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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
# 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:

  • 41

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 + aou + nitrate + silicate 1.7979872 685.8837 8.915509 1982-1999 –> 2000-2012 3.6055366 1598.7717
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou 1.2043383 549.2359 4.445163 1982-1999 –> 2000-2012 2.5928383 1341.9648
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 1.1914188 547.6120 4.887897 1982-1999 –> 2000-2012 2.5535458 1333.7497
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.1051493 524.3568 3.304136 1982-1999 –> 2000-2012 2.4643137 1311.5190
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 1.0709739 511.8023 4.694811 1982-1999 –> 2000-2012 2.4040133 1288.2696
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate 1.1639203 539.7661 4.829575 1982-1999 –> 2000-2012 2.5231488 1324.9495
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.0694684 513.3297 4.624413 1982-1999 –> 2000-2012 2.4024546 1291.7791
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate 1.4974719 622.4328 5.357017 1982-1999 –> 2000-2012 3.3857999 1552.9072
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 1.3240242 583.0704 5.870624 1982-1999 –> 2000-2012 2.7624787 1393.6339
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate 1.5656900 639.4011 4.536433 1982-1999 –> 2000-2012 3.2869598 1530.3775
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou 1.3308655 275.9438 3.290423 2000-2012 –> 2013-2019 2.5352037 825.1797
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 1.3308598 277.9431 3.298957 2000-2012 –> 2013-2019 2.5222786 825.5552
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.1929038 262.8713 2.724893 2000-2012 –> 2013-2019 2.2980531 787.2281
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 1.2518691 268.3979 3.819602 2000-2012 –> 2013-2019 2.3228430 780.2002
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate 1.3246093 277.2087 3.484243 2000-2012 –> 2013-2019 2.4885296 816.9748
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.1901456 262.5102 3.453009 2000-2012 –> 2013-2019 2.2596141 775.8399
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate 1.7639722 319.8951 4.591325 2000-2012 –> 2013-2019 3.2614441 942.3279
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 1.4547154 291.8248 4.033856 2000-2012 –> 2013-2019 2.7787395 874.8952
Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate 1.8139422 324.2528 4.228206 2000-2012 –> 2013-2019 3.5174049 989.9909
Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate 1.7006016 316.1876 3.553807 2000-2012 –> 2013-2019 3.2662915 955.5887
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 3.4355823 6039.8999 15.582115 1982-1999 –> 2000-2012 6.8680661 14878.4970
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.3438101 5980.3843 15.193660 1982-1999 –> 2000-2012 6.6831982 14729.4729
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate 3.9904467 6380.0563 17.799592 1982-1999 –> 2000-2012 7.9826027 15721.3388
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6004284 6148.3804 14.160333 1982-1999 –> 2000-2012 7.1392057 15090.4719
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate 3.9941888 6382.1860 18.954002 1982-1999 –> 2000-2012 8.0810957 15801.5333
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate 3.9996578 6383.2947 18.489476 1982-1999 –> 2000-2012 8.1163779 15824.8311
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate 3.9798872 6374.0362 19.108434 1982-1999 –> 2000-2012 8.0908823 15812.9412
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate 4.4846700 6643.3390 12.328905 1982-1999 –> 2000-2012 9.0127658 16401.8498
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 4.0993827 6441.2487 14.735760 1982-1999 –> 2000-2012 8.2126070 15881.9577
Atlantic (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4.5265699 6666.4676 12.618353 1982-1999 –> 2000-2012 8.9266981 16331.5719
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 3.3529894 3261.1855 10.303799 2000-2012 –> 2013-2019 6.7885717 9301.0854
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.2019551 3206.2174 9.370614 2000-2012 –> 2013-2019 6.5457652 9186.6017
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate 3.9679578 3469.3270 11.496873 2000-2012 –> 2013-2019 7.9584045 9849.3833
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.6537066 3369.3453 10.309180 2000-2012 –> 2013-2019 7.2541351 9517.7258
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate 4.3208649 3572.6391 13.768183 2000-2012 –> 2013-2019 8.9920836 10308.5737
Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate 3.8524592 3432.8157 11.307173 2000-2012 –> 2013-2019 7.8466479 9815.0016
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate 4.0173849 3482.6281 12.004710 2000-2012 –> 2013-2019 8.0170426 9865.9229
Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate 3.8397846 3428.7425 11.206273 2000-2012 –> 2013-2019 7.8196717 9802.7788
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate 4.3535265 3581.9470 12.269478 2000-2012 –> 2013-2019 8.8381966 10225.2860
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 3.9538872 3464.9362 13.426711 2000-2012 –> 2013-2019 8.0532699 9906.1849
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + phosphate 4.5136026 9139.2266 13.183405 1982-1999 –> 2000-2012 8.4434732 20918.2417
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 3.3451130 8206.4897 9.984430 1982-1999 –> 2000-2012 6.5607432 19140.6428
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate 4.7338309 9289.8608 45.693736 1982-1999 –> 2000-2012 9.5892953 21963.8215
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.7333357 9291.5344 46.104044 1982-1999 –> 2000-2012 9.5789970 21958.9623
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.5119495 9140.0837 12.884756 1982-1999 –> 2000-2012 8.4394941 20918.5991
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.2947613 8161.1695 10.455973 1982-1999 –> 2000-2012 6.4445084 19009.9221
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate 4.8320414 9351.9276 44.658364 1982-1999 –> 2000-2012 9.8537335 22166.0101
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate 4.8277491 9351.1548 45.897056 1982-1999 –> 2000-2012 9.8491101 22166.9590
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + phosphate 4.7676872 9310.0956 12.923617 1982-1999 –> 2000-2012 8.9517345 21353.7141
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 3.4179295 8273.6773 10.821627 1982-1999 –> 2000-2012 6.6469078 19225.3197
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + nitrate + silicate 4.4227791 4283.3890 16.771351 2000-2012 –> 2013-2019 9.3931429 13725.3755
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + phosphate 4.9297992 4440.9281 15.796238 2000-2012 –> 2013-2019 9.4434018 13580.1547
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 3.4519208 3919.0679 10.234892 2000-2012 –> 2013-2019 6.7970338 12125.5577
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate 4.1616099 4193.9156 15.650820 2000-2012 –> 2013-2019 8.8954408 13483.7763
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.1033402 4175.1876 16.778173 2000-2012 –> 2013-2019 8.8366759 13466.7220
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.9284457 4442.5244 16.114540 2000-2012 –> 2013-2019 9.4403952 13582.6082
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.4268245 3910.3417 10.584934 2000-2012 –> 2013-2019 6.7215859 12071.5112
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate 4.2871781 4235.6139 15.861123 2000-2012 –> 2013-2019 9.1192195 13587.5415
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate 4.2047959 4209.0915 17.180581 2000-2012 –> 2013-2019 9.0325449 13560.2463
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 3.5774973 3971.5950 11.143465 2000-2012 –> 2013-2019 6.9954268 12245.2722
Atlantic (26.75,27] cstar_tref ~ sal + aou + nitrate + silicate 4.3465805 15435.6713 37.756764 1982-1999 –> 2000-2012 8.8806195 35967.3944
Atlantic (26.75,27] cstar_tref ~ sal + aou + phosphate 4.1695168 15211.5845 14.663913 1982-1999 –> 2000-2012 7.5033660 33588.2934
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 2.2365224 11887.4160 19.548166 1982-1999 –> 2000-2012 4.2545625 26751.1156
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + nitrate 4.9745169 16156.2446 47.728105 1982-1999 –> 2000-2012 9.9474496 37334.9286
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.1845458 15234.7979 36.946982 1982-1999 –> 2000-2012 8.5135566 35444.5097
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 4.0989955 15122.4938 22.072268 1982-1999 –> 2000-2012 7.4297426 33494.6841
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.1203301 11604.5250 15.079101 1982-1999 –> 2000-2012 3.8780807 25503.3052
