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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
        }
        
        # # plot model diagnostics, if activated
        # if (params_local$plot_all_figures == "y") {
        #   p_model <- ggnostic(
        #     i_lm_fit,
        #     columnsY = c(params_local$MLR_target, ".fitted", ".resid"),
        #     title = paste(
        #       "| era:",
        #       i_era,
        #       "| 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_basin,
        #       i_gamma_slab,
        #       i_predictors,
        #       "predictors.png",
        #       sep = "_"
        #     ),
        #     width = 14,
        #     height = 8
        #   )
        #   
        #   rm(p_model)
        #   
        # }
        
      }
      
      
    }
  }
  
}

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 + temp + aou + nitrate + phosphate_star 10.5575872 28626.886 63.050056 1982-1999 –> 2000-2012 21.1931930 67864.543
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 10.7281865 28746.359 91.140123 1982-1999 –> 2000-2012 21.6160774 68225.082
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 10.7062203 28732.827 86.310318 1982-1999 –> 2000-2012 21.5857949 68205.628
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 10.7107430 28734.028 85.842165 1982-1999 –> 2000-2012 21.6001123 68214.158
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 10.5667578 28633.465 71.794012 1982-1999 –> 2000-2012 21.1806255 67849.910
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10.5828372 28644.988 70.204395 1982-1999 –> 2000-2012 21.2458817 67909.359
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 10.5582716 28625.377 61.749332 1982-1999 –> 2000-2012 21.2127741 67879.439
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10.5582548 28627.365 61.878811 1982-1999 –> 2000-2012 21.1882927 67859.593
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 10.7063014 28730.885 86.366762 1982-1999 –> 2000-2012 21.5874871 68203.221
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10.5661938 28633.061 70.073531 1982-1999 –> 2000-2012 21.2082466 67877.001
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 10.4171268 15018.410 43.672382 2000-2012 –> 2013-2019 20.9747140 43645.296
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 10.6087022 15089.085 80.966971 2000-2012 –> 2013-2019 21.3368886 43835.445
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 10.5576078 15071.832 67.399599 2000-2012 –> 2013-2019 21.2638281 43804.659
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 10.5584420 15070.147 68.292053 2000-2012 –> 2013-2019 21.2691850 43804.175
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 10.4897132 15046.102 58.713059 2000-2012 –> 2013-2019 21.0564710 43679.568
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10.4540542 15032.522 47.864414 2000-2012 –> 2013-2019 21.0368914 43677.511
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 10.4329430 15022.461 43.266261 2000-2012 –> 2013-2019 20.9912146 43647.838
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10.4183847 15018.892 45.400115 2000-2012 –> 2013-2019 20.9766395 43646.257
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 10.5719619 15075.250 71.114915 2000-2012 –> 2013-2019 21.2782633 43806.135
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10.4557916 15033.185 49.503350 2000-2012 –> 2013-2019 21.0219854 43666.246
Atlantic (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 6.3562108 21439.440 26.744973 1982-1999 –> 2000-2012 13.0316619 51825.328
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.3279771 21412.254 31.468879 1982-1999 –> 2000-2012 12.9893953 51780.875
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.9122873 20966.788 29.944245 1982-1999 –> 2000-2012 12.0905428 50645.994
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 6.0966811 21168.134 50.531465 1982-1999 –> 2000-2012 12.7381104 51509.239
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.3322879 21416.719 29.951410 1982-1999 –> 2000-2012 12.9523194 51728.276
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 6.1712906 21245.878 31.111428 1982-1999 –> 2000-2012 12.5921151 51275.687
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 6.4040328 21488.580 39.376408 1982-1999 –> 2000-2012 13.3127267 52188.921
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6.1303087 21204.196 33.570072 1982-1999 –> 2000-2012 12.5185407 51189.410
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 6.4607837 21546.422 34.664582 1982-1999 –> 2000-2012 13.1931417 52010.033
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6.3473228 21432.266 27.073796 1982-1999 –> 2000-2012 12.9997416 51788.509
Atlantic (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 6.2476084 11371.474 30.426723 2000-2012 –> 2013-2019 12.6038192 32810.914
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.1974492 11345.309 30.004666 2000-2012 –> 2013-2019 12.5254263 32757.563
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 5.7676016 11094.155 34.681519 2000-2012 –> 2013-2019 11.6798889 32060.943
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 5.8961710 11171.186 40.664822 2000-2012 –> 2013-2019 11.9928521 32339.321
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.2202901 11358.162 32.702388 2000-2012 –> 2013-2019 12.5525779 32774.881
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 6.0682459 11269.696 34.705115 2000-2012 –> 2013-2019 12.2395365 32515.574
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 6.3435259 11424.708 40.936824 2000-2012 –> 2013-2019 12.7475587 32913.289
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6.0452855 11258.451 36.762483 2000-2012 –> 2013-2019 12.1755942 32462.647
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 6.3539826 11430.463 37.327750 2000-2012 –> 2013-2019 12.8147663 32976.885
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6.2434346 11371.139 30.012859 2000-2012 –> 2013-2019 12.5907574 32803.405
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 4.6047453 14865.863 60.745482 1982-1999 –> 2000-2012 8.8109029 35174.672
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.4483741 14693.668 70.217322 1982-1999 –> 2000-2012 8.4450488 34641.352
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.4527212 14698.593 69.463219 1982-1999 –> 2000-2012 8.4425140 34634.027
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.5510964 14808.774 67.576840 1982-1999 –> 2000-2012 8.6345026 34909.059
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.5852616 14846.483 67.218401 1982-1999 –> 2000-2012 8.7113205 35020.628
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.4756104 14724.445 70.432781 1982-1999 –> 2000-2012 8.5104971 34739.765
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 4.5417654 14796.426 75.569129 1982-1999 –> 2000-2012 8.5834981 34821.796
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.5372065 14793.363 74.368914 1982-1999 –> 2000-2012 8.5787069 34820.324
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 4.5771077 14835.509 70.879808 1982-1999 –> 2000-2012 8.6749224 34958.830
Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.6022314 14863.109 69.903673 1982-1999 –> 2000-2012 8.7361500 35048.781
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 4.3402383 7448.571 33.587810 2000-2012 –> 2013-2019 8.9449836 22314.434
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.1512783 7335.906 32.158850 2000-2012 –> 2013-2019 8.5996524 22029.574
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.1602854 7341.489 31.728400 2000-2012 –> 2013-2019 8.6130066 22040.082
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.2653099 7405.712 31.320320 2000-2012 –> 2013-2019 8.8164063 22214.486
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.2952576 7423.735 31.225822 2000-2012 –> 2013-2019 8.8805192 22270.219
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.1395505 7328.618 30.758464 2000-2012 –> 2013-2019 8.6151608 22053.063
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 4.2442711 7390.974 30.318794 2000-2012 –> 2013-2019 8.7860365 22187.401
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.2420743 7391.641 30.352636 2000-2012 –> 2013-2019 8.7792808 22185.003
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 4.2897259 7418.416 30.541763 2000-2012 –> 2013-2019 8.8668336 22253.925
Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.3122752 7431.921 30.576652 2000-2012 –> 2013-2019 8.9145065 22295.030
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 4.3227416 19782.437 38.757627 1982-1999 –> 2000-2012 8.2483296 45273.779
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.2118340 19606.186 47.675501 1982-1999 –> 2000-2012 7.9061586 44544.319
