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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, 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, "oxygen") &
      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, "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()

lm_rm <- lm_rm_ph %>%
  select(-lm_coeff_filter) %>%
  unique()

lm_all <- anti_join(lm_all, lm_rm)

# remove temp sal predictor combination
lm_all <- lm_all %>%
# filter(!(
#   str_detect(lm_coeff, "temp") &
#     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")
# )) %>%
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 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
)

# lm_full <- lm(paste(
#   params_local$MLR_target,
#   paste(params_local$MLR_predictors, collapse = " + "),
#   sep = " ~ "
# ),
# data = GLODAP_basin_era_slab)
# 
# lm_full <-
#   loess(
#     cstar_tref ~ sal + temp + aou + phosphate,
#     span = 0.1,
#     degree = 1,
#     data = GLODAP_basin_era_slab
#   )

3 Apply predictor threshold

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

Minimum: 2
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:

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:

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, n_predictors, 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	n_predictors	model	nr_obs	rmse	aic	resid_max	eras	rmse_sum	aic_sum
Atlantic	(-Inf,26]	2	cstar_tref ~ sal + aou	158	1.9502753	667.4633	7.221775	1982-1999 –> 2000-2012	4.052696	1574.8669
Atlantic	(-Inf,26]	3	cstar_tref ~ sal + aou + phosphate	158	1.9223248	664.9017	6.746550	1982-1999 –> 2000-2012	3.989270	1567.2259
Atlantic	(-Inf,26]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	158	1.0492038	475.5626	4.357844	1982-1999 –> 2000-2012	2.385552	1198.4564
Atlantic	(-Inf,26]	3	cstar_tref ~ sal + aou + phosphate_star	158	1.7232695	630.3592	5.488825	1982-1999 –> 2000-2012	3.603284	1493.2499
Atlantic	(-Inf,26]	3	cstar_tref ~ sal + aou + silicate	158	1.9454291	668.6771	7.421781	1982-1999 –> 2000-2012	4.045497	1577.6150
Atlantic	(-Inf,26]	4	cstar_tref ~ sal + aou + silicate + phosphate	158	1.8736520	658.7976	7.056359	1982-1999 –> 2000-2012	3.879202	1550.5780
Atlantic	(-Inf,26]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	158	1.0480832	477.2249	4.299021	1982-1999 –> 2000-2012	2.383776	1201.9145
Atlantic	(-Inf,26]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	158	1.5933338	607.5864	5.896294	1982-1999 –> 2000-2012	3.315100	1435.8988
Atlantic	(-Inf,26]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	158	1.4654213	581.1417	7.417048	1982-1999 –> 2000-2012	3.127691	1394.8248
Atlantic	(-Inf,26]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	158	1.4545749	580.7941	7.074044	1982-1999 –> 2000-2012	3.116063	1396.2815
Atlantic	(-Inf,26]	2	cstar_tref ~ sal + aou	72	1.8545661	301.2689	5.145995	2000-2012 –> 2013-2019	3.804842	968.7321
Atlantic	(-Inf,26]	3	cstar_tref ~ sal + aou + phosphate	72	1.8358840	301.8109	4.689169	2000-2012 –> 2013-2019	3.758209	966.7126
Atlantic	(-Inf,26]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	72	1.2725075	251.0296	3.658367	2000-2012 –> 2013-2019	2.321711	726.5922
Atlantic	(-Inf,26]	3	cstar_tref ~ sal + aou + phosphate_star	72	1.7335391	293.5509	3.896954	2000-2012 –> 2013-2019	3.456809	923.9101
Atlantic	(-Inf,26]	3	cstar_tref ~ sal + aou + silicate	72	1.8477634	302.7397	4.871193	2000-2012 –> 2013-2019	3.793192	971.4167
Atlantic	(-Inf,26]	4	cstar_tref ~ sal + aou + silicate + phosphate	72	1.8344756	303.7004	4.732561	2000-2012 –> 2013-2019	3.708128	962.4980
Atlantic	(-Inf,26]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	72	1.1936365	243.8158	3.237974	2000-2012 –> 2013-2019	2.241720	721.0407
Atlantic	(-Inf,26]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	72	1.6918467	292.0453	4.133504	2000-2012 –> 2013-2019	3.285181	899.6317
Atlantic	(-Inf,26]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	72	1.5761474	281.8448	5.713265	2000-2012 –> 2013-2019	3.041569	862.9865
Atlantic	(-Inf,26]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	72	1.5044066	277.1365	5.003414	2000-2012 –> 2013-2019	2.958982	857.9306
Atlantic	(26,26.5]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1046	4.5602677	6154.7812	12.793756	1982-1999 –> 2000-2012	8.993582	15036.4433
Atlantic	(26,26.5]	4	cstar_tref ~ sal + aou + silicate + phosphate	1046	4.9993120	6347.0757	14.797906	1982-1999 –> 2000-2012	9.874105	15518.2748
Atlantic	(26,26.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1046	3.5518213	5633.9468	13.477555	1982-1999 –> 2000-2012	6.998566	13749.8718
Atlantic	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate	1046	4.5165005	6134.6062	12.512217	1982-1999 –> 2000-2012	8.908998	14988.0574
Atlantic	(26,26.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1046	4.2948916	6031.3553	13.012884	1982-1999 –> 2000-2012	8.529991	14775.5085
Atlantic	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1046	4.4942951	6124.2955	12.381481	1982-1999 –> 2000-2012	8.865824	14963.1522
Atlantic	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1046	4.4898702	6122.2348	12.384079	1982-1999 –> 2000-2012	8.854541	14956.3028
Atlantic	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1046	4.4898702	6122.2348	12.384079	1982-1999 –> 2000-2012	8.854541	14956.3028
Atlantic	(26,26.5]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1046	4.4898702	6122.2348	12.384079	1982-1999 –> 2000-2012	8.854541	14956.3028
Atlantic	(26,26.5]	3	cstar_tref ~ temp + silicate + phosphate_star	1046	4.6317409	6185.3148	13.840219	1982-1999 –> 2000-2012	9.396595	15284.9417
Atlantic	(26,26.5]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	567	4.5238837	3332.7028	12.241757	2000-2012 –> 2013-2019	9.084151	9487.4840
Atlantic	(26,26.5]	4	cstar_tref ~ sal + aou + silicate + phosphate	567	4.9425281	3433.0688	14.248584	2000-2012 –> 2013-2019	9.941840	9780.1444
Atlantic	(26,26.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	567	3.6070302	3077.8676	10.902628	2000-2012 –> 2013-2019	7.158851	8711.8144
Atlantic	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate	567	4.4772850	3320.9614	11.976451	2000-2012 –> 2013-2019	8.993786	9455.5676
Atlantic	(26,26.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	567	4.2189568	3255.5690	10.763473	2000-2012 –> 2013-2019	8.513848	9286.9243
Atlantic	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	567	4.4555144	3315.4339	11.876083	2000-2012 –> 2013-2019	8.949810	9439.7294
Atlantic	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	567	4.4550925	3315.3265	11.906159	2000-2012 –> 2013-2019	8.944963	9437.5613
Atlantic	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	567	4.4550925	3315.3265	11.906159	2000-2012 –> 2013-2019	8.944963	9437.5613
Atlantic	(26,26.5]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	567	4.4550925	3315.3265	11.906159	2000-2012 –> 2013-2019	8.944963	9437.5613
Atlantic	(26,26.5]	3	cstar_tref ~ temp + silicate + phosphate_star	567	4.4562951	3313.6326	11.744360	2000-2012 –> 2013-2019	9.088036	9498.9474
Atlantic	(26.5,26.75]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1397	3.3429532	7348.4661	10.697715	1982-1999 –> 2000-2012	6.441567	17034.7612
Atlantic	(26.5,26.75]	4	cstar_tref ~ sal + aou + silicate + phosphate	1397	3.3316510	7339.0038	10.073920	1982-1999 –> 2000-2012	6.478599	17084.0238
Atlantic	(26.5,26.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1397	3.2700730	7288.8799	10.507891	1982-1999 –> 2000-2012	6.329223	16928.5449
Atlantic	(26.5,26.75]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	1397	3.5061205	7481.6156	9.850603	1982-1999 –> 2000-2012	6.846382	17452.8191
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate	1397	3.4027533	7398.0044	10.818893	1982-1999 –> 2000-2012	6.563940	17160.1523
Atlantic	(26.5,26.75]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1397	3.2249399	7250.0489	10.037456	1982-1999 –> 2000-2012	6.207974	16794.1190
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1397	3.4336491	7423.2585	10.906572	1982-1999 –> 2000-2012	6.627923	17224.9109
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1397	3.4413502	7429.5180	10.920943	1982-1999 –> 2000-2012	6.645696	17243.1144
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1397	3.4413502	7429.5180	10.920943	1982-1999 –> 2000-2012	6.645696	17243.1144
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1397	3.4413502	7429.5180	10.920943	1982-1999 –> 2000-2012	6.645696	17243.1144
Atlantic	(26.5,26.75]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	656	3.4323365	3491.6598	11.340269	2000-2012 –> 2013-2019	6.775290	10840.1259
Atlantic	(26.5,26.75]	4	cstar_tref ~ sal + aou + silicate + phosphate	656	3.3850399	3473.4551	10.375376	2000-2012 –> 2013-2019	6.716691	10812.4589
Atlantic	(26.5,26.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	656	3.3455096	3460.0435	10.735554	2000-2012 –> 2013-2019	6.615583	10748.9234
Atlantic	(26.5,26.75]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	656	3.5321626	3529.2737	10.543489	2000-2012 –> 2013-2019	7.038283	11010.8893
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate	656	3.4910702	3513.9207	11.381386	2000-2012 –> 2013-2019	6.893823	10911.9252
Atlantic	(26.5,26.75]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	656	3.3238240	3451.5114	11.113656	2000-2012 –> 2013-2019	6.548764	10701.5603
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	656	3.5219283	3525.4667	11.414557	2000-2012 –> 2013-2019	6.955577	10948.7252
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	656	3.5288346	3528.0369	11.412513	2000-2012 –> 2013-2019	6.970185	10957.5549
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	656	3.5288346	3528.0369	11.412513	2000-2012 –> 2013-2019	6.970185	10957.5549
Atlantic	(26.5,26.75]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	656	3.5288346	3528.0369	11.412513	2000-2012 –> 2013-2019	6.970185	10957.5549
Atlantic	(26.75,27]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2398	2.0935628	10360.8368	14.739529	1982-1999 –> 2000-2012	3.766100	22513.8376
Atlantic	(26.75,27]	4	cstar_tref ~ sal + aou + silicate + phosphate	2398	2.1776482	10549.6945	20.348896	1982-1999 –> 2000-2012	4.132985	23683.7595
Atlantic	(26.75,27]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2398	2.0001820	10143.9994	14.081577	1982-1999 –> 2000-2012	3.653171	22225.1681
Atlantic	(26.75,27]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	2398	2.4457851	11106.6093	34.906111	1982-1999 –> 2000-2012	4.696912	25125.3291
Atlantic	(26.75,27]	4	cstar_tref ~ temp + aou + silicate + phosphate	2398	2.2004206	10599.5875	15.280820	1982-1999 –> 2000-2012	3.988012	23170.3800
Atlantic	(26.75,27]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2398	2.0860637	10345.6268	19.975942	1982-1999 –> 2000-2012	3.599513	21872.9381
Atlantic	(26.75,27]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2398	2.2716861	10752.4544	17.733985	1982-1999 –> 2000-2012	4.110647	23501.1674
Atlantic	(26.75,27]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2398	2.3001008	10812.0716	20.719299	1982-1999 –> 2000-2012	4.158026	23625.2168
Atlantic	(26.75,27]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2398	2.3001008	10812.0716	20.719299	1982-1999 –> 2000-2012	4.158026	23625.2168
Atlantic	(26.75,27]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2398	2.3001008	10812.0716	20.719299	1982-1999 –> 2000-2012	4.158026	23625.2168
Atlantic	(26.75,27]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1263	2.6364762	6045.0524	27.471250	2000-2012 –> 2013-2019	4.730039	16405.8891
Atlantic	(26.75,27]	4	cstar_tref ~ sal + aou + silicate + phosphate	1263	2.5846959	5994.9482	24.744636	2000-2012 –> 2013-2019	4.762344	16544.6427
Atlantic	(26.75,27]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1263	2.5330762	5945.9902	25.891764	2000-2012 –> 2013-2019	4.533258	16089.9896
Atlantic	(26.75,27]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	1263	2.6918036	6097.5128	23.840055	2000-2012 –> 2013-2019	5.137589	17204.1222
Atlantic	(26.75,27]	4	cstar_tref ~ temp + aou + silicate + phosphate	1263	2.7633578	6163.7827	28.240304	2000-2012 –> 2013-2019	4.963778	16763.3702
Atlantic	(26.75,27]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1263	2.2552518	5652.5376	22.583567	2000-2012 –> 2013-2019	4.341316	15998.1644
Atlantic	(26.75,27]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1263	2.8094508	6205.5690	28.490393	2000-2012 –> 2013-2019	5.081137	16958.0234
Atlantic	(26.75,27]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1263	2.8252828	6219.7637	28.536665	2000-2012 –> 2013-2019	5.125384	17031.8354
Atlantic	(26.75,27]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1263	2.8252828	6219.7637	28.536665	2000-2012 –> 2013-2019	5.125384	17031.8354
