eMLR - model fitting

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Last updated: 2020-12-23

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1 Required data

Required are:

• cleaned and prepared GLODAP-based model subsetting file

GLODAP <-
  read_csv(paste(path_version_data,
                 "GLODAPv2.2020_MLR_fitting_ready_model_runA.csv",
                 sep = ""))

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

• sal, temp, aou, oxygen, silicate, phosphate, phosphate_star

# the following code is a workaround to find all predictor combinations
# using the olsrr package and fit all models for one era, slab, and basin

i_basin <- unique(GLODAP$basin)[1]
i_era   <- unique(GLODAP$era)[1]

# subset one basin and era for fitting
GLODAP_basin_era <- GLODAP %>%
  filter(basin == i_basin, era == i_era)

i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
print(i_gamma_slab)

# subset one gamma slab
GLODAP_basin_era_slab <- GLODAP_basin_era %>%
  filter(gamma_slab == i_gamma_slab)

# fit the full linear model, i.e. all predictor combinations
lm_full <- lm(paste(
  params_local$MLR_target,
  paste(params_local$MLR_predictors, collapse = " + "),
  sep = " ~ "
),
data = GLODAP_basin_era_slab)

# fit linear models for all possible predictor combinations
# unfortunately, this functions does not provide model coefficients (yet)
lm_all <- ols_step_all_possible(lm_full)

