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

3 Apply predictor threshold

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

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

This results in a total number of MLR models of:

  • 112

4 Fit all models

Individual linear regression models were fitted for the chosen target variable:

  • cstar_tref

as a function of each predictor combination. Fitting was performed separately within each basin, era, and slab. Model diagnostics, such as the root mean squared error (RMSE), were calculated for each fitted model.

# loop across all basins, era, gamma slabs, and MLRs
# fit all MLR models
for (i_basin in unique(GLODAP$basin)) {
  for (i_era in unique(GLODAP$era)) {
    # i_basin <- unique(GLODAP$basin)[1]
    # i_era   <- unique(GLODAP$era)[1]
    print(i_basin)
    print(i_era)
    
    GLODAP_basin_era <- GLODAP %>%
      filter(basin == i_basin, era == i_era)
    
    for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
      # i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
      print(i_gamma_slab)
      
      GLODAP_basin_era_slab <- GLODAP_basin_era %>%
        filter(gamma_slab == i_gamma_slab)
      
      for (i_predictors in unique(lm_all$predictors)) {
        # i_predictors <- unique(lm_all$predictors)[110]

        # extract one model definition
        i_lm <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(lm_coeff) %>%
          pull()
        
        # extract number of predictors
        i_n_predictors <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(n) %>%
          pull()
        
        # fit model
        i_lm_fit <- lm(as.formula(i_lm),
                       data = GLODAP_basin_era_slab)
        
        # find max predictor correlation
        i_cor_max <- GLODAP_basin_era_slab %>%
          select(!!!syms(str_split(i_predictors, " ",
                                         simplify = TRUE))) %>%
          correlate(quiet = TRUE) %>% 
          select(-term) %>% 
          abs() %>% 
          max(na.rm = TRUE)
        
        # calculate root mean squared error
        i_rmse <- sqrt(
          c(crossprod(i_lm_fit$residuals)) / 
            length(i_lm_fit$residuals)
        )

        # calculate maximum residual
        i_resid_max <- max(abs(i_lm_fit$residuals))
        
        # calculate Akaike information criterion aic
        i_aic <- AIC(i_lm_fit)
        
        # collect model coefficients and diagnostics
        coefficients <- tidy(i_lm_fit)
        
        coefficients <- coefficients %>%
          mutate(
            basin = i_basin,
            era = i_era,
            gamma_slab = i_gamma_slab,
            model = i_lm,
            rmse = i_rmse,
            aic = i_aic,
            resid_max = i_resid_max,
            n_predictors = i_n_predictors,
            na_predictor = anyNA(coefficients$estimate),
            cor_max = i_cor_max
          )
        
        if (exists("lm_all_fitted")) {
          lm_all_fitted <- bind_rows(lm_all_fitted, coefficients)
        }
        
        if (!exists("lm_all_fitted")) {
          lm_all_fitted <- coefficients
        }
        
        # # plot model diagnostics, if activated
        # if (params_local$plot_all_figures == "y") {
        #   p_model <- ggnostic(
        #     i_lm_fit,
        #     columnsY = c(params_local$MLR_target, ".fitted", ".resid"),
        #     title = paste(
        #       "| era:",
        #       i_era,
        #       "| basin:",
        #       i_basin,
        #       "| gamma slab:",
        #       i_gamma_slab,
        #       "| predictors:",
        #       i_predictors
        #     )
        #   )
        #   
        #   ggsave(
        #     plot = p_model,
        #     path = paste(path_version_figures, "eMLR_diagnostics/", sep = ""),
        #     filename = paste(
        #       "MLR_residuals",
        #       i_era,
        #       i_basin,
        #       i_gamma_slab,
        #       i_predictors,
        #       "predictors.png",
        #       sep = "_"
        #     ),
        #     width = 14,
        #     height = 8
        #   )
        #   
        #   rm(p_model)
        #   
        # }
        
      }
      
      
    }
  }
  
}

rm(i_lm_fit, coefficients, i_rmse,
   GLODAP_basin_era, GLODAP_basin_era_slab,
   i_lm,
   i_basin, i_era, i_gamma_slab, i_predictors,
   lm_all,
   i_aic, i_n_predictors, i_resid_max)

5 Prepare coeffcients

Coefficients are prepared for the mapping of Cant and the chosen target variable.

5.1 Formatting

# select relevant columns
lm_all_fitted <- lm_all_fitted %>% 
  select(basin, gamma_slab, era, model, n_predictors, 
         term, estimate, 
         rmse, aic, resid_max, na_predictor, cor_max)

# set coefficient to zero if not fitted (=NA)
lm_all_fitted <- lm_all_fitted %>% 
  mutate(estimate = if_else(is.na(estimate), 0, estimate))

# Prepare model coefficients for mapping of target variable
lm_all_fitted_wide <- lm_all_fitted %>% 
  pivot_wider(values_from = estimate,
              names_from = term,
              names_prefix = "coeff_",
              values_fill = 0)

5.2 Predictor selection

Within each basin and slab, the following number of best linear regression models was selected:

  • 10

The criterion used to select the best models was:

  • rmse

The criterion was summed up for two adjacent eras, and the models with lowest summed values were selected.

Please note, that currently the lm() function produces NAs for some predictors. It is not yet entirely clear when this happens, but presumably it is caused by some form of collinearity between predictors, such that including another predictor does not help to explain the target variable any better. The issues also expresses as exactly identical rmse values of different models. As an interim solution, models with fitted NA predictors were not included.