Atlantic	(26.75,27]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1263	2.8252828	6219.7637	28.536665	2000-2012 –> 2013-2019	5.125384	17031.8354
Atlantic	(27,27.25]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2031	2.4661377	9442.3058	11.932474	1982-1999 –> 2000-2012	4.580400	20773.7445
Atlantic	(27,27.25]	4	cstar_tref ~ sal + aou + silicate + phosphate	2031	1.9148200	8414.4995	9.235730	1982-1999 –> 2000-2012	3.631195	18657.1971
Atlantic	(27,27.25]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2031	1.8904789	8364.5325	9.689213	1982-1999 –> 2000-2012	3.460465	18143.6984
Atlantic	(27,27.25]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	2031	2.1351734	8856.9497	9.523454	1982-1999 –> 2000-2012	4.398726	20544.6841
Atlantic	(27,27.25]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	2031	2.1910052	8961.8003	9.938424	1982-1999 –> 2000-2012	4.583278	20938.3539
Atlantic	(27,27.25]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	2031	2.1910052	8961.8003	9.938424	1982-1999 –> 2000-2012	4.583278	20938.3539
Atlantic	(27,27.25]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	2031	2.1910052	8961.8003	9.938424	1982-1999 –> 2000-2012	4.583278	20938.3539
Atlantic	(27,27.25]	4	cstar_tref ~ temp + aou + silicate + phosphate	2031	2.5774029	9621.5579	12.121441	1982-1999 –> 2000-2012	4.664246	20884.8324
Atlantic	(27,27.25]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2031	2.3112875	9180.8912	13.899054	1982-1999 –> 2000-2012	4.387710	20420.0232
Atlantic	(27,27.25]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2031	2.6153116	9680.8671	12.186629	1982-1999 –> 2000-2012	4.736994	21030.6003
Atlantic	(27,27.25]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1142	3.0519587	5801.3053	14.927443	2000-2012 –> 2013-2019	5.518096	15243.6111
Atlantic	(27,27.25]	4	cstar_tref ~ sal + aou + silicate + phosphate	1142	2.3003827	5155.6000	13.777336	2000-2012 –> 2013-2019	4.215203	13570.0995
Atlantic	(27,27.25]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1142	2.2946948	5151.9457	14.080782	2000-2012 –> 2013-2019	4.185174	13516.4782
Atlantic	(27,27.25]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	1142	2.3424794	5197.0192	15.033313	2000-2012 –> 2013-2019	4.477653	14053.9689
Atlantic	(27,27.25]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	1142	2.3613801	5215.3740	15.167463	2000-2012 –> 2013-2019	4.552385	14177.1744
Atlantic	(27,27.25]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1142	2.3613801	5215.3740	15.167463	2000-2012 –> 2013-2019	4.552385	14177.1744
Atlantic	(27,27.25]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1142	2.3613801	5215.3740	15.167463	2000-2012 –> 2013-2019	4.552385	14177.1744
Atlantic	(27,27.25]	3	cstar_tref ~ sal + silicate + phosphate_star	1142	2.6802915	5502.7096	13.700856	2000-2012 –> 2013-2019	5.426597	15380.0995
Atlantic	(27,27.25]	4	cstar_tref ~ temp + aou + silicate + phosphate	1142	3.1722374	5889.5901	15.110201	2000-2012 –> 2013-2019	5.749640	15511.1479
Atlantic	(27,27.25]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1142	2.8129211	5617.0221	14.119428	2000-2012 –> 2013-2019	5.124209	14797.9132
Atlantic	(27.25,27.5]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2025	3.5064046	10839.7953	14.078762	1982-1999 –> 2000-2012	6.154820	24625.3283
Atlantic	(27.25,27.5]	3	cstar_tref ~ sal + aou + phosphate	2025	3.2329612	10508.9649	22.030264	1982-1999 –> 2000-2012	6.036248	24619.6170
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2025	3.1435193	10397.3400	20.035882	1982-1999 –> 2000-2012	5.563423	23663.4868
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + aou + silicate + phosphate	2025	2.7655192	9878.4761	23.145713	1982-1999 –> 2000-2012	5.304972	23422.1817
Atlantic	(27.25,27.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2025	2.6905754	9769.2091	21.422922	1982-1999 –> 2000-2012	4.857623	22402.1133
Atlantic	(27.25,27.5]	4	cstar_tref ~ temp + aou + silicate + phosphate	2025	3.5798778	10923.7821	14.848059	1982-1999 –> 2000-2012	6.294501	24851.4400
Atlantic	(27.25,27.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2025	3.5042119	10839.2619	16.099080	1982-1999 –> 2000-2012	6.151630	24624.6273
Atlantic	(27.25,27.5]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2025	3.6474870	10999.5567	15.738349	1982-1999 –> 2000-2012	6.430810	25071.0711
Atlantic	(27.25,27.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2025	3.6495556	11001.8530	15.721562	1982-1999 –> 2000-2012	6.439997	25088.0695
Atlantic	(27.25,27.5]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2025	3.6495556	11001.8530	15.721562	1982-1999 –> 2000-2012	6.439997	25088.0695
Atlantic	(27.25,27.5]	3	cstar_tref ~ sal + aou + phosphate	1109	4.0365172	6252.1635	24.705305	2000-2012 –> 2013-2019	7.269478	16761.1284
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1109	3.9583585	6210.7953	22.567034	2000-2012 –> 2013-2019	7.101878	16608.1354
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + aou + silicate + phosphate	1109	3.5932118	5996.1307	25.833019	2000-2012 –> 2013-2019	6.358731	15874.6067
Atlantic	(27.25,27.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1109	3.5374046	5963.4120	24.085736	2000-2012 –> 2013-2019	6.227980	15732.6211
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	1109	3.9960259	6231.8018	29.036696	2000-2012 –> 2013-2019	7.323574	16859.5576
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	1109	3.9750215	6220.1126	28.586368	2000-2012 –> 2013-2019	7.320502	16869.6354
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1109	3.9750215	6220.1126	28.586368	2000-2012 –> 2013-2019	7.320502	16869.6354
Atlantic	(27.25,27.5]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1109	3.9750215	6220.1126	28.586368	2000-2012 –> 2013-2019	7.320502	16869.6354
Atlantic	(27.25,27.5]	3	cstar_tref ~ sal + silicate + phosphate_star	1109	4.0164145	6241.0898	29.775574	2000-2012 –> 2013-2019	7.371016	16899.6395
Atlantic	(27.25,27.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1109	4.0771941	6278.4029	17.990130	2000-2012 –> 2013-2019	7.581406	17117.6648
Atlantic	(27.5,27.75]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2804	3.5998639	15152.6723	18.814168	1982-1999 –> 2000-2012	6.434200	33541.5247
Atlantic	(27.5,27.75]	3	cstar_tref ~ sal + aou + phosphate	2804	2.7836924	13708.7557	13.816311	1982-1999 –> 2000-2012	5.258742	31083.3422
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2804	2.7656318	13674.2524	14.269310	1982-1999 –> 2000-2012	5.031500	30391.3946
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + aou + silicate + phosphate	2804	2.4538915	13003.5694	13.901382	1982-1999 –> 2000-2012	4.821076	30047.3887
Atlantic	(27.5,27.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2804	2.3944064	12867.9502	14.685866	1982-1999 –> 2000-2012	4.494974	29021.3907
Atlantic	(27.5,27.75]	4	cstar_tref ~ temp + aou + silicate + phosphate	2804	3.6637192	15251.2765	18.296963	1982-1999 –> 2000-2012	6.486121	33608.6194
Atlantic	(27.5,27.75]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2804	3.5991348	15153.5364	18.870153	1982-1999 –> 2000-2012	6.410481	33483.5690
Atlantic	(27.5,27.75]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2804	3.7345054	15358.5944	18.056531	1982-1999 –> 2000-2012	6.610860	33857.3474
Atlantic	(27.5,27.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2804	3.7322940	15355.2726	18.019343	1982-1999 –> 2000-2012	6.610979	33860.0731
Atlantic	(27.5,27.75]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2804	3.7322940	15355.2726	18.019343	1982-1999 –> 2000-2012	6.610979	33860.0731
Atlantic	(27.5,27.75]	3	cstar_tref ~ sal + aou + phosphate	1515	3.4259760	8040.4845	14.371977	2000-2012 –> 2013-2019	6.209668	21749.2402
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1515	3.4234258	8040.2283	14.171915	2000-2012 –> 2013-2019	6.189058	21714.4806
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + aou + silicate + phosphate	1515	2.8745087	7510.7055	15.545879	2000-2012 –> 2013-2019	5.328400	20514.2749
Atlantic	(27.5,27.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1515	2.8711798	7509.1946	15.461950	2000-2012 –> 2013-2019	5.265586	20377.1448
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	1515	3.3350768	7961.0058	16.848174	2000-2012 –> 2013-2019	6.580411	22532.2534
Atlantic	(27.5,27.75]	3	cstar_tref ~ sal + oxygen + phosphate	1515	3.7058316	8278.4041	14.544521	2000-2012 –> 2013-2019	7.114299	23122.6925
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	1515	3.2671643	7898.6687	16.135848	2000-2012 –> 2013-2019	6.458907	22376.5370
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1515	3.2671643	7898.6687	16.135848	2000-2012 –> 2013-2019	6.458907	22376.5370
Atlantic	(27.5,27.75]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1515	3.2671643	7898.6687	16.135848	2000-2012 –> 2013-2019	6.458907	22376.5370
Atlantic	(27.5,27.75]	3	cstar_tref ~ sal + silicate + phosphate_star	1515	3.4628831	8072.9513	19.517533	2000-2012 –> 2013-2019	6.742176	22700.5745
Atlantic	(27.75,27.85]	3	cstar_tref ~ aou + phosphate + phosphate_star	1036	2.4092497	4771.9821	15.106834	1982-1999 –> 2000-2012	4.340148	10265.0607
Atlantic	(27.75,27.85]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1036	2.2930064	4671.5184	15.409426	1982-1999 –> 2000-2012	4.214188	10153.2785
Atlantic	(27.75,27.85]	3	cstar_tref ~ sal + aou + phosphate	1036	2.2757763	4653.8902	11.420567	1982-1999 –> 2000-2012	4.249564	10204.9673
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1036	1.9943230	4382.3519	12.367472	1982-1999 –> 2000-2012	3.677620	9515.1410
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + aou + silicate + phosphate	1036	1.7389083	4098.3902	12.226980	1982-1999 –> 2000-2012	3.547586	9420.8408
Atlantic	(27.75,27.85]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1036	1.5641536	3880.9392	12.798383	1982-1999 –> 2000-2012	3.161198	8876.8661
Atlantic	(27.75,27.85]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	1036	2.3534421	4725.4219	15.118939	1982-1999 –> 2000-2012	4.258564	10185.0207
Atlantic	(27.75,27.85]	4	cstar_tref ~ temp + aou + silicate + phosphate	1036	2.3208187	4696.4989	15.540108	1982-1999 –> 2000-2012	4.292705	10247.0312
Atlantic	(27.75,27.85]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1036	2.2923345	4672.9112	15.392219	1982-1999 –> 2000-2012	4.197456	10134.5099
Atlantic	(27.75,27.85]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1036	2.3461625	4719.0029	15.610710	1982-1999 –> 2000-2012	4.360125	10325.2757
Atlantic	(27.75,27.85]	3	cstar_tref ~ sal + aou + phosphate	513	2.6899097	2481.0658	10.612786	2000-2012 –> 2013-2019	4.965686	7134.9560
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	513	2.4147179	2372.3345	11.388027	2000-2012 –> 2013-2019	4.409041	6754.6864
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + aou + silicate + phosphate	513	1.8570079	2102.8906	11.721525	2000-2012 –> 2013-2019	3.595916	6201.2808
Atlantic	(27.75,27.85]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	513	1.7475521	2042.5606	12.039326	2000-2012 –> 2013-2019	3.311706	5923.4997
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	513	2.2786438	2312.8244	11.507801	2000-2012 –> 2013-2019	4.561263	6974.9360
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	513	2.2850958	2315.7255	11.564796	2000-2012 –> 2013-2019	4.587523	6995.7397
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	513	2.2850958	2315.7255	11.564796	2000-2012 –> 2013-2019	4.587523	6995.7397
Atlantic	(27.75,27.85]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	513	2.2850958	2315.7255	11.564796	2000-2012 –> 2013-2019	4.587523	6995.7397
Atlantic	(27.75,27.85]	3	cstar_tref ~ sal + silicate + phosphate_star	513	2.2851991	2313.7719	11.573863	2000-2012 –> 2013-2019	4.593218	6996.8119
Atlantic	(27.75,27.85]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	513	2.6632845	2474.8596	14.123109	2000-2012 –> 2013-2019	4.955619	7147.7708
Atlantic	(27.85,27.95]	3	cstar_tref ~ aou + phosphate + phosphate_star	983	3.4444208	5231.0950	40.406696	1982-1999 –> 2000-2012	6.361383	11892.9889
Atlantic	(27.85,27.95]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	983	3.4332878	5226.7302	38.381356	1982-1999 –> 2000-2012	6.310886	11854.3203
Atlantic	(27.85,27.95]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	983	3.4396213	5230.3536	36.781212	1982-1999 –> 2000-2012	6.169629	11717.2584
Atlantic	(27.85,27.95]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	983	3.4272905	5225.2930	34.214054	1982-1999 –> 2000-2012	6.157169	11714.0714
Atlantic	(27.85,27.95]	3	cstar_tref ~ temp + aou + phosphate	983	3.7051030	5374.5251	49.117027	1982-1999 –> 2000-2012	6.634955	12048.2006
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	983	3.0946626	5022.5819	23.332862	1982-1999 –> 2000-2012	6.011468	11686.3324
