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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 certain predictor combinations
# lm_rm_ph <- lm_all %>%
#   filter(str_detect(lm_coeff, "phosphate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "oxygen") &
#       str_detect(lm_coeff_filter, "phosphate")
#   )

# lm_rm_si <- lm_all %>%
#   filter(str_detect(lm_coeff, "silicate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "silicate_star")) %>%
#   filter(str_detect(lm_coeff_filter, "silicate"))

# lm_rm_o2 <- lm_all %>%
#   filter(str_detect(lm_coeff, "phosphate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "phosphate") &
#       str_detect(lm_coeff_filter, "oxygen")
#   )

# lm_rm <- bind_rows(lm_rm_ph, lm_rm_o2) %>%
#   select(-lm_coeff_filter) %>%
#   unique()


# remove temp sal predictor combination
lm_all <- lm_all %>%
  # filter(!(
  #   str_detect(lm_coeff, "temp") &
  #     str_detect(lm_coeff, "phosphate_star")
  # )) %>%
  mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
  filter(!(str_detect(lm_coeff_filter, "nitrate") &
             str_detect(lm_coeff_filter, "phosphate")
  )) %>%
  filter(!(
    str_detect(lm_coeff_filter, "temp") &
      str_detect(lm_coeff_filter, "sal")
  )) %>%
  filter(!(
    str_detect(lm_coeff_filter, "oxygen") &
      str_detect(lm_coeff_filter, "aou")
  )) %>%
  select(-lm_coeff_filter)

# lm_rm <- lm_rm_ph %>%
#   select(-lm_coeff_filter) %>%
#   unique()
# 
# lm_all <- anti_join(lm_all, lm_rm)

# remove helper objects
rm(
  i_gamma_slab,
  i_era,
  i_basin,
  GLODAP_basin_era,
  GLODAP_basin_era_slab,
  lm_full,
  lm_rm_ph,
  lm_rm_si,
  lm_rm_o2,
  lm_rm
)

3 Apply predictor threshold

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

  • Minimum: 3
  • Maximum: 9
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:

  • 45

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)
      
      # number of observations used for each fitting model
      i_nr_obs = nrow(GLODAP_basin_era_slab)
      
      for (i_predictors in unique(lm_all$predictors)) {
        #i_predictors <- unique(lm_all$predictors)[1]
        
        # 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()
        
        if (i_nr_obs > i_n_predictors) {
          # fit model
          if (params_local$MLR_type == "rlm") {
            i_lm_fit <- MASS::rlm(as.formula(i_lm),
                                  data = GLODAP_basin_era_slab)
          }
          
          if (params_local$MLR_type == "lm") {
            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,
              nr_obs = i_nr_obs,
              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_nr_obs,
  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,
    nr_obs,
    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:

  • 5

The criterion used to select the best models was:

  • aic

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, nr_obs, 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)
}

