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

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

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

i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
print(i_gamma_slab)

# subset one gamma slab
GLODAP_basin_era_slab <- GLODAP_basin_era %>%
  filter(gamma_slab == i_gamma_slab)

# fit the full linear model, i.e. all predictor combinations
lm_full <- lm(paste(
  params_local$MLR_target,
  paste(params_local$MLR_predictors, collapse = " + "),
  sep = " ~ "
),
data = GLODAP_basin_era_slab)

# fit linear models for all possible predictor combinations
# unfortunately, this functions does not provide model coefficients (yet)
lm_all <- ols_step_all_possible(lm_full)

# convert to tibble
lm_all <- as_tibble(lm_all)

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

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

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

3 Apply predictor threshold

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

  • Minimum: 2
  • Maximum: 5
lm_all <- lm_all %>% 
  filter(n >= params_local$MLR_predictors_min,
         n <= params_local$MLR_predictors_max)

This results in a total number of MLR models of:

  • 86

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 + phosphate + phosphate_star 1.0669064 510.5238 4.506279 1982-1999 –> 2000-2012 2.3985898 1286.5351
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.0650698 511.9449 4.426016 1982-1999 –> 2000-2012 2.3967507 1289.9554
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 + aou + silicate + phosphate 1.0694684 513.3297 4.624413 1982-1999 –> 2000-2012 2.4024546 1291.7791
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.0708017 513.7483 4.671370 1982-1999 –> 2000-2012 2.4040952 1292.3010
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.0734858 512.5895 4.775202 1982-1999 –> 2000-2012 2.4077143 1289.4562
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.0721782 514.1800 4.711590 1982-1999 –> 2000-2012 2.4062957 1293.0094
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 + aou + silicate + phosphate + phosphate_star 1.1819575 261.4332 3.306338 2000-2012 –> 2013-2019 2.2470273 773.3781
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 + nitrate + silicate 1.1929038 262.8713 2.724893 2000-2012 –> 2013-2019 2.2980531 787.2281
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 + aou + silicate + phosphate 1.1901456 262.5102 3.453009 2000-2012 –> 2013-2019 2.2596141 775.8399
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.1931661 262.9056 3.497480 2000-2012 –> 2013-2019 2.2639678 776.6539
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.1950624 263.1534 3.519214 2000-2012 –> 2013-2019 2.2672406 777.3333
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5385329 6108.9825 13.458633 1982-1999 –> 2000-2012 6.9817398 14959.9600
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 + aou + nitrate + silicate 3.3438101 5980.3843 15.193660 1982-1999 –> 2000-2012 6.6831982 14729.4729
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate 3.9904467 6380.0563 17.799592 1982-1999 –> 2000-2012 7.9826027 15721.3388
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6004284 6148.3804 14.160333 1982-1999 –> 2000-2012 7.1392057 15090.4719
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.6081889 6153.2723 14.267590 1982-1999 –> 2000-2012 7.1588106 15106.4841
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.6380879 6172.0215 14.774574 1982-1999 –> 2000-2012 7.2575738 15189.1618
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6096349 6154.1826 14.304181 1982-1999 –> 2000-2012 7.1649808 15111.8195
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 3.6702662 6190.0286 16.261179 1982-1999 –> 2000-2012 7.5108093 15402.4587
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6126461 3355.3765 10.821609 2000-2012 –> 2013-2019 7.1511790 9464.3590
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 + aou + nitrate + silicate 3.2019551 3206.2174 9.370614 2000-2012 –> 2013-2019 6.5457652 9186.6017
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6537066 3369.3453 10.309180 2000-2012 –> 2013-2019 7.2541351 9517.7258
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.6588360 3371.0793 10.317504 2000-2012 –> 2013-2019 7.2670249 9524.3516
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.6337676 3362.5818 10.363673 2000-2012 –> 2013-2019 7.2718555 9534.6032
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate 3.8397846 3428.7425 11.206273 2000-2012 –> 2013-2019 7.8196717 9802.7788
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6584854 3370.9609 10.318851 2000-2012 –> 2013-2019 7.2681203 9525.1435
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 3.6645903 3371.0217 10.287116 2000-2012 –> 2013-2019 7.3348565 9561.0503
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.3583807 8218.8401 10.684921 1982-1999 –> 2000-2012 6.5236212 19086.3096
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 3.3451130 8206.4897 9.984430 1982-1999 –> 2000-2012 6.5607432 19140.6428
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.2815350 8148.6194 10.449681 1982-1999 –> 2000-2012 6.4073454 18965.1643
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.2947613 8161.1695 10.455973 1982-1999 –> 2000-2012 6.4445084 19009.9221
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.3103382 8175.8853 10.510653 1982-1999 –> 2000-2012 6.4825326 19054.6202
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.3145143 8179.8188 10.520585 1982-1999 –> 2000-2012 6.4936425 19067.7721
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.3258686 8190.4885 11.145018 1982-1999 –> 2000-2012 6.5316513 19113.6924
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 3.4179295 8273.6773 10.821627 1982-1999 –> 2000-2012 6.6469078 19225.3197
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.2593604 8127.4649 9.985777 1982-1999 –> 2000-2012 6.3095645 18840.6336
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 3.4492526 8302.1399 10.919545 1982-1999 –> 2000-2012 6.7116214 19297.2172
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.5190393 3947.3760 11.109784 2000-2012 –> 2013-2019 6.8774200 12166.2161
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 3.4519208 3919.0679 10.234892 2000-2012 –> 2013-2019 6.7970338 12125.5577
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.4178621 3906.4920 10.546763 2000-2012 –> 2013-2019 6.6993971 12055.1115
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.4268245 3910.3417 10.584934 2000-2012 –> 2013-2019 6.7215859 12071.5112
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.4412673 3916.5242 10.744217 2000-2012 –> 2013-2019 6.7516055 12092.4095
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.4448277 3918.0443 10.794175 2000-2012 –> 2013-2019 6.7593420 12097.8631
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.4610820 3924.9641 9.525482 2000-2012 –> 2013-2019 6.7869506 12115.4526
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 3.5774973 3971.5950 11.143465 2000-2012 –> 2013-2019 6.9954268 12245.2722
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.4302888 3911.8270 10.955596 2000-2012 –> 2013-2019 6.6896492 12039.2918
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 3.6090104 3984.4871 11.292419 2000-2012 –> 2013-2019 7.0582630 12286.6269
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.1562430 11692.2135 15.705946 1982-1999 –> 2000-2012 3.8576824 25361.0060
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.0584488 11446.3592 15.019464 1982-1999 –> 2000-2012 3.7431105 25047.7630
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.1203301 11604.5250 15.079101 1982-1999 –> 2000-2012 3.8780807 25503.3052
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.1841990 11763.0024 21.487345 1982-1999 –> 2000-2012 3.9837892 25826.4977
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.2083048 11821.6141 24.431305 1982-1999 –> 2000-2012 4.0228977 25943.2416
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.2438218 11906.8159 15.192665 1982-1999 –> 2000-2012 4.0620723 26042.5430
