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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:

  • 50

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

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

GLODAP_glanced_clean %>% 
  group_by(data_source, era, basin, gamma_slab) %>% 
  count() %>% 
  filter(n < params_local$MLR_number)
# A tibble: 0 x 5
# Groups:   data_source, era, basin, gamma_slab [0]
# … with 5 variables: data_source <chr>, era <chr>, basin <chr>,
#   gamma_slab <chr>, n <int>

6.2 Predictor selection

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

  • 10

The criterion used to select the best models was:

  • rmse

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

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

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

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

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

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


# print table
lm_best_eras %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")
data_source basin gamma_slab model AIC BIC rmse eras rmse_sum aic_sum bic_sum
obs Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 541.5135 558.0996 6.8192844 1981-1999 –> 2000-2012 12.614122 1108.1211 1141.9686
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 308.6142 326.1902 1.2211840 1981-1999 –> 2000-2012 2.955074 590.4398 623.5524
obs Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 541.6622 558.2484 6.8257065 1981-1999 –> 2000-2012 12.616929 1108.1613 1142.0088
obs Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 544.2146 560.8007 6.9368653 1981-1999 –> 2000-2012 13.341763 1128.2388 1162.0863
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 332.4298 347.4949 1.4072882 1981-1999 –> 2000-2012 3.172312 614.6757 643.0579
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate_star 337.7232 352.7884 1.4488200 1981-1999 –> 2000-2012 3.204307 619.2324 647.6146
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 291.9737 309.5497 1.1144816 1981-1999 –> 2000-2012 2.856661 574.4479 607.5605
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate 308.0536 323.1187 1.2308802 1981-1999 –> 2000-2012 3.173415 603.3324 631.7146
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 309.2850 326.8611 1.2256934 1981-1999 –> 2000-2012 2.947439 590.1547 623.2673
obs Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 542.4170 559.0032 6.8583928 1981-1999 –> 2000-2012 12.640501 1108.6420 1142.4895
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 310.2474 327.8234 1.2321915 1981-1999 –> 2000-2012 2.950677 590.8593 623.9718
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + phosphate + phosphate_star 334.6276 349.6928 1.4243859 1981-1999 –> 2000-2012 3.170468 615.4062 643.7884
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate 309.2313 324.2964 1.2388708 1981-1999 –> 2000-2012 3.251652 609.3413 637.7235
mod Atlantic (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 291.6426 309.2186 1.1124559 1981-1999 –> 2000-2012 2.829829 572.1665 605.2791
obs Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate 544.0160 558.2327 7.0164075 1981-1999 –> 2000-2012 13.138067 1118.1703 1147.1824
obs Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate_star 543.9312 558.1479 7.0126414 1981-1999 –> 2000-2012 13.104283 1117.2301 1146.2423
obs Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 545.5342 562.1203 6.9950431 1981-1999 –> 2000-2012 12.945907 1116.7648 1150.6123
obs Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 545.4069 561.9930 6.9894098 1981-1999 –> 2000-2012 12.920100 1116.0466 1149.8941
obs Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 543.7304 557.9471 7.0037362 1981-1999 –> 2000-2012 13.041014 1115.4696 1144.4817
obs Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 545.0304 561.6165 6.9727739 1981-1999 –> 2000-2012 12.866406 1114.5795 1148.4270
obs Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate 4585.2802 4612.6887 6.0052535 1981-1999 –> 2000-2012 10.950792 7765.5759 7818.5648
obs Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 4587.2749 4619.2515 6.0052312 1981-1999 –> 2000-2012 10.921246 7763.2834 7825.1038
obs Atlantic (26,26.5] cstar_tref ~ sal + aou + phosphate 4589.6041 4612.4445 6.0319815 1981-1999 –> 2000-2012 10.980626 7768.5588 7812.7162
obs Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate 4591.0840 4618.4925 6.0297791 1981-1999 –> 2000-2012 10.948946 7765.7656 7818.7545
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate 2301.6672 2325.8079 3.8692305 1981-1999 –> 2000-2012 7.516681 4511.1705 4559.3345
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 2275.5657 2303.7298 3.7398085 1981-1999 –> 2000-2012 7.140226 4430.2635 4486.4548
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2277.2814 2305.4455 3.7475848 1981-1999 –> 2000-2012 7.156675 4434.0424 4490.2338
obs Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + phosphate 4579.6203 4607.0287 5.9814318 1981-1999 –> 2000-2012 10.907721 7755.8210 7808.8098
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate 2320.6907 2344.8314 3.9593762 1981-1999 –> 2000-2012 7.851512 4582.7870 4630.9510
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 2253.5514 2281.7155 3.6414528 1981-1999 –> 2000-2012 6.991161 4396.0789 4452.2702
obs Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 4581.0351 4613.0117 5.9789744 1981-1999 –> 2000-2012 10.880287 7753.8989 7815.7192
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2256.5442 2284.7083 3.6546708 1981-1999 –> 2000-2012 7.020812 4403.0357 4459.2271
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2281.7356 2309.8998 3.7678483 1981-1999 –> 2000-2012 7.197665 4443.4062 4499.5976
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2323.5454 2351.7095 3.9634755 1981-1999 –> 2000-2012 7.352998 4475.6437 4531.8350
mod Atlantic (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2258.5437 2286.7078 3.6635282 1981-1999 –> 2000-2012 7.037165 4406.8368 4463.0282
obs Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate 4530.1645 4557.5730 5.7772617 1981-1999 –> 2000-2012 10.697437 7705.0614 7758.0503
obs Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 4549.2019 4576.6103 5.8550160 1981-1999 –> 2000-2012 10.802275 7729.8627 7782.8516
obs Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4528.2461 4560.2226 5.7613862 1981-1999 –> 2000-2012 10.659221 7700.3644 7762.1848
obs Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4545.6162 4577.5927 5.8320945 1981-1999 –> 2000-2012 10.757108 7723.5451 7785.3654
mod Atlantic (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2362.7992 2386.9399 4.1664540 1981-1999 –> 2000-2012 8.096353 4632.7165 4680.8805
mod Atlantic (26.5,26.75] cstar_tref ~ sal + aou + nitrate + phosphate 3613.8189 3640.5500 4.1069475 1981-1999 –> 2000-2012 7.148456 6379.8646 6432.3895
obs Atlantic (26.5,26.75] cstar_tref ~ sal + aou + phosphate_star 7147.8129 7172.7734 6.4321341 1981-1999 –> 2000-2012 11.372371 11778.8640 11827.0304
mod Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate 3561.5505 3588.2817 3.9416074 1981-1999 –> 2000-2012 6.923786 6306.1635 6358.6883
mod Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate_star 3618.8139 3645.5451 4.1231070 1981-1999 –> 2000-2012 7.349892 6449.1961 6501.7210
obs Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate_star 7138.7712 7168.7238 6.3995781 1981-1999 –> 2000-2012 11.318061 11765.0613 11822.8610
obs Atlantic (26.5,26.75] cstar_tref ~ sal + nitrate + phosphate_star 7142.0444 7167.0049 6.4151051 1981-1999 –> 2000-2012 11.290936 11752.9913 11801.1577
obs Atlantic (26.5,26.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 7135.3053 7165.2579 6.3893930 1981-1999 –> 2000-2012 11.220573 11734.1581 11791.9577
mod Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate 3548.3587 3575.0898 3.9009404 1981-1999 –> 2000-2012 6.710357 6228.0425 6280.5674
mod Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate_star 3551.4826 3578.2138 3.9105325 1981-1999 –> 2000-2012 6.740091 6238.9392 6291.4641
obs Atlantic (26.5,26.75] cstar_tref ~ temp + aou + phosphate_star 6795.8153 6820.7758 5.4714450 1981-1999 –> 2000-2012 9.673332 11178.8669 11227.0333
mod Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate 3536.0175 3562.7487 3.8632759 1981-1999 –> 2000-2012 6.810132 6267.6664 6320.1913
mod Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 3544.8682 3571.5993 3.8902504 1981-1999 –> 2000-2012 6.892958 6296.9448 6349.4697
obs Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 6797.4253 6827.3779 5.4704646 1981-1999 –> 2000-2012 9.643594 11171.9558 11229.7555
mod Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 3557.5549 3584.2861 3.9292455 1981-1999 –> 2000-2012 6.787186 6255.8703 6308.3952
obs Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + phosphate_star 6801.7706 6826.7310 5.4864398 1981-1999 –> 2000-2012 9.704130 11190.5729 11238.7393
mod Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 3591.2074 3617.9386 4.0345863 1981-1999 –> 2000-2012 7.457410 6485.7593 6538.2842
obs Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 6803.4076 6833.3602 5.4855248 1981-1999 –> 2000-2012 9.680832 11186.0584 11243.8581
