Last updated: 2021-03-04

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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:

  • tco2

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] tco2 ~ sal + aou + nitrate + phosphate_star 124 3.3605190 664.4964 8.441841 1982-2000 –> 2001-2010 8.761733 2055.366
Atlantic (-Inf,26] tco2 ~ sal + aou + phosphate + phosphate_star 124 3.3378054 662.8145 8.609812 1982-2000 –> 2001-2010 8.771595 2056.354
Atlantic (-Inf,26] tco2 ~ sal + aou + phosphate_star 124 3.3657676 662.8835 8.634820 1982-2000 –> 2001-2010 8.802006 2054.623
Atlantic (-Inf,26] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 124 3.3377062 664.8071 8.589059 1982-2000 –> 2001-2010 8.734883 2057.345
Atlantic (-Inf,26] tco2 ~ sal + aou + silicate + phosphate_star 124 3.3566163 664.2082 8.456793 1982-2000 –> 2001-2010 8.757765 2055.073
Atlantic (-Inf,26] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 92 3.2279053 490.7020 8.220369 2001-2010 –> 2011-2019 6.580991 1156.649
Atlantic (-Inf,26] tco2 ~ sal + aou + phosphate + phosphate_star 92 3.3361963 494.7737 10.379190 2001-2010 –> 2011-2019 6.674002 1157.588
Atlantic (-Inf,26] tco2 ~ sal + aou + phosphate_star 92 3.3838367 495.3826 10.574694 2001-2010 –> 2011-2019 6.749604 1158.266
Atlantic (-Inf,26] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 92 3.3359691 496.7611 10.412335 2001-2010 –> 2011-2019 6.673675 1161.568
Atlantic (-Inf,26] tco2 ~ sal + aou + silicate + phosphate_star 92 3.3618234 496.1817 10.746574 2001-2010 –> 2011-2019 6.718440 1160.390
Atlantic (26,26.5] tco2 ~ sal + aou + nitrate + phosphate_star 822 4.9624410 4978.2548 14.553617 1982-2000 –> 2001-2010 11.116380 15384.386
Atlantic (26,26.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 822 4.8033507 4926.6867 16.537565 1982-2000 –> 2001-2010 10.917295 15313.875
Atlantic (26,26.5] tco2 ~ sal + aou + silicate + phosphate 822 5.5389846 5158.9526 16.876927 1982-2000 –> 2001-2010 12.092232 15767.017
Atlantic (26,26.5] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 822 4.5671537 4843.7904 16.890064 1982-2000 –> 2001-2010 10.365982 15061.011
Atlantic (26,26.5] tco2 ~ sal + aou + silicate + phosphate_star 822 5.1644880 5043.8640 15.734805 1982-2000 –> 2001-2010 11.436886 15511.237
Atlantic (26,26.5] tco2 ~ sal + aou + nitrate + phosphate_star 710 4.7302030 4233.5275 15.131166 2001-2010 –> 2011-2019 9.692644 9211.782
Atlantic (26,26.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 710 4.5463742 4179.2414 12.411302 2001-2010 –> 2011-2019 9.349725 9105.928
Atlantic (26,26.5] tco2 ~ sal + aou + silicate + phosphate 710 5.3054101 4396.4852 18.142927 2001-2010 –> 2011-2019 10.844395 9555.438
Atlantic (26,26.5] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 710 4.4403719 4145.7409 14.694468 2001-2010 –> 2011-2019 9.007525 8989.531
Atlantic (26,26.5] tco2 ~ sal + aou + silicate + phosphate_star 710 4.9536382 4299.0664 16.921993 2001-2010 –> 2011-2019 10.118126 9342.930
Atlantic (26.5,26.75] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1090 3.9708927 6113.4862 13.628159 1982-2000 –> 2001-2010 8.820754 18071.074
Atlantic (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate 1090 4.0218716 6139.2953 14.060300 1982-2000 –> 2001-2010 8.914940 18130.220
Atlantic (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1090 3.9949329 6126.6444 14.556074 1982-2000 –> 2001-2010 8.833518 18074.959
Atlantic (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate_star 1090 4.0025380 6128.7905 14.304371 1982-2000 –> 2001-2010 8.865561 18095.176
Atlantic (26.5,26.75] tco2 ~ temp + aou + silicate + phosphate_star 1090 4.1086763 6185.8460 13.599749 1982-2000 –> 2001-2010 9.102344 18257.849
Atlantic (26.5,26.75] tco2 ~ aou + silicate + phosphate + phosphate_star 868 4.2260248 4977.3078 13.050743 2001-2010 –> 2011-2019 8.336818 11164.276
Atlantic (26.5,26.75] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 868 4.0854521 4920.5799 12.744041 2001-2010 –> 2011-2019 8.056345 11034.066
Atlantic (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate 868 4.1337309 4938.9744 13.071496 2001-2010 –> 2011-2019 8.155603 11078.270
Atlantic (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 868 4.1009288 4927.1439 13.426886 2001-2010 –> 2011-2019 8.095862 11053.788
Atlantic (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate_star 868 4.1113514 4929.5504 13.229262 2001-2010 –> 2011-2019 8.113889 11058.341
Atlantic (26.75,27] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1822 2.8351727 8982.0348 24.341773 1982-2000 –> 2001-2010 6.304716 26704.729
Atlantic (26.75,27] tco2 ~ sal + aou + silicate + phosphate 1822 3.0347576 9227.9314 39.479887 1982-2000 –> 2001-2010 6.604543 27138.033
Atlantic (26.75,27] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1822 2.8214626 8964.3706 13.393386 1982-2000 –> 2001-2010 6.279824 26665.597
Atlantic (26.75,27] tco2 ~ sal + aou + silicate + phosphate_star 1822 2.8663090 9019.8356 25.537437 1982-2000 –> 2001-2010 6.348124 26764.009
Atlantic (26.75,27] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1822 3.0386740 9234.6310 9.648868 1982-2000 –> 2001-2010 6.789381 27475.501
Atlantic (26.75,27] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1654 3.0664269 8414.5057 21.674380 2001-2010 –> 2011-2019 5.901600 17396.541
Atlantic (26.75,27] tco2 ~ sal + aou + silicate + phosphate 1654 3.1375243 8488.3285 23.560917 2001-2010 –> 2011-2019 6.172282 17716.260
Atlantic (26.75,27] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1654 3.1034629 8454.2200 24.581957 2001-2010 –> 2011-2019 5.924925 17418.591
