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

1 Required data

Required are:

clean version of GLODAPGLODAPv2.2020
observations grid of clean version of GLODAPGLODAPv2.2020
C_ant from GLODAPv2_2016b_MappedClimatologies
annual mean atmospheric pCO₂

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

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

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

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

2 C*

C* serves as a conservative tracer of anthropogenic CO₂ uptake. It is derived from measured DIC by removing the impact of - organic matter formation and respiration - calcification and calcium carbonate dissolution

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

2.1 Stoichiometric ratios

rCP <- 117
rNP <- 16

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

C/P: 117
N/P: 16

2.2 Calculation

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)

2.3 PO₄* calculation

Currently, PO₄* is calculated according to Gruber et al. (2019), ie based on nitrate rather than oxygen.

GLODAP <- GLODAP %>% 
  mutate(phosphate_star = phosphate - 16*nitrate  + 29)

3 Reference year adjustment

The scaling factor for the reference year adjustment is an apriori estiamte of Cant at a given location and depth. Here, Cant from the GLODAP mapped Climatology was used.

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

3.1 Merge GLODAP + Cant

Cant_clim <- Cant_clim %>% 
  drop_na()

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

rm(Cant_clim, GLODAP_obs_grid)

GLODAP_Cant_obs <- full_join(GLODAP, Cant_clim_obs)

rm(Cant_clim_obs)

# GLODAP_Cant_full %>% write_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
#                                           "GLODAP_Cant_full.csv"))
# 
# GLODAP_Cant_full <- read_csv(here::here("data/GLODAPv2_2020/_summarized_data_files",
#                                           "GLODAP_Cant_full.csv"))

The mapped Cant product was merged with GLODAP observation by:

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

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

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

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

rm(GLODAP_Cant_obs)

3.2 Merge GLODAP + atmospheric pCO₂

GLODAP <- left_join(GLODAP, co2_atm)

3.3 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)

3.4 Control plots

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

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

4 Selected section plots

Selected sections are plotted to demonstrate the magnitude of various parameters and corrections relevant to C*.

cruises_meridional <- c("1041")

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

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

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

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

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


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

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

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

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

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

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

lat_section +
  geom_point(aes(col = tco2))

lat_section +
  geom_point(aes(col = talk))

lat_section +
  geom_point(aes(col = phosphate))

lat_section +
  geom_point(aes(col = rCP_phosphate))

lat_section +
  geom_point(aes(col = talk_05))

lat_section +
  geom_point(aes(col = rNP_phosphate_05))

lat_section +
  geom_point(aes(col = Cstar))

lat_section +
  geom_point(aes(col = Cant))

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

rm(mapWorld, lat_section, GLODAP_cruise)

5 MLR

5.1 Isoneutral slabs

slabs_Atl <- c(
-Inf,
26.00,
26.50,
26.75,
27.00,
27.25,
27.50,
27.75,
27.85,
27.95,
28.05,
28.10,
28.15,
28.20,
Inf)

slabs_Ind_Pac <- c(
-Inf,
26.00,
26.50,
26.75,
27.00,
27.25,
27.50,
27.75,
27.85,
27.95,
28.05,
28.10,
Inf)

The following boundaries for isoneutral slabs were defined:

Atlantic: -, 26, 26.5, 26.75, 27, 27.25, 27.5, 27.75, 27.85, 27.95, 28.05, 28.1, 28.15, 28.2,
Indo-Pacific: -, 26, 26.5, 26.75, 27, 27.25, 27.5, 27.75, 27.85, 27.95, 28.05, 28.1,

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

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

GLODAP <- bind_rows(GLODAP_Atl, GLODAP_Ind_Pac)
rm(GLODAP_Atl, GLODAP_Ind_Pac)

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

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

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

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

5.2 Predictor correlation

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

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

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

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

print(i_basin)
print(i_era)

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

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

png(here::here("output/figure/eMLR/predictor_correlation",
               paste("predictor_correlation", i_basin, i_era, i_gamma_slab, ".png", sep = "_")),
    width = 15, height = 15, units = "in", res = 300)

print(p)

dev.off()
  
    }
  }
}

5.3 Model fitting

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

5.3.1 Predictor selection

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


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

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

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

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

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


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

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

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

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

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

n_predictors_max <- 5
n_predictors_min <- 2

all_lm_stats <- all_lm_stats %>% 
  filter(n >= n_predictors_min,
         n <= n_predictors_max) %>% 
  select(basin, era, gamma_slab, predictors, rmse)

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

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

lm_best <- all_lm_stats_wide %>% 
  group_by(basin, gamma_slab) %>% 
  slice_min(rmse_sum, n = 10) %>% 
  ungroup()