# extract diagnostics of each linear model
lm_all <- as_tibble(lm_all$result)

# 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 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:

• 112

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,
   lm_all,
   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 adjecent 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 + oxygen + silicate + phosphate	3.0137882	326.74491	7.994670	1982-1999 –> 2000-2012	5.894284	776.6795
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.0137882	326.74491	7.994670	1982-1999 –> 2000-2012	5.894284	776.6795
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.0137882	326.74491	7.994670	1982-1999 –> 2000-2012	5.894284	776.6795
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + silicate	3.0413252	327.87275	8.707054	1982-1999 –> 2000-2012	6.445396	807.2010
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.0447816	328.01360	8.065597	1982-1999 –> 2000-2012	6.060526	786.0238
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.0482764	328.15584	8.088494	1982-1999 –> 2000-2012	6.089155	787.6268
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate	3.0745536	327.22019	8.380079	1982-1999 –> 2000-2012	6.523518	806.8544
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.0552268	328.43825	8.077230	1982-1999 –> 2000-2012	6.110950	788.7663
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.0552268	328.43825	8.077230	1982-1999 –> 2000-2012	6.110950	788.7663
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.0552268	328.43825	8.077230	1982-1999 –> 2000-2012	6.110950	788.7663
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.8194196	401.35156	6.181648	2000-2012 –> 2013-2019	4.833208	728.0965
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.8194196	401.35156	6.181648	2000-2012 –> 2013-2019	4.833208	728.0965
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate	1.9006328	407.73608	7.693651	2000-2012 –> 2013-2019	5.185096	743.1457
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.8194196	401.35156	6.181648	2000-2012 –> 2013-2019	4.833208	728.0965
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.2923499	335.67694	4.114869	2000-2012 –> 2013-2019	4.333675	663.5497
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.7856004	397.74910	5.831990	2000-2012 –> 2013-2019	4.830382	725.7627
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.7603123	395.01051	5.829413	2000-2012 –> 2013-2019	4.808589	723.1664
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.7411396	392.90785	5.823454	2000-2012 –> 2013-2019	4.796366	721.3461
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.7411396	392.90785	5.823454	2000-2012 –> 2013-2019	4.796366	721.3461
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.7411396	392.90785	5.823454	2000-2012 –> 2013-2019	4.796366	721.3461
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.4325291	3557.38713	13.252235	1982-1999 –> 2000-2012	6.625366	6306.0264
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.4325291	3557.38713	13.252235	1982-1999 –> 2000-2012	6.625366	6306.0264
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.4325291	3557.38713	13.252235	1982-1999 –> 2000-2012	6.625366	6306.0264
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.5259494	3593.26191	14.216183	1982-1999 –> 2000-2012	6.831150	6378.5638
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.5452324	3600.54846	14.289786	1982-1999 –> 2000-2012	6.877535	6394.5066
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.5651780	3608.04377	14.463548	1982-1999 –> 2000-2012	6.914872	6407.5198
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.5651780	3608.04377	14.463548	1982-1999 –> 2000-2012	6.914872	6407.5198
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.5651780	3608.04377	14.463548	1982-1999 –> 2000-2012	6.914872	6407.5198
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.4629374	3569.17045	15.194599	1982-1999 –> 2000-2012	7.081386	6450.4533
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.4629374	3569.17045	15.194599	1982-1999 –> 2000-2012	7.081386	6450.4533
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.8950462	1398.92230	13.288699	2000-2012 –> 2013-2019	6.327575	4956.3094
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.8950462	1398.92230	13.288699	2000-2012 –> 2013-2019	6.327575	4956.3094
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.8950462	1398.92230	13.288699	2000-2012 –> 2013-2019	6.327575	4956.3094
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.9289258	1405.41443	10.885407	2000-2012 –> 2013-2019	6.549352	5034.0028
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate	3.0413110	1424.42478	12.347612	2000-2012 –> 2013-2019	6.741840	5080.2504
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.8189100	1384.05117	12.065902	2000-2012 –> 2013-2019	6.344859	4977.3131
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.8162203	1383.51848	11.952654	2000-2012 –> 2013-2019	6.361453	4984.0669
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.8153913	1383.35419	11.908674	2000-2012 –> 2013-2019	6.380569	4991.3980
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.8153913	1383.35419	11.908674	2000-2012 –> 2013-2019	6.380569	4991.3980
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.8153913	1383.35419	11.908674	2000-2012 –> 2013-2019	6.380569	4991.3980
Atlantic	(26.5,26.75]	cstar_tref ~ aou + oxygen + silicate + phosphate	3.5401579	4696.70981	17.909630	1982-1999 –> 2000-2012	6.282315	8427.9208
Atlantic	(26.5,26.75]	cstar_tref ~ aou + oxygen + silicate + phosphate_star	3.5401579	4696.70981	17.909630	1982-1999 –> 2000-2012	6.282315	8427.9208
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3.5401579	4696.70981	17.909630	1982-1999 –> 2000-2012	6.282315	8427.9208
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.4002855	4628.32518	16.357849	1982-1999 –> 2000-2012	6.136876	8358.4230
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.4002855	4628.32518	16.357849	1982-1999 –> 2000-2012	6.136876	8358.4230
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.4002855	4628.32518	16.357849	1982-1999 –> 2000-2012	6.136876	8358.4230
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.4043401	4630.40591	16.768220	1982-1999 –> 2000-2012	6.246480	8418.4815
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.4069680	4631.75319	20.845609	1982-1999 –> 2000-2012	6.083744	8327.9945
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.4069680	4631.75319	20.845609	1982-1999 –> 2000-2012	6.083744	8327.9945
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.4069680	4631.75319	20.845609	1982-1999 –> 2000-2012	6.083744	8327.9945
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	4.7020088	2322.27026	12.016033	2000-2012 –> 2013-2019	8.102294	6950.5954
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.7020088	2322.27026	12.016033	2000-2012 –> 2013-2019	8.102294	6950.5954
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	4.7020257	2320.27305	12.016734	2000-2012 –> 2013-2019	8.106777	6948.8900
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.7020088	2322.27026	12.016033	2000-2012 –> 2013-2019	8.102294	6950.5954
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.6656211	2316.22609	11.730877	2000-2012 –> 2013-2019	8.069961	6946.6320
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.7129128	2324.07237	12.355878	2000-2012 –> 2013-2019	8.140743	6966.4842
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	4.7154668	2324.49386	12.331972	2000-2012 –> 2013-2019	8.156605	6973.6716
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	4.4236780	2274.79798	11.774653	2000-2012 –> 2013-2019	7.830646	6906.5512
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	4.4236780	2274.79798	11.774653	2000-2012 –> 2013-2019	7.830646	6906.5512
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.4236780	2274.79798	11.774653	2000-2012 –> 2013-2019	7.830646	6906.5512
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.8900011	4775.97519	13.316804	1982-1999 –> 2000-2012	4.947580	8617.1331
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.8900011	4775.97519	13.316804	1982-1999 –> 2000-2012	4.947580	8617.1331
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	2.9058558	4784.47962	12.369485	1982-1999 –> 2000-2012	5.661188	9145.7474
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.8900011	4775.97519	13.316804	1982-1999 –> 2000-2012	4.947580	8617.1331
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.8552298	4752.73449	13.268023	1982-1999 –> 2000-2012	5.154728	8792.6478
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.9730525	4830.37324	15.740864	1982-1999 –> 2000-2012	5.490129	9031.9348
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.0006583	4848.11883	16.303922	1982-1999 –> 2000-2012	5.579794	9093.2289
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.0006583	4848.11883	16.303922	1982-1999 –> 2000-2012	5.579794	9093.2289
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.0006583	4848.11883	16.303922	1982-1999 –> 2000-2012	5.579794	9093.2289
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.6327559	5215.14576	25.585209	1982-1999 –> 2000-2012	5.752888	9109.8512
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.0414721	2889.53427	10.781157	2000-2012 –> 2013-2019	5.931473	7665.5095
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.0414721	2889.53427	10.781157	2000-2012 –> 2013-2019	5.931473	7665.5095
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	3.0625149	2895.36677	12.405570	2000-2012 –> 2013-2019	5.968371	7679.8464
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.0414721	2889.53427	10.781157	2000-2012 –> 2013-2019	5.931473	7665.5095
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate_star	3.3600200	3000.68588	16.778800	2000-2012 –> 2013-2019	6.429235	7890.1781
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.0585678	2895.90171	12.862236	2000-2012 –> 2013-2019	5.913798	7648.6362
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.2494698	2964.68091	14.617396	2000-2012 –> 2013-2019	6.222522	7795.0541
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.2649563	2970.08206	14.546316	2000-2012 –> 2013-2019	6.265615	7818.2009
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.2649563	2970.08206	14.546316	2000-2012 –> 2013-2019	6.265615	7818.2009
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.2649563	2970.08206	14.546316	2000-2012 –> 2013-2019	6.265615	7818.2009
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + phosphate	3.3735808	8886.38784	15.640554	1982-1999 –> 2000-2012	5.740649	16634.1513
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + phosphate_star	3.3735808	8886.38784	15.640554	1982-1999 –> 2000-2012	5.740649	16634.1513
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.1661501	8674.66015	15.700782	1982-1999 –> 2000-2012	5.280404	16041.2962
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.1661501	8674.66015	15.700782	1982-1999 –> 2000-2012	5.280404	16041.2962
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3.3735808	8886.38784	15.640554	1982-1999 –> 2000-2012	5.740649	16634.1513
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.1661501	8674.66015	15.700782	1982-1999 –> 2000-2012	5.280404	16041.2962
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.1287182	8634.60460	14.690529	1982-1999 –> 2000-2012	5.360431	16184.6385
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.1287182	8634.60460	14.690529	1982-1999 –> 2000-2012	5.360431	16184.6385
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.1287182	8634.60460	14.690529	1982-1999 –> 2000-2012	5.360431	16184.6385
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.2735362	8786.99782	16.342242	1982-1999 –> 2000-2012	5.618662	16505.1709
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.6830158	4681.40716	12.069588	2000-2012 –> 2013-2019	5.849166	13356.0673
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.6830158	4681.40716	12.069588	2000-2012 –> 2013-2019	5.849166	13356.0673
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.6830158	4681.40716	12.069588	2000-2012 –> 2013-2019	5.849166	13356.0673
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.4561710	4510.03179	14.456122	2000-2012 –> 2013-2019	5.584889	13144.6364
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.4561710	4510.03179	14.456122	2000-2012 –> 2013-2019	5.584889	13144.6364
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.4561710	4510.03179	14.456122	2000-2012 –> 2013-2019	5.584889	13144.6364
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.7842724	4753.27474	13.011942	2000-2012 –> 2013-2019	6.057809	13540.2726
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.9748984	4881.74792	15.728499	2000-2012 –> 2013-2019	6.440402	13860.6783
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.9798099	4884.94818	15.601615	2000-2012 –> 2013-2019	6.448891	13867.3540
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.9798099	4884.94818	15.601615	2000-2012 –> 2013-2019	6.448891	13867.3540
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + phosphate	3.4902867	11632.48821	15.740420	1982-1999 –> 2000-2012	5.519164	21022.0057
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + phosphate_star	3.4902867	11632.48821	15.740420	1982-1999 –> 2000-2012	5.519164	21022.0057
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.3957003	11514.86703	15.377314	1982-1999 –> 2000-2012	5.261032	20535.7526
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.3957003	11514.86703	15.377314	1982-1999 –> 2000-2012	5.261032	20535.7526
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3.4902867	11632.48821	15.740420	1982-1999 –> 2000-2012	5.519164	21022.0057
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.3957003	11514.86703	15.377314	1982-1999 –> 2000-2012	5.261032	20535.7526
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.8989019	10826.15995	27.601932	1982-1999 –> 2000-2012	4.738523	19785.8361
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.8989019	10826.15995	27.601932	1982-1999 –> 2000-2012	4.738523	19785.8361
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.8989019	10826.15995	27.601932	1982-1999 –> 2000-2012	4.738523	19785.8361
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.6991917	11887.58816	16.180724	1982-1999 –> 2000-2012	5.874788	21587.0119
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + phosphate	3.2028022	5627.36514	12.931480	2000-2012 –> 2013-2019	6.693089	17259.8533
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + phosphate_star	3.2028022	5627.36514	12.931480	2000-2012 –> 2013-2019	6.693089	17259.8533
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.0826864	5546.26470	14.605621	2000-2012 –> 2013-2019	6.478387	17061.1317
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.0826864	5546.26470	14.605621	2000-2012 –> 2013-2019	6.478387	17061.1317
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3.2028022	5627.36514	12.931480	2000-2012 –> 2013-2019	6.693089	17259.8533
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.0826864	5546.26470	14.605621	2000-2012 –> 2013-2019	6.478387	17061.1317
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.3332166	4940.68916	13.543344	2000-2012 –> 2013-2019	5.232119	15766.8491
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.3332166	4940.68916	13.543344	2000-2012 –> 2013-2019	5.232119	15766.8491
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.3332166	4940.68916	13.543344	2000-2012 –> 2013-2019	5.232119	15766.8491
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.2569600	5665.81906	15.210164	2000-2012 –> 2013-2019	6.956152	17553.4072
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + phosphate	2.9715251	13525.17871	15.629326	1982-1999 –> 2000-2012	4.659590	21357.7693
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + phosphate_star	2.9715251	13525.17871	15.629326	1982-1999 –> 2000-2012	4.659590	21357.7693
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.9644868	13514.40167	16.170513	1982-1999 –> 2000-2012	4.648350	21338.9600
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.9644868	13514.40167	16.170513	1982-1999 –> 2000-2012	4.648350	21338.9600
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2.9715251	13525.17871	15.629326	1982-1999 –> 2000-2012	4.659590	21357.7693
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.9644868	13514.40167	16.170513	1982-1999 –> 2000-2012	4.648350	21338.9600