Atlantic (26.75,27] tco2 ~ sal + aou + silicate + phosphate_star 1654 3.1040255 8452.8197 24.714025 2001-2010 –> 2011-2019 5.970334 17472.655
Atlantic (26.75,27] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1654 3.1927188 8548.0160 19.626479 2001-2010 –> 2011-2019 6.231393 17782.647
Atlantic (27,27.25] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1552 2.4103171 7149.1550 17.603433 1982-2000 –> 2001-2010 5.159250 20660.216
Atlantic (27,27.25] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1552 2.4512775 7201.4605 11.915204 1982-2000 –> 2001-2010 5.280384 20872.188
Atlantic (27,27.25] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1552 2.3939819 7128.0469 15.373800 1982-2000 –> 2001-2010 5.242838 20837.412
Atlantic (27,27.25] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1552 2.4316662 7176.5272 14.259774 1982-2000 –> 2001-2010 5.295496 20915.008
Atlantic (27,27.25] tco2 ~ temp + aou + silicate + phosphate_star 1552 2.4395477 7184.5717 12.888675 1982-2000 –> 2001-2010 5.304542 20923.309
Atlantic (27,27.25] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1455 2.8379905 7178.5212 10.757120 2001-2010 –> 2011-2019 5.248308 14327.676
Atlantic (27,27.25] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1455 2.8201726 7160.1936 14.588168 2001-2010 –> 2011-2019 5.271450 14361.654
Atlantic (27,27.25] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1455 2.6705019 7001.5065 11.372134 2001-2010 –> 2011-2019 5.064484 14129.553
Atlantic (27,27.25] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1455 2.7733791 7111.5046 14.737282 2001-2010 –> 2011-2019 5.205045 14288.032
Atlantic (27,27.25] tco2 ~ temp + aou + silicate + phosphate_star 1455 2.8076274 7145.2199 14.224119 2001-2010 –> 2011-2019 5.247175 14329.792
Atlantic (27.25,27.5] tco2 ~ aou + nitrate + silicate + phosphate_star 1572 2.9247915 7847.3565 20.720246 1982-2000 –> 2001-2010 5.839311 23050.037
Atlantic (27.25,27.5] tco2 ~ sal + aou + nitrate + phosphate_star 1572 2.6859094 7579.4757 16.522560 1982-2000 –> 2001-2010 5.268790 22044.795
Atlantic (27.25,27.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1572 2.5870786 7463.6068 17.417094 1982-2000 –> 2001-2010 5.149602 21882.626
Atlantic (27.25,27.5] tco2 ~ temp + aou + nitrate + phosphate_star 1572 2.6415138 7527.0739 14.752115 1982-2000 –> 2001-2010 5.442321 22486.831
Atlantic (27.25,27.5] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1572 2.5298850 7393.3213 15.053663 1982-2000 –> 2001-2010 5.326817 22346.628
Atlantic (27.25,27.5] tco2 ~ sal + aou + nitrate + phosphate_star 1388 3.4358059 7377.2555 14.748017 2001-2010 –> 2011-2019 6.121715 14956.731
Atlantic (27.25,27.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1388 3.3097019 7275.4515 15.363488 2001-2010 –> 2011-2019 5.896781 14739.058
Atlantic (27.25,27.5] tco2 ~ temp + aou + nitrate + phosphate_star 1388 3.2587140 7230.3528 15.542990 2001-2010 –> 2011-2019 5.900228 14757.427
Atlantic (27.25,27.5] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1388 3.0521317 7050.5459 16.476693 2001-2010 –> 2011-2019 5.582017 14443.867
Atlantic (27.25,27.5] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1388 3.6681220 7560.8846 20.622605 2001-2010 –> 2011-2019 6.650131 15471.153
Atlantic (27.5,27.75] tco2 ~ aou + nitrate + silicate + phosphate_star 2162 2.5748492 10237.0903 16.472900 1982-2000 –> 2001-2010 5.117284 28849.185
Atlantic (27.5,27.75] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 2162 2.4691170 10057.7835 16.576072 1982-2000 –> 2001-2010 5.011475 28671.640
Atlantic (27.5,27.75] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 2162 2.4628775 10046.8428 15.426906 1982-2000 –> 2001-2010 5.006852 28665.728
Atlantic (27.5,27.75] tco2 ~ sal + aou + silicate + phosphate_star 2162 2.5253824 10153.2114 16.388237 1982-2000 –> 2001-2010 5.069616 28770.901
Atlantic (27.5,27.75] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 2162 2.5379953 10176.7537 15.455524 1982-2000 –> 2001-2010 5.080305 28790.462
Atlantic (27.5,27.75] tco2 ~ sal + aou + nitrate 1937 2.8167006 9518.7513 19.248743 2001-2010 –> 2011-2019 5.313032 19619.933
Atlantic (27.5,27.75] tco2 ~ sal + aou + nitrate + phosphate_star 1937 2.7720010 9458.7799 20.964307 2001-2010 –> 2011-2019 5.258890 19545.575
Atlantic (27.5,27.75] tco2 ~ sal + aou + nitrate + silicate 1937 2.8145159 9517.7454 19.433708 2001-2010 –> 2011-2019 5.283989 19574.152
Atlantic (27.5,27.75] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1937 2.7687089 9456.1763 20.951649 2001-2010 –> 2011-2019 5.237826 19513.960
Atlantic (27.5,27.75] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1937 2.8475852 9564.9978 17.886641 2001-2010 –> 2011-2019 5.310463 19611.841
Atlantic (27.75,27.85] tco2 ~ aou + silicate + phosphate + phosphate_star 785 1.5331039 2910.5857 13.532786 1982-2000 –> 2001-2010 2.976226 7886.964
Atlantic (27.75,27.85] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 785 1.4359150 2809.7631 11.473740 1982-2000 –> 2001-2010 2.912040 7851.001
Atlantic (27.75,27.85] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 785 1.4284620 2801.5929 11.930917 1982-2000 –> 2001-2010 2.871521 7779.850
Atlantic (27.75,27.85] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 785 1.5174176 2896.4391 11.096265 1982-2000 –> 2001-2010 2.968490 7890.091
Atlantic (27.75,27.85] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 785 1.5192049 2898.2873 13.467254 1982-2000 –> 2001-2010 2.946963 7846.910
Atlantic (27.75,27.85] tco2 ~ sal + aou + nitrate + phosphate_star 694 1.4989101 2543.2634 13.933062 2001-2010 –> 2011-2019 2.934836 5351.038
