlantic	(27.5,27.75]	-0.9882297	-0.9905290	-0.9853573
phosphate	Atlantic	(27.75,27.85]	-0.9821239	-0.9869017	-0.9744831
phosphate	Atlantic	(27.85,27.95]	-0.9680738	-0.9712906	-0.9657589
phosphate	Atlantic	(27.95,28.05]	-0.9512347	-0.9627544	-0.9391833
phosphate	Atlantic	(28.05,28.1]	-0.9441532	-0.9553485	-0.9334168
phosphate	Atlantic	(28.1,28.15]	-0.9593734	-0.9672896	-0.9503788
phosphate	Atlantic	(28.15,28.2]	-0.9843571	-0.9870285	-0.9824927
phosphate	Atlantic	(28.2, Inf]	-0.9828049	-0.9927772	-0.9722113
phosphate	Indo-Pacific	(-Inf,26]	-0.5757096	-0.7038862	-0.5063925
phosphate	Indo-Pacific	(26,26.5]	-0.9334241	-0.9448860	-0.9231474
phosphate	Indo-Pacific	(26.5,26.75]	-0.9484077	-0.9541960	-0.9447109
phosphate	Indo-Pacific	(26.75,27]	-0.9433704	-0.9628345	-0.9204828
phosphate	Indo-Pacific	(27,27.25]	-0.7074515	-0.7269361	-0.6729956
phosphate	Indo-Pacific	(27.25,27.5]	-0.1313102	-0.2527567	-0.0331105
phosphate	Indo-Pacific	(27.5,27.75]	-0.2407063	-0.6995785	0.1761650
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]	-0.5716662	-0.7982668	-0.4395738
phosphate_star	Atlantic	(26,26.5]	-0.8787099	-0.9201545	-0.8431032
phosphate_star	Atlantic	(26.5,26.75]	-0.9183591	-0.9349912	-0.9090733
phosphate_star	Atlantic	(26.75,27]	-0.9092309	-0.9400878	-0.8541407
phosphate_star	Atlantic	(27,27.25]	-0.9150161	-0.9387045	-0.8863060
phosphate_star	Atlantic	(27.25,27.5]	-0.9252870	-0.9479061	-0.9077190
phosphate_star	Atlantic	(27.5,27.75]	-0.9336899	-0.9425117	-0.9257936
phosphate_star	Atlantic	(27.75,27.85]	-0.9113352	-0.9148401	-0.9076138
phosphate_star	Atlantic	(27.85,27.95]	-0.8192714	-0.8483536	-0.7870877
phosphate_star	Atlantic	(27.95,28.05]	-0.8787882	-0.9055045	-0.8355508
phosphate_star	Atlantic	(28.05,28.1]	-0.9194620	-0.9313194	-0.9083668
phosphate_star	Atlantic	(28.1,28.15]	-0.9398605	-0.9518319	-0.9181216
phosphate_star	Atlantic	(28.15,28.2]	-0.9832579	-0.9842676	-0.9822025
phosphate_star	Atlantic	(28.2, Inf]	-0.9647877	-0.9750375	-0.9532374
phosphate_star	Indo-Pacific	(-Inf,26]	-0.4552095	-0.6141218	-0.3489480
phosphate_star	Indo-Pacific	(26,26.5]	-0.8348439	-0.8793879	-0.8084991
phosphate_star	Indo-Pacific	(26.5,26.75]	-0.7768607	-0.8804606	-0.6380077
phosphate_star	Indo-Pacific	(26.75,27]	-0.7137152	-0.8215949	-0.6458558
phosphate_star	Indo-Pacific	(27,27.25]	-0.3862453	-0.5088061	-0.3224569
phosphate_star	Indo-Pacific	(27.25,27.5]	-0.2755320	-0.3886980	-0.1497934
phosphate_star	Indo-Pacific	(27.5,27.75]	-0.4840017	-0.7705701	-0.1416168
phosphate_star	Indo-Pacific	(27.75,27.85]	-0.5007388	-0.7408345	-0.2315430
phosphate_star	Indo-Pacific	(27.85,27.95]	-0.4809896	-0.5537441	-0.3895350
phosphate_star	Indo-Pacific	(27.95,28.05]	-0.5238548	-0.6168542	-0.4006077
phosphate_star	Indo-Pacific	(28.05,28.1]	-0.5996761	-0.6745422	-0.4640165
phosphate_star	Indo-Pacific	(28.1, Inf]	-0.5475604	-0.6637739	-0.4390730
sal	Atlantic	(-Inf,26]	0.3476690	0.2996309	0.4163900
sal	Atlantic	(26,26.5]	0.8134370	0.7831564	0.8666493
sal	Atlantic	(26.5,26.75]	0.7860393	0.6039653	0.8880440
sal	Atlantic	(26.75,27]	0.8524896	0.7396867	0.9102798
sal	Atlantic	(27,27.25]	0.8976174	0.8438029	0.9429090
sal	Atlantic	(27.25,27.5]	0.8895226	0.8214832	0.9378890
sal	Atlantic	(27.5,27.75]	0.8588990	0.8463384	0.8718977
sal	Atlantic	(27.75,27.85]	0.7479073	0.7081495	0.7902278
sal	Atlantic	(27.85,27.95]	0.4598823	0.3083417	0.5464505
sal	Atlantic	(27.95,28.05]	0.5523893	0.2690369	0.7123872
sal	Atlantic	(28.05,28.1]	0.7201343	0.6613456	0.7687060
sal	Atlantic	(28.1,28.15]	0.7890805	0.7499097	0.8441274
sal	Atlantic	(28.15,28.2]	0.9213980	0.9056371	0.9328099