5.3 RMSE tables

5.3.1 per model

lm_best %>%
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")
basin gamma_slab model nr_obs rmse aic resid_max eras rmse_sum aic_sum
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 187 1.5912079 718.4036 5.282024 1982-1992 –> 1993-2008 3.0599555 1204.8809
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 187 1.0781027 570.8088 3.860936 1982-1992 –> 1993-2008 2.2186633 989.0289
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 187 1.0770931 572.4584 3.811461 1982-1992 –> 1993-2008 2.2172836 992.5935
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 187 1.5412172 704.4651 6.354153 1982-1992 –> 1993-2008 2.8865265 1165.9425
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 187 1.5294980 703.6104 6.043070 1982-1992 –> 1993-2008 2.8706272 1166.2724
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 120 1.1639689 388.9858 3.443761 1993-2008 –> 2009-2019 2.2420716 959.7946
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 120 1.1032974 378.1381 3.121374 1993-2008 –> 2009-2019 2.1803906 950.5965
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate_star 120 1.6504991 472.8039 4.220872 1993-2008 –> 2009-2019 3.2426150 1189.4208
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 120 1.5135931 452.0220 6.318368 1993-2008 –> 2009-2019 3.0548103 1156.4871
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 120 1.4696627 446.9532 5.722394 1993-2008 –> 2009-2019 2.9991607 1150.5636
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1315 3.5350907 7066.8118 12.885206 1982-1992 –> 1993-2008 6.8547669 11983.2162
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 1315 4.2250363 7533.7116 14.179773 1982-1992 –> 1993-2008 8.2637201 12815.1246
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 1315 4.0859996 7445.7080 16.579167 1982-1992 –> 1993-2008 8.0382892 12686.6413
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1315 4.0827450 7445.6123 17.035596 1982-1992 –> 1993-2008 8.0316875 12686.9595
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1315 4.3018498 7583.0970 14.193449 1982-1992 –> 1993-2008 8.4406000 12912.3272
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 887 3.5766351 4792.0224 11.509131 1993-2008 –> 2009-2019 7.1117258 11858.8342
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 887 4.1181347 5040.1171 12.061754 1993-2008 –> 2009-2019 8.3431710 12573.8287
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 887 3.9565691 4969.1162 16.433540 1993-2008 –> 2009-2019 8.0425687 12414.8242
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 887 3.9408963 4964.0751 18.038103 1993-2008 –> 2009-2019 8.0236413 12409.6873
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 887 4.2298592 5089.6042 11.623373 1993-2008 –> 2009-2019 8.5317089 12672.7012
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1726 3.1530451 8874.3445 11.763575 1982-1992 –> 1993-2008 6.1942526 14637.2154
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 1726 3.1973454 8922.5076 11.245505 1982-1992 –> 1993-2008 6.2895275 14723.1445
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1726 3.1023316 8820.3713 11.720995 1982-1992 –> 1993-2008 6.1064332 14557.3509
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1726 3.1810445 8906.8633 10.897224 1982-1992 –> 1993-2008 6.2681977 14705.8023
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1726 3.0408539 8751.2775 10.380306 1982-1992 –> 1993-2008 5.9672179 14428.6901
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1088 3.6028024 5888.6155 11.507716 1993-2008 –> 2009-2019 6.7558475 14762.9600
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 1088 3.5167576 5836.0161 11.179635 1993-2008 –> 2009-2019 6.7141030 14758.5237
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1088 3.4970317 5825.7763 11.382695 1993-2008 –> 2009-2019 6.5993633 14646.1476
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1088 3.5173399 5838.3763 9.303961 1993-2008 –> 2009-2019 6.6983844 14745.2396
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1088 3.4808595 5815.6899 10.801616 1993-2008 –> 2009-2019 6.5217135 14566.9674
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2872 1.9010275 11852.2972 13.745547 1982-1992 –> 1993-2008 3.4606631 19038.3516
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2872 1.8314195 11640.0277 12.858470 1982-1992 –> 1993-2008 3.3744409 18786.8495
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2872 2.0203061 12203.8453 16.645169 1982-1992 –> 1993-2008 3.7076860 19694.9900
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2872 2.0086947 12168.7374 13.894756 1982-1992 –> 1993-2008 3.6887866 19641.2175
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2872 1.8931583 11830.4707 21.137549 1982-1992 –> 1993-2008 3.2796149 18565.3766
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2004 2.4497762 9290.2603 27.463653 1993-2008 –> 2009-2019 4.3508038 21142.5576
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 2004 2.4126150 9228.9963 24.703523 1993-2008 –> 2009-2019 4.4762968 21552.8592
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2004 2.3482362 9122.5930 25.940225 1993-2008 –> 2009-2019 4.1796557 20762.6206
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2004 2.5042136 9380.3485 23.426544 1993-2008 –> 2009-2019 4.5245197 21584.1938
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2004 2.1044039 8683.1870 22.765287 1993-2008 –> 2009-2019 3.9975622 20513.6577
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2463 2.0978110 10653.3371 11.326319 1982-1992 –> 1993-2008 4.3907959 17643.0928
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 2463 1.8122952 9930.6619 10.436057 1982-1992 –> 1993-2008 3.4932553 15955.2798
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2463 1.7434002 9741.7460 10.614633 1982-1992 –> 1993-2008 3.2502713 15429.2231
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2463 1.9424432 10274.2919 16.753389 1982-1992 –> 1993-2008 3.4901206 16044.6545
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2463 2.1401881 10751.8537 21.184813 1982-1992 –> 1993-2008 4.1306189 17302.6662
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1770 2.1957025 7821.2597 11.870716 1993-2008 –> 2009-2019 4.2935135 18474.5967
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1770 2.1848856 7801.7771 13.569860 1993-2008 –> 2009-2019 3.9971808 17732.4390
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1770 2.1848757 7803.7610 13.557213 1993-2008 –> 2009-2019 3.9282759 17545.5070
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 1770 2.2804983 7953.3970 14.908620 1993-2008 –> 2009-2019 4.4102467 18679.1632
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1770 2.3928360 8125.6190 19.363213 1993-2008 –> 2009-2019 4.3352791 18399.9109
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 2556 2.4820099 11912.7728 12.362407 1982-1992 –> 1993-2008 5.1593399 20357.1578