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.2280846 19632.596 46.066303 1982-1999 –> 2000-2012 7.9084620 44536.142
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.3366244 19806.427 43.563215 1982-1999 –> 2000-2012 8.1272166 44979.784
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.3634965 19848.791 42.991539 1982-1999 –> 2000-2012 8.1932439 45116.118
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.1043003 19428.818 43.603172 1982-1999 –> 2000-2012 7.7653558 44284.232
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 4.3435969 19815.444 53.665333 1982-1999 –> 2000-2012 8.0637397 44815.258
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.3423066 19815.407 52.902440 1982-1999 –> 2000-2012 8.0624115 44817.128
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 4.3872927 19884.090 48.570324 1982-1999 –> 2000-2012 8.1836189 45069.269
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.4064686 19913.999 47.637651 1982-1999 –> 2000-2012 8.2389166 45185.771
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 4.7695924 10839.716 35.820712 2000-2012 –> 2013-2019 9.0923340 30622.153
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.6217587 10727.361 34.967751 2000-2012 –> 2013-2019 8.8335928 30333.547
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.6664250 10762.293 35.035558 2000-2012 –> 2013-2019 8.8945096 30394.889
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.7963549 10862.039 36.931724 2000-2012 –> 2013-2019 9.1329793 30668.465
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.8186438 10878.878 36.865139 2000-2012 –> 2013-2019 9.1821402 30727.669
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.4891769 10621.648 38.253473 2000-2012 –> 2013-2019 8.5934773 30050.466
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 4.7386197 10816.054 34.713094 2000-2012 –> 2013-2019 9.0822166 30631.498
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.7336343 10814.231 36.217124 2000-2012 –> 2013-2019 9.0759409 30629.637
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 4.8223668 10879.683 36.392816 2000-2012 –> 2013-2019 9.2096594 30763.772
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.8406928 10893.459 36.436307 2000-2012 –> 2013-2019 9.2471614 30807.458
Atlantic (27,27.25] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.3444381 17737.531 50.679824 1982-1999 –> 2000-2012 8.2624310 40894.445
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 4.1948171 17522.414 54.044256 1982-1999 –> 2000-2012 8.1026093 40657.660
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.1946913 17524.230 54.188144 1982-1999 –> 2000-2012 7.9904979 40419.799
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.2327958 17579.736 56.741844 1982-1999 –> 2000-2012 8.1010474 40632.449
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.3384582 17731.076 50.812169 1982-1999 –> 2000-2012 8.2352975 40844.992
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.1928022 17521.465 54.605258 1982-1999 –> 2000-2012 7.9668389 40369.225
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.2278926 17572.622 53.699230 1982-1999 –> 2000-2012 8.0866619 40604.934
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.2316534 17578.079 53.399902 1982-1999 –> 2000-2012 8.1449470 40727.018
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.2288793 17574.054 53.644800 1982-1999 –> 2000-2012 8.1022802 40637.824
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.2908732 17663.382 65.993236 1982-1999 –> 2000-2012 8.1507801 40698.144
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 4.4709997 10214.094 29.072108 2000-2012 –> 2013-2019 8.6658168 27736.508
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.4697970 10215.153 29.099359 2000-2012 –> 2013-2019 8.6644883 27739.383
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.5634306 10287.672 30.547406 2000-2012 –> 2013-2019 8.7962264 27867.408
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.4709902 10216.086 29.071105 2000-2012 –> 2013-2019 8.6637925 27737.552
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.5756236 10297.006 28.590405 2000-2012 –> 2013-2019 8.8035162 27869.628
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.7429078 10420.610 28.629047 2000-2012 –> 2013-2019 9.0842640 28153.785
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.5441879 10272.891 28.334256 2000-2012 –> 2013-2019 8.7758413 27850.970
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.5691046 10292.019 28.560550 2000-2012 –> 2013-2019 8.7979839 27866.073
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate_star 4.6333214 10338.839 29.786712 2000-2012 –> 2013-2019 8.8655583 27915.765
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.5017562 10240.075 31.843798 2000-2012 –> 2013-2019 8.7926294 27903.456
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.6010043 21078.164 66.623050 1982-1999 –> 2000-2012 8.7069871 49757.093
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 4.6357762 21130.012 65.153780 1982-1999 –> 2000-2012 8.7571162 49844.736
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.5997102 21076.153 65.093949 1982-1999 –> 2000-2012 8.6996926 49740.275
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate_star 4.6093296 21089.094 65.051249 1982-1999 –> 2000-2012 8.7368965 49819.102
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.5748236 21037.352 66.117157 1982-1999 –> 2000-2012 8.6771734 49707.318
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.5800589 21045.532 65.725573 1982-1999 –> 2000-2012 8.7033026 49766.930
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.6013778 21076.745 66.298307 1982-1999 –> 2000-2012 8.7290631 49807.043
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.5733877 21035.107 66.695731 1982-1999 –> 2000-2012 8.6984521 49760.975
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.6052139 21082.705 65.069815 1982-1999 –> 2000-2012 8.7328764 49812.948
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.5751809 21037.910 65.750075 1982-1999 –> 2000-2012 8.6992529 49761.343
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.9274130 11616.948 31.774392 2000-2012 –> 2013-2019 9.5649112 32751.616
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.8516041 11557.255 33.173612 2000-2012 –> 2013-2019 9.4526084 32635.419
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.9486455 11633.502 29.447767 2000-2012 –> 2013-2019 9.5483558 32709.654
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate_star 4.9528550 11634.775 29.443309 2000-2012 –> 2013-2019 9.5621846 32723.869
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.8777740 11577.966 31.341619 2000-2012 –> 2013-2019 9.4525976 32615.318
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.8844560 11583.236 30.885449 2000-2012 –> 2013-2019 9.4645149 32628.768
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 4.8872013 11583.400 31.033132 2000-2012 –> 2013-2019 9.4885792 32660.145
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.8297779 11539.895 32.085999 2000-2012 –> 2013-2019 9.4031655 32575.002
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.9491063 11631.860 29.448342 2000-2012 –> 2013-2019 9.5543203 32714.565
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.8759909 11576.558 30.932150 2000-2012 –> 2013-2019 9.4511718 32614.469
Atlantic (27.5,27.75] cstar_tref ~ aou + phosphate + phosphate_star 4.4487249 27139.879 25.581396 1982-1999 –> 2000-2012 8.3078807 61988.768
Atlantic (27.5,27.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.3908580 27019.880 28.326933 1982-1999 –> 2000-2012 8.2499962 61870.711
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.1191019 26424.558 25.729881 1982-1999 –> 2000-2012 7.9371014 61140.565
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.1070637 26399.286 26.804946 1982-1999 –> 2000-2012 7.9217327 61106.314
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 4.2441107 26703.139 25.979081 1982-1999 –> 2000-2012 8.2409629 61995.065
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.0706431 26316.287 25.731912 1982-1999 –> 2000-2012 7.8531769 60916.891
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.2377671 26691.201 26.772930 1982-1999 –> 2000-2012 8.2276222 61963.085
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.4477448 27139.826 25.533284 1982-1999 –> 2000-2012 8.2990968 61965.250
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 4.4852285 27218.025 27.454211 1982-1999 –> 2000-2012 8.5061676 62585.537
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.3908057 27021.769 28.307517 1982-1999 –> 2000-2012 8.2421407 61849.137
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.3586343 14282.456 17.634441 2000-2012 –> 2013-2019 8.4777362 40707.014