Atlantic (27.75,27.85] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 694 1.4756400 2523.5461 13.704523 2001-2010 –> 2011-2019 2.911555 5333.309
Atlantic (27.75,27.85] tco2 ~ sal + aou + phosphate + phosphate_star 694 1.4891144 2534.1627 14.002640 2001-2010 –> 2011-2019 2.925258 5342.176
Atlantic (27.75,27.85] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 694 1.4726370 2520.7186 13.878345 2001-2010 –> 2011-2019 2.901099 5322.311
Atlantic (27.75,27.85] tco2 ~ sal + aou + silicate + phosphate_star 694 1.4759905 2521.8758 13.761862 2001-2010 –> 2011-2019 2.922552 5341.236
Atlantic (27.85,27.95] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 750 2.6692810 3615.1215 23.995265 1982-2000 –> 2001-2010 4.243630 8899.125
Atlantic (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 750 2.6895327 3626.4590 25.833727 1982-2000 –> 2001-2010 4.191313 8777.669
Atlantic (27.85,27.95] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 750 2.8544815 3715.7431 32.204804 1982-2000 –> 2001-2010 4.309205 8777.369
Atlantic (27.85,27.95] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 750 2.2329287 3347.3788 23.454990 1982-2000 –> 2001-2010 3.715054 8461.516
Atlantic (27.85,27.95] tco2 ~ temp + aou + silicate + phosphate_star 750 3.3111420 3936.3475 55.303877 1982-2000 –> 2001-2010 4.802641 9066.226
Atlantic (27.85,27.95] tco2 ~ sal + aou + nitrate + phosphate_star 731 2.0262288 3118.9179 28.426142 2001-2010 –> 2011-2019 4.710233 6740.291
Atlantic (27.85,27.95] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 731 2.0261865 3120.8874 28.412603 2001-2010 –> 2011-2019 4.695468 6736.009
Atlantic (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 731 1.9635808 3075.0015 28.548355 2001-2010 –> 2011-2019 4.653114 6701.461
Atlantic (27.85,27.95] tco2 ~ temp + aou + phosphate + phosphate_star 731 2.1583114 3211.2430 24.481604 2001-2010 –> 2011-2019 4.864486 6844.955
Atlantic (27.85,27.95] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 731 2.0537232 3140.6228 26.196998 2001-2010 –> 2011-2019 4.286652 6488.002
Atlantic (27.95,28.05] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 924 4.1196395 5252.5334 20.941649 1982-2000 –> 2001-2010 8.511758 15516.515
Atlantic (27.95,28.05] tco2 ~ temp + aou + nitrate + phosphate_star 924 3.8437225 5122.4219 16.382441 1982-2000 –> 2001-2010 8.024820 15210.297
Atlantic (27.95,28.05] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 924 3.2071685 4789.8363 15.994347 1982-2000 –> 2001-2010 6.476307 14009.688
Atlantic (27.95,28.05] tco2 ~ temp + nitrate + phosphate_star 924 3.9630495 5176.9199 19.889190 1982-2000 –> 2001-2010 8.318936 15407.610
Atlantic (27.95,28.05] tco2 ~ temp + nitrate + silicate + phosphate_star 924 3.9332438 5164.9688 20.429650 1982-2000 –> 2001-2010 8.246650 15363.005
Atlantic (27.95,28.05] tco2 ~ temp + aou + nitrate + phosphate_star 854 4.0086953 4807.0466 16.883844 2001-2010 –> 2011-2019 7.852418 9929.469
Atlantic (27.95,28.05] tco2 ~ temp + aou + nitrate + silicate 854 4.1778226 4877.6287 21.998666 2001-2010 –> 2011-2019 8.242374 10103.284
Atlantic (27.95,28.05] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 854 3.2053501 4427.0618 16.619663 2001-2010 –> 2011-2019 6.412519 9216.898
Atlantic (27.95,28.05] tco2 ~ temp + nitrate + phosphate_star 854 4.1196667 4851.6860 20.193182 2001-2010 –> 2011-2019 8.082716 10028.606
Atlantic (27.95,28.05] tco2 ~ temp + nitrate + silicate + phosphate_star 854 4.0595672 4828.5854 20.710517 2001-2010 –> 2011-2019 7.992811 9993.554
Atlantic (28.05,28.1] tco2 ~ sal + aou + nitrate + silicate 625 1.1133375 1919.8760 7.631757 1982-2000 –> 2001-2010 2.258027 5462.728
Atlantic (28.05,28.1] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 625 1.0916591 1897.2965 7.911786 1982-2000 –> 2001-2010 2.223390 5416.280
Atlantic (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate 625 1.1117397 1918.0807 7.360564 1982-2000 –> 2001-2010 2.247389 5442.917
Atlantic (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 625 1.0870742 1892.0355 7.779147 1982-2000 –> 2001-2010 2.209818 5392.906
Atlantic (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate_star 625 1.1157696 1922.6036 8.063066 1982-2000 –> 2001-2010 2.280662 5505.205
Atlantic (28.05,28.1] tco2 ~ aou + silicate + phosphate + phosphate_star 553 1.1845765 1768.6862 9.385421 2001-2010 –> 2011-2019 2.288125 3677.522
Atlantic (28.05,28.1] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 553 1.1781886 1764.7059 10.903140 2001-2010 –> 2011-2019 2.269848 3662.002
Atlantic (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 553 1.1729858 1759.8110 10.797416 2001-2010 –> 2011-2019 2.260060 3651.846
Atlantic (28.05,28.1] tco2 ~ temp + aou + silicate + phosphate 553 1.1848805 1768.9699 9.379384 2001-2010 –> 2011-2019 2.288398 3677.772
Atlantic (28.05,28.1] tco2 ~ temp + aou + silicate + phosphate_star 553 1.1840199 1768.1663 9.427247 2001-2010 –> 2011-2019 2.287874 3677.349
Atlantic (28.1,28.15] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 730 0.9583426 2023.5274 8.666162 1982-2000 –> 2001-2010 1.927434 5822.741
Atlantic (28.1,28.15] tco2 ~ sal + aou + silicate + phosphate 730 1.0310561 2128.3023 7.972728 1982-2000 –> 2001-2010 2.049135 6060.045
Atlantic (28.1,28.15] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 730 0.9598337 2025.7972 8.702700 1982-2000 –> 2001-2010 1.925331 5814.875
Atlantic (28.1,28.15] tco2 ~ sal + aou + silicate + phosphate_star 730 0.9603495 2024.5815 8.674619 1982-2000 –> 2001-2010 1.929520 5822.019