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

basin	gamma_slab	predictors	rmse_JGOFS_WOCE	rmse_GO_SHIP	rmse_new_era	rmse_sum
Atlantic	(-Inf,26]	salinity temperature aou oxygen phosphate	7.233104	6.424028	2.765130	16.422262
Atlantic	(-Inf,26]	temperature aou oxygen phosphate phosphate_star	7.238731	6.515207	2.671672	16.425610
Atlantic	(-Inf,26]	temperature oxygen silicate phosphate phosphate_star	7.342865	6.367196	2.734672	16.444733
Atlantic	(-Inf,26]	salinity aou oxygen silicate phosphate	7.363174	6.256378	2.875347	16.494899
Atlantic	(-Inf,26]	salinity temperature oxygen silicate phosphate	7.246124	6.404483	2.852778	16.503385
Atlantic	(-Inf,26]	salinity temperature aou silicate phosphate	7.276259	6.370141	2.857798	16.504198
Atlantic	(-Inf,26]	temperature aou silicate phosphate phosphate_star	7.399728	6.385907	2.744721	16.530356
Atlantic	(-Inf,26]	temperature aou oxygen silicate phosphate	7.055656	6.789733	2.766765	16.612154
Atlantic	(-Inf,26]	salinity temperature oxygen phosphate phosphate_star	7.594469	6.323889	2.711688	16.630046
Atlantic	(-Inf,26]	salinity temperature aou phosphate phosphate_star	7.637863	6.281897	2.717708	16.637469
Atlantic	(26,26.5]	temperature aou oxygen silicate phosphate	5.363576	6.786906	3.120245	15.270727
Atlantic	(26,26.5]	temperature aou oxygen phosphate phosphate_star	5.437464	6.819617	3.180828	15.437908
Atlantic	(26,26.5]	salinity temperature aou oxygen phosphate	5.453636	6.837398	3.164633	15.455668
Atlantic	(26,26.5]	aou oxygen silicate phosphate phosphate_star	5.394684	6.892097	3.178032	15.464813
Atlantic	(26,26.5]	temperature aou oxygen phosphate	5.456491	6.837548	3.181060	15.475099
Atlantic	(26,26.5]	temperature aou silicate phosphate phosphate_star	5.430921	6.955271	3.193715	15.579907
Atlantic	(26,26.5]	salinity aou oxygen phosphate phosphate_star	5.443918	6.941283	3.196238	15.581438
Atlantic	(26,26.5]	salinity aou oxygen silicate phosphate	5.432267	6.973621	3.182424	15.588312
Atlantic	(26,26.5]	aou oxygen phosphate phosphate_star	5.467333	6.943299	3.206234	15.616865
Atlantic	(26,26.5]	aou oxygen silicate phosphate	5.439014	7.001567	3.184956	15.625537
Atlantic	(26.5,26.75]	temperature aou oxygen silicate phosphate	5.219837	5.589322	3.704869	14.514028
Atlantic	(26.5,26.75]	salinity temperature aou silicate phosphate	5.156094	5.583682	3.805535	14.545311
Atlantic	(26.5,26.75]	salinity temperature oxygen silicate phosphate	5.145692	5.566412	3.838208	14.550311
Atlantic	(26.5,26.75]	temperature oxygen silicate phosphate phosphate_star	5.211439	5.585131	3.758446	14.555017
Atlantic	(26.5,26.75]	temperature aou silicate phosphate phosphate_star	5.228077	5.603867	3.730283	14.562227
Atlantic	(26.5,26.75]	aou oxygen silicate phosphate phosphate_star	5.263529	5.643834	3.699733	14.607095
Atlantic	(26.5,26.75]	salinity aou oxygen silicate phosphate	5.201822	5.640533	3.769774	14.612130
Atlantic	(26.5,26.75]	salinity temperature aou oxygen phosphate	5.359083	5.561143	3.703778	14.624004
Atlantic	(26.5,26.75]	temperature aou oxygen phosphate phosphate_star	5.397508	5.580509	3.646853	14.624871
Atlantic	(26.5,26.75]	salinity temperature oxygen phosphate phosphate_star	5.369848	5.574805	3.734403	14.679057
Atlantic	(26.75,27]	salinity temperature oxygen silicate phosphate	4.683879	5.085526	3.618918	13.388323
Atlantic	(26.75,27]	salinity temperature aou silicate phosphate	4.703334	5.094493	3.629813	13.427639
Atlantic	(26.75,27]	salinity temperature oxygen phosphate phosphate_star	4.729705	5.146821	3.618566	13.495093
Atlantic	(26.75,27]	temperature oxygen silicate phosphate phosphate_star	4.734490	5.134443	3.633381	13.502314
Atlantic	(26.75,27]	salinity temperature aou phosphate phosphate_star	4.749608	5.152628	3.629477	13.531713
Atlantic	(26.75,27]	salinity temperature aou oxygen phosphate	4.742004	5.170997	3.622653	13.535654
Atlantic	(26.75,27]	salinity temperature oxygen phosphate	4.742309	5.171062	3.623176	13.536547
Atlantic	(26.75,27]	temperature aou silicate phosphate phosphate_star	4.761655	5.140782	3.647651	13.550089
Atlantic	(26.75,27]	temperature aou oxygen phosphate phosphate_star	4.757625	5.161932	3.641829	13.561385
Atlantic	(26.75,27]	salinity temperature aou phosphate	4.758055	5.173299	3.634027	13.565381
Atlantic	(27,27.25]	temperature oxygen silicate phosphate phosphate_star	5.150199	4.920376	4.425074	14.495649
Atlantic	(27,27.25]	temperature aou oxygen phosphate phosphate_star	5.155952	4.955575	4.485850	14.597377
Atlantic	(27,27.25]	temperature aou silicate phosphate phosphate_star	5.201088	4.956303	4.448113	14.605505
