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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:

  • 10

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)
}


# print table
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 + silicate + phosphate + phosphate_star 0.6869975 122.52544 1.9844368 1982-1999 –> 2000-2012 2.690144 356.3458
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.7937326 137.54471 2.0383256 1982-1999 –> 2000-2012 2.641875 362.9892
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.6839029 122.05592 2.2057626 1982-1999 –> 2000-2012 2.683801 355.7075
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.7425615 130.61405 2.1602026 1982-1999 –> 2000-2012 2.257729 335.3984
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.6796001 121.39953 1.9766954 1982-1999 –> 2000-2012 2.536204 347.3190
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.6802298 121.49586 1.9749797 1982-1999 –> 2000-2012 2.516444 346.2669
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.7256169 128.21337 2.8004232 1982-1999 –> 2000-2012 2.559006 352.8243
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.6785582 121.23996 1.9748939 1982-1999 –> 2000-2012 2.506136 345.5207
Atlantic (-Inf,26] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.7570324 130.62129 2.1365217 1982-1999 –> 2000-2012 2.421801 343.1983
Atlantic (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.6801275 121.48021 1.9354268 1982-1999 –> 2000-2012 2.046535 315.5171
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.8498325 2144.56550 11.3406948 1982-1999 –> 2000-2012 6.934103 3884.2475
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.1899456 2209.75223 12.0912094 1982-1999 –> 2000-2012 7.435090 3983.9070
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.4793012 2261.17231 15.8258932 1982-1999 –> 2000-2012 7.921291 4075.2543
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.9284879 2160.13871 11.8726573 1982-1999 –> 2000-2012 7.116392 3922.2275
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.9475480 2163.86553 12.1138485 1982-1999 –> 2000-2012 7.155016 3930.1025
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.8778213 2150.14325 13.3086856 1982-1999 –> 2000-2012 7.118676 3923.4012
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.9565582 2165.62104 12.1792405 1982-1999 –> 2000-2012 7.171665 3933.4709
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.1420379 2200.89736 16.3315042 1982-1999 –> 2000-2012 7.913574 4076.9708
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.2280733 2216.72740 15.0029847 1982-1999 –> 2000-2012 7.966769 4086.8712
Atlantic (26,26.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.1567343 2201.62456 16.0666928 1982-1999 –> 2000-2012 7.932621 4076.4797
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.2675377 32.07985 0.6378534 2000-2012 –> 2013-2019 4.926310 2323.5015
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.4920821 141.76919 1.2308406 2000-2012 –> 2013-2019 4.341915 2286.3347
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 0.4789695 134.90763 1.0286988 2000-2012 –> 2013-2019 4.961210 2394.5850
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.4784061 136.69576 1.0972823 2000-2012 –> 2013-2019 4.668352 2346.4480
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.2503820 20.15081 0.6595283 2000-2012 –> 2013-2019 4.729683 2281.3231
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.4778251 136.47703 1.4317248 2000-2012 –> 2013-2019 4.406313 2296.6157
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.4795344 137.11981 1.3774552 2000-2012 –> 2013-2019 4.427082 2300.9853
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.6839690 201.03725 1.9596135 2000-2012 –> 2013-2019 4.561790 2351.1805
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.4812056 137.74603 1.3377745 2000-2012 –> 2013-2019 4.437764 2303.3671
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.2521798 21.43860 0.7043631 2000-2012 –> 2013-2019 4.394218 2222.3360
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.9905160 3246.49937 13.2593410 1982-1999 –> 2000-2012 6.701146 5070.5891
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.9779260 3244.85277 13.5952314 1982-1999 –> 2000-2012 6.688495 5070.9256
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.0084838 3253.68374 14.0032583 1982-1999 –> 2000-2012 6.774470 5094.9357
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.0305893 3260.03020 14.2182835 1982-1999 –> 2000-2012 6.830336 5110.3808
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.0364691 3261.71241 14.2638630 1982-1999 –> 2000-2012 6.848145 5115.2518
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.9846366 3246.79788 12.8747444 1982-1999 –> 2000-2012 6.749397 5087.7172
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 4.0512643 3263.93455 13.5684491 1982-1999 –> 2000-2012 6.828831 5106.3200
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.8852070 3217.63649 15.2548013 1982-1999 –> 2000-2012 6.514412 5020.8515
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 4.0825840 3272.82164 13.7715287 1982-1999 –> 2000-2012 6.900688 5126.0738
Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.0905776 3275.07892 13.8099177 1982-1999 –> 2000-2012 6.922985 5132.1281
Atlantic (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 0.9798234 258.14579 3.8914741 2000-2012 –> 2013-2019 4.970339 3504.6452
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.8674123 238.69878 2.7394787 2000-2012 –> 2013-2019 4.845338 3483.5515
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.8549176 236.14515 2.9671259 2000-2012 –> 2013-2019 4.863401 3489.8289
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.8548922 236.13992 2.9919839 2000-2012 –> 2013-2019 4.885482 3496.1701
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.8552375 236.21099 3.0267136 2000-2012 –> 2013-2019 4.891706 3497.9234
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.7134922 204.31843 2.2893069 2000-2012 –> 2013-2019 4.698129 3451.1163
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 0.9604393 254.62902 3.9838339 2000-2012 –> 2013-2019 5.011704 3518.5636
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.9406936 252.97293 4.1222795 2000-2012 –> 2013-2019 4.825901 3470.6094
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 0.9562963 253.86818 4.0126821 2000-2012 –> 2013-2019 5.038880 3526.6898
Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 0.9530338 253.26673 4.0289106 2000-2012 –> 2013-2019 5.043611 3528.3456
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.6434289 4736.64652 13.2021442 1982-1999 –> 2000-2012 4.363980 7796.9468
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5746524 4686.55444 12.6781530 1982-1999 –> 2000-2012 4.294470 7748.1922
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.6417887 4737.42007 12.7501154 1982-1999 –> 2000-2012 4.520566 7936.4359
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.6915218 4774.27350 12.8764385 1982-1999 –> 2000-2012 4.646484 8035.0600
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.7105853 4788.21978 12.8943520 1982-1999 –> 2000-2012 4.697216 8073.9785
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.4891171 4619.79238 8.5989099 1982-1999 –> 2000-2012 4.411351 7854.3434
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2.7687880 4828.20004 13.6671366 1982-1999 –> 2000-2012 4.653162 8029.8379
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.5666100 4680.37242 12.5707309 1982-1999 –> 2000-2012 4.151667 7615.2065
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 2.8213032 4865.32755 13.8024486 1982-1999 –> 2000-2012 4.782180 8128.8085
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.8426578 4880.22770 13.8298897 1982-1999 –> 2000-2012 4.835538 8168.8670
Atlantic (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1.9152368 702.97245 8.1063245 2000-2012 –> 2013-2019 4.558666 5439.6190
Atlantic (26.75,27] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.5382656 631.76443 5.6261134 2000-2012 –> 2013-2019 4.470496 5575.2955
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 1.4667167 613.85627 4.2667700 2000-2012 –> 2013-2019 4.213294 5426.1416
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.4447773 610.82251 4.0999012 2000-2012 –> 2013-2019 4.019430 5297.3769
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate_star 1.5935860 641.56506 4.5327244 2000-2012 –> 2013-2019 4.575265 5616.1408