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2556 2.3873503 11715.9949 13.071874 1982-1992 –> 1993-2008 4.9889636 20061.7414
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2556 2.4573309 11863.6891 19.466291 1982-1992 –> 1993-2008 4.5183208 19392.2634
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 2556 2.0708012 10986.8205 11.916000 1982-1992 –> 1993-2008 3.6794046 17644.0419
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2556 1.9827515 10766.7037 14.981948 1982-1992 –> 1993-2008 3.5899289 17422.8141
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate_star 1702 2.9549498 8530.2384 21.650262 1993-2008 –> 2009-2019 5.6073350 20782.4001
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 1702 2.8677604 8428.2875 16.040376 1993-2008 –> 2009-2019 5.3497703 20341.0603
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1702 2.7136930 8242.3155 17.246937 1993-2008 –> 2009-2019 5.1010433 19958.3104
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 1702 3.0012510 8583.1622 11.700791 1993-2008 –> 2009-2019 5.0720522 19569.9827
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1702 2.7021751 8227.8369 17.252150 1993-2008 –> 2009-2019 4.6849266 18994.5407
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 3460 2.7023085 16708.2710 12.866858 1982-1992 –> 1993-2008 5.0820135 27018.6043
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 3460 2.6481687 16570.2237 13.666909 1982-1992 –> 1993-2008 4.7272415 26274.0013
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 3460 2.4592963 16058.1914 14.220601 1982-1992 –> 1993-2008 4.7709995 26239.8869
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3460 2.3582625 15769.8964 14.132359 1982-1992 –> 1993-2008 4.3029125 25174.4931
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3460 2.9043687 17211.2698 15.225490 1982-1992 –> 1993-2008 5.0440866 27046.6037
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2340 3.1208758 11981.0043 15.244357 1993-2008 –> 2009-2019 5.9241805 28947.1879
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 2340 3.2193610 12122.4083 13.884231 1993-2008 –> 2009-2019 5.9216695 28830.6793
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 2340 3.2193457 12124.3861 13.894909 1993-2008 –> 2009-2019 5.8675145 28694.6098
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2340 2.7289817 11351.0180 14.950042 1993-2008 –> 2009-2019 5.1882780 27409.2094
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2340 2.7164500 11331.4775 14.798604 1993-2008 –> 2009-2019 5.0747125 27101.3739
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 1193 1.9259223 4961.3836 13.824255 1982-1992 –> 1993-2008 3.9074411 8400.9511
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1193 1.8670030 4889.2494 14.766879 1982-1992 –> 1993-2008 3.7937816 8285.1538
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 1193 1.7990244 4798.7527 13.033401 1982-1992 –> 1993-2008 3.4405096 7931.4529
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1193 1.7290527 4704.0982 12.731184 1982-1992 –> 1993-2008 3.5309384 7988.7670
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1193 1.5281875 4411.4480 13.364087 1982-1992 –> 1993-2008 3.1231057 7499.2383
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 861 2.0091785 3656.8962 12.547977 1993-2008 –> 2009-2019 3.9351007 8618.2798
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 861 1.9932243 3645.1678 12.962072 1993-2008 –> 2009-2019 3.8602273 8534.4172
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 861 2.3474123 3924.8181 11.404366 1993-2008 –> 2009-2019 4.1464367 8723.5709
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 861 1.8364097 3502.0651 11.597744 1993-2008 –> 2009-2019 3.5654624 8206.1633
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 861 1.7164355 3387.7222 11.994150 1993-2008 –> 2009-2019 3.2446230 7799.1702
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1212 3.1256168 6213.9741 33.596885 1982-1992 –> 1993-2008 6.0030817 10103.1524
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 1212 3.1444076 6228.5032 36.440631 1982-1992 –> 1993-2008 5.9168209 10059.4396
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1212 3.1254040 6215.8090 32.755095 1982-1992 –> 1993-2008 5.8970811 10048.3296
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 1212 2.9408327 6066.2583 24.326059 1982-1992 –> 1993-2008 5.8494801 9972.3157
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1212 2.9107331 6043.3207 24.066688 1982-1992 –> 1993-2008 5.7748175 9927.1999
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 893 3.6388755 4853.1553 24.564776 1993-2008 –> 2009-2019 6.7644923 11067.1294
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 893 3.2764028 4665.7528 31.808520 1993-2008 –> 2009-2019 6.4208104 10894.2560
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 893 3.2010827 4626.2158 30.563544 1993-2008 –> 2009-2019 6.3264867 10842.0248
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 893 3.5763422 4822.1964 23.280568 1993-2008 –> 2009-2019 6.5171749 10888.4547
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 893 3.5520614 4812.0294 24.376118 1993-2008 –> 2009-2019 6.4627946 10855.3501
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 1472 4.8683406 8848.9803 26.059105 1982-1992 –> 1993-2008 9.5709305 14925.6344
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1472 4.7812917 8797.8635 25.211543 1982-1992 –> 1993-2008 9.4002781 14839.8521
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 1472 4.1624893 8387.8325 23.557762 1982-1992 –> 1993-2008 8.2035339 14154.5955
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1472 3.8135340 8132.0649 28.350855 1982-1992 –> 1993-2008 7.5022337 13714.3553
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1472 4.8366110 8831.7299 22.160697 1982-1992 –> 1993-2008 9.5116528 14898.3749
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 1052 4.3783749 6104.3764 24.778686 1993-2008 –> 2009-2019 9.2467155 14953.3567
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1052 4.3189470 6077.6231 24.715518 1993-2008 –> 2009-2019 9.1002387 14875.4866
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 1052 3.8344411 5825.2725 22.665961 1993-2008 –> 2009-2019 7.9969303 14213.1050
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1052 3.4529907 5606.8092 27.139851 1993-2008 –> 2009-2019 7.2665247 13738.8740
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1052 4.4232551 6127.8335 23.229057 1993-2008 –> 2009-2019 9.2598662 14959.5634
Atlantic (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 984 1.1073655 3005.1751 10.327864 1982-1992 –> 1993-2008 2.0186185 4759.5441
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 984 1.0085337 2821.1941 7.202687 1982-1992 –> 1993-2008 1.8431313 4460.1007
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 984 0.9925669 2791.7881 6.438064 1982-1992 –> 1993-2008 1.8263164 4431.3589
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 984 1.0635401 2925.7059 10.462649 1982-1992 –> 1993-2008 1.9698263 4672.8933
