Last updated: 2021-03-03

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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 + phosphate_star 158 1.6001372 608.9328 6.639741 1982-1999 –> 2000-2012 3.2898388 1429.4249
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 158 1.0492038 475.5626 4.357844 1982-1999 –> 2000-2012 2.3855522 1198.4564
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 158 1.0480832 477.2249 4.299021 1982-1999 –> 2000-2012 2.3837757 1201.9145
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 158 1.4654213 581.1417 7.417048 1982-1999 –> 2000-2012 3.1276914 1394.8248
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 158 1.4545749 580.7941 7.074044 1982-1999 –> 2000-2012 3.1160634 1396.2815
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 72 1.2725075 251.0296 3.658367 2000-2012 –> 2013-2019 2.3217113 726.5922
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 72 1.1936365 243.8158 3.237974 2000-2012 –> 2013-2019 2.2417197 721.0407
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate_star 72 1.6918467 292.0453 4.133504 2000-2012 –> 2013-2019 3.2851805 899.6317
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 72 1.5761474 281.8448 5.713265 2000-2012 –> 2013-2019 3.0415687 862.9865
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 72 1.5044066 277.1365 5.003414 2000-2012 –> 2013-2019 2.9589816 857.9306
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1046 3.5518213 5633.9468 13.477555 1982-1999 –> 2000-2012 6.9985663 13749.8718
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 1046 4.1960266 5980.6362 10.665564 1982-1999 –> 2000-2012 8.3544396 14667.0559
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 1046 4.0405761 5901.6616 14.579174 1982-1999 –> 2000-2012 8.1249524 14533.2897
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1046 4.0338370 5900.1695 15.685804 1982-1999 –> 2000-2012 8.1154929 14531.7655
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1046 4.2948916 6031.3553 13.012884 1982-1999 –> 2000-2012 8.5299909 14775.5085
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 567 3.6070302 3077.8676 10.902628 2000-2012 –> 2013-2019 7.1588515 8711.8144
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 567 4.1023698 3221.7908 12.065595 2000-2012 –> 2013-2019 8.2983964 9202.4270
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 567 3.8959809 3163.2545 13.662757 2000-2012 –> 2013-2019 7.9365570 9064.9161
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 567 3.8631919 3155.6702 14.511046 2000-2012 –> 2013-2019 7.8970289 9055.8397
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 567 4.2189568 3255.5690 10.763473 2000-2012 –> 2013-2019 8.5138484 9286.9243
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1397 3.3429532 7348.4661 10.697715 1982-1999 –> 2000-2012 6.4415667 17034.7612
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 1397 3.3316510 7339.0038 10.073920 1982-1999 –> 2000-2012 6.4785991 17084.0238
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1397 3.2700730 7288.8799 10.507891 1982-1999 –> 2000-2012 6.3292231 16928.5449
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1397 3.3250708 7335.4800 10.297171 1982-1999 –> 2000-2012 6.4698137 17079.8406
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1397 3.2249399 7250.0489 10.037456 1982-1999 –> 2000-2012 6.2079736 16794.1190
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 656 3.4323365 3491.6598 11.340269 2000-2012 –> 2013-2019 6.7752897 10840.1259
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 656 3.3850399 3473.4551 10.375376 2000-2012 –> 2013-2019 6.7166909 10812.4589
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 656 3.3455096 3460.0435 10.735554 2000-2012 –> 2013-2019 6.6155826 10748.9234
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 656 3.4093443 3484.8416 9.603997 2000-2012 –> 2013-2019 6.7344151 10820.3216
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 656 3.3238240 3451.5114 11.113656 2000-2012 –> 2013-2019 6.5487639 10701.5603
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2398 2.0935628 10360.8368 14.739529 1982-1999 –> 2000-2012 3.7661002 22513.8376
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2398 2.0001820 10143.9994 14.081577 1982-1999 –> 2000-2012 3.6531709 22225.1681
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2398 2.1989701 10598.4250 16.309198 1982-1999 –> 2000-2012 3.9946362 23199.5206
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2398 2.2004206 10599.5875 15.280820 1982-1999 –> 2000-2012 3.9880121 23170.3800
