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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
        }
      }
      
      
    }
  }
  
}

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 + silicate + phosphate + phosphate_star 3.7157430 778.82481 11.6224446 1982-1999 –> 2000-2012 5.565314 1069.4342
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.1695411 811.08847 10.3797689 1982-1999 –> 2000-2012 5.983450 1099.0499
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.1422876 869.80224 15.8418940 1982-1999 –> 2000-2012 6.473198 1115.6553
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate 4.5216686 831.78949 10.8147800 1982-1999 –> 2000-2012 6.353461 1119.0852
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6143633 771.07919 9.9371655 1982-1999 –> 2000-2012 5.320572 1050.7161
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.0218008 800.98712 8.8892259 1982-1999 –> 2000-2012 5.709717 1079.1581
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.0201177 800.86992 8.9737612 1982-1999 –> 2000-2012 5.700820 1078.4584
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.8573307 789.29591 10.0374176 1982-1999 –> 2000-2012 5.536752 1066.7806
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 4.0218671 798.99174 8.9098827 1982-1999 –> 2000-2012 5.979213 1095.3035
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.4681306 759.51519 10.3816952 1982-1999 –> 2000-2012 4.754085 1000.6950
Atlantic (-Inf,26] cstar_tref ~ aou + silicate + phosphate + phosphate_star 0.0468375 -70.10658 0.1064196 2000-2012 –> 2013-2019 3.824792 711.3674
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.0435060 -71.79586 0.0900986 2000-2012 –> 2013-2019 3.759249 707.0289
Atlantic (-Inf,26] cstar_tref ~ sal + silicate + phosphate + phosphate_star 0.2369429 10.95012 0.5214388 2000-2012 –> 2013-2019 4.094553 798.2663
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.0433600 -71.96396 0.0842255 2000-2012 –> 2013-2019 3.657723 699.1152
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.0433202 -72.00991 0.0826191 2000-2012 –> 2013-2019 4.065121 728.9772
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.0216632 -106.66016 0.0687276 2000-2012 –> 2013-2019 4.041781 694.2098
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.0432954 -72.03850 0.0848692 2000-2012 –> 2013-2019 3.900626 717.2574
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate 0.0449453 -72.16857 0.0954309 2000-2012 –> 2013-2019 3.670084 697.7441
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.0433087 -72.02317 0.0852984 2000-2012 –> 2013-2019 3.511439 687.4920
Atlantic (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 0.0433507 -73.97465 0.0837621 2000-2012 –> 2013-2019 4.084304 726.3427
Atlantic (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.3504626 2496.72981 15.3845010 1982-1999 –> 2000-2012 8.289535 4768.5357
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.0393186 2434.91251 11.3429723 1982-1999 –> 2000-2012 7.269794 4548.0824
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.4005417 2508.57292 10.8198384 1982-1999 –> 2000-2012 7.788678 4660.3400
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.3610774 2500.82559 14.5816507 1982-1999 –> 2000-2012 7.685525 4637.2218
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.4607573 2520.26109 16.2247201 1982-1999 –> 2000-2012 7.801890 4660.7122
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.7369287 2571.92166 16.2893935 1982-1999 –> 2000-2012 8.101450 4718.0232
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.4941744 2526.67964 16.4879652 1982-1999 –> 2000-2012 7.843104 4669.0189
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.4252331 2513.38488 13.9847129 1982-1999 –> 2000-2012 8.296404 4773.1064
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4.4400276 2514.25524 14.7223105 1982-1999 –> 2000-2012 8.353533 4780.7866
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.2928937 2487.27361 16.5651682 1982-1999 –> 2000-2012 8.137471 4741.4114
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.6073970 865.07016 6.7081923 2000-2012 –> 2013-2019 6.646716 3299.9827
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 2.4169118 835.91164 6.3070367 2000-2012 –> 2013-2019 7.394887 3448.5188
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.4160806 837.78850 6.2531612 2000-2012 –> 2013-2019 6.816622 3346.3614
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.3851950 833.18255 5.9582429 2000-2012 –> 2013-2019 7.352027 3445.8623
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.1200733 790.99934 8.0676360 2000-2012 –> 2013-2019 7.231398 3428.3408
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5193356 852.77028 6.5561436 2000-2012 –> 2013-2019 6.880413 3353.5959
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.5152522 852.18955 6.5332856 2000-2012 –> 2013-2019 6.976009 3372.4506
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.4404910 841.38733 6.1312258 2000-2012 –> 2013-2019 7.177420 3413.3090
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.5203373 852.91259 6.5565146 2000-2012 –> 2013-2019 7.014512 3379.5922
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.0074764 771.46247 5.8979842 2000-2012 –> 2013-2019 6.300370 3258.7361
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.9184635 3971.75543 12.0353156 1982-1999 –> 2000-2012 6.767795 6671.7204
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.8451910 3946.91331 13.0710531 1982-1999 –> 2000-2012 6.671113 6639.8862
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.9437811 3982.91358 11.5895578 1982-1999 –> 2000-2012 6.747894 6667.4417
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.8104453 3934.00551 13.4866988 1982-1999 –> 2000-2012 6.671082 6640.2869
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.8178500 3936.76612 14.0455253 1982-1999 –> 2000-2012 6.715639 6657.1126
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.8253632 3939.56176 14.1731984 1982-1999 –> 2000-2012 6.736107 6664.7700
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.9449398 3981.33131 11.5770530 1982-1999 –> 2000-2012 6.750610 6664.4646
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.7538460 3912.72507 12.7771544 1982-1999 –> 2000-2012 6.494022 6572.1123
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 3.8348858 3941.09720 13.1856308 1982-1999 –> 2000-2012 6.762681 6670.6721
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.8331791 3942.46420 13.3950586 1982-1999 –> 2000-2012 6.650544 6632.1312
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.6781594 658.29031 11.7520825 2000-2012 –> 2013-2019 6.523351 4605.2036
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.6857009 659.04391 11.9692582 2000-2012 –> 2013-2019 6.496146 4593.0494
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.6907528 659.54756 12.0620397 2000-2012 –> 2013-2019 6.508603 4596.3137
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.5376693 643.84947 11.0710908 2000-2012 –> 2013-2019 6.494285 4631.3833
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.6898750 659.46012 12.0436214 2000-2012 –> 2013-2019 6.515238 4599.0219
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.3104390 618.70879 9.1642886 2000-2012 –> 2013-2019 6.064285 4531.4339
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 2.6871318 657.18666 11.8976217 2000-2012 –> 2013-2019 6.522018 4598.2839
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.6727647 657.74992 11.5705001 2000-2012 –> 2013-2019 6.505944 4600.2141
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 2.6930884 657.78008 11.9674733 2000-2012 –> 2013-2019 6.534737 4601.3829
Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.5414074 642.24396 10.9176156 2000-2012 –> 2013-2019 6.527346 4638.2773
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.7507746 6108.49923 14.0258865 1982-1999 –> 2000-2012 4.445394 10355.8589
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5964952 5965.73746 12.9710072 1982-1999 –> 2000-2012 4.253570 10166.3447
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.6309215 5998.77190 12.9713022 1982-1999 –> 2000-2012 4.386687 10325.2639
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.6798004 6044.93958 12.9984609 1982-1999 –> 2000-2012 4.501232 10451.3288
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.7014690 6065.13742 12.9729776 1982-1999 –> 2000-2012 4.550628 10504.4019
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.4487545 5818.81126 8.6122671 1982-1999 –> 2000-2012 4.239821 10188.6188
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2.7772817 6132.55124 14.0905097 1982-1999 –> 2000-2012 4.588642 10524.8755
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.7413511 6101.89273 14.0325064 1982-1999 –> 2000-2012 4.397780 10301.6519
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 2.8223530 6172.92571 14.1157398 1982-1999 –> 2000-2012 4.696825 10639.7754
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.8434709 6191.62167 14.0957532 1982-1999 –> 2000-2012 4.744670 10689.2789
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.7407707 1405.20000 11.3771050 2000-2012 –> 2013-2019 5.491545 7513.6992
Atlantic (26.75,27] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.3300404 1314.00907 8.2961229 2000-2012 –> 2013-2019 5.274348 7595.0304
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 2.3615130 1319.71037 9.4382935 2000-2012 –> 2013-2019 5.129651 7443.9906
