eMLR - model fitting

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Last updated: 2021-01-15

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---

1 Required data

Required are:

• cleaned and prepared GLODAP-based synthetic model subsetting file

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

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

• sal, temp, aou, oxygen, silicate, phosphate, phosphate_star

# the following code is a workaround to find all predictor combinations
# using the olsrr package and fit all models for one era, slab, and basin

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

# subset one basin and era for fitting
GLODAP_basin_era <- GLODAP %>%
  filter(basin == i_basin, era == i_era)

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(paste(
  params_local$MLR_target,
  paste(params_local$MLR_predictors, collapse = " + "),
  sep = " ~ "
),
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)

# convert to tibble
lm_all <- as_tibble(lm_all)

# extract relevant columns and format model formula
lm_all <- lm_all %>% 
  select(n, predictors) %>% 
  mutate(lm_coeff = str_replace_all(predictors, " ", " + "),
         lm_coeff = paste(params_local$MLR_target, "~", lm_coeff))

# remove helper objects
rm(i_gamma_slab,
   i_era,
   i_basin,
   GLODAP_basin_era,
   GLODAP_basin_era_slab,
   lm_full)

3 Apply predictor threshold

Select combinations with a total number of predictors in the range:

• Minimum: 2
  
• Maximum: 5

lm_all <- lm_all %>% 
  filter(n >= params_local$MLR_predictors_min,
         n <= params_local$MLR_predictors_max)

This results in a total number of MLR models of:

• 112

4 Fit all models

Individual linear regression models were fitted for the chosen target variable:

• cstar_tref

as a function of each predictor combination. Fitting was performed separately within each basin, era, and slab. Model diagnostics, such as the root mean squared error (RMSE), were calculated for each fitted model.

# loop across all basins, era, gamma slabs, and MLRs
# fit all MLR 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)
    
    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)
      
      for (i_predictors in unique(lm_all$predictors)) {
        # i_predictors <- unique(lm_all$predictors)[110]

        # extract one model definition
        i_lm <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(lm_coeff) %>%
          pull()
        
        # extract number of predictors
        i_n_predictors <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(n) %>%
          pull()
        
        # fit model
        i_lm_fit <- lm(as.formula(i_lm),
                       data = GLODAP_basin_era_slab)
        
        # find max predictor correlation
        i_cor_max <- GLODAP_basin_era_slab %>%
          select(!!!syms(str_split(i_predictors, " ",
                                         simplify = TRUE))) %>%
          correlate(quiet = TRUE) %>% 
          select(-term) %>% 
          abs() %>% 
          max(na.rm = TRUE)
        
        # calculate root mean squared error
        i_rmse <- sqrt(
          c(crossprod(i_lm_fit$residuals)) / 
            length(i_lm_fit$residuals)
        )

        # calculate maximum residual
        i_resid_max <- max(abs(i_lm_fit$residuals))
        
        # calculate Akaike information criterion aic
        i_aic <- AIC(i_lm_fit)
        
        # collect model coefficients and diagnostics
        coefficients <- tidy(i_lm_fit)
        
        coefficients <- coefficients %>%
          mutate(
            basin = i_basin,
            era = i_era,
            gamma_slab = i_gamma_slab,
            model = i_lm,
            rmse = i_rmse,
            aic = i_aic,
            resid_max = i_resid_max,
            n_predictors = i_n_predictors,
            na_predictor = anyNA(coefficients$estimate),
            cor_max = i_cor_max
          )
        
        if (exists("lm_all_fitted")) {
          lm_all_fitted <- bind_rows(lm_all_fitted, coefficients)
        }
        
        if (!exists("lm_all_fitted")) {
          lm_all_fitted <- coefficients
        }
        
        # plot model diagnostics, if activated
        if (params_local$plot_all_figures == "y") {
          p_model <- ggnostic(
            i_lm_fit,
            columnsY = c(params_local$MLR_target, ".fitted", ".resid"),
            title = paste(
              "| 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(
              "MLR_residuals",
              i_era,
              i_basin,
              i_gamma_slab,
              i_predictors,
              "predictors.png",
              sep = "_"
            ),
            width = 14,
            height = 8
          )
          
          rm(p_model)
          
        }
        
      }
      
      
    }
  }
  
}


rm(i_lm_fit, coefficients, i_rmse,
   GLODAP_basin_era, GLODAP_basin_era_slab,
   i_lm,
   i_basin, i_era, i_gamma_slab, i_predictors,
   lm_all,
   i_aic, i_n_predictors, i_resid_max)

5 Prepare coeffcients

Coefficients are prepared for the mapping of Cant and the chosen target variable.

5.1 Formatting

# select relevant columns
lm_all_fitted <- lm_all_fitted %>% 
  select(basin, gamma_slab, era, model, n_predictors, 
         term, estimate, 
         rmse, aic, resid_max, na_predictor, cor_max)

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

# Prepare model coefficients for mapping of target variable
lm_all_fitted_wide <- lm_all_fitted %>% 
  pivot_wider(values_from = estimate,
              names_from = term,
              names_prefix = "coeff_",
              values_fill = 0)

5.2 Predictor selection

Within each basin and slab, the following number of best linear regression models was selected:

• 10

The criterion used to select the best models was:

• rmse

The criterion was summed up for two adjacent eras, and the models with lowest summed values were selected.

Please note, that currently the lm() function produces NAs for some predictors. It is not yet entirely clear when this happens, but presumably it is caused by some form of collinearity between predictors, such that including another predictor does not help to explain the target variable any better. The issues also expresses as exactly identical rmse values of different models. As an interim solution, models with fitted NA predictors were not included.

# remove models with predictors fitted as NA

lm_all_fitted_wide <- lm_all_fitted_wide %>%
  filter(na_predictor == FALSE)

# calculate RMSE sum for adjacent eras
lm_all_fitted_wide_eras <- lm_all_fitted_wide  %>%
  select(basin, gamma_slab, model, era, rmse, aic, resid_max) %>% 
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> "),
         rmse_sum = rmse + lag(rmse),
         aic_sum = aic + lag(aic)
         ) %>% 
  ungroup() %>% 
  select(-c(era)) %>% 
  drop_na()

# subset models with lowest summed criterion
# chose which criterion is applied

if (params_local$MLR_criterion == "aic") {
  lm_best <- lm_all_fitted_wide_eras %>%
    group_by(basin, gamma_slab, eras) %>%
    slice_min(order_by = aic_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
} else {
  lm_best <- lm_all_fitted_wide_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, model)
}


