eMLR - model fitting

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Last updated: 2020-12-02

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Knit directory: emlr_obs_v_XXX/

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html	b03ddb8	jens-daniel-mueller	2020-12-02	Build site.
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---

path_functions      <- "/nfs/kryo/work/updata/emlr_cant/utilities/functions/"
path_files          <- "/nfs/kryo/work/updata/emlr_cant/utilities/files/"

path_preprocessing    <-
  "/nfs/kryo/work/updata/emlr_cant/observations/preprocessing/"

path_version_data     <-
  paste(
    "/nfs/kryo/work/updata/emlr_cant/observations/",
    params_local$Version_ID,
    "/data/",
    sep = ""
  )

path_version_figures  <-
  paste(
    "/nfs/kryo/work/updata/emlr_cant/observations/",
    params_local$Version_ID,
    "/figures/",
    sep = ""
  )

1 Libraries

Loading libraries specific to the the analysis performed in this section.

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

2 Required data

Required are:

• cleaned and prepared GLODAPv2_2020 file

GLODAP <-
  read_csv(paste(path_version_data,
                 "GLODAPv2.2020_MLR_fitting_ready.csv",
                 sep = ""))

3 Fitting all models

3.1 RMSE calculation

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.

# loops across all basins and eras
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  )
    
    # subset one basin and era for fitting
    GLODAP_basin_era <- GLODAP %>%
      filter(basin == i_basin, era == i_era)
    
    # loop across all gamma slabs in the current basin and 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)
      
      # subset one gamma slab
      GLODAP_basin_era_slab <- GLODAP_basin_era %>% 
        filter(gamma_slab == i_gamma_slab)

      # fit the full linear model, i.e. all predictor combinations
      lm_full <- lm(
        params_local$MLR_full_model,
        data = GLODAP_basin_era_slab)
      
      # fit linear models for all possible predictor combinations
      # unfortunately, this functions does not provide model coefficients (yet)
      lm_all <- ols_step_all_possible(lm_full)
      
      # extract diagnostics of each linear model
      lm_all <- as_tibble(lm_all$result)
      
      # add currect basin, era, and gamma values
      lm_all <- lm_all %>% 
        mutate(basin = i_basin,
               era = i_era,
               gamma_slab = i_gamma_slab)
      
      # expanding table with model diagnostics for all eras, basins, slabs
      if (exists("lm_all_stats")) {
        lm_all_stats <- bind_rows(lm_all_stats, lm_all)
      }
      
      if (!exists("lm_all_stats")) {
        lm_all_stats <- lm_all
      }
      
      rm(lm_full, lm_all)
      
    }
    
  }
  
}

# write model diagnostics to file

lm_all_stats %>% write_csv(paste(path_version_data,
                             "lm_all_stats.csv",
                             sep = ""))

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

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

# lm_all_stats <- read_csv(paste(path_version_data,
#                                "lm_all_stats.csv",
#                                sep = ""))


lm_all_stats <- lm_all_stats %>% 
  filter(n >= params_local$predictors_min,
         n <= params_local$predictors_max)

lm_all_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")

Past versions of eMLR_predictor_model_quality-1.png

Version	Author	Date
b03ddb8	jens-daniel-mueller	2020-12-02
91435ae	jens-daniel-mueller	2020-12-01
196be51	jens-daniel-mueller	2020-11-30

3.2 RMSE alternatives

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

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

Past versions of AIC_RMSE-1.png

Version	Author	Date
b03ddb8	jens-daniel-mueller	2020-12-02
91435ae	jens-daniel-mueller	2020-12-01
196be51	jens-daniel-mueller	2020-11-30

3.3 Predictor selection

Within each basin and slab, the 10 linear regression models with lowest summed RMSE across two adjacent (ie compared) eras were selected.

# select relevant columns
lm_all_stats <- lm_all_stats %>%
  select(basin, era, gamma_slab, predictors, rmse)

# calculate RMSE sum for adjacent eras
lm_all_stats_eras <- lm_all_stats %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, predictors) %>% 
  mutate(rmse_sum = rmse + lag(rmse),
         eras = paste(lag(era), era, sep = " --> ")) %>% 
  ungroup() %>% 
  arrange(basin, gamma_slab, predictors, era) %>% 
  drop_na()

# subset models with lowest RMSE sum
lm_best <- lm_all_stats_eras %>%
  group_by(basin, gamma_slab, eras) %>%
  slice_min(order_by = rmse_sum,
            with_ties = FALSE,
            n = params_local$MLR_number) %>%
  ungroup() %>% 
  arrange(basin, gamma_slab, eras, predictors, era)

