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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 predictor combinations with nitrate and phosphate
lm_all <- lm_all %>%
  mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
  filter(!(
    str_detect(lm_coeff_filter, "nitrate") &
      str_detect(lm_coeff_filter, "phosphate")
  )) %>%
  select(-lm_coeff_filter)

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

3 Apply predictor threshold

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

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

This results in a total number of MLR models of:

  • 86

4 Fit all models

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

  • cstar_tref

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

# loop across all basins, era, gamma slabs, and MLRs
# fit all MLR models
for (i_basin in unique(GLODAP$basin)) {
  for (i_era in unique(GLODAP$era)) {
    # i_basin <- unique(GLODAP$basin)[1]
    # i_era   <- unique(GLODAP$era)[1]
    print(i_basin)
    print(i_era)
    
    GLODAP_basin_era <- GLODAP %>%
      filter(basin == i_basin, era == i_era)
    
    for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
      # i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
      print(i_gamma_slab)
      
      GLODAP_basin_era_slab <- GLODAP_basin_era %>%
        filter(gamma_slab == i_gamma_slab)
      
      for (i_predictors in unique(lm_all$predictors)) {
        # i_predictors <- unique(lm_all$predictors)[110]
        
        # extract one model definition
        i_lm <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(lm_coeff) %>%
          pull()
        
        # extract number of predictors
        i_n_predictors <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(n) %>%
          pull()
        
        # fit model
        i_lm_fit <- lm(as.formula(i_lm),
                       data = GLODAP_basin_era_slab)
        
        # find max predictor correlation
        i_cor_max <- GLODAP_basin_era_slab %>%
          select(!!!syms(str_split(i_predictors, " ",
                                   simplify = TRUE))) %>%
          correlate(quiet = TRUE) %>%
          select(-term) %>%
          abs() %>%
          max(na.rm = TRUE)
        
        # calculate root mean squared error
        i_rmse <- sqrt(c(crossprod(i_lm_fit$residuals)) /
                         length(i_lm_fit$residuals))
        
        # calculate maximum residual
        i_resid_max <- max(abs(i_lm_fit$residuals))
        
        # calculate Akaike information criterion aic
        i_aic <- AIC(i_lm_fit)
        
        # collect model coefficients and diagnostics
        coefficients <- tidy(i_lm_fit)
        
        coefficients <- coefficients %>%
          mutate(
            basin = i_basin,
            era = i_era,
            gamma_slab = i_gamma_slab,
            model = i_lm,
            rmse = i_rmse,
            aic = i_aic,
            resid_max = i_resid_max,
            n_predictors = i_n_predictors,
            na_predictor = anyNA(coefficients$estimate),
            cor_max = i_cor_max
          )
        
        if (exists("lm_all_fitted")) {
          lm_all_fitted <- bind_rows(lm_all_fitted, coefficients)
        }
        
        if (!exists("lm_all_fitted")) {
          lm_all_fitted <- coefficients
        }
      }
      
      
    }
  }
  
}

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

5 Prepare coeffcients

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

5.1 Formatting

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

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

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

5.2 Predictor selection

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

  • 5

The criterion used to select the best models was:

