Last updated: 2021-03-05

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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: 1
  • 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:

  • 71

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 144 1.6213889 559.8398 6.646092 1982-2000 –> 2001-2012 3.3022452 1432.4192
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 144 1.0803349 442.9084 4.422245 1982-2000 –> 2001-2012 2.4107879 1211.6877
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 144 1.0792908 444.6299 4.364420 1982-2000 –> 2001-2012 2.4090948 1215.1926
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 144 1.4853990 534.6111 7.434426 1982-2000 –> 2001-2012 3.1316191 1397.9458
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 144 1.4752559 534.6378 7.105460 1982-2000 –> 2001-2012 3.1208234 1399.7964
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 72 1.2725075 251.0296 3.658367 2001-2012 –> 2013-2019 2.3528424 693.9380
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 72 1.1936365 243.8158 3.237974 2001-2012 –> 2013-2019 2.2729273 688.4457
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate_star 72 1.6918467 292.0453 4.133504 2001-2012 –> 2013-2019 3.3006533 849.6415
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 72 1.5761474 281.8448 5.713265 2001-2012 –> 2013-2019 3.0615464 816.4559
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 72 1.5044066 277.1365 5.003414 2001-2012 –> 2013-2019 2.9796625 811.7743
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 965 3.5684248 5207.7512 13.567052 1982-2000 –> 2001-2012 7.0143785 13753.2705
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 965 4.2156951 5527.4634 10.686857 1982-2000 –> 2001-2012 8.3719641 14672.9663
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 965 4.0638916 5456.6836 14.735216 1982-2000 –> 2001-2012 8.1422678 14541.4191
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 965 4.0587800 5456.2545 15.682846 1982-2000 –> 2001-2012 8.1351009 14541.3709
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 965 4.3185678 5575.9943 13.074519 1982-2000 –> 2001-2012 8.5478832 14779.4578
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 567 3.6070302 3077.8676 10.902628 2001-2012 –> 2013-2019 7.1754549 8285.6188
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 567 4.1023698 3221.7908 12.065595 2001-2012 –> 2013-2019 8.3180650 8749.2541
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 567 3.8959809 3163.2545 13.662757 2001-2012 –> 2013-2019 7.9598725 8619.9381
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 567 3.8631919 3155.6702 14.511046 2001-2012 –> 2013-2019 7.9219719 8611.9247
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 567 4.2189568 3255.5690 10.763473 2001-2012 –> 2013-2019 8.5375246 8831.5633
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1302 3.3940109 6889.0362 10.860084 1982-2000 –> 2001-2012 6.4864456 17051.8588
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 1302 3.3616646 6864.1000 10.233140 1982-2000 –> 2001-2012 6.5158422 17105.6827
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1302 3.3099399 6825.7218 10.639653 1982-2000 –> 2001-2012 6.3681965 16946.2674
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1302 3.3534800 6859.7524 11.898665 1982-2000 –> 2001-2012 6.4966262 17089.3770
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1302 3.2764207 6799.2171 10.182438 1982-2000 –> 2001-2012 6.2537947 16812.9783
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 656 3.4323365 3491.6598 11.340269 2001-2012 –> 2013-2019 6.8263474 10380.6960
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 656 3.3850399 3473.4551 10.375376 2001-2012 –> 2013-2019 6.7467045 10337.5551
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 656 3.3455096 3460.0435 10.735554 2001-2012 –> 2013-2019 6.6554495 10285.7653
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 656 3.4093443 3484.8416 9.603997 2001-2012 –> 2013-2019 6.7628244 10344.5939
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 656 3.3238240 3451.5114 11.113656 2001-2012 –> 2013-2019 6.6002447 10250.7285
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2213 2.1450857 9670.0545 15.049138 1982-2000 –> 2001-2012 3.8199035 22547.4298
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2213 2.0475836 9466.1607 14.355801 1982-2000 –> 2001-2012 3.7023052 22265.2601
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2213 2.2445601 9872.6852 15.948275 1982-2000 –> 2001-2012 4.0409226 23217.9559
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2213 2.2516203 9884.5852 15.577694 1982-2000 –> 2001-2012 4.0399446 23198.0322
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2213 2.1386960 9658.8508 19.434325 1982-2000 –> 2001-2012 3.6604924 21901.0704
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1263 2.6364762 6045.0524 27.471250 2001-2012 –> 2013-2019 4.7815619 15715.1069
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 1263 2.5846959 5994.9482 24.744636 2001-2012 –> 2013-2019 4.8035629 15814.6775
