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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, 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)

# 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 predictor combinations with nitrate and phosphate
lm_all <- lm_all %>%
  mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
  filter(!(
    str_detect(lm_coeff_filter, "nitrate") &
      str_detect(lm_coeff_filter, "phosphate")
  )) %>%
  select(-lm_coeff_filter)

# 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:

  • 41

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,
   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 + nitrate + silicate 1.7979903 683.8843 8.909709 1982-1999 –> 2000-2012 3.6223439 1598.9179
Atlantic (-Inf,26] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1.6618576 659.4298 7.791514 1982-1999 –> 2000-2012 3.3446631 1540.2814
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate 1.4974719 622.4328 5.357017 1982-1999 –> 2000-2012 3.3857999 1552.9072
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 1.4421808 611.7919 5.982825 1982-1999 –> 2000-2012 3.3292711 1543.9726
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 1.3240242 583.0704 5.870624 1982-1999 –> 2000-2012 2.7624787 1393.6339
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.1738491 544.6202 5.347280 1982-1999 –> 2000-2012 2.5568164 1339.5603
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate 1.7034627 665.7381 4.210317 1982-1999 –> 2000-2012 3.6358066 1606.5353
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.0734858 512.5895 4.775202 1982-1999 –> 2000-2012 2.4077143 1289.4562
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate 1.5656900 639.4011 4.536433 1982-1999 –> 2000-2012 3.2869598 1530.3775
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.0721782 514.1800 4.711590 1982-1999 –> 2000-2012 2.4062957 1293.0094
Atlantic (-Inf,26] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1.7566234 321.2438 5.221307 2000-2012 –> 2013-2019 3.4184809 980.6736
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate 1.7639722 319.8951 4.591325 2000-2012 –> 2013-2019 3.2614441 942.3279
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 1.7613908 321.6666 4.606930 2000-2012 –> 2013-2019 3.2035717 933.4585
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 1.4547154 291.8248 4.033856 2000-2012 –> 2013-2019 2.7787395 874.8952
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.2683736 272.4411 3.781825 2000-2012 –> 2013-2019 2.4422228 817.0613
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate 1.8139422 324.2528 4.228206 2000-2012 –> 2013-2019 3.5174049 989.9909
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.2543425 268.7058 3.866039 2000-2012 –> 2013-2019 2.3278283 781.2953
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate 1.7006016 316.1876 3.553807 2000-2012 –> 2013-2019 3.2662915 955.5887
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.1950624 263.1534 3.519214 2000-2012 –> 2013-2019 2.2672406 777.3333
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 1.4745112 293.9334 3.841532 2000-2012 –> 2013-2019 2.9911022 922.6290
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.6699626 6737.3236 24.134098 1982-1999 –> 2000-2012 9.5201102 16726.4934
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate 3.9941888 6382.1860 18.954002 1982-1999 –> 2000-2012 8.0810957 15801.5333
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.6380879 6172.0215 14.774574 1982-1999 –> 2000-2012 7.2575738 15189.1618
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate 3.9996578 6383.2947 18.489476 1982-1999 –> 2000-2012 8.1163779 15824.8311
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate 3.9798872 6374.0362 19.108434 1982-1999 –> 2000-2012 8.0908823 15812.9412
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6096349 6154.1826 14.304181 1982-1999 –> 2000-2012 7.1649808 15111.8195
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 3.6702662 6190.0286 16.261179 1982-1999 –> 2000-2012 7.5108093 15402.4587
Atlantic (26,26.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.5607203 6683.5442 12.386147 1982-1999 –> 2000-2012 9.0295126 16400.1810
Atlantic (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.4995827 6652.8815 12.487038 1982-1999 –> 2000-2012 8.8713413 16296.4592
Atlantic (26,26.5] cstar_tref ~ temp + silicate + phosphate_star 4.6400062 6720.7024 14.056163 1982-1999 –> 2000-2012 9.4040774 16648.2793
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate 4.3208649 3572.6391 13.768183 2000-2012 –> 2013-2019 8.9920836 10308.5737
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.3208048 3574.6219 13.772901 2000-2012 –> 2013-2019 8.9907674 10311.9455
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate 3.8524592 3432.8157 11.307173 2000-2012 –> 2013-2019 7.8466479 9815.0016
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.6337676 3362.5818 10.363673 2000-2012 –> 2013-2019 7.2718555 9534.6032
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate 4.0173849 3482.6281 12.004710 2000-2012 –> 2013-2019 8.0170426 9865.9229
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate 3.8397846 3428.7425 11.206273 2000-2012 –> 2013-2019 7.8196717 9802.7788
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6584854 3370.9609 10.318851 2000-2012 –> 2013-2019 7.2681203 9525.1435
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 3.6645903 3371.0217 10.287116 2000-2012 –> 2013-2019 7.3348565 9561.0503
Atlantic (26,26.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.4677708 3615.9635 11.436708 2000-2012 –> 2013-2019 9.0284911 10299.5078
Atlantic (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.4762926 3618.3188 11.952191 2000-2012 –> 2013-2019 8.9758753 10271.2003
Atlantic (26.5,26.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3.7599643 8571.2458 16.055745 1982-1999 –> 2000-2012 7.4558950 20093.1394
Atlantic (26.5,26.75] cstar_tref ~ sal + phosphate + phosphate_star 4.6007230 9198.8742 15.037023 1982-1999 –> 2000-2012 8.6535871 21108.0001
Atlantic (26.5,26.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.5901940 8427.0917 10.080328 1982-1999 –> 2000-2012 7.0755901 19701.3622
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.9584360 9434.4902 12.648749 1982-1999 –> 2000-2012 9.5242243 21848.7406
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.5723347 8413.5326 14.769892 1982-1999 –> 2000-2012 7.0784660 19714.8460
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.5088881 9137.9660 12.862444 1982-1999 –> 2000-2012 8.4472226 20928.0644
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.3145143 8179.8188 10.520585 1982-1999 –> 2000-2012 6.4936425 19067.7721
Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.7350091 8550.4690 12.839795 1982-1999 –> 2000-2012 7.3636558 19994.7934
Atlantic (26.5,26.75] cstar_tref ~ temp + phosphate + phosphate_star 4.7877531 9323.1993 13.078648 1982-1999 –> 2000-2012 9.0044951 21399.6808
Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.4569950 8309.1353 10.935851 1982-1999 –> 2000-2012 6.7294242 19317.2124
Atlantic (26.5,26.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3.6741700 4010.7907 11.036855 2000-2012 –> 2013-2019 7.4341344 12582.0365
Atlantic (26.5,26.75] cstar_tref ~ sal + phosphate + phosphate_star 4.9668748 4451.9422 17.771118 2000-2012 –> 2013-2019 9.5675978 13650.8164
Atlantic (26.5,26.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.6452671 3999.1812 10.958585 2000-2012 –> 2013-2019 7.2354610 12426.2729
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.5499307 3962.2239 11.624344 2000-2012 –> 2013-2019 7.1222654 12375.7565
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.9284528 4442.5265 16.117406 2000-2012 –> 2013-2019 9.4373408 13580.4926
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.4448277 3918.0443 10.794175 2000-2012 –> 2013-2019 6.7593420 12097.8631
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 4.8905710 4431.1840 13.097021 2000-2012 –> 2013-2019 10.1072178 14024.0592
Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.7721649 4049.4838 12.260256 2000-2012 –> 2013-2019 7.5071739 12599.9528
Atlantic (26.5,26.75] cstar_tref ~ temp + phosphate + phosphate_star 5.2497216 4533.3570 15.529203 2000-2012 –> 2013-2019 10.0374747 13856.5562
Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.6158596 3987.2742 11.314802 2000-2012 –> 2013-2019 7.0728546 12296.4095
Atlantic (26.75,27] cstar_tref ~ sal + nitrate + phosphate_star 4.2854472 15358.0329 34.087567 1982-1999 –> 2000-2012 7.9275476 34353.9494
Atlantic (26.75,27] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.7159919 12924.6314 37.121102 1982-1999 –> 2000-2012 5.2900323 29492.2676
Atlantic (26.75,27] cstar_tref ~ sal + phosphate + phosphate_star 4.1615131 15201.3242 33.539267 1982-1999 –> 2000-2012 7.5797058 33752.9738
Atlantic (26.75,27] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.6046719 12701.1497 38.535734 1982-1999 –> 2000-2012 5.0525068 28916.7749
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.2834678 15357.5658 35.355283 1982-1999 –> 2000-2012 7.9094632 34324.4516
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.5229300 12532.8795 27.083041 1982-1999 –> 2000-2012 4.7945751 28227.4582
Atlantic (26.75,27] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.1614042 15203.1844 33.839590 1982-1999 –> 2000-2012 7.5283011 33650.9606
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.2083048 11821.6141 24.431305 1982-1999 –> 2000-2012 4.0228977 25943.2416
Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.7852538 13059.1020 20.682052 1982-1999 –> 2000-2012 5.2436385 29304.8402
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.3529180 12158.3363 19.498731 1982-1999 –> 2000-2012 4.2391160 26548.9549
Atlantic (26.75,27] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.9099779 7035.5252 27.362241 2000-2012 –> 2013-2019 5.6259698 19960.1567
Atlantic (26.75,27] cstar_tref ~ sal + phosphate + phosphate_star 4.8250300 8461.5415 13.521181 2000-2012 –> 2013-2019 8.9865430 23662.8656