Atlantic	(27,27.25]	salinity temperature oxygen phosphate phosphate_star	5.205096	4.944247	4.501528	14.650871
Atlantic	(27,27.25]	temperature oxygen phosphate phosphate_star	5.243274	4.975377	4.507371	14.726023
Atlantic	(27,27.25]	salinity temperature oxygen silicate phosphate	5.025839	5.042443	4.665827	14.734108
Atlantic	(27,27.25]	salinity temperature aou phosphate phosphate_star	5.259815	4.977166	4.519119	14.756100
Atlantic	(27,27.25]	salinity temperature aou silicate phosphate	5.086705	5.064103	4.676695	14.827503
Atlantic	(27,27.25]	temperature aou phosphate phosphate_star	5.294046	5.010556	4.526341	14.830943
Atlantic	(27,27.25]	aou oxygen silicate phosphate phosphate_star	5.340125	5.046883	4.477069	14.864077
Atlantic	(27.25,27.5]	salinity temperature oxygen phosphate phosphate_star	4.784084	4.325538	3.661619	12.771241
Atlantic	(27.25,27.5]	salinity temperature aou phosphate phosphate_star	4.831010	4.335440	3.672001	12.838450
Atlantic	(27.25,27.5]	temperature aou oxygen phosphate phosphate_star	4.778594	4.486817	3.662943	12.928355
Atlantic	(27.25,27.5]	temperature oxygen silicate phosphate phosphate_star	4.815587	4.464644	3.651525	12.931757
Atlantic	(27.25,27.5]	salinity aou oxygen phosphate phosphate_star	4.909921	4.380487	3.693874	12.984282
Atlantic	(27.25,27.5]	temperature aou silicate phosphate phosphate_star	4.864184	4.466131	3.654361	12.984677
Atlantic	(27.25,27.5]	temperature oxygen phosphate phosphate_star	4.836475	4.492731	3.663888	12.993095
Atlantic	(27.25,27.5]	salinity temperature aou oxygen phosphate	4.690176	4.375626	3.957693	13.023495
Atlantic	(27.25,27.5]	temperature aou phosphate phosphate_star	4.877589	4.486869	3.672726	13.037184
Atlantic	(27.25,27.5]	salinity temperature oxygen silicate phosphate	4.785817	4.370284	3.888408	13.044510
Atlantic	(27.5,27.75]	temperature aou silicate phosphate phosphate_star	4.178798	4.405750	4.230958	12.815506
Atlantic	(27.5,27.75]	temperature oxygen silicate phosphate phosphate_star	4.171250	4.419163	4.233864	12.824277
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate phosphate_star	4.197885	4.399525	4.230411	12.827821
Atlantic	(27.5,27.75]	salinity temperature oxygen silicate phosphate	4.179766	4.394406	4.324356	12.898528
Atlantic	(27.5,27.75]	salinity temperature aou silicate phosphate	4.191718	4.383035	4.326416	12.901169
Atlantic	(27.5,27.75]	salinity aou oxygen silicate phosphate	4.210252	4.376137	4.327749	12.914138
Atlantic	(27.5,27.75]	temperature aou oxygen silicate phosphate	4.183773	4.409376	4.344048	12.937196
Atlantic	(27.5,27.75]	temperature aou silicate phosphate	4.197530	4.418293	4.345437	12.961259
Atlantic	(27.5,27.75]	temperature oxygen silicate phosphate	4.186794	4.431777	4.344048	12.962619
Atlantic	(27.5,27.75]	aou oxygen silicate phosphate	4.219326	4.412680	4.348932	12.980938
Atlantic	(27.75,27.85]	salinity aou oxygen silicate phosphate	4.155188	4.343314	6.006423	14.504925
Atlantic	(27.75,27.85]	salinity temperature oxygen silicate phosphate	4.152518	4.345415	6.018195	14.516128
Atlantic	(27.75,27.85]	salinity oxygen silicate phosphate phosphate_star	4.148845	4.341301	6.027563	14.517708
Atlantic	(27.75,27.85]	salinity temperature aou silicate phosphate	4.156656	4.348980	6.020016	14.525652
Atlantic	(27.75,27.85]	salinity aou silicate phosphate phosphate_star	4.141199	4.359680	6.036728	14.537608
Atlantic	(27.75,27.85]	salinity oxygen silicate phosphate	4.165017	4.346978	6.027909	14.539904
Atlantic	(27.75,27.85]	temperature aou oxygen silicate phosphate	4.221683	4.350846	5.972594	14.545123
Atlantic	(27.75,27.85]	salinity aou silicate phosphate	4.158893	4.364303	6.036854	14.560050
Atlantic	(27.75,27.85]	temperature oxygen silicate phosphate phosphate_star	4.213737	4.380967	6.023641	14.618345
Atlantic	(27.75,27.85]	temperature aou silicate phosphate phosphate_star	4.216149	4.387433	6.025514	14.629095
Atlantic	(27.85,27.95]	salinity aou oxygen silicate phosphate	3.727889	4.172888	4.843709	12.744486
Atlantic	(27.85,27.95]	salinity temperature oxygen silicate phosphate	3.739892	4.187911	4.879615	12.807418
Atlantic	(27.85,27.95]	salinity temperature aou silicate phosphate	3.750570	4.193737	4.879217	12.823524
Atlantic	(27.85,27.95]	salinity temperature silicate phosphate phosphate_star	3.882773	4.290264	4.849271	13.022309
Atlantic	(27.85,27.95]	salinity temperature silicate phosphate	3.980800	4.290271	4.879951	13.151023
Atlantic	(27.85,27.95]	salinity oxygen silicate phosphate phosphate_star	3.771723	4.412669	5.319665	13.504056