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3511248 1319.17978 9.7054936 2000-2012 –> 2013-2019 4.947620 7284.9172
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3502808 1318.97370 9.7259955 2000-2012 –> 2013-2019 4.981202 7317.7456
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3571732 1320.65453 9.7253911 2000-2012 –> 2013-2019 5.036974 7365.5941
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3621341 1321.86130 9.7229606 2000-2012 –> 2013-2019 5.063603 7386.9987
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.1116985 1257.53148 7.7100145 2000-2012 –> 2013-2019 4.560453 7076.3427
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2.7105715 1398.84026 11.3872079 2000-2012 –> 2013-2019 5.487853 7531.3915
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.7092286 1400.55582 11.3868599 2000-2012 –> 2013-2019 5.450580 7502.4485
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.3984268 7812.75531 8.6839053 1982-1999 –> 2000-2012 4.472689 13486.0198
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 2.3836965 7789.80923 11.1528646 1982-1999 –> 2000-2012 3.926285 12681.0324
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3632097 7762.46152 11.5665258 1982-1999 –> 2000-2012 3.714328 12306.6012
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.2734175 7630.75737 7.6597313 1982-1999 –> 2000-2012 4.504367 13495.8347
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3633807 7762.70756 11.6968562 1982-1999 –> 2000-2012 3.739447 12355.0395
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3975013 7811.44300 11.9906390 1982-1999 –> 2000-2012 3.834653 12518.1816
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.5995275 8086.51197 14.9672521 1982-1999 –> 2000-2012 4.302018 13239.5270
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.4130187 7833.37802 12.0644866 1982-1999 –> 2000-2012 3.871668 12579.2253
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate 2.3603637 7756.36452 7.6345089 1982-1999 –> 2000-2012 4.652428 13690.6269
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.3312584 7716.17897 7.9312927 1982-1999 –> 2000-2012 3.830243 12533.8740
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate 1.9350541 1841.58494 7.0085142 2000-2012 –> 2013-2019 4.475433 9847.8409
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.7607091 1760.49656 6.7005862 2000-2012 –> 2013-2019 4.159136 9573.2519
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1.9571184 1851.56230 7.3722852 2000-2012 –> 2013-2019 4.340815 9641.3715
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.9284759 1840.58831 7.9526493 2000-2012 –> 2013-2019 4.291686 9603.0498
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.5768574 1663.44770 5.8447375 2000-2012 –> 2013-2019 3.850275 9294.2051
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.9221597 1837.70138 8.0770761 2000-2012 –> 2013-2019 4.285540 9600.4089
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.9334366 1842.84907 7.9906631 2000-2012 –> 2013-2019 4.330938 9654.2921
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.9352108 1843.65622 7.9779992 2000-2012 –> 2013-2019 4.348230 9677.0342
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate 1.6842095 1719.40664 6.3903461 2000-2012 –> 2013-2019 4.044573 9475.7712
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.6425037 1699.34105 5.9776430 2000-2012 –> 2013-2019 3.973762 9415.5200
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5728335 17007.78187 17.3450655 1982-1999 –> 2000-2012 5.986334 26074.6476
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.2962629 16499.22651 12.7456477 1982-1999 –> 2000-2012 5.545185 25288.1042
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.2681312 16445.12612 10.4358597 1982-1999 –> 2000-2012 5.352186 24934.3341
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5638462 16991.88432 16.8121585 1982-1999 –> 2000-2012 5.954377 26021.1118
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.4999923 16877.76592 18.1775385 1982-1999 –> 2000-2012 6.027418 26126.1728
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.4402100 16769.02118 17.1463764 1982-1999 –> 2000-2012 6.038133 26125.7110
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.4995195 16876.91328 18.1037013 1982-1999 –> 2000-2012 6.038160 26142.7458
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.7344673 17285.06393 12.0356111 1982-1999 –> 2000-2012 6.045714 26179.5358
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 3.4852540 16849.13029 11.4620622 1982-1999 –> 2000-2012 5.569438 25336.5811
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.4752146 16832.92223 10.8687134 1982-1999 –> 2000-2012 5.436399 25082.9503
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 3.7758265 3973.97839 9.9414718 2000-2012 –> 2013-2019 7.117473 20557.5164
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.7620558 3970.70969 10.9685715 2000-2012 –> 2013-2019 7.066227 20485.0619
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.9253190 4031.96882 15.3046388 2000-2012 –> 2013-2019 7.498152 21039.7507
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.1474347 4111.33995 16.5260564 2000-2012 –> 2013-2019 7.443698 20610.5665
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.7606499 3970.17073 9.5663288 2000-2012 –> 2013-2019 7.028781 20415.2969
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.8546103 4005.75659 14.8131093 2000-2012 –> 2013-2019 7.354603 20883.5225
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.8421675 4001.09423 14.4067030 2000-2012 –> 2013-2019 7.282377 20770.1154
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.8591530 4007.45499 14.8582465 2000-2012 –> 2013-2019 7.358672 20884.3683
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate_star 3.8774160 4012.26298 15.5719734 2000-2012 –> 2013-2019 7.445695 21009.9929
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.9815266 4052.47075 8.9147475 2000-2012 –> 2013-2019 7.456741 20885.3930
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3767449 26374.52726 18.0234485 1982-1999 –> 2000-2012 4.145790 41137.7789
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.4263595 26612.90371 20.9674693 1982-1999 –> 2000-2012 4.220243 41479.5292
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.4490817 26720.45109 17.8263155 1982-1999 –> 2000-2012 4.269441 41695.7000
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 2.4533720 26738.64534 18.7342670 1982-1999 –> 2000-2012 4.284748 41756.6260
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3745436 26363.83560 18.1015003 1982-1999 –> 2000-2012 4.089202 40895.5775
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3622820 26304.10177 20.2604840 1982-1999 –> 2000-2012 4.063184 40776.1205
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.3697646 26340.59121 19.8265342 1982-1999 –> 2000-2012 4.071284 40815.3046
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.4513073 26728.93131 18.4737744 1982-1999 –> 2000-2012 4.281454 41741.9365
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3614588 26300.08059 20.0686432 1982-1999 –> 2000-2012 4.062177 40771.2996
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 2.5372542 27126.54253 23.2554110 1982-1999 –> 2000-2012 4.242714 41616.4054
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2.4043203 8007.38851 11.4453086 2000-2012 –> 2013-2019 4.781682 34382.9073
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3771511 7969.81735 11.2454684 2000-2012 –> 2013-2019 4.753896 34344.3446
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.4229714 8036.29529 12.4336305 2000-2012 –> 2013-2019 4.849331 34649.1990
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.4700720 8103.33310 13.5883694 2000-2012 –> 2013-2019 4.919154 34823.7842
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 2.4720179 8104.07513 13.5316161 2000-2012 –> 2013-2019 4.925390 34842.7205
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.4010706 8004.67898 11.2464227 2000-2012 –> 2013-2019 4.775614 34368.5146
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3050798 7862.61544 12.4330800 2000-2012 –> 2013-2019 4.667362 34166.7172
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.3222345 7888.43291 12.5808608 2000-2012 –> 2013-2019 4.691999 34229.0241
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3080871 7867.15519 12.4077220 2000-2012 –> 2013-2019 4.669546 34167.2358
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 2.3559976 7936.69349 13.8243457 2000-2012 –> 2013-2019 4.893252 35063.2360
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.3292682 7707.30895 14.5011028 1982-1999 –> 2000-2012 2.294615 11260.7395
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.2737793 7512.74559 13.6506208 1982-1999 –> 2000-2012 2.228284 11035.2840
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2209499 7323.45178 13.7437305 1982-1999 –> 2000-2012 2.020929 10396.2285
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.3246036 7691.43399 14.5286278 1982-1999 –> 2000-2012 2.259697 11163.4142
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.1572832 7081.60197 11.8450616 1982-1999 –> 2000-2012 1.877062 9884.1471
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2453942 7412.97222 13.7548477 1982-1999 –> 2000-2012 2.078779 10590.3967
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2968965 7595.96958 13.8559473 1982-1999 –> 2000-2012 2.181392 10925.6510
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.2970030 7596.34031 13.8896109 1982-1999 –> 2000-2012 2.181421 10925.7983
