eMLR - model fitting

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Last updated: 2021-02-27

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---

1 Required data

Required are:

• cleaned and prepared GLODAP-based synthetic model subsetting file

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

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

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

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

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

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

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

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

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

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

# convert to tibble
lm_all <- as_tibble(lm_all)

# extract relevant columns and format model formula
lm_all <- lm_all %>% 
  select(n, predictors) %>% 
  mutate(lm_coeff = str_replace_all(predictors, " ", " + "),
         lm_coeff = paste(params_local$MLR_target, "~", lm_coeff))

# remove certain predictor combinations
# lm_rm_ph <- lm_all %>%
#   filter(str_detect(lm_coeff, "phosphate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "nitrate") &
#       str_detect(lm_coeff_filter, "phosphate")
#   ) 

# lm_rm_si <- lm_all %>%
#   filter(str_detect(lm_coeff, "silicate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "silicate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "nitrate") &
#       str_detect(lm_coeff_filter, "silicate")
#   )

# lm_rm_o2 <- lm_all %>%
#   filter(str_detect(lm_coeff, "phosphate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "phosphate") &
#       str_detect(lm_coeff_filter, "oxygen")
#   )

# lm_rm <- bind_rows(lm_rm_ph, lm_rm_o2) %>%
#   select(-lm_coeff_filter) %>%
#   unique()


#remove temp sal predictor combination
lm_all <- lm_all %>%
  mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
  filter(!(
    str_detect(lm_coeff_filter, "nitrate") &
      str_detect(lm_coeff_filter, "phosphate")
  )) %>%
  filter(!(
    str_detect(lm_coeff_filter, "temp") &
      str_detect(lm_coeff_filter, "sal")
  )) %>%
  filter(!(
    str_detect(lm_coeff_filter, "oxygen") &
      str_detect(lm_coeff_filter, "aou")
  )) %>%
  select(-lm_coeff_filter)

# # remove certain predictor combinations
# lm_rm_ph <- lm_all %>%
#   filter(str_detect(lm_coeff, "phosphate_star")) %>%
#   mutate(lm_coeff_filter = str_remove(lm_coeff, "phosphate_star")) %>%
#   filter(
#     str_detect(lm_coeff_filter, "nitrate") &
#       str_detect(lm_coeff_filter, "phosphate")
#   )
# 
# 
# 
# lm_rm <- lm_rm_ph %>%
#   select(-lm_coeff_filter) %>%
#   unique()
# 
# lm_all <- anti_join(lm_all, lm_rm)

# remove helper objects
rm(
  i_gamma_slab,
  i_era,
  i_basin,
  GLODAP_basin_era,
  GLODAP_basin_era_slab,
  lm_full,
  lm_rm_ph,
  lm_rm_si,
  lm_rm_o2,
  lm_rm
)

3 Apply predictor threshold

Select combinations with a total number of predictors in the range:

• Minimum: 3
  
• Maximum: 9

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:

• 74

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)
      
      # number of observations used for each fitting model
      i_nr_obs = nrow(GLODAP_basin_era_slab)
      
      for (i_predictors in unique(lm_all$predictors)) {
        #i_predictors <- unique(lm_all$predictors)[1]
        
        # 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()
        
        if (i_nr_obs > i_n_predictors) {
          # fit model
          if (params_local$MLR_type == "rlm") {
            i_lm_fit <- MASS::rlm(as.formula(i_lm),
                                  data = GLODAP_basin_era_slab)
          }
          
          if (params_local$MLR_type == "lm") {
            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,
              nr_obs = i_nr_obs,
              rmse = i_rmse,
              aic = i_aic,
              resid_max = i_resid_max,
              n_predictors = i_n_predictors,
              na_predictor = anyNA(coefficients$estimate),
              cor_max = i_cor_max
            )
          
          if (exists("lm_all_fitted")) {
            lm_all_fitted <- bind_rows(lm_all_fitted, coefficients)
          }
          
          if (!exists("lm_all_fitted")) {
            lm_all_fitted <- coefficients
          }
        }
      }
    }
  }
}

rm(
  i_lm_fit,
  coefficients,
  i_rmse,
  GLODAP_basin_era,
  GLODAP_basin_era_slab,
  i_lm,
  i_basin,
  i_era,
  i_gamma_slab,
  i_nr_obs,
  i_predictors,
  i_aic,
  i_n_predictors,
  i_resid_max
)

5 Prepare coeffcients

Coefficients are prepared for the mapping of Cant and the chosen target variable.

5.1 Formatting

# select relevant columns
lm_all_fitted <- lm_all_fitted %>%
  select(
    basin,
    gamma_slab,
    era,
    model,
    nr_obs,
    n_predictors,
    term,
    estimate,
    rmse,
    aic,
    resid_max,
    na_predictor,
    cor_max
  )

# set coefficient to zero if not fitted (=NA)
lm_all_fitted <- lm_all_fitted %>%
  mutate(estimate = if_else(is.na(estimate), 0, estimate))

# Prepare model coefficients for mapping of target variable
lm_all_fitted_wide <- lm_all_fitted %>%
  pivot_wider(
    values_from = estimate,
    names_from = term,
    names_prefix = "coeff_",
    values_fill = 0
  )

5.2 Predictor selection

Within each basin and slab, the following number of best linear regression models was selected:

• 10

The criterion used to select the best models was:

• rmse

The criterion was summed up for two adjacent eras, and the models with lowest summed values were selected.

Please note, that currently the lm() function produces NAs for some predictors. It is not yet entirely clear when this happens, but presumably it is caused by some form of collinearity between predictors, such that including another predictor does not help to explain the target variable any better. The issues also expresses as exactly identical rmse values of different models. As an interim solution, models with fitted NA predictors were not included.

# remove models with predictors fitted as NA

lm_all_fitted_wide <- lm_all_fitted_wide %>%
  filter(na_predictor == FALSE)

# calculate RMSE sum for adjacent eras
lm_all_fitted_wide_eras <- lm_all_fitted_wide  %>%
  select(basin, gamma_slab, model, era, nr_obs, 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)
}