Atlantic (26.75,27] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.7728530 6899.2144 22.992642 2000-2012 –> 2013-2019 5.3775249 19600.3641
Atlantic (26.75,27] cstar_tref ~ sal + silicate + phosphate_star 4.3448411 8165.5079 13.984161 2000-2012 –> 2013-2019 8.8672286 23810.9135
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.8509139 6979.6167 28.834681 2000-2012 –> 2013-2019 5.3738439 19512.4962
Atlantic (26.75,27] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.7898034 8442.8484 13.400189 2000-2012 –> 2013-2019 8.9512076 23646.0328
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.6182643 6739.2152 25.400147 2000-2012 –> 2013-2019 4.8265691 18560.8293
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate_star 4.3437790 8166.8175 14.144170 2000-2012 –> 2013-2019 8.8556828 23801.8297
Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.1656429 7273.3363 31.750586 2000-2012 –> 2013-2019 5.9508967 20332.4383
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.8238520 6950.6822 27.989507 2000-2012 –> 2013-2019 5.1767700 19109.0185
Atlantic (27,27.25] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.3260996 10490.2984 11.108468 1982-1999 –> 2000-2012 4.8117446 24767.9771
Atlantic (27,27.25] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.3259642 10490.0289 11.725473 1982-1999 –> 2000-2012 4.8474242 24855.3171
Atlantic (27,27.25] cstar_tref ~ sal + silicate + phosphate_star 2.8572813 11440.5862 13.889698 1982-1999 –> 2000-2012 6.0976822 27340.1346
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.1260865 11858.8756 12.076220 1982-1999 –> 2000-2012 5.7359658 26435.2328
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.0875930 9991.4197 9.273630 1982-1999 –> 2000-2012 3.9667985 22558.3192
Atlantic (27,27.25] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.1403559 11879.9617 12.324688 1982-1999 –> 2000-2012 5.6836626 26298.0816
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.9753004 9735.4214 9.239424 1982-1999 –> 2000-2012 3.6435323 21573.0454
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate_star 2.7672450 11294.3412 11.198274 1982-1999 –> 2000-2012 5.7342966 26656.1919
Atlantic (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.9406926 11575.8124 13.795732 1982-1999 –> 2000-2012 5.5606351 26175.7369
Atlantic (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.6577803 11107.4701 12.305484 1982-1999 –> 2000-2012 4.8597885 24643.1500
Atlantic (27,27.25] cstar_tref ~ sal + nitrate + phosphate_star 3.5282875 6907.6795 12.940347 2000-2012 –> 2013-2019 6.7008552 18832.8909
Atlantic (27,27.25] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.4642713 5985.8285 15.716961 2000-2012 –> 2013-2019 4.7903709 16476.1269
Atlantic (27,27.25] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.4284040 5948.0888 15.043234 2000-2012 –> 2013-2019 4.7543682 16438.1177
Atlantic (27,27.25] cstar_tref ~ sal + silicate + phosphate_star 2.7289547 6246.4344 13.698458 2000-2012 –> 2013-2019 5.5862360 17687.0205
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.5244882 6906.9063 13.292900 2000-2012 –> 2013-2019 6.6505747 18765.7819
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.4270934 5948.6992 14.883828 2000-2012 –> 2013-2019 4.5146864 15940.1189
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3578885 5874.2388 13.876581 2000-2012 –> 2013-2019 4.3331890 15609.6602
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate_star 2.7208616 6240.7895 13.230134 2000-2012 –> 2013-2019 5.4881065 17535.1307
Atlantic (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.4451037 6848.2674 17.171515 2000-2012 –> 2013-2019 6.3857964 18424.0798
Atlantic (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.2422103 6692.0289 15.409856 2000-2012 –> 2013-2019 5.8999906 17799.4990
Atlantic (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.4414699 13270.2570 26.167869 1982-1999 –> 2000-2012 7.1864042 32939.7796
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.3292256 13104.6613 20.574940 1982-1999 –> 2000-2012 6.1757755 30805.8330
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.8849141 12391.2978 22.454726 1982-1999 –> 2000-2012 5.5000493 29486.0028
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.3708296 13166.6825 21.640713 1982-1999 –> 2000-2012 6.2117380 30853.6182
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate_star 3.8254865 13796.5572 25.725729 1982-1999 –> 2000-2012 6.6763703 31506.6461
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.8715160 12368.0505 22.697774 1982-1999 –> 2000-2012 5.4120701 29255.1283
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate_star 2.8875250 12393.8153 22.136811 1982-1999 –> 2000-2012 5.6809689 29959.8451
Atlantic (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.7524941 13702.3480 14.805884 1982-1999 –> 2000-2012 6.9063069 32139.0918
Atlantic (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.7428240 13689.4620 15.565881 1982-1999 –> 2000-2012 6.7872965 31873.0041
Atlantic (27.25,27.5] cstar_tref ~ temp + silicate + phosphate_star 3.7539200 13702.2453 15.039813 1982-1999 –> 2000-2012 7.0257816 32400.6853
Atlantic (27.25,27.5] cstar_tref ~ sal + nitrate + silicate + phosphate_star 4.1247944 7742.8125 27.698535 2000-2012 –> 2013-2019 7.5698240 21018.2325
Atlantic (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.1606971 7766.4373 28.637397 2000-2012 –> 2013-2019 7.6021670 21036.6943
Atlantic (27.25,27.5] cstar_tref ~ sal + silicate + phosphate_star 4.2063208 7794.1663 29.823748 2000-2012 –> 2013-2019 7.6537158 21071.0139
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.1404159 7753.1170 22.742204 2000-2012 –> 2013-2019 7.4696415 20857.7783
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.7367783 7475.5046 24.666793 2000-2012 –> 2013-2019 6.6216924 19866.8023
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.2538270 7826.7812 24.760840 2000-2012 –> 2013-2019 7.6246566 20993.4637
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.7893620 7513.5973 25.813866 2000-2012 –> 2013-2019 6.6608780 19881.6478
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate_star 3.8267602 7538.3690 26.794841 2000-2012 –> 2013-2019 6.7142852 19932.1843
Atlantic (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.4498468 7949.5892 17.124368 2000-2012 –> 2013-2019 8.2023409 21651.9372
Atlantic (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.5292151 7997.7821 18.531955 2000-2012 –> 2013-2019 8.2720390 21687.2441
Atlantic (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.3412263 19754.0788 21.278705 1982-1999 –> 2000-2012 6.9475495 47220.0151
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 2.9290451 18763.9848 19.050781 1982-1999 –> 2000-2012 5.2570526 41782.2579
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.5969033 17860.9019 21.769808 1982-1999 –> 2000-2012 4.7636531 40151.7007
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.8899670 18662.9809 19.678120 1982-1999 –> 2000-2012 5.2131427 41660.1403
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate_star 3.5585243 20225.8993 27.736207 1982-1999 –> 2000-2012 5.9575292 43547.4517
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.5941074 17852.8013 21.972752 1982-1999 –> 2000-2012 4.7598768 40139.0013
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 2.6488317 18007.7901 24.114223 1982-1999 –> 2000-2012 4.8209797 40321.8752
Atlantic (27.5,27.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.7660531 20654.1448 16.683751 1982-1999 –> 2000-2012 6.6902581 45989.4542
Atlantic (27.5,27.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.8081786 20737.7934 17.301318 1982-1999 –> 2000-2012 6.7294558 46062.9233
Atlantic (27.5,27.75] cstar_tref ~ temp + silicate + phosphate_star 3.8541912 20826.1099 19.484374 1982-1999 –> 2000-2012 6.7787783 46160.7471
Atlantic (27.5,27.75] cstar_tref ~ sal + nitrate + phosphate_star 3.7490462 10982.7217 13.645556 2000-2012 –> 2013-2019 7.3209639 31236.8712
Atlantic (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3.3467726 10530.2478 15.254499 2000-2012 –> 2013-2019 6.7176093 30350.6762
Atlantic (27.5,27.75] cstar_tref ~ sal + phosphate + phosphate_star 3.6286512 10852.0293 13.921373 2000-2012 –> 2013-2019 7.1250741 30945.5352
Atlantic (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.3021073 10476.4516 15.251540 2000-2012 –> 2013-2019 6.6433337 30230.5303
Atlantic (27.5,27.75] cstar_tref ~ sal + silicate + phosphate_star 3.5403585 10753.3988 19.039534 2000-2012 –> 2013-2019 7.0129125 30795.3920
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.4807840 10687.4491 13.094023 2000-2012 –> 2013-2019 6.4098291 29451.4339
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.9855177 10074.8976 15.644630 2000-2012 –> 2013-2019 5.5824210 27935.7995
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.3929378 10585.1013 13.596469 2000-2012 –> 2013-2019 6.2829048 29248.0822
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.9665985 10049.4436 15.764128 2000-2012 –> 2013-2019 5.5607059 27902.2449
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 3.1365845 10270.5403 18.803814 2000-2012 –> 2013-2019 5.7854162 28278.3305
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + phosphate_star 2.2223063 5773.0236 12.445344 1982-1999 –> 2000-2012 3.9881562 12447.3603
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.6571869 5012.7080 13.065690 1982-1999 –> 2000-2012 3.2589745 11362.1850
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.2225426 5773.2998 12.472432 1982-1999 –> 2000-2012 4.0025101 12474.3287
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + phosphate_star 2.2234691 5772.3827 12.462708 1982-1999 –> 2000-2012 4.0240370 12509.9828
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.6651339 5025.1368 13.155852 1982-1999 –> 2000-2012 3.2750218 11391.5224
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.7839394 5202.1873 13.100644 1982-1999 –> 2000-2012 3.4925351 11766.0412
Atlantic (27.75,27.85] cstar_tref ~ temp + nitrate + phosphate_star 2.6187304 6197.4699 14.550650 1982-1999 –> 2000-2012 4.6155588 13281.8614