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate 4.2124771 15268.3233 36.502723 1982-1999 –> 2000-2012 8.6160054 35595.5385
Atlantic (26.75,27] cstar_tref ~ temp + aou + phosphate 4.6957961 15846.3370 13.444724 1982-1999 –> 2000-2012 8.4138186 34986.7147
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2.2592103 11941.3136 16.122729 1982-1999 –> 2000-2012 4.0744471 26063.4253
Atlantic (26.75,27] cstar_tref ~ sal + aou + nitrate + silicate 4.0994946 8003.3615 32.947066 2000-2012 –> 2013-2019 8.4460751 23439.0329
Atlantic (26.75,27] cstar_tref ~ sal + aou + phosphate 4.8980193 8503.9409 13.689358 2000-2012 –> 2013-2019 9.0675360 23715.5254
Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 2.5995484 6716.9561 24.264161 2000-2012 –> 2013-2019 4.8360707 18604.3721
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + nitrate 5.0091843 8569.3176 48.195291 2000-2012 –> 2013-2019 9.9837011 24725.5622
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.0308733 7957.6906 35.129593 2000-2012 –> 2013-2019 8.2154191 23192.4885
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 4.7571171 8423.5110 12.957027 2000-2012 –> 2013-2019 8.8561126 23546.0047
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.5714581 6688.2744 25.212987 2000-2012 –> 2013-2019 4.6917882 18292.7994
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate 5.0224444 8574.7833 49.403301 2000-2012 –> 2013-2019 9.9975847 24729.6972
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate 4.0310619 7955.8227 35.024687 2000-2012 –> 2013-2019 8.2435390 23224.1460
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 2.7601533 6886.2508 27.686717 2000-2012 –> 2013-2019 5.0193637 18827.5644
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate 2.6943491 11170.7407 20.001256 1982-1999 –> 2000-2012 5.9141733 27033.2774
Atlantic (27,27.25] cstar_tref ~ sal + aou + phosphate 3.1542666 11898.4258 12.378649 1982-1999 –> 2000-2012 5.6562493 26214.2247
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 1.9771119 9737.6654 9.743648 1982-1999 –> 2000-2012 3.7957715 22102.0078
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate 3.0458635 11738.5074 23.773723 1982-1999 –> 2000-2012 6.1895687 27454.5295
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.2100456 10255.3364 18.140966 1982-1999 –> 2000-2012 4.6462747 24412.0401
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 3.1037168 11825.6250 12.327428 1982-1999 –> 2000-2012 5.5990723 26127.1815
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.9433711 9659.9692 9.780245 1982-1999 –> 2000-2012 3.5783826 21374.4124
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate 3.0549813 11750.3466 23.488242 1982-1999 –> 2000-2012 6.2469989 27557.7663
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate 2.2107803 10254.8753 18.059224 1982-1999 –> 2000-2012 4.7255758 24603.9555
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate 2.6028293 11010.7390 12.226447 1982-1999 –> 2000-2012 4.7596249 24419.3695
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate 3.4419817 6843.9338 35.575880 2000-2012 –> 2013-2019 6.7277524 18931.4729
Atlantic (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate 2.6753770 6197.3962 26.440282 2000-2012 –> 2013-2019 5.3697261 17368.1369
Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 2.3351662 5847.3136 13.611619 2000-2012 –> 2013-2019 4.3122781 15584.9790
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate 3.3904785 6807.1273 35.453401 2000-2012 –> 2013-2019 6.4363421 18545.6348
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.4957442 6020.4946 25.558211 2000-2012 –> 2013-2019 4.7057899 16275.8310
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 3.5625214 6934.5338 14.345929 2000-2012 –> 2013-2019 6.6662382 18760.1589
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.3301867 5843.8189 13.907665 2000-2012 –> 2013-2019 4.2735578 15503.7881
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate 3.5018813 6888.3429 34.806829 2000-2012 –> 2013-2019 6.5568626 18638.6895
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate 2.5779754 6101.9370 24.809555 2000-2012 –> 2013-2019 4.7887557 16356.8123
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate 3.1934757 6653.0446 15.340464 2000-2012 –> 2013-2019 5.7963051 17663.7837
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 2.5924312 11855.4440 13.069770 1982-1999 –> 2000-2012 5.3326841 29283.5153
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + phosphate 3.3144485 13080.4455 21.998383 1982-1999 –> 2000-2012 6.3094355 31144.3891
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 2.8584420 12343.2610 22.990288 1982-1999 –> 2000-2012 5.6118706 29805.7533
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate 3.1549165 12836.0954 17.500848 1982-1999 –> 2000-2012 5.7285284 29813.9451
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.2210980 11085.3993 14.016845 1982-1999 –> 2000-2012 4.0373466 25564.1467
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 3.2597086 12999.2782 20.754816 1982-1999 –> 2000-2012 5.9610120 30324.6193
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.8023109 12246.2184 21.814276 1982-1999 –> 2000-2012 5.2463875 28855.4783
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate 3.2618547 13000.5650 17.438143 1982-1999 –> 2000-2012 5.8397748 29988.4174
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 2.4583415 11590.2168 14.105424 1982-1999 –> 2000-2012 4.3015537 26172.7141
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate 3.6842077 13610.6322 14.643677 1982-1999 –> 2000-2012 6.6635867 31639.0812
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate 3.9643653 7632.6710 16.145757 2000-2012 –> 2013-2019 7.4951803 21028.9245
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate 3.0862675 6952.1260 15.715825 2000-2012 –> 2013-2019 5.6786987 18807.5700
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + phosphate 4.1774829 7775.4129 24.694295 2000-2012 –> 2013-2019 7.4919314 20855.8584
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.7428537 7477.9330 25.719311 2000-2012 –> 2013-2019 6.6012958 19821.1941
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate 3.7245537 7464.5721 17.446910 2000-2012 –> 2013-2019 6.8794702 20300.6675
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8794846 6765.0749 14.381413 2000-2012 –> 2013-2019 5.1005825 17850.4742
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 4.1419372 7754.1184 23.674294 2000-2012 –> 2013-2019 7.4016458 20753.3966
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.7104579 7456.2358 24.789558 2000-2012 –> 2013-2019 6.5127688 19702.4542
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate 3.8937891 7583.7038 15.641480 2000-2012 –> 2013-2019 7.1556437 20584.2688
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate 3.1786481 7032.5254 12.434604 2000-2012 –> 2013-2019 5.6369895 18622.7422
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate 3.5616302 20232.4599 16.468611 1982-1999 –> 2000-2012 6.7873765 46563.0850
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate 3.0167581 18985.8722 14.881585 1982-1999 –> 2000-2012 5.9316343 44288.7113
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 2.9055285 18701.3647 17.392654 1982-1999 –> 2000-2012 5.4605671 42663.2585
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 2.6619219 18044.8615 19.625058 1982-1999 –> 2000-2012 5.1381309 41690.2927
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate 3.4731721 20045.3316 15.793395 1982-1999 –> 2000-2012 6.3001385 45036.9780
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.8224707 18487.2649 13.827754 1982-1999 –> 2000-2012 5.1809520 41639.6960
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 2.8874703 18656.4814 17.295800 1982-1999 –> 2000-2012 5.2261995 41721.4481
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.6041209 17881.7733 19.658847 1982-1999 –> 2000-2012 4.7997322 40307.0382
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate 3.2816362 19618.7506 16.377780 1982-1999 –> 2000-2012 5.7538359 43247.7147
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 3.7636868 20649.4183 17.527626 1982-1999 –> 2000-2012 6.6603602 45888.5987
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate 4.0997077 11340.7363 18.415139 2000-2012 –> 2013-2019 7.6613379 31573.1962
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate 3.3616336 10547.9878 16.630404 2000-2012 –> 2013-2019 6.3783917 29533.8600
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + phosphate 3.4148343 10608.8583 13.555597 2000-2012 –> 2013-2019 6.3203628 29310.2230
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 3.0011240 10093.7734 14.392043 2000-2012 –> 2013-2019 5.6630459 28138.6349