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2398 2.0860637 10345.6268 19.975942 1982-1999 –> 2000-2012 3.5995129 21872.9381
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1263 2.6364762 6045.0524 27.471250 2000-2012 –> 2013-2019 4.7300390 16405.8891
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 1263 2.5846959 5994.9482 24.744636 2000-2012 –> 2013-2019 4.7623441 16544.6427
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1263 2.5330762 5945.9902 25.891764 2000-2012 –> 2013-2019 4.5332582 16089.9896
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1263 2.6623762 6071.7460 22.596317 2000-2012 –> 2013-2019 4.8613463 16670.1710
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1263 2.2552518 5652.5376 22.583567 2000-2012 –> 2013-2019 4.3413155 15998.1644
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2031 2.0909522 8773.9389 9.715574 1982-1999 –> 2000-2012 4.3252336 20395.7044
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 2031 1.9148200 8414.4995 9.235730 1982-1999 –> 2000-2012 3.6311952 18657.1971
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2031 1.8904789 8364.5325 9.689213 1982-1999 –> 2000-2012 3.4604645 18143.6984
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2031 2.0594140 8712.2044 13.384239 1982-1999 –> 2000-2012 3.7359927 18834.3973
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2031 2.3112875 9180.8912 13.899054 1982-1999 –> 2000-2012 4.3877097 20420.0232
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1142 2.2408412 5097.7041 11.555324 2000-2012 –> 2013-2019 4.3317934 13871.6430
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1142 2.3003827 5155.6000 13.777336 2000-2012 –> 2013-2019 4.2152027 13570.0995
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1142 2.2946948 5151.9457 14.080782 2000-2012 –> 2013-2019 4.1851737 13516.4782
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 1142 2.3424794 5197.0192 15.033313 2000-2012 –> 2013-2019 4.4776528 14053.9689
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1142 2.5328202 5377.4530 21.355986 2000-2012 –> 2013-2019 4.5922342 14089.6574
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 2025 2.5285742 9515.7061 13.358360 1982-1999 –> 2000-2012 5.1450783 23231.4624
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2025 2.4514644 9392.2776 12.813379 1982-1999 –> 2000-2012 4.9864330 22927.8111
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2025 2.6905754 9769.2091 21.422922 1982-1999 –> 2000-2012 4.8576234 22402.1133
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 2025 2.4063497 9315.0504 11.614926 1982-1999 –> 2000-2012 4.1264292 20616.3452
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2025 2.2547324 9053.4778 15.509020 1982-1999 –> 2000-2012 3.9706310 20342.7650
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate_star 1109 3.0051254 5599.7139 21.412798 2000-2012 –> 2013-2019 5.7555576 15456.0350
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 1109 3.0025580 5597.8181 16.245244 2000-2012 –> 2013-2019 5.5311321 15113.5242
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1109 2.7952620 5441.1451 16.992150 2000-2012 –> 2013-2019 5.2467264 14833.4228
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 1109 3.1081847 5674.5038 12.222568 2000-2012 –> 2013-2019 5.5145344 14989.5543
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1109 2.7923328 5438.8197 16.610907 2000-2012 –> 2013-2019 5.0470652 14492.2975
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 2804 2.7836924 13708.7557 13.816311 1982-1999 –> 2000-2012 5.2587422 31083.3422
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 2804 2.7656318 13674.2524 14.269310 1982-1999 –> 2000-2012 5.0314996 30391.3946
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2804 2.4538915 13003.5694 13.901382 1982-1999 –> 2000-2012 4.8210764 30047.3887
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2804 2.3944064 12867.9502 14.685866 1982-1999 –> 2000-2012 4.4949743 29021.3907
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2804 3.1165165 14346.1100 16.244315 1982-1999 –> 2000-2012 5.5026775 31451.5564
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate 1515 3.2789491 7909.5783 16.534959 2000-2012 –> 2013-2019 6.1058258 21706.6649
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1515 3.2267256 7862.9314 14.600864 2000-2012 –> 2013-2019 6.0506408 21656.1398
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 1515 3.4234258 8040.2283 14.171915 2000-2012 –> 2013-2019 6.1890576 21714.4806
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 1515 2.8745087 7510.7055 15.545879 2000-2012 –> 2013-2019 5.3284002 20514.2749