5.3 RMSE tables

5.3.1 per model

lm_best %>%
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

basin	gamma_slab	model	nr_obs	rmse	aic	resid_max	eras	rmse_sum	aic_sum
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate_star	158	1.6001372	608.9328	6.639741	1982-1999 –> 2000-2012	3.2898388	1429.4249
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	158	1.5921923	609.3599	6.118408	1982-1999 –> 2000-2012	3.2779521	1430.8804
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	158	1.0492038	475.5626	4.357844	1982-1999 –> 2000-2012	2.3855522	1198.4564
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	158	1.0480832	477.2249	4.299021	1982-1999 –> 2000-2012	2.3837757	1201.9145
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate_star	158	1.5933338	607.5864	5.896294	1982-1999 –> 2000-2012	3.3151005	1435.8988
Atlantic	(-Inf,26]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	158	1.6581469	620.1860	7.643496	1982-1999 –> 2000-2012	3.3615952	1444.0487
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + nitrate + silicate	158	1.6268394	614.1625	8.329023	1982-1999 –> 2000-2012	3.2947666	1429.2589
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	158	1.6216413	615.1512	8.073641	1982-1999 –> 2000-2012	3.2856343	1431.2652
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	158	1.4654213	581.1417	7.417048	1982-1999 –> 2000-2012	3.1276914	1394.8248
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	158	1.4545749	580.7941	7.074044	1982-1999 –> 2000-2012	3.1160634	1396.2815
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate_star	72	1.7037742	293.0570	4.337445	2000-2012 –> 2013-2019	3.3039114	901.9898
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	72	1.6825475	293.2516	3.600013	2000-2012 –> 2013-2019	3.2747398	902.6116
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	72	1.2725075	251.0296	3.658367	2000-2012 –> 2013-2019	2.3217113	726.5922
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	72	1.1936365	243.8158	3.237974	2000-2012 –> 2013-2019	2.2417197	721.0407
Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate_star	72	1.6918467	292.0453	4.133504	2000-2012 –> 2013-2019	3.2851805	899.6317
Atlantic	(-Inf,26]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	72	1.7638716	298.0488	5.052184	2000-2012 –> 2013-2019	3.4220185	918.2347
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + nitrate + silicate	72	1.7125308	293.7952	5.378554	2000-2012 –> 2013-2019	3.3393703	907.9577
Atlantic	(-Inf,26]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	72	1.7102518	295.6034	5.514006	2000-2012 –> 2013-2019	3.3318930	910.7546
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + phosphate + phosphate_star	72	1.5761474	281.8448	5.713265	2000-2012 –> 2013-2019	3.0415687	862.9865
Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	72	1.5044066	277.1365	5.003414	2000-2012 –> 2013-2019	2.9589816	857.9306
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1046	3.5518213	5633.9468	13.477555	1982-1999 –> 2000-2012	6.9985663	13749.8718
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1046	4.1960266	5980.6362	10.665564	1982-1999 –> 2000-2012	8.3544396	14667.0559
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	1046	4.0405761	5901.6616	14.579174	1982-1999 –> 2000-2012	8.1249524	14533.2897
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1046	4.0338370	5900.1695	15.685804	1982-1999 –> 2000-2012	8.1154929	14531.7655
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1046	4.2948916	6031.3553	13.012884	1982-1999 –> 2000-2012	8.5299909	14775.5085
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	1046	4.1683330	5966.7833	10.579872	1982-1999 –> 2000-2012	8.3007589	14634.0829
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + silicate	1046	3.9974267	5879.2009	14.350644	1982-1999 –> 2000-2012	8.0360096	14476.4398
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1046	3.9825944	5873.4242	15.972464	1982-1999 –> 2000-2012	8.0211559	14472.6469
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate	1046	4.4898702	6122.2348	12.384079	1982-1999 –> 2000-2012	8.8545410	14956.3028
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	1046	4.4898702	6122.2348	12.384079	1982-1999 –> 2000-2012	8.8545410	14956.3028
Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	567	3.6070302	3077.8676	10.902628	2000-2012 –> 2013-2019	7.1588515	8711.8144
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate	567	4.3273734	3280.3418	12.473922	2000-2012 –> 2013-2019	8.8059117	9395.2899
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	567	4.1023698	3221.7908	12.065595	2000-2012 –> 2013-2019	8.2983964	9202.4270
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate	567	3.8959809	3163.2545	13.662757	2000-2012 –> 2013-2019	7.9365570	9064.9161
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	567	3.8631919	3155.6702	14.511046	2000-2012 –> 2013-2019	7.8970289	9055.8397
Atlantic	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	567	4.2189568	3255.5690	10.763473	2000-2012 –> 2013-2019	8.5138484	9286.9243
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate	567	4.2852908	3269.2599	12.306864	2000-2012 –> 2013-2019	8.7190363	9363.1793
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	567	4.0757597	3214.4111	11.944274	2000-2012 –> 2013-2019	8.2440926	9181.1944
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + silicate	567	3.8537522	3150.8959	13.395954	2000-2012 –> 2013-2019	7.8511788	9030.0968
Atlantic	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	567	3.8005103	3137.1198	14.416820	2000-2012 –> 2013-2019	7.7831048	9010.5440
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1397	3.3429532	7348.4661	10.697715	1982-1999 –> 2000-2012	6.4415667	17034.7612
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	1397	3.3316510	7339.0038	10.073920	1982-1999 –> 2000-2012	6.4785991	17084.0238
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1397	3.2700730	7288.8799	10.507891	1982-1999 –> 2000-2012	6.3292231	16928.5449
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1397	3.3250708	7335.4800	10.297171	1982-1999 –> 2000-2012	6.4698137	17079.8406
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate	1397	3.4027533	7398.0044	10.818893	1982-1999 –> 2000-2012	6.5639402	17160.1523
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1397	3.2249399	7250.0489	10.037456	1982-1999 –> 2000-2012	6.2079736	16794.1190
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	1397	3.4336491	7423.2585	10.906572	1982-1999 –> 2000-2012	6.6279234	17224.9109
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1397	3.3402414	7348.1986	9.940278	1982-1999 –> 2000-2012	6.4993586	17109.8616
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + silicate + phosphate	1397	3.4413502	7429.5180	10.920943	1982-1999 –> 2000-2012	6.6456964	17243.1144
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	1397	3.4413502	7429.5180	10.920943	1982-1999 –> 2000-2012	6.6456964	17243.1144
Atlantic	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	656	3.4323365	3491.6598	11.340269	2000-2012 –> 2013-2019	6.7752897	10840.1259
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	656	3.3850399	3473.4551	10.375376	2000-2012 –> 2013-2019	6.7166909	10812.4589
Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	656	3.3455096	3460.0435	10.735554	2000-2012 –> 2013-2019	6.6155826	10748.9234
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	656	3.4093443	3484.8416	9.603997	2000-2012 –> 2013-2019	6.7344151	10820.3216
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate	656	3.4910702	3513.9207	11.381386	2000-2012 –> 2013-2019	6.8938235	10911.9252
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	656	3.3238240	3451.5114	11.113656	2000-2012 –> 2013-2019	6.5487639	10701.5603
Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	656	3.5219283	3525.4667	11.414557	2000-2012 –> 2013-2019	6.9555774	10948.7252
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	656	3.4254447	3491.0228	9.732422	2000-2012 –> 2013-2019	6.7656861	10839.2215
Atlantic	(26.5,26.75]	cstar_tref ~ temp + oxygen + silicate + phosphate	656	3.5288346	3528.0369	11.412513	2000-2012 –> 2013-2019	6.9701847	10957.5549
Atlantic	(26.5,26.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	656	3.5288346	3528.0369	11.412513	2000-2012 –> 2013-2019	6.9701847	10957.5549
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2398	2.0935628	10360.8368	14.739529	1982-1999 –> 2000-2012	3.7661002	22513.8376
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	2398	2.1776482	10549.6945	20.348896	1982-1999 –> 2000-2012	4.1329846	23683.7595
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2398	2.0001820	10143.9994	14.081577	1982-1999 –> 2000-2012	3.6531709	22225.1681
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2398	2.1989701	10598.4250	16.309198	1982-1999 –> 2000-2012	3.9946362	23199.5206
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	2398	2.2004206	10599.5875	15.280820	1982-1999 –> 2000-2012	3.9880121	23170.3800
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2398	2.0860637	10345.6268	19.975942	1982-1999 –> 2000-2012	3.5995129	21872.9381
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	2398	2.2716861	10752.4544	17.733985	1982-1999 –> 2000-2012	4.1106467	23501.1674
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2398	2.2396447	10686.3266	20.763751	1982-1999 –> 2000-2012	4.0590677	23369.9626
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + silicate + phosphate	2398	2.3001008	10812.0716	20.719299	1982-1999 –> 2000-2012	4.1580260	23625.2168
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	2398	2.3001008	10812.0716	20.719299	1982-1999 –> 2000-2012	4.1580260	23625.2168
Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1263	2.6364762	6045.0524	27.471250	2000-2012 –> 2013-2019	4.7300390	16405.8891
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1263	2.6666494	6075.7970	21.456447	2000-2012 –> 2013-2019	5.1089531	17177.5749
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	1263	2.5846959	5994.9482	24.744636	2000-2012 –> 2013-2019	4.7623441	16544.6427
Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1263	2.5330762	5945.9902	25.891764	2000-2012 –> 2013-2019	4.5332582	16089.9896
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1263	2.6623762	6071.7460	22.596317	2000-2012 –> 2013-2019	4.8613463	16670.1710
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	1263	2.7633578	6163.7827	28.240304	2000-2012 –> 2013-2019	4.9637784	16763.3702
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1263	2.2552518	5652.5376	22.583567	2000-2012 –> 2013-2019	4.3413155	15998.1644
Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	1263	2.8094508	6205.5690	28.490393	2000-2012 –> 2013-2019	5.0811370	16958.0234
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1263	2.6917313	6099.4450	22.955194	2000-2012 –> 2013-2019	4.9313760	16785.7717
Atlantic	(26.75,27]	cstar_tref ~ temp + oxygen + silicate + phosphate	1263	2.8252828	6219.7637	28.536665	2000-2012 –> 2013-2019	5.1253837	17031.8354
Atlantic	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2031	2.4661377	9442.3058	11.932474	1982-1999 –> 2000-2012	4.5803997	20773.7445
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2031	2.0909522	8773.9389	9.715574	1982-1999 –> 2000-2012	4.3252336	20395.7044
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	2031	1.9148200	8414.4995	9.235730	1982-1999 –> 2000-2012	3.6311952	18657.1971
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2031	1.8904789	8364.5325	9.689213	1982-1999 –> 2000-2012	3.4604645	18143.6984
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	2031	2.1351734	8856.9497	9.523454	1982-1999 –> 2000-2012	4.3987260	20544.6841
Atlantic	(27,27.25]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	2031	2.2040749	8985.9589	10.013233	1982-1999 –> 2000-2012	4.5689583	20902.3812
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	2031	2.1902432	8962.3874	9.942899	1982-1999 –> 2000-2012	4.5538173	20877.9179
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2031	2.0594140	8712.2044	13.384239	1982-1999 –> 2000-2012	3.7359927	18834.3973
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2031	2.3112875	9180.8912	13.899054	1982-1999 –> 2000-2012	4.3877097	20420.0232
Atlantic	(27,27.25]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2031	2.1067869	8804.5844	12.394761	1982-1999 –> 2000-2012	3.8168590	19030.0700
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1142	2.2408412	5097.7041	11.555324	2000-2012 –> 2013-2019	4.3317934	13871.6430
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	1142	2.3003827	5155.6000	13.777336	2000-2012 –> 2013-2019	4.2152027	13570.0995
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1142	2.2946948	5151.9457	14.080782	2000-2012 –> 2013-2019	4.1851737	13516.4782
Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	1142	2.3424794	5197.0192	15.033313	2000-2012 –> 2013-2019	4.4776528	14053.9689
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1142	2.3332715	5190.0234	13.840333	2000-2012 –> 2013-2019	4.5235147	14152.4108
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + silicate + phosphate	1142	2.3613801	5215.3740	15.167463	2000-2012 –> 2013-2019	4.5523853	14177.1744
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + silicate + phosphate + phosphate_star	1142	2.3613801	5215.3740	15.167463	2000-2012 –> 2013-2019	4.5523853	14177.1744
Atlantic	(27,27.25]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1142	2.3613801	5215.3740	15.167463	2000-2012 –> 2013-2019	4.5523853	14177.1744
Atlantic	(27,27.25]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1142	2.3613801	5215.3740	15.167463	2000-2012 –> 2013-2019	4.5523853	14177.1744
Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1142	2.5328202	5377.4530	21.355986	2000-2012 –> 2013-2019	4.5922342	14089.6574
Atlantic	(27.25,27.5]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	2025	2.7504322	9856.3212	19.941044	1982-1999 –> 2000-2012	5.5340146	23928.3716
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	2025	2.5285742	9515.7061	13.358360	1982-1999 –> 2000-2012	5.1450783	23231.4624
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2025	2.4514644	9392.2776	12.813379	1982-1999 –> 2000-2012	4.9864330	22927.8111
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2025	3.1435193	10397.3400	20.035882	1982-1999 –> 2000-2012	5.5634228	23663.4868