Atlantic (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.3770603 5947.9185 15.403746 1982-1999 –> 2000-2012 4.3200104 12942.6238
Atlantic (27.75,27.85] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.3738277 5944.3829 15.442862 1982-1999 –> 2000-2012 4.3152567 12936.4632
Atlantic (27.75,27.85] cstar_tref ~ temp + silicate + phosphate_star 2.3964633 5967.0388 15.329180 1982-1999 –> 2000-2012 4.3789514 13027.2709
Atlantic (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.3378964 2987.8654 11.548426 2000-2012 –> 2013-2019 4.6871892 8905.2568
Atlantic (27.75,27.85] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.3377954 2987.8087 11.566112 2000-2012 –> 2013-2019 4.6899808 8908.3969
Atlantic (27.75,27.85] cstar_tref ~ sal + silicate + phosphate_star 2.3379998 2985.9234 11.557145 2000-2012 –> 2013-2019 4.6939508 8908.6674
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + phosphate_star 2.6582659 3156.3556 11.374209 2000-2012 –> 2013-2019 4.8805722 8929.3792
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.8065490 2651.5883 12.287919 2000-2012 –> 2013-2019 3.4637358 7664.2963
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.6204894 3137.5771 11.418425 2000-2012 –> 2013-2019 4.8430320 8910.8770
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + phosphate_star 2.7005504 3175.0611 11.136292 2000-2012 –> 2013-2019 4.9240196 8947.4438
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.8147710 2657.5459 12.344435 2000-2012 –> 2013-2019 3.4799048 7682.6828
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.8598127 2687.7116 12.393512 2000-2012 –> 2013-2019 3.6437522 7889.8989
Atlantic (27.75,27.85] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.7211808 3187.0458 15.318370 2000-2012 –> 2013-2019 5.0950085 9131.4288
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.6930174 6760.0467 51.548127 1982-1999 –> 2000-2012 6.8009830 15502.9884
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.6929286 6761.9872 51.770459 1982-1999 –> 2000-2012 6.7739173 15477.1139
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.6898682 6757.9345 52.824150 1982-1999 –> 2000-2012 6.7985203 15501.6314
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + phosphate_star 3.8170523 6839.8405 64.167224 1982-1999 –> 2000-2012 6.9258084 15581.6519
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6885920 6759.0780 51.842587 1982-1999 –> 2000-2012 6.7722781 15477.1976
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 3.8121369 6838.6500 65.381085 1982-1999 –> 2000-2012 6.8988667 15558.1436
Atlantic (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 3.6935815 6758.4249 52.651033 1982-1999 –> 2000-2012 6.8886539 15593.9001
Atlantic (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.6934228 6760.3185 52.865066 1982-1999 –> 2000-2012 6.8872126 15596.4205
Atlantic (27.85,27.95] cstar_tref ~ temp + phosphate + phosphate_star 3.6900930 6756.0853 53.517133 1982-1999 –> 2000-2012 6.8850481 15591.4349
Atlantic (27.85,27.95] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.6889515 6757.3193 52.772225 1982-1999 –> 2000-2012 6.8829288 15593.6220
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.5681621 3822.4407 26.866261 2000-2012 –> 2013-2019 7.2611795 10582.4874
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.3786842 3747.1776 25.710784 2000-2012 –> 2013-2019 7.0716128 10509.1648
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.5559519 3817.5868 25.414800 2000-2012 –> 2013-2019 7.2458201 10575.5213
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + phosphate_star 3.5700168 3821.1765 27.665985 2000-2012 –> 2013-2019 7.3870691 10661.0170
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.3848830 3749.7732 25.267436 2000-2012 –> 2013-2019 7.0734751 10508.8512
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 3.3930561 3751.1881 23.807090 2000-2012 –> 2013-2019 7.2051930 10589.8381
Atlantic (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 3.8304377 3920.8753 24.016081 2000-2012 –> 2013-2019 7.5240191 10679.3003
Atlantic (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.7739214 3901.8273 24.304529 2000-2012 –> 2013-2019 7.4673442 10662.1458
Atlantic (27.85,27.95] cstar_tref ~ temp + phosphate + phosphate_star 3.8171204 3915.9437 24.075083 2000-2012 –> 2013-2019 7.5072134 10672.0290
Atlantic (27.85,27.95] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.7719859 3901.1009 24.309174 2000-2012 –> 2013-2019 7.4609374 10658.4201
Atlantic (27.95,28.05] cstar_tref ~ sal + phosphate + phosphate_star 4.2751880 10767.6377 29.066843 1982-1999 –> 2000-2012 8.6506919 25860.3805
Atlantic (27.95,28.05] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.2750292 10769.4986 29.048330 1982-1999 –> 2000-2012 8.6504609 25864.1553
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.0457075 10562.9648 26.287164 1982-1999 –> 2000-2012 8.3429060 25563.6234
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.9616144 10486.2807 25.618789 1982-1999 –> 2000-2012 8.1821218 25395.1179
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.8926869 10418.5310 26.101297 1982-1999 –> 2000-2012 8.0317475 25223.8434
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.8739353 10402.4424 25.781312 1982-1999 –> 2000-2012 7.9982193 25191.1218
Atlantic (27.95,28.05] cstar_tref ~ temp + nitrate + phosphate_star 4.0630136 10576.9547 26.261050 1982-1999 –> 2000-2012 8.4119762 25637.9979
Atlantic (27.95,28.05] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.0053913 10525.4480 25.714774 1982-1999 –> 2000-2012 8.3098120 25534.8555
Atlantic (27.95,28.05] cstar_tref ~ temp + phosphate + phosphate_star 3.9274783 10449.8627 26.075741 1982-1999 –> 2000-2012 8.1439617 25349.7300
Atlantic (27.95,28.05] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.9201578 10444.8739 25.878178 1982-1999 –> 2000-2012 8.1332632 25342.5656
Atlantic (27.95,28.05] cstar_tref ~ sal + phosphate + phosphate_star 4.0791808 5569.2747 27.397808 2000-2012 –> 2013-2019 8.3543688 16336.9124
Atlantic (27.95,28.05] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.0726928 5568.1421 27.472110 2000-2012 –> 2013-2019 8.3477221 16337.6407
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.0086790 5536.9638 24.749523 2000-2012 –> 2013-2019 8.0543865 16099.9286
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.8978424 5483.7838 24.848984 2000-2012 –> 2013-2019 7.8594568 15970.0645
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.8060168 5434.8667 24.881092 2000-2012 –> 2013-2019 7.6987037 15853.3978
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.7787244 5422.7037 24.911551 2000-2012 –> 2013-2019 7.6526597 15825.1461
Atlantic (27.95,28.05] cstar_tref ~ temp + nitrate + phosphate_star 4.0650928 5562.4662 25.338914 2000-2012 –> 2013-2019 8.1281065 16139.4209
Atlantic (27.95,28.05] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.0000660 5532.7308 24.974102 2000-2012 –> 2013-2019 8.0054574 16058.1788
Atlantic (27.95,28.05] cstar_tref ~ temp + phosphate + phosphate_star 3.8970705 5479.3940 24.721111 2000-2012 –> 2013-2019 7.8245488 15929.2567
Atlantic (27.95,28.05] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.8891197 5477.3748 24.726316 2000-2012 –> 2013-2019 7.8092775 15922.2487
Atlantic (28.05,28.1] cstar_tref ~ sal + phosphate + phosphate_star 1.4199571 4437.4520 6.640338 1982-1999 –> 2000-2012 2.7317962 9988.4804
Atlantic (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.4104398 4422.6259 6.078163 1982-1999 –> 2000-2012 2.7219625 9974.8634
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + phosphate_star 1.2202055 4060.1304 8.465170 1982-1999 –> 2000-2012 2.2981844 8969.5490
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.1765015 3970.8722 7.269305 1982-1999 –> 2000-2012 2.2369827 8828.6461
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.1566552 3926.3062 7.730772 1982-1999 –> 2000-2012 2.1978100 8721.7900
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.1514385 3916.9963 7.337089 1982-1999 –> 2000-2012 2.1925930 8714.4792
Atlantic (28.05,28.1] cstar_tref ~ temp + nitrate + phosphate_star 1.2837257 4185.1002 11.567407 1982-1999 –> 2000-2012 2.4309000 9296.4558
Atlantic (28.05,28.1] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1.2777623 4175.4504 11.562349 1982-1999 –> 2000-2012 2.4248501 9288.5588
Atlantic (28.05,28.1] cstar_tref ~ temp + phosphate + phosphate_star 1.2679910 4154.2435 11.799512 1982-1999 –> 2000-2012 2.4216483 9284.0721
Atlantic (28.05,28.1] cstar_tref ~ temp + silicate + phosphate + phosphate_star 1.2636645 4147.6919 11.820325 1982-1999 –> 2000-2012 2.4016116 9234.5745
Atlantic (28.05,28.1] cstar_tref ~ sal + phosphate + phosphate_star 1.5421334 2577.0180 7.095010 2000-2012 –> 2013-2019 2.9620905 7014.4700
Atlantic (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.5018197 2542.3038 5.965893 2000-2012 –> 2013-2019 2.9122595 6964.9297
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + phosphate_star 1.3501543 2394.7522 9.099186 2000-2012 –> 2013-2019 2.5703598 6454.8826
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.2625424 2303.7635 7.403175 2000-2012 –> 2013-2019 2.4390438 6274.6357
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.2569957 2295.6610 8.240693 2000-2012 –> 2013-2019 2.4136509 6221.9671
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2343138 2272.4229 7.428694 2000-2012 –> 2013-2019 2.3857523 6189.4192
Atlantic (28.05,28.1] cstar_tref ~ temp + nitrate + phosphate_star 1.4180322 2460.7372 12.397956 2000-2012 –> 2013-2019 2.7017580 6645.8374
Atlantic (28.05,28.1] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1.3992066 2444.2137 12.463663 2000-2012 –> 2013-2019 2.6769690 6619.6640
Atlantic (28.05,28.1] cstar_tref ~ temp + phosphate + phosphate_star 1.3844179 2427.4865 12.684212 2000-2012 –> 2013-2019 2.6524089 6581.7300
Atlantic (28.05,28.1] cstar_tref ~ temp + silicate + phosphate + phosphate_star 1.3841026 2429.1709 12.680122 2000-2012 –> 2013-2019 2.6477671 6576.8627