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1263 2.5330762 5945.9902 25.891764 2001-2012 –> 2013-2019 4.5806598 15412.1509
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1263 2.6623762 6071.7460 22.596317 2001-2012 –> 2013-2019 4.9069363 15944.4312
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1263 2.2552518 5652.5376 22.583567 2001-2012 –> 2013-2019 4.3939478 15311.3884
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1865 2.1174041 8104.8526 9.753017 1982-2000 –> 2001-2012 4.3335559 20419.3564
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1865 1.9611264 7816.8666 9.080920 1982-2000 –> 2001-2012 3.6654535 18670.8795
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1865 1.9418541 7782.0299 9.454811 1982-2000 –> 2001-2012 3.5012152 18144.3245
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1865 2.0955192 8066.0998 13.262470 1982-2000 –> 2001-2012 3.7745248 18838.9766
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1865 2.3561908 8503.4232 13.662829 1982-2000 –> 2001-2012 4.4264830 20439.7967
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1142 2.2408412 5097.7041 11.555324 2001-2012 –> 2013-2019 4.3582453 13202.5567
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1142 2.3003827 5155.6000 13.777336 2001-2012 –> 2013-2019 4.2615090 12972.4666
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1142 2.2946948 5151.9457 14.080782 2001-2012 –> 2013-2019 4.2365489 12933.9756
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 1142 2.3424794 5197.0192 15.033313 2001-2012 –> 2013-2019 4.5073450 13382.5562
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1142 2.5328202 5377.4530 21.355986 2001-2012 –> 2013-2019 4.6283394 13443.5528
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 1851 2.5474089 8726.5645 13.485514 1982-2000 –> 2001-2012 5.1585703 23258.3545
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1851 2.4547971 8591.4698 13.504128 1982-2000 –> 2001-2012 4.9910350 22947.5524
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1851 2.7774733 9048.6575 21.608848 1982-2000 –> 2001-2012 4.9327912 22411.3534
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 1851 2.4655849 8605.7029 10.664952 1982-2000 –> 2001-2012 4.1969565 20629.4743
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1851 2.2791194 8316.5779 15.349588 1982-2000 –> 2001-2012 4.0077725 20332.7575
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate_star 1109 3.0051254 5599.7139 21.412798 2001-2012 –> 2013-2019 5.7534889 14607.3673
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 1109 3.0025580 5597.8181 16.245244 2001-2012 –> 2013-2019 5.5499669 14324.3826
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1109 2.7952620 5441.1451 16.992150 2001-2012 –> 2013-2019 5.2500591 14032.6149
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 1109 3.1081847 5674.5038 12.222568 2001-2012 –> 2013-2019 5.5737696 14280.2067
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1109 2.7923328 5438.8197 16.610907 2001-2012 –> 2013-2019 5.0714522 13755.3976
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 2584 2.8260559 12712.0168 13.997376 1982-2000 –> 2001-2012 5.2956729 31092.3137
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 2584 2.8139410 12691.8148 14.365371 1982-2000 –> 2001-2012 5.0740864 30373.1944
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2584 2.4775904 12033.9309 14.087302 1982-2000 –> 2001-2012 4.8389252 30061.6643
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2584 2.4274089 11930.1828 14.801336 1982-2000 –> 2001-2012 4.5222592 29012.9733
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2584 3.1776583 13322.0293 16.456627 1982-2000 –> 2001-2012 5.5625226 31430.1722
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate 1515 3.2789491 7909.5783 16.534959 2001-2012 –> 2013-2019 6.1269356 20663.5449
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1515 3.2267256 7862.9314 14.600864 2001-2012 –> 2013-2019 6.0734103 20616.5351
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 1515 3.4234258 8040.2283 14.171915 2001-2012 –> 2013-2019 6.2373668 20732.0430
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 1515 2.8745087 7510.7055 15.545879 2001-2012 –> 2013-2019 5.3520991 19544.6364
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1515 2.8711798 7509.1946 15.461950 2001-2012 –> 2013-2019 5.2985887 19439.3774
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 966 1.9166493 4010.3069 13.295221 1982-2000 –> 2001-2012 3.9275919 9909.0739
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 966 1.8712552 3965.9987 14.088491 1982-2000 –> 2001-2012 3.8291308 9792.4187
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 966 2.0249243 4116.4777 12.386002 1982-2000 –> 2001-2012 3.7124536 9527.8049
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 966 1.7342245 3817.0718 12.249045 1982-2000 –> 2001-2012 3.5462253 9426.2409
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 966 1.5617184 3616.6493 12.825761 1982-2000 –> 2001-2012 3.1630309 8884.1879
