eMLR - model fitting

workflowr

• Summary
• Checks
• Past versions

Last updated: 2021-04-08

Checks: 7 0

Knit directory: emlr_obs_v_XXX/

This reproducible R Markdown analysis was created with workflowr (version 1.6.2). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

---

R Markdown file: up-to-date

Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Environment: empty

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

Seed: set.seed(20200707)

The command set.seed(20200707) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Session information: recorded

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Cache: none

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

File paths: relative

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Repository version: 05a66fd

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version 05a66fd. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:

Ignored files:
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/

Untracked files:
    Untracked:  code/previous_script_versions/analysis_this_study.Rmd
    Untracked:  code/previous_script_versions/analysis_this_study_vs_Gruber_2019.Rmd
    Untracked:  code/previous_script_versions/mapping_target_variable.Rmd
    Untracked:  data/

Unstaged changes:
    Modified:   analysis/_site.yml
    Deleted:    analysis/analysis_this_study.Rmd
    Deleted:    analysis/analysis_this_study_vs_Gruber_2019.Rmd
    Deleted:    analysis/mapping_target_variable.Rmd
    Modified:   code/Workflowr_project_managment.R

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.

---

These are the previous versions of the repository in which changes were made to the R Markdown (analysis/eMLR_model_fitting.Rmd) and HTML (docs/eMLR_model_fitting.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File	Version	Author	Date	Message
html	c0895f8	jens-daniel-mueller	2021-04-07	Build site.
html	156d5b7	jens-daniel-mueller	2021-04-07	Build site.
html	eb827c9	jens-daniel-mueller	2021-04-07	Build site.
html	d3c3fde	jens-daniel-mueller	2021-03-26	Build site.
Rmd	88fa519	jens-daniel-mueller	2021-03-26	included model data
html	594d503	jens-daniel-mueller	2021-03-26	Build site.
Rmd	e4ef0f6	jens-daniel-mueller	2021-03-26	included model data
html	06bfaf7	jens-daniel-mueller	2021-03-26	Build site.
Rmd	6d2102a	jens-daniel-mueller	2021-03-26	included model data
html	2eb881a	jens-daniel-mueller	2021-03-26	Build site.
Rmd	a9e976a	jens-daniel-mueller	2021-03-26	included model data
html	03b6009	jens-daniel-mueller	2021-03-23	removed before copying template
html	de6256b	jens-daniel-mueller	2021-03-23	Build site.
html	f155edd	jens-daniel-mueller	2021-03-23	Build site.
html	380d215	jens-daniel-mueller	2021-03-21	Build site.
html	33b385b	jens-daniel-mueller	2021-03-20	Build site.
Rmd	6c5618b	jens-daniel-mueller	2021-03-20	rerun with vif threshold
html	108d6b2	jens-daniel-mueller	2021-03-20	Build site.
Rmd	2b99ba0	jens-daniel-mueller	2021-03-20	included vif removel option
html	330dcd0	jens-daniel-mueller	2021-03-20	Build site.
Rmd	4df8990	jens-daniel-mueller	2021-03-20	added vif calculation and plots
html	83a13de	jens-daniel-mueller	2021-03-20	Build site.
html	cf98c6d	jens-daniel-mueller	2021-03-16	Build site.
html	a1d52ff	jens-daniel-mueller	2021-03-15	Build site.
html	0bade3b	jens-daniel-mueller	2021-03-15	Build site.
html	27c1f4b	jens-daniel-mueller	2021-03-14	Build site.
html	af75ebf	jens-daniel-mueller	2021-03-14	Build site.
html	5017709	jens-daniel-mueller	2021-03-11	Build site.
html	585b07f	jens-daniel-mueller	2021-03-11	Build site.
html	6482ed7	jens-daniel-mueller	2021-03-11	Build site.
html	85a5ed2	jens-daniel-mueller	2021-03-10	Build site.
html	00688a1	jens-daniel-mueller	2021-03-05	Build site.
html	6c0bec6	jens-daniel-mueller	2021-03-05	Build site.
html	3c2ec33	jens-daniel-mueller	2021-03-05	Build site.
html	af70b94	jens-daniel-mueller	2021-03-04	Build site.
Rmd	c9cf1fd	jens-daniel-mueller	2021-03-04	rebuild with NA in Cant replaced by 0
html	27ae473	jens-daniel-mueller	2021-02-24	Build site.
Rmd	7f77d91	jens-daniel-mueller	2021-02-24	removed log10 color scale
html	fec3558	jens-daniel-mueller	2021-02-24	Build site.
Rmd	9ebedac	jens-daniel-mueller	2021-02-24	latitudinal residual plots
html	4bc00ea	jens-daniel-mueller	2021-02-24	Build site.
Rmd	de11bfe	jens-daniel-mueller	2021-02-24	clean up purrr approach and residual plots
html	42eca5d	jens-daniel-mueller	2021-02-24	Build site.
Rmd	06a2f3b	jens-daniel-mueller	2021-02-24	purrr residual plots by basin
html	a1ba577	jens-daniel-mueller	2021-02-24	Build site.
Rmd	9ae7d87	jens-daniel-mueller	2021-02-24	loop residual plots by basin
html	071743d	jens-daniel-mueller	2021-02-24	Build site.
Rmd	c45672c	jens-daniel-mueller	2021-02-24	added residual plots
html	ac1a836	jens-daniel-mueller	2021-02-24	Build site.
Rmd	5f655e0	jens-daniel-mueller	2021-02-24	added plots back to after switching to map aproach
html	b03fbd3	jens-daniel-mueller	2021-02-24	Build site.
Rmd	c69736b	jens-daniel-mueller	2021-02-24	added plots back to after switching to map aproach
html	86406d5	jens-daniel-mueller	2021-02-24	Build site.
Rmd	1b3c171	jens-daniel-mueller	2021-02-24	introduced purrr::map to model fitting, rebuild all
html	3d3b4cc	jens-daniel-mueller	2021-02-23	Build site.
Rmd	cbfc388	jens-daniel-mueller	2021-02-23	introduced purrr::map to model fitting
html	7b672f7	jens-daniel-mueller	2021-01-11	Build site.
html	33ba23c	jens-daniel-mueller	2021-01-07	Build site.
Rmd	0ad30ba	jens-daniel-mueller	2021-01-07	removed GLODAP gamma filter, target variable mapped by eras+era
html	318609d	jens-daniel-mueller	2020-12-23	adapted more variable predictor selection
html	9d0b2d0	jens-daniel-mueller	2020-12-23	Build site.
html	0aa2b50	jens-daniel-mueller	2020-12-23	remove html before duplication
html	39113c3	jens-daniel-mueller	2020-12-23	Build site.
Rmd	bef9220	jens-daniel-mueller	2020-12-23	rebuild before sensitivity test
html	2886da0	jens-daniel-mueller	2020-12-19	Build site.
html	02f0ee9	jens-daniel-mueller	2020-12-18	cleaned up for copying template
html	965dba3	jens-daniel-mueller	2020-12-18	Build site.
html	5d452fe	jens-daniel-mueller	2020-12-18	Build site.
Rmd	ca65bf5	jens-daniel-mueller	2020-12-18	rebuild after final cleaning
html	7bcb4eb	jens-daniel-mueller	2020-12-18	Build site.
html	d397028	jens-daniel-mueller	2020-12-18	Build site.
Rmd	7e1b1c0	jens-daniel-mueller	2020-12-18	rebuild without na predictors
html	7131186	jens-daniel-mueller	2020-12-17	Build site.
Rmd	737d904	jens-daniel-mueller	2020-12-17	rebuild without na predictors
html	22b07fb	jens-daniel-mueller	2020-12-17	Build site.
html	a84ff3c	jens-daniel-mueller	2020-12-17	Build site.
Rmd	40369db	jens-daniel-mueller	2020-12-17	model selection criterion added
html	5b48ef5	jens-daniel-mueller	2020-12-17	Build site.
Rmd	e6ed2bc	jens-daniel-mueller	2020-12-17	plotted model results
html	f3a708f	jens-daniel-mueller	2020-12-17	Build site.
Rmd	7c8ace9	jens-daniel-mueller	2020-12-17	new MLR fitting routine, rmse corrected
html	e4ca289	jens-daniel-mueller	2020-12-16	Build site.
Rmd	3d5a3e2	jens-daniel-mueller	2020-12-16	new MLR fitting routine
html	158fe26	jens-daniel-mueller	2020-12-15	Build site.
html	7a9a4cb	jens-daniel-mueller	2020-12-15	Build site.
html	61b263c	jens-daniel-mueller	2020-12-15	Build site.
html	4d612dd	jens-daniel-mueller	2020-12-15	Build site.
html	e91cebd	jens-daniel-mueller	2020-12-15	Build site.
Rmd	d7992c4	jens-daniel-mueller	2020-12-15	eMLR target variable selection
html	953caf3	jens-daniel-mueller	2020-12-15	Build site.
html	42daf5c	jens-daniel-mueller	2020-12-14	Build site.
Rmd	923aa7f	jens-daniel-mueller	2020-12-14	rebuild with new path and auto folder creation
html	984697e	jens-daniel-mueller	2020-12-12	Build site.
html	3ebff89	jens-daniel-mueller	2020-12-12	Build site.
html	ba112d3	jens-daniel-mueller	2020-12-11	Build site.
Rmd	91b2b29	jens-daniel-mueller	2020-12-11	selectable basinmask, try 5
html	b01a367	jens-daniel-mueller	2020-12-09	Build site.
Rmd	71c63b0	jens-daniel-mueller	2020-12-09	rerun with variable predictor assignment
html	24a632f	jens-daniel-mueller	2020-12-07	Build site.
html	92dca91	jens-daniel-mueller	2020-12-07	Build site.
html	6a8004b	jens-daniel-mueller	2020-12-07	Build site.
html	70bf1a5	jens-daniel-mueller	2020-12-07	Build site.
html	7555355	jens-daniel-mueller	2020-12-07	Build site.
html	143d6fa	jens-daniel-mueller	2020-12-07	Build site.
html	abc6818	jens-daniel-mueller	2020-12-03	Build site.
Rmd	992ba15	jens-daniel-mueller	2020-12-03	rebuild with variable inventory depth
html	c8c2e7b	jens-daniel-mueller	2020-12-03	Build site.
Rmd	83203db	jens-daniel-mueller	2020-12-03	calculate cant with variable inventory depth
html	090e4d5	jens-daniel-mueller	2020-12-02	Build site.
html	7c25f7a	jens-daniel-mueller	2020-12-02	Build site.
html	ec8dc38	jens-daniel-mueller	2020-12-02	Build site.
html	c987de1	jens-daniel-mueller	2020-12-02	Build site.
html	f8358f8	jens-daniel-mueller	2020-12-02	Build site.
html	b03ddb8	jens-daniel-mueller	2020-12-02	Build site.
Rmd	9183e8f	jens-daniel-mueller	2020-12-02	revised assignment of era to eras
html	22d0127	jens-daniel-mueller	2020-12-01	Build site.
html	0ff728b	jens-daniel-mueller	2020-12-01	Build site.
html	91435ae	jens-daniel-mueller	2020-12-01	Build site.
Rmd	17d09be	jens-daniel-mueller	2020-12-01	auto eras naming
html	cf19652	jens-daniel-mueller	2020-11-30	Build site.
Rmd	0895ad6	jens-daniel-mueller	2020-11-30	rebuild with all plot output
Rmd	2842970	jens-daniel-mueller	2020-11-30	cleaned for eMLR part only
html	196be51	jens-daniel-mueller	2020-11-30	Build site.
Rmd	7a4b015	jens-daniel-mueller	2020-11-30	first rebuild on ETH server
Rmd	bc61ce3	Jens Müller	2020-11-30	Initial commit

---

1 Required data

Required are:

• cleaned and prepared GLODAPv2_2020 file

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

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

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

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

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

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

i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[3]
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)

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

# remove helper objects
rm(i_gamma_slab,
   i_era,
   i_basin,
   GLODAP_basin_era,
   GLODAP_basin_era_slab,
   lm_full)

3 Apply predictor threshold

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

• Minimum: 2
  
• Maximum: 5

lm_all <- lm_all %>% 
  filter(n >= params_local$MLR_predictors_min,
         n <= params_local$MLR_predictors_max)

This results in a total number of MLR models of:

• 112

4 Fit all models

Individual linear regression models were fitted for the chosen target variable:

• cstar_tref

as a function of each predictor combination. Fitting was performed separately within each basin, era, and slab. Model diagnostics, such as the root mean squared error (RMSE), were calculated for each fitted model.

# prepare nested data frame

GLODAP %>%
  filter_all(any_vars(is.na(.)))