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1515 2.8711798 7509.1946 15.461950 2000-2012 –> 2013-2019 5.2655862 20377.1448
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2019 3.3909827 10674.5554 68.328717 1982-1999 –> 2000-2012 6.1980295 23708.6473
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 2019 3.2048031 10444.5331 70.971683 1982-1999 –> 2000-2012 5.5427147 22505.1934
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2019 3.1293776 10350.3620 75.777120 1982-1999 –> 2000-2012 5.4394680 22349.4303
Atlantic (27.75,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 2019 3.3411879 10612.8198 25.685074 1982-1999 –> 2000-2012 6.1847456 23713.5586
Atlantic (27.75,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2019 3.3050381 10570.8928 25.903285 1982-1999 –> 2000-2012 6.1484255 23673.3136
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1082 3.3022278 5669.6916 29.934451 2000-2012 –> 2013-2019 6.6932106 16344.2471
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + phosphate 1082 3.3138753 5673.3109 30.016585 2000-2012 –> 2013-2019 6.8721651 16538.3376
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 1082 3.1773806 5584.2907 28.891889 2000-2012 –> 2013-2019 6.3821837 16028.8238
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + silicate + phosphate 1082 3.1157062 5541.8734 29.351308 2000-2012 –> 2013-2019 6.6673566 16401.3585
Atlantic (27.75,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1082 2.8568070 5356.1437 27.643773 2000-2012 –> 2013-2019 5.9861846 15706.5057
Atlantic (27.95,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 2008 3.7134933 10979.3408 26.949010 1982-1999 –> 2000-2012 7.5860998 26253.1971
Atlantic (27.95,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2008 3.6635469 10926.9592 26.570037 1982-1999 –> 2000-2012 7.5149161 26172.5485
Atlantic (27.95,28.1] cstar_tref ~ temp + aou + nitrate + phosphate_star 2008 3.5043423 10746.5326 24.807965 1982-1999 –> 2000-2012 6.9860313 25434.7067
Atlantic (27.95,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2008 3.3865256 10611.1920 24.787113 1982-1999 –> 2000-2012 6.5190666 24719.7417
Atlantic (27.95,28.1] cstar_tref ~ temp + aou + silicate + phosphate 2008 3.8340769 11107.6748 26.418466 1982-1999 –> 2000-2012 7.8262845 26548.9439
Atlantic (27.95,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 1100 3.5377603 5913.3512 25.267363 2000-2012 –> 2013-2019 7.2512536 16892.6920
Atlantic (27.95,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1100 3.4740033 5875.3415 25.419145 2000-2012 –> 2013-2019 7.1375502 16802.3007
Atlantic (27.95,28.1] cstar_tref ~ temp + aou + nitrate + phosphate_star 1100 3.3726433 5808.1978 24.185522 2000-2012 –> 2013-2019 6.8769856 16554.7304
Atlantic (27.95,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1100 3.2335924 5717.5709 26.004951 2000-2012 –> 2013-2019 6.6201180 16328.7630
Atlantic (27.95,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1100 3.7182889 6024.8447 28.147294 2000-2012 –> 2013-2019 7.5486989 17130.6767
Atlantic (28.1,28.15] cstar_tref ~ aou + silicate + phosphate + phosphate_star 936 0.8652007 2397.1990 9.973159 1982-1999 –> 2000-2012 1.5501093 5104.0130
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 936 0.8394339 2342.6013 6.649159 1982-1999 –> 2000-2012 1.5477300 5138.3794
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 936 0.7732900 2186.9596 6.039973 1982-1999 –> 2000-2012 1.4451653 4844.0128
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 936 0.7598609 2156.1646 5.927820 1982-1999 –> 2000-2012 1.3893138 4646.2932
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 936 0.7856962 2218.7544 10.025704 1982-1999 –> 2000-2012 1.3744859 4535.9182
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 497 0.9633503 1387.3108 6.933462 2000-2012 –> 2013-2019 1.8027842 3729.9121
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 497 0.8714406 1285.6430 6.181914 2000-2012 –> 2013-2019 1.6447306 3472.6026
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 497 0.8712585 1287.4353 6.182326 2000-2012 –> 2013-2019 1.6311195 3443.5998
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 497 0.9653756 1387.3983 11.632299 2000-2012 –> 2013-2019 1.8224628 3766.9596
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 497 0.8791505 1296.3985 11.933687 2000-2012 –> 2013-2019 1.6648467 3515.1529
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1540 0.5939756 2777.9061 2.353787 1982-1999 –> 2000-2012 1.1267120 6300.3123
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1540 0.5471615 2527.0561 2.040783 1982-1999 –> 2000-2012 1.0648603 5924.1022