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 513 2.0314562 2195.0114 12.644220 2001-2012 –> 2013-2019 3.9481055 6205.3183
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 513 2.0209724 2191.7028 12.956555 2001-2012 –> 2013-2019 3.8922276 6157.7014
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 513 2.4147179 2372.3345 11.388027 2001-2012 –> 2013-2019 4.4396421 6488.8122
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 513 1.8570079 2102.8906 11.721525 2001-2012 –> 2013-2019 3.5912324 5919.9624
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 513 1.7475521 2042.5606 12.039326 2001-2012 –> 2013-2019 3.3092705 5659.2099
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 912 3.5064247 4888.5286 38.572383 1982-2000 –> 2001-2012 6.3783451 11862.1380
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 912 3.5127698 4891.8263 36.343656 1982-2000 –> 2001-2012 6.2345455 11714.3340
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 912 3.4971891 4885.7181 33.515759 1982-2000 –> 2001-2012 6.2189648 11710.2257
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 912 3.1396295 4686.9911 23.273919 1982-2000 –> 2001-2012 6.0449276 11693.1164
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 912 3.1193769 4677.1870 23.061744 1982-2000 –> 2001-2012 5.9782159 11639.9495
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 569 3.7372699 3127.0405 23.268863 2001-2012 –> 2013-2019 7.2436946 8015.5691
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 569 3.4103854 3022.8793 30.447244 2001-2012 –> 2013-2019 6.9231552 7914.7056
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 569 3.3215129 2994.8304 29.207068 2001-2012 –> 2013-2019 6.8187020 7880.5485
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 569 3.6730463 3107.3144 22.693963 2001-2012 –> 2013-2019 6.8126758 7794.3054
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 569 3.6600265 3105.2733 23.151675 2001-2012 –> 2013-2019 6.7794034 7782.4603
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 1112 4.6921323 6605.7722 25.753441 1982-2000 –> 2001-2012 9.4680529 17163.9817
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1112 4.6182121 6572.4563 24.942643 1982-2000 –> 2001-2012 9.3090925 17069.1363
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 1112 4.1027935 6307.2691 22.048472 1982-2000 –> 2001-2012 8.1309718 16263.3949
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1112 3.8714870 6180.2117 25.188136 1982-2000 –> 2001-2012 7.4237387 15693.7472
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1112 4.5892293 6558.4550 21.577430 1982-2000 –> 2001-2012 9.3871384 17134.9069
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 666 4.2792874 3840.4697 24.913097 2001-2012 –> 2013-2019 8.8974994 10412.9260
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 666 3.8465745 3696.4739 22.933854 2001-2012 –> 2013-2019 7.9493681 10003.7431
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 666 3.5060655 3575.0128 26.986021 2001-2012 –> 2013-2019 7.3775525 9755.2245
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 666 4.4290548 3886.2901 23.783433 2001-2012 –> 2013-2019 9.0182841 10444.7452
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate_star 666 4.4290672 3884.2939 23.826635 2001-2012 –> 2013-2019 9.0686107 10464.9991
Atlantic (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 744 1.1782992 2367.5197 10.986680 1982-2000 –> 2001-2012 2.1370558 5507.6559
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 744 1.0672991 2220.2959 7.740850 1982-2000 –> 2001-2012 1.9699850 5223.5153
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 744 1.0357559 2177.6562 6.775510 1982-2000 –> 2001-2012 1.9379618 5181.6674
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 744 1.1237430 2296.9782 11.320799 1982-2000 –> 2001-2012 2.0687173 5404.2169
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 744 1.0613363 2213.9593 12.198642 1982-2000 –> 2001-2012 1.9057470 5067.5555
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 434 1.1676572 1380.1780 6.819178 2001-2012 –> 2013-2019 2.3080390 3701.0269
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 434 1.1212849 1343.0032 8.929761 2001-2012 –> 2013-2019 2.1885840 3563.2991
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 434 1.0586072 1295.0748 7.429722 2001-2012 –> 2013-2019 2.0943631 3472.7310
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 434 1.1480057 1363.4454 12.833810 2001-2012 –> 2013-2019 2.2717487 3660.4237
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 434 1.1075442 1334.3006 13.578379 2001-2012 –> 2013-2019 2.1688805 3548.2600
Atlantic (28.1,28.15] cstar_tref ~ aou + silicate + phosphate + phosphate_star 867 0.8274144 2143.9338 11.197656 1982-2000 –> 2001-2012 1.5361983 5087.8080
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 867 0.8246169 2140.0612 8.145751 1982-2000 –> 2001-2012 1.5416690 5117.5743
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 867 0.7589728 1994.2207 7.286861 1982-2000 –> 2001-2012 1.4374788 4818.9978
