eMLR - model fitting

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Last updated: 2021-04-15

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Knit directory: emlr_obs_v_XXX/

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---

1 Required data

Required are:

• cleaned and prepared GLODAPv2_2020 file

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

2 Predictor combinations

Find all possible combinations of following considered predictor variables:

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

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

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

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

• 200

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
mod	Atlantic	(-Inf,26]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	258.7811	276.0424	0.9879227	2000-2012 –> 2007-2019	4.645171	1033.1629	1071.016
obs	Atlantic	(-Inf,26]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	895.5390	915.7715	6.6533333	2000-2012 –> 2007-2019	14.195650	1370.4277	1406.093
mod	Atlantic	(-Inf,26]	cstar_tref ~ nitrate + silicate + phosphate + phosphate_star	258.8623	273.6577	0.9998102	2000-2012 –> 2007-2019	4.659212	1031.4090	1063.854
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	898.8452	919.0777	6.7365453	2000-2012 –> 2007-2019	13.804409	1365.0278	1400.693
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	217.4219	234.6832	0.7789198	2000-2012 –> 2007-2019	4.513870	997.6903	1035.543
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	226.6841	243.9455	0.8215060	2000-2012 –> 2007-2019	4.462998	999.8570	1037.710
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	227.0874	241.8828	0.8329313	2000-2012 –> 2007-2019	4.701703	1015.2126	1047.658
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate	900.6621	918.0042	6.8339069	2000-2012 –> 2007-2019	13.965820	1366.0535	1396.624
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	899.1822	919.4146	6.7450847	2000-2012 –> 2007-2019	13.871646	1366.4730	1402.138
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	899.2173	919.4497	6.7459753	2000-2012 –> 2007-2019	13.871044	1366.4801	1402.145
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	892.6750	912.9074	6.5820801	2000-2012 –> 2007-2019	13.644192	1358.7485	1394.414
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	217.1153	234.3766	0.7775483	2000-2012 –> 2007-2019	4.422657	990.5662	1028.419
obs	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	899.5019	919.7344	6.7531974	2000-2012 –> 2007-2019	13.915791	1367.4686	1403.134
mod	Atlantic	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	217.6930	234.9543	0.7801342	2000-2012 –> 2007-2019	4.648433	1007.7839	1045.637
mod	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	256.1120	273.3734	0.9728842	2000-2012 –> 2007-2019	4.628315	1030.3547	1068.208
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	894.2196	914.4520	6.6204123	2000-2012 –> 2007-2019	14.135378	1368.6215	1404.287
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	893.9032	914.1356	6.6125418	2000-2012 –> 2007-2019	14.120540	1368.1808	1403.846
mod	Atlantic	(-Inf,26]	cstar_tref ~ temp + aou + silicate + phosphate	263.3646	278.1600	1.0260181	2000-2012 –> 2007-2019	4.683132	1035.7361	1068.181
mod	Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	259.3619	276.6233	0.9912260	2000-2012 –> 2007-2019	4.608109	1030.6362	1068.489
obs	Atlantic	(-Inf,26]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	892.4294	912.6619	6.5760075	2000-2012 –> 2007-2019	14.059826	1366.2748	1401.940
mod	Atlantic	(26,26.5]	cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star	2391.4517	2419.9791	3.7201522	2000-2012 –> 2007-2019	8.209448	4718.5942	4774.991
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	2349.5786	2378.1060	3.5453418	2000-2012 –> 2007-2019	8.022200	4674.5237	4730.921
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	4536.8744	4568.6515	6.3536807	2000-2012 –> 2007-2019	12.033565	9158.4437	9222.372
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	2349.8289	2378.3564	3.5463621	2000-2012 –> 2007-2019	8.080428	4684.8306	4741.228
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	4546.1729	4577.9500	6.3965123	2000-2012 –> 2007-2019	12.166190	9190.6430	9254.571
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	2305.3046	2333.8320	3.3694344	2000-2012 –> 2007-2019	7.887484	4637.5035	4693.901
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4630.3195	4662.0966	6.7974831	2000-2012 –> 2007-2019	12.616168	9287.1381	9351.067
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	2305.9894	2334.5168	3.3720877	2000-2012 –> 2007-2019	7.995582	4656.4601	4712.857
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	2350.6933	2379.2208	3.5498874	2000-2012 –> 2007-2019	8.150510	4697.2364	4753.634
obs	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	4573.5995	4605.3766	6.5245354	2000-2012 –> 2007-2019	12.403996	9245.5886	9309.517
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	2294.8476	2323.3751	3.3291780	2000-2012 –> 2007-2019	8.233204	4691.9718	4748.369
mod	Atlantic	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	2306.3639	2334.8913	3.3735396	2000-2012 –> 2007-2019	8.030716	4662.5834	4718.981
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate	4545.5920	4572.8295	6.4030742	2000-2012 –> 2007-2019	12.091693	9167.4047	9222.201
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	4556.7974	4584.0349	6.4551266	2000-2012 –> 2007-2019	12.228850	9200.2907	9255.086
mod	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	2387.4235	2415.9509	3.7029672	2000-2012 –> 2007-2019	8.250122	4724.7082	4781.106
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	4546.1676	4577.9447	6.3964877	2000-2012 –> 2007-2019	12.055528	9162.3691	9226.297
mod	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	2381.4985	2410.0260	3.6778346	2000-2012 –> 2007-2019	8.270700	4726.7050	4783.102
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	4556.6936	4588.4707	6.4453214	2000-2012 –> 2007-2019	12.182259	9192.8552	9256.784
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	4577.6799	4604.9174	6.5532631	2000-2012 –> 2007-2019	12.453773	9252.8867	9307.683
obs	Atlantic	(26,26.5]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	4574.9339	4606.7110	6.5308295	2000-2012 –> 2007-2019	12.373248	9237.6957	9301.624
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	6932.2333	6967.0021	6.3047502	2000-2012 –> 2007-2019	11.422791	13128.9984	13198.212
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	6927.8675	6962.6362	6.2917921	2000-2012 –> 2007-2019	11.413321	13126.0128	13195.226
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	3123.4060	3153.5499	4.1293116	2000-2012 –> 2007-2019	7.116336	6213.5825	6274.644
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6959.0203	6993.7890	6.3848425	2000-2012 –> 2007-2019	11.497641	13153.7091	13222.923
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	3130.7355	3160.8794	4.1570191	2000-2012 –> 2007-2019	7.145267	6221.4133	6282.474
obs	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6959.9210	6994.6898	6.3875533	2000-2012 –> 2007-2019	11.509645	13158.2890	13227.502
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	3160.8860	3191.0299	4.2729644	2000-2012 –> 2007-2019	7.401369	6307.6670	6368.728
mod	Atlantic	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	3132.0890	3162.2329	4.1621558	2000-2012 –> 2007-2019	7.160512	6226.9001	6287.961
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate	6950.0737	6979.8755	6.3639753	2000-2012 –> 2007-2019	11.484718	13145.9080	13205.234
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate_star	6947.1722	6976.9740	6.3552794	2000-2012 –> 2007-2019	11.481851	13145.3115	13204.637
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	3096.8392	3126.9831	4.0304213	2000-2012 –> 2007-2019	7.147803	6239.2999	6300.361
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	6950.2158	6984.9845	6.3584057	2000-2012 –> 2007-2019	11.472547	13145.4367	13214.650
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	3101.2891	3131.4331	4.0468189	2000-2012 –> 2007-2019	7.144867	6236.1350	6297.196
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	6949.1394	6983.9081	6.3551811	2000-2012 –> 2007-2019	11.481440	13149.1550	13218.369
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate	3133.2386	3159.0763	4.1741340	2000-2012 –> 2007-2019	7.312122	6281.7637	6334.102
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	3139.3471	3165.1847	4.1974631	2000-2012 –> 2007-2019	7.332321	6286.6506	6338.989
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	6947.5824	6977.3842	6.3565080	2000-2012 –> 2007-2019	11.484393	13146.2403	13205.566
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	3105.4814	3135.6253	4.0623278	2000-2012 –> 2007-2019	7.162779	6241.2764	6302.337
obs	Atlantic	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	6949.5277	6984.2964	6.3563442	2000-2012 –> 2007-2019	11.483759	13149.9998	13219.213
mod	Atlantic	(26.5,26.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	3140.4993	3166.3370	4.2018784	2000-2012 –> 2007-2019	7.344043	6290.6524	6342.990
mod	Atlantic	(26.75,27]	cstar_tref ~ aou + silicate + phosphate + phosphate_star	5506.4160	5536.4995	2.8621476	2000-2012 –> 2007-2019	5.513820	10570.0285	10629.880
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	5290.7567	5325.8542	2.5953046	2000-2012 –> 2007-2019	5.247555	10356.8289	10426.655
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + aou + silicate + phosphate	5435.7775	5465.8610	2.7726689	2000-2012 –> 2007-2019	5.506313	10563.6289	10623.480
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5391.4988	5426.5962	2.7155692	2000-2012 –> 2007-2019	5.262828	10372.3467	10442.173
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	7760.4421	7796.3584	5.3636156	2000-2012 –> 2007-2019	10.930609	14792.3483	14863.406
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5419.7582	5454.8556	2.7502948	2000-2012 –> 2007-2019	5.352225	10445.4135	10515.240
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	7750.5595	7786.4758	5.3424550	2000-2012 –> 2007-2019	10.849399	14758.1939	14829.252
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	7748.3320	7784.2483	5.3376968	2000-2012 –> 2007-2019	10.841777	14754.8025	14825.860
mod	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	5431.0021	5466.0995	2.7642348	2000-2012 –> 2007-2019	5.390817	10476.5542	10546.381
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	7750.2150	7786.1313	5.3417187	2000-2012 –> 2007-2019	10.846403	14756.9311	14827.989
obs	Atlantic	(26.75,27]	cstar_tref ~ sal + temp + silicate + phosphate_star	7764.0473	7794.8327	5.3756548	2000-2012 –> 2007-2019	10.914011	14782.4111	14843.318
mod	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	5107.8219	5142.9194	2.3903721	2000-2012 –> 2007-2019	4.740477	9918.6928	9988.519