Atlantic (28.1,28.15] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1.1944893 4476.2537 5.508118 1982-1999 –> 2000-2012 2.2854108 10171.7516
Atlantic (28.1,28.15] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.1758428 4432.2627 5.321626 1982-1999 –> 2000-2012 2.2506006 10071.4244
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.8168537 3413.7344 5.415135 1982-1999 –> 2000-2012 1.5096886 7395.8884
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8127139 3401.5284 5.436958 1982-1999 –> 2000-2012 1.5031113 7372.3809
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.8094433 3388.2539 5.337970 1982-1999 –> 2000-2012 1.5291408 7513.9673
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.7991765 3354.5633 5.281963 1982-1999 –> 2000-2012 1.4793572 7269.1497
Atlantic (28.1,28.15] cstar_tref ~ temp + nitrate + phosphate_star 1.0041836 3989.0251 11.262598 1982-1999 –> 2000-2012 1.7847351 8419.0736
Atlantic (28.1,28.15] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1.0012941 3982.9680 11.290660 1982-1999 –> 2000-2012 1.7779735 8396.2484
Atlantic (28.1,28.15] cstar_tref ~ temp + phosphate + phosphate_star 0.9922627 3955.6345 11.094893 1982-1999 –> 2000-2012 1.7951476 8492.1500
Atlantic (28.1,28.15] cstar_tref ~ temp + silicate + phosphate + phosphate_star 0.9841578 3934.7027 11.044040 1982-1999 –> 2000-2012 1.7472134 8281.1951
Atlantic (28.1,28.15] cstar_tref ~ sal + phosphate + phosphate_star 1.2047793 2295.8546 7.707298 2000-2012 –> 2013-2019 2.3940527 6757.8724
Atlantic (28.1,28.15] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.2038209 2296.7213 7.694622 2000-2012 –> 2013-2019 2.3796637 6728.9840
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.9317137 1931.8494 7.194852 2000-2012 –> 2013-2019 1.7485674 5345.5839
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.9073146 1896.0617 7.191330 2000-2012 –> 2013-2019 1.7200285 5297.5901
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.8879019 1863.2634 6.924296 2000-2012 –> 2013-2019 1.6973452 5251.5173
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.8876626 1864.8796 6.919523 2000-2012 –> 2013-2019 1.6868392 5219.4429
Atlantic (28.1,28.15] cstar_tref ~ temp + nitrate + phosphate_star 1.0796456 2139.6936 13.229077 2000-2012 –> 2013-2019 2.0838292 6128.7187
Atlantic (28.1,28.15] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1.0635499 2120.3044 13.323388 2000-2012 –> 2013-2019 2.0648440 6103.2724
Atlantic (28.1,28.15] cstar_tref ~ temp + phosphate + phosphate_star 1.0452943 2093.6496 13.040195 2000-2012 –> 2013-2019 2.0375570 6049.2841
Atlantic (28.1,28.15] cstar_tref ~ temp + silicate + phosphate + phosphate_star 1.0446470 2094.7674 13.019719 2000-2012 –> 2013-2019 2.0288048 6029.4701
Atlantic (28.15,28.2] cstar_tref ~ nitrate + silicate + phosphate_star 1.0984852 6100.8172 25.207735 1982-1999 –> 2000-2012 1.9870940 13543.8191
Atlantic (28.15,28.2] cstar_tref ~ sal + nitrate + phosphate_star 0.9795220 5639.3462 17.854894 1982-1999 –> 2000-2012 1.8567975 13009.0031
Atlantic (28.15,28.2] cstar_tref ~ sal + nitrate + silicate + phosphate_star 0.9238520 5405.7738 12.393045 1982-1999 –> 2000-2012 1.7750136 12604.7588
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.7808204 4728.5734 13.314922 1982-1999 –> 2000-2012 1.4504501 10556.9008
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.7318765 4469.9570 8.923396 1982-1999 –> 2000-2012 1.3696404 10021.6876
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.9139992 5362.6062 15.940803 1982-1999 –> 2000-2012 1.6871376 12012.2245
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.8420102 5034.3229 10.786385 1982-1999 –> 2000-2012 1.5818732 11434.5653
Atlantic (28.15,28.2] cstar_tref ~ temp + nitrate + phosphate_star 0.7817024 4731.1188 13.180268 1982-1999 –> 2000-2012 1.5124562 11056.5732
Atlantic (28.15,28.2] cstar_tref ~ temp + nitrate + silicate + phosphate_star 0.7532490 4583.8413 11.498079 1982-1999 –> 2000-2012 1.3911484 10134.7869
Atlantic (28.15,28.2] cstar_tref ~ temp + silicate + phosphate + phosphate_star 0.8420657 5032.5883 10.652940 1982-1999 –> 2000-2012 1.6154852 11684.2836
Atlantic (28.15,28.2] cstar_tref ~ sal + nitrate + phosphate_star 1.0915705 3258.1348 15.717184 2000-2012 –> 2013-2019 2.0710925 8897.4809
Atlantic (28.15,28.2] cstar_tref ~ sal + nitrate + silicate + phosphate_star 0.9695336 3004.5246 8.802601 2000-2012 –> 2013-2019 1.8933856 8410.2983
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.8948567 2831.7178 11.345676 2000-2012 –> 2013-2019 1.6756771 7560.2912
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8121334 2624.5880 6.619729 2000-2012 –> 2013-2019 1.5440099 7094.5450
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.0582045 3193.2042 13.615812 2000-2012 –> 2013-2019 1.9722037 8555.8104
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.9371442 2933.2680 8.050753 2000-2012 –> 2013-2019 1.7791544 7967.5909
Atlantic (28.15,28.2] cstar_tref ~ temp + nitrate + phosphate_star 0.9051006 2854.2585 11.656522 2000-2012 –> 2013-2019 1.6868030 7585.3772
Atlantic (28.15,28.2] cstar_tref ~ temp + nitrate + silicate + phosphate_star 0.8926946 2826.5024 10.659037 2000-2012 –> 2013-2019 1.6459436 7410.3436
Atlantic (28.15,28.2] cstar_tref ~ temp + phosphate + phosphate_star 1.0947516 3264.4087 12.761753 2000-2012 –> 2013-2019 2.0972762 8997.2067
Atlantic (28.15,28.2] cstar_tref ~ temp + silicate + phosphate + phosphate_star 0.9549110 2971.7598 9.977485 2000-2012 –> 2013-2019 1.7969767 8004.3482
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + phosphate_star 0.7398276 9453.7232 13.150206 1982-1999 –> 2000-2012 1.6907735 25706.7481
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 0.5622126 7135.8848 5.894035 1982-1999 –> 2000-2012 1.1169813 16995.1738
Atlantic (28.2, Inf] cstar_tref ~ sal + silicate + phosphate + phosphate_star 0.7042722 9039.5425 6.382879 1982-1999 –> 2000-2012 1.3522082 20741.2271
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.7103820 9112.5322 9.768706 1982-1999 –> 2000-2012 1.4626824 22586.6302
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.5229331 6525.8802 2.014189 1982-1999 –> 2000-2012 0.9707675 13845.9018
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.9039397 11148.6425 12.848198 1982-1999 –> 2000-2012 1.8283510 27067.8022
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.6846615 8802.9111 2.946372 1982-1999 –> 2000-2012 1.2609807 19116.4945
Atlantic (28.2, Inf] cstar_tref ~ temp + nitrate + phosphate_star 0.8427511 10554.3745 5.466214 1982-1999 –> 2000-2012 1.5955855 24034.8920
Atlantic (28.2, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 0.8248184 10374.6275 8.259432 1982-1999 –> 2000-2012 1.5317220 23110.0439
Atlantic (28.2, Inf] cstar_tref ~ temp + silicate + phosphate + phosphate_star 0.9118653 11222.4079 8.851589 1982-1999 –> 2000-2012 1.6940813 25159.3007
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + phosphate_star 0.8650243 6117.2722 12.857130 2000-2012 –> 2013-2019 1.6048518 15570.9954
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 0.5986382 4354.6000 4.314619 2000-2012 –> 2013-2019 1.1608508 11490.4847
Atlantic (28.2, Inf] cstar_tref ~ sal + silicate + phosphate + phosphate_star 0.7825632 5638.9955 4.752826 2000-2012 –> 2013-2019 1.4868354 14678.5380
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.8377518 5965.6932 10.184414 2000-2012 –> 2013-2019 1.5481338 15078.2254
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.5828792 4228.7081 2.387587 2000-2012 –> 2013-2019 1.1058122 10754.5883
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.0970635 7258.4935 13.949039 2000-2012 –> 2013-2019 2.0010032 18407.1360
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.7777060 5611.1473 3.110185 2000-2012 –> 2013-2019 1.4623675 14414.0584
Atlantic (28.2, Inf] cstar_tref ~ temp + nitrate + phosphate_star 1.0789365 7176.6193 5.655216 2000-2012 –> 2013-2019 1.9216876 17730.9937
Atlantic (28.2, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1.0397993 7001.4900 10.093673 2000-2012 –> 2013-2019 1.8646176 17376.1175
Atlantic (28.2, Inf] cstar_tref ~ temp + silicate + phosphate + phosphate_star 1.1371137 7430.3880 10.396041 2000-2012 –> 2013-2019 2.0489790 18652.7959
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 6.4566916 36911.6486 32.494484 1982-1999 –> 2000-2012 13.3359797 88374.0121
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 7.9447879 39241.9842 36.536151 1982-1999 –> 2000-2012 16.1735886 93457.5006
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.4521690 36905.7755 32.726328 1982-1999 –> 2000-2012 13.3217883 88348.5214
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 6.5004682 36987.5719 30.432796 1982-1999 –> 2000-2012 13.2889149 88245.6217
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate_star 6.5020932 36988.3804 30.694955 1982-1999 –> 2000-2012 13.3815421 88449.1031
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.4520118 36905.5018 29.937685 1982-1999 –> 2000-2012 13.1783795 88024.3492
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 6.4908437 36970.9237 31.083318 1982-1999 –> 2000-2012 13.3640974 88419.7990
Indo-Pacific (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate_star 7.7806284 39007.3879 29.995151 1982-1999 –> 2000-2012 16.0906764 93373.9161
Indo-Pacific (-Inf,26] cstar_tref ~ temp + phosphate + phosphate_star 7.8078537 39044.6353 32.330438 1982-1999 –> 2000-2012 15.9938566 93178.0040
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 7.4261688 38483.4867 28.396384 1982-1999 –> 2000-2012 15.1909526 91806.9026
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 5.9978940 19055.7781 27.345614 2000-2012 –> 2013-2019 12.4545857 55967.4267
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 7.5257367 20401.8692 29.624509 2000-2012 –> 2013-2019 15.4705245 59643.8535
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.9955754 19055.4845 27.200018 2000-2012 –> 2013-2019 12.4477444 55961.2600
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 6.1930562 19245.7224 25.777825 2000-2012 –> 2013-2019 12.6935244 56233.2943
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate_star 6.2839535 19330.1554 24.325749 2000-2012 –> 2013-2019 12.7860467 56318.5358