# plot table for website
kable(lm_best) %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

basin	era	gamma_slab	predictors	rmse	rmse_sum	eras
Atlantic	(1999,2012]	(-Inf,26]	sal aou oxygen silicate phosphate	6.446770	12.518444	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal aou oxygen silicate phosphate_star	6.446770	12.518444	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal aou silicate phosphate phosphate_star	6.446770	12.518444	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal tem aou oxygen phosphate	6.573543	12.631831	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal tem aou oxygen phosphate_star	6.573543	12.631831	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal tem aou silicate phosphate	6.509788	12.547537	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal tem aou silicate phosphate_star	6.517120	12.548096	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal tem oxygen silicate phosphate	6.523111	12.543418	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal tem oxygen silicate phosphate_star	6.523111	12.543418	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(-Inf,26]	sal tem silicate phosphate phosphate_star	6.523111	12.543418	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(-Inf,26]	sal aou oxygen silicate phosphate	2.728721	9.175491	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal aou oxygen silicate phosphate_star	2.728721	9.175491	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal aou silicate phosphate phosphate_star	2.728721	9.175491	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal tem aou oxygen phosphate	2.596383	9.169926	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal tem aou oxygen phosphate_star	2.596383	9.169926	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal tem aou phosphate phosphate_star	2.596383	9.169926	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal tem aou silicate phosphate	2.690482	9.200270	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal tem aou silicate phosphate_star	2.685370	9.202490	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal tem oxygen silicate phosphate	2.684320	9.207431	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(-Inf,26]	sal tem oxygen silicate phosphate_star	2.684320	9.207431	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(26,26.5]	sal tem aou oxygen phosphate	5.136319	9.963518	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	sal tem aou oxygen phosphate_star	5.136319	9.963518	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	sal tem aou phosphate phosphate_star	5.136319	9.963518	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	tem aou oxygen phosphate	5.142191	9.978025	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	tem aou oxygen phosphate phosphate_star	5.142191	9.978025	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	tem aou oxygen phosphate_star	5.142191	9.978025	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	tem aou oxygen silicate phosphate	5.130892	9.934180	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	tem aou oxygen silicate phosphate_star	5.130892	9.934180	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	tem aou phosphate phosphate_star	5.142191	9.978025	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26,26.5]	tem aou silicate phosphate phosphate_star	5.130892	9.934180	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(26,26.5]	sal tem aou oxygen phosphate	2.727349	7.863668	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	sal tem aou oxygen phosphate_star	2.727349	7.863668	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	sal tem aou phosphate phosphate_star	2.727349	7.863668	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	tem aou oxygen phosphate	2.808370	7.950562	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	tem aou oxygen phosphate phosphate_star	2.808370	7.950562	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	tem aou oxygen phosphate_star	2.808370	7.950562	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	tem aou oxygen silicate phosphate	2.801538	7.932431	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	tem aou oxygen silicate phosphate_star	2.801538	7.932431	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	tem aou phosphate phosphate_star	2.808370	7.950562	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26,26.5]	tem aou silicate phosphate phosphate_star	2.801538	7.932431	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(26.5,26.75]	sal tem aou oxygen phosphate	4.248296	8.008264	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	sal tem aou oxygen phosphate_star	4.248296	8.008264	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	sal tem aou phosphate phosphate_star	4.248296	8.008264	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	sal tem aou silicate phosphate_star	4.206024	8.080635	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	sal tem oxygen silicate phosphate	4.202137	8.067419	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	sal tem oxygen silicate phosphate_star	4.202137	8.067419	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	sal tem silicate phosphate phosphate_star	4.202137	8.067419	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	tem aou oxygen silicate phosphate	4.235850	8.028528	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	tem aou oxygen silicate phosphate_star	4.235850	8.028528	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.5,26.75]	tem aou silicate phosphate phosphate_star	4.235850	8.028528	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(26.5,26.75]	sal tem aou oxygen phosphate	3.119708	7.368005	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	sal tem aou oxygen phosphate_star	3.119708	7.368005	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	sal tem aou phosphate phosphate_star	3.119708	7.368005	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	sal tem aou silicate phosphate_star	3.164120	7.370144	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	sal tem oxygen silicate phosphate	3.164229	7.366366	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	sal tem oxygen silicate phosphate_star	3.164229	7.366366	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	sal tem silicate phosphate phosphate_star	3.164229	7.366366	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	tem aou oxygen silicate phosphate	3.114510	7.350360	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	tem aou oxygen silicate phosphate_star	3.114510	7.350360	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.5,26.75]	tem aou silicate phosphate phosphate_star	3.114510	7.350360	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(26.75,27]	sal tem aou oxygen phosphate	4.360414	8.713407	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem aou oxygen phosphate_star	4.360414	8.713407	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem aou phosphate phosphate_star	4.360414	8.713407	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem aou phosphate_star	4.367359	8.720793	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem aou silicate phosphate	4.356613	8.692939	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem aou silicate phosphate_star	4.333963	8.660576	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem oxygen phosphate_star	4.367851	8.721622	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem oxygen silicate phosphate	4.333964	8.660787	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem oxygen silicate phosphate_star	4.333964	8.660787	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(26.75,27]	sal tem silicate phosphate phosphate_star	4.333964	8.660787	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(26.75,27]	sal tem aou silicate phosphate	3.678809	8.035422	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	sal tem aou silicate phosphate_star	3.681923	8.015886	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	sal tem oxygen silicate phosphate	3.682514	8.016478	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	sal tem oxygen silicate phosphate_star	3.682514	8.016478	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	sal tem silicate phosphate phosphate_star	3.682514	8.016478	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	tem aou oxygen silicate phosphate	3.695972	8.064147	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	tem aou oxygen silicate phosphate_star	3.695972	8.064147	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	tem aou silicate phosphate phosphate_star	3.695972	8.064147	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	tem aou silicate phosphate_star	3.699295	8.069753	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(26.75,27]	tem oxygen silicate phosphate	3.699843	8.070358	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(27,27.25]	sal tem aou silicate phosphate_star	4.709058	9.907592	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	sal tem oxygen silicate phosphate	4.714825	9.912489	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	sal tem oxygen silicate phosphate_star	4.714825	9.912489	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	sal tem silicate phosphate phosphate_star	4.714825	9.912489	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	tem aou oxygen silicate phosphate	4.701316	9.949449	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	tem aou oxygen silicate phosphate_star	4.701316	9.949449	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	tem aou silicate phosphate phosphate_star	4.701316	9.949449	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	tem aou silicate phosphate_star	4.743110	9.994747	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	tem oxygen silicate phosphate_star	4.748900	10.000240	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27,27.25]	tem silicate phosphate phosphate_star	4.748900	10.000240	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(27,27.25]	sal aou oxygen silicate phosphate	4.737076	9.698728	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	sal aou oxygen silicate phosphate_star	4.737076	9.698728	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	sal tem aou silicate phosphate	4.760680	9.541862	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	sal tem aou silicate phosphate_star	4.782627	9.491685	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	sal tem oxygen silicate phosphate	4.783279	9.498103	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	sal tem oxygen silicate phosphate_star	4.783279	9.498103	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	sal tem silicate phosphate phosphate_star	4.783279	9.498103	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	tem aou oxygen silicate phosphate	4.869536	9.570852	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	tem aou oxygen silicate phosphate_star	4.869536	9.570852	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27,27.25]	tem aou silicate phosphate phosphate_star	4.869536	9.570852	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem aou oxygen phosphate	4.179194	8.762928	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem aou oxygen phosphate_star	4.179194	8.762928	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem aou phosphate phosphate_star	4.179194	8.762928	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem aou silicate phosphate_star	4.178656	8.768145	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem oxygen phosphate	4.182260	8.772177	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem oxygen phosphate phosphate_star	4.182260	8.772177	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem oxygen phosphate_star	4.182260	8.772177	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem oxygen silicate phosphate	4.181959	8.768776	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem oxygen silicate phosphate_star	4.181959	8.768776	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.25,27.5]	sal tem silicate phosphate phosphate_star	4.181959	8.768776	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(27.25,27.5]	sal aou oxygen silicate phosphate	3.859668	8.123212	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	sal aou oxygen silicate phosphate_star	3.859668	8.123212	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	sal aou silicate phosphate phosphate_star	3.859668	8.123212	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	sal tem aou silicate phosphate	3.901209	8.101716	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	sal tem oxygen silicate phosphate	3.935914	8.117873	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	sal tem oxygen silicate phosphate_star	3.935914	8.117873	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	sal tem silicate phosphate phosphate_star	3.935914	8.117873	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	tem aou oxygen silicate phosphate	3.843413	8.114852	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	tem aou oxygen silicate phosphate_star	3.843413	8.114852	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.25,27.5]	tem aou silicate phosphate phosphate_star	3.843413	8.114852	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(27.5,27.75]	sal aou oxygen silicate phosphate	4.348180	8.668369	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	sal aou oxygen silicate phosphate_star	4.348180	8.668369	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	sal aou silicate phosphate phosphate_star	4.348180	8.668369	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	sal tem aou silicate phosphate	4.337363	8.668546	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	sal tem oxygen silicate phosphate	4.338995	8.688911	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	sal tem oxygen silicate phosphate_star	4.338995	8.688911	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	sal tem silicate phosphate phosphate_star	4.338995	8.688911	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	tem aou oxygen silicate phosphate	4.379270	8.700742	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	tem aou oxygen silicate phosphate_star	4.379270	8.700742	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.5,27.75]	tem aou silicate phosphate phosphate_star	4.379270	8.700742	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(27.5,27.75]	sal aou oxygen silicate phosphate	4.454236	8.802417	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	sal aou silicate phosphate phosphate_star	4.454236	8.802417	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	sal tem aou silicate phosphate	4.442462	8.779824	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	sal tem aou silicate phosphate_star	4.412547	8.763975	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	sal tem oxygen silicate phosphate	4.427796	8.766791	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	sal tem oxygen silicate phosphate_star	4.427796	8.766791	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	sal tem silicate phosphate phosphate_star	4.427796	8.766791	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	tem aou oxygen silicate phosphate	4.404808	8.784078	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	tem aou oxygen silicate phosphate_star	4.404808	8.784078	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.5,27.75]	tem aou silicate phosphate phosphate_star	4.404808	8.784078	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(27.75,27.85]	sal aou oxygen silicate phosphate	4.690259	8.988176	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal aou oxygen silicate phosphate_star	4.690259	8.988176	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal aou silicate phosphate	4.691904	8.990229	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal aou silicate phosphate phosphate_star	4.690259	8.988176	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal oxygen silicate phosphate	4.695498	9.012822	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal oxygen silicate phosphate phosphate_star	4.695498	9.012822	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal tem aou silicate phosphate	4.690017	8.985914	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal tem oxygen silicate phosphate	4.691036	8.997614	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal tem oxygen silicate phosphate_star	4.691036	8.997614	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.75,27.85]	sal tem silicate phosphate phosphate_star	4.691036	8.997614	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(27.75,27.85]	sal aou oxygen silicate phosphate	6.730359	11.420618	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	sal aou oxygen silicate phosphate_star	6.730359	11.420618	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	sal aou silicate phosphate phosphate_star	6.730359	11.420618	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	sal tem aou silicate phosphate	6.762289	11.452306	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	sal tem aou silicate phosphate_star	6.727605	11.423909	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	sal tem oxygen silicate phosphate_star	6.762002	11.453038	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	sal tem silicate phosphate phosphate_star	6.762002	11.453038	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	tem aou oxygen silicate phosphate	6.650617	11.367302	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	tem aou oxygen silicate phosphate_star	6.650617	11.367302	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.75,27.85]	tem aou silicate phosphate phosphate_star	6.650617	11.367302	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(27.85,27.95]	sal aou oxygen silicate phosphate	4.885371	8.591569	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal aou oxygen silicate phosphate_star	4.885371	8.591569	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal aou silicate phosphate phosphate_star	4.885371	8.591569	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal aou silicate phosphate_star	4.938351	8.649773	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal tem aou silicate phosphate	4.887553	8.604430	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal tem aou silicate phosphate_star	4.884559	8.591987	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal tem oxygen silicate phosphate	4.886511	8.600076	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal tem oxygen silicate phosphate_star	4.886511	8.600076	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal tem silicate phosphate	4.981469	8.801289	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.85,27.95]	sal tem silicate phosphate phosphate_star	4.886511	8.600076	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(27.85,27.95]	sal aou oxygen silicate phosphate	4.893184	9.778555	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal aou oxygen silicate phosphate_star	4.893184	9.778555	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal aou silicate phosphate phosphate_star	4.893184	9.778555	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal aou silicate phosphate_star	5.019136	9.957487	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal tem aou silicate phosphate	4.928597	9.816150	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal tem aou silicate phosphate_star	4.908498	9.793057	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal tem oxygen silicate phosphate	4.930139	9.816650	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal tem oxygen silicate phosphate_star	4.930139	9.816650	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal tem silicate phosphate	4.938165	9.919634	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.85,27.95]	sal tem silicate phosphate phosphate_star	4.930139	9.816650	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(27.95,28.05]	sal aou oxygen silicate phosphate	5.738505	9.286373	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal aou oxygen silicate phosphate_star	5.738505	9.286373	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal aou silicate phosphate phosphate_star	5.738505	9.286373	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal aou silicate phosphate_star	5.740725	9.294228	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal oxygen silicate phosphate_star	5.801487	9.450195	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal tem aou silicate phosphate	5.770190	9.347012	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal tem aou silicate phosphate_star	5.740490	9.291199	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal tem oxygen silicate phosphate	5.757240	9.323109	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal tem oxygen silicate phosphate_star	5.757240	9.323109	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(27.95,28.05]	sal tem silicate phosphate phosphate_star	5.757240	9.323109	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(27.95,28.05]	sal aou oxygen silicate phosphate	5.077554	10.816059	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal aou oxygen silicate phosphate_star	5.077554	10.816059	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal aou silicate phosphate phosphate_star	5.077554	10.816059	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal aou silicate phosphate_star	5.095028	10.835754	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal tem aou oxygen phosphate	4.909342	10.758163	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal tem aou oxygen phosphate_star	4.909342	10.758163	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal tem aou phosphate phosphate_star	4.909342	10.758163	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal tem aou silicate phosphate_star	5.093985	10.834475	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal tem oxygen silicate phosphate_star	5.150494	10.907734	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(27.95,28.05]	sal tem silicate phosphate phosphate_star	5.150494	10.907734	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(28.05,28.1]	sal tem aou oxygen phosphate	5.932755	9.452717	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	sal tem aou oxygen phosphate_star	5.932755	9.452717	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	sal tem aou phosphate phosphate_star	5.932755	9.452717	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	sal tem aou silicate phosphate_star	6.097779	9.683318	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	tem aou oxygen phosphate	6.026452	9.696971	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	tem aou oxygen phosphate phosphate_star	6.026452	9.696971	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	tem aou oxygen