Atlantic	(27.85,27.95]	salinity oxygen silicate phosphate	3.788228	4.442442	5.332826	13.563495
Atlantic	(27.85,27.95]	salinity aou silicate phosphate phosphate_star	3.896036	4.600259	5.378794	13.875090
Atlantic	(27.85,27.95]	salinity aou silicate phosphate	3.924500	4.616418	5.383425	13.924343
Atlantic	(27.85,27.95]	temperature aou oxygen silicate phosphate	4.214755	4.849638	5.263138	14.327531
Atlantic	(27.95,28.05]	salinity aou oxygen silicate phosphate	3.487770	4.416875	4.820087	12.724732
Atlantic	(27.95,28.05]	salinity temperature oxygen silicate phosphate	3.498901	4.435697	4.910557	12.845155
Atlantic	(27.95,28.05]	salinity oxygen silicate phosphate phosphate_star	3.570396	4.433626	4.875191	12.879213
Atlantic	(27.95,28.05]	salinity temperature aou silicate phosphate	3.508118	4.459459	4.931814	12.899391
Atlantic	(27.95,28.05]	salinity temperature aou oxygen phosphate	3.755336	4.422690	4.799080	12.977106
Atlantic	(27.95,28.05]	salinity oxygen silicate phosphate	3.570686	4.452825	5.020607	13.044118
Atlantic	(27.95,28.05]	salinity temperature silicate phosphate phosphate_star	3.755808	4.829486	4.861915	13.447209
Atlantic	(27.95,28.05]	salinity aou silicate phosphate phosphate_star	3.750648	4.607306	5.100329	13.458284
Atlantic	(27.95,28.05]	salinity aou silicate phosphate	3.757788	4.616897	5.190912	13.565597
Atlantic	(27.95,28.05]	salinity temperature silicate phosphate	3.758011	4.835232	4.988962	13.582204
Atlantic	(28.05,28.1]	salinity temperature aou oxygen phosphate	3.539499	4.427871	4.144983	12.112354
Atlantic	(28.05,28.1]	temperature aou oxygen silicate phosphate	3.643192	4.386906	4.117142	12.147240
Atlantic	(28.05,28.1]	temperature aou oxygen phosphate phosphate_star	3.737328	4.517341	4.186888	12.441557
Atlantic	(28.05,28.1]	temperature aou oxygen phosphate	3.737933	4.520827	4.228193	12.486953
Atlantic	(28.05,28.1]	salinity temperature oxygen silicate phosphate	3.531111	4.629803	4.415293	12.576206
Atlantic	(28.05,28.1]	salinity temperature oxygen phosphate phosphate_star	3.554312	4.684188	4.356252	12.594752
Atlantic	(28.05,28.1]	salinity oxygen silicate phosphate phosphate_star	3.548422	4.631248	4.447473	12.627143
Atlantic	(28.05,28.1]	salinity temperature oxygen phosphate	3.557078	4.688580	4.416199	12.661857
Atlantic	(28.05,28.1]	salinity aou oxygen silicate phosphate	3.554108	4.635135	4.529410	12.718653
Atlantic	(28.05,28.1]	salinity oxygen silicate phosphate	3.555467	4.648734	4.534233	12.738434
Atlantic	(28.1,28.15]	salinity temperature oxygen silicate phosphate	3.349308	4.010613	4.254217	11.614139
Atlantic	(28.1,28.15]	salinity temperature aou oxygen phosphate	3.440411	4.008819	4.211635	11.660865
Atlantic	(28.1,28.15]	temperature aou oxygen silicate phosphate	3.436793	4.025910	4.216057	11.678759
Atlantic	(28.1,28.15]	temperature oxygen silicate phosphate phosphate_star	3.430280	4.041063	4.243363	11.714706
Atlantic	(28.1,28.15]	salinity temperature oxygen phosphate phosphate_star	3.448754	4.022449	4.243864	11.715066
Atlantic	(28.1,28.15]	salinity temperature oxygen phosphate	3.449525	4.022451	4.254795	11.726772
Atlantic	(28.1,28.15]	temperature oxygen silicate phosphate	3.437071	4.041093	4.255279	11.733443
Atlantic	(28.1,28.15]	salinity temperature aou silicate phosphate	3.390856	4.077688	4.319062	11.787606
Atlantic	(28.1,28.15]	temperature aou oxygen phosphate phosphate_star	3.542289	4.045605	4.211446	11.799340
Atlantic	(28.1,28.15]	temperature aou oxygen phosphate	3.542305	4.046629	4.220084	11.809018
Atlantic	(28.15,28.2]	salinity temperature aou oxygen phosphate	3.719163	3.681081	2.836143	10.236388
Atlantic	(28.15,28.2]	salinity temperature aou silicate phosphate	3.739761	3.698785	2.835064	10.273611
Atlantic	(28.15,28.2]	salinity temperature aou phosphate phosphate_star	3.727244	3.710071	2.837066	10.274381
Atlantic	(28.15,28.2]	salinity temperature aou phosphate	3.740143	3.711047	2.837785	10.288975
Atlantic	(28.15,28.2]	salinity aou oxygen silicate phosphate	3.713912	3.687702	2.914045	10.315659
Atlantic	(28.15,28.2]	salinity temperature oxygen silicate phosphate	3.775192	3.734735	2.836415	10.346342
Atlantic	(28.15,28.2]	salinity aou oxygen phosphate phosphate_star	3.705570	3.688287	2.955392	10.349249
Atlantic	(28.15,28.2]	salinity aou oxygen phosphate	3.719217	3.688379	2.956477	10.364073
Atlantic	(28.15,28.2]	salinity temperature oxygen phosphate phosphate_star	3.777038	3.755312	2.835243	10.367592
Atlantic	(28.15,28.2]	salinity temperature oxygen phosphate	3.784450	3.757169	2.836701	10.378319
Atlantic	(28.2, Inf]	salinity temperature aou oxygen phosphate	3.337999	3.143686	2.685083	9.166769