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 867 0.7462906 1967.0013 7.177232 1982-2000 –> 2001-2012 1.3847056 4627.6300
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 867 0.7346900 1939.8357 11.369467 1982-2000 –> 2001-2012 1.3579973 4535.1318
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 497 0.9633503 1387.3108 6.933462 2001-2012 –> 2013-2019 1.7879673 3527.3721
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 497 0.8714406 1285.6430 6.181914 2001-2012 –> 2013-2019 1.6304134 3279.8636
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 497 0.8712585 1287.4353 6.182326 2001-2012 –> 2013-2019 1.6175491 3254.4366
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 497 0.9653756 1387.3983 11.632299 2001-2012 –> 2013-2019 1.7819394 3508.4422
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 497 0.8791505 1296.3985 11.933687 2001-2012 –> 2013-2019 1.6138405 3236.2342
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1433 0.6021846 2625.0680 2.355115 1982-2000 –> 2001-2012 1.1346056 6313.6038
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1433 0.5547520 2391.9328 2.089595 1982-2000 –> 2001-2012 1.0715876 5943.9629
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 1433 0.6122065 2672.3730 2.236451 1982-2000 –> 2001-2012 1.1735415 6607.4509
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 1433 0.5813926 2524.3627 2.238918 1982-2000 –> 2001-2012 1.1295113 6348.3641
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1433 0.5651818 2445.3159 2.369816 1982-2000 –> 2001-2012 1.1127395 6266.5434
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 819 0.7431790 1850.0329 4.262643 2001-2012 –> 2013-2019 1.3453636 4475.1008
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 819 0.7372762 1838.9708 4.731734 2001-2012 –> 2013-2019 1.2920281 4230.9036
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 819 0.8686623 2105.5896 7.748139 2001-2012 –> 2013-2019 1.4808689 4777.9626
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 819 0.8619250 2092.8357 8.363302 2001-2012 –> 2013-2019 1.4433175 4617.1984
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 819 0.8613203 2093.6861 8.208278 2001-2012 –> 2013-2019 1.4265021 4539.0020
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 2485 0.3673688 2085.2212 1.986972 1982-2000 –> 2001-2012 0.6725630 3914.6684
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 2485 0.3601450 1988.5189 1.958481 1982-2000 –> 2001-2012 0.6617242 3726.5727
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 2485 0.3664309 2074.5165 1.983944 1982-2000 –> 2001-2012 0.6704517 3875.7695
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2485 0.3518295 1874.4192 1.922124 1982-2000 –> 2001-2012 0.6508414 3547.4638
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2485 0.5450062 4049.5423 3.149665 1982-2000 –> 2001-2012 1.0039906 9081.4265
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 1557 0.4186021 1716.7958 2.479100 2001-2012 –> 2013-2019 0.7859709 3802.0170
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 1557 0.3991609 1570.7062 2.411345 2001-2012 –> 2013-2019 0.7593059 3559.2251
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 1557 0.4110188 1661.8663 2.465092 2001-2012 –> 2013-2019 0.7774497 3736.3828
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1557 0.3901368 1501.4981 2.457959 2001-2012 –> 2013-2019 0.7419663 3375.9172
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1557 0.7057457 3347.3447 8.527267 2001-2012 –> 2013-2019 1.2507519 7396.8870
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 4881 6.2143686 31697.5256 29.835795 1982-2000 –> 2001-2012 12.7449630 81800.1602
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4881 6.1712600 31631.5713 29.388714 1982-2000 –> 2001-2012 12.6509949 81617.3670
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4881 7.1785132 33107.4809 31.204086 1982-2000 –> 2001-2012 14.7061688 85371.8181
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4881 7.2855079 33251.9083 28.991912 1982-2000 –> 2001-2012 14.8610962 85612.7255
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4881 7.3711072 33363.9360 28.325070 1982-2000 –> 2001-2012 15.0843095 85996.3902
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 2816 5.9520247 18049.4373 24.894024 2001-2012 –> 2013-2019 12.1663933 49746.9629
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2816 5.8778725 17980.8313 24.128023 2001-2012 –> 2013-2019 12.0491324 49612.4026
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2816 6.9521542 18926.2002 25.907885 2001-2012 –> 2013-2019 14.1306674 52033.6812
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2816 7.0001768 18964.9700 25.465195 2001-2012 –> 2013-2019 14.2856846 52216.8783
Indo-Pacific (-Inf,26] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2816 7.1344030 19069.9395 24.441528 2001-2012 –> 2013-2019 14.5055102 52433.8756
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5096 4.9373668 30748.7349 41.521617 1982-2000 –> 2001-2012 9.5682410 78820.0569
