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1 Required data

Required are:

  • cleaned and prepared GLODAPv2_2020 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, nitrate, 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)

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

# 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.

GLODAP %>% 
  # filter(basin %in% unique(GLODAP$basin)[1],
  #        era %in% unique(GLODAP$era)[c(1,2)],
  #        gamma_slab %in% unique(GLODAP$gamma_slab)[c(5,6)]) %>% 
  filter_all(any_vars(is.na(.)))

GLODAP_nested <- GLODAP %>% 
  # filter(basin %in% unique(GLODAP$basin)[1],
  #        era %in% unique(GLODAP$era)[c(1,2)],
  #        gamma_slab %in% unique(GLODAP$gamma_slab)[c(5,6)]) %>% 
  drop_na() %>% 
  group_by(gamma_slab, era, basin) %>% 
  nest()

GLODAP_nested_lm <- expand_grid(
  GLODAP_nested,
  lm_all
)

GLODAP_nested_lm_fit <- GLODAP_nested_lm %>% 
  mutate(
    fit = map2(.x = data, .y = model, 
               ~ lm(as.formula(.y), data = .x)),
    tidied = map(fit, tidy),
    glanced = map(fit, glance),
    augmented = map(fit, augment)
  )

print(object.size(GLODAP_nested), units = "MB")
print(object.size(GLODAP_nested_lm), units = "MB")
print(object.size(GLODAP_nested_lm_fit), units = "MB")

# GLODAP_glanced <- GLODAP_nested_lm_fit %>% 
#   select(-c(data, fit, tidied, augmented)) %>% 
#   unnest(glanced)

GLODAP_tidy <- GLODAP_nested_lm_fit %>%
  select(-c(data, fit, glanced, augmented)) %>%
  unnest(tidied)

GLODAP_augmented <- GLODAP_nested_lm_fit %>% 
  select(-c(data, fit, tidied, glanced)) %>% 
  unnest(augmented) 

print(object.size(GLODAP_augmented), units = "MB")

lm_rmse <- GLODAP_augmented %>%
  group_by(gamma_slab, era, basin, model) %>%
  summarise(rmse = sqrt(c(crossprod(.resid)) / length(.resid))) %>%
  ungroup()

# GLODAP_data <- GLODAP_nested_lm_fit %>% 
#   select(-c(fit, tidied, glanced, augmented)) %>% 
#   unnest(data) 

# GLODAP_augmented %>% 
#   ggplot(aes(phosphate, .resid)) +
#   geom_bin2d(bins = 100) +
#   geom_hline(yintercept = 0, col = "white") +
#   scale_fill_viridis_c() +
#   geom_smooth(col = "red") +
#   ylim(-30,30)