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2.2592103 11941.3136 16.122729 1982-1999 –> 2000-2012 4.0744471 26063.4253
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.1484086 11674.7761 22.760365 1982-1999 –> 2000-2012 3.7156404 24770.2584
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 2.3267471 12098.6080 16.537660 1982-1999 –> 2000-2012 4.1938950 26418.1489
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.3529180 12158.3363 19.498731 1982-1999 –> 2000-2012 4.2391160 26548.9549
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.6328416 6752.8943 26.902311 2000-2012 –> 2013-2019 4.7890846 18445.1078
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 2.5995484 6716.9561 24.264161 2000-2012 –> 2013-2019 4.8360707 18604.3721
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5343371 6647.2107 25.445252 2000-2012 –> 2013-2019 4.5927859 18093.5699
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5714581 6688.2744 25.212987 2000-2012 –> 2013-2019 4.6917882 18292.7994
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.6068856 6726.9156 25.377739 2000-2012 –> 2013-2019 4.7910846 18489.9181
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.6182643 6739.2152 25.400147 2000-2012 –> 2013-2019 4.8265691 18560.8293
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.6675005 6791.8272 22.032035 2000-2012 –> 2013-2019 4.9113223 18698.6431
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2.7601533 6886.2508 27.686717 2000-2012 –> 2013-2019 5.0193637 18827.5644
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.3244729 6403.1075 22.917547 2000-2012 –> 2013-2019 4.4728815 18077.8835
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 2.8080839 6934.8691 27.945041 2000-2012 –> 2013-2019 5.1348310 19033.4771
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.2099022 10255.0358 10.956753 1982-1999 –> 2000-2012 4.5729303 24224.9117
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1.9771119 9737.6654 9.743648 1982-1999 –> 2000-2012 3.7957715 22102.0078
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.9362557 9642.9858 10.006513 1982-1999 –> 2000-2012 3.5913896 21432.3384
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 2.2579994 10352.7242 10.229612 1982-1999 –> 2000-2012 4.6474158 24388.6087
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.2100456 10255.3364 18.140966 1982-1999 –> 2000-2012 4.6462747 24412.0401
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.9433711 9659.9692 9.780245 1982-1999 –> 2000-2012 3.5783826 21374.4124
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.9684366 9719.3048 9.339418 1982-1999 –> 2000-2012 3.6251231 21514.3993
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.0875930 9991.4197 9.273630 1982-1999 –> 2000-2012 3.9667985 22558.3192
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.9753004 9735.4214 9.239424 1982-1999 –> 2000-2012 3.6435323 21573.0454
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.0626276 9935.7160 14.340241 1982-1999 –> 2000-2012 3.8028987 22032.2421
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.3167718 5828.9576 11.607001 2000-2012 –> 2013-2019 4.5266740 16083.9934
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 2.3351662 5847.3136 13.611619 2000-2012 –> 2013-2019 4.3122781 15584.9790
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3340849 5848.1214 13.744520 2000-2012 –> 2013-2019 4.2703405 15491.1072
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 2.4058006 5924.0180 14.914910 2000-2012 –> 2013-2019 4.6638001 16276.7422
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.4957442 6020.4946 25.558211 2000-2012 –> 2013-2019 4.7057899 16275.8310
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3301867 5843.8189 13.907665 2000-2012 –> 2013-2019 4.2735578 15503.7881
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3540156 5870.0075 13.884121 2000-2012 –> 2013-2019 4.3224522 15589.3122
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.4270934 5948.6992 14.883828 2000-2012 –> 2013-2019 4.5146864 15940.1189
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3578885 5874.2388 13.876581 2000-2012 –> 2013-2019 4.3331890 15609.6602
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.5559660 6081.8672 20.913985 2000-2012 –> 2013-2019 4.6185935 16017.5832
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 2.5924312 11855.4440 13.069770 1982-1999 –> 2000-2012 5.3326841 29283.5153
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.5177324 11711.4321 13.933174 1982-1999 –> 2000-2012 5.1453479 28840.3020
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.7833837 12212.3738 21.243153 1982-1999 –> 2000-2012 5.1761193 28669.2869
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.2210980 11085.3993 14.016845 1982-1999 –> 2000-2012 4.0373466 25564.1467
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.8023109 12246.2184 21.814276 1982-1999 –> 2000-2012 5.2463875 28855.4783
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.8696680 12364.8356 22.709098 1982-1999 –> 2000-2012 5.4021054 29228.9501
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.8849141 12391.2978 22.454726 1982-1999 –> 2000-2012 5.5000493 29486.0028
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.8715160 12368.0505 22.697774 1982-1999 –> 2000-2012 5.4120701 29255.1283
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 2.4583415 11590.2168 14.105424 1982-1999 –> 2000-2012 4.3015537 26172.7141
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.3175625 11297.7160 17.497059 1982-1999 –> 2000-2012 4.1483759 25833.7791
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate_star 3.1237522 6985.0356 21.378502 2000-2012 –> 2013-2019 5.9681741 19303.7417
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 3.0862675 6952.1260 15.715825 2000-2012 –> 2013-2019 5.6786987 18807.5700
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.8793827 6764.9784 17.147392 2000-2012 –> 2013-2019 5.3971151 18476.4106
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.7428537 7477.9330 25.719311 2000-2012 –> 2013-2019 6.6012958 19821.1941
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6849392 7437.4229 23.980995 2000-2012 –> 2013-2019 6.4683230 19649.7968
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8794846 6765.0749 14.381413 2000-2012 –> 2013-2019 5.1005825 17850.4742
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.7104579 7456.2358 24.789558 2000-2012 –> 2013-2019 6.5127688 19702.4542
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.7367783 7475.5046 24.666793 2000-2012 –> 2013-2019 6.6216924 19866.8023
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 3.1786481 7032.5254 12.434604 2000-2012 –> 2013-2019 5.6369895 18622.7422
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.8693849 6755.4967 17.402553 2000-2012 –> 2013-2019 5.1869474 18053.2127
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2.6619219 18044.8615 19.625058 1982-1999 –> 2000-2012 5.1381309 41690.2927
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.6166199 17917.7807 18.949567 1982-1999 –> 2000-2012 4.8633639 40576.9908
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 + nitrate + silicate 2.8224707 18487.2649 13.827754 1982-1999 –> 2000-2012 5.1809520 41639.6960
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 + silicate + phosphate 2.6041209 17881.7733 19.658847 1982-1999 –> 2000-2012 4.7997322 40307.0382
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.5947071 17854.5397 22.096079 1982-1999 –> 2000-2012 4.7604163 40140.4569
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.5969033 17860.9019 21.769808 1982-1999 –> 2000-2012 4.7636531 40151.7007
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.5941074 17852.8013 21.972752 1982-1999 –> 2000-2012 4.7598768 40139.0013
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 2.6488317 18007.7901 24.114223 1982-1999 –> 2000-2012 4.8209797 40321.8752
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 3.0011240 10093.7734 14.392043 2000-2012 –> 2013-2019 5.6630459 28138.6349