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	2025	2.7655192	9878.4761	23.145713	1982-1999 –> 2000-2012	5.3049716	23422.1817
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2025	2.6905754	9769.2091	21.422922	1982-1999 –> 2000-2012	4.8576234	22402.1133
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	2025	2.4063497	9315.0504	11.614926	1982-1999 –> 2000-2012	4.1264292	20616.3452
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2025	2.2547324	9053.4778	15.509020	1982-1999 –> 2000-2012	3.9706310	20342.7650
Atlantic	(27.25,27.5]	cstar_tref ~ temp + oxygen + nitrate + silicate	2025	2.4916281	9456.0932	10.104738	1982-1999 –> 2000-2012	4.3239984	21121.3969
Atlantic	(27.25,27.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2025	2.3326197	9191.0186	10.601623	1982-1999 –> 2000-2012	4.1616629	20847.8613
Atlantic	(27.25,27.5]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	1109	3.0051254	5599.7139	21.412798	2000-2012 –> 2013-2019	5.7555576	15456.0350
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	1109	3.0025580	5597.8181	16.245244	2000-2012 –> 2013-2019	5.5311321	15113.5242
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1109	2.7952620	5441.1451	16.992150	2000-2012 –> 2013-2019	5.2467264	14833.4228
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	1109	3.5932118	5996.1307	25.833019	2000-2012 –> 2013-2019	6.3587310	15874.6067
Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1109	3.5374046	5963.4120	24.085736	2000-2012 –> 2013-2019	6.2279800	15732.6211
Atlantic	(27.25,27.5]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1109	3.6764640	6048.9339	20.304506	2000-2012 –> 2013-2019	6.9782970	16647.2699
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate	1109	3.1081847	5674.5038	12.222568	2000-2012 –> 2013-2019	5.5145344	14989.5543
Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1109	2.7923328	5438.8197	16.610907	2000-2012 –> 2013-2019	5.0470652	14492.2975
Atlantic	(27.25,27.5]	cstar_tref ~ temp + oxygen + nitrate + silicate	1109	3.2001964	5739.2103	12.589120	2000-2012 –> 2013-2019	5.6918245	15195.3035
Atlantic	(27.25,27.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1109	2.8746758	5503.2804	14.300893	2000-2012 –> 2013-2019	5.2072955	14694.2990
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate	2804	2.8268767	13797.0865	15.595608	1982-1999 –> 2000-2012	5.6266381	32094.2808
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2804	2.8239152	13793.2083	15.894239	1982-1999 –> 2000-2012	5.5291200	31835.8277
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	2804	2.7836924	13708.7557	13.816311	1982-1999 –> 2000-2012	5.2587422	31083.3422
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2804	2.7656318	13674.2524	14.269310	1982-1999 –> 2000-2012	5.0314996	30391.3946
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	2804	2.4538915	13003.5694	13.901382	1982-1999 –> 2000-2012	4.8210764	30047.3887
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2804	2.3944064	12867.9502	14.685866	1982-1999 –> 2000-2012	4.4949743	29021.3907
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate	2804	3.1926743	14479.5041	16.493618	1982-1999 –> 2000-2012	5.5799379	31586.4005
Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2804	3.1165165	14346.1100	16.244315	1982-1999 –> 2000-2012	5.5026775	31451.5564
Atlantic	(27.5,27.75]	cstar_tref ~ temp + oxygen + nitrate + silicate	2804	3.2454298	14571.4129	16.872661	1982-1999 –> 2000-2012	5.6444387	31714.9618
Atlantic	(27.5,27.75]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2804	3.1572781	14418.9826	16.810973	1982-1999 –> 2000-2012	5.5460908	31532.7237
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate	1515	3.2789491	7909.5783	16.534959	2000-2012 –> 2013-2019	6.1058258	21706.6649
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1515	3.2267256	7862.9314	14.600864	2000-2012 –> 2013-2019	6.0506408	21656.1398
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	1515	3.4259760	8040.4845	14.371977	2000-2012 –> 2013-2019	6.2096684	21749.2402
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1515	3.4234258	8040.2283	14.171915	2000-2012 –> 2013-2019	6.1890576	21714.4806
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	1515	2.8745087	7510.7055	15.545879	2000-2012 –> 2013-2019	5.3284002	20514.2749
Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1515	2.8711798	7509.1946	15.461950	2000-2012 –> 2013-2019	5.2655862	20377.1448
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + nitrate + phosphate_star	1515	2.9543301	7593.6977	23.012182	2000-2012 –> 2013-2019	5.8568749	21538.9217
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1515	2.8464806	7483.0164	22.421750	2000-2012 –> 2013-2019	5.7223980	21378.5562
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate	1515	3.2671643	7898.6687	16.135848	2000-2012 –> 2013-2019	6.4589075	22376.5370
Atlantic	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate + phosphate_star	1515	3.2671643	7898.6687	16.135848	2000-2012 –> 2013-2019	6.4589075	22376.5370
Atlantic	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1036	2.2930064	4671.5184	15.409426	1982-1999 –> 2000-2012	4.2141877	10153.2785
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	1036	1.9259602	4310.0805	13.267819	1982-1999 –> 2000-2012	3.9306085	9904.1154
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1036	1.8800580	4262.0997	14.057027	1982-1999 –> 2000-2012	3.8317057	9787.3967
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate	1036	2.2757763	4653.8902	11.420567	1982-1999 –> 2000-2012	4.2495639	10204.9673
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1036	1.9943230	4382.3519	12.367472	1982-1999 –> 2000-2012	3.6776199	9515.1410
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	1036	1.7389083	4098.3902	12.226980	1982-1999 –> 2000-2012	3.5475856	9420.8408
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1036	1.5641536	3880.9392	12.798383	1982-1999 –> 2000-2012	3.1611985	8876.8661
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + nitrate + phosphate_star	1036	2.0673590	4456.8761	14.204780	1982-1999 –> 2000-2012	4.2394980	10262.7546
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1036	2.0673322	4458.8492	14.257932	1982-1999 –> 2000-2012	4.2060587	10225.8028
Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1036	2.2923345	4672.9112	15.392219	1982-1999 –> 2000-2012	4.1974560	10134.5099
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	513	2.0314562	2195.0114	12.644220	2000-2012 –> 2013-2019	3.9574164	6505.0919
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	513	2.0209724	2191.7028	12.956555	2000-2012 –> 2013-2019	3.9010304	6453.8025
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate + phosphate_star	513	2.4147179	2372.3345	11.388027	2000-2012 –> 2013-2019	4.4090409	6754.6864
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	513	1.8570079	2102.8906	11.721525	2000-2012 –> 2013-2019	3.5959162	6201.2808
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	513	1.7475521	2042.5606	12.039326	2000-2012 –> 2013-2019	3.3117057	5923.4997
Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate_star	513	2.2786438	2312.8244	11.507801	2000-2012 –> 2013-2019	4.5612635	6974.9360
Atlantic	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	513	2.2842561	2315.3484	11.539783	2000-2012 –> 2013-2019	4.5828767	6991.9337
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + nitrate + phosphate_star	513	2.1177551	2237.6968	14.216180	2000-2012 –> 2013-2019	4.1851141	6694.5729
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	513	2.0908491	2226.5780	12.385110	2000-2012 –> 2013-2019	4.1581813	6685.4273
Atlantic	(27.75,27.85]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	513	2.2850958	2315.7255	11.564796	2000-2012 –> 2013-2019	4.5875235	6995.7397
Atlantic	(27.85,27.95]	cstar_tref ~ aou + phosphate + phosphate_star	983	3.4444208	5231.0950	40.406696	1982-1999 –> 2000-2012	6.3613830	11892.9889
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	983	3.4332878	5226.7302	38.381356	1982-1999 –> 2000-2012	6.3108859	11854.3203
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	983	3.4396213	5230.3536	36.781212	1982-1999 –> 2000-2012	6.1696286	11717.2584
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	983	3.4272905	5225.2930	34.214054	1982-1999 –> 2000-2012	6.1571686	11714.0714
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	983	3.7119861	5382.1740	36.399240	1982-1999 –> 2000-2012	6.6375507	12055.9363
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate	983	3.7051030	5374.5251	49.117027	1982-1999 –> 2000-2012	6.6349552	12048.2006
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	983	3.0946626	5022.5819	23.332862	1982-1999 –> 2000-2012	6.0114682	11686.3324
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate	983	3.6929852	5370.0846	46.749916	1982-1999 –> 2000-2012	6.6056230	12030.0144
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	983	3.0757549	5012.5332	23.130965	1982-1999 –> 2000-2012	5.9400103	11629.7050
Atlantic	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	983	3.8137613	5435.3521	51.408459	1982-1999 –> 2000-2012	6.7226058	12093.7996
Atlantic	(27.85,27.95]	cstar_tref ~ aou + phosphate + phosphate_star	569	3.7400627	3125.8905	23.720140	2000-2012 –> 2013-2019	7.1844835	8356.9855
Atlantic	(27.85,27.95]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	569	3.7372699	3127.0405	23.268863	2000-2012 –> 2013-2019	7.1705577	8353.7707
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	569	3.6673760	3107.5562	28.923043	2000-2012 –> 2013-2019	7.3896551	8495.1743
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + phosphate + phosphate_star	569	3.4103854	3022.8793	30.447244	2000-2012 –> 2013-2019	6.8500067	8253.2329
Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	569	3.3215129	2994.8304	29.207068	2000-2012 –> 2013-2019	6.7488034	8220.1234
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	569	3.8223998	3154.6717	23.042368	2000-2012 –> 2013-2019	7.5343859	8536.8458
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate	569	3.8337887	3154.0574	23.962464	2000-2012 –> 2013-2019	7.5388917	8528.5825
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	569	3.6730463	3107.3144	22.693963	2000-2012 –> 2013-2019	6.7677089	8129.8962
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate	569	3.8181580	3151.4082	23.646089	2000-2012 –> 2013-2019	7.5111432	8521.4928
Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	569	3.6600265	3105.2733	23.151675	2000-2012 –> 2013-2019	6.7357814	8117.8065
Atlantic	(27.95,28.05]	cstar_tref ~ oxygen + nitrate + silicate + phosphate_star	1204	4.7603831	7186.0742	34.069173	1982-1999 –> 2000-2012	8.7956135	16630.6086
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1204	4.6143746	7111.0606	26.067945	1982-1999 –> 2000-2012	9.4462340	17159.5181
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1204	4.5430532	7075.5511	25.262696	1982-1999 –> 2000-2012	9.2883301	17065.3992
Atlantic	(27.95,28.05]	cstar_tref ~ sal + oxygen + nitrate + phosphate_star	1204	4.4957529	7048.3486	26.854357	1982-1999 –> 2000-2012	8.6410505	16583.0894
Atlantic	(27.95,28.05]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1204	4.1957717	6884.0621	30.223807	1982-1999 –> 2000-2012	7.7898469	15942.5131
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1204	4.0815088	6815.5758	22.528945	1982-1999 –> 2000-2012	8.1122385	16256.3696
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1204	3.8590720	6682.6316	25.099675	1982-1999 –> 2000-2012	7.3908813	15682.5017
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1204	4.5224648	7064.6136	21.845213	1982-1999 –> 2000-2012	9.3768338	17130.6504
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	1204	4.1566877	6859.5262	23.454537	1982-1999 –> 2000-2012	8.2856315	16381.0167
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1204	3.9591041	6744.2548	25.125796	1982-1999 –> 2000-2012	7.5958976	15842.3119
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	666	4.3483289	3859.7886	24.917815	2000-2012 –> 2013-2019	8.9627036	10970.8492
Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	666	4.2792874	3840.4697	24.913097	2000-2012 –> 2013-2019	8.8223406	10916.0208
Atlantic	(27.95,28.05]	cstar_tref ~ sal + oxygen + nitrate + phosphate_star	666	3.9013752	3715.3165	28.636553	2000-2012 –> 2013-2019	8.3971281	10763.6651
Atlantic	(27.95,28.05]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	666	3.4861342	3567.4190	32.154120	2000-2012 –> 2013-2019	7.6819059	10451.4811
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate_star	666	3.8465745	3696.4739	22.933854	2000-2012 –> 2013-2019	7.9280833	10512.0498
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	666	3.5060655	3575.0128	26.986021	2000-2012 –> 2013-2019	7.3651375	10257.6443
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	666	4.4290548	3886.2901	23.783433	2000-2012 –> 2013-2019	8.9515196	10950.9038
Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate_star	666	4.4290672	3884.2939	23.826635	2000-2012 –> 2013-2019	8.9990669	10972.0855
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	666	3.9030940	3715.9032	23.856002	2000-2012 –> 2013-2019	8.0597817	10575.4294
Atlantic	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	666	3.5394291	3587.6281	27.891571	2000-2012 –> 2013-2019	7.4985332	10331.8828
Atlantic	(28.05,28.1]	cstar_tref ~ aou + phosphate + phosphate_star	804	1.1608853	2531.5393	11.005507	1982-1999 –> 2000-2012	2.1206840	5506.7947
Atlantic	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	804	1.1604167	2532.8901	10.979649	1982-1999 –> 2000-2012	2.1134849	5495.0017
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	804	1.1335334	2497.1994	6.397009	1982-1999 –> 2000-2012	2.1255963	5547.6063
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	804	1.0598757	2387.1610	7.838670	1982-1999 –> 2000-2012	1.9527650	5208.9110
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	804	1.0324411	2346.9902	6.945256	1982-1999 –> 2000-2012	1.9247967	5169.4535
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate	804	1.1795166	2557.1414	11.041510	1982-1999 –> 2000-2012	2.1507145	5557.8051
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	804	1.1065403	2456.4443	11.331523	1982-1999 –> 2000-2012	2.0473492	5390.6954
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	804	1.1772969	2556.1127	10.971289	1982-1999 –> 2000-2012	2.1453194	5551.7285