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

basin	gamma_slab	model	rmse	aic	resid_max	eras	rmse_sum	aic_sum
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen	0.7809678	133.85859	2.0772701	1982-1999 –> 2000-2012	2.4182795	344.70599
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.7425615	130.61405	2.1602026	1982-1999 –> 2000-2012	2.2577295	335.39839
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.7425615	130.61405	2.1602026	1982-1999 –> 2000-2012	2.2577295	335.39839
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + silicate	0.6812955	121.65866	1.8480163	1982-1999 –> 2000-2012	2.3184984	334.49915
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.7425615	130.61405	2.1602026	1982-1999 –> 2000-2012	2.2577295	335.39839
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + phosphate	0.7570324	130.62129	2.1365217	1982-1999 –> 2000-2012	2.4218012	343.19827
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.6801275	121.48021	1.9354268	1982-1999 –> 2000-2012	2.0465353	315.51708
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.6801275	121.48021	1.9354268	1982-1999 –> 2000-2012	2.0465353	315.51708
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	0.7570324	130.62129	2.1365217	1982-1999 –> 2000-2012	2.4218012	343.19827
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.6801275	121.48021	1.9354268	1982-1999 –> 2000-2012	2.0465353	315.51708
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.0440426	-71.18296	0.0902802	2000-2012 –> 2013-2019	0.7310401	51.34248
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + silicate	0.0481951	-66.67802	0.1236976	2000-2012 –> 2013-2019	0.7294906	54.98064
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.0439239	-71.31794	0.0921668	2000-2012 –> 2013-2019	0.7235239	50.08159
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.0438963	-71.34931	0.0930618	2000-2012 –> 2013-2019	0.7241262	50.14655
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.0439039	-71.34072	0.0953370	2000-2012 –> 2013-2019	0.7224621	49.89925
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.0439039	-71.34072	0.0953370	2000-2012 –> 2013-2019	0.7224621	49.89925
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.0439039	-71.34072	0.0953370	2000-2012 –> 2013-2019	0.7224621	49.89925
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.0438948	-71.35101	0.0947611	2000-2012 –> 2013-2019	0.7240223	50.12919
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.0438948	-71.35101	0.0947611	2000-2012 –> 2013-2019	0.7240223	50.12919
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.0438948	-71.35101	0.0947611	2000-2012 –> 2013-2019	0.7240223	50.12919
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.8498325	2144.56550	11.3406948	1982-1999 –> 2000-2012	6.9328661	3894.15496
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.8498325	2144.56550	11.3406948	1982-1999 –> 2000-2012	6.9328661	3894.15496
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.8498325	2144.56550	11.3406948	1982-1999 –> 2000-2012	6.9328661	3894.15496
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.9284879	2160.13871	11.8726573	1982-1999 –> 2000-2012	7.1140315	3932.03563
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.9475480	2163.86553	12.1138485	1982-1999 –> 2000-2012	7.1523363	3939.87021
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.9565582	2165.62104	12.1792405	1982-1999 –> 2000-2012	7.1688705	3943.22499
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.9565582	2165.62104	12.1792405	1982-1999 –> 2000-2012	7.1688705	3943.22499
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.9565582	2165.62104	12.1792405	1982-1999 –> 2000-2012	7.1688705	3943.22499
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	4.2280733	2216.72740	15.0029847	1982-1999 –> 2000-2012	7.9674374	4097.94391
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.2280733	2216.72740	15.0029847	1982-1999 –> 2000-2012	7.9674374	4097.94391
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.4590247	797.72173	5.6105742	2000-2012 –> 2013-2019	6.3088572	2942.28722
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.4590247	797.72173	5.6105742	2000-2012 –> 2013-2019	6.3088572	2942.28722
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.4590247	797.72173	5.6105742	2000-2012 –> 2013-2019	6.3088572	2942.28722
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.3555704	783.19385	5.5005819	2000-2012 –> 2013-2019	6.2840584	2943.33256
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.3472685	782.00050	5.4836198	2000-2012 –> 2013-2019	6.2948165	2945.86604
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.3584706	783.60974	5.5099605	2000-2012 –> 2013-2019	6.3150288	2949.23077
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.3584706	783.60974	5.5099605	2000-2012 –> 2013-2019	6.3150288	2949.23077
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.8825144	707.42284	6.0035096	2000-2012 –> 2013-2019	6.1105877	2924.15024
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.8825144	707.42284	6.0035096	2000-2012 –> 2013-2019	6.1105877	2924.15024
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.8825144	707.42284	6.0035096	2000-2012 –> 2013-2019	6.1105877	2924.15024
Atlantic	(26.5,26.75]	cstar_tref ~ aou + oxygen + silicate + phosphate	3.9971830	3270.86201	13.2209042	1982-1999 –> 2000-2012	6.7152620	5106.68538
Atlantic	(26.5,26.75]	cstar_tref ~ aou + oxygen + silicate + phosphate_star	3.9971830	3270.86201	13.2209042	1982-1999 –> 2000-2012	6.7152620	5106.68538
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3.9971830	3270.86201	13.2209042	1982-1999 –> 2000-2012	6.7152620	5106.68538
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.9846842	3269.22284	13.5499402	1982-1999 –> 2000-2012	6.7026507	5107.01503
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.9846842	3269.22284	13.5499402	1982-1999 –> 2000-2012	6.7026507	5107.01503
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.9846842	3269.22284	13.5499402	1982-1999 –> 2000-2012	6.7026507	5107.01503
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.0153437	3278.12944	13.9597422	1982-1999 –> 2000-2012	6.7892579	5131.28468
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.8917538	3241.80180	15.2756633	1982-1999 –> 2000-2012	6.5276151	5056.46577
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.8917538	3241.80180	15.2756633	1982-1999 –> 2000-2012	6.5276151	5056.46577
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.8917538	3241.80180	15.2756633	1982-1999 –> 2000-2012	6.5276151	5056.46577
Atlantic	(26.5,26.75]	cstar_tref ~ aou + oxygen + silicate + phosphate	2.7166201	582.72518	11.2366719	2000-2012 –> 2013-2019	6.7138031	3853.58718
Atlantic	(26.5,26.75]	cstar_tref ~ aou + oxygen + silicate + phosphate_star	2.7166201	582.72518	11.2366719	2000-2012 –> 2013-2019	6.7138031	3853.58718
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2.7166201	582.72518	11.2366719	2000-2012 –> 2013-2019	6.7138031	3853.58718
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.6726733	580.87619	10.6080611	2000-2012 –> 2013-2019	6.6573575	3850.09903
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.6726733	580.87619	10.6080611	2000-2012 –> 2013-2019	6.6573575	3850.09903
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.6726733	580.87619	10.6080611	2000-2012 –> 2013-2019	6.6573575	3850.09903
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.6856638	582.02048	10.9520865	2000-2012 –> 2013-2019	6.7010075	3860.14993
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	2.7163585	584.70246	11.1980846	2000-2012 –> 2013-2019	6.6081124	3826.50425
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	2.7163585	584.70246	11.1980846	2000-2012 –> 2013-2019	6.6081124	3826.50425
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.7163585	584.70246	11.1980846	2000-2012 –> 2013-2019	6.6081124	3826.50425
Atlantic	(26.75,27]	cstar_tref ~ aou + oxygen + silicate + phosphate	2.6380588	4770.85189	13.1434793	1982-1999 –> 2000-2012	4.3586100	7831.15223
Atlantic	(26.75,27]	cstar_tref ~ aou + oxygen + silicate + phosphate_star	2.6380588	4770.85189	13.1434793	1982-1999 –> 2000-2012	4.3586100	7831.15223
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2.6380588	4770.85189	13.1434793	1982-1999 –> 2000-2012	4.3586100	7831.15223
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.5691297	4720.11143	12.6389106	1982-1999 –> 2000-2012	4.2889475	7781.74921
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.5691297	4720.11143	12.6389106	1982-1999 –> 2000-2012	4.2889475	7781.74921
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.5691297	4720.11143	12.6389106	1982-1999 –> 2000-2012	4.2889475	7781.74921
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.6363187	4771.53751	12.7136994	1982-1999 –> 2000-2012	4.5150960	7970.55330
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	2.5608624	4713.69092	12.5196205	1982-1999 –> 2000-2012	4.1459188	7648.52496
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	2.5608624	4713.69092	12.5196205	1982-1999 –> 2000-2012	4.1459188	7648.52496
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.5608624	4713.69092	12.5196205	1982-1999 –> 2000-2012	4.1459188	7648.52496
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.2973153	1080.82219	9.6340579	2000-2012 –> 2013-2019	4.8664450	5800.93361
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.2973153	1080.82219	9.6340579	2000-2012 –> 2013-2019	4.8664450	5800.93361
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	2.2974853	1078.85727	9.5903640	2000-2012 –> 2013-2019	5.0380876	5925.67282
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.2973153	1080.82219	9.6340579	2000-2012 –> 2013-2019	4.8664450	5800.93361
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.2956660	1080.48177	9.7242563	2000-2012 –> 2013-2019	4.9319847	5852.01928
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.2879976	1078.89578	9.6274708	2000-2012 –> 2013-2019	4.9741211	5887.71467
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.2882592	1078.94997	9.6030520	2000-2012 –> 2013-2019	4.9934989	5901.89501
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.2882592	1078.94997	9.6030520	2000-2012 –> 2013-2019	4.9934989	5901.89501
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.2882592	1078.94997	9.6030520	2000-2012 –> 2013-2019	4.9934989	5901.89501
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.6722178	1152.47562	11.8382781	2000-2012 –> 2013-2019	5.2330802	5866.16654
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.1681177	5403.89723	11.0657725	1982-1999 –> 2000-2012	3.5456671	8819.85977
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.1681177	5403.89723	11.0657725	1982-1999 –> 2000-2012	3.5456671	8819.85977
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	2.1744607	5409.07786	10.7496732	1982-1999 –> 2000-2012	3.6870811	9005.99955
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.1681177	5403.89723	11.0657725	1982-1999 –> 2000-2012	3.5456671	8819.85977
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.1739219	5410.46873	10.8429707	1982-1999 –> 2000-2012	3.5833317	8871.15495
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.2101379	5451.07992	10.8680275	1982-1999 –> 2000-2012	3.6631803	8971.40175
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.2185242	5460.38904	10.8660375	1982-1999 –> 2000-2012	3.6843877	8997.89417