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5096 4.5759017 29975.8536 43.758131 1982-2000 –> 2001-2012 8.8099690 76590.5919
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5096 4.8101119 30484.6033 49.048369 1982-2000 –> 2001-2012 9.2049909 77706.2847
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 5096 4.9357595 30745.4164 40.229458 1982-2000 –> 2001-2012 9.5401955 78723.5164
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5096 4.9268192 30728.9386 40.974753 1982-2000 –> 2001-2012 9.5310926 78708.4635
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2918 4.8175903 17468.7156 40.382988 2001-2012 –> 2013-2019 9.7549572 48217.4505
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2918 4.4724496 17036.8813 46.310491 2001-2012 –> 2013-2019 9.0483513 47012.7349
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2918 4.5715543 17164.7889 45.715284 2001-2012 –> 2013-2019 9.3816663 47649.3923
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 2918 4.8142859 17464.7112 37.043514 2001-2012 –> 2013-2019 9.7500453 48210.1276
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2918 4.8065118 17457.2797 38.739984 2001-2012 –> 2013-2019 9.7333310 48186.2182
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4184 4.0625793 23616.0912 22.275517 1982-2000 –> 2001-2012 8.0116440 60756.0715
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4184 3.9432208 23368.5557 20.385022 1982-2000 –> 2001-2012 7.7043985 59862.4007
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4184 4.0095095 23508.0591 29.332337 1982-2000 –> 2001-2012 8.0113472 60826.5427
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4184 3.9599665 23404.0169 25.942445 1982-2000 –> 2001-2012 7.8351530 60294.9025
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4184 4.0095098 23506.0598 29.343437 1982-2000 –> 2001-2012 8.0794624 61046.9490
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2447 4.4033896 14211.0265 24.538450 2001-2012 –> 2013-2019 8.4659689 37827.1177
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2447 4.2938981 14089.7973 24.434470 2001-2012 –> 2013-2019 8.2371189 37458.3531
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2447 4.3225383 14122.3318 31.664753 2001-2012 –> 2013-2019 8.3320478 37630.3909
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2447 4.2923135 14087.9909 22.815590 2001-2012 –> 2013-2019 8.2522800 37492.0079
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2447 4.3388127 14138.7232 34.446250 2001-2012 –> 2013-2019 8.3483226 37644.7831
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4962 4.5534369 29137.1620 18.939535 1982-2000 –> 2001-2012 8.5582793 73620.0540
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4962 4.3364534 28652.6180 22.008744 1982-2000 –> 2001-2012 8.0394196 71893.6582
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4962 4.3192831 28615.2456 21.108747 1982-2000 –> 2001-2012 8.0079944 71797.1675
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4962 4.2311566 28408.6718 23.234746 1982-2000 –> 2001-2012 7.9242593 71607.4469
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4962 4.1948398 28325.1244 21.547407 1982-2000 –> 2001-2012 7.8600939 71405.9570
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2868 4.9018613 17269.0630 18.494849 2001-2012 –> 2013-2019 9.4552982 46406.2250
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 2868 4.6612052 16980.3073 20.095371 2001-2012 –> 2013-2019 8.9976586 45632.9253
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2868 4.6499950 16968.4956 19.282213 2001-2012 –> 2013-2019 8.9692781 45583.7412
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 2868 4.5774010 16876.2410 16.522089 2001-2012 –> 2013-2019 8.8085576 45284.9128
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2868 4.5537010 16848.4650 17.066955 2001-2012 –> 2013-2019 8.7485407 45173.5894
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5959 4.3992827 34580.7292 44.861548 1982-2000 –> 2001-2012 8.0019405 85063.7361
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5959 4.0971941 33732.8931 54.460349 1982-2000 –> 2001-2012 7.5380948 83357.3996
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 5959 4.3648841 34485.1746 48.474013 1982-2000 –> 2001-2012 8.0109883 85190.2018
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5959 3.9847135 33401.1323 33.390135 1982-2000 –> 2001-2012 7.3040408 82353.4105
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 5959 4.5171137 34893.7426 77.524087 1982-2000 –> 2001-2012 8.1317640 85436.8545
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3470 5.1328308 21210.8952 31.173698 2001-2012 –> 2013-2019 9.5785110 55914.6607
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3470 5.0789520 21139.6617 33.597697 2001-2012 –> 2013-2019 9.4782346 55720.3908
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3470 4.9716940 20991.5322 35.708885 2001-2012 –> 2013-2019 9.0688881 54724.4254
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 3470 5.1322261 21210.0776 39.784583 2001-2012 –> 2013-2019 9.4971102 55695.2522