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate 4.0926132 11335.8014 18.205055 2000-2012 –> 2013-2019 7.5657853 31381.1330
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.3187334 10498.5610 16.109561 2000-2012 –> 2013-2019 6.1412041 28985.8259
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 3.4093268 10604.3954 13.379528 2000-2012 –> 2013-2019 6.2967972 29260.8768
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.0000950 10094.4003 14.405089 2000-2012 –> 2013-2019 5.6042159 27976.1735
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate 4.0709495 11314.5505 18.311761 2000-2012 –> 2013-2019 7.3525857 30933.3011
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 4.4894333 11706.3427 18.881946 2000-2012 –> 2013-2019 8.2531201 32355.7611
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 1.9328237 5410.4375 13.304351 1982-1999 –> 2000-2012 3.8998084 12446.3534
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate 2.2983963 5858.4881 11.332919 1982-1999 –> 2000-2012 4.2541777 12873.2575
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.7700096 5181.8213 12.243782 1982-1999 –> 2000-2012 3.5500394 11882.9673
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate 2.8376475 6408.0523 13.351113 1982-1999 –> 2000-2012 5.1420463 13974.6503
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.7589195 5167.4921 14.092507 1982-1999 –> 2000-2012 3.4890179 11775.2677
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 2.1041418 5631.0745 12.284382 1982-1999 –> 2000-2012 3.7864540 12142.9635
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.6156555 4946.7689 12.930476 1982-1999 –> 2000-2012 3.1746413 11205.4577
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate 2.3052431 5868.2158 16.105208 1982-1999 –> 2000-2012 4.2386435 12846.4055
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + phosphate 2.5432252 6121.4613 14.467755 1982-1999 –> 2000-2012 4.4857227 13113.3859
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate 2.3522550 5920.6652 15.245745 1982-1999 –> 2000-2012 4.2629364 12859.2328
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 2.0476770 2813.9656 12.694233 2000-2012 –> 2013-2019 3.9805007 8224.4031
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + phosphate 2.6579239 3154.1868 10.578892 2000-2012 –> 2013-2019 4.9563202 9012.6749
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 1.8581579 2686.5437 11.776253 2000-2012 –> 2013-2019 3.6281675 7868.3650
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate 3.2741846 3429.7697 12.197003 2000-2012 –> 2013-2019 6.1118321 9837.8220
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.9432112 2747.2639 13.161242 2000-2012 –> 2013-2019 3.7021307 7914.7560
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 2.5005533 3076.1111 11.287467 2000-2012 –> 2013-2019 4.6046950 8707.1856
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.7606499 2617.8234 12.187032 2000-2012 –> 2013-2019 3.3763054 7564.5923
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate 2.6941847 3173.9648 15.520638 2000-2012 –> 2013-2019 4.9994278 9042.1807
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + phosphate 2.9882417 3307.8743 13.997842 2000-2012 –> 2013-2019 5.5314669 9429.3356
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate 2.7013116 3177.4308 15.102614 2000-2012 –> 2013-2019 5.0535666 9098.0960
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate 4.0521030 6987.8002 64.166443 1982-1999 –> 2000-2012 7.3767129 15959.1950
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate 4.0487901 6987.7750 62.452143 1982-1999 –> 2000-2012 7.3341874 15920.5923
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 3.7067356 6769.2272 37.186586 1982-1999 –> 2000-2012 7.0943846 15806.8627
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.6208361 6713.1733 46.326798 1982-1999 –> 2000-2012 6.8137290 15550.3147
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 3.5749853 6679.6194 50.360961 1982-1999 –> 2000-2012 6.6621117 15399.5524
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5723212 6679.7736 48.930358 1982-1999 –> 2000-2012 6.6446587 15385.2836
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + nitrate 3.7074767 6767.7221 38.501157 1982-1999 –> 2000-2012 7.1060293 15814.3477
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 3.6208361 6711.1733 46.318352 1982-1999 –> 2000-2012 6.8889725 15625.9752
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate 3.5752685 6677.8155 49.566127 1982-1999 –> 2000-2012 6.7520165 15493.6198
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 3.5724467 6677.8606 48.371030 1982-1999 –> 2000-2012 6.7491780 15495.6468
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + phosphate 3.7579621 3893.8265 26.025630 2000-2012 –> 2013-2019 7.8100651 10881.6267
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate 3.5923822 3832.0198 25.669438 2000-2012 –> 2013-2019 7.6411723 10819.7948
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 3.9675233 3972.6661 25.160550 2000-2012 –> 2013-2019 7.6742589 10741.8933
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.5054092 3799.3160 25.395176 2000-2012 –> 2013-2019 7.1262453 10512.4893
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 3.5052511 3797.2522 25.574745 2000-2012 –> 2013-2019 7.0802364 10476.8716
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.3614399 3739.9320 25.280442 2000-2012 –> 2013-2019 6.9337610 10419.7056
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + nitrate 4.0924012 4014.5477 24.608372 2000-2012 –> 2013-2019 7.7998778 10782.2698
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 3.8372921 3925.4070 24.980562 2000-2012 –> 2013-2019 7.4581282 10636.5803
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + phosphate 3.7724012 3899.2568 23.929748 2000-2012 –> 2013-2019 7.3476697 10577.0723
Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 3.7397860 3888.9612 24.138528 2000-2012 –> 2013-2019 7.3122327 10566.8218
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate 4.1709717 10675.1900 28.517619 1982-1999 –> 2000-2012 8.4403823 25640.0486
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate 4.1688521 10675.2859 28.441753 1982-1999 –> 2000-2012 8.4362902 25639.7369
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate 4.2530249 10750.1675 27.334932 1982-1999 –> 2000-2012 8.8151921 26062.5637
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.1177015 10631.0392 26.286322 1982-1999 –> 2000-2012 8.5565155 25802.6264
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 3.8938747 10419.6738 26.237305 1982-1999 –> 2000-2012 8.0350175 25227.6067
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.8776148 10405.9987 25.952066 1982-1999 –> 2000-2012 8.0063456 25200.2924
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate 4.2689973 10762.2094 27.307160 1982-1999 –> 2000-2012 8.8813092 26129.5584
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate 4.1640643 10670.9812 26.391442 1982-1999 –> 2000-2012 8.6908999 25942.8716
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate 3.9280155 10450.3750 26.218377 1982-1999 –> 2000-2012 8.1455204 25351.5044
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 3.9221329 10446.7607 26.049458 1982-1999 –> 2000-2012 8.1372873 25346.9858
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate 4.0037631 5532.5489 26.960221 2000-2012 –> 2013-2019 8.1747349 16207.7390
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate 3.9932278 5529.3636 27.039948 2000-2012 –> 2013-2019 8.1620800 16204.6495
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate 4.2022398 5629.7666 26.242521 2000-2012 –> 2013-2019 8.4552647 16379.9341
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.0477544 5558.0544 25.389885 2000-2012 –> 2013-2019 8.1654559 16189.0936
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 3.8042578 5433.9570 24.996323 2000-2012 –> 2013-2019 7.6981324 15853.6308
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.7794327 5423.0725 25.038717 2000-2012 –> 2013-2019 7.6570474 15829.0712
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate 4.2598613 5654.5686 27.061030 2000-2012 –> 2013-2019 8.5288586 16416.7780
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate 4.1549762 5607.5066 26.603877 2000-2012 –> 2013-2019 8.3190405 16278.4878
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate 3.8942491 5477.9688 24.850256 2000-2012 –> 2013-2019 7.8222647 15928.3438
Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 3.8875793 5476.5952 24.862579 2000-2012 –> 2013-2019 7.8097122 15923.3560
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate 1.2846751 4186.9499 6.259752 1982-1999 –> 2000-2012 2.4182987 9259.3546
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1.2706915 4161.5664 5.681836 1982-1999 –> 2000-2012 2.4033631 9233.2173