Atlantic (28.1,28.15] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 730 1.0223245 2117.8856 4.558204 1982-2000 –> 2001-2010 2.105628 6221.032
Atlantic (28.1,28.15] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 634 1.0426481 1866.1705 8.046985 2001-2010 –> 2011-2019 2.000991 3889.698
Atlantic (28.1,28.15] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 634 1.0441064 1867.9428 8.125753 2001-2010 –> 2011-2019 2.003940 3893.740
Atlantic (28.1,28.15] tco2 ~ sal + aou + silicate + phosphate_star 634 1.0445623 1866.4963 8.084222 2001-2010 –> 2011-2019 2.004912 3891.078
Atlantic (28.1,28.15] tco2 ~ temp + aou + nitrate + phosphate_star 634 1.0725186 1899.9864 5.998753 2001-2010 –> 2011-2019 2.114794 4044.090
Atlantic (28.1,28.15] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 634 1.0589537 1885.8468 5.558966 2001-2010 –> 2011-2019 2.081278 4003.732
Atlantic (28.15,28.2] tco2 ~ sal + aou + nitrate + phosphate_star 1187 1.1460251 3704.1351 5.303922 1982-2000 –> 2001-2010 2.429933 11496.298
Atlantic (28.15,28.2] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1187 1.0721072 3547.8523 4.448836 1982-2000 –> 2001-2010 2.229493 10858.360
Atlantic (28.15,28.2] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1187 1.2787062 3966.2052 3.559950 1982-2000 –> 2001-2010 2.746435 12384.180
Atlantic (28.15,28.2] tco2 ~ temp + aou + nitrate + phosphate_star 1187 0.8787989 3073.8413 3.236014 1982-2000 –> 2001-2010 1.795025 9293.043
Atlantic (28.15,28.2] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1187 0.8771064 3071.2646 3.150407 1982-2000 –> 2001-2010 1.780008 9224.170
Atlantic (28.15,28.2] tco2 ~ sal + aou + nitrate + phosphate_star 1065 1.3482098 3670.7354 10.174007 2001-2010 –> 2011-2019 2.494235 7374.871
Atlantic (28.15,28.2] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1065 1.1919905 3410.4195 6.276861 2001-2010 –> 2011-2019 2.264098 6958.272
Atlantic (28.15,28.2] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1065 1.4665649 3851.9648 10.817584 2001-2010 –> 2011-2019 2.745271 7818.170
Atlantic (28.15,28.2] tco2 ~ temp + aou + nitrate + phosphate_star 1065 0.9236713 2865.2191 5.661281 2001-2010 –> 2011-2019 1.802470 5939.060
Atlantic (28.15,28.2] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1065 0.9167518 2851.2027 5.115247 2001-2010 –> 2011-2019 1.793858 5922.467
Atlantic (28.2, Inf] tco2 ~ sal + aou + phosphate + phosphate_star 2075 1.9499417 8671.9626 6.858475 1982-2000 –> 2001-2010 3.822134 24720.893
Atlantic (28.2, Inf] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 2075 1.9335739 8638.9806 7.065373 1982-2000 –> 2001-2010 3.736760 24395.555
Atlantic (28.2, Inf] tco2 ~ sal + silicate + phosphate + phosphate_star 2075 1.9467935 8665.2572 6.908914 1982-2000 –> 2001-2010 3.761556 24469.991
Atlantic (28.2, Inf] tco2 ~ temp + aou + nitrate + phosphate_star 2075 1.4292334 7382.7186 11.703298 1982-2000 –> 2001-2010 2.781529 20881.896
Atlantic (28.2, Inf] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 2075 1.2506421 6830.7720 8.001194 1982-2000 –> 2001-2010 2.520755 19840.526
Atlantic (28.2, Inf] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1967 2.0301459 8381.7997 6.973980 2001-2010 –> 2011-2019 3.963720 17020.780
Atlantic (28.2, Inf] tco2 ~ sal + silicate + phosphate + phosphate_star 1967 2.0449366 8408.3572 7.173934 2001-2010 –> 2011-2019 3.991730 17073.614
Atlantic (28.2, Inf] tco2 ~ temp + aou + nitrate + phosphate_star 1967 1.4557462 7071.3945 6.693418 2001-2010 –> 2011-2019 2.884980 14454.113
Atlantic (28.2, Inf] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1967 1.1973473 6304.6512 5.494230 2001-2010 –> 2011-2019 2.447989 13135.423
Atlantic (28.2, Inf] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1967 2.0170198 8356.2814 7.041599 2001-2010 –> 2011-2019 4.007400 17115.428
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + nitrate + phosphate_star 4077 9.5194278 29955.7163 42.038091 1982-2000 –> 2001-2010 20.074713 87356.308
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 4077 9.5115547 29950.9696 39.771493 1982-2000 –> 2001-2010 20.030316 87300.875
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + phosphate + phosphate_star 4077 8.1686373 28707.8881 28.903677 1982-2000 –> 2001-2010 17.228273 83785.953
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 4077 8.1674502 28708.7031 28.988967 1982-2000 –> 2001-2010 17.226814 83788.312
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + silicate + phosphate_star 4077 9.9190367 30291.0175 30.863782 1982-2000 –> 2001-2010 20.742383 88072.806
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + nitrate + phosphate_star 3620 9.5306262 26607.7704 36.539652 2001-2010 –> 2011-2019 19.050054 56563.487
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 3620 9.4929250 26581.0737 31.514343 2001-2010 –> 2011-2019 19.004480 56532.043
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + phosphate + phosphate_star 3620 7.9556678 25300.0395 26.043615 2001-2010 –> 2011-2019 16.124305 54007.928
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 3620 7.9556513 25302.0245 26.056743 2001-2010 –> 2011-2019 16.123102 54010.728
Indo-Pacific (-Inf,26] tco2 ~ sal + aou + silicate + phosphate_star 3620 9.8050630 26813.3029 30.613000 2001-2010 –> 2011-2019 19.724100 57104.320
Indo-Pacific (26,26.5] tco2 ~ sal + aou + nitrate + phosphate_star 4220 6.8060143 28174.1296 56.062420 1982-2000 –> 2001-2010 13.804181 82968.330
Indo-Pacific (26,26.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 4220 6.7144513 28061.8135 46.226026 1982-2000 –> 2001-2010 13.656856 82727.759