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3470 4.4723380 20256.9380 25.616236 2001-2012 –> 2013-2019 8.4570515 53658.0703
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 5405 3.5002342 28895.8165 32.348639 1982-2000 –> 2001-2012 6.4076154 70349.6528
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5405 3.7736996 29709.0091 32.665481 1982-2000 –> 2001-2012 6.8314356 72003.2800
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 5405 3.7938958 29764.7083 31.805016 1982-2000 –> 2001-2012 6.8522496 72060.3464
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5405 3.7142636 29537.3961 32.974793 1982-2000 –> 2001-2012 6.7813081 71882.3309
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5405 3.4131680 28623.5237 33.365958 1982-2000 –> 2001-2012 6.3227040 70089.7087
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3127 3.9776245 17522.8442 31.036835 2001-2012 –> 2013-2019 7.4778587 46418.6607
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3127 4.3037583 18015.6837 32.127293 2001-2012 –> 2013-2019 8.0774578 47724.6928
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 3127 4.3425043 18069.7354 30.551097 2001-2012 –> 2013-2019 8.1364001 47834.4437
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3127 4.2454019 17930.3030 31.035584 2001-2012 –> 2013-2019 7.9596655 47467.6991
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3127 3.8437243 17308.6883 33.232474 2001-2012 –> 2013-2019 7.2568923 45932.2121
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 5382 3.3514439 28305.3418 24.159198 1982-2000 –> 2001-2012 5.6719070 67018.0957
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5382 3.3168416 28193.6303 9.294607 1982-2000 –> 2001-2012 5.6635178 67098.6737
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 5382 3.4725174 28685.3406 22.445770 1982-2000 –> 2001-2012 5.8399549 67739.1621
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 5382 3.4761715 28696.6616 29.228334 1982-2000 –> 2001-2012 5.8707708 67945.7608
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 5382 3.5287932 28858.3841 25.429685 1982-2000 –> 2001-2012 5.9130550 68033.4254
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3104 3.9417327 17337.7899 25.386634 2001-2012 –> 2013-2019 7.2931766 45643.1317
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3104 3.7804110 17078.3721 11.020697 2001-2012 –> 2013-2019 7.0972526 45272.0023
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3104 4.0989818 17578.6356 23.944569 2001-2012 –> 2013-2019 7.5714992 46263.9762
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 3104 4.1948886 17722.2154 32.318244 2001-2012 –> 2013-2019 7.6710601 46418.8770
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3104 4.0127640 17448.6640 19.751773 2001-2012 –> 2013-2019 7.4630446 46066.8540
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2156 2.7985695 10567.9784 21.832325 1982-2000 –> 2001-2012 4.7718819 24397.5037
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2156 2.7959069 10565.8738 22.237131 1982-2000 –> 2001-2012 4.7633978 24377.9470
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2156 2.7922972 10560.3032 22.404634 1982-2000 –> 2001-2012 4.7717904 24412.4187
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate 2156 2.8115219 10587.8893 21.390063 1982-2000 –> 2001-2012 4.7958849 24454.1823
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2156 2.6997759 10415.0067 21.666915 1982-2000 –> 2001-2012 4.6514713 24174.0083
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1264 3.1358059 6490.2930 31.989646 2001-2012 –> 2013-2019 5.9265656 17048.2212
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1264 3.1693826 6517.2176 30.950746 2001-2012 –> 2013-2019 5.9652894 17083.0915
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 1264 3.1488202 6498.7630 29.448400 2001-2012 –> 2013-2019 5.9396792 17054.8446
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 1264 3.1128492 6469.7178 31.766441 2001-2012 –> 2013-2019 5.9028656 17024.4974
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1264 3.0665742 6433.8549 28.861392 2001-2012 –> 2013-2019 5.7663501 16848.8616
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 2680 2.7758132 13089.7691 29.064449 1982-2000 –> 2001-2012 4.9251554 31609.8356
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2680 2.7701319 13080.7874 28.621230 1982-2000 –> 2001-2012 4.9183028 31598.2348
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2680 2.8030717 13144.1476 34.550032 1982-2000 –> 2001-2012 4.9778552 31765.9299
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + phosphate_star 2680 2.7902414 13115.5573 31.981362 1982-2000 –> 2001-2012 4.9421829 31643.8655
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2680 2.7823104 13102.3002 31.200569 1982-2000 –> 2001-2012 4.9333601 31629.0961
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 1542 3.3165597 8085.5004 32.079445 2001-2012 –> 2013-2019 6.0923729 21175.2695
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 1542 3.3046795 8074.4335 31.424170 2001-2012 –> 2013-2019 6.0760726 21155.6606