phosphate_star	6.026452	9.696971	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	tem aou oxygen silicate phosphate	5.936568	9.582293	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	tem aou oxygen silicate phosphate_star	5.936568	9.582293	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.05,28.1]	tem aou silicate phosphate phosphate_star	5.936568	9.582293	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(28.05,28.1]	sal tem aou oxygen phosphate	4.579117	10.511872	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	sal tem aou oxygen phosphate_star	4.579117	10.511872	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	sal tem aou phosphate phosphate_star	4.579117	10.511872	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	tem aou oxygen phosphate	4.580169	10.606621	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	tem aou oxygen phosphate phosphate_star	4.580169	10.606621	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	tem aou oxygen phosphate_star	4.580169	10.606621	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	tem aou oxygen silicate phosphate	4.519272	10.455840	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	tem aou oxygen silicate phosphate_star	4.519272	10.455840	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	tem aou phosphate phosphate_star	4.580169	10.606621	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.05,28.1]	tem aou silicate phosphate phosphate_star	4.519272	10.455840	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem aou oxygen phosphate	6.663587	10.125704	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem aou oxygen phosphate_star	6.663587	10.125704	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem aou phosphate phosphate_star	6.663587	10.125704	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem aou phosphate_star	6.673994	10.144965	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem aou silicate phosphate_star	6.666140	10.107288	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem oxygen silicate phosphate	6.667478	10.108027	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem oxygen silicate phosphate_star	6.667478	10.108027	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem phosphate phosphate_star	6.673367	10.146370	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem silicate phosphate phosphate_star	6.667478	10.108027	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.1,28.15]	sal tem silicate phosphate_star	6.669045	10.116689	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(28.1,28.15]	sal tem aou oxygen phosphate	4.691179	11.354767	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	sal tem aou oxygen phosphate_star	4.691179	11.354767	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	sal tem aou phosphate phosphate_star	4.691179	11.354767	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	sal tem aou silicate phosphate_star	4.743879	11.410019	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	sal tem oxygen silicate phosphate	4.746503	11.413981	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	sal tem oxygen silicate phosphate_star	4.746503	11.413981	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	sal tem silicate phosphate phosphate_star	4.746503	11.413981	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	tem aou oxygen silicate phosphate	4.687568	11.399807	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	tem aou oxygen silicate phosphate_star	4.687568	11.399807	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.1,28.15]	tem aou silicate phosphate phosphate_star	4.687568	11.399807	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(28.15,28.2]	sal aou oxygen silicate phosphate	3.512680	6.995892	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	sal aou oxygen silicate phosphate_star	3.512680	6.995892	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	sal aou silicate phosphate phosphate_star	3.512680	6.995892	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	sal tem aou oxygen phosphate	3.511563	6.978371	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	sal tem aou oxygen phosphate_star	3.511563	6.978371	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	sal tem aou phosphate phosphate_star	3.511563	6.978371	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	sal tem aou silicate phosphate	3.513504	6.984252	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	tem aou oxygen silicate phosphate	3.523840	7.006837	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	tem aou oxygen silicate phosphate_star	3.523840	7.006837	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.15,28.2]	tem aou silicate phosphate phosphate_star	3.523840	7.006837	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(28.15,28.2]	sal aou oxygen silicate phosphate	2.921525	6.434205	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal aou oxygen silicate phosphate_star	2.921525	6.434205	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal aou silicate phosphate phosphate_star	2.921525	6.434205	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal tem aou oxygen phosphate	2.910600	6.422163	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal tem aou oxygen phosphate_star	2.910600	6.422163	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal tem aou phosphate	2.910619	6.446814	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal tem aou phosphate phosphate_star	2.910600	6.422163	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal tem aou silicate phosphate	2.904569	6.418073	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal tem oxygen silicate phosphate_star	2.912375	6.460174	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.15,28.2]	sal tem silicate phosphate phosphate_star	2.912375	6.460174	(1999,2012] –> (2012,Inf]
Atlantic	(1999,2012]	(28.2, Inf]	sal aou oxygen phosphate	3.025095	5.874140	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal aou oxygen phosphate phosphate_star	3.025095	5.874140	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal aou oxygen phosphate_star	3.025095	5.874140	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal aou oxygen silicate phosphate	3.020253	5.861716	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal aou oxygen silicate phosphate_star	3.020253	5.861716	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal aou phosphate phosphate_star	3.025095	5.874140	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal aou silicate phosphate phosphate_star	3.020253	5.861716	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal tem aou oxygen phosphate	3.022294	5.870065	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal tem aou oxygen phosphate_star	3.022294	5.870065	(1981,1999] –> (1999,2012]
Atlantic	(1999,2012]	(28.2, Inf]	sal tem aou phosphate phosphate_star	3.022294	5.870065	(1981,1999] –> (1999,2012]
Atlantic	(2012,Inf]	(28.2, Inf]	sal aou oxygen silicate phosphate	2.879832	5.900085	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal aou oxygen silicate phosphate_star	2.879832	5.900085	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal aou silicate phosphate	2.899339	5.919967	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal aou silicate phosphate phosphate_star	2.879832	5.900085	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal oxygen silicate phosphate_star	2.880829	5.920535	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal silicate phosphate phosphate_star	2.880829	5.920535	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal tem aou silicate phosphate	2.899066	5.919534	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal tem oxygen silicate phosphate	2.880233	5.916931	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal tem oxygen silicate phosphate_star	2.880233	5.916931	(1999,2012] –> (2012,Inf]
Atlantic	(2012,Inf]	(28.2, Inf]	sal tem silicate phosphate phosphate_star	2.880233	5.916931	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal aou oxygen silicate phosphate	6.382846	17.782020	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal aou oxygen silicate phosphate_star	6.382846	17.782020	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal aou silicate phosphate phosphate_star	6.382846	17.782020	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal tem aou phosphate phosphate_star	6.772556	18.516934	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal tem aou silicate phosphate	6.499343	17.930861	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal tem aou silicate phosphate_star	6.538589	17.987478	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal tem oxygen silicate phosphate	6.555662	18.010692	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal tem oxygen silicate phosphate_star	6.555662	18.010692	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal tem silicate phosphate phosphate_star	6.555662	18.010692	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(-Inf,26]	sal tem silicate phosphate_star	6.777762	18.372964	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal aou oxygen silicate phosphate	5.446200	11.829046	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal aou oxygen silicate phosphate_star	5.446200	11.829046	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal aou silicate phosphate phosphate_star	5.446200	11.829046	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal tem aou oxygen phosphate	5.867660	12.640216	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal tem aou oxygen phosphate_star	5.867660	12.640216	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal tem aou silicate phosphate	5.680341	12.179684	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal tem aou silicate phosphate_star	5.748744	12.287333	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal tem oxygen silicate phosphate	5.791662	12.347324	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal tem oxygen silicate phosphate_star	5.791662	12.347324	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(-Inf,26]	sal tem silicate phosphate phosphate_star	5.791662	12.347324	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(26,26.5]	sal aou oxygen silicate phosphate	4.746536	12.220507	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal aou oxygen silicate phosphate_star	4.746536	12.220507	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal aou silicate phosphate phosphate_star	4.746536	12.220507	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal tem aou oxygen phosphate	4.964585	12.614270	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal tem aou silicate phosphate	4.759256	12.298676	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal tem aou silicate phosphate_star	4.787274	12.360645	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal tem oxygen silicate phosphate	4.788708	12.363756	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal tem oxygen silicate phosphate_star	4.788708	12.363756	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal tem silicate phosphate phosphate_star	4.788708	12.363756	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26,26.5]	sal tem silicate phosphate_star	4.809740	12.399154	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal aou oxygen silicate phosphate	3.951995	8.698531	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal aou