GLODAP_nested <- GLODAP %>% 
  # filter(gamma_slab %in% unique(GLODAP$gamma_slab)[c(5,6)]) %>%
  group_by(gamma_slab, era, basin, data_source) %>% 
  nest()

# expand with model definitions

GLODAP_nested_lm <- expand_grid(
  GLODAP_nested,
  lm_all
)

# fit models and extract tidy model output
GLODAP_nested_lm_fit <- GLODAP_nested_lm %>% 
  mutate(
    fit = map2(.x = data, .y = model, 
               ~ lm(as.formula(.y), data = .x)),
    tidied = map(fit, tidy),
    glanced = map(fit, glance),
    augmented = map(fit, augment),
    vif = map(fit, ols_vif_tol)
  )


# test parallel processing
# 
# library(parallel)
# library(multidplyr)
# 
# n_cores <- detectCores()
# system.time(
# cluster <- new_cluster(5)
# )
# 
# cluster
# 
# system.time(
#   GLODAP_nested_lm <-
#     expand_grid(GLODAP,
#                 lm_all) %>%
#     group_by(gamma_slab, era, basin, data_source, model, predictors, n) %>%
#     partition(cluster)
# )
# 
# GLODAP_nested_lm 
# 
# cluster %>%
#   cluster_library(c("tidyverse",
#                     "broom",
#                     "olsrr",
#                     "purrr"))
# 
# cluster_call(cluster, search())
# 
# system.time(
# GLODAP_nested_lm_fit <- GLODAP_nested_lm %>% 
#   mutate(
#     fit = map2(.x = data, .y = model, 
#                ~ lm(as.formula(.y), data = .x)),
#     tidied = map(fit, tidy),
#     glanced = map(fit, glance),
#     augmented = map(fit, augment),
#     vif = map(fit, ols_vif_tol)
#   )
# )
# 
# system.time(
# GLODAP_nested_lm_fit <- GLODAP_nested_lm_fit %>% 
#   collect()
# )
# 
# 
# 
# library(furrr)
# 
# plan(sequential)
# plan(multisession, workers = 5)
# 
# # This does run in parallel!
# system.time(
# GLODAP_nested_lm_fit <- GLODAP_nested_lm %>% 
#   mutate(
#     fit = future_map2(.x = data, .y = model, 
#                ~ lm(as.formula(.y), data = .x))
#     # tidied = future_map(fit, tidy),
#     # glanced = future_map(fit, glance),
#     # augmented = future_map(fit, augment),
#     # vif = future_map(fit, ols_vif_tol)
#   )
# )



# print(object.size(GLODAP_nested), units = "MB")
# print(object.size(GLODAP_nested_lm), units = "MB")
# print(object.size(GLODAP_nested_lm_fit), units = "MB")

5 Tidy models

# extract glanced model output (model diagnostics, such as AIC)
GLODAP_glanced <- GLODAP_nested_lm_fit %>%
  select(-c(data, fit, tidied, augmented, vif)) %>%
  unnest(glanced) %>% 
  rename(n_predictors = n)

# extract tidy model output (model coefficients)
GLODAP_tidy <- GLODAP_nested_lm_fit %>%
  select(-c(data, fit, glanced, augmented, vif)) %>%
  unnest(tidied)

# extract augmented model output (fitted values and residuals)
GLODAP_augmented <- GLODAP_nested_lm_fit %>% 
  select(-c(data, fit, tidied, glanced, vif)) %>% 
  unnest(augmented) 

# print(object.size(GLODAP_augmented), units = "MB")

# extract VIC from output
GLODAP_glanced_vif <- GLODAP_nested_lm_fit %>%
  select(-c(data, fit, tidied, augmented, glanced)) %>%
  unnest(vif)

# calculte max vif per model
GLODAP_glanced_vif_max <- GLODAP_glanced_vif %>% 
  group_by(data_source, era, basin, gamma_slab, model, n) %>% 
  summarise(vif_max = max(VIF)) %>% 
  ungroup()

# calculate RMSE from augmented output
GLODAP_glanced_rmse <- GLODAP_augmented %>%
  group_by(data_source, era, basin, gamma_slab, model) %>%
  summarise(rmse = sqrt(c(crossprod(.resid)) / length(.resid))) %>%
  ungroup()

# add RMSE and vif_max to glanced output
GLODAP_glanced <- full_join(GLODAP_glanced, GLODAP_glanced_rmse)
GLODAP_glanced <- full_join(GLODAP_glanced, GLODAP_glanced_vif_max)
rm(GLODAP_glanced_rmse)
rm(GLODAP_glanced_vif_max)


# extract input data
GLODAP_data <- GLODAP_nested_lm_fit %>%
  select(-c(fit, tidied, glanced, augmented, vif)) %>%
  unnest(data)

# append input data with augmented data
GLODAP_augmented <- bind_cols(
  GLODAP_data,
  GLODAP_augmented %>% select(.fitted, .resid)
)

rm(GLODAP, GLODAP_nested, GLODAP_nested_lm, GLODAP_nested_lm_fit, lm_all,
   GLODAP_data)

6 Prepare coeffcients

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

6.1 VIF threshold

To avoid multicollinearity among predictors, models were excluded with a VIF above:

• 50

After removing models affected by multicollinearity, the targeted number of MLRs (10) was undercut in following fitting units:

GLODAP_glanced_clean <- GLODAP_glanced %>% 
  filter(vif_max <= params_local$vif_max)

GLODAP_glanced_clean %>% 
  group_by(data_source, era, basin, gamma_slab) %>% 
  count() %>% 
  filter(n < params_local$MLR_number)

# A tibble: 0 x 5
# Groups:   data_source, era, basin, gamma_slab [0]
# … with 5 variables: data_source <chr>, era <chr>, basin <chr>,
#   gamma_slab <chr>, n <int>

6.2 Predictor selection

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

• 10

The criterion used to select the best models was:

• rmse

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

# calculate RMSE sum for adjacent eras
lm_all_eras <- GLODAP_glanced_clean  %>%
  select(data_source, basin, gamma_slab, model, era, AIC, BIC, rmse) %>% 
  arrange(era) %>% 
  group_by(data_source, basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> "),
         rmse_sum = rmse + lag(rmse),
         aic_sum = AIC + lag(AIC),
         bic_sum = BIC + lag(BIC)
         ) %>% 
  ungroup() %>% 
  select(-c(era)) %>% 
  drop_na()

# subset models with lowest summed criterion
# chose which criterion is applied

if (params_local$MLR_criterion == "aic") {
  lm_best_eras <- lm_all_eras %>%
    group_by(data_source, basin, gamma_slab, eras) %>%
    slice_min(order_by = aic_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
} 

if (params_local$MLR_criterion == "bic") {
  lm_best_eras <- lm_all_eras %>%
    group_by(data_source, basin, gamma_slab, eras) %>%
    slice_min(order_by = bic_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
}

if (params_local$MLR_criterion == "rmse") {
  lm_best_eras <- lm_all_eras %>%
    group_by(data_source, basin, gamma_slab, eras) %>%
    slice_min(order_by = rmse_sum,
              with_ties = FALSE,
              n = params_local$MLR_number) %>%
    ungroup() %>%
    arrange(basin, gamma_slab, eras, model)
}