obs Atlantic (26.5,26.75] cstar_tref ~ temp + phosphate_star 6988.6053 7008.5737 5.9838265 1981-1999 –> 2000-2012 11.403100 11759.4407 11797.9738
mod Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3547.1269 3573.8581 3.8971647 1981-1999 –> 2000-2012 6.917434 6305.5484 6358.0733
obs Atlantic (26.5,26.75] cstar_tref ~ temp + silicate + phosphate_star 6888.4249 6913.3854 5.7093337 1981-1999 –> 2000-2012 10.343144 11421.3762 11469.5426
mod Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate 5474.0389 5504.3240 2.6009090 1981-1999 –> 2000-2012 4.844554 10020.2929 10080.1316
mod Atlantic (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate_star 5728.4774 5758.7626 2.9051541 1981-1999 –> 2000-2012 5.609342 10654.8520 10714.6907
obs Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate_star 7831.9953 7862.8190 5.4149721 1981-1999 –> 2000-2012 10.238559 13386.0247 13445.8336
mod Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 5298.8674 5334.2000 2.4080804 1981-1999 –> 2000-2012 4.272928 9470.6192 9540.4310
mod Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5346.7179 5382.0505 2.4587042 1981-1999 –> 2000-2012 4.392537 9592.4264 9662.2382
obs Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7764.6932 7800.6542 5.2678545 1981-1999 –> 2000-2012 10.076765 13315.0790 13384.8560
obs Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + phosphate_star 7835.7211 7866.5448 5.4229967 1981-1999 –> 2000-2012 10.234120 13384.9588 13444.7678
mod Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 5508.2706 5543.6032 2.6376141 1981-1999 –> 2000-2012 5.139520 10278.3489 10348.1607
obs Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 7761.8302 7797.7911 5.2618634 1981-1999 –> 2000-2012 10.056887 13306.8599 13376.6370
mod Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5367.2364 5402.5690 2.4807366 1981-1999 –> 2000-2012 4.443354 9643.0277 9712.8395
obs Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate_star 7786.8389 7817.6625 5.3186526 1981-1999 –> 2000-2012 10.230193 13374.3333 13434.1422
obs Atlantic (26.75,27] cstar_tref ~ temp + aou + phosphate_star 7846.0891 7871.7755 5.4497202 1981-1999 –> 2000-2012 10.300737 13408.6202 13458.4609
mod Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate 5393.2828 5423.5679 2.5111722 1981-1999 –> 2000-2012 4.417248 9607.5565 9667.3952
mod Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 5436.7615 5467.0466 2.5590943 1981-1999 –> 2000-2012 4.532160 9721.3631 9781.2018
obs Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 7797.8216 7828.6453 5.3419201 1981-1999 –> 2000-2012 10.188297 13360.5805 13420.3894
obs Atlantic (26.75,27] cstar_tref ~ temp + nitrate + phosphate_star 7851.1938 7876.8802 5.4607885 1981-1999 –> 2000-2012 10.288712 13404.8871 13454.7279
mod Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 5678.0371 5708.3222 2.8421359 1981-1999 –> 2000-2012 5.471619 10547.3749 10607.2136
obs Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 7789.6681 7820.4917 5.3246367 1981-1999 –> 2000-2012 10.141005 13340.9237 13400.7326
mod Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 5456.3098 5486.5949 2.5809374 1981-1999 –> 2000-2012 4.582097 9769.6960 9829.5347
obs Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 7796.6855 7827.5092 5.3395086 1981-1999 –> 2000-2012 10.187331 13359.9967 13419.8056
mod Atlantic (27,27.25] cstar_tref ~ sal + aou + phosphate 7562.6550 7589.2610 2.9406557 1981-1999 –> 2000-2012 5.120320 13120.6836 13172.9918
mod Atlantic (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 6914.5323 6946.4595 2.3717899 1981-1999 –> 2000-2012 4.439178 12341.0788 12403.8486
mod Atlantic (27,27.25] cstar_tref ~ sal + nitrate + silicate + phosphate_star 7101.5047 7133.4318 2.5230649 1981-1999 –> 2000-2012 4.687869 12644.2662 12707.0361
mod Atlantic (27,27.25] cstar_tref ~ sal + silicate + phosphate + phosphate_star 7060.1154 7092.0426 2.4887671 1981-1999 –> 2000-2012 4.709571 12667.3383 12730.1081
mod Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate 7560.6110 7592.5381 2.9367257 1981-1999 –> 2000-2012 5.112734 13116.4023 13179.1722
obs Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + phosphate_star 14705.3906 14739.9712 5.4922000 1981-1999 –> 2000-2012 10.844807 26131.1716 26198.8672
mod Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6582.7814 6620.0298 2.1239500 1981-1999 –> 2000-2012 3.603569 11167.0459 11240.2774
obs Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 14577.4978 14617.8420 5.3426800 1981-1999 –> 2000-2012 10.510819 25876.0071 25954.9853
mod Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6798.3052 6835.5535 2.2808510 1981-1999 –> 2000-2012 4.019402 11789.6087 11862.8402
obs Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 14609.2786 14649.6227 5.3788824 1981-1999 –> 2000-2012 10.516682 25886.0853 25965.0635
obs Atlantic (27,27.25] cstar_tref ~ sal + temp + phosphate + phosphate_star 14713.7052 14748.2859 5.5019123 1981-1999 –> 2000-2012 10.855793 26140.3635 26208.0591
mod Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6615.7330 6652.9813 2.1472205 1981-1999 –> 2000-2012 3.648968 11237.4660 11310.6975
obs Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 14582.0832 14622.4273 5.3478882 1981-1999 –> 2000-2012 10.514500 25879.5032 25958.4814
obs Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate_star 14699.6548 14734.2355 5.4855101 1981-1999 –> 2000-2012 10.690065 26022.0455 26089.7410
obs Atlantic (27,27.25] cstar_tref ~ temp + aou + phosphate_star 14741.8643 14770.6815 5.5372853 1981-1999 –> 2000-2012 10.944234 26202.8783 26259.2913
mod Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate_star 7481.5251 7513.4522 2.8609179 1981-1999 –> 2000-2012 4.780530 12720.8849 12783.6547
obs Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate_star 14647.4654 14682.0461 5.4250120 1981-1999 –> 2000-2012 10.720496 26033.6983 26101.3939
obs Atlantic (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 14702.1139 14736.6946 5.4883773 1981-1999 –> 2000-2012 10.768073 26077.3403 26145.0359
mod Atlantic (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 7492.9071 7524.8343 2.8717064 1981-1999 –> 2000-2012 4.812134 12759.4887 12822.2586
obs Atlantic (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 14653.0594 14687.6401 5.4314646 1981-1999 –> 2000-2012 10.726627 26039.0680 26106.7636
mod Atlantic (27.25,27.5] cstar_tref ~ sal + aou + phosphate 16303.1983 16333.2684 3.5820449 1981-1999 –> 2000-2012 6.556087 25716.4075 25774.1567
mod Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate 16645.8784 16681.9625 3.7896810 1981-1999 –> 2000-2012 6.608318 25859.9382 25929.2372
mod Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 16263.5589 16299.6429 3.5574597 1981-1999 –> 2000-2012 6.121303 25122.5110 25191.8100
obs Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 16117.8421 16153.4147 4.4016067 1981-1999 –> 2000-2012 8.967424 29548.5073 29618.4820
mod Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate_star 16190.8243 16226.9083 3.5149191 1981-1999 –> 2000-2012 6.254077 25297.6797 25366.9787
obs Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate_star 16083.6923 16119.2649 4.3746159 1981-1999 –> 2000-2012 8.951217 29525.1332 29595.1079
obs Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 16084.7826 16126.2840 4.3738992 1981-1999 –> 2000-2012 8.946346 29524.0753 29605.7124
mod Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 16066.5250 16102.6090 3.4433939 1981-1999 –> 2000-2012 6.197860 25194.2686 25263.5676
mod Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 16184.4544 16220.5384 3.5112179 1981-1999 –> 2000-2012 6.253761 25295.9390 25365.2380
obs Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 16090.0540 16125.6266 4.3796314 1981-1999 –> 2000-2012 8.951785 29527.0538 29597.0285
mod Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate_star 16722.8539 16752.9239 3.8395082 1981-1999 –> 2000-2012 6.601640 25859.0138 25916.7630
obs Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 16090.1463 16131.6477 4.3781268 1981-1999 –> 2000-2012 8.946505 29525.3724 29607.0095
mod Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate 16866.1314 16896.2014 3.9315831 1981-1999 –> 2000-2012 6.752677 26081.4562 26139.2054
obs Atlantic (27.25,27.5] cstar_tref ~ temp + aou + phosphate 16276.4859 16306.1297 4.5308249 1981-1999 –> 2000-2012 9.164489 29772.5307 29830.8430
obs Atlantic (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate 16264.3565 16299.9291 4.5193090 1981-1999 –> 2000-2012 9.118589 29728.3780 29798.3527
mod Atlantic (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate_star 17075.7317 17111.8158 4.0689256 1981-1999 –> 2000-2012 6.813638 26190.1806 26259.4796
obs Atlantic (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate_star 16249.4198 16284.9924 4.5071670 1981-1999 –> 2000-2012 9.110902 29717.8640 29787.8387
obs Atlantic (27.25,27.5] cstar_tref ~ temp + phosphate + phosphate_star 16271.1993 16300.8431 4.5265127 1981-1999 –> 2000-2012 9.169344 29776.2720 29834.5842
mod Atlantic (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 17074.3927 17110.4768 4.0680246 1981-1999 –> 2000-2012 6.824939 26205.4665 26274.7656