# # 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
#   )
# 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 adjecent 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_rmse  %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> "),
         rmse_sum = rmse + lag(rmse)
         ) %>% 
  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")
gamma_slab basin model rmse eras rmse_sum
(-Inf,26] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 6.901466 1982-1999 –> 2000-2012 12.807857
(-Inf,26] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7.217422 1982-1999 –> 2000-2012 13.267957
(-Inf,26] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 6.961989 1982-1999 –> 2000-2012 12.846097
(-Inf,26] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.967437 1982-1999 –> 2000-2012 12.847216
(-Inf,26] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 7.136236 1982-1999 –> 2000-2012 13.160079
(-Inf,26] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6.994268 1982-1999 –> 2000-2012 12.863175
(-Inf,26] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 7.200241 1982-1999 –> 2000-2012 13.043712
(-Inf,26] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7.189271 1982-1999 –> 2000-2012 13.202551
(-Inf,26] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7.183121 1982-1999 –> 2000-2012 13.175607
(-Inf,26] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7.163047 1982-1999 –> 2000-2012 13.117181
(-Inf,26] Atlantic cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 6.945624 2000-2012 –> 2013-2019 14.156964
(-Inf,26] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 7.047372 2000-2012 –> 2013-2019 13.948838
(-Inf,26] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.919649 2000-2012 –> 2013-2019 14.137071
(-Inf,26] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 7.052707 2000-2012 –> 2013-2019 14.014696
(-Inf,26] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 7.053006 2000-2012 –> 2013-2019 14.020443
(-Inf,26] Atlantic cstar_tref ~ sal + temp + aou + nitrate + silicate 6.849967 2000-2012 –> 2013-2019 13.805204
(-Inf,26] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 7.055954 2000-2012 –> 2013-2019 14.050221
(-Inf,26] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 6.923432 2000-2012 –> 2013-2019 14.112703
(-Inf,26] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6.913161 2000-2012 –> 2013-2019 14.096281
(-Inf,26] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 6.883305 2000-2012 –> 2013-2019 14.046352
(26,26.5] Atlantic cstar_tref ~ aou + nitrate + phosphate + phosphate_star 5.461580 1982-1999 –> 2000-2012 10.349824
(26,26.5] Atlantic cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 5.460806 1982-1999 –> 2000-2012 10.328188
(26,26.5] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.449533 1982-1999 –> 2000-2012 10.333577
(26,26.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 5.595354 1982-1999 –> 2000-2012 10.501369
(26,26.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.668480 1982-1999 –> 2000-2012 10.600656
(26,26.5] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.672809 1982-1999 –> 2000-2012 10.485241
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate 5.595568 1982-1999 –> 2000-2012 10.501616
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.405341 1982-1999 –> 2000-2012 10.227093
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 5.581556 1982-1999 –> 2000-2012 10.468166
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.648629 1982-1999 –> 2000-2012 10.561557
(26,26.5] Atlantic cstar_tref ~ aou + nitrate + phosphate + phosphate_star 7.048254 2000-2012 –> 2013-2019 12.509834
(26,26.5] Atlantic cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 7.042845 2000-2012 –> 2013-2019 12.503651
(26,26.5] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 6.717929 2000-2012 –> 2013-2019 12.167462
(26,26.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 6.742082 2000-2012 –> 2013-2019 12.337436
(26,26.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.742965 2000-2012 –> 2013-2019 12.411445
(26,26.5] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6.761371 2000-2012 –> 2013-2019 12.542132
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate 7.046893 2000-2012 –> 2013-2019 12.642461
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 7.046599 2000-2012 –> 2013-2019 12.451940
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7.042239 2000-2012 –> 2013-2019 12.623796
(26,26.5] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7.042643 2000-2012 –> 2013-2019 12.691271
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.218068 1982-1999 –> 2000-2012 9.303712
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.242126 1982-1999 –> 2000-2012 9.121238
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 5.226952 1982-1999 –> 2000-2012 9.322765
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.237147 1982-1999 –> 2000-2012 9.290792
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 5.219559 1982-1999 –> 2000-2012 9.291792
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + phosphate + phosphate_star 5.243349 1982-1999 –> 2000-2012 9.329778
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.239509 1982-1999 –> 2000-2012 9.282844
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.272305 1982-1999 –> 2000-2012 9.204879
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + phosphate + phosphate_star 5.273396 1982-1999 –> 2000-2012 9.218245
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.265284 1982-1999 –> 2000-2012 9.201894
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 7.380291 2000-2012 –> 2013-2019 12.611754
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 7.376551 2000-2012 –> 2013-2019 12.594619
(26.5,26.75] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 7.365686 2000-2012 –> 2013-2019 12.585245
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate 7.491668 2000-2012 –> 2013-2019 12.773279
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 7.416970 2000-2012 –> 2013-2019 12.689274
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate_star 7.483768 2000-2012 –> 2013-2019 12.757489
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7.491640 2000-2012 –> 2013-2019 12.756794
(26.5,26.75] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7.483495 2000-2012 –> 2013-2019 12.756141
(26.5,26.75] Atlantic cstar_tref ~ temp + nitrate + phosphate + phosphate_star 7.474357 2000-2012 –> 2013-2019 12.749889
(26.5,26.75] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7.474144 2000-2012 –> 2013-2019 12.749324
(26.75,27] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.382671 1982-1999 –> 2000-2012 10.245473
(26.75,27] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 5.435928 1982-1999 –> 2000-2012 10.290717
(26.75,27] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.378582 1982-1999 –> 2000-2012 10.232802
(26.75,27] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.384566 1982-1999 –> 2000-2012 10.221549
(26.75,27] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.376777 1982-1999 –> 2000-2012 10.232040
(26.75,27] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.407867 1982-1999 –> 2000-2012 10.259738
(26.75,27] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.440886 1982-1999 –> 2000-2012 10.289409
(26.75,27] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.357636 1982-1999 –> 2000-2012 10.245974
(26.75,27] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 5.440904 1982-1999 –> 2000-2012 10.288834
(26.75,27] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate_star 5.441043 1982-1999 –> 2000-2012 10.300335
(26.75,27] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6.035075 2000-2012 –> 2013-2019 11.417746
(26.75,27] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.005890 2000-2012 –> 2013-2019 11.384472
(26.75,27] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.026915 2000-2012 –> 2013-2019 11.411480
(26.75,27] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.004702 2000-2012 –> 2013-2019 11.381479
(26.75,27] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 6.028263 2000-2012 –> 2013-2019 11.436131
(26.75,27] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.988403 2000-2012 –> 2013-2019 11.429289
(26.75,27] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.988961 2000-2012 –> 2013-2019 11.346597
(26.75,27] Atlantic cstar_tref ~ temp + aou + silicate + phosphate_star 6.006705 2000-2012 –> 2013-2019 11.449134
(26.75,27] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 5.985030 2000-2012 –> 2013-2019 11.425934
(26.75,27] Atlantic cstar_tref ~ temp + silicate + phosphate + phosphate_star 6.005559 2000-2012 –> 2013-2019 11.446717
(27,27.25] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.428459 1982-1999 –> 2000-2012 10.895441
(27,27.25] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 5.400919 1982-1999 –> 2000-2012 10.779965
(27,27.25] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.332359 1982-1999 –> 2000-2012 10.674002