  • rmse

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

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

# remove models with predictors fitted as NA

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

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

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

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 rmse aic resid_max eras rmse_sum aic_sum
Atlantic (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 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 1.0480832 477.2249 4.299021 1982-1999 –> 2000-2012 2.3837757 1201.9145
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.0458289 476.5445 4.199297 1982-1999 –> 2000-2012 2.3833703 1201.8095
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0447877 476.2297 3.991338 1982-1999 –> 2000-2012 2.3809752 1201.0734
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.0538228 478.9507 4.496846 1982-1999 –> 2000-2012 2.3907671 1204.0299
Atlantic (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.1936365 243.8158 3.237974 2000-2012 –> 2013-2019 2.2417197 721.0407
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.1377961 236.9166 2.786570 2000-2012 –> 2013-2019 2.1836250 713.4610
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.1990801 244.4710 3.379652 2000-2012 –> 2013-2019 2.2529029 723.4217
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2012446 244.7307 3.425080 2000-2012 –> 2013-2019 2.2566374 724.1518
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2024324 244.8730 3.445295 2000-2012 –> 2013-2019 2.2595421 724.8078
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5518213 5633.9468 13.477555 1982-1999 –> 2000-2012 6.9985663 13749.8718
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 3.4447540 5567.9148 15.626500 1982-1999 –> 2000-2012 6.8794929 13671.1971
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.3758183 5527.6256 14.515788 1982-1999 –> 2000-2012 6.7415640 13571.0193
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.3139957 5488.9589 14.956164 1982-1999 –> 2000-2012 6.6524475 13507.5183
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6117860 5668.9708 14.137864 1982-1999 –> 2000-2012 7.1481878 13863.2182
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.6070302 3077.8676 10.902628 2000-2012 –> 2013-2019 7.1588515 8711.8144
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 3.3369968 2987.6271 10.231047 2000-2012 –> 2013-2019 6.7817508 8555.5419
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.2984682 2976.4579 9.956192 2000-2012 –> 2013-2019 6.6742865 8504.0835
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.1723161 2932.2362 9.432214 2000-2012 –> 2013-2019 6.4863118 8421.1950
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6470365 3090.3758 10.325180 2000-2012 –> 2013-2019 7.2588226 8759.3466
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.2700730 7288.8799 10.507891 1982-1999 –> 2000-2012 6.3292231 16928.5449
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.2846060 7301.2695 10.500101 1982-1999 –> 2000-2012 6.3669620 16969.6063
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.3014232 7315.5384 10.543653 1982-1999 –> 2000-2012 6.4059223 17011.0331
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.3059150 7319.3372 10.550809 1982-1999 –> 2000-2012 6.4173056 17023.2446
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.2249399 7250.0489 10.037456 1982-1999 –> 2000-2012 6.2079736 16794.1190
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.3455096 3460.0435 10.735554 2000-2012 –> 2013-2019 6.6155826 10748.9234
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.3565540 3464.3677 10.767824 2000-2012 –> 2013-2019 6.6411600 10765.6372
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.3723676 3470.5343 10.887326 2000-2012 –> 2013-2019 6.6737908 10786.0727
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.3762721 3472.0524 10.919163 2000-2012 –> 2013-2019 6.6821871 10791.3896
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 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 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 2.0001820 10143.9994 14.081577 1982-1999 –> 2000-2012 3.6531709 22225.1681
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.0669164 10301.4026 14.196373 1982-1999 –> 2000-2012 3.7902516 22644.2987
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.1361037 10459.3140 22.290539 1982-1999 –> 2000-2012 3.8999248 22948.0383
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 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 2.6364762 6045.0524 27.471250 2000-2012 –> 2013-2019 4.7300390 16405.8891
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5330762 5945.9902 25.891764 2000-2012 –> 2013-2019 4.5332582 16089.9896
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5653762 5977.9963 25.592327 2000-2012 –> 2013-2019 4.6322925 16279.3988
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.5985873 6010.4878 25.748151 2000-2012 –> 2013-2019 4.7346911 16469.8018
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.2552518 5652.5376 22.583567 2000-2012 –> 2013-2019 4.3413155 15998.1644
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 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 1.8904789 8364.5325 9.689213 1982-1999 –> 2000-2012 3.4604645 18143.6984
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.8979717 8380.6003 9.355072 1982-1999 –> 2000-2012 3.4547428 18115.6267
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.9187787 8424.8886 8.642107 1982-1999 –> 2000-2012 3.5002075 18241.9782
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.9234272 8434.7175 8.493771 1982-1999 –> 2000-2012 3.5167839 18291.0461
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 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 2.2946948 5151.9457 14.080782 2000-2012 –> 2013-2019 4.1851737 13516.4782
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.2882847 5145.5566 14.231726 2000-2012 –> 2013-2019 4.1862565 13526.1569