# print table
lm_best_eras %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")

data_source	basin	gamma_slab	model	AIC	BIC	rmse	eras	rmse_sum	aic_sum	bic_sum
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	541.5135	558.0996	6.8192844	1981-1999 –> 2000-2012	12.614122	1108.1211	1141.9686
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	379.0069	396.5829	1.7978544	1981-1999 –> 2000-2012	4.161384	702.9638	736.0763
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	541.6622	558.2484	6.8257065	1981-1999 –> 2000-2012	12.616929	1108.1613	1142.0088
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	544.2146	560.8007	6.9368653	1981-1999 –> 2000-2012	13.341763	1128.2388	1162.0863
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate	394.7760	409.8411	1.9822371	1981-1999 –> 2000-2012	4.347936	716.8576	745.2398
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate	375.4371	390.5023	1.7824140	1981-1999 –> 2000-2012	4.142894	697.2184	725.6006
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	336.7548	354.3308	1.4253816	1981-1999 –> 2000-2012	3.779220	660.1529	693.2655
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate	377.4402	392.5053	1.8021394	1981-1999 –> 2000-2012	4.207849	701.8027	730.1849
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	378.6614	396.2374	1.7944441	1981-1999 –> 2000-2012	4.146037	701.9296	735.0422
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	542.4170	559.0032	6.8583928	1981-1999 –> 2000-2012	12.640501	1108.6420	1142.4895
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + silicate	366.5474	381.6126	1.6974452	1981-1999 –> 2000-2012	4.018520	686.0392	714.4214
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	332.3644	349.9404	1.3914084	1981-1999 –> 2000-2012	3.686542	652.3276	685.4402
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate	353.4047	368.4699	1.5791893	1981-1999 –> 2000-2012	4.020140	679.7451	708.1273
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	335.9618	353.5378	1.4191847	1981-1999 –> 2000-2012	3.757812	658.4782	691.5908
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + phosphate	544.0160	558.2327	7.0164075	1981-1999 –> 2000-2012	13.138067	1118.1703	1147.1824
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + phosphate_star	543.9312	558.1479	7.0126414	1981-1999 –> 2000-2012	13.104283	1117.2301	1146.2423
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	545.5342	562.1203	6.9950431	1981-1999 –> 2000-2012	12.945907	1116.7648	1150.6123
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	545.4069	561.9930	6.9894098	1981-1999 –> 2000-2012	12.920100	1116.0466	1149.8941
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	543.7304	557.9471	7.0037362	1981-1999 –> 2000-2012	13.041014	1115.4696	1144.4817
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	545.0304	561.6165	6.9727739	1981-1999 –> 2000-2012	12.866406	1114.5795	1148.4270
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + aou + nitrate + phosphate	4585.2802	4612.6887	6.0052535	1981-1999 –> 2000-2012	10.950792	7765.5759	7818.5648
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	4587.2749	4619.2515	6.0052312	1981-1999 –> 2000-2012	10.921246	7763.2834	7825.1038
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + aou + phosphate	4589.6041	4612.4445	6.0319815	1981-1999 –> 2000-2012	10.980626	7768.5588	7812.7162
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + aou + silicate + phosphate	4591.0840	4618.4925	6.0297791	1981-1999 –> 2000-2012	10.948946	7765.7656	7818.7545
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate	2374.9437	2399.0844	4.2281652	1981-1999 –> 2000-2012	8.085084	4629.6774	4677.8414
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	2333.5748	2361.7389	4.0118938	1981-1999 –> 2000-2012	7.746311	4564.1644	4620.3557
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	2335.7955	2363.9596	4.0226942	1981-1999 –> 2000-2012	7.762891	4567.6377	4623.8291
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + phosphate	4579.6203	4607.0287	5.9814318	1981-1999 –> 2000-2012	10.907721	7755.8210	7808.8098
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate	2402.0346	2426.1753	4.3691386	1981-1999 –> 2000-2012	8.480128	4708.4424	4756.6064
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2324.6147	2352.7788	3.9686096	1981-1999 –> 2000-2012	7.713237	4557.4158	4613.6071
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4581.0351	4613.0117	5.9789744	1981-1999 –> 2000-2012	10.880287	7753.8989	7815.7192
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2327.8990	2356.0631	3.9844209	1981-1999 –> 2000-2012	7.741673	4563.4264	4619.6177
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	2339.9576	2368.1217	4.0430151	1981-1999 –> 2000-2012	7.803492	4576.1799	4632.3712
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	2385.4931	2413.6572	4.2721554	1981-1999 –> 2000-2012	8.080626	4631.9878	4688.1792
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2329.7261	2357.8902	3.9932442	1981-1999 –> 2000-2012	7.757551	4566.7731	4622.9644
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate	4530.1645	4557.5730	5.7772617	1981-1999 –> 2000-2012	10.697437	7705.0614	7758.0503
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	4549.2019	4576.6103	5.8550160	1981-1999 –> 2000-2012	10.802275	7729.8627	7782.8516
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	4528.2461	4560.2226	5.7613862	1981-1999 –> 2000-2012	10.659221	7700.3644	7762.1848
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4545.6162	4577.5927	5.8320945	1981-1999 –> 2000-2012	10.757108	7723.5451	7785.3654
mod	Atlantic	(26,26.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	2415.2379	2439.3786	4.4395387	1981-1999 –> 2000-2012	8.688187	4748.3248	4796.4889
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + nitrate + phosphate	3592.1295	3618.8607	4.0375120	1981-1999 –> 2000-2012	7.372588	6458.4257	6510.9506
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + nitrate + phosphate_star	3635.3105	3662.0417	4.1769280	1981-1999 –> 2000-2012	7.711636	6564.8579	6617.3828
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + phosphate_star	7147.8129	7172.7734	6.4321341	1981-1999 –> 2000-2012	11.372371	11778.8640	11827.0304
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate	3528.1642	3554.8954	3.8394976	1981-1999 –> 2000-2012	7.187481	6398.6632	6451.1880
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	3590.9848	3617.7160	4.0338804	1981-1999 –> 2000-2012	7.599718	6530.0720	6582.5969
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	7138.7712	7168.7238	6.3995781	1981-1999 –> 2000-2012	11.318061	11765.0613	11822.8610
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + nitrate + phosphate_star	7142.0444	7167.0049	6.4151051	1981-1999 –> 2000-2012	11.290936	11752.9913	11801.1577
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	7135.3053	7165.2579	6.3893930	1981-1999 –> 2000-2012	11.220573	11734.1581	11791.9577
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate	3522.0842	3548.8154	3.8211889	1981-1999 –> 2000-2012	6.941593	6315.9924	6368.5173
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	3525.2522	3551.9834	3.8307178	1981-1999 –> 2000-2012	6.976325	6327.9128	6380.4377
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + phosphate_star	6795.8153	6820.7758	5.4714450	1981-1999 –> 2000-2012	9.673332	11178.8669	11227.0333
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate	3497.6945	3524.4256	3.7486182	1981-1999 –> 2000-2012	7.093534	6367.1958	6419.7207
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	3506.6414	3533.3726	3.7750781	1981-1999 –> 2000-2012	7.182645	6396.3329	6448.8578
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	6797.4253	6827.3779	5.4704646	1981-1999 –> 2000-2012	9.643594	11171.9558	11229.7555
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	3530.8865	3557.6176	3.8477233	1981-1999 –> 2000-2012	7.032438	6346.9902	6399.5151
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate_star	6801.7706	6826.7310	5.4864398	1981-1999 –> 2000-2012	9.704130	11190.5729	11238.7393
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	6803.4076	6833.3602	5.4855248	1981-1999 –> 2000-2012	9.680832	11186.0584	11243.8581
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + phosphate_star	6988.6053	7008.5737	5.9838265	1981-1999 –> 2000-2012	11.403100	11759.4407	11797.9738
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	3508.8205	3535.5517	3.7815508	1981-1999 –> 2000-2012	7.210554	6405.3351	6457.8600
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + silicate + phosphate_star	6888.4249	6913.3854	5.7093337	1981-1999 –> 2000-2012	10.343144	11421.3762	11469.5426
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	5525.4648	5555.7499	2.6597179	1981-1999 –> 2000-2012	5.338074	10432.2976	10492.1363
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate_star	5733.4711	5763.7562	2.9114685	1981-1999 –> 2000-2012	5.941199	10891.2820	10951.1207
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	5813.9846	5844.2697	3.0151919	1981-1999 –> 2000-2012	6.237828	11097.4700	11157.3087
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + phosphate_star	7831.9953	7862.8190	5.4149721	1981-1999 –> 2000-2012	10.238559	13386.0247	13445.8336
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5419.8927	5455.2253	2.5381859	1981-1999 –> 2000-2012	4.967468	10129.9968	10199.8086
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5448.5041	5483.8367	2.5699574	1981-1999 –> 2000-2012	5.044082	10195.8478	10265.6596
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	7764.6932	7800.6542	5.2678545	1981-1999 –> 2000-2012	10.076765	13315.0790	13384.8560
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + phosphate_star	7835.7211	7866.5448	5.4229967	1981-1999 –> 2000-2012	10.234120	13384.9588	13444.7678
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	5561.4893	5596.8219	2.6993563	1981-1999 –> 2000-2012	5.893118	10828.6506	10898.4623
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	7761.8302	7797.7911	5.2618634	1981-1999 –> 2000-2012	10.056887	13306.8599	13376.6370
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5460.7795	5496.1121	2.5837103	1981-1999 –> 2000-2012	5.080795	10226.9304	10296.7422
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate_star	7786.8389	7817.6625	5.3186526	1981-1999 –> 2000-2012	10.230193	13374.3333	13434.1422
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + phosphate_star	7846.0891	7871.7755	5.4497202	1981-1999 –> 2000-2012	10.300737	13408.6202	13458.4609
mod	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	5550.8741	5581.1592	2.6892642	1981-1999 –> 2000-2012	5.187018	10315.5706	10375.4093
mod	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	5576.1638	5606.4489	2.7189972	1981-1999 –> 2000-2012	5.259875	10375.7120	10435.5507
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	7797.8216	7828.6453	5.3419201	1981-1999 –> 2000-2012	10.188297	13360.5805	13420.3894
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + phosphate_star	7851.1938	7876.8802	5.4607885	1981-1999 –> 2000-2012	10.288712	13404.8871	13454.7279
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	7789.6681	7820.4917	5.3246367	1981-1999 –> 2000-2012	10.141005	13340.9237	13400.7326
mod	Atlantic	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	5587.6432	5617.9283	2.7326017	1981-1999 –> 2000-2012	5.295745	10404.9551	10464.7938
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	7796.6855	7827.5092	5.3395086	1981-1999 –> 2000-2012	10.187331	13359.9967	13419.8056
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + aou + phosphate	7779.8598	7806.4657	3.1596446	1981-1999 –> 2000-2012	6.139833	14127.4343	14179.7425
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	7450.8642	7482.7913	2.8320571	1981-1999 –> 2000-2012	5.562158	13579.2154	13641.9852
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	7574.5672	7606.4944	2.9503105	1981-1999 –> 2000-2012	5.833691	13840.7917	13903.5615
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	7549.1836	7581.1108	2.9256491	1981-1999 –> 2000-2012	5.780549	13790.3533	13853.1231
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate	7781.2466	7813.1737	3.1590039	1981-1999 –> 2000-2012	6.138882	14130.5588	14193.3286
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate_star	14705.3906	14739.9712	5.4922000	1981-1999 –> 2000-2012	10.844807	26131.1716	26198.8672
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	7167.1223	7204.3706	2.5767063	1981-1999 –> 2000-2012	4.973144	12968.4572	13041.6887
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14577.4978	14617.8420	5.3426800	1981-1999 –> 2000-2012	10.510819	25876.0071	25954.9853
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	7304.5700	7341.8183	2.6965259	1981-1999 –> 2000-2012	5.350250	13363.3037	13436.5352
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	14609.2786	14649.6227	5.3788824	1981-1999 –> 2000-2012	10.516682	25886.0853	25965.0635
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + phosphate + phosphate_star	14713.7052	14748.2859	5.5019123	1981-1999 –> 2000-2012	10.855793	26140.3635	26208.0591
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	7188.7733	7226.0217	2.5952211	1981-1999 –> 2000-2012	5.001491	13000.4422	13073.6737
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	14582.0832	14622.4273	5.3478882	1981-1999 –> 2000-2012	10.514500	25879.5032	25958.4814
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate_star	14699.6548	14734.2355	5.4855101	1981-1999 –> 2000-2012	10.690065	26022.0455	26089.7410
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + phosphate_star	14741.8643	14770.6815	5.5372853	1981-1999 –> 2000-2012	10.944234	26202.8783	26259.2913
mod	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate_star	7806.6185	7838.5456	3.1856201	1981-1999 –> 2000-2012	5.985246	13998.4418	14061.2116
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate_star	14647.4654	14682.0461	5.4250120	1981-1999 –> 2000-2012	10.720496	26033.6983	26101.3939
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	14702.1139	14736.6946	5.4883773	1981-1999 –> 2000-2012	10.768073	26077.3403	26145.0359
mod	Atlantic	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	7816.6345	7848.5617	3.1961889	1981-1999 –> 2000-2012	6.007480	14018.9529	14081.7228
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	14653.0594	14687.6401	5.4314646	1981-1999 –> 2000-2012	10.726627	26039.0680	26106.7636
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate	16992.7385	17022.8086	4.0147811	1981-1999 –> 2000-2012	7.732934	27242.8950	27300.6441
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + phosphate	16623.6975	16653.7675	3.7770525	1981-1999 –> 2000-2012	7.462376	26840.6141	26898.3632
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate	16808.5558	16844.6398	3.8930327	1981-1999 –> 2000-2012	7.122830	26532.9658	26602.2648
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	16543.0470	16579.1310	3.7257705	1981-1999 –> 2000-2012	7.124624	26458.6753	26527.9743
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	16117.8421	16153.4147	4.4016067	1981-1999 –> 2000-2012	8.967424	29548.5073	29618.4820
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate_star	16510.0137	16546.0977	3.7054696	1981-1999 –> 2000-2012	7.259279	26592.7343	26662.0333
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate_star	16083.6923	16119.2649	4.3746159	1981-1999 –> 2000-2012	8.951217	29525.1332	29595.1079
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	16084.7826	16126.2840	4.3738992	1981-1999 –> 2000-2012	8.946346	29524.0753	29605.7124
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate_star	16380.8230	16416.9071	3.6271313	1981-1999 –> 2000-2012	7.197554	26481.0241	26550.3231
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	16501.3432	16537.4272	3.7001595	1981-1999 –> 2000-2012	7.257243	26587.5151	26656.8141
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	16090.0540	16125.6266	4.3796314	1981-1999 –> 2000-2012	8.951785	29527.0538	29597.0285
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + phosphate_star	17054.5702	17084.6402	4.0560504	1981-1999 –> 2000-2012	7.632767	27159.3726	27217.1217
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	16090.1463	16131.6477	4.3781268	1981-1999 –> 2000-2012	8.946505	29525.3724	29607.0095
mod	Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate	16937.9869	16968.0569	3.9785880	1981-1999 –> 2000-2012	7.208941	26661.0416	26718.7907
obs	Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + phosphate	16276.4859	16306.1297	4.5308249	1981-1999 –> 2000-2012	9.164489	29772.5307	29830.8430
obs	Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate	16264.3565	16299.9291	4.5193090	1981-1999 –> 2000-2012	9.118589	29728.3780	29798.3527
obs	Atlantic	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate_star	16249.4198	16284.9924	4.5071670	1981-1999 –> 2000-2012	9.110902	29717.8640	29787.8387
mod	Atlantic	(27.25,27.5]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	17110.7363	17146.8203	4.0925518	1981-1999 –> 2000-2012	7.790098	27342.0625	27411.3615
obs	Atlantic	(27.25,27.5]	cstar_tref ~ temp + phosphate + phosphate_star	16271.1993	16300.8431	4.5265127	1981-1999 –> 2000-2012	9.169344	29776.2720	29834.5842
obs	Atlantic	(27.25,27.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	16249.0602	16284.6328	4.5068750	1981-1999 –> 2000-2012	9.106900	29713.8215	29783.7962
obs	Atlantic	(27.5,27.75]	cstar_tref ~ aou + silicate + phosphate	18683.9780	18714.2697	4.6450625	1981-1999 –> 2000-2012	9.225980	31763.0614	31821.8839
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	27864.3469	27904.1919	2.8359752	1981-1999 –> 2000-2012	5.258536	44555.5956	44632.6060
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	18592.5074	18628.8574	4.5768692	1981-1999 –> 2000-2012	9.021270	31539.1406	31609.7275
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate	28003.5131	28043.3581	2.8710679	1981-1999 –> 2000-2012	5.161273	44287.9928	44365.0032
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate	18694.4118	18730.7618	4.6512653	1981-1999 –> 2000-2012	9.236588	31779.7667	31850.3536
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate_star	27997.5976	28037.4425	2.8695674	1981-1999 –> 2000-2012	5.174926	44329.8245	44406.8348
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	27812.9519	27859.4377	2.8226251	1981-1999 –> 2000-2012	5.021160	43803.6768	43893.5222
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	18387.4008	18429.8091	4.4293158	1981-1999 –> 2000-2012	8.779538	31240.8517	31323.2032
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	27790.7576	27837.2434	2.8170944	1981-1999 –> 2000-2012	5.018189	43789.9053	43879.7507
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	18419.2686	18461.6769	4.4517065	1981-1999 –> 2000-2012	8.841047	31312.5025	31394.8540
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + phosphate_star	28034.4396	28074.2845	2.8789252	1981-1999 –> 2000-2012	5.186547	44373.7701	44450.7804
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	27791.3204	27837.8062	2.8172345	1981-1999 –> 2000-2012	5.017907	43789.0787	43878.9241