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2940803 7586.15232 13.8372287 1982-1999 –> 2000-2012 2.177316 10912.1862
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.3349947 7724.72219 14.2518081 1982-1999 –> 2000-2012 2.242644 11118.5036
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.1611436 1754.86179 6.3279907 2000-2012 –> 2013-2019 2.490412 9462.1707
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.0596571 1651.34115 5.6573384 2000-2012 –> 2013-2019 2.333436 9164.0867
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.9898089 1577.65164 4.1700830 2000-2012 –> 2013-2019 2.210759 8901.1034
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.1432901 1737.66202 5.6044887 2000-2012 –> 2013-2019 2.467894 9429.0960
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8646329 1427.57205 4.1528944 2000-2012 –> 2013-2019 2.021916 8509.1740
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.0085041 1598.42139 4.5828734 2000-2012 –> 2013-2019 2.253898 9011.3936
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.0368634 1629.20400 4.8858946 2000-2012 –> 2013-2019 2.333760 9225.1736
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.0389848 1631.47267 4.8887698 2000-2012 –> 2013-2019 2.335988 9227.8130
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.0360834 1628.36868 4.8819267 2000-2012 –> 2013-2019 2.330164 9214.5210
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.0449033 1635.77785 4.7743287 2000-2012 –> 2013-2019 2.379898 9360.5000
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5168636 10730.77254 25.6903592 1982-1999 –> 2000-2012 3.550239 14876.5068
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.5892375 10860.50172 25.0130387 1982-1999 –> 2000-2012 3.598190 14938.1664
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.3147654 10347.73767 24.1330874 1982-1999 –> 2000-2012 3.214239 14098.5159
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5458372 10783.14972 25.6739741 1982-1999 –> 2000-2012 3.616719 15030.3490
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.5831202 10849.67787 25.7937670 1982-1999 –> 2000-2012 3.699058 15214.1686
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.5966987 10873.66913 25.8948349 1982-1999 –> 2000-2012 3.715332 15245.0255
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.5775169 10839.74068 25.7657690 1982-1999 –> 2000-2012 3.692214 15201.0669
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 2.6558064 10974.66309 26.1066195 1982-1999 –> 2000-2012 3.781014 15360.6969
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 2.5188258 10732.33870 25.3922217 1982-1999 –> 2000-2012 3.553730 14880.2794
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.5023540 10704.31585 24.9834553 1982-1999 –> 2000-2012 3.534450 14846.5240
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate 1.3106919 1704.87271 10.5067660 2000-2012 –> 2013-2019 3.914321 12588.7386
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.1008666 1532.06633 8.1911686 2000-2012 –> 2013-2019 3.617730 12262.8389
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.9553182 1389.97422 5.6365835 2000-2012 –> 2013-2019 3.544556 12250.4759
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.7176818 1103.38401 4.1212589 2000-2012 –> 2013-2019 3.032447 11451.1217
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.1618869 1586.12180 8.9271708 2000-2012 –> 2013-2019 3.707724 12369.2715
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2178630 1633.26831 9.2669612 2000-2012 –> 2013-2019 3.800983 12482.9462
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.2323913 1645.15072 9.4203821 2000-2012 –> 2013-2019 3.829090 12518.8199
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2112182 1627.78633 9.1985964 2000-2012 –> 2013-2019 3.788735 12467.5270
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.0560548 1488.42553 7.4896536 2000-2012 –> 2013-2019 3.574880 12220.7642
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.0540817 1488.55168 7.3881297 2000-2012 –> 2013-2019 3.556436 12192.8675
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.9626837 14446.22953 21.0190853 1982-1999 –> 2000-2012 7.365546 23490.6153
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.8499388 12744.71059 20.8261663 1982-1999 –> 2000-2012 5.095582 20369.3218
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.9816453 14470.87089 21.2715235 1982-1999 –> 2000-2012 7.418253 23548.9647
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.9642547 14448.27549 20.6868696 1982-1999 –> 2000-2012 7.362401 23487.9236
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.9672344 14452.15401 20.5008938 1982-1999 –> 2000-2012 7.364860 23491.2787
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.0461468 14551.82377 20.3984153 1982-1999 –> 2000-2012 7.380980 23525.2253
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.9225928 14393.73902 20.5432444 1982-1999 –> 2000-2012 7.197838 23307.5510
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.9673372 14452.28781 20.4951428 1982-1999 –> 2000-2012 7.365022 23491.4713
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 2.9146782 12858.65875 20.3966194 1982-1999 –> 2000-2012 5.224532 20577.5750
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.2197383 11454.68429 18.9115639 1982-1999 –> 2000-2012 3.848312 17981.7774
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.8074396 1476.93255 4.4406262 2000-2012 –> 2013-2019 4.770123 15923.1621
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.7712628 1421.28392 4.1289238 2000-2012 –> 2013-2019 3.621202 14165.9945
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.4677174 814.08358 1.9962155 2000-2012 –> 2013-2019 4.449363 15284.9545
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.8622742 1556.69846 4.8674697 2000-2012 –> 2013-2019 4.826529 16004.9740
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.9301937 1648.74335 5.3255769 2000-2012 –> 2013-2019 4.852786 16042.4824
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.9057952 1616.47571 5.2670953 2000-2012 –> 2013-2019 4.873132 16068.7635
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 1.2220101 1977.99490 5.8067357 2000-2012 –> 2013-2019 4.136688 14836.6537
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.9631224 1690.97560 4.5099323 2000-2012 –> 2013-2019 3.182861 13145.6599
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.6841610 1273.80318 4.7300205 2000-2012 –> 2013-2019 4.792529 15904.4039
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.6634913 1238.56059 4.4878684 2000-2012 –> 2013-2019 4.771782 15871.0635
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.2063951 4571.46041 9.6649319 1982-1999 –> 2000-2012 1.908526 6622.4491
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.1998723 4558.07400 9.1782678 1982-1999 –> 2000-2012 1.901844 6610.6288
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.2515065 4677.64729 9.5569018 1982-1999 –> 2000-2012 1.979716 6800.4384
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.2355326 4639.19053 9.5073603 1982-1999 –> 2000-2012 1.954007 6734.2225
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.1103192 4337.93730 10.1705292 1982-1999 –> 2000-2012 1.775962 6288.7831
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2319044 4632.84452 9.1292364 1982-1999 –> 2000-2012 1.948822 6725.7236
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.2503780 4673.08697 9.3746864 1982-1999 –> 2000-2012 1.984636 6809.7101
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2477333 4669.07789 9.0414562 1982-1999 –> 2000-2012 1.978101 6797.5338
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.1125312 4341.58552 10.1383916 1982-1999 –> 2000-2012 1.858504 6508.5040
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.9975611 4034.01738 8.4021900 1982-1999 –> 2000-2012 1.613983 5837.8272
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.4586243 489.00330 2.3150734 2000-2012 –> 2013-2019 1.665019 5060.4637
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.4573188 488.87668 2.2346065 2000-2012 –> 2013-2019 1.657191 5046.9507
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.5040076 561.39589 2.3617698 2000-2012 –> 2013-2019 1.755514 5239.0432
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 0.4978417 550.21313 2.6760984 2000-2012 –> 2013-2019 1.733374 5189.4037
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.3663661 323.45309 1.9343769 2000-2012 –> 2013-2019 1.476685 4661.3904
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.4932024 545.22878 2.5114765 2000-2012 –> 2013-2019 1.725107 5178.0733
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.5193456 583.75963 2.6572139 2000-2012 –> 2013-2019 1.767079 5252.8375
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.5222321 587.89438 2.2745084 2000-2012 –> 2013-2019 1.735029 5176.3754
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.4659792 500.87185 3.4701251 2000-2012 –> 2013-2019 1.578510 4842.4574
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.3035623 183.17040 2.4546731 2000-2012 –> 2013-2019 1.301123 4217.1878
Atlantic (28.1,28.15] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1.2814148 7266.36316 10.5366436 1982-1999 –> 2000-2012 1.945897 9654.3319
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2414415 7130.44143 8.4388242 1982-1999 –> 2000-2012 1.867915 9381.8746
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.2369464 7114.65494 11.7081027 1982-1999 –> 2000-2012 1.917424 9560.5714