mod	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	5118.3666	5153.4640	2.4017324	2000-2012 –> 2007-2019	4.758635	9935.3316	10005.158
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	7747.9507	7783.8669	5.3368828	2000-2012 –> 2007-2019	10.887979	14773.4568	14844.514
mod	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate	5558.7574	5588.8409	2.9303066	2000-2012 –> 2007-2019	5.610689	10645.0921	10704.943
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + aou + silicate + phosphate_star	7748.7469	7779.5322	5.3428553	2000-2012 –> 2007-2019	10.927770	14785.8462	14846.753
mod	Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	5143.7212	5178.8186	2.4292699	2000-2012 –> 2007-2019	4.813741	9985.2240	10055.050
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	7748.1426	7784.0589	5.3372925	2000-2012 –> 2007-2019	10.896347	14776.8552	14847.913
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	7746.3335	7777.1188	5.3377000	2000-2012 –> 2007-2019	10.910911	14778.7377	14839.644
obs	Atlantic	(26.75,27]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	7748.4178	7779.2032	5.3421520	2000-2012 –> 2007-2019	10.925338	14784.8241	14845.731
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate	6861.4768	6893.3881	2.3445844	2000-2012 –> 2007-2019	4.955173	13709.3263	13772.859
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	6713.8718	6745.7830	2.2326015	2000-2012 –> 2007-2019	4.740419	13446.2932	13509.826
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	13254.6739	13294.1041	5.9717246	2000-2012 –> 2007-2019	11.604826	26148.6477	26227.443
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + nitrate + silicate	6548.7348	6585.9645	2.1122436	2000-2012 –> 2007-2019	4.447505	13078.2723	13152.394
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6715.4109	6752.6406	2.2322603	2000-2012 –> 2007-2019	4.713780	13419.5353	13493.657
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6819.9849	6857.2147	2.3110172	2000-2012 –> 2007-2019	4.816171	13551.3521	13625.474
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	13296.9875	13336.4177	6.0332220	2000-2012 –> 2007-2019	11.560100	26113.0619	26191.858
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	13267.6255	13307.0557	5.9904813	2000-2012 –> 2007-2019	11.641620	26174.6814	26253.477
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	7017.3661	7054.5959	2.4673198	2000-2012 –> 2007-2019	5.179555	13976.9956	14051.118
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	13318.0886	13357.5188	6.0641260	2000-2012 –> 2007-2019	11.628544	26161.8628	26240.658
mod	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6847.3637	6884.5935	2.3320918	2000-2012 –> 2007-2019	4.850663	13594.0838	13668.206
obs	Atlantic	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	13297.8348	13337.2650	6.0344599	2000-2012 –> 2007-2019	11.567995	26118.8348	26197.630
mod	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate	6724.5385	6756.4497	2.2405115	2000-2012 –> 2007-2019	4.649732	13341.6856	13405.219
mod	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	6725.8827	6763.1125	2.2400244	2000-2012 –> 2007-2019	4.633585	13326.2878	13400.410
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	13236.9181	13276.3483	5.9461060	2000-2012 –> 2007-2019	11.616901	26158.1823	26236.978
mod	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	6722.0685	6759.2983	2.2371934	2000-2012 –> 2007-2019	4.617847	13306.9344	13381.056
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	13192.9610	13232.3912	5.8831550	2000-2012 –> 2007-2019	11.469129	26052.5562	26131.352
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + aou + silicate + phosphate_star	13300.1783	13333.9757	6.0408097	2000-2012 –> 2007-2019	11.645094	26171.1653	26238.704
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	13203.7461	13243.1763	5.8985385	2000-2012 –> 2007-2019	11.499020	26073.9553	26152.751
obs	Atlantic	(27,27.25]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	13301.0165	13334.8138	6.0420357	2000-2012 –> 2007-2019	11.654300	26177.8259	26245.365
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate	14672.0134	14707.5077	3.5122132	2000-2012 –> 2007-2019	6.912094	29747.2826	29818.507
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	14396.2019	14431.6962	3.3398164	2000-2012 –> 2007-2019	7.036247	29948.1470	30019.372
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	16487.1380	16528.1970	5.7069166	2000-2012 –> 2007-2019	10.199508	31107.9787	31189.806
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	16487.8967	16528.9557	5.7077474	2000-2012 –> 2007-2019	10.172362	31077.5033	31159.331
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + silicate	14613.0477	14654.4577	3.4733560	2000-2012 –> 2007-2019	6.795834	29559.0503	29642.146
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate	16520.4782	16555.6716	5.7457441	2000-2012 –> 2007-2019	10.254396	31157.1616	31227.299
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + phosphate_star	16520.1143	16555.3078	5.7453430	2000-2012 –> 2007-2019	10.232419	31132.8134	31202.951
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	14398.1951	14439.6051	3.3398122	2000-2012 –> 2007-2019	7.027126	29938.0639	30021.159
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	16512.6302	16553.6892	5.7348979	2000-2012 –> 2007-2019	10.242289	31149.9155	31231.743
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14231.9498	14273.3598	3.2400147	2000-2012 –> 2007-2019	6.850007	29651.0214	29734.117
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	16514.5095	16555.5685	5.7369662	2000-2012 –> 2007-2019	10.224041	31129.2071	31211.034
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	16482.3595	16523.4185	5.7016868	2000-2012 –> 2007-2019	10.172483	31078.8842	31160.712
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate_star	14590.2279	14625.7222	3.4601849	2000-2012 –> 2007-2019	7.044360	29966.3885	30037.613
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	14208.9659	14250.3759	3.2264540	2000-2012 –> 2007-2019	6.764905	29513.9430	29597.038
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	14608.6546	14644.1489	3.4718395	2000-2012 –> 2007-2019	7.147138	30127.9197	30199.144
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + phosphate + phosphate_star	16516.7942	16551.9876	5.7416843	2000-2012 –> 2007-2019	10.231838	31132.9210	31203.059
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	14233.9735	14275.3835	3.2412114	2000-2012 –> 2007-2019	6.851335	29653.2523	29736.348
obs	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	16510.6369	16551.6959	5.7327050	2000-2012 –> 2007-2019	10.222730	31128.6209	31210.448
mod	Atlantic	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	14303.0963	14338.5906	3.2835520	2000-2012 –> 2007-2019	6.975408	29847.9822	29919.207
obs	Atlantic	(27.25,27.5]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	16511.8001	16552.8591	5.7339846	2000-2012 –> 2007-2019	10.350644	31268.8496	31350.677
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	18173.4467	18215.4632	5.0520335	2000-2012 –> 2007-2019	9.951039	35826.1874	35910.088
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + phosphate	24504.7991	24537.6594	2.4590287	2000-2012 –> 2007-2019	4.928844	48558.6955	48624.314
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	23624.9552	23664.3875	2.2620921	2000-2012 –> 2007-2019	4.681105	47465.7403	47544.482
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate	24503.7997	24543.2321	2.4583306	2000-2012 –> 2007-2019	4.916479	48510.6894	48589.431
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + phosphate_star	24307.3983	24346.8307	2.4130486	2000-2012 –> 2007-2019	4.846278	48208.8331	48287.575
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	23626.4176	23672.4220	2.2619770	2000-2012 –> 2007-2019	4.673830	47438.5245	47530.390
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	18150.4346	18192.4511	5.0326168	2000-2012 –> 2007-2019	9.763498	35598.4003	35682.301
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	23347.1813	23393.1857	2.2029698	2000-2012 –> 2007-2019	4.587598	47041.7921	47133.658
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	18160.0234	18202.0399	5.0406984	2000-2012 –> 2007-2019	9.788788	35629.2800	35713.181
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	23467.2904	23513.2948	2.2281598	2000-2012 –> 2007-2019	4.621461	47199.4762	47291.342
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + phosphate + phosphate_star	24310.0644	24349.4967	2.4136576	2000-2012 –> 2007-2019	4.846688	48210.6530	48289.395
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	23355.6156	23401.6200	2.2047294	2000-2012 –> 2007-2019	4.589665	47051.5592	47143.425
obs	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	18149.4075	18191.4240	5.0317519	2000-2012 –> 2007-2019	9.766358	35601.9883	35685.889
mod	Atlantic	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	23920.7294	23960.1617	2.3263218	2000-2012 –> 2007-2019	4.880410	48323.8912	48402.633
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	18124.8016	18166.8181	5.0110765	2000-2012 –> 2007-2019	9.794753	35637.8447	35721.745
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	18142.6894	18184.7059	5.0260985	2000-2012 –> 2007-2019	9.834846	35686.3858	35770.286
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate	18149.5259	18185.5401	5.0335359	2000-2012 –> 2007-2019	9.820214	35664.2475	35736.162
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + aou + silicate + phosphate_star	18158.8195	18194.8336	5.0413699	2000-2012 –> 2007-2019	9.852756	35703.7322	35775.647
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	18125.4502	18167.4668	5.0116204	2000-2012 –> 2007-2019	9.801890	35646.5700	35730.471
obs	Atlantic	(27.5,27.75]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	18148.3223	18184.3364	5.0325222	2000-2012 –> 2007-2019	9.826360	35671.8091	35743.724
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate	6848.0502	6881.5283	1.3864314	2000-2012 –> 2007-2019	2.711797	13720.3790	13787.513
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	11836.6862	11875.5002	5.5129631	2000-2012 –> 2007-2019	10.240763	23502.4882	23580.367
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	6581.1708	6614.6488	1.2950925	2000-2012 –> 2007-2019	2.572862	13305.9666	13373.101
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + aou + silicate + phosphate	11836.0397	11869.3089	5.5149364	2000-2012 –> 2007-2019	10.294548	23542.5675	23609.321
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	11826.8217	11865.6358	5.4986025	2000-2012 –> 2007-2019	10.236224	23500.7585	23578.637
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	7352.5816	7386.0596	1.5770745	2000-2012 –> 2007-2019	3.097407	14778.5389	14845.673
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	7342.6622	7376.1402	1.5730848	2000-2012 –> 2007-2019	3.095073	14773.0119	14840.146
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	11825.9448	11859.2140	5.5002356	2000-2012 –> 2007-2019	10.295187	23545.0327	23611.786