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + phosphate + phosphate_star	27988.6469	28028.4918	2.8672985	1981-1999 –> 2000-2012	5.171298	44316.6013	44393.6117
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + phosphate + phosphate_star	18734.4136	18770.7635	4.6807983	1981-1999 –> 2000-2012	9.324607	31876.0933	31946.6802
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	27785.8002	27832.2859	2.8158605	1981-1999 –> 2000-2012	5.016722	43784.1802	43874.0256
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	18396.0543	18438.4626	4.4353848	1981-1999 –> 2000-2012	8.807726	31272.0441	31354.3955
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	28452.0983	28491.9433	2.9871678	1981-1999 –> 2000-2012	5.191297	44459.2195	44536.2299
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate	18457.5258	18493.8757	4.4801535	1981-1999 –> 2000-2012	8.837676	31316.4288	31387.0157
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	18497.2408	18533.5907	4.5083956	1981-1999 –> 2000-2012	8.905834	31396.6660	31467.2529
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	18469.7622	18506.1122	4.4888362	1981-1999 –> 2000-2012	8.869077	31351.7734	31422.3603
obs	Atlantic	(27.75,27.85]	cstar_tref ~ aou + silicate + phosphate	12705.3851	12733.6998	4.7778932	1981-1999 –> 2000-2012	9.464258	19057.4798	19110.6715
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	9288.1473	9322.3572	1.9696184	1981-1999 –> 2000-2012	3.463428	13843.5360	13908.5217
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	9247.6399	9281.8498	1.9516663	1981-1999 –> 2000-2012	3.481873	13863.1166	13928.1023
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate_star	12708.3409	12742.3185	4.7789663	1981-1999 –> 2000-2012	9.364158	19015.7295	19079.5597
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	9587.7409	9621.9508	2.1076211	1981-1999 –> 2000-2012	3.901736	14600.3531	14665.3388
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate	12947.7136	12976.0283	5.0578313	1981-1999 –> 2000-2012	10.136630	19471.9023	19525.0940
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	9593.3918	9627.6017	2.1103149	1981-1999 –> 2000-2012	3.910137	14613.9314	14678.9171
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	12623.7112	12657.6888	4.6848761	1981-1999 –> 2000-2012	9.199378	18897.8508	18961.6809
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + nitrate + silicate	9285.5146	9325.4262	1.9675569	1981-1999 –> 2000-2012	3.442050	13810.4175	13886.2342
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	9211.8506	9251.7621	1.9350663	1981-1999 –> 2000-2012	3.410825	13738.8945	13814.7112
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	9270.4206	9310.3321	1.9608553	1981-1999 –> 2000-2012	3.462648	13841.1142	13916.9308
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	12619.5078	12659.1483	4.6780526	1981-1999 –> 2000-2012	9.189044	18893.9826	18968.4511
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	9268.9589	9308.8704	1.9602076	1981-1999 –> 2000-2012	3.460326	13836.8673	13912.6839
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate	12934.0713	12968.0489	5.0392760	1981-1999 –> 2000-2012	10.041806	19427.8793	19491.7094
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	9266.4855	9306.3971	1.9591120	1981-1999 –> 2000-2012	3.460057	13835.7686	13911.5853
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate_star	9355.5207	9389.7306	1.9998434	1981-1999 –> 2000-2012	3.523022	13959.5070	14024.4927
obs	Atlantic	(27.75,27.85]	cstar_tref ~ silicate + phosphate	12987.0654	13009.7171	5.1072132	1981-1999 –> 2000-2012	10.280377	19548.6507	19591.2041
obs	Atlantic	(27.75,27.85]	cstar_tref ~ silicate + phosphate + phosphate_star	12777.7647	12806.0794	4.8598432	1981-1999 –> 2000-2012	9.663291	19182.6676	19235.8594
obs	Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate_star	12624.2971	12658.2747	4.6855211	1981-1999 –> 2000-2012	9.236976	18915.8818	18979.7120
obs	Atlantic	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate	12937.5104	12965.8251	5.0457203	1981-1999 –> 2000-2012	10.084667	19444.8407	19498.0325
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + nitrate + silicate	11506.2343	11540.5358	3.1264081	1981-1999 –> 2000-2012	4.739283	16791.7738	16857.4976
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate	11320.6628	11354.9643	2.9998828	1981-1999 –> 2000-2012	4.557858	16509.9285	16575.6523
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate	27179.7433	27218.1148	5.2078619	1981-1999 –> 2000-2012	9.394845	40277.4618	40350.2642
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate_star	26616.8399	26655.2114	4.8870011	1981-1999 –> 2000-2012	8.935741	39560.4499	39633.2523
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate	27495.6579	27527.6342	5.3982986	1981-1999 –> 2000-2012	9.904559	40928.6819	40989.3506
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	26967.8164	27006.1879	5.0846605	1981-1999 –> 2000-2012	9.183234	39967.5775	40040.3799
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + nitrate + silicate	11495.8854	11535.9037	3.1178251	1981-1999 –> 2000-2012	4.675852	16687.2432	16763.9209
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate	11366.6829	11400.9843	3.0307743	1981-1999 –> 2000-2012	4.676438	16708.1721	16773.8959
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	11269.9969	11310.0153	2.9649165	1981-1999 –> 2000-2012	4.421416	16274.0254	16350.7031
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	11315.4405	11355.4589	2.9950634	1981-1999 –> 2000-2012	4.482611	16378.1087	16454.7864
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	26526.2458	26571.0126	4.8361483	1981-1999 –> 2000-2012	8.884809	39471.7662	39556.7024
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	11336.6781	11376.6964	3.0092572	1981-1999 –> 2000-2012	4.498517	16402.5439	16479.2216
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + phosphate + phosphate_star	11414.9299	11449.2313	3.0635022	1981-1999 –> 2000-2012	4.757615	16837.0818	16902.8056
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate	26688.1490	26726.5205	4.9265284	1981-1999 –> 2000-2012	9.124726	39798.1448	39870.9472
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	11306.3229	11346.3413	2.9889904	1981-1999 –> 2000-2012	4.475389	16366.8417	16443.5194
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	26552.1668	26596.9336	4.8503306	1981-1999 –> 2000-2012	8.906955	39506.7067	39591.6429
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate_star	11488.7721	11523.0735	3.1142781	1981-1999 –> 2000-2012	4.613281	16570.7650	16636.4888
obs	Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate	27620.5035	27658.8750	5.4737369	1981-1999 –> 2000-2012	9.897787	40971.0161	41043.8186
obs	Atlantic	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate_star	27519.4568	27557.8283	5.4116088	1981-1999 –> 2000-2012	9.801300	40834.1834	40906.9858
obs	Atlantic	(27.85,27.95]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	27611.6236	27649.9951	5.4682487	1981-1999 –> 2000-2012	9.883209	40952.6965	41025.4989
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate	30446.3967	30478.6966	6.0732290	1981-1999 –> 2000-2012	10.298207	48405.4587	48468.0153
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + phosphate_star	30396.7283	30429.0282	6.0413722	1981-1999 –> 2000-2012	10.260547	48347.1643	48409.7210
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate	30319.2756	30358.0356	5.9907592	1981-1999 –> 2000-2012	10.100717	48107.1119	48182.1799
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate_star	29984.8340	30023.5939	5.7823201	1981-1999 –> 2000-2012	9.670184	47424.0214	47499.0893
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	30353.3949	30392.1548	6.0124417	1981-1999 –> 2000-2012	10.169362	48212.5374	48287.6054
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + phosphate + phosphate_star	30356.7420	30389.0420	6.0158469	1981-1999 –> 2000-2012	10.204249	48261.2363	48323.7930
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate	14468.0508	14503.0524	4.2409188	1981-1999 –> 2000-2012	7.834519	23470.0974	23537.6081
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate	30385.0233	30423.7832	6.0326114	1981-1999 –> 2000-2012	10.221907	48292.8565	48367.9245
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate_star	14478.2910	14513.2926	4.2495304	1981-1999 –> 2000-2012	7.854999	23491.3236	23558.8343
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate_star	30325.3214	30364.0813	5.9945955	1981-1999 –> 2000-2012	10.151771	48184.8497	48259.9177
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	14447.0239	14487.8591	4.2216175	1981-1999 –> 2000-2012	7.723549	23364.9716	23443.7341
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14449.1806	14490.0158	4.2234215	1981-1999 –> 2000-2012	7.725868	23367.6178	23446.3803
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + phosphate + phosphate_star	30340.0896	30378.8495	6.0039770	1981-1999 –> 2000-2012	10.167411	48209.0587	48284.1267
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + phosphate_star	14513.0326	14542.2006	4.2805732	1981-1999 –> 2000-2012	7.946298	23579.2909	23635.5498
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate	30407.7412	30446.5011	6.0471405	1981-1999 –> 2000-2012	10.207519	48272.1034	48347.1714
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	14448.4207	14483.4223	4.2244591	1981-1999 –> 2000-2012	7.842736	23473.2693	23540.7800
mod	Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate	14714.8926	14744.0606	4.4552139	1981-1999 –> 2000-2012	8.111462	23772.5259	23828.7848
mod	Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate_star	14745.9561	14775.1241	4.4827141	1981-1999 –> 2000-2012	8.166603	23828.6841	23884.9430
mod	Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	14698.6861	14733.6877	4.4391743	1981-1999 –> 2000-2012	8.019191	23688.1134	23755.6241
mod	Atlantic	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate_star	14722.0941	14757.0957	4.4598069	1981-1999 –> 2000-2012	8.056941	23727.4155	23794.9262
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate	5601.5619	5627.7436	1.8109702	1981-1999 –> 2000-2012	2.968265	8478.6855	8528.9673
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate	5540.4187	5566.6004	1.7715466	1981-1999 –> 2000-2012	2.782392	8169.6758	8219.9576
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate	23410.1840	23441.1079	6.3203548	1981-1999 –> 2000-2012	10.323369	35659.8953	35719.2570
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate_star	5925.2264	5951.4081	2.0347493	1981-1999 –> 2000-2012	3.299495	8965.0059	9015.2877
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + phosphate_star	23331.4390	23362.3629	6.2513400	1981-1999 –> 2000-2012	10.280354	35609.3910	35668.7526
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate_star	5877.8518	5909.2699	1.9989043	1981-1999 –> 2000-2012	3.257372	8910.5148	8970.8529
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + nitrate + phosphate_star	23352.2419	23383.1659	6.2694988	1981-1999 –> 2000-2012	10.286907	35617.6101	35676.9717
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + phosphate + phosphate_star	23335.2471	23366.1711	6.2546602	1981-1999 –> 2000-2012	10.277557	35606.5710	35665.9326
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate	23411.7941	23448.9028	6.3200112	1981-1999 –> 2000-2012	10.308406	35647.5459	35718.7799
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate_star	23279.4496	23316.5583	6.2044579	1981-1999 –> 2000-2012	10.086700	35397.5324	35468.7664
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + phosphate_star	23283.5776	23320.6864	6.2080300	1981-1999 –> 2000-2012	10.090963	35402.4367	35473.6707
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + phosphate + phosphate_star	23294.2061	23331.3148	6.2172368	1981-1999 –> 2000-2012	10.098045	35410.6776	35481.9116
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + phosphate_star	5631.0565	5657.2382	1.8303001	1981-1999 –> 2000-2012	2.895985	8357.1002	8407.3820
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + phosphate_star	23351.3166	23382.2406	6.2686900	1981-1999 –> 2000-2012	10.151806	35468.3810	35527.7427
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate	5751.1970	5782.6151	1.9098164	1981-1999 –> 2000-2012	3.380469	9069.3068	9129.6449
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	5540.2328	5571.6509	1.7701532	1981-1999 –> 2000-2012	2.728534	8073.8504	8134.1885
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	23326.7736	23363.8823	6.2455330	1981-1999 –> 2000-2012	10.127883	35444.9775	35516.2114
mod	Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate_star	5316.4955	5342.6772	1.6343530	1981-1999 –> 2000-2012	2.659109	7970.7919	8021.0736
mod	Atlantic	(28.05,28.1]	cstar_tref ~ temp + phosphate_star	5629.4036	5650.3490	1.8305288	1981-1999 –> 2000-2012	2.923265	8399.3705	8439.5959
mod	Atlantic	(28.05,28.1]	cstar_tref ~ temp + silicate + phosphate_star	5554.4101	5580.5918	1.7804915	1981-1999 –> 2000-2012	2.830166	8252.7208	8303.0026
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + nitrate	7931.3351	7959.6521	1.5548875	1981-1999 –> 2000-2012	2.675787	11452.0650	11505.5979
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate	8064.2108	8092.5279	1.6041746	1981-1999 –> 2000-2012	2.817869	11767.0825	11820.6154
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + aou + phosphate_star	18077.4254	18106.8802	7.1041360	1981-1999 –> 2000-2012	10.877251	26366.3994	26422.4435
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + nitrate + phosphate_star	18063.6684	18093.1232	7.0858782	1981-1999 –> 2000-2012	10.855130	26349.5550	26405.5992
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + phosphate	18877.7996	18901.3634	8.2545605	1981-1999 –> 2000-2012	13.098847	27917.9691	27962.8044
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + phosphate_star	18162.4145	18185.9784	7.2206787	1981-1999 –> 2000-2012	11.026922	26475.7360	26520.5713
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + silicate + phosphate	7828.4217	7856.7388	1.5177573	1981-1999 –> 2000-2012	3.074029	12100.6418	12154.1747
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + silicate + phosphate_star	18104.2120	18133.6667	7.1398211	1981-1999 –> 2000-2012	10.932116	26408.4683	26464.5125
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate_star	7733.5123	7767.4927	1.4836042	1981-1999 –> 2000-2012	2.302982	10538.6901	10602.9295
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + nitrate	8019.6325	8047.9496	1.5874676	1981-1999 –> 2000-2012	2.680095	11481.8610	11535.3938
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate	7761.1053	7789.4224	1.4939512	1981-1999 –> 2000-2012	2.308580	10550.9712	10604.5040
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate_star	7794.2299	7822.5470	1.5056185	1981-1999 –> 2000-2012	2.340130	10639.3175	10692.8503
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate_star	17858.2374	17887.6922	6.8187541	1981-1999 –> 2000-2012	10.397884	25988.1290	26044.1732
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate_star	7669.8753	7703.8558	1.4615962	1981-1999 –> 2000-2012	2.292183	10506.1693	10570.4087
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + nitrate + phosphate_star	17861.6815	17891.1362	6.8231483	1981-1999 –> 2000-2012	10.413292	26000.8337	26056.8778
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + phosphate	18863.1870	18886.7508	8.2320285	1981-1999 –> 2000-2012	13.086443	27909.6516	27954.4869
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + phosphate_star	17875.0884	17898.6522	6.8428407	1981-1999 –> 2000-2012	10.479858	26051.3370	26096.1723
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + silicate + phosphate	8001.1520	8029.4690	1.5805926	1981-1999 –> 2000-2012	3.226479	12401.5804	12455.1133
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + silicate + phosphate_star	9353.3017	9381.6188	2.1713628	1981-1999 –> 2000-2012	3.056256	12332.6318	12386.1646
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + silicate + phosphate_star	17841.6127	17871.0675	6.7975824	1981-1999 –> 2000-2012	10.339493	25939.9974	25996.0415
mod	Atlantic	(28.15,28.2]	cstar_tref ~ aou + nitrate	12923.6546	12948.6976	1.2842591	1981-1999 –> 2000-2012	2.431645	19260.0767	19307.5888
mod	Atlantic	(28.15,28.2]	cstar_tref ~ aou + nitrate + silicate	12493.3852	12524.6890	1.2144834	1981-1999 –> 2000-2012	2.249940	18414.4574	18473.8475
mod	Atlantic	(28.15,28.2]	cstar_tref ~ aou + phosphate	12779.8123	12804.8553	1.2606064	1981-1999 –> 2000-2012	2.477566	19355.5988	19403.1108
mod	Atlantic	(28.15,28.2]	cstar_tref ~ aou + silicate + phosphate	12670.1872	12701.4910	1.2425520	1981-1999 –> 2000-2012	2.409202	19076.3110	19135.7011
mod	Atlantic	(28.15,28.2]	cstar_tref ~ nitrate + silicate + phosphate_star	12698.1503	12729.4541	1.2470504	1981-1999 –> 2000-2012	2.491026	19365.2136	19424.6037
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + phosphate	12766.6360	12797.9398	1.2581365	1981-1999 –> 2000-2012	2.472976	19337.3312	19396.7213
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + aou + phosphate_star	6543.3631	6568.5833	4.1852604	1981-1999 –> 2000-2012	8.098929	9514.9152	9561.5186
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + nitrate + phosphate_star	12468.7337	12500.0375	1.2106205	1981-1999 –> 2000-2012	2.378063	18877.6188	18937.0089
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + phosphate	6986.0687	7006.2449	5.0814369	1981-1999 –> 2000-2012	9.346854	10047.1938	10084.4765
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + phosphate_star	6947.1096	6967.2858	4.9957932	1981-1999 –> 2000-2012	9.084774	9963.2868	10000.5695
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + silicate + phosphate_star	6624.7550	6649.9752	4.3365549	1981-1999 –> 2000-2012	8.314911	9613.7500	9660.3533
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate_star	11947.5086	11985.0731	1.1314674	1981-1999 –> 2000-2012	1.993552	17125.5115	17196.7796
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + phosphate_star	13536.1043	13567.4081	1.3896777	1981-1999 –> 2000-2012	2.258242	18742.5531	18801.9432
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + phosphate_star	6385.7489	6410.9690	3.9071250	1981-1999 –> 2000-2012	7.487823	9262.6930	9309.2963
mod	Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + phosphate_star	12616.0210	12647.3248	1.2338845	1981-1999 –> 2000-2012	2.321168	18735.6758	18795.0658
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + phosphate_star	6303.9209	6329.1410	3.7700952	1981-1999 –> 2000-2012	7.378012	9188.9224	9235.5258
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + nitrate + phosphate_star	6323.3941	6348.6143	3.8022630	1981-1999 –> 2000-2012	7.410373	9208.4526	9255.0560
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + phosphate	6984.5804	7004.7565	5.0781382	1981-1999 –> 2000-2012	9.372734	10052.9593	10090.2420
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + phosphate_star	6387.1022	6407.2783	3.9128456	1981-1999 –> 2000-2012	7.520995	9270.1724	9307.4551
