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1 Required data

Required are:

  • cleaned and prepared GLODAP-based synthetic model subsetting file
GLODAP <-
  read_csv(paste(path_version_data,
                 "GLODAPv2.2020_MLR_fitting_ready.csv",
                 sep = ""))

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

  • sal, temp, aou, nitrate, 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 + aou + nitrate + phosphate_star 1.6008674 646.8667 6.790466 1982-1999 –> 2000-2012 3.2738747 1525.1022
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.0669064 510.5238 4.506279 1982-1999 –> 2000-2012 2.3985898 1286.5351
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou 1.2043383 549.2359 4.445163 1982-1999 –> 2000-2012 2.5928383 1341.9648
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 1.1914188 547.6120 4.887897 1982-1999 –> 2000-2012 2.5535458 1333.7497
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.0589440 510.0068 4.281729 1982-1999 –> 2000-2012 2.3921140 1288.5180
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 1.0709739 511.8023 4.694811 1982-1999 –> 2000-2012 2.4040133 1288.2696
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0646493 511.8122 4.234683 1982-1999 –> 2000-2012 2.3962400 1289.7923
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 1.0721408 512.1682 4.734438 1982-1999 –> 2000-2012 2.4055121 1288.7470
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 ~ temp + aou + phosphate + phosphate_star 1.4525065 614.1890 7.640069 1982-1999 –> 2000-2012 3.1079737 1487.7028
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.2474664 267.8483 3.699851 2000-2012 –> 2013-2019 2.3143729 778.3721
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou 1.3308655 275.9438 3.290423 2000-2012 –> 2013-2019 2.5352037 825.1797
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 1.3308598 277.9431 3.298957 2000-2012 –> 2013-2019 2.5222786 825.5552
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.1385676 255.5987 2.813203 2000-2012 –> 2013-2019 2.1975116 765.6055
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 1.2518691 268.3979 3.819602 2000-2012 –> 2013-2019 2.3228430 780.2002
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.2437146 269.3784 3.455189 2000-2012 –> 2013-2019 2.3083639 781.1906
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 1.2527613 268.5090 3.836054 2000-2012 –> 2013-2019 2.3249022 780.6773
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 + phosphate + phosphate_star 1.2543425 268.7058 3.866039 2000-2012 –> 2013-2019 2.3278283 781.2953
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.6305700 309.6274 5.571504 2000-2012 –> 2013-2019 3.0830765 923.8165
Atlantic (26,26.5] cstar_tref ~ aou + nitrate 5.1314812 6947.4443 14.848543 1982-1999 –> 2000-2012 10.2186362 17091.3917
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + phosphate_star 4.9765702 6879.7997 14.946791 1982-1999 –> 2000-2012 9.9603277 16957.4080
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate 4.9231441 6855.2768 13.989569 1982-1999 –> 2000-2012 9.8406880 16888.3732
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate_star 4.9229900 6857.2056 14.032761 1982-1999 –> 2000-2012 9.8355206 16888.9076
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 3.4355823 6039.8999 15.582115 1982-1999 –> 2000-2012 6.8680661 14878.4970
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.3858067 6008.7418 14.762595 1982-1999 –> 2000-2012 6.7501440 14782.6021
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate 4.6712187 6735.9346 24.240953 1982-1999 –> 2000-2012 9.5388356 16735.0697
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 ~ temp + aou + nitrate 4.4846700 6643.3390 12.328905 1982-1999 –> 2000-2012 9.0127658 16401.8498
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 4.2216419 6508.0176 10.554565 1982-1999 –> 2000-2012 8.3922815 15994.8600
Atlantic (26,26.5] cstar_tref ~ aou + nitrate 5.1351471 3784.0381 14.011825 2000-2012 –> 2013-2019 10.2666283 10731.4824
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + phosphate_star 4.9164927 3732.2560 13.437923 2000-2012 –> 2013-2019 9.8930629 10612.0557
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate 4.8482706 3714.9849 14.229714 2000-2012 –> 2013-2019 9.7714148 10570.2617
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate_star 4.8469652 3716.6521 14.127046 2000-2012 –> 2013-2019 9.7699552 10573.8577
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 3.3529894 3261.1855 10.303799 2000-2012 –> 2013-2019 6.7885717 9301.0854
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.3151019 3249.1396 9.885919 2000-2012 –> 2013-2019 6.7009086 9257.8815
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 ~ temp + aou + nitrate 4.3535265 3581.9470 12.269478 2000-2012 –> 2013-2019 8.8381966 10225.2860
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 4.1356021 3520.4743 11.928557 2000-2012 –> 2013-2019 8.3572440 10028.4919
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + nitrate + phosphate_star 3.8581710 8651.6912 22.167333 1982-1999 –> 2000-2012 7.5404489 20157.9599
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + phosphate 4.5136026 9139.2266 13.183405 1982-1999 –> 2000-2012 8.4434732 20918.2417
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.5125633 9140.5081 12.951490 1982-1999 –> 2000-2012 8.4384142 20917.2025
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + phosphate_star 4.5784974 9183.7653 14.778635 1982-1999 –> 2000-2012 8.5948874 21054.7228
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.6383187 8470.6359 25.007220 1982-1999 –> 2000-2012 7.1163833 19738.0159
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.5119495 9140.0837 12.884756 1982-1999 –> 2000-2012 8.4394941 20918.5991
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.5081383 9139.4472 12.842841 1982-1999 –> 2000-2012 8.4234361 20906.7771
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate_star 4.5091781 9138.1667 12.865162 1982-1999 –> 2000-2012 8.4453102 20925.9034
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 ~ temp + aou + nitrate + phosphate_star 3.6758919 8500.6912 27.143927 1982-1999 –> 2000-2012 7.2077869 19830.9151
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + nitrate + phosphate_star 3.8726485 4088.1294 13.664375 2000-2012 –> 2013-2019 7.7308195 12739.8206
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.9282930 4442.4789 16.129130 2000-2012 –> 2013-2019 9.4408563 13582.9870
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate 4.1616099 4193.9156 15.650820 2000-2012 –> 2013-2019 8.8954408 13483.7763
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.6354401 3997.2130 10.381965 2000-2012 –> 2013-2019 7.2737588 12467.8489
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.9284457 4442.5244 16.114540 2000-2012 –> 2013-2019 9.4403952 13582.6082
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.9281680 4444.4416 16.116414 2000-2012 –> 2013-2019 9.4363063 13583.8888
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate_star 4.9283363 4442.4918 16.117618 2000-2012 –> 2013-2019 9.4375144 13580.6585
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 ~ temp + aou + nitrate 4.2871781 4235.6139 15.861123 2000-2012 –> 2013-2019 9.1192195 13587.5415
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.6394258 3996.8237 10.582046 2000-2012 –> 2013-2019 7.3153177 12497.5149
Atlantic (26.75,27] cstar_tref ~ sal + aou + nitrate + phosphate_star 3.7347203 14625.5052 28.460129 1982-1999 –> 2000-2012 6.9198923 32684.7740
Atlantic (26.75,27] cstar_tref ~ sal + aou + phosphate 4.1695168 15211.5845 14.663913 1982-1999 –> 2000-2012 7.5033660 33588.2934