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + nitrate + silicate	6789.6040	6828.6618	1.3651952	2000-2012 –> 2007-2019	2.685986	13649.9828	13728.306
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6426.6398	6465.6975	1.2443458	2000-2012 –> 2007-2019	2.492284	13058.1378	13136.461
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate	11831.3656	11870.1796	5.5052128	2000-2012 –> 2007-2019	10.284102	23539.3005	23617.179
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6573.5000	6612.5578	1.2918981	2000-2012 –> 2007-2019	2.590586	13365.8020	13444.125
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	11817.5302	11856.3442	5.4851102	2000-2012 –> 2007-2019	10.270431	23530.7372	23608.616
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	6580.1733	6619.2310	1.2941015	2000-2012 –> 2007-2019	2.592580	13371.8261	13450.149
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6566.8234	6605.8811	1.2896973	2000-2012 –> 2007-2019	2.585566	13350.3590	13428.682
obs	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	11827.4180	11866.2320	5.4994695	2000-2012 –> 2007-2019	10.279734	23536.4813	23614.360
mod	Atlantic	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate_star	6663.1273	6696.6054	1.3224826	2000-2012 –> 2007-2019	2.653068	13551.3109	13618.445
obs	Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	11854.8587	11893.6727	5.5395166	2000-2012 –> 2007-2019	10.273443	23525.7371	23603.616
obs	Atlantic	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	11840.4966	11879.3106	5.5185202	2000-2012 –> 2007-2019	10.255398	23513.8186	23591.698
obs	Atlantic	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	11850.7208	11889.5348	5.5334591	2000-2012 –> 2007-2019	10.267265	23521.4998	23599.379
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	24548.2139	24592.3089	5.1131810	2000-2012 –> 2007-2019	10.367227	50355.3257	50443.804
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	23892.7237	23936.8187	4.7129468	2000-2012 –> 2007-2019	9.665891	49205.2798	49293.758
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate	9357.8967	9391.1308	2.9056941	2000-2012 –> 2007-2019	5.558500	19292.9384	19359.990
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + aou + silicate + phosphate_star	23903.4605	23941.2562	4.7204170	2000-2012 –> 2007-2019	9.673380	49214.0486	49289.887
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	24288.9707	24333.0657	4.9509801	2000-2012 –> 2007-2019	10.083536	49900.0354	49988.514
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	24334.7267	24372.5224	4.9804681	2000-2012 –> 2007-2019	10.117960	49951.8460	50027.684
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + nitrate + silicate	9462.3243	9501.0975	2.9859372	2000-2012 –> 2007-2019	5.800795	19645.0794	19723.306
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate	9456.9897	9490.2239	2.9832903	2000-2012 –> 2007-2019	5.670081	19444.7827	19511.834
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate_star	9536.7089	9569.9431	3.0472170	2000-2012 –> 2007-2019	5.787203	19605.7460	19672.798
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	9201.8915	9240.6646	2.7861191	2000-2012 –> 2007-2019	5.396666	19072.3877	19150.615
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	23821.4000	23865.4950	4.6713329	2000-2012 –> 2007-2019	9.599077	49091.2095	49179.688
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	9252.8089	9291.5821	2.8241050	2000-2012 –> 2007-2019	5.472410	19182.8143	19261.041
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	23776.4319	23820.5269	4.6452853	2000-2012 –> 2007-2019	9.555175	49015.8247	49104.303
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	23921.8677	23965.9627	4.7300574	2000-2012 –> 2007-2019	9.723404	49302.5034	49390.982
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	9266.9029	9305.6761	2.8347107	2000-2012 –> 2007-2019	5.502653	19227.5228	19305.750
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + phosphate + phosphate_star	9518.2289	9551.4630	3.0322770	2000-2012 –> 2007-2019	5.757384	19564.7028	19631.755
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate	23933.2173	23971.0131	4.7379157	2000-2012 –> 2007-2019	9.740112	49326.6918	49402.530
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	9246.8205	9285.5937	2.8196107	2000-2012 –> 2007-2019	5.460620	19165.3929	19243.620
obs	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	23812.7176	23856.8126	4.6662923	2000-2012 –> 2007-2019	9.589829	49075.3701	49163.848
mod	Atlantic	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate_star	9316.2886	9349.5228	2.8737170	2000-2012 –> 2007-2019	5.628951	19408.3231	19475.375
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	26546.5125	26590.9788	5.5283837	2000-2012 –> 2007-2019	11.633277	54805.7682	54894.920
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	26094.7711	26139.2374	5.2415859	2000-2012 –> 2007-2019	11.145270	54060.7790	54149.931
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + aou + silicate + phosphate_star	26165.2290	26203.3429	5.2865648	2000-2012 –> 2007-2019	11.207099	54154.1747	54230.591
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	26224.5094	26268.9756	5.3223952	2000-2012 –> 2007-2019	11.275365	54263.2604	54352.412
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	26496.9509	26535.0648	5.4974635	2000-2012 –> 2007-2019	11.663356	54841.2010	54917.617
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	26311.1116	26349.2255	5.3782971	2000-2012 –> 2007-2019	11.347540	54371.7503	54448.166
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate	11709.1544	11743.3398	3.4414243	2000-2012 –> 2007-2019	7.536612	24852.2171	24920.901
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate_star	11740.6492	11774.8346	3.4661123	2000-2012 –> 2007-2019	7.570566	24894.2036	24962.888
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	11576.1671	11616.0501	3.3375876	2000-2012 –> 2007-2019	7.408451	24693.5747	24773.706
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	26259.3050	26303.7712	5.3442792	2000-2012 –> 2007-2019	11.297930	54299.0579	54388.210
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	11586.8958	11626.7789	3.3457247	2000-2012 –> 2007-2019	7.418882	24706.9192	24787.050
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	26165.5334	26209.9996	5.2855078	2000-2012 –> 2007-2019	11.205733	54156.0224	54245.174
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + phosphate_star	11822.5337	11856.7191	3.5311315	2000-2012 –> 2007-2019	7.669602	25014.4011	25083.085
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	11576.0546	11615.9376	3.3375024	2000-2012 –> 2007-2019	7.374991	24655.2489	24735.380
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	26498.8145	26543.2807	5.4973751	2000-2012 –> 2007-2019	11.656134	54834.9359	54924.088
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + phosphate + phosphate_star	11735.4223	11769.6078	3.4620029	2000-2012 –> 2007-2019	7.565429	24887.8133	24956.497
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + phosphate_star	11851.8126	11880.3005	3.5562888	2000-2012 –> 2007-2019	7.694916	25041.8559	25099.093
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	11586.7118	11626.5948	3.3455849	2000-2012 –> 2007-2019	7.418731	24706.7218	24786.853
obs	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	26222.7158	26267.1820	5.3212696	2000-2012 –> 2007-2019	11.259836	54240.2715	54329.423
mod	Atlantic	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	11585.4438	11619.6293	3.3461408	2000-2012 –> 2007-2019	7.419316	24703.4874	24772.171
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	21443.8168	21486.7601	5.5976235	2000-2012 –> 2007-2019	12.008371	42508.7151	42594.181
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate_star	21493.3808	21530.1893	5.6400934	2000-2012 –> 2007-2019	12.059579	42565.0288	42638.285
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	21538.0850	21574.8936	5.6771740	2000-2012 –> 2007-2019	12.111778	42624.8441	42698.101
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	21522.3962	21565.3395	5.6624727	2000-2012 –> 2007-2019	12.080496	42594.5809	42680.047
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + nitrate + silicate	4336.3032	4372.2641	1.3484934	2000-2012 –> 2007-2019	2.697230	8793.3265	8865.441
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate	4146.4266	4177.2502	1.2514655	2000-2012 –> 2007-2019	2.500110	8402.0453	8463.857
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate_star	4197.7847	4228.6084	1.2772737	2000-2012 –> 2007-2019	2.545873	8494.4034	8556.215
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + phosphate_star	21537.2744	21574.0829	5.6764995	2000-2012 –> 2007-2019	12.095273	42608.2104	42681.467
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	4144.1639	4180.1248	1.2493470	2000-2012 –> 2007-2019	2.491775	8388.8753	8460.989
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	4190.6962	4226.6572	1.2726682	2000-2012 –> 2007-2019	2.537532	8481.6895	8553.803
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	21446.8181	21489.7614	5.6000868	2000-2012 –> 2007-2019	11.984478	42485.2516	42570.718
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	21513.2864	21556.2298	5.6549164	2000-2012 –> 2007-2019	12.079977	42592.5111	42677.977
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + phosphate_star	21520.5054	21557.3140	5.6625634	2000-2012 –> 2007-2019	12.088989	42599.0946	42672.351
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	21452.4219	21495.3652	5.6046887	2000-2012 –> 2007-2019	12.019754	42521.6456	42607.111
obs	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	21514.2468	21557.1901	5.6557125	2000-2012 –> 2007-2019	12.071513	42584.2061	42669.672
mod	Atlantic	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	4335.0608	4365.8844	1.3488995	2000-2012 –> 2007-2019	2.798478	8976.5476	9038.360
mod	Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate	4181.9671	4207.6535	1.2702783	2000-2012 –> 2007-2019	2.555680	8510.6133	8562.123
mod	Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + phosphate_star	4234.9524	4260.6388	1.2973132	2000-2012 –> 2007-2019	2.606575	8611.1601	8662.670
mod	Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate	4183.9666	4214.7902	1.2702780	2000-2012 –> 2007-2019	2.545667	8494.3900	8556.202
mod	Atlantic	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate_star	4236.3031	4267.1268	1.2969784	2000-2012 –> 2007-2019	2.599272	8600.7102	8662.522
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + nitrate	6280.3062	6313.7258	1.2182769	2000-2012 –> 2007-2019	2.578827	13116.7283	13183.681
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	16934.1717	16975.3400	5.9130687	2000-2012 –> 2007-2019	12.843857	34024.6742	34106.736
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + nitrate + silicate	6121.9714	6160.9609	1.1689346	2000-2012 –> 2007-2019	2.527044	12953.2989	13031.410