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.0010230 10095.6386 14.411490 2000-2012 –> 2013-2019 5.6176429 28013.4193
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 + nitrate + silicate 3.3187334 10498.5610 16.109561 2000-2012 –> 2013-2019 6.1412041 28985.8259
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 + silicate + phosphate 3.0000950 10094.4003 14.405089 2000-2012 –> 2013-2019 5.6042159 27976.1735
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.9648162 10047.0373 15.888668 2000-2012 –> 2013-2019 5.5595233 27901.5769
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.9855177 10074.8976 15.644630 2000-2012 –> 2013-2019 5.5824210 27935.7995
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.9665985 10049.4436 15.764128 2000-2012 –> 2013-2019 5.5607059 27902.2449
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 3.1365845 10270.5403 18.803814 2000-2012 –> 2013-2019 5.7854162 28278.3305
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.7700096 5181.8213 12.243782 1982-1999 –> 2000-2012 3.5500394 11882.9673
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5878549 4901.6758 12.822888 1982-1999 –> 2000-2012 3.1163377 11094.1297
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 + nitrate + silicate 1.7589195 5167.4921 14.092507 1982-1999 –> 2000-2012 3.4890179 11775.2677
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 + silicate + phosphate 1.6156555 4946.7689 12.930476 1982-1999 –> 2000-2012 3.1746413 11205.4577
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.6610165 5018.7049 13.140037 1982-1999 –> 2000-2012 3.2673240 11377.6273
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.6571869 5012.7080 13.065690 1982-1999 –> 2000-2012 3.2589745 11362.1850
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.6651339 5025.1368 13.155852 1982-1999 –> 2000-2012 3.2750218 11391.5224
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.7839394 5202.1873 13.100644 1982-1999 –> 2000-2012 3.4925351 11766.0412
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.8581579 2686.5437 11.776253 2000-2012 –> 2013-2019 3.6281675 7868.3650
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.7304708 2595.1396 12.144692 2000-2012 –> 2013-2019 3.3183257 7496.8155
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 + nitrate + silicate 1.9432112 2747.2639 13.161242 2000-2012 –> 2013-2019 3.7021307 7914.7560
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 + silicate + phosphate 1.7606499 2617.8234 12.187032 2000-2012 –> 2013-2019 3.3763054 7564.5923
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.8117847 2655.3852 12.335194 2000-2012 –> 2013-2019 3.4728013 7674.0901
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.8065490 2651.5883 12.287919 2000-2012 –> 2013-2019 3.4637358 7664.2963
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.8147710 2657.5459 12.344435 2000-2012 –> 2013-2019 3.4799048 7682.6828
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.8598127 2687.7116 12.393512 2000-2012 –> 2013-2019 3.6437522 7889.8989
Atlantic (27.85,27.95] 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 ~ aou + silicate + phosphate + phosphate_star 3.3547203 6522.1640 37.787209 1982-1999 –> 2000-2012 6.5127716 15319.7804
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 + aou + silicate + phosphate + phosphate_star 3.3547202 6524.1639 37.769942 1982-1999 –> 2000-2012 6.4198126 15221.5995
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 + silicate + phosphate 3.5723212 6679.7736 48.930358 1982-1999 –> 2000-2012 6.6446587 15385.2836
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 ~ temp + aou + silicate + phosphate + phosphate_star 3.1015239 6329.8603 23.435647 1982-1999 –> 2000-2012 6.2545453 15124.0252
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 ~ aou + silicate + phosphate + phosphate_star 3.6760448 3864.6187 23.747093 2000-2012 –> 2013-2019 7.0307651 10386.7827
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 + aou + silicate + phosphate + phosphate_star 3.3388618 3730.3890 25.099121 2000-2012 –> 2013-2019 6.6935821 10254.5529
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 + 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 + silicate + phosphate 3.3614399 3739.9320 25.280442 2000-2012 –> 2013-2019 6.9337610 10419.7056
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.3786842 3747.1776 25.710784 2000-2012 –> 2013-2019 7.0716128 10509.1648
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.6198780 3842.8164 23.176587 2000-2012 –> 2013-2019 6.7363232 10182.5601
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.6162841 3843.4099 23.009079 2000-2012 –> 2013-2019 6.7178080 10173.2702
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.8909023 10418.8133 26.501166 1982-1999 –> 2000-2012 8.0292647 25225.2468
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 + 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 + aou + silicate + phosphate 3.8776148 10405.9987 25.952066 1982-1999 –> 2000-2012 8.0063456 25200.2924
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.8714512 10400.0396 25.669358 1982-1999 –> 2000-2012 7.9933467 25185.7007
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.8926869 10418.5310 26.101297 1982-1999 –> 2000-2012 8.0317475 25223.8434
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.8739353 10402.4424 25.781312 1982-1999 –> 2000-2012 7.9982193 25191.1218
Atlantic (27.95,28.05] cstar_tref ~ temp + 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 + nitrate + silicate + phosphate_star 3.3840311 9895.9711 24.001342 1982-1999 –> 2000-2012 6.6687908 23498.8599
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.7829465 5424.9013 25.453790 2000-2012 –> 2013-2019 7.6738488 15843.7146
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 + silicate + phosphate 3.7794327 5423.0725 25.038717 2000-2012 –> 2013-2019 7.6570474 15829.0712
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.7782083 5422.4349 24.786112 2000-2012 –> 2013-2019 7.6496595 15822.4744
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.8060168 5434.8667 24.881092 2000-2012 –> 2013-2019 7.6987037 15853.3978
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.7787244 5422.7037 24.911551 2000-2012 –> 2013-2019 7.6526597 15825.1461
Atlantic (27.95,28.05] cstar_tref ~ temp + 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 + nitrate + silicate + phosphate_star 3.2118152 5102.8048 25.221935 2000-2012 –> 2013-2019 6.5958463 14998.7759
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 + aou + silicate + phosphate + phosphate_star 1.1400058 3892.0296 7.508830 1982-1999 –> 2000-2012 2.1717216 8659.6599
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 + silicate + phosphate 1.1473329 3908.0592 7.366582 1982-1999 –> 2000-2012 2.1841723 8691.9281
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.1559549 3926.7909 7.275281 1982-1999 –> 2000-2012 2.2007441 8735.6975
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.1566552 3926.3062 7.730772 1982-1999 –> 2000-2012 2.1978100 8721.7900
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.1514385 3916.9963 7.337089 1982-1999 –> 2000-2012 2.1925930 8714.4792
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.0870369 3772.9900 12.684409 1982-1999 –> 2000-2012 2.1112381 8516.6574
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 + aou + silicate + phosphate + phosphate_star 1.2235483 2260.2814 7.594756 2000-2012 –> 2013-2019 2.3635541 6152.3110
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 + silicate + phosphate 1.2310580 2268.7621 7.450137 2000-2012 –> 2013-2019 2.3783909 6176.8213
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2386232 2277.2534 7.367325 2000-2012 –> 2013-2019 2.3945781 6204.0443
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.2569957 2295.6610 8.240693 2000-2012 –> 2013-2019 2.4136509 6221.9671
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2343138 2272.4229 7.428694 2000-2012 –> 2013-2019 2.3857523 6189.4192
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.2275125 2264.7647 13.894436 2000-2012 –> 2013-2019 2.3145494 6037.7546