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 1540 0.6019966 2819.2202 2.184553 1982-1999 –> 2000-2012 1.1657858 6593.6216
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 1540 0.5718023 2660.7281 2.192349 1982-1999 –> 2000-2012 1.1224532 6330.2485
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1540 0.5576121 2585.3284 2.314250 1982-1999 –> 2000-2012 1.1076613 6251.9858
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 819 0.7431790 1850.0329 4.262643 2000-2012 –> 2013-2019 1.3371546 4627.9389
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 819 0.7372762 1838.9708 4.731734 2000-2012 –> 2013-2019 1.2844377 4366.0269
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 819 0.8686623 2105.5896 7.748139 2000-2012 –> 2013-2019 1.4706590 4924.8098
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 819 0.8619250 2092.8357 8.363302 2000-2012 –> 2013-2019 1.4337273 4753.5638
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 819 0.8613203 2093.6861 8.208278 2000-2012 –> 2013-2019 1.4189324 4679.0145
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 2693 0.3593168 2139.5581 1.966552 1982-1999 –> 2000-2012 0.6655852 3898.5165
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 2693 0.3540505 2062.0339 1.937681 1982-1999 –> 2000-2012 0.6560011 3717.6111
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 2693 0.3588037 2133.8610 1.963165 1982-1999 –> 2000-2012 0.6635911 3858.8422
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2693 0.3463114 1944.9979 1.900529 1982-1999 –> 2000-2012 0.6453988 3531.8596
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2693 0.5306498 4243.5482 3.091584 1982-1999 –> 2000-2012 0.9896559 9009.4595
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 1557 0.4186021 1716.7958 2.479100 2000-2012 –> 2013-2019 0.7779188 3856.3538
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 1557 0.3991609 1570.7062 2.411345 2000-2012 –> 2013-2019 0.7532114 3632.7401
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 1557 0.4110188 1661.8663 2.465092 2000-2012 –> 2013-2019 0.7698225 3795.7273
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1557 0.3901368 1501.4981 2.457959 2000-2012 –> 2013-2019 0.7364483 3446.4960
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1557 0.7057457 3347.3447 8.527267 2000-2012 –> 2013-2019 1.2363955 7590.8929
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 5288 6.2360939 34376.5179 29.968567 1982-1999 –> 2000-2012 12.7656352 81794.3473
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5288 6.1928478 34304.9200 29.527354 1982-1999 –> 2000-2012 12.6716991 81612.6324
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5288 7.1987438 35896.7294 31.371808 1982-1999 –> 2000-2012 14.7271008 85364.2640
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5288 7.2933052 36034.7494 29.166512 1982-1999 –> 2000-2012 14.8774849 85608.5624
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 5288 7.3907730 36173.1511 28.492599 1982-1999 –> 2000-2012 15.1050761 85989.6943
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 2816 5.9520247 18049.4373 24.894024 2000-2012 –> 2013-2019 12.1881186 52425.9552
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2816 5.8778725 17980.8313 24.128023 2000-2012 –> 2013-2019 12.0707203 52285.7513
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2816 6.9521542 18926.2002 25.907885 2000-2012 –> 2013-2019 14.1508980 54822.9297
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2816 7.0001768 18964.9700 25.465195 2000-2012 –> 2013-2019 14.2934820 54999.7194
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2816 7.1344030 19069.9395 24.441528 2000-2012 –> 2013-2019 14.5251760 55243.0906
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5525 4.8905258 33230.9339 41.688307 1982-1999 –> 2000-2012 9.5377100 78823.9388
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5525 4.5360650 32401.5327 43.772780 1982-1999 –> 2000-2012 8.7824377 76605.3494
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5525 4.7555301 32923.6260 49.041150 1982-1999 –> 2000-2012 9.1671720 77716.3587
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 5525 4.8893893 33228.3657 40.409229 1982-1999 –> 2000-2012 9.5091497 78730.0815
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5525 4.8803203 33209.8508 41.154556 1982-1999 –> 2000-2012 9.4999894 78713.2617
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2918 4.8175903 17468.7156 40.382988 2000-2012 –> 2013-2019 9.7081161 50699.6495
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2918 4.4724496 17036.8813 46.310491 2000-2012 –> 2013-2019 9.0085146 49438.4140