Atlantic	(28.2, Inf]	salinity aou oxygen silicate phosphate	3.358320	3.145049	2.767527	9.270896
Atlantic	(28.2, Inf]	salinity temperature aou silicate phosphate	3.425561	3.148993	2.696506	9.271059
Atlantic	(28.2, Inf]	salinity aou oxygen phosphate phosphate_star	3.376522	3.141055	2.763926	9.281502
Atlantic	(28.2, Inf]	salinity aou oxygen phosphate	3.378104	3.145072	2.767543	9.290719
Atlantic	(28.2, Inf]	salinity temperature aou phosphate phosphate_star	3.471029	3.143746	2.692778	9.307553
Atlantic	(28.2, Inf]	salinity temperature aou phosphate	3.472721	3.149181	2.700720	9.322622
Atlantic	(28.2, Inf]	salinity temperature oxygen silicate phosphate	3.502342	3.144268	2.676045	9.322655
Atlantic	(28.2, Inf]	temperature aou oxygen silicate phosphate	3.361576	3.278500	2.736479	9.376555
Atlantic	(28.2, Inf]	temperature aou oxygen phosphate phosphate_star	3.384056	3.283704	2.751414	9.419175
Indo-Pacific	(-Inf,26]	salinity aou oxygen phosphate phosphate_star	11.652593	6.872465	4.747255	23.272313
Indo-Pacific	(-Inf,26]	salinity temperature aou phosphate phosphate_star	11.725349	6.849543	4.968075	23.542968
Indo-Pacific	(-Inf,26]	salinity temperature oxygen phosphate phosphate_star	11.771329	6.883678	5.114532	23.769539
Indo-Pacific	(-Inf,26]	salinity aou oxygen silicate phosphate	11.591824	7.146475	5.644898	24.383197
Indo-Pacific	(-Inf,26]	salinity temperature aou silicate phosphate	11.662658	7.221472	5.848813	24.732943
Indo-Pacific	(-Inf,26]	salinity temperature aou oxygen phosphate_star	12.532453	7.048097	5.305447	24.885997
Indo-Pacific	(-Inf,26]	salinity temperature oxygen silicate phosphate	11.701156	7.270085	5.949523	24.920764
Indo-Pacific	(-Inf,26]	salinity temperature oxygen silicate phosphate_star	12.564249	7.054970	5.319566	24.938785
Indo-Pacific	(-Inf,26]	salinity temperature aou silicate phosphate_star	12.593023	7.092992	5.270621	24.956636
Indo-Pacific	(-Inf,26]	salinity temperature oxygen phosphate_star	12.574223	7.054989	5.382004	25.011216
Indo-Pacific	(26,26.5]	salinity temperature aou phosphate phosphate_star	7.884709	5.129658	3.991869	17.006237
Indo-Pacific	(26,26.5]	salinity aou oxygen phosphate phosphate_star	7.825697	5.232341	3.950876	17.008915
Indo-Pacific	(26,26.5]	salinity aou oxygen silicate phosphate	7.863872	5.215921	3.936596	17.016389
Indo-Pacific	(26,26.5]	salinity temperature oxygen phosphate phosphate_star	7.925778	5.121998	4.024452	17.072228
Indo-Pacific	(26,26.5]	salinity temperature aou silicate phosphate	7.935808	5.171091	4.013896	17.120795
Indo-Pacific	(26,26.5]	salinity temperature oxygen silicate phosphate	7.972957	5.179160	4.053536	17.205653
Indo-Pacific	(26,26.5]	salinity temperature aou oxygen phosphate	7.969753	5.311089	4.249030	17.529872
Indo-Pacific	(26,26.5]	salinity temperature aou phosphate	8.020770	5.323834	4.291014	17.635619
Indo-Pacific	(26,26.5]	salinity aou oxygen phosphate	7.970078	5.414262	4.254610	17.638950
Indo-Pacific	(26,26.5]	salinity temperature oxygen phosphate	8.051221	5.312575	4.311661	17.675457
Indo-Pacific	(26.5,26.75]	salinity aou oxygen phosphate phosphate_star	5.643270	5.441635	4.201758	15.286663
Indo-Pacific	(26.5,26.75]	salinity temperature aou phosphate phosphate_star	5.744701	5.481610	4.285316	15.511626
Indo-Pacific	(26.5,26.75]	salinity temperature oxygen phosphate phosphate_star	5.810017	5.522181	4.347636	15.679835
Indo-Pacific	(26.5,26.75]	salinity aou oxygen silicate phosphate	5.905584	5.702333	4.562541	16.170458
Indo-Pacific	(26.5,26.75]	salinity temperature aou oxygen phosphate	5.986932	5.709024	4.619676	16.315632
Indo-Pacific	(26.5,26.75]	salinity aou oxygen phosphate	5.988940	5.709065	4.635932	16.333936
Indo-Pacific	(26.5,26.75]	salinity temperature aou silicate phosphate	6.048583	5.719303	4.660956	16.428842
Indo-Pacific	(26.5,26.75]	aou oxygen silicate phosphate phosphate_star	6.137998	5.852677	4.450257	16.440932
Indo-Pacific	(26.5,26.75]	salinity temperature aou phosphate	6.075088	5.745923	4.716630	16.537642
Indo-Pacific	(26.5,26.75]	temperature aou oxygen phosphate phosphate_star	6.114876	5.850423	4.573040	16.538338
Indo-Pacific	(26.75,27]	temperature aou oxygen phosphate phosphate_star	6.512153	4.907927	4.030310	15.450390
Indo-Pacific	(26.75,27]	salinity aou oxygen phosphate phosphate_star	6.562262	4.957194	4.045916	15.565373
Indo-Pacific	(26.75,27]	aou oxygen silicate phosphate phosphate_star	6.519772	4.958933	4.154753	15.633458
Indo-Pacific	(26.75,27]	temperature aou oxygen silicate phosphate	6.525639	4.983289	4.221813	15.730741