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.2185242	5460.38904	10.8660375	1982-1999 –> 2000-2012	3.6843877	8997.89417
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.2185242	5460.38904	10.8660375	1982-1999 –> 2000-2012	3.6843877	8997.89417
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.5056792	5759.57098	13.4813560	1982-1999 –> 2000-2012	4.0916232	9451.08246
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.9401521	1633.56643	8.2521474	2000-2012 –> 2013-2019	4.1082698	7037.46366
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.9401521	1633.56643	8.2521474	2000-2012 –> 2013-2019	4.1082698	7037.46366
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1.9675418	1642.47288	7.8365467	2000-2012 –> 2013-2019	4.1420026	7051.55074
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.9401521	1633.56643	8.2521474	2000-2012 –> 2013-2019	4.1082698	7037.46366
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	1.9587182	1638.97601	8.4879296	2000-2012 –> 2013-2019	4.2753819	7203.76176
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.9349428	1631.47469	8.3015637	2000-2012 –> 2013-2019	4.1088648	7041.94342
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.9442717	1635.21662	8.2716662	2000-2012 –> 2013-2019	4.1544096	7086.29654
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.9457224	1635.79688	8.2653400	2000-2012 –> 2013-2019	4.1642466	7096.18592
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.9457224	1635.79688	8.2653400	2000-2012 –> 2013-2019	4.1642466	7096.18592
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.9457224	1635.79688	8.2653400	2000-2012 –> 2013-2019	4.1642466	7096.18592
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.3097058	12036.20688	19.2757793	1982-1999 –> 2000-2012	4.6260814	16586.25872
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.3097058	12036.20688	19.2757793	1982-1999 –> 2000-2012	4.6260814	16586.25872
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	3.3097080	12034.20996	19.2853994	1982-1999 –> 2000-2012	4.7971149	16909.38511
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.3097058	12036.20688	19.2757793	1982-1999 –> 2000-2012	4.6260814	16586.25872
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.3988366	12158.34044	18.6106791	1982-1999 –> 2000-2012	5.1225724	17430.41251
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.2964181	12017.71780	18.7257268	1982-1999 –> 2000-2012	4.5415081	16418.67388
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.2252527	11917.40944	20.1109707	1982-1999 –> 2000-2012	4.5144786	16411.65128
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.2251848	11917.31269	20.0696031	1982-1999 –> 2000-2012	4.5302883	16444.33423
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.2251848	11917.31269	20.0696031	1982-1999 –> 2000-2012	4.5302883	16444.33423
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.2251848	11917.31269	20.0696031	1982-1999 –> 2000-2012	4.5302883	16444.33423
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.7459411	3153.59467	10.2400948	2000-2012 –> 2013-2019	7.0556469	15189.80155
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.7459411	3153.59467	10.2400948	2000-2012 –> 2013-2019	7.0556469	15189.80155
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	3.8687655	3188.56759	11.9597599	2000-2012 –> 2013-2019	7.1784735	15222.77755
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.7459411	3153.59467	10.2400948	2000-2012 –> 2013-2019	7.0556469	15189.80155
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.8596491	3187.86397	11.8244046	2000-2012 –> 2013-2019	7.1560672	15205.58177
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.7261089	3147.51126	9.2111956	2000-2012 –> 2013-2019	6.9513616	15064.92070
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.7231009	3146.58577	9.2453403	2000-2012 –> 2013-2019	6.9482857	15063.89845
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.7231009	3146.58577	9.2453403	2000-2012 –> 2013-2019	6.9482857	15063.89845
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.7231009	3146.58577	9.2453403	2000-2012 –> 2013-2019	6.9482857	15063.89845
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	3.7301991	3146.76857	9.1869755	2000-2012 –> 2013-2019	6.9792901	15096.02271
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.4006938	18867.22503	19.3346654	1982-1999 –> 2000-2012	4.0408521	29395.26477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.4006938	18867.22503	19.3346654	1982-1999 –> 2000-2012	4.0408521	29395.26477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.4006938	18867.22503	19.3346654	1982-1999 –> 2000-2012	4.0408521	29395.26477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.5343071	19312.22400	19.2526571	1982-1999 –> 2000-2012	4.1791520	29855.93995
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.3932563	18841.73164	19.5514846	1982-1999 –> 2000-2012	3.9172781	28966.29209
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.3595962	18725.35691	21.8075049	1982-1999 –> 2000-2012	3.7816419	28469.42314
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.3602820	18727.74461	21.6593084	1982-1999 –> 2000-2012	3.7815198	28468.68874
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.3602820	18727.74461	21.6593084	1982-1999 –> 2000-2012	3.7815198	28468.68874
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.3602820	18727.74461	21.6593084	1982-1999 –> 2000-2012	3.7815198	28468.68874
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.4822913	19139.83859	24.4123097	1982-1999 –> 2000-2012	3.9137287	28918.07017
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.0796279	5133.68348	10.6683765	2000-2012 –> 2013-2019	4.4803217	24000.90851
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.0796279	5133.68348	10.6683765	2000-2012 –> 2013-2019	4.4803217	24000.90851
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	2.1231849	5181.01682	10.9452919	2000-2012 –> 2013-2019	4.5271787	24057.52764
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.0796279	5133.68348	10.6683765	2000-2012 –> 2013-2019	4.4803217	24000.90851
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.1008012	5157.79241	10.8268946	2000-2012 –> 2013-2019	4.4940575	23999.52406
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.0544696	5104.71587	10.4705213	2000-2012 –> 2013-2019	4.4140658	23830.07278
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.0546389	5104.91193	10.4908237	2000-2012 –> 2013-2019	4.4149209	23832.65654
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.0546389	5104.91193	10.4908237	2000-2012 –> 2013-2019	4.4149209	23832.65654
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.0546389	5104.91193	10.4908237	2000-2012 –> 2013-2019	4.4149209	23832.65654
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.0714609	5122.31846	10.3444180	2000-2012 –> 2013-2019	4.5537522	24262.15705
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.1913083	5424.00423	6.7089315	1982-1999 –> 2000-2012	1.8511426	7374.12625
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.1913083	5424.00423	6.7089315	1982-1999 –> 2000-2012	1.8511426	7374.12625
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.1913083	5424.00423	6.7089315	1982-1999 –> 2000-2012	1.8511426	7374.12625
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.1707506	5364.92475	6.5856147	1982-1999 –> 2000-2012	1.8927577	7488.83602
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.1707506	5364.92475	6.5856147	1982-1999 –> 2000-2012	1.8927577	7488.83602
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.1707506	5364.92475	6.5856147	1982-1999 –> 2000-2012	1.8927577	7488.83602
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.2272623	5524.92083	6.8273131	1982-1999 –> 2000-2012	1.9110354	7543.82293
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.2873675	5687.19989	7.1263801	1982-1999 –> 2000-2012	2.0097888	7812.21797
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.2873675	5687.19989	7.1263801	1982-1999 –> 2000-2012	2.0097888	7812.21797
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.2873675	5687.19989	7.1263801	1982-1999 –> 2000-2012	2.0097888	7812.21797
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.0257425	1108.82129	3.8752299	2000-2012 –> 2013-2019	2.2170508	6532.82552
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.0257425	1108.82129	3.8752299	2000-2012 –> 2013-2019	2.2170508	6532.82552
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.0257425	1108.82129	3.8752299	2000-2012 –> 2013-2019	2.2170508	6532.82552
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.8362449	953.99945	5.2034351	2000-2012 –> 2013-2019	2.0069955	6318.92420
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.8362449	953.99945	5.2034351	2000-2012 –> 2013-2019	2.0069955	6318.92420
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.8362449	953.99945	5.2034351	2000-2012 –> 2013-2019	2.0069955	6318.92420
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.0502397	1126.71139	4.1044281	2000-2012 –> 2013-2019	2.2775020	6651.63222
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.0779195	1146.43030	4.3526831	2000-2012 –> 2013-2019	2.3652871	6833.63018
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.0779195	1146.43030	4.3526831	2000-2012 –> 2013-2019	2.3652871	6833.63018
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.0779195	1146.43030	4.3526831	2000-2012 –> 2013-2019	2.3652871	6833.63018
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.5036202	5841.53725	10.9113376	1982-1999 –> 2000-2012	2.6226425	9013.27141
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.2840781	5338.04484	9.1027355	1982-1999 –> 2000-2012	2.2240530	8150.25392
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.2840781	5338.04484	9.1027355	1982-1999 –> 2000-2012	2.2240530	8150.25392
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.2840781	5338.04484	9.1027355	1982-1999 –> 2000-2012	2.2240530	8150.25392
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + phosphate	1.5687650	5974.83491	8.4432988	1982-1999 –> 2000-2012	2.6151504	9006.18074
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + phosphate_star	1.5687650	5974.83491	8.4432988	1982-1999 –> 2000-2012	2.6151504	9006.18074
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.5639527	5967.03418	8.5210370	1982-1999 –> 2000-2012	2.6097355	8999.19239
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.5639527	5967.03418	8.5210370	1982-1999 –> 2000-2012	2.6097355	8999.19239
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.5687650	5974.83491	8.4432988	1982-1999 –> 2000-2012	2.6151504	9006.18074
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.5639527	5967.03418	8.5210370	1982-1999 –> 2000-2012	2.6097355	8999.19239
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.1281279	1023.91074	6.5436144	2000-2012 –> 2013-2019	2.6317481	6865.44798
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.7238751	732.84618	3.7436233	2000-2012 –> 2013-2019	2.0079532	6070.89102
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.7238751	732.84618	3.7436233	2000-2012 –> 2013-2019	2.0079532	6070.89102
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.7238751	732.84618	3.7436233	2000-2012 –> 2013-2019	2.0079532	6070.89102