(27,27.25] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.370951 1982-1999 –> 2000-2012 10.684161
(27,27.25] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.338179 1982-1999 –> 2000-2012 10.678097
(27,27.25] Atlantic cstar_tref ~ sal + temp + silicate + phosphate_star 5.506324 1982-1999 –> 2000-2012 10.904833
(27,27.25] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.368613 1982-1999 –> 2000-2012 10.851333
(27,27.25] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.388886 1982-1999 –> 2000-2012 10.799945
(27,27.25] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.344687 1982-1999 –> 2000-2012 10.813132
(27,27.25] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 5.404332 1982-1999 –> 2000-2012 10.822723
(27,27.25] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 7.420420 2000-2012 –> 2013-2019 12.848879
(27,27.25] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 7.512168 2000-2012 –> 2013-2019 12.913087
(27,27.25] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7.497589 2000-2012 –> 2013-2019 12.829948
(27,27.25] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 7.429456 2000-2012 –> 2013-2019 12.877562
(27,27.25] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 7.482608 2000-2012 –> 2013-2019 12.853558
(27,27.25] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7.497446 2000-2012 –> 2013-2019 12.835625
(27,27.25] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7.428956 2000-2012 –> 2013-2019 12.901783
(27,27.25] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7.391449 2000-2012 –> 2013-2019 12.780334
(27,27.25] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7.499307 2000-2012 –> 2013-2019 12.843994
(27,27.25] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7.401831 2000-2012 –> 2013-2019 12.806163
(27.25,27.5] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.451293 1982-1999 –> 2000-2012 9.089033
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.388044 1982-1999 –> 2000-2012 9.019600
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.357842 1982-1999 –> 2000-2012 9.028179
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + phosphate 4.412906 1982-1999 –> 2000-2012 9.143955
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.391370 1982-1999 –> 2000-2012 9.116691
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 4.409697 1982-1999 –> 2000-2012 9.138929
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.390880 1982-1999 –> 2000-2012 9.153335
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4.365533 1982-1999 –> 2000-2012 9.016608
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + phosphate + phosphate_star 4.394774 1982-1999 –> 2000-2012 9.152330
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.393479 1982-1999 –> 2000-2012 9.147065
(27.25,27.5] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 7.428170 2000-2012 –> 2013-2019 11.879463
(27.25,27.5] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7.445225 2000-2012 –> 2013-2019 11.912517
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 7.450782 2000-2012 –> 2013-2019 11.838826
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 7.494790 2000-2012 –> 2013-2019 11.852632
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + phosphate 7.497556 2000-2012 –> 2013-2019 11.910463
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 7.405055 2000-2012 –> 2013-2019 11.796425
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 7.481493 2000-2012 –> 2013-2019 11.891190
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 7.473331 2000-2012 –> 2013-2019 11.838864
(27.25,27.5] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7.511381 2000-2012 –> 2013-2019 11.904860
(27.25,27.5] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7.364817 2000-2012 –> 2013-2019 11.890186
(27.5,27.75] Atlantic cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4.371045 1982-1999 –> 2000-2012 9.014373
(27.5,27.75] Atlantic cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.403508 1982-1999 –> 2000-2012 9.078354
(27.5,27.75] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.364128 1982-1999 –> 2000-2012 9.029025
(27.5,27.75] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 4.354863 1982-1999 –> 2000-2012 9.019904
(27.5,27.75] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.372114 1982-1999 –> 2000-2012 9.061612
(27.5,27.75] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.357921 1982-1999 –> 2000-2012 9.035232
(27.5,27.75] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4.369861 1982-1999 –> 2000-2012 9.015257
(27.5,27.75] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.397956 1982-1999 –> 2000-2012 9.076851
(27.5,27.75] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.402253 1982-1999 –> 2000-2012 9.077089
(27.5,27.75] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 4.375091 1982-1999 –> 2000-2012 9.034563
(27.5,27.75] Atlantic cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 6.462587 2000-2012 –> 2013-2019 10.833632
(27.5,27.75] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.509849 2000-2012 –> 2013-2019 10.873977
(27.5,27.75] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 6.508170 2000-2012 –> 2013-2019 10.863032
(27.5,27.75] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.514530 2000-2012 –> 2013-2019 10.886643
(27.5,27.75] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.507467 2000-2012 –> 2013-2019 10.865388
(27.5,27.75] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 6.466532 2000-2012 –> 2013-2019 10.836393
(27.5,27.75] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6.497457 2000-2012 –> 2013-2019 10.895413
(27.5,27.75] Atlantic cstar_tref ~ temp + aou + silicate + phosphate 6.510308 2000-2012 –> 2013-2019 10.912612
(27.5,27.75] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6.510090 2000-2012 –> 2013-2019 10.912342
(27.5,27.75] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 6.470887 2000-2012 –> 2013-2019 10.845978
(27.75,27.85] Atlantic cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4.663654 1982-1999 –> 2000-2012 9.435526
(27.75,27.85] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate 4.636874 1982-1999 –> 2000-2012 9.367800
(27.75,27.85] Atlantic cstar_tref ~ sal + aou + silicate + phosphate 4.664060 1982-1999 –> 2000-2012 9.419511
(27.75,27.85] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.662831 1982-1999 –> 2000-2012 9.417270
(27.75,27.85] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 4.636937 1982-1999 –> 2000-2012 9.376109
(27.75,27.85] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 4.663183 1982-1999 –> 2000-2012 9.414587
(27.75,27.85] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.662372 1982-1999 –> 2000-2012 9.425139
(27.75,27.85] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4.657806 1982-1999 –> 2000-2012 9.431622
(27.75,27.85] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.647812 1982-1999 –> 2000-2012 9.434206
(27.75,27.85] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 4.653842 1982-1999 –> 2000-2012 9.431782
(27.75,27.85] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate 7.716381 2000-2012 –> 2013-2019 12.353255
(27.75,27.85] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 7.643066 2000-2012 –> 2013-2019 12.380697
(27.75,27.85] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7.643268 2000-2012 –> 2013-2019 12.306099
(27.75,27.85] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 7.714219 2000-2012 –> 2013-2019 12.351157
(27.75,27.85] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 7.664258 2000-2012 –> 2013-2019 12.327441
(27.75,27.85] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7.644854 2000-2012 –> 2013-2019 12.309105
(27.75,27.85] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7.665162 2000-2012 –> 2013-2019 12.327533
(27.75,27.85] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7.722498 2000-2012 –> 2013-2019 12.380304
(27.75,27.85] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7.703930 2000-2012 –> 2013-2019 12.351742
(27.75,27.85] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7.723003 2000-2012 –> 2013-2019 12.376845
(27.85,27.95] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4.974593 1982-1999 –> 2000-2012 9.088464
(27.85,27.95] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.911509 1982-1999 –> 2000-2012 9.075460
(27.85,27.95] Atlantic cstar_tref ~ sal + aou + silicate + phosphate_star 4.974769 1982-1999 –> 2000-2012 9.139290
(27.85,27.95] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 5.171299 1982-1999 –> 2000-2012 9.358673
(27.85,27.95] Atlantic cstar_tref ~ sal + silicate + phosphate + phosphate_star 5.182745 1982-1999 –> 2000-2012 9.400108
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 4.914835 1982-1999 –> 2000-2012 9.089378
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.911124 1982-1999 –> 2000-2012 9.075467
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate 4.978761 1982-1999 –> 2000-2012 9.153894
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + silicate + phosphate 4.982514 1982-1999 –> 2000-2012 9.292880