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2530901 7171.08645 8.2970301 1982-1999 –> 2000-2012 1.895029 9479.8793
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2680821 7222.84500 8.1045846 1982-1999 –> 2000-2012 1.926566 9591.4858
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.3244699 7412.18601 7.9595343 1982-1999 –> 2000-2012 1.990185 9806.5161
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2578789 7187.68640 8.2995962 1982-1999 –> 2000-2012 1.912022 9540.7714
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.2341617 7104.84623 9.1289970 1982-1999 –> 2000-2012 1.921539 9574.4893
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.2457624 7143.56261 10.0772817 1982-1999 –> 2000-2012 1.934072 9614.3959
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.0463114 6386.23996 13.2216360 1982-1999 –> 2000-2012 1.605131 8368.8873
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.4973335 872.21018 2.7426610 2000-2012 –> 2013-2019 1.816803 8265.9355
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.4558820 770.30033 2.5586933 2000-2012 –> 2013-2019 1.697323 7900.7418
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.4747730 818.78002 2.5422329 2000-2012 –> 2013-2019 1.807189 8256.9973
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.4889575 853.92974 2.5312615 2000-2012 –> 2013-2019 1.725904 7968.5847
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.4758200 821.41001 2.6505916 2000-2012 –> 2013-2019 1.728910 7992.4965
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.4924304 862.38040 2.7400276 2000-2012 –> 2013-2019 1.760512 8085.2254
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.4886151 853.09337 2.6850304 2000-2012 –> 2013-2019 1.813085 8265.2794
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.4915160 860.16118 2.7275486 2000-2012 –> 2013-2019 1.749395 8047.8476
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.5027910 885.24131 2.4159092 2000-2012 –> 2013-2019 1.748553 8028.8039
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.3510299 458.23312 1.5308964 2000-2012 –> 2013-2019 1.397341 6844.4731
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1.0239654 11325.03634 10.0713781 1982-1999 –> 2000-2012 1.752560 15900.5597
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.9974202 11121.05927 10.9135453 1982-1999 –> 2000-2012 1.680000 15428.4996
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.9901441 11061.64274 10.4644296 1982-1999 –> 2000-2012 1.696461 15508.6053
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.9882850 11048.90447 11.0178760 1982-1999 –> 2000-2012 1.690886 15476.0297
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.9836449 11011.99923 11.4124061 1982-1999 –> 2000-2012 1.665575 15315.4955
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.7074070 8426.81472 25.1442843 1982-1999 –> 2000-2012 1.480997 13252.4293
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.9924500 11079.88419 12.1601275 1982-1999 –> 2000-2012 1.710761 15596.5576
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.9879264 11044.05824 12.5376868 1982-1999 –> 2000-2012 1.685216 15437.7662
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.9877273 11044.47831 12.4614387 1982-1999 –> 2000-2012 1.684138 15434.9659
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.8820857 10157.41074 14.4692946 1982-1999 –> 2000-2012 1.762684 15519.3987
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.5708385 1956.88425 3.8247927 2000-2012 –> 2013-2019 1.594804 13281.9206
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.5015991 1665.87872 3.7963984 2000-2012 –> 2013-2019 1.499019 12786.9380
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.5043984 1676.48947 3.1777295 2000-2012 –> 2013-2019 1.494543 12738.1322
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.4910756 1617.83272 2.8182608 2000-2012 –> 2013-2019 1.479361 12666.7372
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.4770310 1552.08083 2.9850549 2000-2012 –> 2013-2019 1.460676 12564.0801
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.5341662 1808.42327 1.7901428 2000-2012 –> 2013-2019 1.241573 10235.2380
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.5182786 1738.00369 2.4138473 2000-2012 –> 2013-2019 1.510729 12817.8879
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.5319793 1797.12708 2.2762501 2000-2012 –> 2013-2019 1.519906 12841.1853
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.5132009 1717.69371 2.2392848 2000-2012 –> 2013-2019 1.500928 12762.1720
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.6375558 2209.35746 2.6288442 2000-2012 –> 2013-2019 1.519641 12366.7682
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.6857088 12799.21135 4.6631787 1982-1999 –> 2000-2012 1.251907 18641.0827
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.6852020 12792.13325 4.5957378 1982-1999 –> 2000-2012 1.243518 18539.8387
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.6681014 12481.82136 4.3880344 1982-1999 –> 2000-2012 1.231293 18289.1696
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.6430160 12013.93859 4.7384749 1982-1999 –> 2000-2012 1.198149 17724.4244
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.6853958 12795.60544 4.5801711 1982-1999 –> 2000-2012 1.251406 18637.2062
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.6851890 12793.89939 4.6108902 1982-1999 –> 2000-2012 1.232301 18404.5333
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.6632917 12395.11228 4.6788294 1982-1999 –> 2000-2012 1.226029 18198.9205
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.7809467 14400.01156 4.4982162 1982-1999 –> 2000-2012 1.522527 22096.9812
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate 0.8126068 14885.94470 11.2556158 1982-1999 –> 2000-2012 1.614911 23120.8254
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.7993430 14685.88306 12.2774847 1982-1999 –> 2000-2012 1.596379 22877.5736
Atlantic (28.2, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate_star 0.5317035 1784.93021 2.3987251 2000-2012 –> 2013-2019 1.339972 16605.1449
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.4994889 1642.17894 2.2408837 2000-2012 –> 2013-2019 1.185198 14441.3903
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.4916692 1608.64417 2.2371754 2000-2012 –> 2013-2019 1.176871 14400.7774
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.4848682 1577.27569 2.0976552 2000-2012 –> 2013-2019 1.152969 14059.0970
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.4170953 1240.20955 1.7831480 2000-2012 –> 2013-2019 1.060111 13254.1481
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.4884497 1593.84915 1.8837425 2000-2012 –> 2013-2019 1.173846 14389.4546
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.4880178 1593.85694 1.9519856 2000-2012 –> 2013-2019 1.173207 14387.7563
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.4664236 1491.93687 1.8579337 2000-2012 –> 2013-2019 1.129715 13887.0491
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate 0.5395203 1817.79709 2.6697122 2000-2012 –> 2013-2019 1.352127 16703.7418
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.5251805 1759.13187 2.4826026 2000-2012 –> 2013-2019 1.324523 16445.0149
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.7654055 22385.26370 24.2989469 1982-1999 –> 2000-2012 11.189956 30588.6706
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.5408507 22106.94692 21.7225889 1982-1999 –> 2000-2012 10.875813 30268.4893
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.7227414 22334.85501 57.5578307 1982-1999 –> 2000-2012 10.874756 30404.4869
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.3213079 23034.77309 23.3540880 1982-1999 –> 2000-2012 11.670241 31201.2044
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.6715371 22271.43733 25.6058626 1982-1999 –> 2000-2012 10.881959 30370.7622
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.0944052 22778.84131 20.4679940 1982-1999 –> 2000-2012 11.281895 30866.5477
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.2645822 22973.16869 20.3950622 1982-1999 –> 2000-2012 11.621881 31145.7159
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.4315501 23158.76742 24.7263577 1982-1999 –> 2000-2012 12.004255 31435.1487
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.3035684 23016.94396 20.7376644 1982-1999 –> 2000-2012 11.691855 31204.6833
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 6.4395289 23165.51544 23.8176246 1982-1999 –> 2000-2012 12.012685 31440.1103
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.7721701 14755.39388 23.2437254 2000-2012 –> 2013-2019 11.537576 37140.6576
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.3459697 14400.86831 23.1125386 2000-2012 –> 2013-2019 10.886820 36507.8152
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 4.3874791 13480.47871 15.8772758 2000-2012 –> 2013-2019 10.562664 36350.2305
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.3175536 13407.80452 15.5562020 2000-2012 –> 2013-2019 10.040295 35742.6595
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.0486703 13108.93607 14.2992052 2000-2012 –> 2013-2019 9.868867 35562.9398
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.3022204 15163.73886 22.1727520 2000-2012 –> 2013-2019 12.623528 38198.5120
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.4783258 14514.54262 24.6945811 2000-2012 –> 2013-2019 11.149863 36785.9799
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.8629911 14829.95755 22.6875052 2000-2012 –> 2013-2019 11.957396 37608.7989