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + phosphate	0.9986613	941.94492	6.6630775	2000-2012 –> 2013-2019	2.5674264	6916.77984
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + phosphate_star	0.9986613	941.94492	6.6630775	2000-2012 –> 2013-2019	2.5674264	6916.77984
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.9914174	939.16921	7.0181098	2000-2012 –> 2013-2019	2.5553701	6906.20339
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.9914174	939.16921	7.0181098	2000-2012 –> 2013-2019	2.5553701	6906.20339
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	0.9986613	941.94492	6.6630775	2000-2012 –> 2013-2019	2.5674264	6916.77984
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.9914174	939.16921	7.0181098	2000-2012 –> 2013-2019	2.5553701	6906.20339
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	4.3701951	11247.52274	18.6148284	1982-1999 –> 2000-2012	7.9966536	18208.18531
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.3701951	11247.52274	18.6148284	1982-1999 –> 2000-2012	7.9966536	18208.18531
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.3701951	11247.52274	18.6148284	1982-1999 –> 2000-2012	7.9966536	18208.18531
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	4.3956104	11270.03344	18.8597477	1982-1999 –> 2000-2012	8.1481834	18318.41525
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	4.3956104	11270.03344	18.8597477	1982-1999 –> 2000-2012	8.1481834	18318.41525
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.3749103	11251.70889	18.5325206	1982-1999 –> 2000-2012	7.9950015	18207.86217
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.3798004	11256.04564	18.4996250	1982-1999 –> 2000-2012	7.9992669	18211.75609
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	4.3801291	11256.33695	18.5032040	1982-1999 –> 2000-2012	7.9996326	18212.07359
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	4.3801291	11256.33695	18.5032040	1982-1999 –> 2000-2012	7.9996326	18212.07359
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.3801291	11256.33695	18.5032040	1982-1999 –> 2000-2012	7.9996326	18212.07359
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.8639435	1060.15171	3.9247030	2000-2012 –> 2013-2019	5.2341387	12307.67444
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.4967798	605.28933	2.0457321	2000-2012 –> 2013-2019	4.8923902	11875.32277
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.4967798	605.28933	2.0457321	2000-2012 –> 2013-2019	4.8923902	11875.32277
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.4967798	605.28933	2.0457321	2000-2012 –> 2013-2019	4.8923902	11875.32277
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate	0.6632053	840.79619	4.0362195	2000-2012 –> 2013-2019	5.1977363	12229.61909
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate_star	0.6632053	840.79619	4.0362195	2000-2012 –> 2013-2019	5.1977363	12229.61909
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.6507941	827.26751	3.9028273	2000-2012 –> 2013-2019	5.1851958	12217.97970
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.6507941	827.26751	3.9028273	2000-2012 –> 2013-2019	5.1851958	12217.97970
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	0.6632053	840.79619	4.0362195	2000-2012 –> 2013-2019	5.1977363	12229.61909
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.6507941	827.26751	3.9028273	2000-2012 –> 2013-2019	5.1851958	12217.97970
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.2438107	3677.87092	8.6924605	1982-1999 –> 2000-2012	2.0084695	5367.16333
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.1332606	3469.55601	8.5938983	1982-1999 –> 2000-2012	1.8480430	5060.63896
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.1332606	3469.55601	8.5938983	1982-1999 –> 2000-2012	1.8480430	5060.63896
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.1332606	3469.55601	8.5938983	1982-1999 –> 2000-2012	1.8480430	5060.63896
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + phosphate	1.1338392	3468.69836	8.5895417	1982-1999 –> 2000-2012	1.8597697	5080.31460
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + phosphate_star	1.1338392	3468.69836	8.5895417	1982-1999 –> 2000-2012	1.8597697	5080.31460
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.0289069	3253.36077	8.0287550	1982-1999 –> 2000-2012	1.6922335	4735.66502
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.0289069	3253.36077	8.0287550	1982-1999 –> 2000-2012	1.6922335	4735.66502
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.1338392	3468.69836	8.5895417	1982-1999 –> 2000-2012	1.8597697	5080.31460
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.0289069	3253.36077	8.0287550	1982-1999 –> 2000-2012	1.6922335	4735.66502
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.4619130	357.96985	2.0547931	2000-2012 –> 2013-2019	1.7057238	4035.84077
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.3756068	247.93433	1.8452256	2000-2012 –> 2013-2019	1.5088675	3717.49033
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.3756068	247.93433	1.8452256	2000-2012 –> 2013-2019	1.5088675	3717.49033
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.3756068	247.93433	1.8452256	2000-2012 –> 2013-2019	1.5088675	3717.49033
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + phosphate	0.4593185	352.97327	3.0361973	2000-2012 –> 2013-2019	1.5931578	3821.67163
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + phosphate_star	0.4593185	352.97327	3.0361973	2000-2012 –> 2013-2019	1.5931578	3821.67163
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.3036156	134.73516	2.4071938	2000-2012 –> 2013-2019	1.3325226	3388.09593
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.3036156	134.73516	2.4071938	2000-2012 –> 2013-2019	1.3325226	3388.09593
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	0.4593185	352.97327	3.0361973	2000-2012 –> 2013-2019	1.5931578	3821.67163
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.3036156	134.73516	2.4071938	2000-2012 –> 2013-2019	1.3325226	3388.09593
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.0456312	4755.93189	6.5487221	1982-1999 –> 2000-2012	1.6842745	6419.83177
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.0456312	4755.93189	6.5487221	1982-1999 –> 2000-2012	1.6842745	6419.83177
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.0456312	4755.93189	6.5487221	1982-1999 –> 2000-2012	1.6842745	6419.83177
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.9991957	4608.75378	6.6178803	1982-1999 –> 2000-2012	1.6824680	6387.48418
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.9991957	4608.75378	6.6178803	1982-1999 –> 2000-2012	1.6824680	6387.48418
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.9991957	4608.75378	6.6178803	1982-1999 –> 2000-2012	1.6824680	6387.48418
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.8831303	4208.68546	7.3212528	1982-1999 –> 2000-2012	1.4033503	5523.92510
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.8831303	4208.68546	7.3212528	1982-1999 –> 2000-2012	1.4033503	5523.92510
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.0112951	4645.75173	6.7220596	1982-1999 –> 2000-2012	1.6981345	6431.33415
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.8831303	4208.68546	7.3212528	1982-1999 –> 2000-2012	1.4033503	5523.92510
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.4128857	441.48317	1.5372758	2000-2012 –> 2013-2019	1.4585168	5197.41505
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.4128857	441.48317	1.5372758	2000-2012 –> 2013-2019	1.4585168	5197.41505
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.4128857	441.48317	1.5372758	2000-2012 –> 2013-2019	1.4585168	5197.41505
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.4564022	521.64615	1.8669196	2000-2012 –> 2013-2019	1.4555979	5130.39993
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.4564022	521.64615	1.8669196	2000-2012 –> 2013-2019	1.4555979	5130.39993
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.4564022	521.64615	1.8669196	2000-2012 –> 2013-2019	1.4555979	5130.39993
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + oxygen + phosphate_star	0.4630860	531.27683	1.9104036	2000-2012 –> 2013-2019	1.4743811	5177.02856
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.2797729	130.12915	1.2331882	2000-2012 –> 2013-2019	1.1629032	4338.81461
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.2797729	130.12915	1.2331882	2000-2012 –> 2013-2019	1.1629032	4338.81461
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.2797729	130.12915	1.2331882	2000-2012 –> 2013-2019	1.1629032	4338.81461
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.8959016	7954.47796	11.9690641	1982-1999 –> 2000-2012	1.7475653	11758.70326
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.8959016	7954.47796	11.9690641	1982-1999 –> 2000-2012	1.7475653	11758.70326
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.8959016	7954.47796	11.9690641	1982-1999 –> 2000-2012	1.7475653	11758.70326
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.7236679	6659.39884	22.8046471	1982-1999 –> 2000-2012	1.5498097	10371.98357
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.7236679	6659.39884	22.8046471	1982-1999 –> 2000-2012	1.5498097	10371.98357
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.7236679	6659.39884	22.8046471	1982-1999 –> 2000-2012	1.5498097	10371.98357
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.9183865	8104.84010	11.8495950	1982-1999 –> 2000-2012	1.7830432	11954.66991
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.7863775	7163.51009	12.6015457	1982-1999 –> 2000-2012	1.6256286	10923.51391
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.7863775	7163.51009	12.6015457	1982-1999 –> 2000-2012	1.6256286	10923.51391
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.7863775	7163.51009	12.6015457	1982-1999 –> 2000-2012	1.6256286	10923.51391
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.6111236	1629.78548	2.4002237	2000-2012 –> 2013-2019	1.5070252	9584.26344
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.6111236	1629.78548	2.4002237	2000-2012 –> 2013-2019	1.5070252	9584.26344
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.6111236	1629.78548	2.4002237	2000-2012 –> 2013-2019	1.5070252	9584.26344
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.5480112	1439.68341	1.6829609	2000-2012 –> 2013-2019	1.2716791	8099.08224
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.5480112	1439.68341	1.6829609	2000-2012 –> 2013-2019	1.2716791	8099.08224
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.5480112	1439.68341	1.6829609	2000-2012 –> 2013-2019	1.2716791	8099.08224
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.6326753	1690.22922	2.5384461	2000-2012 –> 2013-2019	1.5510618	9795.06932
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.5876275	1561.41018	2.0095964	2000-2012 –> 2013-2019	1.3740050	8724.92028
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.5876275	1561.41018	2.0095964	2000-2012 –> 2013-2019	1.3740050	8724.92028
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.5876275	1561.41018	2.0095964	2000-2012 –> 2013-2019	1.3740050	8724.92028
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.8662496	14627.03325	4.5498357	1982-1999 –> 2000-2012	1.7234469	20891.92838
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.8662496	14627.03325	4.5498357	1982-1999 –> 2000-2012	1.7234469	20891.92838