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.4556896 613.33570 4.1998082 2000-2012 –> 2013-2019 4.097478 5350.7558
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.4792530 618.69891 4.3098683 2000-2012 –> 2013-2019 4.170775 5392.9724
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.4979120 622.88557 4.3924471 2000-2012 –> 2013-2019 4.208497 5411.1054
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.4054166 601.59695 5.5797114 2000-2012 –> 2013-2019 3.894534 5221.3893
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.8823471 699.18697 9.4143111 2000-2012 –> 2013-2019 4.448957 5379.5594
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.1851961 5374.76908 8.6590868 1982-1999 –> 2000-2012 4.112873 9427.2134
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 2.1776058 5364.29288 10.7828072 1982-1999 –> 2000-2012 3.684981 8936.1270
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.1709172 5358.79901 11.1074919 1982-1999 –> 2000-2012 3.547196 8755.5731
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.9977674 5156.31999 8.9262174 1982-1999 –> 2000-2012 4.223618 9488.6449
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.1769654 5365.57639 10.8846203 1982-1999 –> 2000-2012 3.584662 8806.2740
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.2131293 5405.71093 10.9107855 1982-1999 –> 2000-2012 3.664355 8905.6723
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.3529009 5554.89524 13.3245705 1982-1999 –> 2000-2012 4.066422 9378.1684
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.2215346 5414.94517 10.9088576 1982-1999 –> 2000-2012 3.685525 8931.9482
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.0305857 5196.01214 9.0014257 1982-1999 –> 2000-2012 3.597430 8845.1449
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.5042296 5706.73631 13.5019784 1982-1999 –> 2000-2012 4.087463 9376.1175
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.7380523 1224.62605 6.9461183 2000-2012 –> 2013-2019 3.923249 6599.3951
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1.9751882 1301.15575 6.0440411 2000-2012 –> 2013-2019 4.152794 6665.4486
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.9511903 1295.65017 5.9655197 2000-2012 –> 2013-2019 4.122108 6654.4492
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 1.9781768 1302.08407 6.1992116 2000-2012 –> 2013-2019 4.298498 6821.0137
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.4550223 1115.49130 5.7219429 2000-2012 –> 2013-2019 3.452790 6271.8113
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.9396341 1292.00286 5.9933663 2000-2012 –> 2013-2019 4.116600 6657.5792
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.9611113 1298.76419 6.0197160 2000-2012 –> 2013-2019 4.174241 6704.4751
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.9633018 1299.44962 6.0215930 2000-2012 –> 2013-2019 4.184836 6714.3948
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate 1.4601623 1115.65647 5.6218791 2000-2012 –> 2013-2019 3.493486 6312.9511
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.4601335 1117.64436 5.6195162 2000-2012 –> 2013-2019 3.490719 6313.6565
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.3611268 11626.18212 19.3613010 1982-1999 –> 2000-2012 4.847674 16488.9167
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.3607609 11627.70159 19.4887616 1982-1999 –> 2000-2012 4.676954 16167.2210
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.2952970 11540.87337 13.7707569 1982-1999 –> 2000-2012 5.094149 16915.1381
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.1966121 11406.66666 10.1142689 1982-1999 –> 2000-2012 4.988835 16771.0673
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.4560798 11751.15032 18.7535837 1982-1999 –> 2000-2012 5.180090 17011.8667
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.3517878 11615.90064 18.8661511 1982-1999 –> 2000-2012 4.597047 16007.3917
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.2781228 11517.80856 20.2126766 1982-1999 –> 2000-2012 4.568056 16003.4779
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.2514857 11481.79523 19.4800372 1982-1999 –> 2000-2012 4.616573 16118.7750
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.2781177 11517.80174 20.1739420 1982-1999 –> 2000-2012 4.583984 16036.2740
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.4170689 11701.04347 9.6831060 1982-1999 –> 2000-2012 4.999467 16732.7390
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 2.7209796 2044.74162 16.7465636 2000-2012 –> 2013-2019 5.996055 13556.4453
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.6756927 2032.64335 16.8992454 2000-2012 –> 2013-2019 5.905816 13485.3421
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.3747936 1932.43322 16.8184924 2000-2012 –> 2013-2019 5.571406 13339.0999
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.9097491 2103.08453 16.6482028 2000-2012 –> 2013-2019 6.261537 13718.9852
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.8408023 2082.94104 13.7070791 2000-2012 –> 2013-2019 6.118925 13600.7496
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.8683950 2091.06057 13.1189880 2000-2012 –> 2013-2019 6.119881 13572.8558
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.8379208 2082.08857 13.5798835 2000-2012 –> 2013-2019 6.116039 13599.8903
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate_star 2.9084827 2100.71887 11.4541160 2000-2012 –> 2013-2019 6.210359 13648.3962
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 2.5175069 1979.45442 16.2204686 2000-2012 –> 2013-2019 5.944365 13691.1249
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.3350914 1918.27125 17.8915346 2000-2012 –> 2013-2019 5.752160 13619.3147
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3742449 17785.11527 19.7700725 1982-1999 –> 2000-2012 4.014158 28300.8513
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.5191026 18245.99071 22.6025088 1982-1999 –> 2000-2012 3.866083 27681.8101
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.5458535 18328.19386 18.1627018 1982-1999 –> 2000-2012 4.191166 28861.9690
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 2.5580862 18363.49626 19.7842592 1982-1999 –> 2000-2012 4.208034 28910.7113
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3717098 17776.80138 19.9641386 1982-1999 –> 2000-2012 3.895509 27889.5183
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3699314 17770.96390 22.0826120 1982-1999 –> 2000-2012 3.791695 27503.3144
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.3725304 17779.49368 21.7326573 1982-1999 –> 2000-2012 3.788911 27491.0263
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 2.5547454 18353.32668 19.5330791 1982-1999 –> 2000-2012 4.205167 28902.1176
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3687540 17767.09676 21.9288321 1982-1999 –> 2000-2012 3.789706 27496.3125
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 2.4908191 18156.12326 24.6829920 1982-1999 –> 2000-2012 3.922036 27922.8418
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 2.4253110 3635.30015 15.3125112 2000-2012 –> 2013-2019 4.975831 21975.7464
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2.3041759 3554.75607 9.7753758 2000-2012 –> 2013-2019 4.682061 21349.7944
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.2491988 3518.79380 9.7978942 2000-2012 –> 2013-2019 4.623444 21303.9091
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.4431232 3648.80316 15.7504820 2000-2012 –> 2013-2019 4.962226 21894.7939
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.4230826 3635.85508 15.3561078 2000-2012 –> 2013-2019 4.968936 21964.0489
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.2714707 3534.28343 9.9105276 2000-2012 –> 2013-2019 4.643180 21311.0848
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.2246429 3501.53693 9.5192421 2000-2012 –> 2013-2019 4.594574 21272.5008
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.2245250 3501.45360 9.6871879 2000-2012 –> 2013-2019 4.597055 21280.9473
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.2249872 3501.78021 9.5414589 2000-2012 –> 2013-2019 4.593741 21268.8770
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 2.2499563 3517.32316 9.5658104 2000-2012 –> 2013-2019 4.740775 21673.4464
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.3565679 5589.08105 6.9535067 1982-1999 –> 2000-2012 2.253712 8126.9118
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.2984197 5445.39947 6.4801627 1982-1999 –> 2000-2012 2.113953 7797.5384