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.913841 1982-1999 –> 2000-2012 9.084490
(27.85,27.95] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 5.417747 2000-2012 –> 2013-2019 10.392340
(27.85,27.95] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.362794 2000-2012 –> 2013-2019 10.274303
(27.85,27.95] Atlantic cstar_tref ~ sal + aou + silicate + phosphate_star 5.441394 2000-2012 –> 2013-2019 10.416163
(27.85,27.95] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 5.652592 2000-2012 –> 2013-2019 10.823891
(27.85,27.95] Atlantic cstar_tref ~ sal + silicate + phosphate + phosphate_star 5.689318 2000-2012 –> 2013-2019 10.872063
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 5.370894 2000-2012 –> 2013-2019 10.285729
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.364829 2000-2012 –> 2013-2019 10.275953
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate 5.312474 2000-2012 –> 2013-2019 10.291236
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + silicate + phosphate 5.378703 2000-2012 –> 2013-2019 10.361217
(27.85,27.95] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.371446 2000-2012 –> 2013-2019 10.285287
(27.95,28.05] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate 5.955215 1982-1999 –> 2000-2012 10.047152
(27.95,28.05] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 5.722130 1982-1999 –> 2000-2012 9.609778
(27.95,28.05] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.736088 1982-1999 –> 2000-2012 9.624880
(27.95,28.05] Atlantic cstar_tref ~ sal + aou + silicate + phosphate_star 5.739255 1982-1999 –> 2000-2012 9.628448
(27.95,28.05] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 5.784076 1982-1999 –> 2000-2012 9.729408
(27.95,28.05] Atlantic cstar_tref ~ sal + silicate + phosphate + phosphate_star 5.802947 1982-1999 –> 2000-2012 9.748402
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.823956 1982-1999 –> 2000-2012 9.916769
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 5.767852 1982-1999 –> 2000-2012 9.681437
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.738639 1982-1999 –> 2000-2012 9.627826
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.755226 1982-1999 –> 2000-2012 9.657068
(27.95,28.05] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 6.520771 2000-2012 –> 2013-2019 12.242901
(27.95,28.05] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.546216 2000-2012 –> 2013-2019 12.282305
(27.95,28.05] Atlantic cstar_tref ~ sal + aou + silicate + phosphate_star 6.601357 2000-2012 –> 2013-2019 12.340613
(27.95,28.05] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 6.644621 2000-2012 –> 2013-2019 12.428697
(27.95,28.05] Atlantic cstar_tref ~ sal + silicate + phosphate + phosphate_star 6.736281 2000-2012 –> 2013-2019 12.539228
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6.455828 2000-2012 –> 2013-2019 12.279784
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 6.634293 2000-2012 –> 2013-2019 12.402145
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.576288 2000-2012 –> 2013-2019 12.314927
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate 6.491018 2000-2012 –> 2013-2019 12.472280
(27.95,28.05] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.620148 2000-2012 –> 2013-2019 12.375374
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.114213 1982-1999 –> 2000-2012 9.978572
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.909336 1982-1999 –> 2000-2012 9.711211
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + aou + phosphate_star 6.115820 1982-1999 –> 2000-2012 9.983778
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.076665 1982-1999 –> 2000-2012 9.944508
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6.119701 1982-1999 –> 2000-2012 9.978328
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.104332 1982-1999 –> 2000-2012 9.971979
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.111266 1982-1999 –> 2000-2012 9.976509
(28.05,28.1] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.998766 1982-1999 –> 2000-2012 9.913766
(28.05,28.1] Atlantic cstar_tref ~ temp + aou + phosphate + phosphate_star 5.998766 1982-1999 –> 2000-2012 9.915482
(28.05,28.1] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.905011 1982-1999 –> 2000-2012 9.809069
(28.05,28.1] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 6.953530 2000-2012 –> 2013-2019 13.117268
(28.05,28.1] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 7.010296 2000-2012 –> 2013-2019 13.112118
(28.05,28.1] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7.010978 2000-2012 –> 2013-2019 13.123214
(28.05,28.1] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 6.986937 2000-2012 –> 2013-2019 13.101770
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6.662463 2000-2012 –> 2013-2019 12.571799
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6.986231 2000-2012 –> 2013-2019 13.105932
(28.05,28.1] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 7.011765 2000-2012 –> 2013-2019 13.116097
(28.05,28.1] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 6.865174 2000-2012 –> 2013-2019 12.863940
(28.05,28.1] Atlantic cstar_tref ~ temp + aou + phosphate + phosphate_star 6.925755 2000-2012 –> 2013-2019 12.924521
(28.05,28.1] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6.793526 2000-2012 –> 2013-2019 12.698537
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.644854 1982-1999 –> 2000-2012 10.333901
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6.632841 1982-1999 –> 2000-2012 10.315142
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + aou + phosphate_star 6.646183 1982-1999 –> 2000-2012 10.339960
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.635782 1982-1999 –> 2000-2012 10.300604
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6.642775 1982-1999 –> 2000-2012 10.330540
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate_star 6.648644 1982-1999 –> 2000-2012 10.338328
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.633629 1982-1999 –> 2000-2012 10.307143
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + phosphate + phosphate_star 6.645257 1982-1999 –> 2000-2012 10.340518
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.637483 1982-1999 –> 2000-2012 10.301195
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + silicate + phosphate_star 6.639544 1982-1999 –> 2000-2012 10.314827
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 8.407980 2000-2012 –> 2013-2019 15.052834
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 8.178101 2000-2012 –> 2013-2019 14.810943
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 8.331092 2000-2012 –> 2013-2019 14.973868
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + phosphate + phosphate_star 8.430686 2000-2012 –> 2013-2019 15.075943
(28.1,28.15] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 8.430675 2000-2012 –> 2013-2019 15.068158
(28.1,28.15] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 8.127710 2000-2012 –> 2013-2019 14.822795
(28.1,28.15] Atlantic cstar_tref ~ temp + aou + phosphate + phosphate_star 8.180080 2000-2012 –> 2013-2019 14.875218
(28.1,28.15] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 8.125508 2000-2012 –> 2013-2019 14.798703
(28.1,28.15] Atlantic cstar_tref ~ temp + nitrate + phosphate + phosphate_star 8.355469 2000-2012 –> 2013-2019 15.060287
(28.1,28.15] Atlantic cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 8.348093 2000-2012 –> 2013-2019 15.035359
(28.15,28.2] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.547214 1982-1999 –> 2000-2012 7.686954
(28.15,28.2] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.544237 1982-1999 –> 2000-2012 7.707813
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 3.545668 1982-1999 –> 2000-2012 7.690879
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.533409 1982-1999 –> 2000-2012 7.694024
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 3.523780 1982-1999 –> 2000-2012 7.673626
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.551753 1982-1999 –> 2000-2012 7.713679
(28.15,28.2] Atlantic cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3.561607 1982-1999 –> 2000-2012 7.694376
(28.15,28.2] Atlantic cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.558439 1982-1999 –> 2000-2012 7.694880
(28.15,28.2] Atlantic cstar_tref ~ temp + aou + silicate + phosphate 3.558948 1982-1999 –> 2000-2012 7.715330
(28.15,28.2] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.547460 1982-1999 –> 2000-2012 7.700246
(28.15,28.2] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.783801 2000-2012 –> 2013-2019 6.328038
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate 2.771759 2000-2012 –> 2013-2019 6.317427
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.776193 2000-2012 –> 2013-2019 6.373325
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + phosphate 2.772593 2000-2012 –> 2013-2019 6.318291
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.771506 2000-2012 –> 2013-2019 6.304915
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 2.756933 2000-2012 –> 2013-2019 6.280713