obs Atlantic (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 16249.0602 16284.6328 4.5068750 1981-1999 –> 2000-2012 9.106900 29713.8215 29783.7962
obs Atlantic (27.5,27.75] cstar_tref ~ aou + silicate + phosphate 18683.9780 18714.2697 4.6450625 1981-1999 –> 2000-2012 9.225980 31763.0614 31821.8839
mod Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 25790.6855 25830.5304 2.3611186 1981-1999 –> 2000-2012 4.435620 41358.9804 41435.9907
obs Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 18592.5074 18628.8574 4.5768692 1981-1999 –> 2000-2012 9.021270 31539.1406 31609.7275
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 26152.1553 26192.0003 2.4377579 1981-1999 –> 2000-2012 4.290267 40901.0269 40978.0372
obs Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 18694.4118 18730.7618 4.6512653 1981-1999 –> 2000-2012 9.236588 31779.7667 31850.3536
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 26105.5919 26145.4369 2.4277476 1981-1999 –> 2000-2012 4.279467 40851.3762 40928.3866
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 25773.7324 25820.2182 2.3571673 1981-1999 –> 2000-2012 4.089350 40038.3748 40128.2202
obs Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 18387.4008 18429.8091 4.4293158 1981-1999 –> 2000-2012 8.779538 31240.8517 31323.2032
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 25701.2258 25747.7116 2.3421121 1981-1999 –> 2000-2012 4.057803 39896.6071 39986.4525
obs Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 18419.2686 18461.6769 4.4517065 1981-1999 –> 2000-2012 8.841047 31312.5025 31394.8540
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 26206.9334 26246.7783 2.4495871 1981-1999 –> 2000-2012 4.309565 40984.9376 41061.9479
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 25735.3364 25781.8222 2.3491828 1981-1999 –> 2000-2012 4.065787 39934.5701 40024.4155
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 26097.7992 26137.6441 2.4260763 1981-1999 –> 2000-2012 4.276559 40838.7470 40915.7573
obs Atlantic (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 18734.4136 18770.7635 4.6807983 1981-1999 –> 2000-2012 9.324607 31876.0933 31946.6802
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 25698.4208 25744.9065 2.3415316 1981-1999 –> 2000-2012 4.057023 39892.9626 39982.8080
obs Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 18396.0543 18438.4626 4.4353848 1981-1999 –> 2000-2012 8.807726 31272.0441 31354.3955
mod Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 26426.7666 26466.6115 2.4976399 1981-1999 –> 2000-2012 4.220544 40650.5231 40727.5334
obs Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 18457.5258 18493.8757 4.4801535 1981-1999 –> 2000-2012 8.837676 31316.4288 31387.0157
obs Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate_star 18497.2408 18533.5907 4.5083956 1981-1999 –> 2000-2012 8.905834 31396.6660 31467.2529
obs Atlantic (27.5,27.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 18469.7622 18506.1122 4.4888362 1981-1999 –> 2000-2012 8.869077 31351.7734 31422.3603
obs Atlantic (27.75,27.85] cstar_tref ~ aou + silicate + phosphate 12705.3851 12733.6998 4.7778932 1981-1999 –> 2000-2012 9.464258 19057.4798 19110.6715
mod Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate 7512.3178 7546.5277 1.3184169 1981-1999 –> 2000-2012 2.283350 10976.8898 11041.8755
mod Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 7341.0485 7375.2584 1.2683515 1981-1999 –> 2000-2012 2.211126 10747.6354 10812.6211
obs Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate_star 12708.3409 12742.3185 4.7789663 1981-1999 –> 2000-2012 9.364158 19015.7295 19079.5597
mod Atlantic (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate_star 8110.0146 8144.2245 1.5091324 1981-1999 –> 2000-2012 2.879606 12450.3164 12515.3021
obs Atlantic (27.75,27.85] cstar_tref ~ sal + silicate + phosphate 12947.7136 12976.0283 5.0578313 1981-1999 –> 2000-2012 10.136630 19471.9023 19525.0940
obs Atlantic (27.75,27.85] cstar_tref ~ sal + silicate + phosphate + phosphate_star 12623.7112 12657.6888 4.6848761 1981-1999 –> 2000-2012 9.199378 18897.8508 18961.6809
mod Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + silicate 7499.4669 7539.3784 1.3139985 1981-1999 –> 2000-2012 2.243851 10873.6055 10949.4221
mod Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 8964.7473 8998.9572 1.8307734 1981-1999 –> 2000-2012 2.882904 12645.2567 12710.2424
mod Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 7241.0642 7280.9758 1.2394472 1981-1999 –> 2000-2012 2.076616 10353.1219 10428.9386
mod Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7418.8667 7458.7783 1.2902757 1981-1999 –> 2000-2012 2.176811 10673.9336 10749.7502
obs Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 12619.5078 12659.1483 4.6780526 1981-1999 –> 2000-2012 9.189044 18893.9826 18968.4511
mod Atlantic (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 7418.6690 7458.5806 1.2902181 1981-1999 –> 2000-2012 2.176512 10673.0557 10748.8723
obs Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate 12934.0713 12968.0489 5.0392760 1981-1999 –> 2000-2012 10.041806 19427.8793 19491.7094
mod Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7410.1313 7450.0429 1.2877305 1981-1999 –> 2000-2012 2.172943 10661.4716 10737.2882
mod Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 7524.4202 7558.6301 1.3220285 1981-1999 –> 2000-2012 2.236008 10853.5825 10918.5682
obs Atlantic (27.75,27.85] cstar_tref ~ silicate + phosphate 12987.0654 13009.7171 5.1072132 1981-1999 –> 2000-2012 10.280377 19548.6507 19591.2041
obs Atlantic (27.75,27.85] cstar_tref ~ silicate + phosphate + phosphate_star 12777.7647 12806.0794 4.8598432 1981-1999 –> 2000-2012 9.663291 19182.6676 19235.8594
obs Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate_star 12624.2971 12658.2747 4.6855211 1981-1999 –> 2000-2012 9.236976 18915.8818 18979.7120
obs Atlantic (27.75,27.85] cstar_tref ~ temp + silicate + phosphate 12937.5104 12965.8251 5.0457203 1981-1999 –> 2000-2012 10.084667 19444.8407 19498.0325
mod Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate 10715.3030 10749.6045 2.6216641 1981-1999 –> 2000-2012 3.864553 15276.4323 15342.1561
obs Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate 27179.7433 27218.1148 5.2078619 1981-1999 –> 2000-2012 9.394845 40277.4618 40350.2642
obs Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate_star 26616.8399 26655.2114 4.8870011 1981-1999 –> 2000-2012 8.935741 39560.4499 39633.2523
obs Atlantic (27.85,27.95] cstar_tref ~ sal + silicate + phosphate 27495.6579 27527.6342 5.3982986 1981-1999 –> 2000-2012 9.904559 40928.6819 40989.3506
obs Atlantic (27.85,27.95] cstar_tref ~ sal + silicate + phosphate + phosphate_star 26967.8164 27006.1879 5.0846605 1981-1999 –> 2000-2012 9.183234 39967.5775 40040.3799
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + silicate 10939.5373 10979.5556 2.7546285 1981-1999 –> 2000-2012 4.021142 15555.0110 15631.6888
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 10831.7799 10866.0814 2.6905324 1981-1999 –> 2000-2012 3.940739 15409.2272 15474.9510
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate_star 10927.5065 10961.8079 2.7484842 1981-1999 –> 2000-2012 4.064752 15648.1007 15713.8245
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 10615.3907 10655.4091 2.5628547 1981-1999 –> 2000-2012 3.649194 14804.2621 14880.9399
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10679.8304 10719.8487 2.5998849 1981-1999 –> 2000-2012 3.730494 14979.7434 15056.4212
obs Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 26526.2458 26571.0126 4.8361483 1981-1999 –> 2000-2012 8.884809 39471.7662 39556.7024
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10703.4180 10743.4363 2.6135728 1981-1999 –> 2000-2012 3.747032 15010.3283 15087.0061
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + phosphate + phosphate_star 10904.5858 10938.8873 2.7344956 1981-1999 –> 2000-2012 4.046240 15615.6090 15681.3328
obs Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate 26688.1490 26726.5205 4.9265284 1981-1999 –> 2000-2012 9.124726 39798.1448 39870.9472
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10670.3206 10710.3389 2.5943866 1981-1999 –> 2000-2012 3.723708 14967.0638 15043.7415
obs Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 26552.1668 26596.9336 4.8503306 1981-1999 –> 2000-2012 8.906955 39506.7067 39591.6429
mod Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 10799.1992 10833.5006 2.6710884 1981-1999 –> 2000-2012 3.812003 15122.3375 15188.0613
obs Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 27620.5035 27658.8750 5.4737369 1981-1999 –> 2000-2012 9.897787 40971.0161 41043.8186
obs Atlantic (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate_star 27519.4568 27557.8283 5.4116088 1981-1999 –> 2000-2012 9.801300 40834.1834 40906.9858
obs Atlantic (27.85,27.95] cstar_tref ~ temp + silicate + phosphate + phosphate_star 27611.6236 27649.9951 5.4682487 1981-1999 –> 2000-2012 9.883209 40952.6965 41025.4989
obs Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate 30446.3967 30478.6966 6.0732290 1981-1999 –> 2000-2012 10.298207 48405.4587 48468.0153
obs Atlantic (27.95,28.05] cstar_tref ~ sal + aou + phosphate_star 30396.7283 30429.0282 6.0413722 1981-1999 –> 2000-2012 10.260547 48347.1643 48409.7210