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2129656 5227.22996 6.7299404 1982-1999 –> 2000-2012 1.871257 7168.8314
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.3420440 5554.27002 7.0942827 1982-1999 –> 2000-2012 2.198812 8003.4091
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.1949278 5178.77657 6.5850604 1982-1999 –> 2000-2012 1.916780 7297.9008
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2500487 5324.61950 6.8504419 1982-1999 –> 2000-2012 1.932154 7334.6632
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.3139417 5485.83113 7.1958200 1982-1999 –> 2000-2012 2.034934 7602.6618
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.3138795 5485.67821 7.1917099 1982-1999 –> 2000-2012 2.035477 7604.1233
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.3113548 5479.45780 7.1502712 1982-1999 –> 2000-2012 2.032052 7595.4995
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.3400096 5547.36398 7.8584620 1982-1999 –> 2000-2012 2.063365 7668.4960
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.1488318 868.72630 5.0419593 2000-2012 –> 2013-2019 2.447252 6314.1258
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.0165068 803.42082 3.1798837 2000-2012 –> 2013-2019 2.229472 6030.6508
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.8806360 724.50519 3.7228068 2000-2012 –> 2013-2019 2.447088 6778.8145
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8599956 711.46079 5.0940172 2000-2012 –> 2013-2019 2.054923 5890.2374
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.0461453 819.22795 3.5405548 2000-2012 –> 2013-2019 2.296194 6143.8475
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.0755760 834.48719 3.7717337 2000-2012 –> 2013-2019 2.389518 6320.3183
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.0727121 833.02077 3.7565756 2000-2012 –> 2013-2019 2.386592 6318.6990
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.0761036 834.75691 3.7751058 2000-2012 –> 2013-2019 2.387458 6314.2147
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 1.0786442 834.05387 3.7597740 2000-2012 –> 2013-2019 2.418654 6381.4179
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.9573298 770.43217 5.6789632 2000-2012 –> 2013-2019 2.499910 6775.0780
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5256091 5692.66874 10.8737589 1982-1999 –> 2000-2012 2.569182 8708.7726
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.9002648 6369.91368 19.1051493 1982-1999 –> 2000-2012 2.891979 9281.3224
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.3019106 5203.66711 9.0765853 1982-1999 –> 2000-2012 2.222783 7962.8467
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5913110 5822.70387 11.0594737 1982-1999 –> 2000-2012 2.668254 8903.4586
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.6563898 5946.31744 11.1891375 1982-1999 –> 2000-2012 2.774910 9104.8782
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.6625235 5957.71655 11.2261613 1982-1999 –> 2000-2012 2.782621 9119.1720
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.6503799 5935.10750 11.1258276 1982-1999 –> 2000-2012 2.768213 9092.4059
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 1.7056647 6034.72323 11.9905586 1982-1999 –> 2000-2012 2.827454 9197.2800
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.5843269 5807.13886 8.3836632 1982-1999 –> 2000-2012 2.629844 8825.0655
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.5788892 5798.53573 8.5359223 1982-1999 –> 2000-2012 2.623705 8817.0844
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.1438177 744.05571 5.9924546 2000-2012 –> 2013-2019 2.669427 6436.7245
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.8515724 605.38583 4.1848260 2000-2012 –> 2013-2019 2.751837 6975.2995
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.7666199 555.99193 3.6736419 2000-2012 –> 2013-2019 2.068531 5759.6590
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2116338 771.12689 6.4619187 2000-2012 –> 2013-2019 2.802945 6593.8308
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2703568 793.37109 6.6654833 2000-2012 –> 2013-2019 2.926747 6739.6885
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.2989690 803.83943 6.8835856 2000-2012 –> 2013-2019 2.961492 6761.5560
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2598878 789.48176 6.5878827 2000-2012 –> 2013-2019 2.910268 6724.5893
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 1.4124328 841.19851 7.7469454 2000-2012 –> 2013-2019 3.118098 6875.9217
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.0964793 722.19020 6.3060746 2000-2012 –> 2013-2019 2.680806 6529.3291
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.0954227 723.73708 6.4534540 2000-2012 –> 2013-2019 2.674312 6522.2728
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.4550954 11013.43898 18.6661485 1982-1999 –> 2000-2012 8.064477 17940.3699
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.0088610 9531.40857 15.6201568 1982-1999 –> 2000-2012 5.151553 15124.4100
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.4591913 11016.90891 18.5680851 1982-1999 –> 2000-2012 8.058887 17936.9664
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.4637785 11020.79130 18.5359021 1982-1999 –> 2000-2012 8.061415 17939.3851
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.5594163 11098.83871 20.5827006 1982-1999 –> 2000-2012 8.125404 17992.8298
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.3963621 10963.32740 20.6293783 1982-1999 –> 2000-2012 7.779153 17724.4095
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.4640627 11021.03173 18.5393599 1982-1999 –> 2000-2012 8.061224 17939.2873
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.1454317 9697.02337 16.1871024 1982-1999 –> 2000-2012 5.386245 15402.5621
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.2906491 8501.59373 12.3869725 1982-1999 –> 2000-2012 3.813608 13221.2740
Atlantic (27.95,28.05] cstar_tref ~ temp + nitrate + silicate + phosphate_star 4.6124998 11142.54727 21.6977876 1982-1999 –> 2000-2012 8.105547 17983.6729
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.7052324 583.08605 2.6380008 2000-2012 –> 2013-2019 5.160328 11596.5250
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.6090338 505.06630 2.7410760 2000-2012 –> 2013-2019 3.617895 10036.4749
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.4282354 317.69557 1.7580876 2000-2012 –> 2013-2019 4.907630 11351.6739
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.7717527 631.03884 3.2511944 2000-2012 –> 2013-2019 5.230944 11647.9477
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.8233219 665.45022 3.5360274 2000-2012 –> 2013-2019 5.287100 11686.2415
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8487831 681.65306 3.5788543 2000-2012 –> 2013-2019 5.245145 11644.9805
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.8140349 659.41520 3.5104036 2000-2012 –> 2013-2019 5.278098 11680.4469
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 1.0018614 767.86467 3.4924624 2000-2012 –> 2013-2019 4.147293 10464.8880
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.8248152 666.41425 4.0059800 2000-2012 –> 2013-2019 3.115464 9168.0080
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.7112986 587.64258 3.8532384 2000-2012 –> 2013-2019 5.336360 11742.4594
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.3339554 3726.62135 9.0930907 1982-1999 –> 2000-2012 2.048873 5309.4799
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.3255248 3714.82538 8.5768042 1982-1999 –> 2000-2012 2.039678 5298.1328
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.3823460 3806.16000 8.9508089 1982-1999 –> 2000-2012 2.115333 5427.2112
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.3649815 3776.65283 8.9359361 1982-1999 –> 2000-2012 2.087687 5375.2214
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.2354271 3561.65308 9.6650488 1982-1999 –> 2000-2012 1.913368 5069.5058
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.3603360 3771.23451 8.5384560 1982-1999 –> 2000-2012 2.082165 5370.0429
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.3797191 3800.02097 8.8056306 1982-1999 –> 2000-2012 2.111005 5415.7033
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.3762430 3796.53186 8.4509691 1982-1999 –> 2000-2012 2.107077 5413.3169
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.2354727 3559.73332 9.6559647 1982-1999 –> 2000-2012 1.932109 5105.0313