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + silicate + phosphate_star	6354.3150	6379.5352	3.8539061	1981-1999 –> 2000-2012	7.456109	9237.6300	9284.2333
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	13182.7605	13216.2364	0.7287453	1981-1999 –> 2000-2012	1.276325	18631.9182	18695.9477
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + phosphate	14316.7008	14346.2409	3.3599864	1981-1999 –> 2000-2012	6.648067	20291.4289	20346.1761
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	16381.9892	16422.1602	0.9523376	1981-1999 –> 2000-2012	1.818564	24887.6810	24964.5164
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + nitrate	13183.7323	13223.9033	0.7286826	1981-1999 –> 2000-2012	1.275548	18626.2085	18703.0439
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate	14276.0598	14311.5080	3.3337428	1981-1999 –> 2000-2012	6.478355	20150.8021	20216.4987
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate_star	14235.1447	14270.5928	3.3087541	1981-1999 –> 2000-2012	6.526855	20162.6954	20228.3920
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14209.0833	14250.4395	3.2917241	1981-1999 –> 2000-2012	6.370960	20037.7990	20114.4450
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate_star	14479.6667	14519.8377	0.8121644	1981-1999 –> 2000-2012	1.821391	24002.9619	24079.7973
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate_star	14388.3991	14423.8472	3.4033282	1981-1999 –> 2000-2012	6.627327	20320.1358	20385.8324
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	14435.3234	14482.1896	0.8090203	1981-1999 –> 2000-2012	1.537751	21791.8911	21881.5324
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + phosphate + phosphate_star	14233.6361	14269.0842	3.3078363	1981-1999 –> 2000-2012	6.515643	20153.8627	20219.5593
mod	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate	14730.6961	14770.8671	0.8294086	1981-1999 –> 2000-2012	1.610885	22550.6724	22627.5078
obs	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + phosphate	14647.1153	14676.6554	3.5704700	1981-1999 –> 2000-2012	6.816908	20592.7070	20647.4541
obs	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + phosphate_star	14584.5586	14614.0987	3.5296320	1981-1999 –> 2000-2012	6.822711	20562.7595	20617.5067
mod	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + silicate + phosphate	16322.6226	16362.7937	0.9476174	1981-1999 –> 2000-2012	1.880604	25322.7843	25399.6197
obs	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + silicate + phosphate	14642.0734	14677.5215	3.5658494	1981-1999 –> 2000-2012	6.657654	20478.1007	20543.7972
mod	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + silicate + phosphate_star	16373.2551	16413.4261	0.9516417	1981-1999 –> 2000-2012	1.891087	25419.3636	25496.1990
obs	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + silicate + phosphate_star	14586.5572	14622.0053	3.5296311	1981-1999 –> 2000-2012	6.628816	20428.0351	20493.7317
mod	Atlantic	(28.2, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	15607.3575	15647.5285	0.8925531	1981-1999 –> 2000-2012	1.767430	24179.2307	24256.0661
mod	Atlantic	(28.2, Inf]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	16353.6255	16393.7966	0.9500795	1981-1999 –> 2000-2012	1.887703	25386.8063	25463.6417
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate	29056.6374	29095.1031	6.1172617	1981-1999 –> 2000-2012	17.651722	41418.8688	41489.5935
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	21938.3560	21981.4556	5.6062819	1981-1999 –> 2000-2012	10.571579	29801.9836	29881.2686
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	28905.0082	28949.8848	6.0136354	1981-1999 –> 2000-2012	17.330997	41208.5118	41291.0239
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	22038.2953	22081.3949	5.6871764	1981-1999 –> 2000-2012	10.785506	29970.6135	30049.8985
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	28920.0014	28964.8780	6.0236709	1981-1999 –> 2000-2012	17.349151	41225.7969	41308.3090
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	29056.8104	29101.6870	6.1160189	1981-1999 –> 2000-2012	17.604854	41408.3746	41490.8868
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate	22730.6876	22767.6301	6.2824125	1981-1999 –> 2000-2012	11.552082	30746.8817	30814.8403
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + phosphate	29906.2592	29944.7249	6.7234470	1981-1999 –> 2000-2012	18.440368	42318.6517	42389.3764
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	22470.6681	22513.7677	6.0508208	1981-1999 –> 2000-2012	11.150258	30403.5504	30482.8354
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	29474.8006	29519.6772	6.4070315	1981-1999 –> 2000-2012	17.724582	41778.3577	41860.8698
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	22661.1572	22704.2567	6.2183231	1981-1999 –> 2000-2012	11.500315	30685.4192	30764.7042
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	29532.0794	29576.9560	6.4479744	1981-1999 –> 2000-2012	17.779669	41839.6283	41922.1405
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	22165.4945	22208.5941	5.7918266	1981-1999 –> 2000-2012	10.949532	30127.8946	30207.1797
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate_star	22877.0517	22913.9942	6.4156169	1981-1999 –> 2000-2012	11.943368	31017.4654	31085.4240
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	22863.6654	22906.7650	6.4014822	1981-1999 –> 2000-2012	11.917095	31000.3677	31079.6527
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	29848.1828	29893.0594	6.6786768	1981-1999 –> 2000-2012	18.117203	42185.7212	42268.2334
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	22705.9163	22749.0159	6.2583492	1981-1999 –> 2000-2012	11.573581	30746.4767	30825.7617
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	29558.3191	29603.1957	6.4668178	1981-1999 –> 2000-2012	17.803469	41867.2655	41949.7777
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate_star	22867.5383	22904.4808	6.4068737	1981-1999 –> 2000-2012	11.924096	31002.9987	31070.9573
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate_star	29891.8053	29930.2710	6.7126483	1981-1999 –> 2000-2012	18.183525	42236.3701	42307.0948
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	18131.9209	18174.2243	4.4419940	1981-1999 –> 2000-2012	8.033539	28202.2797	28283.2964
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	18262.1445	18304.3619	4.7031826	1981-1999 –> 2000-2012	12.046995	29927.4320	30007.7468
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + phosphate_star	18641.7087	18677.8951	5.0042242	1981-1999 –> 2000-2012	12.530738	30388.8915	30457.7328
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	17541.6585	17583.9619	4.0402127	1981-1999 –> 2000-2012	7.975403	27952.6696	28033.6863
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	18433.8725	18476.0900	4.8363616	1981-1999 –> 2000-2012	12.157004	30088.3720	30168.6869
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	18191.8389	18234.1423	4.4849494	1981-1999 –> 2000-2012	8.093357	28279.6593	28360.6761
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	18269.5288	18311.7462	4.7088331	1981-1999 –> 2000-2012	12.058785	29937.6695	30017.9844
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate_star	18505.4550	18541.6413	4.8945744	1981-1999 –> 2000-2012	12.383595	30235.5886	30304.4299
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	18438.9639	18481.2673	4.6665480	1981-1999 –> 2000-2012	9.086854	29283.3536	29364.3704
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	18437.4469	18479.6644	4.8391733	1981-1999 –> 2000-2012	12.213729	30116.9966	30197.3115
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	18641.2088	18677.3951	5.0038174	1981-1999 –> 2000-2012	12.530511	30388.4734	30457.3147
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + phosphate_star	18649.8933	18680.0486	5.0125182	1981-1999 –> 2000-2012	12.539765	30395.4084	30452.7762
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	17590.2994	17632.6028	4.0719006	1981-1999 –> 2000-2012	8.020343	28013.8432	28094.8599
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	18436.2336	18478.4511	4.8382187	1981-1999 –> 2000-2012	12.161663	30092.0397	30172.3546
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	18480.1057	18516.3657	4.6989962	1981-1999 –> 2000-2012	9.126511	29328.5701	29398.0131
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	18460.8140	18497.0003	4.8591747	1981-1999 –> 2000-2012	12.235505	30139.1853	30208.0266
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	17957.8828	18000.1862	4.3195444	1981-1999 –> 2000-2012	8.232825	28348.0795	28429.0962
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate_star	18359.5152	18395.7753	4.6088578	1981-1999 –> 2000-2012	9.200246	29343.4701	29412.9130
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	17983.6650	18025.9684	4.3374689	1981-1999 –> 2000-2012	8.262754	28385.2805	28466.2973
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	18385.4149	18421.6750	4.6280703	1981-1999 –> 2000-2012	9.225626	29374.3745	29443.8174
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate_star	19911.9883	19948.3818	5.5126277	1981-1999 –> 2000-2012	11.434049	31083.3157	31152.4962
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	16269.2583	16310.8573	4.3419290	1981-1999 –> 2000-2012	7.876019	24654.5712	24733.6418
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate_star	16862.4255	16898.0818	4.8260689	1981-1999 –> 2000-2012	8.364744	25249.7864	25317.5612
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate_star	19641.1955	19677.5890	5.2830525	1981-1999 –> 2000-2012	11.074446	30735.0325	30804.2131
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	16548.8263	16590.4253	4.5629783	1981-1999 –> 2000-2012	8.096539	24933.6715	25012.7421
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	19570.9336	19613.3927	5.2234225	1981-1999 –> 2000-2012	11.014732	30666.7201	30747.4307
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	16547.1318	16582.7881	4.5632259	1981-1999 –> 2000-2012	8.172188	24995.8956	25063.6704
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	20143.2734	20179.6669	5.7165914	1981-1999 –> 2000-2012	11.601181	31292.8248	31362.0054
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	17188.0568	17223.7131	5.1134322	1981-1999 –> 2000-2012	8.603384	25532.1328	25599.9076
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	19983.8282	20020.2217	5.5751897	1981-1999 –> 2000-2012	11.404834	31100.6403	31169.8209
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	16580.0176	16621.6166	4.5883283	1981-1999 –> 2000-2012	7.964947	24823.0272	24902.0978
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	19964.3819	20006.8409	5.5564391	1981-1999 –> 2000-2012	11.385934	31083.1041	31163.8147
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	16821.2373	16856.8936	4.7908910	1981-1999 –> 2000-2012	8.637368	25468.9900	25536.7648
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	17204.2734	17239.9297	5.1281821	1981-1999 –> 2000-2012	8.633431	25562.0040	25629.7788
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	19991.4598	20027.8533	5.5818773	1981-1999 –> 2000-2012	11.419687	31113.1566	31182.3371
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate_star	20047.5857	20077.9136	5.6330770	1981-1999 –> 2000-2012	11.660481	31278.8252	31336.4756
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	16603.3478	16644.9468	4.6073813	1981-1999 –> 2000-2012	8.005086	24865.7924	24944.8630
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	19969.5548	20012.0139	5.5609561	1981-1999 –> 2000-2012	11.398741	31093.2366	31173.9472
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	20001.3997	20037.7932	5.5905997	1981-1999 –> 2000-2012	11.617580	31234.3943	31303.5748
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	16835.4151	16871.0714	4.8029709	1981-1999 –> 2000-2012	8.656750	25489.0888	25556.8636
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ aou + silicate + phosphate	30154.9864	30187.3953	5.4972445	1981-1999 –> 2000-2012	12.063467	49686.3749	49748.7434
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ nitrate + silicate + phosphate + phosphate_star	30384.6099	30423.5005	5.6284270	1981-1999 –> 2000-2012	12.342632	50049.8019	50124.6441
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate_star	30493.4052	30532.2959	5.6922283	1981-1999 –> 2000-2012	12.253179	50022.0428	50096.8850
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	30498.9597	30537.8504	5.6955050	1981-1999 –> 2000-2012	12.143022	49924.4551	49999.2973
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	30355.7850	30394.6757	5.6116432	1981-1999 –> 2000-2012	12.147597	49861.8479	49936.6901
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + nitrate + phosphate_star	23171.4001	23209.1778	4.3470068	1981-1999 –> 2000-2012	7.626093	34865.7472	34937.8131
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	23118.4467	23162.5208	4.3173154	1981-1999 –> 2000-2012	7.586258	34800.9079	34884.9848
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate_star	24100.9824	24138.7602	4.8813628	1981-1999 –> 2000-2012	8.778028	36568.7277	36640.7935
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate_star	23582.4927	23620.2705	4.5756956	1981-1999 –> 2000-2012	8.032194	35513.0029	35585.0688
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate_star	30040.3384	30079.2290	5.4312081	1981-1999 –> 2000-2012	11.858479	49447.2339	49522.0761
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	23528.3767	23572.4507	4.5437832	1981-1999 –> 2000-2012	7.976997	35430.5912	35514.6680
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	30111.6940	30150.5847	5.4715089	1981-1999 –> 2000-2012	11.980756	49593.5424	49668.3846
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	23566.9972	23604.7749	4.5668612	1981-1999 –> 2000-2012	8.038444	35517.0247	35589.0906
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + phosphate_star	23669.4243	23700.9058	4.6267294	1981-1999 –> 2000-2012	8.186832	35730.3029	35790.3578
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + phosphate_star	30206.1845	30238.5933	5.5264815	1981-1999 –> 2000-2012	12.092991	49737.8309	49800.1994
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	23518.5656	23562.6397	4.5382267	1981-1999 –> 2000-2012	7.991259	35446.5789	35530.6557
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	23557.1743	23594.9521	4.5612697	1981-1999 –> 2000-2012	8.117130	35614.7080	35686.7739
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	29807.6358	29846.5264	5.3018315	1981-1999 –> 2000-2012	11.648086	49139.5111	49214.3533
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	24098.7645	24136.5422	4.8800127	1981-1999 –> 2000-2012	8.974642	36788.6151	36860.6810
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	30075.0049	30113.8956	5.4507501	1981-1999 –> 2000-2012	11.950645	49548.3495	49623.1917
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	39513.7673	39554.4742	4.9767297	1981-1999 –> 2000-2012	11.263029	63525.6349	63603.6122
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	39902.6576	39943.3644	5.1271045	1981-1999 –> 2000-2012	11.330912	63817.1990	63895.1763
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	39413.1972	39453.9040	4.9385646	1981-1999 –> 2000-2012	11.196746	63392.0347	63470.0120
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate_star	30246.6272	30285.9726	4.4144647	1981-1999 –> 2000-2012	7.998424	45034.8462	45109.6881
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + phosphate_star	40022.9612	40063.6680	5.1745370	1981-1999 –> 2000-2012	11.995210	64635.9523	64713.9297
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	39329.4794	39376.9707	4.9062669	1981-1999 –> 2000-2012	11.174043	63321.6049	63412.5784
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + nitrate + phosphate_star	27358.4545	27397.7999	3.3451039	1981-1999 –> 2000-2012	6.383482	41241.3529	41316.1948
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	26807.4979	26853.4009	3.1720882	1981-1999 –> 2000-2012	5.964588	40229.7884	40317.1039
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	39396.1220	39443.6133	4.9313589	1981-1999 –> 2000-2012	11.077605	63243.9815	63334.9550
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate_star	39993.3029	40034.0097	5.1628029	1981-1999 –> 2000-2012	11.744421	64343.4211	64421.3985
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + phosphate_star	26873.0250	26912.3704	3.1927277	1981-1999 –> 2000-2012	5.859613	40041.0020	40115.8438
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	26746.7649	26792.6679	3.1536393	1981-1999 –> 2000-2012	5.810074	39895.2170	39982.5325
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate_star	40058.6968	40099.4036	5.1887109	1981-1999 –> 2000-2012	11.572101	64183.4926	64261.4699
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	26892.8271	26932.1725	3.1988056	1981-1999 –> 2000-2012	5.878872	40087.8310	40162.6729
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + phosphate_star	27426.7658	27459.5536	3.3677695	1981-1999 –> 2000-2012	6.446616	41380.1969	41442.5651
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	26763.1357	26809.0387	3.1586017	1981-1999 –> 2000-2012	5.827289	39936.8149	40024.1304
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	26911.3010	26950.6464	3.2044862	1981-1999 –> 2000-2012	6.041761	40418.7925	40493.6343
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	39966.4998	40007.2066	5.1522214	1981-1999 –> 2000-2012	11.399752	63932.7873	64010.7646
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	30224.1093	30263.4547	4.4049280	1981-1999 –> 2000-2012	8.012075	45047.6826	45122.5245
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	40017.8800	40058.5868	5.1725247	1981-1999 –> 2000-2012	11.539920	64124.1910	64202.1683
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	35031.4986	35079.1415	3.3337409	1981-1999 –> 2000-2012	6.014707	53232.9830	53324.2901
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	34747.3475	34794.9904	3.2635330	1981-1999 –> 2000-2012	5.898129	52816.8954	52908.2025
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	36008.1629	36048.9996	3.5873123	1981-1999 –> 2000-2012	6.360578	54463.6106	54541.8738
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	40208.4146	40249.4433	4.4692749	1981-1999 –> 2000-2012	10.400338	65416.8565	65495.5558
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	34395.6388	34443.2817	3.1786772	1981-1999 –> 2000-2012	5.770052	52340.1026	52431.4096
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	40898.9032	40939.9319	4.6988588	1981-1999 –> 2000-2012	10.305518	65664.3323	65743.0315
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	39834.5430	39882.4098	4.3490503	1981-1999 –> 2000-2012	9.973738	64627.2576	64719.0734
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	34420.7753	34468.4181	3.1846679	1981-1999 –> 2000-2012	5.784731	52390.5505	52481.8576
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate_star	35128.5449	35169.3817	3.3585666	1981-1999 –> 2000-2012	6.252214	53905.3175	53983.5807
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	33683.7836	33731.4265	3.0136219	1981-1999 –> 2000-2012	5.503214	51325.2410	51416.5481