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + aou + silicate + phosphate	983	3.6929852	5370.0846	46.749916	1982-1999 –> 2000-2012	6.605623	12030.0144
Atlantic	(27.85,27.95]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	983	3.0757549	5012.5332	23.130965	1982-1999 –> 2000-2012	5.940010	11629.7050
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	983	3.8308048	5442.1184	50.328170	1982-1999 –> 2000-2012	6.776013	12131.7618
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	983	3.8308048	5442.1184	50.328170	1982-1999 –> 2000-2012	6.776013	12131.7618
Atlantic	(27.85,27.95]	3	cstar_tref ~ aou + phosphate + phosphate_star	569	3.7400627	3125.8905	23.720140	2000-2012 –> 2013-2019	7.184483	8356.9855
Atlantic	(27.85,27.95]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	569	3.7372699	3127.0405	23.268863	2000-2012 –> 2013-2019	7.170558	8353.7707
Atlantic	(27.85,27.95]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	569	3.4103854	3022.8793	30.447244	2000-2012 –> 2013-2019	6.850007	8253.2329
Atlantic	(27.85,27.95]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	569	3.3215129	2994.8304	29.207068	2000-2012 –> 2013-2019	6.748803	8220.1234
Atlantic	(27.85,27.95]	3	cstar_tref ~ temp + aou + phosphate	569	3.8337887	3154.0574	23.962464	2000-2012 –> 2013-2019	7.538892	8528.5825
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	569	3.6730463	3107.3144	22.693963	2000-2012 –> 2013-2019	6.767709	8129.8962
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + aou + silicate + phosphate	569	3.8181580	3151.4082	23.646089	2000-2012 –> 2013-2019	7.511143	8521.4928
Atlantic	(27.85,27.95]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	569	3.6600265	3105.2733	23.151675	2000-2012 –> 2013-2019	6.735781	8117.8065
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	569	3.8608548	3164.0633	23.852541	2000-2012 –> 2013-2019	7.691660	8606.1817
Atlantic	(27.85,27.95]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	569	3.8608548	3164.0633	23.852541	2000-2012 –> 2013-2019	7.691660	8606.1817
Atlantic	(27.95,28.05]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1204	4.6141408	7110.9386	25.515496	1982-1999 –> 2000-2012	9.520857	17210.9282
Atlantic	(27.95,28.05]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1204	4.6143746	7111.0606	26.067945	1982-1999 –> 2000-2012	9.446234	17159.5181
Atlantic	(27.95,28.05]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1204	4.5430532	7075.5511	25.262696	1982-1999 –> 2000-2012	9.288330	17065.3992
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	1204	4.6354269	7122.0217	25.001956	1982-1999 –> 2000-2012	9.572341	17242.5778
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate	1204	4.5804981	7093.3170	24.656039	1982-1999 –> 2000-2012	9.465022	17178.1118
Atlantic	(27.95,28.05]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1204	4.5224648	7064.6136	21.845213	1982-1999 –> 2000-2012	9.376834	17130.6504
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1204	4.5699997	7087.7916	24.379873	1982-1999 –> 2000-2012	9.447168	17167.5348
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1204	4.5725557	7089.1381	24.432332	1982-1999 –> 2000-2012	9.450955	17169.7271
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1204	4.5725557	7089.1381	24.432332	1982-1999 –> 2000-2012	9.450955	17169.7271
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1204	4.5725557	7089.1381	24.432332	1982-1999 –> 2000-2012	9.450955	17169.7271
Atlantic	(27.95,28.05]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	666	4.4357083	3886.2896	24.809832	2000-2012 –> 2013-2019	9.049849	10997.2283
Atlantic	(27.95,28.05]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	666	4.3483289	3859.7886	24.917815	2000-2012 –> 2013-2019	8.962704	10970.8492
Atlantic	(27.95,28.05]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	666	4.2792874	3840.4697	24.913097	2000-2012 –> 2013-2019	8.822341	10916.0208
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	666	4.4563090	3892.4615	25.112416	2000-2012 –> 2013-2019	9.091736	11014.4832
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate	666	4.4296661	3884.4740	24.087584	2000-2012 –> 2013-2019	9.010164	10977.7910
Atlantic	(27.95,28.05]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	666	4.4290548	3886.2901	23.783433	2000-2012 –> 2013-2019	8.951520	10950.9038
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	666	4.4290672	3884.2939	23.826635	2000-2012 –> 2013-2019	8.999067	10972.0855
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	666	4.4291749	3884.3263	23.917524	2000-2012 –> 2013-2019	9.001731	10973.4643
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	666	4.4291749	3884.3263	23.917524	2000-2012 –> 2013-2019	9.001731	10973.4643
Atlantic	(27.95,28.05]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	666	4.4291749	3884.3263	23.917524	2000-2012 –> 2013-2019	9.001731	10973.4643
Atlantic	(28.05,28.1]	3	cstar_tref ~ aou + phosphate + phosphate_star	804	1.1608853	2531.5393	11.005507	1982-1999 –> 2000-2012	2.120684	5506.7947
Atlantic	(28.05,28.1]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	804	1.1604167	2532.8901	10.979649	1982-1999 –> 2000-2012	2.113485	5495.0017
Atlantic	(28.05,28.1]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	804	1.0598757	2387.1610	7.838670	1982-1999 –> 2000-2012	1.952765	5208.9110
Atlantic	(28.05,28.1]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	804	1.0324411	2346.9902	6.945256	1982-1999 –> 2000-2012	1.924797	5169.4535
Atlantic	(28.05,28.1]	3	cstar_tref ~ temp + aou + phosphate	804	1.1795166	2557.1414	11.041510	1982-1999 –> 2000-2012	2.150714	5557.8051
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	804	1.1065403	2456.4443	11.331523	1982-1999 –> 2000-2012	2.047349	5390.6954
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + aou + silicate + phosphate	804	1.1772969	2556.1127	10.971289	1982-1999 –> 2000-2012	2.145319	5551.7285
Atlantic	(28.05,28.1]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	804	1.0436142	2364.2985	12.188672	1982-1999 –> 2000-2012	1.882891	5054.7923
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	804	1.1824509	2563.1368	10.968185	1982-1999 –> 2000-2012	2.157405	5574.1061
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	804	1.1824509	2563.1368	10.968185	1982-1999 –> 2000-2012	2.157405	5574.1061
Atlantic	(28.05,28.1]	3	cstar_tref ~ aou + phosphate + phosphate_star	434	1.2192680	1413.7202	12.282594	2000-2012 –> 2013-2019	2.380153	3945.2595
Atlantic	(28.05,28.1]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	434	1.2132881	1411.4526	12.215619	2000-2012 –> 2013-2019	2.373705	3944.3427
Atlantic	(28.05,28.1]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	434	1.1212849	1343.0032	8.929761	2000-2012 –> 2013-2019	2.181161	3730.1642
Atlantic	(28.05,28.1]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	434	1.0586072	1295.0748	7.429722	2000-2012 –> 2013-2019	2.091048	3642.0650
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	434	1.1480057	1363.4454	12.833810	2000-2012 –> 2013-2019	2.254546	3819.8898
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + aou + silicate + phosphate	434	1.2303737	1423.5906	12.182262	2000-2012 –> 2013-2019	2.407671	3979.7033
Atlantic	(28.05,28.1]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	434	1.1075442	1334.3006	13.578379	2000-2012 –> 2013-2019	2.151158	3698.5991
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	434	1.2341739	1426.2674	12.180217	2000-2012 –> 2013-2019	2.416625	3989.4043
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	434	1.2341739	1426.2674	12.180217	2000-2012 –> 2013-2019	2.416625	3989.4043
Atlantic	(28.05,28.1]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	434	1.2341739	1426.2674	12.180217	2000-2012 –> 2013-2019	2.416625	3989.4043
Atlantic	(28.1,28.15]	3	cstar_tref ~ aou + phosphate + phosphate_star	936	0.8709417	2407.5796	9.946705	1982-1999 –> 2000-2012	1.591247	5242.9037
Atlantic	(28.1,28.15]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	936	0.8652007	2397.1990	9.973159	1982-1999 –> 2000-2012	1.550109	5104.0130
Atlantic	(28.1,28.15]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	936	0.7732900	2186.9596	6.039973	1982-1999 –> 2000-2012	1.445165	4844.0128
Atlantic	(28.1,28.15]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	936	0.7598609	2156.1646	5.927820	1982-1999 –> 2000-2012	1.389314	4646.2932
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	936	0.8570872	2379.5613	9.929510	1982-1999 –> 2000-2012	1.575478	5209.9919
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + aou + silicate + phosphate	936	0.8783084	2425.3470	10.051818	1982-1999 –> 2000-2012	1.576700	5182.6502
Atlantic	(28.1,28.15]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	936	0.7856962	2218.7544	10.025704	1982-1999 –> 2000-2012	1.374486	4535.9182
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	936	0.8830714	2435.4712	10.082608	1982-1999 –> 2000-2012	1.588411	5218.4149
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	936	0.8830714	2435.4712	10.082608	1982-1999 –> 2000-2012	1.588411	5218.4149
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	936	0.8830714	2435.4712	10.082608	1982-1999 –> 2000-2012	1.588411	5218.4149
Atlantic	(28.1,28.15]	3	cstar_tref ~ aou + phosphate + phosphate_star	497	1.0350290	1454.6478	11.396766	2000-2012 –> 2013-2019	1.905971	3862.2274
Atlantic	(28.1,28.15]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	497	1.0349299	1456.5526	11.397933	2000-2012 –> 2013-2019	1.900131	3853.7516
Atlantic	(28.1,28.15]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	497	0.8714406	1285.6430	6.181914	2000-2012 –> 2013-2019	1.644731	3472.6026
Atlantic	(28.1,28.15]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	497	0.8712585	1287.4353	6.182326	2000-2012 –> 2013-2019	1.631120	3443.5998
Atlantic	(28.1,28.15]	3	cstar_tref ~ temp + aou + phosphate	497	1.0551579	1473.7932	11.501643	2000-2012 –> 2013-2019	1.935758	3902.0192
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	497	0.9653756	1387.3983	11.632299	2000-2012 –> 2013-2019	1.822463	3766.9596
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + aou + silicate + phosphate	497	1.0549100	1475.5596	11.494491	2000-2012 –> 2013-2019	1.933218	3900.9066
Atlantic	(28.1,28.15]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	497	0.8791505	1296.3985	11.933687	2000-2012 –> 2013-2019	1.664847	3515.1529
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	497	1.0602381	1480.5675	11.532519	2000-2012 –> 2013-2019	1.943310	3916.0387
Atlantic	(28.1,28.15]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	497	1.0602381	1480.5675	11.532519	2000-2012 –> 2013-2019	1.943310	3916.0387
Atlantic	(28.15,28.2]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1540	0.7514019	3502.0216	2.306367	1982-1999 –> 2000-2012	1.535911	8745.9426
Atlantic	(28.15,28.2]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1540	0.7103431	3328.9486	2.687186	1982-1999 –> 2000-2012	1.488766	8538.2298
Atlantic	(28.15,28.2]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1540	0.7055495	3310.0933	2.511827	1982-1999 –> 2000-2012	1.442265	8276.4329
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	1540	0.8620248	3925.0394	2.618817	1982-1999 –> 2000-2012	1.806413	9993.9715
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + aou + silicate + phosphate	1540	0.7569911	3524.8470	2.346351	1982-1999 –> 2000-2012	1.546083	8794.6784
Atlantic	(28.15,28.2]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1540	0.7016940	3293.2166	2.285566	1982-1999 –> 2000-2012	1.464622	8415.0657
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1540	0.7628987	3548.7902	2.378988	1982-1999 –> 2000-2012	1.557131	8847.4995
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1540	0.7591252	3533.5181	2.362963	1982-1999 –> 2000-2012	1.550927	8818.5971
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1540	0.7591252	3533.5181	2.362963	1982-1999 –> 2000-2012	1.550927	8818.5971
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1540	0.7591252	3533.5181	2.362963	1982-1999 –> 2000-2012	1.550927	8818.5971
Atlantic	(28.15,28.2]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	819	0.9417136	2237.8528	6.997675	2000-2012 –> 2013-2019	1.693115	5739.8744
Atlantic	(28.15,28.2]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	819	1.0621809	2435.0324	11.038429	2000-2012 –> 2013-2019	1.772524	5763.9810
Atlantic	(28.15,28.2]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	819	0.9381573	2233.6552	6.391027	2000-2012 –> 2013-2019	1.643707	5543.7484
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	819	1.1027685	2496.4568	9.381846	2000-2012 –> 2013-2019	1.964793	6421.4962
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + aou + silicate + phosphate	819	0.9555104	2261.6765	7.212608	2000-2012 –> 2013-2019	1.712501	5786.5235