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3093184 5166.4549 14.219293 2000-2012 –> 2013-2019 4.2280971 13591.3435
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3127467 5169.8432 14.213647 2000-2012 –> 2013-2019 4.2361739 13604.5606
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.6905754 9769.2091 21.422922 1982-1999 –> 2000-2012 4.8576234 22402.1133
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.1625100 8884.3428 12.574713 1982-1999 –> 2000-2012 3.8613513 20116.1247
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.7127786 9802.4934 22.028851 1982-1999 –> 2000-2012 4.9396802 22592.2216
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 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 2.2547324 9053.4778 15.509020 1982-1999 –> 2000-2012 3.9706310 20342.7650
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 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 2.7952620 5441.1451 16.992150 2000-2012 –> 2013-2019 5.2467264 14833.4228
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8205406 5461.1132 14.090309 2000-2012 –> 2013-2019 4.9830506 14345.4560
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 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 2.7923328 5438.8197 16.610907 2000-2012 –> 2013-2019 5.0470652 14492.2975
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3944064 12867.9502 14.685866 1982-1999 –> 2000-2012 4.4949743 29021.3907
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3920617 12862.4560 14.587684 1982-1999 –> 2000-2012 4.4588552 28894.8448
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.4132697 12911.9574 14.216479 1982-1999 –> 2000-2012 4.4797512 28943.2189
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.4148672 12915.6685 14.181558 1982-1999 –> 2000-2012 4.4833272 28954.0764
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.4122515 12909.5908 14.214259 1982-1999 –> 2000-2012 4.4796273 28944.0833
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.8711798 7509.1946 15.461950 2000-2012 –> 2013-2019 5.2655862 20377.1448
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.8690598 7506.9564 15.594453 2000-2012 –> 2013-2019 5.2611214 20369.4124
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.8670393 7504.8218 16.960962 2000-2012 –> 2013-2019 5.2803090 20416.7793
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.8833164 7521.9755 16.841839 2000-2012 –> 2013-2019 5.2981836 20437.6440
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.8660787 7503.8064 16.855872 2000-2012 –> 2013-2019 5.2783302 20413.3972
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5641536 3880.9392 12.798383 1982-1999 –> 2000-2012 3.1611985 8876.8661
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.6216292 3955.7103 16.087961 1982-1999 –> 2000-2012 3.2308513 8971.6904
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.6994499 4052.8317 11.282662 1982-1999 –> 2000-2012 3.2672503 8999.9679
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5917451 3917.1705 12.897616 1982-1999 –> 2000-2012 3.2211161 8966.0004
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.6298056 3966.1312 13.022129 1982-1999 –> 2000-2012 3.3011800 9082.1552
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.7475521 2042.5606 12.039326 2000-2012 –> 2013-2019 3.3117057 5923.4997
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.7754726 2058.8233 12.075398 2000-2012 –> 2013-2019 3.3672178 5975.9938
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.8242119 2086.6088 12.213063 2000-2012 –> 2013-2019 3.4614785 6062.2038
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.8185913 2083.4428 12.157352 2000-2012 –> 2013-2019 3.4483969 6049.5740
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.8275241 2088.4700 12.223997 2000-2012 –> 2013-2019 3.4690021 6069.3878
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.4396213 5230.3536 36.781212 1982-1999 –> 2000-2012 6.1696286 11717.2584
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.4272905 5225.2930 34.214054 1982-1999 –> 2000-2012 6.1571686 11714.0714
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.9304503 4917.3900 22.456892 1982-1999 –> 2000-2012 5.6593028 11405.1644
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.0946626 5022.5819 23.332862 1982-1999 –> 2000-2012 6.0114682 11686.3324
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.0757549 5012.5332 23.130965 1982-1999 –> 2000-2012 5.9400103 11629.7050
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.4103854 3022.8793 30.447244 2000-2012 –> 2013-2019 6.8500067 8253.2329
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.3215129 2994.8304 29.207068 2000-2012 –> 2013-2019 6.7488034 8220.1234
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.3261262 2996.4099 29.121490 2000-2012 –> 2013-2019 6.2565764 7913.7999
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.6730463 3107.3144 22.693963 2000-2012 –> 2013-2019 6.7677089 8129.8962
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.6600265 3105.2733 23.151675 2000-2012 –> 2013-2019 6.7357814 8117.8065
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.9558395 6742.2684 22.787482 1982-1999 –> 2000-2012 7.7155699 15951.7623
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.4923146 7048.5063 24.290391 1982-1999 –> 2000-2012 9.2008204 17012.2786
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.4965817 7050.7925 24.338742 1982-1999 –> 2000-2012 9.2082047 17016.7832
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 4.0815088 6815.5758 22.528945 1982-1999 –> 2000-2012 8.1122385 16256.3696
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.8590720 6682.6316 25.099675 1982-1999 –> 2000-2012 7.3908813 15682.5017
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.5357472 3586.2418 25.590197 2000-2012 –> 2013-2019 7.4915867 10328.5101
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.2577904 3833.7616 24.198809 2000-2012 –> 2013-2019 8.7501050 10882.2679
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.2605747 3834.6323 24.285919 2000-2012 –> 2013-2019 8.7571564 10885.4248
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.8465745 3696.4739 22.933854 2000-2012 –> 2013-2019 7.9280833 10512.0498