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.9886907 14928.55513 23.0125451 2000-2012 –> 2013-2019 12.253273 37901.7238
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.0578772 14981.94499 22.8467868 2000-2012 –> 2013-2019 12.361446 37998.8890
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.9631962 18959.63969 42.7616751 1982-1999 –> 2000-2012 9.408167 31056.9154
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.0822204 19108.27548 41.4870083 1982-1999 –> 2000-2012 9.226750 30914.9769
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.3479270 18131.53578 42.0595096 1982-1999 –> 2000-2012 8.036978 29456.8618
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.0388885 19056.57006 48.6546252 1982-1999 –> 2000-2012 8.667973 30313.8499
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.0420514 19060.50582 39.2672753 1982-1999 –> 2000-2012 9.168022 30850.5740
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.4747310 18311.83732 45.6939866 1982-1999 –> 2000-2012 8.257034 29740.8136
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.6164707 18507.42497 45.4472805 1982-1999 –> 2000-2012 8.482496 30027.3037
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.6457871 18547.12871 45.3990753 1982-1999 –> 2000-2012 8.525346 30081.5172
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.8493499 18816.09619 47.7728679 1982-1999 –> 2000-2012 8.695080 30314.1218
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.9572552 18954.12749 43.6492837 1982-1999 –> 2000-2012 9.387293 31039.4312
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.0852363 8869.68093 23.0855667 2000-2012 –> 2013-2019 9.048433 27829.3206
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6832700 8547.06554 21.6998729 2000-2012 –> 2013-2019 8.031197 26678.6013
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.8177145 8659.42252 21.7415384 2000-2012 –> 2013-2019 8.292445 26971.2598
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.8624792 8695.95661 21.4596482 2000-2012 –> 2013-2019 8.478950 27203.3816
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.8860703 8715.04007 21.4796508 2000-2012 –> 2013-2019 8.531857 27262.1688
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.1672547 8933.97827 23.0307743 2000-2012 –> 2013-2019 9.016605 27750.0745
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4.1413669 8912.44852 23.0391292 2000-2012 –> 2013-2019 9.134665 27910.0134
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.0695369 8859.61392 23.2034791 2000-2012 –> 2013-2019 9.026792 27813.7414
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate_star 4.1676161 8932.25006 23.1118050 2000-2012 –> 2013-2019 9.241026 28029.6430
Indo-Pacific (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.1848389 8945.17474 23.1123850 2000-2012 –> 2013-2019 9.279262 28068.4915
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.9946221 17328.15762 19.4579347 1982-1999 –> 2000-2012 8.235805 26977.5304
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.5693494 16821.12957 21.6588089 1982-1999 –> 2000-2012 7.508124 26108.7324
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.2192822 17581.82691 21.9131857 1982-1999 –> 2000-2012 8.166825 26880.4940
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.7445763 17036.38066 55.9118692 1982-1999 –> 2000-2012 7.956130 26653.6453
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.8140931 17119.58111 21.1436161 1982-1999 –> 2000-2012 7.978596 26682.0316
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.9024011 17223.55604 20.9506779 1982-1999 –> 2000-2012 8.198752 26937.6122
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.9181253 17241.87326 19.6105317 1982-1999 –> 2000-2012 8.255703 27002.0921
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.9053976 17227.05122 20.8416638 1982-1999 –> 2000-2012 8.209603 26949.9464
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 4.9189839 17240.87172 19.6035363 1982-1999 –> 2000-2012 8.311582 27059.8165
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.7146600 17000.19968 43.9883906 1982-1999 –> 2000-2012 7.945945 26640.2130
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.7100507 7918.03386 21.8010872 2000-2012 –> 2013-2019 8.789270 25342.2635
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5451616 7788.37649 19.7349280 2000-2012 –> 2013-2019 8.114511 24609.5061
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.7982781 7988.09650 18.5979298 2000-2012 –> 2013-2019 8.542854 25024.4772
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.7304235 7935.89300 21.4314919 2000-2012 –> 2013-2019 8.544517 25055.4741
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.7762361 7971.24162 21.8459421 2000-2012 –> 2013-2019 8.678637 25194.7977
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.6953346 7908.52395 22.1564846 2000-2012 –> 2013-2019 8.613460 25150.3972
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.7851273 7978.05228 21.8652306 2000-2012 –> 2013-2019 8.690525 25205.1035
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 4.0244288 8153.58711 19.2691506 2000-2012 –> 2013-2019 8.943413 25394.4588
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.7572018 7956.60730 23.9123714 2000-2012 –> 2013-2019 9.017412 25583.1140
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.2381376 7526.04122 19.4999763 2000-2012 –> 2013-2019 7.952798 24526.2409
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.5588006 23899.28051 15.3718083 1982-1999 –> 2000-2012 7.739248 36476.8155
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.5412128 23869.83119 16.1306254 1982-1999 –> 2000-2012 7.684804 36392.5083
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.7080354 24163.35038 15.2653297 1982-1999 –> 2000-2012 7.724499 36484.6598
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.4777336 23755.30007 21.3090816 1982-1999 –> 2000-2012 7.582354 36217.1267
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.9831390 24623.38819 18.6218552 1982-1999 –> 2000-2012 8.152123 37183.3093
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.9396880 24554.13438 17.6779382 1982-1999 –> 2000-2012 8.098146 37099.8261
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate_star 4.8883353 24467.11023 16.9293325 1982-1999 –> 2000-2012 8.211247 37258.3973
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.8823376 24459.12175 16.8837817 1982-1999 –> 2000-2012 8.182710 37219.2088
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.5985146 23969.85036 22.8061442 1982-1999 –> 2000-2012 7.847860 36651.9290
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.5799137 23938.87357 23.0318022 1982-1999 –> 2000-2012 7.812873 36598.2902
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.2289400 10986.37364 14.9558290 2000-2012 –> 2013-2019 9.017217 35285.2223
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.6678062 11365.13201 12.8969501 2000-2012 –> 2013-2019 9.226607 35264.4125
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.2142535 10975.02862 14.5689514 2000-2012 –> 2013-2019 8.755466 34844.8598
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.4507686 11184.49080 18.1269496 2000-2012 –> 2013-2019 8.928502 34939.7909
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.2823232 11042.24045 15.8934616 2000-2012 –> 2013-2019 9.047470 35303.6912
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.3147438 11065.42582 16.3686788 2000-2012 –> 2013-2019 9.202988 35534.3851
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.3057065 11057.38281 16.2141714 2000-2012 –> 2013-2019 9.163718 35475.8665
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.3205844 11070.61479 16.3708206 2000-2012 –> 2013-2019 9.202922 35529.7365
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.4899011 11216.07068 19.0245711 2000-2012 –> 2013-2019 9.088416 35185.9210
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.1838292 10947.23466 15.8308289 2000-2012 –> 2013-2019 8.763743 34886.1082
Indo-Pacific (27,27.25] cstar_tref ~ aou + phosphate + phosphate_star 5.0776466 32000.19519 32.2307425 1982-1999 –> 2000-2012 8.192146 46507.3044
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.9077251 31644.46257 28.1678921 1982-1999 –> 2000-2012 8.021946 46153.0654
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.0533422 31951.76778 33.4840544 1982-1999 –> 2000-2012 8.070378 46280.4801
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.8814707 31590.08719 29.4107130 1982-1999 –> 2000-2012 7.898453 45920.6994
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.3648408 32582.44310 33.8977089 1982-1999 –> 2000-2012 7.868005 45853.7108
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.1464738 29874.97852 25.5860452 1982-1999 –> 2000-2012 7.056197 44000.1959
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate_star 5.3737309 32597.84475 34.7706749 1982-1999 –> 2000-2012 7.974407 46083.9493
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.0700911 31988.54473 31.0905611 1982-1999 –> 2000-2012 7.660722 45454.6917
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.1688532 29929.55081 24.4541368 1982-1999 –> 2000-2012 7.144560 44180.0001
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.6716803 28596.86912 20.7917312 1982-1999 –> 2000-2012 6.611020 42779.5481
Indo-Pacific (27,27.25] cstar_tref ~ aou + phosphate + phosphate_star 4.9621881 16654.52712 20.5960993 2000-2012 –> 2013-2019 10.039835 48654.7223
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.9066017 16594.45579 19.6633213 2000-2012 –> 2013-2019 9.814327 48238.9184
