eMLR - model fitting

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Last updated: 2021-01-11

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---

1 Required data

Required are:

• cleaned and prepared GLODAPv2_2020 file

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

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

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

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

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

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

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

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

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

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

# 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 + nitrate + phosphate + phosphate_star	6.901466	489.7955	31.989457	1982-1999 –> 2000-2012	12.807857	1034.161
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	7.217422	496.1520	31.653586	1982-1999 –> 2000-2012	13.267957	1044.520
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	6.961989	491.0353	31.822907	1982-1999 –> 2000-2012	12.846097	1034.773
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	6.967437	491.1464	31.817625	1982-1999 –> 2000-2012	12.847216	1034.762
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	7.136236	494.5456	32.610924	1982-1999 –> 2000-2012	13.160079	1042.180
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	6.994268	491.6922	31.757131	1982-1999 –> 2000-2012	12.863175	1035.001
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	7.200241	495.8135	31.521168	1982-1999 –> 2000-2012	13.043712	1038.401
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	7.189271	495.5970	31.435904	1982-1999 –> 2000-2012	13.202551	1042.940
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	7.183121	495.4755	31.414627	1982-1999 –> 2000-2012	13.175607	1042.243
Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	7.163047	495.0781	31.356568	1982-1999 –> 2000-2012	13.117181	1040.780
Atlantic	(-Inf,26]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	6.945624	571.2704	25.480413	2000-2012 –> 2013-2019	14.156964	1067.303
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	7.047372	573.6845	25.557489	2000-2012 –> 2013-2019	13.948838	1063.480
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	6.919649	570.6484	24.814403	2000-2012 –> 2013-2019	14.137071	1066.800
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	7.052707	573.8101	25.632476	2000-2012 –> 2013-2019	14.014696	1064.845
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	7.053006	573.8171	25.631237	2000-2012 –> 2013-2019	14.020443	1064.964
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	6.849967	568.9683	23.970969	2000-2012 –> 2013-2019	13.805204	1059.866
Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	7.055954	573.8865	25.677561	2000-2012 –> 2013-2019	14.050221	1065.579
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	6.923432	570.7391	25.591870	2000-2012 –> 2013-2019	14.112703	1066.336
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	6.913161	570.4927	25.615129	2000-2012 –> 2013-2019	14.096281	1065.968
Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	6.883305	569.7742	25.520200	2000-2012 –> 2013-2019	14.046352	1064.852
Atlantic	(26,26.5]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	5.461580	4705.7150	27.508531	1982-1999 –> 2000-2012	10.349824	7819.671
Atlantic	(26,26.5]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	5.460806	4707.5016	27.439920	1982-1999 –> 2000-2012	10.328188	7819.044
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	5.449533	4704.3895	27.627401	1982-1999 –> 2000-2012	10.333577	7819.459
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	5.595354	4744.1579	28.662211	1982-1999 –> 2000-2012	10.501369	7863.859
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	5.668480	4763.7126	29.611179	1982-1999 –> 2000-2012	10.600656	7888.902
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.672809	4764.8621	27.240431	1982-1999 –> 2000-2012	10.485241	7864.688
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate	5.595568	4742.2156	28.710839	1982-1999 –> 2000-2012	10.501616	7859.924
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.405341	4692.1270	26.364337	1982-1999 –> 2000-2012	10.227093	7793.949
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	5.581556	4740.4397	28.447928	1982-1999 –> 2000-2012	10.468166	7856.051
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5.648629	4758.4291	28.798979	1982-1999 –> 2000-2012	10.561557	7879.584
Atlantic	(26,26.5]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	7.048254	1522.5299	31.846401	2000-2012 –> 2013-2019	12.509834	6228.245
Atlantic	(26,26.5]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	7.042845	1524.1859	31.659719	2000-2012 –> 2013-2019	12.503651	6231.688
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	6.717929	1503.0259	30.587996	2000-2012 –> 2013-2019	12.167462	6207.415
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	6.742082	1504.6337	30.902036	2000-2012 –> 2013-2019	12.337436	6248.792
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	6.742965	1504.6923	30.862911	2000-2012 –> 2013-2019	12.411445	6268.405
Atlantic	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	6.761371	1505.9136	31.037048	2000-2012 –> 2013-2019	12.542132	6299.165
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate	7.046893	1522.4434	31.864787	2000-2012 –> 2013-2019	12.642461	6264.659
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	7.046599	1524.4247	31.875965	2000-2012 –> 2013-2019	12.451940	6216.552
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	7.042239	1524.1474	31.692077	2000-2012 –> 2013-2019	12.623796	6264.587
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	7.042643	1524.1731	31.718774	2000-2012 –> 2013-2019	12.691271	6282.602
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	5.218068	6856.3345	31.316310	1982-1999 –> 2000-2012	9.303712	11098.656
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.242126	6866.5829	31.603854	1982-1999 –> 2000-2012	9.121238	11031.302
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.226952	6860.1244	31.682938	1982-1999 –> 2000-2012	9.322765	11106.165
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.237147	6864.4659	31.413731	1982-1999 –> 2000-2012	9.290792	11095.024
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	5.219559	6856.9711	31.199031	1982-1999 –> 2000-2012	9.291792	11094.374
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + phosphate + phosphate_star	5.243349	6865.1031	31.491794	1982-1999 –> 2000-2012	9.329778	11105.711
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.239509	6865.4707	31.387200	1982-1999 –> 2000-2012	9.282844	11092.219
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.272305	6879.3728	31.962505	1982-1999 –> 2000-2012	9.204879	11064.569
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5.273396	6877.8338	31.975276	1982-1999 –> 2000-2012	9.218245	11065.692
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5.265284	6876.4041	32.082762	1982-1999 –> 2000-2012	9.201894	11063.135
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	7.380291	1620.3433	33.746997	2000-2012 –> 2013-2019	12.611754	8482.390
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	7.376551	1620.1050	33.808938	2000-2012 –> 2013-2019	12.594619	8476.440
Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	7.365686	1619.4122	33.903597	2000-2012 –> 2013-2019	12.585245	8476.383
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate	7.491668	1625.3831	32.400618	2000-2012 –> 2013-2019	12.773279	8506.685
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	7.416970	1622.6733	33.571880	2000-2012 –> 2013-2019	12.689274	8502.046
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	7.483768	1624.8872	32.521858	2000-2012 –> 2013-2019	12.757489	8502.858
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	7.491640	1627.3813	32.403216	2000-2012 –> 2013-2019	12.756794	8503.731
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	7.483495	1626.8701	32.532918	2000-2012 –> 2013-2019	12.756141	8506.387
Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	7.474357	1624.2958	32.578936	2000-2012 –> 2013-2019	12.749889	8503.032
Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	7.474144	1626.2824	32.587440	2000-2012 –> 2013-2019	12.749324	8506.870
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.382671	8011.2738	31.556447	1982-1999 –> 2000-2012	10.245473	13504.284
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.435928	8036.6554	31.303060	1982-1999 –> 2000-2012	10.290717	13526.655
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.378582	8009.3144	31.209812	1982-1999 –> 2000-2012	10.232802	13499.099
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	5.384566	8012.1810	31.187756	1982-1999 –> 2000-2012	10.221549	13495.470
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.376777	8008.4492	31.183263	1982-1999 –> 2000-2012	10.232040	13498.627
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.407867	8023.3133	30.420316	1982-1999 –> 2000-2012	10.259738	13512.214
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5.440886	8039.0057	30.354436	1982-1999 –> 2000-2012	10.289409	13526.647
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5.357636	7999.2555	30.082233	1982-1999 –> 2000-2012	10.245974	13501.830
Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	5.440904	8039.0141	30.389609	1982-1999 –> 2000-2012	10.288834	13526.432
Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	5.441043	8037.0803	30.373411	1982-1999 –> 2000-2012	10.300335	13526.772
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	6.035075	2310.6002	38.579373	2000-2012 –> 2013-2019	11.417746	10321.874
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6.005890	2307.1390	38.587713	2000-2012 –> 2013-2019	11.384472	10316.453
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	6.026915	2309.6341	38.376311	2000-2012 –> 2013-2019	11.411480	10321.815
Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6.004702	2306.9977	38.611358	2000-2012 –> 2013-2019	11.381479	10315.447
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	6.028263	2309.7938	38.675885	2000-2012 –> 2013-2019	11.436131	10333.107
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5.988403	2305.0570	38.473897	2000-2012 –> 2013-2019	11.429289	10344.063
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5.988961	2305.1236	38.969850	2000-2012 –> 2013-2019	11.346597	10304.379
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	6.006705	2305.2358	38.450034	2000-2012 –> 2013-2019	11.449134	10342.973
Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	5.985030	2304.6548	38.527950	2000-2012 –> 2013-2019	11.425934	10343.669
Atlantic	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	6.005559	2305.0996	38.469541	2000-2012 –> 2013-2019	11.446717	10342.234
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	5.428459	15013.2836	34.582688	1982-1999 –> 2000-2012	10.895441	28788.658
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.400919	14988.7580	34.251655	1982-1999 –> 2000-2012	10.779965	28692.557
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.332359	14927.1551	34.467700	1982-1999 –> 2000-2012	10.674002	28600.154
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	5.370951	14961.9272	34.760812	1982-1999 –> 2000-2012	10.684161	28611.368
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.338179	14932.4154	34.436121	1982-1999 –> 2000-2012	10.678097	28603.988
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate_star	5.506324	15079.9581	34.548620	1982-1999 –> 2000-2012	10.904833	28797.699
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.368613	14959.8284	34.084947	1982-1999 –> 2000-2012	10.851333	28747.891
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5.388886	14978.0024	32.575615	1982-1999 –> 2000-2012	10.799945	28707.993
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5.344687	14938.2903	33.624230	1982-1999 –> 2000-2012	10.813132	28714.845
Atlantic	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	5.404332	14991.8040	32.546984	1982-1999 –> 2000-2012	10.822723	28727.771
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	7.420420	4114.9626	49.297141	2000-2012 –> 2013-2019	12.848879	19128.246
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	7.512168	4129.6842	48.491261	2000-2012 –> 2013-2019	12.913087	19118.442
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	7.497589	4127.3570	48.699698	2000-2012 –> 2013-2019	12.829948	19054.512
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	7.429456	4116.4206	49.124556	2000-2012 –> 2013-2019	12.877562	19147.125
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	7.482608	4124.9608	48.690328	2000-2012 –> 2013-2019	12.853558	19086.888
Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	7.497446	4127.3341	48.702277	2000-2012 –> 2013-2019	12.835625	19059.749
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	7.428956	4116.3399	49.766188	2000-2012 –> 2013-2019	12.901783	19168.875
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	7.391449	4110.2762	50.000979	2000-2012 –> 2013-2019	12.780334	19088.279
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	7.499307	4127.6314	49.406647	2000-2012 –> 2013-2019	12.843994	19065.922
Atlantic	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	7.401831	4111.9578	49.902433	2000-2012 –> 2013-2019	12.806163	19103.762
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.451293	16252.0546	29.010400	1982-1999 –> 2000-2012	9.089033	30529.845
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	4.388044	16172.2556	29.043519	1982-1999 –> 2000-2012	9.019600	30443.601
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	4.357842	16133.7447	29.157326	1982-1999 –> 2000-2012	9.028179	30445.365
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	4.412906	16201.7599	29.215351	1982-1999 –> 2000-2012	9.143955	30573.763
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.391370	16176.4811	29.359098	1982-1999 –> 2000-2012	9.116691	30544.633
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.409697	16199.7034	29.262732	1982-1999 –> 2000-2012	9.138929	30571.851
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.390880	16175.8588	29.367069	1982-1999 –> 2000-2012	9.153335	30581.819
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	4.365533	16143.5772	29.114394	1982-1999 –> 2000-2012	9.016608	30435.235
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	4.394774	16178.8019	29.302833	1982-1999 –> 2000-2012	9.152330	30577.791
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.393479	16179.1581	29.332596	1982-1999 –> 2000-2012	9.147065	30576.115
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	7.428170	4602.4522	40.519886	2000-2012 –> 2013-2019	11.879463	20854.507
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	7.445225	4605.5253	40.099019	2000-2012 –> 2013-2019	11.912517	20877.586
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	7.450782	4606.5251	40.546326	2000-2012 –> 2013-2019	11.838826	20778.781
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	7.494790	4614.4165	40.421331	2000-2012 –> 2013-2019	11.852632	20748.161
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	7.497556	4612.9110	40.426170	2000-2012 –> 2013-2019	11.910463	20814.671
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	7.405055	4598.2758	40.968520	2000-2012 –> 2013-2019	11.796425	20774.757
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	7.481493	4612.0371	40.210960	2000-2012 –> 2013-2019	11.891190	20811.740
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	7.473331	4610.5744	40.488423	2000-2012 –> 2013-2019	11.838864	20754.152
Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	7.511381	4617.3796	40.155855	2000-2012 –> 2013-2019	11.904860	20796.538
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	7.364817	4590.9747	40.460267	2000-2012 –> 2013-2019	11.890186	20935.058
Atlantic	(27.5,27.75]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	4.371045	18396.3108	39.480256	1982-1999 –> 2000-2012	9.014373	32183.584
Atlantic	(27.5,27.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4.403508	18441.3120	39.485064	1982-1999 –> 2000-2012	9.078354	32258.122
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.364128	18386.2516	39.397157	1982-1999 –> 2000-2012	9.029025	32195.129
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.354863	18372.7510	39.561546	1982-1999 –> 2000-2012	9.019904	32181.773
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.372114	18397.8643	39.732165	1982-1999 –> 2000-2012	9.061612	32231.263
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.357921	18377.2112	39.635847	1982-1999 –> 2000-2012	9.035232	32198.478
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	4.369861	18394.5904	39.564712	1982-1999 –> 2000-2012	9.015257	32183.939
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4.397956	18435.2976	39.682165	1982-1999 –> 2000-2012	9.076851	32258.145
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.402253	18441.5006	39.550881	1982-1999 –> 2000-2012	9.077089	32260.301
Atlantic	(27.5,27.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	4.375091	18402.1881	39.636335	1982-1999 –> 2000-2012	9.034563	32205.641
Atlantic	(27.5,27.75]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	6.462587	5269.9493	44.043668	2000-2012 –> 2013-2019	10.833632	23666.260
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	6.509849	5281.6076	43.273670	2000-2012 –> 2013-2019	10.873977	23667.859
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6.508170	5281.1949	43.278721	2000-2012 –> 2013-2019	10.863032	23653.946
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6.514530	5282.7576	43.425543	2000-2012 –> 2013-2019	10.886643	23680.622
Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6.507467	5281.0220	43.322719	2000-2012 –> 2013-2019	10.865388	23658.233
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	6.466532	5270.9255	44.012019	2000-2012 –> 2013-2019	10.836393	23665.516
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	6.497457	5278.5590	43.842819	2000-2012 –> 2013-2019	10.895413	23713.857
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate	6.510308	5279.7204	43.179262	2000-2012 –> 2013-2019	10.912612	23719.296
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	6.510090	5281.6669	43.192055	2000-2012 –> 2013-2019	10.912342	23723.167
Atlantic	(27.5,27.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	6.470887	5272.0027	43.986541	2000-2012 –> 2013-2019	10.845978	23674.191
Atlantic	(27.75,27.85]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	4.663654	12600.4703	47.036142	1982-1999 –> 2000-2012	9.435526	19245.720
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	4.636874	12575.9729	46.856876	1982-1999 –> 2000-2012	9.367800	19202.057
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	4.664060	12598.8411	47.841640	1982-1999 –> 2000-2012	9.419511	19234.425
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.662831	12599.7197	47.791748	1982-1999 –> 2000-2012	9.417270	19236.830
Atlantic	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	4.636937	12576.0306	46.670710	1982-1999 –> 2000-2012	9.376109	19205.988