obs Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate 30319.2756 30358.0356 5.9907592 1981-1999 –> 2000-2012 10.100717 48107.1119 48182.1799
obs Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate_star 29984.8340 30023.5939 5.7823201 1981-1999 –> 2000-2012 9.670184 47424.0214 47499.0893
obs Atlantic (27.95,28.05] cstar_tref ~ sal + nitrate + silicate + phosphate_star 30353.3949 30392.1548 6.0124417 1981-1999 –> 2000-2012 10.169362 48212.5374 48287.6054
obs Atlantic (27.95,28.05] cstar_tref ~ sal + phosphate + phosphate_star 30356.7420 30389.0420 6.0158469 1981-1999 –> 2000-2012 10.204249 48261.2363 48323.7930
mod Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 14237.8361 14272.8377 4.0518550 1981-1999 –> 2000-2012 7.532749 23133.7068 23201.2174
obs Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 30385.0233 30423.7832 6.0326114 1981-1999 –> 2000-2012 10.221907 48292.8565 48367.9245
mod Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 14253.8973 14288.8989 4.0647673 1981-1999 –> 2000-2012 7.555341 23159.0204 23226.5311
obs Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 30325.3214 30364.0813 5.9945955 1981-1999 –> 2000-2012 10.151771 48184.8497 48259.9177
mod Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 14187.2744 14228.1096 4.0098844 1981-1999 –> 2000-2012 7.433485 23029.8458 23108.6082
mod Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 14190.7948 14231.6300 4.0126818 1981-1999 –> 2000-2012 7.436701 23033.7734 23112.5358
obs Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 30340.0896 30378.8495 6.0039770 1981-1999 –> 2000-2012 10.167411 48209.0587 48284.1267
mod Atlantic (27.95,28.05] cstar_tref ~ sal + temp + phosphate_star 14275.8750 14305.0430 4.0841206 1981-1999 –> 2000-2012 7.630730 23232.0635 23288.3224
obs Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate 30407.7412 30446.5011 6.0471405 1981-1999 –> 2000-2012 10.207519 48272.1034 48347.1714
mod Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate_star 14190.7184 14225.7200 4.0142112 1981-1999 –> 2000-2012 7.534434 23124.0242 23191.5349
mod Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate 14514.8747 14544.0427 4.2821356 1981-1999 –> 2000-2012 7.837882 23479.6364 23535.8953
mod Atlantic (27.95,28.05] cstar_tref ~ temp + aou + phosphate_star 14553.4560 14582.6240 4.3149889 1981-1999 –> 2000-2012 7.897861 23543.5405 23599.7994
mod Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 14474.1443 14509.1459 4.2460411 1981-1999 –> 2000-2012 7.757215 23398.8741 23466.3848
mod Atlantic (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate_star 14500.9635 14535.9651 4.2686597 1981-1999 –> 2000-2012 7.798540 23443.3984 23510.9091
mod Atlantic (28.05,28.1] cstar_tref ~ sal + aou + nitrate 5198.4253 5224.6070 1.5663455 1981-1999 –> 2000-2012 2.537735 7754.7415 7805.0233
mod Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate 5110.7871 5136.9688 1.5177029 1981-1999 –> 2000-2012 2.365077 7416.8803 7467.1621
obs Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate 23410.1840 23441.1079 6.3203548 1981-1999 –> 2000-2012 10.323369 35659.8953 35719.2570
mod Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate_star 5641.1600 5667.3417 1.8369689 1981-1999 –> 2000-2012 2.964707 8470.8871 8521.1689
obs Atlantic (28.05,28.1] cstar_tref ~ sal + aou + phosphate_star 23331.4390 23362.3629 6.2513400 1981-1999 –> 2000-2012 10.280354 35609.3910 35668.7526
mod Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate_star 5596.4226 5627.8406 1.8063221 1981-1999 –> 2000-2012 2.914601 8396.2623 8456.6004
obs Atlantic (28.05,28.1] cstar_tref ~ sal + nitrate + phosphate_star 23352.2419 23383.1659 6.2694988 1981-1999 –> 2000-2012 10.286907 35617.6101 35676.9717
obs Atlantic (28.05,28.1] cstar_tref ~ sal + phosphate + phosphate_star 23335.2471 23366.1711 6.2546602 1981-1999 –> 2000-2012 10.277557 35606.5710 35665.9326
obs Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 23411.7941 23448.9028 6.3200112 1981-1999 –> 2000-2012 10.308406 35647.5459 35718.7799
obs Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 23279.4496 23316.5583 6.2044579 1981-1999 –> 2000-2012 10.086700 35397.5324 35468.7664
obs Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + phosphate_star 23283.5776 23320.6864 6.2080300 1981-1999 –> 2000-2012 10.090963 35402.4367 35473.6707
obs Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 23294.2061 23331.3148 6.2172368 1981-1999 –> 2000-2012 10.098045 35410.6776 35481.9116
mod Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate_star 5061.7056 5087.8873 1.4911237 1981-1999 –> 2000-2012 2.437879 7570.9643 7621.2461
obs Atlantic (28.05,28.1] cstar_tref ~ sal + temp + phosphate_star 23351.3166 23382.2406 6.2686900 1981-1999 –> 2000-2012 10.151806 35468.3810 35527.7427
mod Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate 5429.1579 5460.5759 1.7007721 1981-1999 –> 2000-2012 3.030017 8562.0606 8622.3987
mod Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 4930.6679 4962.0859 1.4213971 1981-1999 –> 2000-2012 2.270734 7242.9988 7303.3369
obs Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 23326.7736 23363.8823 6.2455330 1981-1999 –> 2000-2012 10.127883 35444.9775 35516.2114
mod Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate_star 4664.2858 4690.4675 1.2923604 1981-1999 –> 2000-2012 2.184037 7063.7397 7114.0215
mod Atlantic (28.05,28.1] cstar_tref ~ temp + phosphate_star 5059.7087 5080.6540 1.4911254 1981-1999 –> 2000-2012 2.473761 7635.1132 7675.3386
mod Atlantic (28.05,28.1] cstar_tref ~ temp + silicate + phosphate_star 4945.5612 4971.7429 1.4300671 1981-1999 –> 2000-2012 2.379982 7460.9229 7511.2047
mod Atlantic (28.1,28.15] cstar_tref ~ sal + aou + nitrate 7554.3771 7582.6942 1.4231516 1981-1999 –> 2000-2012 2.309548 10537.5919 10591.1247
mod Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate 7730.2059 7758.5229 1.4831491 1981-1999 –> 2000-2012 2.525882 11085.4012 11138.9341
obs Atlantic (28.1,28.15] cstar_tref ~ sal + aou + phosphate_star 18077.4254 18106.8802 7.1041360 1981-1999 –> 2000-2012 10.877251 26366.3994 26422.4435
obs Atlantic (28.1,28.15] cstar_tref ~ sal + nitrate + phosphate_star 18063.6684 18093.1232 7.0858782 1981-1999 –> 2000-2012 10.855130 26349.5550 26405.5992
obs Atlantic (28.1,28.15] cstar_tref ~ sal + phosphate 18877.7996 18901.3634 8.2545605 1981-1999 –> 2000-2012 13.098847 27917.9691 27962.8044
obs Atlantic (28.1,28.15] cstar_tref ~ sal + phosphate_star 18162.4145 18185.9784 7.2206787 1981-1999 –> 2000-2012 11.026922 26475.7360 26520.5713
mod Atlantic (28.1,28.15] cstar_tref ~ sal + silicate + phosphate 7513.5660 7541.8831 1.4095765 1981-1999 –> 2000-2012 2.766492 11471.8752 11525.4080
obs Atlantic (28.1,28.15] cstar_tref ~ sal + silicate + phosphate_star 18104.2120 18133.6667 7.1398211 1981-1999 –> 2000-2012 10.932116 26408.4683 26464.5125
mod Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 7321.4424 7355.4228 1.3467563 1981-1999 –> 2000-2012 2.061990 9815.3281 9879.5676
mod Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate 7668.4744 7696.7914 1.4618018 1981-1999 –> 2000-2012 2.437894 10872.4304 10925.9632
mod Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate 7361.4483 7389.7653 1.3601080 1981-1999 –> 2000-2012 2.108882 9958.2792 10011.8120
mod Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate_star 7403.7644 7432.0815 1.3736922 1981-1999 –> 2000-2012 2.139802 10053.0093 10106.5421
obs Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate_star 17858.2374 17887.6922 6.8187541 1981-1999 –> 2000-2012 10.397884 25988.1290 26044.1732
mod Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate_star 7267.9341 7301.9145 1.3299381 1981-1999 –> 2000-2012 2.066217 9828.2288 9892.4682
obs Atlantic (28.1,28.15] cstar_tref ~ temp + nitrate + phosphate_star 17861.6815 17891.1362 6.8231483 1981-1999 –> 2000-2012 10.413292 26000.8337 26056.8778
obs Atlantic (28.1,28.15] cstar_tref ~ temp + phosphate 18863.1870 18886.7508 8.2320285 1981-1999 –> 2000-2012 13.086443 27909.6516 27954.4869
obs Atlantic (28.1,28.15] cstar_tref ~ temp + phosphate_star 17875.0884 17898.6522 6.8428407 1981-1999 –> 2000-2012 10.479858 26051.3370 26096.1723
mod Atlantic (28.1,28.15] cstar_tref ~ temp + silicate + phosphate 7729.3132 7757.6303 1.4828382 1981-1999 –> 2000-2012 2.986498 11922.7773 11976.3101
mod Atlantic (28.1,28.15] cstar_tref ~ temp + silicate + phosphate_star 9087.2528 9115.5698 2.0398430 1981-1999 –> 2000-2012 2.907882 12022.5438 12076.0767
obs Atlantic (28.1,28.15] cstar_tref ~ temp + silicate + phosphate_star 17841.6127 17871.0675 6.7975824 1981-1999 –> 2000-2012 10.339493 25939.9974 25996.0415
mod Atlantic (28.15,28.2] cstar_tref ~ aou + nitrate 12588.9875 12614.0305 1.2298991 1981-1999 –> 2000-2012 2.335690 18775.2732 18822.7853
mod Atlantic (28.15,28.2] cstar_tref ~ aou + nitrate + silicate 12087.6845 12118.9883 1.1524489 1981-1999 –> 2000-2012 2.162436 17907.4945 17966.8846
mod Atlantic (28.15,28.2] cstar_tref ~ aou + phosphate 12341.8952 12366.9382 1.1912460 1981-1999 –> 2000-2012 2.389258 18853.8773 18901.3894
mod Atlantic (28.15,28.2] cstar_tref ~ aou + silicate + phosphate 12233.7440 12265.0478 1.1744087 1981-1999 –> 2000-2012 2.307839 18522.4082 18581.7983