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.8142064 16489.70866 22.2711859 2000-2012 –> 2013-2019 9.867548 48441.4764
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.7827589 16455.59808 21.4414170 2000-2012 –> 2013-2019 9.664230 48045.6853
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.2972622 15865.81072 20.2008233 2000-2012 –> 2013-2019 8.443736 45740.7892
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.8195457 16497.81630 21.9711610 2000-2012 –> 2013-2019 9.962637 48636.6066
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.8298880 16509.62754 22.0795829 2000-2012 –> 2013-2019 10.093400 48891.6635
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.9597396 16655.80766 18.1961531 2000-2012 –> 2013-2019 10.029831 48644.3524
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.4079647 16003.95735 18.7475642 2000-2012 –> 2013-2019 8.576818 45933.5082
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.0871660 15589.61481 16.4872879 2000-2012 –> 2013-2019 7.758846 44186.4839
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.4517924 35969.15344 11.6911369 1982-1999 –> 2000-2012 6.080326 55113.7769
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.8507873 37446.90025 16.4963012 1982-1999 –> 2000-2012 6.528382 56737.8379
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6748105 36816.11355 13.3334567 1982-1999 –> 2000-2012 6.349404 56100.0566
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 3.6791037 36829.90885 13.2597076 1982-1999 –> 2000-2012 6.420989 56311.1351
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.7280078 37008.54369 13.2517692 1982-1999 –> 2000-2012 6.443079 56410.9513
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6169559 36601.44042 12.5311130 1982-1999 –> 2000-2012 6.291869 55886.3408
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.6604389 36763.10401 13.0977542 1982-1999 –> 2000-2012 6.385718 56197.6096
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6358223 36671.82028 12.7551434 1982-1999 –> 2000-2012 6.347107 56065.0362
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.0129098 38006.78118 16.4280806 1982-1999 –> 2000-2012 6.465099 56594.4576
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.1147927 34579.40804 18.6816804 1982-1999 –> 2000-2012 5.434756 52722.5357
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.4464446 19064.85215 12.1898536 2000-2012 –> 2013-2019 6.898237 55034.0056
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.9219849 19989.86713 13.8873535 2000-2012 –> 2013-2019 7.772772 57436.7674
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5468500 19270.80858 14.5162115 2000-2012 –> 2013-2019 7.221660 56086.9221
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 3.6423417 19459.34659 13.2148529 2000-2012 –> 2013-2019 7.321445 56289.2554
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.8196432 19800.23330 12.7125839 2000-2012 –> 2013-2019 7.547651 56808.7770
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.4911198 19157.22329 14.0847477 2000-2012 –> 2013-2019 7.108076 55758.6637
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.5150104 19206.13586 14.4333343 2000-2012 –> 2013-2019 7.175449 55969.2399
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate 3.5089944 19191.85027 15.4428512 2000-2012 –> 2013-2019 7.518358 57184.6727
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.4939468 19163.02850 14.2194095 2000-2012 –> 2013-2019 7.129769 55834.8488
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.3732656 18910.92772 15.0704776 2000-2012 –> 2013-2019 6.488058 53490.3358
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.3019582 40836.15492 17.1014420 1982-1999 –> 2000-2012 5.669575 61039.9948
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.0925934 39812.95654 11.3071718 1982-1999 –> 2000-2012 5.533656 60287.2218
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3.3498155 41058.92022 16.2359915 1982-1999 –> 2000-2012 5.815261 61619.1667
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.4915863 41706.38301 19.0279623 1982-1999 –> 2000-2012 5.949087 62238.0573
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.0574294 39634.33375 10.7392732 1982-1999 –> 2000-2012 5.491844 60084.4594
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.0651411 39673.68194 10.8635211 1982-1999 –> 2000-2012 5.525182 60216.5010
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.6071739 42217.10231 18.1320297 1982-1999 –> 2000-2012 5.919399 62211.3835
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.0574323 39632.34817 10.7344778 1982-1999 –> 2000-2012 5.640553 60605.3245
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.0573661 39634.00993 10.7559073 1982-1999 –> 2000-2012 5.513383 60162.3384
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.1603287 40151.37948 22.4307281 1982-1999 –> 2000-2012 5.418097 59934.6867
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.4536974 21775.53054 11.8397608 2000-2012 –> 2013-2019 6.755656 62611.6855
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.7775261 19991.92627 12.6535686 2000-2012 –> 2013-2019 5.870120 59804.8828
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3.5033590 21890.40093 11.8152144 2000-2012 –> 2013-2019 6.853174 62949.3212
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8135744 20097.48512 14.3111891 2000-2012 –> 2013-2019 6.087478 60800.3590
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate 2.8173406 20106.43561 14.5356193 2000-2012 –> 2013-2019 6.123767 60961.7131
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.7652705 19955.72636 12.1300751 2000-2012 –> 2013-2019 5.822700 59590.0601
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.7660611 19958.06629 12.1887745 2000-2012 –> 2013-2019 5.831202 59631.7482
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.0358466 20717.90461 8.6609996 2000-2012 –> 2013-2019 6.093279 60350.2528
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.7638488 19951.51668 12.0658586 2000-2012 –> 2013-2019 5.821215 59585.5266
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.5075308 21902.14304 14.3391041 2000-2012 –> 2013-2019 6.667859 62053.5225
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 3.0677546 15484.97589 9.4410754 1982-1999 –> 2000-2012 5.099601 23025.4279
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.0437562 15439.13213 9.0966403 1982-1999 –> 2000-2012 5.066137 22965.0632
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.9372055 15222.05151 10.3915969 1982-1999 –> 2000-2012 5.040767 22887.2253
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.0710965 15493.60879 7.4743037 1982-1999 –> 2000-2012 5.069315 22977.0155
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.0132568 15377.78041 10.1706781 1982-1999 –> 2000-2012 5.037039 22906.1625
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.9355479 15218.61243 10.0959981 1982-1999 –> 2000-2012 5.062506 22922.9208
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.9353583 15218.21892 9.9809728 1982-1999 –> 2000-2012 5.073967 22941.8531
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.9353531 15218.20829 9.9183776 1982-1999 –> 2000-2012 5.075286 22944.0337
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.0043004 15359.64612 8.4236570 1982-1999 –> 2000-2012 5.007455 22851.7815
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.0122539 15375.75242 7.7555229 1982-1999 –> 2000-2012 4.956218 22761.7690
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5025762 7382.56158 9.5778344 2000-2012 –> 2013-2019 5.439782 22604.6131
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.8888455 7835.27495 8.5188488 2000-2012 –> 2013-2019 5.959942 23328.8837
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8574884 7800.85254 10.4214853 2000-2012 –> 2013-2019 5.870745 23178.6329
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5172249 7400.96949 9.0295724 2000-2012 –> 2013-2019 5.452773 22619.5819
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.5218467 7406.75514 8.8637263 2000-2012 –> 2013-2019 5.457205 22624.9741
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.5248435 7410.50093 8.7703862 2000-2012 –> 2013-2019 5.460197 22628.7092
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.9322555 7882.31680 9.5171902 2000-2012 –> 2013-2019 5.936556 23241.9629
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.9042191 7852.01505 9.1455598 2000-2012 –> 2013-2019 5.916473 23227.7675
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate_star 2.9461588 7895.23611 9.5514753 2000-2012 –> 2013-2019 5.965932 23284.1768
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.9436569 7892.55660 9.5383334 2000-2012 –> 2013-2019 5.962518 23279.6580
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate 3.0056846 18822.16809 12.4065276 1982-1999 –> 2000-2012 4.748232 26407.5323
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.0056690 18824.12926 12.4231028 1982-1999 –> 2000-2012 4.725968 26362.2008
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 3.0690005 18977.80860 11.6955004 1982-1999 –> 2000-2012 4.766916 26463.6414
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.0672483 18975.54479 11.8064399 1982-1999 –> 2000-2012 4.708344 26332.8094
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.0006454 18811.64033 12.1807025 1982-1999 –> 2000-2012 4.640054 26164.9609
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate 3.0795605 19001.45410 11.5018057 1982-1999 –> 2000-2012 4.879486 26709.0923