oxygen silicate phosphate_star	3.951995	8.698531	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal aou silicate phosphate phosphate_star	3.951995	8.698531	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal tem aou phosphate phosphate_star	4.310251	9.274837	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal tem aou silicate phosphate	4.049322	8.808578	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal tem aou silicate phosphate_star	4.098276	8.885551	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal tem oxygen silicate phosphate	4.097894	8.886602	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal tem oxygen silicate phosphate_star	4.097894	8.886602	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal tem silicate phosphate phosphate_star	4.097894	8.886602	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26,26.5]	sal tem silicate phosphate_star	4.098581	8.908321	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal aou oxygen phosphate	5.365868	11.066878	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal aou oxygen phosphate phosphate_star	5.365868	11.066878	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal aou oxygen phosphate_star	5.365868	11.066878	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal aou oxygen silicate phosphate	5.365268	10.995337	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal aou oxygen silicate phosphate_star	5.365268	10.995337	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal aou phosphate phosphate_star	5.365868	11.066878	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal aou silicate phosphate phosphate_star	5.365268	10.995337	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal tem aou oxygen phosphate	5.365041	11.066011	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal tem aou oxygen phosphate_star	5.365041	11.066011	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.5,26.75]	sal tem aou phosphate phosphate_star	5.365041	11.066011	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal aou oxygen phosphate	4.664114	10.029982	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal aou oxygen phosphate phosphate_star	4.664114	10.029982	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal aou oxygen phosphate_star	4.664114	10.029982	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal aou oxygen silicate phosphate	4.589254	9.954522	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal aou oxygen silicate phosphate_star	4.589254	9.954522	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal aou phosphate phosphate_star	4.664114	10.029982	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal aou silicate phosphate phosphate_star	4.589254	9.954522	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal tem aou oxygen phosphate	4.648956	10.013996	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal tem aou oxygen phosphate_star	4.648956	10.013996	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.5,26.75]	sal tem aou phosphate phosphate_star	4.648956	10.013996	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(26.75,27]	sal tem aou oxygen phosphate	5.005957	11.349111	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	sal tem aou oxygen phosphate_star	5.005957	11.349111	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	sal tem aou phosphate phosphate_star	5.005957	11.349111	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	tem aou oxygen phosphate	5.012107	11.355314	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	tem aou oxygen phosphate phosphate_star	5.012107	11.355314	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	tem aou oxygen phosphate_star	5.012107	11.355314	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	tem aou oxygen silicate phosphate	4.981285	11.301194	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	tem aou oxygen silicate phosphate_star	4.981285	11.301194	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	tem aou phosphate phosphate_star	5.012107	11.355314	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(26.75,27]	tem aou silicate phosphate phosphate_star	4.981285	11.301194	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(26.75,27]	sal tem aou oxygen phosphate	4.315630	9.321587	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	sal tem aou oxygen phosphate_star	4.315630	9.321587	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	sal tem aou phosphate phosphate_star	4.315630	9.321587	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	tem aou oxygen phosphate	4.324421	9.336528	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	tem aou oxygen phosphate phosphate_star	4.324421	9.336528	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	tem aou oxygen phosphate_star	4.324421	9.336528	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	tem aou oxygen silicate phosphate	4.308653	9.289937	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	tem aou oxygen silicate phosphate_star	4.308653	9.289937	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	tem aou phosphate phosphate_star	4.324421	9.336528	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(26.75,27]	tem aou silicate phosphate phosphate_star	4.308653	9.289937	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(27,27.25]	sal aou oxygen silicate phosphate	4.773061	10.941716	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	sal aou oxygen silicate phosphate_star	4.773061	10.941716	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	sal aou silicate phosphate phosphate_star	4.773061	10.941716	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	sal tem aou oxygen phosphate	4.749776	10.783988	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	sal tem aou oxygen phosphate_star	4.749776	10.783988	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	sal tem aou phosphate phosphate_star	4.749776	10.783988	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	tem aou oxygen silicate phosphate	4.693978	10.646400	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	tem aou oxygen silicate phosphate_star	4.693978	10.646400	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	tem aou phosphate phosphate_star	4.880383	10.979896	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27,27.25]	tem aou silicate phosphate phosphate_star	4.693978	10.646400	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(27,27.25]	sal aou oxygen silicate phosphate	4.158213	8.931275	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	sal aou oxygen silicate phosphate_star	4.158213	8.931275	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	sal aou silicate phosphate phosphate_star	4.158213	8.931275	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	sal tem aou oxygen phosphate	4.170069	8.919845	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	sal tem aou oxygen phosphate_star	4.170069	8.919845	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	sal tem aou phosphate phosphate_star	4.170069	8.919845	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	sal tem aou silicate phosphate	4.173867	8.954467	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	tem aou oxygen silicate phosphate	4.083208	8.777186	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	tem aou oxygen silicate phosphate_star	4.083208	8.777186	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27,27.25]	tem aou silicate phosphate phosphate_star	4.083208	8.777186	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(27.25,27.5]	sal tem aou oxygen phosphate	4.312410	9.143720	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	sal tem aou oxygen phosphate_star	4.312410	9.143720	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	sal tem aou phosphate phosphate_star	4.312410	9.143720	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	tem aou oxygen phosphate	4.350064	9.199345	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	tem aou oxygen phosphate phosphate_star	4.350064	9.199345	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	tem aou oxygen phosphate_star	4.350064	9.199345	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	tem aou oxygen silicate phosphate	4.103948	8.901021	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	tem aou oxygen silicate phosphate_star	4.103948	8.901021	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	tem aou phosphate phosphate_star	4.350064	9.199345	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.25,27.5]	tem aou silicate phosphate phosphate_star	4.103948	8.901021	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal aou oxygen silicate phosphate	3.270995	7.499409	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal aou oxygen silicate phosphate_star	3.270995	7.499409	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal aou silicate phosphate	3.304707	7.594365	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal aou silicate phosphate phosphate_star	3.270995	7.499409	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal tem aou silicate phosphate	3.274877	7.531761	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal tem aou silicate phosphate_star	3.283048	7.585998	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal tem oxygen silicate phosphate	3.281384	7.574943	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal tem oxygen silicate phosphate_star	3.281384	7.574943	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	sal tem silicate phosphate phosphate_star	3.281384	7.574943	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.25,27.5]	tem aou oxygen silicate phosphate_star	3.574838	7.678787	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(27.5,27.75]	sal aou oxygen silicate phosphate	3.806972	8.516369	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	sal aou oxygen silicate phosphate_star	3.806972	8.516369	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	sal aou silicate phosphate phosphate_star	3.806972	8.516369	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	sal tem aou oxygen phosphate	4.021376	8.498585	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	sal tem aou oxygen phosphate_star	4.021376	8.498585	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	sal tem aou phosphate phosphate_star	4.021376	8.498585	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	tem aou oxygen phosphate_star	4.089631	8.566857	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	tem aou oxygen silicate phosphate	4.017873	8.477925	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	tem aou oxygen silicate phosphate_star	4.017873	8.477925	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.5,27.75]	tem aou silicate phosphate phosphate_star	4.017873	8.477925	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal aou oxygen silicate phosphate	2.976658	6.783630	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal aou oxygen silicate phosphate_star	2.976658	6.783630	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal aou silicate phosphate	3.117945	7.099913	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal aou silicate phosphate phosphate_star	2.976658	6.783630	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal tem aou silicate phosphate	2.975163	6.780257	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal tem aou silicate phosphate_star	2.974569	6.788626	