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.5060655 3575.0128 26.986021 2000-2012 –> 2013-2019 7.3651375 10257.6443
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.0324411 2346.9902 6.945256 1982-1999 –> 2000-2012 1.9247967 5169.4535
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.0374154 2354.7189 6.772617 1982-1999 –> 2000-2012 1.9399611 5201.6173
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.9934328 2285.0583 8.087713 1982-1999 –> 2000-2012 1.8641000 5054.5716
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.0379653 2355.5710 6.801673 1982-1999 –> 2000-2012 1.9363554 5192.5380
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.0436142 2364.2985 12.188672 1982-1999 –> 2000-2012 1.8828911 5054.7923
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.0586072 1295.0748 7.429722 2000-2012 –> 2013-2019 2.0910483 3642.0650
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.0605845 1296.6946 7.328068 2000-2012 –> 2013-2019 2.0979999 3651.4134
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0174317 1260.6390 9.169936 2000-2012 –> 2013-2019 2.0108645 3545.6973
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.0645856 1299.9629 7.272475 2000-2012 –> 2013-2019 2.1025508 3655.5339
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.0672164 1302.1053 7.231208 2000-2012 –> 2013-2019 2.1084324 3662.7045
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.7598609 2156.1646 5.927820 1982-1999 –> 2000-2012 1.3893138 4646.2932
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.7694118 2179.5475 5.861659 1982-1999 –> 2000-2012 1.4115736 4721.4486
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.7641038 2166.5883 5.828897 1982-1999 –> 2000-2012 1.3992369 4679.9843
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.7666596 2172.8394 5.792427 1982-1999 –> 2000-2012 1.4061667 4704.0109
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.7856962 2218.7544 10.025704 1982-1999 –> 2000-2012 1.3744859 4535.9182
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 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 0.8712585 1287.4353 6.182326 2000-2012 –> 2013-2019 1.6311195 3443.5998
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8492568 1262.0116 6.971050 2000-2012 –> 2013-2019 1.6225461 3450.9696
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.8778689 1294.9484 6.059947 2000-2012 –> 2013-2019 1.6419727 3461.5366
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.8812870 1298.8112 6.030679 2000-2012 –> 2013-2019 1.6479466 3471.6506
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.5471615 2527.0561 2.040783 1982-1999 –> 2000-2012 1.0648603 5924.1022
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.5816010 2713.0610 2.059205 1982-1999 –> 2000-2012 1.1102087 6200.8612
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.5814763 2714.4005 2.081606 1982-1999 –> 2000-2012 1.1063265 6172.4699
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.5693363 2649.4158 2.047829 1982-1999 –> 2000-2012 1.0976310 6136.5816
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 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 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 0.7372762 1838.9708 4.731734 2000-2012 –> 2013-2019 1.2844377 4366.0269
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.7638188 1894.9037 5.281723 2000-2012 –> 2013-2019 1.3454198 4607.9647
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.7409497 1847.1121 4.370070 2000-2012 –> 2013-2019 1.3224260 4561.5126
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.7570242 1882.2675 4.592474 2000-2012 –> 2013-2019 1.3263604 4531.6833
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.3540505 2062.0339 1.937681 1982-1999 –> 2000-2012 0.6560011 3717.6111
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.3463114 1944.9979 1.900529 1982-1999 –> 2000-2012 0.6453988 3531.8596
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.3592615 2140.7296 1.976601 1982-1999 –> 2000-2012 0.6633222 3847.9927
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3473235 1960.7157 2.119236 1982-1999 –> 2000-2012 0.6492687 3618.1601
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.3584097 2129.9437 2.006883 1982-1999 –> 2000-2012 0.6622526 3833.8894
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.3991609 1570.7062 2.411345 2000-2012 –> 2013-2019 0.7532114 3632.7401
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 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 0.3901368 1501.4981 2.457959 2000-2012 –> 2013-2019 0.7364483 3446.4960
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3803071 1422.0335 2.702200 2000-2012 –> 2013-2019 0.7276306 3382.7492
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.4078439 1639.7187 2.585072 2000-2012 –> 2013-2019 0.7662535 3769.6624
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 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 6.1928478 34304.9200 29.527354 1982-1999 –> 2000-2012 12.6716991 81612.6324
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6.0656694 34085.4664 34.021650 1982-1999 –> 2000-2012 12.4290401 81134.4469
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6.2323348 34372.1408 29.869481 1982-1999 –> 2000-2012 12.7604050 81788.7288
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.3160008 34513.1739 29.849776 1982-1999 –> 2000-2012 12.9032362 82059.5576
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 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 5.8778725 17980.8313 24.128023 2000-2012 –> 2013-2019 12.0707203 52285.7513
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.7800044 17886.2676 29.028201 2000-2012 –> 2013-2019 11.8456737 51971.7340
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.9502121 18049.7219 24.771202 2000-2012 –> 2013-2019 12.1825468 52421.8627
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.9876308 18085.0286 24.907000 2000-2012 –> 2013-2019 12.3036316 52598.2025
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.5360650 32401.5327 43.772780 1982-1999 –> 2000-2012 8.7824377 76605.3494