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.8662496	14627.03325	4.5498357	1982-1999 –> 2000-2012	1.7234469	20891.92838
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.8671911	14639.48021	4.5268433	1982-1999 –> 2000-2012	1.7244049	20904.47039
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.8714105	14695.09389	4.6117260	1982-1999 –> 2000-2012	1.7292468	20963.67220
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.8697380	14673.08243	4.5703170	1982-1999 –> 2000-2012	1.7272286	20939.66817
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.8697380	14673.08243	4.5703170	1982-1999 –> 2000-2012	1.7272286	20939.66817
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.8697380	14673.08243	4.5703170	1982-1999 –> 2000-2012	1.7272286	20939.66817
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.8499989	14410.04126	6.2570512	1982-1999 –> 2000-2012	1.7301985	20805.80379
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.8499989	14410.04126	6.2570512	1982-1999 –> 2000-2012	1.7301985	20805.80379
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.5606895	1607.30470	2.2306790	2000-2012 –> 2013-2019	1.4269391	16234.33795
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.5606895	1607.30470	2.2306790	2000-2012 –> 2013-2019	1.4269391	16234.33795
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.5606895	1607.30470	2.2306790	2000-2012 –> 2013-2019	1.4269391	16234.33795
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	0.5217253	1470.74315	1.8633030	2000-2012 –> 2013-2019	1.4205311	16520.50612
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	0.5217253	1470.74315	1.8633030	2000-2012 –> 2013-2019	1.4205311	16520.50612
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	0.5217253	1470.74315	1.8633030	2000-2012 –> 2013-2019	1.4205311	16520.50612
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.5605984	1606.99660	2.2413317	2000-2012 –> 2013-2019	1.4277896	16246.47681
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.5607556	1607.52819	2.2624780	2000-2012 –> 2013-2019	1.4304937	16280.61061
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.5607556	1607.52819	2.2624780	2000-2012 –> 2013-2019	1.4304937	16280.61061
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.5607556	1607.52819	2.2624780	2000-2012 –> 2013-2019	1.4304937	16280.61061
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + phosphate	5.9171365	16737.61137	24.5984660	1982-1999 –> 2000-2012	11.2468945	23867.95792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + phosphate_star	5.9171365	16737.61137	24.5984660	1982-1999 –> 2000-2012	11.2468945	23867.95792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	5.6769089	16522.76715	22.3359678	1982-1999 –> 2000-2012	10.8818433	23600.55920
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	5.6769089	16522.76715	22.3359678	1982-1999 –> 2000-2012	10.8818433	23600.55920
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5.9171365	16737.61137	24.5984660	1982-1999 –> 2000-2012	11.2468945	23867.95792
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.6769089	16522.76715	22.3359678	1982-1999 –> 2000-2012	10.8818433	23600.55920
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	5.8480540	16678.16846	26.0845534	1982-1999 –> 2000-2012	10.9088253	23691.30149
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	5.8480540	16678.16846	26.0845534	1982-1999 –> 2000-2012	10.9088253	23691.30149
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.8480540	16678.16846	26.0845534	1982-1999 –> 2000-2012	10.9088253	23691.30149
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6.0570773	16861.90814	20.7269795	1982-1999 –> 2000-2012	11.0381157	23838.48419
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + phosphate	5.6899852	13583.56331	23.7304247	2000-2012 –> 2013-2019	11.6071217	30321.17468
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + phosphate_star	5.6899852	13583.56331	23.7304247	2000-2012 –> 2013-2019	11.6071217	30321.17468
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	5.3293238	13304.11614	23.1544130	2000-2012 –> 2013-2019	11.0062327	29826.88329
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	5.3293238	13304.11614	23.1544130	2000-2012 –> 2013-2019	11.0062327	29826.88329
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5.6899852	13583.56331	23.7304247	2000-2012 –> 2013-2019	11.6071217	30321.17468
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.3293238	13304.11614	23.1544130	2000-2012 –> 2013-2019	11.0062327	29826.88329
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	5.5249053	13459.02356	24.6947128	2000-2012 –> 2013-2019	11.3729593	30137.19202
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	5.5249053	13459.02356	24.6947128	2000-2012 –> 2013-2019	11.3729593	30137.19202
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.5249053	13459.02356	24.6947128	2000-2012 –> 2013-2019	11.3729593	30137.19202
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.7109991	13601.40718	27.8143638	2000-2012 –> 2013-2019	11.7680765	30463.31532
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	4.5110722	15314.22584	40.6005388	1982-1999 –> 2000-2012	8.2922673	24306.39013
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.5110722	15314.22584	40.6005388	1982-1999 –> 2000-2012	8.2922673	24306.39013
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.5110722	15314.22584	40.6005388	1982-1999 –> 2000-2012	8.2922673	24306.39013
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	5.1444850	16001.39767	37.8739439	1982-1999 –> 2000-2012	9.3025479	25303.86196
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	5.1444850	16001.39767	37.8739439	1982-1999 –> 2000-2012	9.3025479	25303.86196
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.6207613	15439.87458	44.1201629	1982-1999 –> 2000-2012	8.4761720	24495.52151
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.7524715	15586.86539	44.0182509	1982-1999 –> 2000-2012	8.6919815	24712.98869
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	4.7786338	15615.57758	43.9855669	1982-1999 –> 2000-2012	8.7310367	24752.37206
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	4.7786338	15615.57758	43.9855669	1982-1999 –> 2000-2012	8.7310367	24752.37206
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.7786338	15615.57758	43.9855669	1982-1999 –> 2000-2012	8.7310367	24752.37206
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.6943928	8033.17047	20.9215804	2000-2012 –> 2013-2019	8.2054650	23347.39632
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.6943928	8033.17047	20.9215804	2000-2012 –> 2013-2019	8.2054650	23347.39632
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.6943928	8033.17047	20.9215804	2000-2012 –> 2013-2019	8.2054650	23347.39632
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.7518193	8078.54979	20.8916072	2000-2012 –> 2013-2019	8.3725806	23518.42438
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.7775516	8098.65902	20.7211356	2000-2012 –> 2013-2019	8.5300231	23685.52440
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.7899589	8108.30605	20.7125254	2000-2012 –> 2013-2019	8.5685927	23723.88363
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.7899589	8108.30605	20.7125254	2000-2012 –> 2013-2019	8.5685927	23723.88363
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.7899589	8108.30605	20.7125254	2000-2012 –> 2013-2019	8.5685927	23723.88363
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	4.0665720	8315.55589	22.3051985	2000-2012 –> 2013-2019	9.1091067	24212.26780
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	4.0665720	8315.55589	22.3051985	2000-2012 –> 2013-2019	9.1091067	24212.26780
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	4.5997234	13896.42221	18.8796432	1982-1999 –> 2000-2012	7.7744021	20881.20674
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.5997234	13896.42221	18.8796432	1982-1999 –> 2000-2012	7.7744021	20881.20674
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.5997234	13896.42221	18.8796432	1982-1999 –> 2000-2012	7.7744021	20881.20674
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	4.6539490	13951.66992	15.2426036	1982-1999 –> 2000-2012	8.0653809	21131.22930
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	4.6539490	13951.66992	15.2426036	1982-1999 –> 2000-2012	8.0653809	21131.22930
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.6539490	13951.66992	15.2426036	1982-1999 –> 2000-2012	8.0653809	21131.22930
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.8140395	14111.09950	19.3742196	1982-1999 –> 2000-2012	8.2074636	21276.32638
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	4.7431591	14041.17605	15.8965320	1982-1999 –> 2000-2012	8.1819584	21242.37292
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	4.7431591	14041.17605	15.8965320	1982-1999 –> 2000-2012	8.1819584	21242.37292
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.7431591	14041.17605	15.8965320	1982-1999 –> 2000-2012	8.1819584	21242.37292
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.2330242	6904.48361	16.5464518	2000-2012 –> 2013-2019	7.8327476	20800.90582
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.2330242	6904.48361	16.5464518	2000-2012 –> 2013-2019	7.8327476	20800.90582
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.2330242	6904.48361	16.5464518	2000-2012 –> 2013-2019	7.8327476	20800.90582
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.4239406	7056.98403	14.2361648	2000-2012 –> 2013-2019	8.0778895	21008.65395
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.4239406	7056.98403	14.2361648	2000-2012 –> 2013-2019	8.0778895	21008.65395
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.4239406	7056.98403	14.2361648	2000-2012 –> 2013-2019	8.0778895	21008.65395
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.4057129	7042.79608	18.0529528	2000-2012 –> 2013-2019	8.2197523	21153.89558
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.0927721	6786.60086	18.0189689	2000-2012 –> 2013-2019	7.8359312	20827.77690
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.0927721	6786.60086	18.0189689	2000-2012 –> 2013-2019	7.8359312	20827.77690
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.0927721	6786.60086	18.0189689	2000-2012 –> 2013-2019	7.8359312	20827.77690
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + phosphate	4.3828503	19570.09837	15.0604193	1982-1999 –> 2000-2012	7.5865761	29713.61662
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + phosphate_star	4.3828503	19570.09837	15.0604193	1982-1999 –> 2000-2012	7.5865761	29713.61662
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	4.3817574	19570.41455	15.2521912	1982-1999 –> 2000-2012	7.5408394	29660.89541
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.3817574	19570.41455	15.2521912	1982-1999 –> 2000-2012	7.5408394	29660.89541
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4.3828503	19570.09837	15.0604193	1982-1999 –> 2000-2012	7.5865761	29713.61662
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.3817574	19570.41455	15.2521912	1982-1999 –> 2000-2012	7.5408394	29660.89541
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	4.2959923	19436.94559	21.1850201	1982-1999 –> 2000-2012	7.4358571	29503.49548