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.663183	12600.0407	47.786581	1982-1999 –> 2000-2012	9.414587	19235.731
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.662372	12599.3007	47.830778	1982-1999 –> 2000-2012	9.425139	19240.304
Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	4.657806	12595.1328	47.059363	1982-1999 –> 2000-2012	9.431622	19241.289
Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4.647812	12585.9960	47.093313	1982-1999 –> 2000-2012	9.434206	19238.004
Atlantic	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	4.653842	12591.5108	47.081754	1982-1999 –> 2000-2012	9.431782	19239.587
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	7.716381	3254.6978	53.594379	2000-2012 –> 2013-2019	12.353255	15830.671
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	7.643066	3245.7622	53.225487	2000-2012 –> 2013-2019	12.380697	15913.182
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	7.643268	3245.7869	53.160594	2000-2012 –> 2013-2019	12.306099	15845.507
Atlantic	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	7.714219	3254.4356	53.444046	2000-2012 –> 2013-2019	12.351157	15830.466
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	7.664258	3248.3539	53.292748	2000-2012 –> 2013-2019	12.327441	15848.395
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	7.644854	3245.9811	53.233859	2000-2012 –> 2013-2019	12.309105	15846.996
Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	7.665162	3248.4642	53.272046	2000-2012 –> 2013-2019	12.327533	15847.765
Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	7.722498	3255.4395	53.748299	2000-2012 –> 2013-2019	12.380304	15850.572
Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	7.703930	3253.1863	53.692403	2000-2012 –> 2013-2019	12.351742	15839.182
Atlantic	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	7.723003	3255.5008	53.723758	2000-2012 –> 2013-2019	12.376845	15847.012
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	4.974593	25857.0159	86.528000	1982-1999 –> 2000-2012	9.088464	38858.876
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.911509	25747.9224	85.823432	1982-1999 –> 2000-2012	9.075460	38805.250
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate_star	4.974769	25855.3178	86.407196	1982-1999 –> 2000-2012	9.139290	38911.272
Atlantic	(27.85,27.95]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	5.171299	26188.5093	87.998624	1982-1999 –> 2000-2012	9.358673	39271.551
Atlantic	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5.182745	26205.4092	87.067742	1982-1999 –> 2000-2012	9.400108	39319.161
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.914835	25753.7099	85.738067	1982-1999 –> 2000-2012	9.089378	38822.682
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.911124	25747.2525	85.784435	1982-1999 –> 2000-2012	9.075467	38805.011
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	4.978761	25864.1748	85.232204	1982-1999 –> 2000-2012	9.153894	38933.795
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate	4.982514	25868.6155	85.710178	1982-1999 –> 2000-2012	9.292880	39082.358
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.913841	25751.9810	85.746207	1982-1999 –> 2000-2012	9.084490	38816.675
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	5.417747	8419.7047	37.174165	2000-2012 –> 2013-2019	10.392340	34276.721
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.362794	8392.1376	36.124924	2000-2012 –> 2013-2019	10.274303	34140.060
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate_star	5.441394	8429.4810	36.888570	2000-2012 –> 2013-2019	10.416163	34284.799
Atlantic	(27.85,27.95]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	5.652592	8534.4466	38.211945	2000-2012 –> 2013-2019	10.823891	34722.956
Atlantic	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5.689318	8549.9583	37.990732	2000-2012 –> 2013-2019	10.872063	34755.368
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.370894	8396.2185	36.030625	2000-2012 –> 2013-2019	10.285729	34149.928
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.364829	8393.1634	36.081270	2000-2012 –> 2013-2019	10.275953	34140.416
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	5.312474	8366.6459	36.084095	2000-2012 –> 2013-2019	10.291236	34230.821
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate	5.378703	8398.1471	36.126109	2000-2012 –> 2013-2019	10.361217	34266.763
Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.371446	8396.4962	36.030957	2000-2012 –> 2013-2019	10.285287	34148.477
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	5.955215	30944.1547	99.933163	1982-1999 –> 2000-2012	10.047152	48966.586
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	5.722130	30558.6275	98.336544	1982-1999 –> 2000-2012	9.609778	48254.927
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.736088	30582.1535	96.971949	1982-1999 –> 2000-2012	9.624880	48280.326
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate_star	5.739255	30585.4841	97.240056	1982-1999 –> 2000-2012	9.628448	48282.312
Atlantic	(27.95,28.05]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	5.784076	30662.5997	99.159330	1982-1999 –> 2000-2012	9.729408	48452.690
Atlantic	(27.95,28.05]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5.802947	30692.0522	98.117203	1982-1999 –> 2000-2012	9.748402	48480.342
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.823956	30728.9471	97.509768	1982-1999 –> 2000-2012	9.916769	48752.740
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.767852	30635.4768	97.155585	1982-1999 –> 2000-2012	9.681437	48374.119
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5.738639	30586.4468	97.122933	1982-1999 –> 2000-2012	9.627826	48285.265
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5.755226	30614.3165	97.162369	1982-1999 –> 2000-2012	9.657068	48333.823
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	6.520771	8591.3969	66.899008	2000-2012 –> 2013-2019	12.242901	39150.024
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	6.546216	8601.5383	60.308730	2000-2012 –> 2013-2019	12.282305	39183.692
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate_star	6.601357	8621.3808	64.290824	2000-2012 –> 2013-2019	12.340613	39206.865
Atlantic	(27.95,28.05]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	6.644621	8640.3910	73.358913	2000-2012 –> 2013-2019	12.428697	39302.991
Atlantic	(27.95,28.05]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	6.736281	8674.0666	70.875908	2000-2012 –> 2013-2019	12.539228	39366.119
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	6.455828	8565.3323	65.179632	2000-2012 –> 2013-2019	12.279784	39294.279
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6.634293	8636.3405	63.014629	2000-2012 –> 2013-2019	12.402145	39271.817
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6.576288	8613.4729	62.019436	2000-2012 –> 2013-2019	12.314927	39199.920
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	6.491018	8579.4878	57.697152	2000-2012 –> 2013-2019	12.472280	39565.786
Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6.620148	8630.7824	63.720596	2000-2012 –> 2013-2019	12.375374	39245.099
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	6.114213	23957.9176	96.242539	1982-1999 –> 2000-2012	9.978572	36229.647
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.909336	23705.2294	96.582137	1982-1999 –> 2000-2012	9.711211	35904.841
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate_star	6.115820	23957.8665	96.788647	1982-1999 –> 2000-2012	9.983778	36231.714
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6.076665	23912.2472	98.646271	1982-1999 –> 2000-2012	9.944508	36187.962
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	6.119701	23964.5696	95.907812	1982-1999 –> 2000-2012	9.978328	36229.732
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	6.104332	23945.9268	95.731880	1982-1999 –> 2000-2012	9.971979	36221.418
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6.111266	23954.3432	98.003225	1982-1999 –> 2000-2012	9.976509	36227.084
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.998766	23816.5903	97.150484	1982-1999 –> 2000-2012	9.913766	36145.917
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5.998766	23814.5904	97.148018	1982-1999 –> 2000-2012	9.915482	36143.856
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5.905011	23699.8007	99.874380	1982-1999 –> 2000-2012	9.809069	36016.746
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	6.953530	6952.0163	33.885771	2000-2012 –> 2013-2019	13.117268	30969.745
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	7.010296	6968.8141	34.622969	2000-2012 –> 2013-2019	13.112118	30911.691
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	7.010978	6969.0149	34.284903	2000-2012 –> 2013-2019	13.123214	30924.535
Atlantic	(28.05,28.1]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	6.986937	6961.9182	34.379110	2000-2012 –> 2013-2019	13.101770	30920.588
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	6.662463	6863.6739	33.843111	2000-2012 –> 2013-2019	12.571799	30568.903
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	6.986231	6961.7096	34.673672	2000-2012 –> 2013-2019	13.105932	30926.279
Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	7.011765	6969.2468	34.851907	2000-2012 –> 2013-2019	13.116097	30915.174
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	6.865174	6925.5961	33.932419	2000-2012 –> 2013-2019	12.863940	30742.186
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	6.925755	6941.7473	34.572648	2000-2012 –> 2013-2019	12.924521	30756.338