mod Atlantic (28.15,28.2] cstar_tref ~ nitrate + silicate + phosphate_star 12323.5651 12354.8689 1.1881204 1981-1999 –> 2000-2012 2.390461 18852.2101 18911.6002
mod Atlantic (28.15,28.2] cstar_tref ~ sal + aou + phosphate 12340.7260 12372.0297 1.1907582 1981-1999 –> 2000-2012 2.386068 18845.5279 18904.9180
obs Atlantic (28.15,28.2] cstar_tref ~ sal + aou + phosphate_star 6543.3631 6568.5833 4.1852604 1981-1999 –> 2000-2012 8.098929 9514.9152 9561.5186
mod Atlantic (28.15,28.2] cstar_tref ~ sal + nitrate + phosphate_star 11982.2251 12013.5288 1.1368490 1981-1999 –> 2000-2012 2.255910 18219.0117 18278.4018
obs Atlantic (28.15,28.2] cstar_tref ~ sal + phosphate 6986.0687 7006.2449 5.0814369 1981-1999 –> 2000-2012 9.346854 10047.1938 10084.4765
obs Atlantic (28.15,28.2] cstar_tref ~ sal + phosphate_star 6947.1096 6967.2858 4.9957932 1981-1999 –> 2000-2012 9.084774 9963.2868 10000.5695
obs Atlantic (28.15,28.2] cstar_tref ~ sal + silicate + phosphate_star 6624.7550 6649.9752 4.3365549 1981-1999 –> 2000-2012 8.314911 9613.7500 9660.3533
mod Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate_star 11441.0876 11478.6521 1.0597886 1981-1999 –> 2000-2012 1.924770 16632.7314 16703.9995
mod Atlantic (28.15,28.2] cstar_tref ~ sal + temp + phosphate_star 13130.9225 13162.2262 1.3187829 1981-1999 –> 2000-2012 2.199200 18392.4823 18451.8723
obs Atlantic (28.15,28.2] cstar_tref ~ sal + temp + phosphate_star 6385.7489 6410.9690 3.9071250 1981-1999 –> 2000-2012 7.487823 9262.6930 9309.2963
mod Atlantic (28.15,28.2] cstar_tref ~ temp + aou + phosphate_star 12106.0629 12137.3666 1.1551893 1981-1999 –> 2000-2012 2.234245 18194.8351 18254.2252
obs Atlantic (28.15,28.2] cstar_tref ~ temp + aou + phosphate_star 6303.9209 6329.1410 3.7700952 1981-1999 –> 2000-2012 7.378012 9188.9224 9235.5258
obs Atlantic (28.15,28.2] cstar_tref ~ temp + nitrate + phosphate_star 6323.3941 6348.6143 3.8022630 1981-1999 –> 2000-2012 7.410373 9208.4526 9255.0560
obs Atlantic (28.15,28.2] cstar_tref ~ temp + phosphate 6984.5804 7004.7565 5.0781382 1981-1999 –> 2000-2012 9.372734 10052.9593 10090.2420
obs Atlantic (28.15,28.2] cstar_tref ~ temp + phosphate_star 6387.1022 6407.2783 3.9128456 1981-1999 –> 2000-2012 7.520995 9270.1724 9307.4551
obs Atlantic (28.15,28.2] cstar_tref ~ temp + silicate + phosphate_star 6354.3150 6379.5352 3.8539061 1981-1999 –> 2000-2012 7.456109 9237.6300 9284.2333
mod Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate 12414.1746 12447.6505 0.6833429 1981-1999 –> 2000-2012 1.257678 18181.0509 18245.0804
obs Atlantic (28.2, Inf] cstar_tref ~ sal + aou + phosphate 14316.7008 14346.2409 3.3599864 1981-1999 –> 2000-2012 6.648067 20291.4289 20346.1761
mod Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 15769.4475 15809.6186 0.9047443 1981-1999 –> 2000-2012 1.776291 24315.9229 24392.7583
mod Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate 12404.4635 12444.6346 0.6826734 1981-1999 –> 2000-2012 1.256836 18171.3394 18248.1748
obs Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate 14276.0598 14311.5080 3.3337428 1981-1999 –> 2000-2012 6.478355 20150.8021 20216.4987
obs Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate_star 14235.1447 14270.5928 3.3087541 1981-1999 –> 2000-2012 6.526855 20162.6954 20228.3920
obs Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 14209.0833 14250.4395 3.2917241 1981-1999 –> 2000-2012 6.370960 20037.7990 20114.4450
mod Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 14008.7098 14048.8808 0.7807739 1981-1999 –> 2000-2012 1.813743 23686.8730 23763.7084
obs Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 14388.3991 14423.8472 3.4033282 1981-1999 –> 2000-2012 6.627327 20320.1358 20385.8324
mod Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 13917.4540 13964.3202 0.7747036 1981-1999 –> 2000-2012 1.527263 21488.3072 21577.9485
obs Atlantic (28.2, Inf] cstar_tref ~ sal + temp + phosphate + phosphate_star 14233.6361 14269.0842 3.3078363 1981-1999 –> 2000-2012 6.515643 20153.8627 20219.5593
mod Atlantic (28.2, Inf] cstar_tref ~ temp + aou + nitrate + silicate 14491.6095 14531.7805 0.8129766 1981-1999 –> 2000-2012 1.627885 22590.5755 22667.4109
obs Atlantic (28.2, Inf] cstar_tref ~ temp + aou + phosphate 14647.1153 14676.6554 3.5704700 1981-1999 –> 2000-2012 6.816908 20592.7070 20647.4541
obs Atlantic (28.2, Inf] cstar_tref ~ temp + aou + phosphate_star 14584.5586 14614.0987 3.5296320 1981-1999 –> 2000-2012 6.822711 20562.7595 20617.5067
mod Atlantic (28.2, Inf] cstar_tref ~ temp + aou + silicate + phosphate 16076.5580 16116.7291 0.9283012 1981-1999 –> 2000-2012 1.894676 25310.8953 25387.7307
obs Atlantic (28.2, Inf] cstar_tref ~ temp + aou + silicate + phosphate 14642.0734 14677.5215 3.5658494 1981-1999 –> 2000-2012 6.657654 20478.1007 20543.7972
mod Atlantic (28.2, Inf] cstar_tref ~ temp + aou + silicate + phosphate_star 16130.8462 16171.0172 0.9325287 1981-1999 –> 2000-2012 1.905028 25407.2552 25484.0906
obs Atlantic (28.2, Inf] cstar_tref ~ temp + aou + silicate + phosphate_star 14586.5572 14622.0053 3.5296311 1981-1999 –> 2000-2012 6.628816 20428.0351 20493.7317
mod Atlantic (28.2, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 15383.8376 15424.0087 0.8760107 1981-1999 –> 2000-2012 1.783491 24199.3923 24276.2277
mod Atlantic (28.2, Inf] cstar_tref ~ temp + silicate + phosphate + phosphate_star 16110.5550 16150.7260 0.9309464 1981-1999 –> 2000-2012 1.901674 25374.8215 25451.6569
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 29056.6374 29095.1031 6.1172617 1981-1999 –> 2000-2012 17.651722 41418.8688 41489.5935
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 22001.3258 22044.4254 5.6571168 1981-1999 –> 2000-2012 10.639695 29873.9796 29953.2646
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 28905.0082 28949.8848 6.0136354 1981-1999 –> 2000-2012 17.330997 41208.5118 41291.0239
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 22103.1638 22146.2634 5.7403070 1981-1999 –> 2000-2012 10.859380 30046.0310 30125.3160
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 28920.0014 28964.8780 6.0236709 1981-1999 –> 2000-2012 17.349151 41225.7969 41308.3090
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 29056.8104 29101.6870 6.1160189 1981-1999 –> 2000-2012 17.604854 41408.3746 41490.8868
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 22786.0270 22822.9695 6.3324481 1981-1999 –> 2000-2012 11.622372 30812.1876 30880.1462
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + phosphate 29906.2592 29944.7249 6.7234470 1981-1999 –> 2000-2012 18.440368 42318.6517 42389.3764
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 22524.2396 22567.3392 6.0974664 1981-1999 –> 2000-2012 11.222446 30470.1026 30549.3876
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 29474.8006 29519.6772 6.4070315 1981-1999 –> 2000-2012 17.724582 41778.3577 41860.8698
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 22716.6456 22759.7451 6.2679821 1981-1999 –> 2000-2012 11.579852 30755.5620 30834.8471
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 29532.0794 29576.9560 6.4479744 1981-1999 –> 2000-2012 17.779669 41839.6283 41922.1405
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 22232.2239 22275.3235 5.8474946 1981-1999 –> 2000-2012 11.027110 30205.6370 30284.9220
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate_star 22933.8301 22970.7726 6.4680474 1981-1999 –> 2000-2012 12.012928 31082.2822 31150.2408
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 22919.6292 22962.7288 6.4530435 1981-1999 –> 2000-2012 11.986877 31064.8999 31144.1850
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 29848.1828 29893.0594 6.6786768 1981-1999 –> 2000-2012 18.117203 42185.7212 42268.2334
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 22762.0087 22805.1083 6.3088740 1981-1999 –> 2000-2012 11.653761 30817.0237 30896.3088
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 29558.3191 29603.1957 6.4668178 1981-1999 –> 2000-2012 17.803469 41867.2655 41949.7777
mod Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 22923.2209 22960.1634 6.4582182 1981-1999 –> 2000-2012 11.992823 31066.8535 31134.8121
obs Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate_star 29891.8053 29930.2710 6.7126483 1981-1999 –> 2000-2012 18.183525 42236.3701 42307.0948
mod Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 18204.7598 18247.0632 4.4942667 1981-1999 –> 2000-2012 8.074703 28263.5694 28344.5862
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 18262.1445 18304.3619 4.7031826 1981-1999 –> 2000-2012 12.046995 29927.4320 30007.7468
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + phosphate_star 18641.7087 18677.8951 5.0042242 1981-1999 –> 2000-2012 12.530738 30388.8915 30457.7328
mod Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 17613.8771 17656.1805 4.0873501 1981-1999 –> 2000-2012 8.026873 28028.9899 28110.0066
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 18433.8725 18476.0900 4.8363616 1981-1999 –> 2000-2012 12.157004 30088.3720 30168.6869
mod Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 18274.4335 18316.7369 4.5448435 1981-1999 –> 2000-2012 8.142263 28350.8843 28431.9011
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 18269.5288 18311.7462 4.7088331 1981-1999 –> 2000-2012 12.058785 29937.6695 30017.9844