# remove models with predictors fitted as NA

lm_all_fitted_wide <- lm_all_fitted_wide %>%
  filter(na_predictor == FALSE)
# calculate RMSE sum for adjacent eras
lm_all_fitted_wide_eras <- lm_all_fitted_wide  %>%
  select(basin, gamma_slab, model, era, rmse, aic, resid_max) %>% 
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> "),
         rmse_sum = rmse + lag(rmse),
         aic_sum = aic + lag(aic)
         ) %>% 
  ungroup() %>% 
  select(-c(era)) %>% 
  drop_na()

# subset models with lowest summed criterion
# chose which criterion is applied

if (params_local$MLR_criterion == "aic") {
  lm_best <- lm_all_fitted_wide_eras %>%
    group_by(basin, gamma_slab, eras) %>%
    slice_min(order_by = aic_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
} else {
  lm_best <- lm_all_fitted_wide_eras %>%
    group_by(basin, gamma_slab, eras) %>%
    slice_min(order_by = rmse_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
}


# print table
lm_best %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")
basin gamma_slab model rmse aic resid_max eras rmse_sum aic_sum
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 1.0529313 508.0936 4.021817 1982-1999 –> 2000-2012 2.3845411 1286.0801
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.0669064 510.5238 4.506279 1982-1999 –> 2000-2012 2.3985898 1286.5351
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.0650698 511.9449 4.426016 1982-1999 –> 2000-2012 2.3967507 1289.9554
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 1.0574420 509.5299 4.227758 1982-1999 –> 2000-2012 2.3903131 1287.9406
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.0589440 510.0068 4.281729 1982-1999 –> 2000-2012 2.3921140 1288.5180
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 1.0709739 511.8023 4.694811 1982-1999 –> 2000-2012 2.4040133 1288.2696
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0646493 511.8122 4.234683 1982-1999 –> 2000-2012 2.3962400 1289.7923
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.0694684 513.3297 4.624413 1982-1999 –> 2000-2012 2.4024546 1291.7791
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.0708017 513.7483 4.671370 1982-1999 –> 2000-2012 2.4040952 1292.3010
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 1.0605961 510.5306 4.333869 1982-1999 –> 2000-2012 2.3945656 1289.3103
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 1.1285639 254.2220 2.798637 2000-2012 –> 2013-2019 2.1814952 762.3155
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.1819575 261.4332 3.306338 2000-2012 –> 2013-2019 2.2470273 773.3781
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 1.1357044 255.2059 2.761390 2000-2012 –> 2013-2019 2.1931464 764.7358
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.1385676 255.5987 2.813203 2000-2012 –> 2013-2019 2.1975116 765.6055
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.1929038 262.8713 2.724893 2000-2012 –> 2013-2019 2.2980531 787.2281
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.2437146 269.3784 3.455189 2000-2012 –> 2013-2019 2.3083639 781.1906
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.1901456 262.5102 3.453009 2000-2012 –> 2013-2019 2.2596141 775.8399
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.1931661 262.9056 3.497480 2000-2012 –> 2013-2019 2.2639678 776.6539
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 1.1417526 256.0345 2.864096 2000-2012 –> 2013-2019 2.2023487 766.5651
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.1950624 263.1534 3.519214 2000-2012 –> 2013-2019 2.2672406 777.3333
Atlantic (26,26.8] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.8890327 14988.1178 17.924664 1982-1999 –> 2000-2012 7.7302552 35875.8233
Atlantic (26,26.8] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.8093271 14876.4608 35.094315 1982-1999 –> 2000-2012 7.5543650 35572.7063
Atlantic (26,26.8] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.9527677 15075.7677 12.077204 1982-1999 –> 2000-2012 7.6801708 35736.3775
Atlantic (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate 3.9016580 15005.5940 34.479878 1982-1999 –> 2000-2012 7.7462780 35899.9743
Atlantic (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.9178675 15027.9487 34.551996 1982-1999 –> 2000-2012 7.7812613 35959.1070
Atlantic (26,26.8] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.0773464 15243.0835 12.235786 1982-1999 –> 2000-2012 7.9517081 36195.6453
Atlantic (26,26.8] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 3.9571830 15081.7873 34.091338 1982-1999 –> 2000-2012 7.8588609 36087.3938
Atlantic (26,26.8] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.9171389 15026.9458 19.265703 1982-1999 –> 2000-2012 7.7858304 35968.4500
Atlantic (26,26.8] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.9335417 15049.4774 20.037089 1982-1999 –> 2000-2012 7.8206681 36026.8731
Atlantic (26,26.8] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3.9537134 15077.0576 19.792862 1982-1999 –> 2000-2012 7.8585277 36088.7307
Atlantic (26,26.8] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 3.9880919 7594.8924 11.221907 2000-2012 –> 2013-2019 8.0029119 22752.6485
Atlantic (26,26.8] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.9766030 7589.0857 10.789211 2000-2012 –> 2013-2019 7.8656357 22577.2035
Atlantic (26,26.8] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.6938392 7389.4868 10.426509 2000-2012 –> 2013-2019 7.5031663 22265.9476
Atlantic (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate 3.7903241 7459.2615 10.303387 2000-2012 –> 2013-2019 7.6919822 22464.8555
Atlantic (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.8027479 7468.1166 10.282146 2000-2012 –> 2013-2019 7.7206154 22496.0653
Atlantic (26,26.8] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 3.8477109 7499.9242 10.304416 2000-2012 –> 2013-2019 7.8048939 22581.7116
Atlantic (26,26.8] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3.9836624 7593.8852 10.957736 2000-2012 –> 2013-2019 7.9973746 22752.1534
Atlantic (26,26.8] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.9827716 7593.2800 10.489451 2000-2012 –> 2013-2019 7.8999104 22620.2258
Atlantic (26,26.8] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.9885200 7597.1828 10.434835 2000-2012 –> 2013-2019 7.9220617 22646.6603
Atlantic (26,26.8] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 4.0053015 7608.5443 10.301486 2000-2012 –> 2013-2019 7.9590149 22685.6019
Atlantic (26.8,27.2] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2.6049278 23706.1447 12.821629 1982-1999 –> 2000-2012 4.7227741 52194.8778
Atlantic (26.8,27.2] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.7988071 24419.8743 15.180973 1982-1999 –> 2000-2012 5.0446380 53676.7874
Atlantic (26.8,27.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 2.7087789 24095.9017 12.446419 1982-1999 –> 2000-2012 5.2917970 55190.9183