Atlantic	(28.15,28.2]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	819	0.8478245	2067.8177	6.287814	2000-2012 –> 2013-2019	1.549519	5361.0343
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	819	0.9645019	2277.0184	7.305998	2000-2012 –> 2013-2019	1.727401	5825.8086
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	819	0.9599097	2269.2008	7.293954	2000-2012 –> 2013-2019	1.719035	5802.7189
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	819	0.9599097	2269.2008	7.293954	2000-2012 –> 2013-2019	1.719035	5802.7189
Atlantic	(28.15,28.2]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	819	0.9599097	2269.2008	7.293954	2000-2012 –> 2013-2019	1.719035	5802.7189
Atlantic	(28.2, Inf]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2693	0.8593664	6838.1015	5.693506	1982-1999 –> 2000-2012	1.607617	15228.9593
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + aou + silicate + phosphate	2693	0.7445250	6065.4852	2.717163	1982-1999 –> 2000-2012	1.382026	13267.4629
Atlantic	(28.2, Inf]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2693	0.7404046	6037.5946	2.951204	1982-1999 –> 2000-2012	1.374822	13205.5921
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	2693	0.7721739	6261.8769	7.611345	1982-1999 –> 2000-2012	1.461405	14042.9241
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	2693	0.7721739	6261.8769	7.611345	1982-1999 –> 2000-2012	1.461405	14042.9241
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	2693	0.7721739	6261.8769	7.611345	1982-1999 –> 2000-2012	1.461405	14042.9241
Atlantic	(28.2, Inf]	4	cstar_tref ~ temp + aou + silicate + phosphate	2693	0.8645161	6870.2803	5.772725	1982-1999 –> 2000-2012	1.618469	15317.4782
Atlantic	(28.2, Inf]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2693	0.6982481	5721.8554	7.872375	1982-1999 –> 2000-2012	1.337148	12942.1058
Atlantic	(28.2, Inf]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2693	0.8714327	6913.2000	5.866418	1982-1999 –> 2000-2012	1.633520	15440.0494
Atlantic	(28.2, Inf]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2693	0.8714327	6913.2000	5.866418	1982-1999 –> 2000-2012	1.633520	15440.0494
Atlantic	(28.2, Inf]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1557	1.0649426	4626.5104	8.696200	2000-2012 –> 2013-2019	1.924309	11464.6119
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + aou + silicate + phosphate	1557	0.8505933	3926.6635	2.632616	2000-2012 –> 2013-2019	1.595118	9992.1487
Atlantic	(28.2, Inf]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1557	0.8341145	3867.7431	2.739508	2000-2012 –> 2013-2019	1.574519	9905.3377
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	1557	0.8922942	4075.7052	6.658049	2000-2012 –> 2013-2019	1.754731	10933.0163
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	1557	0.8389904	3883.8932	2.971888	2000-2012 –> 2013-2019	1.611164	10145.7701
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1557	0.8389904	3883.8932	2.971888	2000-2012 –> 2013-2019	1.611164	10145.7701
Atlantic	(28.2, Inf]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1557	0.8389904	3883.8932	2.971888	2000-2012 –> 2013-2019	1.611164	10145.7701
Atlantic	(28.2, Inf]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	1557	1.0196005	4491.0202	19.690960	2000-2012 –> 2013-2019	1.889935	11397.4279
Atlantic	(28.2, Inf]	4	cstar_tref ~ temp + aou + silicate + phosphate	1557	1.0748512	4655.3501	9.198412	2000-2012 –> 2013-2019	1.939367	11525.6305
Atlantic	(28.2, Inf]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1557	0.7915199	3704.5208	11.936972	2000-2012 –> 2013-2019	1.489768	9426.3762
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5288	7.7270410	36643.7160	27.677067	1982-1999 –> 2000-2012	15.807897	87128.0807
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	5288	6.2360939	34376.5179	29.968567	1982-1999 –> 2000-2012	12.765635	81794.3473
Indo-Pacific	(-Inf,26]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5288	6.1928478	34304.9200	29.527354	1982-1999 –> 2000-2012	12.671699	81612.6324
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	5288	7.5866534	36449.8006	30.398788	1982-1999 –> 2000-2012	15.509135	86649.4191
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + aou + silicate + phosphate	5288	7.4813073	36301.9161	28.357780	1982-1999 –> 2000-2012	15.294363	86301.4501
Indo-Pacific	(-Inf,26]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5288	7.2933052	36034.7494	29.166512	1982-1999 –> 2000-2012	14.877485	85608.5624
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	5288	7.4060853	36195.0399	28.515322	1982-1999 –> 2000-2012	15.143432	86054.4924
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	5288	7.3907730	36173.1511	28.492599	1982-1999 –> 2000-2012	15.105076	85989.6943
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	5288	7.3907730	36173.1511	28.492599	1982-1999 –> 2000-2012	15.105076	85989.6943
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	5288	7.3907730	36173.1511	28.492599	1982-1999 –> 2000-2012	15.105076	85989.6943
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2816	5.9520247	18049.4373	24.894024	2000-2012 –> 2013-2019	12.188119	52425.9552
Indo-Pacific	(-Inf,26]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2816	5.8778725	17980.8313	24.128023	2000-2012 –> 2013-2019	12.070720	52285.7513
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	2816	7.3755420	19257.1519	27.689978	2000-2012 –> 2013-2019	14.962195	55706.9524
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + aou + silicate + phosphate	2816	7.2293095	19144.3661	24.250881	2000-2012 –> 2013-2019	14.710617	55446.2822
Indo-Pacific	(-Inf,26]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2816	7.0001768	18964.9700	25.465195	2000-2012 –> 2013-2019	14.293482	54999.7194
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2816	7.1474074	19080.1961	24.474615	2000-2012 –> 2013-2019	14.553493	55275.2360
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2816	7.1344030	19069.9395	24.441528	2000-2012 –> 2013-2019	14.525176	55243.0906
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2816	7.1344030	19069.9395	24.441528	2000-2012 –> 2013-2019	14.525176	55243.0906
Indo-Pacific	(-Inf,26]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2816	7.1344030	19069.9395	24.441528	2000-2012 –> 2013-2019	14.525176	55243.0906
Indo-Pacific	(-Inf,26]	3	cstar_tref ~ temp + silicate + phosphate_star	2816	7.3741321	19254.0751	27.379074	2000-2012 –> 2013-2019	15.195870	56024.6147
Indo-Pacific	(26,26.5]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5525	4.8905258	33230.9339	41.688307	1982-1999 –> 2000-2012	9.537710	78823.9388
Indo-Pacific	(26,26.5]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	5525	5.0675025	33623.7421	44.531956	1982-1999 –> 2000-2012	9.845665	79645.4511
Indo-Pacific	(26,26.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5525	4.5360650	32401.5327	43.772780	1982-1999 –> 2000-2012	8.782438	76605.3494
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	5525	5.4891091	34506.8347	46.051915	1982-1999 –> 2000-2012	10.700297	81866.6037
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate	5525	4.8893893	33228.3657	40.409229	1982-1999 –> 2000-2012	9.509150	78730.0815
Indo-Pacific	(26,26.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5525	4.8803203	33209.8508	41.154556	1982-1999 –> 2000-2012	9.499989	78713.2617
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	5525	4.9245814	33307.6149	49.529819	1982-1999 –> 2000-2012	9.555972	78848.1124
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	5525	4.9304894	33320.8635	50.805047	1982-1999 –> 2000-2012	9.566622	78877.1440
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	5525	4.9304894	33320.8635	50.805047	1982-1999 –> 2000-2012	9.566622	78877.1440
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	5525	4.9304894	33320.8635	50.805047	1982-1999 –> 2000-2012	9.566622	78877.1440
Indo-Pacific	(26,26.5]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2918	4.8175903	17468.7156	40.382988	2000-2012 –> 2013-2019	9.708116	50699.6495
Indo-Pacific	(26,26.5]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2918	5.0324162	17723.3190	47.734928	2000-2012 –> 2013-2019	10.099919	51347.0611
Indo-Pacific	(26,26.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2918	4.4724496	17036.8813	46.310491	2000-2012 –> 2013-2019	9.008515	49438.4140
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate	2918	4.8142859	17464.7112	37.043514	2000-2012 –> 2013-2019	9.703675	50693.0769
Indo-Pacific	(26,26.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2918	4.8065118	17457.2797	38.739984	2000-2012 –> 2013-2019	9.686832	50667.1305
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2918	4.8483037	17505.8034	34.431113	2000-2012 –> 2013-2019	9.772885	50813.4183
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2918	4.8517131	17509.9060	34.225344	2000-2012 –> 2013-2019	9.782203	50830.7695
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2918	4.8517131	17509.9060	34.225344	2000-2012 –> 2013-2019	9.782203	50830.7695
Indo-Pacific	(26,26.5]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2918	4.8517131	17509.9060	34.225344	2000-2012 –> 2013-2019	9.782203	50830.7695
Indo-Pacific	(26,26.5]	3	cstar_tref ~ temp + silicate + phosphate_star	2918	5.0016139	17685.4884	31.434569	2000-2012 –> 2013-2019	10.282583	51763.1714
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	4544	4.0473152	25612.8259	22.127132	1982-1999 –> 2000-2012	7.996383	60742.2745
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	4544	4.2282325	26010.2468	17.683523	1982-1999 –> 2000-2012	8.162414	61092.2007
Indo-Pacific	(26.5,26.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	4544	3.9265162	25339.4488	20.226531	1982-1999 –> 2000-2012	7.683911	59845.1956
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	4544	4.2651270	26089.2026	19.530570	1982-1999 –> 2000-2012	8.331264	61586.0455
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate	4544	4.1322494	25801.5670	26.615035	1982-1999 –> 2000-2012	8.153897	61160.0507
Indo-Pacific	(26.5,26.75]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	4544	3.9477481	25388.4579	23.151958	1982-1999 –> 2000-2012	7.824940	60288.9073
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	4544	4.2139237	25979.4400	32.785894	1982-1999 –> 2000-2012	8.307920	61562.1542
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	4544	4.2095240	25969.9463	32.334600	1982-1999 –> 2000-2012	8.306431	61561.5980
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	4544	4.2095240	25969.9463	32.334600	1982-1999 –> 2000-2012	8.306431	61561.5980
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	4544	4.2095240	25969.9463	32.334600	1982-1999 –> 2000-2012	8.306431	61561.5980
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2447	4.4033896	14211.0265	24.538450	2000-2012 –> 2013-2019	8.450705	39823.8524
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2447	4.6312511	14457.9407	20.916727	2000-2012 –> 2013-2019	8.859483	40468.1875
Indo-Pacific	(26.5,26.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2447	4.2938981	14089.7973	24.434470	2000-2012 –> 2013-2019	8.220414	39429.2462
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	2447	4.6619310	14490.2543	19.589333	2000-2012 –> 2013-2019	8.927058	40579.4569
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate	2447	4.4871872	14303.2855	23.916608	2000-2012 –> 2013-2019	8.619437	40104.8525
Indo-Pacific	(26.5,26.75]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2447	4.2923135	14087.9909	22.815590	2000-2012 –> 2013-2019	8.240061	39476.4489
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2447	4.5629428	14385.2194	23.337978	2000-2012 –> 2013-2019	8.776867	40364.6594
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2447	4.5556780	14377.4214	23.174250	2000-2012 –> 2013-2019	8.765202	40347.3676
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2447	4.5556780	14377.4214	23.174250	2000-2012 –> 2013-2019	8.765202	40347.3676
Indo-Pacific	(26.5,26.75]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2447	4.5556780	14377.4214	23.174250	2000-2012 –> 2013-2019	8.765202	40347.3676
Indo-Pacific	(26.75,27]	3	cstar_tref ~ aou + phosphate + phosphate_star	5354	4.5403612	31405.2681	19.876020	1982-1999 –> 2000-2012	8.549339	73701.4539
Indo-Pacific	(26.75,27]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5354	4.5232238	31366.7748	18.928405	1982-1999 –> 2000-2012	8.520208	73619.8323
Indo-Pacific	(26.75,27]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	5354	4.3077986	30844.2463	21.980567	1982-1999 –> 2000-2012	7.995606	71884.6902
Indo-Pacific	(26.75,27]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5354	4.2906105	30803.4359	21.052395	1982-1999 –> 2000-2012	7.964508	71788.9629
Indo-Pacific	(26.75,27]	3	cstar_tref ~ temp + aou + phosphate	5354	4.7325547	31849.2068	22.112703	1982-1999 –> 2000-2012	8.938048	74866.1886