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.8926817	13382.28814	13.031928	1982-1999 –> 2000-2012	4.580524	21216.3477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.8926817	13382.28814	13.031928	1982-1999 –> 2000-2012	4.580524	21216.3477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.8926817	13382.28814	13.031928	1982-1999 –> 2000-2012	4.580524	21216.3477
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.1146098	13780.56856	18.140550	1982-1999 –> 2000-2012	4.928769	21905.1901
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + phosphate	3.2105966	6620.27040	16.334010	2000-2012 –> 2013-2019	6.182122	20145.4491
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + phosphate_star	3.2105966	6620.27040	16.334010	2000-2012 –> 2013-2019	6.182122	20145.4491
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.1899867	6605.80967	15.437839	2000-2012 –> 2013-2019	6.154473	20120.2113
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.1899867	6605.80967	15.437839	2000-2012 –> 2013-2019	6.154473	20120.2113
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3.2105966	6620.27040	16.334010	2000-2012 –> 2013-2019	6.182122	20145.4491
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.1899867	6605.80967	15.437839	2000-2012 –> 2013-2019	6.154473	20120.2113
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.9528323	6408.35377	17.555520	2000-2012 –> 2013-2019	5.845514	19790.6419
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.9528323	6408.35377	17.555520	2000-2012 –> 2013-2019	5.845514	19790.6419
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.9528323	6408.35377	17.555520	2000-2012 –> 2013-2019	5.845514	19790.6419
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.2980559	6690.96645	17.256616	2000-2012 –> 2013-2019	6.412666	20471.5350
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + phosphate	2.7684205	9609.75455	14.018479	1982-1999 –> 2000-2012	4.483048	13534.1069
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + phosphate_star	2.7684205	9609.75455	14.018479	1982-1999 –> 2000-2012	4.483048	13534.1069
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.6202653	9395.15921	14.156873	1982-1999 –> 2000-2012	4.120295	13054.3567
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.6202653	9395.15921	14.156873	1982-1999 –> 2000-2012	4.120295	13054.3567
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2.7684205	9609.75455	14.018479	1982-1999 –> 2000-2012	4.483048	13534.1069
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.6202653	9395.15921	14.156873	1982-1999 –> 2000-2012	4.120295	13054.3567
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.7450905	9578.42762	14.817033	1982-1999 –> 2000-2012	4.448108	13491.2049
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.7450905	9578.42762	14.817033	1982-1999 –> 2000-2012	4.448108	13491.2049
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.7450905	9578.42762	14.817033	1982-1999 –> 2000-2012	4.448108	13491.2049
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.6286257	9407.70394	13.544033	1982-1999 –> 2000-2012	4.211805	13174.6950
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.6492573	3216.12549	12.813959	2000-2012 –> 2013-2019	5.269523	12611.2847
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.6492573	3216.12549	12.813959	2000-2012 –> 2013-2019	5.269523	12611.2847
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.6492573	3216.12549	12.813959	2000-2012 –> 2013-2019	5.269523	12611.2847
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.6548936	3218.96906	15.360490	2000-2012 –> 2013-2019	5.399984	12797.3967
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.6548936	3218.96906	15.360490	2000-2012 –> 2013-2019	5.399984	12797.3967
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.6548936	3218.96906	15.360490	2000-2012 –> 2013-2019	5.399984	12797.3967
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.6770664	3230.09723	12.429388	2000-2012 –> 2013-2019	5.305692	12637.8012
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.8087411	3294.34102	12.517117	2000-2012 –> 2013-2019	5.525811	12832.3646
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.8087411	3294.34102	12.517117	2000-2012 –> 2013-2019	5.525811	12832.3646
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.8087411	3294.34102	12.517117	2000-2012 –> 2013-2019	5.525811	12832.3646
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + phosphate	3.7553630	23599.74630	34.428083	1982-1999 –> 2000-2012	7.250745	35179.8382
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + phosphate_star	3.7553630	23599.74630	34.428083	1982-1999 –> 2000-2012	7.250745	35179.8382
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.6368882	23325.99601	37.910361	1982-1999 –> 2000-2012	6.895314	34603.9880
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.6368882	23325.99601	37.910361	1982-1999 –> 2000-2012	6.895314	34603.9880
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3.7553630	23599.74630	34.428083	1982-1999 –> 2000-2012	7.250745	35179.8382
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.6368882	23325.99601	37.910361	1982-1999 –> 2000-2012	6.895314	34603.9880
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.5644120	23152.84366	34.507704	1982-1999 –> 2000-2012	6.947887	34593.9745
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.5644120	23152.84366	34.507704	1982-1999 –> 2000-2012	6.947887	34593.9745
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.5644120	23152.84366	34.507704	1982-1999 –> 2000-2012	6.947887	34593.9745
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.6664907	23395.72867	37.747658	1982-1999 –> 2000-2012	7.000709	34773.3305
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.8894284	6060.43632	17.323098	2000-2012 –> 2013-2019	5.526317	29386.4323
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.8894284	6060.43632	17.323098	2000-2012 –> 2013-2019	5.526317	29386.4323
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate	1.9165048	6100.29734	16.463010	2000-2012 –> 2013-2019	5.703613	29772.4531
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.8894284	6060.43632	17.323098	2000-2012 –> 2013-2019	5.526317	29386.4323
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.8846937	6053.05475	26.804799	2000-2012 –> 2013-2019	5.449106	29205.8984
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.8846937	6053.05475	26.804799	2000-2012 –> 2013-2019	5.449106	29205.8984
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.8846937	6053.05475	26.804799	2000-2012 –> 2013-2019	5.449106	29205.8984
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.9044702	6083.76488	16.984513	2000-2012 –> 2013-2019	5.570961	29479.4935
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.0103668	6242.96639	17.346599	2000-2012 –> 2013-2019	5.765004	29843.0489
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.0103668	6242.96639	17.346599	2000-2012 –> 2013-2019	5.765004	29843.0489
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + phosphate	1.9213550	18804.76044	14.618070	1982-1999 –> 2000-2012	3.317188	29250.7286
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + phosphate_star	1.9213550	18804.76044	14.618070	1982-1999 –> 2000-2012	3.317188	29250.7286
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.8788710	18603.95918	15.818698	1982-1999 –> 2000-2012	3.135124	28424.6250
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.8788710	18603.95918	15.818698	1982-1999 –> 2000-2012	3.135124	28424.6250
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1.9213550	18804.76044	14.618070	1982-1999 –> 2000-2012	3.317188	29250.7286
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.8788710	18603.95918	15.818698	1982-1999 –> 2000-2012	3.135124	28424.6250
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.6419648	17381.52744	15.514416	1982-1999 –> 2000-2012	2.924492	27325.4360
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.6419648	17381.52744	15.514416	1982-1999 –> 2000-2012	2.924492	27325.4360
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.6419648	17381.52744	15.514416	1982-1999 –> 2000-2012	2.924492	27325.4360
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.8993345	18702.20986	15.640521	1982-1999 –> 2000-2012	3.226282	28848.8442
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.3652637	5744.70775	16.260046	2000-2012 –> 2013-2019	3.244135	24348.6669
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.3652637	5744.70775	16.260046	2000-2012 –> 2013-2019	3.244135	24348.6669
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate	1.3652660	5742.71334	16.251745	2000-2012 –> 2013-2019	3.277007	24501.9752
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.3652637	5744.70775	16.260046	2000-2012 –> 2013-2019	3.244135	24348.6669
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.2976681	5576.52860	18.227237	2000-2012 –> 2013-2019	2.939633	22958.0560
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.2976681	5576.52860	18.227237	2000-2012 –> 2013-2019	2.939633	22958.0560
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.2976681	5576.52860	18.227237	2000-2012 –> 2013-2019	2.939633	22958.0560
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.3610240	5734.40659	15.789822	2000-2012 –> 2013-2019	3.260359	24436.6164
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.4386639	5918.14798	16.158092	2000-2012 –> 2013-2019	3.421576	25010.9375
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.4386639	5918.14798	16.158092	2000-2012 –> 2013-2019	3.421576	25010.9375
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + phosphate	1.5941223	12586.69662	16.467256	1982-1999 –> 2000-2012	2.994151	20041.7249
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + phosphate_star	1.5941223	12586.69662	16.467256	1982-1999 –> 2000-2012	2.994151	20041.7249
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.5846950	12549.13433	17.272849	1982-1999 –> 2000-2012	2.974717	19975.7484
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.5846950	12549.13433	17.272849	1982-1999 –> 2000-2012	2.974717	19975.7484
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1.5941223	12586.69662	16.467256	1982-1999 –> 2000-2012	2.994151	20041.7249
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.5846950	12549.13433	17.272849	1982-1999 –> 2000-2012	2.974717	19975.7484
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.5760663	12512.71680	14.494025	1982-1999 –> 2000-2012	2.873442	19646.8713
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.5760663	12512.71680	14.494025	1982-1999 –> 2000-2012	2.873442	19646.8713
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.5760663	12512.71680	14.494025	1982-1999 –> 2000-2012	2.873442	19646.8713
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.5800215	12529.43443	17.638713	1982-1999 –> 2000-2012	3.017468	20098.2949
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.4935712	5408.80171	7.291169	2000-2012 –> 2013-2019	3.078266	17957.9360
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.4935712	5408.80171	7.291169	2000-2012 –> 2013-2019	3.078266	17957.9360
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	1.5136487	5446.38034	9.188469	2000-2012 –> 2013-2019	3.105892	18025.2091
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.4935712	5408.80171	7.291169	2000-2012 –> 2013-2019	3.078266	17957.9360
Atlantic	(28.05,28.1]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1.5054137	5430.21064	7.387464	2000-2012 –> 2013-2019	3.125984	18126.6608
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.4863789	5394.49406	7.121216	2000-2012 –> 2013-2019	3.066400	17923.9285
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.5113038	5443.78498	7.211391	2000-2012 –> 2013-2019	3.121967	18101.3341
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.5007859	5423.08483	7.129042	2000-2012 –> 2013-2019	3.098000	18024.7064
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.5007859	5423.08483	7.129042	2000-2012 –> 2013-2019	3.098000	18024.7064
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.5007859	5423.08483	7.129042	2000-2012 –> 2013-2019	3.098000	18024.7064
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.1042005	7901.84018	13.016637	1982-1999 –> 2000-2012	2.035116	11965.9792
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.1042005	7901.84018	13.016637	1982-1999 –> 2000-2012	2.035116	11965.9792
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.1042005	7901.84018	13.016637	1982-1999 –> 2000-2012	2.035116	11965.9792
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.1493797	8110.20426	13.038831	1982-1999 –> 2000-2012	2.090179	12206.0911
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.1493797	8110.20426	13.038831	1982-1999 –> 2000-2012	2.090179	12206.0911
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.0986632	7875.71789	13.171393	1982-1999 –> 2000-2012	2.030840	11943.9265
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.1099987	7929.05333	12.898965	1982-1999 –> 2000-2012	2.056001	12041.5191
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.1024839	7893.75627	13.047644	1982-1999 –> 2000-2012	2.043449	11990.1715
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.1024839	7893.75627	13.047644	1982-1999 –> 2000-2012	2.043449	11990.1715
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.1024839	7893.75627	13.047644	1982-1999 –> 2000-2012	2.043449	11990.1715
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.0160437	2410.20771	5.105046	2000-2012 –> 2013-2019	2.120244	10312.0479
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.0160437	2410.20771	5.105046	2000-2012 –> 2013-2019	2.120244	10312.0479
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.0160437	2410.20771	5.105046	2000-2012 –> 2013-2019	2.120244	10312.0479
Atlantic	(28.1,28.15]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1.0252308	2423.24004	4.972206	2000-2012 –> 2013-2019	2.132244	10336.2990
Atlantic	(28.1,28.15]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1.0252308	2423.24004	4.972206	2000-2012 –> 2013-2019	2.132244	10336.2990
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.0079363	2396.82864	4.796288	2000-2012 –> 2013-2019	2.106600	10272.5465
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.0173376	2412.33306	5.216816	2000-2012 –> 2013-2019	2.127336	10341.3864
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.0107402	2401.46779	4.964931	2000-2012 –> 2013-2019	2.113224	10295.2241
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.0107402	2401.46779	4.964931	2000-2012 –> 2013-2019	2.113224	10295.2241
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.0107402	2401.46779	4.964931	2000-2012 –> 2013-2019	2.113224	10295.2241
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.1809348	3596.65330	18.708707	1982-1999 –> 2000-2012	1.865046	4691.5295
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.1809348	3596.65330	18.708707	1982-1999 –> 2000-2012	1.865046	4691.5295
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate	1.2092179	3648.14180	16.207852	1982-1999 –> 2000-2012	1.969739	4851.1359
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.1809348	3596.65330	18.708707	1982-1999 –> 2000-2012	1.865046	4691.5295
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.2927485	3801.10262	18.346462	1982-1999 –> 2000-2012	2.009502	4944.4542
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.1804735	3595.77045	18.994708	1982-1999 –> 2000-2012	1.865303	4691.7373
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.1841352	3602.76978	18.190388	1982-1999 –> 2000-2012	1.877353	4711.3979
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.1818720	3598.44622	18.527842	1982-1999 –> 2000-2012	1.871055	4701.0037
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.1818720	3598.44622	18.527842	1982-1999 –> 2000-2012	1.871055	4701.0037
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.1818720	3598.44622	18.527842	1982-1999 –> 2000-2012	1.871055	4701.0037
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.4453789	384.94612	1.627049	2000-2012 –> 2013-2019	1.626314	3981.5994
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.4453789	384.94612	1.627049	2000-2012 –> 2013-2019	1.626314	3981.5994
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate	0.5003339	453.68700	2.426112	2000-2012 –> 2013-2019	1.709552	4101.8288
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.4453789	384.94612	1.627049	2000-2012 –> 2013-2019	1.626314	3981.5994