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate	5802.5990	5836.0186	1.0770799	2000-2012 –> 2007-2019	2.415824	12575.1684	12642.121
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate_star	5860.3953	5893.8148	1.0932525	2000-2012 –> 2007-2019	2.441354	12660.4916	12727.444
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + phosphate_star	16938.6737	16973.9608	5.9203355	2000-2012 –> 2007-2019	12.851605	34027.5297	34097.868
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate	5759.0365	5798.0260	1.0644994	2000-2012 –> 2007-2019	2.310333	12249.3494	12327.461
mod	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	5829.2497	5868.2392	1.0839482	2000-2012 –> 2007-2019	2.344601	12366.2953	12444.407
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	16925.8330	16967.0012	5.9037621	2000-2012 –> 2007-2019	12.817824	34004.0365	34086.098
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	16919.0256	16960.1938	5.8961755	2000-2012 –> 2007-2019	12.810314	33997.2859	34079.347
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + phosphate + phosphate_star	16932.2237	16967.5108	5.9131267	2000-2012 –> 2007-2019	12.842853	34019.9463	34090.285
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	16927.0536	16968.2219	5.9051236	2000-2012 –> 2007-2019	12.823114	34008.1486	34090.210
obs	Atlantic	(28.1,28.15]	cstar_tref ~ sal + temp + silicate + phosphate_star	16925.1202	16960.4073	5.9051978	2000-2012 –> 2007-2019	12.827141	34007.1231	34077.462
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	16929.7310	16970.8993	5.9081107	2000-2012 –> 2007-2019	12.843618	34023.6979	34105.759
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate	5890.0208	5917.8704	1.1022045	2000-2012 –> 2007-2019	2.474699	12758.9873	12814.781
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + phosphate_star	5964.2542	5992.1038	1.1235064	2000-2012 –> 2007-2019	2.510066	12873.5150	12929.309
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate	5865.2711	5898.6907	1.0946279	2000-2012 –> 2007-2019	2.413825	12579.7124	12646.665
mod	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate_star	5949.5913	5983.0108	1.1186893	2000-2012 –> 2007-2019	2.458066	12724.0270	12790.979
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + aou + silicate + phosphate_star	16935.1767	16970.4638	5.9164260	2000-2012 –> 2007-2019	12.852505	34027.5632	34097.902
obs	Atlantic	(28.1,28.15]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	16929.2283	16964.5154	5.9097819	2000-2012 –> 2007-2019	12.847552	34022.8558	34093.194
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + nitrate	8923.7283	8960.5544	0.8900878	2000-2012 –> 2007-2019	1.904720	18863.9052	18937.631
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	6375.3904	6410.8197	3.7022118	2000-2012 –> 2007-2019	7.463525	12096.3002	12166.358
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate	9377.7898	9414.6160	0.9511616	2000-2012 –> 2007-2019	2.027022	19723.7946	19797.520
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + phosphate	6349.9753	6380.3433	3.6652247	2000-2012 –> 2007-2019	7.396289	12052.0903	12112.140
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate	6334.1472	6369.5766	3.6373110	2000-2012 –> 2007-2019	7.345756	12025.6139	12095.672
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	9389.6225	9432.5863	0.9525295	2000-2012 –> 2007-2019	2.028254	19736.7505	19822.764
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	6350.0582	6385.4876	3.6622129	2000-2012 –> 2007-2019	7.396669	12056.0630	12126.121
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + nitrate + phosphate_star	9063.1442	9099.9703	0.9084107	2000-2012 –> 2007-2019	1.946090	19158.8806	19232.606
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	9047.6506	9090.6144	0.9060911	2000-2012 –> 2007-2019	1.938923	19112.9588	19198.972
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + phosphate + phosphate_star	6369.2989	6399.6669	3.6957220	2000-2012 –> 2007-2019	7.452603	12085.7563	12145.806
mod	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	9342.2771	9385.2409	0.9459610	2000-2012 –> 2007-2019	2.013777	19638.2953	19724.308
obs	Atlantic	(28.15,28.2]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	6344.3410	6379.7703	3.6532454	2000-2012 –> 2007-2019	7.377359	12044.5775	12114.636
mod	Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate	9150.6464	9181.3348	0.9203720	2000-2012 –> 2007-2019	1.972968	19343.2395	19404.677
mod	Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + nitrate + silicate	8789.0459	8825.8721	0.8727381	2000-2012 –> 2007-2019	1.889485	18743.6404	18817.366
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + phosphate	6363.6681	6388.9748	3.6899724	2000-2012 –> 2007-2019	7.425429	12066.2299	12116.271
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate	6347.0190	6377.3870	3.6605812	2000-2012 –> 2007-2019	7.373109	12038.7744	12098.824
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + aou + silicate + phosphate_star	6368.4976	6398.8656	3.6944523	2000-2012 –> 2007-2019	7.438960	12078.0930	12138.143
mod	Atlantic	(28.15,28.2]	cstar_tref ~ temp + nitrate + phosphate_star	9251.8349	9282.5234	0.9340848	2000-2012 –> 2007-2019	1.978176	19388.2410	19449.679
mod	Atlantic	(28.15,28.2]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	9106.1024	9142.9286	0.9141322	2000-2012 –> 2007-2019	1.947147	19170.6389	19244.364
obs	Atlantic	(28.15,28.2]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	6361.3148	6391.6828	3.6830905	2000-2012 –> 2007-2019	7.415616	12064.2442	12124.294
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate	13113.6675	13147.5791	0.6611677	2000-2012 –> 2007-2019	1.347520	24247.9381	24314.760
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + aou + nitrate + silicate	12950.4488	12991.1428	0.6528410	2000-2012 –> 2007-2019	1.316268	23724.2335	23804.420
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + nitrate + phosphate_star	16127.9370	16161.8486	0.8331670	2000-2012 –> 2007-2019	1.735883	30185.9642	30252.786
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	14109.6495	14151.0030	3.2351657	2000-2012 –> 2007-2019	6.485868	26660.6787	26742.553
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	16097.4579	16138.1518	0.8310938	2000-2012 –> 2007-2019	1.721728	30013.7236	30093.910
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + nitrate	13047.3841	13088.0781	0.6577136	2000-2012 –> 2007-2019	1.343062	24168.0311	24248.217
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	14067.9209	14109.2744	3.2104265	2000-2012 –> 2007-2019	6.482076	26649.9487	26731.823
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	14113.1613	14154.5148	3.2372563	2000-2012 –> 2007-2019	6.481380	26654.4142	26736.288
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + nitrate + silicate	12896.5149	12943.9911	0.6500458	2000-2012 –> 2007-2019	1.308308	23588.9066	23682.457
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate	14067.6457	14103.0916	3.2114453	2000-2012 –> 2007-2019	6.490803	26659.0304	26729.208
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + phosphate_star	14111.5589	14147.0049	3.2374932	2000-2012 –> 2007-2019	6.482582	26652.2473	26722.425
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	14037.7646	14079.1182	3.1926659	2000-2012 –> 2007-2019	6.471385	26630.2086	26712.083
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14024.4789	14065.8324	3.1848725	2000-2012 –> 2007-2019	6.426493	26562.0063	26643.880
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	14085.8077	14127.1612	3.2210076	2000-2012 –> 2007-2019	6.468164	26631.5696	26713.444
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate_star	15534.8574	15575.5514	0.7959889	2000-2012 –> 2007-2019	1.550613	27682.9459	27763.132
mod	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	15499.9737	15547.4499	0.7937399	2000-2012 –> 2007-2019	1.547210	27633.7312	27727.282
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + phosphate + phosphate_star	14083.8079	14119.2538	3.2210077	2000-2012 –> 2007-2019	6.470987	26631.7635	26701.941
obs	Atlantic	(28.2, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	14012.4727	14053.8262	3.1778460	2000-2012 –> 2007-2019	6.427104	26561.3568	26643.231
mod	Atlantic	(28.2, Inf]	cstar_tref ~ temp + aou + nitrate + silicate	14911.6435	14952.3374	0.7588302	2000-2012 –> 2007-2019	1.569213	27820.3655	27900.552
mod	Atlantic	(28.2, Inf]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	16433.9533	16474.6472	0.8528259	2000-2012 –> 2007-2019	1.708034	29917.1237	29997.310
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	26137.8744	26182.3998	5.1334134	2000-2012 –> 2007-2019	10.460697	47720.1312	47807.756
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star	34050.8990	34097.1725	5.3737497	2000-2012 –> 2007-2019	11.331738	62872.3119	62963.462
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + phosphate + phosphate_star	27063.5881	27101.7527	5.7216085	2000-2012 –> 2007-2019	11.493958	49203.5837	49278.691
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	26743.1160	26787.6414	5.5098795	2000-2012 –> 2007-2019	11.049537	48598.0737	48685.699
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star	35219.3417	35265.6152	5.9772516	2000-2012 –> 2007-2019	12.255669	64511.8008	64602.951
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate	27167.8262	27205.9909	5.7917745	2000-2012 –> 2007-2019	11.983665	49797.2674	49872.374
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate	34383.7973	34423.4603	5.5402092	2000-2012 –> 2007-2019	11.657471	63440.4348	63518.563
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	26578.9258	26623.4512	5.4051042	2000-2012 –> 2007-2019	11.062221	48580.2516	48667.877
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	34283.5187	34329.7922	5.4888324	2000-2012 –> 2007-2019	11.502468	63188.5268	63279.677
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	26667.8591	26712.3845	5.4616057	2000-2012 –> 2007-2019	11.201913	48771.0229	48858.648
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	34301.7503	34348.0238	5.4979556	2000-2012 –> 2007-2019	11.521626	63221.7517	63312.902
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	26697.1467	26741.6721	5.4803419	2000-2012 –> 2007-2019	11.310844	48909.0693	48996.694
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + nitrate + silicate	34382.9979	34429.2714	5.5387966	2000-2012 –> 2007-2019	11.654815	63439.8083	63530.958
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	27464.6518	27509.1772	5.9949244	2000-2012 –> 2007-2019	12.092391	49988.8914	50076.516
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate	35466.9404	35513.2139	6.1135948	2000-2012 –> 2007-2019	12.520626	64941.7410	65032.891
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	27631.2647	27675.7901	6.1128646	2000-2012 –> 2007-2019	12.380847	50347.9102	50435.535
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	35534.4121	35580.6856	6.1512852	2000-2012 –> 2007-2019	12.599260	65066.4915	65157.642