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	5354	4.2057274	30587.4712	23.104196	1982-1999 –> 2000-2012	7.885923	71596.7963
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + aou + silicate + phosphate	5354	4.7085076	31796.6584	21.818996	1982-1999 –> 2000-2012	8.895315	74748.5682
Indo-Pacific	(26.75,27]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5354	4.1702723	30498.8181	21.453131	1982-1999 –> 2000-2012	7.822736	71396.2141
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	5354	4.8218019	32051.2593	23.312826	1982-1999 –> 2000-2012	9.148674	75498.8053
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	5354	4.8218019	32051.2593	23.312826	1982-1999 –> 2000-2012	9.148674	75498.8053
Indo-Pacific	(26.75,27]	3	cstar_tref ~ aou + phosphate + phosphate_star	2868	4.9134802	17280.6429	19.343238	2000-2012 –> 2013-2019	9.453841	48685.9111
Indo-Pacific	(26.75,27]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2868	4.9018613	17269.0630	18.494849	2000-2012 –> 2013-2019	9.425085	48635.8378
Indo-Pacific	(26.75,27]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2868	4.6612052	16980.3073	20.095371	2000-2012 –> 2013-2019	8.969004	47824.5536
Indo-Pacific	(26.75,27]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2868	4.6499950	16968.4956	19.282213	2000-2012 –> 2013-2019	8.940606	47771.9315
Indo-Pacific	(26.75,27]	3	cstar_tref ~ temp + aou + phosphate	2868	5.1322867	17530.5538	18.555267	2000-2012 –> 2013-2019	9.864841	49379.7605
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	2868	4.5774010	16876.2410	16.522089	2000-2012 –> 2013-2019	8.783128	47463.7121
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + aou + silicate + phosphate	2868	5.1132156	17511.1996	17.396394	2000-2012 –> 2013-2019	9.821723	49307.8580
Indo-Pacific	(26.75,27]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2868	4.5537010	16848.4650	17.066955	2000-2012 –> 2013-2019	8.723973	47347.2831
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2868	5.2254515	17635.7438	17.046500	2000-2012 –> 2013-2019	10.047253	49687.0031
Indo-Pacific	(26.75,27]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2868	5.2254515	17635.7438	17.046500	2000-2012 –> 2013-2019	10.047253	49687.0031
Indo-Pacific	(27,27.25]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	6466	4.4389355	37635.7547	39.385070	1982-1999 –> 2000-2012	8.090056	85614.5068
Indo-Pacific	(27,27.25]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	6466	4.7089499	38399.3937	56.109262	1982-1999 –> 2000-2012	8.486198	86978.3817
Indo-Pacific	(27,27.25]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	6466	4.3929768	37503.1646	41.945012	1982-1999 –> 2000-2012	7.958712	85065.6810
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	6466	4.3599345	37403.5276	46.003290	1982-1999 –> 2000-2012	7.968003	85172.6402
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + aou + silicate + phosphate	6466	4.5799992	38040.3224	37.420573	1982-1999 –> 2000-2012	8.364560	86653.4940
Indo-Pacific	(27,27.25]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	6466	3.9500266	36128.6900	31.512269	1982-1999 –> 2000-2012	7.252857	82337.5496
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	6466	4.7461789	38501.2320	36.893307	1982-1999 –> 2000-2012	8.687012	87829.5354
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	6466	4.6882058	38342.2992	36.052942	1982-1999 –> 2000-2012	8.593789	87511.8009
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	6466	4.6882058	38342.2992	36.052942	1982-1999 –> 2000-2012	8.593789	87511.8009
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	6466	4.6882058	38342.2992	36.052942	1982-1999 –> 2000-2012	8.593789	87511.8009
Indo-Pacific	(27,27.25]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3470	5.1328308	21210.8952	31.173698	2000-2012 –> 2013-2019	9.571766	58846.6499
Indo-Pacific	(27,27.25]	4	cstar_tref ~ sal + aou + silicate + phosphate	3470	5.3345972	21478.4743	22.271388	2000-2012 –> 2013-2019	10.081157	59980.7427
Indo-Pacific	(27,27.25]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3470	5.0789520	21139.6617	33.597697	2000-2012 –> 2013-2019	9.471929	58642.8263
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	3470	5.1322261	21210.0776	39.784583	2000-2012 –> 2013-2019	9.492161	58613.6052
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + aou + silicate + phosphate	3470	5.2457410	21361.9039	28.969816	2000-2012 –> 2013-2019	9.825740	59402.2264
Indo-Pacific	(27,27.25]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3470	4.4723380	20256.9380	25.616236	2000-2012 –> 2013-2019	8.422365	56385.6280
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	3470	5.4066556	21571.5906	28.251741	2000-2012 –> 2013-2019	10.152835	60072.8226
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	3470	5.3226341	21462.8935	27.632792	2000-2012 –> 2013-2019	10.010840	59805.1927
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	3470	5.3226341	21462.8935	27.632792	2000-2012 –> 2013-2019	10.010840	59805.1927
Indo-Pacific	(27,27.25]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	3470	5.3226341	21462.8935	27.632792	2000-2012 –> 2013-2019	10.010840	59805.1927
Indo-Pacific	(27.25,27.5]	3	cstar_tref ~ aou + silicate + phosphate	5847	3.9594704	32695.3009	33.448037	1982-1999 –> 2000-2012	7.223782	73775.0697
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5847	3.9594630	32697.2790	33.418727	1982-1999 –> 2000-2012	7.221070	73765.9675
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + aou + silicate + phosphate	5847	3.8461151	32357.6286	30.339456	1982-1999 –> 2000-2012	7.021167	73001.7908
Indo-Pacific	(27.25,27.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5847	3.6920890	31881.6814	32.521736	1982-1999 –> 2000-2012	6.762564	71999.2104
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	5847	3.7105782	31938.0962	31.726047	1982-1999 –> 2000-2012	6.781708	72056.9912
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	5847	3.7568967	32083.1670	30.801943	1982-1999 –> 2000-2012	6.844184	72284.8816
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	5847	3.7568967	32083.1670	30.801943	1982-1999 –> 2000-2012	6.844184	72284.8816
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5847	3.7568967	32083.1670	30.801943	1982-1999 –> 2000-2012	6.844184	72284.8816
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ temp + aou + silicate + phosphate	5847	3.9564842	32688.4779	34.034247	1982-1999 –> 2000-2012	7.220526	73768.9438
Indo-Pacific	(27.25,27.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5847	3.3461863	30731.3292	33.390589	1982-1999 –> 2000-2012	6.270480	70078.9213
Indo-Pacific	(27.25,27.5]	3	cstar_tref ~ aou + silicate + phosphate	3127	4.6475693	18492.3392	32.264940	2000-2012 –> 2013-2019	8.607040	51187.6401
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	3127	4.6475485	18494.3112	32.208168	2000-2012 –> 2013-2019	8.607012	51191.5902
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + aou + silicate + phosphate	3127	4.5032127	18297.0049	28.659822	2000-2012 –> 2013-2019	8.349328	50654.6335
Indo-Pacific	(27.25,27.5]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3127	4.3037583	18015.6837	32.127293	2000-2012 –> 2013-2019	7.995847	49897.3651
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	3127	4.3425043	18069.7354	30.551097	2000-2012 –> 2013-2019	8.053082	50007.8316
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	3127	4.4121255	18169.2074	29.187384	2000-2012 –> 2013-2019	8.169022	50252.3744
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	3127	4.4121255	18169.2074	29.187384	2000-2012 –> 2013-2019	8.169022	50252.3744
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	3127	4.4121255	18169.2074	29.187384	2000-2012 –> 2013-2019	8.169022	50252.3744
Indo-Pacific	(27.25,27.5]	4	cstar_tref ~ temp + aou + silicate + phosphate	3127	4.6438859	18489.3806	33.023859	2000-2012 –> 2013-2019	8.600370	51177.8584
Indo-Pacific	(27.25,27.5]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3127	3.8437243	17308.6883	33.232474	2000-2012 –> 2013-2019	7.189910	48040.0175
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	5836	3.5070701	31219.6540	20.172306	1982-1999 –> 2000-2012	6.135140	69895.5542
Indo-Pacific	(27.5,27.75]	3	cstar_tref ~ sal + aou + phosphate_star	5836	3.5667966	31414.7582	27.481765	1982-1999 –> 2000-2012	6.196586	70099.2635
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + aou + silicate + phosphate	5836	3.5684756	31422.2510	27.037264	1982-1999 –> 2000-2012	6.053853	69193.2287
Indo-Pacific	(27.5,27.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	5836	3.2280103	30253.8699	9.417658	1982-1999 –> 2000-2012	5.571568	67074.4342
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	5836	3.3807244	30791.3972	22.456992	1982-1999 –> 2000-2012	5.742317	67734.2326
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	5836	3.4363673	30981.9413	25.357370	1982-1999 –> 2000-2012	5.813590	68031.7039
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	5836	3.4363673	30981.9413	25.357370	1982-1999 –> 2000-2012	5.813590	68031.7039
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5836	3.4363673	30981.9413	25.357370	1982-1999 –> 2000-2012	5.813590	68031.7039
Indo-Pacific	(27.5,27.75]	3	cstar_tref ~ sal + silicate + phosphate_star	5836	3.6584353	31710.8495	29.513815	1982-1999 –> 2000-2012	6.169877	69648.9367
Indo-Pacific	(27.5,27.75]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	5836	3.3691828	30753.4813	15.287781	1982-1999 –> 2000-2012	5.812132	68247.3438
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	3104	4.1222456	17613.7695	17.053811	2000-2012 –> 2013-2019	7.629316	48833.4235
Indo-Pacific	(27.5,27.75]	3	cstar_tref ~ sal + aou + phosphate_star	3104	4.3065788	17883.3432	29.304857	2000-2012 –> 2013-2019	7.873375	49298.1014
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + aou + silicate + phosphate	3104	4.3322538	17922.2442	26.788532	2000-2012 –> 2013-2019	7.900729	49344.4952
Indo-Pacific	(27.5,27.75]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	3104	3.7804110	17078.3721	11.020697	2000-2012 –> 2013-2019	7.008421	47332.2420
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	3104	4.0989818	17578.6356	23.944569	2000-2012 –> 2013-2019	7.479706	48370.0328
Indo-Pacific	(27.5,27.75]	3	cstar_tref ~ sal + oxygen + phosphate	3104	4.3404132	17931.9253	30.547742	2000-2012 –> 2013-2019	7.914689	49371.1324
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	3104	4.2088784	17742.8844	27.865993	2000-2012 –> 2013-2019	7.645246	48724.8257
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	3104	4.2088784	17742.8844	27.865993	2000-2012 –> 2013-2019	7.645246	48724.8257
Indo-Pacific	(27.5,27.75]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	3104	4.2088784	17742.8844	27.865993	2000-2012 –> 2013-2019	7.645246	48724.8257
Indo-Pacific	(27.5,27.75]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	3104	4.0127640	17448.6640	19.751773	2000-2012 –> 2013-2019	7.381947	48202.1453
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2317	2.7304690	11242.0909	21.046900	1982-1999 –> 2000-2012	4.662358	24262.9999
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2317	2.7697926	11308.3527	23.085715	1982-1999 –> 2000-2012	4.708540	24351.4525
Indo-Pacific	(27.75,27.85]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2317	2.7290365	11241.6591	21.325228	1982-1999 –> 2000-2012	4.650760	24231.5321
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	2317	2.7408402	11259.6589	23.487260	1982-1999 –> 2000-2012	4.687996	24329.8596
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ temp + aou + silicate + phosphate	2317	2.7417874	11261.2601	20.642191	1982-1999 –> 2000-2012	4.687075	24325.4494
Indo-Pacific	(27.75,27.85]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2317	2.6406178	11089.0349	20.968772	1982-1999 –> 2000-2012	4.548200	24032.6569
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2317	2.7384695	11255.6490	20.449118	1982-1999 –> 2000-2012	4.689522	24338.3683
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2317	2.7373185	11253.7009	20.385504	1982-1999 –> 2000-2012	4.689757	24340.8662
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2317	2.7373185	11253.7009	20.385504	1982-1999 –> 2000-2012	4.689757	24340.8662
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2317	2.7373185	11253.7009	20.385504	1982-1999 –> 2000-2012	4.689757	24340.8662
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1264	3.1716141	6516.9969	31.692509	2000-2012 –> 2013-2019	5.941407	17825.3496
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ sal + aou + silicate + phosphate	1264	3.1874884	6529.6183	29.149027	2000-2012 –> 2013-2019	5.940246	17809.3821
Indo-Pacific	(27.75,27.85]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1264	3.1693826	6517.2176	30.950746	2000-2012 –> 2013-2019	5.898419	17758.8767