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate 1.2936655 4206.3983 9.435540 1982-1999 –> 2000-2012 2.4514785 9350.0136
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.2043636 4029.4343 7.444928 1982-1999 –> 2000-2012 2.2941696 8976.6218
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.1516323 3915.4175 7.717827 1982-1999 –> 2000-2012 2.1885741 8697.6100
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.1473329 3908.0592 7.366582 1982-1999 –> 2000-2012 2.1841723 8691.9281
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate 1.3258191 4265.8245 11.593273 1982-1999 –> 2000-2012 2.5118674 9486.4203
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate 1.2909720 4201.1835 11.407720 1982-1999 –> 2000-2012 2.4509282 9350.8611
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate 1.2638184 4145.9966 11.794931 1982-1999 –> 2000-2012 2.4143248 9266.8597
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate 1.2587069 4137.8566 11.813569 1982-1999 –> 2000-2012 2.3910640 9208.5971
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate 1.4300984 2472.4809 6.552824 2000-2012 –> 2013-2019 2.7147735 6659.4308
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1.3792748 2424.3280 5.516656 2000-2012 –> 2013-2019 2.6499663 6585.8944
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate 1.4210472 2465.6810 10.070826 2000-2012 –> 2013-2019 2.7147127 6672.0793
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.2881510 2331.5948 7.630773 2000-2012 –> 2013-2019 2.4925145 6361.0292
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 1.2523837 2290.5663 8.224435 2000-2012 –> 2013-2019 2.4040160 6205.9837
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.2310580 2268.7621 7.450137 2000-2012 –> 2013-2019 2.3783909 6176.8213
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate 1.4602809 2501.4283 12.504427 2000-2012 –> 2013-2019 2.7861000 6767.2528
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate 1.4100747 2454.9376 12.389456 2000-2012 –> 2013-2019 2.7010467 6656.1211
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate 1.3809322 2423.9925 12.682790 2000-2012 –> 2013-2019 2.6447506 6569.9890
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate 1.3804589 2425.5174 12.676516 2000-2012 –> 2013-2019 2.6391658 6563.3740
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate 1.0001664 3979.8173 4.627289 1982-1999 –> 2000-2012 1.8581749 8768.9361
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate 0.9888141 3945.9001 4.185494 1982-1999 –> 2000-2012 1.8632874 8804.7541
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate 0.9817677 3927.9043 4.115779 1982-1999 –> 2000-2012 1.8217506 8636.8917
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate 0.8942682 3666.9003 6.143180 1982-1999 –> 2000-2012 1.6402112 7927.7920
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.8395288 3492.2913 5.824235 1982-1999 –> 2000-2012 1.5581767 7614.4971
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate 0.8093116 3387.7988 5.388705 1982-1999 –> 2000-2012 1.5303121 7520.3390
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.7972728 3347.8948 5.317335 1982-1999 –> 2000-2012 1.4740772 7243.7012
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + silicate 1.0248213 4047.9053 11.699294 1982-1999 –> 2000-2012 1.8261966 8579.3178
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate 0.9893063 3947.2916 11.077933 1982-1999 –> 2000-2012 1.7905572 8476.1182
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate 0.9800064 3922.8835 11.017377 1982-1999 –> 2000-2012 1.7375651 8242.0905
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate + silicate 1.0914734 2157.2091 6.686857 2000-2012 –> 2013-2019 2.0916398 6137.0264
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate 1.0653838 2120.7577 5.937265 2000-2012 –> 2013-2019 2.0541979 6066.6578
Atlantic (28.1,28.15] cstar_tref ~ sal + aou + silicate + phosphate 1.0653280 2122.6831 5.942134 2000-2012 –> 2013-2019 2.0470957 6050.5874
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate 1.0014374 2034.6139 8.283117 2000-2012 –> 2013-2019 1.8957056 5701.5141
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.9300484 1931.3019 7.718437 2000-2012 –> 2013-2019 1.7695772 5423.5932
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate 0.8849636 1858.5432 6.958491 2000-2012 –> 2013-2019 1.6942752 5246.3420
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.8845179 1859.8258 6.949110 2000-2012 –> 2013-2019 1.6817907 5207.7206
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + silicate 1.0793517 2141.3059 13.714359 2000-2012 –> 2013-2019 2.1041730 6189.2112
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate 1.0412125 2088.0780 13.015802 2000-2012 –> 2013-2019 2.0305188 6035.3696
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate 1.0403664 2088.9203 12.990054 2000-2012 –> 2013-2019 2.0203727 6011.8038
Atlantic (28.15,28.2] cstar_tref ~ aou + nitrate + silicate 1.0150968 5782.9722 23.217271 1982-1999 –> 2000-2012 1.7510028 12148.5721
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate 0.7725648 4683.7802 10.144436 1982-1999 –> 2000-2012 1.4056175 10189.1442
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate 0.7587494 4613.1336 8.276041 1982-1999 –> 2000-2012 1.3877901 10084.1700
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.6659083 4087.6614 7.918388 1982-1999 –> 2000-2012 1.2147171 8779.0476
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.6658899 4089.5505 7.861172 1982-1999 –> 2000-2012 1.2128558 8763.7158
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate 0.9135168 5360.4806 16.031405 1982-1999 –> 2000-2012 1.6851590 11999.0304
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.8391352 5020.5527 10.759834 1982-1999 –> 2000-2012 1.5756525 11394.8979
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate 0.7737979 4690.2010 12.224785 1982-1999 –> 2000-2012 1.3748519 9899.1864
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.7176256 4388.7903 12.118912 1982-1999 –> 2000-2012 1.2777278 9196.5647
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate 0.8392335 5019.0245 10.583301 1982-1999 –> 2000-2012 1.6103451 11653.6435
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate 0.8796573 2792.7830 8.993340 2000-2012 –> 2013-2019 1.6522222 7476.5631
Atlantic (28.15,28.2] cstar_tref ~ sal + aou + nitrate + silicate 0.8313687 2673.0573 6.109030 2000-2012 –> 2013-2019 1.5901181 7286.1909
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate 0.7635202 2489.5089 6.905498 2000-2012 –> 2013-2019 1.4294285 6577.1703
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.7554349 2468.5561 5.925970 2000-2012 –> 2013-2019 1.4213248 6558.1065
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate 1.0583864 3193.5748 13.696345 2000-2012 –> 2013-2019 1.9719032 8554.0554
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.9345422 2927.2734 8.025563 2000-2012 –> 2013-2019 1.7736773 7947.8262
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate 0.9385901 2932.5919 11.306237 2000-2012 –> 2013-2019 1.7123881 7622.7930
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate 0.8758629 2785.4631 11.227380 2000-2012 –> 2013-2019 1.5934885 7174.2534
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + phosphate 1.0976795 3270.1673 12.858640 2000-2012 –> 2013-2019 2.1040742 9018.4770
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate 0.9517195 2964.5419 9.909076 2000-2012 –> 2013-2019 1.7909530 7983.5664
Atlantic (28.2, Inf] cstar_tref ~ aou + nitrate + silicate 0.7727177 9821.2700 15.271565 1982-1999 –> 2000-2012 1.5695877 23976.4397
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.3566263 3287.5171 1.988203 1982-1999 –> 2000-2012 0.6691525 6334.2006
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.3534411 3213.7066 1.988553 1982-1999 –> 2000-2012 0.6596790 6021.1606
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + silicate + phosphate 0.6990396 8976.5255 2.842565 1982-1999 –> 2000-2012 1.2827011 19438.3524
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.3560111 3274.9265 2.045845 1982-1999 –> 2000-2012 0.6669547 6263.3605
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.3509290 3155.4335 2.134668 1982-1999 –> 2000-2012 0.6570626 5960.8427
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate 0.9013505 11124.4041 12.898765 1982-1999 –> 2000-2012 1.8248495 27031.8462
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.6816066 8765.1232 2.911507 1982-1999 –> 2000-2012 1.2555193 19029.0472
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate 0.6753154 8684.7681 6.816568 1982-1999 –> 2000-2012 1.2318027 18580.7669
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + silicate + phosphate 0.9046595 11155.3685 8.739880 1982-1999 –> 2000-2012 1.6782928 24961.3237