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.5877220 32526.6595 39.934460 1982-1999 –> 2000-2012 8.8818706 76903.0425
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.6579284 32694.4781 38.557719 1982-1999 –> 2000-2012 9.0054183 77261.2754
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.6658266 32713.1992 39.207721 1982-1999 –> 2000-2012 9.0244249 77319.3567
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.7555301 32923.6260 49.041150 1982-1999 –> 2000-2012 9.1671720 77716.3587
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.4724496 17036.8813 46.310491 2000-2012 –> 2013-2019 9.0085146 49438.4140
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.5594237 17149.2824 39.840874 2000-2012 –> 2013-2019 9.1471456 49675.9420
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.6381187 17249.1516 36.657339 2000-2012 –> 2013-2019 9.2960471 49943.6297
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.6426236 17254.8173 36.476302 2000-2012 –> 2013-2019 9.3084502 49968.0165
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.5715543 17164.7889 45.715284 2000-2012 –> 2013-2019 9.3270844 50088.4149
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.9265162 25339.4488 20.226531 1982-1999 –> 2000-2012 7.6839109 59845.1956
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.0209885 25555.5176 28.598406 1982-1999 –> 2000-2012 7.9073574 60485.6979
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.0407862 25600.1536 20.538812 1982-1999 –> 2000-2012 7.8931648 60419.8596
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.9296720 25346.7499 27.085865 1982-1999 –> 2000-2012 7.8142638 60271.1781
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.9477481 25388.4579 23.151958 1982-1999 –> 2000-2012 7.8249401 60288.9073
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.2938981 14089.7973 24.434470 2000-2012 –> 2013-2019 8.2204143 39429.2462
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.2783866 14072.0860 34.710261 2000-2012 –> 2013-2019 8.2080586 39418.8360
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 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 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 4.3388127 14138.7232 34.446250 2000-2012 –> 2013-2019 8.3606936 39694.2577
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 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 4.2906105 30803.4359 21.052395 1982-1999 –> 2000-2012 7.9645082 71788.9629
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.1643941 30483.7138 22.734855 1982-1999 –> 2000-2012 7.7513405 71108.4774
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 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 4.1702723 30498.8181 21.453131 1982-1999 –> 2000-2012 7.8227361 71396.2141
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 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 4.6499950 16968.4956 19.282213 2000-2012 –> 2013-2019 8.9406055 47771.9315
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.5360260 16826.1577 17.606576 2000-2012 –> 2013-2019 8.7004201 47309.8716
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 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 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 4.3929768 37503.1646 41.945012 1982-1999 –> 2000-2012 7.9587117 85065.6810
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.2956539 37213.4453 48.286060 1982-1999 –> 2000-2012 7.8087443 84513.0773
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 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 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 3.9500266 36128.6900 31.512269 1982-1999 –> 2000-2012 7.2528573 82337.5496
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.0789520 21139.6617 33.597697 2000-2012 –> 2013-2019 9.4719288 58642.8263
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.0651721 21120.8069 42.030410 2000-2012 –> 2013-2019 9.3608260 58334.2522
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 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 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 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 3.4261572 31007.5182 32.305003 1982-1999 –> 2000-2012 6.3475428 70339.4077
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6349919 31699.4240 32.897992 1982-1999 –> 2000-2012 6.6737213 71652.9104
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6434273 31726.5299 33.075508 1982-1999 –> 2000-2012 6.6965461 71754.5823
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 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 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 3.9776245 17522.8442 31.036835 2000-2012 –> 2013-2019 7.4037817 48530.3624
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.2298938 17907.4158 32.750414 2000-2012 –> 2013-2019 7.8648856 49606.8398
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.2332498 17912.3758 32.987685 2000-2012 –> 2013-2019 7.8766771 49638.9057
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 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 3.8437243 17308.6883 33.232474 2000-2012 –> 2013-2019 7.1899105 48040.0175
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.2280103 30253.8699 9.417658 1982-1999 –> 2000-2012 5.5715676 67074.4342
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.1735450 30055.2512 8.689085 1982-1999 –> 2000-2012 5.4890819 66680.8347
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.1804225 30080.5185 8.700790 1982-1999 –> 2000-2012 5.5093045 66799.2566
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.1824417 30085.9266 11.982022 1982-1999 –> 2000-2012 5.5582386 67125.9669
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.1698959 30041.8225 8.686571 1982-1999 –> 2000-2012 5.4929254 66719.7736
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.6736333 16900.5032 10.209719 2000-2012 –> 2013-2019 6.8651581 47021.6955
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate 3.7197021 16975.8697 10.325293 2000-2012 –> 2013-2019 6.9432174 47211.4751