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.773282 2000-2012 –> 2013-2019 6.337780
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2.770329 2000-2012 –> 2013-2019 6.357685
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + phosphate + phosphate_star 2.771640 2000-2012 –> 2013-2019 6.359878
(28.15,28.2] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.761732 2000-2012 –> 2013-2019 6.313485
(28.2, Inf] Atlantic cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.203518 1982-1999 –> 2000-2012 6.333156
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.046855 1982-1999 –> 2000-2012 6.195966
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate 3.045390 1982-1999 –> 2000-2012 6.305506
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + phosphate + phosphate_star 3.051649 1982-1999 –> 2000-2012 6.226811
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + silicate + phosphate 3.051416 1982-1999 –> 2000-2012 6.324743
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.051085 1982-1999 –> 2000-2012 6.187020
(28.2, Inf] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.051559 1982-1999 –> 2000-2012 6.223436
(28.2, Inf] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 3.050729 1982-1999 –> 2000-2012 6.256676
(28.2, Inf] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.060899 1982-1999 –> 2000-2012 6.315086
(28.2, Inf] Atlantic cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.196909 1982-1999 –> 2000-2012 6.338973
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2.890878 2000-2012 –> 2013-2019 5.937733
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + nitrate + silicate + phosphate 2.883988 2000-2012 –> 2013-2019 5.929378
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + silicate + phosphate 2.884370 2000-2012 –> 2013-2019 5.935786
(28.2, Inf] Atlantic cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.860314 2000-2012 –> 2013-2019 5.911400
(28.2, Inf] Atlantic cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 2.862602 2000-2012 –> 2013-2019 5.929777
(28.2, Inf] Atlantic cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.862641 2000-2012 –> 2013-2019 5.934837
(28.2, Inf] Atlantic cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.887976 2000-2012 –> 2013-2019 5.939535
(28.2, Inf] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate 2.884348 2000-2012 –> 2013-2019 5.935076
(28.2, Inf] Atlantic cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.856816 2000-2012 –> 2013-2019 5.929672
(28.2, Inf] Atlantic cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.860484 2000-2012 –> 2013-2019 5.921383
(-Inf,26] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.952614 1982-1999 –> 2000-2012 17.829783
(-Inf,26] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.273330 1982-1999 –> 2000-2012 17.844829
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 6.002633 1982-1999 –> 2000-2012 17.973264
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.012245 1982-1999 –> 2000-2012 18.011336
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + silicate 6.104074 1982-1999 –> 2000-2012 18.610577
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 6.396171 1982-1999 –> 2000-2012 18.035387
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.436101 1982-1999 –> 2000-2012 18.104831
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6.062980 1982-1999 –> 2000-2012 18.092030
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.658204 1982-1999 –> 2000-2012 18.461982
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.454052 1982-1999 –> 2000-2012 18.137058
(-Inf,26] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.536916 2000-2012 –> 2013-2019 10.489530
(-Inf,26] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.481318 2000-2012 –> 2013-2019 11.754648
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate 4.884956 2000-2012 –> 2013-2019 10.990263
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.784056 2000-2012 –> 2013-2019 10.786689
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.805216 2000-2012 –> 2013-2019 10.817461
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + silicate 4.878066 2000-2012 –> 2013-2019 10.982141
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 5.714558 2000-2012 –> 2013-2019 12.110729
(-Inf,26] Indo-Pacific cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4.942149 2000-2012 –> 2013-2019 11.005129
(-Inf,26] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.442136 2000-2012 –> 2013-2019 12.065652
(-Inf,26] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 5.396961 2000-2012 –> 2013-2019 12.079369
(26,26.5] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.849393 1982-1999 –> 2000-2012 12.345384
(26,26.5] Indo-Pacific cstar_tref ~ sal + aou + phosphate + phosphate_star 5.114211 1982-1999 –> 2000-2012 12.978506
(26,26.5] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.887104 1982-1999 –> 2000-2012 12.525119
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.817151 1982-1999 –> 2000-2012 12.456025
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.832549 1982-1999 –> 2000-2012 12.553273
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.083018 1982-1999 –> 2000-2012 12.930845
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 4.916514 1982-1999 –> 2000-2012 12.737700
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.949101 1982-1999 –> 2000-2012 12.861671
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4.837051 1982-1999 –> 2000-2012 12.585523
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.949923 1982-1999 –> 2000-2012 12.881883
(26,26.5] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.130189 2000-2012 –> 2013-2019 8.979582
(26,26.5] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.030688 2000-2012 –> 2013-2019 8.917793
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.204764 2000-2012 –> 2013-2019 9.021915
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.243048 2000-2012 –> 2013-2019 9.075598
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 4.142558 2000-2012 –> 2013-2019 9.059072
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.195720 2000-2012 –> 2013-2019 9.144821
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4.250336 2000-2012 –> 2013-2019 9.087387
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.135552 2000-2012 –> 2013-2019 9.056822
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.195824 2000-2012 –> 2013-2019 9.145746
(26,26.5] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate_star 4.195824 2000-2012 –> 2013-2019 9.150514
(26.5,26.75] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 5.808327 1982-1999 –> 2000-2012 12.090369
(26.5,26.75] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 5.800853 1982-1999 –> 2000-2012 12.054660
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.411260 1982-1999 –> 2000-2012 11.271803
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + aou + phosphate + phosphate_star 5.672335 1982-1999 –> 2000-2012 12.087296
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.670897 1982-1999 –> 2000-2012 11.901538
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 5.477894 1982-1999 –> 2000-2012 11.550295
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.521924 1982-1999 –> 2000-2012 11.709021
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.667857 1982-1999 –> 2000-2012 12.057955
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 5.527312 1982-1999 –> 2000-2012 11.750107
(26.5,26.75] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.768508 1982-1999 –> 2000-2012 11.974173
(26.5,26.75] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4.978989 2000-2012 –> 2013-2019 10.779842
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.895823 2000-2012 –> 2013-2019 10.307083
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + aou + phosphate + phosphate_star 5.120286 2000-2012 –> 2013-2019 10.792621
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.034496 2000-2012 –> 2013-2019 10.705393
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.938988 2000-2012 –> 2013-2019 10.416882
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.973672 2000-2012 –> 2013-2019 10.495596
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.111282 2000-2012 –> 2013-2019 10.779139
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4.975450 2000-2012 –> 2013-2019 10.502761
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + nitrate + phosphate_star 4.983552 2000-2012 –> 2013-2019 10.559708
(26.5,26.75] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.941502 2000-2012 –> 2013-2019 10.460892
(26.75,27] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 5.525180 1982-1999 –> 2000-2012 12.581190
(26.75,27] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 5.451019 1982-1999 –> 2000-2012 12.477020
(26.75,27] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.579009 1982-1999 –> 2000-2012 12.698265
(26.75,27] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.466015 1982-1999 –> 2000-2012 12.458943