Atlantic (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.1467394 15184.3331 24.984206 1982-1999 –> 2000-2012 7.4805816 33563.0271
Atlantic (26.75,27] cstar_tref ~ sal + aou + phosphate_star 4.1572197 15195.8121 32.153748 1982-1999 –> 2000-2012 7.5564443 33708.4984
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.6953595 14570.9275 22.462355 1982-1999 –> 2000-2012 6.7423252 32321.5870
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 4.0989955 15122.4938 22.072268 1982-1999 –> 2000-2012 7.4297426 33494.6841
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.0012559 14995.6201 17.950724 1982-1999 –> 2000-2012 7.1910740 33067.0948
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate_star 4.1563847 15196.7395 32.972535 1982-1999 –> 2000-2012 7.5186737 33634.9263
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 ~ temp + aou + nitrate + phosphate_star 3.8728810 14819.4847 25.358928 1982-1999 –> 2000-2012 7.0423664 32844.1841
Atlantic (26.75,27] cstar_tref ~ sal + aou + nitrate + phosphate_star 4.2006852 8072.2218 23.344251 2000-2012 –> 2013-2019 7.9354055 22697.7270
Atlantic (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.8162976 8458.4260 13.458339 2000-2012 –> 2013-2019 8.9630370 23642.7590
Atlantic (26.75,27] cstar_tref ~ sal + aou + phosphate_star 4.8256128 8461.8826 13.525401 2000-2012 –> 2013-2019 8.9828325 23657.6947
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 + temp + aou + nitrate + phosphate_star 4.1931422 8069.1463 24.255984 2000-2012 –> 2013-2019 7.8885018 22640.0738
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 4.7571171 8423.5110 12.957027 2000-2012 –> 2013-2019 8.8561126 23546.0047
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.4959581 8266.0593 14.771202 2000-2012 –> 2013-2019 8.4972140 23261.6794
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate_star 4.7891497 8442.4630 13.376941 2000-2012 –> 2013-2019 8.9455345 23639.2024
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 ~ temp + aou + nitrate + phosphate_star 4.3344610 8160.7531 30.368032 2000-2012 –> 2013-2019 8.2073420 22980.2378
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.9132787 11532.4479 13.636805 1982-1999 –> 2000-2012 5.6820035 26470.6284
Atlantic (27,27.25] cstar_tref ~ sal + aou + phosphate 3.1542666 11898.4258 12.378649 1982-1999 –> 2000-2012 5.6562493 26214.2247
Atlantic (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.1184894 11847.6100 12.349352 1982-1999 –> 2000-2012 5.6120278 26144.7053
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.7675932 11296.9238 15.178784 1982-1999 –> 2000-2012 5.0411312 25030.3725
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 3.1037168 11825.6250 12.327428 1982-1999 –> 2000-2012 5.5990723 26127.1815
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.0864272 11801.7611 14.801070 1982-1999 –> 2000-2012 5.5794808 26099.6654
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate_star 3.1409425 11880.8266 12.335352 1982-1999 –> 2000-2012 5.6801885 26289.1606
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 + phosphate + phosphate_star 3.1403559 11879.9617 12.324688 1982-1999 –> 2000-2012 5.6836626 26298.0816
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate_star 2.9737250 11627.5305 17.412698 1982-1999 –> 2000-2012 5.4731130 25938.9753
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + phosphate_star 3.1961019 6655.1605 16.487850 2000-2012 –> 2013-2019 6.1093806 18187.6084
Atlantic (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.6003514 6961.7227 14.040691 2000-2012 –> 2013-2019 6.7188408 18809.3327
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 + temp + aou + nitrate 3.3904785 6807.1273 35.453401 2000-2012 –> 2013-2019 6.4363421 18545.6348
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.1837119 6647.1628 17.518601 2000-2012 –> 2013-2019 5.9513051 17944.0866
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 3.5625214 6934.5338 14.345929 2000-2012 –> 2013-2019 6.6662382 18760.1589
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.4976981 6889.2662 14.539662 2000-2012 –> 2013-2019 6.5841253 18691.0273
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 ~ temp + aou + nitrate 3.5018813 6888.3429 34.806829 2000-2012 –> 2013-2019 6.5568626 18638.6895
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.4965569 6886.4263 32.622774 2000-2012 –> 2013-2019 6.4702819 18513.9568
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.2222258 12941.5204 19.954756 1982-1999 –> 2000-2012 5.8391044 30039.0078
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate 3.1549165 12836.0954 17.500848 1982-1999 –> 2000-2012 5.7285284 29813.9451
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.0728018 12706.3924 13.387049 1982-1999 –> 2000-2012 5.5397331 29382.4439
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 3.2597086 12999.2782 20.754816 1982-1999 –> 2000-2012 5.9610120 30324.6193
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.1547217 12837.7871 24.173728 1982-1999 –> 2000-2012 5.6945595 29722.8412
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate_star 3.3798005 13179.9556 21.743287 1982-1999 –> 2000-2012 6.2193540 30863.4680
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 + phosphate + phosphate_star 3.3708296 13166.6825 21.640713 1982-1999 –> 2000-2012 6.2117380 30853.6182
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate 3.2618547 13000.5650 17.438143 1982-1999 –> 2000-2012 5.8397748 29988.4174
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.2618518 13002.5606 17.418942 1982-1999 –> 2000-2012 5.7950108 29866.7198
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate_star 3.9617160 7632.8487 16.691319 2000-2012 –> 2013-2019 7.4851875 21020.7046
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + phosphate 4.1774829 7775.4129 24.694295 2000-2012 –> 2013-2019 7.4919314 20855.8584
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.1023489 7727.9382 22.640986 2000-2012 –> 2013-2019 7.3245748 20669.4587
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate 3.7245537 7464.5721 17.446910 2000-2012 –> 2013-2019 6.8794702 20300.6675
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.7110206 7456.6491 16.288274 2000-2012 –> 2013-2019 6.7838224 20163.0416
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 4.1419372 7754.1184 23.674294 2000-2012 –> 2013-2019 7.4016458 20753.3966
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.0182270 7673.4584 26.251071 2000-2012 –> 2013-2019 7.1729488 20511.2455
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 ~ temp + aou + nitrate 3.8937891 7583.7038 15.641480 2000-2012 –> 2013-2019 7.1556437 20584.2688
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.8766670 7573.6904 17.071967 2000-2012 –> 2013-2019 7.1385188 20576.2510
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 2.9055285 18701.3647 17.392654 1982-1999 –> 2000-2012 5.4605671 42663.2585
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.8915485 18667.0949 16.912660 1982-1999 –> 2000-2012 5.2661255 41886.6424
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate 3.4731721 20045.3316 15.793395 1982-1999 –> 2000-2012 6.3001385 45036.9780
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.8133808 18463.0073 25.621580 1982-1999 –> 2000-2012 5.1271232 41420.8200
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 2.8874703 18656.4814 17.295800 1982-1999 –> 2000-2012 5.2261995 41721.4481
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.8832635 18647.5174 18.355780 1982-1999 –> 2000-2012 5.2036450 41634.4475
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 2.8932810 18671.5992 19.992092 1982-1999 –> 2000-2012 5.2171354 41671.7274