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	4.2959923	19436.94559	21.1850201	1982-1999 –> 2000-2012	7.4358571	29503.49548
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.2959923	19436.94559	21.1850201	1982-1999 –> 2000-2012	7.4358571	29503.49548
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.4209585	19630.55230	22.4314004	1982-1999 –> 2000-2012	7.6657778	29826.05719
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.8037880	9738.92388	12.2952264	2000-2012 –> 2013-2019	8.1855454	29309.33842
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.8037880	9738.92388	12.2952264	2000-2012 –> 2013-2019	8.1855454	29309.33842
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.8037880	9738.92388	12.2952264	2000-2012 –> 2013-2019	8.1855454	29309.33842
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.8936510	9821.34889	15.8177101	2000-2012 –> 2013-2019	8.1896432	29258.29448
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.8936510	9821.34889	15.8177101	2000-2012 –> 2013-2019	8.1896432	29258.29448
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.8936510	9821.34889	15.8177101	2000-2012 –> 2013-2019	8.1896432	29258.29448
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + oxygen + phosphate_star	3.9598723	9878.88056	16.8972842	2000-2012 –> 2013-2019	8.3822217	29509.55681
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.7693127	9706.78414	14.7360756	2000-2012 –> 2013-2019	8.1902712	29337.33644
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.7693127	9706.78414	14.7360756	2000-2012 –> 2013-2019	8.1902712	29337.33644
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.7693127	9706.78414	14.7360756	2000-2012 –> 2013-2019	8.1902712	29337.33644
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.8811487	26608.23286	27.9807981	1982-1999 –> 2000-2012	7.8983021	38219.10062
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	4.1321620	25133.66821	24.8385028	1982-1999 –> 2000-2012	7.0550807	36598.69969
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	4.1321620	25133.66821	24.8385028	1982-1999 –> 2000-2012	7.0550807	36598.69969
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.1321620	25133.66821	24.8385028	1982-1999 –> 2000-2012	7.0550807	36598.69969
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + phosphate	4.1639450	25199.49383	23.5758399	1982-1999 –> 2000-2012	7.1407117	36746.42544
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + phosphate_star	4.1639450	25199.49383	23.5758399	1982-1999 –> 2000-2012	7.1407117	36746.42544
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.5773624	23857.43128	16.0385121	1982-1999 –> 2000-2012	6.5289804	35367.36942
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.5773624	23857.43128	16.0385121	1982-1999 –> 2000-2012	6.5289804	35367.36942
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4.1639450	25199.49383	23.5758399	1982-1999 –> 2000-2012	7.1407117	36746.42544
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.5773624	23857.43128	16.0385121	1982-1999 –> 2000-2012	6.5289804	35367.36942
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.6921182	15300.62560	20.2340983	2000-2012 –> 2013-2019	9.5732669	41908.85846
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	4.2265824	14761.87306	19.4557796	2000-2012 –> 2013-2019	8.3587444	39895.54128
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	4.2265824	14761.87306	19.4557796	2000-2012 –> 2013-2019	8.3587444	39895.54128
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.2265824	14761.87306	19.4557796	2000-2012 –> 2013-2019	8.3587444	39895.54128
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + phosphate	4.3231966	14876.40573	18.1291512	2000-2012 –> 2013-2019	8.4871416	40075.89955
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + phosphate_star	4.3231966	14876.40573	18.1291512	2000-2012 –> 2013-2019	8.4871416	40075.89955
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.9209008	14374.80029	15.9055025	2000-2012 –> 2013-2019	7.4982632	38232.23158
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.9209008	14374.80029	15.9055025	2000-2012 –> 2013-2019	7.4982632	38232.23158
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4.3231966	14876.40573	18.1291512	2000-2012 –> 2013-2019	8.4871416	40075.89955
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.9209008	14374.80029	15.9055025	2000-2012 –> 2013-2019	7.4982632	38232.23158
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.5890979	30623.12741	11.8601893	1982-1999 –> 2000-2012	6.2013888	45111.97410
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.5890979	30623.12741	11.8601893	1982-1999 –> 2000-2012	6.2013888	45111.97410
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.5890979	30623.12741	11.8601893	1982-1999 –> 2000-2012	6.2013888	45111.97410
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + silicate	3.0844293	28903.21389	13.8988234	1982-1999 –> 2000-2012	6.0885567	44242.35773
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.5333545	30445.46369	11.3858029	1982-1999 –> 2000-2012	6.1456335	44934.28268
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.5521641	30505.72452	11.5994102	1982-1999 –> 2000-2012	6.2050185	45088.31716
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate	3.1933345	29295.04781	17.3970223	1982-1999 –> 2000-2012	6.2000755	44637.48242
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.1093132	28994.41341	18.0861691	1982-1999 –> 2000-2012	5.3556466	42565.01245
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.1093132	28994.41341	18.0861691	1982-1999 –> 2000-2012	5.3556466	42565.01245
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.1093132	28994.41341	18.0861691	1982-1999 –> 2000-2012	5.3556466	42565.01245
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.9674206	17169.38673	11.9858738	2000-2012 –> 2013-2019	6.0518499	46072.60062
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.4387736	18178.34160	13.7873631	2000-2012 –> 2013-2019	6.9721280	48623.80529
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.4626480	18225.69346	14.1337349	2000-2012 –> 2013-2019	7.0378726	48804.86347
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.4424625	18185.67954	13.9244017	2000-2012 –> 2013-2019	6.9946266	48691.40406
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.4424625	18185.67954	13.9244017	2000-2012 –> 2013-2019	6.9946266	48691.40406
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.4424625	18185.67954	13.9244017	2000-2012 –> 2013-2019	6.9946266	48691.40406
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate	3.3739326	18046.06006	15.7011643	2000-2012 –> 2013-2019	6.5672671	47341.10787
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.3521746	18003.78126	14.9487549	2000-2012 –> 2013-2019	6.4614878	46998.19467
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.3521746	18003.78126	14.9487549	2000-2012 –> 2013-2019	6.4614878	46998.19467
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.3521746	18003.78126	14.9487549	2000-2012 –> 2013-2019	6.4614878	46998.19467
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.0324520	33468.59862	10.6583319	1982-1999 –> 2000-2012	5.3455127	48734.33749
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.8595827	32691.93562	16.9783126	1982-1999 –> 2000-2012	5.1651164	47935.65360
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.9966623	33311.50296	10.1288040	1982-1999 –> 2000-2012	5.2982339	48543.60043
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.0054406	33350.20721	10.2540003	1982-1999 –> 2000-2012	5.3340552	48661.22392
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.9972209	33313.96925	10.1530334	1982-1999 –> 2000-2012	5.3211866	48611.48443
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.9972209	33313.96925	10.1530334	1982-1999 –> 2000-2012	5.3211866	48611.48443
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.9972209	33313.96925	10.1530334	1982-1999 –> 2000-2012	5.3211866	48611.48443
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.0506844	33547.91724	20.5284776	1982-1999 –> 2000-2012	5.1485462	48153.91200
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.0506844	33547.91724	20.5284776	1982-1999 –> 2000-2012	5.1485462	48153.91200
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.0506844	33547.91724	20.5284776	1982-1999 –> 2000-2012	5.1485462	48153.91200
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.7574902	19012.88985	12.6480309	2000-2012 –> 2013-2019	5.7899422	52481.48847
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.7574902	19012.88985	12.6480309	2000-2012 –> 2013-2019	5.7899422	52481.48847
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.7574902	19012.88985	12.6480309	2000-2012 –> 2013-2019	5.7899422	52481.48847
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.7499572	18991.53044	11.4294859	2000-2012 –> 2013-2019	5.6095399	51683.46607
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.7447079	18976.61186	12.1505620	2000-2012 –> 2013-2019	5.7413703	52288.11481
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.7455471	18978.99873	12.2093988	2000-2012 –> 2013-2019	5.7509877	52329.20594
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.7432404	18972.43604	12.0931425	2000-2012 –> 2013-2019	5.7404613	52286.40530
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.7432404	18972.43604	12.0931425	2000-2012 –> 2013-2019	5.7404613	52286.40530
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate	2.9944894	19654.68141	8.4412807	2000-2012 –> 2013-2019	5.9931860	52973.16393
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.7432404	18972.43604	12.0931425	2000-2012 –> 2013-2019	5.7404613	52286.40530
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.1679730	13414.27883	9.0214032	1982-1999 –> 2000-2012	4.7844113	18624.39065
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.1679730	13414.27883	9.0214032	1982-1999 –> 2000-2012	4.7844113	18624.39065
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + silicate	3.1166679	13329.21260	9.8754952	1982-1999 –> 2000-2012	4.8010415	18651.96162
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.1679730	13414.27883	9.0214032	1982-1999 –> 2000-2012	4.7844113	18624.39065
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + phosphate	3.2261932	13507.15762	8.4447285	1982-1999 –> 2000-2012	4.8439305	18717.46738
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate	3.1403948	13366.72560	9.8600442	1982-1999 –> 2000-2012	4.8314447	18698.29785
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	2.9949800	13121.71449	7.6320448	1982-1999 –> 2000-2012	4.5310097	18192.22406
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	2.9949800	13121.71449	7.6320448	1982-1999 –> 2000-2012	4.5310097	18192.22406
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	3.2261932	13507.15762	8.4447285	1982-1999 –> 2000-2012	4.8439305	18717.46738
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.9949800	13121.71449	7.6320448	1982-1999 –> 2000-2012	4.5310097	18192.22406
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.4782579	7086.54298	9.5043297	2000-2012 –> 2013-2019	5.4128162	20102.07446
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.4782579	7086.54298	9.5043297	2000-2012 –> 2013-2019	5.4128162	20102.07446
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.4782579	7086.54298	9.5043297	2000-2012 –> 2013-2019	5.4128162	20102.07446