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.1120038 19169.5741 24.949991 2000-2012 –> 2013-2019 12.5640157 56075.0760
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 6.1129613 19168.5034 25.112435 2000-2012 –> 2013-2019 12.6038050 56139.4271
Indo-Pacific (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate_star 7.4069617 20307.5008 26.295197 2000-2012 –> 2013-2019 15.1875901 59314.8887
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 7.1702245 20114.8095 24.195783 2000-2012 –> 2013-2019 14.5963933 58598.2961
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate_star 7.4245925 20319.6039 27.220325 2000-2012 –> 2013-2019 15.2834028 59437.3308
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 5.0574576 36331.5595 44.678439 1982-1999 –> 2000-2012 10.1805234 87280.7713
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.9348402 36040.3125 37.710730 1982-1999 –> 2000-2012 10.0275321 86892.3010
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 5.1401100 36525.2436 40.707207 1982-1999 –> 2000-2012 9.9893962 86558.0343
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + phosphate_star 5.1406159 36524.4193 40.866191 1982-1999 –> 2000-2012 10.2857026 87543.2004
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7055211 35471.7817 39.423783 1982-1999 –> 2000-2012 9.1078292 83892.9940
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 4.9352282 36039.2517 37.912905 1982-1999 –> 2000-2012 10.0798477 87058.5174
Indo-Pacific (26,26.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 5.3378298 36976.2171 45.312009 1982-1999 –> 2000-2012 10.8878816 89261.2133
Indo-Pacific (26,26.5] cstar_tref ~ temp + phosphate + phosphate_star 5.5694650 37481.7660 53.223437 1982-1999 –> 2000-2012 10.8635408 88976.8690
Indo-Pacific (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 5.0021764 36200.2413 50.654439 1982-1999 –> 2000-2012 9.7072225 85729.1828
Indo-Pacific (26,26.5] cstar_tref ~ temp + silicate + phosphate_star 5.3525355 37007.0884 44.448120 1982-1999 –> 2000-2012 11.0212909 89643.1995
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.9835684 19148.6859 43.364005 2000-2012 –> 2013-2019 10.0410260 55480.2455
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.7937328 18905.0044 37.001566 2000-2012 –> 2013-2019 9.7285730 54945.3169
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 5.2207786 19442.8472 38.490821 2000-2012 –> 2013-2019 10.3608886 55968.0908
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + phosphate_star 5.3410378 19584.9120 42.375550 2000-2012 –> 2013-2019 10.4816537 56109.3313
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7403369 18834.1457 36.682469 2000-2012 –> 2013-2019 9.4458580 54305.9273
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 4.8209449 18938.8131 35.204419 2000-2012 –> 2013-2019 9.7561731 54978.0648
Indo-Pacific (26,26.5] cstar_tref ~ temp + nitrate + phosphate_star 5.3811809 19632.2802 39.505130 2000-2012 –> 2013-2019 10.9048719 57015.4430
Indo-Pacific (26,26.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 5.1100800 19307.2716 32.285755 2000-2012 –> 2013-2019 10.4479098 56283.4886
Indo-Pacific (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.9535006 19110.4031 34.415843 2000-2012 –> 2013-2019 9.9556770 55310.6444
Indo-Pacific (26,26.5] cstar_tref ~ temp + silicate + phosphate_star 5.1135724 19309.5935 31.704587 2000-2012 –> 2013-2019 10.4661078 56316.6819
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.3558684 28818.3495 29.623845 1982-1999 –> 2000-2012 8.4247316 67964.3918
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.2059512 28471.3051 25.457852 1982-1999 –> 2000-2012 8.2380439 67493.4699
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.5815752 29321.8207 24.757970 1982-1999 –> 2000-2012 8.7939772 68948.5883
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.3227555 28744.2995 22.662236 1982-1999 –> 2000-2012 8.3705239 67820.2670
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 4.3733096 28858.1744 24.620781 1982-1999 –> 2000-2012 8.4382350 67990.7907
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + phosphate_star 4.5023515 29145.9833 33.667012 1982-1999 –> 2000-2012 8.7921077 69023.0685
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.3514595 28808.2570 30.277835 1982-1999 –> 2000-2012 8.6003177 68554.5116
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + phosphate + phosphate_star 4.7386236 29655.7131 32.269037 1982-1999 –> 2000-2012 9.1855765 70031.8253
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.4743412 29085.7885 29.769847 1982-1999 –> 2000-2012 8.7401403 68887.2191
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + silicate + phosphate_star 4.5272679 29200.9839 31.908671 1982-1999 –> 2000-2012 8.8116937 69060.8290
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.7394847 16070.3318 38.779535 2000-2012 –> 2013-2019 9.0953531 44888.6813
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.5305607 15828.9753 33.448696 2000-2012 –> 2013-2019 8.7365118 44300.2804
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.9493395 16304.2041 28.099633 2000-2012 –> 2013-2019 9.5309148 45626.0247
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.6524894 15972.3285 26.300399 2000-2012 –> 2013-2019 8.9752449 44716.6280
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 4.8325633 16175.3154 30.682274 2000-2012 –> 2013-2019 9.2058729 45033.4898
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + phosphate_star 4.8767412 16222.4382 40.323775 2000-2012 –> 2013-2019 9.3790927 45368.4214
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.6594536 15978.4026 35.975237 2000-2012 –> 2013-2019 9.0109131 44786.6597
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + phosphate + phosphate_star 5.1133077 16478.1376 36.756350 2000-2012 –> 2013-2019 9.8519313 46133.8507
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.7938206 16131.8652 33.974265 2000-2012 –> 2013-2019 9.2681618 45217.6537
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + silicate + phosphate_star 4.9660989 16320.4518 38.245575 2000-2012 –> 2013-2019 9.4933668 45521.4357
Indo-Pacific (26.75,27] cstar_tref ~ sal + silicate + phosphate + phosphate_star 5.6324347 38631.5836 28.024978 1982-1999 –> 2000-2012 10.9345286 91709.8073
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + phosphate_star 5.7537222 38892.9982 34.979030 1982-1999 –> 2000-2012 10.2193717 89019.9201
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.6079327 38580.0908 34.029827 1982-1999 –> 2000-2012 10.0492617 88615.1373
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.8270931 36738.3550 21.354008 1982-1999 –> 2000-2012 9.0452926 85885.3385
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7909596 36648.1617 19.879630 1982-1999 –> 2000-2012 8.9806257 85680.4708
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate_star 6.0315739 39471.6639 35.188322 1982-1999 –> 2000-2012 10.7026990 90371.8827
Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + phosphate_star 6.0839183 39575.6884 31.918135 1982-1999 –> 2000-2012 10.9205466 91072.4266
Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 5.9215112 39245.6959 31.011715 1982-1999 –> 2000-2012 10.7271928 90634.0919
Indo-Pacific (26.75,27] cstar_tref ~ temp + phosphate + phosphate_star 5.0220127 37222.0796 23.121518 1982-1999 –> 2000-2012 9.5429235 87558.4176
Indo-Pacific (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.9780973 37116.3116 22.786640 1982-1999 –> 2000-2012 9.4626255 87315.7514
Indo-Pacific (26.75,27] cstar_tref ~ sal + phosphate + phosphate_star 6.0902654 21157.2315 22.636223 2000-2012 –> 2013-2019 11.8513857 60063.9964
Indo-Pacific (26.75,27] cstar_tref ~ sal + silicate + phosphate + phosphate_star 5.9800226 21039.4711 23.659498 2000-2012 –> 2013-2019 11.6124573 59671.0547
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + phosphate 5.9556761 21010.7251 30.994780 2000-2012 –> 2013-2019 11.7198085 59923.9034
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + phosphate + phosphate_star 5.1943369 20116.0232 22.193470 2000-2012 –> 2013-2019 10.0214300 56854.3782
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate 5.9063235 20958.1715 33.378839 2000-2012 –> 2013-2019 11.6240650 59774.1988
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.1689570 20085.9117 20.758325 2000-2012 –> 2013-2019 9.9599166 56734.0734
Indo-Pacific (26.75,27] cstar_tref ~ temp + phosphate 6.0282121 21088.0903 30.439397 2000-2012 –> 2013-2019 11.8536692 60129.1198
Indo-Pacific (26.75,27] cstar_tref ~ temp + phosphate + phosphate_star 5.3788177 20342.8251 19.535742 2000-2012 –> 2013-2019 10.4008304 57564.9047
Indo-Pacific (26.75,27] cstar_tref ~ temp + silicate + phosphate 5.9754651 21032.4727 32.933145 2000-2012 –> 2013-2019 11.7500727 59967.9291
Indo-Pacific (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 5.3476448 20306.7194 17.971375 2000-2012 –> 2013-2019 10.3257421 57423.0309
Indo-Pacific (27,27.25] cstar_tref ~ sal + silicate + phosphate + phosphate_star 5.0394866 47219.5022 19.219188 1982-1999 –> 2000-2012 9.4868387 109596.2442
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.7949096 46445.9991 74.545242 1982-1999 –> 2000-2012 8.7811626 106477.9496
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.6445272 45952.5578 75.011259 1982-1999 –> 2000-2012 8.2923633 104086.0006
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + phosphate + phosphate_star 5.1381732 47521.0307 58.017971 1982-1999 –> 2000-2012 9.4450617 109210.2732
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.6875333 46095.8627 39.776509 1982-1999 –> 2000-2012 8.6326854 105907.7910
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate_star 6.0112963 49961.1775 76.391973 1982-1999 –> 2000-2012 10.6325971 113159.8249
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + phosphate_star 4.8353636 46574.6252 73.954993 1982-1999 –> 2000-2012 8.8649515 106836.1994
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.6885919 46097.3735 74.666491 1982-1999 –> 2000-2012 8.3845011 104509.2823