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	6.793526	6903.9213	34.201090	2000-2012 –> 2013-2019	12.698537	30603.722
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	6.644854	17989.1513	95.346030	1982-1999 –> 2000-2012	10.333901	26317.735
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	6.632841	17979.3331	95.155758	1982-1999 –> 2000-2012	10.315142	26302.330
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate_star	6.646183	17988.2361	95.426477	1982-1999 –> 2000-2012	10.339960	26318.731
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6.635782	17981.7378	95.582750	1982-1999 –> 2000-2012	10.300604	26290.215
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	6.642775	17987.4536	95.287756	1982-1999 –> 2000-2012	10.330540	26314.977
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + nitrate + phosphate_star	6.648644	17990.2452	95.493555	1982-1999 –> 2000-2012	10.338328	26317.356
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	6.633629	17979.9770	95.445994	1982-1999 –> 2000-2012	10.307143	26295.683
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + phosphate + phosphate_star	6.645257	17987.4803	95.410632	1982-1999 –> 2000-2012	10.340518	26319.201
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6.637483	17983.1287	95.566579	1982-1999 –> 2000-2012	10.301195	26290.680
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + silicate + phosphate_star	6.639544	17982.8134	95.473191	1982-1999 –> 2000-2012	10.314827	26297.989
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	8.407980	5023.9452	38.417935	2000-2012 –> 2013-2019	15.052834	23013.096
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	8.178101	4984.8027	38.143771	2000-2012 –> 2013-2019	14.810943	22964.136
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	8.331092	5010.9735	37.768667	2000-2012 –> 2013-2019	14.973868	22998.427
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + phosphate + phosphate_star	8.430686	5025.7532	39.455255	2000-2012 –> 2013-2019	15.075943	23013.234
Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	8.430675	5027.7514	39.452112	2000-2012 –> 2013-2019	15.068158	23010.880
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	8.127710	4976.0755	37.576369	2000-2012 –> 2013-2019	14.822795	23006.089
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	8.180080	4983.1443	38.109235	2000-2012 –> 2013-2019	14.875218	23011.201
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	8.125508	4975.6929	38.121227	2000-2012 –> 2013-2019	14.798703	22987.937
Atlantic	(28.1,28.15]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	8.355469	5013.0991	38.036301	2000-2012 –> 2013-2019	15.060287	23048.995
Atlantic	(28.1,28.15]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	8.348093	5013.8519	37.956187	2000-2012 –> 2013-2019	15.035359	23037.525
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	3.547214	6195.1024	25.313058	1982-1999 –> 2000-2012	7.686954	9355.348
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.544237	6193.1700	25.060451	1982-1999 –> 2000-2012	7.707813	9359.776
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	3.545668	6194.0992	25.464382	1982-1999 –> 2000-2012	7.690879	9355.808
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.533409	6186.1261	25.332635	1982-1999 –> 2000-2012	7.694024	9351.944
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.523780	6179.8447	25.390538	1982-1999 –> 2000-2012	7.673626	9342.791
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.551753	6198.0464	25.459225	1982-1999 –> 2000-2012	7.713679	9364.214
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	3.561607	6204.4239	24.994567	1982-1999 –> 2000-2012	7.694376	9362.802
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	3.558439	6202.3756	25.195805	1982-1999 –> 2000-2012	7.694880	9361.738
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate	3.558948	6200.7049	25.101071	1982-1999 –> 2000-2012	7.715330	9363.395
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.547460	6195.2620	25.002778	1982-1999 –> 2000-2012	7.700246	9358.993
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.783801	1015.5299	8.965589	2000-2012 –> 2013-2019	6.328038	7208.700
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	2.771759	1013.7525	9.471845	2000-2012 –> 2013-2019	6.317427	7207.852
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	2.776193	1014.4078	9.560464	2000-2012 –> 2013-2019	6.373325	7241.680
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate	2.772593	1011.8758	9.455044	2000-2012 –> 2013-2019	6.318291	7203.994
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.771506	1013.7150	9.477876	2000-2012 –> 2013-2019	6.304915	7199.841
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.756933	1011.5535	9.349321	2000-2012 –> 2013-2019	6.280713	7191.398
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.773282	1013.9777	9.470941	2000-2012 –> 2013-2019	6.337780	7220.270
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	2.770329	1013.5410	9.505900	2000-2012 –> 2013-2019	6.357685	7234.547
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + phosphate + phosphate_star	2.771640	1011.7349	9.486362	2000-2012 –> 2013-2019	6.359878	7231.307
Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.761732	1012.2665	9.405195	2000-2012 –> 2013-2019	6.313485	7210.313
Atlantic	(28.2, Inf]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	3.203518	13074.5988	42.155242	1982-1999 –> 2000-2012	6.333156	18807.317
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	3.046855	12821.0924	41.542169	1982-1999 –> 2000-2012	6.195966	18567.668
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	3.045390	12818.6609	41.487796	1982-1999 –> 2000-2012	6.305506	18642.628
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3.051649	12827.0411	41.430143	1982-1999 –> 2000-2012	6.226811	18590.022
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	3.051416	12826.6558	41.387740	1982-1999 –> 2000-2012	6.324743	18657.657
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.051085	12828.1081	41.396198	1982-1999 –> 2000-2012	6.187020	18565.316
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	3.051559	12828.8932	41.376804	1982-1999 –> 2000-2012	6.223436	18591.561
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.050729	12827.5168	41.272131	1982-1999 –> 2000-2012	6.256676	18614.052
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.060899	12844.3443	40.822683	1982-1999 –> 2000-2012	6.315086	18664.245
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.196909	13064.1580	41.607716	1982-1999 –> 2000-2012	6.338973	18805.728
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	2.890878	1725.5443	9.064250	2000-2012 –> 2013-2019	5.937733	14546.637
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	2.883988	1723.8977	9.631241	2000-2012 –> 2013-2019	5.929378	14542.559
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	2.884370	1721.9891	9.468133	2000-2012 –> 2013-2019	5.935786	14548.645
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.860314	1718.2103	8.894454	2000-2012 –> 2013-2019	5.911400	14546.318
Atlantic	(28.2, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	2.862602	1718.7620	8.988262	2000-2012 –> 2013-2019	5.929777	14573.462
Atlantic	(28.2, Inf]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	2.862641	1716.7714	9.042808	2000-2012 –> 2013-2019	5.934837	14577.741
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.887976	1724.8511	8.868844	2000-2012 –> 2013-2019	5.939535	14553.744
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.884348	1723.9837	9.431204	2000-2012 –> 2013-2019	5.935076	14551.501
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.856816	1717.3660	8.910804	2000-2012 –> 2013-2019	5.929672	14581.422
Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.860484	1718.2512	8.881052	2000-2012 –> 2013-2019	5.921383	14562.595
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	5.952614	29165.6039	66.419585	1982-1999 –> 2000-2012	17.829783	41895.959
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	6.273330	29643.2481	62.367337	1982-1999 –> 2000-2012	17.844829	42288.449
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	6.002633	29241.7664	64.366738	1982-1999 –> 2000-2012	17.973264	41997.722
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	6.012245	29256.3307	64.278499	1982-1999 –> 2000-2012	18.011336	42020.042
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	6.104074	29394.3003	65.092963	1982-1999 –> 2000-2012	18.610577	42293.282
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6.396171	29819.7552	60.560084	1982-1999 –> 2000-2012	18.035387	42484.014
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6.436101	29876.4014	60.219070	1982-1999 –> 2000-2012	18.104831	42548.931
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	6.062980	29332.8161	63.632956	1982-1999 –> 2000-2012	18.092030	42104.671
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	6.658204	30185.2033	60.526374	1982-1999 –> 2000-2012	18.461982	42895.315
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6.454052	29901.7522	60.114464	1982-1999 –> 2000-2012	18.137058	42578.275
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.536916	16967.9794	34.918851	2000-2012 –> 2013-2019	10.489530	46133.583
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.481318	18061.7234	38.352102	2000-2012 –> 2013-2019	11.754648	47704.971
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate	4.884956	17393.4918	35.706692	2000-2012 –> 2013-2019	10.990263	46787.630
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	4.784056	17274.7703	28.182502	2000-2012 –> 2013-2019	10.786689	46516.537