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	804	1.0436142	2364.2985	12.188672	1982-1999 –> 2000-2012	1.8828911	5054.7923
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	804	1.1823967	2565.0630	11.000864	1982-1999 –> 2000-2012	2.1548805	5572.5740
Atlantic	(28.05,28.1]	cstar_tref ~ aou + phosphate + phosphate_star	434	1.2192680	1413.7202	12.282594	2000-2012 –> 2013-2019	2.3801533	3945.2595
Atlantic	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	434	1.2132881	1411.4526	12.215619	2000-2012 –> 2013-2019	2.3737048	3944.3427
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	434	1.1676572	1380.1780	6.819178	2000-2012 –> 2013-2019	2.3011906	3877.3774
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate + phosphate_star	434	1.1212849	1343.0032	8.929761	2000-2012 –> 2013-2019	2.1811606	3730.1642
Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	434	1.0586072	1295.0748	7.429722	2000-2012 –> 2013-2019	2.0910483	3642.0650
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate + phosphate_star	434	1.1480057	1363.4454	12.833810	2000-2012 –> 2013-2019	2.2545460	3819.8898
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	434	1.2303737	1423.5906	12.182262	2000-2012 –> 2013-2019	2.4076706	3979.7033
Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	434	1.1075442	1334.3006	13.578379	2000-2012 –> 2013-2019	2.1511584	3698.5991
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	434	1.2338376	1428.0309	12.265693	2000-2012 –> 2013-2019	2.4162343	3993.0939
Atlantic	(28.05,28.1]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	434	1.2341739	1426.2674	12.180217	2000-2012 –> 2013-2019	2.4166248	3989.4043
Atlantic	(28.1,28.15]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	936	0.8652007	2397.1990	9.973159	1982-1999 –> 2000-2012	1.5501093	5104.0130
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	936	0.8394339	2342.6013	6.649159	1982-1999 –> 2000-2012	1.5477300	5138.3794
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	936	0.7732900	2186.9596	6.039973	1982-1999 –> 2000-2012	1.4451653	4844.0128
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	936	0.7598609	2156.1646	5.927820	1982-1999 –> 2000-2012	1.3893138	4646.2932
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	936	0.8570872	2379.5613	9.929510	1982-1999 –> 2000-2012	1.5754781	5209.9919
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate	936	0.8783084	2425.3470	10.051818	1982-1999 –> 2000-2012	1.5766996	5182.6502
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	936	0.7856962	2218.7544	10.025704	1982-1999 –> 2000-2012	1.3744859	4535.9182
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	936	0.8807386	2432.5195	9.872456	1982-1999 –> 2000-2012	1.5856244	5215.7966
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + silicate + phosphate	936	0.8830714	2435.4712	10.082608	1982-1999 –> 2000-2012	1.5884109	5218.4149
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	936	0.8830714	2435.4712	10.082608	1982-1999 –> 2000-2012	1.5884109	5218.4149
Atlantic	(28.1,28.15]	cstar_tref ~ aou + phosphate + phosphate_star	497	1.0350290	1454.6478	11.396766	2000-2012 –> 2013-2019	1.9059708	3862.2274
Atlantic	(28.1,28.15]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	497	1.0349299	1456.5526	11.397933	2000-2012 –> 2013-2019	1.9001307	3853.7516
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	497	0.9633503	1387.3108	6.933462	2000-2012 –> 2013-2019	1.8027842	3729.9121
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate + phosphate_star	497	0.8714406	1285.6430	6.181914	2000-2012 –> 2013-2019	1.6447306	3472.6026
Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	497	0.8712585	1287.4353	6.182326	2000-2012 –> 2013-2019	1.6311195	3443.5998
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate	497	1.0551579	1473.7932	11.501643	2000-2012 –> 2013-2019	1.9357585	3902.0192
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate + phosphate_star	497	0.9653756	1387.3983	11.632299	2000-2012 –> 2013-2019	1.8224628	3766.9596
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate	497	1.0549100	1475.5596	11.494491	2000-2012 –> 2013-2019	1.9332185	3900.9066
Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	497	0.8791505	1296.3985	11.933687	2000-2012 –> 2013-2019	1.6648467	3515.1529
Atlantic	(28.1,28.15]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	497	1.0490759	1472.0472	11.035771	2000-2012 –> 2013-2019	1.9298146	3904.5667
Atlantic	(28.15,28.2]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	1540	0.5623454	2609.3623	2.430575	1982-1999 –> 2000-2012	1.1578520	6627.2122
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1540	0.5939756	2777.9061	2.353787	1982-1999 –> 2000-2012	1.1267120	6300.3123
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate	1540	0.6375040	2995.7309	2.402197	1982-1999 –> 2000-2012	1.2354501	7031.7649
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1540	0.5471615	2527.0561	2.040783	1982-1999 –> 2000-2012	1.0648603	5924.1022
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1540	0.6019966	2819.2202	2.184553	1982-1999 –> 2000-2012	1.1657858	6593.6216
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	1540	0.5718023	2660.7281	2.192349	1982-1999 –> 2000-2012	1.1224532	6330.2485
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1540	0.5576121	2585.3284	2.314250	1982-1999 –> 2000-2012	1.1076613	6251.9858
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	1540	0.6051750	2835.4386	2.198295	1982-1999 –> 2000-2012	1.1760176	6665.1429
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + nitrate + silicate	1540	0.5772872	2690.1312	2.226077	1982-1999 –> 2000-2012	1.1364464	6427.8538
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1540	0.5669166	2636.2981	2.345127	1982-1999 –> 2000-2012	1.1259531	6375.0445
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + phosphate_star	819	0.7431790	1850.0329	4.262643	2000-2012 –> 2013-2019	1.3371546	4627.9389
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate	819	0.8257916	2022.6871	4.712442	2000-2012 –> 2013-2019	1.4632956	5018.4180
Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	819	0.7372762	1838.9708	4.731734	2000-2012 –> 2013-2019	1.2844377	4366.0269
Atlantic	(28.15,28.2]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	819	0.8297177	2032.4562	5.671364	2000-2012 –> 2013-2019	1.4482931	4937.3514
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + phosphate_star	819	0.8686623	2105.5896	7.748139	2000-2012 –> 2013-2019	1.4706590	4924.8098
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	819	0.8619250	2092.8357	8.363302	2000-2012 –> 2013-2019	1.4337273	4753.5638
Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	819	0.8613203	2093.6861	8.208278	2000-2012 –> 2013-2019	1.4189324	4679.0145
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	819	0.8724916	2112.7945	7.808630	2000-2012 –> 2013-2019	1.4776666	4948.2331
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + nitrate + silicate	819	0.8696972	2107.5398	8.465903	2000-2012 –> 2013-2019	1.4469843	4797.6710
Atlantic	(28.15,28.2]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	819	0.8677435	2105.8561	8.181408	2000-2012 –> 2013-2019	1.4346601	4742.1542
Atlantic	(28.2, Inf]	cstar_tref ~ aou + nitrate + silicate + phosphate_star	2693	0.5320594	4255.8361	3.167207	1982-1999 –> 2000-2012	1.0002835	9167.3239
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	2693	0.3593168	2139.5581	1.966552	1982-1999 –> 2000-2012	0.6655852	3898.5165
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	2693	0.3540505	2062.0339	1.937681	1982-1999 –> 2000-2012	0.6560011	3717.6111
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	2693	0.3588037	2133.8610	1.963165	1982-1999 –> 2000-2012	0.6635911	3858.8422
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2693	0.3463114	1944.9979	1.900529	1982-1999 –> 2000-2012	0.6453988	3531.8596
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + nitrate + phosphate_star	2693	0.4644953	3524.3978	6.704526	1982-1999 –> 2000-2012	0.9658160	8942.8000
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate	2693	0.4778466	3677.0273	6.696866	1982-1999 –> 2000-2012	0.9678429	8925.8507
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	2693	0.4618076	3495.1416	7.084808	1982-1999 –> 2000-2012	0.9515248	8741.7369
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2693	0.5306498	4243.5482	3.091584	1982-1999 –> 2000-2012	0.9896559	9009.4595
Atlantic	(28.2, Inf]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2693	0.5451838	4389.0814	3.304918	1982-1999 –> 2000-2012	1.0135140	9304.2502
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	1557	0.4186021	1716.7958	2.479100	2000-2012 –> 2013-2019	0.7779188	3856.3538
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1557	0.3991609	1570.7062	2.411345	2000-2012 –> 2013-2019	0.7532114	3632.7401
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	1557	0.4110188	1661.8663	2.465092	2000-2012 –> 2013-2019	0.7698225	3795.7273
Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1557	0.3901368	1501.4981	2.457959	2000-2012 –> 2013-2019	0.7364483	3446.4960
Atlantic	(28.2, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	1557	0.6309055	2996.2688	2.438558	2000-2012 –> 2013-2019	1.2382861	7965.2135
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + nitrate	1557	0.5156492	2366.0835	7.293748	2000-2012 –> 2013-2019	1.0111620	6236.6407
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + nitrate + phosphate_star	1557	0.4442799	1904.1849	3.889221	2000-2012 –> 2013-2019	0.9087752	5428.5827
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate	1557	0.4718588	2091.7254	3.398074	2000-2012 –> 2013-2019	0.9497054	5768.7527
Atlantic	(28.2, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1557	0.4385296	1865.6176	5.067855	2000-2012 –> 2013-2019	0.9003372	5360.7592
Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1557	0.7057457	3347.3447	8.527267	2000-2012 –> 2013-2019	1.2363955	7590.8929
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5288	6.2360939	34376.5179	29.968567	1982-1999 –> 2000-2012	12.7656352	81794.3473
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5288	6.1928478	34304.9200	29.527354	1982-1999 –> 2000-2012	12.6716991	81612.6324
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5288	7.1987438	35896.7294	31.371808	1982-1999 –> 2000-2012	14.7271008	85364.2640
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5288	7.2933052	36034.7494	29.166512	1982-1999 –> 2000-2012	14.8774849	85608.5624
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate_star	5288	7.4060853	36195.0399	28.515322	1982-1999 –> 2000-2012	15.1434323	86054.4924
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	5288	7.1609299	35841.0290	31.554355	1982-1999 –> 2000-2012	14.6425732	85219.0198
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate	5288	7.3907730	36173.1511	28.492599	1982-1999 –> 2000-2012	15.1050761	85989.6943
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	5288	7.3907730	36173.1511	28.492599	1982-1999 –> 2000-2012	15.1050761	85989.6943
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	5288	7.3907730	36173.1511	28.492599	1982-1999 –> 2000-2012	15.1050761	85989.6943
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	5288	7.3907730	36173.1511	28.492599	1982-1999 –> 2000-2012	15.1050761	85989.6943
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2816	5.9520247	18049.4373	24.894024	2000-2012 –> 2013-2019	12.1881186	52425.9552
Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2816	5.8778725	17980.8313	24.128023	2000-2012 –> 2013-2019	12.0707203	52285.7513
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2816	6.9521542	18926.2002	25.907885	2000-2012 –> 2013-2019	14.1508980	54822.9297
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2816	7.0001768	18964.9700	25.465195	2000-2012 –> 2013-2019	14.2934820	54999.7194
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate_star	2816	7.1474074	19080.1961	24.474615	2000-2012 –> 2013-2019	14.5534927	55275.2360
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2816	6.9178353	18898.3293	26.006595	2000-2012 –> 2013-2019	14.0787652	54739.3584
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate	2816	7.1344030	19069.9395	24.441528	2000-2012 –> 2013-2019	14.5251760	55243.0906
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	2816	7.1344030	19069.9395	24.441528	2000-2012 –> 2013-2019	14.5251760	55243.0906
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2816	7.1344030	19069.9395	24.441528	2000-2012 –> 2013-2019	14.5251760	55243.0906
Indo-Pacific	(-Inf,26]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2816	7.1344030	19069.9395	24.441528	2000-2012 –> 2013-2019	14.5251760	55243.0906
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5525	4.8905258	33230.9339	41.688307	1982-1999 –> 2000-2012	9.5377100	78823.9388
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5525	4.5360650	32401.5327	43.772780	1982-1999 –> 2000-2012	8.7824377	76605.3494
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5525	4.7555301	32923.6260	49.041150	1982-1999 –> 2000-2012	9.1671720	77716.3587
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	5525	4.8893893	33228.3657	40.409229	1982-1999 –> 2000-2012	9.5091497	78730.0815
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5525	4.8803203	33209.8508	41.154556	1982-1999 –> 2000-2012	9.4999894	78713.2617
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate_star	5525	4.9245814	33307.6149	49.529819	1982-1999 –> 2000-2012	9.5559722	78848.1124
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	5525	4.7637711	32942.7584	51.203206	1982-1999 –> 2000-2012	9.1789275	77747.7736
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate	5525	4.9304894	33320.8635	50.805047	1982-1999 –> 2000-2012	9.5666218	78877.1440
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	5525	4.9304894	33320.8635	50.805047	1982-1999 –> 2000-2012	9.5666218	78877.1440
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	5525	4.9304894	33320.8635	50.805047	1982-1999 –> 2000-2012	9.5666218	78877.1440
Indo-Pacific	(26,26.5]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2918	4.8175903	17468.7156	40.382988	2000-2012 –> 2013-2019	9.7081161	50699.6495
Indo-Pacific	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2918	4.4724496	17036.8813	46.310491	2000-2012 –> 2013-2019	9.0085146	49438.4140
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2918	4.5715543	17164.7889	45.715284	2000-2012 –> 2013-2019	9.3270844	50088.4149