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2918 4.5715543 17164.7889 45.715284 2000-2012 –> 2013-2019 9.3270844 50088.4149
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 2918 4.8142859 17464.7112 37.043514 2000-2012 –> 2013-2019 9.7036752 50693.0769
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2918 4.8065118 17457.2797 38.739984 2000-2012 –> 2013-2019 9.6868321 50667.1305
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4544 4.0473152 25612.8259 22.127132 1982-1999 –> 2000-2012 7.9963826 60742.2745
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4544 3.9265162 25339.4488 20.226531 1982-1999 –> 2000-2012 7.6839109 59845.1956
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4544 4.0218289 25557.4171 33.030413 1982-1999 –> 2000-2012 8.0127086 60821.3190
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4544 3.9477481 25388.4579 23.151958 1982-1999 –> 2000-2012 7.8249401 60288.9073
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4544 4.0218809 25555.5345 32.963712 1982-1999 –> 2000-2012 8.0834114 61038.1226
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2447 4.4033896 14211.0265 24.538450 2000-2012 –> 2013-2019 8.4507048 39823.8524
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2447 4.2938981 14089.7973 24.434470 2000-2012 –> 2013-2019 8.2204143 39429.2462
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2447 4.3225383 14122.3318 31.664753 2000-2012 –> 2013-2019 8.3443672 39679.7489
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2447 4.2923135 14087.9909 22.815590 2000-2012 –> 2013-2019 8.2400615 39476.4489
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2447 4.3388127 14138.7232 34.446250 2000-2012 –> 2013-2019 8.3606936 39694.2577
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5354 4.5232238 31366.7748 18.928405 1982-1999 –> 2000-2012 8.5202080 73619.8323
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 5354 4.3077986 30844.2463 21.980567 1982-1999 –> 2000-2012 7.9956057 71884.6902
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5354 4.2906105 30803.4359 21.052395 1982-1999 –> 2000-2012 7.9645082 71788.9629
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 5354 4.2057274 30587.4712 23.104196 1982-1999 –> 2000-2012 7.8859232 71596.7963
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5354 4.1702723 30498.8181 21.453131 1982-1999 –> 2000-2012 7.8227361 71396.2141
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2868 4.9018613 17269.0630 18.494849 2000-2012 –> 2013-2019 9.4250851 48635.8378
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 2868 4.6612052 16980.3073 20.095371 2000-2012 –> 2013-2019 8.9690038 47824.5536
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2868 4.6499950 16968.4956 19.282213 2000-2012 –> 2013-2019 8.9406055 47771.9315
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 2868 4.5774010 16876.2410 16.522089 2000-2012 –> 2013-2019 8.7831284 47463.7121
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2868 4.5537010 16848.4650 17.066955 2000-2012 –> 2013-2019 8.7239733 47347.2831
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6466 4.3929768 37503.1646 41.945012 1982-1999 –> 2000-2012 7.9587117 85065.6810
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6466 4.1535561 36778.4265 49.359080 1982-1999 –> 2000-2012 7.5202091 83325.5519
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 6466 4.3599345 37403.5276 46.003290 1982-1999 –> 2000-2012 7.9680032 85172.6402
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6466 3.9500266 36128.6900 31.512269 1982-1999 –> 2000-2012 7.2528573 82337.5496
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 6466 4.6663213 38281.7913 72.764927 1982-1999 –> 2000-2012 8.1605463 85484.2572
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3470 5.1328308 21210.8952 31.173698 2000-2012 –> 2013-2019 9.5717663 58846.6499
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3470 5.0789520 21139.6617 33.597697 2000-2012 –> 2013-2019 9.4719288 58642.8263
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3470 4.9716940 20991.5322 35.708885 2000-2012 –> 2013-2019 9.1252501 57769.9588
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 3470 5.1322261 21210.0776 39.784583 2000-2012 –> 2013-2019 9.4921606 58613.6052
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3470 4.4723380 20256.9380 25.616236 2000-2012 –> 2013-2019 8.4223646 56385.6280
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 5847 3.4261572 31007.5182 32.305003 1982-1999 –> 2000-2012 6.3475428 70339.4077
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5847 3.6920890 31881.6814 32.521736 1982-1999 –> 2000-2012 6.7625645 71999.2104