mod	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	26817.4292	26861.9546	5.5579666	2000-2012 –> 2007-2019	11.405461	49049.6531	49137.278
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	34435.3635	34481.6370	5.5652800	2000-2012 –> 2007-2019	11.641797	63433.9083	63525.058
obs	Indo-Pacific	(-Inf,26]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	35563.8535	35610.1271	6.1678042	2000-2012 –> 2007-2019	12.634622	65122.1727	65213.323
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	19412.9151	19455.6902	4.4540397	2000-2012 –> 2007-2019	8.756530	37346.1676	37431.246
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	19877.3486	19920.1656	4.6914437	2000-2012 –> 2007-2019	9.377616	38117.2098	38202.244
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	19674.6425	19717.4175	4.6325612	2000-2012 –> 2007-2019	9.126828	37879.4023	37964.481
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	19912.2953	19955.1123	4.7159779	2000-2012 –> 2007-2019	9.419161	38174.4398	38259.474
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + phosphate	20280.1515	20316.8518	4.9836308	2000-2012 –> 2007-2019	9.976784	38908.2397	38981.126
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	18584.1316	18626.9067	3.9328703	2000-2012 –> 2007-2019	7.839791	35916.9211	36002.000
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	20064.6636	20107.4806	4.8244553	2000-2012 –> 2007-2019	9.623503	38450.9034	38535.938
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	18834.9827	18877.7577	4.0838282	2000-2012 –> 2007-2019	8.171178	36448.8598	36533.938
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	20114.1324	20156.9494	4.8602080	2000-2012 –> 2007-2019	9.696570	38548.0049	38633.039
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	19728.7194	19771.4945	4.6703291	2000-2012 –> 2007-2019	9.215173	38003.1529	38088.231
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	19919.7012	19962.5182	4.7211936	2000-2012 –> 2007-2019	9.430027	38189.2300	38274.264
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + phosphate_star	20061.0072	20097.7075	4.8232627	2000-2012 –> 2007-2019	9.717837	38566.4622	38639.349
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	19995.6580	20038.4750	4.7750216	2000-2012 –> 2007-2019	9.614195	38433.1050	38518.139
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	18885.6843	18928.4594	4.1150365	2000-2012 –> 2007-2019	8.240020	36556.6239	36641.702
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	20113.6014	20156.4184	4.8598228	2000-2012 –> 2007-2019	9.698041	38549.8350	38634.869
obs	Indo-Pacific	(26,26.5]	cstar_tref ~ sal + temp + silicate + phosphate_star	20113.1716	20149.8719	4.8609618	2000-2012 –> 2007-2019	9.720137	38573.9855	38646.872
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	19207.9673	19250.7424	4.3190632	2000-2012 –> 2007-2019	8.598351	37107.5534	37192.632
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	19339.6220	19382.3971	4.4052919	2000-2012 –> 2007-2019	8.727953	37301.9954	37387.074
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + aou + silicate + phosphate	19579.6291	19616.2935	4.5683127	2000-2012 –> 2007-2019	9.118204	37858.9740	37931.898
mod	Indo-Pacific	(26,26.5]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	19390.2439	19433.0190	4.4389035	2000-2012 –> 2007-2019	8.788875	37391.8295	37476.908
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	19027.6822	19070.2351	4.6089745	2000-2012 –> 2007-2019	9.070562	35449.9968	35534.149
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	21464.7062	21507.7977	5.2567924	2000-2012 –> 2007-2019	10.362981	40891.1340	40976.685
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	21540.4939	21583.5854	5.3142801	2000-2012 –> 2007-2019	10.478611	41038.9992	41124.550
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + phosphate	21957.3443	21994.2799	5.6435208	2000-2012 –> 2007-2019	11.105715	41810.8242	41884.153
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	18562.2019	18604.7549	4.2881709	2000-2012 –> 2007-2019	8.478065	34630.7883	34714.940
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	21949.9680	21993.0595	5.6359318	2000-2012 –> 2007-2019	11.091057	41797.2040	41882.755
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	18755.9483	18798.5013	4.4188928	2000-2012 –> 2007-2019	8.726190	34980.1205	35064.273
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	21549.9824	21593.0739	5.3215216	2000-2012 –> 2007-2019	10.495505	41060.3760	41145.927
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + phosphate_star	21635.5930	21672.5286	5.3888530	2000-2012 –> 2007-2019	10.671905	41276.7885	41350.118
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	19038.3805	19080.9335	4.6166232	2000-2012 –> 2007-2019	9.139605	35537.6394	35621.791
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	21578.4077	21621.4993	5.3432746	2000-2012 –> 2007-2019	10.566697	41149.3413	41234.892
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	18771.3360	18813.8890	4.4294442	2000-2012 –> 2007-2019	8.747089	35009.0180	35093.170
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	21997.4866	22040.5782	5.6744977	2000-2012 –> 2007-2019	11.166650	41887.7853	41973.336
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	19037.5697	19074.0436	4.6174742	2000-2012 –> 2007-2019	9.140645	35535.0644	35607.195
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + phosphate	21967.9006	22004.8362	5.6520770	2000-2012 –> 2007-2019	11.172748	41889.1704	41962.499
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	18916.8818	18959.4348	4.5305002	2000-2012 –> 2007-2019	8.982111	35326.5933	35410.745
obs	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	21966.8534	22009.9450	5.6496059	2000-2012 –> 2007-2019	11.160421	41878.7483	41964.299
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	19085.2736	19127.8266	4.6502990	2000-2012 –> 2007-2019	9.212175	35632.7392	35716.891
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + aou + silicate + phosphate	19123.8800	19160.3540	4.6796585	2000-2012 –> 2007-2019	9.317724	35762.5982	35834.728
mod	Indo-Pacific	(26.5,26.75]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	19110.0013	19152.5542	4.6681557	2000-2012 –> 2007-2019	9.248710	35680.4718	35764.624
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	32650.7147	32696.8073	5.1130288	2000-2012 –> 2007-2019	10.514840	62640.6691	62732.134
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	23912.1942	23956.8381	3.7757988	2000-2012 –> 2007-2019	7.921380	46705.1851	46793.903
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	32534.7278	32580.8204	5.0578932	2000-2012 –> 2007-2019	10.330670	62291.3248	62382.790
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	24181.3257	24225.9696	3.8944549	2000-2012 –> 2007-2019	8.151807	47187.6302	47276.348
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	32795.8603	32841.9530	5.1828728	2000-2012 –> 2007-2019	10.567874	62755.7309	62847.196
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + aou + silicate + phosphate	32849.8995	32895.9922	5.2091195	2000-2012 –> 2007-2019	10.575990	62777.2185	62868.684
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	24197.0262	24241.6701	3.9014910	2000-2012 –> 2007-2019	8.153808	47193.8411	47282.559
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + nitrate + phosphate_star	24339.5715	24377.8377	3.9668686	2000-2012 –> 2007-2019	8.247317	47387.2552	47463.299
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	24222.7042	24267.3481	3.9130259	2000-2012 –> 2007-2019	8.165363	47219.5570	47308.275
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	32487.4827	32533.5754	5.0356055	2000-2012 –> 2007-2019	10.286689	62204.2865	62295.752
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate	24802.0025	24840.2687	4.1834750	2000-2012 –> 2007-2019	8.561157	48029.7845	48105.829
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + phosphate	32589.3838	32628.8918	5.0847505	2000-2012 –> 2007-2019	10.403978	62428.6378	62507.036
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	24455.7306	24500.3745	4.0192760	2000-2012 –> 2007-2019	8.373961	47643.2807	47731.999
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	32377.0474	32423.1401	4.9838904	2000-2012 –> 2007-2019	10.209426	62046.7779	62138.243
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	24692.5938	24737.2378	4.1302325	2000-2012 –> 2007-2019	8.608487	48104.4961	48193.214
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	32553.8851	32599.9778	5.0669586	2000-2012 –> 2007-2019	10.366266	62358.9249	62450.390
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	24707.1925	24751.8364	4.1371704	2000-2012 –> 2007-2019	8.609803	48109.0226	48197.741
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	32552.8008	32598.8934	5.0664451	2000-2012 –> 2007-2019	10.367808	62361.5837	62453.049
mod	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	24819.2826	24857.5488	4.1917944	2000-2012 –> 2007-2019	8.687722	48260.7654	48336.809
obs	Indo-Pacific	(26.75,27]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	32551.9933	32591.5013	5.0670099	2000-2012 –> 2007-2019	10.368841	62359.6290	62438.028
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	39964.6386	40012.3545	4.6765550	2000-2012 –> 2007-2019	9.529719	79151.9493	79247.157
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	40180.7651	40228.4810	4.7520826	2000-2012 –> 2007-2019	9.719334	79671.6277	79766.835
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate	39962.7151	40003.6145	4.6765816	2000-2012 –> 2007-2019	9.529764	79148.0750	79229.681
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + aou + silicate + phosphate_star	40212.3440	40253.2433	4.7639261	2000-2012 –> 2007-2019	9.740656	79726.1113	79807.717
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	40099.9662	40147.6821	4.7237049	2000-2012 –> 2007-2019	9.649486	79481.3041	79576.511
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	40129.0166	40169.9159	4.7345901	2000-2012 –> 2007-2019	9.673155	79542.2138	79623.820
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	28148.0020	28194.5112	2.8833560	2000-2012 –> 2007-2019	5.857392	54284.2366	54376.649
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	40574.8474	40622.5633	4.8929525	2000-2012 –> 2007-2019	9.923804	80231.9198	80327.127
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	28580.6932	28627.2024	2.9953588	2000-2012 –> 2007-2019	6.058453	55024.1420	55116.554
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	40125.8625	40173.5784	4.7327816	2000-2012 –> 2007-2019	9.639048	79455.3420	79550.549
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	28608.0077	28654.5170	3.0025735	2000-2012 –> 2007-2019	6.073434	55077.8206	55170.233
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	28789.8224	28836.3317	3.0510416	2000-2012 –> 2007-2019	6.152787	55363.8295	55456.242
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	40288.1108	40335.8267	4.7900478	2000-2012 –> 2007-2019	9.721407	79684.2328	79779.440