Indo-Pacific (27,27.25] cstar_tref ~ temp + phosphate + phosphate_star 5.1583935 47580.0968 56.486933 1982-1999 –> 2000-2012 9.5102084 109489.6410
Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.6885848 46097.3497 39.304596 1982-1999 –> 2000-2012 8.6479291 105984.2034
Indo-Pacific (27,27.25] cstar_tref ~ sal + silicate + phosphate + phosphate_star 5.6078593 26181.5139 19.526433 2000-2012 –> 2013-2019 10.6473459 73401.0161
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + phosphate_star 6.4087108 27292.9438 72.736018 2000-2012 –> 2013-2019 11.2036204 73738.9429
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.3540594 27223.6379 72.729427 2000-2012 –> 2013-2019 10.9985866 73176.1957
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + phosphate + phosphate_star 6.1217767 26911.5650 51.751919 2000-2012 –> 2013-2019 11.2599499 74432.5958
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.3928334 25857.9827 33.129925 2000-2012 –> 2013-2019 10.0803668 71953.8454
Indo-Pacific (27,27.25] cstar_tref ~ silicate + phosphate + phosphate_star 6.1099917 26893.5212 25.654698 2000-2012 –> 2013-2019 11.7960333 75987.8244
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + phosphate_star 6.4675542 27367.0425 70.937775 2000-2012 –> 2013-2019 11.3029178 73941.6677
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 6.4142098 27300.0848 70.919059 2000-2012 –> 2013-2019 11.1028017 73397.4584
Indo-Pacific (27,27.25] cstar_tref ~ temp + phosphate + phosphate_star 6.1404106 26934.8698 50.336526 2000-2012 –> 2013-2019 11.2988041 74514.9666
Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 5.3936438 25857.2339 32.776574 2000-2012 –> 2013-2019 10.0822286 71954.5835
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + nitrate + silicate + phosphate_star 4.3863331 42610.0471 37.537275 1982-1999 –> 2000-2012 7.9109458 95467.6198
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.6841067 40045.0553 31.160905 1982-1999 –> 2000-2012 6.6782498 89684.7454
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.3469879 42477.5757 51.492832 1982-1999 –> 2000-2012 8.0591404 96357.8749
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.1089389 41651.5834 53.387405 1982-1999 –> 2000-2012 7.5136674 93828.4621
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate 3.5938483 39680.3794 35.540744 1982-1999 –> 2000-2012 6.8910642 91222.2502
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.5492843 39498.9338 33.569547 1982-1999 –> 2000-2012 6.5016885 88863.6767
Indo-Pacific (27.25,27.5] cstar_tref ~ silicate + phosphate + phosphate_star 3.9351604 41012.2634 35.607565 1982-1999 –> 2000-2012 7.2095092 92414.8384
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.2421808 42118.7633 55.530735 1982-1999 –> 2000-2012 7.7752377 95023.5440
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate 4.0418997 41405.7355 38.573314 1982-1999 –> 2000-2012 7.7414847 95217.1318
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3.9327845 41005.3840 35.069241 1982-1999 –> 2000-2012 7.1514683 92071.6936
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate 4.9150615 23551.8962 35.387418 2000-2012 –> 2013-2019 9.3787949 66417.1093
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.2938391 22497.5043 29.598350 2000-2012 –> 2013-2019 7.9779458 62542.5596
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 5.0049184 23695.5336 64.468819 2000-2012 –> 2013-2019 9.3519062 66173.1093
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.8497861 23451.3722 66.556121 2000-2012 –> 2013-2019 8.9587250 65102.9556
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate 4.1120690 22159.3373 34.196766 2000-2012 –> 2013-2019 7.7059173 61839.7167
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.1066786 22151.0822 33.387214 2000-2012 –> 2013-2019 7.6559629 61650.0160
Indo-Pacific (27.25,27.5] cstar_tref ~ silicate + phosphate + phosphate_star 4.5758155 22992.7581 34.303587 2000-2012 –> 2013-2019 8.5109759 64005.0215
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.9779639 23653.3152 68.668246 2000-2012 –> 2013-2019 9.2201447 65772.0785
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate 4.6309905 23086.4634 36.813025 2000-2012 –> 2013-2019 8.6728902 64492.1989
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.5749090 22993.2091 33.918111 2000-2012 –> 2013-2019 8.5076935 63998.5931
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3.2954563 40719.7999 30.456038 1982-1999 –> 2000-2012 5.6083801 89208.3020
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.3685543 41061.7850 26.570147 1982-1999 –> 2000-2012 5.6872759 89604.0491
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate_star 3.6246811 42202.1153 31.661725 1982-1999 –> 2000-2012 6.0838920 92005.5761
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.4358441 41370.0996 22.880176 1982-1999 –> 2000-2012 6.0176859 92220.5394
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate 3.3028597 40754.7798 20.873590 1982-1999 –> 2000-2012 5.8809155 91573.7066
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.2472499 40492.0922 24.685745 1982-1999 –> 2000-2012 5.5601714 88982.5727
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.4160317 41279.9530 20.132542 1982-1999 –> 2000-2012 5.9971179 92124.1076
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.0631121 39580.1107 12.814094 1982-1999 –> 2000-2012 5.3715286 88026.7251
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.0476098 39503.0203 9.397780 1982-1999 –> 2000-2012 5.3021483 87444.4940
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 3.5349231 41813.2497 23.431683 1982-1999 –> 2000-2012 5.9914287 91595.0752
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 4.0348535 23249.2565 35.011617 2000-2012 –> 2013-2019 7.3303098 63969.0564
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.1229178 23427.5561 30.585387 2000-2012 –> 2013-2019 7.4914721 64489.3411
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate 4.0994214 23378.3594 23.627616 2000-2012 –> 2013-2019 7.5652930 64882.0982
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.0965337 23374.5402 25.506334 2000-2012 –> 2013-2019 7.5323777 64744.6397
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate 3.9605093 23095.6795 23.241015 2000-2012 –> 2013-2019 7.2633690 63850.4592
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.9481443 23071.8571 26.890775 2000-2012 –> 2013-2019 7.1953942 63563.9492
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + phosphate 4.0122714 23200.9088 21.973611 2000-2012 –> 2013-2019 7.4402502 64533.2835
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.0037155 23185.2803 18.625094 2000-2012 –> 2013-2019 7.4197471 64465.2332
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.6764968 22481.1829 17.935126 2000-2012 –> 2013-2019 6.7396089 62061.2936
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.5747323 22251.3804 10.907617 2000-2012 –> 2013-2019 6.6223421 61754.4007
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.6510327 15739.8427 24.146895 1982-1999 –> 2000-2012 4.8134036 35274.7846
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.6594156 15760.5852 22.987839 1982-1999 –> 2000-2012 4.8228648 35299.9709
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate 2.6702885 15787.3916 28.291824 1982-1999 –> 2000-2012 4.8221484 35278.8979
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.6467606 15731.2467 24.736227 1982-1999 –> 2000-2012 4.7461667 35004.7731
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate 2.6785181 15807.6085 27.539897 1982-1999 –> 2000-2012 4.8319452 35305.6047
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.6561934 15754.6200 23.637730 1982-1999 –> 2000-2012 4.7537252 35020.1848
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 2.6677616 15781.1714 25.028220 1982-1999 –> 2000-2012 4.7671809 35052.7536
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.6593135 15760.3330 23.663705 1982-1999 –> 2000-2012 4.7609594 35041.3641
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.6742233 15797.0656 22.252997 1982-1999 –> 2000-2012 4.7746561 35072.9500
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + silicate + phosphate_star 2.6880054 15828.8383 23.690269 1982-1999 –> 2000-2012 4.7896734 35107.9634
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3.0828431 9331.0238 29.216505 2000-2012 –> 2013-2019 5.7338757 25070.8666
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.1047580 9356.9638 28.278040 2000-2012 –> 2013-2019 5.7641736 25117.5490
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + silicate + phosphate_star 3.1137279 9365.5283 29.491419 2000-2012 –> 2013-2019 5.7881837 25161.1651
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.1177496 9372.2551 29.043142 2000-2012 –> 2013-2019 5.8222334 25243.2468
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate 3.1366102 9394.3413 35.206965 2000-2012 –> 2013-2019 5.8068987 25181.7330
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.0827974 9332.9695 29.138730 2000-2012 –> 2013-2019 5.7295579 25064.2162
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.1163780 9370.6437 29.441495 2000-2012 –> 2013-2019 5.8167146 25231.5531
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.1047122 9358.9097 28.180344 2000-2012 –> 2013-2019 5.7609056 25113.5296
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 3.1135288 9367.2941 29.650786 2000-2012 –> 2013-2019 5.7812904 25148.4656
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.1412078 9399.7051 26.707078 2000-2012 –> 2013-2019 5.8005213 25160.0380
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + phosphate_star 2.7586348 19710.1611 34.012716 1982-1999 –> 2000-2012 4.8770280 43900.1434
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.7582987 19711.1748 33.775588 1982-1999 –> 2000-2012 4.8681472 43858.1163
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.7883318 19796.8281 35.822574 1982-1999 –> 2000-2012 4.9304076 44110.7040
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.7818432 19779.9711 35.788093 1982-1999 –> 2000-2012 4.9032809 43987.9579