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 + 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 + aou + nitrate + phosphate_star 3.7478257 10983.4181 13.842903 2000-2012 –> 2013-2019 7.2087214 31002.1220
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 3.4148343 10608.8583 13.555597 2000-2012 –> 2013-2019 6.3203628 29310.2230
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.4049889 10599.2975 13.234065 2000-2012 –> 2013-2019 6.2965374 29266.3924
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 + temp + aou + nitrate + phosphate_star 3.1178660 10248.5737 21.014934 2000-2012 –> 2013-2019 5.9312469 28711.5810
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 3.4093268 10604.3954 13.379528 2000-2012 –> 2013-2019 6.2967972 29260.8768
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.3929098 10587.0683 13.656392 2000-2012 –> 2013-2019 6.2761734 29234.5857
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 3.3933170 10585.5487 13.888126 2000-2012 –> 2013-2019 6.2865980 29257.1479
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 + phosphate + phosphate_star 3.3929378 10585.1013 13.596469 2000-2012 –> 2013-2019 6.2829048 29248.0822
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate 2.2983963 5858.4881 11.332919 1982-1999 –> 2000-2012 4.2541777 12873.2575
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.0098007 5511.8987 12.302204 1982-1999 –> 2000-2012 3.6222614 11881.6368
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.7701030 5183.9584 15.104695 1982-1999 –> 2000-2012 3.3654426 11519.9147
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 2.1041418 5631.0745 12.284382 1982-1999 –> 2000-2012 3.7864540 12142.9635
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.7052880 5087.0433 11.194363 1982-1999 –> 2000-2012 3.2193048 11247.6217
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate_star 2.2231633 5774.0252 12.468928 1982-1999 –> 2000-2012 4.0002799 12469.6811
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 + 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 ~ temp + aou + phosphate + phosphate_star 2.3985643 5971.3155 14.446654 1982-1999 –> 2000-2012 4.2874047 12871.3457
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate 2.6579239 3154.1868 10.578892 2000-2012 –> 2013-2019 4.9563202 9012.6749
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.3943710 3019.1815 11.376380 2000-2012 –> 2013-2019 4.4041717 8531.0802
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.8708815 2697.4969 15.992073 2000-2012 –> 2013-2019 3.6409845 7881.4553
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 2.5005533 3076.1111 11.287467 2000-2012 –> 2013-2019 4.6046950 8707.1856
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.8588432 2689.0275 10.382841 2000-2012 –> 2013-2019 3.5641313 7776.0708
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate_star 2.6285872 3141.6252 11.410199 2000-2012 –> 2013-2019 4.8517505 8915.6504
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 + 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 ~ temp + aou + phosphate + phosphate_star 2.7699895 3210.3701 13.544935 2000-2012 –> 2013-2019 5.1685538 9181.6856
Atlantic (27.85,27.95] cstar_tref ~ aou + phosphate + phosphate_star 3.3583056 6522.8087 38.951768 1982-1999 –> 2000-2012 6.5202987 15322.6912
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.3582501 6524.7678 39.373477 1982-1999 –> 2000-2012 6.4297050 15227.2952
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.6716112 6747.6531 45.858691 1982-1999 –> 2000-2012 6.7088414 15413.8582
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 3.5749853 6679.6194 50.360961 1982-1999 –> 2000-2012 6.6621117 15399.5524
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.9405148 6197.8675 22.293581 1982-1999 –> 2000-2012 6.0055909 14895.2849
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate_star 3.7093246 6770.9560 54.305858 1982-1999 –> 2000-2012 6.8180537 15514.7376
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 + phosphate + phosphate_star 3.6898682 6757.9345 52.824150 1982-1999 –> 2000-2012 6.7985203 15501.6314
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate 3.5752685 6677.8155 49.566127 1982-1999 –> 2000-2012 6.7520165 15493.6198
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.1164452 6339.7437 23.637863 1982-1999 –> 2000-2012 6.2780482 15141.2042
Atlantic (27.85,27.95] cstar_tref ~ aou + phosphate + phosphate_star 3.6881750 3867.2835 23.611024 2000-2012 –> 2013-2019 7.0464806 10390.0923
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.4493114 3774.4722 25.312421 2000-2012 –> 2013-2019 6.8075615 10299.2401
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.2717396 3701.6327 24.633954 2000-2012 –> 2013-2019 6.9433508 10449.2858
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 3.5052511 3797.2522 25.574745 2000-2012 –> 2013-2019 7.0802364 10476.8716
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.3332865 3728.0226 24.407223 2000-2012 –> 2013-2019 6.2738014 9925.8900
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate_star 3.5585069 3818.6039 25.635405 2000-2012 –> 2013-2019 7.2678316 10589.5599
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 + phosphate + phosphate_star 3.5559519 3817.5868 25.414800 2000-2012 –> 2013-2019 7.2458201 10575.5213
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate 3.7724012 3899.2568 23.929748 2000-2012 –> 2013-2019 7.3476697 10577.0723
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.6198780 3842.8164 23.176587 2000-2012 –> 2013-2019 6.7363232 10182.5601
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.9005315 10426.0723 26.690347 1982-1999 –> 2000-2012 8.0471829 25240.9310
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.5218348 10045.4907 24.004911 1982-1999 –> 2000-2012 7.0630981 24040.1196
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 3.8938747 10419.6738 26.237305 1982-1999 –> 2000-2012 8.0350175 25227.6067
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.8916445 10419.5277 25.815150 1982-1999 –> 2000-2012 8.0275541 25222.8724
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 3.8919974 10417.8674 25.981905 1982-1999 –> 2000-2012 8.0298954 25221.7162
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 ~ temp + aou + nitrate + phosphate_star 3.6324901 10159.3780 24.215864 1982-1999 –> 2000-2012 7.3632160 24423.5486
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.9273983 10451.7864 25.996572 1982-1999 –> 2000-2012 8.1434520 25353.1227
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate_star 3.9274126 10449.7999 25.963125 1982-1999 –> 2000-2012 8.1435742 25349.2697
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 ~ aou + phosphate + phosphate_star 3.8859537 5473.7721 25.458541 2000-2012 –> 2013-2019 7.8207491 15930.6072
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.8005114 5432.0180 25.380343 2000-2012 –> 2013-2019 7.7010429 15858.0903
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.2788996 5143.4865 24.102906 2000-2012 –> 2013-2019 6.8007344 15188.9772
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 3.8042578 5433.9570 24.996323 2000-2012 –> 2013-2019 7.6981324 15853.6308
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.7996986 5433.5970 25.677376 2000-2012 –> 2013-2019 7.6913431 15853.1247
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 3.8086257 5436.2153 24.729450 2000-2012 –> 2013-2019 7.7006231 15854.0827
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 ~ temp + aou + nitrate + phosphate_star 3.5146493 5278.1284 23.980176 2000-2012 –> 2013-2019 7.1471394 15437.5065