obs	Indo-Pacific	(27,27.25]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	40091.5386	40139.2545	4.7207548	2000-2012 –> 2007-2019	9.616483	79392.9270	79488.134
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + phosphate	28493.1865	28533.0516	2.9728856	2000-2012 –> 2007-2019	6.030686	54916.6235	54995.834
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + phosphate_star	28862.3178	28902.1829	3.0711257	2000-2012 –> 2007-2019	6.204814	55541.0046	55620.215
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	28364.2364	28410.7456	2.9387951	2000-2012 –> 2007-2019	5.918158	54519.1029	54611.515
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	28808.2250	28854.7343	3.0559907	2000-2012 –> 2007-2019	6.143031	55332.7522	55425.164
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	28880.6805	28920.5456	3.0760967	2000-2012 –> 2007-2019	6.215732	55579.1081	55658.319
mod	Indo-Pacific	(27,27.25]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	28822.4878	28868.9970	3.0598320	2000-2012 –> 2007-2019	6.151555	55362.7990	55455.211
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	37631.3069	37679.5935	3.1621491	2000-2012 –> 2007-2019	6.194835	71399.2784	71495.208
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	42442.9627	42491.4418	4.0608245	2000-2012 –> 2007-2019	8.405152	82262.5297	82358.876
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	42953.1790	43001.6581	4.2009091	2000-2012 –> 2007-2019	8.729066	83344.0090	83440.355
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate	42443.7757	42485.3292	4.0615839	2000-2012 –> 2007-2019	8.413017	82283.8694	82366.452
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + aou + silicate + phosphate_star	42967.0205	43008.5740	4.2053351	2000-2012 –> 2007-2019	8.750075	83406.2377	83488.820
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	38198.2870	38246.5737	3.2870504	2000-2012 –> 2007-2019	6.481552	72660.2215	72756.151
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	42726.1834	42774.6626	4.1379984	2000-2012 –> 2007-2019	8.574117	82833.9561	82930.302
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	42765.0565	42806.6100	4.1492562	2000-2012 –> 2007-2019	8.618531	82973.4711	83056.053
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	38072.5488	38120.8354	3.2589322	2000-2012 –> 2007-2019	6.394862	72287.4382	72383.368
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate	42365.7316	42414.2107	4.0400309	2000-2012 –> 2007-2019	8.345467	82061.3462	82157.692
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	42525.7774	42574.2565	4.0832403	2000-2012 –> 2007-2019	8.432291	82360.3204	82456.666
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	38090.2675	38138.5541	3.2628799	2000-2012 –> 2007-2019	6.404621	72329.8727	72425.802
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	37441.5208	37489.8075	3.1214100	2000-2012 –> 2007-2019	6.077612	70868.4886	70964.418
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	42543.1970	42591.6761	4.0879710	2000-2012 –> 2007-2019	8.442085	82393.7805	82490.126
obs	Indo-Pacific	(27.25,27.5]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	42493.5852	42542.0643	4.0745120	2000-2012 –> 2007-2019	8.415348	82302.0684	82398.414
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + phosphate_star	38259.1521	38300.5406	3.3011994	2000-2012 –> 2007-2019	6.494072	72712.2760	72794.501
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	37805.1842	37853.4708	3.1999398	2000-2012 –> 2007-2019	6.289751	71822.2834	71918.213
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + nitrate + phosphate + phosphate_star	38283.5750	38324.9635	3.3067126	2000-2012 –> 2007-2019	6.507454	72769.5589	72851.784
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	37802.3942	37850.6808	3.1993298	2000-2012 –> 2007-2019	6.290861	71826.9203	71922.850
mod	Indo-Pacific	(27.25,27.5]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	37804.9111	37846.2996	3.2003174	2000-2012 –> 2007-2019	6.295299	71842.3298	71924.555
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	41436.0857	41485.2004	2.9905370	2000-2012 –> 2007-2019	5.892006	79760.7345	79858.502
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	47159.2352	47208.6216	3.7958454	2000-2012 –> 2007-2019	7.858582	90630.4099	90728.442
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	41502.5193	41551.6340	3.0026211	2000-2012 –> 2007-2019	5.904742	79830.6327	79928.400
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate	47253.8786	47296.2098	3.8173262	2000-2012 –> 2007-2019	7.892223	90769.0925	90853.120
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + aou + silicate + phosphate_star	42171.1677	42213.2660	3.1273785	2000-2012 –> 2007-2019	6.147630	81112.5933	81196.394
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	41467.4347	41516.5494	2.9962332	2000-2012 –> 2007-2019	5.893944	79772.0960	79869.864
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	42239.1552	42281.2536	3.1403117	2000-2012 –> 2007-2019	6.172931	81243.6062	81327.407
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	47891.1916	47940.5780	3.9615946	2000-2012 –> 2007-2019	7.969355	91152.4699	91250.502
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	47923.3848	47972.7712	3.9690486	2000-2012 –> 2007-2019	7.985877	91219.4802	91317.512
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate	46689.2658	46738.6523	3.6930966	2000-2012 –> 2007-2019	7.544843	89338.8336	89436.866
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	42005.5996	42054.7144	3.0957291	2000-2012 –> 2007-2019	6.091861	80825.3686	80923.136
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	46743.7703	46793.1568	3.7048688	2000-2012 –> 2007-2019	7.570924	89450.4637	89548.496
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate	41790.8547	41839.9695	3.0556369	2000-2012 –> 2007-2019	6.032823	80512.7944	80610.562
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	41871.2555	41920.3703	3.0705863	2000-2012 –> 2007-2019	6.037344	80539.0803	80636.848
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	46757.0654	46806.4518	3.7077460	2000-2012 –> 2007-2019	7.565478	89430.5571	89528.589
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate	41978.9717	42021.0700	3.0911045	2000-2012 –> 2007-2019	6.097192	80847.8997	80931.701
mod	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	41963.6109	42012.7256	3.0878488	2000-2012 –> 2007-2019	6.076223	80743.3978	80841.165
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	46737.0416	46786.4281	3.7034135	2000-2012 –> 2007-2019	7.568230	89438.8005	89536.832
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ sal + temp + silicate + phosphate_star	47019.6018	47061.9330	3.7654623	2000-2012 –> 2007-2019	7.655483	89819.5026	89903.530
obs	Indo-Pacific	(27.5,27.75]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	47815.1052	47864.4917	3.9440334	2000-2012 –> 2007-2019	7.988199	91215.6956	91313.728
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	14723.8278	14766.2979	2.4305645	2000-2012 –> 2007-2019	4.764242	28254.5403	28339.013
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + nitrate	14730.2565	14766.6594	2.4337797	2000-2012 –> 2007-2019	4.767568	28259.2522	28331.657
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	14422.7825	14465.2525	2.3184716	2000-2012 –> 2007-2019	4.556740	27704.5411	27789.014
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + nitrate + silicate	14713.7182	14756.1883	2.4267138	2000-2012 –> 2007-2019	4.752848	28225.1218	28309.594
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + phosphate_star	14616.1262	14652.5291	2.3906027	2000-2012 –> 2007-2019	4.687653	28050.4923	28122.897
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	14590.3018	14632.7718	2.3801930	2000-2012 –> 2007-2019	4.675511	28022.1676	28106.640
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	23990.2298	24035.1530	3.4204881	2000-2012 –> 2007-2019	6.934613	45410.0629	45499.044
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	14440.5556	14483.0256	2.3249433	2000-2012 –> 2007-2019	4.569176	27738.1868	27822.659
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	14728.1076	14770.5776	2.4321965	2000-2012 –> 2007-2019	4.770284	28270.0819	28354.554
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	23978.4428	24023.3660	3.4160371	2000-2012 –> 2007-2019	6.923255	45382.5355	45471.517
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + phosphate + phosphate_star	14620.9113	14657.3142	2.3923975	2000-2012 –> 2007-2019	4.691504	28060.6145	28133.019
mod	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	14598.4987	14640.9687	2.3832549	2000-2012 –> 2007-2019	4.681057	28036.8162	28121.289
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	23988.2781	24033.2012	3.4197507	2000-2012 –> 2007-2019	6.933033	45406.1919	45495.173
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ sal + temp + silicate + phosphate_star	24007.9141	24046.4197	3.4279344	2000-2012 –> 2007-2019	6.953094	45450.8285	45527.098
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	24034.6824	24079.6056	3.4373268	2000-2012 –> 2007-2019	6.964617	45484.4307	45573.412
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	23990.6603	24035.5834	3.4206508	2000-2012 –> 2007-2019	6.932563	45405.4543	45494.436
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + aou + silicate + phosphate_star	24008.2629	24046.7685	3.4280665	2000-2012 –> 2007-2019	6.950079	45444.0315	45520.301
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	23991.5052	24036.4284	3.4209701	2000-2012 –> 2007-2019	6.933085	45406.7615	45495.743
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	23990.2505	24028.7561	3.4212518	2000-2012 –> 2007-2019	6.933535	45403.8898	45480.160
obs	Indo-Pacific	(27.75,27.85]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	24005.6050	24044.1105	3.4270600	2000-2012 –> 2007-2019	6.947972	45438.8731	45515.143
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou	17142.3777	17173.8002	2.1025450	2000-2012 –> 2007-2019	4.181836	32974.8795	33037.353
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + phosphate_star	16965.1139	17002.8209	2.0555133	2000-2012 –> 2007-2019	4.072202	32574.7433	32649.711
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate	17144.0408	17181.7478	2.1024556	2000-2012 –> 2007-2019	4.177032	32961.8455	33036.813
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate	33250.1233	33297.5457	3.1592513	2000-2012 –> 2007-2019	6.302496	62280.5434	62374.452
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	16966.7045	17010.6961	2.0554071	2000-2012 –> 2007-2019	4.066596	32558.2446	32645.707
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	33255.9741	33303.3965	3.1606805	2000-2012 –> 2007-2019	6.310227	62309.0608	62402.969
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate	17284.6321	17322.3391	2.1400912	2000-2012 –> 2007-2019	4.245886	33212.3064	33287.274
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	17153.2659	17197.2574	2.1043735	2000-2012 –> 2007-2019	4.161243	32910.0163	32997.479