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.0770059 18997.25817 11.6429362 1982-1999 –> 2000-2012 4.811806 26565.5292
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 3.0228132 18864.59410 11.8571713 1982-1999 –> 2000-2012 4.775474 26472.1574
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.0170744 18852.40653 12.0805525 1982-1999 –> 2000-2012 4.731779 26377.9834
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.1802522 19245.66230 16.5887426 1982-1999 –> 2000-2012 4.843431 26654.2002
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + silicate + phosphate_star 3.0119386 9679.51715 10.7624172 2000-2012 –> 2013-2019 6.029079 28530.0872
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate 2.9788303 9635.13901 11.8200738 2000-2012 –> 2013-2019 6.048789 28613.2784
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.9650939 9619.41830 13.2452400 2000-2012 –> 2013-2019 6.032362 28593.0113
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate 2.9699450 9625.68588 12.0059060 2000-2012 –> 2013-2019 5.975630 28447.8540
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.9454199 9595.89410 14.1197218 2000-2012 –> 2013-2019 5.951089 28420.0234
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 2.9371478 9583.11137 12.1029056 2000-2012 –> 2013-2019 6.006148 28560.9200
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.9354423 9582.88443 11.5172591 2000-2012 –> 2013-2019 6.002691 28558.4292
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8607188 9484.02387 12.9908230 2000-2012 –> 2013-2019 5.861364 28295.6642
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 3.0128665 9680.69810 11.2347214 2000-2012 –> 2013-2019 6.035680 28545.2922
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.0119349 9681.51235 10.7320038 2000-2012 –> 2013-2019 6.029009 28533.9189
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.7500817 17645.29216 8.2713471 1982-1999 –> 2000-2012 3.465930 26805.1032
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.7154103 17468.96143 8.3458403 1982-1999 –> 2000-2012 3.413667 26582.6472
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate 1.6774802 17267.69329 8.5079103 1982-1999 –> 2000-2012 3.378669 26387.4340
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.6736073 17249.09380 8.2877260 1982-1999 –> 2000-2012 3.324674 26231.1767
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.6259969 16991.89172 8.5737922 1982-1999 –> 2000-2012 3.276889 25973.4807
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.7307324 17548.21010 8.2521401 1982-1999 –> 2000-2012 3.357818 26461.9651
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.7273327 17530.68729 8.3485620 1982-1999 –> 2000-2012 3.450909 26713.4856
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.7313003 17551.13397 8.3131877 1982-1999 –> 2000-2012 3.464729 26760.5494
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.7995421 17893.66738 9.8915704 1982-1999 –> 2000-2012 3.438115 26838.2774
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.7074921 17427.72935 8.5902681 1982-1999 –> 2000-2012 3.246810 26082.5270
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.5528592 8647.36521 6.0949324 2000-2012 –> 2013-2019 3.334976 26456.3163
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5602026 8669.27464 9.2479005 2000-2012 –> 2013-2019 3.275613 26138.2361
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate 1.5853128 8741.42107 11.3323789 2000-2012 –> 2013-2019 3.262793 26009.1144
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.5701495 8698.78781 10.2930742 2000-2012 –> 2013-2019 3.243757 25947.8816
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.5113392 8521.50462 9.8586276 2000-2012 –> 2013-2019 3.137336 25513.3963
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5629599 8677.47443 9.1995601 2000-2012 –> 2013-2019 3.290293 26208.1617
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5636915 8679.64797 9.1718596 2000-2012 –> 2013-2019 3.294992 26230.7819
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5636729 8679.59251 8.6745343 2000-2012 –> 2013-2019 3.327320 26395.6968
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5637500 8679.82157 9.1648433 2000-2012 –> 2013-2019 3.296193 26236.8371
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.6126161 8822.72190 9.8649669 2000-2012 –> 2013-2019 3.320108 26250.4513
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1.6407753 9992.15615 9.0333908 1982-1999 –> 2000-2012 3.233653 15578.4505
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5581820 9724.85745 7.0858716 1982-1999 –> 2000-2012 3.144407 15300.7725
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5658754 9750.53797 7.1506719 1982-1999 –> 2000-2012 3.158560 15338.4740
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5685180 9759.32981 7.1849109 1982-1999 –> 2000-2012 3.163750 15351.9924
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5675216 9756.01643 7.2064206 1982-1999 –> 2000-2012 3.168392 15359.1161
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5683251 9758.68843 7.1802919 1982-1999 –> 2000-2012 3.162925 15350.1788
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 1.5710203 9765.64127 7.2593140 1982-1999 –> 2000-2012 3.203430 15424.4510
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.6631189 10064.67965 9.0858589 1982-1999 –> 2000-2012 3.263789 15667.4085
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate 1.6623000 10060.11173 9.1608837 1982-1999 –> 2000-2012 3.263842 15662.4513
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.5089126 9557.32907 6.8617741 1982-1999 –> 2000-2012 3.062577 15071.8912
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1.3986811 4622.74248 7.9016227 2000-2012 –> 2013-2019 3.039456 14614.8986
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2948994 4422.13238 5.8556737 2000-2012 –> 2013-2019 2.853081 14146.9898
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.3076003 4447.78330 5.4420741 2000-2012 –> 2013-2019 2.913799 14330.8899
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2981980 4428.81848 5.8103375 2000-2012 –> 2013-2019 2.864073 14179.3564
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2991096 4430.66314 5.7962963 2000-2012 –> 2013-2019 2.867628 14189.9930
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.2985783 4429.58809 5.7983381 2000-2012 –> 2013-2019 2.866100 14185.6045
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 1.3404592 4511.00664 4.9998005 2000-2012 –> 2013-2019 3.066020 14765.8612
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2988539 4430.14594 5.7896261 2000-2012 –> 2013-2019 2.867179 14188.8344
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 1.3164852 4463.57959 6.7665728 2000-2012 –> 2013-2019 2.887506 14229.2209
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.2951634 4422.66825 6.5370347 2000-2012 –> 2013-2019 2.804076 13979.9973
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate_star 1.7712033 105740.60614 8.6592218 1982-1999 –> 2000-2012 3.797368 175672.0867
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.6085955 100627.84945 9.5731035 1982-1999 –> 2000-2012 3.628556 170460.4362
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5623441 99078.29304 9.2748974 1982-1999 –> 2000-2012 3.953797 174465.5018
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.7379556 104736.11128 8.4598170 1982-1999 –> 2000-2012 3.589606 171706.2019
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5625467 99085.18096 9.2763881 1982-1999 –> 2000-2012 3.952592 174453.0191
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5627628 99092.52721 9.2776863 1982-1999 –> 2000-2012 3.952403 174454.7869
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5697516 99329.52872 9.0069451 1982-1999 –> 2000-2012 3.869460 173429.6458
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5627475 99092.00641 9.2780323 1982-1999 –> 2000-2012 3.952240 174452.2236
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate_star 1.7903476 106311.61521 6.7288963 1982-1999 –> 2000-2012 3.874523 177171.8768
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.5141500 97414.06935 7.8231764 1982-1999 –> 2000-2012 3.414454 165237.5303
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.4642019 56271.77579 8.6153265 2000-2012 –> 2013-2019 3.072797 156899.6252
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.3416924 53539.19697 8.6970660 2000-2012 –> 2013-2019 2.945212 153997.1795
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2907039 52330.44548 9.5505299 2000-2012 –> 2013-2019 2.853048 151408.7385
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2910467 52338.74526 9.5507250 2000-2012 –> 2013-2019 2.853593 151423.9262
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2915111 52349.98225 9.5538193 2000-2012 –> 2013-2019 2.854274 151442.5095
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.3033432 52634.97466 9.7868520 2000-2012 –> 2013-2019 2.873095 151964.5034
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2914640 52348.84310 9.5526995 2000-2012 –> 2013-2019 2.854211 151440.8495
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.3195818 53019.91856 10.4469688 2000-2012 –> 2013-2019 2.889565 152355.2751
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.4206974 55329.19962 11.8641876 2000-2012 –> 2013-2019 2.934847 152743.2690
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.3445589 53607.89224 10.0268171 2000-2012 –> 2013-2019 2.940396 153812.7767