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate 3.8942491 5477.9688 24.850256 2000-2012 –> 2013-2019 7.8222647 15928.3438
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.8845316 5475.0518 25.855251 2000-2012 –> 2013-2019 7.8119300 15926.8382
Atlantic (28.05,28.1] cstar_tref ~ aou + phosphate + phosphate_star 1.2502980 4119.0857 11.775302 1982-1999 –> 2000-2012 2.3946308 9222.3121
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.1424109 3895.3026 7.780828 1982-1999 –> 2000-2012 2.1747704 8662.9775
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.1406889 3893.5285 6.982709 1982-1999 –> 2000-2012 2.1810442 8688.4940
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.1516323 3915.4175 7.717827 1982-1999 –> 2000-2012 2.1885741 8697.6100
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0888369 3777.1296 7.899696 1982-1999 –> 2000-2012 2.1067240 8500.5259
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 1.1629032 3939.7851 7.727641 1982-1999 –> 2000-2012 2.2078272 8747.1147
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 + phosphate + phosphate_star 1.1566552 3926.3062 7.730772 1982-1999 –> 2000-2012 2.1978100 8721.7900
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate 1.2638184 4145.9966 11.794931 1982-1999 –> 2000-2012 2.4143248 9266.8597
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.2129605 4045.2306 12.073160 1982-1999 –> 2000-2012 2.3511400 9132.7826
Atlantic (28.05,28.1] cstar_tref ~ aou + phosphate + phosphate_star 1.3649159 2407.8235 12.696647 2000-2012 –> 2013-2019 2.6152139 6526.9092
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.2401088 2276.9148 8.299177 2000-2012 –> 2013-2019 2.3825197 6172.2174
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.2105055 2245.4275 6.979690 2000-2012 –> 2013-2019 2.3511944 6138.9560
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.2523837 2290.5663 8.224435 2000-2012 –> 2013-2019 2.4040160 6205.9837
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.1579193 2183.8706 8.562264 2000-2012 –> 2013-2019 2.2467562 5961.0002
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 1.2646618 2304.0882 8.233229 2000-2012 –> 2013-2019 2.4275650 6243.8732
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 + phosphate + phosphate_star 1.2569957 2295.6610 8.240693 2000-2012 –> 2013-2019 2.4136509 6221.9671
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate 1.3809322 2423.9925 12.682790 2000-2012 –> 2013-2019 2.6447506 6569.9890
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.3166795 2359.9555 13.296424 2000-2012 –> 2013-2019 2.5296400 6405.1861
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.8096172 3388.8543 5.467126 1982-1999 –> 2000-2012 1.5326899 7532.2260
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate 0.8942682 3666.9003 6.143180 1982-1999 –> 2000-2012 1.6402112 7927.7920
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.8057853 3377.5898 5.336769 1982-1999 –> 2000-2012 1.4985105 7361.1456
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate 0.8093116 3387.7988 5.388705 1982-1999 –> 2000-2012 1.5303121 7520.3390
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8093116 3389.7988 5.389161 1982-1999 –> 2000-2012 1.5276146 7510.1929
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 0.8097628 3389.3574 5.294503 1982-1999 –> 2000-2012 1.5288629 7511.9370
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 + phosphate + phosphate_star 0.8094433 3388.2539 5.337970 1982-1999 –> 2000-2012 1.5291408 7513.9673
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.9935553 3961.2743 11.148118 1982-1999 –> 2000-2012 1.7737885 8391.7836
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.9685962 3890.1390 11.042213 1982-1999 –> 2000-2012 1.7669350 8407.2241
Atlantic (28.1,28.15] cstar_tref ~ aou + phosphate + phosphate_star 1.0250134 2065.7493 12.951158 2000-2012 –> 2013-2019 2.0065851 5991.0955
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.8792018 1849.2415 7.100581 2000-2012 –> 2013-2019 1.6888190 5238.0959
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate 1.0014374 2034.6139 8.283117 2000-2012 –> 2013-2019 1.8957056 5701.5141
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.8910485 1870.3010 6.797078 2000-2012 –> 2013-2019 1.6968339 5247.8908
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate 0.8849636 1858.5432 6.958491 2000-2012 –> 2013-2019 1.6942752 5246.3420
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8569972 1814.8160 8.112716 2000-2012 –> 2013-2019 1.6663088 5204.6147
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 0.8918397 1869.5648 6.850193 2000-2012 –> 2013-2019 1.7016025 5258.9221
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 + phosphate + phosphate_star 0.8879019 1863.2634 6.924296 2000-2012 –> 2013-2019 1.6973452 5251.5173
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.9596419 1973.9067 13.374384 2000-2012 –> 2013-2019 1.9282382 5864.0457
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate 0.7725648 4683.7802 10.144436 1982-1999 –> 2000-2012 1.4056175 10189.1442
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.6770043 4154.1936 6.501489 1982-1999 –> 2000-2012 1.2437371 9029.2149
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.9125392 5356.1700 16.336972 1982-1999 –> 2000-2012 1.6806939 11968.8363
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.6659083 4087.6614 7.918388 1982-1999 –> 2000-2012 1.2147171 8779.0476
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.6608030 4058.6769 7.164936 1982-1999 –> 2000-2012 1.2088659 8744.2901
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.9123305 5357.2491 16.566693 1982-1999 –> 2000-2012 1.6734607 11919.4226
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 ~ temp + aou + nitrate 0.7737979 4690.2010 12.224785 1982-1999 –> 2000-2012 1.3748519 9899.1864
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.7289031 4451.5668 11.454276 1982-1999 –> 2000-2012 1.3019921 9390.3168
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 ~ sal + aou + nitrate 0.8796573 2792.7830 8.993340 2000-2012 –> 2013-2019 1.6522222 7476.5631
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.7438009 2433.0944 5.353850 2000-2012 –> 2013-2019 1.4208051 6587.2880
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.7635202 2489.5089 6.905498 2000-2012 –> 2013-2019 1.4294285 6577.1703
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.7400734 2424.2628 5.601071 2000-2012 –> 2013-2019 1.4008765 6482.9398
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate 1.0583864 3193.5748 13.696345 2000-2012 –> 2013-2019 1.9719032 8554.0554
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0580589 3194.9076 13.461997 2000-2012 –> 2013-2019 1.9703894 8552.1567
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 ~ temp + aou + nitrate 0.9385901 2932.5919 11.306237 2000-2012 –> 2013-2019 1.7123881 7622.7930
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.8821824 2800.9631 10.600095 2000-2012 –> 2013-2019 1.6110855 7252.5299
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 (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.3566263 3287.5171 1.988203 1982-1999 –> 2000-2012 0.6691525 6334.2006
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.3501288 3134.1416 1.949898 1982-1999 –> 2000-2012 0.6565772 5949.7518
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 + temp + aou + nitrate 0.3560111 3274.9265 2.045845 1982-1999 –> 2000-2012 0.6669547 6263.3605
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3395940 2877.9930 2.205103 1982-1999 –> 2000-2012 0.6447888 5646.9529
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8255740 10384.3655 17.517649 1982-1999 –> 2000-2012 1.7449265 26240.3984