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.7943969 3337.7911 5.398179 1982-1999 –> 2000-2012 1.4671003 7210.6600
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 + 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 + aou + silicate + phosphate 0.7972728 3347.8948 5.317335 1982-1999 –> 2000-2012 1.4740772 7243.7012
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.8011440 3361.4382 5.239412 1982-1999 –> 2000-2012 1.4841616 7291.7327
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.8168537 3413.7344 5.415135 1982-1999 –> 2000-2012 1.5096886 7395.8884
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8127139 3401.5284 5.436958 1982-1999 –> 2000-2012 1.5031113 7372.3809
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.8094433 3388.2539 5.337970 1982-1999 –> 2000-2012 1.5291408 7513.9673
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.7991765 3354.5633 5.281963 1982-1999 –> 2000-2012 1.4793572 7269.1497
Atlantic (28.1,28.15] cstar_tref ~ 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 + aou + silicate + phosphate + phosphate_star 0.8779548 1849.2204 7.088283 2000-2012 –> 2013-2019 1.6723517 5187.0115
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 + aou + silicate + phosphate 0.8845179 1859.8258 6.949110 2000-2012 –> 2013-2019 1.6817907 5207.7206
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.8918126 1871.5215 6.848206 2000-2012 –> 2013-2019 1.6929566 5232.9597
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.8879019 1863.2634 6.924296 2000-2012 –> 2013-2019 1.6973452 5251.5173
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.8876626 1864.8796 6.919523 2000-2012 –> 2013-2019 1.6868392 5219.4429
Atlantic (28.15,28.2] cstar_tref ~ aou + nitrate + silicate + phosphate_star 0.7770053 4708.8542 16.122287 1982-1999 –> 2000-2012 1.3657554 9801.6574
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 + nitrate + silicate + phosphate_star 0.6531656 4011.8744 7.988766 1982-1999 –> 2000-2012 1.1941366 8623.0669
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 + nitrate + silicate 0.6658899 4089.5505 7.861172 1982-1999 –> 2000-2012 1.2128558 8763.7158
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.7318765 4469.9570 8.923396 1982-1999 –> 2000-2012 1.3696404 10021.6876
Atlantic (28.15,28.2] cstar_tref ~ 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 + aou + nitrate + silicate 0.7176256 4388.7903 12.118912 1982-1999 –> 2000-2012 1.2777278 9196.5647
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.7173564 4389.2800 12.253531 1982-1999 –> 2000-2012 1.2757504 9181.6009
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 + aou + nitrate + silicate 0.8313687 2673.0573 6.109030 2000-2012 –> 2013-2019 1.5901181 7286.1909
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.7354711 2410.8135 6.061562 2000-2012 –> 2013-2019 1.3886368 6422.6879
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 + nitrate + silicate 0.7554349 2468.5561 5.925970 2000-2012 –> 2013-2019 1.4213248 6558.1065
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8121334 2624.5880 6.619729 2000-2012 –> 2013-2019 1.5440099 7094.5450
Atlantic (28.15,28.2] cstar_tref ~ 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 + aou + nitrate + silicate 0.8758629 2785.4631 11.227380 2000-2012 –> 2013-2019 1.5934885 7174.2534
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.8756887 2787.0340 11.132298 2000-2012 –> 2013-2019 1.5930451 7176.3139
Atlantic (28.2, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate_star 0.5786277 7379.0689 6.882067 1982-1999 –> 2000-2012 1.1067223 16653.5526
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 + aou + nitrate + silicate 0.3534411 3213.7066 1.988553 1982-1999 –> 2000-2012 0.6596790 6021.1606
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.3490030 3108.9287 2.067840 1982-1999 –> 2000-2012 0.6550932 5912.6573
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 + nitrate + silicate 0.3509290 3155.4335 2.134668 1982-1999 –> 2000-2012 0.6570626 5960.8427
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.5229331 6525.8802 2.014189 1982-1999 –> 2000-2012 0.9707675 13845.9018
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.5696464 7248.8817 8.521425 1982-1999 –> 2000-2012 1.0936375 16432.7869
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 + aou + nitrate + silicate 0.4165997 2616.6231 2.435991 2000-2012 –> 2013-2019 0.7700408 5830.3298
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.4134611 2582.3694 2.655486 2000-2012 –> 2013-2019 0.7624641 5691.2982
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 0.5986382 4354.6000 4.314619 2000-2012 –> 2013-2019 1.1608508 11490.4847
Atlantic (28.2, Inf] cstar_tref ~ sal + 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 + nitrate + silicate 0.4031930 2461.8100 2.685125 2000-2012 –> 2013-2019 0.7541221 5617.2435
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.5828792 4228.7081 2.387587 2000-2012 –> 2013-2019 1.1058122 10754.5883
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.7432499 5393.9015 11.501170 2000-2012 –> 2013-2019 1.3128963 12642.7832
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 + aou + silicate + phosphate + phosphate_star 6.2388929 36528.0930 29.366420 1982-1999 –> 2000-2012 12.7725705 87200.2068
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 + aou + silicate + phosphate 6.3773992 36774.8088 29.718986 1982-1999 –> 2000-2012 13.0347184 87735.0625
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.4461499 36895.2887 29.845366 1982-1999 –> 2000-2012 13.1621308 87990.3838
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 + silicate + phosphate + phosphate_star 6.4520118 36905.5018 29.937685 1982-1999 –> 2000-2012 13.1783795 88024.3492
Indo-Pacific (-Inf,26] cstar_tref ~ sal + 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 + aou + silicate + phosphate + phosphate_star 5.9243606 18984.6030 23.875073 2000-2012 –> 2013-2019 12.1632535 55512.6960
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 + silicate + phosphate 6.0470335 19106.1797 24.650519 2000-2012 –> 2013-2019 12.4244327 55880.9886
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.1110238 19168.6229 24.877741 2000-2012 –> 2013-2019 12.5571737 56063.9116
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 5.9978940 19055.7781 27.345614 2000-2012 –> 2013-2019 12.4545857 55967.4267
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.9955754 19055.4845 27.200018 2000-2012 –> 2013-2019 12.4477444 55961.2600
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.1120038 19169.5741 24.949991 2000-2012 –> 2013-2019 12.5640157 56075.0760
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.9432773 36058.7225 42.584321 1982-1999 –> 2000-2012 9.6357525 85543.0229
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.5539940 35080.7012 44.753312 1982-1999 –> 2000-2012 8.8237082 82991.6211
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 + silicate + phosphate 4.6161138 35242.5790 40.891373 1982-1999 –> 2000-2012 8.9414393 83369.4242
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.6965239 35448.9144 39.546419 1982-1999 –> 2000-2012 9.0854971 83819.5071
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7055211 35471.7817 39.423783 1982-1999 –> 2000-2012 9.1078292 83892.9940
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.8068077 35726.2342 48.677503 1982-1999 –> 2000-2012 9.2716544 84382.8177
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4.9509994 36077.3723 41.437095 1982-1999 –> 2000-2012 9.6267773 85502.1927
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.9361025 36043.3683 42.245436 1982-1999 –> 2000-2012 9.6093231 85461.0601
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate_star 4.9950409 36183.1857 49.382037 1982-1999 –> 2000-2012 9.6928243 85686.3507
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.9160569 19062.4030 39.841092 2000-2012 –> 2013-2019 9.8593342 55121.1254
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.5800051 18616.4801 45.821666 2000-2012 –> 2013-2019 9.1339991 53697.1812