Indo-Pacific (26,26.5] tco2 ~ sal + aou + phosphate + phosphate_star 4220 6.0851001 27229.1576 45.296377 1982-2000 –> 2001-2010 12.510483 80633.008
Indo-Pacific (26,26.5] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 4220 6.0427775 27172.2513 44.940298 1982-2000 –> 2001-2010 12.426446 80472.052
Indo-Pacific (26,26.5] tco2 ~ sal + aou + silicate + phosphate_star 4220 6.8504103 28229.0053 45.364215 1982-2000 –> 2001-2010 13.930929 83213.688
Indo-Pacific (26,26.5] tco2 ~ sal + aou + nitrate + phosphate_star 3794 6.7823516 25304.7953 51.923082 2001-2010 –> 2011-2019 13.588366 53478.925
Indo-Pacific (26,26.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 3794 6.6603343 25169.0411 38.723674 2001-2010 –> 2011-2019 13.374786 53230.855
Indo-Pacific (26,26.5] tco2 ~ sal + aou + phosphate + phosphate_star 3794 6.0845120 24480.9102 43.121045 2001-2010 –> 2011-2019 12.169612 51710.068
Indo-Pacific (26,26.5] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 3794 6.0268281 24410.6294 42.723824 2001-2010 –> 2011-2019 12.069605 51582.881
Indo-Pacific (26,26.5] tco2 ~ sal + aou + silicate + phosphate_star 3794 6.8085975 25334.1021 26.280781 2001-2010 –> 2011-2019 13.659008 53563.107
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + nitrate + phosphate_star 3488 4.9441918 21059.6527 21.624807 1982-2000 –> 2001-2010 10.377044 62440.864
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 3488 4.8143112 20875.9478 22.854058 1982-2000 –> 2001-2010 10.099677 61893.222
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + phosphate + phosphate_star 3488 5.1191863 21302.2919 16.124201 1982-2000 –> 2001-2010 10.512436 62586.228
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 3488 5.1185227 21303.3875 15.919141 1982-2000 –> 2001-2010 10.494317 62546.220
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate_star 3488 5.2856923 21525.5803 16.226763 1982-2000 –> 2001-2010 10.905985 63357.785
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + nitrate + phosphate_star 3143 5.3172798 19435.1138 23.054367 2001-2010 –> 2011-2019 10.261472 40494.767
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 3143 5.2286251 19331.4241 24.125422 2001-2010 –> 2011-2019 10.042936 40207.372
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + phosphate + phosphate_star 3143 5.4574819 19598.7110 21.124913 2001-2010 –> 2011-2019 10.576668 40901.003
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 3143 5.4553558 19598.2617 21.470929 2001-2010 –> 2011-2019 10.573878 40901.649
Indo-Pacific (26.5,26.75] tco2 ~ sal + aou + silicate + phosphate_star 3143 5.7155883 19889.1854 17.177316 2001-2010 –> 2011-2019 11.001281 41414.766
Indo-Pacific (26.75,27] tco2 ~ sal + aou + nitrate + phosphate_star 4075 5.7353755 25811.5728 23.325930 1982-2000 –> 2001-2010 11.506265 76083.357
Indo-Pacific (26.75,27] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 4075 4.9326551 24584.7498 18.952402 1982-2000 –> 2001-2010 9.890572 72452.468
Indo-Pacific (26.75,27] tco2 ~ sal + aou + phosphate + phosphate_star 4075 5.4752786 25433.3308 21.463618 1982-2000 –> 2001-2010 10.949113 74867.703
Indo-Pacific (26.75,27] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 4075 5.0545550 24783.7110 16.612212 1982-2000 –> 2001-2010 10.084663 72880.497
Indo-Pacific (26.75,27] tco2 ~ sal + aou + silicate + phosphate_star 4075 5.4392449 25379.5171 24.512979 1982-2000 –> 2001-2010 10.864077 74671.395
Indo-Pacific (26.75,27] tco2 ~ sal + aou + nitrate + phosphate_star 3755 6.1664525 24329.8474 21.714913 2001-2010 –> 2011-2019 11.901828 50141.420
Indo-Pacific (26.75,27] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 3755 5.3590929 23277.9768 18.154205 2001-2010 –> 2011-2019 10.291748 47862.727
Indo-Pacific (26.75,27] tco2 ~ sal + aou + phosphate + phosphate_star 3755 5.9178176 24020.7661 23.255394 2001-2010 –> 2011-2019 11.393096 49454.097
Indo-Pacific (26.75,27] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 3755 5.5301448 23513.9356 17.845607 2001-2010 –> 2011-2019 10.584700 48297.647
Indo-Pacific (26.75,27] tco2 ~ sal + aou + silicate + phosphate_star 3755 5.9479389 24058.8945 18.254926 2001-2010 –> 2011-2019 11.387184 49438.412
Indo-Pacific (27,27.25] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 5035 4.2360138 28839.9914 27.363505 1982-2000 –> 2001-2010 8.411507 82080.611
Indo-Pacific (27,27.25] tco2 ~ sal + aou + silicate + phosphate 5035 5.3395007 31169.2917 21.249743 1982-2000 –> 2001-2010 10.503717 88379.502
Indo-Pacific (27,27.25] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 5035 4.9399278 30388.0327 27.538227 1982-2000 –> 2001-2010 9.704201 86093.833
Indo-Pacific (27,27.25] tco2 ~ sal + aou + silicate + phosphate_star 5035 5.1274683 30761.2542 18.261929 1982-2000 –> 2001-2010 10.054513 87092.865
Indo-Pacific (27,27.25] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 5035 4.9628088 30434.5678 38.749303 1982-2000 –> 2001-2010 10.003790 87195.416
Indo-Pacific (27,27.25] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 4394 4.7003588 26084.2820 20.866311 2001-2010 –> 2011-2019 8.936373 54924.273
Indo-Pacific (27,27.25] tco2 ~ sal + aou + silicate + phosphate 4394 5.7587531 27866.9678 24.811907 2001-2010 –> 2011-2019 11.098254 59036.259
Indo-Pacific (27,27.25] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 4394 5.4707388 27418.0791 20.815364 2001-2010 –> 2011-2019 10.410666 57806.112
Indo-Pacific (27,27.25] tco2 ~ sal + aou + silicate + phosphate_star 4394 5.5796043 27589.2396 21.578895 2001-2010 –> 2011-2019 10.707073 58350.494
Indo-Pacific (27,27.25] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 4394 5.3672998 27250.3275 26.470255 2001-2010 –> 2011-2019 10.330109 57684.895