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal tem oxygen silicate phosphate	2.974597	6.787567	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal tem oxygen silicate phosphate_star	2.974597	6.787567	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal tem silicate phosphate phosphate_star	2.974597	6.787567	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.5,27.75]	sal tem silicate phosphate_star	3.072150	6.917647	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(27.75,27.85]	sal tem aou oxygen phosphate	3.368877	7.474893	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	sal tem aou oxygen phosphate_star	3.368877	7.474893	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	sal tem aou phosphate phosphate_star	3.368877	7.474893	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	tem aou oxygen phosphate	3.369535	7.482781	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	tem aou oxygen phosphate phosphate_star	3.369535	7.482781	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	tem aou oxygen phosphate_star	3.369535	7.482781	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	tem aou oxygen silicate phosphate	3.311254	7.424455	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	tem aou oxygen silicate phosphate_star	3.311254	7.424455	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	tem aou phosphate phosphate_star	3.369535	7.482781	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.75,27.85]	tem aou silicate phosphate phosphate_star	3.311254	7.424455	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	sal tem aou silicate phosphate	2.877533	6.234006	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	sal tem aou silicate phosphate_star	2.866808	6.201961	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	sal tem oxygen silicate phosphate	2.866847	6.200557	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	sal tem oxygen silicate phosphate_star	2.866847	6.200557	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	sal tem silicate phosphate phosphate_star	2.866847	6.200557	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	sal tem silicate phosphate_star	2.866886	6.226521	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	tem aou oxygen silicate phosphate	2.908008	6.219262	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	tem aou oxygen silicate phosphate_star	2.908008	6.219262	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	tem aou silicate phosphate phosphate_star	2.908008	6.219262	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.75,27.85]	tem silicate phosphate phosphate_star	2.919082	6.257604	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(27.85,27.95]	aou oxygen silicate phosphate	3.020440	7.317989	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	aou oxygen silicate phosphate phosphate_star	3.020440	7.317989	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	aou oxygen silicate phosphate_star	3.020440	7.317989	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	aou silicate phosphate phosphate_star	3.020440	7.317989	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	sal aou oxygen silicate phosphate	3.020316	7.316696	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	sal aou oxygen silicate phosphate_star	3.020316	7.316696	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	sal aou silicate phosphate phosphate_star	3.020316	7.316696	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	tem aou oxygen silicate phosphate	3.015558	7.313092	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	tem aou oxygen silicate phosphate_star	3.015558	7.313092	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.85,27.95]	tem aou silicate phosphate phosphate_star	3.015558	7.313092	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	sal tem aou silicate phosphate	2.866566	5.882913	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	sal tem aou silicate phosphate_star	2.859085	5.882181	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	sal tem oxygen silicate phosphate	2.859051	5.883043	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	sal tem oxygen silicate phosphate_star	2.859051	5.883043	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	sal tem silicate phosphate phosphate_star	2.859051	5.883043	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	sal tem silicate phosphate_star	2.859166	5.903344	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	tem aou oxygen silicate phosphate	2.884353	5.899911	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	tem aou oxygen silicate phosphate_star	2.884353	5.899911	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	tem aou silicate phosphate	2.886725	5.903075	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.85,27.95]	tem aou silicate phosphate phosphate_star	2.884353	5.899911	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal aou oxygen phosphate	2.882262	7.140450	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal aou oxygen phosphate phosphate_star	2.882262	7.140450	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal aou oxygen phosphate_star	2.882262	7.140450	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal aou oxygen silicate phosphate	2.860814	7.117364	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal aou oxygen silicate phosphate_star	2.860814	7.117364	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal aou phosphate phosphate_star	2.882262	7.140450	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal aou silicate phosphate phosphate_star	2.860814	7.117364	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal tem aou oxygen phosphate	2.875437	7.126786	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal tem aou oxygen phosphate_star	2.875437	7.126786	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(27.95,28.05]	sal tem aou phosphate phosphate_star	2.875437	7.126786	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	sal aou oxygen silicate phosphate	3.058382	5.919197	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	sal aou oxygen silicate phosphate_star	3.058382	5.919197	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	sal aou silicate phosphate phosphate_star	3.058382	5.919197	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	sal tem aou oxygen phosphate	3.085178	5.960615	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	sal tem aou oxygen phosphate_star	3.085178	5.960615	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	sal tem aou phosphate phosphate_star	3.085178	5.960615	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	sal tem aou silicate phosphate	3.046502	5.933889	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	tem aou oxygen silicate phosphate	3.088661	5.959650	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	tem aou oxygen silicate phosphate_star	3.088661	5.959650	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(27.95,28.05]	tem aou silicate phosphate phosphate_star	3.088661	5.959650	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal aou oxygen phosphate	2.846988	6.907189	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal aou oxygen phosphate phosphate_star	2.846988	6.907189	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal aou oxygen phosphate_star	2.846988	6.907189	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal aou oxygen silicate phosphate	2.829597	6.881145	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal aou oxygen silicate phosphate_star	2.829597	6.881145	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal aou phosphate phosphate_star	2.846988	6.907189	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal aou silicate phosphate phosphate_star	2.829597	6.881145	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal tem aou oxygen phosphate	2.845020	6.897846	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal tem aou oxygen phosphate_star	2.845020	6.897846	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.05,28.1]	sal tem aou phosphate phosphate_star	2.845020	6.897846	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal aou oxygen phosphate	2.818529	5.665517	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal aou oxygen phosphate phosphate_star	2.818529	5.665517	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal aou oxygen phosphate_star	2.818529	5.665517	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal aou oxygen silicate phosphate	2.816657	5.646255	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal aou oxygen silicate phosphate_star	2.816657	5.646255	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal aou phosphate phosphate_star	2.818529	5.665517	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal aou silicate phosphate phosphate_star	2.816657	5.646255	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal tem aou oxygen phosphate	2.809125	5.654146	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal tem aou oxygen phosphate_star	2.809125	5.654146	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.05,28.1]	sal tem aou phosphate phosphate_star	2.809125	5.654146	(1999,2012] –> (2012,Inf]
Indo-Pacific	(1999,2012]	(28.1, Inf]	aou oxygen silicate phosphate	3.119228	6.935474	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	aou oxygen silicate phosphate phosphate_star	3.119228	6.935474	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	aou oxygen silicate phosphate_star	3.119228	6.935474	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	aou silicate phosphate phosphate_star	3.119228	6.935474	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	sal aou oxygen silicate phosphate	3.118070	6.915110	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	sal aou oxygen silicate phosphate_star	3.118070	6.915110	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	sal aou silicate phosphate phosphate_star	3.118070	6.915110	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	tem aou oxygen silicate phosphate	3.066430	6.834195	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	tem aou oxygen silicate phosphate_star	3.066430	6.834195	(1981,1999] –> (1999,2012]
Indo-Pacific	(1999,2012]	(28.1, Inf]	tem aou silicate phosphate phosphate_star	3.066430	6.834195	(1981,1999] –> (1999,2012]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	aou oxygen silicate phosphate	2.697320	5.816548	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	aou oxygen silicate phosphate phosphate_star	2.697320	5.816548	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	aou oxygen silicate phosphate_star	2.697320	5.816548	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	aou silicate phosphate phosphate_star	2.697320	5.816548	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	sal aou oxygen silicate phosphate	2.608983	5.727053	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	sal aou oxygen silicate phosphate_star	2.608983	5.727053	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	sal aou silicate phosphate phosphate_star	2.608983	5.727053	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	tem aou oxygen silicate phosphate	2.650916	5.717346	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	tem aou oxygen silicate phosphate_star	2.650916	5.717346	(1999,2012] –> (2012,Inf]
Indo-Pacific	(2012,Inf]	(28.1, Inf]	tem aou silicate phosphate phosphate_star	2.650916	5.717346	(1999,2012] –> (2012,Inf]