Atlantic (26.8,27.2] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.4952938 23277.4496 12.395986 1982-1999 –> 2000-2012 4.5472903 51351.5796
Atlantic (26.8,27.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5926602 23659.0811 11.819352 1982-1999 –> 2000-2012 4.7711050 52518.1196
Atlantic (26.8,27.2] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.6956406 24047.4269 16.030288 1982-1999 –> 2000-2012 4.9917184 53596.7763
Atlantic (26.8,27.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.7291979 24170.7744 18.335328 1982-1999 –> 2000-2012 5.0677790 53960.8811
Atlantic (26.8,27.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 2.8307542 24535.0326 13.200750 1982-1999 –> 2000-2012 5.1366416 54140.3412
Atlantic (26.8,27.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.9021450 24783.3550 15.154767 1982-1999 –> 2000-2012 5.3019287 54912.5616
Atlantic (26.8,27.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.6069906 23714.0366 43.074769 1982-1999 –> 2000-2012 4.8105108 52723.3009
Atlantic (26.8,27.2] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.1662044 13894.8061 17.068745 2000-2012 –> 2013-2019 5.7711322 37600.9508
Atlantic (26.8,27.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 3.0839375 13752.6967 17.006646 2000-2012 –> 2013-2019 5.7927164 37848.5984
Atlantic (26.8,27.2] cstar_tref ~ sal + aou + silicate + phosphate 3.1017187 13781.7308 19.605376 2000-2012 –> 2013-2019 5.8105956 37875.9932
Atlantic (26.8,27.2] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.0569199 13705.1978 21.445281 2000-2012 –> 2013-2019 5.5522137 36982.6474
Atlantic (26.8,27.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.0954121 13772.7440 20.313104 2000-2012 –> 2013-2019 5.6880723 37431.8252
Atlantic (26.8,27.2] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.1772794 13913.6548 20.412323 2000-2012 –> 2013-2019 5.8729200 37961.0816
Atlantic (26.8,27.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.3115817 14137.1353 23.434895 2000-2012 –> 2013-2019 6.1922401 38846.4009
Atlantic (26.8,27.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.2014731 13954.6027 20.350140 2000-2012 –> 2013-2019 5.9306710 38125.3770
Atlantic (26.8,27.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.3844672 14254.6528 18.021890 2000-2012 –> 2013-2019 6.2152213 38789.6854
Atlantic (26.8,27.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.8811712 13385.5769 24.655222 2000-2012 –> 2013-2019 5.4881618 37099.6135
Atlantic (27.2,27.8] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.1757893 32231.2271 20.869331 1982-1999 –> 2000-2012 5.7146447 73000.8298
Atlantic (27.2,27.8] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.1759618 32229.9070 21.151860 1982-1999 –> 2000-2012 5.7369712 73148.1435
Atlantic (27.2,27.8] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.9166117 31165.8648 21.944476 1982-1999 –> 2000-2012 5.3273116 71037.4244
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate 3.2032099 32338.8125 22.469231 1982-1999 –> 2000-2012 5.7568597 73209.1532
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.1110548 31973.5090 14.366119 1982-1999 –> 2000-2012 5.5786023 72249.1763
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.1200544 32009.6572 19.335570 1982-1999 –> 2000-2012 5.6799906 72922.6269
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.9646699 31370.3827 22.962120 1982-1999 –> 2000-2012 5.4033109 71441.7419
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.1602554 32169.8665 24.980092 1982-1999 –> 2000-2012 5.7574391 73333.2896
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.1435113 32103.3869 24.153462 1982-1999 –> 2000-2012 5.7512899 73337.3942
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.1484843 32123.1682 24.748967 1982-1999 –> 2000-2012 5.7503303 73317.6875
Atlantic (27.2,27.8] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.0138129 18916.4175 24.683522 2000-2012 –> 2013-2019 7.1896022 51147.6445
Atlantic (27.2,27.8] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 3.7123766 18391.0106 26.346727 2000-2012 –> 2013-2019 6.7824309 50198.5018
Atlantic (27.2,27.8] cstar_tref ~ sal + aou + silicate + phosphate 3.7338343 18427.7983 28.528346 2000-2012 –> 2013-2019 6.8169993 50286.6170
Atlantic (27.2,27.8] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.7204750 18405.6760 27.646487 2000-2012 –> 2013-2019 6.6370867 49571.5407
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.7919939 18533.8194 17.331054 2000-2012 –> 2013-2019 6.9030487 50507.3284
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.8425282 18622.9148 22.550614 2000-2012 –> 2013-2019 6.9625826 50632.5719
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.7335455 18429.2778 28.438479 2000-2012 –> 2013-2019 6.6982154 49799.6606
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.9472747 18803.9173 30.746162 2000-2012 –> 2013-2019 7.1075301 50973.7838
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.9021439 18726.5271 28.929716 2000-2012 –> 2013-2019 7.0456552 50829.9140
Atlantic (27.2,27.8] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.9191116 18755.7277 30.301004 2000-2012 –> 2013-2019 7.0675959 50878.8959
Atlantic (27.8,27.9] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3.0476531 12868.0168 81.780590 1982-1999 –> 2000-2012 5.4914003 28542.0711
Atlantic (27.8,27.9] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.1183048 12982.3012 73.984632 1982-1999 –> 2000-2012 5.6425583 28873.8548
Atlantic (27.8,27.9] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.0218764 12824.9189 79.766840 1982-1999 –> 2000-2012 5.5111994 28624.1076
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + nitrate + phosphate 3.1640789 13058.2419 89.496383 1982-1999 –> 2000-2012 5.6267083 28784.4207
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + phosphate 3.2406006 13177.4937 80.912266 1982-1999 –> 2000-2012 5.8188571 29212.3973
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.5738885 12010.7440 32.175994 1982-1999 –> 2000-2012 5.0229280 27699.4484
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.1570872 13047.0173 87.178381 1982-1999 –> 2000-2012 5.6929871 28971.7441
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.3141969 13293.4387 93.760615 1982-1999 –> 2000-2012 5.9197878 29401.7604
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 3.2960446 13265.5714 95.572250 1982-1999 –> 2000-2012 5.7925628 29084.3057
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.3120399 13290.1354 92.752085 1982-1999 –> 2000-2012 5.9084877 29374.6519
Atlantic (27.8,27.9] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2.7163855 6610.9605 24.468703 2000-2012 –> 2013-2019 5.7640386 19478.9773
Atlantic (27.8,27.9] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.8361089 6728.6215 27.328764 2000-2012 –> 2013-2019 5.8579853 19553.5405
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + nitrate + phosphate 2.7301970 6624.7960 24.747403 2000-2012 –> 2013-2019 5.8942760 19683.0379