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.1146372 3337.76924 8.1067583 1982-1999 –> 2000-2012 1.744671 4739.3563
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.4291476 225.15010 1.7846102 2000-2012 –> 2013-2019 1.763103 3951.7715
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.4195171 218.70700 1.7112354 2000-2012 –> 2013-2019 1.745042 3933.5324
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.4499877 244.79012 1.7810074 2000-2012 –> 2013-2019 1.832334 4050.9501
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 0.4659034 255.72009 1.9728635 2000-2012 –> 2013-2019 1.830885 4032.3729
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.3366016 136.79097 1.5570948 2000-2012 –> 2013-2019 1.572029 3698.4441
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.4484156 243.48821 1.8624228 2000-2012 –> 2013-2019 1.808752 4014.7227
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.4681852 259.53759 1.9383973 2000-2012 –> 2013-2019 1.844428 4056.0695
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.4733482 263.61742 2.3906660 2000-2012 –> 2013-2019 1.810598 3997.6065
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.4580099 249.36351 2.6788983 2000-2012 –> 2013-2019 1.693483 3809.0968
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.3431583 143.96758 2.4199022 2000-2012 –> 2013-2019 1.457796 3481.7368
Atlantic (28.1,28.15] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1.3070563 5281.30084 11.6805718 1982-1999 –> 2000-2012 1.991624 7052.9314
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2890323 5239.92190 10.1610007 1982-1999 –> 2000-2012 1.902057 6826.7865
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.3148856 5301.95783 12.4917692 1982-1999 –> 2000-2012 1.976645 7018.2538
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.3018181 5270.75581 9.9780068 1982-1999 –> 2000-2012 1.924254 6883.3978
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.3160440 5304.70901 9.8277627 1982-1999 –> 2000-2012 1.952681 6955.5194
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.3060962 5281.00535 9.9808255 1982-1999 –> 2000-2012 1.937269 6917.2336
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.1940208 5000.73188 9.4611998 1982-1999 –> 2000-2012 1.864047 6738.0331
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.3210021 5314.45632 11.2440371 1982-1999 –> 2000-2012 1.986640 7038.6403
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate 1.3282485 5331.54617 11.7999299 1982-1999 –> 2000-2012 2.046531 7184.5216
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.1193241 4798.91706 13.5869094 1982-1999 –> 2000-2012 1.624702 6059.0587
Atlantic (28.1,28.15] cstar_tref ~ aou + silicate + phosphate + phosphate_star 0.4895828 408.06216 1.7039831 2000-2012 –> 2013-2019 1.796639 5689.3630
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.4037117 299.67895 1.7095319 2000-2012 –> 2013-2019 1.775615 5732.2484
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.3856113 275.89937 1.4310718 2000-2012 –> 2013-2019 1.674644 5515.8213
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.3922726 285.52476 1.6867747 2000-2012 –> 2013-2019 1.707158 5587.4826
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.4043632 302.58522 1.4758757 2000-2012 –> 2013-2019 1.706181 5573.3410
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.4200192 323.93378 1.5314873 2000-2012 –> 2013-2019 1.736063 5628.6428
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.4178209 320.98475 1.5136772 2000-2012 –> 2013-2019 1.723917 5601.9901
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.5341289 459.00314 1.6821036 2000-2012 –> 2013-2019 1.728150 5459.7350
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 0.4126692 312.01225 1.6827518 2000-2012 –> 2013-2019 1.733671 5626.4686
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.2771681 90.32370 1.1114077 2000-2012 –> 2013-2019 1.396492 4889.2408
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 1.0048762 8438.06575 11.5293844 1982-1999 –> 2000-2012 1.652106 11389.9139
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.9937731 8374.31211 12.3479982 1982-1999 –> 2000-2012 1.640860 11327.5014
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.9600630 8168.08193 11.7993448 1982-1999 –> 2000-2012 1.614205 11151.6709
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.9555765 8142.36133 12.5573844 1982-1999 –> 2000-2012 1.601177 11088.6785
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.9583722 8159.65070 12.3221925 1982-1999 –> 2000-2012 1.610870 11137.7183
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.7654124 6829.15714 25.0683926 1982-1999 –> 2000-2012 1.549113 10354.6870
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.9576736 8153.33518 13.3268283 1982-1999 –> 2000-2012 1.669683 11390.2070
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.9653568 8200.62438 13.8491542 1982-1999 –> 2000-2012 1.691710 11497.0935
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.9572758 8152.87609 13.2107909 1982-1999 –> 2000-2012 1.668265 11387.4629
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.8182781 7224.40533 13.5294387 1982-1999 –> 2000-2012 1.621210 10822.3698
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.6358764 860.38018 2.3162524 2000-2012 –> 2013-2019 1.596021 9030.9686
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.6284098 848.03313 3.0550910 2000-2012 –> 2013-2019 1.588473 9016.1151
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.5673141 760.43649 2.1629643 2000-2012 –> 2013-2019 1.522891 8902.7978
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.5172736 679.54551 2.2423627 2000-2012 –> 2013-2019 1.475646 8839.1962
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.4842522 621.75921 1.6393860 2000-2012 –> 2013-2019 1.249665 7450.9164
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.6682826 903.92347 2.0565213 2000-2012 –> 2013-2019 1.627562 9069.1740
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.5689706 760.99054 2.2087785 2000-2012 –> 2013-2019 1.526644 8914.3257
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.5200793 682.28413 2.2713444 2000-2012 –> 2013-2019 1.485436 8882.9085
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.5159584 677.31541 2.3130401 2000-2012 –> 2013-2019 1.473234 8830.1915
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 0.7477977 1002.40453 1.7226763 2000-2012 –> 2013-2019 1.566076 8226.8099
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.6790836 12178.48882 4.5921194 1982-1999 –> 2000-2012 1.226230 16168.4505
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.6784036 12168.67486 4.5156779 1982-1999 –> 2000-2012 1.196928 15898.5425
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.6615632 11872.26055 4.3245696 1982-1999 –> 2000-2012 1.196177 15751.1882
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.6380153 11446.88016 4.6598571 1982-1999 –> 2000-2012 1.145340 15072.2337
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.6786319 12172.64357 4.4942970 1982-1999 –> 2000-2012 1.220970 16121.5480
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.6783961 12170.54493 4.5269884 1982-1999 –> 2000-2012 1.189030 15827.6076
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.6572459 11797.05538 4.5957727 1982-1999 –> 2000-2012 1.191738 15676.8736
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.7749638 13739.88315 4.4228123 1982-1999 –> 2000-2012 1.459062 18823.5170
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate 0.8108738 14272.01531 11.1403370 1982-1999 –> 2000-2012 1.532409 19613.5430
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.7986185 14094.43368 12.1243589 1982-1999 –> 2000-2012 1.510631 19373.1539
Atlantic (28.2, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate_star 0.4501223 993.95159 1.5648889 2000-2012 –> 2013-2019 1.258437 15228.6924
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.4547557 1008.15284 2.0609851 2000-2012 –> 2013-2019 1.133839 13186.6417
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.4444906 974.03342 1.9381796 2000-2012 –> 2013-2019 1.122894 13142.7083
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.4449066 975.51344 1.8686116 2000-2012 –> 2013-2019 1.106470 12847.7740
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.4267565 911.62170 1.5887800 2000-2012 –> 2013-2019 1.064772 12358.5019
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.4542792 1008.49415 1.9878249 2000-2012 –> 2013-2019 1.132911 13181.1377