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.4923267	7103.75193	8.9701919	2000-2012 –> 2013-2019	5.4253579	20116.57147
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.4967804	7109.17935	8.8090180	2000-2012 –> 2013-2019	5.4296020	20121.62661
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.4996524	7112.67420	8.7188128	2000-2012 –> 2013-2019	5.4324523	20125.08297
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.4996524	7112.67420	8.7188128	2000-2012 –> 2013-2019	5.4324523	20125.08297
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.4996524	7112.67420	8.7188128	2000-2012 –> 2013-2019	5.4324523	20125.08297
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	2.8722373	7535.05058	8.9679710	2000-2012 –> 2013-2019	5.8672173	20656.76507
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	2.8722373	7535.05058	8.9679710	2000-2012 –> 2013-2019	5.8672173	20656.76507
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.1541570	16251.88061	17.8351326	1982-1999 –> 2000-2012	4.9538488	22197.25415
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.2949562	16528.05985	17.9094571	1982-1999 –> 2000-2012	4.7655574	21876.48639
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.2949562	16528.05985	17.9094571	1982-1999 –> 2000-2012	4.7655574	21876.48639
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.2949562	16528.05985	17.9094571	1982-1999 –> 2000-2012	4.7655574	21876.48639
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + phosphate	3.3086868	16552.35818	17.7290191	1982-1999 –> 2000-2012	4.7813942	21903.01538
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + phosphate_star	3.3086868	16552.35818	17.7290191	1982-1999 –> 2000-2012	4.7813942	21903.01538
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.1574651	16258.50971	17.2112577	1982-1999 –> 2000-2012	4.5916452	21532.80599
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.1574651	16258.50971	17.2112577	1982-1999 –> 2000-2012	4.5916452	21532.80599
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	3.3086868	16552.35818	17.7290191	1982-1999 –> 2000-2012	4.7813942	21903.01538
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.1574651	16258.50971	17.2112577	1982-1999 –> 2000-2012	4.5916452	21532.80599
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.3105153	9552.09060	9.3111647	2000-2012 –> 2013-2019	6.4646724	25803.97121
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.3105153	9552.09060	9.3111647	2000-2012 –> 2013-2019	6.4646724	25803.97121
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.3105153	9552.09060	9.3111647	2000-2012 –> 2013-2019	6.4646724	25803.97121
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.3444727	9589.29868	9.4041251	2000-2012 –> 2013-2019	6.5013077	25846.54623
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.3596636	9605.82162	9.4523390	2000-2012 –> 2013-2019	6.5193746	25868.82796
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.3664542	9613.18354	9.4679657	2000-2012 –> 2013-2019	6.5273716	25878.60401
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.3664542	9613.18354	9.4679657	2000-2012 –> 2013-2019	6.5273716	25878.60401
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.3664542	9613.18354	9.4679657	2000-2012 –> 2013-2019	6.5273716	25878.60401
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.4615597	9714.75830	9.8097748	2000-2012 –> 2013-2019	6.6190247	25973.26800
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.4615597	9714.75830	9.8097748	2000-2012 –> 2013-2019	6.6190247	25973.26800
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.6868896	15020.42271	8.4972367	1982-1999 –> 2000-2012	3.4770441	22230.88341
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.6905568	15037.20482	8.5730976	1982-1999 –> 2000-2012	3.3434758	21960.85175
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.6905568	15037.20482	8.5730976	1982-1999 –> 2000-2012	3.3434758	21960.85175
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.6905568	15037.20482	8.5730976	1982-1999 –> 2000-2012	3.3434758	21960.85175
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate	1.7421644	15267.58806	10.4344233	1982-1999 –> 2000-2012	3.3977152	22194.95603
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate_star	1.7421644	15267.58806	10.4344233	1982-1999 –> 2000-2012	3.3977152	22194.95603
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.6609148	14900.50096	9.0532945	1982-1999 –> 2000-2012	3.1884612	21540.49536
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.6609148	14900.50096	9.0532945	1982-1999 –> 2000-2012	3.1884612	21540.49536
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.7421644	15267.58806	10.4344233	1982-1999 –> 2000-2012	3.3977152	22194.95603
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.6609148	14900.50096	9.0532945	1982-1999 –> 2000-2012	3.1884612	21540.49536
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.5684161	8263.78728	9.1231543	2000-2012 –> 2013-2019	3.2553057	23284.20999
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.5684161	8263.78728	9.1231543	2000-2012 –> 2013-2019	3.2553057	23284.20999
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.5684161	8263.78728	9.1231543	2000-2012 –> 2013-2019	3.2553057	23284.20999
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.5711791	8271.55624	9.0746907	2000-2012 –> 2013-2019	3.2716587	23353.98826
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.5719412	8273.69666	9.0469574	2000-2012 –> 2013-2019	3.2769267	23376.57902
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.5719951	8273.84817	9.0399522	2000-2012 –> 2013-2019	3.2783238	23382.81616
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.5719951	8273.84817	9.0399522	2000-2012 –> 2013-2019	3.2783238	23382.81616
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.5719951	8273.84817	9.0399522	2000-2012 –> 2013-2019	3.2783238	23382.81616
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.6205132	8408.02173	9.7347045	2000-2012 –> 2013-2019	3.2814280	23308.52268
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.6205132	8408.02173	9.7347045	2000-2012 –> 2013-2019	3.2814280	23308.52268
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.5548808	8206.92595	7.3193185	1982-1999 –> 2000-2012	3.0992837	12361.81446
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.5548808	8206.92595	7.3193185	1982-1999 –> 2000-2012	3.0992837	12361.81446
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.5548808	8206.92595	7.3193185	1982-1999 –> 2000-2012	3.0992837	12361.81446
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.5610214	8224.28432	7.3829130	1982-1999 –> 2000-2012	3.1157460	12394.05355
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.5627952	8229.28564	7.4071916	1982-1999 –> 2000-2012	3.1210987	12404.19167
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.5627952	8229.28564	7.4071916	1982-1999 –> 2000-2012	3.1210987	12404.19167
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.5627952	8229.28564	7.4071916	1982-1999 –> 2000-2012	3.1210987	12404.19167
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.5307379	8138.00775	6.1987387	1982-1999 –> 2000-2012	2.9717656	12138.12294
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.5307379	8138.00775	6.1987387	1982-1999 –> 2000-2012	2.9717656	12138.12294
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.5307379	8138.00775	6.1987387	1982-1999 –> 2000-2012	2.9717656	12138.12294
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.2902622	4188.41727	5.8262405	2000-2012 –> 2013-2019	2.8451430	12395.34322
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.2902622	4188.41727	5.8262405	2000-2012 –> 2013-2019	2.8451430	12395.34322
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.2902622	4188.41727	5.8262405	2000-2012 –> 2013-2019	2.8451430	12395.34322
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.2934477	4194.56700	5.7870805	2000-2012 –> 2013-2019	2.8544691	12418.85132
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.2941037	4195.83169	5.7686036	2000-2012 –> 2013-2019	2.8568989	12425.11733
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.2941037	4195.83169	5.7686036	2000-2012 –> 2013-2019	2.8568989	12425.11733
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.2941037	4195.83169	5.7686036	2000-2012 –> 2013-2019	2.8568989	12425.11733
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.2940968	4195.81825	6.4737894	2000-2012 –> 2013-2019	2.8248346	12333.82600
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.2940968	4195.81825	6.4737894	2000-2012 –> 2013-2019	2.8248346	12333.82600
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.2940968	4195.81825	6.4737894	2000-2012 –> 2013-2019	2.8248346	12333.82600
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.5457119	89059.68970	9.6225706	1982-1999 –> 2000-2012	2.8533113	132024.68257
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.5457119	89059.68970	9.6225706	1982-1999 –> 2000-2012	2.8533113	132024.68257
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	1.5862780	90301.63353	10.1419768	1982-1999 –> 2000-2012	3.0021288	135289.49705
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.5457119	89059.68970	9.6225706	1982-1999 –> 2000-2012	2.8533113	132024.68257
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.5458590	89064.25855	9.6237779	1982-1999 –> 2000-2012	2.8526421	132013.35434
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.5460122	89069.01719	9.6248630	1982-1999 –> 2000-2012	2.8517894	131998.50803
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.5460006	89068.65692	9.6251167	1982-1999 –> 2000-2012	2.8518187	131998.94619
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.5460006	89068.65692	9.6251167	1982-1999 –> 2000-2012	2.8518187	131998.94619
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.5460006	89068.65692	9.6251167	1982-1999 –> 2000-2012	2.8518187	131998.94619
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate_star	1.5530253	89284.34511	9.2818343	1982-1999 –> 2000-2012	2.8718943	132465.81043
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.2904044	49641.61538	9.2901765	2000-2012 –> 2013-2019	2.8361163	138701.30508
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.2904044	49641.61538	9.2901765	2000-2012 –> 2013-2019	2.8361163	138701.30508
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.2904044	49641.61538	9.2901765	2000-2012 –> 2013-2019	2.8361163	138701.30508
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.2907334	49649.17197	9.2905994	2000-2012 –> 2013-2019	2.8365924	138713.43051
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.2911776	49659.37507	9.2937847	2000-2012 –> 2013-2019	2.8371898	138728.39227
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.2911324	49658.33768	9.2927061	2000-2012 –> 2013-2019	2.8371331	138726.99460
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.2911324	49658.33768	9.2927061	2000-2012 –> 2013-2019	2.8371331	138726.99460
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.2911324	49658.33768	9.2927061	2000-2012 –> 2013-2019	2.8371331	138726.99460
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate_star	1.3186734	50282.10445	10.1511497	2000-2012 –> 2013-2019	2.8716987	139566.44956
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.3443327	50855.46644	9.7413986	2000-2012 –> 2013-2019	2.9266322	141038.51664