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.8537508 6745.5384 26.191802 2000-2012 –> 2013-2019 6.2596436 20177.4555
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.8265818 6719.4422 23.123666 2000-2012 –> 2013-2019 5.4004703 18730.1862
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.8894257 6779.4298 27.966117 2000-2012 –> 2013-2019 6.0465128 19826.4472
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.9696416 6854.1321 28.539746 2000-2012 –> 2013-2019 6.2838384 20147.5707
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2.7566583 6651.1087 25.015350 2000-2012 –> 2013-2019 6.0527029 19916.6800
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.9580732 6843.4843 28.659117 2000-2012 –> 2013-2019 6.2701132 20133.6197
Atlantic (27.8,27.9] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.9761188 6860.0758 28.456667 2000-2012 –> 2013-2019 6.2861048 20147.0636
Atlantic (27.9,28.1] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3.0353096 15816.7662 27.753840 1982-1999 –> 2000-2012 5.9985122 37094.9816
Atlantic (27.9,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 2.9530508 15645.1048 28.365399 1982-1999 –> 2000-2012 5.7793567 36521.8369
Atlantic (27.9,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate 3.0307699 15805.4146 30.200762 1982-1999 –> 2000-2012 6.0340957 37195.7905
Atlantic (27.9,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 2.9853149 15712.9983 28.583363 1982-1999 –> 2000-2012 5.8488618 36700.8426
Atlantic (27.9,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.9182477 15571.0319 25.339640 1982-1999 –> 2000-2012 5.9356573 37003.1184
Atlantic (27.9,28.1] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2.9580799 15655.7362 26.215211 1982-1999 –> 2000-2012 6.0384664 37263.1540
Atlantic (27.9,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 3.0172724 15779.5271 30.280490 1982-1999 –> 2000-2012 6.0161720 37159.3844
Atlantic (27.9,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3.0318909 15809.7251 27.198793 1982-1999 –> 2000-2012 5.9844675 37057.4479
Atlantic (27.9,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.0451837 15837.0585 25.723841 1982-1999 –> 2000-2012 5.9839591 37045.0131
Atlantic (27.9,28.1] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3.0317310 15809.3955 27.104322 1982-1999 –> 2000-2012 5.9821775 37050.9927
Atlantic (27.9,28.1] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2.9459116 8396.8428 26.617676 2000-2012 –> 2013-2019 5.9812212 24213.6091
Atlantic (27.9,28.1] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2.7824213 8205.3402 26.236983 2000-2012 –> 2013-2019 5.7755555 23934.6822
Atlantic (27.9,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 2.6535975 8046.3431 28.239775 2000-2012 –> 2013-2019 5.6066483 23691.4478
Atlantic (27.9,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate 2.6733422 8069.2069 29.469179 2000-2012 –> 2013-2019 5.7041121 23874.6214
Atlantic (27.9,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 2.6655502 8061.4167 28.790431 2000-2012 –> 2013-2019 5.6508651 23774.4150
Atlantic (27.9,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate 2.7619183 8180.5338 25.763326 2000-2012 –> 2013-2019 5.7285528 23854.3129
Atlantic (27.9,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.7184662 8127.3473 24.745497 2000-2012 –> 2013-2019 5.6367139 23698.3792
Atlantic (27.9,28.1] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2.7562851 8173.6860 25.631013 2000-2012 –> 2013-2019 5.7143649 23829.4222
Atlantic (27.9,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 2.6475444 8038.6835 29.634210 2000-2012 –> 2013-2019 5.6648168 23818.2106
Atlantic (27.9,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 2.9588859 8411.5821 26.124471 2000-2012 –> 2013-2019 5.9907769 24221.3072
Atlantic (28.1,28.2] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 0.8439233 8536.3485 7.593862 1982-1999 –> 2000-2012 1.5746245 19036.3713
Atlantic (28.1,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.8861600 8867.5073 6.460803 1982-1999 –> 2000-2012 1.6606546 19917.7882
Atlantic (28.1,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.8664944 8716.4085 7.542880 1982-1999 –> 2000-2012 1.6308643 19643.8388
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.8504911 8587.2347 7.418466 1982-1999 –> 2000-2012 1.5896611 19194.5910
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate 0.8504032 8588.5299 7.510925 1982-1999 –> 2000-2012 1.5878841 19176.1792
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.8504903 8589.2286 7.426875 1982-1999 –> 2000-2012 1.5886548 19185.6683
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.8501907 8586.8249 7.612598 1982-1999 –> 2000-2012 1.5889554 19190.9765
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 0.8563499 8636.0690 7.491839 1982-1999 –> 2000-2012 1.6020058 19328.3136
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8859848 8868.1583 8.112323 1982-1999 –> 2000-2012 1.6617056 19935.4496
Atlantic (28.1,28.2] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 0.8231615 8366.4182 13.869518 1982-1999 –> 2000-2012 1.4598735 17560.0637
Atlantic (28.1,28.2] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 0.9482691 4903.6413 8.416903 2000-2012 –> 2013-2019 1.7921924 13439.9898
Atlantic (28.1,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.9843129 5035.1948 7.395627 2000-2012 –> 2013-2019 1.8704729 13902.7021
Atlantic (28.1,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.9627538 4957.9118 8.657656 2000-2012 –> 2013-2019 1.8292482 13674.3202
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.9560785 4931.0032 8.225577 2000-2012 –> 2013-2019 1.8065695 13518.2379
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate 0.9559603 4932.5607 8.338042 2000-2012 –> 2013-2019 1.8063635 13521.0906
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.9560784 4933.0029 8.222789 2000-2012 –> 2013-2019 1.8065687 13522.2316
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.9552180 4929.7799 8.585688 2000-2012 –> 2013-2019 1.8054087 13516.6049
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 0.9617924 4954.3351 8.348077 2000-2012 –> 2013-2019 1.8181423 13590.4041
Atlantic (28.1,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.9823514 5030.0538 8.939639 2000-2012 –> 2013-2019 1.8683362 13898.2120
Atlantic (28.1,28.2] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 0.8670608 4583.1265 15.561133 2000-2012 –> 2013-2019 1.6902223 12949.5447
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate 0.3429184 2958.3108 2.037539 1982-1999 –> 2000-2012 0.6478106 5713.4989
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 0.3391792 2867.6653 2.211193 1982-1999 –> 2000-2012 0.6440319 5623.3136
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.3501288 3134.1416 1.949898 1982-1999 –> 2000-2012 0.6565772 5949.7518