Indo-Pacific	(26.75,27]	aou oxygen phosphate phosphate_star	6.598292	5.006942	4.154785	15.760018
Indo-Pacific	(26.75,27]	salinity temperature aou oxygen phosphate	6.549695	5.020274	4.249159	15.819127
Indo-Pacific	(26.75,27]	temperature aou oxygen phosphate	6.552943	5.020844	4.262915	15.836701
Indo-Pacific	(26.75,27]	temperature aou silicate phosphate phosphate_star	6.552474	5.026245	4.289949	15.868669
Indo-Pacific	(26.75,27]	temperature oxygen silicate phosphate phosphate_star	6.589732	5.091516	4.384008	16.065256
Indo-Pacific	(26.75,27]	salinity temperature aou phosphate phosphate_star	6.677586	5.136264	4.252461	16.066312
Indo-Pacific	(27,27.25]	temperature aou oxygen silicate phosphate	6.057890	4.532863	4.048207	14.638960
Indo-Pacific	(27,27.25]	salinity temperature aou oxygen phosphate	6.083955	4.607439	4.166144	14.857539
Indo-Pacific	(27,27.25]	temperature aou oxygen phosphate phosphate_star	6.113241	4.648067	4.163487	14.924795
Indo-Pacific	(27,27.25]	salinity aou oxygen silicate phosphate	6.431710	4.541014	4.107446	15.080171
Indo-Pacific	(27,27.25]	temperature aou oxygen phosphate	6.115680	4.747192	4.304603	15.167475
Indo-Pacific	(27,27.25]	salinity aou silicate phosphate phosphate_star	6.509533	4.544592	4.121767	15.175892
Indo-Pacific	(27,27.25]	salinity temperature aou silicate phosphate	6.562627	4.548385	4.119478	15.230490
Indo-Pacific	(27,27.25]	salinity aou silicate phosphate	6.576878	4.548729	4.126122	15.251729
Indo-Pacific	(27,27.25]	salinity aou oxygen phosphate phosphate_star	6.431281	4.709064	4.174627	15.314973
Indo-Pacific	(27,27.25]	salinity temperature oxygen silicate phosphate	6.676758	4.583771	4.146776	15.407305
Indo-Pacific	(27.25,27.5]	temperature aou oxygen silicate phosphate	4.835968	3.913969	3.527790	12.277728
Indo-Pacific	(27.25,27.5]	salinity aou oxygen silicate phosphate	5.251519	3.924282	3.243081	12.418882
Indo-Pacific	(27.25,27.5]	temperature aou oxygen phosphate phosphate_star	4.863065	4.084331	3.647515	12.594911
Indo-Pacific	(27.25,27.5]	salinity temperature aou oxygen phosphate	4.862194	4.131183	3.627177	12.620554
Indo-Pacific	(27.25,27.5]	salinity temperature aou silicate phosphate	5.578168	3.945800	3.247152	12.771119
Indo-Pacific	(27.25,27.5]	temperature aou oxygen phosphate	4.866519	4.177465	3.729263	12.773247
Indo-Pacific	(27.25,27.5]	salinity aou oxygen phosphate phosphate_star	5.202101	4.189161	3.564507	12.955770
Indo-Pacific	(27.25,27.5]	salinity temperature oxygen silicate phosphate	5.801738	3.975890	3.253916	13.031545
Indo-Pacific	(27.25,27.5]	aou oxygen silicate phosphate phosphate_star	5.231115	4.179514	3.679102	13.089731
Indo-Pacific	(27.25,27.5]	salinity aou silicate phosphate phosphate_star	5.925597	3.952449	3.239888	13.117934
Indo-Pacific	(27.5,27.75]	salinity aou oxygen silicate phosphate	4.688828	3.618102	2.968149	11.275080
Indo-Pacific	(27.5,27.75]	salinity temperature aou silicate phosphate	4.857991	3.616196	2.966581	11.440767
Indo-Pacific	(27.5,27.75]	temperature aou oxygen silicate phosphate	4.414022	3.841294	3.290961	11.546277
Indo-Pacific	(27.5,27.75]	salinity temperature oxygen silicate phosphate	4.986342	3.619099	2.965966	11.571407
Indo-Pacific	(27.5,27.75]	salinity temperature aou oxygen phosphate	4.436909	3.849001	3.371011	11.656920
Indo-Pacific	(27.5,27.75]	temperature aou oxygen phosphate phosphate_star	4.435934	3.911470	3.405050	11.752454
Indo-Pacific	(27.5,27.75]	temperature aou oxygen phosphate	4.437170	3.916272	3.429891	11.783332
Indo-Pacific	(27.5,27.75]	salinity aou oxygen phosphate phosphate_star	4.689603	3.835711	3.334569	11.859882
Indo-Pacific	(27.5,27.75]	salinity aou oxygen phosphate	4.689770	3.851583	3.372534	11.913887
Indo-Pacific	(27.5,27.75]	aou oxygen silicate phosphate phosphate_star	4.694510	3.840147	3.409260	11.943917
Indo-Pacific	(27.75,27.85]	temperature aou oxygen silicate phosphate	4.269432	3.241574	2.903747	10.414753
Indo-Pacific	(27.75,27.85]	salinity temperature oxygen silicate phosphate	4.308811	3.258512	2.865015	10.432338
Indo-Pacific	(27.75,27.85]	salinity temperature aou silicate phosphate	4.285667	3.281811	2.876268	10.443746
Indo-Pacific	(27.75,27.85]	salinity aou oxygen silicate phosphate	4.262144	3.320317	2.896917	10.479378
Indo-Pacific	(27.75,27.85]	temperature aou silicate phosphate phosphate_star	4.300544	3.271219	2.918998	10.490761
Indo-Pacific	(27.75,27.85]	temperature oxygen silicate phosphate phosphate_star	4.326772	3.254352	2.911216	10.492339
Indo-Pacific	(27.75,27.85]	aou oxygen silicate phosphate phosphate_star	4.272132	3.304968	2.938537	10.515636