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	33250.4676	33297.8900	3.1593354	2000-2012 –> 2007-2019	6.302529	62280.7044	62374.613
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + phosphate + phosphate_star	16973.0626	17010.7696	2.0575763	2000-2012 –> 2007-2019	4.076674	32591.4722	32666.440
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate	17265.7153	17303.4223	2.1349883	2000-2012 –> 2007-2019	4.240715	33193.1507	33268.118
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	16974.3591	17018.3506	2.0573936	2000-2012 –> 2007-2019	4.070515	32572.9647	32660.427
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	33257.2030	33304.6253	3.1609808	2000-2012 –> 2007-2019	6.311187	62312.6598	62406.568
mod	Indo-Pacific	(27.85,27.95]	cstar_tref ~ sal + temp + silicate + phosphate_star	17155.6370	17193.3441	2.1055346	2000-2012 –> 2007-2019	4.162932	32912.2740	32987.242
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	33239.1639	33286.5863	3.1565759	2000-2012 –> 2007-2019	6.291675	62240.2205	62334.129
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	33251.3463	33298.7686	3.1595500	2000-2012 –> 2007-2019	6.302974	62282.4113	62376.319
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate	33250.4968	33291.1445	3.1598310	2000-2012 –> 2007-2019	6.303706	62281.1885	62361.681
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + aou + silicate + phosphate_star	33259.5238	33300.1715	3.1620368	2000-2012 –> 2007-2019	6.312795	62314.9628	62395.456
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	33252.0013	33299.4237	3.1597100	2000-2012 –> 2007-2019	6.303171	62283.2010	62377.109
obs	Indo-Pacific	(27.85,27.95]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	33251.7626	33292.4103	3.1601402	2000-2012 –> 2007-2019	6.303601	62280.9629	62361.456
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou	20827.2589	20859.9360	1.8685742	2000-2012 –> 2007-2019	3.734442	38923.0114	38987.666
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + phosphate_star	20534.5939	20573.8064	1.8152833	2000-2012 –> 2007-2019	3.559262	38034.1951	38111.781
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate	20754.5383	20793.7508	1.8549145	2000-2012 –> 2007-2019	3.715133	38825.4464	38903.032
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate	56793.8194	56845.0444	3.0977365	2000-2012 –> 2007-2019	6.087606	104908.8876	105010.274
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	20332.0446	20377.7926	1.7791864	2000-2012 –> 2007-2019	3.491976	37673.8682	37764.385
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	56954.2440	57005.4689	3.1201320	2000-2012 –> 2007-2019	6.145987	105298.2042	105399.591
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + phosphate_star	20836.7095	20875.9220	1.8699417	2000-2012 –> 2007-2019	3.684449	38687.3300	38764.915
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate	20875.7675	20914.9801	1.8771271	2000-2012 –> 2007-2019	3.792135	39203.6846	39281.270
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	20425.3033	20471.0513	1.7955539	2000-2012 –> 2007-2019	3.540507	37931.8506	38022.367
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	56910.6912	56961.9161	3.1140360	2000-2012 –> 2007-2019	6.130146	105192.9390	105294.326
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + phosphate + phosphate_star	20539.7006	20578.9132	1.8161938	2000-2012 –> 2007-2019	3.561533	38046.2061	38123.792
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	20335.6746	20381.4226	1.7798207	2000-2012 –> 2007-2019	3.493736	37683.3205	37773.837
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	56952.0514	57003.2763	3.1198248	2000-2012 –> 2007-2019	6.145104	105292.3714	105393.758
mod	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	20434.9956	20474.2082	1.7976166	2000-2012 –> 2007-2019	3.556662	38010.7644	38088.350
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ sal + temp + silicate + phosphate_star	56952.6679	56996.5750	3.1201914	2000-2012 –> 2007-2019	6.146152	105295.2975	105382.200
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate	56818.2021	56869.4270	3.1011299	2000-2012 –> 2007-2019	6.092437	104942.4647	105043.851
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star	56978.5110	57029.7359	3.1235337	2000-2012 –> 2007-2019	6.147701	105311.7964	105413.183
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + aou + silicate + phosphate	56940.7455	56984.6526	3.1185214	2000-2012 –> 2007-2019	6.133717	105215.1889	105302.092
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star	56967.3987	57018.6236	3.1219755	2000-2012 –> 2007-2019	6.143658	105284.9625	105386.349
obs	Indo-Pacific	(27.95,28.05]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	56990.7970	57034.7041	3.1255381	2000-2012 –> 2007-2019	6.153120	105343.6720	105430.575
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	48433.3615	48483.6250	2.9310537	2000-2012 –> 2007-2019	5.799341	86541.0618	86639.971
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star	48702.3173	48752.5808	2.9719465	2000-2012 –> 2007-2019	5.898387	87119.2427	87218.152
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + aou + silicate + phosphate	48470.6596	48513.7426	2.9369934	2000-2012 –> 2007-2019	5.817764	86643.2651	86728.044
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star	48605.2785	48655.5420	2.9571270	2000-2012 –> 2007-2019	5.861942	86907.9387	87006.848
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	48684.0888	48727.1718	2.9694629	2000-2012 –> 2007-2019	5.898700	87113.7300	87198.509
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate	48459.2064	48509.4699	2.9349586	2000-2012 –> 2007-2019	5.807094	86587.5619	86686.471
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	10801.1119	10842.9840	1.5276831	2000-2012 –> 2007-2019	3.082713	20474.4828	20557.387
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	48626.2376	48676.5011	2.9603216	2000-2012 –> 2007-2019	5.861099	86907.4654	87006.374
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate	11198.7279	11234.6183	1.6356103	2000-2012 –> 2007-2019	3.374838	21451.3244	21522.385
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	10790.0581	10831.9303	1.5248012	2000-2012 –> 2007-2019	3.079021	20460.7214	20543.626
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	48795.6025	48845.8660	2.9862626	2000-2012 –> 2007-2019	5.913008	87214.1349	87313.044
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate	11159.0847	11194.9751	1.6245714	2000-2012 –> 2007-2019	3.341804	21345.6019	21416.663
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	10800.2686	10842.1407	1.5274630	2000-2012 –> 2007-2019	3.082306	20473.0132	20555.917
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	48595.5049	48645.7684	2.9556385	2000-2012 –> 2007-2019	5.851779	86852.0889	86950.998
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	10822.4874	10858.3778	1.5337954	2000-2012 –> 2007-2019	3.091279	20502.0415	20573.102
obs	Indo-Pacific	(28.05,28.1]	cstar_tref ~ sal + temp + silicate + phosphate_star	48848.8449	48891.9279	2.9947730	2000-2012 –> 2007-2019	5.922941	87272.8628	87357.642
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + aou + silicate + phosphate_star	11146.4047	11182.2951	1.6210563	2000-2012 –> 2007-2019	3.271900	21128.2120	21199.273
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + nitrate + silicate + phosphate_star	11152.0539	11187.9443	1.6226214	2000-2012 –> 2007-2019	3.276466	21143.2925	21214.353
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + silicate + phosphate + phosphate_star	11144.2719	11180.1623	1.6204658	2000-2012 –> 2007-2019	3.270719	21124.2242	21195.285
mod	Indo-Pacific	(28.05,28.1]	cstar_tref ~ temp + silicate + phosphate_star	11173.0532	11202.9619	1.6290089	2000-2012 –> 2007-2019	3.285500	21170.5926	21229.810
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + phosphate	54322.3135	54366.0584	2.9642143	2000-2012 –> 2007-2019	5.972857	102781.9716	102868.740
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + nitrate + silicate + phosphate	54280.6982	54331.7339	2.9582559	2000-2012 –> 2007-2019	5.952235	102648.4404	102749.671
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + phosphate	54696.8930	54733.3471	3.0161619	2000-2012 –> 2007-2019	6.117461	103737.5929	103809.900
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	118943.0103	118993.1745	1.5893072	2000-2012 –> 2007-2019	3.179081	218898.5318	218997.816
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate	54467.6186	54511.3635	2.9841517	2000-2012 –> 2007-2019	6.029534	103160.5855	103247.354
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + aou + silicate + phosphate_star	122230.0570	122280.2211	1.6741741	2000-2012 –> 2007-2019	3.348048	224922.3069	225021.591
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + nitrate + silicate + phosphate_star	122798.0123	122848.1765	1.6892904	2000-2012 –> 2007-2019	3.383181	226121.3782	226220.662
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + silicate + phosphate + phosphate_star	121467.5395	121517.7036	1.6540919	2000-2012 –> 2007-2019	3.306831	223485.2169	223584.501
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate	54168.6011	54219.6368	2.9429968	2000-2012 –> 2007-2019	5.895536	102268.4325	102369.663
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + phosphate_star	55002.0512	55053.0869	3.0583597	2000-2012 –> 2007-2019	6.139794	103923.2367	104024.467
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + nitrate + silicate	123965.8284	124024.3533	1.7207481	2000-2012 –> 2007-2019	3.443967	228202.5449	228318.376
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + phosphate	54376.0975	54419.8424	2.9715784	2000-2012 –> 2007-2019	5.970127	102771.1587	102857.928
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	117545.0657	117603.5906	1.5544818	2000-2012 –> 2007-2019	3.102690	216096.0460	216211.877
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate	54315.0889	54366.1246	2.9629531	2000-2012 –> 2007-2019	5.954141	102664.9026	102766.133
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + aou + silicate + phosphate_star	117553.4857	117612.0105	1.5546890	2000-2012 –> 2007-2019	3.103104	216111.5623	216227.393
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star	54838.6784	54889.7141	3.0353954	2000-2012 –> 2007-2019	6.088523	103582.4700	103683.700
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	117883.0031	117941.5280	1.5628179	2000-2012 –> 2007-2019	3.117773	216664.8611	216780.692
obs	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star	54936.6495	54987.6852	3.0491458	2000-2012 –> 2007-2019	6.133700	103877.2859	103978.516
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star	117552.8324	117611.3572	1.5546729	2000-2012 –> 2007-2019	3.103074	216110.4276	216226.259
mod	Indo-Pacific	(28.1, Inf]	cstar_tref ~ sal + temp + silicate + phosphate_star	117934.0523	117984.2165	1.5641306	2000-2012 –> 2007-2019	3.119230	216718.8295	216818.113