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 2.7876272 19794.7827 35.479611 1982-1999 –> 2000-2012 4.9369283 44146.1837
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 2.7606894 19714.1870 33.644807 1982-1999 –> 2000-2012 4.8793078 43903.3543
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.7599939 19714.1477 33.348940 1982-1999 –> 2000-2012 4.8710511 43865.4716
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + phosphate + phosphate_star 2.7892718 19797.5562 35.546323 1982-1999 –> 2000-2012 4.9313547 44109.4690
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.7841513 19784.6838 35.371389 1982-1999 –> 2000-2012 4.9069213 43997.6673
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + silicate + phosphate_star 2.7912149 19803.1930 34.917282 1982-1999 –> 2000-2012 4.9442507 44171.9419
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate 3.1019057 10938.2921 39.850258 2000-2012 –> 2013-2019 5.8609553 30647.6701
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + phosphate_star 3.0936018 10928.8082 38.482684 2000-2012 –> 2013-2019 5.8522366 30638.9693
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate 3.0891329 10922.6153 38.170291 2000-2012 –> 2013-2019 5.8479314 30633.2568
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.0826259 10915.5819 37.073345 2000-2012 –> 2013-2019 5.8409245 30626.7566
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.0995226 10936.9996 39.588543 2000-2012 –> 2013-2019 5.8878544 30733.8277
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate 3.1040234 10943.2158 41.295870 2000-2012 –> 2013-2019 5.8858859 30721.2429
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.0952649 10933.1108 39.663019 2000-2012 –> 2013-2019 5.8771082 30713.0819
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 3.1214466 10965.1950 36.992838 2000-2012 –> 2013-2019 5.8821359 30679.3820
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate 3.1116928 10951.7877 36.563283 2000-2012 –> 2013-2019 5.8722516 30665.5916
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3.1049348 10944.4735 35.452205 2000-2012 –> 2013-2019 5.8649287 30658.6212
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate 2.2436028 17828.1719 8.852520 1982-1999 –> 2000-2012 4.2347576 41525.9800
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.2419974 17824.4454 8.822692 1982-1999 –> 2000-2012 4.2017336 41345.5145
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate 2.2670056 17909.1871 8.527904 1982-1999 –> 2000-2012 4.2831797 41745.3231
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate 2.2613688 17891.2706 8.718979 1982-1999 –> 2000-2012 4.2547756 41601.7815
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.2584202 17882.8325 8.669948 1982-1999 –> 2000-2012 4.2270436 41454.7490
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate_star 2.2644434 17902.1400 8.476091 1982-1999 –> 2000-2012 4.2518453 41578.7467
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + nitrate + silicate 2.3179901 18087.1121 8.514118 1982-1999 –> 2000-2012 4.3482065 42001.2475
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.3167477 18084.8230 8.486770 1982-1999 –> 2000-2012 4.3124717 41808.3899
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.3235661 18108.3331 8.376556 1982-1999 –> 2000-2012 4.3211223 41842.2126
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + silicate + phosphate_star 2.3278426 18121.0436 8.104514 1982-1999 –> 2000-2012 4.3418446 41945.0660
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.5451771 10417.5797 9.467334 2000-2012 –> 2013-2019 4.8712589 28534.5697
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate 2.4800741 10302.9977 8.895172 2000-2012 –> 2013-2019 4.7236769 28131.1695
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.4526233 10255.7797 8.813300 2000-2012 –> 2013-2019 4.6946206 28080.2251
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + phosphate 2.5436228 10412.8783 9.085960 2000-2012 –> 2013-2019 4.8662386 28515.9391
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.4986199 10335.9419 9.196589 2000-2012 –> 2013-2019 4.8157896 28422.2221
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate 2.5057678 10346.5741 8.977222 2000-2012 –> 2013-2019 4.7727734 28255.7612
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate 2.5033719 10344.3440 8.939868 2000-2012 –> 2013-2019 4.7647407 28235.6146
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.4690447 10285.2882 9.057342 2000-2012 –> 2013-2019 4.7274648 28168.1207
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate_star 2.4710154 10286.8163 9.091710 2000-2012 –> 2013-2019 4.7354587 28188.9563
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.5463405 10419.6004 9.433968 2000-2012 –> 2013-2019 4.8630882 28504.4235
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate 1.9305303 10730.0972 8.904916 1982-1999 –> 2000-2012 3.6488255 25493.0981
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1.9270503 10722.7836 8.984059 1982-1999 –> 2000-2012 3.5873970 25229.5958
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate 1.9298811 10728.3610 8.794546 1982-1999 –> 2000-2012 3.6092888 25319.0807
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.9179397 10698.3211 8.633406 1982-1999 –> 2000-2012 3.5605064 25124.1057
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate_star 1.9759679 10850.1840 9.235029 1982-1999 –> 2000-2012 3.6602117 25462.5448
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate 1.9080141 10671.5377 8.771278 1982-1999 –> 2000-2012 3.6231246 25422.5771
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.9072203 10671.3898 8.712059 1982-1999 –> 2000-2012 3.5597902 25144.8684
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 1.8952781 10636.9658 8.797017 1982-1999 –> 2000-2012 3.5744229 25228.5072
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.8951582 10638.6392 8.762353 1982-1999 –> 2000-2012 3.5277325 25020.5004
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 1.9571597 10802.8141 9.092021 1982-1999 –> 2000-2012 3.6343973 25385.8026
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate 2.1766290 6455.1644 8.977398 2000-2012 –> 2013-2019 4.1071594 17185.2617
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.0718737 6312.4479 8.608198 2000-2012 –> 2013-2019 3.9989240 17035.2315
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.0728445 6313.8223 8.661407 2000-2012 –> 2013-2019 3.9907842 17012.1434
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate_star 2.1325340 6395.1160 8.995016 2000-2012 –> 2013-2019 4.1085019 17245.3000
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate 2.1112028 6367.6201 9.021283 2000-2012 –> 2013-2019 4.0192169 17039.1578
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.0624051 6301.0085 8.735205 2000-2012 –> 2013-2019 3.9696254 16972.3983
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate 2.1759220 6454.2112 9.682023 2000-2012 –> 2013-2019 4.1334731 17256.0578
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 2.1263116 6388.5425 9.434007 2000-2012 –> 2013-2019 4.0215897 17025.5083
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.0613801 6299.5499 8.800503 2000-2012 –> 2013-2019 3.9565382 16938.1891
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 2.1229628 6383.9180 9.128128 2000-2012 –> 2013-2019 4.0801225 17186.7321
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1.7945525 79827.1553 8.869720 1982-1999 –> 2000-2012 3.4573054 186401.9740
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.7262480 78281.3797 9.253351 1982-1999 –> 2000-2012 3.3100058 182165.0975
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + silicate + phosphate_star 1.8530483 81102.8845 7.845127 1982-1999 –> 2000-2012 3.5807596 189794.5006
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 1.8222960 80438.2702 11.787044 1982-1999 –> 2000-2012 3.4882621 187119.8291
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5281199 73427.1334 14.378394 1982-1999 –> 2000-2012 2.8513606 167376.6806
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5314910 73514.9130 14.185270 1982-1999 –> 2000-2012 2.8636761 167836.9173
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.5317666 73520.0807 14.250129 1982-1999 –> 2000-2012 2.8640890 167845.7842
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + phosphate_star 1.8228918 80449.2936 12.036224 1982-1999 –> 2000-2012 3.5415805 188851.4249
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1.7791251 79483.2299 14.398530 1982-1999 –> 2000-2012 3.2837701 180533.8043
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + silicate + phosphate + phosphate_star 1.8881552 81852.4991 14.924924 1982-1999 –> 2000-2012 3.4986767 186662.7118
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1.9449714 44646.9235 12.859642 2000-2012 –> 2013-2019 3.7395239 124474.0788
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.8802282 43921.9031 13.117569 2000-2012 –> 2013-2019 3.6064761 122203.2828
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + silicate + phosphate_star 2.0014061 45257.4791 13.609980 2000-2012 –> 2013-2019 3.8544544 126360.3636
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 1.9870127 45104.9067 18.529833 2000-2012 –> 2013-2019 3.8093087 125543.1769
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.7344727 42195.8521 17.075855 2000-2012 –> 2013-2019 3.2625926 115622.9856
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.0537644 45812.5344 17.840504 2000-2012 –> 2013-2019 3.9510900 127858.0309
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.7322017 42167.7935 16.574226 2000-2012 –> 2013-2019 3.2636927 115682.7065
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.7349951 42200.3016 16.913655 2000-2012 –> 2013-2019 3.2667617 115720.3823
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + phosphate_star 2.0496261 45767.3380 21.123590 2000-2012 –> 2013-2019 3.8725179 126216.6316
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.0492147 45765.0389 20.958257 2000-2012 –> 2013-2019 3.8283398 125248.2688