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	1264	3.1779674	6522.0559	29.072248	2000-2012 –> 2013-2019	5.916047	17777.0445
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	1264	3.1768073	6521.1329	29.025171	2000-2012 –> 2013-2019	5.911793	17770.8822
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1264	3.1768073	6521.1329	29.025171	2000-2012 –> 2013-2019	5.911793	17770.8822
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1264	3.1768073	6521.1329	29.025171	2000-2012 –> 2013-2019	5.911793	17770.8822
Indo-Pacific	(27.75,27.85]	3	cstar_tref ~ sal + silicate + phosphate_star	1264	3.1799375	6521.6226	29.845922	2000-2012 –> 2013-2019	5.933455	17800.6665
Indo-Pacific	(27.75,27.85]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	1264	3.1128492	6469.7178	31.766441	2000-2012 –> 2013-2019	5.853689	17729.3767
Indo-Pacific	(27.75,27.85]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1264	3.0665742	6433.8549	28.861392	2000-2012 –> 2013-2019	5.707192	17522.8898
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2907	2.7916993	14230.6545	33.332942	1982-1999 –> 2000-2012	4.935430	31738.1725
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2907	2.7949337	14237.3865	33.577486	1982-1999 –> 2000-2012	4.955391	31807.2408
Indo-Pacific	(27.85,27.95]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2907	2.7913452	14231.9170	33.450567	1982-1999 –> 2000-2012	4.933683	31736.2227
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	2907	2.7938709	14235.1753	33.889830	1982-1999 –> 2000-2012	4.953379	31801.5053
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + aou + silicate + phosphate	2907	2.7953002	14238.1489	33.042313	1982-1999 –> 2000-2012	4.942185	31757.4596
Indo-Pacific	(27.85,27.95]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2907	2.7856872	14220.1201	34.100919	1982-1999 –> 2000-2012	4.926975	31720.4944
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2907	2.7945654	14236.6204	33.041333	1982-1999 –> 2000-2012	4.942281	31759.0352
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2907	2.7948101	14237.1294	33.015412	1982-1999 –> 2000-2012	4.942986	31761.2604
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2907	2.7948101	14237.1294	33.015412	1982-1999 –> 2000-2012	4.942986	31761.2604
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2907	2.7948101	14237.1294	33.015412	1982-1999 –> 2000-2012	4.942986	31761.2604
Indo-Pacific	(27.85,27.95]	3	cstar_tref ~ aou + phosphate + phosphate_star	1542	3.3195387	8086.2692	35.090356	2000-2012 –> 2013-2019	6.114488	22321.6887
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1542	3.3126052	8081.8211	35.442498	2000-2012 –> 2013-2019	6.104304	22312.4755
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1542	3.3135799	8082.7283	35.646015	2000-2012 –> 2013-2019	6.108513	22320.1148
Indo-Pacific	(27.85,27.95]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1542	3.3089038	8080.3731	35.834119	2000-2012 –> 2013-2019	6.100249	22312.2901
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	1542	3.2669990	8039.0671	37.333823	2000-2012 –> 2013-2019	6.060870	22274.2424
Indo-Pacific	(27.85,27.95]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1542	3.2637446	8037.9935	37.426960	2000-2012 –> 2013-2019	6.049432	22258.1136
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1542	3.3192220	8087.9751	34.929845	2000-2012 –> 2013-2019	6.113787	22324.5955
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1542	3.3201728	8088.8583	34.874578	2000-2012 –> 2013-2019	6.114983	22325.9877
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1542	3.3201728	8088.8583	34.874578	2000-2012 –> 2013-2019	6.114983	22325.9877
Indo-Pacific	(27.85,27.95]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1542	3.3201728	8088.8583	34.874578	2000-2012 –> 2013-2019	6.114983	22325.9877
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	2467	2.2624239	11041.3418	8.237248	1982-1999 –> 2000-2012	4.184588	25738.2975
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	2467	2.2511588	11016.7129	7.786842	1982-1999 –> 2000-2012	4.236774	25943.8015
Indo-Pacific	(27.95,28.05]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	2467	2.2115502	10931.1275	8.468880	1982-1999 –> 2000-2012	4.102269	25513.2034
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate	2467	2.2777752	11074.7074	8.288880	1982-1999 –> 2000-2012	4.210664	25811.0912
Indo-Pacific	(27.95,28.05]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	2467	2.1886299	10879.7253	7.878228	1982-1999 –> 2000-2012	4.064290	25405.1370
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	2467	2.2787563	11076.8322	8.277324	1982-1999 –> 2000-2012	4.213757	25820.9529
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	2467	2.2789172	11077.1806	8.289996	1982-1999 –> 2000-2012	4.213832	25820.9878
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	2467	2.2789172	11077.1806	8.289996	1982-1999 –> 2000-2012	4.213832	25820.9878
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2467	2.2789172	11077.1806	8.289996	1982-1999 –> 2000-2012	4.213832	25820.9878
Indo-Pacific	(27.95,28.05]	3	cstar_tref ~ temp + silicate + phosphate_star	2467	2.2794555	11076.3459	8.377885	1982-1999 –> 2000-2012	4.214682	25819.2952
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1354	2.5384577	6377.1411	7.728054	2000-2012 –> 2013-2019	4.800882	17418.4829
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ sal + aou + phosphate + phosphate_star	1354	2.4939482	6329.2376	8.352020	2000-2012 –> 2013-2019	4.745107	17345.9505
Indo-Pacific	(27.95,28.05]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1354	2.4779038	6313.7598	8.329809	2000-2012 –> 2013-2019	4.689454	17244.8873
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + aou + phosphate + phosphate_star	1354	2.4648617	6297.4690	8.721893	2000-2012 –> 2013-2019	4.716500	17315.2334
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate	1354	2.5573875	6397.2602	7.772823	2000-2012 –> 2013-2019	4.835163	17471.9676
Indo-Pacific	(27.95,28.05]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1354	2.4266912	6257.2052	8.523746	2000-2012 –> 2013-2019	4.615321	17136.9304
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	1354	2.5567349	6396.5691	7.765420	2000-2012 –> 2013-2019	4.835491	17473.4013
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1354	2.5570958	6396.9513	7.768822	2000-2012 –> 2013-2019	4.836013	17474.1319
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1354	2.5570958	6396.9513	7.768822	2000-2012 –> 2013-2019	4.836013	17474.1319
Indo-Pacific	(27.95,28.05]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	1354	2.5570958	6396.9513	7.768822	2000-2012 –> 2013-2019	4.836013	17474.1319
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	1718	1.8848420	7065.3607	9.810959	1982-1999 –> 2000-2012	3.584409	17034.4465
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ sal + aou + silicate + phosphate	1718	1.9503440	7182.7407	8.816710	1982-1999 –> 2000-2012	3.570913	16908.7065
Indo-Pacific	(28.05,28.1]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	1718	1.8450332	6994.0133	9.467590	1982-1999 –> 2000-2012	3.441478	16645.3685
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	1718	1.9539957	7189.1680	8.935869	1982-1999 –> 2000-2012	3.595080	16979.3910
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	1718	1.9539957	7189.1680	8.935869	1982-1999 –> 2000-2012	3.595080	16979.3910
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	1718	1.9539957	7189.1680	8.935869	1982-1999 –> 2000-2012	3.595080	16979.3910
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + aou + silicate + phosphate	1718	1.8950101	7083.8471	9.849801	1982-1999 –> 2000-2012	3.603161	17078.6673
Indo-Pacific	(28.05,28.1]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	1718	1.8032691	6915.3424	9.697645	1982-1999 –> 2000-2012	3.429878	16662.3098
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	1718	1.8961482	7085.9101	9.843194	1982-1999 –> 2000-2012	3.606103	17086.1201
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	1718	1.8961482	7085.9101	9.843194	1982-1999 –> 2000-2012	3.606103	17086.1201
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	966	2.1066397	4192.9110	9.987464	2000-2012 –> 2013-2019	3.991482	11258.2717
Indo-Pacific	(28.05,28.1]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	966	2.0390556	4131.9137	9.747515	2000-2012 –> 2013-2019	3.884089	11125.9270
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	966	2.1032628	4189.8117	9.400527	2000-2012 –> 2013-2019	4.057259	11378.9797
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + aou + silicate + phosphate	966	2.1188554	4204.0818	10.037184	2000-2012 –> 2013-2019	4.013866	11287.9289
Indo-Pacific	(28.05,28.1]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	966	2.0001288	4094.6740	9.111786	2000-2012 –> 2013-2019	3.803398	11010.0164
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	966	2.1192706	4204.4603	10.033932	2000-2012 –> 2013-2019	4.015802	11291.0651
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate	966	2.1186866	4203.9279	10.028459	2000-2012 –> 2013-2019	4.014835	11289.8379
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + oxygen + silicate + phosphate_star	966	2.1186866	4203.9279	10.028459	2000-2012 –> 2013-2019	4.014835	11289.8379
Indo-Pacific	(28.05,28.1]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	966	2.1186866	4203.9279	10.028459	2000-2012 –> 2013-2019	4.014835	11289.8379
Indo-Pacific	(28.05,28.1]	3	cstar_tref ~ temp + silicate + phosphate_star	966	2.1380335	4219.4899	10.237607	2000-2012 –> 2013-2019	4.045323	11323.5296
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	14627	1.6310156	55832.7692	18.423930	1982-1999 –> 2000-2012	3.030668	127227.2398
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + aou + silicate + phosphate	14627	1.4320006	52025.9353	13.806990	1982-1999 –> 2000-2012	2.708801	119684.1812
Indo-Pacific	(28.1, Inf]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	14627	1.3378772	50039.0036	16.225048	1982-1999 –> 2000-2012	2.509014	114186.0580
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	14627	1.6072254	55402.9247	9.839246	1982-1999 –> 2000-2012	3.103039	129499.7490
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	14627	1.6072254	55402.9247	9.839246	1982-1999 –> 2000-2012	3.103039	129499.7490
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	14627	1.6072254	55402.9247	9.839246	1982-1999 –> 2000-2012	3.103039	129499.7490
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ temp + aou + silicate + phosphate	14627	1.6564391	56285.2493	18.364072	1982-1999 –> 2000-2012	3.077562	128298.8415
Indo-Pacific	(28.1, Inf]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	14627	1.3940533	51242.2624	17.034744	1982-1999 –> 2000-2012	2.634077	117713.8450
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	14627	1.6670006	56471.1807	18.226788	1982-1999 –> 2000-2012	3.099984	128822.7887
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ temp + silicate + phosphate + phosphate_star	14627	1.6697977	56520.2259	18.221976	1982-1999 –> 2000-2012	3.105173	128939.6726
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ aou + silicate + phosphate + phosphate_star	7804	1.8640423	31878.6342	16.201195	2000-2012 –> 2013-2019	3.495058	87711.4034
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + aou + silicate + phosphate	7804	1.5693631	29192.8476	10.689506	2000-2012 –> 2013-2019	3.001364	81218.7829
Indo-Pacific	(28.1, Inf]	5	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	7804	1.4923380	28409.3615	12.644005	2000-2012 –> 2013-2019	2.830215	78448.3652
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + aou + silicate + phosphate_star	7804	1.7461744	30859.1181	9.861265	2000-2012 –> 2013-2019	3.396520	87036.5449
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate	7804	1.7050926	30487.5244	9.446823	2000-2012 –> 2013-2019	3.312318	85890.4491
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + oxygen + silicate + phosphate_star	7804	1.7050926	30487.5244	9.446823	2000-2012 –> 2013-2019	3.312318	85890.4491
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ sal + silicate + phosphate + phosphate_star	7804	1.7050926	30487.5244	9.446823	2000-2012 –> 2013-2019	3.312318	85890.4491
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ temp + aou + silicate + phosphate	7804	1.8922532	32113.0803	16.180287	2000-2012 –> 2013-2019	3.548692	88398.3296
Indo-Pacific	(28.1, Inf]	5	cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star	7804	1.5521124	29022.3323	13.774789	2000-2012 –> 2013-2019	2.946166	80264.5947
Indo-Pacific	(28.1, Inf]	4	cstar_tref ~ temp + aou + silicate + phosphate_star	7804	1.9004563	32180.5960	16.022465	2000-2012 –> 2013-2019	3.567457	88651.7767