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	4.805216	17300.2964	28.617133	2000-2012 –> 2013-2019	10.817461	46556.627
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	4.878066	17387.3280	38.376277	2000-2012 –> 2013-2019	10.982141	46781.628
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5.714558	18302.7503	39.170421	2000-2012 –> 2013-2019	12.110729	48122.506
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	4.942149	17462.8168	25.710633	2000-2012 –> 2013-2019	11.005129	46795.633
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.442136	18020.2290	35.339365	2000-2012 –> 2013-2019	12.065652	48157.889
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	5.396961	17972.0156	28.325896	2000-2012 –> 2013-2019	12.079369	48190.247
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.849393	18684.2488	43.598044	1982-1999 –> 2000-2012	12.345384	32548.209
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5.114211	19013.3895	33.213041	1982-1999 –> 2000-2012	12.978506	33068.838
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.887104	18732.4939	46.201109	1982-1999 –> 2000-2012	12.525119	32672.169
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	4.817151	18642.7033	43.037393	1982-1999 –> 2000-2012	12.456025	32582.832
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	4.832549	18662.5790	42.435084	1982-1999 –> 2000-2012	12.553273	32645.702
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.083018	18977.2860	32.970444	1982-1999 –> 2000-2012	12.930845	33026.279
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.916514	18769.8605	43.256587	1982-1999 –> 2000-2012	12.737700	32805.136
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.949101	18811.0040	41.891274	1982-1999 –> 2000-2012	12.861671	32893.140
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	4.837051	18668.3781	42.168203	1982-1999 –> 2000-2012	12.585523	32665.974
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.949923	18812.0380	41.709124	1982-1999 –> 2000-2012	12.881883	32904.047
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.130189	8911.6526	20.356650	2000-2012 –> 2013-2019	8.979582	27595.901
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.030688	8835.1781	20.029230	2000-2012 –> 2013-2019	8.917793	27567.672
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	4.204764	8967.7711	21.638633	2000-2012 –> 2013-2019	9.021915	27610.474
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	4.243048	8996.1956	22.174811	2000-2012 –> 2013-2019	9.075598	27658.775
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.142558	8921.0302	19.443420	2000-2012 –> 2013-2019	9.059072	27690.891
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.195720	8961.0191	19.149768	2000-2012 –> 2013-2019	9.144821	27772.023
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	4.250336	9001.5772	22.309663	2000-2012 –> 2013-2019	9.087387	27669.955
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	4.135552	8915.7219	20.896799	2000-2012 –> 2013-2019	9.056822	27691.604
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.195824	8961.0964	19.074590	2000-2012 –> 2013-2019	9.145746	27773.134
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	4.195824	8959.0966	19.069926	2000-2012 –> 2013-2019	9.150514	27775.130
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	5.808327	20765.8498	73.130660	1982-1999 –> 2000-2012	12.090369	33791.357
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	5.800853	20759.4410	71.100824	1982-1999 –> 2000-2012	12.054660	33768.948
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	5.411260	20305.4559	78.693240	1982-1999 –> 2000-2012	11.271803	33055.430
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5.672335	20611.1420	63.475935	1982-1999 –> 2000-2012	12.087296	33720.317
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.670897	20611.4869	62.548911	1982-1999 –> 2000-2012	11.901538	33606.164
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	5.477894	20385.3753	77.150240	1982-1999 –> 2000-2012	11.550295	33277.255
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	5.521924	20437.6519	75.972424	1982-1999 –> 2000-2012	11.709021	33404.304
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.667857	20607.9849	63.367505	1982-1999 –> 2000-2012	12.057955	33703.643
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	5.527312	20444.0199	75.396308	1982-1999 –> 2000-2012	11.750107	33433.662
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.768508	20722.9285	72.833308	1982-1999 –> 2000-2012	11.974173	33701.556
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	4.978989	8294.1648	46.495087	2000-2012 –> 2013-2019	10.779842	29053.606
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.895823	8248.0448	43.752886	2000-2012 –> 2013-2019	10.307083	28553.501
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5.120286	8368.7834	37.263205	2000-2012 –> 2013-2019	10.792621	28979.925
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.034496	8324.5196	41.005692	2000-2012 –> 2013-2019	10.705393	28936.007
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	4.938988	8272.0789	42.435810	2000-2012 –> 2013-2019	10.416882	28657.454
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	4.973672	8291.2393	41.685157	2000-2012 –> 2013-2019	10.495596	28728.891
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.111282	8365.9647	37.710877	2000-2012 –> 2013-2019	10.779139	28973.950
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	4.975450	8292.2178	41.478156	2000-2012 –> 2013-2019	10.502761	28736.238
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate_star	4.983552	8294.6731	39.745697	2000-2012 –> 2013-2019	10.559708	28794.144
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	4.941502	8273.4721	40.026671	2000-2012 –> 2013-2019	10.460892	28708.127
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	5.525180	30925.4096	116.391371	1982-1999 –> 2000-2012	12.581190	52098.472
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	5.451019	30793.8708	102.547528	1982-1999 –> 2000-2012	12.477020	51942.192
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5.579009	31021.2196	90.607385	1982-1999 –> 2000-2012	12.698265	52250.267
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	5.466015	30821.0196	118.163610	1982-1999 –> 2000-2012	12.458943	51939.739
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5.547168	30966.6582	90.772916	1982-1999 –> 2000-2012	12.584590	52125.170
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	5.535395	30945.6631	105.111721	1982-1999 –> 2000-2012	12.573541	52104.820
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	5.428964	30753.8071	113.083373	1982-1999 –> 2000-2012	12.459585	51906.254
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	5.507089	30894.9992	96.309702	1982-1999 –> 2000-2012	12.665790	52160.714
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5.538147	30948.5742	104.881884	1982-1999 –> 2000-2012	12.603547	52129.980
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5.477472	30841.7122	93.656622	1982-1999 –> 2000-2012	12.462776	51953.587
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	4.406959	13576.5245	24.507363	2000-2012 –> 2013-2019	9.932139	44501.934
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	4.383580	13553.6637	25.099274	2000-2012 –> 2013-2019	9.834599	44347.534
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.364438	13533.2085	24.688894	2000-2012 –> 2013-2019	9.830453	44354.228
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	4.502440	13678.7104	23.596522	2000-2012 –> 2013-2019	10.127855	44783.787
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.578805	13757.3204	24.430883	2000-2012 –> 2013-2019	10.114201	44702.983
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	4.629702	13808.9882	22.152595	2000-2012 –> 2013-2019	10.156203	44738.760
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	4.354659	13522.7238	25.219650	2000-2012 –> 2013-2019	9.783623	44276.531
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	4.516169	13692.9400	23.835235	2000-2012 –> 2013-2019	10.023257	44587.939
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4.579988	13756.5281	24.439877	2000-2012 –> 2013-2019	10.118135	44705.102
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.579878	13758.4153	24.409136	2000-2012 –> 2013-2019	10.057350	44600.128
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	5.121705	40371.1752	62.628938	1982-1999 –> 2000-2012	11.805717	65631.518
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	5.038754	40157.2800	61.103109	1982-1999 –> 2000-2012	11.720812	65417.398
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5.091368	40292.6264	60.515699	1982-1999 –> 2000-2012	11.838390	65624.353
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	5.008753	40078.3204	62.721695	1982-1999 –> 2000-2012	11.692533	65340.398
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.900925	39790.5700	60.724604	1982-1999 –> 2000-2012	11.647917	65124.262
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.887741	39754.9522	64.837369	1982-1999 –> 2000-2012	11.456942	64885.477
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.918292	39837.3387	60.366137	1982-1999 –> 2000-2012	11.799717	65321.130
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	4.891258	39764.4640	64.991465	1982-1999 –> 2000-2012	11.468504	64904.300
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5.007658	40073.4281	65.563341	1982-1999 –> 2000-2012	11.595081	65223.027
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.825345	39585.0765	63.130137	1982-1999 –> 2000-2012	11.410953	64734.579