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1542 3.2946985 8067.1049 31.554855 2001-2012 –> 2013-2019 6.0648304 21147.8923
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1542 3.2637446 8037.9935 37.426960 2001-2012 –> 2013-2019 6.0668164 21182.1411
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1542 3.2965108 8066.8008 32.540164 2001-2012 –> 2013-2019 6.0788211 21169.1009
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2315 2.2833414 10404.3981 8.268281 1982-2000 –> 2001-2012 4.2090832 25745.1039
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2315 2.2095949 10254.3920 8.091231 1982-2000 –> 2001-2012 4.1830067 25777.8031
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2315 2.2291592 10295.2068 8.513948 1982-2000 –> 2001-2012 4.1240522 25518.5722
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2315 2.2885822 10417.0129 8.100060 1982-2000 –> 2001-2012 4.2273602 25809.5765
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2315 2.2090564 10253.2635 7.916875 1982-2000 –> 2001-2012 4.0869121 25409.8840
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate_star 1354 2.4060015 6232.0181 8.104133 2001-2012 –> 2013-2019 4.6312562 16517.1081
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1354 2.4007452 6228.0956 8.259744 2001-2012 –> 2013-2019 4.6103401 16482.4876
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1354 2.4779038 6313.7598 8.329809 2001-2012 –> 2013-2019 4.7070630 16608.9667
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 1354 2.4648617 6297.4690 8.721893 2001-2012 –> 2013-2019 4.7314392 16667.7491
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1354 2.4266912 6257.2052 8.523746 2001-2012 –> 2013-2019 4.6357476 16510.4687
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1579 1.9459787 6597.4940 9.561773 1982-2000 –> 2001-2012 3.6052255 16981.1719
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1579 1.9606240 6619.1718 8.938549 1982-2000 –> 2001-2012 3.5936594 16915.0870
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1579 1.8448339 6428.9331 9.646517 1982-2000 –> 2001-2012 3.4539344 16647.3234
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1579 1.8640624 6461.6782 10.350963 1982-2000 –> 2001-2012 3.4825621 16711.4381
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1579 1.8045187 6359.1560 9.968863 1982-2000 –> 2001-2012 3.4389356 16661.6258
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 966 2.1066397 4192.9110 9.987464 2001-2012 –> 2013-2019 3.9876724 10681.2095
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 966 2.0390556 4131.9137 9.747515 2001-2012 –> 2013-2019 3.8838895 10560.8467
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 966 2.0868098 4176.6389 10.548800 2001-2012 –> 2013-2019 3.9508722 10638.3172
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate 966 2.1188554 4204.0818 10.037184 2001-2012 –> 2013-2019 4.0097537 10708.8999
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 966 2.0001288 4094.6740 9.111786 2001-2012 –> 2013-2019 3.8046474 10453.8300
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 13532 1.4478536 48430.0561 13.741302 1982-2000 –> 2001-2012 2.7234565 119690.6973
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 13532 1.3507384 46552.9828 16.223864 1982-2000 –> 2001-2012 2.5232392 114203.3814
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 13532 1.3898784 47326.0612 12.981276 1982-2000 –> 2001-2012 2.5152099 113216.5745
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 13532 1.4027407 47575.3660 17.038930 1982-2000 –> 2001-2012 2.6457586 117728.9334
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 13532 1.5832480 50849.4761 17.438936 1982-2000 –> 2001-2012 2.9146956 123946.5781
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 7804 1.6305548 29791.8606 9.567306 2001-2012 –> 2013-2019 3.1645931 79788.7991
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 7804 1.5693631 29192.8476 10.689506 2001-2012 –> 2013-2019 3.0172166 77622.9037
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7804 1.4923380 28409.3615 12.644005 2001-2012 –> 2013-2019 2.8430764 74962.3443
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7804 1.5858456 29357.9189 10.996188 2001-2012 –> 2013-2019 2.9757240 76683.9801
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7804 1.5521124 29022.3323 13.774789 2001-2012 –> 2013-2019 2.9548530 76597.6983

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 –> 2001-2012 2.8749141 1331.4083
Atlantic (-Inf,26] 2001-2012 –> 2013-2019 2.7935264 772.0511
Atlantic (26,26.5] 1982-2000 –> 2001-2012 8.0423189 14457.6969
Atlantic (26,26.5] 2001-2012 –> 2013-2019 7.9825778 8619.6598
Atlantic (26.5,26.75] 1982-2000 –> 2001-2012 6.4241811 17001.2328
Atlantic (26.5,26.75] 2001-2012 –> 2013-2019 6.7183141 10319.8678
Atlantic (26.75,27] 1982-2000 –> 2001-2012 3.8527137 22625.9497
Atlantic (26.75,27] 2001-2012 –> 2013-2019 4.6933337 15639.5510
Atlantic (27,27.25] 1982-2000 –> 2001-2012 3.9402465 19302.6667
Atlantic (27,27.25] 2001-2012 –> 2013-2019 4.3983975 13187.0216