Atlantic (28.2, Inf] cstar_tref ~ aou + nitrate + silicate 1.0713973 7143.0033 20.055030 2000-2012 –> 2013-2019 1.8441150 16964.2733
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 0.4264163 2726.2777 2.452673 2000-2012 –> 2013-2019 0.7830427 6013.7947
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate 0.4165997 2616.6231 2.435991 2000-2012 –> 2013-2019 0.7700408 5830.3298
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + phosphate 1.0955880 7250.0416 14.560516 2000-2012 –> 2013-2019 1.9969442 18372.4989
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + silicate + phosphate 0.8107101 5808.3957 2.835865 2000-2012 –> 2013-2019 1.5097497 14784.9213
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 0.4234133 2694.3964 2.563266 2000-2012 –> 2013-2019 0.7794244 5969.3229
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 0.4031930 2461.8100 2.685125 2000-2012 –> 2013-2019 0.7541221 5617.2435
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate 1.0946010 7247.7208 13.987805 2000-2012 –> 2013-2019 1.9959515 18372.1249
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 0.7742414 5589.7429 3.139424 2000-2012 –> 2013-2019 1.4558480 14354.8661
Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate 0.8922617 6267.8955 8.940761 2000-2012 –> 2013-2019 1.5675771 14952.6635
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 7.4439384 38510.3404 59.558635 1982-1999 –> 2000-2012 15.1437988 91704.7035
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 7.2111316 38155.3258 53.102312 1982-1999 –> 2000-2012 14.6039978 90726.3344
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.4254929 36857.2246 30.208689 1982-1999 –> 2000-2012 13.1429671 87953.7368
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.3773992 36774.8088 29.718986 1982-1999 –> 2000-2012 13.0347184 87735.0625
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate 7.9657308 39269.5641 37.182876 1982-1999 –> 2000-2012 16.2238251 93537.6988
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 7.9447879 39241.9842 36.536151 1982-1999 –> 2000-2012 16.1735886 93457.5006
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate 7.9825970 39293.3294 35.188077 1982-1999 –> 2000-2012 16.2706483 93617.1192
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate 7.9763193 39286.4896 34.895002 1982-1999 –> 2000-2012 16.2454705 93577.1896
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + phosphate 7.9224355 39208.3276 34.751322 1982-1999 –> 2000-2012 16.2286578 93565.7783
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate 7.5119852 38612.5848 28.234413 1982-1999 –> 2000-2012 15.3711529 92121.7026
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 7.3614676 20270.9536 55.451975 2000-2012 –> 2013-2019 14.8054059 58781.2940
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 7.0553702 20021.0201 43.011672 2000-2012 –> 2013-2019 14.2665018 58176.3459
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 6.1276808 19182.7699 25.473564 2000-2012 –> 2013-2019 12.5531737 56039.9945
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 6.0470335 19106.1797 24.650519 2000-2012 –> 2013-2019 12.4244327 55880.9886
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate 7.6102296 20466.0979 39.358896 2000-2012 –> 2013-2019 15.5759604 59735.6620
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate 7.5257367 20401.8692 29.624509 2000-2012 –> 2013-2019 15.4705245 59643.8535
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + phosphate 7.5388760 20410.2170 29.018857 2000-2012 –> 2013-2019 15.5214730 59703.5464
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate 7.5147450 20393.1990 28.562745 2000-2012 –> 2013-2019 15.4910643 59679.6886
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + phosphate 7.7891700 20603.9633 26.336030 2000-2012 –> 2013-2019 15.7116055 59812.2909
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + silicate + phosphate 7.2631462 20191.1907 23.989973 2000-2012 –> 2013-2019 14.7751314 58803.7754
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + phosphate 6.7452272 39770.2402 51.652901 1982-1999 –> 2000-2012 13.2192397 94622.6941
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate 6.3014575 38959.1285 52.803670 1982-1999 –> 2000-2012 12.3563662 92696.8419
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 7.1019307 40389.9387 30.362985 1982-1999 –> 2000-2012 13.7702665 95739.8683
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate 5.0755511 36374.2283 42.154614 1982-1999 –> 2000-2012 9.8723949 86225.5866
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate 7.1020120 40388.0754 30.000569 1982-1999 –> 2000-2012 13.7703574 95736.0291
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.6161138 35242.5790 40.891373 1982-1999 –> 2000-2012 8.9414393 83369.4242
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate 7.2318998 40604.6167 27.390766 1982-1999 –> 2000-2012 14.0506186 96324.6653
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + phosphate 5.5548314 37450.3318 43.347669 1982-1999 –> 2000-2012 10.8577694 88973.3433
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate 7.2319785 40602.7468 27.030682 1982-1999 –> 2000-2012 14.0506989 96320.7993
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4.9509994 36077.3723 41.437095 1982-1999 –> 2000-2012 9.6267773 85502.1927
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + phosphate 6.7896451 21103.0171 24.825428 2000-2012 –> 2013-2019 13.5348723 60873.2574
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate 6.2703895 20601.7193 22.631273 2000-2012 –> 2013-2019 12.5718470 59560.8478
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 7.1769795 21457.9833 27.375653 2000-2012 –> 2013-2019 14.2789102 61847.9220
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate 5.1575902 19365.8149 41.629135 2000-2012 –> 2013-2019 10.2331412 55740.0431
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate 7.1837795 21461.9741 27.422147 2000-2012 –> 2013-2019 14.2857915 61850.0495
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.6574285 18722.5251 39.739545 2000-2012 –> 2013-2019 9.2735423 53965.1042
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate 7.2201288 21493.9024 28.576222 2000-2012 –> 2013-2019 14.4108091 62030.2246
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate 7.1688463 21448.8104 29.891200 2000-2012 –> 2013-2019 14.4255932 62094.4072
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + phosphate 5.5799356 19861.7203 38.179164 2000-2012 –> 2013-2019 11.1347670 57312.0521
Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate 4.9136860 19059.3514 36.964086 2000-2012 –> 2013-2019 9.8646854 55136.7237
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + phosphate 5.5776295 31278.3421 31.889129 1982-1999 –> 2000-2012 11.0205041 74454.6095
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate 5.5776232 31280.3308 31.865797 1982-1999 –> 2000-2012 10.9997964 74405.7596
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate 4.9506579 30091.9624 32.324509 1982-1999 –> 2000-2012 9.6749059 71306.8189
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 4.7904695 29766.1604 31.618768 1982-1999 –> 2000-2012 9.4237878 70713.5296
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.5015798 29146.2749 20.161616 1982-1999 –> 2000-2012 8.6448420 68543.5662
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.2360966 28542.4799 19.954055 1982-1999 –> 2000-2012 8.2115795 67368.5892
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate 5.4794452 31105.3459 25.154367 1982-1999 –> 2000-2012 10.9317815 74309.6964
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + phosphate 4.6434034 29453.4120 27.329374 1982-1999 –> 2000-2012 8.9974513 69536.7690
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 4.3727026 28856.7911 24.913709 1982-1999 –> 2000-2012 8.5429722 68344.1730
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + silicate + phosphate 5.6071189 31332.8944 29.367547 1982-1999 –> 2000-2012 11.2655048 75049.5969
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + phosphate 6.0100775 17348.4066 35.574082 2000-2012 –> 2013-2019 11.5877070 48626.7487
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + silicate + phosphate 6.0081850 17348.7066 35.993474 2000-2012 –> 2013-2019 11.5858082 48629.0374
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate 5.3586017 16731.0694 37.172152 2000-2012 –> 2013-2019 10.3092596 46823.0318
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 5.1514754 16520.2807 36.539159 2000-2012 –> 2013-2019 9.9419449 46286.4411
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate 4.8695214 16216.4407 23.726262 2000-2012 –> 2013-2019 9.3711012 45362.7157
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.5675473 15872.8646 23.790924 2000-2012 –> 2013-2019 8.8036439 44415.3445