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 ~ temp + aou + nitrate + phosphate_star 0.8411465 10540.2697 5.176159 1982-1999 –> 2000-2012 1.4858560 22182.7090
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.8671400 10797.4423 15.747147 1982-1999 –> 2000-2012 1.8076321 26921.2787
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 ~ sal + aou + nitrate 0.4264163 2726.2777 2.452673 2000-2012 –> 2013-2019 0.7830427 6013.7947
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.4135856 2581.8126 2.572196 2000-2012 –> 2013-2019 0.7637143 5715.9542
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 + temp + aou + nitrate 0.4234133 2694.3964 2.563266 2000-2012 –> 2013-2019 0.7794244 5969.3229
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3788945 2163.8268 2.767863 2000-2012 –> 2013-2019 0.7184885 5041.8198
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0201828 6912.1841 18.023648 2000-2012 –> 2013-2019 1.8457568 17296.5497
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 ~ temp + aou + nitrate + phosphate_star 1.0783793 7176.1433 6.138344 2000-2012 –> 2013-2019 1.9195258 17716.4129
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.0456896 7028.5710 16.663467 2000-2012 –> 2013-2019 1.9128297 17826.0133
Atlantic (28.2, Inf] cstar_tref ~ temp + nitrate + phosphate_star 1.0789365 7176.6193 5.655216 2000-2012 –> 2013-2019 1.9216876 17730.9937
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 6.2801597 36600.1682 29.818984 1982-1999 –> 2000-2012 12.8626803 87384.7542
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 7.4439384 38510.3404 59.558635 1982-1999 –> 2000-2012 15.1437988 91704.7035
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.1136918 36300.3175 34.053133 1982-1999 –> 2000-2012 12.5238257 86679.0210
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.4254929 36857.2246 30.208689 1982-1999 –> 2000-2012 13.1429671 87953.7368
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6.2733617 36589.9990 29.675295 1982-1999 –> 2000-2012 12.8523383 87368.3078
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 6.4996394 36986.1393 30.371328 1982-1999 –> 2000-2012 13.2827179 88232.0298
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 + 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 ~ temp + aou + nitrate + phosphate_star 7.6057593 38751.9786 35.245120 1982-1999 –> 2000-2012 15.5892140 92502.2596
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.9966384 19054.5361 24.645119 2000-2012 –> 2013-2019 12.2767981 55654.7043
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 7.3614676 20270.9536 55.451975 2000-2012 –> 2013-2019 14.8054059 58781.2940
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.8220861 18881.3024 29.808032 2000-2012 –> 2013-2019 11.9357779 55181.6200
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.1276808 19182.7699 25.473564 2000-2012 –> 2013-2019 12.5531737 56039.9945
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.9924378 19052.3794 24.457831 2000-2012 –> 2013-2019 12.2657995 55642.3784
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 6.1981371 19250.5871 25.753337 2000-2012 –> 2013-2019 12.6977765 56236.7264
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 + 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 ~ temp + aou + nitrate + phosphate_star 7.4523302 20343.7241 28.148100 2000-2012 –> 2013-2019 15.0580895 59095.7027
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.0821327 36389.7116 45.752274 1982-1999 –> 2000-2012 9.8846246 86260.7052
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.8747891 35894.0278 52.864020 1982-1999 –> 2000-2012 9.3529781 84600.3995
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate 5.0755511 36374.2283 42.154614 1982-1999 –> 2000-2012 9.8723949 86225.5866
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.0503378 36316.7276 44.104781 1982-1999 –> 2000-2012 9.8271348 86100.2061
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate_star 5.1403010 36525.6875 40.738339 1982-1999 –> 2000-2012 9.9855379 86544.5393
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 + 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 ~ temp + aou + nitrate + phosphate_star 5.3202775 36936.8638 52.741465 1982-1999 –> 2000-2012 10.2721051 87318.8129
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + phosphate + phosphate_star 5.5544660 37451.5457 43.207070 1982-1999 –> 2000-2012 10.8475114 88945.4006
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.1348826 19337.9016 47.814448 2000-2012 –> 2013-2019 10.2170153 55727.6131
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.8891471 19029.6802 50.582408 2000-2012 –> 2013-2019 9.7639362 54923.7079
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate 5.1575902 19365.8149 41.629135 2000-2012 –> 2013-2019 10.2331412 55740.0431
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.1225304 19324.6658 45.747890 2000-2012 –> 2013-2019 10.1728682 55641.3934
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate_star 5.2238663 19446.5875 38.433198 2000-2012 –> 2013-2019 10.3641674 55972.2750
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 + 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 ~ temp + aou + nitrate + phosphate_star 5.2685050 19500.4144 47.812939 2000-2012 –> 2013-2019 10.5887824 56437.2781
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 (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.3778171 28868.4409 17.580971 1982-1999 –> 2000-2012 8.4344625 67972.7841
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.3142836 28724.7487 25.568471 1982-1999 –> 2000-2012 8.3693163 67825.5785
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.5015798 29146.2749 20.161616 1982-1999 –> 2000-2012 8.6448420 68543.5662
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.3446226 28794.5866 21.561021 1982-1999 –> 2000-2012 8.3961243 67883.3368
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate_star 4.5956715 29352.4363 25.721857 1982-1999 –> 2000-2012 8.8115218 68990.5501
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 + 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 ~ temp + aou + nitrate + phosphate_star 4.4610680 29056.1803 31.666714 1982-1999 –> 2000-2012 8.7354817 68885.5844
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.4220261 28968.5770 19.561170 1982-1999 –> 2000-2012 8.6086164 68510.1185
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 ~ aou + phosphate + phosphate_star 4.9188516 16268.8496 24.629168 2000-2012 –> 2013-2019 9.4722187 45527.1213
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.7452825 16076.9312 20.815315 2000-2012 –> 2013-2019 9.1230996 44945.3721
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.6104347 15923.3131 30.090850 2000-2012 –> 2013-2019 8.9247183 44648.0618
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.8695214 16216.4407 23.726262 2000-2012 –> 2013-2019 9.3711012 45362.7157
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.7197611 16049.8208 20.737804 2000-2012 –> 2013-2019 9.0643837 44844.4074
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 + 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 ~ temp + aou + nitrate + phosphate_star 4.7548764 16087.8337 36.535410 2000-2012 –> 2013-2019 9.2159445 45144.0140
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.7999532 16138.7663 19.442145 2000-2012 –> 2013-2019 9.2219793 45107.3433
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 (26.75,27] cstar_tref ~ aou + phosphate + phosphate_star 4.6964246 36399.6301 19.956325 1982-1999 –> 2000-2012 8.8547652 85298.9295
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.4690269 35792.6601 21.903442 1982-1999 –> 2000-2012 8.3066735 83314.3453