Atlantic	(28.15,28.2]	cstar_tref ~ sal + oxygen + silicate + phosphate	0.5536934	515.29893	2.307351	2000-2012 –> 2013-2019	1.748242	4135.8573
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.4449228	384.32315	1.585609	2000-2012 –> 2013-2019	1.625396	3980.0936
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.4442848	383.45068	1.573843	2000-2012 –> 2013-2019	1.628420	3986.2205
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.4443785	383.57881	1.577982	2000-2012 –> 2013-2019	1.626251	3982.0250
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.4443785	383.57881	1.577982	2000-2012 –> 2013-2019	1.626251	3982.0250
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.4443785	383.57881	1.577982	2000-2012 –> 2013-2019	1.626251	3982.0250
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.1028496	6948.97397	24.558356	1982-1999 –> 2000-2012	2.313407	10601.6174
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.1028496	6948.97397	24.558356	1982-1999 –> 2000-2012	2.313407	10601.6174
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	1.1906175	7297.07328	25.354171	1982-1999 –> 2000-2012	2.409798	10963.7592
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.1028496	6948.97397	24.558356	1982-1999 –> 2000-2012	2.313407	10601.6174
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + silicate + phosphate	1.6825949	8878.36868	26.186199	1982-1999 –> 2000-2012	2.981532	12688.2640
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.0852558	6875.44841	24.206468	1982-1999 –> 2000-2012	2.297896	10531.9767
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.0174664	6580.55393	23.062651	1982-1999 –> 2000-2012	2.213323	10205.5850
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.0389244	6675.97319	23.440881	1982-1999 –> 2000-2012	2.241472	10313.6130
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.0389244	6675.97319	23.440881	1982-1999 –> 2000-2012	2.241472	10313.6130
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.0389244	6675.97319	23.440881	1982-1999 –> 2000-2012	2.241472	10313.6130
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.4069512	735.58854	1.686609	2000-2012 –> 2013-2019	1.509801	7684.5625
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.4069512	735.58854	1.686609	2000-2012 –> 2013-2019	1.509801	7684.5625
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	0.5016472	1023.96360	3.146531	2000-2012 –> 2013-2019	1.692265	8321.0369
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.4069512	735.58854	1.686609	2000-2012 –> 2013-2019	1.509801	7684.5625
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + silicate + phosphate	0.5194026	1072.24121	3.750891	2000-2012 –> 2013-2019	2.201998	9950.6099
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.4050963	729.24767	1.811744	2000-2012 –> 2013-2019	1.490352	7604.6961
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.4231162	789.65631	1.713957	2000-2012 –> 2013-2019	1.440583	7370.2102
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.4144929	761.07587	1.630054	2000-2012 –> 2013-2019	1.453417	7437.0491
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.4144929	761.07587	1.630054	2000-2012 –> 2013-2019	1.453417	7437.0491
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.4144929	761.07587	1.630054	2000-2012 –> 2013-2019	1.453417	7437.0491
Indian	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.8137223	1125.90453	5.005862	1982-1999 –> 2000-2012	3.931516	3131.3343
Indian	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.6902574	1086.98830	4.986531	1982-1999 –> 2000-2012	3.776832	3078.7848
Indian	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.6745568	1081.83685	4.994461	1982-1999 –> 2000-2012	3.755222	3071.0297
Indian	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.6745568	1081.83685	4.994461	1982-1999 –> 2000-2012	3.755222	3071.0297
Indian	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.6745568	1081.83685	4.994461	1982-1999 –> 2000-2012	3.755222	3071.0297
Indian	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.5150504	1026.58175	5.740969	1982-1999 –> 2000-2012	3.886953	3136.0370
Indian	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.5150504	1026.58175	5.740969	1982-1999 –> 2000-2012	3.886953	3136.0370
Indian	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.5150504	1026.58175	5.740969	1982-1999 –> 2000-2012	3.886953	3136.0370
Indian	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1.8449747	1133.33506	5.331546	1982-1999 –> 2000-2012	4.556643	3363.6845
Indian	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1.8449747	1133.33506	5.331546	1982-1999 –> 2000-2012	4.556643	3363.6845
Indian	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.8585915	107.71926	2.491671	2000-2012 –> 2013-2019	2.672314	1233.6238
Indian	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.7749909	100.13856	2.354419	2000-2012 –> 2013-2019	2.465248	1187.1269
Indian	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.7713676	99.79178	2.320083	2000-2012 –> 2013-2019	2.445924	1181.6286
Indian	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.7713676	99.79178	2.320083	2000-2012 –> 2013-2019	2.445924	1181.6286
Indian	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.7713676	99.79178	2.320083	2000-2012 –> 2013-2019	2.445924	1181.6286
Indian	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.7975978	102.26629	2.075175	2000-2012 –> 2013-2019	2.312648	1128.8480
Indian	(-Inf,26]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.7975978	102.26629	2.075175	2000-2012 –> 2013-2019	2.312648	1128.8480
Indian	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.7975978	102.26629	2.075175	2000-2012 –> 2013-2019	2.312648	1128.8480
Indian	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	0.8861532	108.05741	2.614005	2000-2012 –> 2013-2019	2.731128	1241.3925
Indian	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	0.8861532	108.05741	2.614005	2000-2012 –> 2013-2019	2.731128	1241.3925
Indian	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.0676672	2094.99878	7.478229	1982-1999 –> 2000-2012	4.692806	5680.3392
Indian	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.0676672	2094.99878	7.478229	1982-1999 –> 2000-2012	4.692806	5680.3392
Indian	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.8852519	2005.40996	7.387017	1982-1999 –> 2000-2012	4.003894	5269.6412
Indian	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.8412306	1982.49151	7.375508	1982-1999 –> 2000-2012	3.844507	5162.8482
Indian	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.8367337	1980.11952	7.364605	1982-1999 –> 2000-2012	3.829460	5152.5659
Indian	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.8367337	1980.11952	7.364605	1982-1999 –> 2000-2012	3.829460	5152.5659
Indian	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.8367337	1980.11952	7.364605	1982-1999 –> 2000-2012	3.829460	5152.5659
Indian	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.7875163	1953.77269	7.234424	1982-1999 –> 2000-2012	4.357202	5507.1305
Indian	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.7875163	1953.77269	7.234424	1982-1999 –> 2000-2012	4.357202	5507.1305
Indian	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.7875163	1953.77269	7.234424	1982-1999 –> 2000-2012	4.357202	5507.1305
Indian	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.7214011	107.94455	1.885792	2000-2012 –> 2013-2019	2.562632	2090.4361
Indian	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.7217689	107.98839	1.887966	2000-2012 –> 2013-2019	2.558502	2088.1079
Indian	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.7217689	107.98839	1.887966	2000-2012 –> 2013-2019	2.558502	2088.1079
Indian	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.7217689	107.98839	1.887966	2000-2012 –> 2013-2019	2.558502	2088.1079
Indian	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.7205011	107.83720	1.751789	2000-2012 –> 2013-2019	2.508017	2061.6099
Indian	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.7205011	107.83720	1.751789	2000-2012 –> 2013-2019	2.508017	2061.6099
Indian	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.7205011	107.83720	1.751789	2000-2012 –> 2013-2019	2.508017	2061.6099
Indian	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate	0.7829647	112.98729	2.231539	2000-2012 –> 2013-2019	2.631252	2097.1893
Indian	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	0.7829647	112.98729	2.231539	2000-2012 –> 2013-2019	2.631252	2097.1893
Indian	(26,26.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	0.7829647	112.98729	2.231539	2000-2012 –> 2013-2019	2.631252	2097.1893
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.2016074	3750.14966	11.118232	1982-1999 –> 2000-2012	4.591859	8024.1766
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.2016074	3750.14966	11.118232	1982-1999 –> 2000-2012	4.591859	8024.1766
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.8180925	3426.30110	9.174254	1982-1999 –> 2000-2012	4.491880	7908.8291
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.7801994	3390.66335	8.694337	1982-1999 –> 2000-2012	4.348315	7798.1898
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.7752847	3385.98568	8.595445	1982-1999 –> 2000-2012	4.334736	7787.2263
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.7752847	3385.98568	8.595445	1982-1999 –> 2000-2012	4.334736	7787.2263
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.7752847	3385.98568	8.595445	1982-1999 –> 2000-2012	4.334736	7787.2263
Indian	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.6606457	3273.03737	7.730338	1982-1999 –> 2000-2012	3.970823	7483.6866
Indian	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.6606457	3273.03737	7.730338	1982-1999 –> 2000-2012	3.970823	7483.6866
Indian	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.6606457	3273.03737	7.730338	1982-1999 –> 2000-2012	3.970823	7483.6866
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.6895625	160.61368	2.206988	2000-2012 –> 2013-2019	2.469762	3551.2770
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.6884424	160.38608	2.203971	2000-2012 –> 2013-2019	2.463727	3546.3718
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.6884424	160.38608	2.203971	2000-2012 –> 2013-2019	2.463727	3546.3718
Indian	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.6884424	160.38608	2.203971	2000-2012 –> 2013-2019	2.463727	3546.3718
Indian	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.6572573	153.89624	2.087755	2000-2012 –> 2013-2019	2.317903	3426.9336
Indian	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.6572573	153.89624	2.087755	2000-2012 –> 2013-2019	2.317903	3426.9336
Indian	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.6572573	153.89624	2.087755	2000-2012 –> 2013-2019	2.317903	3426.9336
Indian	(26.5,26.75]	cstar_tref ~ temp + oxygen + silicate + phosphate	0.7101175	162.72591	2.039060	2000-2012 –> 2013-2019	2.511206	3571.1277
Indian	(26.5,26.75]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	0.7101175	162.72591	2.039060	2000-2012 –> 2013-2019	2.511206	3571.1277
Indian	(26.5,26.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	0.7101175	162.72591	2.039060	2000-2012 –> 2013-2019	2.511206	3571.1277
Indian	(26.75,27]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.3013628	6730.77603	10.254913	1982-1999 –> 2000-2012	5.226964	15906.9801
Indian	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.2190287	6622.13623	7.804462	1982-1999 –> 2000-2012	4.873469	15440.7901
Indian	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.1907887	6583.94278	7.838360	1982-1999 –> 2000-2012	4.714716	15217.2611
Indian	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.1862662	6577.78067	7.839924	1982-1999 –> 2000-2012	4.699293	15195.1883
Indian	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.1862662	6577.78067	7.839924	1982-1999 –> 2000-2012	4.699293	15195.1883
Indian	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.1862662	6577.78067	7.839924	1982-1999 –> 2000-2012	4.699293	15195.1883
Indian	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.2742337	6693.41458	10.961689	1982-1999 –> 2000-2012	4.868233	15425.3985
Indian	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	2.2466073	6658.96878	8.375828	1982-1999 –> 2000-2012	5.136043	15789.4484
Indian	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	2.2466073	6658.96878	8.375828	1982-1999 –> 2000-2012	5.136043	15789.4484
Indian	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.2466073	6658.96878	8.375828	1982-1999 –> 2000-2012	5.136043	15789.4484
Indian	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.5481184	971.68506	6.375446	2000-2012 –> 2013-2019	3.767147	7593.8213
Indian	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.5442665	970.39959	6.459540	2000-2012 –> 2013-2019	3.735055	7554.3424
Indian	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.5442433	970.39184	6.459378	2000-2012 –> 2013-2019	3.730510	7548.1725
Indian	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.5442433	970.39184	6.459378	2000-2012 –> 2013-2019	3.730510	7548.1725
Indian	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.5442433	970.39184	6.459378	2000-2012 –> 2013-2019	3.730510	7548.1725
Indian	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate_star	1.5443252	968.41921	6.473427	2000-2012 –> 2013-2019	3.818559	7661.8338
Indian	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.5844558	983.65664	6.386094	2000-2012 –> 2013-2019	3.831063	7642.6254
Indian	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.5844558	983.65664	6.386094	2000-2012 –> 2013-2019	3.831063	7642.6254
Indian	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.5844558	983.65664	6.386094	2000-2012 –> 2013-2019	3.831063	7642.6254
Indian	(26.75,27]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1.5853938	981.96202	6.456018	2000-2012 –> 2013-2019	3.846875	7658.6078
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.0613838	3480.26734	8.107145	1982-1999 –> 2000-2012	4.166146	9291.4852
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.0613838	3480.26734	8.107145	1982-1999 –> 2000-2012	4.166146	9291.4852
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.0345960	3459.10354	6.864727	1982-1999 –> 2000-2012	4.186229	9329.3478
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.0613838	3480.26734	8.107145	1982-1999 –> 2000-2012	4.166146	9291.4852
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.0352041	3459.58704	6.341175	1982-1999 –> 2000-2012	4.242958	9398.8376
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.0301210	3455.54094	6.725734	1982-1999 –> 2000-2012	4.141868	9275.6381
Indian	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.0267098	3452.81989	7.058210	1982-1999 –> 2000-2012	4.137584	9271.8094
Indian	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.0267098	3452.81989	7.058210	1982-1999 –> 2000-2012	4.137584	9271.8094
Indian	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.0267098	3452.81989	7.058210	1982-1999 –> 2000-2012	4.137584	9271.8094
Indian	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.1687447	3560.41485	7.071436	1982-1999 –> 2000-2012	4.280528	9378.5579
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.1295286	516.28087	3.491771	2000-2012 –> 2013-2019	3.190912	3996.5482
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.1295286	516.28087	3.491771	2000-2012 –> 2013-2019	3.190912	3996.5482
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.1292386	516.19719	3.510267	2000-2012 –> 2013-2019	3.163835	3975.3007
Indian	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.1295286	516.28087	3.491771	2000-2012 –> 2013-2019	3.190912	3996.5482
Indian	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.1489266	521.83192	3.642926	2000-2012 –> 2013-2019	3.175636	3974.6518
Indian	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.1489266	521.83192	3.642926	2000-2012 –> 2013-2019	3.175636	3974.6518
Indian	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.1489266	521.83192	3.642926	2000-2012 –> 2013-2019	3.175636	3974.6518
Indian	(27,27.25]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.1413743	519.68193	3.473289	2000-2012 –> 2013-2019	3.192979	3992.2555
Indian	(27,27.25]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.1413743	519.68193	3.473289	2000-2012 –> 2013-2019	3.192979	3992.2555
Indian	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.1413743	519.68193	3.473289	2000-2012 –> 2013-2019	3.192979	3992.2555