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.7040372 16951.6707 10.351471 2000-2012 –> 2013-2019 6.8775822 47006.9218
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.7079082 16958.1551 10.354380 2000-2012 –> 2013-2019 6.8883307 47038.6736
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6928602 16932.9096 10.332716 2000-2012 –> 2013-2019 6.8627561 46974.7321
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 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 2.7290365 11241.6591 21.325228 1982-1999 –> 2000-2012 4.6507603 24231.5321
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.7364990 11254.3133 24.038402 1982-1999 –> 2000-2012 4.6592663 24247.5857
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 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 + phosphate_star 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 3.1358059 6490.2930 31.989646 2000-2012 –> 2013-2019 5.8629052 17728.6613
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.0327595 6405.8242 34.844332 2000-2012 –> 2013-2019 5.7692585 17660.1374
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.1487768 6500.7281 29.551108 2000-2012 –> 2013-2019 5.8739654 17735.8488
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 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 3.0665742 6433.8549 28.861392 2000-2012 –> 2013-2019 5.7071919 17522.8898
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.7472776 14139.3979 28.705900 1982-1999 –> 2000-2012 4.8676515 31561.0562
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.7620867 14170.6537 31.227540 1982-1999 –> 2000-2012 4.8825340 31592.5900
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 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 2.7457460 14136.1557 28.208152 1982-1999 –> 2000-2012 4.8664196 31558.9474
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 2.7621671 14168.8231 31.138313 1982-1999 –> 2000-2012 4.8840444 31594.1657
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.3042832 8076.0636 32.744068 2000-2012 –> 2013-2019 6.0515609 22215.4615
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.2978683 8070.0705 32.004378 2000-2012 –> 2013-2019 6.0457481 22210.7427
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 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 3.2946985 8067.1049 31.554855 2000-2012 –> 2013-2019 6.0404446 22203.2606
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.2637446 8037.9935 37.426960 2000-2012 –> 2013-2019 6.0494318 22258.1136
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.2115502 10931.1275 8.468880 1982-1999 –> 2000-2012 4.1022689 25513.2034
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.1868435 10875.6962 8.583791 1982-1999 –> 2000-2012 4.0752629 25449.1497
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.2194485 10948.7174 8.518833 1982-1999 –> 2000-2012 4.1159015 25552.2518
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.2177921 10945.0336 8.776951 1982-1999 –> 2000-2012 4.1134423 25545.5679
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 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 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 2.4007452 6228.0956 8.259744 2000-2012 –> 2013-2019 4.5943605 17119.0470
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.3941382 6220.6327 8.284045 2000-2012 –> 2013-2019 4.5799766 17094.0607
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.4833521 6319.7076 8.863057 2000-2012 –> 2013-2019 4.6701956 17195.4038
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 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 + phosphate_star 1.8450332 6994.0133 9.467590 1982-1999 –> 2000-2012 3.4414783 16645.3685
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.8511670 7005.4174 9.474435 1982-1999 –> 2000-2012 3.4501316 16664.8274
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.8524675 7007.8305 9.472903 1982-1999 –> 2000-2012 3.4530954 16672.5512
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.8521019 7007.1522 9.467448 1982-1999 –> 2000-2012 3.4524360 16670.9355
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.8032691 6915.3424 9.697645 1982-1999 –> 2000-2012 3.4298781 16662.3098
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.0390556 4131.9137 9.747515 2000-2012 –> 2013-2019 3.8840888 11125.9270
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.0453970 4137.9128 9.764284 2000-2012 –> 2013-2019 3.8965640 11143.3302
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.0456543 4138.1559 9.760669 2000-2012 –> 2013-2019 3.8981218 11145.9864
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.0451030 4137.6351 9.755580 2000-2012 –> 2013-2019 3.8972049 11144.7873
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.0001288 4094.6740 9.111786 2000-2012 –> 2013-2019 3.8033978 11010.0164
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.3376755 50034.5935 16.199862 1982-1999 –> 2000-2012 2.5064341 114098.9931
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.3331929 49936.3988 16.466261 1982-1999 –> 2000-2012 2.4904010 113596.8674
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.3376755 50034.5945 16.199920 1982-1999 –> 2000-2012 2.5064212 114098.5423
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.3376891 50032.8912 16.220724 1982-1999 –> 2000-2012 2.5073460 114126.5367
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.3692488 50717.0570 13.004762 1982-1999 –> 2000-2012 2.4951048 113260.4541
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.4923380 28409.3615 12.644005 2000-2012 –> 2013-2019 2.8302151 78448.3652
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.4925685 28411.7727 12.628703 2000-2012 –> 2013-2019 2.8303164 78447.9491
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.4928857 28415.0892 12.611716 2000-2012 –> 2013-2019 2.8305612 78449.6827
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.4959833 28447.4412 13.045112 2000-2012 –> 2013-2019 2.8291763 78383.8400
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.4928764 28414.9925 12.611567 2000-2012 –> 2013-2019 2.8305520 78449.5870