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	2918	4.8142859	17464.7112	37.043514	2000-2012 –> 2013-2019	9.7036752	50693.0769
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2918	4.8065118	17457.2797	38.739984	2000-2012 –> 2013-2019	9.6868321	50667.1305
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate_star	2918	4.8483037	17505.8034	34.431113	2000-2012 –> 2013-2019	9.7728851	50813.4183
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2918	4.5779873	17172.9954	45.249093	2000-2012 –> 2013-2019	9.3417584	50115.7538
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate	2918	4.8517131	17509.9060	34.225344	2000-2012 –> 2013-2019	9.7822025	50830.7695
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2918	4.8517131	17509.9060	34.225344	2000-2012 –> 2013-2019	9.7822025	50830.7695
Indo-Pacific	(26,26.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2918	4.8517131	17509.9060	34.225344	2000-2012 –> 2013-2019	9.7822025	50830.7695
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4544	4.0473152	25612.8259	22.127132	1982-1999 –> 2000-2012	7.9963826	60742.2745
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	4544	4.2282325	26010.2468	17.683523	1982-1999 –> 2000-2012	8.1624139	61092.2007
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4544	3.9265162	25339.4488	20.226531	1982-1999 –> 2000-2012	7.6839109	59845.1956
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	4544	4.1123307	25757.6541	34.883768	1982-1999 –> 2000-2012	8.1714906	61232.8996
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4544	4.0218289	25557.4171	33.030413	1982-1999 –> 2000-2012	8.0127086	60821.3190
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate	4544	4.1322494	25801.5670	26.615035	1982-1999 –> 2000-2012	8.1538965	61160.0507
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4544	3.9477481	25388.4579	23.151958	1982-1999 –> 2000-2012	7.8249401	60288.9073
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	4544	4.0218809	25555.5345	32.963712	1982-1999 –> 2000-2012	8.0834114	61038.1226
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	4544	4.1104968	25753.6003	34.578793	1982-1999 –> 2000-2012	8.1719835	61236.0528
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	4544	4.0218771	25557.5260	32.942351	1982-1999 –> 2000-2012	8.0175184	60836.4236
Indo-Pacific	(26.5,26.75]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2447	4.4033896	14211.0265	24.538450	2000-2012 –> 2013-2019	8.4507048	39823.8524
Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2447	4.2938981	14089.7973	24.434470	2000-2012 –> 2013-2019	8.2204143	39429.2462
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2447	4.4145039	14223.3635	32.302554	2000-2012 –> 2013-2019	8.5268346	39981.0176
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2447	4.3225383	14122.3318	31.664753	2000-2012 –> 2013-2019	8.3443672	39679.7489
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate	2447	4.4871872	14303.2855	23.916608	2000-2012 –> 2013-2019	8.6194367	40104.8525
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2447	4.2923135	14087.9909	22.815590	2000-2012 –> 2013-2019	8.2400615	39476.4489
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate_star	2447	4.4875150	14301.6430	39.084814	2000-2012 –> 2013-2019	8.6154803	40091.7829
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2447	4.3388127	14138.7232	34.446250	2000-2012 –> 2013-2019	8.3606936	39694.2577
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	2447	4.4113430	14219.8580	32.128406	2000-2012 –> 2013-2019	8.5218397	39973.4583
Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2447	4.3205048	14120.0290	31.479242	2000-2012 –> 2013-2019	8.3423820	39677.5550
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + phosphate + phosphate_star	5354	4.5403612	31405.2681	19.876020	1982-1999 –> 2000-2012	8.5493390	73701.4539
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5354	4.5232238	31366.7748	18.928405	1982-1999 –> 2000-2012	8.5202080	73619.8323
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	5354	4.3077986	30844.2463	21.980567	1982-1999 –> 2000-2012	7.9956057	71884.6902
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5354	4.2906105	30803.4359	21.052395	1982-1999 –> 2000-2012	7.9645082	71788.9629
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5354	4.7202960	31825.4340	21.967294	1982-1999 –> 2000-2012	8.9654213	74987.6940
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate	5354	4.7325547	31849.2068	22.112703	1982-1999 –> 2000-2012	8.9380478	74866.1886
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	5354	4.2057274	30587.4712	23.104196	1982-1999 –> 2000-2012	7.8859232	71596.7963
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	5354	4.7085076	31796.6584	21.818996	1982-1999 –> 2000-2012	8.8953150	74748.5682
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5354	4.1702723	30498.8181	21.453131	1982-1999 –> 2000-2012	7.8227361	71396.2141
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	5354	4.6674184	31704.8041	20.858437	1982-1999 –> 2000-2012	8.8798032	74750.4482
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + phosphate + phosphate_star	2868	4.9134802	17280.6429	19.343238	2000-2012 –> 2013-2019	9.4538414	48685.9111
Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2868	4.9018613	17269.0630	18.494849	2000-2012 –> 2013-2019	9.4250851	48635.8378
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + phosphate + phosphate_star	2868	4.6612052	16980.3073	20.095371	2000-2012 –> 2013-2019	8.9690038	47824.5536
Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2868	4.6499950	16968.4956	19.282213	2000-2012 –> 2013-2019	8.9406055	47771.9315
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2868	5.1164605	17516.8386	19.185056	2000-2012 –> 2013-2019	9.8367565	49342.2726
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2868	4.5774010	16876.2410	16.522089	2000-2012 –> 2013-2019	8.7831284	47463.7121
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	2868	5.1132156	17511.1996	17.396394	2000-2012 –> 2013-2019	9.8217232	49307.8580
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2868	4.5537010	16848.4650	17.066955	2000-2012 –> 2013-2019	8.7239733	47347.2831
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	2868	5.1160215	17514.3463	20.245716	2000-2012 –> 2013-2019	9.8562356	49382.8696
Indo-Pacific	(26.75,27]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2868	5.0448252	17435.9616	18.619356	2000-2012 –> 2013-2019	9.7122436	49140.7657
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	6466	4.4389355	37635.7547	39.385070	1982-1999 –> 2000-2012	8.0900559	85614.5068
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + phosphate + phosphate_star	6466	4.7089499	38399.3937	56.109262	1982-1999 –> 2000-2012	8.4861976	86978.3817
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	6466	4.3929768	37503.1646	41.945012	1982-1999 –> 2000-2012	7.9587117	85065.6810
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	6466	4.1535561	36778.4265	49.359080	1982-1999 –> 2000-2012	7.5202091	83325.5519
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	6466	4.3599345	37403.5276	46.003290	1982-1999 –> 2000-2012	7.9680032	85172.6402
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate	6466	4.5799992	38040.3224	37.420573	1982-1999 –> 2000-2012	8.3645596	86653.4940
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	6466	3.9500266	36128.6900	31.512269	1982-1999 –> 2000-2012	7.2528573	82337.5496
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	6466	4.6663213	38281.7913	72.764927	1982-1999 –> 2000-2012	8.1605463	85484.2572
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	6466	4.7286162	38453.2900	65.782175	1982-1999 –> 2000-2012	8.5031493	87019.5720
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	6466	4.1253304	36690.2467	48.506869	1982-1999 –> 2000-2012	7.4805153	83177.0650
Indo-Pacific	(27,27.25]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3470	5.1328308	21210.8952	31.173698	2000-2012 –> 2013-2019	9.5717663	58846.6499
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3470	5.0789520	21139.6617	33.597697	2000-2012 –> 2013-2019	9.4719288	58642.8263
Indo-Pacific	(27,27.25]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	3470	5.1816896	21278.6438	20.340514	2000-2012 –> 2013-2019	9.8693827	59621.5287
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3470	4.9716940	20991.5322	35.708885	2000-2012 –> 2013-2019	9.1252501	57769.9588
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + phosphate + phosphate_star	3470	5.1322261	21210.0776	39.784583	2000-2012 –> 2013-2019	9.4921606	58613.6052
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate	3470	5.2457410	21361.9039	28.969816	2000-2012 –> 2013-2019	9.8257402	59402.2264
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3470	4.4723380	20256.9380	25.616236	2000-2012 –> 2013-2019	8.4223646	56385.6280
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	3470	4.9160028	20913.3540	34.970533	2000-2012 –> 2013-2019	9.0413332	57603.6007
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	3470	5.3226341	21462.8935	27.632792	2000-2012 –> 2013-2019	10.0108400	59805.1927
Indo-Pacific	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	3470	5.3226341	21462.8935	27.632792	2000-2012 –> 2013-2019	10.0108400	59805.1927
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	5847	3.4261572	31007.5182	32.305003	1982-1999 –> 2000-2012	6.3475428	70339.4077
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5847	3.6920890	31881.6814	32.521736	1982-1999 –> 2000-2012	6.7625645	71999.2104
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	5847	3.7105782	31938.0962	31.726047	1982-1999 –> 2000-2012	6.7817085	72056.9912
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	5847	3.4222130	30994.0484	31.732058	1982-1999 –> 2000-2012	6.3354476	70281.8372
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + silicate + phosphate	5847	3.7568967	32083.1670	30.801943	1982-1999 –> 2000-2012	6.8441839	72284.8816
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + silicate + phosphate + phosphate_star	5847	3.7568967	32083.1670	30.801943	1982-1999 –> 2000-2012	6.8441839	72284.8816
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5847	3.7568967	32083.1670	30.801943	1982-1999 –> 2000-2012	6.8441839	72284.8816
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5847	3.6356816	31701.6427	32.976030	1982-1999 –> 2000-2012	6.7191704	71885.9262
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5847	3.3461863	30731.3292	33.390589	1982-1999 –> 2000-2012	6.2704796	70078.9213
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	5847	3.6204935	31652.6884	33.074778	1982-1999 –> 2000-2012	6.6947648	71789.7182
Indo-Pacific	(27.25,27.5]	cstar_tref ~ oxygen + nitrate + silicate + phosphate_star	3127	4.3080384	18019.9002	34.741395	2000-2012 –> 2013-2019	8.0052965	49915.9424
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	3127	3.9776245	17522.8442	31.036835	2000-2012 –> 2013-2019	7.4037817	48530.3624
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3127	4.3037583	18015.6837	32.127293	2000-2012 –> 2013-2019	7.9958473	49897.3651
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	3127	4.3425043	18069.7354	30.551097	2000-2012 –> 2013-2019	8.0530824	50007.8316
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	3127	3.9789503	17524.9283	30.123196	2000-2012 –> 2013-2019	7.4011633	48518.9767
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + silicate + phosphate	3127	4.4121255	18169.2074	29.187384	2000-2012 –> 2013-2019	8.1690222	50252.3744
Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	3127	4.4121255	18169.2074	29.187384	2000-2012 –> 2013-2019	8.1690222	50252.3744
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3127	4.2454019	17930.3030	31.035584	2000-2012 –> 2013-2019	7.8810835	49631.9457
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3127	3.8437243	17308.6883	33.232474	2000-2012 –> 2013-2019	7.1899105	48040.0175
Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	3127	4.2264297	17902.2919	31.188098	2000-2012 –> 2013-2019	7.8469231	49554.9803
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	5836	3.2683124	30398.6938	24.119856	1982-1999 –> 2000-2012	5.5822735	67013.2424
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5836	3.2280103	30253.8699	9.417658	1982-1999 –> 2000-2012	5.5715676	67074.4342
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	5836	3.3807244	30791.3972	22.456992	1982-1999 –> 2000-2012	5.7423173	67734.2326
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	5836	3.3957705	30843.2286	29.089521	1982-1999 –> 2000-2012	5.7808728	67946.6354
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	5836	3.2980912	30504.5604	26.307453	1982-1999 –> 2000-2012	5.6183359	67163.0675
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate	5836	3.4363673	30981.9413	25.357370	1982-1999 –> 2000-2012	5.8135896	68031.7039
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate + phosphate_star	5836	3.4363673	30981.9413	25.357370	1982-1999 –> 2000-2012	5.8135896	68031.7039
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	5836	3.4363673	30981.9413	25.357370	1982-1999 –> 2000-2012	5.8135896	68031.7039
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5836	3.4363673	30981.9413	25.357370	1982-1999 –> 2000-2012	5.8135896	68031.7039
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5836	3.3691828	30753.4813	15.287781	1982-1999 –> 2000-2012	5.8121319	68247.3438
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	3104	3.9417327	17337.7899	25.386634	2000-2012 –> 2013-2019	7.2100451	47736.4837
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate + phosphate_star	3104	4.1222456	17613.7695	17.053811	2000-2012 –> 2013-2019	7.6293157	48833.4235
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3104	3.7804110	17078.3721	11.020697	2000-2012 –> 2013-2019	7.0084214	47332.2420
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	3104	4.0989818	17578.6356	23.944569	2000-2012 –> 2013-2019	7.4797062	48370.0328
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	3104	4.1948886	17722.2154	32.318244	2000-2012 –> 2013-2019	7.5906591	48565.4440
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	3104	4.0075075	17440.5265	28.440018	2000-2012 –> 2013-2019	7.3055987	47945.0868
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate	3104	4.2088784	17742.8844	27.865993	2000-2012 –> 2013-2019	7.6452457	48724.8257