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen	2.1535433	4554.61824	9.715364	1982-1999 –> 2000-2012	3.920420	11091.7337
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.0709842	4475.38800	10.121577	1982-1999 –> 2000-2012	3.821579	10984.1187
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.0709842	4475.38800	10.121577	1982-1999 –> 2000-2012	3.821579	10984.1187
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.1528307	4555.93056	9.660340	1982-1999 –> 2000-2012	3.799251	10863.3035
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.0709842	4475.38800	10.121577	1982-1999 –> 2000-2012	3.821579	10984.1187
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.1768279	4578.96544	13.131069	1982-1999 –> 2000-2012	3.853496	10946.0869
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + phosphate	2.1724061	4572.74014	12.960982	1982-1999 –> 2000-2012	4.000030	11220.7969
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.1492729	4552.49355	12.713194	1982-1999 –> 2000-2012	3.824417	10916.6308
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.1492729	4552.49355	12.713194	1982-1999 –> 2000-2012	3.824417	10916.6308
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.1492729	4552.49355	12.713194	1982-1999 –> 2000-2012	3.824417	10916.6308
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen	1.4243534	877.05637	3.968532	2000-2012 –> 2013-2019	3.577897	5431.6746
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.3698833	860.02807	4.714511	2000-2012 –> 2013-2019	3.440867	5335.4161
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.3698833	860.02807	4.714511	2000-2012 –> 2013-2019	3.440867	5335.4161
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.3615867	857.06355	4.660015	2000-2012 –> 2013-2019	3.514417	5412.9941
Indian	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.3698833	860.02807	4.714511	2000-2012 –> 2013-2019	3.440867	5335.4161
Indian	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate	1.3625635	855.41350	4.781260	2000-2012 –> 2013-2019	3.520708	5414.4673
Indian	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.3620277	857.22158	4.811855	2000-2012 –> 2013-2019	3.480259	5379.4838
Indian	(27.25,27.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.3620277	857.22158	4.811855	2000-2012 –> 2013-2019	3.480259	5379.4838
Indian	(27.25,27.5]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.4963653	901.12504	5.747944	2000-2012 –> 2013-2019	3.615149	5421.9291
Indian	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.3620277	857.22158	4.811855	2000-2012 –> 2013-2019	3.480259	5379.4838
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	2.2212560	6199.46168	10.103497	1982-1999 –> 2000-2012	4.059068	14080.2158
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	2.2212560	6199.46168	10.103497	1982-1999 –> 2000-2012	4.059068	14080.2158
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.1553147	6115.38197	7.879156	1982-1999 –> 2000-2012	3.827135	13628.8466
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.2212560	6199.46168	10.103497	1982-1999 –> 2000-2012	4.059068	14080.2158
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.4659995	6491.08470	13.750915	1982-1999 –> 2000-2012	4.138298	14005.6575
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.0546669	5981.95586	10.627821	1982-1999 –> 2000-2012	3.724431	13490.6447
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.0316506	5950.52602	10.464618	1982-1999 –> 2000-2012	3.701650	13459.7621
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.0316506	5950.52602	10.464618	1982-1999 –> 2000-2012	3.701650	13459.7621
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.0316506	5950.52602	10.464618	1982-1999 –> 2000-2012	3.701650	13459.7621
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.1815640	6147.15588	11.438627	1982-1999 –> 2000-2012	3.852414	13656.3675
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.2820607	994.43544	3.777652	2000-2012 –> 2013-2019	3.503317	7193.8971
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.2820607	994.43544	3.777652	2000-2012 –> 2013-2019	3.503317	7193.8971
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.2820607	994.43544	3.777652	2000-2012 –> 2013-2019	3.503317	7193.8971
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.2462176	977.76232	4.141713	2000-2012 –> 2013-2019	3.300884	6959.7182
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.2313355	970.69826	4.127012	2000-2012 –> 2013-2019	3.262986	6921.2243
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.2313355	970.69826	4.127012	2000-2012 –> 2013-2019	3.262986	6921.2243
Indian	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.2313355	970.69826	4.127012	2000-2012 –> 2013-2019	3.262986	6921.2243
Indian	(27.5,27.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.5813860	1117.81725	5.805160	2000-2012 –> 2013-2019	3.645336	7112.3507
Indian	(27.5,27.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.5813860	1117.81725	5.805160	2000-2012 –> 2013-2019	3.645336	7112.3507
Indian	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.5813860	1117.81725	5.805160	2000-2012 –> 2013-2019	3.645336	7112.3507
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.2289295	3278.07613	16.290711	1982-1999 –> 2000-2012	3.906662	6754.3262
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.2289295	3278.07613	16.290711	1982-1999 –> 2000-2012	3.906662	6754.3262
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	2.2350634	3280.11597	16.639824	1982-1999 –> 2000-2012	4.126590	6968.8211
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.2289295	3278.07613	16.290711	1982-1999 –> 2000-2012	3.906662	6754.3262
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.2055731	3262.59112	14.602654	1982-1999 –> 2000-2012	3.940823	6799.1122
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.0553214	3158.87505	9.283664	1982-1999 –> 2000-2012	3.835923	6741.5261
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.0555230	3159.01923	9.092907	1982-1999 –> 2000-2012	3.849570	6755.1212
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.0555230	3159.01923	9.092907	1982-1999 –> 2000-2012	3.849570	6755.1212
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.0555230	3159.01923	9.092907	1982-1999 –> 2000-2012	3.849570	6755.1212
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.0555308	3157.02476	9.124077	1982-1999 –> 2000-2012	3.877634	6778.8712
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.1069136	534.01584	5.142488	2000-2012 –> 2013-2019	3.335843	3812.0920
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.1069136	534.01584	5.142488	2000-2012 –> 2013-2019	3.335843	3812.0920
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	1.2185721	564.88345	4.334351	2000-2012 –> 2013-2019	3.453635	3844.9994
Indian	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.1069136	534.01584	5.142488	2000-2012 –> 2013-2019	3.335843	3812.0920
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.0988807	531.52488	5.156122	2000-2012 –> 2013-2019	3.304454	3794.1160
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.0836042	526.73708	5.082026	2000-2012 –> 2013-2019	3.138926	3685.6121
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.0796289	525.48013	5.074631	2000-2012 –> 2013-2019	3.135152	3684.4994
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.0796289	525.48013	5.074631	2000-2012 –> 2013-2019	3.135152	3684.4994
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.0796289	525.48013	5.074631	2000-2012 –> 2013-2019	3.135152	3684.4994
Indian	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate_star	1.2734990	579.96172	4.671403	2000-2012 –> 2013-2019	3.329030	3736.9865
Indian	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.9233666	4184.90742	11.949556	1982-1999 –> 2000-2012	3.625381	8974.3465
Indian	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.9233666	4184.90742	11.949556	1982-1999 –> 2000-2012	3.625381	8974.3465
Indian	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.9233666	4184.90742	11.949556	1982-1999 –> 2000-2012	3.625381	8974.3465
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + silicate	2.2273706	4480.15777	7.567306	1982-1999 –> 2000-2012	3.670175	8865.1281
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.9141778	4175.27211	11.882841	1982-1999 –> 2000-2012	3.719254	9108.6288
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.8680107	4126.15097	10.691490	1982-1999 –> 2000-2012	3.672738	9059.0351
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.8662571	4124.26130	10.588591	1982-1999 –> 2000-2012	3.673270	9060.2435
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.8662571	4124.26130	10.588591	1982-1999 –> 2000-2012	3.673270	9060.2435
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.8662571	4124.26130	10.588591	1982-1999 –> 2000-2012	3.673270	9060.2435
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate_star	1.8851564	4142.53399	10.657065	1982-1999 –> 2000-2012	3.692208	9076.5694
Indian	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.3662633	1011.06637	5.753624	2000-2012 –> 2013-2019	3.289630	5195.9738
Indian	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.3662633	1011.06637	5.753624	2000-2012 –> 2013-2019	3.289630	5195.9738
Indian	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.3662633	1011.06637	5.753624	2000-2012 –> 2013-2019	3.289630	5195.9738
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.2512930	960.43481	4.239151	2000-2012 –> 2013-2019	3.343603	5314.7358
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.3725954	1013.72976	5.886282	2000-2012 –> 2013-2019	3.286773	5189.0019
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.3663013	1011.08240	5.900477	2000-2012 –> 2013-2019	3.234312	5137.2334
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.3661054	1010.99981	5.921863	2000-2012 –> 2013-2019	3.232362	5135.2611
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.3661054	1010.99981	5.921863	2000-2012 –> 2013-2019	3.232362	5135.2611
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.3661054	1010.99981	5.921863	2000-2012 –> 2013-2019	3.232362	5135.2611
Indian	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate_star	1.3665432	1009.18436	5.832087	2000-2012 –> 2013-2019	3.251699	5151.7183
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.3402924	5300.11960	4.957701	1982-1999 –> 2000-2012	2.577949	12511.9372
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.3402924	5300.11960	4.957701	1982-1999 –> 2000-2012	2.577949	12511.9372
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.3626180	5351.13364	5.111233	1982-1999 –> 2000-2012	2.529732	12304.1485
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.3402924	5300.11960	4.957701	1982-1999 –> 2000-2012	2.577949	12511.9372
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate	1.3695116	5364.71680	5.313498	1982-1999 –> 2000-2012	2.659175	12756.0578
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate_star	1.3695116	5364.71680	5.313498	1982-1999 –> 2000-2012	2.659175	12756.0578
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.3257643	5266.46462	5.194024	1982-1999 –> 2000-2012	2.612482	12649.7210
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.3257643	5266.46462	5.194024	1982-1999 –> 2000-2012	2.612482	12649.7210
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.3695116	5364.71680	5.313498	1982-1999 –> 2000-2012	2.659175	12756.0578
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.3257643	5266.46462	5.194024	1982-1999 –> 2000-2012	2.612482	12649.7210
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.0893150	1689.99917	3.615224	2000-2012 –> 2013-2019	2.429607	6990.1188
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.0893150	1689.99917	3.615224	2000-2012 –> 2013-2019	2.429607	6990.1188
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.0644848	1664.31240	3.484328	2000-2012 –> 2013-2019	2.427103	7015.4460
Indian	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.0893150	1689.99917	3.615224	2000-2012 –> 2013-2019	2.429607	6990.1188
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate	1.0902259	1688.93032	3.530056	2000-2012 –> 2013-2019	2.459738	7053.6471
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + phosphate_star	1.0902259	1688.93032	3.530056	2000-2012 –> 2013-2019	2.459738	7053.6471
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.0524485	1651.64444	3.175651	2000-2012 –> 2013-2019	2.378213	6918.1091
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.0524485	1651.64444	3.175651	2000-2012 –> 2013-2019	2.378213	6918.1091
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.0902259	1688.93032	3.530056	2000-2012 –> 2013-2019	2.459738	7053.6471
Indian	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.0524485	1651.64444	3.175651	2000-2012 –> 2013-2019	2.378213	6918.1091
Indian	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.8979040	2772.86248	5.629412	1982-1999 –> 2000-2012	1.789906	7128.7422
Indian	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.8979040	2772.86248	5.629412	1982-1999 –> 2000-2012	1.789906	7128.7422
Indian	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.8979040	2772.86248	5.629412	1982-1999 –> 2000-2012	1.789906	7128.7422
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.9006054	2779.18305	5.683654	1982-1999 –> 2000-2012	1.798165	7155.7347
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.9004595	2778.84198	5.674306	1982-1999 –> 2000-2012	1.799893	7162.3331
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.9004595	2778.84198	5.674306	1982-1999 –> 2000-2012	1.799893	7162.3331
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.9004595	2778.84198	5.674306	1982-1999 –> 2000-2012	1.799893	7162.3331
Indian	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	0.8700316	2706.51565	4.947197	1982-1999 –> 2000-2012	1.778364	7122.7718
Indian	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	0.8700316	2706.51565	4.947197	1982-1999 –> 2000-2012	1.778364	7122.7718
Indian	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	0.8700316	2706.51565	4.947197	1982-1999 –> 2000-2012	1.778364	7122.7718
Indian	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.0494164	1082.10174	5.650684	2000-2012 –> 2013-2019	1.947320	3854.9642
Indian	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.0494164	1082.10174	5.650684	2000-2012 –> 2013-2019	1.947320	3854.9642
Indian	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.0494164	1082.10174	5.650684	2000-2012 –> 2013-2019	1.947320	3854.9642
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.0501314	1082.59762	5.665438	2000-2012 –> 2013-2019	1.950737	3861.7807
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.0499750	1082.48914	5.655886	2000-2012 –> 2013-2019	1.950434	3861.3311
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.0499750	1082.48914	5.655886	2000-2012 –> 2013-2019	1.950434	3861.3311
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate	1.0506794	1080.97740	5.725801	2000-2012 –> 2013-2019	1.951357	3858.3291
Indian	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.0499750	1082.48914	5.655886	2000-2012 –> 2013-2019	1.950434	3861.3311
Indian	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.0878981	1108.31939	4.644792	2000-2012 –> 2013-2019	1.957930	3814.8350
Indian	(28.05,28.1]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.0878981	1108.31939	4.644792	2000-2012 –> 2013-2019	1.957930	3814.8350
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.4343342	14400.60402	13.183810	1982-1999 –> 2000-2012	2.302844	26041.5039
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.4343342	14400.60402	13.183810	1982-1999 –> 2000-2012	2.302844	26041.5039
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.4343342	14400.60402	13.183810	1982-1999 –> 2000-2012	2.302844	26041.5039
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.4306196	14379.64102	15.062588	1982-1999 –> 2000-2012	2.317490	26210.8743
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.4312695	14383.31259	15.080060	1982-1999 –> 2000-2012	2.319621	26229.7228
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.4312695	14383.31259	15.080060	1982-1999 –> 2000-2012	2.319621	26229.7228
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.4312695	14383.31259	15.080060	1982-1999 –> 2000-2012	2.319621	26229.7228
Indian	(28.1, Inf]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.4232824	14338.07413	13.264412	1982-1999 –> 2000-2012	2.278161	25835.0443