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 2.3848881 1201.4567
Atlantic (-Inf,26] 2000-2012 –> 2013-2019 2.2388854 721.3766
Atlantic (26,26.5] 1982-1999 –> 2000-2012 6.8840517 13672.5649
Atlantic (26,26.5] 2000-2012 –> 2013-2019 6.8720046 8590.3963
Atlantic (26.5,26.75] 1982-1999 –> 2000-2012 6.3454773 16945.3096
Atlantic (26.5,26.75] 2000-2012 –> 2013-2019 6.6322969 10758.7166
Atlantic (26.75,27] 1982-1999 –> 2000-2012 3.7417921 22440.8562
Atlantic (26.75,27] 2000-2012 –> 2013-2019 4.5943193 16248.6488
Atlantic (27,27.25] 1982-1999 –> 2000-2012 3.5126788 18289.9093
Atlantic (27,27.25] 2000-2012 –> 2013-2019 4.2101808 13561.7278
Atlantic (27.25,27.5] 1982-1999 –> 2000-2012 4.3511430 21213.9140
Atlantic (27.25,27.5] 2000-2012 –> 2013-2019 5.2645017 14754.8510
Atlantic (27.5,27.75] 1982-1999 –> 2000-2012 4.4793070 28951.5228
Atlantic (27.5,27.75] 2000-2012 –> 2013-2019 5.2767061 20402.8755
Atlantic (27.75,27.85] 1982-1999 –> 2000-2012 3.2363192 8979.3360
Atlantic (27.75,27.85] 2000-2012 –> 2013-2019 3.4115602 6016.1318
Atlantic (27.85,27.95] 1982-1999 –> 2000-2012 5.9875157 11630.5063
Atlantic (27.85,27.95] 2000-2012 –> 2013-2019 6.6717754 8126.9718
Atlantic (27.95,28.05] 1982-1999 –> 2000-2012 8.3255430 16383.9391
Atlantic (27.95,28.05] 2000-2012 –> 2013-2019 8.0584138 10573.1794
Atlantic (28.05,28.1] 1982-1999 –> 2000-2012 1.9096209 5134.5946
Atlantic (28.05,28.1] 2000-2012 –> 2013-2019 2.0821792 3631.4828
Atlantic (28.1,28.15] 1982-1999 –> 2000-2012 1.3961554 4657.5310
Atlantic (28.1,28.15] 2000-2012 –> 2013-2019 1.6376631 3460.0719
Atlantic (28.15,28.2] 1982-1999 –> 2000-2012 1.0973376 6137.2001
Atlantic (28.15,28.2] 2000-2012 –> 2013-2019 1.3231597 4539.0253
Atlantic (28.2, Inf] 1982-1999 –> 2000-2012 0.6552487 3709.9026
Atlantic (28.2, Inf] 2000-2012 –> 2013-2019 0.7506733 3605.4750
Indo-Pacific (-Inf,26] 1982-1999 –> 2000-2012 12.7060031 81677.9426
Indo-Pacific (-Inf,26] 2000-2012 –> 2013-2019 12.1181382 52340.7011
Indo-Pacific (26,26.5] 1982-1999 –> 2000-2012 8.9722647 77161.0765
Indo-Pacific (26,26.5] 2000-2012 –> 2013-2019 9.2174484 49822.8834
Indo-Pacific (26.5,26.75] 1982-1999 –> 2000-2012 7.8247274 60262.1677
Indo-Pacific (26.5,26.75] 2000-2012 –> 2013-2019 8.2747191 39539.7075
Indo-Pacific (26.75,27] 1982-1999 –> 2000-2012 7.8840227 71555.0282
Indo-Pacific (26.75,27] 2000-2012 –> 2013-2019 8.8234262 47543.4704
Indo-Pacific (27,27.25] 1982-1999 –> 2000-2012 7.7017051 84082.9000
Indo-Pacific (27,27.25] 2000-2012 –> 2013-2019 9.1745060 57949.2541
Indo-Pacific (27.25,27.5] 1982-1999 –> 2000-2012 6.5414920 71142.3496
Indo-Pacific (27.25,27.5] 2000-2012 –> 2013-2019 7.6432677 49089.6142
Indo-Pacific (27.5,27.75] 1982-1999 –> 2000-2012 5.5242236 66880.0532
Indo-Pacific (27.5,27.75] 2000-2012 –> 2013-2019 6.8874089 47050.6996
Indo-Pacific (27.75,27.85] 1982-1999 –> 2000-2012 4.6368258 24210.1522
Indo-Pacific (27.75,27.85] 2000-2012 –> 2013-2019 5.8134021 17675.3828
Indo-Pacific (27.85,27.95] 1982-1999 –> 2000-2012 4.8741505 31574.1399
Indo-Pacific (27.85,27.95] 2000-2012 –> 2013-2019 6.0480595 22220.3708
Indo-Pacific (27.95,28.05] 1982-1999 –> 2000-2012 4.0942330 25493.0619
Indo-Pacific (27.95,28.05] 2000-2012 –> 2013-2019 4.6154320 17141.2080
Indo-Pacific (28.05,28.1] 1982-1999 –> 2000-2012 3.4454039 16663.1985
Indo-Pacific (28.05,28.1] 2000-2012 –> 2013-2019 3.8758755 11114.0095
Indo-Pacific (28.1, Inf] 1982-1999 –> 2000-2012 2.5011414 113836.2787
Indo-Pacific (28.1, Inf] 2000-2012 –> 2013-2019 2.8301642 78435.8848