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.4378294 952.14581 2.3570728 2000-2012 –> 2013-2019 1.116226 13122.6907
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.4448646 977.36411 1.8488413 2000-2012 –> 2013-2019 1.102110 12774.4195
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate 0.4698081 1061.66895 1.5717936 2000-2012 –> 2013-2019 1.280682 15333.6843
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.4182040 879.59547 1.6653982 2000-2012 –> 2013-2019 1.216822 14974.0291
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.8788276 16716.38927 24.7102565 1982-1999 –> 2000-2012 11.164825 23556.3650
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.6447816 16505.67236 22.4725361 1982-1999 –> 2000-2012 10.813017 23297.7666
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.8892665 16727.67850 44.4742950 1982-1999 –> 2000-2012 10.970776 23482.3051
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.2416255 17029.93820 23.2632894 1982-1999 –> 2000-2012 11.433970 23830.3364
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.8157682 16661.92181 26.1111201 1982-1999 –> 2000-2012 10.851627 23396.5686
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 6.3865665 17150.13657 23.5313799 1982-1999 –> 2000-2012 11.828361 24054.4234
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.0163238 16839.44063 20.8733316 1982-1999 –> 2000-2012 10.995581 23549.0619
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6.1470699 16952.01005 22.9824705 1982-1999 –> 2000-2012 11.332591 23751.4970
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.3719990 17140.17989 23.5540972 1982-1999 –> 2000-2012 11.837461 24056.0751
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6.1765125 16977.02897 23.5744309 1982-1999 –> 2000-2012 11.400750 23792.9845
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.6853690 13510.62459 23.6747249 2000-2012 –> 2013-2019 11.564197 30227.0139
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.3223262 13230.47030 23.0804439 2000-2012 –> 2013-2019 10.967108 29736.1427
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 4.2460706 12262.45145 16.0136752 2000-2012 –> 2013-2019 10.793759 29543.0446
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.2434104 12261.77165 16.4254233 2000-2012 –> 2013-2019 10.132677 28989.4502
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.9002982 11901.24386 14.3350324 2000-2012 –> 2013-2019 10.050924 28856.2818
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.0448303 13772.77495 26.1705474 2000-2012 –> 2013-2019 12.286456 30802.7132
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.5191033 13385.71024 24.6378243 2000-2012 –> 2013-2019 11.334872 30047.6320
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.7061331 13528.21298 27.5315978 2000-2012 –> 2013-2019 11.722457 30367.6536
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.8187367 13611.77284 29.5949842 2000-2012 –> 2013-2019 11.965807 30563.7829
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.8700780 13649.33638 30.2766170 2000-2012 –> 2013-2019 12.046590 30626.3654
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.1722841 15972.46228 39.8511551 1982-1999 –> 2000-2012 9.378551 24693.7801
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.5032117 15252.47754 40.4744945 1982-1999 –> 2000-2012 8.342611 23697.4538
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.0998014 15900.90632 47.2712918 1982-1999 –> 2000-2012 8.619244 24080.4918
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.1341694 15935.91265 37.7492516 1982-1999 –> 2000-2012 9.322262 24646.0238
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.6123030 15377.23436 43.9787355 1982-1999 –> 2000-2012 8.508341 23866.8756
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.7434863 15523.40518 43.8818180 1982-1999 –> 2000-2012 8.721759 24076.7534
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.1558818 15957.90777 38.9034677 1982-1999 –> 2000-2012 9.634204 24872.3781
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7693627 15551.76017 43.8495858 1982-1999 –> 2000-2012 8.760615 24115.0433
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 5.1622458 15962.33699 38.9395182 1982-1999 –> 2000-2012 9.658966 24887.3118
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.8906367 15682.63249 46.4559387 1982-1999 –> 2000-2012 8.772397 24161.0757
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.0780188 8293.58005 22.3634021 2000-2012 –> 2013-2019 9.116485 24129.4221
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.7055665 8014.76738 20.8655954 2000-2012 –> 2013-2019 8.208778 23267.2449
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.7655878 8061.87819 20.8331851 2000-2012 –> 2013-2019 8.377891 23439.1126
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.7919676 8082.34674 20.6606615 2000-2012 –> 2013-2019 8.535454 23605.7519
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.8043799 8091.92839 20.6531455 2000-2012 –> 2013-2019 8.573743 23643.6886
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.1023332 8313.00962 21.9710538 2000-2012 –> 2013-2019 8.992970 23995.6421
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4.0912940 8303.10908 22.1144132 2000-2012 –> 2013-2019 9.146066 24155.7913
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.0780046 8295.56981 22.3515988 2000-2012 –> 2013-2019 9.107144 24123.7549
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate_star 4.1027486 8311.30654 22.0525908 2000-2012 –> 2013-2019 9.229533 24237.7166
Indo-Pacific (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.1100351 8316.50913 21.9941004 2000-2012 –> 2013-2019 9.254812 24261.1792
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.8945360 14247.41268 17.3590254 1982-1999 –> 2000-2012 8.349712 20720.3256
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.5792922 13934.24644 18.7286909 1982-1999 –> 2000-2012 7.794183 20234.0052
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.0223808 14371.47698 20.2004134 1982-1999 –> 2000-2012 8.328090 20738.9299
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.6353942 13991.89142 15.3087346 1982-1999 –> 2000-2012 8.065684 20449.2389
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.7897998 14147.01208 19.2570538 1982-1999 –> 2000-2012 8.232886 20613.4071
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.8650027 14220.76149 19.1617485 1982-1999 –> 2000-2012 8.451284 20786.1739
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.8526656 14208.74137 18.4639585 1982-1999 –> 2000-2012 8.413952 20757.1583
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.8661678 14221.89511 19.0628053 1982-1999 –> 2000-2012 8.458219 20791.2137
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 4.8689786 14222.62869 18.4949663 1982-1999 –> 2000-2012 8.500870 20816.7507
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.7291174 14086.65351 15.8951232 1982-1999 –> 2000-2012 8.228443 20592.4201
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.4957027 7104.77613 19.1678607 2000-2012 –> 2013-2019 8.553330 21507.3593
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.2584428 6920.09918 16.6705200 2000-2012 –> 2013-2019 7.837735 20854.3456
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.4562515 7076.63113 14.3411426 2000-2012 –> 2013-2019 8.091646 21068.5226
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.4319686 7057.90474 18.1822538 2000-2012 –> 2013-2019 8.221768 21204.9168
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.4812795 7095.79486 18.6137498 2000-2012 –> 2013-2019 8.346282 21316.5563
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.3840924 7020.59248 19.4181539 2000-2012 –> 2013-2019 8.236758 21229.3338
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.4851419 7098.74004 18.5844497 2000-2012 –> 2013-2019 8.351310 21320.6351
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 3.5317033 7131.98914 17.1812619 2000-2012 –> 2013-2019 8.400682 21354.6178
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.5607135 7155.71703 20.9830561 2000-2012 –> 2013-2019 8.712285 21647.4267
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.1134216 6799.17921 18.0981616 2000-2012 –> 2013-2019 7.842539 20885.8327
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.6271044 19894.96076 13.2410188 1982-1999 –> 2000-2012 8.010945 29429.9597
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.3375013 19459.46470 15.1634098 1982-1999 –> 2000-2012 7.506199 28757.3205