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	39850.5836	39898.4504	4.3541143	1981-1999 –> 2000-2012	9.937713	64585.5527	64677.3685
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	39808.4832	39856.3500	4.3408359	1981-1999 –> 2000-2012	9.956417	64588.4360	64680.2518
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	40477.9313	40518.9600	4.5575220	1981-1999 –> 2000-2012	10.203582	65298.5155	65377.2148
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	34641.5534	34682.3902	3.2382579	1981-1999 –> 2000-2012	5.849143	52640.7360	52718.9992
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + silicate + phosphate_star	40786.9639	40827.9926	4.6608541	1981-1999 –> 2000-2012	10.289583	65583.3350	65662.0343
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	34675.0213	34715.8581	3.2463863	1981-1999 –> 2000-2012	5.867793	52704.6180	52782.8812
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	34300.5397	34341.3765	3.1565871	1981-1999 –> 2000-2012	5.701514	52106.2329	52184.4961
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	40676.2582	40717.2869	4.6235706	1981-1999 –> 2000-2012	10.216104	65421.8193	65500.5185
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	40762.6619	40803.6906	4.6526440	1981-1999 –> 2000-2012	10.274028	65548.7495	65627.4487
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + silicate + phosphate_star	41129.8560	41164.0466	4.7789455	1981-1999 –> 2000-2012	10.425034	65948.4801	66014.0629
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	38385.6888	38434.3417	2.9129757	1981-1999 –> 2000-2012	5.357209	58020.3822	58113.5045
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	39008.1950	39049.8975	3.0333561	1981-1999 –> 2000-2012	5.581408	58993.8029	59073.6220
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	38365.9301	38414.5829	2.9092459	1981-1999 –> 2000-2012	5.345335	57972.3080	58065.4304
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	39216.2109	39257.9133	3.0745479	1981-1999 –> 2000-2012	5.543554	58934.4588	59014.2779
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	39076.2426	39117.9450	3.0467699	1981-1999 –> 2000-2012	5.588120	59039.5071	59119.3263
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	39973.5960	40022.2489	3.2288915	1981-1999 –> 2000-2012	5.713844	59748.4622	59841.5846
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate	43424.9659	43466.6621	4.0510955	1981-1999 –> 2000-2012	9.086489	69317.0446	69396.8871
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate_star	43494.4991	43536.1953	4.0694210	1981-1999 –> 2000-2012	9.214970	69571.0838	69650.9264
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	42706.6934	42755.3389	3.8660550	1981-1999 –> 2000-2012	8.993198	68754.7240	68847.8737
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	39985.3165	40033.9693	3.2313463	1981-1999 –> 2000-2012	5.723193	59783.6874	59876.8097
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	38744.5103	38793.1631	2.9815461	1981-1999 –> 2000-2012	5.611747	59001.3232	59094.4455
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	38745.8330	38794.4859	2.9818018	1981-1999 –> 2000-2012	5.377747	58211.2398	58304.3622
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	42673.4917	42722.1372	3.8577322	1981-1999 –> 2000-2012	9.024720	68787.5247	68880.6743
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + phosphate + phosphate_star	43504.4601	43546.1563	4.0720530	1981-1999 –> 2000-2012	9.236215	69611.8294	69691.6719
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate	38900.6749	38942.3773	3.0122815	1981-1999 –> 2000-2012	5.664018	59224.6703	59304.4895
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	42701.7588	42750.4044	3.8648169	1981-1999 –> 2000-2012	9.004862	68771.2185	68864.3681
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	42799.9008	42841.5970	3.8900208	1981-1999 –> 2000-2012	9.113531	69004.6952	69084.5378
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + phosphate	43665.4162	43700.1630	4.1153535	1981-1999 –> 2000-2012	9.156404	69565.0669	69631.6024
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	43521.1464	43562.8426	4.0764658	1981-1999 –> 2000-2012	9.203987	69567.8070	69647.6495
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	43524.7875	43566.4837	4.0774294	1981-1999 –> 2000-2012	9.217605	69592.4634	69672.3059
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou	13717.0960	13741.0974	2.4101829	1981-1999 –> 2000-2012	4.673051	21571.9520	21617.8343
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + phosphate_star	13682.9496	13712.9513	2.3956195	1981-1999 –> 2000-2012	4.647468	21522.6718	21580.0247
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + phosphate + phosphate_star	13716.4042	13746.4060	2.4090954	1981-1999 –> 2000-2012	4.677284	21581.5039	21638.8568
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + silicate	13725.9928	13749.9942	2.4137810	1981-1999 –> 2000-2012	4.626085	21501.5273	21547.4096
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate_star	13659.0696	13689.0713	2.3860466	1981-1999 –> 2000-2012	4.582270	21410.9992	21468.3521
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou	13697.1984	13727.2002	2.4013499	1981-1999 –> 2000-2012	4.652779	21536.2665	21593.6194
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate	21595.3757	21633.1400	3.5929854	1981-1999 –> 2000-2012	7.841756	33155.6159	33227.0305
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate_star	13476.0209	13512.0230	2.3131500	1981-1999 –> 2000-2012	4.487419	21194.6862	21263.5097
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate_star	21571.7953	21609.5596	3.5824104	1981-1999 –> 2000-2012	7.841681	33141.9822	33213.3968
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	21419.8331	21463.8915	3.5141252	1981-1999 –> 2000-2012	7.773392	32992.0167	33075.3337
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	21404.0927	21448.1510	3.5072177	1981-1999 –> 2000-2012	7.779455	32988.5300	33071.8470
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + phosphate + phosphate_star	13481.3317	13517.3338	2.3152108	1981-1999 –> 2000-2012	4.492974	21205.6332	21274.4566
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + phosphate + phosphate_star	21568.7772	21606.5415	3.5810592	1981-1999 –> 2000-2012	7.843392	33141.8609	33213.2754
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate	13727.9925	13757.9942	2.4137809	1981-1999 –> 2000-2012	4.625229	21504.1701	21561.5230
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	21417.9139	21461.9722	3.5132822	1981-1999 –> 2000-2012	7.775568	32992.9523	33076.2693
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate_star	13574.1615	13610.1636	2.3515290	1981-1999 –> 2000-2012	4.517596	21279.5609	21348.3843
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + phosphate	21594.6317	21626.1020	3.5935495	1981-1999 –> 2000-2012	7.846186	33156.5364	33216.0485
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate_star	21435.7686	21473.5329	3.5220124	1981-1999 –> 2000-2012	7.784750	33009.2343	33080.6489
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	21413.6392	21451.4035	3.5122834	1981-1999 –> 2000-2012	7.793517	33004.5535	33075.9681
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	21433.2682	21471.0325	3.5209118	1981-1999 –> 2000-2012	7.786482	33009.4111	33080.8256
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + silicate	16075.7009	16100.5414	2.1497684	1981-1999 –> 2000-2012	4.138568	24079.8599	24126.8946
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate_star	16074.4007	16105.4513	2.1488041	1981-1999 –> 2000-2012	4.130845	24067.6370	24126.4304
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou	15866.8524	15897.9030	2.0890233	1981-1999 –> 2000-2012	4.059070	23837.0477	23895.8411
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate	29193.8919	29233.7368	3.1895452	1981-1999 –> 2000-2012	7.548178	45800.7887	45876.4060
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate_star	15652.0983	15689.3591	2.0283656	1981-1999 –> 2000-2012	3.860895	23349.6161	23420.1682
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	29030.4201	29076.9059	3.1432445	1981-1999 –> 2000-2012	7.501796	45639.2091	45727.4293
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	29053.0867	29099.5725	3.1495469	1981-1999 –> 2000-2012	7.519479	45676.8447	45765.0650
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + phosphate_star	16035.9781	16073.2388	2.1370284	1981-1999 –> 2000-2012	4.110039	24013.8801	24084.4321
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	29030.2368	29076.7226	3.1431935	1981-1999 –> 2000-2012	7.486170	45618.4784	45706.6987
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + phosphate + phosphate_star	15661.8987	15699.1595	2.0310698	1981-1999 –> 2000-2012	3.867647	23367.7912	23438.3433
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate	15991.5609	16022.6115	2.1247411	1981-1999 –> 2000-2012	4.099139	23970.1322	24028.9256
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	29055.4569	29101.9427	3.1502066	1981-1999 –> 2000-2012	7.523558	45683.7044	45771.9246
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate_star	15820.3249	15857.5856	2.0752874	1981-1999 –> 2000-2012	3.979153	23662.8075	23733.3596
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate	29231.1849	29264.3890	3.2006397	1981-1999 –> 2000-2012	7.559659	45836.5901	45899.6046
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + phosphate_star	16382.7169	16413.7675	2.2407823	1981-1999 –> 2000-2012	4.101179	24135.5264	24194.3198
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate	29030.6917	29070.5367	3.1438755	1981-1999 –> 2000-2012	7.502638	45637.7587	45713.3761
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate_star	29055.4390	29095.2840	3.1507585	1981-1999 –> 2000-2012	7.521226	45677.9002	45753.5176
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	29029.2003	29069.0452	3.1434612	1981-1999 –> 2000-2012	7.489222	45619.1208	45694.7382
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + phosphate + phosphate_star	16394.3500	16425.4006	2.2443288	1981-1999 –> 2000-2012	4.108652	24155.1629	24213.9563
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	29058.4992	29098.3442	3.1516107	1981-1999 –> 2000-2012	7.525711	45685.7295	45761.3469
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + silicate	18742.0926	18767.6745	2.0076236	1981-1999 –> 2000-2012	3.998524	28579.5919	28628.1918
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + silicate + phosphate_star	18732.8878	18764.8652	2.0050846	1981-1999 –> 2000-2012	3.982788	28541.3680	28602.1178
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou	18158.9431	18190.9205	1.8792317	1981-1999 –> 2000-2012	3.848385	27947.2163	28007.9661
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	48523.2304	48573.3922	3.0543408	1981-1999 –> 2000-2012	7.417217	80737.5396	80834.0736
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate	48593.1556	48636.1514	3.0658449	1981-1999 –> 2000-2012	7.438763	80831.0609	80913.8044
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate_star	17627.4351	17665.8079	1.7693405	1981-1999 –> 2000-2012	3.537937	26916.7124	26989.6122
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	48115.0682	48165.2299	2.9898696	1981-1999 –> 2000-2012	7.340417	80297.8677	80394.4018
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	48343.9602	48394.1220	3.0258547	1981-1999 –> 2000-2012	7.418358	80633.6206	80730.1547
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + phosphate_star	18005.6345	18044.0074	1.8465554	1981-1999 –> 2000-2012	3.735351	27601.5858	27674.4856
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	48282.2477	48332.4095	3.0161102	1981-1999 –> 2000-2012	7.405732	80564.6011	80661.1351
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + phosphate + phosphate_star	17635.7100	17674.0829	1.7709949	1981-1999 –> 2000-2012	3.543001	26933.9707	27006.8704
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate	18398.6473	18430.6247	1.9308031	1981-1999 –> 2000-2012	3.891991	28168.0158	28228.7656
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	48340.3200	48390.4818	3.0252791	1981-1999 –> 2000-2012	7.423303	80643.9649	80740.4990
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	17724.7539	17763.1268	1.7888955	1981-1999 –> 2000-2012	3.596167	27114.9230	27187.8227
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	48342.6296	48385.6254	3.0259606	1981-1999 –> 2000-2012	7.448537	80706.2581	80789.0016
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + phosphate	48545.4891	48588.4849	3.0582160	1981-1999 –> 2000-2012	7.443461	80814.7356	80897.4791
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	48124.2626	48174.4244	2.9913068	1981-1999 –> 2000-2012	7.373224	80387.0581	80483.5921
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + phosphate_star	18965.2447	18997.2221	2.0584009	1981-1999 –> 2000-2012	3.882290	28396.1020	28456.8518
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	48274.4434	48317.4392	3.0151953	1981-1999 –> 2000-2012	7.425847	80608.0114	80690.7549
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + phosphate + phosphate_star	18983.1135	19015.0909	2.0625593	1981-1999 –> 2000-2012	3.890456	28424.2101	28484.9599
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	38107.7002	38156.3458	2.8682870	1981-1999 –> 2000-2012	7.088181	60145.4988	60237.9388
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	38172.6055	38214.3017	2.8807705	1981-1999 –> 2000-2012	7.103252	60213.1265	60292.3608
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + silicate + phosphate_star	10667.8490	10697.1577	1.8847702	1981-1999 –> 2000-2012	3.804854	16759.2069	16814.9738
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	38576.8123	38625.4579	2.9569696	1981-1999 –> 2000-2012	7.088099	60450.8304	60543.2704
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate	38682.5851	38724.2813	2.9777276	1981-1999 –> 2000-2012	7.109407	60555.6286	60634.8629
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate_star	10203.8736	10239.0440	1.7229831	1981-1999 –> 2000-2012	3.593562	16220.5408	16287.4611
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	38128.3555	38177.0011	2.8721352	1981-1999 –> 2000-2012	6.993776	59984.6582	60077.0982
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	38281.2279	38329.8734	2.9007770	1981-1999 –> 2000-2012	7.066811	60220.0650	60312.5050
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + phosphate_star	10324.3789	10359.5492	1.7634409	1981-1999 –> 2000-2012	3.623592	16324.6337	16391.5540
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	38418.5324	38467.1779	2.9267455	1981-1999 –> 2000-2012	7.126796	60420.0188	60512.4588
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + phosphate + phosphate_star	10206.2903	10241.4607	1.7237853	1981-1999 –> 2000-2012	3.594175	16222.6617	16289.5820
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate	10397.1485	10426.4571	1.7890198	1981-1999 –> 2000-2012	3.692885	16463.6019	16519.3688
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	38256.5840	38305.2295	2.8961405	1981-1999 –> 2000-2012	7.070321	60210.4709	60302.9109
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	9736.8798	9772.0502	1.5747748	1981-1999 –> 2000-2012	3.234513	15402.4360	15469.3563
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	38424.0178	38465.7140	2.9281678	1981-1999 –> 2000-2012	7.141421	60447.6838	60526.9181
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	38383.8566	38432.5022	2.9201654	1981-1999 –> 2000-2012	7.097052	60342.7364	60435.1764
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate_star	10477.1272	10506.4358	1.8167916	1981-1999 –> 2000-2012	3.698308	16508.9119	16564.6788
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + nitrate + phosphate_star	10519.8876	10549.1962	1.8318162	1981-1999 –> 2000-2012	3.691981	16518.1646	16573.9315
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + phosphate + phosphate_star	10482.1399	10511.4485	1.8185465	1981-1999 –> 2000-2012	3.700031	16513.8748	16569.6417
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + silicate + phosphate_star	10118.5855	10147.8942	1.6955642	1981-1999 –> 2000-2012	3.364715	15798.7460	15854.5129
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate_star	102958.0965	103007.2161	1.6822764	1981-1999 –> 2000-2012	4.209044	179980.6264	180075.9814
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	103595.7104	103644.8300	1.7026024	1981-1999 –> 2000-2012	4.209771	180362.6125	180457.9674
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	102274.0240	102323.1436	1.6607390	1981-1999 –> 2000-2012	4.186175	179279.2510	179374.6059
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	48099.8315	48150.0261	2.9525389	1981-1999 –> 2000-2012	6.872030	89330.3575	89428.9168
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	48921.1855	48971.3802	3.0814348	1981-1999 –> 2000-2012	7.070512	90412.1612	90510.7205
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + phosphate	48395.0612	48438.0852	2.9985488	1981-1999 –> 2000-2012	6.932741	89678.9949	89763.4743
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	48349.8136	48400.0083	2.9911874	1981-1999 –> 2000-2012	6.921415	89620.8232	89719.3825
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	98819.6831	98876.9893	1.5560636	1981-1999 –> 2000-2012	3.994196	174671.9771	174783.2245
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	48743.7917	48793.9863	3.0531280	1981-1999 –> 2000-2012	7.056331	90287.0854	90385.6447
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate_star	107720.4725	107769.5921	1.8401584	1981-1999 –> 2000-2012	4.186496	182310.9285	182406.2835
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate_star	48979.4986	49022.5226	3.0911186	1981-1999 –> 2000-2012	7.105786	90563.1142	90647.5936
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	99059.1224	99116.4285	1.5630974	1981-1999 –> 2000-2012	3.909311	173649.8480	173761.0954
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	48940.6364	48990.8311	3.0845545	1981-1999 –> 2000-2012	7.097693	90520.6161	90619.1753
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	98819.1657	98876.4719	1.5560484	1981-1999 –> 2000-2012	3.994029	174669.4149	174780.6623
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate_star	99065.5953	99114.7149	1.5633469	1981-1999 –> 2000-2012	4.029064	175285.2107	175380.5656
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + phosphate	48876.7753	48919.7993	3.0746436	1981-1999 –> 2000-2012	7.001614	90133.5149	90217.9943
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	48708.3455	48758.5401	3.0475031	1981-1999 –> 2000-2012	6.962253	89920.9577	90019.5170
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + aou + silicate + phosphate	49371.7659	49414.7899	3.1548478	1981-1999 –> 2000-2012	7.089040	90655.6981	90740.1775
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + phosphate_star	107734.9779	107775.9109	1.8407306	1981-1999 –> 2000-2012	4.198047	182476.6854	182556.1478
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	105776.9548	105826.0744	1.7740121	1981-1999 –> 2000-2012	4.123040	180405.0301	180500.3850