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 984 0.9817662 2770.2558 11.546709 1982-1992 –> 1993-2008 1.8022525 4388.7555
Atlantic (28.05,28.1] cstar_tref ~ aou + phosphate + phosphate_star 673 1.1376904 2093.5256 12.561330 1993-2008 –> 2009-2019 2.2451598 5096.8853
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 673 1.0731011 2016.8552 9.691677 1993-2008 –> 2009-2019 2.0816348 4838.0493
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 673 1.0390706 1975.4790 8.643193 1993-2008 –> 2009-2019 2.0316375 4767.2670
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 673 1.0632974 2004.5018 13.201907 1993-2008 –> 2009-2019 2.1268375 4930.2077
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 673 1.0029755 1927.8904 13.995196 1993-2008 –> 2009-2019 1.9847418 4698.1462
Atlantic (28.1,28.15] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1137 0.7992305 2729.0496 9.214513 1982-1992 –> 1993-2008 1.4502223 4366.1044
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1137 0.7860789 2693.3187 5.763904 1982-1992 –> 1993-2008 1.4514111 4368.1521
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 1137 0.7214219 2496.1344 5.265422 1982-1992 –> 1993-2008 1.3646504 4113.4904
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1137 0.6997497 2428.7741 5.252605 1982-1992 –> 1993-2008 1.2937291 3917.3358
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1137 0.7098230 2461.2763 9.375947 1982-1992 –> 1993-2008 1.2811913 3886.1110
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 770 0.8961317 2030.2768 7.973080 1993-2008 –> 2009-2019 1.6822106 4723.5955
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 770 0.8166830 1885.3088 7.028213 1993-2008 –> 2009-2019 1.5381050 4381.4433
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 770 0.8154600 1885.0009 7.017951 1993-2008 –> 2009-2019 1.5152097 4313.7750
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 770 0.8766659 1994.4562 11.848627 1993-2008 –> 2009-2019 1.6794266 4733.5277
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 770 0.7933963 1842.7593 12.250467 1993-2008 –> 2009-2019 1.5032193 4304.0356
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1906 0.6036128 3496.6107 7.529280 1982-1992 –> 1993-2008 1.0852274 5407.0179
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1906 0.5866004 3389.6293 9.003397 1982-1992 –> 1993-2008 1.0347774 5103.5820
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 1906 0.6499700 3778.6733 12.009128 1982-1992 –> 1993-2008 1.1246717 5649.2064
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 1906 0.6345989 3687.4404 12.704542 1982-1992 –> 1993-2008 1.0885999 5435.0019
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1906 0.6334483 3682.5228 13.033942 1982-1992 –> 1993-2008 1.0824254 5401.3942
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1298 0.7148302 2824.0606 5.571969 1993-2008 –> 2009-2019 1.3184430 6320.6713
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1298 0.7054925 2791.9262 6.356481 1993-2008 –> 2009-2019 1.2920929 6181.5555
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 1298 0.8189368 3177.0178 9.752451 1993-2008 –> 2009-2019 1.4689068 6955.6911
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 1298 0.8075260 3140.5916 10.459046 1993-2008 –> 2009-2019 1.4421249 6828.0319
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1298 0.8075158 3142.5587 10.484177 1993-2008 –> 2009-2019 1.4409641 6825.0815
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 3337 0.3411789 2303.1216 3.699396 1982-1992 –> 1993-2008 0.6291122 3101.9863
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 3337 0.3356854 2196.7846 2.531077 1982-1992 –> 1993-2008 0.6205144 2948.4811
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 3337 0.3400551 2283.1024 3.045934 1982-1992 –> 1993-2008 0.6271763 3071.1552
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3337 0.3308491 2101.9325 3.344175 1982-1992 –> 1993-2008 0.6122090 2800.0421
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3337 0.5238862 5169.3833 11.930561 1982-1992 –> 1993-2008 0.9445172 7691.5158
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 2356 0.4048932 2435.7681 2.383068 1993-2008 –> 2009-2019 0.7460721 4738.8897
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 2356 0.3912592 2276.3681 2.329236 1993-2008 –> 2009-2019 0.7269446 4473.1527
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 2356 0.4002060 2382.9022 2.376657 1993-2008 –> 2009-2019 0.7402611 4666.0045
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2356 0.3839474 2189.4776 2.545602 1993-2008 –> 2009-2019 0.7147965 4291.4101
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2356 0.6695335 4809.7061 10.072546 1993-2008 –> 2009-2019 1.1934197 9979.0895
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 6436 6.3858313 42142.3161 30.798168 1982-1992 –> 1993-2008 12.8754792 71111.9647
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6436 6.3346761 42040.7868 30.310376 1982-1992 –> 1993-2008 12.7788413 70950.5151
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6436 7.3288812 43917.3208 32.107268 1982-1992 –> 1993-2008 14.8383972 74174.0252
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6436 7.4228947 44081.3903 30.028356 1982-1992 –> 1993-2008 14.9641797 74375.2615
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 6436 7.5249713 44255.1947 29.299980 1982-1992 –> 1993-2008 15.2131727 74716.9328
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 4459 6.0310286 28691.0048 24.778598 1993-2008 –> 2009-2019 12.4168599 70833.3208
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4459 5.9692539 28601.1884 24.098032 1993-2008 –> 2009-2019 12.3039300 70641.9752
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4459 7.0467156 30081.0385 25.923585 1993-2008 –> 2009-2019 14.3755968 73998.3593
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4459 7.1134116 30165.0489 25.398300 1993-2008 –> 2009-2019 14.5363063 74246.4393
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4459 7.2315127 30309.8953 24.429455 1993-2008 –> 2009-2019 14.7564840 74565.0900
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 6798 4.6865739 40305.6541 41.627876 1982-1992 –> 1993-2008 9.3568841 68397.7700
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6798 4.3273493 39223.4189 44.342767 1982-1992 –> 1993-2008 8.5870707 66444.6167
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6798 4.5085294 39781.0705 48.566481 1982-1992 –> 1993-2008 8.9535296 67406.1456
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 6798 4.6887161 40311.8671 39.905392 1982-1992 –> 1993-2008 9.3230872 68330.7039
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6798 4.6778572 40282.3428 40.951686 1982-1992 –> 1993-2008 9.3118879 68302.4829
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4614 4.9091889 27788.7162 41.959096 1993-2008 –> 2009-2019 9.5957628 68094.3703