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.3368038 19460.38112 15.3154320 1982-1999 –> 2000-2012 7.457257 28704.8502
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.4883426 19691.80368 13.9921590 1982-1999 –> 2000-2012 7.599424 28925.4147
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.2495218 19323.38982 21.2569544 1982-1999 –> 2000-2012 7.375870 28574.6728
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.7944639 20134.36615 18.5516358 1982-1999 –> 2000-2012 8.006388 29481.1355
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.7734236 20106.73166 17.5713226 1982-1999 –> 2000-2012 7.983665 29453.6096
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.6816206 19975.88328 16.3311968 1982-1999 –> 2000-2012 7.958048 29396.4314
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.3829499 19529.69857 22.4963529 1982-1999 –> 2000-2012 7.656452 28945.0227
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.3819085 19530.09744 22.5534439 1982-1999 –> 2000-2012 7.606324 28892.8787
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.8974123 9783.84771 13.1476264 2000-2012 –> 2013-2019 8.524517 29678.8085
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.1580082 10011.41505 14.0131777 2000-2012 –> 2013-2019 8.495510 29470.8798
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.8515106 9744.19232 12.4088939 2000-2012 –> 2013-2019 8.188314 29204.5734
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.9424165 9826.21512 16.0460137 2000-2012 –> 2013-2019 8.191938 29149.6049
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.9480880 9836.85390 13.6483393 2000-2012 –> 2013-2019 8.533722 29673.1538
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.9928745 9870.92996 14.0974714 2000-2012 –> 2013-2019 8.713075 29902.1113
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.9786142 9858.35035 13.9274083 2000-2012 –> 2013-2019 8.662209 29837.0751
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.0069208 9883.27698 14.1524460 2000-2012 –> 2013-2019 8.688541 29859.1603
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.0075434 9881.82322 17.1289126 2000-2012 –> 2013-2019 8.390493 29411.5218
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.8154542 9711.12179 14.9440193 2000-2012 –> 2013-2019 8.197363 29241.2192
Indo-Pacific (27,27.25] cstar_tref ~ aou + phosphate + phosphate_star 5.1272710 27045.79598 31.1002502 1982-1999 –> 2000-2012 8.022031 37702.8930
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.9061541 26657.48335 26.7325621 1982-1999 –> 2000-2012 7.800463 37315.9116
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.0992462 26999.26883 32.3831587 1982-1999 –> 2000-2012 7.898574 37514.5516
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.8750894 26603.24358 28.0171555 1982-1999 –> 2000-2012 7.674404 37120.5061
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.4464941 27584.56487 31.9461789 1982-1999 –> 2000-2012 7.930782 37589.6512
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.1175553 25107.99035 24.7855935 1982-1999 –> 2000-2012 6.873540 35558.3310
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate_star 5.4551094 27596.55909 32.7696363 1982-1999 –> 2000-2012 7.988130 37682.9850
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.1088926 27018.00237 28.9822154 1982-1999 –> 2000-2012 7.635904 37096.2389
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.1496432 25174.72176 23.5155063 1982-1999 –> 2000-2012 6.971702 35724.7007
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.5598114 23819.27256 15.9687197 1982-1999 –> 2000-2012 6.371953 34356.1491
Indo-Pacific (27,27.25] cstar_tref ~ aou + phosphate + phosphate_star 4.9486070 15534.82169 20.3416770 2000-2012 –> 2013-2019 10.075878 42580.6177
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.8524808 15435.91678 19.0689871 2000-2012 –> 2013-2019 9.758635 42093.4001
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.8184140 15399.67606 21.9017060 2000-2012 –> 2013-2019 9.917660 42398.9449
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.7571383 15335.84034 20.6677390 2000-2012 –> 2013-2019 9.632228 41939.0839
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.2854132 14798.65599 19.8816771 2000-2012 –> 2013-2019 8.402969 39906.6463
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.8045283 15386.83061 21.2785181 2000-2012 –> 2013-2019 9.947149 42463.0929
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.8162235 15399.33701 21.3934631 2000-2012 –> 2013-2019 10.081910 42684.9849
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.9657540 15556.61498 17.9612885 2000-2012 –> 2013-2019 10.074647 42574.6173
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.3845451 14914.29362 18.5285404 2000-2012 –> 2013-2019 8.534188 40089.0154
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.9757965 14412.89780 16.0587779 2000-2012 –> 2013-2019 7.535608 38232.1704
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.3848794 29968.76777 11.0720416 1982-1999 –> 2000-2012 5.931237 42729.8785
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.7814759 31224.74693 16.1463953 1982-1999 –> 2000-2012 6.395053 44124.9772
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5814452 30609.68000 11.8352381 1982-1999 –> 2000-2012 6.153868 43425.9487
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 3.5873833 30626.48934 11.7071771 1982-1999 –> 2000-2012 6.323636 43775.1481
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.6420608 30798.23726 12.7423962 1982-1999 –> 2000-2012 6.338487 43867.4869
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5251580 30429.81953 11.3555983 1982-1999 –> 2000-2012 6.134025 43322.2807
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.5671158 30564.16126 11.8020452 1982-1999 –> 2000-2012 6.247353 43602.7957
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.5439747 30490.26393 11.5691907 1982-1999 –> 2000-2012 6.210170 43500.4492
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.9454438 31708.69083 15.1038103 1982-1999 –> 2000-2012 6.213448 43842.8249
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.1055927 28991.03277 18.1092286 1982-1999 –> 2000-2012 5.277244 40890.0471
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.4534928 18165.04078 12.1670983 2000-2012 –> 2013-2019 6.838372 48133.8085
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.9332582 19051.24073 13.8690039 2000-2012 –> 2013-2019 7.714734 50275.9877
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5440853 18341.84489 14.4077540 2000-2012 –> 2013-2019 7.125531 48951.5249
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate_star 3.6426960 18527.23214 13.1181427 2000-2012 –> 2013-2019 7.230079 49153.7215
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 3.8243938 18859.59125 12.6599691 2000-2012 –> 2013-2019 7.466455 49657.8285
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.4889740 18234.83379 13.9696458 2000-2012 –> 2013-2019 7.014132 48664.6533
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.5127982 18281.29976 14.3170633 2000-2012 –> 2013-2019 7.079914 48845.4610
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate 3.5128411 18279.38312 15.5360695 2000-2012 –> 2013-2019 7.506069 50122.7589
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.4921618 18241.06943 14.1039559 2000-2012 –> 2013-2019 7.036136 48731.3334
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.4011722 18060.80464 15.1116820 2000-2012 –> 2013-2019 6.506765 47051.8374
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.2060797 34205.32181 16.1165127 1982-1999 –> 2000-2012 5.236692 47246.7579
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.0241735 33432.42665 10.6465044 1982-1999 –> 2000-2012 5.257381 47056.2655
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3.2443712 34360.42069 15.2302073 1982-1999 –> 2000-2012 5.494044 48027.2467
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.2154899 34244.10260 12.3691526 1982-1999 –> 2000-2012 5.552832 48147.0464
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.9884236 33275.07418 10.1176771 1982-1999 –> 2000-2012 5.209188 46864.6948
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.9972234 33313.98033 10.2433594 1982-1999 –> 2000-2012 5.246259 46981.0716
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.4538395 35190.28016 20.2840591 1982-1999 –> 2000-2012 5.504505 48291.8996
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 2.9905721 33282.58365 10.2297238 1982-1999 –> 2000-2012 5.341173 47218.1685