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + oxygen + silicate + phosphate + phosphate_star	3104	4.2088784	17742.8844	27.865993	2000-2012 –> 2013-2019	7.6452457	48724.8257
Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	3104	4.2088784	17742.8844	27.865993	2000-2012 –> 2013-2019	7.6452457	48724.8257
Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3104	4.0127640	17448.6640	19.751773	2000-2012 –> 2013-2019	7.3819468	48202.1453
Indo-Pacific	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2317	2.7304690	11242.0909	21.046900	1982-1999 –> 2000-2012	4.6623579	24262.9999
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2317	2.7290365	11241.6591	21.325228	1982-1999 –> 2000-2012	4.6507603	24231.5321
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2317	2.7271269	11238.4154	21.453348	1982-1999 –> 2000-2012	4.6635446	24275.9866
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	2317	2.7408402	11259.6589	23.487260	1982-1999 –> 2000-2012	4.6879961	24329.8596
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate	2317	2.7417874	11261.2601	20.642191	1982-1999 –> 2000-2012	4.6870749	24325.4494
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2317	2.6406178	11089.0349	20.968772	1982-1999 –> 2000-2012	4.5482001	24032.6569
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate_star	2317	2.7384695	11255.6490	20.449118	1982-1999 –> 2000-2012	4.6895219	24338.3683
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2317	2.7269514	11238.1171	21.350081	1982-1999 –> 2000-2012	4.6654113	24282.2891
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2317	2.7373185	11253.7009	20.385504	1982-1999 –> 2000-2012	4.6897567	24340.8662
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2317	2.7373185	11253.7009	20.385504	1982-1999 –> 2000-2012	4.6897567	24340.8662
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1264	3.1358059	6490.2930	31.989646	2000-2012 –> 2013-2019	5.8629052	17728.6613
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1264	3.1693826	6517.2176	30.950746	2000-2012 –> 2013-2019	5.8984191	17758.8767
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	1264	3.1488202	6498.7630	29.448400	2000-2012 –> 2013-2019	5.8762396	17735.6753
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1264	3.1390093	6492.8741	31.279189	2000-2012 –> 2013-2019	5.8653527	17729.9579
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + oxygen + silicate + phosphate	1264	3.1768073	6521.1329	29.025171	2000-2012 –> 2013-2019	5.9117926	17770.8822
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + oxygen + silicate + phosphate + phosphate_star	1264	3.1768073	6521.1329	29.025171	2000-2012 –> 2013-2019	5.9117926	17770.8822
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1264	3.1768073	6521.1329	29.025171	2000-2012 –> 2013-2019	5.9117926	17770.8822
Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1264	3.1768073	6521.1329	29.025171	2000-2012 –> 2013-2019	5.9117926	17770.8822
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1264	3.1128492	6469.7178	31.766441	2000-2012 –> 2013-2019	5.8536894	17729.3767
Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1264	3.0665742	6433.8549	28.861392	2000-2012 –> 2013-2019	5.7071919	17522.8898
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	2907	2.7487099	14140.4282	28.492785	1982-1999 –> 2000-2012	4.8701028	31563.9400
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	2907	2.7484328	14139.8421	28.396374	1982-1999 –> 2000-2012	4.9240749	31765.8662
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2907	2.7457460	14136.1557	28.208152	1982-1999 –> 2000-2012	4.8664196	31558.9474
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2907	2.7856872	14220.1201	34.100919	1982-1999 –> 2000-2012	4.9269749	31720.4944
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + phosphate_star	2907	2.7674113	14177.8510	31.750508	1982-1999 –> 2000-2012	4.8898936	31603.4801
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	2907	2.7621671	14168.8231	31.138313	1982-1999 –> 2000-2012	4.8840444	31594.1657
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate	2907	2.7499312	14141.0108	28.547833	1982-1999 –> 2000-2012	4.9295241	31779.5857
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	2907	2.7472864	14137.4165	28.371289	1982-1999 –> 2000-2012	4.8684199	31559.9473
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate + silicate	2907	2.7476621	14138.2115	28.325089	1982-1999 –> 2000-2012	4.9235034	31764.9698
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2907	2.7445406	14133.6026	28.109511	1982-1999 –> 2000-2012	4.8649180	31555.2745
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + phosphate_star	1542	3.3165597	8085.5004	32.079445	2000-2012 –> 2013-2019	6.0652696	22225.9286
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate	1542	3.3046795	8074.4335	31.424170	2000-2012 –> 2013-2019	6.0531124	22214.2756
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1542	3.2946985	8067.1049	31.554855	2000-2012 –> 2013-2019	6.0404446	22203.2606
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1542	3.2669990	8039.0671	37.333823	2000-2012 –> 2013-2019	6.0608699	22274.2424
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1542	3.2637446	8037.9935	37.426960	2000-2012 –> 2013-2019	6.0494318	22258.1136
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	1542	3.2965108	8066.8008	32.540164	2000-2012 –> 2013-2019	6.0586779	22235.6239
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate	1542	3.3252514	8091.5720	31.716600	2000-2012 –> 2013-2019	6.0751825	22232.5829
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate + phosphate_star	1542	3.3151344	8084.1748	31.858968	2000-2012 –> 2013-2019	6.0624208	22221.5913
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate + silicate	1542	3.3028816	8072.7552	31.234941	2000-2012 –> 2013-2019	6.0505437	22210.9666
Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1542	3.2939987	8066.4498	31.381712	2000-2012 –> 2013-2019	6.0385393	22200.0524
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2467	2.2624239	11041.3418	8.237248	1982-1999 –> 2000-2012	4.1845877	25738.2975
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	2467	2.1936153	10890.9515	8.036190	1982-1999 –> 2000-2012	4.1649943	25769.0539
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2467	2.2115502	10931.1275	8.468880	1982-1999 –> 2000-2012	4.1022689	25513.2034
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2467	2.2668883	11053.0683	8.062293	1982-1999 –> 2000-2012	4.2018862	25799.1794
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	2467	2.2777752	11074.7074	8.288880	1982-1999 –> 2000-2012	4.2106641	25811.0912
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2467	2.1886299	10879.7253	7.878228	1982-1999 –> 2000-2012	4.0642895	25405.1370
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate_star	2467	2.2787563	11076.8322	8.277324	1982-1999 –> 2000-2012	4.2137568	25820.9529
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	2467	2.2685749	11056.7379	8.088917	1982-1999 –> 2000-2012	4.2034596	25802.4346
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2467	2.2789172	11077.1806	8.289996	1982-1999 –> 2000-2012	4.2138321	25820.9878
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2467	2.2789172	11077.1806	8.289996	1982-1999 –> 2000-2012	4.2138321	25820.9878
Indo-Pacific	(27.95,28.05]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1354	2.5384577	6377.1411	7.728054	2000-2012 –> 2013-2019	4.8008817	17418.4829
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + phosphate_star	1354	2.4060015	6232.0181	8.104133	2000-2012 –> 2013-2019	4.6173063	17160.5981
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1354	2.4007452	6228.0956	8.259744	2000-2012 –> 2013-2019	4.5943605	17119.0470
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate + phosphate_star	1354	2.4939482	6329.2376	8.352020	2000-2012 –> 2013-2019	4.7451070	17345.9505
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1354	2.4779038	6313.7598	8.329809	2000-2012 –> 2013-2019	4.6894540	17244.8873
Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1354	2.5167285	6355.8608	8.981549	2000-2012 –> 2013-2019	4.8166120	17480.2273
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1354	2.5359986	6376.5164	7.886317	2000-2012 –> 2013-2019	4.8028869	17429.5848
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate + phosphate_star	1354	2.4648617	6297.4690	8.721893	2000-2012 –> 2013-2019	4.7165003	17315.2334
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1354	2.4266912	6257.2052	8.523746	2000-2012 –> 2013-2019	4.6153211	17136.9304
Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1354	2.5387308	6379.4324	7.893914	2000-2012 –> 2013-2019	4.8073057	17436.1703
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1718	1.8848420	7065.3607	9.810959	1982-1999 –> 2000-2012	3.5844089	17034.4465
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	1718	1.9453032	7175.8486	9.430189	1982-1999 –> 2000-2012	3.5919535	16985.3663
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	1718	1.9503440	7182.7407	8.816710	1982-1999 –> 2000-2012	3.5709134	16908.7065
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1718	1.8450332	6994.0133	9.467590	1982-1999 –> 2000-2012	3.4414783	16645.3685
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	1718	1.9538428	7190.8991	8.874628	1982-1999 –> 2000-2012	3.5863843	16956.4621
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + silicate + phosphate	1718	1.9539957	7189.1680	8.935869	1982-1999 –> 2000-2012	3.5950802	16979.3910
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1718	1.9539957	7189.1680	8.935869	1982-1999 –> 2000-2012	3.5950802	16979.3910
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	1718	1.8612616	7024.1034	10.244079	1982-1999 –> 2000-2012	3.4707315	16716.9636
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1718	1.8032691	6915.3424	9.697645	1982-1999 –> 2000-2012	3.4298781	16662.3098
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	1718	1.8584907	7018.9844	10.244915	1982-1999 –> 2000-2012	3.4634280	16697.4390
Indo-Pacific	(28.05,28.1]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	966	2.1066397	4192.9110	9.987464	2000-2012 –> 2013-2019	3.9914816	11258.2717
Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	966	2.0390556	4131.9137	9.747515	2000-2012 –> 2013-2019	3.8840888	11125.9270
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	966	2.0868098	4176.6389	10.548800	2000-2012 –> 2013-2019	3.9480714	11200.7423
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	966	2.1188554	4204.0818	10.037184	2000-2012 –> 2013-2019	4.0138656	11287.9289
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	966	2.0001288	4094.6740	9.111786	2000-2012 –> 2013-2019	3.8033978	11010.0164
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	966	2.0835440	4173.6130	10.558303	2000-2012 –> 2013-2019	3.9420347	11192.5974
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + silicate + phosphate	966	2.1186866	4203.9279	10.028459	2000-2012 –> 2013-2019	4.0148349	11289.8379
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + silicate + phosphate + phosphate_star	966	2.1186866	4203.9279	10.028459	2000-2012 –> 2013-2019	4.0148349	11289.8379
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + oxygen + silicate + phosphate_star	966	2.1186866	4203.9279	10.028459	2000-2012 –> 2013-2019	4.0148349	11289.8379
Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	966	2.1186866	4203.9279	10.028459	2000-2012 –> 2013-2019	4.0148349	11289.8379
Indo-Pacific	(28.1, Inf]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	14627	1.6310156	55832.7692	18.423930	1982-1999 –> 2000-2012	3.0306685	127227.2398
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + nitrate + silicate + phosphate_star	14627	1.4377139	52142.4183	8.775636	1982-1999 –> 2000-2012	2.6704554	118372.4597
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	14627	1.5209342	53790.5541	8.043162	1982-1999 –> 2000-2012	2.9137573	124988.0837
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	14627	1.4320006	52025.9353	13.806990	1982-1999 –> 2000-2012	2.7088012	119684.1812
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	14627	1.3378772	50039.0036	16.225048	1982-1999 –> 2000-2012	2.5090135	114186.0580
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	14627	1.3133686	49498.1312	9.366747	1982-1999 –> 2000-2012	2.4634246	112906.4588
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	14627	1.3692488	50717.0570	13.004762	1982-1999 –> 2000-2012	2.4951048	113260.4541
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	14627	1.3940533	51242.2624	17.034744	1982-1999 –> 2000-2012	2.6340769	117713.8450
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	14627	1.5669226	54659.9964	17.476131	1982-1999 –> 2000-2012	2.8961915	123956.0907
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	14627	1.3591254	50499.9672	12.907049	1982-1999 –> 2000-2012	2.4770940	112757.4410
Indo-Pacific	(28.1, Inf]	cstar_tref ~ oxygen + nitrate + silicate + phosphate_star	7804	1.6277929	29763.4008	8.895830	2000-2012 –> 2013-2019	3.0655068	81905.8190
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	7804	1.6305548	29791.8606	9.567306	2000-2012 –> 2013-2019	3.1514890	83582.4147
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	7804	1.5693631	29192.8476	10.689506	2000-2012 –> 2013-2019	3.0013637	81218.7829
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	7804	1.4923380	28409.3615	12.644005	2000-2012 –> 2013-2019	2.8302151	78448.3652
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + nitrate + silicate + phosphate_star	7804	1.4569278	28034.5504	8.140875	2000-2012 –> 2013-2019	2.7702964	77532.6816
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + oxygen + silicate + phosphate_star	7804	1.7050926	30487.5244	9.446823	2000-2012 –> 2013-2019	3.3123180	85890.4491
Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	7804	1.7050926	30487.5244	9.446823	2000-2012 –> 2013-2019	3.3123180	85890.4491
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	7804	1.5858456	29357.9189	10.996188	2000-2012 –> 2013-2019	2.9550945	80074.9759
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	7804	1.5521124	29022.3323	13.774789	2000-2012 –> 2013-2019	2.9461657	80264.5947
Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + oxygen + nitrate + silicate + phosphate_star	7804	1.5743591	29244.4567	10.872611	2000-2012 –> 2013-2019	2.9334846	79744.4239