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.2886301 14204.535 20.173180 2000-2012 –> 2013-2019 8.3956938 40603.821
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.5094431 14452.354 18.761309 2000-2012 –> 2013-2019 8.9058657 41486.035
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 4.4429163 14376.992 17.590954 2000-2012 –> 2013-2019 8.6870269 41080.131
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.3142627 14233.950 17.959451 2000-2012 –> 2013-2019 8.3849059 40550.237
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 4.6146996 14564.243 17.400039 2000-2012 –> 2013-2019 9.0585297 41695.864
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.3855025 14314.790 19.893970 2000-2012 –> 2013-2019 8.6232695 41005.991
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.5531963 14500.015 19.844378 2000-2012 –> 2013-2019 8.9886939 41616.148
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 4.5753254 14521.946 17.529994 2000-2012 –> 2013-2019 8.9863194 41584.460
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.5202464 14464.165 19.826891 2000-2012 –> 2013-2019 8.9255209 41516.589
Atlantic (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.1721364 9317.195 14.893472 1982-1999 –> 2000-2012 8.4758675 21263.128
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.0778809 9242.518 16.276224 1982-1999 –> 2000-2012 8.0906410 20898.219
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.0406583 9214.551 16.334315 1982-1999 –> 2000-2012 8.0445142 20863.042
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 4.2898651 9408.133 16.530153 1982-1999 –> 2000-2012 8.4615713 21224.888
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.7562610 8976.041 14.087279 1982-1999 –> 2000-2012 7.6031123 20458.679
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.2130971 9351.122 16.937590 1982-1999 –> 2000-2012 8.3488164 21133.957
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.2904728 9410.596 17.312273 1982-1999 –> 2000-2012 8.4870713 21254.017
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.2762164 9399.719 17.246416 1982-1999 –> 2000-2012 8.4616337 21232.079
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.7628450 8979.764 14.557143 1982-1999 –> 2000-2012 7.6479920 20501.472
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.7599162 8979.219 14.484282 1982-1999 –> 2000-2012 7.6286393 20485.364
Atlantic (27.75,27.85] cstar_tref ~ aou + phosphate + phosphate_star 4.1445920 4714.270 13.948117 2000-2012 –> 2013-2019 8.4038385 14096.995
Atlantic (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.0388813 4673.485 14.891606 2000-2012 –> 2013-2019 8.2110177 13990.679
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.0584521 4681.490 15.493116 2000-2012 –> 2013-2019 8.1363330 13924.008
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.9871985 4654.157 15.817435 2000-2012 –> 2013-2019 8.0278567 13868.709
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.5543841 4463.871 12.813732 2000-2012 –> 2013-2019 7.3106451 13439.912
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.1899680 4736.302 16.471906 2000-2012 –> 2013-2019 8.4030651 14087.424
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.2766163 4770.199 16.852259 2000-2012 –> 2013-2019 8.5670891 14180.795
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.2589892 4763.359 16.785675 2000-2012 –> 2013-2019 8.5352056 14163.078
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.6320423 4497.663 14.833751 2000-2012 –> 2013-2019 7.3948874 13477.427
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.6320254 4499.655 14.841997 2000-2012 –> 2013-2019 7.3919417 13478.875
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.9339971 8985.697 25.993007 1982-1999 –> 2000-2012 7.6975412 21358.023
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.9626364 9009.039 26.019754 1982-1999 –> 2000-2012 7.7604963 21422.246
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.9050901 8963.964 26.269255 1982-1999 –> 2000-2012 7.6675026 21336.935
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.8808090 8943.893 25.014037 1982-1999 –> 2000-2012 7.6446148 21318.531
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.9909289 9033.933 26.695958 1982-1999 –> 2000-2012 7.7662367 21422.315
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.0202035 9057.452 27.081094 1982-1999 –> 2000-2012 7.8018713 21453.415
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.0192168 9056.662 26.913519 1982-1999 –> 2000-2012 7.8011931 21452.993
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.8809291 8941.992 25.054054 1982-1999 –> 2000-2012 7.6482358 21318.818
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 4.0247203 9059.066 34.924596 1982-1999 –> 2000-2012 7.8006237 21446.158
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.8283943 8900.134 25.423818 1982-1999 –> 2000-2012 7.5818670 21262.390
Atlantic (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 4.2596517 5186.099 25.712670 2000-2012 –> 2013-2019 8.1936488 14171.796
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 4.3560499 5226.470 25.532185 2000-2012 –> 2013-2019 8.3186863 14235.509
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.2549591 5186.111 25.532540 2000-2012 –> 2013-2019 8.1600492 14150.075
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4.1996363 5162.501 24.490381 2000-2012 –> 2013-2019 8.0804453 14106.394
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.2926502 5202.020 25.689561 2000-2012 –> 2013-2019 8.2835791 14235.954
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.3305124 5217.862 26.053635 2000-2012 –> 2013-2019 8.3507159 14275.315
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.3043936 5206.949 25.746866 2000-2012 –> 2013-2019 8.3236105 14263.611
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 4.2037075 5162.249 24.716089 2000-2012 –> 2013-2019 8.0846366 14104.242
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 4.3015254 5203.746 25.967112 2000-2012 –> 2013-2019 8.3262458 14262.812
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.1937476 5159.970 24.979641 2000-2012 –> 2013-2019 8.0221419 14060.104
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.3666353 12256.763 24.734830 1982-1999 –> 2000-2012 6.8055160 28943.723
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 3.6270788 12601.252 26.533358 1982-1999 –> 2000-2012 7.5059696 30042.585
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.6244523 12599.884 26.032900 1982-1999 –> 2000-2012 7.4949417 30029.595
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 3.6249976 12598.584 26.259424 1982-1999 –> 2000-2012 7.4996196 30032.998
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6167030 12589.931 26.325101 1982-1999 –> 2000-2012 7.4926457 30028.487
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.6114058 12583.116 26.028426 1982-1999 –> 2000-2012 7.4813228 30011.898
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.6258377 12599.661 26.393820 1982-1999 –> 2000-2012 7.5020876 30036.715
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.6136873 12586.053 26.157561 1982-1999 –> 2000-2012 7.4858797 30018.527
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.4775250 12405.456 25.192484 1982-1999 –> 2000-2012 7.0844145 29390.065
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.3451491 12226.992 25.075094 1982-1999 –> 2000-2012 6.6398161 28644.824
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.5591426 6460.923 25.640211 2000-2012 –> 2013-2019 7.1866900 19064.776
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.1846183 6194.296 24.436207 2000-2012 –> 2013-2019 6.5512536 18451.059
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 3.5739596 6468.885 25.161042 2000-2012 –> 2013-2019 7.2010384 19070.138
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.5708989 6468.831 25.759121 2000-2012 –> 2013-2019 7.1953512 19068.715
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5563070 6459.011 25.210691 2000-2012 –> 2013-2019 7.1730100 19048.943
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.5555409 6458.495 24.944211 2000-2012 –> 2013-2019 7.1669467 19041.611
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 3.5753500 6469.818 25.042041 2000-2012 –> 2013-2019 7.2011877 19069.479
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.5558370 6458.695 25.082189 2000-2012 –> 2013-2019 7.1695244 19044.747
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate_star 3.3805955 6335.503 24.525160 2000-2012 –> 2013-2019 6.8581205 18740.959
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.2130169 6215.585 24.010914 2000-2012 –> 2013-2019 6.5581660 18442.577
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.1452903 3963.785 7.856079 1982-1999 –> 2000-2012 2.1806877 8810.870