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 + silicate + phosphate 4.6574285 18722.5251 39.739545 2000-2012 –> 2013-2019 9.2735423 53965.1042
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.7355004 18827.6881 36.855147 2000-2012 –> 2013-2019 9.4320243 54276.6026
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.7937328 18905.0044 37.001566 2000-2012 –> 2013-2019 9.7285730 54945.3169
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7403369 18834.1457 36.682469 2000-2012 –> 2013-2019 9.4458580 54305.9273
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 4.8209449 18938.8131 35.204419 2000-2012 –> 2013-2019 9.7561731 54978.0648
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.6921156 18769.4646 45.154919 2000-2012 –> 2013-2019 9.4989234 54495.6988
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.9051301 19050.3267 38.488949 2000-2012 –> 2013-2019 9.8412326 55093.6949
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.2530081 28580.1873 22.088300 1982-1999 –> 2000-2012 8.3293645 67751.7414
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.0892195 28190.7985 20.072352 1982-1999 –> 2000-2012 7.9721607 66690.3175
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 + 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 + silicate + phosphate 4.2360966 28542.4799 19.954055 1982-1999 –> 2000-2012 8.2115795 67368.5892
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.3283079 28757.0921 23.063837 1982-1999 –> 2000-2012 8.3732971 67823.5361
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.3558684 28818.3495 29.623845 1982-1999 –> 2000-2012 8.4247316 67964.3918
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.2059512 28471.3051 25.457852 1982-1999 –> 2000-2012 8.2380439 67493.4699
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.3227555 28744.2995 22.662236 1982-1999 –> 2000-2012 8.3705239 67820.2670
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.1256713 28279.2431 22.364969 1982-1999 –> 2000-2012 8.1263545 67192.9706
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.5664310 15869.5452 24.381318 2000-2012 –> 2013-2019 8.8194391 44449.7325
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.4241171 15700.6380 23.915080 2000-2012 –> 2013-2019 8.5133365 43891.4365
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 + silicate + phosphate 4.5675473 15872.8646 23.790924 2000-2012 –> 2013-2019 8.8036439 44415.3445
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.6634756 15985.0601 27.009578 2000-2012 –> 2013-2019 8.9917834 44742.1522
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.5305607 15828.9753 33.448696 2000-2012 –> 2013-2019 8.7365118 44300.2804
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.6524894 15972.3285 26.300399 2000-2012 –> 2013-2019 8.9752449 44716.6280
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.6288162 15944.7918 34.660703 2000-2012 –> 2013-2019 8.9783869 44750.7221
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.4602774 15744.5790 23.480597 2000-2012 –> 2013-2019 8.5859487 44023.8221
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.6594536 15978.4026 35.975237 2000-2012 –> 2013-2019 9.0109131 44786.6597
Indo-Pacific (26.75,27] 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 ~ aou + silicate + phosphate + phosphate_star 4.6600497 36306.2261 18.631871 1982-1999 –> 2000-2012 8.7902595 85090.8415
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 + aou + silicate + phosphate + phosphate_star 4.4299290 35686.8420 20.567849 1982-1999 –> 2000-2012 8.2355276 83066.3715
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 + silicate + phosphate 4.6904849 36388.1022 20.587989 1982-1999 –> 2000-2012 8.7566764 84906.1856
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7909596 36648.1617 19.879630 1982-1999 –> 2000-2012 8.9806257 85680.4708
Indo-Pacific (26.75,27] cstar_tref ~ 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 ~ temp + aou + silicate + phosphate + phosphate_star 4.3524014 35470.2051 23.266241 1982-1999 –> 2000-2012 8.1741859 82922.6919
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 ~ aou + silicate + phosphate + phosphate_star 5.0323654 19908.3367 20.355745 2000-2012 –> 2013-2019 9.6924151 56214.5628
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 + aou + silicate + phosphate + phosphate_star 4.8272468 19637.5164 21.530173 2000-2012 –> 2013-2019 9.2571758 55324.3583
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 + silicate + phosphate 5.0760152 19966.9571 21.685280 2000-2012 –> 2013-2019 9.7665001 56355.0592
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.1689570 20085.9117 20.758325 2000-2012 –> 2013-2019 9.9599166 56734.0734
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.8134874 19616.8027 28.200886 2000-2012 –> 2013-2019 9.2282396 55259.5358
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.7660416 19553.8606 26.508381 2000-2012 –> 2013-2019 9.1184429 55024.0656
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.4247843 45196.9766 41.955348 1982-1999 –> 2000-2012 8.1249236 103633.3899
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.3779276 45033.4517 44.485161 1982-1999 –> 2000-2012 7.9995288 103012.2726
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 + aou + silicate + phosphate 4.5714513 45705.9846 41.262834 1982-1999 –> 2000-2012 8.3880300 104808.1355
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.6445272 45952.5578 75.011259 1982-1999 –> 2000-2012 8.2923633 104086.0006
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.1791804 44311.0866 51.794122 1982-1999 –> 2000-2012 7.6800403 101563.5385
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 + aou + silicate + phosphate 4.5743610 45713.8775 40.477243 1982-1999 –> 2000-2012 8.4103418 104922.6546
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.0073313 43658.2318 33.755013 1982-1999 –> 2000-2012 7.3874781 100158.9966
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.6885919 46097.3735 74.666491 1982-1999 –> 2000-2012 8.3845011 104509.2823
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.1723556 25508.4330 36.033755 2000-2012 –> 2013-2019 9.5971399 70705.4095
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.1179855 25422.4495 38.508960 2000-2012 –> 2013-2019 9.4959131 70455.9013
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 + aou + silicate + phosphate 5.3049828 25721.2332 34.661205 2000-2012 –> 2013-2019 9.8764341 71427.2178
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.3928334 25857.9827 33.129925 2000-2012 –> 2013-2019 10.0803668 71953.8454
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.0612734 25329.6746 41.047414 2000-2012 –> 2013-2019 9.2404538 69640.7612
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 (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate 5.3069909 25722.3843 34.100429 2000-2012 –> 2013-2019 9.8813519 71436.2618
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.5859941 24508.6376 29.369756 2000-2012 –> 2013-2019 8.5933254 68166.8694
Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 5.3936438 25857.2339 32.776574 2000-2012 –> 2013-2019 10.0822286 71954.5835
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.3410751 38610.1487 32.628605 1982-1999 –> 2000-2012 6.1643125 87092.3486
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.7883105 40455.1240 30.730003 1982-1999 –> 2000-2012 6.8816109 90737.5631
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6005006 39709.5681 33.071824 1982-1999 –> 2000-2012 6.5718587 89200.5563
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 3.6276227 39817.9010 32.134599 1982-1999 –> 2000-2012 6.6005742 89317.4660
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.6841067 40045.0553 31.160905 1982-1999 –> 2000-2012 6.6782498 89684.7454
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5414587 39466.4822 33.401271 1982-1999 –> 2000-2012 6.4799341 88737.9332
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.5702464 39585.5086 33.491300 1982-1999 –> 2000-2012 6.5347769 89031.1136