Indian	(28.1, Inf]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.4232824	14338.07413	13.264412	1982-1999 –> 2000-2012	2.278161	25835.0443
Indian	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.4232824	14338.07413	13.264412	1982-1999 –> 2000-2012	2.278161	25835.0443
Indian	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.1427426	4848.07925	10.137181	2000-2012 –> 2013-2019	2.571369	19216.4513
Indian	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.1427426	4848.07925	10.137181	2000-2012 –> 2013-2019	2.571369	19216.4513
Indian	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.1427426	4848.07925	10.137181	2000-2012 –> 2013-2019	2.571369	19216.4513
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.0850464	4686.74788	8.111481	2000-2012 –> 2013-2019	2.486109	18897.6250
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.1422561	4846.75314	10.000537	2000-2012 –> 2013-2019	2.572876	19226.3942
Indian	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.1429712	4848.70212	10.086697	2000-2012 –> 2013-2019	2.574241	19232.0147
Indian	(28.1, Inf]	cstar_tref ~ temp + aou + oxygen + silicate	1.0851361	4685.00532	8.177916	2000-2012 –> 2013-2019	2.534701	19168.9975
Indian	(28.1, Inf]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.0825004	4679.43248	7.760230	2000-2012 –> 2013-2019	2.505783	19017.5066
Indian	(28.1, Inf]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.0825004	4679.43248	7.760230	2000-2012 –> 2013-2019	2.505783	19017.5066
Indian	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.0825004	4679.43248	7.760230	2000-2012 –> 2013-2019	2.505783	19017.5066
Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	5.1514464	22699.84669	24.395440	1982-1999 –> 2000-2012	10.213379	29506.7413
Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	5.1514464	22699.84669	24.395440	1982-1999 –> 2000-2012	10.213379	29506.7413
Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.1514464	22699.84669	24.395440	1982-1999 –> 2000-2012	10.213379	29506.7413
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + silicate	5.8786241	23679.35812	26.591310	1982-1999 –> 2000-2012	11.381510	30672.8459
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.4441162	23109.74986	22.979344	1982-1999 –> 2000-2012	10.631768	29971.4506
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.5216644	23214.66938	22.917726	1982-1999 –> 2000-2012	10.750787	30094.1580
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	5.5452661	23246.30911	23.096604	1982-1999 –> 2000-2012	10.789151	30132.0956
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	5.5452661	23246.30911	23.096604	1982-1999 –> 2000-2012	10.789151	30132.0956
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.5452661	23246.30911	23.096604	1982-1999 –> 2000-2012	10.789151	30132.0956
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate_star	5.6883325	23433.26447	26.269509	1982-1999 –> 2000-2012	11.068980	30374.5676
Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	4.9013810	16091.18640	44.918260	2000-2012 –> 2013-2019	10.052827	38791.0331
Pacific	(-Inf,26]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.9013810	16091.18640	44.918260	2000-2012 –> 2013-2019	10.052827	38791.0331
Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.9013810	16091.18640	44.918260	2000-2012 –> 2013-2019	10.052827	38791.0331
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + oxygen + silicate	5.6110733	16813.82888	34.963827	2000-2012 –> 2013-2019	11.489697	40493.1870
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.2056081	16412.99952	24.484860	2000-2012 –> 2013-2019	10.649724	39522.7494
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.3070500	16516.13653	22.653677	2000-2012 –> 2013-2019	10.828714	39730.8059
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	5.3457426	16554.95720	22.601977	2000-2012 –> 2013-2019	10.891009	39801.2663
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	5.3457426	16554.95720	22.601977	2000-2012 –> 2013-2019	10.891009	39801.2663
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.3457426	16554.95720	22.601977	2000-2012 –> 2013-2019	10.891009	39801.2663
Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate_star	5.7316657	16925.46462	24.037951	2000-2012 –> 2013-2019	11.419998	40358.7291
Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.3265322	12620.37947	46.177070	1982-1999 –> 2000-2012	6.042042	17213.9168
Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.3265322	12620.37947	46.177070	1982-1999 –> 2000-2012	6.042042	17213.9168
Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.3265322	12620.37947	46.177070	1982-1999 –> 2000-2012	6.042042	17213.9168
Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.2798440	12552.39242	44.076612	1982-1999 –> 2000-2012	5.933001	17101.9328
Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.3195289	12610.24239	42.353591	1982-1999 –> 2000-2012	6.003179	17181.4270
Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.3290176	12623.97195	42.075415	1982-1999 –> 2000-2012	6.025723	17204.3481
Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.3290176	12623.97195	42.075415	1982-1999 –> 2000-2012	6.025723	17204.3481
Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.3290176	12623.97195	42.075415	1982-1999 –> 2000-2012	6.025723	17204.3481
Pacific	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.6573309	13076.38308	36.721470	1982-1999 –> 2000-2012	6.480115	17743.3013
Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.6573309	13076.38308	36.721470	1982-1999 –> 2000-2012	6.480115	17743.3013
Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.2252672	7581.84659	25.175824	2000-2012 –> 2013-2019	6.551799	20202.2261
Pacific	(26,26.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.2252672	7581.84659	25.175824	2000-2012 –> 2013-2019	6.551799	20202.2261
Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.2252672	7581.84659	25.175824	2000-2012 –> 2013-2019	6.551799	20202.2261
Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.3184266	7665.05039	24.324136	2000-2012 –> 2013-2019	6.598271	20217.4428
Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.3740581	7713.62993	23.564835	2000-2012 –> 2013-2019	6.693587	20323.8723
Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.3905276	7727.85818	23.488966	2000-2012 –> 2013-2019	6.719545	20351.8301
Pacific	(26,26.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.3905276	7727.85818	23.488966	2000-2012 –> 2013-2019	6.719545	20351.8301
Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.3905276	7727.85818	23.488966	2000-2012 –> 2013-2019	6.719545	20351.8301
Pacific	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.5607391	7870.98527	22.542773	2000-2012 –> 2013-2019	7.218070	20947.3684
Pacific	(26,26.5]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.5607391	7870.98527	22.542773	2000-2012 –> 2013-2019	7.218070	20947.3684
Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.1662804	10942.85818	38.132847	1982-1999 –> 2000-2012	5.393605	14570.5942
Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.1662804	10942.85818	38.132847	1982-1999 –> 2000-2012	5.393605	14570.5942
Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.1662804	10942.85818	38.132847	1982-1999 –> 2000-2012	5.393605	14570.5942
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.2518949	11056.24975	39.542494	1982-1999 –> 2000-2012	5.587612	14761.3447
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.3605515	11195.93542	38.109774	1982-1999 –> 2000-2012	5.763858	14947.4717
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.3736548	11212.47457	37.907133	1982-1999 –> 2000-2012	5.787355	14971.0362
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.3736548	11212.47457	37.907133	1982-1999 –> 2000-2012	5.787355	14971.0362
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.3736548	11212.47457	37.907133	1982-1999 –> 2000-2012	5.787355	14971.0362
Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.6481143	11544.88294	33.427372	1982-1999 –> 2000-2012	6.193120	15389.6831
Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.6481143	11544.88294	33.427372	1982-1999 –> 2000-2012	6.193120	15389.6831
Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.9529644	5838.06954	27.335453	2000-2012 –> 2013-2019	6.119245	16780.9277
Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.9529644	5838.06954	27.335453	2000-2012 –> 2013-2019	6.119245	16780.9277
Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.9529644	5838.06954	27.335453	2000-2012 –> 2013-2019	6.119245	16780.9277
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.0757276	5932.89347	25.238307	2000-2012 –> 2013-2019	6.327623	16989.1432
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.1573307	5993.85329	23.079627	2000-2012 –> 2013-2019	6.517882	17189.7887
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.1633303	5998.27279	22.868253	2000-2012 –> 2013-2019	6.536985	17210.7474
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.1633303	5998.27279	22.868253	2000-2012 –> 2013-2019	6.536985	17210.7474
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.1633303	5998.27279	22.868253	2000-2012 –> 2013-2019	6.536985	17210.7474
Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	3.2751633	6077.15295	17.242300	2000-2012 –> 2013-2019	6.945687	17646.0628
Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.3927355	6161.25876	14.660001	2000-2012 –> 2013-2019	7.040850	17706.1417
Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.6044923	16258.53237	44.805450	1982-1999 –> 2000-2012	6.218060	21555.3663
Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.6044923	16258.53237	44.805450	1982-1999 –> 2000-2012	6.218060	21555.3663
Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.6044923	16258.53237	44.805450	1982-1999 –> 2000-2012	6.218060	21555.3663
Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.4515616	15997.80060	15.719580	1982-1999 –> 2000-2012	6.141803	21358.8251
Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.5119850	16102.17136	12.969515	1982-1999 –> 2000-2012	6.307773	21548.6278
Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.5120952	16102.36005	12.939564	1982-1999 –> 2000-2012	6.308959	21549.6707
Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.5120952	16102.36005	12.939564	1982-1999 –> 2000-2012	6.308959	21549.6707
Pacific	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.5120952	16102.36005	12.939564	1982-1999 –> 2000-2012	6.308959	21549.6707
Pacific	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate_star	3.5120954	16100.36034	12.938043	1982-1999 –> 2000-2012	6.309383	21546.0077
Pacific	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	3.6382715	16314.62978	23.320798	1982-1999 –> 2000-2012	6.365938	21706.3241
Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.5078655	10207.08312	22.333095	2000-2012 –> 2013-2019	7.112358	26465.6155
Pacific	(26.75,27]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.5078655	10207.08312	22.333095	2000-2012 –> 2013-2019	7.112358	26465.6155
Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.5078655	10207.08312	22.333095	2000-2012 –> 2013-2019	7.112358	26465.6155
Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.6330811	10340.78277	22.571647	2000-2012 –> 2013-2019	7.084643	26338.5834
Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.7015795	10411.98536	21.996428	2000-2012 –> 2013-2019	7.213565	26514.1567
Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.6936094	10403.76862	21.790810	2000-2012 –> 2013-2019	7.205705	26506.1287
Pacific	(26.75,27]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.6936094	10403.76862	21.790810	2000-2012 –> 2013-2019	7.205705	26506.1287
Pacific	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.6936094	10403.76862	21.790810	2000-2012 –> 2013-2019	7.205705	26506.1287
Pacific	(26.75,27]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	3.5854975	10290.52592	14.068224	2000-2012 –> 2013-2019	7.223769	26605.1557
Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.5854975	10290.52592	14.068224	2000-2012 –> 2013-2019	7.223769	26605.1557
Pacific	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	3.5776420	28701.29221	57.045235	1982-1999 –> 2000-2012	6.386911	40180.2032
Pacific	(27,27.25]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	3.5776420	28701.29221	57.045235	1982-1999 –> 2000-2012	6.386911	40180.2032
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.5320097	28564.57936	41.031347	1982-1999 –> 2000-2012	6.354331	40065.1656
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.5320097	28564.57936	41.031347	1982-1999 –> 2000-2012	6.354331	40065.1656
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.5320097	28564.57936	41.031347	1982-1999 –> 2000-2012	6.354331	40065.1656
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.4566101	28334.76659	39.948732	1982-1999 –> 2000-2012	6.294305	39860.7538
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.4526501	28322.55853	40.290268	1982-1999 –> 2000-2012	6.342401	39933.5471
Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.4521042	28320.87438	40.297799	1982-1999 –> 2000-2012	6.335948	39922.2945
Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.4521042	28320.87438	40.297799	1982-1999 –> 2000-2012	6.335948	39922.2945
Pacific	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.4521042	28320.87438	40.297799	1982-1999 –> 2000-2012	6.335948	39922.2945
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	3.3272232	15148.09637	28.262076	2000-2012 –> 2013-2019	6.859233	43712.6757
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	3.3272232	15148.09637	28.262076	2000-2012 –> 2013-2019	6.859233	43712.6757
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.3272232	15148.09637	28.262076	2000-2012 –> 2013-2019	6.859233	43712.6757
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.3089461	15116.29112	29.009691	2000-2012 –> 2013-2019	6.765556	43451.0577
Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.3163044	15129.11693	29.266221	2000-2012 –> 2013-2019	6.768955	43451.6755
Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + phosphate	3.3431063	15173.59396	29.150371	2000-2012 –> 2013-2019	6.875162	43736.3110
Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	3.3146036	15126.15485	29.206304	2000-2012 –> 2013-2019	6.766708	43447.0292
Pacific	(27,27.25]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	3.3146036	15126.15485	29.206304	2000-2012 –> 2013-2019	6.766708	43447.0292
Pacific	(27,27.25]	cstar_tref ~ sal + temp + phosphate + phosphate_star	3.3431063	15173.59396	29.150371	2000-2012 –> 2013-2019	6.875162	43736.3110
Pacific	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.3146036	15126.15485	29.206304	2000-2012 –> 2013-2019	6.766708	43447.0292
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.0994229	23205.89129	50.664824	1982-1999 –> 2000-2012	3.694701	31733.2340
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.0994229	23205.89129	50.664824	1982-1999 –> 2000-2012	3.694701	31733.2340
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	2.1143072	23279.72381	54.620808	1982-1999 –> 2000-2012	3.719949	31834.2962
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.0994229	23205.89129	50.664824	1982-1999 –> 2000-2012	3.694701	31733.2340
Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + silicate + phosphate	2.1570388	23494.50225	57.937740	1982-1999 –> 2000-2012	3.753004	32021.7905
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.1027150	23222.71023	48.240993	1982-1999 –> 2000-2012	3.692765	31735.2365
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.1172531	23296.66950	43.764447	1982-1999 –> 2000-2012	3.714532	31829.6705
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	2.1148251	23284.35300	44.651543	1982-1999 –> 2000-2012	3.710712	31813.4200
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	2.1148251	23284.35300	44.651543	1982-1999 –> 2000-2012	3.710712	31813.4200
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.1148251	23284.35300	44.651543	1982-1999 –> 2000-2012	3.710712	31813.4200
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + phosphate	1.6515360	12607.58533	14.946156	2000-2012 –> 2013-2019	3.763588	35875.8535
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + phosphate_star	1.6515360	12607.58533	14.946156	2000-2012 –> 2013-2019	3.763588	35875.8535
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.6508181	12606.73407	14.817519	2000-2012 –> 2013-2019	3.750241	35812.6254