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4614 4.5485519 27086.6215 45.085074 1993-2008 –> 2009-2019 8.8759012 66310.0404
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4614 4.7038052 27396.3397 47.887037 1993-2008 –> 2009-2019 9.2123346 67177.4102
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4614 4.8959995 27763.8901 40.766362 1993-2008 –> 2009-2019 9.5847155 68075.7572
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4614 4.8929016 27760.0494 41.227023 1993-2008 –> 2009-2019 9.5707588 68042.3922
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5607 4.0261247 31542.8842 22.557650 1982-1992 –> 1993-2008 7.8711871 52773.5522
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 5607 4.1537322 31892.7942 17.379345 1982-1992 –> 1993-2008 7.9513108 53028.1285
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5607 3.8993595 31186.1260 19.228653 1982-1992 –> 1993-2008 7.5361845 51991.6263
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5607 4.0565286 31629.2502 36.803680 1982-1992 –> 1993-2008 7.9284448 52915.3130
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5607 3.9432595 31311.6707 20.122261 1982-1992 –> 1993-2008 7.7255392 52418.0352
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3836 4.3185308 22121.5823 25.159708 1993-2008 –> 2009-2019 8.3446556 53664.4666
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3836 4.1788159 21871.2707 25.715301 1993-2008 –> 2009-2019 8.0781754 53057.3967
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3836 4.2292460 21963.3024 33.372085 1993-2008 –> 2009-2019 8.2857745 53592.5526
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3836 4.1844077 21881.5300 23.557925 1993-2008 –> 2009-2019 8.1276672 53193.2007
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3836 4.2320442 21966.3768 34.676735 1993-2008 –> 2009-2019 8.2965306 53615.6042
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 6552 4.3109375 37752.7509 17.610979 1982-1992 –> 1993-2008 8.1721643 63142.7900
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 6552 4.0592592 36964.4810 20.644577 1982-1992 –> 1993-2008 7.5998000 61560.1245
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6552 4.0414175 36908.7578 19.658194 1982-1992 –> 1993-2008 7.5722097 61481.1397
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 6552 3.9901204 36739.3663 19.107282 1982-1992 –> 1993-2008 7.5390950 61356.8083
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6552 3.9537237 36621.2870 17.324677 1982-1992 –> 1993-2008 7.4824065 61188.1934
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4620 4.8346391 27683.4439 18.928175 1993-2008 –> 2009-2019 9.1455766 65436.1948
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4620 4.6186014 27261.0415 21.294506 1993-2008 –> 2009-2019 8.6778606 64225.5225
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4620 4.6042741 27234.3336 20.417790 1993-2008 –> 2009-2019 8.6456915 64143.0914
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4620 4.5195678 27060.7592 22.587891 1993-2008 –> 2009-2019 8.5096882 63800.1256
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4620 4.4910489 27004.2693 21.096126 1993-2008 –> 2009-2019 8.4447726 63625.5563
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7975 4.1236653 45243.1111 37.463865 1982-1992 –> 1993-2008 7.3887895 73517.3974
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7975 3.9356639 44498.8389 45.991457 1982-1992 –> 1993-2008 6.9422331 71877.1953
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 7975 4.1366419 45291.2244 41.611464 1982-1992 –> 1993-2008 7.4370854 73680.3543
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7975 3.7252527 43622.4677 26.948414 1982-1992 –> 1993-2008 6.8055605 71263.9610
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 7975 4.3688352 46162.2876 67.019674 1982-1992 –> 1993-2008 7.4002795 73628.1256
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5368 4.9996749 32523.9515 33.137375 1993-2008 –> 2009-2019 9.1852348 78002.6865
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5368 4.9630411 32446.9967 35.215683 1993-2008 –> 2009-2019 9.0867065 77690.1078
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5368 4.8065903 32103.1149 38.756934 1993-2008 –> 2009-2019 8.7422542 76601.9538
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 5368 4.9677680 32455.2170 41.181662 1993-2008 –> 2009-2019 9.1044099 77746.4414
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5368 4.3759429 31095.3701 26.859631 1993-2008 –> 2009-2019 8.1011956 74717.8378
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 7106 3.2411458 36892.2275 31.445110 1982-1992 –> 1993-2008 6.0368444 60519.9760
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7106 3.4566301 37807.0148 31.170733 1982-1992 –> 1993-2008 6.3714162 61837.3075
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 7106 3.4724036 37869.7205 30.743556 1982-1992 –> 1993-2008 6.3885787 61902.6105
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7106 3.4356714 37720.5807 32.455127 1982-1992 –> 1993-2008 6.3686298 61810.8496
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7106 3.2025543 36721.9934 32.476878 1982-1992 –> 1993-2008 5.9660058 60237.7867
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4935 3.7984566 27191.3742 30.763268 1993-2008 –> 2009-2019 7.0396023 64083.6016
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4935 4.1106150 27970.8855 32.033024 1993-2008 –> 2009-2019 7.5672451 65777.9003
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 4935 4.1456000 28052.5325 30.395240 1993-2008 –> 2009-2019 7.6180036 65922.2530
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4935 4.0646343 27859.8589 30.502849 1993-2008 –> 2009-2019 7.5003057 65580.4397
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4935 3.6825512 26885.5122 32.539426 1993-2008 –> 2009-2019 6.8851054 63607.5056
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 7265 2.8794810 35998.2513 30.291013 1982-1992 –> 1993-2008 4.9895832 57253.1908
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7265 2.8744343 35972.7628 31.734535 1982-1992 –> 1993-2008 5.0096047 57343.5356
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 7265 2.9623897 36408.7029 29.485869 1982-1992 –> 1993-2008 5.1079867 57825.2539
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 7265 2.9948059 36566.8351 29.742882 1982-1992 –> 1993-2008 5.1761853 58145.6065
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 7265 3.0022281 36602.8009 28.897569 1982-1992 –> 1993-2008 5.1600431 58075.0449
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4876 3.8360163 26962.4128 26.671827 1993-2008 –> 2009-2019 6.7154973 62960.6642
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4876 3.7213482 26666.4554 10.513159 1993-2008 –> 2009-2019 6.5957825 62639.2182
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 4876 3.9928783 27351.2531 24.983842 1993-2008 –> 2009-2019 6.9552681 63759.9559