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.5492843 39498.9338 33.569547 1982-1999 –> 2000-2012 6.5016885 88863.6767
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.5962591 39692.2384 33.645030 1982-1999 –> 2000-2012 6.6115668 89472.8886
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.3267764 38547.0941 33.862527 1982-1999 –> 2000-2012 6.1814837 87247.9800
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.8645078 21675.9023 31.423341 2000-2012 –> 2013-2019 7.2055829 60286.0510
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.1766045 22283.0815 32.589678 2000-2012 –> 2013-2019 7.7771051 61992.6496
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 4.2181404 22358.4466 30.995118 2000-2012 –> 2013-2019 7.8457631 62176.3477
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.2938391 22497.5043 29.598350 2000-2012 –> 2013-2019 7.9779458 62542.5596
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.1032514 22144.5551 33.161694 2000-2012 –> 2013-2019 7.6447101 61611.0373
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.1338823 22202.6998 33.279262 2000-2012 –> 2013-2019 7.7041287 61788.2084
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate 4.1120690 22159.3373 34.196766 2000-2012 –> 2013-2019 7.7059173 61839.7167
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.1066786 22151.0822 33.387214 2000-2012 –> 2013-2019 7.6559629 61650.0160
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.1716917 22273.8800 31.636730 2000-2012 –> 2013-2019 7.7679508 61966.1184
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.7917291 21527.2650 33.525325 2000-2012 –> 2013-2019 7.1185055 60074.3591
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.1665684 40099.8982 25.053065 1982-1999 –> 2000-2012 5.4126159 87960.3441
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.1083250 39810.5151 10.089971 1982-1999 –> 2000-2012 5.3835324 87947.9588
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3.2953018 40719.0689 23.187702 1982-1999 –> 2000-2012 5.5939901 89074.9955
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.0654649 39594.0798 11.583687 1982-1999 –> 2000-2012 5.5343465 89485.8209
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate 3.1037038 39785.3228 10.315295 1982-1999 –> 2000-2012 5.5838689 89772.9833
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.0515401 39523.1104 9.456817 1982-1999 –> 2000-2012 5.2990528 87397.5594
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.0584885 39558.5637 9.504795 1982-1999 –> 2000-2012 5.3187867 87554.8273
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.2472499 40492.0922 24.685745 1982-1999 –> 2000-2012 5.5601714 88982.5727
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.0631121 39580.1107 12.814094 1982-1999 –> 2000-2012 5.3715286 88026.7251
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.0476098 39503.0203 9.397780 1982-1999 –> 2000-2012 5.3021483 87444.4940
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.8192180 22797.6918 27.801018 2000-2012 –> 2013-2019 6.9857864 62897.5899
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6620606 22450.6932 12.124587 2000-2012 –> 2013-2019 6.7703856 62261.2083
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.5489940 22191.7072 10.708006 2000-2012 –> 2013-2019 6.6144589 61785.7870
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate 3.5990796 22305.4345 10.796496 2000-2012 –> 2013-2019 6.7027833 62090.7573
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5857892 22276.8837 11.095529 2000-2012 –> 2013-2019 6.6373294 61799.9940
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.5893554 22285.0923 11.103375 2000-2012 –> 2013-2019 6.6478438 61843.6560
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate 3.9605093 23095.6795 23.241015 2000-2012 –> 2013-2019 7.2633690 63850.4592
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.9481443 23071.8571 26.890775 2000-2012 –> 2013-2019 7.1953942 63563.9492
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.6764968 22481.1829 17.935126 2000-2012 –> 2013-2019 6.7396089 62061.2936
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.5747323 22251.3804 10.907617 2000-2012 –> 2013-2019 6.6223421 61754.4007
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.6639007 15771.6562 22.864245 1982-1999 –> 2000-2012 4.7506750 34989.3863
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.6510177 15741.8056 24.056369 1982-1999 –> 2000-2012 4.7356239 34952.2697
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.6593461 15762.4135 23.912453 1982-1999 –> 2000-2012 4.7528486 35010.8379
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.6573761 15757.5448 23.706051 1982-1999 –> 2000-2012 4.7545379 35021.5368
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.6467606 15731.2467 24.736227 1982-1999 –> 2000-2012 4.7461667 35004.7731
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.6561934 15754.6200 23.637730 1982-1999 –> 2000-2012 4.7537252 35020.1848
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 2.6677616 15781.1714 25.028220 1982-1999 –> 2000-2012 4.7671809 35052.7536
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.6591998 15762.0521 23.846206 1982-1999 –> 2000-2012 4.7566374 35027.2164
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.5894484 15587.4191 22.616594 1982-1999 –> 2000-2012 4.6493209 34691.4864
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.6593135 15760.3330 23.663705 1982-1999 –> 2000-2012 4.7609594 35041.3641
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.0795402 9329.0983 30.362926 2000-2012 –> 2013-2019 5.7305656 25070.9231
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.1032714 9357.2099 28.842289 2000-2012 –> 2013-2019 5.7542891 25099.0156
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate_star 3.1060870 9358.5309 28.182934 2000-2012 –> 2013-2019 5.7692100 25128.2689
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3.0828431 9331.0238 29.216505 2000-2012 –> 2013-2019 5.7338757 25070.8666
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.1047580 9356.9638 28.278040 2000-2012 –> 2013-2019 5.7641736 25117.5490
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + 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 + silicate + phosphate_star 3.1060122 9360.4427 28.288842 2000-2012 –> 2013-2019 5.7633883 25117.9875
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.0827974 9332.9695 29.138730 2000-2012 –> 2013-2019 5.7295579 25064.2162
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.1047122 9358.9097 28.180344 2000-2012 –> 2013-2019 5.7609056 25113.5296
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.0638417 9310.3829 25.606619 2000-2012 –> 2013-2019 5.6532901 24897.8020
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.7768689 19763.4849 35.768682 1982-1999 –> 2000-2012 4.8904390 43928.0663
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.7754984 19761.4892 36.065886 1982-1999 –> 2000-2012 4.8884009 43924.5497
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 + nitrate + phosphate_star 2.7586348 19710.1611 34.012716 1982-1999 –> 2000-2012 4.8770280 43900.1434
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.7582987 19711.1748 33.775588 1982-1999 –> 2000-2012 4.8681472 43858.1163
Indo-Pacific (27.85,27.95] cstar_tref ~ 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 + nitrate + silicate + phosphate_star 2.7460735 19675.2212 30.486126 1982-1999 –> 2000-2012 4.8570747 43828.2496
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.7622174 19722.6658 36.840204 1982-1999 –> 2000-2012 4.8659967 43837.5037
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 2.7606894 19714.1870 33.644807 1982-1999 –> 2000-2012 4.8793078 43903.3543
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.7599939 19714.1477 33.348940 1982-1999 –> 2000-2012 4.8710511 43865.4716
Indo-Pacific (27.85,27.95] cstar_tref ~ 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 + nitrate + silicate 3.0859175 10920.1539 36.636123 2000-2012 –> 2013-2019 5.8395905 30617.7436