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.9889979 33277.61687 10.1421194 1982-1999 –> 2000-2012 5.233648 46932.7532
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.0421573 33510.87985 20.5245758 1982-1999 –> 2000-2012 5.078814 46570.5186
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 3.4912150 20812.31553 11.8470025 2000-2012 –> 2013-2019 6.697295 55017.6373
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.8040309 19104.37283 12.8427971 2000-2012 –> 2013-2019 5.828204 52536.7995
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3.5389071 20916.03854 11.7486107 2000-2012 –> 2013-2019 6.783278 55276.4592
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8182534 19143.79534 14.0538853 2000-2012 –> 2013-2019 6.033743 53387.8979
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate 2.8344254 19186.38030 14.6028909 2000-2012 –> 2013-2019 6.106937 53661.0756
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.7904199 19066.45792 12.3385782 2000-2012 –> 2013-2019 5.778844 52341.5321
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.7912594 19068.80155 12.3967568 2000-2012 –> 2013-2019 5.788483 52382.7819
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.0642350 19793.83464 8.6039584 2000-2012 –> 2013-2019 6.054807 53076.4183
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.7887743 19061.86119 12.2782252 2000-2012 –> 2013-2019 5.777772 52339.4781
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.5488965 20940.00229 14.5586275 2000-2012 –> 2013-2019 6.591054 54450.8821
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.0020270 13116.84949 8.4128587 1982-1999 –> 2000-2012 4.646451 17996.3243
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.9316135 12995.33363 9.8665209 1982-1999 –> 2000-2012 4.557179 17847.5111
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.0327255 13171.79497 7.1653693 1982-1999 –> 2000-2012 4.492929 17751.4823
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.1691461 13400.77335 9.0529633 1982-1999 –> 2000-2012 4.456443 17660.3404
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.9300222 12992.50810 9.6105624 1982-1999 –> 2000-2012 4.606634 17923.2207
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.9297975 12992.10908 9.5068443 1982-1999 –> 2000-2012 4.634454 17964.9559
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.9297671 12992.05509 9.4494442 1982-1999 –> 2000-2012 4.641085 17974.8089
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.9798968 13080.34476 8.1158384 1982-1999 –> 2000-2012 4.528911 17810.0002
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.2292613 13496.56294 8.4669179 1982-1999 –> 2000-2012 4.516832 17754.6696
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.9935809 13104.18755 7.6294875 1982-1999 –> 2000-2012 4.276829 17355.7539
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5122401 7113.90392 9.6533539 2000-2012 –> 2013-2019 5.443854 20109.2376
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.8927197 7541.76561 8.5735240 2000-2012 –> 2013-2019 5.925445 20713.5606
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8717147 7519.65436 10.5831602 2000-2012 –> 2013-2019 5.858344 20611.7429
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5262216 7130.74241 9.1131126 2000-2012 –> 2013-2019 5.456244 20123.2505
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.5307179 7136.13763 8.9482479 2000-2012 –> 2013-2019 5.460515 20128.2467
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.5335899 7139.57883 8.8566147 2000-2012 –> 2013-2019 5.463357 20131.6339
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.9401276 7591.08584 9.5053416 2000-2012 –> 2013-2019 5.920024 20671.4306
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.9121242 7562.04991 9.1004241 2000-2012 –> 2013-2019 5.905705 20666.2375
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate_star 2.9539853 7603.35245 9.5384459 2000-2012 –> 2013-2019 5.953542 20715.9181
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2.9515129 7600.81195 9.5251173 2000-2012 –> 2013-2019 5.950261 20711.9752
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate 2.9439987 15763.85083 12.4143678 1982-1999 –> 2000-2012 4.681823 21205.5608
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.9425239 15762.69199 12.2302547 1982-1999 –> 2000-2012 4.665761 21183.1886
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 2.9972509 15876.86094 11.7573905 1982-1999 –> 2000-2012 4.645333 21172.5499
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.9968713 15878.06255 11.6991105 1982-1999 –> 2000-2012 4.585532 21074.6222
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.9395547 15756.32764 12.1720814 1982-1999 –> 2000-2012 4.566183 21017.9312
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.2963064 16478.41586 17.9003963 1982-1999 –> 2000-2012 4.668008 21270.5802
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.0084886 15900.45258 11.4861017 1982-1999 –> 2000-2012 4.692867 21256.1354
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.9597782 15799.54923 11.8690724 1982-1999 –> 2000-2012 4.643145 21155.5775
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.3097304 16502.03633 17.7211518 1982-1999 –> 2000-2012 4.685803 21300.9627
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.1542854 16200.78405 17.1829443 1982-1999 –> 2000-2012 4.504044 20948.5356
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + silicate + phosphate_star 2.9868284 9164.89461 10.1207112 2000-2012 –> 2013-2019 5.948252 24965.9465
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate 2.9252623 9087.03918 11.6244412 2000-2012 –> 2013-2019 5.923050 24963.0284
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.8715322 9021.52233 14.3166435 2000-2012 –> 2013-2019 5.869318 24899.5089
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate 2.9198871 9082.34084 11.4921145 2000-2012 –> 2013-2019 5.863886 24846.1917
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.8481123 8993.69689 14.5983138 2000-2012 –> 2013-2019 5.790636 24756.3889
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 2.8674795 9016.37871 12.0637520 2000-2012 –> 2013-2019 5.864730 24893.2397
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.8604062 9009.38378 13.3126745 2000-2012 –> 2013-2019 5.857278 24887.4463
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.7930108 8922.54572 11.8257838 2000-2012 –> 2013-2019 5.732565 24678.8734
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 2.9812457 9158.08086 10.6000925 2000-2012 –> 2013-2019 5.941312 24956.2433
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.9749384 9152.36756 11.8702656 2000-2012 –> 2013-2019 5.934717 24951.9168
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.7129068 15136.70313 8.4831831 1982-1999 –> 2000-2012 3.549719 22040.4023
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.6842950 15008.52718 8.4784051 1982-1999 –> 2000-2012 3.501198 21877.1715
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate 1.6507753 14851.17867 8.5824558 1982-1999 –> 2000-2012 3.423110 21633.3821
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.6504798 14851.79528 8.5203422 1982-1999 –> 2000-2012 3.407031 21605.5845
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.6061006 14641.15468 8.5984924 1982-1999 –> 2000-2012 3.327053 21325.3311
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.6886702 15028.57588 8.5486172 1982-1999 –> 2000-2012 3.367080 21627.6467
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.6978511 15070.47733 8.4606304 1982-1999 –> 2000-2012 3.542319 21990.3171
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.7023273 15090.82439 8.4183323 1982-1999 –> 2000-2012 3.557153 22029.7034
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 1.7403070 15259.34461 10.4004200 1982-1999 –> 2000-2012 3.421055 21861.1487
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.6586609 14890.00689 9.0156615 1982-1999 –> 2000-2012 3.201801 21203.3827
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5832896 8286.66417 9.1473557 2000-2012 –> 2013-2019 3.267585 23295.1914
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate 1.6125704 8365.36613 11.2159046 2000-2012 –> 2013-2019 3.263346 23216.5448
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.5969718 8324.55821 10.1906284 2000-2012 –> 2013-2019 3.247452 23176.3535
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.5363563 8154.14270 9.7433999 2000-2012 –> 2013-2019 3.142457 22795.2974