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.179970	18260.5503	27.372736	2000-2012 –> 2013-2019	9.188724	58338.871
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	4.157633	18226.2355	18.443765	2000-2012 –> 2013-2019	9.078207	58069.709
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	4.164075	18234.1511	18.274664	2000-2012 –> 2013-2019	9.084773	58075.956
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.131051	18185.1610	20.611055	2000-2012 –> 2013-2019	9.031977	57975.731
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.147629	18210.8090	27.378395	2000-2012 –> 2013-2019	9.035370	57965.761
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.147870	18211.1812	19.334833	2000-2012 –> 2013-2019	9.066162	58048.520
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4.184060	18266.8121	18.875743	2000-2012 –> 2013-2019	9.158629	58254.586
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	4.178544	18258.3643	18.773380	2000-2012 –> 2013-2019	9.142160	58216.992
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	4.164460	18236.7435	31.462832	2000-2012 –> 2013-2019	9.055719	58001.208
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.115378	18160.8170	22.221764	2000-2012 –> 2013-2019	8.940723	57745.893
Indo-Pacific	(27.25,27.5]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	4.620524	41174.4761	48.897069	1982-1999 –> 2000-2012	9.988679	66558.351
Indo-Pacific	(27.25,27.5]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	4.533720	40911.7979	48.878189	1982-1999 –> 2000-2012	9.901091	66296.478
Indo-Pacific	(27.25,27.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4.577427	41043.6951	48.581928	1982-1999 –> 2000-2012	9.973915	66470.662
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.534323	40913.6525	49.780705	1982-1999 –> 2000-2012	9.885777	66274.021
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4.334099	40283.3710	50.294102	1982-1999 –> 2000-2012	9.716268	65690.589
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.443130	40630.1134	48.929247	1982-1999 –> 2000-2012	9.571162	65641.378
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4.362208	40373.5915	50.462559	1982-1999 –> 2000-2012	9.980814	66132.742
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	4.379105	40427.5473	48.812079	1982-1999 –> 2000-2012	9.513160	65448.420
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4.480920	40746.3121	48.308966	1982-1999 –> 2000-2012	9.619501	65772.399
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.230264	39944.9489	48.670568	1982-1999 –> 2000-2012	9.355803	64952.233
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	3.312844	19090.0758	14.312700	2000-2012 –> 2013-2019	7.707336	59566.574
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	3.346851	19162.5274	13.999761	2000-2012 –> 2013-2019	7.749101	59661.642
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.298733	19058.9573	14.930407	2000-2012 –> 2013-2019	7.632832	59342.328
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	3.361704	19196.8070	13.889169	2000-2012 –> 2013-2019	7.839568	59935.598
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	3.434659	19351.3206	14.862761	2000-2012 –> 2013-2019	7.946828	60194.622
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.302981	19068.3399	14.903485	2000-2012 –> 2013-2019	7.665189	59441.931
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.310956	19085.9191	14.910566	2000-2012 –> 2013-2019	7.716433	59597.260
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	3.361829	19197.0784	15.290837	2000-2012 –> 2013-2019	7.779105	59745.748
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.309446	19082.5932	14.903450	2000-2012 –> 2013-2019	7.706352	59566.755
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.587543	19670.7998	27.674118	2000-2012 –> 2013-2019	7.817807	59615.749
Indo-Pacific	(27.5,27.75]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	4.095478	44036.1271	34.608647	1982-1999 –> 2000-2012	9.145887	71025.111
Indo-Pacific	(27.5,27.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4.095543	44034.3762	34.570597	1982-1999 –> 2000-2012	9.147793	71024.596
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	4.087125	44004.3553	38.385918	1982-1999 –> 2000-2012	9.124486	70970.372
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4.112763	44099.6707	37.553543	1982-1999 –> 2000-2012	9.159725	71080.593
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.883195	43207.8378	34.583772	1982-1999 –> 2000-2012	8.923066	70178.279
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	4.105823	44075.3862	37.547709	1982-1999 –> 2000-2012	8.975517	70740.873
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.882307	43204.2783	34.687697	1982-1999 –> 2000-2012	9.086666	70459.845
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	4.158120	44272.3515	39.566088	1982-1999 –> 2000-2012	9.007566	70900.847
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + phosphate + phosphate_star	4.172579	44324.3716	38.806383	1982-1999 –> 2000-2012	9.042509	70988.289
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4.095252	44035.2708	34.599504	1982-1999 –> 2000-2012	8.964944	70700.753
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	3.083594	21259.9453	15.210098	2000-2012 –> 2013-2019	7.107683	65022.420
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	3.171443	21492.4493	15.376356	2000-2012 –> 2013-2019	7.228876	65381.336
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.026597	21104.1990	22.247122	2000-2012 –> 2013-2019	6.909792	64312.037
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	3.168356	21486.3185	13.652231	2000-2012 –> 2013-2019	7.368456	65914.998
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.026042	21102.6688	22.753924	2000-2012 –> 2013-2019	6.908349	64306.947
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.026397	21103.6470	23.229528	2000-2012 –> 2013-2019	6.917997	64345.130
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	3.060610	21197.4914	25.949338	2000-2012 –> 2013-2019	6.954167	64446.800
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.026290	21103.3532	23.158305	2000-2012 –> 2013-2019	6.916765	64340.337
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	3.128095	21377.5610	30.765980	2000-2012 –> 2013-2019	7.054100	64754.019
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.343940	21936.5857	24.258655	2000-2012 –> 2013-2019	7.439193	65971.856
Indo-Pacific	(27.75,27.85]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	3.583312	21737.5229	38.238653	1982-1999 –> 2000-2012	7.958234	33573.997
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.557619	21679.5225	38.838487	1982-1999 –> 2000-2012	7.956487	33538.289
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3.538930	21637.0691	38.459313	1982-1999 –> 2000-2012	7.954226	33511.060
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	3.532281	21621.9108	37.859684	1982-1999 –> 2000-2012	7.965906	33512.820
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3.538040	21635.0428	38.483351	1982-1999 –> 2000-2012	7.957556	33512.935
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	3.597614	21769.6274	41.515566	1982-1999 –> 2000-2012	7.964170	33598.284
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	3.552789	21668.5725	38.017221	1982-1999 –> 2000-2012	7.954566	33530.039
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3.536932	21632.5168	37.743687	1982-1999 –> 2000-2012	7.957935	33511.784
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.523331	21601.4639	37.566666	1982-1999 –> 2000-2012	7.899190	33438.813
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	3.537090	21632.8779	37.848528	1982-1999 –> 2000-2012	7.961453	33515.246
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.915987	10533.1345	12.141959	2000-2012 –> 2013-2019	6.473606	32212.657
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.905267	10517.5696	12.090762	2000-2012 –> 2013-2019	6.444197	32154.639
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	2.906046	10518.7033	12.202456	2000-2012 –> 2013-2019	6.438327	32140.614
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.905413	10517.7821	12.098928	2000-2012 –> 2013-2019	6.443453	32152.825
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.906142	10516.8432	12.177090	2000-2012 –> 2013-2019	6.456809	32178.599
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2.951336	10584.0566	13.177670	2000-2012 –> 2013-2019	6.488268	32216.573
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.948812	10580.4406	13.172097	2000-2012 –> 2013-2019	6.472143	32181.905
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	2.951787	10584.7027	13.180334	2000-2012 –> 2013-2019	6.488878	32217.581
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2.954488	10586.5679	13.203818	2000-2012 –> 2013-2019	6.491657	32217.624
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2.961005	10595.8790	13.213333	2000-2012 –> 2013-2019	6.506318	32245.472
Indo-Pacific	(27.85,27.95]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	3.199014	29433.9782	21.345052	1982-1999 –> 2000-2012	7.654412	46300.913
Indo-Pacific	(27.85,27.95]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	3.157695	29287.8282	21.722876	1982-1999 –> 2000-2012	7.613090	46156.760
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	3.186171	29390.1365	21.583591	1982-1999 –> 2000-2012	7.636116	46251.987
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	3.163197	29307.6662	21.918267	1982-1999 –> 2000-2012	7.652391	46220.326
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	3.198333	29433.5512	21.283188	1982-1999 –> 2000-2012	7.653635	46302.363