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate 5.6974599 17064.0606 25.082320 2000-2012 –> 2013-2019 11.1769051 48169.4065
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + phosphate 5.0161354 16374.5678 31.933839 2000-2012 –> 2013-2019 9.6595388 45827.9798
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 4.6927690 16016.8614 29.306095 2000-2012 –> 2013-2019 9.0654716 44873.6524
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + silicate + phosphate 5.8344464 17190.3113 29.594597 2000-2012 –> 2013-2019 11.4415652 48523.2057
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate 5.4456283 38215.7329 27.338641 1982-1999 –> 2000-2012 10.4328372 90239.4921
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 5.3239132 37940.3753 26.164674 1982-1999 –> 2000-2012 10.1907916 89546.2913
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 4.7283178 36484.6734 22.062270 1982-1999 –> 2000-2012 8.8243027 85126.2509
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.6904849 36388.1022 20.587989 1982-1999 –> 2000-2012 8.7566764 84906.1856
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + phosphate 5.7641324 38913.1782 36.037619 1982-1999 –> 2000-2012 11.4271210 93121.3629
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate 5.7177415 38816.0273 38.733330 1982-1999 –> 2000-2012 11.3249393 92856.0190
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate 4.9094485 36943.9289 22.137235 1982-1999 –> 2000-2012 9.2842785 86715.6471
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 4.8642728 36832.5001 21.820620 1982-1999 –> 2000-2012 9.2021901 86460.5623
Indo-Pacific (26.75,27] cstar_tref ~ temp + phosphate 5.8254571 39041.0295 35.675767 1982-1999 –> 2000-2012 11.5852591 93538.6073
Indo-Pacific (26.75,27] cstar_tref ~ temp + silicate + phosphate 5.7746075 38935.4563 38.524744 1982-1999 –> 2000-2012 11.4738060 93253.2059
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + phosphate 5.8156915 20854.7904 20.405141 2000-2012 –> 2013-2019 11.2613198 59070.5234
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 5.7166755 20744.2090 17.949660 2000-2012 –> 2013-2019 11.0405887 58684.5843
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate 5.1020985 19998.5590 23.101966 2000-2012 –> 2013-2019 9.8304163 56483.2325
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.0760152 19966.9571 21.685280 2000-2012 –> 2013-2019 9.7665001 56355.0592
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + phosphate 5.9556761 21010.7251 30.994780 2000-2012 –> 2013-2019 11.7198085 59923.9034
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate 5.9063235 20958.1715 33.378839 2000-2012 –> 2013-2019 11.6240650 59774.1988
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate 5.2720580 20211.3918 20.906662 2000-2012 –> 2013-2019 10.1815066 57155.3207
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 5.2408292 20174.4422 19.374295 2000-2012 –> 2013-2019 10.1051020 57006.9423
Indo-Pacific (26.75,27] cstar_tref ~ temp + phosphate 6.0282121 21088.0903 30.439397 2000-2012 –> 2013-2019 11.8536692 60129.1198
Indo-Pacific (26.75,27] cstar_tref ~ temp + silicate + phosphate 5.9754651 21032.4727 32.933145 2000-2012 –> 2013-2019 11.7500727 59967.9291
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate 5.4102480 48321.2661 23.787305 1982-1999 –> 2000-2012 10.0768549 111726.9065
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + phosphate 5.5723879 48780.3787 43.918282 1982-1999 –> 2000-2012 10.3952507 112891.5625
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 4.7724806 46373.1003 28.177801 1982-1999 –> 2000-2012 8.8711472 107000.7964
Indo-Pacific (27,27.25] cstar_tref ~ sal + silicate + phosphate 5.7971766 49395.2607 20.286669 1982-1999 –> 2000-2012 11.2575539 116165.9903
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 4.9913500 47070.2756 58.596198 1982-1999 –> 2000-2012 9.1433335 107974.8398
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.5714513 45705.9846 41.262834 1982-1999 –> 2000-2012 8.3880300 104808.1355
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate 5.7726133 49331.2421 20.739011 1982-1999 –> 2000-2012 11.2034561 115987.7883
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate 5.0177033 47150.1501 56.857416 1982-1999 –> 2000-2012 9.2227483 108324.7484
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate 4.5743610 45713.8775 40.477243 1982-1999 –> 2000-2012 8.4103418 104922.6546
Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate 5.8122276 49435.5750 20.671037 1982-1999 –> 2000-2012 11.2616431 116163.2563
Indo-Pacific (27,27.25] cstar_tref ~ aou + silicate + phosphate 5.9346592 26651.1030 25.733957 2000-2012 –> 2013-2019 11.3449073 74972.3691
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 5.4320894 25916.3705 25.868863 2000-2012 –> 2013-2019 10.2045700 72289.4708
Indo-Pacific (27,27.25] cstar_tref ~ sal + silicate + phosphate 6.0413646 26799.4749 20.588999 2000-2012 –> 2013-2019 11.8385412 76194.7356
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 6.0018615 26746.8542 52.822574 2000-2012 –> 2013-2019 10.9932115 73817.1299
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 5.3049828 25721.2332 34.661205 2000-2012 –> 2013-2019 9.8764341 71427.2178
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate 6.0411204 26801.1383 20.564861 2000-2012 –> 2013-2019 11.8137337 76132.3804
Indo-Pacific (27,27.25] cstar_tref ~ silicate + phosphate 6.1377278 26929.2313 24.517450 2000-2012 –> 2013-2019 11.9589160 76386.7580
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + phosphate 6.0251868 26777.1492 51.235865 2000-2012 –> 2013-2019 11.0428901 73927.2993
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate 5.3069909 25722.3843 34.100429 2000-2012 –> 2013-2019 9.8813519 71436.2618
Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate 6.0546914 26817.8212 21.214851 2000-2012 –> 2013-2019 11.8669189 76253.3962
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + silicate + phosphate 3.9190528 40951.9609 34.177695 1982-1999 –> 2000-2012 7.1155061 91879.5418
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + phosphate 4.3663641 42540.9627 38.469768 1982-1999 –> 2000-2012 8.0632455 96337.9371
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 3.7883105 40455.1240 30.730003 1982-1999 –> 2000-2012 6.8816109 90737.5631
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate 4.4637334 42865.2131 37.832365 1982-1999 –> 2000-2012 8.7058964 99376.4382
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 4.3568233 42510.8027 35.609066 1982-1999 –> 2000-2012 8.0447550 96261.9602
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5414587 39466.4822 33.401271 1982-1999 –> 2000-2012 6.4799341 88737.9332
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate 3.5938483 39680.3794 35.540744 1982-1999 –> 2000-2012 6.8910642 91222.2502
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + phosphate 4.7253319 43702.5259 42.264885 1982-1999 –> 2000-2012 8.6791975 98825.3031
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate 3.9158318 40941.8725 34.793882 1982-1999 –> 2000-2012 7.1117275 91868.0123
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate 4.0418997 41405.7355 38.573314 1982-1999 –> 2000-2012 7.7414847 95217.1318
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + silicate + phosphate 4.5622714 22969.5830 33.091043 2000-2012 –> 2013-2019 8.4813242 63921.5439
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + phosphate 4.9910727 23671.8758 43.020389 2000-2012 –> 2013-2019 9.3574368 66212.8385
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 4.3920697 22674.3423 29.076246 2000-2012 –> 2013-2019 8.1803801 63129.4663
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + silicate 4.8345575 23426.7845 41.083495 2000-2012 –> 2013-2019 9.2339369 66082.4952
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 4.9756375 23649.6608 38.994228 2000-2012 –> 2013-2019 9.3324608 66160.4635
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate 4.8658993 23475.3041 43.592247 2000-2012 –> 2013-2019 9.2855373 66196.5598
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4.1032514 22144.5551 33.161694 2000-2012 –> 2013-2019 7.6447101 61611.0373
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate 4.1120690 22159.3373 34.196766 2000-2012 –> 2013-2019 7.7059173 61839.7167
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate 4.5607941 22969.0511 33.574406 2000-2012 –> 2013-2019 8.4766259 63910.9236
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate 4.6309905 23086.4634 36.813025 2000-2012 –> 2013-2019 8.6728902 64492.1989
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 3.5328728 41804.2060 27.969728 1982-1999 –> 2000-2012 5.9840627 91539.5128
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou 3.4427756 41399.5154 14.751361 1982-1999 –> 2000-2012 6.2247416 93851.0938