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.6508181	12606.73407	14.817519	2000-2012 –> 2013-2019	3.750241	35812.6254
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1.6515360	12607.58533	14.946156	2000-2012 –> 2013-2019	3.763588	35875.8535
Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.6508181	12606.73407	14.817519	2000-2012 –> 2013-2019	3.750241	35812.6254
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.6515259	12609.54538	14.931698	2000-2012 –> 2013-2019	3.761798	35870.7630
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.6515259	12609.54538	14.931698	2000-2012 –> 2013-2019	3.761798	35870.7630
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.6515259	12609.54538	14.931698	2000-2012 –> 2013-2019	3.761798	35870.7630
Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.6510487	12607.65014	14.777215	2000-2012 –> 2013-2019	3.753764	35830.3604
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	4.8312543	36816.79680	29.753980	1982-1999 –> 2000-2012	6.710438	46161.3767
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	4.8312543	36816.79680	29.753980	1982-1999 –> 2000-2012	6.710438	46161.3767
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.8312543	36816.79680	29.753980	1982-1999 –> 2000-2012	6.710438	46161.3767
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	4.9200114	37038.56949	31.124104	1982-1999 –> 2000-2012	6.966481	46769.3386
Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate	5.0755540	37421.15582	32.253106	1982-1999 –> 2000-2012	7.104514	47112.8098
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.8543959	36875.53488	30.563953	1982-1999 –> 2000-2012	6.787026	46347.7723
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.8396839	36838.22539	30.129784	1982-1999 –> 2000-2012	6.848342	46486.1030
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	4.8486043	36860.86086	30.406364	1982-1999 –> 2000-2012	6.853005	46499.0804
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	4.8486043	36860.86086	30.406364	1982-1999 –> 2000-2012	6.853005	46499.0804
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.8486043	36860.86086	30.406364	1982-1999 –> 2000-2012	6.853005	46499.0804
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	5.8483180	28845.45847	49.884782	2000-2012 –> 2013-2019	10.679572	65662.2553
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	5.8483180	28845.45847	49.884782	2000-2012 –> 2013-2019	10.679572	65662.2553
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.8483180	28845.45847	49.884782	2000-2012 –> 2013-2019	10.679572	65662.2553
Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	5.9162536	28948.00286	44.202869	2000-2012 –> 2013-2019	10.836265	65986.5724
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.9599707	29016.64511	49.925940	2000-2012 –> 2013-2019	10.814367	65892.1800
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.8806482	28895.36127	48.653949	2000-2012 –> 2013-2019	10.720332	65733.5867
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	5.9168139	28950.86013	48.888236	2000-2012 –> 2013-2019	10.765418	65811.7210
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	5.9168139	28950.86013	48.888236	2000-2012 –> 2013-2019	10.765418	65811.7210
Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.9168139	28950.86013	48.888236	2000-2012 –> 2013-2019	10.765418	65811.7210
Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5.4475367	28202.85182	48.646637	2000-2012 –> 2013-2019	10.979993	66685.5308
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen	1.5749196	11479.37983	24.857440	1982-1999 –> 2000-2012	3.544625	16100.1961
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.4086636	10798.39286	26.804013	1982-1999 –> 2000-2012	3.087734	15070.3118
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.4086636	10798.39286	26.804013	1982-1999 –> 2000-2012	3.087734	15070.3118
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.4651251	11038.98219	21.991742	1982-1999 –> 2000-2012	3.203399	15387.0670
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.4086636	10798.39286	26.804013	1982-1999 –> 2000-2012	3.087734	15070.3118
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + phosphate	1.8596033	12496.60502	29.170631	1982-1999 –> 2000-2012	3.863876	17155.6606
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.8333965	12411.71598	30.507996	1982-1999 –> 2000-2012	3.821656	17055.1399
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.8333965	12411.71598	30.507996	1982-1999 –> 2000-2012	3.821656	17055.1399
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.8596033	12496.60502	29.170631	1982-1999 –> 2000-2012	3.863876	17155.6606
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.8333965	12411.71598	30.507996	1982-1999 –> 2000-2012	3.821656	17055.1399
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen	1.6222688	7124.53247	17.847497	2000-2012 –> 2013-2019	3.197188	18603.9123
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.5189308	6880.50128	19.525347	2000-2012 –> 2013-2019	2.927595	17678.8941
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.5189308	6880.50128	19.525347	2000-2012 –> 2013-2019	2.927595	17678.8941
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.4562172	6722.89016	14.194308	2000-2012 –> 2013-2019	2.921342	17761.8724
Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.5189308	6880.50128	19.525347	2000-2012 –> 2013-2019	2.927595	17678.8941
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + phosphate	1.8258860	7566.51254	23.533384	2000-2012 –> 2013-2019	3.685489	20063.1176
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate	1.8136594	7543.39777	22.668648	2000-2012 –> 2013-2019	3.647056	19955.1137
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + oxygen + silicate + phosphate_star	1.8136594	7543.39777	22.668648	2000-2012 –> 2013-2019	3.647056	19955.1137
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1.8258860	7566.51254	23.533384	2000-2012 –> 2013-2019	3.685489	20063.1176
Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1.8136594	7543.39777	22.668648	2000-2012 –> 2013-2019	3.647056	19955.1137
Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	2.4051309	20154.68081	47.259125	1982-1999 –> 2000-2012	3.935979	26116.1888
Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	2.4051309	20154.68081	47.259125	1982-1999 –> 2000-2012	3.935979	26116.1888
Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate	2.4166243	20194.49021	46.895047	1982-1999 –> 2000-2012	3.958855	26177.8818
Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.4051309	20154.68081	47.259125	1982-1999 –> 2000-2012	3.935979	26116.1888
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen	1.9451108	18290.93816	26.206868	1982-1999 –> 2000-2012	3.956817	25131.1181
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.8743577	17967.98413	28.472358	1982-1999 –> 2000-2012	3.700669	24498.4513
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.8743577	17967.98413	28.472358	1982-1999 –> 2000-2012	3.700669	24498.4513
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.6576747	16890.58757	19.473162	1982-1999 –> 2000-2012	3.299018	23076.7869
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.8743577	17967.98413	28.472358	1982-1999 –> 2000-2012	3.700669	24498.4513
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.3996870	20134.80797	43.799057	1982-1999 –> 2000-2012	3.941579	26119.4902
Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.2680572	8802.98847	9.175164	2000-2012 –> 2013-2019	3.673188	28957.6693
Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.2680572	8802.98847	9.175164	2000-2012 –> 2013-2019	3.673188	28957.6693
Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.2680572	8802.98847	9.175164	2000-2012 –> 2013-2019	3.673188	28957.6693
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen	1.6089122	10064.20026	14.448409	2000-2012 –> 2013-2019	3.554023	28355.1384
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.4698348	9586.49366	16.259616	2000-2012 –> 2013-2019	3.344193	27554.4778
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.4698348	9586.49366	16.259616	2000-2012 –> 2013-2019	3.344193	27554.4778
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.3980900	9320.96584	9.449663	2000-2012 –> 2013-2019	3.055765	26211.5534
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.4698348	9586.49366	16.259616	2000-2012 –> 2013-2019	3.344193	27554.4778
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.2877479	8884.74800	8.599853	2000-2012 –> 2013-2019	3.687435	29019.5560
Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.3034001	8948.85229	8.494312	2000-2012 –> 2013-2019	3.694521	29052.2995
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.2300871	25445.00802	12.943271	1982-1999 –> 2000-2012	2.134182	34224.4885
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.2300871	25445.00802	12.943271	1982-1999 –> 2000-2012	2.134182	34224.4885
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate	1.2318471	25465.36974	11.941972	1982-1999 –> 2000-2012	2.196749	34675.7149
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.2300871	25445.00802	12.943271	1982-1999 –> 2000-2012	2.134182	34224.4885
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.2316661	25465.07059	12.262414	1982-1999 –> 2000-2012	2.140123	34276.5609
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.2379759	25544.99030	12.146381	1982-1999 –> 2000-2012	2.151757	34395.3365
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.2354927	25513.58705	12.070447	1982-1999 –> 2000-2012	2.149040	34362.2316
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.2354927	25513.58705	12.070447	1982-1999 –> 2000-2012	2.149040	34362.2316
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.2354927	25513.58705	12.070447	1982-1999 –> 2000-2012	2.149040	34362.2316
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	1.3214898	26564.00105	17.975522	1982-1999 –> 2000-2012	2.241858	35460.1146
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.8453987	11698.26147	6.536769	2000-2012 –> 2013-2019	2.075486	37143.2695
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.8453987	11698.26147	6.536769	2000-2012 –> 2013-2019	2.075486	37143.2695
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate	0.8732985	11999.52258	5.272273	2000-2012 –> 2013-2019	2.105146	37464.8923
Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.8453987	11698.26147	6.536769	2000-2012 –> 2013-2019	2.075486	37143.2695
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + oxygen + silicate	0.9038019	12322.19084	4.181612	2000-2012 –> 2013-2019	2.063302	36842.9429
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.8515572	11766.05436	6.464399	2000-2012 –> 2013-2019	2.083223	37231.1249
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.8607850	11866.72175	6.353072	2000-2012 –> 2013-2019	2.098761	37411.7121
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.8593885	11851.55669	6.327135	2000-2012 –> 2013-2019	2.094881	37365.1437
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.8593885	11851.55669	6.327135	2000-2012 –> 2013-2019	2.094881	37365.1437
Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.8593885	11851.55669	6.327135	2000-2012 –> 2013-2019	2.094881	37365.1437
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.7056488	13989.98847	16.184369	1982-1999 –> 2000-2012	1.377054	18457.6973
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.7056488	13989.98847	16.184369	1982-1999 –> 2000-2012	1.377054	18457.6973
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	0.7397577	14604.39355	10.907158	1982-1999 –> 2000-2012	1.494326	19579.6967
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.7056488	13989.98847	16.184369	1982-1999 –> 2000-2012	1.377054	18457.6973
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.7095402	14061.80146	16.013755	1982-1999 –> 2000-2012	1.383438	18545.6816
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.7146235	14155.01804	16.182185	1982-1999 –> 2000-2012	1.390584	18652.2370
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.7145361	14153.42175	16.136551	1982-1999 –> 2000-2012	1.390604	18651.3329
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.7145361	14153.42175	16.136551	1982-1999 –> 2000-2012	1.390604	18651.3329
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.7145361	14153.42175	16.136551	1982-1999 –> 2000-2012	1.390604	18651.3329
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	0.7150620	14161.02937	16.636984	1982-1999 –> 2000-2012	1.395249	18683.4431
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	0.5993430	9058.77731	5.576006	2000-2012 –> 2013-2019	1.304992	23048.7658
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	0.5993430	9058.77731	5.576006	2000-2012 –> 2013-2019	1.304992	23048.7658
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	0.6292212	9541.90300	6.657797	2000-2012 –> 2013-2019	1.368979	24146.2965
Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	0.5993430	9058.77731	5.576006	2000-2012 –> 2013-2019	1.304992	23048.7658
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	0.5987240	9048.47300	5.574015	2000-2012 –> 2013-2019	1.308264	23110.2745
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	0.5981422	9038.77750	5.580037	2000-2012 –> 2013-2019	1.312766	23193.7955
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	0.5980981	9038.04270	5.582077	2000-2012 –> 2013-2019	1.312634	23191.4645
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	0.5980981	9038.04270	5.582077	2000-2012 –> 2013-2019	1.312634	23191.4645
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	0.5980981	9038.04270	5.582077	2000-2012 –> 2013-2019	1.312634	23191.4645
Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	0.6092722	9220.62653	5.062029	2000-2012 –> 2013-2019	1.324334	23381.6559
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.9538780	23245.12893	15.556421	1982-1999 –> 2000-2012	3.223813	32079.1781
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.9538780	23245.12893	15.556421	1982-1999 –> 2000-2012	3.223813	32079.1781
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.9561794	23258.22173	14.237058	1982-1999 –> 2000-2012	3.217844	32057.5132
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.9538780	23245.12893	15.556421	1982-1999 –> 2000-2012	3.223813	32079.1781
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.9620588	23291.59959	12.529955	1982-1999 –> 2000-2012	3.230655	32120.0379
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.9618987	23290.69189	12.595295	1982-1999 –> 2000-2012	3.230511	32119.1987
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate	1.9635633	23298.12441	11.894626	1982-1999 –> 2000-2012	3.231509	32121.8367
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate	1.9623484	23293.24086	12.484949	1982-1999 –> 2000-2012	3.230270	32118.8519
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + oxygen + silicate + phosphate_star	1.9623484	23293.24086	12.484949	1982-1999 –> 2000-2012	3.230270	32118.8519
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.9623484	23293.24086	12.484949	1982-1999 –> 2000-2012	3.230270	32118.8519
Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate	1.0285374	9037.96786	6.535296	2000-2012 –> 2013-2019	2.991710	32335.8771
Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + oxygen + silicate + phosphate_star	1.0285374	9037.96786	6.535296	2000-2012 –> 2013-2019	2.991710	32335.8771
Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1.0285374	9037.96786	6.535296	2000-2012 –> 2013-2019	2.991710	32335.8771
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate	1.0334539	9067.70551	9.829961	2000-2012 –> 2013-2019	2.987332	32312.8344
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + phosphate_star	1.0334539	9067.70551	9.829961	2000-2012 –> 2013-2019	2.987332	32312.8344
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + oxygen + silicate	1.0221851	8999.33478	9.036276	2000-2012 –> 2013-2019	2.978365	32257.5565
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	1.0334539	9067.70551	9.829961	2000-2012 –> 2013-2019	2.987332	32312.8344
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	1.0290904	9041.32013	6.525257	2000-2012 –> 2013-2019	2.991149	32332.9197
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	1.0294175	9043.30142	6.527749	2000-2012 –> 2013-2019	2.991316	32333.9933
Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	1.0296013	9044.41528	6.513144	2000-2012 –> 2013-2019	2.991950	32337.6561