5.3.2 per fitting unit

lm_best %>%
  group_by(basin, gamma_slab, eras) %>% 
  summarise(rmse_sum_mean = mean(rmse_sum),
            ais_sum_mean = mean(aic_sum)) %>% 
  ungroup() %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

basin	gamma_slab	eras	rmse_sum_mean	ais_sum_mean
Atlantic	(-Inf,26]	1982-1999 –> 2000-2012	3.0837970	1379.225
Atlantic	(-Inf,26]	2000-2012 –> 2013-2019	3.0521095	860.973
Atlantic	(26,26.5]	1982-1999 –> 2000-2012	8.2190449	14575.327
Atlantic	(26,26.5]	2000-2012 –> 2013-2019	8.1208007	9130.223
Atlantic	(26.5,26.75]	1982-1999 –> 2000-2012	6.4909791	17090.244
Atlantic	(26.5,26.75]	2000-2012 –> 2013-2019	6.7946199	10853.837
Atlantic	(26.75,27]	1982-1999 –> 2000-2012	3.9620183	23078.717
Atlantic	(26.75,27]	2000-2012 –> 2013-2019	4.8438931	16642.543
Atlantic	(27,27.25]	1982-1999 –> 2000-2012	4.1459356	19857.982
Atlantic	(27,27.25]	2000-2012 –> 2013-2019	4.4535113	13996.296
Atlantic	(27.25,27.5]	1982-1999 –> 2000-2012	4.7974265	22250.380
Atlantic	(27.25,27.5]	2000-2012 –> 2013-2019	5.7559144	15302.893
Atlantic	(27.5,27.75]	1982-1999 –> 2000-2012	5.3035196	31075.927
Atlantic	(27.5,27.75]	2000-2012 –> 2013-2019	5.9646267	21538.850
Atlantic	(27.75,27.85]	1982-1999 –> 2000-2012	3.9255483	9848.567
Atlantic	(27.75,27.85]	2000-2012 –> 2013-2019	4.1250069	6618.097
Atlantic	(27.85,27.95]	1982-1999 –> 2000-2012	6.3551279	11872.263
Atlantic	(27.85,27.95]	2000-2012 –> 2013-2019	7.1431418	8351.391
Atlantic	(27.95,28.05]	1982-1999 –> 2000-2012	8.4722558	16467.398
Atlantic	(27.95,28.05]	2000-2012 –> 2013-2019	8.2666200	10670.201
Atlantic	(28.05,28.1]	1982-1999 –> 2000-2012	2.0618482	5405.536
Atlantic	(28.05,28.1]	2000-2012 –> 2013-2019	2.2973492	3861.990
Atlantic	(28.1,28.15]	1982-1999 –> 2000-2012	1.5221428	5031.389
Atlantic	(28.1,28.15]	2000-2012 –> 2013-2019	1.8170837	3735.170
Atlantic	(28.15,28.2]	1982-1999 –> 2000-2012	1.1419192	6452.729
Atlantic	(28.15,28.2]	2000-2012 –> 2013-2019	1.4215811	4779.518
Atlantic	(28.2, Inf]	1982-1999 –> 2000-2012	0.8519213	6909.825
Atlantic	(28.2, Inf]	2000-2012 –> 2013-2019	0.9282062	5308.216
Indo-Pacific	(-Inf,26]	1982-1999 –> 2000-2012	14.5248230	84961.210
Indo-Pacific	(-Inf,26]	2000-2012 –> 2013-2019	13.9436181	54552.131
Indo-Pacific	(26,26.5]	1982-1999 –> 2000-2012	9.3931224	78381.631
Indo-Pacific	(26,26.5]	2000-2012 –> 2013-2019	9.5895473	50500.817
Indo-Pacific	(26.5,26.75]	1982-1999 –> 2000-2012	8.0278657	60829.345
Indo-Pacific	(26.5,26.75]	2000-2012 –> 2013-2019	8.4242215	39793.222
Indo-Pacific	(26.75,27]	1982-1999 –> 2000-2012	8.4416907	73334.085
Indo-Pacific	(26.75,27]	2000-2012 –> 2013-2019	9.3522596	48490.299
Indo-Pacific	(27,27.25]	1982-1999 –> 2000-2012	7.9784805	85082.870
Indo-Pacific	(27,27.25]	2000-2012 –> 2013-2019	9.4841606	58649.641
Indo-Pacific	(27.25,27.5]	1982-1999 –> 2000-2012	6.6444230	71528.666
Indo-Pacific	(27.25,27.5]	2000-2012 –> 2013-2019	7.8115133	49460.217
Indo-Pacific	(27.5,27.75]	1982-1999 –> 2000-2012	5.7361857	67730.577
Indo-Pacific	(27.5,27.75]	2000-2012 –> 2013-2019	7.4541430	48315.934
Indo-Pacific	(27.75,27.85]	1982-1999 –> 2000-2012	4.6634380	24276.087
Indo-Pacific	(27.75,27.85]	2000-2012 –> 2013-2019	5.8710968	17728.897
Indo-Pacific	(27.85,27.95]	1982-1999 –> 2000-2012	4.8947876	31646.667
Indo-Pacific	(27.85,27.95]	2000-2012 –> 2013-2019	6.0554492	22227.664
Indo-Pacific	(27.95,28.05]	1982-1999 –> 2000-2012	4.1773571	25730.133
Indo-Pacific	(27.95,28.05]	2000-2012 –> 2013-2019	4.7205736	17308.711
Indo-Pacific	(28.05,28.1]	1982-1999 –> 2000-2012	3.5329337	16856.584
Indo-Pacific	(28.05,28.1]	2000-2012 –> 2013-2019	3.9642279	11223.484
Indo-Pacific	(28.1, Inf]	1982-1999 –> 2000-2012	2.6798588	118505.231
Indo-Pacific	(28.1, Inf]	2000-2012 –> 2013-2019	3.0278252	81455.296

5.4 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)

5.5 Plot selected model residuals

# plot model diagnostics, if activated
if (params_local$plot_all_figures == "y") {
  # mutate predictors column
  lm_best_plot <- lm_best_target %>%
    select(basin, gamma_slab, model, eras, era) %>%
    mutate(
      predictors = str_remove(model, paste(params_local$MLR_target, "~ ")),
      predictors = str_replace_all(predictors, "\\+ ", "")
    )
  
  # loop across all basins, era, gamma slabs, and MLRs
  # fit all MLR models
  for (i_basin in unique(GLODAP$basin)) {
    for (i_era in unique(GLODAP$era)) {
      #i_basin <- unique(GLODAP$basin)[1]
      #i_era   <- unique(GLODAP$era)[2]
      print(i_basin)
      print(i_era)
      
      GLODAP_basin_era <- GLODAP %>%
        filter(basin == i_basin, era == i_era)
      
      for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
        #i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
        print(i_gamma_slab)
        
        GLODAP_basin_era_slab <- GLODAP_basin_era %>%
          filter(gamma_slab == i_gamma_slab)
        
        lm_best_basin_era_slab <- lm_best_plot %>%
          filter(basin == i_basin, era == i_era, gamma_slab == i_gamma_slab)
        
        for (i_eras in unique(lm_best_basin_era_slab$eras)) {
          #i_eras <- unique(lm_best_basin_era_slab$eras)[1]
          print(i_eras)
          
          lm_best_basin_era_slab_eras <- lm_best_basin_era_slab %>%
            filter(eras == i_eras)
          
          for (i_predictors in unique(lm_best_basin_era_slab_eras$predictors)) {
            #i_predictors <- unique(lm_best_basin_era_slab$predictors)[1]
            print(i_predictors)
            # extract one model definition
            i_lm <- lm_all %>%
              filter(predictors == i_predictors) %>%
              select(lm_coeff) %>%
              pull()
            
             # fit model
          if (params_local$MLR_type == "rlm") {
            i_lm_fit <- MASS::rlm(as.formula(i_lm),
                                  data = GLODAP_basin_era_slab)
          }
          
          if (params_local$MLR_type == "lm") {
            i_lm_fit <- lm(as.formula(i_lm),
                           data = GLODAP_basin_era_slab)
          }
            
            # plot model diagnostics vs predictors
            
            p_model_predictors <- ggnostic(
              i_lm_fit,
              columnsY = c(params_local$MLR_target, ".fitted", ".resid"),
              title = paste(
                "era:",
                i_era,
                "| eras:",
                i_eras,
                "| basin:",
                i_basin,
                "| gamma slab:",
                i_gamma_slab,
                "| predictors:",
                i_predictors
              )
            )
            
            ggsave(
              plot = p_model_predictors,
              path = paste(path_version_figures, "eMLR_diagnostics/", sep = ""),
              filename = paste(
                "MLR_residuals",
                i_era,
                i_eras,
                i_basin,
                i_gamma_slab,
                i_predictors,
                "predictors.png",
                sep = "_"
              ),
              width = 14,
              height = 8
            )

            rm(p_model_predictors)
            
            
            # plot model diagnostics vs location
            
            GLODAP_basin_era_slab <- GLODAP_basin_era_slab %>%
              mutate(fitted = i_lm_fit$fitted.values,
                     residuals = i_lm_fit$residuals)
            
            GLODAP_basin_era_slab_long <- GLODAP_basin_era_slab %>% 
              pivot_longer(cols = c(params_local$MLR_target , fitted, residuals),
                           names_to = "estimate",
                           values_to = "value"
              ) %>% 
              pivot_longer(cols = c(lat, lon, depth),
                           names_to = "coordinate_type",
                           values_to = "coordinate_value"
              )

             p_model_coordinate <- GLODAP_basin_era_slab_long %>%
              ggplot(aes(coordinate_value, value)) +
              geom_bin2d() +
              scale_fill_viridis_c() +
              labs(
                title = paste(
                  "era:",
                  i_era,
                  "| eras:",
                  i_eras,
                  "| basin:",
                  i_basin,
                  "| gamma slab:",
                  i_gamma_slab,
                  "| predictors:",
                  i_predictors
                )
              ) +
              facet_grid(estimate~coordinate_type,
                         scales = "free")

            ggsave(
              plot = p_model_coordinate,
              path = paste(path_version_figures, "eMLR_diagnostics", sep = ""),
              filename = paste(
                "Location_MLR_residuals",
                i_era,
                i_eras,
                i_basin,
                i_gamma_slab,
                i_predictors,
                "predictors.png",
                sep = "_"
              ),
              width = 14,
              height = 8
            )

            rm(p_model_coordinate)
            
          }
          
        }
        
      }
    }
  }
  
  rm(
    lm_best_plot,
    lm_best_basin_era_slab,
    i_rmse,
    GLODAP_basin_era,
    GLODAP_basin_era_slab,
    i_lm,
    lm_all_fitted,
    i_basin,
    i_era,
    i_gamma_slab,
    i_predictors,
    lm_all,
    i_aic,
    i_n_predictors,
    i_resid_max
  )
  
}

Individual residual plots of the MLR models for each basin, era, eras and neutral density (gamma) slab are available at:

/nfs/kryo/work/jenmueller/emlr_cant/model/v_XXX/figures/eMLR_diagnostics/

5.6 Cant coeffcients

A data frame of coefficient offsets is prepared to facilitate the direct mapping of Cant.

# pivot long format
lm_best_long <- lm_best_target %>%
  pivot_longer(cols = starts_with("coeff_"),
               names_to = "term",
               values_to = "estimate",
               names_prefix = "coeff_")

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

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

5.7 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 3 - 9).