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.8057070 36685.8730 23.033151 1982-1999 –> 2000-2012 9.0009170 85740.9133
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 4.7283178 36484.6734 22.062270 1982-1999 –> 2000-2012 8.8243027 85126.2509
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.3764564 35537.8328 24.155271 1982-1999 –> 2000-2012 8.1555956 82797.4266
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate_star 4.8778936 36866.8104 21.608442 1982-1999 –> 2000-2012 9.1239182 86126.8140
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 ~ temp + aou + nitrate + phosphate_star 5.0029956 37177.5280 22.523309 1982-1999 –> 2000-2012 9.4960231 87409.5164
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate 4.9094485 36943.9289 22.137235 1982-1999 –> 2000-2012 9.2842785 86715.6471
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.4147522 35642.7332 25.003944 1982-1999 –> 2000-2012 8.2874817 83320.8516
Indo-Pacific (26.75,27] cstar_tref ~ aou + phosphate + phosphate_star 5.0571210 19938.5085 21.624849 2000-2012 –> 2013-2019 9.7535456 56338.1386
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.8557206 19674.0738 23.134484 2000-2012 –> 2013-2019 9.3247475 55466.7339
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.1729842 20091.0175 24.828846 2000-2012 –> 2013-2019 9.9786913 56776.8906
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 5.1020985 19998.5590 23.101966 2000-2012 –> 2013-2019 9.8304163 56483.2325
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.7804239 19573.6147 27.468474 2000-2012 –> 2013-2019 9.1568804 55111.4474
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate_star 5.2565739 20194.1083 22.513870 2000-2012 –> 2013-2019 10.1344675 57060.9187
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 ~ temp + aou + nitrate + phosphate_star 5.3586249 20320.1667 22.503297 2000-2012 –> 2013-2019 10.3616205 57497.6948
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate 5.2720580 20211.3918 20.906662 2000-2012 –> 2013-2019 10.1815066 57155.3207
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.8134874 19616.8027 28.200886 2000-2012 –> 2013-2019 9.2282396 55259.5358
Indo-Pacific (27,27.25] cstar_tref ~ aou + phosphate + phosphate_star 4.8181808 46519.2759 56.606395 1982-1999 –> 2000-2012 8.8470371 106776.9600
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.7207687 46203.7115 59.058113 1982-1999 –> 2000-2012 8.6211002 105768.8735
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.7678501 46360.0076 70.647423 1982-1999 –> 2000-2012 8.7224759 106223.3160
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 4.9913500 47070.2756 58.596198 1982-1999 –> 2000-2012 9.1433335 107974.8398
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.3906586 45078.5995 51.228310 1982-1999 –> 2000-2012 8.0583032 103328.0536
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 ~ temp + aou + nitrate + phosphate_star 4.7965711 46451.3860 69.209155 1982-1999 –> 2000-2012 8.8054915 106604.8049
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate 5.0177033 47150.1501 56.857416 1982-1999 –> 2000-2012 9.2227483 108324.7484
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.4560374 45306.4093 48.916173 1982-1999 –> 2000-2012 8.2124151 104065.9656
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 ~ aou + phosphate + phosphate_star 5.8184141 26486.3992 51.803496 2000-2012 –> 2013-2019 10.6365949 73005.6751
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.7045985 26323.9179 54.516444 2000-2012 –> 2013-2019 10.4253672 72527.6294
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.9925950 26735.9896 59.012569 2000-2012 –> 2013-2019 10.7604452 73095.9971
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 6.0018615 26746.8542 52.822574 2000-2012 –> 2013-2019 10.9932115 73817.1299
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.1786096 25520.4940 46.466105 2000-2012 –> 2013-2019 9.5692682 70599.0935
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 + phosphate + phosphate_star 6.1217767 26911.5650 51.751919 2000-2012 –> 2013-2019 11.2599499 74432.5958
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate_star 6.0130013 26762.2935 57.523834 2000-2012 –> 2013-2019 10.8095724 73213.6795
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate 6.0251868 26777.1492 51.235865 2000-2012 –> 2013-2019 11.0428901 73927.2993
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 5.2479146 25629.1814 44.123913 2000-2012 –> 2013-2019 9.7039521 70935.5907
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate_star 4.3760286 42575.4681 32.395972 1982-1999 –> 2000-2012 8.1047266 96543.5014
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + phosphate 4.3663641 42540.9627 38.469768 1982-1999 –> 2000-2012 8.0632455 96337.9371
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.3646187 42537.0846 37.180522 1982-1999 –> 2000-2012 8.0577449 96316.0095
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.3109542 42357.1980 44.188380 1982-1999 –> 2000-2012 8.0128949 96185.1518
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 4.3568233 42510.8027 35.609066 1982-1999 –> 2000-2012 8.0447550 96261.9602
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.0020160 41263.9420 45.979688 1982-1999 –> 2000-2012 7.5600065 94309.4582
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate_star 4.3875706 42614.1943 34.554605 1982-1999 –> 2000-2012 8.0942850 96465.5719
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 + phosphate + phosphate_star 4.3817389 42594.6402 34.628733 1982-1999 –> 2000-2012 8.0871857 96439.2698
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.1174048 41679.8438 51.572373 1982-1999 –> 2000-2012 7.8052794 95430.6955
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate_star 4.9610903 23626.7698 37.773275 2000-2012 –> 2013-2019 9.3371189 66202.2380
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + phosphate 4.9910727 23671.8758 43.020389 2000-2012 –> 2013-2019 9.3574368 66212.8385
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.9875747 23668.3947 41.020153 2000-2012 –> 2013-2019 9.3521934 66205.4793
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + phosphate + phosphate_star 5.0010701 23687.5201 36.587876 2000-2012 –> 2013-2019 9.3912231 66308.3650
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.8948364 23523.6593 50.857213 2000-2012 –> 2013-2019 9.2057906 65880.8573
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 4.9756375 23649.6608 38.994228 2000-2012 –> 2013-2019 9.3324608 66160.4635
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.4976285 22862.0174 49.856387 2000-2012 –> 2013-2019 8.4996446 64125.9595
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 + phosphate + phosphate_star 4.9997169 23687.4044 37.927937 2000-2012 –> 2013-2019 9.3814558 66282.0446
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.6119274 23056.2148 55.495361 2000-2012 –> 2013-2019 8.7293322 64736.0586
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + phosphate_star 3.5222328 41757.1886 30.628430 1982-1999 –> 2000-2012 6.1017712 92588.4616
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.4299624 41343.3924 20.186961 1982-1999 –> 2000-2012 6.0110351 92187.4345
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + phosphate_star 3.5317985 41797.4651 29.576568 1982-1999 –> 2000-2012 6.1130683 92641.1470
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + phosphate_star 3.5223359 41755.6447 30.754935 1982-1999 –> 2000-2012 6.1103205 92655.1152
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.4151795 41278.0641 19.238138 1982-1999 –> 2000-2012 5.9929213 92096.3757