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 5847 3.7105782 31938.0962 31.726047 1982-1999 –> 2000-2012 6.7817085 72056.9912
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5847 3.6356816 31701.6427 32.976030 1982-1999 –> 2000-2012 6.7191704 71885.9262
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5847 3.3461863 30731.3292 33.390589 1982-1999 –> 2000-2012 6.2704796 70078.9213
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3127 3.9776245 17522.8442 31.036835 2000-2012 –> 2013-2019 7.4037817 48530.3624
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3127 4.3037583 18015.6837 32.127293 2000-2012 –> 2013-2019 7.9958473 49897.3651
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 3127 4.3425043 18069.7354 30.551097 2000-2012 –> 2013-2019 8.0530824 50007.8316
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3127 4.2454019 17930.3030 31.035584 2000-2012 –> 2013-2019 7.8810835 49631.9457
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3127 3.8437243 17308.6883 33.232474 2000-2012 –> 2013-2019 7.1899105 48040.0175
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 5836 3.2683124 30398.6938 24.119856 1982-1999 –> 2000-2012 5.5822735 67013.2424
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5836 3.2280103 30253.8699 9.417658 1982-1999 –> 2000-2012 5.5715676 67074.4342
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 5836 3.3807244 30791.3972 22.456992 1982-1999 –> 2000-2012 5.7423173 67734.2326
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 5836 3.3957705 30843.2286 29.089521 1982-1999 –> 2000-2012 5.7808728 67946.6354
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 5836 3.4363673 30981.9413 25.357370 1982-1999 –> 2000-2012 5.8135896 68031.7039
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3104 3.9417327 17337.7899 25.386634 2000-2012 –> 2013-2019 7.2100451 47736.4837
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3104 3.7804110 17078.3721 11.020697 2000-2012 –> 2013-2019 7.0084214 47332.2420
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3104 4.0989818 17578.6356 23.944569 2000-2012 –> 2013-2019 7.4797062 48370.0328
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3104 4.1948886 17722.2154 32.318244 2000-2012 –> 2013-2019 7.5906591 48565.4440
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3104 4.0127640 17448.6640 19.751773 2000-2012 –> 2013-2019 7.3819468 48202.1453
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2317 2.7304690 11242.0909 21.046900 1982-1999 –> 2000-2012 4.6623579 24262.9999
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2317 2.7290365 11241.6591 21.325228 1982-1999 –> 2000-2012 4.6507603 24231.5321
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2317 2.7271269 11238.4154 21.453348 1982-1999 –> 2000-2012 4.6635446 24275.9866
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate 2317 2.7417874 11261.2601 20.642191 1982-1999 –> 2000-2012 4.6870749 24325.4494
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2317 2.6406178 11089.0349 20.968772 1982-1999 –> 2000-2012 4.5482001 24032.6569
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1264 3.1358059 6490.2930 31.989646 2000-2012 –> 2013-2019 5.8629052 17728.6613
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1264 3.1693826 6517.2176 30.950746 2000-2012 –> 2013-2019 5.8984191 17758.8767
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1264 3.1488202 6498.7630 29.448400 2000-2012 –> 2013-2019 5.8762396 17735.6753
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 1264 3.1128492 6469.7178 31.766441 2000-2012 –> 2013-2019 5.8536894 17729.3767
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1264 3.0665742 6433.8549 28.861392 2000-2012 –> 2013-2019 5.7071919 17522.8898
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 2907 2.7487099 14140.4282 28.492785 1982-1999 –> 2000-2012 4.8701028 31563.9400
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2907 2.7457460 14136.1557 28.208152 1982-1999 –> 2000-2012 4.8664196 31558.9474
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2907 2.7856872 14220.1201 34.100919 1982-1999 –> 2000-2012 4.9269749 31720.4944
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 2907 2.7674113 14177.8510 31.750508 1982-1999 –> 2000-2012 4.8898936 31603.4801
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2907 2.7621671 14168.8231 31.138313 1982-1999 –> 2000-2012 4.8840444 31594.1657
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate 1542 3.3281826 8094.2894 31.958774 2000-2012 –> 2013-2019 6.0790784 22237.3394