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.3534411 3213.7066 1.988553 1982-1999 –> 2000-2012 0.6596790 6021.1606
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 0.3255418 2520.8956 2.143799 1982-1999 –> 2000-2012 0.6303960 5276.6069
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.3490030 3108.9287 2.067840 1982-1999 –> 2000-2012 0.6550932 5912.6573
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 0.3393669 2872.3409 2.206547 1982-1999 –> 2000-2012 0.6442495 5629.1521
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3395940 2877.9930 2.205103 1982-1999 –> 2000-2012 0.6447888 5646.9529
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.3509290 3155.4335 2.134668 1982-1999 –> 2000-2012 0.6570626 5960.8427
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 0.3379706 2837.5014 2.209241 1982-1999 –> 2000-2012 0.6389390 5440.9641
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate 0.3950700 2362.2400 2.495027 2000-2012 –> 2013-2019 0.7379884 5320.5508
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 0.3783565 2157.0140 2.771724 2000-2012 –> 2013-2019 0.7175357 5024.6793
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.4135856 2581.8126 2.572196 2000-2012 –> 2013-2019 0.7637143 5715.9542
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.4165997 2616.6231 2.435991 2000-2012 –> 2013-2019 0.7700408 5830.3298
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 0.3619309 1944.2398 2.679695 2000-2012 –> 2013-2019 0.6874727 4465.1354
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.4134611 2582.3694 2.655486 2000-2012 –> 2013-2019 0.7624641 5691.2982
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 0.3786330 2160.5167 2.768969 2000-2012 –> 2013-2019 0.7179999 5032.8576
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3788945 2163.8268 2.767863 2000-2012 –> 2013-2019 0.7184885 5041.8198
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.4031930 2461.8100 2.685125 2000-2012 –> 2013-2019 0.7541221 5617.2435
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 0.3777333 2149.1120 2.771424 2000-2012 –> 2013-2019 0.7157039 4986.6135
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.9368924 35970.5975 33.206006 1982-1999 –> 2000-2012 12.1836597 85952.5079
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 6.2801597 36600.1682 29.818984 1982-1999 –> 2000-2012 12.8626803 87384.7542
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.2388929 36528.0930 29.366420 1982-1999 –> 2000-2012 12.7725705 87200.2068
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 6.0579613 36197.4241 33.818877 1982-1999 –> 2000-2012 12.4174769 86454.2748
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.1136918 36300.3175 34.053133 1982-1999 –> 2000-2012 12.5238257 86679.0210
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.4254929 36857.2246 30.208689 1982-1999 –> 2000-2012 13.1429671 87953.7368
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6.2733617 36589.9990 29.675295 1982-1999 –> 2000-2012 12.8523383 87368.3078
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.3773992 36774.8088 29.718986 1982-1999 –> 2000-2012 13.0347184 87735.0625
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.4461499 36895.2887 29.845366 1982-1999 –> 2000-2012 13.1621308 87990.3838
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6.1369641 36343.0072 34.054990 1982-1999 –> 2000-2012 12.5721086 86781.5633
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.6641426 18718.1540 28.268543 2000-2012 –> 2013-2019 11.6010350 54688.7514
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.9966384 19054.5361 24.645119 2000-2012 –> 2013-2019 12.2767981 55654.7043
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.9243606 18984.6030 23.875073 2000-2012 –> 2013-2019 12.1632535 55512.6960
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 5.7682183 18826.1621 29.166503 2000-2012 –> 2013-2019 11.8261796 55023.5862
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.8220861 18881.3024 29.808032 2000-2012 –> 2013-2019 11.9357779 55181.6200
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.9924378 19052.3794 24.457831 2000-2012 –> 2013-2019 12.2657995 55642.3784
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.0470335 19106.1797 24.650519 2000-2012 –> 2013-2019 12.4244327 55880.9886
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 5.8363044 18895.7715 29.341398 2000-2012 –> 2013-2019 11.9732685 55238.7787
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 5.9978940 19055.7781 27.345614 2000-2012 –> 2013-2019 12.4545857 55967.4267
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.9955754 19055.4845 27.200018 2000-2012 –> 2013-2019 12.4477444 55961.2600
Indo-Pacific (26,26.8] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.6199548 64645.4743 37.089849 1982-1999 –> 2000-2012 9.0638277 153579.9948
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.8242499 65593.7003 56.356823 1982-1999 –> 2000-2012 9.3833055 155310.0229
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.8681188 65792.0728 56.308779 1982-1999 –> 2000-2012 9.4419727 155607.4044
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.6498108 64786.6354 35.212652 1982-1999 –> 2000-2012 9.0460965 153392.2260
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.7432544 65222.6575 34.972147 1982-1999 –> 2000-2012 9.2002384 154247.1855
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4.8704518 65802.5724 56.209203 1982-1999 –> 2000-2012 9.4490013 155649.2531
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.8917582 65896.2291 54.417884 1982-1999 –> 2000-2012 9.6943665 157200.5895
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.7457183 65234.0380 40.259916 1982-1999 –> 2000-2012 9.5072391 156277.8943
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7474245 65241.9151 35.164825 1982-1999 –> 2000-2012 9.2147567 154337.2958
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + silicate + phosphate_star 4.7747259 65365.5765 33.757204 1982-1999 –> 2000-2012 9.5399697 156431.3124
Indo-Pacific (26,26.8] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.7381641 34888.0729 37.416197 2000-2012 –> 2013-2019 9.3581189 99533.5472
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate 4.9385239 35373.6429 43.798277 2000-2012 –> 2013-2019 9.7627738 100967.3432
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.0112464 35545.0263 42.147309 2000-2012 –> 2013-2019 9.8793651 101337.0991
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.8112061 35067.4275 35.106247 2000-2012 –> 2013-2019 9.4610169 99854.0629
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.9254596 35342.5872 41.789883 2000-2012 –> 2013-2019 9.6687140 100565.2447
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 5.0111174 35544.7247 42.003616 2000-2012 –> 2013-2019 9.8815692 101347.2971
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + nitrate + phosphate_star 5.0112471 35543.0280 42.156824 2000-2012 –> 2013-2019 9.9030053 101439.2572