5.3 Target variable coefficients

A data frame to map the target variable is prepared.

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

eras_backward <- lm_all_fitted_wide %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_era <- full_join(eras_backward, eras_forward) %>% 
  filter(str_detect(eras, "NA") == FALSE)

# extend best model selection from eras to era
lm_best_target <- full_join(
  lm_best %>% select(basin, gamma_slab, model, eras),
  eras_era)

lm_best_target <- left_join(lm_best_target, lm_all_fitted_wide)

rm(eras_era, eras_forward, eras_backward,
   lm_all_fitted)

5.4 Plot selected model residuals

# plot model diagnostics, if activated
if (params_local$plot_all_figures == "y") {
  # mutate predictors column
  lm_best_plot <- lm_best_target %>%
    select(basin, gamma_slab, model, eras, era) %>%
    mutate(
      predictors = str_remove(model, paste(params_local$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)[2]
      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_eras in unique(lm_best_basin_era_slab$eras)) {
          #i_eras <- unique(lm_best_basin_era_slab$eras)[1]
          print(i_eras)
          
          lm_best_basin_era_slab_eras <- lm_best_basin_era_slab %>%
            filter(eras == i_eras)
          
          for (i_predictors in unique(lm_best_basin_era_slab_eras$predictors)) {
            #i_predictors <- unique(lm_best_basin_era_slab$predictors)[1]
            print(i_predictors)
            # extract one model definition
            i_lm <- lm_all %>%
              filter(predictors == i_predictors) %>%
              select(lm_coeff) %>%
              pull()
            
            # fit model
            i_lm_fit <- lm(as.formula(i_lm),
                           data = GLODAP_basin_era_slab)
            
            p_model <- ggnostic(
              i_lm_fit,
              columnsY = c(params_local$MLR_target, ".fitted", ".resid"),
              title = paste(
                "era:",
                i_era,
                "| eras:",
                i_eras,
                "| 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_eras,
                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
  )
  
}

Individual residual plots of the MLR models for each basin, era, eras and neutral density (gamma) slab are available at:

/nfs/kryo/work/jenmueller/emlr_cant/model/v_XXX/figures/eMLR_diagnostics/

5.5 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)

5.6 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
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
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
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
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
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
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
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
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,
              values_fill = 0)

# 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] 7 2 5 7 9 9 9
(26,26.5] 8 3 6 8 6 9 8
(26.5,26.75] 9 3 6 8 5 8 8
(26.75,27] 8 1 7 8 4 10 8
(27,27.25] 8 5 4 6 8 10 7
(27.25,27.5] 8 6 3 7 7 8 9
(27.5,27.75] 6 2 5 9 10 6 9
(27.75,27.85] 7 3 5 7 10 9 7
(27.85,27.95] 7 2 6 9 8 7 9
(27.95,28.05] 7 5 4 9 8 6 9
(28.05,28.1] 8 1 9 8 8 4 8
(28.1,28.15] 8 2 7 9 6 8 8
(28.15,28.2] 10 8 2 7 6 5 8
(28.2, Inf] 9 10 0 5 8 6 6
total 110.00 53.00 69.00 107.00 103.00 105.00 113.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 6 1 8 8 6 10 7
(26,26.5] 8 4 5 7 9 7 9
(26.5,26.75] 7 3 5 8 5 10 9
(26.75,27] 9 2 7 7 6 10 6
(27,27.25] 9 5 4 5 8 10 6
(27.25,27.5] 7 6 2 8 9 9 7
(27.5,27.75] 7 2 5 8 10 7 8
(27.75,27.85] 7 3 5 7 10 9 7
(27.85,27.95] 8 2 7 8 8 7 8
(27.95,28.05] 8 4 6 9 6 6 9
(28.05,28.1] 9 2 8 8 7 5 8
(28.1,28.15] 8 2 7 9 8 6 8
(28.15,28.2] 10 8 2 7 6 5 8
(28.2, Inf] 10 10 0 5 7 6 5
total 113.00 54.00 71.00 104.00 105.00 107.00 105.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 7 2 6 8 10 6 8
(26,26.5] 9 2 7 9 7 7 7
(26.5,26.75] 7 2 6 9 9 7 8
(26.75,27] 8 5 5 10 6 4 8
(27,27.25] 10 3 7 10 4 4 6
(27.25,27.5] 8 2 6 8 8 10 5
(27.5,27.75] 6 2 6 8 9 10 6
(27.75,27.85] 9 5 4 7 8 9 7
(27.85,27.95] 10 9 1 5 5 6 8
(27.95,28.05] 10 3 6 7 8 5 8
(28.05,28.1] 7 2 6 8 6 10 8
(28.1, Inf] 8 6 3 9 7 8 7
total 99.00 43.00 63.00 98.00 87.00 86.00 86.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 9 3 6 6 10 5 8
(26,26.5] 8 1 7 8 4 10 8
(26.5,26.75] 7 2 6 9 7 9 8
(26.75,27] 9 1 8 9 6 7 7
(27,27.25] 9 1 9 9 5 6 6
(27.25,27.5] 7 1 7 7 9 10 5
(27.5,27.75] 8 2 5 6 9 10 7
(27.75,27.85] 8 3 5 8 6 9 9
(27.85,27.95] 10 10 0 5 7 6 5
(27.95,28.05] 8 5 4 7 9 8 8
(28.05,28.1] 6 2 6 7 8 10 8
(28.1, Inf] 7 3 5 8 8 10 7
total 96.00 34.00 68.00 89.00 88.00 100.00 86.00

6.4 RMSE alternatives

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

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

Version Author Date
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
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
ecf335c Donghe-Zhu 2021-01-31
a618965 Donghe-Zhu 2021-01-31
59e006e Donghe-Zhu 2021-01-31
a1c8f87 Donghe-Zhu 2021-01-31
ae5c18f Donghe-Zhu 2021-01-31
b50fe52 Donghe-Zhu 2021-01-31
ac99ae5 jens-daniel-mueller 2021-01-29
b5bdcaf Donghe-Zhu 2021-01-29
442010d Donghe-Zhu 2021-01-29
372adf5 Donghe-Zhu 2021-01-29
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] fs_1.5.0                 webshot_0.5.2            RColorBrewer_1.1-2      
 [4] httr_1.4.2               rprojroot_2.0.2          tools_4.0.3             
 [7] backports_1.1.10         R6_2.5.0                 nortest_1.0-4           
[10] DBI_1.1.0                colorspace_2.0-0         withr_2.3.0             
[13] gridExtra_2.3            tidyselect_1.1.0         curl_4.3                
[16] compiler_4.0.3           git2r_0.27.1             cli_2.2.0               
[19] rvest_0.3.6              xml2_1.3.2               sass_0.2.0              
[22] labeling_0.4.2           scales_1.1.1             checkmate_2.0.0         
[25] goftest_1.2-2            digest_0.6.27            foreign_0.8-80          
[28] rmarkdown_2.5            rio_0.5.16               pkgconfig_2.0.3         
[31] htmltools_0.5.0          highr_0.8                dbplyr_1.4.4            
[34] rlang_0.4.10             readxl_1.3.1             rstudioapi_0.13         
[37] farver_2.0.3             generics_0.1.0           jsonlite_1.7.2          
[40] zip_2.1.1                car_3.0-10               magrittr_2.0.1          
[43] Matrix_1.2-18            Rcpp_1.0.5               munsell_0.5.0           
[46] fansi_0.4.1              abind_1.4-5              lifecycle_0.2.0         
[49] stringi_1.5.3            whisker_0.4              yaml_2.2.1              
[52] carData_3.0-4            plyr_1.8.6               grid_4.0.3              
[55] blob_1.2.1               parallel_4.0.3           promises_1.1.1          
[58] crayon_1.3.4             lattice_0.20-41          haven_2.3.1             
[61] hms_0.5.3                pillar_1.4.7             reprex_0.3.0            
[64] glue_1.4.2               evaluate_0.14            RcppArmadillo_0.10.1.2.2
[67] data.table_1.13.6        modelr_0.1.8             vctrs_0.3.6             
[70] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[73] reshape_0.8.8            assertthat_0.2.1         xfun_0.20               
[76] openxlsx_4.2.3           RcppEigen_0.3.3.9.1      later_1.1.0.1           
[79] viridisLite_0.3.0        ellipsis_0.3.1           here_1.0.1