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.6522119 8474.31945 10.4855832 2000-2012 –> 2013-2019 3.340882 23502.8953
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5861329 8294.56560 9.0977828 2000-2012 –> 2013-2019 3.283984 23365.0429
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5868838 8296.65027 9.0695503 2000-2012 –> 2013-2019 3.289211 23387.4747
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5865283 8295.66334 8.5945618 2000-2012 –> 2013-2019 3.324705 23547.5448
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5869380 8296.80046 9.0624015 2000-2012 –> 2013-2019 3.290603 23393.6936
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.6367966 8433.03690 9.7696994 2000-2012 –> 2013-2019 3.295457 23323.0438
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1.6301531 8386.41877 8.4075126 1982-1999 –> 2000-2012 3.194768 12381.6961
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5359575 8127.12615 7.2494345 1982-1999 –> 2000-2012 3.078983 12094.7531
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.5801895 8251.76168 8.0261139 1982-1999 –> 2000-2012 3.190652 12310.6727
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5426004 8146.07166 7.3145744 1982-1999 –> 2000-2012 3.096396 12128.5423
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5447871 8152.29014 7.3457551 1982-1999 –> 2000-2012 3.103066 12140.9089
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5441104 8150.36681 7.3600899 1982-1999 –> 2000-2012 3.091018 12123.3564
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5446596 8151.92784 7.3417904 1982-1999 –> 2000-2012 3.102034 12139.3069
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 1.5461457 8154.14926 7.4026344 1982-1999 –> 2000-2012 3.127578 12172.2428
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate 1.6509297 8442.01641 8.5271739 1982-1999 –> 2000-2012 3.231705 12459.2226
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.5073086 8044.46994 6.4785885 1982-1999 –> 2000-2012 2.931331 11840.8225
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 1.4057043 4396.61666 8.1565303 2000-2012 –> 2013-2019 3.035857 12783.0354
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.3010438 4205.80672 6.0878618 2000-2012 –> 2013-2019 2.837001 12332.9329
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.3134709 4229.49632 5.6581916 2000-2012 –> 2013-2019 2.893660 12481.2580
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.3043983 4212.22348 6.0453500 2000-2012 –> 2013-2019 2.846999 12358.2951
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.3053374 4214.01708 6.0318147 2000-2012 –> 2013-2019 2.850125 12366.3072
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.3044599 4212.34131 6.0190625 2000-2012 –> 2013-2019 2.848570 12362.7081
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 1.3526890 4300.81416 4.9670454 2000-2012 –> 2013-2019 3.045676 12853.2636
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.3050972 4213.55846 6.0249300 2000-2012 –> 2013-2019 2.849757 12365.4863
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 1.3208040 4241.37059 6.9545356 2000-2012 –> 2013-2019 2.866950 12395.5199
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.3038982 4211.26789 6.7565463 2000-2012 –> 2013-2019 2.811207 12255.7378
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.5873437 89274.99992 9.7500059 1982-1999 –> 2000-2012 3.233193 135416.7068
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.5848976 89199.81705 10.0617134 1982-1999 –> 2000-2012 3.003301 131761.2118
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5424042 87912.13817 9.5209242 1982-1999 –> 2000-2012 2.857471 128655.5318
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5425430 87916.40796 9.5219774 1982-1999 –> 2000-2012 2.856820 128645.3420
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5426882 87920.87526 9.5229429 1982-1999 –> 2000-2012 2.855968 128631.5437
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5490514 88116.20896 9.2452570 1982-1999 –> 2000-2012 2.876643 129087.6737
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5426778 87920.55485 9.5231863 1982-1999 –> 2000-2012 2.856002 128632.0510
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.5491568 88117.43652 9.1927832 1982-1999 –> 2000-2012 2.878439 129117.5097
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.4861751 86149.85882 7.4928876 1982-1999 –> 2000-2012 2.803095 126927.1285
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.5793562 89035.60813 9.4267114 1982-1999 –> 2000-2012 3.034699 132217.5815
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.4706222 53629.38304 8.6388573 2000-2012 –> 2013-2019 3.057966 142904.3830
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.3484194 51049.96500 8.6530985 2000-2012 –> 2013-2019 2.933317 140249.7820
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2967733 49891.67118 9.4901170 2000-2012 –> 2013-2019 2.839177 137803.8094
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2971131 49899.45571 9.4905403 2000-2012 –> 2013-2019 2.839656 137815.8637
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2975674 49909.86077 9.4937692 2000-2012 –> 2013-2019 2.840256 137830.7360
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.3092860 50176.97187 9.7211962 2000-2012 –> 2013-2019 2.858337 138293.1808
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2975212 49908.80146 9.4926591 2000-2012 –> 2013-2019 2.840199 137829.3563
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.3254741 50540.05605 10.3712645 2000-2012 –> 2013-2019 2.874631 138657.4926
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.4284939 52765.86376 11.8019856 2000-2012 –> 2013-2019 2.914669 138915.7226
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.3512909 51115.16667 9.9517102 2000-2012 –> 2013-2019 2.930647 140150.7748

5.3 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)

5.4 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)
            
            p_model <- 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,
              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)
            
          }
          
        }
        
      }
    }
  }
  
  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/

5.5 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)

5.6 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
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
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
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
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] 8 3 6 8 8 7 9
(26,26.5] 7 5 4 8 7 9 9
(26.5,26.75] 8 1 7 8 4 10 8
(26.75,27] 8 1 7 8 4 10 8
(27,27.25] 8 4 5 7 8 10 7
(27.25,27.5] 8 4 5 7 9 8 8
(27.5,27.75] 6 2 5 9 10 6 9
(27.75,27.85] 7 3 5 7 10 9 7
(27.85,27.95] 7 2 6 9 8 7 9
(27.95,28.05] 6 6 3 9 7 7 9
(28.05,28.1] 8 1 9 8 8 4 8
(28.1,28.15] 9 1 8 8 5 8 8
(28.15,28.2] 10 8 2 7 6 5 8
(28.2, Inf] 9 10 0 5 8 6 6
total 109.00 51.00 72.00 108.00 102.00 106.00 113.00
Atlantic - 2000-2012 --> 2013-2019
(26,26.5] 8 6 3 7 9 8 8
(26.5,26.75] 8 1 7 8 4 10 8
(26.75,27] 9 2 6 8 7 10 5
(27,27.25] 9 4 4 6 8 10 6
(27.25,27.5] 7 6 2 6 8 10 8
(27.5,27.75] 7 2 6 8 10 7 7
(27.75,27.85] 7 2 6 8 9 8 8
(27.85,27.95] 7 2 6 9 8 7 9
(27.95,28.05] 8 4 5 9 7 7 9
(28.05,28.1] 9 2 8 8 7 5 8
(28.1,28.15] 9 1 8 9 6 7 7
(28.15,28.2] 9 7 3 7 6 6 9
(28.2, Inf] 10 10 0 5 7 6 5
total 107.00 49.00 64.00 98.00 96.00 101.00 97.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 8 2 6 8 10 5 8
(26,26.5] 7 3 5 9 9 7 8
(26.5,26.75] 7 2 6 9 9 7 8
(26.75,27] 8 4 6 10 6 5 7
(27,27.25] 10 3 7 10 4 4 6
(27.25,27.5] 8 2 6 8 8 10 5
(27.5,27.75] 7 3 5 7 9 10 7
(27.75,27.85] 9 2 7 9 6 7 8
(27.85,27.95] 10 7 3 7 6 5 8
(27.95,28.05] 10 3 6 7 8 5 8
(28.05,28.1] 7 2 6 7 7 10 8
(28.1, Inf] 7 3 5 8 8 10 7
total 98.00 36.00 68.00 99.00 90.00 85.00 88.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 9 3 6 6 10 5 8
(26,26.5] 8 1 7 8 4 10 8
(26.5,26.75] 7 2 6 9 7 9 8
(26.75,27] 9 1 8 9 6 7 7
(27,27.25] 9 1 9 9 5 6 6
(27.25,27.5] 7 1 7 7 9 10 5
(27.5,27.75] 8 2 5 6 9 10 7
(27.75,27.85] 8 3 5 8 6 9 9
(27.85,27.95] 10 10 0 5 7 6 5
(27.95,28.05] 8 4 5 7 9 7 9
(28.05,28.1] 6 2 6 7 8 10 8
(28.1, Inf] 7 3 5 8 8 10 7
total 96.00 33.00 69.00 89.00 88.00 99.00 87.00

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
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
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] 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