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.8028438 35047.0323 39.334231 2000-2012 –> 2013-2019 9.5485621 100281.0702
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.9239888 35339.0857 41.490198 2000-2012 –> 2013-2019 9.6714133 100581.0008
Indo-Pacific (26,26.8] cstar_tref ~ sal + temp + silicate + phosphate_star 4.9275027 35345.4493 42.358810 2000-2012 –> 2013-2019 9.7022286 100711.0258
Indo-Pacific (26.8,27.2] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4.5795336 81813.8219 34.801865 1982-1999 –> 2000-2012 8.5516150 189873.0313
Indo-Pacific (26.8,27.2] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.7886149 83053.7301 33.349845 1982-1999 –> 2000-2012 8.9291782 192714.9439
Indo-Pacific (26.8,27.2] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4.8295980 83292.7959 45.368888 1982-1999 –> 2000-2012 8.9093005 192384.2516
Indo-Pacific (26.8,27.2] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.9176703 83793.5132 43.210781 1982-1999 –> 2000-2012 9.0702458 193566.5823
Indo-Pacific (26.8,27.2] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.7371486 82755.1342 36.785071 1982-1999 –> 2000-2012 8.7534986 191242.2911
Indo-Pacific (26.8,27.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.6565455 82277.7345 40.769086 1982-1999 –> 2000-2012 8.6285536 190336.2311
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4.7350846 82743.0111 38.131037 1982-1999 –> 2000-2012 8.8754037 192403.9473
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4.7380874 82760.6466 33.937656 1982-1999 –> 2000-2012 8.8483849 192140.5852
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.7560441 82863.8732 36.970104 1982-1999 –> 2000-2012 8.9114400 192663.1588
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.5137641 81411.4136 31.307713 1982-1999 –> 2000-2012 8.4468954 189090.1265
Indo-Pacific (26.8,27.2] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 5.1129226 45414.6620 38.741744 2000-2012 –> 2013-2019 9.6924562 127228.4838
Indo-Pacific (26.8,27.2] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.3461176 46076.3907 36.840632 2000-2012 –> 2013-2019 10.1347325 129130.1208
Indo-Pacific (26.8,27.2] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5.4336533 46320.0907 48.460676 2000-2012 –> 2013-2019 10.2632513 129612.8866
Indo-Pacific (26.8,27.2] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.3224960 46012.4896 39.131883 2000-2012 –> 2013-2019 10.0596447 128767.6238
Indo-Pacific (26.8,27.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.2455588 45795.7988 42.954185 2000-2012 –> 2013-2019 9.9021043 128073.5333
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 5.2853539 45908.2742 41.361839 2000-2012 –> 2013-2019 10.0204386 128651.2852
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 5.2749045 45878.8224 37.966053 2000-2012 –> 2013-2019 10.0129919 128639.4689
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + phosphate + phosphate_star 5.3051466 45961.9005 40.029218 2000-2012 –> 2013-2019 10.0611907 128825.7737
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.0451120 45215.9674 34.042217 2000-2012 –> 2013-2019 9.5588760 126627.3810
Indo-Pacific (26.8,27.2] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 5.3883644 46195.5309 37.019791 2000-2012 –> 2013-2019 10.2500015 129672.2592
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 3.6311940 82054.4668 35.438607 1982-1999 –> 2000-2012 6.4340072 182995.3260
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.4872184 80829.0205 31.145000 1982-1999 –> 2000-2012 6.2166685 180677.0600
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6724121 82396.3547 32.077068 1982-1999 –> 2000-2012 6.5157353 183928.4591
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + silicate + phosphate_star 3.7333729 82893.0309 30.468524 1982-1999 –> 2000-2012 6.5781398 184444.0506
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 3.5110881 81035.6466 30.468186 1982-1999 –> 2000-2012 6.2335009 180777.3192
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5551878 81413.7232 32.908179 1982-1999 –> 2000-2012 6.3364189 182036.0933
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.5989799 81784.5499 33.006624 1982-1999 –> 2000-2012 6.4275883 183102.8720
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 3.4841970 80802.7655 34.064284 1982-1999 –> 2000-2012 6.4875823 184591.3607
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + silicate + phosphate 3.5678878 81519.7339 33.667524 1982-1999 –> 2000-2012 6.5791832 185414.7023
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.5618307 81470.2678 33.134929 1982-1999 –> 2000-2012 6.3680145 182460.6458
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 4.2684165 46155.0368 39.014604 2000-2012 –> 2013-2019 7.8996105 128209.5036
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4.0818001 45436.3622 29.917429 2000-2012 –> 2013-2019 7.5690185 126265.3827
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.2806890 46201.1922 32.074435 2000-2012 –> 2013-2019 7.9531011 128597.5469
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + aou + silicate + phosphate_star 4.4049957 46659.3727 29.189160 2000-2012 –> 2013-2019 8.1383686 129552.4037
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 4.1297449 45624.0905 31.749891 2000-2012 –> 2013-2019 7.6408330 126659.7371
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.1330172 45636.8236 33.253329 2000-2012 –> 2013-2019 7.6882050 127050.5468
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.1728802 45791.1337 33.395820 2000-2012 –> 2013-2019 7.7718600 127575.6836
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 3.9857466 45053.5372 33.202756 2000-2012 –> 2013-2019 7.4699436 125856.3026
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + silicate + phosphate 4.1369757 45650.2135 32.731002 2000-2012 –> 2013-2019 7.7048636 127169.9474
Indo-Pacific (27.2,27.8] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.1270636 45613.6495 33.571282 2000-2012 –> 2013-2019 7.6888944 127083.9174
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2.8482817 36170.3565 34.472962 1982-1999 –> 2000-2012 5.0269370 80264.7475
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.8354017 36103.8955 36.169899 1982-1999 –> 2000-2012 4.9934882 80008.0179
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + nitrate + phosphate 2.8494127 36176.1785 34.292463 1982-1999 –> 2000-2012 5.0349683 80333.9972
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.8201792 36024.9560 36.836244 1982-1999 –> 2000-2012 4.9998907 80129.0692
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.8358069 36105.9905 36.038293 1982-1999 –> 2000-2012 5.0018154 80083.6091
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.8333838 36093.4557 35.912394 1982-1999 –> 2000-2012 5.0034524 80108.6361
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.8335276 36094.1996 35.912551 1982-1999 –> 2000-2012 5.0075779 80146.1495