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate 3.4405718 41391.5342 13.750548 1982-1999 –> 2000-2012 6.2108870 93754.9906
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.0654649 39594.0798 11.583687 1982-1999 –> 2000-2012 5.5343465 89485.8209
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 3.4148074 41274.3653 20.377962 1982-1999 –> 2000-2012 5.9940251 92102.9689
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate 3.1037038 39785.3228 10.315295 1982-1999 –> 2000-2012 5.5838689 89772.9833
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.0515401 39523.1104 9.456817 1982-1999 –> 2000-2012 5.2990528 87397.5594
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate 3.3028597 40754.7798 20.873590 1982-1999 –> 2000-2012 5.8809155 91573.7066
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.0631121 39580.1107 12.814094 1982-1999 –> 2000-2012 5.3715286 88026.7251
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 3.6184811 42177.4289 12.135101 1982-1999 –> 2000-2012 6.1990521 93017.2973
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou 4.0061172 23188.2326 17.454607 2000-2012 –> 2013-2019 7.4488928 64587.7479
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate 4.0042660 23186.4157 16.509857 2000-2012 –> 2013-2019 7.4448379 64577.9499
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.5489940 22191.7072 10.708006 2000-2012 –> 2013-2019 6.6144589 61785.7870
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 4.0047653 23187.4452 18.787997 2000-2012 –> 2013-2019 7.4195726 64461.8106
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate 3.5990796 22305.4345 10.796496 2000-2012 –> 2013-2019 6.7027833 62090.7573
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.5857892 22276.8837 11.095529 2000-2012 –> 2013-2019 6.6373294 61799.9940
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate 4.0994214 23378.3594 23.627616 2000-2012 –> 2013-2019 7.5652930 64882.0982
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate 3.9605093 23095.6795 23.241015 2000-2012 –> 2013-2019 7.2633690 63850.4592
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + phosphate 4.0122714 23200.9088 21.973611 2000-2012 –> 2013-2019 7.4402502 64533.2835
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 3.6764968 22481.1829 17.935126 2000-2012 –> 2013-2019 6.7396089 62061.2936
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 2.6745231 15797.8022 23.410175 1982-1999 –> 2000-2012 4.8141268 35238.3925
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.6648488 15775.9942 26.404732 1982-1999 –> 2000-2012 4.7914178 35164.1130
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate 2.6667147 15778.5927 25.609058 1982-1999 –> 2000-2012 4.8169962 35263.5579
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.6593461 15762.4135 23.912453 1982-1999 –> 2000-2012 4.7528486 35010.8379
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate 2.6702885 15787.3916 28.291824 1982-1999 –> 2000-2012 4.8221484 35278.8979
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate 2.6829881 15816.5638 27.916191 1982-1999 –> 2000-2012 4.8387010 35322.0165
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate 2.6785181 15807.6085 27.539897 1982-1999 –> 2000-2012 4.8319452 35305.6047
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate 2.6825266 15817.4336 25.563216 1982-1999 –> 2000-2012 4.8099572 35207.1635
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate 2.6864966 15825.1496 24.327295 1982-1999 –> 2000-2012 4.8378237 35312.4487
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate 2.6774761 15805.0523 22.507350 1982-1999 –> 2000-2012 4.7742163 35065.2519
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 3.1547838 9415.4979 32.949167 2000-2012 –> 2013-2019 5.8437897 25248.7812
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate 3.1556060 9414.4520 32.344271 2000-2012 –> 2013-2019 5.8447741 25246.1317
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 3.1167043 9371.0272 28.094421 2000-2012 –> 2013-2019 5.7912275 25168.8294
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.1332958 9392.4698 33.494753 2000-2012 –> 2013-2019 5.7981447 25168.4640
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 3.1211609 9376.2597 29.742172 2000-2012 –> 2013-2019 5.8231163 25241.1065
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate 3.1369066 9394.6874 32.212819 2000-2012 –> 2013-2019 5.8036213 25173.2801
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.1106952 9365.9599 28.585907 2000-2012 –> 2013-2019 5.7700413 25128.3734
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate 3.1366102 9394.3413 35.206965 2000-2012 –> 2013-2019 5.8068987 25181.7330
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate 3.1526928 9411.0698 34.845105 2000-2012 –> 2013-2019 5.8356809 25227.6336
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate 3.1519024 9412.1516 34.650683 2000-2012 –> 2013-2019 5.8304205 25219.7602
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 2.7536733 19695.5905 31.796793 1982-1999 –> 2000-2012 4.9296408 44184.4050
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.7536730 19697.5897 31.792295 1982-1999 –> 2000-2012 4.9203073 44140.5025
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 2.7883121 19796.7709 35.862322 1982-1999 –> 2000-2012 4.9294286 44105.6548
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate 2.7836452 19783.2124 36.365501 1982-1999 –> 2000-2012 4.9579823 44263.6740
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.7818621 19780.0261 35.843695 1982-1999 –> 2000-2012 4.9008972 43975.3844
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate 2.7561880 19700.9787 31.466823 1982-1999 –> 2000-2012 4.9321580 44187.8064
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 2.7560792 19702.6593 31.389425 1982-1999 –> 2000-2012 4.9232487 44146.3244
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + phosphate 2.7892458 19797.4810 35.590601 1982-1999 –> 2000-2012 4.9303624 44104.3650
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate 2.7860915 19788.3223 35.962177 1982-1999 –> 2000-2012 4.9607553 44268.4583
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 2.7841548 19784.6940 35.431765 1982-1999 –> 2000-2012 4.9044360 43984.6039
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate 3.0952577 10931.1007 37.417437 2000-2012 –> 2013-2019 5.8489309 30626.6911
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 3.0859175 10920.1539 36.636123 2000-2012 –> 2013-2019 5.8395905 30617.7436
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 3.1011175 10939.2033 39.710912 2000-2012 –> 2013-2019 5.8894295 30735.9742
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 3.0965763 10934.9254 39.767905 2000-2012 –> 2013-2019 5.8784384 30714.9514
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate 3.1019057 10938.2921 39.850258 2000-2012 –> 2013-2019 5.8609553 30647.6701
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate 3.0891329 10922.6153 38.170291 2000-2012 –> 2013-2019 5.8479314 30633.2568
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate 3.1040234 10943.2158 41.295870 2000-2012 –> 2013-2019 5.8858859 30721.2429
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate 3.1246326 10969.5655 36.088189 2000-2012 –> 2013-2019 5.8808206 30670.5441
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate 3.1094905 10950.7545 35.259684 2000-2012 –> 2013-2019 5.8655697 30653.4138
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate 3.1116928 10951.7877 36.563283 2000-2012 –> 2013-2019 5.8722516 30665.5916
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.2426483 17826.7679 8.852835 1982-1999 –> 2000-2012 4.1979448 41322.3483
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate 2.2589943 17882.8660 8.624166 1982-1999 –> 2000-2012 4.2750025 41720.0772
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.2586209 17883.5434 8.671942 1982-1999 –> 2000-2012 4.2267749 41452.7800
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate 2.2436028 17828.1719 8.852520 1982-1999 –> 2000-2012 4.2347576 41525.9800
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate 2.2670056 17909.1871 8.527904 1982-1999 –> 2000-2012 4.2831797 41745.3231
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate 2.2613688 17891.2706 8.718979 1982-1999 –> 2000-2012 4.2547756 41601.7815
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate 2.3179629 18089.0183 8.513568 1982-1999 –> 2000-2012 4.3180940 41837.3740
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 2.3238474 18109.3018 8.378052 1982-1999 –> 2000-2012 4.3206146 41838.7407
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + nitrate + silicate 2.3179901 18087.1121 8.514118 1982-1999 –> 2000-2012 4.3482065 42001.2475
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + silicate + phosphate 2.3256944 18113.6577 8.393067 1982-1999 –> 2000-2012 4.3512725 42002.0886