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

6.1.1 All models

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

Version Author Date
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
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
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
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 4 5 2 3
(26,26.5] 5 3 2 2 5 3 4
(26.5,26.75] 4 0 4 4 4 5 4
(26.75,27] 5 0 4 4 3 5 3
(27,27.25] 4 0 4 3 5 5 3
(27.25,27.5] 5 3 2 2 3 5 4
(27.5,27.75] 3 1 3 4 5 5 4
(27.75,27.85] 4 2 3 4 5 3 4
(27.85,27.95] 5 0 5 5 3 2 3
(27.95,28.05] 4 3 1 5 3 3 5
(28.05,28.1] 5 1 4 4 4 3 4
(28.1,28.15] 4 1 4 4 4 4 4
(28.15,28.2] 5 5 0 3 4 3 4
(28.2, Inf] 5 5 0 3 5 2 3
total 63.00 25.00 40.00 51.00 58.00 50.00 52.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 4 1 3 4 5 4 4
(26,26.5] 5 3 2 2 5 3 4
(26.5,26.75] 4 0 4 4 4 5 4
(26.75,27] 5 0 4 4 3 5 3
(27,27.25] 4 0 4 3 5 5 3
(27.25,27.5] 5 5 0 2 3 5 3
(27.5,27.75] 3 1 3 4 5 5 4
(27.75,27.85] 3 1 3 4 5 5 4
(27.85,27.95] 5 0 5 5 3 2 3
(27.95,28.05] 4 3 1 5 3 3 5
(28.05,28.1] 4 1 4 4 5 3 4
(28.1,28.15] 4 0 5 4 5 3 3
(28.15,28.2] 5 5 0 3 5 2 3
(28.2, Inf] 5 5 0 3 5 3 2
total 60.00 25.00 38.00 51.00 61.00 53.00 49.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 5 1 4 4 5 2 3
(26,26.5] 4 1 3 4 4 5 4
(26.5,26.75] 4 2 3 4 4 4 4
(26.75,27] 5 0 5 5 3 2 3
(27,27.25] 5 1 4 5 2 3 4
(27.25,27.5] 4 2 3 4 3 5 4
(27.5,27.75] 3 0 4 3 5 5 4
(27.75,27.85] 5 1 4 5 2 4 3
(27.85,27.95] 3 5 0 5 2 3 5
(27.95,28.05] 4 2 3 3 4 5 4
(28.05,28.1] 4 0 4 4 4 5 4
(28.1, Inf] 2 2 1 5 4 5 5
total 48.00 17.00 38.00 51.00 42.00 48.00 47.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 5 1 4 4 5 2 3
(26,26.5] 4 1 3 4 4 5 4
(26.5,26.75] 3 3 2 5 2 5 4
(26.75,27] 5 0 5 5 3 2 3
(27,27.25] 5 1 4 5 2 3 4
(27.25,27.5] 4 2 3 4 3 5 4
(27.5,27.75] 4 1 2 2 5 5 5
(27.75,27.85] 4 2 3 5 3 3 4
(27.85,27.95] 5 4 1 3 2 4 5
(27.95,28.05] 5 4 1 4 4 3 3
(28.05,28.1] 4 0 4 4 4 5 4
(28.1, Inf] 3 1 3 4 5 5 4
total 51.00 20.00 35.00 49.00 42.00 47.00 47.00

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
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
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_0.7.3      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.3   
[21] tidyverse_1.3.0  workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] nlme_3.1-149             fs_1.5.0                 webshot_0.5.2           
 [4] RColorBrewer_1.1-2       httr_1.4.2               rprojroot_2.0.2         
 [7] tools_4.0.3              backports_1.1.10         R6_2.5.0                
[10] mgcv_1.8-33              nortest_1.0-4            DBI_1.1.0               
[13] colorspace_2.0-0         withr_2.3.0              gridExtra_2.3           
[16] tidyselect_1.1.0         curl_4.3                 compiler_4.0.3          
[19] git2r_0.27.1             cli_2.2.0                rvest_0.3.6             
[22] xml2_1.3.2               sass_0.2.0               labeling_0.4.2          
[25] scales_1.1.1             checkmate_2.0.0          goftest_1.2-2           
[28] digest_0.6.27            foreign_0.8-80           rmarkdown_2.5           
[31] rio_0.5.16               pkgconfig_2.0.3          htmltools_0.5.0         
[34] highr_0.8                dbplyr_1.4.4             rlang_0.4.10            
[37] readxl_1.3.1             rstudioapi_0.13          farver_2.0.3            
[40] generics_0.1.0           jsonlite_1.7.2           zip_2.1.1               
[43] car_3.0-10               magrittr_2.0.1           Matrix_1.2-18           
[46] Rcpp_1.0.5               munsell_0.5.0            fansi_0.4.1             
[49] abind_1.4-5              lifecycle_0.2.0          stringi_1.5.3           
[52] whisker_0.4              yaml_2.2.1               carData_3.0-4           
[55] plyr_1.8.6               grid_4.0.3               blob_1.2.1              
[58] parallel_4.0.3           promises_1.1.1           crayon_1.3.4            
[61] lattice_0.20-41          splines_4.0.3            haven_2.3.1             
[64] hms_0.5.3                pillar_1.4.7             reprex_0.3.0            
[67] glue_1.4.2               evaluate_0.14            RcppArmadillo_0.10.1.2.2
[70] data.table_1.13.6        modelr_0.1.8             vctrs_0.3.6             
[73] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[76] reshape_0.8.8            assertthat_0.2.1         xfun_0.20               
[79] openxlsx_4.2.3           RcppEigen_0.3.3.9.1      later_1.1.0.1           
[82] viridisLite_0.3.0        ellipsis_0.3.1           here_1.0.1