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.8332168 36092.5910 35.893479 1982-1999 –> 2000-2012 5.0046659 80120.5281
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + silicate + phosphate_star 2.8335702 36092.4202 35.966529 1982-1999 –> 2000-2012 5.0286896 80335.8196
Indo-Pacific (27.8,27.9] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.8288658 36070.0540 35.663023 1982-1999 –> 2000-2012 4.9609466 79731.0031
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 3.2619062 20683.5347 42.052061 2000-2012 –> 2013-2019 6.0962975 56782.2037
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.2562933 20669.8499 39.928836 2000-2012 –> 2013-2019 6.0916950 56773.7454
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.2496245 20653.5600 39.978779 2000-2012 –> 2013-2019 6.0971681 56820.1163
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.1692189 20454.4785 40.940090 2000-2012 –> 2013-2019 5.9893980 56479.4345
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.2508193 20656.4811 39.746171 2000-2012 –> 2013-2019 6.0866262 56762.4715
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.2445752 20641.2039 39.567399 2000-2012 –> 2013-2019 6.0779590 56734.6596
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 3.2502667 20655.1301 39.767367 2000-2012 –> 2013-2019 6.0975419 56820.3040
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.2423743 20635.8121 40.235128 2000-2012 –> 2013-2019 6.0759019 56730.0118
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.2440939 20640.0250 39.539922 2000-2012 –> 2013-2019 6.0773106 56732.6159
Indo-Pacific (27.8,27.9] cstar_tref ~ sal + temp + silicate + phosphate_star 3.2457468 20642.0726 39.732509 2000-2012 –> 2013-2019 6.0793170 56734.4929
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.1497875 28763.8559 9.090062 1982-1999 –> 2000-2012 4.0365372 67315.2492
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.1452171 28735.8437 9.090571 1982-1999 –> 2000-2012 4.0411647 67378.4894
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.1542792 28791.3276 9.110385 1982-1999 –> 2000-2012 4.0444431 67376.6450
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.1543768 28791.9239 9.105887 1982-1999 –> 2000-2012 4.0455476 67387.2340
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + nitrate + silicate 2.1455127 28735.6571 9.069301 1982-1999 –> 2000-2012 4.0738926 67694.5677
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 2.1279997 28629.7803 8.688730 1982-1999 –> 2000-2012 4.0494159 67522.8074
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.1439932 28728.3326 8.974954 1982-1999 –> 2000-2012 4.0335617 67307.7384
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.1540557 28789.9619 9.104070 1982-1999 –> 2000-2012 4.0449001 67382.0337
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 2.1607357 28828.7155 9.138491 1982-1999 –> 2000-2012 4.0619310 67521.2255
Indo-Pacific (27.9,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.1490185 28759.1465 8.506487 1982-1999 –> 2000-2012 4.0341289 67294.2300
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.3308618 16676.6391 8.794806 2000-2012 –> 2013-2019 4.5047731 45587.3695
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3484670 16731.9910 9.300589 2000-2012 –> 2013-2019 4.4982546 45495.8469
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.3705243 16800.7576 9.489054 2000-2012 –> 2013-2019 4.5157414 45536.6013
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3536974 16748.3557 9.325255 2000-2012 –> 2013-2019 4.5079767 45539.6833
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3528743 16745.7827 9.319013 2000-2012 –> 2013-2019 4.5072512 45537.7066
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 2.3261398 16661.7216 8.688527 2000-2012 –> 2013-2019 4.4541395 45291.5019
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.3403400 16706.4907 9.157466 2000-2012 –> 2013-2019 4.4843332 45434.8233
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3525686 16744.8270 9.317052 2000-2012 –> 2013-2019 4.5066244 45534.7889
Indo-Pacific (27.9,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 2.3576049 16758.5576 9.351008 2000-2012 –> 2013-2019 4.5183406 45587.2731
Indo-Pacific (27.9,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.3589130 16764.6377 8.470486 2000-2012 –> 2013-2019 4.5079314 45523.7842
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate 1.5361773 73634.6174 8.733378 1982-1999 –> 2000-2012 2.8079755 165389.8842
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 1.5089135 72923.3001 10.415983 1982-1999 –> 2000-2012 2.7513833 163390.6644
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 1.3948961 69793.5465 10.490447 1982-1999 –> 2000-2012 2.5772322 157518.1298
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 1.4354153 70934.1635 8.449386 1982-1999 –> 2000-2012 2.6823797 161601.1701
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5314928 73514.9585 14.185354 1982-1999 –> 2000-2012 2.8636804 167837.0700
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5281199 73427.1334 14.378394 1982-1999 –> 2000-2012 2.8513606 167376.6806
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5314910 73514.9130 14.185270 1982-1999 –> 2000-2012 2.8636761 167836.9173
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 1.5143319 73066.0856 10.220413 1982-1999 –> 2000-2012 2.7611966 163728.6687
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.5308210 73497.4825 10.138151 1982-1999 –> 2000-2012 2.7926269 164818.6463
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 1.5184453 73174.1397 10.078924 1982-1999 –> 2000-2012 2.7707584 164077.7898
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 1.7716198 42649.6756 20.936949 2000-2012 –> 2013-2019 3.2805333 115572.9757
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 1.6072486 40564.3886 17.629482 2000-2012 –> 2013-2019 3.0021447 110357.9351
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.7314864 42158.9485 16.581456 2000-2012 –> 2013-2019 3.2626842 115666.2325
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 1.6318563 40889.7931 17.025774 2000-2012 –> 2013-2019 3.0672716 111823.9566
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.7317874 42162.6704 16.576870 2000-2012 –> 2013-2019 3.2630874 115672.6150
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.7322153 42167.9616 16.575055 2000-2012 –> 2013-2019 3.2637081 115682.9201
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 1.7038406 41814.2505 16.464704 2000-2012 –> 2013-2019 3.2660027 116119.0319
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.7344727 42195.8521 17.075855 2000-2012 –> 2013-2019 3.2625926 115622.9856
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.7322017 42167.7935 16.574226 2000-2012 –> 2013-2019 3.2636927 115682.7065
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.7349951 42200.3016 16.913655 2000-2012 –> 2013-2019 3.2667617 115720.3823