3.4 Correlations RMSE between eras

3.4.1 All models

max_rmse <-
  max(c(lm_all_stats_eras$rmse,
        lm_all_stats_eras$rmse_sum - lm_all_stats_eras$rmse))

lm_all_stats_eras %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0,max_rmse),
              ylim = c(0,max_rmse)) +
  facet_grid(eras ~ basin)

Past versions of rmse_correlation_across_eras_all_models-1.png

Version	Author	Date
b03ddb8	jens-daniel-mueller	2020-12-02
91435ae	jens-daniel-mueller	2020-12-01
196be51	jens-daniel-mueller	2020-11-30

rm(max_rmse)

3.4.2 Best models

max_rmse <-
  max(c(lm_best$rmse,
        lm_best$rmse_sum - lm_best$rmse))

lm_best %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0,max_rmse),
              ylim = c(0,max_rmse)) +
  facet_grid(eras ~ basin)

Past versions of rmse_correlation_across_eras_10_models-1.png

Version	Author	Date
b03ddb8	jens-daniel-mueller	2020-12-02
91435ae	jens-daniel-mueller	2020-12-01
196be51	jens-daniel-mueller	2020-11-30

rm(max_rmse)

# this code tests the rmse output of the ols_step_all_possible() function used
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))

4 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.

# format model formula
lm_best <- lm_best %>% 
  mutate(lm_coeff = str_replace_all(predictors, " ", " + "),
         lm_coeff = paste("cstar ~", lm_coeff))


# create table with two era belonging to one eras
eras_forward <- lm_all_stats %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, predictors) %>% 
  mutate(eras = paste(era, lead(era), sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_backward <- lm_all_stats %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, predictors) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_era <- full_join(eras_backward, eras_forward) %>% 
  filter(str_detect(eras, "NA") == FALSE)

# extend best model selection from eras to era
lm_best <- lm_best %>% 
  select(-era)

lm_best <- full_join(lm_best, eras_era)
rm(eras_era, eras_forward, eras_backward, lm_all_stats, lm_all_stats_eras)