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.1434240 3961.639 7.617210 1982-1999 –> 2000-2012 2.1777269 8807.207
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.1445566 3964.156 7.098268 1982-1999 –> 2000-2012 2.1878569 8838.531
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.1539339 3982.897 7.793043 1982-1999 –> 2000-2012 2.1935256 8843.429
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.0969227 3856.099 7.984041 1982-1999 –> 2000-2012 2.1199059 8665.066
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.1503897 3977.078 7.475629 1982-1999 –> 2000-2012 2.1896561 8838.569
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.1587105 3995.398 7.383063 1982-1999 –> 2000-2012 2.2057523 8881.680
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.1587003 3993.376 7.804613 1982-1999 –> 2000-2012 2.2022344 8866.496
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.1543181 3985.744 7.445439 1982-1999 –> 2000-2012 2.1977982 8860.692
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.0988130 3860.476 12.830493 1982-1999 –> 2000-2012 2.1264897 8684.667
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 1.2411391 2300.955 8.337261 2000-2012 –> 2013-2019 2.3864294 6264.740
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.2253654 2285.049 7.652933 2000-2012 –> 2013-2019 2.3687894 6246.688
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1.2121956 2269.920 7.034687 2000-2012 –> 2013-2019 2.3567522 6234.076
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.2532958 2314.601 8.261466 2000-2012 –> 2013-2019 2.4072298 6297.499
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1.1608824 2209.367 8.608460 2000-2012 –> 2013-2019 2.2578052 6065.466
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2328310 2293.552 7.507202 2000-2012 –> 2013-2019 2.3832207 6270.630
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.2403370 2302.050 7.424044 2000-2012 –> 2013-2019 2.3990475 6297.448
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 1.2578537 2319.684 8.277328 2000-2012 –> 2013-2019 2.4165540 6313.059
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.2360529 2297.206 7.485595 2000-2012 –> 2013-2019 2.3903710 6282.950
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.2285868 2288.724 13.954771 2000-2012 –> 2013-2019 2.3273998 6149.200
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.7943969 3337.791 5.398179 1982-1999 –> 2000-2012 1.4660700 7204.875
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.8057853 3377.590 5.336769 1982-1999 –> 2000-2012 1.4978939 7357.785
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8093116 3389.799 5.389161 1982-1999 –> 2000-2012 1.5272515 7508.285
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 0.8097628 3389.357 5.294503 1982-1999 –> 2000-2012 1.5286050 7510.583
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.7972728 3347.895 5.317335 1982-1999 –> 2000-2012 1.4730354 7237.888
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.8011440 3361.438 5.239412 1982-1999 –> 2000-2012 1.4831193 7285.969
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + phosphate_star 0.8168537 3413.734 5.415135 1982-1999 –> 2000-2012 1.5091190 7392.784
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8127139 3401.528 5.436958 1982-1999 –> 2000-2012 1.5022580 7367.714
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.8094433 3388.254 5.337970 1982-1999 –> 2000-2012 1.5289113 7512.764
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.7991765 3354.563 5.281963 1982-1999 –> 2000-2012 1.4783259 7263.423
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate + phosphate_star 0.8792018 1849.242 7.100581 2000-2012 –> 2013-2019 1.6888190 5238.096
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 0.8779548 1849.220 7.088283 2000-2012 –> 2013-2019 1.6723517 5187.011
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.8910485 1870.301 6.797078 2000-2012 –> 2013-2019 1.6968339 5247.891
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate 0.8849636 1858.543 6.958491 2000-2012 –> 2013-2019 1.6942752 5246.342
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 0.8569972 1814.816 8.112716 2000-2012 –> 2013-2019 1.6663088 5204.615
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 0.8918397 1869.565 6.850193 2000-2012 –> 2013-2019 1.7016025 5258.922
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.8845179 1859.826 6.949110 2000-2012 –> 2013-2019 1.6817907 5207.721
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 0.8918126 1871.521 6.848206 2000-2012 –> 2013-2019 1.6929566 5232.960
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 0.8879019 1863.263 6.924296 2000-2012 –> 2013-2019 1.6973452 5251.517
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 0.8876626 1864.880 6.919523 2000-2012 –> 2013-2019 1.6868392 5219.443
Atlantic (28.15,28.2] cstar_tref ~ aou + nitrate + silicate + phosphate_star 0.7770053 4708.854 16.122287 1982-1999 –> 2000-2012 1.3639427 9784.037
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.6770043 4154.194 6.501489 1982-1999 –> 2000-2012 1.2420162 9011.838
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.6531656 4011.874 7.988766 1982-1999 –> 2000-2012 1.1926888 8607.754
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.6659083 4087.661 7.918388 1982-1999 –> 2000-2012 1.2126228 8757.200
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.6608030 4058.677 7.164936 1982-1999 –> 2000-2012 1.2068834 8723.583
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.6658899 4089.550 7.861172 1982-1999 –> 2000-2012 1.2107104 8741.259
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.7318765 4469.957 8.923396 1982-1999 –> 2000-2012 1.3674125 10001.692
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.7289031 4451.567 11.454276 1982-1999 –> 2000-2012 1.2994157 9364.571
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.7176256 4388.790 12.118912 1982-1999 –> 2000-2012 1.2754303 9173.078
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.7173564 4389.280 12.253531 1982-1999 –> 2000-2012 1.2736240 9159.800
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.7438009 2433.094 5.353850 2000-2012 –> 2013-2019 1.4208051 6587.288
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate 0.8313687 2673.057 6.109030 2000-2012 –> 2013-2019 1.5901181 7286.191
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.7354711 2410.813 6.061562 2000-2012 –> 2013-2019 1.3886368 6422.688
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.7635202 2489.509 6.905498 2000-2012 –> 2013-2019 1.4294285 6577.170
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.7400734 2424.263 5.601071 2000-2012 –> 2013-2019 1.4008765 6482.940
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.7554349 2468.556 5.925970 2000-2012 –> 2013-2019 1.4213248 6558.107
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.8121334 2624.588 6.619729 2000-2012 –> 2013-2019 1.5440099 7094.545
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate_star 0.8821824 2800.963 10.600095 2000-2012 –> 2013-2019 1.6110855 7252.530
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.8758629 2785.463 11.227380 2000-2012 –> 2013-2019 1.5934885 7174.253
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.8756887 2787.034 11.132298 2000-2012 –> 2013-2019 1.5930451 7176.314
Atlantic (28.2, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate_star 0.5786277 7379.069 6.882067 1982-1999 –> 2000-2012 1.1040322 16592.944
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.3566263 3287.517 1.988203 1982-1999 –> 2000-2012 0.6689778 6327.561
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.3501288 3134.142 1.949898 1982-1999 –> 2000-2012 0.6565248 5947.722
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.3534411 3213.707 1.988553 1982-1999 –> 2000-2012 0.6595794 6017.300
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.3490030 3108.929 2.067840 1982-1999 –> 2000-2012 0.6550151 5909.629
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.3560111 3274.927 2.045845 1982-1999 –> 2000-2012 0.6667174 6254.300
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3395940 2877.993 2.205103 1982-1999 –> 2000-2012 0.6448938 5651.035
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.3509290 3155.433 2.134668 1982-1999 –> 2000-2012 0.6569886 5957.976
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.5229331 6525.880 2.014189 1982-1999 –> 2000-2012 0.9694721 13811.525
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.5696464 7248.882 8.521425 1982-1999 –> 2000-2012 1.0907040 16366.159
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.4264163 2726.278 2.452673 2000-2012 –> 2013-2019 0.7830427 6013.795
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate_star 0.4135856 2581.813 2.572196 2000-2012 –> 2013-2019 0.7637143 5715.954