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)
# mutate predictors column
lm_best_plot <- lm_best_target %>%
  select(basin, gamma_slab, model, eras, era) %>%
  mutate(predictors = str_remove(model, paste(params_local$MLR_target, "~ ")),
         predictors = str_replace_all(predictors, "\\+ ", ""))

# 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)
      
      lm_best_basin_era_slab <- lm_best_plot %>%
        filter(basin == i_basin, era == i_era, gamma_slab == i_gamma_slab)
      
      for (i_predictors in unique(lm_best_basin_era_slab$predictors)) {
        #i_predictors <- unique(lm_best_basin_era_slab$predictors)[1]
        print(i_predictors)
        # 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(lm_best_plot, lm_best_basin_era_slab, i_rmse,
   GLODAP_basin_era, GLODAP_basin_era_slab,
   i_lm, lm_all_fitted, 
   i_basin, i_era, i_gamma_slab, i_predictors,
   lm_all,
   i_aic, i_n_predictors, i_resid_max)

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")

Version Author Date
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
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")

Version Author Date
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
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)

Version Author Date
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
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)

Version Author Date
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
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")
  )
nitrate phosphate phosphate_star sal silicate temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26] 6 4 5 10 6 8
(26,26.5] 4 3 7 7 9 10
(26.5,26.75] 4 6 10 7 6 7
(26.75,27] 5 5 10 8 6 6
(27,27.25] 4 4 10 8 8 7
(27.25,27.5] 3 4 10 7 7 9
(27.5,27.75] 3 4 10 7 7 9
(27.75,27.85] 4 3 10 6 6 10
(27.85,27.95] 4 4 10 6 5 10
(27.95,28.05] 4 6 10 6 5 8
(28.05,28.1] 4 6 10 6 5 8
(28.1,28.15] 5 5 10 6 6 8
(28.15,28.2] 7 3 10 6 6 7
(28.2, Inf] 6 4 10 7 6 7
total 63.00 61.00 132.00 97.00 88.00 114.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 5 4 6 10 6 9
(26,26.5] 5 3 6 8 8 10
(26.5,26.75] 3 6 10 7 7 7
(26.75,27] 3 5 10 8 8 6
(27,27.25] 5 3 10 8 8 6
(27.25,27.5] 4 4 10 8 8 7
(27.5,27.75] 4 4 10 10 6 5
(27.75,27.85] 3 4 10 9 7 7
(27.85,27.95] 4 4 10 6 5 10
(27.95,28.05] 4 6 10 6 5 8
(28.05,28.1] 4 6 10 6 5 8
(28.1,28.15] 4 6 10 6 5 8
(28.15,28.2] 6 4 10 6 5 8
(28.2, Inf] 6 4 10 7 6 7
total 60.00 63.00 132.00 105.00 89.00 106.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 4 4 9 7 6 10
(26,26.5] 3 4 10 6 6 10
(26.5,26.75] 4 4 10 5 6 10
(26.75,27] 4 5 10 6 6 9
(27,27.25] 4 5 10 6 6 9
(27.25,27.5] 4 6 8 6 9 7
(27.5,27.75] 4 4 8 10 8 7
(27.75,27.85] 4 4 8 7 10 8
(27.85,27.95] 4 4 10 5 6 10
(27.95,28.05] 4 3 6 6 10 10
(28.05,28.1] 4 4 6 10 10 5
(28.1, Inf] 5 3 10 7 8 7
total 48.00 50.00 105.00 81.00 91.00 102.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 4 3 9 7 7 10
(26,26.5] 4 3 10 6 6 10
(26.5,26.75] 4 4 10 5 6 10
(26.75,27] NA 10 6 6 5 8
(27,27.25] 4 6 10 5 6 8
(27.25,27.5] 3 7 7 6 9 7
(27.5,27.75] 5 5 6 10 6 8
(27.75,27.85] 5 3 9 9 8 7
(27.85,27.95] 7 3 6 7 6 10
(27.95,28.05] 4 4 6 9 8 9
(28.05,28.1] 4 3 6 10 10 6
(28.1, Inf] 5 3 10 8 7 7
total — 54.00 95.00 88.00 84.00 100.00

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)

Version Author Date
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
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)

Version Author Date
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
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 

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_0.7.3      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_3.3.3   
[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_2.0-0         withr_2.3.0             
[13] gridExtra_2.3            tidyselect_1.1.0         curl_4.3                
[16] compiler_4.0.3           git2r_0.27.1             cli_2.2.0               
[19] rvest_0.3.6              xml2_1.3.2               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_0.4.10             readxl_1.3.1             rstudioapi_0.13         
[37] farver_2.0.3             generics_0.1.0           jsonlite_1.7.2          
[40] zip_2.1.1                car_3.0-10               magrittr_2.0.1          
[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_0.10.1.2.2
[67] data.table_1.13.6        modelr_0.1.8             vctrs_0.3.6             
[70] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[73] reshape_0.8.8            assertthat_0.2.1         xfun_0.20               
[76] openxlsx_4.2.3           RcppEigen_0.3.3.9.1      later_1.1.0.1           
[79] viridisLite_0.3.0        ellipsis_0.3.1           here_1.0.1