6.3 Target variable coefficients

A data frame to map the target variable is prepared.

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

eras_backward <- GLODAP_glanced %>%
  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 <- full_join(
  lm_best_eras %>% select(data_source, basin, gamma_slab, model, eras),
  eras_era) %>% 
  drop_na() %>% 
  arrange(era, basin, gamma_slab, data_source)

lm_best <- left_join(
  lm_best,
  GLODAP_tidy %>% select(data_source, basin, gamma_slab, era, model, term, estimate))

rm(eras_era, eras_forward, eras_backward)

6.4 Cant coeffcients

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

# subtract coefficients of adjacent era  
lm_best_cant <- lm_best %>%
  arrange(era) %>%
  group_by(data_source, 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 to wide format
lm_best_cant <- lm_best_cant %>%
  pivot_wider(values_from = delta_coeff,
              names_from = term,
              names_prefix = "delta_coeff_",
              values_fill = 0)

6.5 Write files

# create table of target varaible coefficients in wide format
lm_best_target <- lm_best %>% 
  pivot_wider(names_from = "term",
              names_prefix = "coeff_",
              values_from = "estimate",
              values_fill = 0
              )


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

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

7 Model diagnotics

7.1 Selection criterion vs predictors

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

7.1.1 All models

GLODAP_glanced %>%
  group_split(era) %>%
  map(
    ~ ggplot(data = .x,
             aes(
               as.factor(n_predictors),
               !!sym(params_local$MLR_criterion),
               col = data_source
             )) +
      geom_hline(yintercept = c(0, 10)) +
      geom_boxplot() +
      facet_grid(gamma_slab ~ basin) +
      scale_color_brewer(palette = "Set1") +
      ylim(c(0, NA)) +
      labs(x = "Number of predictors",
           title = paste("Era:", unique(.x$era)))
  )

[[1]]

Past versions of eMLR_predictor_model_quality_all-1.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
f3a708f	jens-daniel-mueller	2020-12-17

[[2]]

Past versions of eMLR_predictor_model_quality_all-2.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26

7.1.2 Best models

left_join(lm_best_target %>% select(basin, gamma_slab, era, model),
          GLODAP_glanced) %>%
  group_split(era) %>%
  imap(
  ~ ggplot(data = .x,
         aes("",
             !!sym(params_local$MLR_criterion),
             col = data_source)) +
  geom_hline(yintercept = c(0, 10)) +
  geom_boxplot() +
  facet_grid(gamma_slab ~ basin) +
  scale_color_brewer(palette = "Set1") +
  ylim(c(0, NA)) +
  labs(x = "Number of predictors pooled",
           title = paste("Era:", unique(.x$era)))
  )

[[1]]

Past versions of eMLR_predictor_model_quality_best-1.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
f3a708f	jens-daniel-mueller	2020-12-17

[[2]]

Past versions of eMLR_predictor_model_quality_best-2.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26

7.2 RMSE correlation between eras

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

7.2.1 All models

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

lm_all_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)) +
  geom_abline(slope = 1,
              col = 'red') +
  facet_grid(data_source ~ basin)

Past versions of rmse_correlation_across_eras_all_models-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17
e4ca289	jens-daniel-mueller	2020-12-16
158fe26	jens-daniel-mueller	2020-12-15
7a9a4cb	jens-daniel-mueller	2020-12-15
61b263c	jens-daniel-mueller	2020-12-15
984697e	jens-daniel-mueller	2020-12-12
3ebff89	jens-daniel-mueller	2020-12-12
ba112d3	jens-daniel-mueller	2020-12-11
24a632f	jens-daniel-mueller	2020-12-07
6a8004b	jens-daniel-mueller	2020-12-07
70bf1a5	jens-daniel-mueller	2020-12-07
7555355	jens-daniel-mueller	2020-12-07
143d6fa	jens-daniel-mueller	2020-12-07
090e4d5	jens-daniel-mueller	2020-12-02
7c25f7a	jens-daniel-mueller	2020-12-02
b03ddb8	jens-daniel-mueller	2020-12-02
91435ae	jens-daniel-mueller	2020-12-01
196be51	jens-daniel-mueller	2020-11-30

rm(max_rmse)

7.2.2 Best models

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

lm_best_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)) +
  geom_abline(slope = 1,
              col = 'red') +
  facet_grid(data_source ~ basin)

Past versions of rmse_correlation_across_eras_best_models-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
a84ff3c	jens-daniel-mueller	2020-12-17

rm(max_rmse)

7.3 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_cant %>% 
  pivot_longer(starts_with("delta_coeff_"),
               names_to = "term",
               names_prefix = "delta_coeff_",
               values_to = "delta_coeff") %>% 
  filter(term != "(Intercept)",
         delta_coeff != 0) %>% 
  group_by(data_source, basin, gamma_slab) %>% 
  count(term) %>% 
  ungroup() %>% 
  pivot_wider(values_from = n, names_from = term)