Indo-Pacific (27.25,27.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 4525 3.5875103 24416.3927 18.754136 1982-2000 –> 2001-2010 7.002290 68551.445
Indo-Pacific (27.25,27.5] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 4525 4.1422755 25717.6635 20.568862 1982-2000 –> 2001-2010 8.057321 72131.467
Indo-Pacific (27.25,27.5] tco2 ~ sal + silicate + phosphate + phosphate_star 4525 4.2181033 25879.8332 18.598230 1982-2000 –> 2001-2010 8.133334 72292.422
Indo-Pacific (27.25,27.5] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 4525 3.6925082 24677.4627 19.149427 1982-2000 –> 2001-2010 7.426427 70301.724
Indo-Pacific (27.25,27.5] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 4525 3.9439688 25273.6908 20.036154 1982-2000 –> 2001-2010 7.970319 72154.756
Indo-Pacific (27.25,27.5] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 4007 3.9808975 22456.7728 21.549652 2001-2010 –> 2011-2019 7.568408 46873.165
Indo-Pacific (27.25,27.5] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 4007 3.9873654 22469.7829 18.413943 2001-2010 –> 2011-2019 7.679874 47147.246
Indo-Pacific (27.25,27.5] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 4007 4.1988497 22883.9456 20.580479 2001-2010 –> 2011-2019 8.142818 48157.636
Indo-Pacific (27.25,27.5] tco2 ~ temp + aou + silicate + phosphate_star 4007 4.4894269 23418.1979 23.637014 2001-2010 –> 2011-2019 8.600847 49066.198
Indo-Pacific (27.25,27.5] tco2 ~ temp + silicate + phosphate + phosphate_star 4007 4.5289001 23488.3530 24.449319 2001-2010 –> 2011-2019 8.676859 49216.424
Indo-Pacific (27.5,27.75] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 4480 3.5185656 23999.8478 17.594722 1982-2000 –> 2001-2010 6.600451 67570.258
Indo-Pacific (27.5,27.75] tco2 ~ sal + silicate + phosphate + phosphate_star 4480 3.6341366 24287.4185 15.265632 1982-2000 –> 2001-2010 6.743912 68010.043
Indo-Pacific (27.5,27.75] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 4480 3.3593876 23585.0471 11.600497 1982-2000 –> 2001-2010 6.528719 67634.402
Indo-Pacific (27.5,27.75] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 4480 3.3928106 23673.7508 16.407331 1982-2000 –> 2001-2010 6.608237 67970.278
Indo-Pacific (27.5,27.75] tco2 ~ temp + aou + silicate + phosphate_star 4480 3.4649885 23860.3647 17.339052 1982-2000 –> 2001-2010 6.686353 68186.477
Indo-Pacific (27.5,27.75] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 4006 3.8517158 22186.8673 10.883762 2001-2010 –> 2011-2019 7.211103 45771.914
Indo-Pacific (27.5,27.75] tco2 ~ temp + aou + silicate + phosphate 4006 4.0882668 22662.4018 16.853159 2001-2010 –> 2011-2019 7.593036 46625.049
Indo-Pacific (27.5,27.75] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 4006 3.8702367 22225.3007 16.356122 2001-2010 –> 2011-2019 7.263047 45899.052
Indo-Pacific (27.5,27.75] tco2 ~ temp + aou + silicate + phosphate_star 4006 4.0354161 22558.1522 17.384353 2001-2010 –> 2011-2019 7.500405 46418.517
Indo-Pacific (27.5,27.75] tco2 ~ temp + silicate + phosphate + phosphate_star 4006 4.0834359 22652.9289 17.745094 2001-2010 –> 2011-2019 7.587279 46613.207
Indo-Pacific (27.75,27.85] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1772 2.6986815 8561.0714 14.917753 1982-2000 –> 2001-2010 5.113328 23721.508
Indo-Pacific (27.75,27.85] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1772 2.7005974 8563.5865 16.729055 1982-2000 –> 2001-2010 5.107830 23703.776
Indo-Pacific (27.75,27.85] tco2 ~ sal + aou + silicate + phosphate_star 1772 2.7512933 8627.4981 15.469195 1982-2000 –> 2001-2010 5.203883 23888.588
Indo-Pacific (27.75,27.85] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1772 2.6855562 8543.7927 16.757679 1982-2000 –> 2001-2010 5.172788 23899.229
Indo-Pacific (27.75,27.85] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1772 2.3889834 8129.0740 12.693411 1982-2000 –> 2001-2010 4.701482 23004.922
Indo-Pacific (27.75,27.85] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1648 3.0800680 8398.6621 10.744839 2001-2010 –> 2011-2019 5.778749 16959.733
Indo-Pacific (27.75,27.85] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1648 3.1203862 8441.5269 11.287184 2001-2010 –> 2011-2019 5.820984 17005.113
Indo-Pacific (27.75,27.85] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1648 3.0784426 8396.9223 10.426959 2001-2010 –> 2011-2019 5.763999 16940.715
Indo-Pacific (27.75,27.85] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1648 2.8053609 8090.7515 15.199695 2001-2010 –> 2011-2019 5.194344 16219.826
Indo-Pacific (27.75,27.85] tco2 ~ temp + aou + silicate + phosphate_star 1648 3.1523358 8473.1031 11.052261 2001-2010 –> 2011-2019 5.894117 17088.327
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 2176 2.1694170 9559.6638 11.639858 1982-2000 –> 2001-2010 4.175899 27498.898
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate 2176 2.3177648 9845.5259 14.205950 1982-2000 –> 2001-2010 4.418653 28172.370
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 2176 2.1471672 9514.7986 10.872997 1982-2000 –> 2001-2010 4.118588 27304.650
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate_star 2176 2.1855157 9589.8396 12.222087 1982-2000 –> 2001-2010 4.202768 27572.437
Indo-Pacific (27.85,27.95] tco2 ~ sal + silicate + phosphate + phosphate_star 2176 2.2856459 9784.7955 14.160172 1982-2000 –> 2001-2010 4.373784 28060.056
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 2046 2.5041365 9576.5231 9.169674 2001-2010 –> 2011-2019 4.673553 19136.187
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate 2046 2.6838002 9858.0571 16.302501 2001-2010 –> 2011-2019 5.001565 19703.583