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
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
02b976d	Donghe-Zhu	2021-02-24
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

6.1.2 Best models

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

Past versions of eMLR_predictor_model_quality_best-1.png

Version	Author	Date
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
e2ffc14	Donghe-Zhu	2021-02-05
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

6.2 RMSE correlation between eras

RMSE was plotted to compare the agreement for one model applied to two adjacent eras (ie check whether the same predictor combination performs equal in both eras).

6.2.1 All models

# find max rmse to scale axis
max_rmse <-
  max(c(lm_all_fitted_wide_eras$rmse,
        lm_all_fitted_wide_eras$rmse_sum - lm_all_fitted_wide_eras$rmse))

lm_all_fitted_wide_eras %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0,max_rmse),
              ylim = c(0,max_rmse)) +
  facet_grid(eras ~ basin)

Past versions of rmse_correlation_across_eras_all_models-1.png

Version	Author	Date
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
02b976d	Donghe-Zhu	2021-02-24
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

rm(max_rmse)

6.2.2 Best models

# find max rmse to scale axis
max_rmse <-
  max(c(lm_best$rmse,
        lm_best$rmse_sum - lm_best$rmse))

lm_best %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0,max_rmse),
              ylim = c(0,max_rmse)) +
  facet_grid(eras ~ basin)

Past versions of rmse_correlation_across_eras_best_models-1.png

Version	Author	Date
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
e2ffc14	Donghe-Zhu	2021-02-05
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

rm(max_rmse)

6.3 Predictor counts

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

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

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

	aou	nitrate	oxygen	phosphate	phosphate_star	sal	silicate	temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26]	7	5	2	4	9	8	7	2
(26,26.5]	5	6	5	4	6	1	8	9
(26.5,26.75]	7	2	3	7	6	2	10	7
(26.75,27]	7	2	3	7	6	2	10	7
(27,27.25]	7	5	2	4	9	6	10	3
(27.25,27.5]	8	7	2	3	6	5	9	4
(27.5,27.75]	8	6	2	4	5	6	8	4
(27.75,27.85]	8	4	2	6	7	8	7	1
(27.85,27.95]	9	2	1	8	8	2	6	6
(27.95,28.05]	5	7	5	3	10	4	6	5
(28.05,28.1]	9	2	1	8	8	3	6	5
(28.1,28.15]	7	2	3	8	7	3	8	6
(28.15,28.2]	7	10	3	0	7	3	7	6
(28.2, Inf]	6	10	4	0	7	7	7	2
total	100.00	70.00	38.00	66.00	101.00	60.00	109.00	67.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26]	7	5	2	4	9	8	7	2
(26,26.5]	6	8	4	2	6	1	6	9
(26.5,26.75]	7	2	2	7	7	2	10	7
(26.75,27]	8	3	2	6	7	3	10	6
(27,27.25]	5	3	4	5	7	9	10	1
(27.25,27.5]	7	8	3	2	6	5	10	4
(27.5,27.75]	6	4	4	6	5	10	7	0
(27.75,27.85]	6	5	3	3	8	10	8	0
(27.85,27.95]	10	2	0	8	8	3	6	5
(27.95,28.05]	6	6	4	3	10	4	6	6
(28.05,28.1]	8	2	2	7	9	3	7	5
(28.1,28.15]	9	2	1	8	8	3	6	5
(28.15,28.2]	6	10	4	0	7	4	7	6
(28.2, Inf]	5	10	4	0	6	9	6	1
total	96.00	70.00	39.00	61.00	103.00	74.00	106.00	57.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26]	5	2	4	6	8	2	9	8
(26,26.5]	6	2	4	6	7	1	10	8
(26.5,26.75]	7	5	2	5	9	2	7	7
(26.75,27]	9	2	1	8	8	2	6	6
(27,27.25]	7	4	2	6	9	2	7	7
(27.25,27.5]	5	4	4	5	8	7	10	3
(27.5,27.75]	4	3	4	5	8	9	10	1
(27.75,27.85]	7	2	2	6	9	1	9	8
(27.85,27.95]	4	9	4	1	7	0	6	10
(27.95,28.05]	7	3	2	5	9	2	10	7
(28.05,28.1]	6	4	4	5	8	6	10	3
(28.1, Inf]	6	6	3	4	9	4	10	4
total	73.00	46.00	36.00	62.00	99.00	38.00	104.00	72.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26]	5	2	4	6	8	2	9	8
(26,26.5]	6	2	3	6	8	1	10	8
(26.5,26.75]	6	6	2	4	9	1	7	8
(26.75,27]	8	3	2	7	9	2	6	6
(27,27.25]	6	3	3	6	9	2	9	7
(27.25,27.5]	5	5	5	3	9	6	10	3
(27.5,27.75]	5	3	3	6	8	9	9	1
(27.75,27.85]	4	3	4	6	8	8	9	2
(27.85,27.95]	5	8	4	2	7	0	6	10
(27.95,28.05]	8	5	2	5	10	5	7	4
(28.05,28.1]	5	2	4	7	7	1	10	8
(28.1, Inf]	5	5	4	4	9	6	10	3
total	68.00	47.00	40.00	62.00	101.00	43.00	102.00	68.00

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
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
02b976d	Donghe-Zhu	2021-02-24
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

lm_best %>% 
  ggplot(aes(rmse, aic, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras~basin)

Past versions of aic_vs_rmse_selected_models-1.png

Version	Author	Date
adbc9bc	Donghe-Zhu	2021-02-27
5937141	Donghe-Zhu	2021-02-27
4414bbf	Donghe-Zhu	2021-02-27
a265efb	Donghe-Zhu	2021-02-27
19edd1e	Donghe-Zhu	2021-02-27
f20483f	Donghe-Zhu	2021-02-26
6a2c7b3	Donghe-Zhu	2021-02-25
354c224	Donghe-Zhu	2021-02-24
1a0a88a	Donghe-Zhu	2021-02-24
57f701e	Donghe-Zhu	2021-02-24
06f3149	Donghe-Zhu	2021-02-16
401eab3	Donghe-Zhu	2021-02-15
e3bba84	Donghe-Zhu	2021-02-15
5dce4b1	Donghe-Zhu	2021-02-15
4469a0c	Donghe-Zhu	2021-02-13
5ae6a69	Donghe-Zhu	2021-02-10
05385dc	Donghe-Zhu	2021-02-10
f791ae4	Donghe-Zhu	2021-02-09
f71ae34	Donghe-Zhu	2021-02-09
c011832	Donghe-Zhu	2021-02-09
a145fa7	Donghe-Zhu	2021-02-09
c344e42	Donghe-Zhu	2021-02-08
2f095d7	Donghe-Zhu	2021-02-07
1fad5f1	Donghe-Zhu	2021-02-07
ca03c39	Donghe-Zhu	2021-02-07
e2ffc14	Donghe-Zhu	2021-02-05
cd7c52c	Donghe-Zhu	2021-02-04
bcf84f4	Donghe-Zhu	2021-02-02
a518739	Donghe-Zhu	2021-02-01
61666de	Donghe-Zhu	2021-01-31
865b582	Donghe-Zhu	2021-01-31
3e68089	Donghe-Zhu	2021-01-31
ecf335c	Donghe-Zhu	2021-01-31
a618965	Donghe-Zhu	2021-01-31
59e006e	Donghe-Zhu	2021-01-31
a1c8f87	Donghe-Zhu	2021-01-31
ae5c18f	Donghe-Zhu	2021-01-31
b50fe52	Donghe-Zhu	2021-01-31
ac99ae5	jens-daniel-mueller	2021-01-29
b5bdcaf	Donghe-Zhu	2021-01-29
442010d	Donghe-Zhu	2021-01-29
372adf5	Donghe-Zhu	2021-01-29
af8788e	Donghe-Zhu	2021-01-29
21c91c9	Donghe-Zhu	2021-01-29
eded038	Donghe-Zhu	2021-01-29
541d4dd	Donghe-Zhu	2021-01-29
6a75576	Donghe-Zhu	2021-01-28
16fba40	Donghe-Zhu	2021-01-28
12bc567	Donghe-Zhu	2021-01-27
ceed31b	Donghe-Zhu	2021-01-27
342402d	Donghe-Zhu	2021-01-27
5bad5c2	Donghe-Zhu	2021-01-27
61efb56	Donghe-Zhu	2021-01-25
48f638e	Donghe-Zhu	2021-01-25
c1cec47	Donghe-Zhu	2021-01-25
05ffb0c	Donghe-Zhu	2021-01-25
8b97165	Donghe-Zhu	2021-01-25
c569946	Donghe-Zhu	2021-01-24
a2f0d56	Donghe-Zhu	2021-01-23
28509fc	Donghe-Zhu	2021-01-23
4c28e4a	Donghe-Zhu	2021-01-22
24cc264	jens-daniel-mueller	2021-01-22
7891955	Donghe-Zhu	2021-01-21
d4cf1cb	Donghe-Zhu	2021-01-21
1f3e5b6	jens-daniel-mueller	2021-01-20
0e7bdf1	jens-daniel-mueller	2021-01-15
4571843	jens-daniel-mueller	2021-01-14
b3564aa	jens-daniel-mueller	2021-01-14
8d032c3	jens-daniel-mueller	2021-01-14
17dee1d	jens-daniel-mueller	2021-01-13
7cdea0c	jens-daniel-mueller	2021-01-06
fa85b93	jens-daniel-mueller	2021-01-06
e5cb81a	Donghe-Zhu	2021-01-05
a499f10	Donghe-Zhu	2021-01-05
fb8a752	Donghe-Zhu	2020-12-23
8fae0b2	Donghe-Zhu	2020-12-21
c8b76b3	jens-daniel-mueller	2020-12-19

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_0.7.5      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.3   
[21] tidyverse_1.3.0  workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] fs_1.5.0                 webshot_0.5.2            RColorBrewer_1.1-2      
 [4] httr_1.4.2               rprojroot_2.0.2          tools_4.0.3             
 [7] backports_1.1.10         R6_2.5.0                 nortest_1.0-4           
[10] DBI_1.1.0                colorspace_2.0-0         withr_2.3.0             
[13] gridExtra_2.3            tidyselect_1.1.0         curl_4.3                
[16] compiler_4.0.3           git2r_0.27.1             cli_2.2.0               
[19] rvest_0.3.6              xml2_1.3.2               sass_0.2.0              
[22] labeling_0.4.2           scales_1.1.1             checkmate_2.0.0         
[25] goftest_1.2-2            digest_0.6.27            foreign_0.8-80          
[28] rmarkdown_2.5            rio_0.5.16               pkgconfig_2.0.3         
[31] htmltools_0.5.0          highr_0.8                dbplyr_1.4.4            
[34] rlang_0.4.10             readxl_1.3.1             rstudioapi_0.13         
[37] farver_2.0.3             generics_0.1.0           jsonlite_1.7.2          
[40] zip_2.1.1                car_3.0-10               magrittr_2.0.1          
[43] Matrix_1.2-18            Rcpp_1.0.5               munsell_0.5.0           
[46] fansi_0.4.1              abind_1.4-5              lifecycle_0.2.0         
[49] stringi_1.5.3            whisker_0.4              yaml_2.2.1              
[52] carData_3.0-4            plyr_1.8.6               grid_4.0.3              
[55] blob_1.2.1               parallel_4.0.3           promises_1.1.1          
[58] crayon_1.3.4             lattice_0.20-41          haven_2.3.1             
[61] hms_0.5.3                pillar_1.4.7             reprex_0.3.0            
[64] glue_1.4.2               evaluate_0.14            RcppArmadillo_0.10.1.2.2
[67] data.table_1.13.6        modelr_0.1.8             vctrs_0.3.6             
[70] httpuv_1.5.4             cellranger_1.1.0         gtable_0.3.0            
[73] reshape_0.8.8            assertthat_0.2.1         xfun_0.20               
[76] openxlsx_4.2.3           RcppEigen_0.3.3.9.1      later_1.1.0.1           
[79] viridisLite_0.3.0        ellipsis_0.3.1           here_1.0.1