sal	Atlantic	(28.2, Inf]	0.9543662	0.9265982	0.9766301
sal	Indo-Pacific	(-Inf,26]	0.1443403	0.1303290	0.1546539
sal	Indo-Pacific	(26,26.5]	0.4048335	0.2625329	0.6255706
sal	Indo-Pacific	(26.5,26.75]	0.4337514	0.2106493	0.7113481
sal	Indo-Pacific	(26.75,27]	0.4462745	0.2980179	0.6668893
sal	Indo-Pacific	(27,27.25]	0.0010683	-0.1258426	0.1903493
sal	Indo-Pacific	(27.25,27.5]	-0.3890946	-0.5729609	-0.2139092
sal	Indo-Pacific	(27.5,27.75]	-0.5985513	-0.8858929	-0.3342618
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]	-0.3471374	-0.6218264	-0.0855565
silicate	Atlantic	(26,26.5]	-0.7481636	-0.8500649	-0.6412899
silicate	Atlantic	(26.5,26.75]	-0.8145445	-0.8354718	-0.8011666
silicate	Atlantic	(26.75,27]	-0.7479592	-0.7773250	-0.7169040
silicate	Atlantic	(27,27.25]	-0.8410861	-0.8435366	-0.8390693
silicate	Atlantic	(27.25,27.5]	-0.8874037	-0.9011691	-0.8665235
silicate	Atlantic	(27.5,27.75]	-0.8936111	-0.9056000	-0.8753326
silicate	Atlantic	(27.75,27.85]	-0.9132461	-0.9248236	-0.9008202
silicate	Atlantic	(27.85,27.95]	-0.9059987	-0.9207020	-0.8981879
silicate	Atlantic	(27.95,28.05]	-0.9005218	-0.9282317	-0.8789909
silicate	Atlantic	(28.05,28.1]	-0.9106977	-0.9301316	-0.8980040
silicate	Atlantic	(28.1,28.15]	-0.9403432	-0.9538044	-0.9304294
silicate	Atlantic	(28.15,28.2]	-0.9749233	-0.9794229	-0.9692107
silicate	Atlantic	(28.2, Inf]	-0.9593603	-0.9901692	-0.9269682
silicate	Indo-Pacific	(-Inf,26]	-0.5180154	-0.6288626	-0.4567030
silicate	Indo-Pacific	(26,26.5]	-0.7760733	-0.8161663	-0.7162793
silicate	Indo-Pacific	(26.5,26.75]	-0.7668757	-0.8437098	-0.6341042
silicate	Indo-Pacific	(26.75,27]	-0.7701662	-0.7995253	-0.7182576
silicate	Indo-Pacific	(27,27.25]	-0.4271802	-0.5036758	-0.3849373
silicate	Indo-Pacific	(27.25,27.5]	0.2548866	0.1935102	0.2881561
silicate	Indo-Pacific	(27.5,27.75]	0.1382496	-0.3023333	0.5405623
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]	0.1189611	-0.0827931	0.3088210
tem	Atlantic	(26,26.5]	0.7722566	0.7200321	0.8169447
tem	Atlantic	(26.5,26.75]	0.8217590	0.7343439	0.8735358
tem	Atlantic	(26.75,27]	0.8467874	0.7556874	0.8971559
tem	Atlantic	(27,27.25]	0.8729027	0.8324803	0.9066721
tem	Atlantic	(27.25,27.5]	0.8645627	0.8039766	0.9128891
tem	Atlantic	(27.5,27.75]	0.8114848	0.7840849	0.8284506
tem	Atlantic	(27.75,27.85]	0.7115430	0.6959796	0.7324943
tem	Atlantic	(27.85,27.95]	0.4041541	0.2469741	0.5506878
tem	Atlantic	(27.95,28.05]	0.5128440	0.3266584	0.6569443
tem	Atlantic	(28.05,28.1]	0.5874385	0.4727863	0.6720668
tem	Atlantic	(28.1,28.15]	0.5908305	0.5110488	0.7279052
tem	Atlantic	(28.15,28.2]	0.6764127	0.6108550	0.7130884
tem	Atlantic	(28.2, Inf]	-0.0562982	-0.1283263	0.0232188
tem	Indo-Pacific	(-Inf,26]	-0.0028059	-0.0794153	0.0631445
tem	Indo-Pacific	(26,26.5]	0.4465913	0.3214697	0.6341563
tem	Indo-Pacific	(26.5,26.75]	0.4292183	0.2218006	0.6913863
tem	Indo-Pacific	(26.75,27]	0.4893808	0.3790500	0.6861830
tem	Indo-Pacific	(27,27.25]	0.1391987	0.0326513	0.3300104
tem	Indo-Pacific	(27.25,27.5]	-0.3363825	-0.5117782	-0.1917468
tem	Indo-Pacific	(27.5,27.75]	-0.6372165	-0.8870304	-0.3884786
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

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 ~ sal + tem + aou + oxygen + phosphate_star, data = .)

lm_2 <- GLODAP %>% 
  filter(basin == "Atlantic",
         gamma_slab == "(-Inf,26]",
         era == "new_era") %>% 
  lm(Cstar ~ sal + tem + 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?
• test model selection based on AIC

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