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 2046 2.5040317 9576.3520 11.437380 2001-2010 –> 2011-2019 4.651199 19091.151
Indo-Pacific (27.85,27.95] tco2 ~ sal + aou + silicate + phosphate_star 2046 2.5358782 9626.0661 9.601261 2001-2010 –> 2011-2019 4.721394 19215.906
Indo-Pacific (27.85,27.95] tco2 ~ sal + silicate + phosphate + phosphate_star 2046 2.6167053 9754.4568 15.632590 2001-2010 –> 2011-2019 4.902351 19539.252
Indo-Pacific (27.95,28.05] tco2 ~ sal + aou + nitrate + silicate + phosphate_star 1910 2.5326413 8984.1289 10.635014 1982-2000 –> 2001-2010 4.895147 25837.436
Indo-Pacific (27.95,28.05] tco2 ~ sal + aou + silicate + phosphate 1910 2.4473448 8851.2592 11.276362 1982-2000 –> 2001-2010 4.685415 25302.703
Indo-Pacific (27.95,28.05] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1910 2.3837799 8752.7312 11.039288 1982-2000 –> 2001-2010 4.588994 25096.882
Indo-Pacific (27.95,28.05] tco2 ~ sal + silicate + phosphate + phosphate_star 1910 2.3942259 8767.4342 11.103208 1982-2000 –> 2001-2010 4.605596 25130.186
Indo-Pacific (27.95,28.05] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1910 2.3812311 8748.6446 11.619988 1982-2000 –> 2001-2010 4.737939 25583.794
Indo-Pacific (27.95,28.05] tco2 ~ sal + aou + silicate + phosphate 1759 2.7277472 8534.0545 11.098056 2001-2010 –> 2011-2019 5.175092 17385.314
Indo-Pacific (27.95,28.05] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1759 2.6290892 8406.4564 10.426828 2001-2010 –> 2011-2019 5.012869 17159.188
Indo-Pacific (27.95,28.05] tco2 ~ sal + silicate + phosphate + phosphate_star 1759 2.6513438 8434.1101 10.481761 2001-2010 –> 2011-2019 5.045570 17201.544
Indo-Pacific (27.95,28.05] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1759 2.5446660 8291.6356 10.515274 2001-2010 –> 2011-2019 4.925897 17040.280
Indo-Pacific (27.95,28.05] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1759 2.6965454 8495.5814 10.885952 2001-2010 –> 2011-2019 5.237534 17492.280
Indo-Pacific (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate 1321 2.1825949 5822.9549 9.823222 1982-2000 –> 2001-2010 4.273427 17449.867
Indo-Pacific (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1321 2.1590063 5796.2458 10.068181 1982-2000 –> 2001-2010 4.249824 17425.123
Indo-Pacific (28.05,28.1] tco2 ~ sal + silicate + phosphate + phosphate_star 1321 2.1615371 5797.3409 9.979929 1982-2000 –> 2001-2010 4.254876 17430.707
Indo-Pacific (28.05,28.1] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1321 2.2087296 5856.4027 11.527943 1982-2000 –> 2001-2010 4.314869 17524.602
Indo-Pacific (28.05,28.1] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1321 2.2047564 5851.6458 11.780195 1982-2000 –> 2001-2010 4.279925 17440.057
Indo-Pacific (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate 1224 2.2743358 5497.0539 8.864542 2001-2010 –> 2011-2019 4.456931 11320.009
Indo-Pacific (28.05,28.1] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 1224 2.2484361 5471.0165 9.462538 2001-2010 –> 2011-2019 4.407442 11267.262
Indo-Pacific (28.05,28.1] tco2 ~ sal + silicate + phosphate + phosphate_star 1224 2.2500144 5470.7344 9.295047 2001-2010 –> 2011-2019 4.411551 11268.075
Indo-Pacific (28.05,28.1] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 1224 2.2515546 5474.4095 10.500183 2001-2010 –> 2011-2019 4.460284 11330.812
Indo-Pacific (28.05,28.1] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 1224 2.1996608 5417.3277 11.300012 2001-2010 –> 2011-2019 4.404417 11268.973
Indo-Pacific (28.1, Inf] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 11307 4.4336277 65779.0552 26.692619 1982-2000 –> 2001-2010 8.737398 189162.563
Indo-Pacific (28.1, Inf] tco2 ~ sal + silicate + phosphate + phosphate_star 11307 4.4488355 65854.4906 25.037276 1982-2000 –> 2001-2010 8.766154 189370.709
Indo-Pacific (28.1, Inf] tco2 ~ temp + aou + nitrate + silicate 11307 4.3980583 65594.8992 25.053413 1982-2000 –> 2001-2010 8.689127 188849.726
Indo-Pacific (28.1, Inf] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 11307 4.3745293 65475.5929 26.581131 1982-2000 –> 2001-2010 8.647787 188554.157
Indo-Pacific (28.1, Inf] tco2 ~ temp + aou + silicate + phosphate + phosphate_star 11307 4.4562512 65894.1541 26.139500 1982-2000 –> 2001-2010 8.781353 189489.570
Indo-Pacific (28.1, Inf] tco2 ~ sal + aou + silicate + phosphate + phosphate_star 10029 4.6819050 59438.7056 27.824489 2001-2010 –> 2011-2019 9.115533 125217.761
Indo-Pacific (28.1, Inf] tco2 ~ temp + aou + nitrate + silicate 10029 4.6436251 59272.0346 25.610462 2001-2010 –> 2011-2019 9.041683 124866.934
Indo-Pacific (28.1, Inf] tco2 ~ temp + aou + nitrate + silicate + phosphate_star 10029 4.6198155 59170.9251 27.758708 2001-2010 –> 2011-2019 8.994345 124646.518
Indo-Pacific (28.1, Inf] tco2 ~ temp + nitrate + silicate 10029 4.6563906 59325.0990 27.615312 2001-2010 –> 2011-2019 9.080866 125053.426
Indo-Pacific (28.1, Inf] tco2 ~ temp + nitrate + silicate + phosphate_star 10029 4.6546770 59319.7160 28.534212 2001-2010 –> 2011-2019 9.079099 125049.765

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] 1982-2000 –> 2001-2010 8.765596 2055.752
Atlantic (-Inf,26] 2001-2010 –> 2011-2019 6.679342 1158.892
Atlantic (26,26.5] 1982-2000 –> 2001-2010 11.185755 15407.505
Atlantic (26,26.5] 2001-2010 –> 2011-2019 9.802483 9241.122
Atlantic (26.5,26.75] 1982-2000 –> 2001-2010 8.907423 18125.856
Atlantic (26.5,26.75] 2001-2010 –> 2011-2019 8.151703 11077.748
Atlantic (26.75,27] 1982-2000 –> 2001-2010 6.465317 26949.574
Atlantic (26.75,27] 2001-2010 –> 2011-2019 6.040107 17557.339