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 3.4148074 41274.3653 20.377962 1982-1999 –> 2000-2012 5.9940251 92102.9689
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.4000976 41209.0730 21.784129 1982-1999 –> 2000-2012 5.9786950 92034.5105
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 3.4165862 41282.4834 20.110300 1982-1999 –> 2000-2012 5.9974164 92124.5075
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 + 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 + aou + phosphate + phosphate_star 4.0271627 23233.5010 18.466600 2000-2012 –> 2013-2019 7.4571251 64576.8934
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou 4.0061172 23188.2326 17.454607 2000-2012 –> 2013-2019 7.4488928 64587.7479
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate 4.0042660 23186.4157 16.509857 2000-2012 –> 2013-2019 7.4448379 64577.9499
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.0034014 23186.6325 17.583942 2000-2012 –> 2013-2019 7.4185809 64464.6965
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 4.0047653 23187.4452 18.787997 2000-2012 –> 2013-2019 7.4195726 64461.8106
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.9855759 23149.7809 20.503092 2000-2012 –> 2013-2019 7.3856736 64358.8539
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 4.0051598 23188.2587 18.559686 2000-2012 –> 2013-2019 7.4217460 64470.7421
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 + 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 (27.75,27.85] cstar_tref ~ aou + phosphate + phosphate_star 2.7106771 15884.0200 24.679481 1982-1999 –> 2000-2012 4.8614803 35369.1481
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.6953757 15848.8283 25.933360 1982-1999 –> 2000-2012 4.8392829 35307.3298
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.6995543 15861.0057 25.608111 1982-1999 –> 2000-2012 4.8465562 35334.3653
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 2.7019554 15864.8468 25.781084 1982-1999 –> 2000-2012 4.8505512 35342.8214
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.6594820 15762.7493 26.827961 1982-1999 –> 2000-2012 4.7971147 35197.1243
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate_star 2.6995598 15859.0190 25.639446 1982-1999 –> 2000-2012 4.8497340 35343.5396
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + phosphate_star 2.7044838 15870.9918 24.480023 1982-1999 –> 2000-2012 4.8683230 35411.9842
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.7003367 15860.9095 25.612602 1982-1999 –> 2000-2012 4.8517720 35350.6569
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + phosphate_star 2.7178496 15903.3813 24.549368 1982-1999 –> 2000-2012 4.8716457 35402.9046
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 2.6853351 15824.3085 25.085906 1982-1999 –> 2000-2012 4.8333906 35300.0414
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + phosphate_star 3.1064942 9359.0110 31.069308 2000-2012 –> 2013-2019 5.8118538 25232.1299
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.1139668 9367.8093 29.988091 2000-2012 –> 2013-2019 5.8093426 25216.6376
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + phosphate_star 3.1163067 9368.5599 29.361222 2000-2012 –> 2013-2019 5.8216844 25239.7230
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.1064941 9361.0109 31.066032 2000-2012 –> 2013-2019 5.8060485 25222.0166
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 3.1211609 9376.2597 29.742172 2000-2012 –> 2013-2019 5.8231163 25241.1065
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.0203461 9258.0230 31.461684 2000-2012 –> 2013-2019 5.6798281 25020.7723
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate_star 3.1162269 9370.4661 29.470450 2000-2012 –> 2013-2019 5.8157867 25229.4852
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 + 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 ~ temp + aou + phosphate + phosphate_star 3.1181258 9372.6970 27.929897 2000-2012 –> 2013-2019 5.8034609 25197.0054
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + phosphate + phosphate_star 2.7844532 19783.5613 35.931948 1982-1999 –> 2000-2012 4.9241993 44083.3104
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.7840796 19784.4754 36.091427 1982-1999 –> 2000-2012 4.9237602 44085.8833
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.7431168 19666.5017 30.871068 1982-1999 –> 2000-2012 4.8615079 43858.4733
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 2.7883121 19796.7709 35.862322 1982-1999 –> 2000-2012 4.9294286 44105.6548
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.7808061 19776.9530 36.506954 1982-1999 –> 2000-2012 4.9204734 44080.2912
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate_star 2.7878875 19795.5385 35.848297 1982-1999 –> 2000-2012 4.9294830 44106.9148
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 ~ temp + aou + nitrate + phosphate_star 2.7461187 19673.3544 30.533650 1982-1999 –> 2000-2012 4.8647366 43864.5191
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 2.7808876 19775.1902 36.445124 1982-1999 –> 2000-2012 4.9206286 44076.9123
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 ~ sal + aou + phosphate + phosphate_star 3.0890675 10922.5246 39.968381 2000-2012 –> 2013-2019 5.8731471 30707.0000
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 3.0952577 10931.1007 37.417437 2000-2012 –> 2013-2019 5.8489309 30626.6911
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.0928060 10929.7061 37.733847 2000-2012 –> 2013-2019 5.8359228 30596.2078
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.0413356 10857.8121 41.543177 2000-2012 –> 2013-2019 5.8221417 30634.7650
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 ~ temp + aou + nitrate 3.1246326 10969.5655 36.088189 2000-2012 –> 2013-2019 5.8808206 30670.5441
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.1211113 10966.7348 36.495833 2000-2012 –> 2013-2019 5.8672300 30640.0893
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.0546560 10874.5340 40.601759 2000-2012 –> 2013-2019 5.8355436 30649.7242
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 (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.2544478 17866.7489 7.902572 1982-1999 –> 2000-2012 4.3575547 42179.2859
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.3145227 18077.1362 8.308708 1982-1999 –> 2000-2012 4.4086901 42341.8029
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.2511224 17856.9397 7.824021 1982-1999 –> 2000-2012 4.3311036 42047.2198
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 2.3173507 18086.9050 8.353684 1982-1999 –> 2000-2012 4.4120821 42354.5979
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.3050446 18046.3084 8.034260 1982-1999 –> 2000-2012 4.3989891 42311.7793
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 2.3167720 18084.9070 8.346039 1982-1999 –> 2000-2012 4.4114595 42352.3647
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + phosphate 2.3226158 18103.0608 8.354841 1982-1999 –> 2000-2012 4.4363275 42470.1223
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.3171697 18086.2802 8.351281 1982-1999 –> 2000-2012 4.4119950 42354.4769
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 2.3405256 18166.5125 7.538133 1982-1999 –> 2000-2012 4.4448393 42485.4965
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 2.3281019 18123.9346 7.763781 1982-1999 –> 2000-2012 4.4315235 42438.1536
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.4029551 10163.3105 8.501463 2000-2012 –> 2013-2019 4.6574030 28030.0593
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.4946372 10328.8879 9.144701 2000-2012 –> 2013-2019 4.8091599 28406.0241
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.4016759 10162.9558 8.333752 2000-2012 –> 2013-2019 4.6527983 28019.8955