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 + phosphate_star 3.0936018 10928.8082 38.482684 2000-2012 –> 2013-2019 5.8522366 30638.9693
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate 3.0891329 10922.6153 38.170291 2000-2012 –> 2013-2019 5.8479314 30633.2568
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.0826259 10915.5819 37.073345 2000-2012 –> 2013-2019 5.8409245 30626.7566
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.1048401 10946.3428 35.696250 2000-2012 –> 2013-2019 5.8509136 30621.5640
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 + aou + silicate + phosphate + phosphate_star 3.0518298 10872.5687 40.735383 2000-2012 –> 2013-2019 5.8140473 30595.2345
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.2143379 17725.1356 8.493771 1982-1999 –> 2000-2012 4.2244267 41531.3014
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.2539713 17867.0577 8.649145 1982-1999 –> 2000-2012 4.2188053 41417.3211
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.2426483 17826.7679 8.852835 1982-1999 –> 2000-2012 4.1979448 41322.3483
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.2586209 17883.5434 8.671942 1982-1999 –> 2000-2012 4.2267749 41452.7800
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.2587157 17883.8792 8.665561 1982-1999 –> 2000-2012 4.2277417 41458.0938
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate 2.2436028 17828.1719 8.852520 1982-1999 –> 2000-2012 4.2347576 41525.9800
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.2419974 17824.4454 8.822692 1982-1999 –> 2000-2012 4.2017336 41345.5145
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.2584202 17882.8325 8.669948 1982-1999 –> 2000-2012 4.2270436 41454.7490
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate_star 2.2644434 17902.1400 8.476091 1982-1999 –> 2000-2012 4.2518453 41578.7467
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.2544584 17868.7863 8.194285 1982-1999 –> 2000-2012 4.2163154 41402.0101
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 + nitrate + silicate + phosphate_star 2.3842351 10130.7263 8.366988 2000-2012 –> 2013-2019 4.5985730 27855.8620
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.4636685 10275.6491 8.995974 2000-2012 –> 2013-2019 4.7176398 28142.7068
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 + nitrate + silicate 2.4750570 10296.0430 8.900837 2000-2012 –> 2013-2019 4.7177053 28122.8109
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.4692392 10285.6366 9.060557 2000-2012 –> 2013-2019 4.7279549 28169.5158
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate 2.4800741 10302.9977 8.895172 2000-2012 –> 2013-2019 4.7236769 28131.1695
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.4526233 10255.7797 8.813300 2000-2012 –> 2013-2019 4.6946206 28080.2251
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.4690447 10285.2882 9.057342 2000-2012 –> 2013-2019 4.7274648 28168.1207
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.4590057 10267.2720 8.013161 2000-2012 –> 2013-2019 4.7134641 28136.0583
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.9269949 10724.6353 8.965614 1982-1999 –> 2000-2012 3.5762170 25182.8526
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1.9234948 10713.2506 8.647099 1982-1999 –> 2000-2012 3.5598308 25110.4332
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.8928438 10632.3315 8.764850 1982-1999 –> 2000-2012 3.5243069 25009.0683
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate_star 1.9323668 10737.0055 8.825899 1982-1999 –> 2000-2012 3.5832870 25200.9675
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.9179397 10698.3211 8.633406 1982-1999 –> 2000-2012 3.5605064 25124.1057
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.8951875 10638.7192 8.767010 1982-1999 –> 2000-2012 3.5273132 25018.5120
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.8958513 10640.5267 8.767085 1982-1999 –> 2000-2012 3.5288463 25024.3270
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.9072203 10671.3898 8.712059 1982-1999 –> 2000-2012 3.5597902 25144.8684
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 1.8952781 10636.9658 8.797017 1982-1999 –> 2000-2012 3.5744229 25228.5072
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.8951582 10638.6392 8.762353 1982-1999 –> 2000-2012 3.5277325 25020.5004
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.0709455 6313.1331 8.713211 2000-2012 –> 2013-2019 3.9979404 17037.7684
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.0594409 6296.7886 8.802893 2000-2012 –> 2013-2019 3.9522847 16929.1201
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.0718737 6312.4479 8.608198 2000-2012 –> 2013-2019 3.9989240 17035.2315
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.0728445 6313.8223 8.661407 2000-2012 –> 2013-2019 3.9907842 17012.1434
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.0619981 6300.4294 8.794721 2000-2012 –> 2013-2019 3.9698425 16973.5081
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate 2.0621507 6298.6466 8.806887 2000-2012 –> 2013-2019 3.9888742 17020.5547
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.0621501 6300.6457 8.807529 2000-2012 –> 2013-2019 3.9573376 16939.3649
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.0621491 6300.6443 8.805830 2000-2012 –> 2013-2019 3.9580004 16941.1710
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.0624051 6301.0085 8.735205 2000-2012 –> 2013-2019 3.9696254 16972.3983
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.0613801 6299.5499 8.800503 2000-2012 –> 2013-2019 3.9565382 16938.1891
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.6396635 76233.5531 7.832848 1982-1999 –> 2000-2012 3.1325623 176852.8215
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.5851502 74884.6921 12.511212 1982-1999 –> 2000-2012 2.9820417 171826.9471
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5311977 73507.2840 14.214366 1982-1999 –> 2000-2012 2.8643992 167871.4547
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5313000 73509.9446 14.202239 1982-1999 –> 2000-2012 2.8640690 167856.1779
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5314928 73514.9585 14.185354 1982-1999 –> 2000-2012 2.8636804 167837.0700
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5281199 73427.1334 14.378394 1982-1999 –> 2000-2012 2.8513606 167376.6806
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5314910 73514.9130 14.185270 1982-1999 –> 2000-2012 2.8636761 167836.9173
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.5317666 73520.0807 14.250129 1982-1999 –> 2000-2012 2.8640890 167845.7842
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.5308210 73497.4825 10.138151 1982-1999 –> 2000-2012 2.7926269 164818.6463
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.5798847 74754.1507 14.936959 1982-1999 –> 2000-2012 2.9694396 171407.2658
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.7989953 42978.0695 14.155567 2000-2012 –> 2013-2019 3.4386588 119211.6226
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.7754628 42694.0808 15.096407 2000-2012 –> 2013-2019 3.3606130 117578.7729
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.7314864 42158.9485 16.581456 2000-2012 –> 2013-2019 3.2626842 115666.2325
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.7317874 42162.6704 16.576870 2000-2012 –> 2013-2019 3.2630874 115672.6150
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.7322153 42167.9616 16.575055 2000-2012 –> 2013-2019 3.2637081 115682.9201
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.7344727 42195.8521 17.075855 2000-2012 –> 2013-2019 3.2625926 115622.9856
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.7322017 42167.7935 16.574226 2000-2012 –> 2013-2019 3.2636927 115682.7065
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.7349951 42200.3016 16.913655 2000-2012 –> 2013-2019 3.2667617 115720.3823
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.7932852 42909.9867 20.922377 2000-2012 –> 2013-2019 3.3241063 116407.4692
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.7819870 42774.6330 17.106634 2000-2012 –> 2013-2019 3.3618717 117528.7837