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	3.155971	29281.6042	21.787156	1982-1999 –> 2000-2012	7.623839	46166.711
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3.163651	29309.2995	21.821907	1982-1999 –> 2000-2012	7.646141	46213.312
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.163377	29308.3156	21.511462	1982-1999 –> 2000-2012	7.660087	46230.654
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	3.163728	29309.5799	21.842099	1982-1999 –> 2000-2012	7.647595	46215.369
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	3.163748	29307.6502	21.858105	1982-1999 –> 2000-2012	7.655102	46221.093
Indo-Pacific	(27.85,27.95]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	2.954551	15182.8527	22.483930	2000-2012 –> 2013-2019	6.112246	44470.681
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.932958	15138.3865	23.084398	2000-2012 –> 2013-2019	6.096134	44445.978
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2.923830	15119.4903	22.759449	2000-2012 –> 2013-2019	6.092631	44447.329
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	2.921662	15114.9946	22.831131	2000-2012 –> 2013-2019	6.084859	44422.661
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2.923856	15119.5461	22.777845	2000-2012 –> 2013-2019	6.093261	44449.554
Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate_star	2.923879	15117.5926	22.812577	2000-2012 –> 2013-2019	6.105234	44488.488
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	2.939477	15151.8461	22.221957	2000-2012 –> 2013-2019	6.095448	44433.450
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2.935312	15143.2512	21.956729	2000-2012 –> 2013-2019	6.098963	44452.551
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	2.935509	15143.6577	22.002954	2000-2012 –> 2013-2019	6.099238	44453.238
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2.941718	15154.4654	23.167958	2000-2012 –> 2013-2019	6.105466	44462.116
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	3.002390	48318.9347	51.461957	1982-1999 –> 2000-2012	7.495788	81075.642
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	2.986021	48216.0691	50.857103	1982-1999 –> 2000-2012	7.479359	80974.626
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2.995182	48272.8258	51.512685	1982-1999 –> 2000-2012	7.504853	81070.051
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	3.002150	48319.4048	51.435634	1982-1999 –> 2000-2012	7.467956	81009.076
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3.005961	48341.7370	51.802881	1982-1999 –> 2000-2012	7.476073	81040.210
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.982881	48195.8902	51.210008	1982-1999 –> 2000-2012	7.443665	80872.951
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.999181	48300.4227	51.518311	1982-1999 –> 2000-2012	7.455914	80967.300
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.006200	48345.2637	51.459611	1982-1999 –> 2000-2012	7.495734	81094.328
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	2.997284	48288.2854	51.259385	1982-1999 –> 2000-2012	7.487518	81039.098
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.994442	48270.0890	51.454948	1982-1999 –> 2000-2012	7.497463	81052.772
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	3.072230	27163.6986	102.801466	2000-2012 –> 2013-2019	6.074619	75482.633
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	3.071881	27164.4857	102.792406	2000-2012 –> 2013-2019	6.057902	75380.555
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	3.068017	27151.0408	102.737395	2000-2012 –> 2013-2019	6.070168	75470.446
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.072589	27166.9486	102.768499	2000-2012 –> 2013-2019	6.055470	75362.839
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3.059974	27122.9945	103.233246	2000-2012 –> 2013-2019	6.066175	75468.258
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	3.059308	27120.6672	103.790092	2000-2012 –> 2013-2019	6.090229	75623.026
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	3.066327	27145.1506	103.158494	2000-2012 –> 2013-2019	6.063611	75433.436
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	3.058372	27117.3999	103.438234	2000-2012 –> 2013-2019	6.065583	75469.108
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.101504	27267.0217	103.847171	2000-2012 –> 2013-2019	6.095946	75537.111
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	3.061166	27127.1530	103.717226	2000-2012 –> 2013-2019	6.097839	75665.879
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	2.932177	38609.7481	26.396358	1982-1999 –> 2000-2012	7.071476	60542.417
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	2.930554	38603.1774	25.941756	1982-1999 –> 2000-2012	7.064024	60526.969
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2.942203	38662.5588	23.975034	1982-1999 –> 2000-2012	7.085728	60603.107
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	2.920762	38551.3958	26.062983	1982-1999 –> 2000-2012	7.032468	60434.430
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2.927141	38583.1484	24.388801	1982-1999 –> 2000-2012	7.039276	60464.990
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.910460	38496.7256	21.962744	1982-1999 –> 2000-2012	7.022207	60379.838
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.925242	38575.1118	24.648296	1982-1999 –> 2000-2012	7.035558	60455.535
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.920574	38550.4021	19.725935	1982-1999 –> 2000-2012	7.047339	60461.658
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	2.931644	38608.9344	26.302110	1982-1999 –> 2000-2012	7.066823	60535.917
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.940409	38655.1231	23.154936	1982-1999 –> 2000-2012	7.082978	60595.889
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + nitrate + phosphate + phosphate_star	2.855172	26830.0550	16.300721	2000-2012 –> 2013-2019	5.787349	65439.803
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	2.830862	26739.1407	16.057897	2000-2012 –> 2013-2019	5.761415	65342.318
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	2.808480	26652.8892	15.912241	2000-2012 –> 2013-2019	5.729242	65204.285
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	2.812612	26668.8624	15.877047	2000-2012 –> 2013-2019	5.740233	65256.550
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2.843530	26785.6598	15.374309	2000-2012 –> 2013-2019	5.770671	65368.808
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	2.849122	26807.0059	15.327096	2000-2012 –> 2013-2019	5.795265	65490.270
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.841222	26778.8359	15.411872	2000-2012 –> 2013-2019	5.751682	65275.561
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.834318	26752.3979	15.478455	2000-2012 –> 2013-2019	5.759560	65327.510
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2.849121	26809.0017	15.327196	2000-2012 –> 2013-2019	5.769695	65359.404
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	2.846628	26799.4915	16.182518	2000-2012 –> 2013-2019	5.778272	65408.426
Indo-Pacific	(28.1, Inf]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	3.134411	50104.3433	31.391291	1982-1999 –> 2000-2012	7.103890	91830.163
Indo-Pacific	(28.1, Inf]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3.256294	50848.3740	32.242547	1982-1999 –> 2000-2012	7.240790	92628.495
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	3.401257	51702.1435	31.893030	1982-1999 –> 2000-2012	7.414067	93589.838
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3.254223	50837.9350	32.349095	1982-1999 –> 2000-2012	7.237476	92615.400
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	3.435319	51897.0100	32.184178	1982-1999 –> 2000-2012	7.369602	93490.039
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + phosphate	3.475266	52121.1057	32.794252	1982-1999 –> 2000-2012	7.412950	93725.017
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star	3.436796	51905.4162	32.358838	1982-1999 –> 2000-2012	7.365221	93476.231
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	3.340850	51351.7018	32.493241	1982-1999 –> 2000-2012	7.267894	92917.270
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3.194108	50473.2965	31.641880	1982-1999 –> 2000-2012	7.118973	92030.592
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	3.424303	51834.2004	32.880725	1982-1999 –> 2000-2012	7.428214	93688.796
Indo-Pacific	(28.1, Inf]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	2.710158	22743.2168	13.842857	2000-2012 –> 2013-2019	5.844570	72847.560
Indo-Pacific	(28.1, Inf]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2.726148	22796.5575	15.016465	2000-2012 –> 2013-2019	5.982441	73644.932
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate	2.707531	22732.0916	20.481063	2000-2012 –> 2013-2019	6.167224	74765.367
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	2.674858	22619.8699	22.788041	2000-2012 –> 2013-2019	6.076115	74322.013
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	2.707209	22732.9721	20.145662	2000-2012 –> 2013-2019	6.123153	74519.382
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2.646133	22518.2907	21.150238	2000-2012 –> 2013-2019	5.900356	73356.226
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	2.706303	22729.8248	20.808757	2000-2012 –> 2013-2019	6.141622	74626.835
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + phosphate + phosphate_star	2.666540	22590.5669	22.702732	2000-2012 –> 2013-2019	6.199150	75033.727
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	2.844736	23199.1564	13.010841	2000-2012 –> 2013-2019	6.185585	74550.858
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2.683780	22651.1975	14.810256	2000-2012 –> 2013-2019	5.877887	73124.494