(26.75,27] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.547168 1982-1999 –> 2000-2012 12.584590
(26.75,27] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.535395 1982-1999 –> 2000-2012 12.573541
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.428964 1982-1999 –> 2000-2012 12.459585
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 5.507089 1982-1999 –> 2000-2012 12.665790
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + phosphate + phosphate_star 5.538147 1982-1999 –> 2000-2012 12.603547
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.477472 1982-1999 –> 2000-2012 12.462776
(26.75,27] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 4.406959 2000-2012 –> 2013-2019 9.932139
(26.75,27] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4.383580 2000-2012 –> 2013-2019 9.834599
(26.75,27] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.364438 2000-2012 –> 2013-2019 9.830453
(26.75,27] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.502440 2000-2012 –> 2013-2019 10.127855
(26.75,27] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.578805 2000-2012 –> 2013-2019 10.114201
(26.75,27] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.629702 2000-2012 –> 2013-2019 10.156203
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4.354659 2000-2012 –> 2013-2019 9.783623
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4.516169 2000-2012 –> 2013-2019 10.023257
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + phosphate + phosphate_star 4.579988 2000-2012 –> 2013-2019 10.118135
(26.75,27] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.579878 2000-2012 –> 2013-2019 10.057350
(27,27.25] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 5.121705 1982-1999 –> 2000-2012 11.805717
(27,27.25] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 5.038754 1982-1999 –> 2000-2012 11.720812
(27,27.25] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.091368 1982-1999 –> 2000-2012 11.838390
(27,27.25] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.008753 1982-1999 –> 2000-2012 11.692533
(27,27.25] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.900925 1982-1999 –> 2000-2012 11.647917
(27,27.25] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.887741 1982-1999 –> 2000-2012 11.456942
(27,27.25] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 4.918292 1982-1999 –> 2000-2012 11.799717
(27,27.25] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4.891258 1982-1999 –> 2000-2012 11.468504
(27,27.25] Indo-Pacific cstar_tref ~ temp + aou + phosphate + phosphate_star 5.007658 1982-1999 –> 2000-2012 11.595081
(27,27.25] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.825345 1982-1999 –> 2000-2012 11.410953
(27,27.25] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.179970 2000-2012 –> 2013-2019 9.188724
(27,27.25] Indo-Pacific cstar_tref ~ sal + aou + nitrate + silicate + phosphate 4.157633 2000-2012 –> 2013-2019 9.078207
(27,27.25] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate 4.164075 2000-2012 –> 2013-2019 9.084773
(27,27.25] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.131051 2000-2012 –> 2013-2019 9.031977
(27,27.25] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.147629 2000-2012 –> 2013-2019 9.035370
(27,27.25] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 4.147870 2000-2012 –> 2013-2019 9.066162
(27,27.25] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.184060 2000-2012 –> 2013-2019 9.158629
(27,27.25] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.178544 2000-2012 –> 2013-2019 9.142160
(27,27.25] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4.164460 2000-2012 –> 2013-2019 9.055719
(27,27.25] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.115378 2000-2012 –> 2013-2019 8.940723
(27.25,27.5] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 4.620524 1982-1999 –> 2000-2012 9.988679
(27.25,27.5] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4.533720 1982-1999 –> 2000-2012 9.901091
(27.25,27.5] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.577427 1982-1999 –> 2000-2012 9.973915
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.534323 1982-1999 –> 2000-2012 9.885777
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.334099 1982-1999 –> 2000-2012 9.716268
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.443130 1982-1999 –> 2000-2012 9.571162
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 4.362208 1982-1999 –> 2000-2012 9.980814
(27.25,27.5] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4.379105 1982-1999 –> 2000-2012 9.513160
(27.25,27.5] Indo-Pacific cstar_tref ~ temp + aou + phosphate + phosphate_star 4.480920 1982-1999 –> 2000-2012 9.619501
(27.25,27.5] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.230264 1982-1999 –> 2000-2012 9.355803
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + aou + nitrate + silicate + phosphate 3.312844 2000-2012 –> 2013-2019 7.707336
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate 3.346851 2000-2012 –> 2013-2019 7.749101
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.298733 2000-2012 –> 2013-2019 7.632832
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 3.361704 2000-2012 –> 2013-2019 7.839568
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.434659 2000-2012 –> 2013-2019 7.946828
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 3.302981 2000-2012 –> 2013-2019 7.665189
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.310956 2000-2012 –> 2013-2019 7.716433
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.361829 2000-2012 –> 2013-2019 7.779105
(27.25,27.5] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.309446 2000-2012 –> 2013-2019 7.706352
(27.25,27.5] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.587543 2000-2012 –> 2013-2019 7.817807
(27.5,27.75] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4.095478 1982-1999 –> 2000-2012 9.145887
(27.5,27.75] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.095543 1982-1999 –> 2000-2012 9.147793
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.087125 1982-1999 –> 2000-2012 9.124486
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + aou + phosphate + phosphate_star 4.112763 1982-1999 –> 2000-2012 9.159725
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.883195 1982-1999 –> 2000-2012 8.923066
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.105823 1982-1999 –> 2000-2012 8.975517
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 3.882307 1982-1999 –> 2000-2012 9.086666
(27.5,27.75] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4.158120 1982-1999 –> 2000-2012 9.007566
(27.5,27.75] Indo-Pacific cstar_tref ~ temp + aou + phosphate + phosphate_star 4.172579 1982-1999 –> 2000-2012 9.042509
(27.5,27.75] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.095252 1982-1999 –> 2000-2012 8.964944
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + aou + nitrate + silicate + phosphate 3.083594 2000-2012 –> 2013-2019 7.107683
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate 3.171443 2000-2012 –> 2013-2019 7.228876
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.026597 2000-2012 –> 2013-2019 6.909792
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 3.168356 2000-2012 –> 2013-2019 7.368456
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 3.026042 2000-2012 –> 2013-2019 6.908349
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.026397 2000-2012 –> 2013-2019 6.917997
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.060610 2000-2012 –> 2013-2019 6.954167
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.026290 2000-2012 –> 2013-2019 6.916765
(27.5,27.75] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate_star 3.128095 2000-2012 –> 2013-2019 7.054100
(27.5,27.75] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.343940 2000-2012 –> 2013-2019 7.439193
(27.75,27.85] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.583312 1982-1999 –> 2000-2012 7.958234
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 3.557619 1982-1999 –> 2000-2012 7.956487
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.538930 1982-1999 –> 2000-2012 7.954226
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.532281 1982-1999 –> 2000-2012 7.965906
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.538040 1982-1999 –> 2000-2012 7.957556
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3.597614 1982-1999 –> 2000-2012 7.964170
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.552789 1982-1999 –> 2000-2012 7.954566
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.536932 1982-1999 –> 2000-2012 7.957935
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.523331 1982-1999 –> 2000-2012 7.899190
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3.537090 1982-1999 –> 2000-2012 7.961453
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 2.915987 2000-2012 –> 2013-2019 6.473606
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.905267 2000-2012 –> 2013-2019 6.444197
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.906046 2000-2012 –> 2013-2019 6.438327