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
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19

6.1.2 Best models

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

Version Author Date
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19

6.2 RMSE correlation between eras

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

6.2.1 All models

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

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

Version Author Date
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 
rm(max_rmse)

6.2.2 Best models

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

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

Version Author Date
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 
rm(max_rmse)

6.3 Predictor counts

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

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

# print table
lm_all_stats %>%
  gt(rowname_col = "gamma_slab",
     groupname_col = c("basin", "eras")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )
aou nitrate phosphate phosphate_star sal silicate temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26] 8 1 7 8 10 4 8
(26,26.5] 7 4 3 6 10 8 9
(26.5,26.75] 9 1 7 7 5 10 7
(26.75,27] 8 1 7 8 4 10 8
(27,27.25] 8 4 4 7 9 10 6
(27.25,27.5] 8 6 3 6 8 10 7
(27.5,27.75] 7 3 5 7 10 8 8
(27.75,27.85] 7 3 5 7 10 8 8
(27.85,27.95] 10 1 9 8 6 4 6
(27.95,28.05] 8 3 5 9 8 5 9
(28.05,28.1] 8 1 8 8 9 5 8
(28.1,28.15] 6 3 5 9 10 5 9
(28.15,28.2] 9 10 NA 7 6 6 7
(28.2, Inf] 9 10 NA 6 8 6 5
total 112.00 51.00 — 103.00 113.00 99.00 105.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 9 2 6 7 10 5 8
(26,26.5] 6 4 4 6 10 8 9
(26.5,26.75] 9 1 7 7 5 10 7
(26.75,27] 9 1 7 7 5 10 7
(27,27.25] 8 4 4 7 9 10 6
(27.25,27.5] 9 7 3 5 7 10 5
(27.5,27.75] 7 3 5 7 10 8 8
(27.75,27.85] 7 3 5 7 10 8 8
(27.85,27.95] 9 2 8 9 6 5 6
(27.95,28.05] 8 3 6 8 8 5 9
(28.05,28.1] 8 1 8 8 9 5 8
(28.1,28.15] 8 1 7 8 10 4 8
(28.15,28.2] 9 10 NA 6 7 6 7
(28.2, Inf] 8 10 NA 6 9 6 5
total 114.00 52.00 — 98.00 115.00 100.00 101.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 8 1 7 8 10 4 8
(26,26.5] 9 2 6 8 5 9 8
(26.5,26.75] 7 3 6 9 8 7 8
(26.75,27] 9 NA 10 8 6 5 6
(27,27.25] 8 3 7 8 4 8 8
(27.25,27.5] 8 2 6 8 8 10 5
(27.5,27.75] 7 3 4 6 10 10 7
(27.75,27.85] 6 3 5 9 6 10 8
(27.85,27.95] 6 7 3 10 4 6 8
(27.95,28.05] 6 4 4 7 9 10 8
(28.05,28.1] 6 2 6 7 10 10 5
(28.1, Inf] 7 3 5 8 8 10 7
total 87.00 — 69.00 96.00 88.00 99.00 86.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 7 3 6 8 10 5 8
(26,26.5] 7 3 5 9 7 9 8
(26.5,26.75] 7 4 5 9 6 9 8
(26.75,27] 9 NA 10 8 6 5 6
(27,27.25] 8 1 9 8 4 8 8
(27.25,27.5] 7 2 6 8 8 10 6
(27.5,27.75] 6 4 4 5 10 10 8
(27.75,27.85] 6 3 5 10 9 9 5
(27.85,27.95] 7 7 3 7 7 5 10
(27.95,28.05] 7 6 3 8 9 8 7
(28.05,28.1] 6 4 4 7 10 10 6
(28.1, Inf] 7 3 5 8 8 10 7
total 84.00 — 65.00 95.00 94.00 98.00 87.00

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
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 
lm_best %>% 
  ggplot(aes(rmse, aic, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras~basin)

Version Author Date
af8788e Donghe-Zhu 2021-01-29
21c91c9 Donghe-Zhu 2021-01-29
eded038 Donghe-Zhu 2021-01-29
541d4dd Donghe-Zhu 2021-01-29
6a75576 Donghe-Zhu 2021-01-28
16fba40 Donghe-Zhu 2021-01-28
12bc567 Donghe-Zhu 2021-01-27
ceed31b Donghe-Zhu 2021-01-27
342402d Donghe-Zhu 2021-01-27
5bad5c2 Donghe-Zhu 2021-01-27
61efb56 Donghe-Zhu 2021-01-25
48f638e Donghe-Zhu 2021-01-25
c1cec47 Donghe-Zhu 2021-01-25
05ffb0c Donghe-Zhu 2021-01-25
8b97165 Donghe-Zhu 2021-01-25
c569946 Donghe-Zhu 2021-01-24
a2f0d56 Donghe-Zhu 2021-01-23
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 

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

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

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

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

other attached packages:
 [1] gt_0.2.2         corrr_0.4.3      broom_0.7.3      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.3   
[21] tidyverse_1.3.0  workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] nlme_3.1-149             fs_1.5.0                 webshot_0.5.2           
 [4] RColorBrewer_1.1-2       httr_1.4.2               rprojroot_2.0.2         
 [7] tools_4.0.3              backports_1.1.10         R6_2.5.0                
[10] mgcv_1.8-33              nortest_1.0-4            DBI_1.1.0               
[13] colorspace_2.0-0         withr_2.3.0              gridExtra_2.3           
[16] tidyselect_1.1.0         curl_4.3                 compiler_4.0.3          
[19] git2r_0.27.1             cli_2.2.0                rvest_0.3.6             
[22] xml2_1.3.2               sass_0.2.0               labeling_0.4.2          
[25] scales_1.1.1             checkmate_2.0.0          goftest_1.2-2           
[28] digest_0.6.27            foreign_0.8-80           rmarkdown_2.5           
[31] rio_0.5.16               pkgconfig_2.0.3          htmltools_0.5.0         
[34] highr_0.8                dbplyr_1.4.4             rlang_0.4.10            
[37] readxl_1.3.1             rstudioapi_0.13          farver_2.0.3            
[40] generics_0.1.0           jsonlite_1.7.2           zip_2.1.1               
[43] car_3.0-10               magrittr_2.0.1           Matrix_1.2-18           
[46] Rcpp_1.0.5               munsell_0.5.0            fansi_0.4.1             
[49] abind_1.4-5              lifecycle_0.2.0          stringi_1.5.3           
[52] whisker_0.4              yaml_2.2.1               carData_3.0-4           
[55] plyr_1.8.6               grid_4.0.3               blob_1.2.1              
[58] parallel_4.0.3           promises_1.1.1           crayon_1.3.4            
[61] lattice_0.20-41          splines_4.0.3            haven_2.3.1             
[64] hms_0.5.3                pillar_1.4.7             reprex_0.3.0            
[67] glue_1.4.2               evaluate_0.14            RcppArmadillo_0.10.1.2.2
[70] data.table_1.13.6        modelr_0.1.8             vctrs_0.3.6             
[73] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[76] reshape_0.8.8            assertthat_0.2.1         xfun_0.20               
[79] openxlsx_4.2.3           RcppEigen_0.3.3.9.1      later_1.1.0.1           
[82] viridisLite_0.3.0        ellipsis_0.3.1           here_1.0.1