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

	aou	nitrate	phosphate	phosphate_star	sal	silicate	temp
Atlantic - mod
(-Inf,26]	4	5	6	4	10	6	10
(26,26.5]	6	5	5	6	9	6	10
(26.5,26.75]	8	5	6	6	4	5	6
(26.75,27]	6	1	6	7	7	10	7
(27,27.25]	5	2	5	8	8	8	6
(27.25,27.5]	6	5	3	5	8	1	8
(27.5,27.75]	5	2	5	7	10	6	9
(27.75,27.85]	5	4	4	6	10	10	6
(27.85,27.95]	6	3	5	5	10	8	8
(27.95,28.05]	8	NA	4	6	6	5	10
(28.05,28.1]	5	1	2	7	7	4	6
(28.1,28.15]	7	2	4	4	4	4	7
(28.15,28.2]	7	4	3	5	4	3	3
(28.2, Inf]	5	7	2	6	5	7	8
total	83.00	—	60.00	82.00	102.00	83.00	104.00
Indo-Pacific - mod
(-Inf,26]	5	5	5	7	10	5	10
(26,26.5]	4	5	4	10	6	8	10
(26.5,26.75]	4	6	3	10	4	7	10
(26.75,27]	2	8	3	10	3	6	10
(27,27.25]	3	8	3	10	3	5	10
(27.25,27.5]	3	9	4	10	7	5	7
(27.5,27.75]	3	7	5	8	10	8	5
(27.75,27.85]	4	NA	2	6	10	4	5
(27.85,27.95]	3	1	2	7	8	4	8
(27.95,28.05]	3	1	2	7	8	4	8
(28.05,28.1]	2	2	2	9	6	4	9
(28.1, Inf]	2	5	2	10	8	8	7
total	38.00	—	37.00	104.00	83.00	68.00	99.00
Atlantic - obs
(-Inf,26]	7	10	6	6	4	4	10
(26,26.5]	10	6	8	2	6	5	6
(26.5,26.75]	4	4	NA	10	4	5	6
(26.75,27]	4	4	1	10	5	6	10
(27,27.25]	4	2	3	10	6	7	10
(27.25,27.5]	6	NA	7	7	5	5	10
(27.5,27.75]	7	NA	8	5	6	8	8
(27.75,27.85]	4	NA	7	5	5	10	4
(27.85,27.95]	5	NA	7	6	7	10	6
(27.95,28.05]	6	1	6	6	10	4	4
(28.05,28.1]	4	2	4	8	10	1	6
(28.1,28.15]	2	2	2	8	5	2	5
(28.15,28.2]	2	1	2	8	5	2	6
(28.2, Inf]	8	1	5	6	6	3	9
total	73.00	—	—	97.00	84.00	72.00	100.00
Indo-Pacific - obs
(-Inf,26]	7	5	4	5	10	6	10
(26,26.5]	3	4	3	10	10	4	10
(26.5,26.75]	3	8	2	10	4	5	10
(26.75,27]	4	5	4	9	3	8	5
(27,27.25]	4	3	2	10	7	9	7
(27.25,27.5]	3	2	4	9	6	9	9
(27.5,27.75]	5	1	5	8	7	6	10
(27.75,27.85]	5	2	5	8	6	6	10
(27.85,27.95]	6	2	6	6	5	8	10
(27.95,28.05]	7	4	7	4	7	7	10
(28.05,28.1]	7	4	7	4	9	8	8
(28.1, Inf]	7	7	7	4	7	4	10
total	61.00	47.00	56.00	87.00	81.00	80.00	109.00

7.4 RMSE alternatives

7.4.1 AIC

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

lm_all_eras %>% 
  ggplot(aes(rmse, AIC, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(data_source~basin)

Past versions of aic_vs_rmse_all_models-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17

lm_best_eras %>% 
  ggplot(aes(rmse, AIC, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(data_source~basin)

Past versions of aic_vs_rmse_selected_models-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
ac1a836	jens-daniel-mueller	2021-02-24
b03fbd3	jens-daniel-mueller	2021-02-24
3d3b4cc	jens-daniel-mueller	2021-02-23
7b672f7	jens-daniel-mueller	2021-01-11
33ba23c	jens-daniel-mueller	2021-01-07
318609d	jens-daniel-mueller	2020-12-23
9d0b2d0	jens-daniel-mueller	2020-12-23
0aa2b50	jens-daniel-mueller	2020-12-23
2886da0	jens-daniel-mueller	2020-12-19
02f0ee9	jens-daniel-mueller	2020-12-18
7bcb4eb	jens-daniel-mueller	2020-12-18
7131186	jens-daniel-mueller	2020-12-17
5b48ef5	jens-daniel-mueller	2020-12-17

7.4.2 AIC vs BIC

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

lm_all_eras %>% 
  ggplot(aes(AIC, BIC, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(data_source~basin)

Past versions of BIC_vs_AIC_all_models-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20

7.5 RMSE vs VIF

GLODAP_glanced %>% 
  ggplot(aes(rmse, log10(vif_max),col=data_source)) +
  geom_hline(yintercept = 1) +
  geom_point() +
  scale_color_brewer(palette = "Set1") +
  facet_grid(gamma_slab~basin)

Past versions of rmse_vs_VIF_all_models-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20

7.6 Residual patterns

7.6.1 Fitted vs actual models

Plotted are fitted vs actual target variable values, here: rparams_local$MLR_target`

GLODAP_augmented_best <- left_join(
  lm_best_target %>% select(data_source, basin, gamma_slab, era, model),
  GLODAP_augmented
)

# calculate equal axis limits and binwidth
axis_lims <- GLODAP_augmented %>%
  summarise(
    max_value = max(
      c(max(.fitted, max(!!sym(params_local$MLR_target))))
      ),
    min_value = min(
      c(min(.fitted, min(!!sym(params_local$MLR_target))))
    )
  )

i_binwidth <- 1
# binwidth_value <- (axis_lims$max_value - axis_lims$min_value) / 40
axis_lims <- c(axis_lims$min_value, axis_lims$max_value)

GLODAP_augmented %>%
  ggplot(aes(cstar_tref, .fitted)) +
  geom_bin2d(binwidth = i_binwidth) +
  scale_fill_viridis_c() +
  geom_abline(slope = 1,
              col = 'red') +
  coord_equal(xlim = axis_lims,
              ylim = axis_lims) +
  labs(title = "All models") +
  facet_wrap(~data_source)

Past versions of fitted_vs_actual_all-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

GLODAP_augmented_best %>%
  ggplot(aes(cstar_tref, .fitted)) +
  geom_bin2d(binwidth = i_binwidth) +
  scale_fill_viridis_c() +
  geom_abline(slope = 1,
              col = 'red') +
  coord_equal(xlim = axis_lims,
              ylim = axis_lims) +
  labs(title = "Selected models") +
  facet_wrap(~data_source)

Past versions of fitted_vs_actual_best-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

rm(binwidth_value, axis_lims)

7.6.2 Pooled

In the following, we present residual patterns vs latitude across all domains.

i_ylim <- c(-30,30)

GLODAP_augmented_best %>%
  ggplot(aes(lat, .resid)) +
  geom_bin2d(binwidth = i_binwidth) +
  geom_hline(yintercept = 0, col = "white") +
  scale_fill_viridis_c() +
  labs(
    title = paste(
      "Target variable:",
      params_local$MLR_target,
      "| Selected models",
      "| All domains"
    )
  ) +
  facet_wrap(~data_source)

Past versions of residual_patterns_full_range-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

Due to the few large residuals, we limit the y axis range for the plots below.

GLODAP_augmented_best %>%
  ggplot(aes(lat, .resid)) +
  geom_bin2d(binwidth = i_binwidth) +
  geom_hline(yintercept = 0, col = "white") +
  scale_fill_viridis_c() +
  coord_cartesian(ylim = i_ylim) +
  labs(
    title = paste(
      "Target variable:",
      params_local$MLR_target,
      "| Selected models",
      "| All domains"
    )
  ) +
  facet_wrap(~data_source)

Past versions of residual_patterns_y_range_limit-1.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
4bc00ea	jens-daniel-mueller	2021-02-24

7.6.3 By model domain

In the following, we present residual patterns vs latitude for separate model domains, ie basins, density slabs and eras.

GLODAP_augmented_best %>% 
  group_split(basin, era) %>% 
  map(~ ggplot(data = .x, aes(lat, .resid)) +
      geom_bin2d(binwidth = i_binwidth) +
      geom_hline(yintercept = 0, col = "black") +
      scale_fill_viridis_c() +
      facet_grid(gamma_slab ~ data_source) +
      coord_cartesian(ylim = i_ylim) +
      labs(
        title = paste(
          "Target:",
          params_local$MLR_target,
          "| best models | basin:",
          unique(.x$basin),
          "| era:",
          unique(.x$era)
        )
      ))

[[1]]

Past versions of residual_patterns_by_model_domain-1.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
a1ba577	jens-daniel-mueller	2021-02-24
071743d	jens-daniel-mueller	2021-02-24

[[2]]

Past versions of residual_patterns_by_model_domain-2.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
27ae473	jens-daniel-mueller	2021-02-24
a1ba577	jens-daniel-mueller	2021-02-24

[[3]]

Past versions of residual_patterns_by_model_domain-3.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26

[[4]]

Past versions of residual_patterns_by_model_domain-4.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26

7.6.4 Latitudinal mean

GLODAP_augmented_best <- GLODAP_augmented_best %>%
  mutate(lat_grid = as.numeric(as.character(cut(
    lat,
    seq(-90, 90, 10),
    seq(-85, 85, 10)
  ))))

lat_residual <- GLODAP_augmented_best %>%
  group_by(data_source, basin, gamma_slab, era, lat_grid) %>% 
  summarise(.resid_mean = mean(.resid)) %>% 
  ungroup()

lat_residual %>%
  group_split(basin) %>% 
  map(
  ~ggplot(data = .x,
          aes(lat_grid, .resid_mean, col=era)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 0, col = "black") +
  facet_grid(gamma_slab ~ data_source) +
    labs(title = paste("Basin:", unique(.x$basin)))
  )

[[1]]

Past versions of latitudinal_residual-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
fec3558	jens-daniel-mueller	2021-02-24

[[2]]

Past versions of latitudinal_residual-2.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26

7.6.5 Latitudinal offset

# calculate residual offset for adjacent eras
lat_residual_offset <- lat_residual  %>%
  select(data_source, basin, gamma_slab, era, lat_grid, .resid_mean) %>% 
  arrange(era) %>% 
  group_by(basin, gamma_slab, lat_grid) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> "),
         .resid_mean_offset = .resid_mean - lag(.resid_mean)
         ) %>% 
  ungroup() %>% 
  select(-era) %>% 
  drop_na() %>% 
  filter(eras != paste(unique(lat_residual$era)[1],
                       unique(lat_residual$era)[3],
                       sep = " --> "))

lat_residual_offset %>%
  ggplot(aes(lat_grid, .resid_mean_offset, col=eras)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 0, col = "black") +
  facet_grid(gamma_slab ~ basin)

Past versions of latitudinal_residual_offset-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
06bfaf7	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
f155edd	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
83a13de	jens-daniel-mueller	2021-03-20
cf98c6d	jens-daniel-mueller	2021-03-16
a1d52ff	jens-daniel-mueller	2021-03-15
0bade3b	jens-daniel-mueller	2021-03-15
27c1f4b	jens-daniel-mueller	2021-03-14
af75ebf	jens-daniel-mueller	2021-03-14
5017709	jens-daniel-mueller	2021-03-11
585b07f	jens-daniel-mueller	2021-03-11
85a5ed2	jens-daniel-mueller	2021-03-10
6c0bec6	jens-daniel-mueller	2021-03-05
3c2ec33	jens-daniel-mueller	2021-03-05
af70b94	jens-daniel-mueller	2021-03-04
fec3558	jens-daniel-mueller	2021-02-24

8 VIF

GLODAP_glanced %>% 
  ggplot(aes(as.factor(n),
             log10(vif_max),
             col=data_source)) + 
  geom_hline(yintercept = log10(params_local$vif_max)) +
  scale_color_brewer(palette = "Set1") +
  geom_violin() +
  facet_grid(gamma_slab~basin)

Past versions of vif_distribution_n_predictors-1.png

Version	Author	Date
594d503	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
330dcd0	jens-daniel-mueller	2021-03-20

GLODAP_glanced_vif %>% 
  ggplot(aes(Variables,
             log10(VIF),
             col = data_source)) + 
  geom_hline(yintercept = log10(params_local$vif_max)) +
  geom_violin() +
  scale_color_brewer(palette = "Set1") +
  facet_grid(gamma_slab~basin) +
  coord_flip()

Past versions of vif_distribution_type_predictor-1.png

Version	Author	Date
d3c3fde	jens-daniel-mueller	2021-03-26
594d503	jens-daniel-mueller	2021-03-26
2eb881a	jens-daniel-mueller	2021-03-26
03b6009	jens-daniel-mueller	2021-03-23
de6256b	jens-daniel-mueller	2021-03-23
380d215	jens-daniel-mueller	2021-03-21
33b385b	jens-daniel-mueller	2021-03-20
108d6b2	jens-daniel-mueller	2021-03-20
330dcd0	jens-daniel-mueller	2021-03-20

Session information

sessionInfo()

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

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

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

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

other attached packages:
 [1] gt_0.2.2         corrr_0.4.3      broom_0.7.5      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.5      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         utf8_1.1.4               R6_2.5.0                
[10] nortest_1.0-4            DBI_1.1.0                colorspace_1.4-1        
[13] withr_2.3.0              gridExtra_2.3            tidyselect_1.1.0        
[16] curl_4.3                 compiler_4.0.3           git2r_0.27.1            
[19] cli_2.1.0                rvest_0.3.6              xml2_1.3.2              
[22] sass_0.2.0               labeling_0.4.2           scales_1.1.1            
[25] checkmate_2.0.0          goftest_1.2-2            digest_0.6.27           
[28] foreign_0.8-80           rmarkdown_2.5            rio_0.5.16              
[31] pkgconfig_2.0.3          htmltools_0.5.0          highr_0.8               
[34] dbplyr_1.4.4             rlang_0.4.10             readxl_1.3.1            
[37] rstudioapi_0.13          farver_2.0.3             generics_0.0.2          
[40] jsonlite_1.7.1           zip_2.1.1                car_3.0-10              
[43] magrittr_1.5             Matrix_1.2-18            Rcpp_1.0.5              
[46] munsell_0.5.0            fansi_0.4.1              abind_1.4-5             
[49] lifecycle_1.0.0          stringi_1.5.3            whisker_0.4             
[52] yaml_2.2.1               carData_3.0-4            plyr_1.8.6              
[55] grid_4.0.3               blob_1.2.1               parallel_4.0.3          
[58] promises_1.1.1           crayon_1.3.4             lattice_0.20-41         
[61] haven_2.3.1              hms_0.5.3                pillar_1.4.7            
[64] reprex_0.3.0             glue_1.4.2               evaluate_0.14           
[67] RcppArmadillo_0.10.1.2.0 data.table_1.13.2        modelr_0.1.8            
[70] vctrs_0.3.5              httpuv_1.5.4             cellranger_1.1.0        
[73] gtable_0.3.0             reshape_0.8.8            assertthat_0.2.1        
[76] xfun_0.18                openxlsx_4.2.3           RcppEigen_0.3.3.7.0     
[79] later_1.1.0.1            viridisLite_0.3.0        ellipsis_0.3.1          
[82] here_0.1