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.4165997 2616.623 2.435991 2000-2012 –> 2013-2019 0.7700408 5830.330
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 0.4134611 2582.369 2.655486 2000-2012 –> 2013-2019 0.7624641 5691.298
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 0.5986382 4354.600 4.314619 2000-2012 –> 2013-2019 1.1608508 11490.485
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.4234133 2694.396 2.563266 2000-2012 –> 2013-2019 0.7794244 5969.323
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 0.3788945 2163.827 2.767863 2000-2012 –> 2013-2019 0.7184885 5041.820
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.4031930 2461.810 2.685125 2000-2012 –> 2013-2019 0.7541221 5617.243
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 0.5828792 4228.708 2.387587 2000-2012 –> 2013-2019 1.1058122 10754.588
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 0.7432499 5393.901 11.501170 2000-2012 –> 2013-2019 1.3128963 12642.783
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 10.4882268 172356.531 92.831315 1982-1999 –> 2000-2012 21.3951083 415243.125
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 10.2862280 171467.315 66.576487 1982-1999 –> 2000-2012 21.0486572 413503.634
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 10.4951090 172384.524 93.690179 1982-1999 –> 2000-2012 21.4221318 415386.779
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10.4824853 172331.494 94.545971 1982-1999 –> 2000-2012 21.3923909 415235.767
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 10.4884105 172355.331 92.622681 1982-1999 –> 2000-2012 21.4099359 415325.493
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10.4762747 172304.395 94.081927 1982-1999 –> 2000-2012 21.3931484 415249.388
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 10.5078939 172440.190 94.069543 1982-1999 –> 2000-2012 21.4361179 415449.455
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate_star 10.5766263 172736.298 88.716461 1982-1999 –> 2000-2012 21.5052947 415746.156
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10.4868406 172350.487 94.566926 1982-1999 –> 2000-2012 21.3900034 415215.333
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 10.4880098 172353.584 94.258498 1982-1999 –> 2000-2012 21.4048884 415296.606
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 10.2463399 92132.167 54.962320 2000-2012 –> 2013-2019 20.7345667 264488.697
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 10.0478675 91651.144 51.215602 2000-2012 –> 2013-2019 20.3340955 263118.459
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 10.2504743 92140.088 54.836267 2000-2012 –> 2013-2019 20.7455833 264524.612
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 10.3594733 92402.208 58.622248 2000-2012 –> 2013-2019 20.9691369 265285.107
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10.2172475 92062.243 55.546258 2000-2012 –> 2013-2019 20.6997328 264393.737
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 10.2576752 92157.357 55.200848 2000-2012 –> 2013-2019 20.7460857 264512.689
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10.2125628 92050.965 55.741861 2000-2012 –> 2013-2019 20.6888375 264355.360
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 10.2730208 92194.120 55.100855 2000-2012 –> 2013-2019 20.7809147 264634.310
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10.2270355 92085.791 55.787383 2000-2012 –> 2013-2019 20.7138761 264436.278
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 10.2379683 92110.066 56.104038 2000-2012 –> 2013-2019 20.7259781 264463.651
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 6.2155935 58141.363 86.294407 1982-1999 –> 2000-2012 12.2865995 138708.490
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.1329963 57903.794 90.613313 1982-1999 –> 2000-2012 12.0794333 137954.659
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.9470535 57352.451 85.562687 1982-1999 –> 2000-2012 11.7267951 136692.542
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.9781351 57445.801 81.936586 1982-1999 –> 2000-2012 11.8015383 136974.023
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6.0874574 57770.327 80.024131 1982-1999 –> 2000-2012 12.2974017 138905.098
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.9854695 57467.759 81.493668 1982-1999 –> 2000-2012 11.8269662 137073.530
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6.2630395 58279.543 76.105653 1982-1999 –> 2000-2012 12.4109413 139163.308
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 6.1973306 58088.668 79.874521 1982-1999 –> 2000-2012 12.2805188 138705.906
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6.1798982 58040.224 82.762938 1982-1999 –> 2000-2012 12.2298444 138522.484
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate_star 6.2800446 58326.100 75.746719 1982-1999 –> 2000-2012 12.4524972 139307.492
Indo-Pacific (26,26.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 6.1777631 30758.601 72.339044 2000-2012 –> 2013-2019 12.3933566 88899.965
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6.0889516 30623.183 77.475055 2000-2012 –> 2013-2019 12.2219479 88526.977
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.9120481 30343.384 74.612926 2000-2012 –> 2013-2019 11.8591016 87695.835
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.9557070 30413.207 72.105343 2000-2012 –> 2013-2019 11.9338422 87859.009
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.9900743 30467.812 71.393377 2000-2012 –> 2013-2019 12.0775316 88238.139
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.9596759 30419.530 71.948109 2000-2012 –> 2013-2019 11.9451454 87887.288
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 5.9900925 30465.841 71.376438 2000-2012 –> 2013-2019 12.1108505 88331.864
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6.2106448 30810.979 64.063128 2000-2012 –> 2013-2019 12.4736843 89090.522
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 6.1570594 30726.744 67.345255 2000-2012 –> 2013-2019 12.3543900 88815.412
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6.1405606 30703.280 69.482672 2000-2012 –> 2013-2019 12.3204588 88743.504
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.1406760 38959.233 60.336685 1982-1999 –> 2000-2012 10.1328060 93090.438
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.1568018 38999.147 62.194346 1982-1999 –> 2000-2012 10.1201533 93026.980
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.0424678 38715.414 63.111528 1982-1999 –> 2000-2012 9.9193163 92430.881
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.1492495 38982.470 62.014400 1982-1999 –> 2000-2012 10.1121144 93010.550
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.1310275 38937.291 62.186090 1982-1999 –> 2000-2012 10.0686920 92874.349
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.2324641 39186.773 61.126911 1982-1999 –> 2000-2012 10.2528011 93420.721
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.2126711 39138.474 65.281353 1982-1999 –> 2000-2012 10.2260144 93347.497
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.2206228 39157.900 61.068273 1982-1999 –> 2000-2012 10.2427428 93398.198
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 5.1747030 39043.310 60.845962 1982-1999 –> 2000-2012 10.1863837 93244.402
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.0671854 38777.731 61.877526 1982-1999 –> 2000-2012 9.9913392 92665.798
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.5125769 21993.826 50.883935 2000-2012 –> 2013-2019 10.6532529 60953.059
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.6589926 22178.161 51.213629 2000-2012 –> 2013-2019 10.8157944 61177.308
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.4918214 21969.300 52.261729 2000-2012 –> 2013-2019 10.5342892 60684.714
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.6549752 22175.167 50.813792 2000-2012 –> 2013-2019 10.8042248 61157.637
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.5405560 22031.427 52.564529 2000-2012 –> 2013-2019 10.6715835 60968.718
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.6234307 22135.831 52.410852 2000-2012 –> 2013-2019 10.8558949 61322.604
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.6546212 22174.727 55.710742 2000-2012 –> 2013-2019 10.8672923 61313.201
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.6092258 22118.046 52.324828 2000-2012 –> 2013-2019 10.8298485 61275.946
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 5.6630212 22183.165 49.697103 2000-2012 –> 2013-2019 10.8377242 61226.475
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.4985565 21977.918 51.258896 2000-2012 –> 2013-2019 10.5657418 60755.650
Indo-Pacific (26.75,27] cstar_tref ~ aou + phosphate + phosphate_star 5.5045084 46715.116 48.087099 1982-1999 –> 2000-2012 10.7643694 111575.922