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 18505.4550 18541.6413 4.8945744 1981-1999 –> 2000-2012 12.383595 30235.5886 30304.4299
mod Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 18528.9866 18571.2900 4.7345126 1981-1999 –> 2000-2012 9.133029 29354.9542 29435.9710
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 18437.4469 18479.6644 4.8391733 1981-1999 –> 2000-2012 12.213729 30116.9966 30197.3115
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 18641.2088 18677.3951 5.0038174 1981-1999 –> 2000-2012 12.530511 30388.4734 30457.3147
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + phosphate_star 18649.8933 18680.0486 5.0125182 1981-1999 –> 2000-2012 12.539765 30395.4084 30452.7762
mod Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 17670.9396 17713.2430 4.1249836 1981-1999 –> 2000-2012 8.077511 28098.3392 28179.3560
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 18436.2336 18478.4511 4.8382187 1981-1999 –> 2000-2012 12.161663 30092.0397 30172.3546
mod Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 18564.5173 18600.7774 4.7631387 1981-1999 –> 2000-2012 9.171424 29396.7552 29466.1981
obs Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 18460.8140 18497.0003 4.8591747 1981-1999 –> 2000-2012 12.235505 30139.1853 30208.0266
mod Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 17962.3733 18004.6767 4.3226610 1981-1999 –> 2000-2012 8.238920 28355.4062 28436.4229
mod Indo-Pacific (26,26.5] cstar_tref ~ temp + aou + silicate + phosphate_star 18402.3459 18438.6060 4.6406730 1981-1999 –> 2000-2012 9.240249 29392.9429 29462.3858
mod Indo-Pacific (26,26.5] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 18001.5856 18043.8890 4.3499717 1981-1999 –> 2000-2012 8.278286 28406.0767 28487.0935
mod Indo-Pacific (26,26.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 18435.8089 18472.0690 4.6656825 1981-1999 –> 2000-2012 9.271373 29431.3584 29500.8013
obs Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate_star 19911.9883 19948.3818 5.5126277 1981-1999 –> 2000-2012 11.434049 31083.3157 31152.4962
mod Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 16224.1723 16265.7713 4.3072969 1981-1999 –> 2000-2012 7.830458 24599.8160 24678.8866
mod Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 16812.3390 16847.9953 4.7833249 1981-1999 –> 2000-2012 8.289814 25171.1737 25238.9485
obs Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 19641.1955 19677.5890 5.2830525 1981-1999 –> 2000-2012 11.074446 30735.0325 30804.2131
mod Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 16499.2590 16540.8580 4.5229815 1981-1999 –> 2000-2012 8.025471 24856.5310 24935.6015
obs Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 19570.9336 19613.3927 5.2234225 1981-1999 –> 2000-2012 11.014732 30666.7201 30747.4307
mod Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 16497.4947 16533.1511 4.5231710 1981-1999 –> 2000-2012 8.112224 24928.9889 24996.7637
obs Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate_star 20143.2734 20179.6669 5.7165914 1981-1999 –> 2000-2012 11.601181 31292.8248 31362.0054
mod Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate_star 17151.9235 17187.5798 5.0807193 1981-1999 –> 2000-2012 8.536878 25465.6222 25533.3970
obs Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate_star 19983.8282 20020.2217 5.5751897 1981-1999 –> 2000-2012 11.404834 31100.6403 31169.8209
mod Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 16547.4656 16589.0646 4.5618756 1981-1999 –> 2000-2012 7.910673 24764.6450 24843.7156
obs Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 19964.3819 20006.8409 5.5564391 1981-1999 –> 2000-2012 11.385934 31083.1041 31163.8147
mod Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate_star 16787.1809 16822.8372 4.7619979 1981-1999 –> 2000-2012 8.595211 25424.1492 25491.9240
mod Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 17167.9260 17203.5823 5.0951811 1981-1999 –> 2000-2012 8.566956 25495.6992 25563.4740
obs Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 19991.4598 20027.8533 5.5818773 1981-1999 –> 2000-2012 11.419687 31113.1566 31182.3371
obs Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + phosphate_star 20047.5857 20077.9136 5.6330770 1981-1999 –> 2000-2012 11.660481 31278.8252 31336.4756
mod Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 16570.4705 16612.0695 4.5805542 1981-1999 –> 2000-2012 7.950656 24807.4487 24886.5193
obs Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 19969.5548 20012.0139 5.5609561 1981-1999 –> 2000-2012 11.398741 31093.2366 31173.9472
obs Indo-Pacific (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate_star 20001.3997 20037.7932 5.5905997 1981-1999 –> 2000-2012 11.617580 31234.3943 31303.5748
mod Indo-Pacific (26.5,26.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 16801.1416 16836.7979 4.7738208 1981-1999 –> 2000-2012 8.613991 25443.7704 25511.5452
obs Indo-Pacific (26.75,27] cstar_tref ~ aou + silicate + phosphate 30154.9864 30187.3953 5.4972445 1981-1999 –> 2000-2012 12.063467 49686.3749 49748.7434
obs Indo-Pacific (26.75,27] cstar_tref ~ nitrate + silicate + phosphate + phosphate_star 30384.6099 30423.5005 5.6284270 1981-1999 –> 2000-2012 12.342632 50049.8019 50124.6441
obs Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + silicate + phosphate_star 30493.4052 30532.2959 5.6922283 1981-1999 –> 2000-2012 12.253179 50022.0428 50096.8850
obs Indo-Pacific (26.75,27] cstar_tref ~ sal + nitrate + silicate + phosphate_star 30498.9597 30537.8504 5.6955050 1981-1999 –> 2000-2012 12.143022 49924.4551 49999.2973
obs Indo-Pacific (26.75,27] cstar_tref ~ sal + silicate + phosphate + phosphate_star 30355.7850 30394.6757 5.6116432 1981-1999 –> 2000-2012 12.147597 49861.8479 49936.6901
mod Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + phosphate_star 23047.6837 23085.4615 4.2804480 1981-1999 –> 2000-2012 7.543248 34719.7156 34791.7815
mod Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 22996.8528 23040.9269 4.2523367 1981-1999 –> 2000-2012 7.503124 34654.3526 34738.4295
mod Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate_star 24016.5173 24054.2951 4.8302103 1981-1999 –> 2000-2012 8.732303 36490.5008 36562.5666
mod Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate_star 23463.9557 23501.7334 4.5085467 1981-1999 –> 2000-2012 7.958765 35386.3150 35458.3808
obs Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate_star 30040.3384 30079.2290 5.4312081 1981-1999 –> 2000-2012 11.858479 49447.2339 49522.0761
mod Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 23411.9023 23455.9764 4.4782546 1981-1999 –> 2000-2012 7.906930 35308.1884 35392.2652
obs Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 30111.6940 30150.5847 5.4715089 1981-1999 –> 2000-2012 11.980756 49593.5424 49668.3846
mod Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 23448.2399 23486.0176 4.4997183 1981-1999 –> 2000-2012 7.965644 35390.9579 35463.0238
mod Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + phosphate_star 23551.1787 23582.6602 4.5589973 1981-1999 –> 2000-2012 8.116102 35608.2811 35668.3360
obs Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + phosphate_star 30206.1845 30238.5933 5.5264815 1981-1999 –> 2000-2012 12.092991 49737.8309 49800.1994
mod Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 23401.8302 23445.9042 4.4726326 1981-1999 –> 2000-2012 7.921673 35324.6592 35408.7360
mod Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 23441.4828 23479.2606 4.4959279 1981-1999 –> 2000-2012 8.047744 35493.9166 35565.9825
obs Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 29807.6358 29846.5264 5.3018315 1981-1999 –> 2000-2012 11.648086 49139.5111 49214.3533
mod Indo-Pacific (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 24004.3807 24042.1585 4.8229046 1981-1999 –> 2000-2012 8.929714 36707.5444 36779.6102
obs Indo-Pacific (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 30075.0049 30113.8956 5.4507501 1981-1999 –> 2000-2012 11.950645 49548.3495 49623.1917
obs Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate_star 39513.7673 39554.4742 4.9767297 1981-1999 –> 2000-2012 11.263029 63525.6349 63603.6122
obs Indo-Pacific (27,27.25] cstar_tref ~ sal + nitrate + silicate + phosphate_star 39902.6576 39943.3644 5.1271045 1981-1999 –> 2000-2012 11.330912 63817.1990 63895.1763
obs Indo-Pacific (27,27.25] cstar_tref ~ sal + silicate + phosphate + phosphate_star 39413.1972 39453.9040 4.9385646 1981-1999 –> 2000-2012 11.196746 63392.0347 63470.0120
mod Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate_star 30107.9931 30147.3385 4.3560764 1981-1999 –> 2000-2012 7.944106 44902.4339 44977.2758
obs Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate_star 40022.9612 40063.6680 5.1745370 1981-1999 –> 2000-2012 11.995210 64635.9523 64713.9297
obs Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 39329.4794 39376.9707 4.9062669 1981-1999 –> 2000-2012 11.174043 63321.6049 63412.5784
mod Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + phosphate_star 27167.1259 27206.4714 3.2841963 1981-1999 –> 2000-2012 6.321885 41048.7794 41123.6213
mod Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 26574.0071 26619.9101 3.1017453 1981-1999 –> 2000-2012 5.884349 39976.8353 40064.1508