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 1542 3.3165597 8085.5004 32.079445 2000-2012 –> 2013-2019 6.0652696 22225.9286
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 1542 3.3046795 8074.4335 31.424170 2000-2012 –> 2013-2019 6.0531124 22214.2756
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1542 3.2946985 8067.1049 31.554855 2000-2012 –> 2013-2019 6.0404446 22203.2606
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1542 3.2965108 8066.8008 32.540164 2000-2012 –> 2013-2019 6.0586779 22235.6239
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2467 2.2624239 11041.3418 8.237248 1982-1999 –> 2000-2012 4.1845877 25738.2975
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2467 2.1936153 10890.9515 8.036190 1982-1999 –> 2000-2012 4.1649943 25769.0539
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2467 2.2115502 10931.1275 8.468880 1982-1999 –> 2000-2012 4.1022689 25513.2034
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2467 2.2668883 11053.0683 8.062293 1982-1999 –> 2000-2012 4.2018862 25799.1794
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2467 2.1886299 10879.7253 7.878228 1982-1999 –> 2000-2012 4.0642895 25405.1370
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate_star 1354 2.4060015 6232.0181 8.104133 2000-2012 –> 2013-2019 4.6173063 17160.5981
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1354 2.4007452 6228.0956 8.259744 2000-2012 –> 2013-2019 4.5943605 17119.0470
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1354 2.4779038 6313.7598 8.329809 2000-2012 –> 2013-2019 4.6894540 17244.8873
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 1354 2.4648617 6297.4690 8.721893 2000-2012 –> 2013-2019 4.7165003 17315.2334
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1354 2.4266912 6257.2052 8.523746 2000-2012 –> 2013-2019 4.6153211 17136.9304
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1718 1.9503440 7182.7407 8.816710 1982-1999 –> 2000-2012 3.5709134 16908.7065
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1718 1.8450332 6994.0133 9.467590 1982-1999 –> 2000-2012 3.4414783 16645.3685
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1718 1.9539957 7189.1680 8.935869 1982-1999 –> 2000-2012 3.5950802 16979.3910
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1718 1.8612616 7024.1034 10.244079 1982-1999 –> 2000-2012 3.4707315 16716.9636
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1718 1.8032691 6915.3424 9.697645 1982-1999 –> 2000-2012 3.4298781 16662.3098
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 966 2.1066397 4192.9110 9.987464 2000-2012 –> 2013-2019 3.9914816 11258.2717
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 966 2.0390556 4131.9137 9.747515 2000-2012 –> 2013-2019 3.8840888 11125.9270
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 966 2.0868098 4176.6389 10.548800 2000-2012 –> 2013-2019 3.9480714 11200.7423
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate 966 2.1188554 4204.0818 10.037184 2000-2012 –> 2013-2019 4.0138656 11287.9289
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 966 2.0001288 4094.6740 9.111786 2000-2012 –> 2013-2019 3.8033978 11010.0164
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 14627 1.4320006 52025.9353 13.806990 1982-1999 –> 2000-2012 2.7088012 119684.1812
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 14627 1.3378772 50039.0036 16.225048 1982-1999 –> 2000-2012 2.5090135 114186.0580
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 14627 1.3692488 50717.0570 13.004762 1982-1999 –> 2000-2012 2.4951048 113260.4541
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 14627 1.3940533 51242.2624 17.034744 1982-1999 –> 2000-2012 2.6340769 117713.8450
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 14627 1.5669226 54659.9964 17.476131 1982-1999 –> 2000-2012 2.8961915 123956.0907
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 7804 1.6305548 29791.8606 9.567306 2000-2012 –> 2013-2019 3.1514890 83582.4147
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 7804 1.5693631 29192.8476 10.689506 2000-2012 –> 2013-2019 3.0013637 81218.7829
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7804 1.4923380 28409.3615 12.644005 2000-2012 –> 2013-2019 2.8302151 78448.3652
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7804 1.5858456 29357.9189 10.996188 2000-2012 –> 2013-2019 2.9550945 80074.9759
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7804 1.5521124 29022.3323 13.774789 2000-2012 –> 2013-2019 2.9461657 80264.5947

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] 1982-1999 –> 2000-2012 2.8605843 1324.1804
Atlantic (-Inf,26] 2000-2012 –> 2013-2019 2.7698324 813.6363