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(starts_with("coeff_"),
               names_to = "term",
               values_to = "estimate",
               names_prefix = "coeff_")

# subtract coefficients of adjacent era  
lm_best_long <- lm_best_long %>%
  arrange(era) %>%
  group_by(basin, gamma_slab, eras, model, term) %>%
  mutate(delta_coeff = estimate - lag(estimate)) %>%
  ungroup() %>%
  arrange(basin, gamma_slab, model, term, eras) %>%
  drop_na() %>%
  select(-c(era,estimate))

# pivot back to wide format
lm_best_cant <- lm_best_long %>%
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

5.5 Write files

lm_best_target %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    era,
    starts_with("coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_target.csv",
                  sep = ""))

lm_best_cant %>%
  select(
    basin,
    gamma_slab,
    model,
    eras,
    starts_with("delta_coeff_")
  ) %>%
  write_csv(paste(path_version_data,
                  "lm_best_cant.csv",
                  sep = ""))

6 Model diagnotics

6.1 Selection criterion vs predictors

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

6.1.1 All models

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

Past versions of eMLR_predictor_model_quality_all-1.png

Version	Author	Date
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
f3a708f	jens-daniel-mueller	2020-12-17

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
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
f3a708f	jens-daniel-mueller	2020-12-17

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
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
e4ca289	jens-daniel-mueller	2020-12-16
158fe26	jens-daniel-mueller	2020-12-15
7a9a4cb	jens-daniel-mueller	2020-12-15
61b263c	jens-daniel-mueller	2020-12-15
984697e	jens-daniel-mueller	2020-12-12
3ebff89	jens-daniel-mueller	2020-12-12
ba112d3	jens-daniel-mueller	2020-12-11
24a632f	jens-daniel-mueller	2020-12-07
6a8004b	jens-daniel-mueller	2020-12-07
70bf1a5	jens-daniel-mueller	2020-12-07
7555355	jens-daniel-mueller	2020-12-07
143d6fa	jens-daniel-mueller	2020-12-07
090e4d5	jens-daniel-mueller	2020-12-02
7c25f7a	jens-daniel-mueller	2020-12-02
b03ddb8	jens-daniel-mueller	2020-12-02
91435ae	jens-daniel-mueller	2020-12-01
196be51	jens-daniel-mueller	2020-11-30

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
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
a84ff3c	jens-daniel-mueller	2020-12-17

rm(max_rmse)

6.3 Predictor counts

The number of models where a particular predictor was included were counted for each basin, density slab and compared eras

# calculate cases of predictor used
lm_all_stats <- lm_best_long %>% 
  filter(term != "(Intercept)",
         delta_coeff != 0) %>% 
  group_by(basin, eras, gamma_slab) %>% 
  count(term) %>% 
  ungroup() %>% 
  pivot_wider(values_from = n, names_from = term)

# print table
lm_all_stats %>%
  gt(rowname_col = "gamma_slab",
     groupname_col = c("basin", "eras")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )

	aou	nitrate	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26]	8	8	8	8	6	4	8
(26,26.5]	10	9	8	7	4	3	7
(26.5,26.75]	7	3	8	9	7	4	10
(26.75,27]	6	5	6	9	5	8	10
(27,27.25]	6	5	5	9	6	8	10
(27.25,27.5]	7	4	8	7	10	3	9
(27.5,27.75]	8	4	8	8	4	10	7
(27.75,27.85]	7	6	9	6	6	10	5
(27.85,27.95]	5	3	7	7	10	10	5
(27.95,28.05]	7	3	7	8	10	9	4
(28.05,28.1]	7	4	6	10	7	4	10
(28.1,28.15]	4	4	4	10	10	4	10
(28.15,28.2]	9	4	10	6	6	6	8
(28.2, Inf]	9	3	10	7	8	7	4
total	100.00	65.00	104.00	111.00	99.00	90.00	107.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26]	8	9	7	7	6	6	7
(26,26.5]	9	10	8	7	4	3	7
(26.5,26.75]	7	10	7	7	3	3	10
(26.75,27]	6	4	6	10	4	8	10
(27,27.25]	6	6	6	8	6	8	10
(27.25,27.5]	8	4	9	7	9	4	8
(27.5,27.75]	8	4	8	7	4	10	8
(27.75,27.85]	7	6	7	7	7	10	6
(27.85,27.95]	5	3	7	7	10	10	5
(27.95,28.05]	6	3	7	8	10	9	5
(28.05,28.1]	7	6	8	10	7	5	6
(28.1,28.15]	5	5	9	10	5	3	10
(28.15,28.2]	7	3	8	7	10	4	9
(28.2, Inf]	7	3	9	7	10	8	4
total	96.00	76.00	106.00	109.00	95.00	91.00	105.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26]	7	6	6	7	10	6	8
(26,26.5]	8	4	8	8	10	4	7
(26.5,26.75]	9	7	9	9	7	2	5
(26.75,27]	10	5	10	9	3	5	5
(27,27.25]	10	4	10	9	4	5	5
(27.25,27.5]	10	4	10	9	4	5	5
(27.5,27.75]	10	3	10	9	5	5	5
(27.75,27.85]	7	6	7	8	4	9	9
(27.85,27.95]	7	9	7	9	2	7	7
(27.95,28.05]	10	4	10	9	5	5	4
(28.05,28.1]	10	4	10	9	5	5	4
(28.1, Inf]	9	7	10	7	3	6	6
total	107.00	63.00	107.00	102.00	62.00	64.00	70.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26]	8	8	7	6	8	4	8
(26,26.5]	6	5	6	8	10	6	8
(26.5,26.75]	7	7	7	9	9	3	6
(26.75,27]	9	7	9	8	4	4	7
(27,27.25]	9	3	9	7	8	7	6
(27.25,27.5]	6	3	8	7	9	10	5
(27.5,27.75]	6	3	7	7	9	10	6
(27.75,27.85]	4	4	5	9	5	10	10
(27.85,27.95]	5	6	5	8	5	10	9
(27.95,28.05]	8	7	9	8	4	7	6
(28.05,28.1]	10	5	10	7	7	5	3
(28.1, Inf]	10	6	10	6	6	6	4
total	88.00	64.00	92.00	90.00	84.00	82.00	78.00

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
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17

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
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17

Session information

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.2

Matrix products: default
BLAS:   /usr/local/R-4.0.3/lib64/R/lib/libRblas.so
LAPACK: /usr/local/R-4.0.3/lib64/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] gt_0.2.2         corrr_0.4.3      broom_0.7.2      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3.9000 GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.2   
[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_1.1.10         R6_2.5.0                 nortest_1.0-4           
[10] DBI_1.1.0                colorspace_1.4-1         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_2.1.0               
[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_0.0.2           jsonlite_1.7.1          
[40] zip_2.1.1                car_3.0-10               magrittr_1.5            
[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_1.13.2        modelr_0.1.8             vctrs_0.3.5             
[70] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[73] reshape_0.8.8            assertthat_0.2.1         xfun_0.18               
[76] openxlsx_4.2.3           RcppEigen_0.3.3.7.0      later_1.1.0.1           
[79] viridisLite_0.3.0        ellipsis_0.3.1           here_0.1