5.3.2 per fitting unit

lm_best %>%
  select(-n_predictors) %>%
  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	3.389813	1439.0912
Atlantic	(-Inf,26]	2000-2012 –> 2013-2019	3.237034	886.1451
Atlantic	(26,26.5]	1982-1999 –> 2000-2012	8.813128	14918.5158
Atlantic	(26,26.5]	2000-2012 –> 2013-2019	8.856521	9397.3295
Atlantic	(26.5,26.75]	1982-1999 –> 2000-2012	6.543270	17140.8674
Atlantic	(26.5,26.75]	2000-2012 –> 2013-2019	6.845457	10884.7273
Atlantic	(26.75,27]	1982-1999 –> 2000-2012	4.042142	23296.8230
Atlantic	(26.75,27]	2000-2012 –> 2013-2019	4.892561	16705.9708
Atlantic	(27,27.25]	1982-1999 –> 2000-2012	4.360957	20326.9842
Atlantic	(27,27.25]	2000-2012 –> 2013-2019	4.835373	14460.4842
Atlantic	(27.25,27.5]	1982-1999 –> 2000-2012	5.967402	24345.6004
Atlantic	(27.25,27.5]	2000-2012 –> 2013-2019	7.119557	16646.2260
Atlantic	(27.5,27.75]	1982-1999 –> 2000-2012	5.876991	32275.4723
Atlantic	(27.5,27.75]	2000-2012 –> 2013-2019	6.280632	21984.0272
Atlantic	(27.75,27.85]	1982-1999 –> 2000-2012	4.029915	9932.7992
Atlantic	(27.75,27.85]	2000-2012 –> 2013-2019	4.415502	6812.1161
Atlantic	(27.85,27.95]	1982-1999 –> 2000-2012	6.374315	11883.6415
Atlantic	(27.85,27.95]	2000-2012 –> 2013-2019	7.189070	8369.4254
Atlantic	(27.95,28.05]	1982-1999 –> 2000-2012	9.446965	17166.3902
Atlantic	(27.95,28.05]	2000-2012 –> 2013-2019	8.989257	10971.9755
Atlantic	(28.05,28.1]	1982-1999 –> 2000-2012	2.065281	5408.3394
Atlantic	(28.05,28.1]	2000-2012 –> 2013-2019	2.308932	3872.8236
Atlantic	(28.1,28.15]	1982-1999 –> 2000-2012	1.526773	5042.1028
Atlantic	(28.1,28.15]	2000-2012 –> 2013-2019	1.832486	3754.9297
Atlantic	(28.15,28.2]	1982-1999 –> 2000-2012	1.549397	8806.7612
Atlantic	(28.15,28.2]	2000-2012 –> 2013-2019	1.722066	5785.0623
Atlantic	(28.2, Inf]	1982-1999 –> 2000-2012	1.497134	14297.0469
Atlantic	(28.2, Inf]	2000-2012 –> 2013-2019	1.700124	10508.1859
Indo-Pacific	(-Inf,26]	1982-1999 –> 2000-2012	14.738487	85311.8067
Indo-Pacific	(-Inf,26]	2000-2012 –> 2013-2019	14.155002	54789.3783
Indo-Pacific	(26,26.5]	1982-1999 –> 2000-2012	9.613109	78986.4231
Indo-Pacific	(26,26.5]	2000-2012 –> 2013-2019	9.760913	50791.4230
Indo-Pacific	(26.5,26.75]	1982-1999 –> 2000-2012	8.138002	61096.1623
Indo-Pacific	(26.5,26.75]	2000-2012 –> 2013-2019	8.638963	40128.8807
Indo-Pacific	(26.75,27]	1982-1999 –> 2000-2012	8.486903	73460.0317
Indo-Pacific	(26.75,27]	2000-2012 –> 2013-2019	9.407671	48579.0854
Indo-Pacific	(27,27.25]	1982-1999 –> 2000-2012	8.258876	86218.7191
Indo-Pacific	(27,27.25]	2000-2012 –> 2013-2019	9.705047	59136.0079
Indo-Pacific	(27.25,27.5]	1982-1999 –> 2000-2012	6.903385	72530.1540
Indo-Pacific	(27.25,27.5]	2000-2012 –> 2013-2019	8.190966	50291.4060
Indo-Pacific	(27.5,27.75]	1982-1999 –> 2000-2012	5.912224	68598.8105
Indo-Pacific	(27.5,27.75]	2000-2012 –> 2013-2019	7.612392	48692.6050
Indo-Pacific	(27.75,27.85]	1982-1999 –> 2000-2012	4.670372	24289.4917
Indo-Pacific	(27.75,27.85]	2000-2012 –> 2013-2019	5.892583	17753.6233
Indo-Pacific	(27.85,27.95]	1982-1999 –> 2000-2012	4.941828	31760.3912
Indo-Pacific	(27.85,27.95]	2000-2012 –> 2013-2019	6.099659	22310.1484
Indo-Pacific	(27.95,28.05]	1982-1999 –> 2000-2012	4.186852	25751.4742
Indo-Pacific	(27.95,28.05]	2000-2012 –> 2013-2019	4.774596	17382.9249
Indo-Pacific	(28.05,28.1]	1982-1999 –> 2000-2012	3.562729	16943.9912
Indo-Pacific	(28.05,28.1]	2000-2012 –> 2013-2019	3.985572	11254.5232
Indo-Pacific	(28.1, Inf]	1982-1999 –> 2000-2012	2.947440	125337.1874
Indo-Pacific	(28.1, Inf]	2000-2012 –> 2013-2019	3.272242	84940.1145