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.905413 2000-2012 –> 2013-2019 6.443453
(27.75,27.85] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate_star 2.906142 2000-2012 –> 2013-2019 6.456809
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.951336 2000-2012 –> 2013-2019 6.488268
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.948812 2000-2012 –> 2013-2019 6.472143
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 2.951787 2000-2012 –> 2013-2019 6.488878
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.954488 2000-2012 –> 2013-2019 6.491657
(27.75,27.85] Indo-Pacific cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.961005 2000-2012 –> 2013-2019 6.506318
(27.85,27.95] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 3.199014 1982-1999 –> 2000-2012 7.654412
(27.85,27.95] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.157695 1982-1999 –> 2000-2012 7.613090
(27.85,27.95] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.186171 1982-1999 –> 2000-2012 7.636116
(27.85,27.95] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.163197 1982-1999 –> 2000-2012 7.652391
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3.198333 1982-1999 –> 2000-2012 7.653635
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.155971 1982-1999 –> 2000-2012 7.623839
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.163651 1982-1999 –> 2000-2012 7.646141
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.163377 1982-1999 –> 2000-2012 7.660087
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3.163728 1982-1999 –> 2000-2012 7.647595
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.163748 1982-1999 –> 2000-2012 7.655102
(27.85,27.95] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2.954551 2000-2012 –> 2013-2019 6.112246
(27.85,27.95] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 2.932958 2000-2012 –> 2013-2019 6.096134
(27.85,27.95] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.923830 2000-2012 –> 2013-2019 6.092631
(27.85,27.95] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.921662 2000-2012 –> 2013-2019 6.084859
(27.85,27.95] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.923856 2000-2012 –> 2013-2019 6.093261
(27.85,27.95] Indo-Pacific cstar_tref ~ sal + temp + silicate + phosphate_star 2.923879 2000-2012 –> 2013-2019 6.105234
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 2.939477 2000-2012 –> 2013-2019 6.095448
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.935312 2000-2012 –> 2013-2019 6.098963
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 2.935509 2000-2012 –> 2013-2019 6.099238
(27.85,27.95] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.941718 2000-2012 –> 2013-2019 6.105466
(27.95,28.05] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 3.002390 1982-1999 –> 2000-2012 7.495788
(27.95,28.05] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2.986021 1982-1999 –> 2000-2012 7.479359
(27.95,28.05] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.995182 1982-1999 –> 2000-2012 7.504853
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.002150 1982-1999 –> 2000-2012 7.467956
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + aou + phosphate + phosphate_star 3.005961 1982-1999 –> 2000-2012 7.476073
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.982881 1982-1999 –> 2000-2012 7.443665
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.999181 1982-1999 –> 2000-2012 7.455914
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 3.006200 1982-1999 –> 2000-2012 7.495734
(27.95,28.05] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 2.997284 1982-1999 –> 2000-2012 7.487518
(27.95,28.05] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.994442 1982-1999 –> 2000-2012 7.497463
(27.95,28.05] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 3.072230 2000-2012 –> 2013-2019 6.074619
(27.95,28.05] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.071881 2000-2012 –> 2013-2019 6.057902
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.068017 2000-2012 –> 2013-2019 6.070168
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.072589 2000-2012 –> 2013-2019 6.055470
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 3.059974 2000-2012 –> 2013-2019 6.066175
(27.95,28.05] Indo-Pacific cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.059308 2000-2012 –> 2013-2019 6.090229
(27.95,28.05] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3.066327 2000-2012 –> 2013-2019 6.063611
(27.95,28.05] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.058372 2000-2012 –> 2013-2019 6.065583
(27.95,28.05] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.101504 2000-2012 –> 2013-2019 6.095946
(27.95,28.05] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3.061166 2000-2012 –> 2013-2019 6.097839
(28.05,28.1] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 2.932177 1982-1999 –> 2000-2012 7.071476
(28.05,28.1] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2.930554 1982-1999 –> 2000-2012 7.064024
(28.05,28.1] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.942203 1982-1999 –> 2000-2012 7.085728
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2.920762 1982-1999 –> 2000-2012 7.032468
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + phosphate + phosphate_star 2.927141 1982-1999 –> 2000-2012 7.039276
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.910460 1982-1999 –> 2000-2012 7.022207
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.925242 1982-1999 –> 2000-2012 7.035558
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 2.920574 1982-1999 –> 2000-2012 7.047339
(28.05,28.1] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 2.931644 1982-1999 –> 2000-2012 7.066823
(28.05,28.1] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.940409 1982-1999 –> 2000-2012 7.082978
(28.05,28.1] Indo-Pacific cstar_tref ~ aou + nitrate + phosphate + phosphate_star 2.855172 2000-2012 –> 2013-2019 5.787349
(28.05,28.1] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2.830862 2000-2012 –> 2013-2019 5.761415
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2.808480 2000-2012 –> 2013-2019 5.729242
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + nitrate + silicate + phosphate 2.812612 2000-2012 –> 2013-2019 5.740233
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + phosphate + phosphate_star 2.843530 2000-2012 –> 2013-2019 5.770671
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate 2.849122 2000-2012 –> 2013-2019 5.795265
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.841222 2000-2012 –> 2013-2019 5.751682
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.834318 2000-2012 –> 2013-2019 5.759560
(28.05,28.1] Indo-Pacific cstar_tref ~ sal + temp + aou + silicate + phosphate 2.849121 2000-2012 –> 2013-2019 5.769695
(28.05,28.1] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 2.846628 2000-2012 –> 2013-2019 5.778272
(28.1, Inf] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.134411 1982-1999 –> 2000-2012 7.103890
(28.1, Inf] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.256294 1982-1999 –> 2000-2012 7.240790
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.401257 1982-1999 –> 2000-2012 7.414067
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.254223 1982-1999 –> 2000-2012 7.237476
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 3.435319 1982-1999 –> 2000-2012 7.369602
(28.1, Inf] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate 3.475266 1982-1999 –> 2000-2012 7.412950
(28.1, Inf] Indo-Pacific cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3.436796 1982-1999 –> 2000-2012 7.365221
(28.1, Inf] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.340850 1982-1999 –> 2000-2012 7.267894
(28.1, Inf] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.194108 1982-1999 –> 2000-2012 7.118973
(28.1, Inf] Indo-Pacific cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3.424303 1982-1999 –> 2000-2012 7.428214
(28.1, Inf] Indo-Pacific cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2.710158 2000-2012 –> 2013-2019 5.844570
(28.1, Inf] Indo-Pacific cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.726148 2000-2012 –> 2013-2019 5.982441
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate 2.707531 2000-2012 –> 2013-2019 6.167224
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2.674858 2000-2012 –> 2013-2019 6.076115
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + aou + nitrate + silicate + phosphate 2.707209 2000-2012 –> 2013-2019 6.123153
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.646133 2000-2012 –> 2013-2019 5.900356
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + temp + aou + nitrate + phosphate 2.706303 2000-2012 –> 2013-2019 6.141622
(28.1, Inf] Indo-Pacific cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.666540 2000-2012 –> 2013-2019 6.199150
(28.1, Inf] Indo-Pacific cstar_tref ~ temp + aou + nitrate + silicate + phosphate 2.844736 2000-2012 –> 2013-2019 6.185585
(28.1, Inf] Indo-Pacific cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.683780 2000-2012 –> 2013-2019 5.877887