5.3 Target variable coefficients

A data frame to map the target variable is prepared.

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

eras_backward <- lm_all_fitted_wide %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  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_target <- full_join(
  lm_best %>% select(basin, gamma_slab, model, eras),
  eras_era)

lm_best_target <- left_join(lm_best_target, lm_all_fitted_wide)

rm(eras_era, eras_forward, eras_backward,
   lm_all_fitted)

5.4 Cant coeffcients

A data frame of coefficient offsets is prepared to facilitate the direct mapping of Cant.

# pivot long format
lm_best_long <- lm_best_target %>%
  pivot_longer(cols = starts_with("coeff_"),
               names_to = "term",
               values_to = "estimate",
               names_prefix = "coeff_")

# subtract coefficients of adjacent era  
lm_best_long <- lm_best_long %>%
  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))

# pivot back to wide format
lm_best_cant <- lm_best_long %>%
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

5.5 Write files

lm_best_target %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    era,
    starts_with("coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_target.csv",
                  sep = ""))

lm_best_cant %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    starts_with("delta_coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_cant.csv",
                  sep = ""))

6 Model diagnotics

6.1 Selection criterion vs predictors

The selection criterion (rmse) was plotted against the number of predictors (limited to 2 - 5).

6.1.1 All models

lm_all_fitted_wide %>%
  ggplot(aes(as.factor(n_predictors),
             !!sym(params_local$MLR_criterion),
             col = basin)) +
  geom_hline(yintercept = 10) +
  geom_boxplot() +
  facet_grid(gamma_slab~era) +
  scale_color_brewer(palette = "Set1") +
  labs(x="Number of predictors")

Past versions of eMLR_predictor_model_quality_all-1.png

Version	Author	Date
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

6.1.2 Best models

lm_best_target %>%
  ggplot(aes("",
             !!sym(params_local$MLR_criterion),
             col = basin)) +
  geom_hline(yintercept = 10) +
  geom_boxplot() +
  facet_grid(gamma_slab~era) +
  scale_color_brewer(palette = "Set1") +
  labs(x="Number of predictors pooled")

Past versions of eMLR_predictor_model_quality_best-1.png

Version	Author	Date
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

6.2 RMSE correlation between eras

RMSE was plotted to compare the agreement for one model applied to two adjacent eras (ie check whether the same predictor combination performs equal in both eras).

6.2.1 All models

# find max rmse to scale axis
max_rmse <-
  max(c(lm_all_fitted_wide_eras$rmse,
        lm_all_fitted_wide_eras$rmse_sum - lm_all_fitted_wide_eras$rmse))

lm_all_fitted_wide_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
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

rm(max_rmse)

6.2.2 Best models

# find max rmse to scale axis
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_best_models-1.png

Version	Author	Date
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

rm(max_rmse)

6.3 Predictor counts

The number of models where a particular predictor was included were counted for each basin, density slab and compared eras

# calculate cases of predictor used
lm_all_stats <- lm_best_long %>% 
  filter(term != "(Intercept)",
         delta_coeff != 0) %>% 
  group_by(basin, eras, gamma_slab) %>% 
  count(term) %>% 
  ungroup() %>% 
  pivot_wider(values_from = n, names_from = term)

# print table
lm_all_stats %>%
  gt(rowname_col = "gamma_slab",
     groupname_col = c("basin", "eras")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )

	aou	oxygen	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26]	10	7	6	5	5	4	10
(26,26.5]	7	5	6	7	8	10	7
(26.5,26.75]	10	6	7	6	4	10	4
(26.75,27]	10	6	7	6	4	10	4
(27,27.25]	7	4	7	6	9	10	6
(27.25,27.5]	7	5	6	6	10	9	6
(27.5,27.75]	6	5	6	6	10	9	7
(27.75,27.85]	7	6	7	6	10	7	7
(27.85,27.95]	10	7	6	7	4	4	9
(27.95,28.05]	7	6	6	6	10	8	7
(28.05,28.1]	10	7	6	7	4	4	9
(28.1,28.15]	10	6	7	7	6	6	7
(28.15,28.2]	10	6	7	6	7	7	7
(28.2, Inf]	7	6	6	6	8	10	7
total	118.00	82.00	90.00	87.00	99.00	108.00	97.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26]	7	6	5	6	7	10	9
(26,26.5]	8	5	6	7	7	10	7
(26.5,26.75]	10	6	7	6	4	10	4
(26.75,27]	7	4	7	6	9	10	6
(27,27.25]	7	4	6	6	10	10	5
(27.25,27.5]	6	4	6	6	10	10	6
(27.5,27.75]	6	4	6	6	10	10	6
(27.75,27.85]	7	6	7	6	10	7	7
(27.85,27.95]	10	6	7	7	4	4	9
(27.95,28.05]	10	7	6	7	4	4	9
(28.05,28.1]	10	7	6	7	4	4	9
(28.1,28.15]	10	7	6	7	6	6	7
(28.15,28.2]	10	6	7	6	7	7	7
(28.2, Inf]	7	6	7	6	10	7	7
total	115.00	78.00	89.00	89.00	102.00	109.00	98.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26]	10	6	7	6	10	4	4
(26,26.5]	7	6	6	6	10	8	7
(26.5,26.75]	10	6	7	6	7	7	7
(26.75,27]	10	6	7	7	9	4	4
(27,27.25]	10	7	6	7	4	4	9
(27.25,27.5]	9	7	5	5	6	10	7
(27.5,27.75]	7	6	5	6	7	10	9
(27.75,27.85]	10	7	6	5	4	5	10
(27.85,27.95]	10	7	6	7	4	4	9
(27.95,28.05]	10	6	7	7	4	4	9
(28.05,28.1]	7	6	7	6	7	10	7
(28.1, Inf]	6	4	6	6	10	10	6
total	106.00	74.00	75.00	74.00	82.00	80.00	88.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26]	10	6	7	6	10	4	4
(26,26.5]	7	6	6	6	8	10	7
(26.5,26.75]	10	6	7	6	7	7	7
(26.75,27]	10	7	6	7	6	6	7
(27,27.25]	10	7	6	7	4	4	9
(27.25,27.5]	7	6	5	5	6	10	10
(27.5,27.75]	6	5	6	5	10	10	7
(27.75,27.85]	7	6	6	6	8	10	7
(27.85,27.95]	7	6	6	6	8	10	7
(27.95,28.05]	7	5	7	6	8	10	7
(28.05,28.1]	7	6	7	6	7	10	7
(28.1, Inf]	6	4	6	7	9	10	7
total	94.00	70.00	75.00	73.00	91.00	101.00	86.00

6.4 RMSE alternatives

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

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

Past versions of aic_vs_rmse_all_models-1.png

Version	Author	Date
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

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

Past versions of aic_vs_rmse_selected_models-1.png

Version	Author	Date
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

Session information

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.2

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] gt_0.2.2         corrr_0.4.3      broom_0.7.2      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.2   
[21] tidyverse_1.3.0  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_1.4-1         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_2.1.0               
[19] rvest_0.3.6              xml2_1.3.2               sass_0.2.0              
[22] labeling_0.4.2           scales_1.1.1             checkmate_2.0.0         
[25] goftest_1.2-2            digest_0.6.27            foreign_0.8-80          
[28] rmarkdown_2.5            rio_0.5.16               pkgconfig_2.0.3         
[31] htmltools_0.5.0          highr_0.8                dbplyr_1.4.4            
[34] rlang_0.4.9              readxl_1.3.1             rstudioapi_0.13         
[37] farver_2.0.3             generics_0.0.2           jsonlite_1.7.1          
[40] zip_2.1.1                car_3.0-10               magrittr_1.5            
[43] Matrix_1.2-18            Rcpp_1.0.5               munsell_0.5.0           
[46] fansi_0.4.1              abind_1.4-5              lifecycle_0.2.0         
[49] stringi_1.5.3            whisker_0.4              yaml_2.2.1              
[52] carData_3.0-4            plyr_1.8.6               grid_4.0.3              
[55] blob_1.2.1               parallel_4.0.3           promises_1.1.1          
[58] crayon_1.3.4             lattice_0.20-41          haven_2.3.1             
[61] hms_0.5.3                pillar_1.4.7             reprex_0.3.0            
[64] glue_1.4.2               evaluate_0.14            RcppArmadillo_0.10.1.2.0
[67] data.table_1.13.2        modelr_0.1.8             vctrs_0.3.5             
[70] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[73] reshape_0.8.8            assertthat_0.2.1         xfun_0.18               
[76] openxlsx_4.2.3           RcppEigen_0.3.3.7.0      later_1.1.0.1           
[79] viridisLite_0.3.0        ellipsis_0.3.1           here_0.1