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.4750570 10296.0430 8.900837 2000-2012 –> 2013-2019 4.7177053 28122.8109
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 2.4993302 10337.1989 9.202167 2000-2012 –> 2013-2019 4.8166809 28424.1039
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate 2.4782080 10299.6691 8.969714 2000-2012 –> 2013-2019 4.7372023 28182.5352
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.4698223 10286.6808 9.061996 2000-2012 –> 2013-2019 4.7284432 28170.2242
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate 2.4800741 10302.9977 8.895172 2000-2012 –> 2013-2019 4.7236769 28131.1695
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + phosphate 2.5436228 10412.8783 9.085960 2000-2012 –> 2013-2019 4.8662386 28515.9391
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate 2.5057678 10346.5741 8.977222 2000-2012 –> 2013-2019 4.7727734 28255.7612
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate 2.5033719 10344.3440 8.939868 2000-2012 –> 2013-2019 4.7647407 28235.6146
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate 2.5622745 10447.1854 9.181239 2000-2012 –> 2013-2019 4.8802375 28536.2037
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 2.5528471 10430.8855 9.516387 2000-2012 –> 2013-2019 4.8766946 28540.1873
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate 1.9272978 10723.4465 8.916703 1982-1999 –> 2000-2012 3.6162540 25358.8351
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate 1.9392916 10753.4706 9.013209 1982-1999 –> 2000-2012 3.6785172 25607.5913
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 1.9234948 10713.2506 8.647099 1982-1999 –> 2000-2012 3.5598308 25110.4332
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate 1.9305303 10730.0972 8.904916 1982-1999 –> 2000-2012 3.6488255 25493.0981
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + silicate + phosphate 1.9298811 10728.3610 8.794546 1982-1999 –> 2000-2012 3.6092888 25319.0807
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.9078444 10673.0787 8.778068 1982-1999 –> 2000-2012 3.5966754 25309.9090
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate 1.9267235 10721.9081 8.900889 1982-1999 –> 2000-2012 3.6627324 25564.0967
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.8951875 10638.7192 8.767010 1982-1999 –> 2000-2012 3.5273132 25018.5120
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate 1.9080141 10671.5377 8.771278 1982-1999 –> 2000-2012 3.6231246 25422.5771
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 1.8952781 10636.9658 8.797017 1982-1999 –> 2000-2012 3.5744229 25228.5072
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate 2.0918415 6340.5890 8.709518 2000-2012 –> 2013-2019 4.0191392 17064.0355
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate 2.0924681 6339.4678 8.681398 2000-2012 –> 2013-2019 4.0317597 17092.9385
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 2.0892046 6336.8882 8.651078 2000-2012 –> 2013-2019 4.0126993 17050.1388
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + nitrate + silicate 2.1766290 6455.1644 8.977398 2000-2012 –> 2013-2019 4.1071594 17185.2617
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.0619981 6300.4294 8.794721 2000-2012 –> 2013-2019 3.9698425 16973.5081
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate 2.0621507 6298.6466 8.806887 2000-2012 –> 2013-2019 3.9888742 17020.5547
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 2.0621501 6300.6457 8.807529 2000-2012 –> 2013-2019 3.9573376 16939.3649
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate 2.1112028 6367.6201 9.021283 2000-2012 –> 2013-2019 4.0192169 17039.1578
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate 2.1759220 6454.2112 9.682023 2000-2012 –> 2013-2019 4.1334731 17256.0578
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 2.1263116 6388.5425 9.434007 2000-2012 –> 2013-2019 4.0215897 17025.5083
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate 2.0110755 84364.8045 10.126629 1982-1999 –> 2000-2012 3.9902972 200572.3987
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + phosphate 2.0780284 85667.3651 7.838862 1982-1999 –> 2000-2012 4.0526145 201743.3155
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.5851502 74884.6921 12.511212 1982-1999 –> 2000-2012 2.9820417 171826.9471
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate 2.0324460 84785.8636 8.048238 1982-1999 –> 2000-2012 4.0259034 201389.6991
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 1.9704593 83554.0719 8.870868 1982-1999 –> 2000-2012 3.9046932 198492.4642
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate 1.8989084 82078.7138 12.089701 1982-1999 –> 2000-2012 3.6600779 191832.7828
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate 2.0230134 84600.5637 10.291169 1982-1999 –> 2000-2012 4.0465890 202033.4712
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.5313000 73509.9446 14.202239 1982-1999 –> 2000-2012 2.8640690 167856.1779
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + phosphate 1.9101489 82311.8136 13.163148 1982-1999 –> 2000-2012 3.6905850 192665.4294
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate 1.8775565 81628.2699 15.081098 1982-1999 –> 2000-2012 3.4757193 186012.5831
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate 2.0887988 46174.7807 11.775724 2000-2012 –> 2013-2019 4.0998743 130539.5852
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate 2.0970044 46256.7468 11.881376 2000-2012 –> 2013-2019 4.1360912 131170.5511
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate 1.7754628 42694.0808 15.096407 2000-2012 –> 2013-2019 3.3606130 117578.7729
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + silicate 2.0504835 45780.2956 13.206405 2000-2012 –> 2013-2019 4.0209429 129334.3674
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate 2.0547640 45822.9555 17.826814 2000-2012 –> 2013-2019 3.9536724 127901.6693
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate 2.0730340 46012.5350 13.013946 2000-2012 –> 2013-2019 4.0960474 130613.0987
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 1.7317874 42162.6704 16.576870 2000-2012 –> 2013-2019 3.2630874 115672.6150
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate 2.0866097 46152.3250 12.427657 2000-2012 –> 2013-2019 4.1332309 131215.0453
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + phosphate 2.1603695 46894.2890 21.093310 2000-2012 –> 2013-2019 4.0705185 129206.1025
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate 2.1587864 46880.5889 20.777038 2000-2012 –> 2013-2019 4.0363428 128508.8588

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
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
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
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
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)

# 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 sal silicate temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26] 7 5 3 10 6 9
(26,26.5] 7 5 3 7 8 10
(26.5,26.75] 10 4 6 6 5 8
(26.75,27] 10 4 6 7 6 7
(27,27.25] 10 5 5 7 6 7
(27.25,27.5] 10 5 5 7 6 7
(27.5,27.75] 10 5 5 8 6 6
(27.75,27.85] 10 4 6 7 6 7
(27.85,27.95] 10 4 6 6 5 8
(27.95,28.05] 10 4 6 6 5 8
(28.05,28.1] 10 4 6 6 5 8
(28.1,28.15] 10 4 6 7 6 7
(28.15,28.2] 10 7 3 6 6 7
(28.2, Inf] 10 6 4 7 7 6
total 134.00 66.00 70.00 97.00 83.00 105.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 6 4 4 10 5 10
(26,26.5] 6 6 2 8 7 10
(26.5,26.75] 10 5 5 7 6 7
(26.75,27] 10 5 5 7 6 7
(27,27.25] 10 6 4 7 6 7
(27.25,27.5] 10 6 4 8 5 6
(27.5,27.75] 10 5 5 8 6 6
(27.75,27.85] 10 4 6 7 6 7
(27.85,27.95] 10 4 6 6 5 8
(27.95,28.05] 10 4 6 6 5 8
(28.05,28.1] 10 4 6 6 5 8
(28.1,28.15] 10 4 6 7 6 7
(28.15,28.2] 10 6 4 6 5 8
(28.2, Inf] 10 6 4 8 6 5
total 132.00 69.00 67.00 101.00 79.00 104.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 6 4 6 8 5 10
(26,26.5] 10 2 6 6 7 8
(26.5,26.75] 8 NA 10 5 6 6
(26.75,27] 6 NA 10 6 5 8
(27,27.25] 7 NA 10 6 7 6
(27.25,27.5] 7 NA 10 6 7 6
(27.5,27.75] 8 3 5 9 7 9
(27.75,27.85] 7 3 4 7 10 9
(27.85,27.95] 10 4 4 5 6 10
(27.95,28.05] 5 4 4 6 10 10
(28.05,28.1] 6 4 4 10 10 5
(28.1, Inf] 10 3 6 8 6 7
total 90.00 — 79.00 82.00 86.00 94.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 6 4 6 8 5 10
(26,26.5] 8 2 7 8 7 8
(26.5,26.75] 8 NA 10 5 6 6
(26.75,27] 6 NA 10 6 5 8
(27,27.25] 6 NA 10 5 8 6
(27.25,27.5] 8 1 8 7 8 7
(27.5,27.75] 6 4 4 10 5 10
(27.75,27.85] 7 3 4 10 9 7
(27.85,27.95] 6 7 3 7 6 10
(27.95,28.05] 6 3 5 8 8 10
(28.05,28.1] 6 4 3 10 10 6
(28.1, Inf] 9 3 5 8 8 7
total 82.00 — 75.00 92.00 85.00 95.00

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
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
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