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 = ""))

lm_best %>%
  write_csv(paste(path_version_data,
                  "lm_best.csv",
                  sep = ""))

6 Model diagnotics

6.1 Selection criterion vs predictors

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

Version	Author	Date
2093979	Donghe-Zhu	2021-03-10
b865899	Donghe-Zhu	2021-03-10
cc2a956	Donghe-Zhu	2021-03-10
60689fb	Donghe-Zhu	2021-03-10
dba33c8	Donghe-Zhu	2021-03-09
17f1c4a	Donghe-Zhu	2021-03-09
c024d1a	Donghe-Zhu	2021-03-09
02f7242	Donghe-Zhu	2021-03-09
6f50bc6	Donghe-Zhu	2021-03-09
1691156	Donghe-Zhu	2021-03-08
c0ceaf8	Donghe-Zhu	2021-03-08
058e0a1	Donghe-Zhu	2021-03-08
112dea0	Donghe-Zhu	2021-03-08
1843412	Donghe-Zhu	2021-03-08
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
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")

Version	Author	Date
2093979	Donghe-Zhu	2021-03-10
b865899	Donghe-Zhu	2021-03-10
cc2a956	Donghe-Zhu	2021-03-10
60689fb	Donghe-Zhu	2021-03-10
dba33c8	Donghe-Zhu	2021-03-09
17f1c4a	Donghe-Zhu	2021-03-09
c024d1a	Donghe-Zhu	2021-03-09
02f7242	Donghe-Zhu	2021-03-09
6f50bc6	Donghe-Zhu	2021-03-09
1691156	Donghe-Zhu	2021-03-08
c0ceaf8	Donghe-Zhu	2021-03-08
058e0a1	Donghe-Zhu	2021-03-08
112dea0	Donghe-Zhu	2021-03-08
1843412	Donghe-Zhu	2021-03-08
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c407a50	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
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)

Version	Author	Date
2093979	Donghe-Zhu	2021-03-10
b865899	Donghe-Zhu	2021-03-10
cc2a956	Donghe-Zhu	2021-03-10
dba33c8	Donghe-Zhu	2021-03-09
17f1c4a	Donghe-Zhu	2021-03-09
c024d1a	Donghe-Zhu	2021-03-09
02f7242	Donghe-Zhu	2021-03-09
1691156	Donghe-Zhu	2021-03-08
c0ceaf8	Donghe-Zhu	2021-03-08
058e0a1	Donghe-Zhu	2021-03-08
112dea0	Donghe-Zhu	2021-03-08
1843412	Donghe-Zhu	2021-03-08
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
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)

Version	Author	Date
2093979	Donghe-Zhu	2021-03-10
b865899	Donghe-Zhu	2021-03-10
cc2a956	Donghe-Zhu	2021-03-10
60689fb	Donghe-Zhu	2021-03-10
dba33c8	Donghe-Zhu	2021-03-09
17f1c4a	Donghe-Zhu	2021-03-09
c024d1a	Donghe-Zhu	2021-03-09
02f7242	Donghe-Zhu	2021-03-09
6f50bc6	Donghe-Zhu	2021-03-09
1691156	Donghe-Zhu	2021-03-08
c0ceaf8	Donghe-Zhu	2021-03-08
058e0a1	Donghe-Zhu	2021-03-08
112dea0	Donghe-Zhu	2021-03-08
1843412	Donghe-Zhu	2021-03-08
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c407a50	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
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	phosphate	phosphate_star	sal	silicate	temp	oxygen
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26]	10	6	6	8	5	2	0
(26,26.5]	6	7	7	2	10	7	2
(26.5,26.75]	7	7	7	3	10	6	2
(26.75,27]	7	7	7	3	10	6	2
(27,27.25]	7	7	7	6	10	3	2
(27.25,27.5]	8	8	7	4	8	5	1
(27.5,27.75]	8	8	7	4	8	5	1
(27.75,27.85]	10	9	7	4	6	4	0
(27.85,27.95]	8	10	7	2	6	6	1
(27.95,28.05]	7	8	8	2	8	7	2
(28.05,28.1]	8	9	7	2	6	6	2
(28.1,28.15]	7	9	8	2	7	6	2
(28.15,28.2]	7	8	8	2	8	7	2
(28.2, Inf]	5	8	7	5	10	4	3
total	105.00	111.00	100.00	49.00	112.00	74.00	22.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26]	10	6	6	8	5	2	0
(26,26.5]	6	7	7	2	10	7	2
(26.5,26.75]	7	7	7	3	10	6	2
(26.75,27]	7	7	7	3	10	6	2
(27,27.25]	6	7	7	7	10	2	2
(27.25,27.5]	6	7	7	9	8	1	2
(27.5,27.75]	5	7	6	10	7	0	3
(27.75,27.85]	6	7	7	9	8	1	2
(27.85,27.95]	8	10	7	2	6	6	1
(27.95,28.05]	7	8	8	2	8	7	2
(28.05,28.1]	7	9	8	2	7	6	2
(28.1,28.15]	8	10	7	2	6	6	1
(28.15,28.2]	7	8	8	2	8	7	2
(28.2, Inf]	7	8	7	6	9	3	2
total	97.00	108.00	99.00	67.00	112.00	60.00	25.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26]	7	8	8	2	8	7	2
(26,26.5]	7	8	8	2	8	7	2
(26.5,26.75]	7	8	8	2	8	7	2
(26.75,27]	8	9	8	2	6	6	1
(27,27.25]	7	8	8	2	8	7	2
(27.25,27.5]	7	8	6	6	10	2	2
(27.5,27.75]	6	6	8	9	8	1	2
(27.75,27.85]	7	8	8	2	8	7	2
(27.85,27.95]	7	8	8	2	8	7	2
(27.95,28.05]	6	7	8	2	9	7	2
(28.05,28.1]	5	8	6	5	10	4	4
(28.1, Inf]	6	8	7	5	10	4	2
total	80.00	94.00	91.00	41.00	101.00	66.00	25.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26]	6	7	8	2	8	8	2
(26,26.5]	6	7	8	2	9	7	2
(26.5,26.75]	7	8	8	2	8	7	2
(26.75,27]	8	9	7	2	6	6	2
(27,27.25]	7	8	7	2	9	7	2
(27.25,27.5]	7	8	6	6	10	2	2
(27.5,27.75]	6	7	7	9	7	1	3
(27.75,27.85]	6	7	8	8	8	2	2
(27.85,27.95]	7	8	9	2	7	6	2
(27.95,28.05]	7	8	8	2	8	7	2
(28.05,28.1]	5	7	7	2	10	7	3
(28.1, Inf]	7	7	7	6	10	3	2
total	79.00	91.00	90.00	45.00	100.00	63.00	26.00

6.4 RMSE alternatives

AIC is an alternative criterion to RMSE to judge model quality, but not (yet) taken into account.

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

Version	Author	Date
2093979	Donghe-Zhu	2021-03-10
b865899	Donghe-Zhu	2021-03-10
cc2a956	Donghe-Zhu	2021-03-10
dba33c8	Donghe-Zhu	2021-03-09
17f1c4a	Donghe-Zhu	2021-03-09
c024d1a	Donghe-Zhu	2021-03-09
02f7242	Donghe-Zhu	2021-03-09
1691156	Donghe-Zhu	2021-03-08
c0ceaf8	Donghe-Zhu	2021-03-08
058e0a1	Donghe-Zhu	2021-03-08
112dea0	Donghe-Zhu	2021-03-08
1843412	Donghe-Zhu	2021-03-08
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
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)

Version	Author	Date
2093979	Donghe-Zhu	2021-03-10
b865899	Donghe-Zhu	2021-03-10
cc2a956	Donghe-Zhu	2021-03-10
60689fb	Donghe-Zhu	2021-03-10
dba33c8	Donghe-Zhu	2021-03-09
17f1c4a	Donghe-Zhu	2021-03-09
c024d1a	Donghe-Zhu	2021-03-09
02f7242	Donghe-Zhu	2021-03-09
6f50bc6	Donghe-Zhu	2021-03-09
1691156	Donghe-Zhu	2021-03-08
c0ceaf8	Donghe-Zhu	2021-03-08
058e0a1	Donghe-Zhu	2021-03-08
112dea0	Donghe-Zhu	2021-03-08
1843412	Donghe-Zhu	2021-03-08
3fbbfa4	Donghe-Zhu	2021-03-07
627c8fb	Donghe-Zhu	2021-03-07
9ef3222	Donghe-Zhu	2021-03-05
8c1e978	Donghe-Zhu	2021-03-05
865f68c	Donghe-Zhu	2021-03-05
ee69bc1	Donghe-Zhu	2021-03-05
a79291f	Donghe-Zhu	2021-03-05
e8c6f30	Donghe-Zhu	2021-03-04
59288fe	Donghe-Zhu	2021-03-04
731abc8	Donghe-Zhu	2021-03-04
e2a5a33	Donghe-Zhu	2021-03-04
c7892c1	Donghe-Zhu	2021-03-04
924430b	Donghe-Zhu	2021-03-03
0d0bca1	Donghe-Zhu	2021-03-03
cb63c16	Donghe-Zhu	2021-03-03
ffda45a	Donghe-Zhu	2021-03-03
691ba81	Donghe-Zhu	2021-03-03
c5e45a2	Donghe-Zhu	2021-03-03
89c3e58	Donghe-Zhu	2021-03-03
c407a50	Donghe-Zhu	2021-03-03
c911669	Donghe-Zhu	2021-03-03
b71c719	Donghe-Zhu	2021-03-01
13666ca	Donghe-Zhu	2021-03-01
c6e60fe	Donghe-Zhu	2021-03-01
7a388f7	Donghe-Zhu	2021-03-01
799e913	Donghe-Zhu	2021-03-01
66ff99f	Donghe-Zhu	2021-03-01
ac9bb7a	Donghe-Zhu	2021-02-28
efdc047	Donghe-Zhu	2021-02-28
e9a7418	Donghe-Zhu	2021-02-28
e152917	Donghe-Zhu	2021-02-28
287123c	Donghe-Zhu	2021-02-27
54d5b5b	Donghe-Zhu	2021-02-27
330f064	Donghe-Zhu	2021-02-27
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

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

eMLR - model fitting

Jens Daniel Müller and Donghe Zhu

10 March, 2021