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 Cant coeffcients

A data frame of coefficient offsets is prepared to facilitate the direct mapping of Cant.

# pivot long format
lm_best_long <- lm_best_target %>%
  pivot_longer(cols = starts_with("coeff_"),
               names_to = "term",
               values_to = "estimate",
               names_prefix = "coeff_")

# subtract coefficients of adjacent era  
lm_best_long <- lm_best_long %>%
  arrange(era) %>%
  group_by(basin, gamma_slab, eras, model, term) %>%
  mutate(delta_coeff = estimate - lag(estimate)) %>%
  ungroup() %>%
  arrange(basin, gamma_slab, model, term, eras) %>%
  drop_na() %>%
  select(-c(era,estimate))

# pivot back to wide format
lm_best_cant <- lm_best_long %>%
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

5.5 Write files

lm_best_target %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    era,
    starts_with("coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_target.csv",
                  sep = ""))

lm_best_cant %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    starts_with("delta_coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_cant.csv",
                  sep = ""))

6 Model diagnotics

6.1 Selection criterion vs predictors

The selection criterion (rmse) was plotted against the number of predictors (limited to 2 - 5).

6.1.1 All models

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

Version Author Date
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
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
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
28509fc Donghe-Zhu 2021-01-23
4c28e4a Donghe-Zhu 2021-01-22
24cc264 jens-daniel-mueller 2021-01-22
7891955 Donghe-Zhu 2021-01-21
d4cf1cb Donghe-Zhu 2021-01-21
1f3e5b6 jens-daniel-mueller 2021-01-20
0e7bdf1 jens-daniel-mueller 2021-01-15
4571843 jens-daniel-mueller 2021-01-14
b3564aa jens-daniel-mueller 2021-01-14
8d032c3 jens-daniel-mueller 2021-01-14
17dee1d jens-daniel-mueller 2021-01-13
7cdea0c jens-daniel-mueller 2021-01-06
fa85b93 jens-daniel-mueller 2021-01-06
e5cb81a Donghe-Zhu 2021-01-05
a499f10 Donghe-Zhu 2021-01-05
fb8a752 Donghe-Zhu 2020-12-23
8fae0b2 Donghe-Zhu 2020-12-21
c8b76b3 jens-daniel-mueller 2020-12-19 
rm(max_rmse)

6.3 Predictor counts

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

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

# print table
lm_all_stats %>%
  gt(rowname_col = "gamma_slab",
     groupname_col = c("basin", "eras")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )
aou nitrate phosphate phosphate_star sal silicate temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26] 9 4 8 7 10 3 7
(26,26.8] 8 8 8 7 6 6 7
(26.8,27.2] 9 4 8 7 5 10 6
(27.2,27.8] 8 4 7 7 10 6 7
(27.8,27.9] 8 4 8 7 10 4 7
(27.9,28.1] 5 10 8 6 6 8 6
(28.1,28.2] 8 10 4 7 9 3 7
(28.2, Inf] 9 10 5 5 10 4 4
total 64.00 54.00 56.00 53.00 66.00 44.00 51.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 8 5 7 7 10 5 8
(26,26.8] 8 10 8 8 4 4 7
(26.8,27.2] 8 4 8 6 7 10 6
(27.2,27.8] 8 4 7 6 10 8 6
(27.8,27.9] 7 5 7 8 10 5 8
(27.9,28.1] 6 10 9 5 8 6 5
(28.1,28.2] 8 10 4 7 9 3 7
(28.2, Inf] 9 10 5 5 10 4 4
total 62.00 58.00 55.00 52.00 68.00 45.00 51.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 9 4 8 7 10 3 7
(26,26.8] 5 5 5 8 10 6 9
(26.8,27.2] 10 4 10 9 4 5 5
(27.2,27.8] 6 4 7 6 10 10 5
(27.8,27.9] 7 3 7 8 9 7 8
(27.9,28.1] 5 4 5 6 9 10 9
(28.1, Inf] 6 8 7 7 5 10 6
total 48.00 32.00 49.00 51.00 57.00 51.00 49.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 7 6 7 8 10 3 7
(26,26.8] 5 5 5 8 10 6 9
(26.8,27.2] 9 5 10 9 3 6 6
(27.2,27.8] 6 4 7 6 10 10 5
(27.8,27.9] 6 4 6 8 10 7 8
(27.9,28.1] 6 4 5 7 9 10 8
(28.1, Inf] 5 5 7 7 9 10 6
total 44.00 33.00 47.00 53.00 61.00 52.00 49.00

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
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
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