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.4413211 46544.532 49.207345 1982-1999 –> 2000-2012 10.6365555 111146.952
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.3621069 46325.321 53.158458 1982-1999 –> 2000-2012 10.5245973 110794.574
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.3020944 46159.081 54.152700 1982-1999 –> 2000-2012 10.4005484 110367.443
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 5.5310624 46789.052 50.153534 1982-1999 –> 2000-2012 10.7947334 111667.109
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.3389739 46262.694 53.851578 1982-1999 –> 2000-2012 10.4969346 110715.458
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.4733646 46634.302 51.017342 1982-1999 –> 2000-2012 10.6778428 111276.164
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.5930624 46957.679 50.280670 1982-1999 –> 2000-2012 10.9062036 112034.761
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 5.3681512 46342.162 52.736283 1982-1999 –> 2000-2012 10.5571895 110919.447
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.2897344 46124.194 54.201852 1982-1999 –> 2000-2012 10.4018669 110388.987
Indo-Pacific (26.75,27] cstar_tref ~ aou + phosphate + phosphate_star 5.7251785 25402.757 41.623790 2000-2012 –> 2013-2019 11.2296869 72117.873
Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.6678456 25323.978 42.317099 2000-2012 –> 2013-2019 11.1091667 71868.511
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate + phosphate_star 5.6149712 25248.754 46.179396 2000-2012 –> 2013-2019 10.9770781 71574.075
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.5614812 25173.929 46.743187 2000-2012 –> 2013-2019 10.8635756 71333.009
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 5.7603049 25453.850 42.750166 2000-2012 –> 2013-2019 11.2913673 72242.902
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5.6035408 25234.398 46.909455 2000-2012 –> 2013-2019 10.9425146 71497.092
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.7088071 25383.774 43.400535 2000-2012 –> 2013-2019 11.1821717 72018.075
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.8182397 25536.169 43.149819 2000-2012 –> 2013-2019 11.4113022 72493.847
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 5.6292366 25269.119 46.135960 2000-2012 –> 2013-2019 10.9973878 71611.280
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.5619328 25174.581 47.091579 2000-2012 –> 2013-2019 10.8516672 71298.774
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.8922124 57199.212 46.089182 1982-1999 –> 2000-2012 9.0915563 132384.064
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.9055065 57250.827 45.547718 1982-1999 –> 2000-2012 9.1113868 132476.646
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5.0340146 57742.673 68.670961 1982-1999 –> 2000-2012 9.1005026 132080.732
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.8956290 57212.490 45.678550 1982-1999 –> 2000-2012 9.0961726 132404.867
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.5667093 55889.651 54.430777 1982-1999 –> 2000-2012 8.5023213 129366.041
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate 4.8937227 57203.083 46.083061 1982-1999 –> 2000-2012 9.0986072 132420.665
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.8903930 57192.137 45.952921 1982-1999 –> 2000-2012 9.0922817 132392.947
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate_star 4.9055419 57248.964 45.547901 1982-1999 –> 2000-2012 9.1216808 132536.952
Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 5.0352821 57745.462 68.809325 1982-1999 –> 2000-2012 9.1132612 132155.847
Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.8958637 57211.402 45.679839 1982-1999 –> 2000-2012 9.1056866 132459.901
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate + phosphate_star 5.6374831 32093.954 37.580966 2000-2012 –> 2013-2019 10.5632561 89421.198
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5.6319083 32085.872 37.442218 2000-2012 –> 2013-2019 10.5467354 89372.803
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.6181402 32060.931 38.548425 2000-2012 –> 2013-2019 10.5103526 89260.142
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5.6341420 32089.913 39.129976 2000-2012 –> 2013-2019 10.5396485 89340.740
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5.6218136 32067.591 38.884937 2000-2012 –> 2013-2019 10.5174425 89280.081
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 5.3450584 31553.181 45.165251 2000-2012 –> 2013-2019 9.9117677 87442.832
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate 5.6186053 32059.774 38.663994 2000-2012 –> 2013-2019 10.5123280 89262.857
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 5.6170360 32058.928 38.805319 2000-2012 –> 2013-2019 10.5074290 89251.065
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate_star 5.6342915 32088.183 39.060464 2000-2012 –> 2013-2019 10.5398334 89337.147
Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 5.6218138 32065.591 38.887608 2000-2012 –> 2013-2019 10.5176775 89276.994
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 4.1812255 53195.869 29.778039 1982-1999 –> 2000-2012 7.8041924 122893.338
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.1625970 53114.530 30.014519 1982-1999 –> 2000-2012 7.7849694 122809.773
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.1679377 53138.461 30.029407 1982-1999 –> 2000-2012 7.7892728 122826.330
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.1563929 53086.692 29.835956 1982-1999 –> 2000-2012 7.7747528 122753.396
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.1579580 53093.718 29.884088 1982-1999 –> 2000-2012 7.7745549 122747.874
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.9352137 52066.099 30.758917 1982-1999 –> 2000-2012 7.4322088 120854.296
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate 4.2354424 53436.325 31.463971 1982-1999 –> 2000-2012 7.8700128 123216.133
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.2245689 53390.348 31.286215 1982-1999 –> 2000-2012 7.8536577 123133.291
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate_star 4.2246400 53388.662 31.273980 1982-1999 –> 2000-2012 7.8555175 123142.294
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4.2260097 53394.712 31.325355 1982-1999 –> 2000-2012 7.8552370 123136.638
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4.6526233 29908.811 32.706936 2000-2012 –> 2013-2019 8.7795353 82862.649
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 4.7602243 30138.007 33.267654 2000-2012 –> 2013-2019 8.9414497 83333.876
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.7363961 30089.263 33.496012 2000-2012 –> 2013-2019 8.8989931 83203.793
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.7438903 30103.250 33.718991 2000-2012 –> 2013-2019 8.9230112 83289.722
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.7437448 30104.940 33.604435 2000-2012 –> 2013-2019 8.9116826 83243.401
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.7274842 30070.218 33.075249 2000-2012 –> 2013-2019 8.8838771 83156.910
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.7317313 30079.299 33.284503 2000-2012 –> 2013-2019 8.8896893 83173.017
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4.4643994 29491.220 35.132948 2000-2012 –> 2013-2019 8.3996130 81557.319
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4.8208413 30267.961 33.958610 2000-2012 –> 2013-2019 9.0454102 83658.309
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate_star 4.8209269 30266.141 34.000867 2000-2012 –> 2013-2019 9.0455669 83654.803
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.9368782 61148.461 35.143008 1982-1999 –> 2000-2012 7.0891220 138988.375
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 3.8875170 60871.912 33.395738 1982-1999 –> 2000-2012 7.0308610 138626.107
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.8854310 60862.147 32.718375 1982-1999 –> 2000-2012 6.9921586 138263.100
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.9166776 61037.707 36.901278 1982-1999 –> 2000-2012 7.0919459 139100.264
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 3.9345441 61135.462 34.794397 1982-1999 –> 2000-2012 7.0977204 139080.342
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.9134412 61019.588 34.654284 1982-1999 –> 2000-2012 7.0311931 138527.935
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.8811887 60838.203 32.148133 1982-1999 –> 2000-2012 7.0013567 138370.036
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.9068773 60982.795 31.980497 1982-1999 –> 2000-2012 7.0654781 138885.789
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.8306459 60550.902 36.258393 1982-1999 –> 2000-2012 6.9457284 138033.278