# select required columns
lm_best <- lm_best %>% 
  select(basin, gamma_slab, era, eras, predictors, lm_coeff, rmse_sum)

# run similar loop as for rmse calculation
# to get model coefficients for 10 best models
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_era <- lm_best %>%
      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_best_basin_era_slab <- lm_best_basin_era %>%
        filter(gamma_slab == i_gamma_slab)
      
      for (i_eras in unique(lm_best_basin_era_slab$eras)) {
        # i_eras <- unique(lm_best_basin_era_slab$eras)[1]
        lm_best_basin_era_slab_eras <- lm_best_basin_era_slab %>%
          filter(eras == i_eras)
        
        for (i_predictors in unique(lm_best_basin_era_slab_eras$predictors)) {
          # i_predictors <- unique(lm_best_basin_era_slab_eras$predictors)[2]
          print(i_predictors)
          
          lm_best_single <- lm_best_basin_era_slab_eras %>%
            filter(predictors == i_predictors) %>%
            select(lm_coeff) %>%
            pull()
          
          i_rmse_sum <- lm_best_basin_era_slab_eras %>%
            filter(predictors == i_predictors) %>%
            select(rmse_sum) %>%
            pull()
          
          lm_best_single_formula <- as.formula(lm_best_single)
          
          lm_fit_single <- lm(lm_best_single_formula,
                              data = GLODAP_basin_era_slab)
          

          if (params_local$plot_all_figures == "y") {
          # plotting model diagnostics
          p_model <- ggnostic(
            lm_fit_single,
            columnsY = c("cstar", ".fitted", ".resid"),
            title = paste("eras:", i_eras,
                          "| era:", i_era,
                          "| basin:", i_basin,
                          "| gamma slab:", i_gamma_slab,
                          "| predictors:", i_predictors)
          )

          ggsave(
            plot = p_model,
            path = paste(path_version_figures, "eMLR_diagnostics/", sep = ""),
            filename = paste(
              i_eras,
              i_era,
              i_basin,
              i_gamma_slab,
              i_predictors,
              "eMLR_cstar_residuals.png",
              sep = "_"
          ),
          width = 14,
          height = 8
          )
          
          rm(p_model)
          
          }

          # collect model coefficients in data frame
          coefficients <- tidy(lm_fit_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
            )
          
          if (exists("lm_all")) {
            lm_all <- bind_rows(lm_all, coefficients)
          }
          
          if (!exists("lm_all")) {
            lm_all <- coefficients
          }
          
        }
        
        
      }
    }
    
  }
  
}


rm(lm_fit_single, coefficients, i_rmse_sum,
   GLODAP_basin_era, GLODAP_basin_era_slab,
   lm_best, lm_best_basin_era, lm_best_basin_era_slab, lm_best_basin_era_slab_eras,
   lm_best_single, lm_best_single_formula,
   i_basin, i_era, i_gamma_slab, i_predictors)

4.1 Prepare coeffcients

Coefficients are prepared for the mapping of cstar and cant.

# select relevant columns
lm_all <- lm_all %>% 
  select(basin, gamma_slab, era, eras, model, term, estimate)

# set coefficient to zero if not fitted (=NA)
lm_all <- lm_all %>% 
  mutate(estimate = if_else(is.na(estimate), 0, estimate))


# Prepare model coefficients for mapping of cstar
lm_all_cstar <- lm_all %>% 
  pivot_wider(values_from = estimate,
              names_from = term,
              names_prefix = "coeff_",
              values_fill = 0)


# Prepare model coefficients differences for mapping of cant
# this requires to subtract coefficients of adjacent era
lm_all_long <- lm_all %>% 
  arrange(era) %>% 
  group_by(basin, gamma_slab, eras, model, term) %>% 
  mutate(delta_coeff = estimate - lag(estimate)) %>% 
  ungroup() %>% 
  arrange(basin, gamma_slab, model, term, eras) %>% 
  drop_na() %>% 
  select(-c(era,estimate))


lm_all_cant <- lm_all_long %>%
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

4.2 Write files

lm_all_cstar %>% write_csv(paste(path_version_data,
                                      "lm_all_cstar.csv",
                                      sep = ""))

lm_all_cant %>% write_csv(paste(path_version_data,
                                      "lm_all_cant.csv",
                                      sep = ""))

Session information

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.1

Matrix products: default
BLAS:   /usr/local/R-4.0.3/lib64/R/lib/libRblas.so
LAPACK: /usr/local/R-4.0.3/lib64/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

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

other attached packages:
 [1] corrr_0.4.3      broom_0.7.2      kableExtra_1.3.1 knitr_1.30      
 [5] olsrr_0.5.3.9000 GGally_2.0.0     lubridate_1.7.9  metR_0.9.0      
 [9] scico_1.2.0      patchwork_1.1.0  collapse_1.4.2   forcats_0.5.0   
[13] stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4      readr_1.4.0     
[17] tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.2    tidyverse_1.3.0 
[21] workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] fs_1.5.0                 webshot_0.5.2            RColorBrewer_1.1-2      
 [4] httr_1.4.2               rprojroot_2.0.2          tools_4.0.3             
 [7] backports_1.1.10         R6_2.5.0                 nortest_1.0-4           
[10] DBI_1.1.0                colorspace_2.0-0         withr_2.3.0             
[13] gridExtra_2.3            tidyselect_1.1.0         curl_4.3                
[16] compiler_4.0.3           git2r_0.27.1             cli_2.2.0               
[19] rvest_0.3.6              xml2_1.3.2               labeling_0.4.2          
[22] scales_1.1.1             checkmate_2.0.0          goftest_1.2-2           
[25] digest_0.6.27            foreign_0.8-80           rmarkdown_2.5           
[28] rio_0.5.16               pkgconfig_2.0.3          htmltools_0.5.0         
[31] highr_0.8                dbplyr_1.4.4             rlang_0.4.9             
[34] readxl_1.3.1             rstudioapi_0.13          farver_2.0.3            
[37] generics_0.0.2           jsonlite_1.7.1           zip_2.1.1               
[40] car_3.0-10               magrittr_2.0.1           Matrix_1.2-18           
[43] Rcpp_1.0.5               munsell_0.5.0            fansi_0.4.1             
[46] abind_1.4-5              lifecycle_0.2.0          stringi_1.5.3           
[49] whisker_0.4              yaml_2.2.1               carData_3.0-4           
[52] plyr_1.8.6               grid_4.0.3               blob_1.2.1              
[55] parallel_4.0.3           promises_1.1.1           crayon_1.3.4            
[58] lattice_0.20-41          haven_2.3.1              hms_0.5.3               
[61] pillar_1.4.7             reprex_0.3.0             glue_1.4.2              
[64] evaluate_0.14            RcppArmadillo_0.10.1.2.0 data.table_1.13.2       
[67] modelr_0.1.8             vctrs_0.3.5              httpuv_1.5.4            
[70] cellranger_1.1.0         gtable_0.3.0             reshape_0.8.8           
[73] assertthat_0.2.1         xfun_0.18                openxlsx_4.2.3          
[76] RcppEigen_0.3.3.7.0      later_1.1.0.1            viridisLite_0.3.0       
[79] ellipsis_0.3.1           here_0.1