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_rmse %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(era, lead(era), sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_backward <- lm_rmse %>%
  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,
  GLODAP_tidy %>% select(basin, gamma_slab, era, model, term, estimate))

rm(eras_era, eras_forward, eras_backward)

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(starts_with("coeff_"),
#                names_to = "term",
#                values_to = "estimate",
#                names_prefix = "coeff_")

# subtract coefficients of adjacent era  
lm_best_long <- lm_best_target %>%
  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 <- lm_best_target %>% 
  pivot_wider(names_from = "term",
              names_prefix = "coeff_",
              values_from = "estimate",
              values_fill = 0
              )


lm_best_target %>%
  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")

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")

6.2 RMSE correlation between eras

RMSE was plotted to compare the agreement for one model applied to two adjecent 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)

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)

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")
  )

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

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         utf8_1.1.4               R6_2.5.0                
[10] nortest_1.0-4            DBI_1.1.0                colorspace_1.4-1        
[13] withr_2.3.0              gridExtra_2.3            tidyselect_1.1.0        
[16] curl_4.3                 compiler_4.0.3           git2r_0.27.1            
[19] cli_2.1.0                rvest_0.3.6              xml2_1.3.2              
[22] scales_1.1.1             checkmate_2.0.0          goftest_1.2-2           
[25] digest_0.6.27            foreign_0.8-80           rmarkdown_2.5           
[28] rio_0.5.16               pkgconfig_2.0.3          htmltools_0.5.0         
[31] highr_0.8                dbplyr_1.4.4             rlang_0.4.9             
[34] readxl_1.3.1             rstudioapi_0.13          generics_0.0.2          
[37] jsonlite_1.7.1           zip_2.1.1                car_3.0-10              
[40] magrittr_1.5             Matrix_1.2-18            Rcpp_1.0.5              
[43] munsell_0.5.0            fansi_0.4.1              abind_1.4-5             
[46] lifecycle_0.2.0          stringi_1.5.3            whisker_0.4             
[49] yaml_2.2.1               carData_3.0-4            plyr_1.8.6              
[52] grid_4.0.3               blob_1.2.1               parallel_4.0.3          
[55] promises_1.1.1           crayon_1.3.4             lattice_0.20-41         
[58] haven_2.3.1              hms_0.5.3                pillar_1.4.7            
[61] reprex_0.3.0             glue_1.4.2               evaluate_0.14           
[64] RcppArmadillo_0.10.1.2.0 data.table_1.13.2        modelr_0.1.8            
[67] vctrs_0.3.5              httpuv_1.5.4             cellranger_1.1.0        
[70] gtable_0.3.0             reshape_0.8.8            assertthat_0.2.1        
[73] xfun_0.18                openxlsx_4.2.3           RcppEigen_0.3.3.7.0     
[76] later_1.1.0.1            viridisLite_0.3.0        ellipsis_0.3.1          
[79] here_0.1