Atlantic (27.25,27.5] 1982-2000 –> 2001-2012 4.6574251 21915.8984
Atlantic (27.25,27.5] 2001-2012 –> 2013-2019 5.4397474 14199.9938
Atlantic (27.5,27.75] 1982-2000 –> 2001-2012 5.0586933 30394.0636
Atlantic (27.5,27.75] 2001-2012 –> 2013-2019 5.8176801 20199.2274
Atlantic (27.75,27.85] 1982-2000 –> 2001-2012 3.6356865 9507.9453
Atlantic (27.75,27.85] 2001-2012 –> 2013-2019 3.8360956 6086.2008
Atlantic (27.85,27.95] 1982-2000 –> 2001-2012 6.1709998 11723.9527
Atlantic (27.85,27.95] 2001-2012 –> 2013-2019 6.9155262 7877.5178
Atlantic (27.95,28.05] 1982-2000 –> 2001-2012 8.7437989 16665.0334
Atlantic (27.95,28.05] 2001-2012 –> 2013-2019 8.4622630 10216.3276
Atlantic (28.05,28.1] 1982-2000 –> 2001-2012 2.0038934 5276.9222
Atlantic (28.05,28.1] 2001-2012 –> 2013-2019 2.2063231 3589.1481
Atlantic (28.1,28.15] 1982-2000 –> 2001-2012 1.4516098 4837.4284
Atlantic (28.1,28.15] 2001-2012 –> 2013-2019 1.6863419 3361.2698
Atlantic (28.15,28.2] 1982-2000 –> 2001-2012 1.1243971 6295.9850
Atlantic (28.15,28.2] 2001-2012 –> 2013-2019 1.3976160 4528.0335
Atlantic (28.2, Inf] 1982-2000 –> 2001-2012 0.7319142 4829.1802
Atlantic (28.2, Inf] 2001-2012 –> 2013-2019 0.8630889 4374.0858
Indo-Pacific (-Inf,26] 1982-2000 –> 2001-2012 14.0095065 84079.6922
Indo-Pacific (-Inf,26] 2001-2012 –> 2013-2019 13.4274776 51208.7601
Indo-Pacific (26,26.5] 1982-2000 –> 2001-2012 9.3308978 78109.7827
Indo-Pacific (26,26.5] 2001-2012 –> 2013-2019 9.5336702 47855.1847
Indo-Pacific (26.5,26.75] 1982-2000 –> 2001-2012 7.9284010 60557.3733
Indo-Pacific (26.5,26.75] 2001-2012 –> 2013-2019 8.3271476 37610.5305
Indo-Pacific (26.75,27] 1982-2000 –> 2001-2012 8.0780093 72064.8567
Indo-Pacific (26.75,27] 2001-2012 –> 2013-2019 8.9958666 45616.2787
Indo-Pacific (27,27.25] 1982-2000 –> 2001-2012 7.7973657 84280.3205
Indo-Pacific (27,27.25] 2001-2012 –> 2013-2019 9.2159591 55142.5599
Indo-Pacific (27.25,27.5] 1982-2000 –> 2001-2012 6.6390626 71277.0638
Indo-Pacific (27.25,27.5] 2001-2012 –> 2013-2019 7.7816549 47075.5417
Indo-Pacific (27.5,27.75] 1982-2000 –> 2001-2012 5.7918411 67567.0235
Indo-Pacific (27.5,27.75] 2001-2012 –> 2013-2019 7.4192066 45932.9682
Indo-Pacific (27.75,27.85] 1982-2000 –> 2001-2012 4.7508853 24363.2120
Indo-Pacific (27.75,27.85] 2001-2012 –> 2013-2019 5.9001500 17011.9033
Indo-Pacific (27.85,27.95] 1982-2000 –> 2001-2012 4.9393713 31649.3924
Indo-Pacific (27.85,27.95] 2001-2012 –> 2013-2019 6.0757827 21166.0129
Indo-Pacific (27.95,28.05] 1982-2000 –> 2001-2012 4.1660829 25652.1879
Indo-Pacific (27.95,28.05] 2001-2012 –> 2013-2019 4.6631692 16557.3560
Indo-Pacific (28.05,28.1] 1982-2000 –> 2001-2012 3.5148634 16783.3293
Indo-Pacific (28.05,28.1] 2001-2012 –> 2013-2019 3.9273670 10608.6207
Indo-Pacific (28.1, Inf] 1982-2000 –> 2001-2012 2.6644720 117757.2330
Indo-Pacific (28.1, Inf] 2001-2012 –> 2013-2019 2.9910926 77131.1451

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 1 - 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
ee69bc1 Donghe-Zhu 2021-03-05
a79291f Donghe-Zhu 2021-03-05
e8c6f30 Donghe-Zhu 2021-03-04
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
ee69bc1 Donghe-Zhu 2021-03-05
a79291f Donghe-Zhu 2021-03-05
e8c6f30 Donghe-Zhu 2021-03-04
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
ee69bc1 Donghe-Zhu 2021-03-05
a79291f Donghe-Zhu 2021-03-05
e8c6f30 Donghe-Zhu 2021-03-04
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
ee69bc1 Donghe-Zhu 2021-03-05
a79291f Donghe-Zhu 2021-03-05
e8c6f30 Donghe-Zhu 2021-03-04
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 --> 2001-2012
(-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
(27.75,27.85] 5 2 3 3 5 4 0
(27.85,27.95] 5 0 5 5 2 3 2
(27.95,28.05] 5 2 3 5 2 3 3
(28.05,28.1] 5 0 5 5 2 3 2
(28.1,28.15] 5 1 4 5 3 4 1
(28.15,28.2] 5 5 0 4 2 3 3
(28.2, Inf] 5 5 0 3 4 3 1
total 70.00 28.00 42.00 57.00 37.00 52.00 28.00
Atlantic - 2001-2012 --> 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
(27.75,27.85] 5 2 3 3 5 4 0
(27.85,27.95] 5 0 5 5 2 3 2
(27.95,28.05] 5 2 2 5 1 4 4
(28.05,28.1] 5 1 4 5 3 3 2
(28.1,28.15] 5 1 4 5 3 3 2
(28.15,28.2] 5 5 0 4 2 3 3
(28.2, Inf] 5 5 0 3 4 3 1
total 70.00 30.00 37.00 57.00 39.00 54.00 27.00
Indo-Pacific - 1982-2000 --> 2001-2012
(-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] 5 2 3 4 3 5 2
(28.1, Inf] 4 2 3 4 2 5 3
total 52.00 21.00 37.00 56.00 23.00 54.00 32.00
Indo-Pacific - 2001-2012 --> 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 4 1 4 0 4 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 20.00 38.00 56.00 24.00 52.00 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
ee69bc1 Donghe-Zhu 2021-03-05
a79291f Donghe-Zhu 2021-03-05
e8c6f30 Donghe-Zhu 2021-03-04
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
ee69bc1 Donghe-Zhu 2021-03-05
a79291f Donghe-Zhu 2021-03-05
e8c6f30 Donghe-Zhu 2021-03-04
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
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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
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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