obs Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 39396.1220 39443.6133 4.9313589 1981-1999 –> 2000-2012 11.077605 63243.9815 63334.9550
obs Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate_star 39993.3029 40034.0097 5.1628029 1981-1999 –> 2000-2012 11.744421 64343.4211 64421.3985
mod Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate_star 26678.6868 26718.0322 3.1336886 1981-1999 –> 2000-2012 5.790223 39825.3443 39900.1862
mod Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 26524.5271 26570.4301 3.0870401 1981-1999 –> 2000-2012 5.731760 39648.7495 39736.0650
obs Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate_star 40058.6968 40099.4036 5.1887109 1981-1999 –> 2000-2012 11.572101 64183.4926 64261.4699
mod Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 26698.4276 26737.7730 3.1396356 1981-1999 –> 2000-2012 5.809470 39872.4632 39947.3051
mod Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + phosphate_star 27229.0929 27261.8807 3.3044351 1981-1999 –> 2000-2012 6.382163 41180.5317 41242.8999
mod Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 26540.3112 26586.2142 3.0917235 1981-1999 –> 2000-2012 5.748772 39690.0302 39777.3457
mod Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 26671.4501 26710.7955 3.1315114 1981-1999 –> 2000-2012 5.958579 40159.1853 40234.0272
obs Indo-Pacific (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate_star 39966.4998 40007.2066 5.1522214 1981-1999 –> 2000-2012 11.399752 63932.7873 64010.7646
mod Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 30082.9267 30122.2721 4.3456020 1981-1999 –> 2000-2012 7.956624 44912.3860 44987.2279
obs Indo-Pacific (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 40017.8800 40058.5868 5.1725247 1981-1999 –> 2000-2012 11.539920 64124.1910 64202.1683
mod Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 34753.7669 34801.4098 3.2651026 1981-1999 –> 2000-2012 5.965164 53008.9204 53100.2274
mod Indo-Pacific (27.25,27.5] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 34461.9345 34509.5774 3.1945016 1981-1999 –> 2000-2012 5.847420 52583.8909 52675.1980
mod Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 35781.4392 35822.2759 3.5269032 1981-1999 –> 2000-2012 6.322470 54297.4509 54375.7141
obs Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 40208.4146 40249.4433 4.4692749 1981-1999 –> 2000-2012 10.400338 65416.8565 65495.5558
mod Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 34214.8894 34262.5323 3.1359302 1981-1999 –> 2000-2012 5.729170 52164.7933 52256.1004
obs Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 40898.9032 40939.9319 4.6988588 1981-1999 –> 2000-2012 10.305518 65664.3323 65743.0315
obs Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 39834.5430 39882.4098 4.3490503 1981-1999 –> 2000-2012 9.973738 64627.2576 64719.0734
mod Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 34239.6053 34287.2481 3.1417414 1981-1999 –> 2000-2012 5.744088 52216.0175 52307.3246
mod Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate_star 34958.0151 34998.8518 3.3159379 1981-1999 –> 2000-2012 6.232916 53795.5140 53873.7772
mod Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 33426.9678 33474.6107 2.9562025 1981-1999 –> 2000-2012 5.451763 51086.5299 51177.8370
obs Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 39850.5836 39898.4504 4.3541143 1981-1999 –> 2000-2012 9.937713 64585.5527 64677.3685
obs Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 39808.4832 39856.3500 4.3408359 1981-1999 –> 2000-2012 9.956417 64588.4360 64680.2518
obs Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate_star 40477.9313 40518.9600 4.5575220 1981-1999 –> 2000-2012 10.203582 65298.5155 65377.2148
mod Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 34453.1239 34493.9606 3.1928723 1981-1999 –> 2000-2012 5.807390 52462.8218 52541.0850
obs Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate_star 40786.9639 40827.9926 4.6608541 1981-1999 –> 2000-2012 10.289583 65583.3350 65662.0343
mod Indo-Pacific (27.25,27.5] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 34485.9840 34526.8207 3.2007411 1981-1999 –> 2000-2012 5.826328 52527.6305 52605.8937
mod Indo-Pacific (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 34037.4187 34078.2554 3.0949816 1981-1999 –> 2000-2012 5.650998 51875.9916 51954.2548
obs Indo-Pacific (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate_star 40676.2582 40717.2869 4.6235706 1981-1999 –> 2000-2012 10.216104 65421.8193 65500.5185
obs Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate + phosphate_star 40762.6619 40803.6906 4.6526440 1981-1999 –> 2000-2012 10.274028 65548.7495 65627.4487
obs Indo-Pacific (27.25,27.5] cstar_tref ~ temp + silicate + phosphate_star 41129.8560 41164.0466 4.7789455 1981-1999 –> 2000-2012 10.425034 65948.4801 66014.0629
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 38328.1134 38376.7662 2.9021208 1981-1999 –> 2000-2012 5.351820 57981.7575 58074.8798
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate_star 38941.4256 38983.1281 3.0202516 1981-1999 –> 2000-2012 5.573254 58943.5002 59023.3193
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 38304.6613 38353.3141 2.8977110 1981-1999 –> 2000-2012 5.338981 57929.0624 58022.1848
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + nitrate + silicate + phosphate_star 39164.7476 39206.4500 3.0643053 1981-1999 –> 2000-2012 5.538744 58901.6429 58981.4620
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + silicate + phosphate + phosphate_star 39004.4509 39046.1534 3.0326197 1981-1999 –> 2000-2012 5.578396 58982.4763 59062.2954
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 39883.4223 39932.0751 3.2100670 1981-1999 –> 2000-2012 5.693285 59652.3655 59745.4879
obs Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate 43424.9659 43466.6621 4.0510955 1981-1999 –> 2000-2012 9.086489 69317.0446 69396.8871
obs Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate_star 43494.4991 43536.1953 4.0694210 1981-1999 –> 2000-2012 9.214970 69571.0838 69650.9264
obs Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 42706.6934 42755.3389 3.8660550 1981-1999 –> 2000-2012 8.993198 68754.7240 68847.8737
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 39895.2776 39943.9304 3.2125356 1981-1999 –> 2000-2012 5.702848 59688.4230 59781.5454
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 38721.9397 38770.5925 2.9771857 1981-1999 –> 2000-2012 5.616944 59009.5253 59102.6476
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 38667.8248 38716.4776 2.9667572 1981-1999 –> 2000-2012 5.364894 58140.9868 58234.1092
obs Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 42673.4917 42722.1372 3.8577322 1981-1999 –> 2000-2012 9.024720 68787.5247 68880.6743
obs Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 43504.4601 43546.1563 4.0720530 1981-1999 –> 2000-2012 9.236215 69611.8294 69691.6719
mod Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate 38868.9281 38910.6305 3.0060870 1981-1999 –> 2000-2012 5.667100 59222.5508 59302.3699
obs Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 42701.7588 42750.4044 3.8648169 1981-1999 –> 2000-2012 9.004862 68771.2185 68864.3681
obs Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 42799.9008 42841.5970 3.8900208 1981-1999 –> 2000-2012 9.113531 69004.6952 69084.5378
obs Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + phosphate 43665.4162 43700.1630 4.1153535 1981-1999 –> 2000-2012 9.156404 69565.0669 69631.6024
obs Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate_star 43521.1464 43562.8426 4.0764658 1981-1999 –> 2000-2012 9.203987 69567.8070 69647.6495
obs Indo-Pacific (27.5,27.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 43524.7875 43566.4837 4.0774294 1981-1999 –> 2000-2012 9.217605 69592.4634 69672.3059
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou 13681.7649 13705.7663 2.3959471 1981-1999 –> 2000-2012 4.680294 21569.7809 21615.6632
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + phosphate_star 13646.0064 13676.0082 2.3808261 1981-1999 –> 2000-2012 4.655990 21521.8839 21579.2368
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + phosphate + phosphate_star 13679.9211 13709.9228 2.3944034 1981-1999 –> 2000-2012 4.685951 21580.9830 21638.3358
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + silicate 13696.5211 13720.5225 2.4018825 1981-1999 –> 2000-2012 4.632756 21501.3948 21547.2771
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + silicate + phosphate_star 13627.6016 13657.6034 2.3734902 1981-1999 –> 2000-2012 4.590462 21412.5350 21469.8879
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou 13661.8898 13691.8915 2.3871752 1981-1999 –> 2000-2012 4.657808 21530.7702 21588.1230
obs Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate 21595.3757 21633.1400 3.5929854 1981-1999 –> 2000-2012 7.841756 33155.6159 33227.0305
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate_star 13434.3660 13470.3681 2.2970504 1981-1999 –> 2000-2012 4.491825 21185.9784 21254.8019
obs Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate_star 21571.7953 21609.5596 3.5824104 1981-1999 –> 2000-2012 7.841681 33141.9822 33213.3968