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 4876 3.9962227 27359.4179 32.475641 1993-2008 –> 2009-2019 6.9910287 63926.2529
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4876 3.9296820 27197.6711 19.536419 1993-2008 –> 2009-2019 6.9459896 63870.4538
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2788 2.4933735 13018.4390 22.624788 1982-1992 –> 1993-2008 4.3134343 20690.0399
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2788 2.4929801 13019.5593 22.773035 1982-1992 –> 1993-2008 4.3057860 20677.9986
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2788 2.4979762 13030.7226 22.835181 1982-1992 –> 1993-2008 4.3287333 20726.5670
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate 2788 2.5043660 13042.9678 22.239783 1982-1992 –> 1993-2008 4.3345354 20735.5932
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2788 2.4321048 12881.7106 22.637596 1982-1992 –> 1993-2008 4.2374678 20524.5325
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2026 2.9681471 10171.8633 31.686491 1993-2008 –> 2009-2019 5.4789572 23231.1605
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2026 3.0026006 10218.6269 30.980275 1993-2008 –> 2009-2019 5.4955807 23238.1862
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2026 2.9867207 10195.1402 28.760017 1993-2008 –> 2009-2019 5.4979539 23253.3770
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 2026 2.9577599 10155.6582 31.706119 1993-2008 –> 2009-2019 5.4757667 23228.9150
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2026 2.9108359 10092.8590 29.031327 1993-2008 –> 2009-2019 5.3429407 22974.5697
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 3469 2.5703392 16406.3302 27.787216 1982-1992 –> 1993-2008 4.6637078 27228.4727
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 3469 2.5836669 16442.2123 27.958955 1982-1992 –> 1993-2008 4.7526315 27442.0863
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3469 2.5689132 16404.4802 27.600046 1982-1992 –> 1993-2008 4.6607332 27224.9150
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 3469 2.5878626 16451.4700 30.886761 1982-1992 –> 1993-2008 4.6894270 27291.1888
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3469 2.5850284 16445.8672 30.474042 1982-1992 –> 1993-2008 4.6854344 27284.8241
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 2485 2.9891703 12506.2540 34.512839 1993-2008 –> 2009-2019 5.5595095 28912.5842
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 2485 2.9841143 12497.8404 33.884360 1993-2008 –> 2009-2019 5.5677813 28940.0527
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2485 2.9784354 12490.3733 34.058594 1993-2008 –> 2009-2019 5.5473487 28894.8535
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate 2485 2.9853115 12497.8339 34.872500 1993-2008 –> 2009-2019 5.5736889 28950.6840
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2485 2.9786599 12488.7479 33.688880 1993-2008 –> 2009-2019 5.5636883 28934.6151
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3072 2.1148668 13331.7641 8.238928 1982-1992 –> 1993-2008 3.9911438 22237.1702
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3072 2.0749251 13216.6178 8.528292 1982-1992 –> 1993-2008 3.9253820 22063.8572
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3072 2.1229719 13357.2655 8.128455 1982-1992 –> 1993-2008 4.0097090 22288.8107
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 3072 2.1285108 13371.2747 8.292371 1982-1992 –> 1993-2008 4.0140784 22298.1278
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3072 2.0554623 13158.7150 7.890540 1982-1992 –> 1993-2008 3.8937921 21977.4053
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate_star 2121 2.3344559 9627.4152 8.114849 1993-2008 –> 2009-2019 4.4727265 23026.7973
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2121 2.3295082 9620.4150 8.254005 1993-2008 –> 2009-2019 4.4325761 22919.8056
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2121 2.4048197 9755.3859 8.396749 1993-2008 –> 2009-2019 4.4797448 22972.0037
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 2121 2.3980224 9741.3788 8.922395 1993-2008 –> 2009-2019 4.5416890 23156.2461
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2121 2.3597710 9675.1682 8.699549 1993-2008 –> 2009-2019 4.4152333 22833.8833
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 2199 1.8375273 8928.3263 8.449480 1982-1992 –> 1993-2008 3.3890506 14734.1184
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2199 1.7846557 8801.9254 8.739544 1982-1992 –> 1993-2008 3.3095186 14555.6740
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2199 1.8469499 8950.8212 8.602045 1982-1992 –> 1993-2008 3.4272622 14813.9384
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2199 1.8054086 8852.7727 9.673566 1982-1992 –> 1993-2008 3.3374653 14621.1964
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2199 1.7752040 8778.5713 8.477926 1982-1992 –> 1993-2008 3.3270688 14587.0496
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1480 2.0189887 6291.7443 9.987210 1993-2008 –> 2009-2019 3.8723298 15257.7581
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1480 2.0327227 6313.8114 8.811078 1993-2008 –> 2009-2019 3.8816044 15271.2301
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1480 1.9639299 6211.9027 9.739216 1993-2008 –> 2009-2019 3.7485856 15013.8281
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1480 1.9976364 6262.2735 10.515985 1993-2008 –> 2009-2019 3.8030450 15115.0461
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1480 1.9240869 6151.2346 9.194710 1993-2008 –> 2009-2019 3.6992909 14929.8059
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 18043 1.3671615 62501.2311 13.366519 1982-1992 –> 1993-2008 2.6097448 103102.3720
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 18043 1.2702370 59849.7143 15.786355 1982-1992 –> 1993-2008 2.4055399 98212.8629
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 18043 1.2708060 59865.8737 12.761589 1982-1992 –> 1993-2008 2.3495296 96960.8149
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 18043 1.3327544 61583.4402 16.560255 1982-1992 –> 1993-2008 2.5369785 101408.6731
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 18043 1.4716303 65158.3946 17.138652 1982-1992 –> 1993-2008 2.7505941 106475.4348
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 12319 1.6225597 46898.7219 9.024654 1993-2008 –> 2009-2019 3.0837161 111801.3647
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 12319 1.5499918 45769.4022 10.853455 1993-2008 –> 2009-2019 2.9171533 108270.6333
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 12319 1.4654909 44390.2118 13.078916 1993-2008 –> 2009-2019 2.7357280 104239.9261
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 12319 1.5412287 45631.7127 12.618266 1993-2008 –> 2009-2019 2.8120347 105497.5864
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 12319 1.5232127 45342.0128 14.186735 1993-2008 –> 2009-2019 2.8559671 106925.4530