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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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]	5	5	10	7	5	10	5
(26,26.5]	7	7	6	7	7	7	9
(26.5,26.75]	6	4	6	7	4	10	10
(26.75,27]	8	4	8	5	5	10	7
(27,27.25]	8	6	4	4	7	10	8
(27.25,27.5]	5	4	4	6	10	8	8
(27.5,27.75]	6	1	6	6	10	6	8
(27.75,27.85]	5	4	4	6	10	10	6
(27.85,27.95]	6	2	5	6	10	7	9
(27.95,28.05]	4	2	4	8	10	5	10
(28.05,28.1]	9	1	4	5	6	6	10
(28.1,28.15]	10	2	4	4	6	5	10
(28.15,28.2]	5	7	2	6	6	5	10
(28.2, Inf]	5	10	NA	5	8	6	6
total	89.00	59.00	—	82.00	104.00	105.00	116.00
Indo-Pacific - mod
(-Inf,26]	9	6	6	6	10	4	7
(26,26.5]	7	6	7	6	6	7	10
(26.5,26.75]	6	5	6	6	6	9	10
(26.75,27]	5	10	5	7	5	5	10
(27,27.25]	6	10	6	7	4	4	10
(27.25,27.5]	4	10	5	9	5	6	8
(27.5,27.75]	4	5	6	7	10	10	5
(27.75,27.85]	6	6	3	8	10	5	9
(27.85,27.95]	4	2	3	6	10	7	10
(27.95,28.05]	4	3	2	7	10	6	10
(28.05,28.1]	2	3	3	8	6	10	10
(28.1, Inf]	5	3	4	7	10	10	6
total	62.00	69.00	56.00	84.00	92.00	83.00	105.00
Atlantic - obs
(-Inf,26]	8	10	6	6	6	5	8
(26,26.5]	7	9	7	6	4	4	10
(26.5,26.75]	8	8	6	6	4	5	10
(26.75,27]	4	4	4	9	5	10	10
(27,27.25]	5	6	5	9	5	8	10
(27.25,27.5]	6	4	7	7	9	4	10
(27.5,27.75]	7	4	7	6	4	10	9
(27.75,27.85]	6	5	8	6	7	10	6
(27.85,27.95]	5	4	7	6	10	10	5
(27.95,28.05]	5	5	5	8	10	10	4
(28.05,28.1]	5	5	3	10	10	6	7
(28.1,28.15]	5	4	2	10	7	7	10
(28.15,28.2]	7	1	7	6	6	6	10
(28.2, Inf]	6	4	7	7	10	4	9
total	84.00	73.00	81.00	102.00	97.00	99.00	118.00
Indo-Pacific - obs
(-Inf,26]	8	6	6	6	10	5	8
(26,26.5]	5	5	5	7	10	5	10
(26.5,26.75]	6	7	7	5	8	4	10
(26.75,27]	7	9	6	5	5	7	9
(27,27.25]	6	5	6	7	10	9	4
(27.25,27.5]	6	4	6	7	10	10	4
(27.5,27.75]	7	5	6	5	9	8	8
(27.75,27.85]	4	5	4	9	4	10	10
(27.85,27.95]	6	5	5	7	4	10	10
(27.95,28.05]	5	5	5	7	5	10	10
(28.05,28.1]	5	4	6	7	10	10	5
(28.1, Inf]	8	6	8	3	10	4	6
total	73.00	66.00	70.00	75.00	95.00	92.00	94.00

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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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
29edae5	jens-daniel-mueller	2021-04-14
099d566	jens-daniel-mueller	2021-04-14
bb44686	jens-daniel-mueller	2021-04-14
bf40480	jens-daniel-mueller	2021-04-13
9f31fe3	jens-daniel-mueller	2021-04-13
338dd3c	jens-daniel-mueller	2021-04-09
a79ca2c	jens-daniel-mueller	2021-04-09
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