Indo-Pacific	(27.75,27.85]	temperature oxygen silicate phosphate	4.327841	3.271370	2.916579	10.515790
Indo-Pacific	(27.75,27.85]	temperature aou silicate phosphate	4.302407	3.293390	2.924736	10.520533
Indo-Pacific	(27.75,27.85]	temperature aou oxygen phosphate phosphate_star	4.261066	3.299139	3.000201	10.560406
Indo-Pacific	(27.85,27.95]	temperature aou silicate phosphate phosphate_star	4.303730	2.964754	2.889269	10.157754
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate phosphate_star	4.288887	2.967361	2.903249	10.159496
Indo-Pacific	(27.85,27.95]	salinity temperature aou silicate phosphate	4.321113	2.980023	2.878668	10.179804
Indo-Pacific	(27.85,27.95]	temperature oxygen silicate phosphate phosphate_star	4.322979	2.972074	2.886339	10.181392
Indo-Pacific	(27.85,27.95]	salinity aou oxygen silicate phosphate	4.308082	2.987020	2.896438	10.191540
Indo-Pacific	(27.85,27.95]	temperature aou oxygen silicate phosphate	4.314832	2.983036	2.896340	10.194207
Indo-Pacific	(27.85,27.95]	salinity temperature oxygen silicate phosphate	4.340586	2.984254	2.870691	10.195531
Indo-Pacific	(27.85,27.95]	temperature aou silicate phosphate	4.326316	2.983354	2.899097	10.208768
Indo-Pacific	(27.85,27.95]	aou oxygen silicate phosphate	4.314868	2.989308	2.913618	10.217794
Indo-Pacific	(27.85,27.95]	salinity aou oxygen phosphate phosphate_star	4.271402	2.998071	2.959829	10.229302
Indo-Pacific	(27.95,28.05]	salinity aou oxygen silicate phosphate	4.380825	2.852408	3.078449	10.311682
Indo-Pacific	(27.95,28.05]	salinity aou oxygen phosphate phosphate_star	4.381490	2.878636	3.076442	10.336569
Indo-Pacific	(27.95,28.05]	aou oxygen silicate phosphate phosphate_star	4.398487	2.860645	3.079305	10.338437
Indo-Pacific	(27.95,28.05]	salinity temperature aou silicate phosphate	4.399293	2.875842	3.067839	10.342974
Indo-Pacific	(27.95,28.05]	temperature aou oxygen phosphate phosphate_star	4.399165	2.871522	3.076308	10.346995
Indo-Pacific	(27.95,28.05]	aou oxygen phosphate phosphate_star	4.399784	2.878684	3.080077	10.358546
Indo-Pacific	(27.95,28.05]	salinity temperature aou oxygen phosphate	4.381680	2.872244	3.110001	10.363925
Indo-Pacific	(27.95,28.05]	salinity aou oxygen phosphate	4.381858	2.881876	3.110180	10.373914
Indo-Pacific	(27.95,28.05]	temperature aou silicate phosphate phosphate_star	4.422479	2.885926	3.068729	10.377135
Indo-Pacific	(27.95,28.05]	temperature aou oxygen silicate phosphate	4.402331	2.868436	3.112341	10.383108
Indo-Pacific	(28.05,28.1]	salinity aou oxygen phosphate phosphate_star	4.234297	2.857998	2.800839	9.893134
Indo-Pacific	(28.05,28.1]	salinity aou oxygen silicate phosphate	4.231465	2.843034	2.829063	9.903562
Indo-Pacific	(28.05,28.1]	salinity temperature aou oxygen phosphate	4.230598	2.861453	2.819898	9.911949
Indo-Pacific	(28.05,28.1]	salinity aou oxygen phosphate	4.234300	2.864288	2.831678	9.930266
Indo-Pacific	(28.05,28.1]	aou oxygen silicate phosphate phosphate_star	4.232564	2.871417	2.826666	9.930646
Indo-Pacific	(28.05,28.1]	temperature aou oxygen phosphate phosphate_star	4.232111	2.872811	2.844050	9.948973
Indo-Pacific	(28.05,28.1]	salinity temperature aou silicate phosphate	4.271623	2.848117	2.838349	9.958088
Indo-Pacific	(28.05,28.1]	aou oxygen phosphate phosphate_star	4.237606	2.873181	2.851534	9.962321
Indo-Pacific	(28.05,28.1]	temperature aou oxygen silicate phosphate	4.231850	2.881579	2.863461	9.976889
Indo-Pacific	(28.05,28.1]	aou oxygen silicate phosphate	4.233558	2.883351	2.872585	9.989494
Indo-Pacific	(28.1, Inf]	salinity aou oxygen silicate phosphate	3.567664	3.090883	2.618254	9.276801
Indo-Pacific	(28.1, Inf]	temperature aou oxygen silicate phosphate	3.599744	3.042637	2.653758	9.296139
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate phosphate_star	3.633084	2.982321	2.697944	9.313349
Indo-Pacific	(28.1, Inf]	aou oxygen silicate phosphate	3.638971	3.091267	2.706785	9.437024
Indo-Pacific	(28.1, Inf]	salinity aou oxygen phosphate phosphate_star	3.596967	3.202683	2.651638	9.451287
Indo-Pacific	(28.1, Inf]	salinity temperature aou phosphate phosphate_star	3.537341	3.234509	2.701246	9.473096
Indo-Pacific	(28.1, Inf]	salinity temperature aou oxygen phosphate	3.537528	3.314768	2.641163	9.493459
Indo-Pacific	(28.1, Inf]	salinity aou oxygen phosphate	3.597324	3.320281	2.652926	9.570531
Indo-Pacific	(28.1, Inf]	salinity temperature aou silicate phosphate	3.538830	3.348288	2.712252	9.599369
Indo-Pacific	(28.1, Inf]	salinity temperature oxygen phosphate phosphate_star	3.590808	3.275252	2.761419	9.627479