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.9003291 60946.028 31.792644 1982-1999 –> 2000-2012 7.0570468 138830.942
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 4.3189983 33398.648 32.079310 2000-2012 –> 2013-2019 8.2034349 94255.186
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 4.4378806 33711.193 35.854356 2000-2012 –> 2013-2019 8.3253976 94583.105
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 4.4028510 33621.395 32.924586 2000-2012 –> 2013-2019 8.2882820 94483.542
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 4.3708911 33535.001 35.595864 2000-2012 –> 2013-2019 8.2675731 94458.524
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 4.4028518 33619.396 32.905054 2000-2012 –> 2013-2019 8.3199688 94657.563
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4.4249284 33679.335 37.746342 2000-2012 –> 2013-2019 8.3416059 94717.042
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.3875789 33581.143 32.105383 2000-2012 –> 2013-2019 8.2687676 94419.347
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4.4101521 33640.588 31.901265 2000-2012 –> 2013-2019 8.3170294 94623.383
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4.3493399 33479.743 38.780604 2000-2012 –> 2013-2019 8.1799858 94030.644
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4.4002907 33614.656 31.669459 2000-2012 –> 2013-2019 8.3006197 94560.684
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.9400240 20839.951 31.979363 1982-1999 –> 2000-2012 5.3158543 45814.623
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.9104116 20757.524 33.150260 1982-1999 –> 2000-2012 5.2846130 45726.701
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2.9095949 20755.183 34.756486 1982-1999 –> 2000-2012 5.3135522 45860.470
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.9199187 20784.722 32.929345 1982-1999 –> 2000-2012 5.3102950 45828.097
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.9228946 20793.218 32.821528 1982-1999 –> 2000-2012 5.3186049 45860.951
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.9173927 20777.505 32.966910 1982-1999 –> 2000-2012 5.3185885 45870.230
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.9229235 20793.300 32.783498 1982-1999 –> 2000-2012 5.3193510 45864.305
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 2.9229247 20791.304 32.774167 1982-1999 –> 2000-2012 5.3243319 45882.992
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.9315385 20817.846 33.781987 1982-1999 –> 2000-2012 5.3236892 45869.329
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.9263792 20803.155 32.346813 1982-1999 –> 2000-2012 5.2625320 45595.783
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.2900731 12210.431 40.213374 2000-2012 –> 2013-2019 6.2168092 33012.603
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.2867324 12207.683 39.784710 2000-2012 –> 2013-2019 6.1971440 32965.206
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate 3.2681789 12179.223 42.726285 2000-2012 –> 2013-2019 6.2075503 33017.323
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.2680686 12181.066 42.736228 2000-2012 –> 2013-2019 6.2001129 33000.350
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.2535073 12160.193 42.511418 2000-2012 –> 2013-2019 6.1769606 32955.006
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.2568072 12164.932 41.513447 2000-2012 –> 2013-2019 6.1664021 32920.115
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.2949407 12219.341 39.578451 2000-2012 –> 2013-2019 6.2148594 33004.063
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.2979971 12223.675 39.455499 2000-2012 –> 2013-2019 6.2208917 33016.893
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.2769864 12193.803 39.698742 2000-2012 –> 2013-2019 6.1943792 32971.307
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3.2979109 12223.552 39.400818 2000-2012 –> 2013-2019 6.2208344 33016.853
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 2.8265203 22881.092 35.468479 1982-1999 –> 2000-2012 5.1342058 51732.380
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.8264299 22882.794 35.394444 1982-1999 –> 2000-2012 5.1282692 51703.644
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8262171 22882.093 32.727556 1982-1999 –> 2000-2012 5.1377482 51756.674
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.8348176 22910.364 35.116851 1982-1999 –> 2000-2012 5.1463854 51785.147
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.8342910 22908.635 35.104855 1982-1999 –> 2000-2012 5.1466528 51787.811
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.8289872 22891.208 33.891256 1982-1999 –> 2000-2012 5.1451763 51791.532
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.8345096 22909.353 35.093317 1982-1999 –> 2000-2012 5.1473198 51791.008
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 2.8262248 22880.119 32.705349 1982-1999 –> 2000-2012 5.1415616 51773.736
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2.8260168 22881.434 32.487690 1982-1999 –> 2000-2012 5.1404878 51772.269
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.8067480 22817.779 36.933796 1982-1999 –> 2000-2012 5.0905670 51538.122
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + silicate + phosphate + phosphate_star 3.1090074 12727.145 38.817069 2000-2012 –> 2013-2019 5.9355277 35608.237
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + phosphate + phosphate_star 3.1049937 12720.712 39.351852 2000-2012 –> 2013-2019 5.9441530 35643.315
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3.1044900 12721.904 39.342619 2000-2012 –> 2013-2019 5.9309199 35604.698
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3.1162820 12740.784 38.879291 2000-2012 –> 2013-2019 5.9465810 35636.306
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3.0641729 12656.807 41.209954 2000-2012 –> 2013-2019 5.8979866 35563.875
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3.1149620 12738.674 39.033254 2000-2012 –> 2013-2019 5.9492529 35647.309
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3.1167244 12741.491 37.321289 2000-2012 –> 2013-2019 5.9457116 35632.700
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3.1213749 12748.916 37.797873 2000-2012 –> 2013-2019 5.9473918 35630.351
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + phosphate + phosphate_star 3.0676720 12660.490 40.783026 2000-2012 –> 2013-2019 5.9030844 35570.806
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3.0613901 12652.282 41.149366 2000-2012 –> 2013-2019 5.8681381 35470.061
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.2724811 19146.464 8.779881 1982-1999 –> 2000-2012 4.3288445 44642.126
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.3457566 19417.551 9.182020 1982-1999 –> 2000-2012 4.3803835 44786.671
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.3362354 19382.809 9.809318 1982-1999 –> 2000-2012 4.3556697 44662.678
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3502121 19433.760 9.193015 1982-1999 –> 2000-2012 4.3876991 44819.608
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.3501362 19433.484 9.174672 1982-1999 –> 2000-2012 4.3883019 44823.298
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate 2.3362839 19380.986 9.801122 1982-1999 –> 2000-2012 4.3839940 44824.433
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.3287152 19355.268 9.730640 1982-1999 –> 2000-2012 4.3550404 44675.702
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.3498336 19432.384 9.192319 1982-1999 –> 2000-2012 4.3876308 44820.045
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate_star 2.3558402 19452.191 8.614011 1982-1999 –> 2000-2012 4.4113278 44940.781
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.3424710 19405.578 9.079879 1982-1999 –> 2000-2012 4.3758523 44767.406
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate_star 2.4390610 10968.636 9.673874 2000-2012 –> 2013-2019 4.7509971 30260.134
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.4241659 10941.588 10.654765 2000-2012 –> 2013-2019 4.6966470 30088.052
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.5244025 11133.719 10.120786 2000-2012 –> 2013-2019 4.8701591 30551.270
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2.4389768 10970.472 9.648126 2000-2012 –> 2013-2019 4.7508240 30263.642
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.5440851 11170.549 11.078920 2000-2012 –> 2013-2019 4.8803205 30553.358
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5302263 11144.647 10.144807 2000-2012 –> 2013-2019 4.8804384 30578.406
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.5294710 11143.231 10.125535 2000-2012 –> 2013-2019 4.8796071 30576.714
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.5134392 11113.080 10.981064 2000-2012 –> 2013-2019 4.8421544 30468.349