Atlantic (26,26.5] 1982-1999 –> 2000-2012 8.0246884 14451.4983
Atlantic (26,26.5] 2000-2012 –> 2013-2019 7.9609365 9064.3843
Atlantic (26.5,26.75] 1982-1999 –> 2000-2012 6.3854352 16984.2579
Atlantic (26.5,26.75] 2000-2012 –> 2013-2019 6.6781485 10784.6780
Atlantic (26.75,27] 1982-1999 –> 2000-2012 3.8002865 22596.3689
Atlantic (26.75,27] 2000-2012 –> 2013-2019 4.6456606 16341.7714
Atlantic (27,27.25] 1982-1999 –> 2000-2012 3.9081191 19290.2041
Atlantic (27,27.25] 2000-2012 –> 2013-2019 4.3604114 13820.3694
Atlantic (27.25,27.5] 1982-1999 –> 2000-2012 4.6172390 21904.0994
Atlantic (27.25,27.5] 2000-2012 –> 2013-2019 5.4190031 14976.9668
Atlantic (27.5,27.75] 1982-1999 –> 2000-2012 5.0217940 30399.0145
Atlantic (27.5,27.75] 2000-2012 –> 2013-2019 5.7879021 21193.7410
Atlantic (27.75,27.95] 1982-1999 –> 2000-2012 5.9026767 23190.0286
Atlantic (27.75,27.95] 2000-2012 –> 2013-2019 6.5202201 16203.8545
Atlantic (27.95,28.1] 1982-1999 –> 2000-2012 7.2864796 25825.8276
Atlantic (27.95,28.1] 2000-2012 –> 2013-2019 7.0869213 16741.8326
Atlantic (28.1,28.15] 1982-1999 –> 2000-2012 1.4613609 4853.7233
Atlantic (28.1,28.15] 2000-2012 –> 2013-2019 1.7131888 3585.6454
Atlantic (28.15,28.2] 1982-1999 –> 2000-2012 1.1174945 6280.0541
Atlantic (28.15,28.2] 2000-2012 –> 2013-2019 1.3889822 4670.2708
Atlantic (28.2, Inf] 1982-1999 –> 2000-2012 0.7240464 4803.2578
Atlantic (28.2, Inf] 2000-2012 –> 2013-2019 0.8547593 4464.4420
Indo-Pacific (-Inf,26] 1982-1999 –> 2000-2012 14.0293992 84073.9001
Indo-Pacific (-Inf,26] 2000-2012 –> 2013-2019 13.4456790 53955.4892
Indo-Pacific (26,26.5] 1982-1999 –> 2000-2012 9.2992918 78117.7980
Indo-Pacific (26,26.5] 2000-2012 –> 2013-2019 9.4868445 50317.3372
Indo-Pacific (26.5,26.75] 1982-1999 –> 2000-2012 7.9202707 60547.1638
Indo-Pacific (26.5,26.75] 2000-2012 –> 2013-2019 8.3232483 39620.7108
Indo-Pacific (26.75,27] 1982-1999 –> 2000-2012 8.0377962 72057.2992
Indo-Pacific (26.75,27] 2000-2012 –> 2013-2019 8.9683592 47808.6636
Indo-Pacific (27,27.25] 1982-1999 –> 2000-2012 7.7720655 84277.1360
Indo-Pacific (27,27.25] 2000-2012 –> 2013-2019 9.2166941 58051.7336
Indo-Pacific (27.25,27.5] 1982-1999 –> 2000-2012 6.5762932 71272.0914
Indo-Pacific (27.25,27.5] 2000-2012 –> 2013-2019 7.7047411 49221.5045
Indo-Pacific (27.5,27.75] 1982-1999 –> 2000-2012 5.6981242 67560.0497
Indo-Pacific (27.5,27.75] 2000-2012 –> 2013-2019 7.3341557 48041.2696
Indo-Pacific (27.75,27.85] 1982-1999 –> 2000-2012 4.6423876 24225.7250
Indo-Pacific (27.75,27.85] 2000-2012 –> 2013-2019 5.8396890 17695.0960
Indo-Pacific (27.85,27.95] 1982-1999 –> 2000-2012 4.8874870 31608.2055
Indo-Pacific (27.85,27.95] 2000-2012 –> 2013-2019 6.0593166 22223.2856
Indo-Pacific (27.95,28.05] 1982-1999 –> 2000-2012 4.1436053 25644.9742
Indo-Pacific (27.95,28.05] 2000-2012 –> 2013-2019 4.6465884 17195.3393
Indo-Pacific (28.05,28.1] 1982-1999 –> 2000-2012 3.5016163 16782.5479
Indo-Pacific (28.05,28.1] 2000-2012 –> 2013-2019 3.9281810 11176.5773
Indo-Pacific (28.1, Inf] 1982-1999 –> 2000-2012 2.6486376 117760.1258
Indo-Pacific (28.1, Inf] 2000-2012 –> 2013-2019 2.9768656 80717.8267

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
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
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
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
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 - 1982-1999 --> 2000-2012
(-Inf,26] 5 1 4 5 3 2 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
(27.75,27.95] 5 1 4 5 3 3 2
(27.95,28.1] 5 2 3 4 2 3 3
(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 60.00 27.00 33.00 48.00 31.00 45.00 26.00
Atlantic - 2000-2012 --> 2013-2019
(-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 2 3 3 5 4 0
(27.75,27.95] 5 1 4 3 5 3 0
(27.95,28.1] 5 2 3 5 2 3 3
(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 60.00 28.00 30.00 47.00 35.00 46.00 22.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-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] 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 4 1 5 0 3 5
(27.95,28.05] 5 2 3 5 2 5 2
(28.05,28.1] 4 1 4 4 3 5 2
(28.1, Inf] 4 2 3 4 2 5 3
total 51.00 20.00 38.00 56.00 23.00 54.00 32.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-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] 4 5 0 3 0 3 5
(27.95,28.05] 5 2 3 5 3 3 2
(28.05,28.1] 5 1 4 4 1 5 3
(28.1, Inf] 5 2 3 4 3 5 2
total 55.00 21.00 37.00 55.00 24.00 51.00 31.00

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
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
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