rm(n_predictors_max, n_predictors_min)

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

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

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

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

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

      # i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
      print(i_gamma_slab)
      
      GLODAP_basin_era_slab <- GLODAP_basin_era %>% 
        filter(gamma_slab == i_gamma_slab)
      
      lm_best_basin_slab <- lm_best_basin %>% 
        filter(gamma_slab == i_gamma_slab)
      
      for (i_rmse_sum in unique(lm_best_basin_slab$rmse_sum)) {
        
        # i_rmse_sum <- unique(lm_best_basin_slab$rmse_sum)[2]
        
        lm_best_single <- lm_best %>%
          filter(rmse_sum == i_rmse_sum) %>%
          select(lm_coeff) %>%
          pull()
        
        lm_formula <- as.formula(lm_best_single)
        
        model_single <- lm(lm_formula, 
              data = GLODAP_basin_era_slab)
        
        coefficients <- tidy(model_single)
        coefficients <- coefficients %>% 
          mutate(basin = i_basin,
                 era = i_era,
                 gamma_slab = i_gamma_slab,
                 model = lm_best_single,
                 rmse = i_rmse_sum)
        
        print(lm_best_single)
      
      if (exists("all_lm")) {
        all_lm <- bind_rows(all_lm, coefficients)
      }
      
      if (!exists("all_lm")) {
        all_lm <- coefficients
      }
      
      rm(lm_formula, model_single, coefficients)
        
      }
      
 
    }
    
  }
  
}


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

5.3.2 All predictors

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

MLRs_tidied <- MLRs %>% 
  unnest(tidied)

MLRs_tidied

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

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

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

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

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

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

MLRs %>% 
  unnest(glanced)

MLRs %>% 
  unnest(augmented)

6 Open tasks

Check if intercept is modeled

sessionInfo()

R version 4.0.2 (2020-06-22)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18363)

Matrix products: default

locale:
[1] LC_COLLATE=English_Germany.1252  LC_CTYPE=English_Germany.1252   
[3] LC_MONETARY=English_Germany.1252 LC_NUMERIC=C                    
[5] LC_TIME=English_Germany.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] kableExtra_1.1.0 knitr_1.29       olsrr_0.5.3.9000 GGally_2.0.0    
 [5] broom_0.7.0      patchwork_1.0.1  lubridate_1.7.9  forcats_0.5.0   
 [9] stringr_1.4.0    dplyr_1.0.0      purrr_0.3.4      readr_1.3.1     
[13] tidyr_1.1.0      tibble_3.0.3     ggplot2_3.3.2    tidyverse_1.3.0 
[17] 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          maps_3.3.0        
[33] rlang_0.4.7        readxl_1.3.1       rstudioapi_0.11    generics_0.0.2    
[37] farver_2.0.3       jsonlite_1.7.0     zip_2.0.4          car_3.0-8         
[41] magrittr_1.5       Rcpp_1.0.5         munsell_0.5.0      fansi_0.4.1       
[45] abind_1.4-5        lifecycle_0.2.0    stringi_1.4.6      whisker_0.4       
[49] yaml_2.2.1         carData_3.0-4      plyr_1.8.6         grid_4.0.2        
[53] blob_1.2.1         promises_1.1.1     crayon_1.3.4       haven_2.3.1       
[57] hms_0.5.3          pillar_1.4.6       reprex_0.3.0       glue_1.4.1        
[61] evaluate_0.14      data.table_1.13.0  modelr_0.1.8       vctrs_0.3.2       
[65] httpuv_1.5.4       cellranger_1.1.0   gtable_0.3.0       reshape_0.8.8     
[69] assertthat_0.2.1   xfun_0.16          openxlsx_4.1.5     later_1.1.0.1     
[73] viridisLite_0.3.0  ellipsis_0.3.1     here_0.1

Data base

Jens Daniel Müller

29 July, 2020

1 Required data

2 C*

2.1 Stoichiometric ratios

2.2 Calculation

2.3 PO₄* calculation

3 Reference year adjustment

3.1 Merge GLODAP + Cant

3.2 Merge GLODAP + atmospheric pCO₂

3.3 Calculate adjustment

3.4 Control plots

4 Selected section plots

5 MLR

5.1 Isoneutral slabs

5.2 Predictor correlation

5.3 Model fitting

5.3.1 Predictor selection

5.3.2 All predictors

6 Open tasks

Data base

Jens Daniel Müller

29 July, 2020

1 Required data

2 C*

2.1 Stoichiometric ratios

2.2 Calculation

2.3 PO4* calculation

3 Reference year adjustment

3.1 Merge GLODAP + Cant

3.2 Merge GLODAP + atmospheric pCO2

3.3 Calculate adjustment

3.4 Control plots

4 Selected section plots

5 MLR

5.1 Isoneutral slabs

5.2 Predictor correlation

5.3 Model fitting

5.3.1 Predictor selection

5.3.2 All predictors

6 Open tasks

2.3 PO₄* calculation

3.2 Merge GLODAP + atmospheric pCO₂