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 2.4993302 10337.1989 9.202167 2000-2012 –> 2013-2019 4.8166809 28424.1039
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.4733849 10293.0546 8.735427 2000-2012 –> 2013-2019 4.7784294 28339.3630
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 2.4981766 10335.1574 9.192474 2000-2012 –> 2013-2019 4.8149486 28420.0643
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + phosphate_star 2.5251433 10382.6351 9.368552 2000-2012 –> 2013-2019 4.8723580 28571.9785
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 ~ temp + aou + phosphate + phosphate_star 2.5010086 10340.1675 8.337462 2000-2012 –> 2013-2019 4.8291105 28464.1022
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.0732712 11100.3176 9.435149 1982-1999 –> 2000-2012 3.9070575 26354.8863
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate 2.0908608 11141.9272 9.340695 1982-1999 –> 2000-2012 3.9250771 26396.2603
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.0774799 11110.7857 9.143031 1982-1999 –> 2000-2012 3.9116905 26367.0957
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate_star 2.0824080 11121.0164 9.253566 1982-1999 –> 2000-2012 3.9166625 26375.5064
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + phosphate + phosphate_star 2.0874594 11133.5228 9.321489 1982-1999 –> 2000-2012 3.9228354 26392.6131
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.0729334 11101.4765 9.354339 1982-1999 –> 2000-2012 3.9067125 26358.0156
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 2.0784128 11113.1032 9.143891 1982-1999 –> 2000-2012 3.9126064 26369.3434
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.0633659 11077.5965 8.941697 1982-1999 –> 2000-2012 3.8930252 26317.2083
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 2.0780812 11112.2796 9.139160 1982-1999 –> 2000-2012 3.9122511 26368.4225
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.0783583 11112.9679 9.140599 1982-1999 –> 2000-2012 3.9127419 26369.9875
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.2102432 6502.1285 9.296085 2000-2012 –> 2013-2019 4.2835144 17602.4462
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate 2.2465228 6547.8971 9.141200 2000-2012 –> 2013-2019 4.3373835 17689.8242
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.2310190 6529.5787 9.259984 2000-2012 –> 2013-2019 4.3084989 17640.3644
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate_star 2.2327590 6529.8660 9.204427 2000-2012 –> 2013-2019 4.3151670 17650.8824
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + phosphate + phosphate_star 2.2356795 6533.7013 9.167644 2000-2012 –> 2013-2019 4.3231389 17667.2241
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.2074944 6500.4773 9.344478 2000-2012 –> 2013-2019 4.2804278 17601.9539
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 2.2322200 6531.1576 9.262747 2000-2012 –> 2013-2019 4.3106327 17644.2609
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.2122584 6506.8024 9.055467 2000-2012 –> 2013-2019 4.2756243 17584.3989
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 2.2314283 6530.1169 9.255394 2000-2012 –> 2013-2019 4.3095094 17642.3964
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.2317161 6530.4953 9.257027 2000-2012 –> 2013-2019 4.3100744 17643.4633
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.9024272 82152.4604 12.057819 1982-1999 –> 2000-2012 3.6685977 192063.3010
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.7053396 77797.9632 8.898797 1982-1999 –> 2000-2012 3.2455996 180143.9568
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate 1.8989084 82078.7138 12.089701 1982-1999 –> 2000-2012 3.6600779 191832.7828
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.8436806 80905.0017 11.800697 1982-1999 –> 2000-2012 3.5106558 187622.0363
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate_star 1.8979189 82057.9499 12.108084 1982-1999 –> 2000-2012 3.6573377 191757.0338
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 + phosphate + phosphate_star 1.8973256 82045.4965 12.111148 1982-1999 –> 2000-2012 3.6558579 191716.7142
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate_star 1.7445694 78701.9282 8.216785 1982-1999 –> 2000-2012 3.4461327 186552.3949
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.9063255 82234.0005 12.560892 1982-1999 –> 2000-2012 3.6501144 191439.7357
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 ~ sal + aou + nitrate + phosphate_star 2.0479670 45751.9953 15.530355 2000-2012 –> 2013-2019 3.9752817 128422.1848
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.0576445 45852.9566 17.807147 2000-2012 –> 2013-2019 3.9600717 128005.4170
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.8703531 43811.1286 19.368278 2000-2012 –> 2013-2019 3.5756927 121609.0918
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate 2.0547640 45822.9555 17.826814 2000-2012 –> 2013-2019 3.9536724 127901.6693
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.0137196 45392.8361 17.638341 2000-2012 –> 2013-2019 3.8574003 126297.8377
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate_star 2.0542229 45817.3155 17.838726 2000-2012 –> 2013-2019 3.9521418 127875.2654
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 + phosphate + phosphate_star 2.0537644 45812.5344 17.840504 2000-2012 –> 2013-2019 3.9510900 127858.0309
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate_star 1.8708037 43814.2871 19.172451 2000-2012 –> 2013-2019 3.6153731 122516.2154
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

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
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
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
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
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")
  )
aou nitrate phosphate phosphate_star sal temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26] 9 3 5 7 9 8
(26,26.5] 8 10 NA 5 6 6
(26.5,26.75] 9 3 5 8 9 6
(26.75,27] 9 3 5 8 9 6
(27,27.25] 8 4 5 8 9 7
(27.25,27.5] 8 5 4 7 8 9
(27.5,27.75] 7 3 5 7 10 8
(27.75,27.85] 7 2 6 8 9 8
(27.85,27.95] 8 2 7 8 7 8
(27.95,28.05] 8 2 6 9 6 9
(28.05,28.1] 8 2 7 8 7 8
(28.1,28.15] 8 4 5 8 8 9
(28.15,28.2] 8 8 2 7 7 7
(28.2, Inf] 7 8 2 8 7 7
total 112.00 59.00 — 106.00 111.00 106.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 8 3 5 7 9 9
(26,26.5] 8 10 NA 5 6 6
(26.5,26.75] 9 5 4 7 8 8
(26.75,27] 8 3 5 9 9 6
(27,27.25] 8 7 3 7 8 7
(27.25,27.5] 9 6 4 6 8 7
(27.5,27.75] 7 3 6 8 10 6
(27.75,27.85] 7 2 6 8 9 8
(27.85,27.95] 8 2 7 8 7 8
(27.95,28.05] 9 2 7 8 6 8
(28.05,28.1] 8 2 7 8 7 8
(28.1,28.15] 8 3 6 8 8 8
(28.15,28.2] 8 8 2 6 7 8
(28.2, Inf] 7 8 2 8 7 7
total 112.00 64.00 — 103.00 109.00 104.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 7 4 4 8 9 9
(26,26.5] 7 3 5 9 8 9
(26.5,26.75] 7 4 5 9 7 9
(26.75,27] 9 2 7 8 6 8
(27,27.25] 8 4 6 8 5 8
(27.25,27.5] 8 3 6 8 9 7
(27.5,27.75] 7 4 4 9 10 6
(27.75,27.85] 8 3 6 9 7 8
(27.85,27.95] 8 4 5 9 6 8
(27.95,28.05] 8 3 6 8 8 8
(28.05,28.1] 8 2 6 8 10 5
(28.1, Inf] 7 4 5 9 7 9
total 92.00 40.00 65.00 102.00 92.00 94.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 7 4 4 8 9 9
(26,26.5] 6 4 4 9 8 9
(26.5,26.75] 7 4 6 9 6 8
(26.75,27] 9 2 7 8 6 8
(27,27.25] 8 3 7 8 6 8
(27.25,27.5] 7 3 7 8 9 6
(27.5,27.75] 7 3 5 6 10 9
(27.75,27.85] 8 3 5 9 9 7
(27.85,27.95] 7 7 3 7 6 9
(27.95,28.05] 7 3 6 8 9 8
(28.05,28.1] 8 2 6 8 10 5
(28.1, Inf] 7 5 4 9 8 8
total 88.00 43.00 64.00 97.00 96.00 94.00

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
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
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