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.5293485 11143.001 10.143478 2000-2012 –> 2013-2019 4.8791821 30575.385
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2.5179937 11121.665 9.755604 2000-2012 –> 2013-2019 4.8604646 30527.243
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.9266283 10727.803 8.965397 1982-1999 –> 2000-2012 3.5690319 25166.331
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1.9231267 10716.409 8.646954 1982-1999 –> 2000-2012 3.5527796 25094.234
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.8925320 10635.595 8.765524 1982-1999 –> 2000-2012 3.5176470 24994.418
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate_star 1.9319973 10740.173 8.825738 1982-1999 –> 2000-2012 3.5762747 25185.290
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 1.9175767 10701.484 8.633204 1982-1999 –> 2000-2012 3.5535960 25108.677
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.8948715 10641.974 8.767650 1982-1999 –> 2000-2012 3.5206136 25003.704
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.8955349 10643.782 8.767726 1982-1999 –> 2000-2012 3.5221429 25009.522
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.9068949 10674.638 8.711910 1982-1999 –> 2000-2012 3.5531724 25130.910
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 1.8949626 10640.223 8.797762 1982-1999 –> 2000-2012 3.5708582 25228.799
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.8948420 10641.894 8.762994 1982-1999 –> 2000-2012 3.5210383 25005.727
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 2.0709455 6313.133 8.713211 2000-2012 –> 2013-2019 3.9975738 17040.936
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2.0594409 6296.789 8.802893 2000-2012 –> 2013-2019 3.9519730 16932.384
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate_star 2.0718737 6312.448 8.608198 2000-2012 –> 2013-2019 3.9985578 17038.400
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2.0728445 6313.822 8.661407 2000-2012 –> 2013-2019 3.9904212 17015.306
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.0619981 6300.429 8.794721 2000-2012 –> 2013-2019 3.9695158 16976.754
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate 2.0621507 6298.647 8.806887 2000-2012 –> 2013-2019 3.9885577 17023.856
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.0621501 6300.646 8.807529 2000-2012 –> 2013-2019 3.9570216 16942.620
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2.0621491 6300.644 8.805830 2000-2012 –> 2013-2019 3.9576840 16944.426
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2.0624051 6301.008 8.735205 2000-2012 –> 2013-2019 3.9693000 16975.646
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2.0613801 6299.550 8.800503 2000-2012 –> 2013-2019 3.9562221 16941.444
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.6396635 76233.553 7.832848 1982-1999 –> 2000-2012 3.1279813 176682.907
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.5851502 74884.692 12.511212 1982-1999 –> 2000-2012 2.9770393 171628.600
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.5311977 73507.284 14.214366 1982-1999 –> 2000-2012 2.8592163 167656.101
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5313000 73509.945 14.202239 1982-1999 –> 2000-2012 2.8588713 167640.138
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.5314928 73514.959 14.185354 1982-1999 –> 2000-2012 2.8584599 167619.984
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.5281199 73427.133 14.378394 1982-1999 –> 2000-2012 2.8459506 167150.174
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.5314910 73514.913 14.185270 1982-1999 –> 2000-2012 2.8584552 167619.818
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.5317666 73520.081 14.250129 1982-1999 –> 2000-2012 2.8588896 167629.601
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.5308210 73497.483 10.138151 1982-1999 –> 2000-2012 2.7847198 164471.093
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.5798847 74754.151 14.936959 1982-1999 –> 2000-2012 2.9642857 171201.819
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 1.7989953 42978.069 14.155567 2000-2012 –> 2013-2019 3.4386588 119211.623
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.7754628 42694.081 15.096407 2000-2012 –> 2013-2019 3.3606130 117578.773
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 1.7314864 42158.948 16.581456 2000-2012 –> 2013-2019 3.2626842 115666.232
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.7317874 42162.670 16.576870 2000-2012 –> 2013-2019 3.2630874 115672.615
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1.7322153 42167.962 16.575055 2000-2012 –> 2013-2019 3.2637081 115682.920
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1.7344727 42195.852 17.075855 2000-2012 –> 2013-2019 3.2625926 115622.986
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1.7322017 42167.794 16.574226 2000-2012 –> 2013-2019 3.2636927 115682.706
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 1.7349951 42200.302 16.913655 2000-2012 –> 2013-2019 3.2667617 115720.382
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1.7932852 42909.987 20.922377 2000-2012 –> 2013-2019 3.3241063 116407.469
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1.7819870 42774.633 17.106634 2000-2012 –> 2013-2019 3.3618717 117528.784

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)
# 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)[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)
      
      lm_best_basin_era_slab <- lm_best_plot %>%
        filter(basin == i_basin, era == i_era, gamma_slab == i_gamma_slab)
      
      for (i_predictors in unique(lm_best_basin_era_slab$predictors)) {
        #i_predictors <- unique(lm_best_basin_era_slab$predictors)[1]
        print(i_predictors)
        # extract one model definition
        i_lm <- lm_all %>%
          filter(predictors == i_predictors) %>%
          select(lm_coeff) %>%
          pull()
        
        # 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
        }
        
        # plot model diagnostics, if activated
        if (params_local$plot_all_figures == "y") {
          p_model <- ggnostic(
            i_lm_fit,
            columnsY = c(params_local$MLR_target, ".fitted", ".resid"),
            title = paste(
              "| era:",
              i_era,
              "| 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_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)

5.4 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)

5.5 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
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
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
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
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)

# set NaN to zero
lm_all_stats[is.na(lm_all_stats)] <- 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] 6 3 5 8 10 4 10
(26,26.5] 10 5 5 6 4 8 8
(26.5,26.75] 8 1 7 7 5 10 8
(26.75,27] 8 1 7 7 5 10 8
(27,27.25] 8 3 6 8 9 7 7
(27.25,27.5] 6 3 5 8 10 4 10
(27.5,27.75] 10 0 10 7 5 5 6
(27.75,27.85] 9 0 9 8 7 6 7
(27.85,27.95] 8 1 9 8 6 7 7
(27.95,28.05] 8 3 5 8 8 4 10
(28.05,28.1] 8 1 8 8 9 5 8
(28.1,28.15] 6 3 5 9 10 5 9
(28.15,28.2] 9 10 0 7 6 6 7
(28.2, Inf] 9 10 0 6 8 6 5
total 113.00 44.00 81.00 105.00 102.00 87.00 110.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 6 3 5 8 10 4 10
(26,26.5] 10 5 5 6 4 8 8
(26.5,26.75] 8 1 7 7 5 10 8
(26.75,27] 8 1 7 7 5 10 8
(27,27.25] 6 4 4 8 9 8 8
(27.25,27.5] 6 3 5 9 10 5 9
(27.5,27.75] 8 1 7 8 10 4 8
(27.75,27.85] 9 0 9 9 6 6 6
(27.85,27.95] 8 1 9 8 6 7 7
(27.95,28.05] 8 3 6 8 8 5 9
(28.05,28.1] 8 1 8 8 9 5 8
(28.1,28.15] 8 1 7 8 10 4 8
(28.15,28.2] 9 10 0 6 7 6 7
(28.2, Inf] 8 10 0 6 9 6 5
total 110.00 44.00 79.00 106.00 108.00 88.00 109.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 4 3 3 10 10 4 10
(26,26.5] 8 2 6 8 5 10 8
(26.5,26.75] 8 1 8 9 7 7 7
(26.75,27] 9 0 10 8 6 5 6
(27,27.25] 6 3 5 8 4 10 10
(27.25,27.5] 8 1 7 7 5 10 8
(27.5,27.75] 8 2 7 7 10 6 7
(27.75,27.85] 7 2 6 9 7 9 8
(27.85,27.95] 8 4 5 7 6 10 8
(27.95,28.05] 6 4 4 7 9 10 8
(28.05,28.1] 6 2 6 7 10 10 5
(28.1, Inf] 7 3 5 8 8 10 7
total 85.00 27.00 72.00 95.00 87.00 101.00 92.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 5 3 4 9 10 5 10
(26,26.5] 7 2 6 8 6 10 8
(26.5,26.75] 8 1 8 9 7 7 7
(26.75,27] 9 0 10 8 6 5 6
(27,27.25] 8 1 7 8 4 10 8
(27.25,27.5] 8 2 6 8 7 10 6
(27.5,27.75] 6 4 5 8 10 9 5
(27.75,27.85] 8 4 5 7 10 6 8
(27.85,27.95] 9 3 6 10 6 6 7
(27.95,28.05] 8 5 4 8 9 8 7
(28.05,28.1] 6 4 4 7 10 10 6
(28.1, Inf] 7 3 5 8 8 10 7
total 89.00 32.00 70.00 98.00 93.00 96.00 85.00

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
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
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