5.3.2 per fitting unit

lm_best %>%
  group_by(basin, gamma_slab, eras) %>% 
  summarise(rmse_sum_mean = mean(rmse_sum),
            ais_sum_mean = mean(aic_sum)) %>% 
  ungroup() %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")
basin gamma_slab eras rmse_sum_mean ais_sum_mean
Atlantic (-Inf,26] 1982-1992 –> 1993-2008 2.6506112 1103.744
Atlantic (-Inf,26] 1993-2008 –> 2009-2019 2.7438096 1081.373
Atlantic (26,26.5] 1982-1992 –> 1993-2008 7.9258127 12616.854
Atlantic (26,26.5] 1993-2008 –> 2009-2019 8.0105632 12385.975
Atlantic (26.5,26.75] 1982-1992 –> 1993-2008 6.1651258 14610.441
Atlantic (26.5,26.75] 1993-2008 –> 2009-2019 6.6578823 14695.968
Atlantic (26.75,27] 1982-1992 –> 1993-2008 3.5022383 19145.357
Atlantic (26.75,27] 1993-2008 –> 2009-2019 4.3057676 21111.178
Atlantic (27,27.25] 1982-1992 –> 1993-2008 3.7510124 16474.983
Atlantic (27,27.25] 1993-2008 –> 2009-2019 4.1928992 18166.323
Atlantic (27.25,27.5] 1982-1992 –> 1993-2008 4.3871915 18975.604
Atlantic (27.25,27.5] 1993-2008 –> 2009-2019 5.1630255 19929.259
Atlantic (27.5,27.75] 1982-1992 –> 1993-2008 4.7854507 26350.718
Atlantic (27.5,27.75] 1993-2008 –> 2009-2019 5.5952710 28196.612
Atlantic (27.75,27.85] 1982-1992 –> 1993-2008 3.5591553 8021.113
Atlantic (27.75,27.85] 1993-2008 –> 2009-2019 3.7503700 8376.320
Atlantic (27.85,27.95] 1982-1992 –> 1993-2008 5.8882563 10022.087
Atlantic (27.85,27.95] 1993-2008 –> 2009-2019 6.4983518 10909.443
Atlantic (27.95,28.05] 1982-1992 –> 1993-2008 8.8377258 14506.562
Atlantic (27.95,28.05] 1993-2008 –> 2009-2019 8.5740551 14548.077
Atlantic (28.05,28.1] 1982-1992 –> 1993-2008 1.8920290 4542.530
Atlantic (28.05,28.1] 1993-2008 –> 2009-2019 2.0940023 4866.111
Atlantic (28.1,28.15] 1982-1992 –> 1993-2008 1.3682408 4130.239
Atlantic (28.1,28.15] 1993-2008 –> 2009-2019 1.5836342 4491.275
Atlantic (28.15,28.2] 1982-1992 –> 1993-2008 1.0831404 5399.240
Atlantic (28.15,28.2] 1993-2008 –> 2009-2019 1.3925064 6622.206
Atlantic (28.2, Inf] 1982-1992 –> 1993-2008 0.6867058 3922.636
Atlantic (28.2, Inf] 1993-2008 –> 2009-2019 0.8242988 5629.709
Indo-Pacific (-Inf,26] 1982-1992 –> 1993-2008 14.1340140 73065.740
Indo-Pacific (-Inf,26] 1993-2008 –> 2009-2019 13.6778354 72857.037
Indo-Pacific (26,26.5] 1982-1992 –> 1993-2008 9.1064919 67776.344
Indo-Pacific (26,26.5] 1993-2008 –> 2009-2019 9.3678946 67539.994
Indo-Pacific (26.5,26.75] 1982-1992 –> 1993-2008 7.8025333 52625.331
Indo-Pacific (26.5,26.75] 1993-2008 –> 2009-2019 8.2265607 53424.644
Indo-Pacific (26.75,27] 1982-1992 –> 1993-2008 7.6731351 61745.811
Indo-Pacific (26.75,27] 1993-2008 –> 2009-2019 8.6847179 64246.098
Indo-Pacific (27,27.25] 1982-1992 –> 1993-2008 7.1947896 72793.407
Indo-Pacific (27,27.25] 1993-2008 –> 2009-2019 8.8439602 76951.805
Indo-Pacific (27.25,27.5] 1982-1992 –> 1993-2008 6.2262950 61261.706
Indo-Pacific (27.25,27.5] 1993-2008 –> 2009-2019 7.3220524 64994.340
Indo-Pacific (27.5,27.75] 1982-1992 –> 1993-2008 5.0886806 57728.526
Indo-Pacific (27.5,27.75] 1993-2008 –> 2009-2019 6.8407132 63431.309
Indo-Pacific (27.75,27.85] 1982-1992 –> 1993-2008 4.3039914 20670.946
Indo-Pacific (27.75,27.85] 1993-2008 –> 2009-2019 5.4582398 23185.242
Indo-Pacific (27.85,27.95] 1982-1992 –> 1993-2008 4.6903868 27294.297
Indo-Pacific (27.85,27.95] 1993-2008 –> 2009-2019 5.5624033 28926.558
Indo-Pacific (27.95,28.05] 1982-1992 –> 1993-2008 3.9668211 22173.074
Indo-Pacific (27.95,28.05] 1993-2008 –> 2009-2019 4.4683939 22981.747
Indo-Pacific (28.05,28.1] 1982-1992 –> 1993-2008 3.3580731 14662.395
Indo-Pacific (28.05,28.1] 1993-2008 –> 2009-2019 3.8009711 15117.534
Indo-Pacific (28.1, Inf] 1982-1992 –> 1993-2008 2.5304774 101232.032
Indo-Pacific (28.1, Inf] 1993-2008 –> 2009-2019 2.8809198 107346.993

5.4 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)

5.5 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
          if (params_local$MLR_type == "rlm") {
            i_lm_fit <- MASS::rlm(as.formula(i_lm),
                                  data = GLODAP_basin_era_slab)
          }
          
          if (params_local$MLR_type == "lm") {
            i_lm_fit <- lm(as.formula(i_lm),
                           data = GLODAP_basin_era_slab)
          }
            
            # plot model diagnostics vs predictors
            
            p_model_predictors <- 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_predictors,
              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_predictors)
            
            
            # plot model diagnostics vs location
            
            GLODAP_basin_era_slab <- GLODAP_basin_era_slab %>%
              mutate(fitted = i_lm_fit$fitted.values,
                     residuals = i_lm_fit$residuals)
            
            GLODAP_basin_era_slab_long <- GLODAP_basin_era_slab %>% 
              pivot_longer(cols = c(params_local$MLR_target , fitted, residuals),
                           names_to = "estimate",
                           values_to = "value"
              ) %>% 
              pivot_longer(cols = c(lat, lon, depth),
                           names_to = "coordinate_type",
                           values_to = "coordinate_value"
              )

             p_model_coordinate <- GLODAP_basin_era_slab_long %>%
              ggplot(aes(coordinate_value, value)) +
              geom_bin2d() +
              scale_fill_viridis_c() +
              labs(
                title = paste(
                  "era:",
                  i_era,
                  "| eras:",
                  i_eras,
                  "| basin:",
                  i_basin,
                  "| gamma slab:",
                  i_gamma_slab,
                  "| predictors:",
                  i_predictors
                )
              ) +
              facet_grid(estimate~coordinate_type,
                         scales = "free")

            ggsave(
              plot = p_model_coordinate,
              path = paste(path_version_figures, "eMLR_diagnostics", sep = ""),
              filename = paste(
                "Location_MLR_residuals",
                i_era,
                i_eras,
                i_basin,
                i_gamma_slab,
                i_predictors,
                "predictors.png",
                sep = "_"
              ),
              width = 14,
              height = 8
            )

            rm(p_model_coordinate)
            
          }
          
        }
        
      }
    }
  }
  
  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/

5.6 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)

5.7 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 (aic) was plotted against the number of predictors (limited to 3 - 9).