5.3 Target variable coefficients

A data frame to map the target variable is prepared.

# create table with two era belonging to one eras
eras_forward <- lm_all_fitted_wide %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(era, lead(era), sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_backward <- lm_all_fitted_wide %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_era <- full_join(eras_backward, eras_forward) %>% 
  filter(str_detect(eras, "NA") == FALSE)

# extend best model selection from eras to era
lm_best_target <- full_join(
  lm_best %>% select(basin, gamma_slab, model, eras),
  eras_era)

lm_best_target <- left_join(lm_best_target, lm_all_fitted_wide)

rm(eras_era, eras_forward, eras_backward,
   lm_all_fitted)

5.4 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,
    `coeff_(Intercept)`,
    paste("coeff", params_local$MLR_predictors, sep = "_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_target.csv",
                  sep = ""))

lm_best_cant %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    `delta_coeff_(Intercept)`,
    paste("delta_coeff", params_local$MLR_predictors, sep = "_")
  ) %>%
  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")

Past versions of eMLR_predictor_model_quality_all-1.png

Version	Author	Date
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")

Past versions of eMLR_predictor_model_quality_best-1.png

Version	Author	Date
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 adjecent 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)

Past versions of rmse_correlation_across_eras_all_models-1.png

Version	Author	Date
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)

Past versions of rmse_correlation_across_eras_best_models-1.png

Version	Author	Date
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	oxygen	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26]	6	6	5	5	10	10	7
(26,26.5]	7	6	6	6	8	10	7
(26.5,26.75]	10	6	7	6	4	10	4
(26.75,27]	7	5	6	6	9	10	6
(27,27.25]	10	6	7	6	10	4	4
(27.25,27.5]	10	6	7	6	10	4	4
(27.5,27.75]	10	6	7	6	10	4	4
(27.75,27.85]	10	6	7	6	10	4	4
(27.85,27.95]	10	6	7	6	10	4	4
(27.95,28.05]	10	6	7	6	10	4	4
(28.05,28.1]	10	6	7	6	10	4	4
(28.1,28.15]	7	5	6	7	10	8	7
(28.15,28.2]	7	5	7	5	10	9	6
(28.2, Inf]	6	5	7	5	10	10	5
total	120.00	80.00	93.00	82.00	131.00	95.00	70.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26]	7	5	6	5	10	10	6
(26,26.5]	7	5	5	5	10	10	7
(26.5,26.75]	9	5	7	5	7	10	6
(26.75,27]	7	4	6	6	10	10	5
(27,27.25]	8	6	6	6	10	7	7
(27.25,27.5]	10	6	7	6	10	4	4
(27.5,27.75]	10	6	7	6	10	4	4
(27.75,27.85]	7	6	7	6	10	7	7
(27.85,27.95]	8	5	8	5	10	7	6
(27.95,28.05]	8	5	8	5	10	7	6
(28.05,28.1]	6	5	6	6	10	10	5
(28.1,28.15]	5	5	6	7	10	10	5
(28.15,28.2]	6	5	7	5	10	10	5
(28.2, Inf]	6	5	7	5	10	10	5
total	104.00	73.00	93.00	78.00	137.00	116.00	78.00
Indian - 1982-1999 --> 2000-2012
(-Inf,26]	5	5	6	7	5	10	10
(26,26.5]	7	5	7	6	7	10	8
(26.5,26.75]	7	6	6	6	7	8	10
(26.75,27]	6	5	5	6	7	10	10
(27,27.25]	6	5	5	6	10	7	10
(27.25,27.5]	6	7	5	5	10	5	10
(27.5,27.75]	6	5	5	6	10	7	10
(27.75,27.85]	6	4	6	6	10	10	6
(27.85,27.95]	6	5	5	6	10	10	7
(27.95,28.05]	10	7	6	6	4	4	10
(28.05,28.1]	7	6	7	6	7	10	7
(28.1, Inf]	7	6	6	7	7	7	10
total	79.00	66.00	69.00	73.00	94.00	98.00	108.00
Indian - 2000-2012 --> 2013-2019
(-Inf,26]	5	5	6	7	5	10	10
(26,26.5]	4	6	6	7	4	10	10
(26.5,26.75]	4	6	6	7	4	10	10
(26.75,27]	5	5	5	7	6	10	10
(27,27.25]	7	7	6	6	7	7	10
(27.25,27.5]	10	7	5	5	5	5	10
(27.5,27.75]	7	6	6	7	7	7	10
(27.75,27.85]	6	4	6	6	10	10	6
(27.85,27.95]	6	4	6	7	10	9	7
(27.95,28.05]	10	7	6	6	4	4	10
(28.05,28.1]	6	6	7	5	8	10	7
(28.1, Inf]	9	7	5	5	6	10	7
total	79.00	70.00	70.00	75.00	76.00	102.00	107.00
Pacific - 1982-1999 --> 2000-2012
(-Inf,26]	6	5	5	6	10	10	7
(26,26.5]	7	5	6	7	8	10	7
(26.5,26.75]	7	5	7	6	8	10	7
(26.75,27]	6	5	5	7	9	10	7
(27,27.25]	7	6	6	6	10	7	8
(27.25,27.5]	6	5	7	5	10	10	5
(27.5,27.75]	6	5	6	6	10	10	5
(27.75,27.85]	10	7	6	5	5	4	10
(27.85,27.95]	10	6	6	4	10	6	6
(27.95,28.05]	6	4	6	6	10	10	6
(28.05,28.1]	6	4	6	6	10	10	6
(28.1, Inf]	6	6	5	5	10	7	10
total	83.00	63.00	71.00	69.00	110.00	104.00	84.00
Pacific - 2000-2012 --> 2013-2019
(-Inf,26]	6	5	5	6	10	10	7
(26,26.5]	7	6	6	6	8	10	7
(26.5,26.75]	6	5	5	7	9	10	7
(26.75,27]	7	5	7	6	8	10	7
(27,27.25]	5	5	7	6	10	5	10
(27.25,27.5]	10	6	7	6	10	4	4
(27.5,27.75]	7	4	6	7	9	10	6
(27.75,27.85]	10	7	6	5	5	4	10
(27.85,27.95]	9	7	5	5	10	6	7
(27.95,28.05]	7	5	6	5	10	10	6
(28.05,28.1]	6	4	6	6	10	10	6
(28.1, Inf]	9	5	6	6	10	7	7
total	89.00	64.00	72.00	71.00	109.00	96.00	84.00

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)

Past versions of aic_vs_rmse_all_models-1.png

Version	Author	Date
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)

Past versions of aic_vs_rmse_selected_models-1.png

Version	Author	Date
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

Session information

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.1

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_0.5.3.9000 GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.8.0       scico_1.2.0      patchwork_1.1.0  collapse_1.4.2  
[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_3.3.2   
[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_1.2.1          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_0.4.9              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_0.10.1.2.0
[67] data.table_1.13.4        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_0.19               
[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_0.1