Atlantic (27,27.25] 1982-2000 –> 2001-2010 5.256502 20841.627
Atlantic (27,27.25] 2001-2010 –> 2011-2019 5.207292 14287.341
Atlantic (27.25,27.5] 1982-2000 –> 2001-2010 5.405368 22362.183
Atlantic (27.25,27.5] 2001-2010 –> 2011-2019 6.030174 14873.647
Atlantic (27.5,27.75] 1982-2000 –> 2001-2010 5.057106 28749.583
Atlantic (27.5,27.75] 2001-2010 –> 2011-2019 5.280840 19573.092
Atlantic (27.75,27.85] 1982-2000 –> 2001-2010 2.935048 7850.963
Atlantic (27.75,27.85] 2001-2010 –> 2011-2019 2.919060 5338.014
Atlantic (27.85,27.95] 1982-2000 –> 2001-2010 4.252369 8796.381
Atlantic (27.85,27.95] 2001-2010 –> 2011-2019 4.641990 6702.143
Atlantic (27.95,28.05] 1982-2000 –> 2001-2010 7.915694 15101.423
Atlantic (27.95,28.05] 2001-2010 –> 2011-2019 7.716568 9854.362
Atlantic (28.05,28.1] 1982-2000 –> 2001-2010 2.243857 5444.007
Atlantic (28.05,28.1] 2001-2010 –> 2011-2019 2.278861 3669.299
Atlantic (28.1,28.15] 1982-2000 –> 2001-2010 1.987410 5948.143
Atlantic (28.1,28.15] 2001-2010 –> 2011-2019 2.041183 3944.468
Atlantic (28.15,28.2] 1982-2000 –> 2001-2010 2.196178 10651.210
Atlantic (28.15,28.2] 2001-2010 –> 2011-2019 2.219986 6802.568
Atlantic (28.2, Inf] 1982-2000 –> 2001-2010 3.324547 22861.772
Atlantic (28.2, Inf] 2001-2010 –> 2011-2019 3.459164 15759.872
Indo-Pacific (-Inf,26] 1982-2000 –> 2001-2010 19.060500 86060.851
Indo-Pacific (-Inf,26] 2001-2010 –> 2011-2019 18.005208 55643.701
Indo-Pacific (26,26.5] 1982-2000 –> 2001-2010 13.265779 82002.967
Indo-Pacific (26,26.5] 2001-2010 –> 2011-2019 12.972275 52713.167
Indo-Pacific (26.5,26.75] 1982-2000 –> 2001-2010 10.477892 62564.864
Indo-Pacific (26.5,26.75] 2001-2010 –> 2011-2019 10.491247 40783.911
Indo-Pacific (26.75,27] 1982-2000 –> 2001-2010 10.658938 74191.084
Indo-Pacific (26.75,27] 2001-2010 –> 2011-2019 11.111711 49038.860
Indo-Pacific (27,27.25] 1982-2000 –> 2001-2010 9.735546 86168.445
Indo-Pacific (27,27.25] 2001-2010 –> 2011-2019 10.296495 57560.407
Indo-Pacific (27.25,27.5] 1982-2000 –> 2001-2010 7.717938 71086.363
Indo-Pacific (27.25,27.5] 2001-2010 –> 2011-2019 8.133761 48092.134
Indo-Pacific (27.5,27.75] 1982-2000 –> 2001-2010 6.633534 67874.292
Indo-Pacific (27.5,27.75] 2001-2010 –> 2011-2019 7.430974 46265.548
Indo-Pacific (27.75,27.85] 1982-2000 –> 2001-2010 5.059862 23643.605
Indo-Pacific (27.75,27.85] 2001-2010 –> 2011-2019 5.690439 16842.743
Indo-Pacific (27.85,27.95] 1982-2000 –> 2001-2010 4.257938 27721.682
Indo-Pacific (27.85,27.95] 2001-2010 –> 2011-2019 4.790012 19337.216
Indo-Pacific (27.95,28.05] 1982-2000 –> 2001-2010 4.702618 25390.200
Indo-Pacific (27.95,28.05] 2001-2010 –> 2011-2019 5.079392 17255.721
Indo-Pacific (28.05,28.1] 1982-2000 –> 2001-2010 4.274584 17454.071
Indo-Pacific (28.05,28.1] 2001-2010 –> 2011-2019 4.428125 11291.026
Indo-Pacific (28.1, Inf] 1982-2000 –> 2001-2010 8.724364 189085.345
Indo-Pacific (28.1, Inf] 2001-2010 –> 2011-2019 9.062305 124966.881

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
59288fe Donghe-Zhu 2021-03-04
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
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
59288fe Donghe-Zhu 2021-03-04
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
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
59288fe Donghe-Zhu 2021-03-04
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
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
59288fe Donghe-Zhu 2021-03-04
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
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 - 1982-2000 --> 2001-2010
(-Inf,26] 5 1 2 5 5 2 0
(26,26.5] 5 2 2 4 5 4 0
(26.5,26.75] 5 1 2 4 4 5 1
(26.75,27] 5 1 3 4 4 5 1
(27,27.25] 5 2 2 5 2 5 3
(27.25,27.5] 5 5 0 5 2 3 2
(27.5,27.75] 5 3 1 5 3 5 1
(27.75,27.85] 5 2 3 5 2 5 2
(27.85,27.95] 5 2 2 5 2 5 3
(27.95,28.05] 3 5 0 5 1 3 4
(28.05,28.1] 5 2 2 3 5 5 0
(28.1,28.15] 5 2 2 4 4 5 1
(28.15,28.2] 5 4 1 5 3 3 2
(28.2, Inf] 4 2 3 5 3 3 2
total 67.00 34.00 25.00 64.00 45.00 58.00 22.00
Atlantic - 2001-2010 --> 2011-2019
(-Inf,26] 5 1 2 5 5 3 0
(26,26.5] 5 2 2 4 5 4 0
(26.5,26.75] 5 1 3 4 4 5 0
(26.75,27] 5 1 3 4 4 5 1
(27,27.25] 5 2 2 5 2 5 3
(27.25,27.5] 5 4 1 5 2 3 3
(27.5,27.75] 5 4 1 3 5 3 0
(27.75,27.85] 5 2 2 5 5 3 0
(27.85,27.95] 5 2 3 5 3 3 2
(27.95,28.05] 3 5 0 4 0 3 5
(28.05,28.1] 5 1 3 4 2 5 2
(28.1,28.15] 5 3 1 5 3 4 2
(28.15,28.2] 5 4 1 5 3 3 2
(28.2, Inf] 4 2 3 5 2 4 3
total 67.00 34.00 27.00 63.00 45.00 53.00 23.00
Indo-Pacific - 1982-2000 --> 2001-2010
(-Inf,26] 5 2 2 5 5 3 0
(26,26.5] 5 2 2 5 5 3 0
(26.5,26.75] 5 2 2 5 5 3 0
(26.75,27] 5 2 2 5 5 3 0
(27,27.25] 5 2 2 4 4 5 1
(27.25,27.5] 4 2 3 5 3 5 2
(27.5,27.75] 4 1 3 5 2 5 3
(27.75,27.85] 5 2 2 5 3 5 2
(27.85,27.95] 4 1 3 4 5 5 0
(27.95,28.05] 4 2 3 4 4 5 1
(28.05,28.1] 4 1 4 4 3 5 2
(28.1, Inf] 4 2 3 4 2 5 3
total 54.00 21.00 31.00 55.00 46.00 52.00 14.00
Indo-Pacific - 2001-2010 --> 2011-2019
(-Inf,26] 5 2 2 5 5 3 0
(26,26.5] 5 2 2 5 5 3 0
(26.5,26.75] 5 2 2 5 5 3 0
(26.75,27] 5 2 2 5 5 3 0
(27,27.25] 5 2 2 4 4 5 1
(27.25,27.5] 4 2 2 5 1 5 4
(27.5,27.75] 4 1 3 4 0 5 5
(27.75,27.85] 5 2 2 5 2 5 3
(27.85,27.95] 4 1 3 4 5 5 0
(27.95,28.05] 4 1 4 4 3 5 2
(28.05,28.1] 4 1 4 4 3 5 2
(28.1, Inf] 3 4 1 3 1 5 4
total 53.00 22.00 29.00 53.00 39.00 52.00 21.00

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
59288fe Donghe-Zhu 2021-03-04
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
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
59288fe Donghe-Zhu 2021-03-04
731abc8 Donghe-Zhu 2021-03-04
e2a5a33 Donghe-Zhu 2021-03-04
c7892c1 Donghe-Zhu 2021-03-04
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