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
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
02b976d Donghe-Zhu 2021-02-24
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
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
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c407a50 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
e2ffc14 Donghe-Zhu 2021-02-05
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
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
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
02b976d Donghe-Zhu 2021-02-24
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
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
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c407a50 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
e2ffc14 Donghe-Zhu 2021-02-05
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
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 - 1982-1992 --> 1993-2008
(-Inf,26] 5 1 4 5 3 3 2
(26,26.5] 5 3 2 4 1 4 4
(26.5,26.75] 5 1 4 4 2 5 2
(26.75,27] 5 1 4 4 1 5 3
(27,27.25] 5 2 3 4 3 5 2
(27.25,27.5] 5 4 1 3 3 5 2
(27.5,27.75] 5 1 4 3 4 3 1
(27.75,27.85] 5 2 3 3 5 4 0
(27.85,27.95] 5 0 5 5 2 3 2
(27.95,28.05] 5 2 3 5 2 3 3
(28.05,28.1] 5 0 5 5 2 3 2
(28.1,28.15] 5 1 4 5 3 4 1
(28.15,28.2] 5 5 0 4 2 3 3
(28.2, Inf] 5 5 0 3 4 3 1
total 70.00 28.00 42.00 57.00 37.00 53.00 28.00
Atlantic - 1993-2008 --> 2009-2019
(-Inf,26] 5 0 4 5 3 3 2
(26,26.5] 5 3 2 4 1 4 4
(26.5,26.75] 5 1 4 4 2 5 2
(26.75,27] 5 1 4 4 2 5 2
(27,27.25] 5 2 2 4 4 5 1
(27.25,27.5] 5 5 0 3 2 5 2
(27.5,27.75] 5 1 4 3 5 3 0
(27.75,27.85] 5 2 3 3 5 4 0
(27.85,27.95] 5 0 5 5 2 3 2
(27.95,28.05] 5 2 3 5 2 3 3
(28.05,28.1] 5 0 5 5 2 2 2
(28.1,28.15] 5 1 4 5 3 3 2
(28.15,28.2] 5 5 0 4 2 3 3
(28.2, Inf] 5 5 0 3 4 3 1
total 70.00 28.00 40.00 57.00 39.00 51.00 26.00
Indo-Pacific - 1982-1992 --> 1993-2008
(-Inf,26] 4 1 4 5 2 4 3
(26,26.5] 5 1 4 4 1 5 3
(26.5,26.75] 5 1 4 5 2 4 2
(26.75,27] 5 0 5 5 2 3 2
(27,27.25] 4 2 3 5 1 4 4
(27.25,27.5] 5 2 2 5 3 5 2
(27.5,27.75] 3 2 2 5 5 5 0
(27.75,27.85] 5 1 4 4 1 5 3
(27.85,27.95] 3 5 0 4 0 3 5
(27.95,28.05] 5 1 4 4 1 5 3
(28.05,28.1] 4 1 4 4 3 5 2
(28.1, Inf] 4 2 3 4 2 5 3
total 52.00 19.00 39.00 54.00 23.00 53.00 32.00
Indo-Pacific - 1993-2008 --> 2009-2019
(-Inf,26] 4 1 4 5 2 4 3
(26,26.5] 5 1 4 4 1 5 3
(26.5,26.75] 4 2 3 5 1 5 3
(26.75,27] 5 0 5 5 2 3 2
(27,27.25] 5 1 4 5 1 4 3
(27.25,27.5] 5 2 2 5 3 5 2
(27.5,27.75] 4 2 2 5 4 5 1
(27.75,27.85] 4 2 3 5 3 4 2
(27.85,27.95] 3 5 0 3 0 4 5
(27.95,28.05] 5 2 3 5 3 3 2
(28.05,28.1] 5 2 3 5 2 5 2
(28.1, Inf] 5 2 3 4 3 5 2
total 54.00 22.00 36.00 56.00 25.00 52.00 30.00

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
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
02b976d Donghe-Zhu 2021-02-24
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
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
924430b Donghe-Zhu 2021-03-03
0d0bca1 Donghe-Zhu 2021-03-03
cb63c16 Donghe-Zhu 2021-03-03
ffda45a Donghe-Zhu 2021-03-03
691ba81 Donghe-Zhu 2021-03-03
c5e45a2 Donghe-Zhu 2021-03-03
89c3e58 Donghe-Zhu 2021-03-03
c407a50 Donghe-Zhu 2021-03-03
c911669 Donghe-Zhu 2021-03-03
b71c719 Donghe-Zhu 2021-03-01
13666ca Donghe-Zhu 2021-03-01
c6e60fe Donghe-Zhu 2021-03-01
7a388f7 Donghe-Zhu 2021-03-01
799e913 Donghe-Zhu 2021-03-01
66ff99f Donghe-Zhu 2021-03-01
ac9bb7a Donghe-Zhu 2021-02-28
efdc047 Donghe-Zhu 2021-02-28
e9a7418 Donghe-Zhu 2021-02-28
e152917 Donghe-Zhu 2021-02-28
287123c Donghe-Zhu 2021-02-27
54d5b5b Donghe-Zhu 2021-02-27
330f064 Donghe-Zhu 2021-02-27
adbc9bc Donghe-Zhu 2021-02-27
5937141 Donghe-Zhu 2021-02-27
4414bbf Donghe-Zhu 2021-02-27
a265efb Donghe-Zhu 2021-02-27
19edd1e Donghe-Zhu 2021-02-27
f20483f Donghe-Zhu 2021-02-26
6a2c7b3 Donghe-Zhu 2021-02-25
354c224 Donghe-Zhu 2021-02-24
1a0a88a Donghe-Zhu 2021-02-24
57f701e Donghe-Zhu 2021-02-24
06f3149 Donghe-Zhu 2021-02-16
401eab3 Donghe-Zhu 2021-02-15
e3bba84 Donghe-Zhu 2021-02-15
5dce4b1 Donghe-Zhu 2021-02-15
4469a0c Donghe-Zhu 2021-02-13
5ae6a69 Donghe-Zhu 2021-02-10
05385dc Donghe-Zhu 2021-02-10
f791ae4 Donghe-Zhu 2021-02-09
f71ae34 Donghe-Zhu 2021-02-09
c011832 Donghe-Zhu 2021-02-09
a145fa7 Donghe-Zhu 2021-02-09
c344e42 Donghe-Zhu 2021-02-08
2f095d7 Donghe-Zhu 2021-02-07
1fad5f1 Donghe-Zhu 2021-02-07
ca03c39 Donghe-Zhu 2021-02-07
e2ffc14 Donghe-Zhu 2021-02-05
cd7c52c Donghe-Zhu 2021-02-04
bcf84f4 Donghe-Zhu 2021-02-02
a518739 Donghe-Zhu 2021-02-01
61666de Donghe-Zhu 2021-01-31
865b582 Donghe-Zhu 2021-01-31
3e68089 Donghe-Zhu 2021-01-31
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_0.7.5      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