obs Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 21419.8331 21463.8915 3.5141252 1981-1999 –> 2000-2012 7.773392 32992.0167 33075.3337
obs Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 21404.0927 21448.1510 3.5072177 1981-1999 –> 2000-2012 7.779455 32988.5300 33071.8470
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + phosphate + phosphate_star 13439.7031 13475.7052 2.2991069 1981-1999 –> 2000-2012 4.497386 21196.9156 21265.7390
obs Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + phosphate + phosphate_star 21568.7772 21606.5415 3.5810592 1981-1999 –> 2000-2012 7.843392 33141.8609 33213.2754
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate 13698.5211 13728.5228 2.4018825 1981-1999 –> 2000-2012 4.631126 21502.8303 21560.1832
obs Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 21417.9139 21461.9722 3.5132822 1981-1999 –> 2000-2012 7.775568 32992.9523 33076.2693
mod Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 13540.7266 13576.7287 2.3383829 1981-1999 –> 2000-2012 4.522776 21275.6968 21344.5203
obs Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + phosphate 21594.6317 21626.1020 3.5935495 1981-1999 –> 2000-2012 7.846186 33156.5364 33216.0485
obs Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate_star 21435.7686 21473.5329 3.5220124 1981-1999 –> 2000-2012 7.784750 33009.2343 33080.6489
obs Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate_star 21413.6392 21451.4035 3.5122834 1981-1999 –> 2000-2012 7.793517 33004.5535 33075.9681
obs Indo-Pacific (27.75,27.85] cstar_tref ~ temp + silicate + phosphate + phosphate_star 21433.2682 21471.0325 3.5209118 1981-1999 –> 2000-2012 7.786482 33009.4111 33080.8256
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + silicate 15999.2581 16024.0986 2.1275439 1981-1999 –> 2000-2012 4.127985 24025.5728 24072.6075
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + silicate + phosphate_star 15991.8757 16022.9263 2.1248320 1981-1999 –> 2000-2012 4.119510 24009.2376 24068.0310
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou 15832.5018 15863.5524 2.0792909 1981-1999 –> 2000-2012 4.055500 23814.5531 23873.3465
obs Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate 29193.8919 29233.7368 3.1895452 1981-1999 –> 2000-2012 7.548178 45800.7887 45876.4060
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + phosphate_star 15609.6294 15646.8902 2.0166888 1981-1999 –> 2000-2012 3.853490 23315.9852 23386.5372
obs Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 29030.4201 29076.9059 3.1432445 1981-1999 –> 2000-2012 7.501796 45639.2091 45727.4293
obs Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 29053.0867 29099.5725 3.1495469 1981-1999 –> 2000-2012 7.519479 45676.8447 45765.0650
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + phosphate_star 15987.1422 16024.4029 2.1228879 1981-1999 –> 2000-2012 4.103241 23979.1453 24049.6973
obs Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 29030.2368 29076.7226 3.1431935 1981-1999 –> 2000-2012 7.486170 45618.4784 45706.6987
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + phosphate + phosphate_star 15618.4097 15655.6704 2.0190974 1981-1999 –> 2000-2012 3.860152 23333.5448 23404.0969
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate 15938.0885 15969.1391 2.1093519 1981-1999 –> 2000-2012 4.092963 23934.3318 23993.1252
obs Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 29055.4569 29101.9427 3.1502066 1981-1999 –> 2000-2012 7.523558 45683.7044 45771.9246
mod Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 15756.6370 15793.8977 2.0573972 1981-1999 –> 2000-2012 3.969554 23615.6149 23686.1670
obs Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + phosphate 29231.1849 29264.3890 3.2006397 1981-1999 –> 2000-2012 7.559659 45836.5901 45899.6046
mod Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + phosphate_star 16363.1112 16394.1618 2.2348180 1981-1999 –> 2000-2012 4.099648 24124.9541 24183.7475
obs Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 29030.6917 29070.5367 3.1438755 1981-1999 –> 2000-2012 7.502638 45637.7587 45713.3761
obs Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate_star 29055.4390 29095.2840 3.1507585 1981-1999 –> 2000-2012 7.521226 45677.9002 45753.5176
obs Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 29029.2003 29069.0452 3.1434612 1981-1999 –> 2000-2012 7.489222 45619.1208 45694.7382
mod Indo-Pacific (27.85,27.95] cstar_tref ~ temp + phosphate + phosphate_star 16374.0237 16405.0743 2.2381357 1981-1999 –> 2000-2012 4.107088 24144.2498 24203.0432
obs Indo-Pacific (27.85,27.95] cstar_tref ~ temp + silicate + phosphate + phosphate_star 29058.4992 29098.3442 3.1516107 1981-1999 –> 2000-2012 7.525711 45685.7295 45761.3469
mod Indo-Pacific (27.95,28.05] cstar_tref ~ sal + silicate + phosphate_star 18613.4300 18645.4074 1.9782137 1981-1999 –> 2000-2012 3.961363 28434.7361 28495.4859
mod Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou 18095.7525 18127.7299 1.8658675 1981-1999 –> 2000-2012 3.839722 27895.1461 27955.8959
obs Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + nitrate + phosphate 48523.2304 48573.3922 3.0543408 1981-1999 –> 2000-2012 7.417217 80737.5396 80834.0736
obs Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate 48593.1556 48636.1514 3.0658449 1981-1999 –> 2000-2012 7.438763 80831.0609 80913.8044
mod Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate_star 17499.6012 17537.9741 1.7439783 1981-1999 –> 2000-2012 3.519728 26807.7047 26880.6045
obs Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 48115.0682 48165.2299 2.9898696 1981-1999 –> 2000-2012 7.340417 80297.8677 80394.4018
obs Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 48343.9602 48394.1220 3.0258547 1981-1999 –> 2000-2012 7.418358 80633.6206 80730.1547
mod Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + phosphate_star 17850.6206 17888.9934 1.8145077 1981-1999 –> 2000-2012 3.711327 27466.3419 27539.2416
obs Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 48282.2477 48332.4095 3.0161102 1981-1999 –> 2000-2012 7.405732 80564.6011 80661.1351
mod Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + phosphate + phosphate_star 17506.5055 17544.8783 1.7453388 1981-1999 –> 2000-2012 3.524486 26823.5255 26896.4253
mod Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate 18327.3314 18359.3088 1.9153136 1981-1999 –> 2000-2012 3.881058 28107.5227 28168.2725
obs Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 48340.3200 48390.4818 3.0252791 1981-1999 –> 2000-2012 7.423303 80643.9649 80740.4990
mod Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate_star 17575.7688 17614.1416 1.7590458 1981-1999 –> 2000-2012 3.572578 26982.0666 27054.9664
obs Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate_star 48342.6296 48385.6254 3.0259606 1981-1999 –> 2000-2012 7.448537 80706.2581 80789.0016
obs Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate 48545.4891 48588.4849 3.0582160 1981-1999 –> 2000-2012 7.443461 80814.7356 80897.4791
obs Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 48124.2626 48174.4244 2.9913068 1981-1999 –> 2000-2012 7.373224 80387.0581 80483.5921
mod Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate_star 18754.2045 18786.1819 2.0099178 1981-1999 –> 2000-2012 3.843549 28209.9087 28270.6585
obs Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate 48274.4434 48317.4392 3.0151953 1981-1999 –> 2000-2012 7.425847 80608.0114 80690.7549
mod Indo-Pacific (27.95,28.05] cstar_tref ~ temp + nitrate + phosphate_star 18945.0797 18977.0570 2.0537182 1981-1999 –> 2000-2012 3.967923 28601.3556 28662.1054
mod Indo-Pacific (27.95,28.05] cstar_tref ~ temp + phosphate + phosphate_star 18771.4849 18803.4623 2.0138444 1981-1999 –> 2000-2012 3.851476 28237.3528 28298.1026
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 38107.7002 38156.3458 2.8682870 1981-1999 –> 2000-2012 7.088181 60145.4988 60237.9388
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 38172.6055 38214.3017 2.8807705 1981-1999 –> 2000-2012 7.103252 60213.1265 60292.3608
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate 38576.8123 38625.4579 2.9569696 1981-1999 –> 2000-2012 7.088099 60450.8304 60543.2704
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate 38682.5851 38724.2813 2.9777276 1981-1999 –> 2000-2012 7.109407 60555.6286 60634.8629
mod Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 10156.7063 10191.8767 1.7074014 1981-1999 –> 2000-2012 3.579486 16175.7362 16242.6565
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 38128.3555 38177.0011 2.8721352 1981-1999 –> 2000-2012 6.993776 59984.6582 60077.0982
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 38281.2279 38329.8734 2.9007770 1981-1999 –> 2000-2012 7.066811 60220.0650 60312.5050
mod Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + phosphate_star 10265.1716 10300.3420 1.7434456 1981-1999 –> 2000-2012 3.606678 16270.2862 16337.2065
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 38418.5324 38467.1779 2.9267455 1981-1999 –> 2000-2012 7.126796 60420.0188 60512.4588
mod Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + phosphate + phosphate_star 10158.9351 10194.1054 1.7081345 1981-1999 –> 2000-2012 3.580038 16177.6807 16244.6010
mod Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate 10376.7529 10406.0615 1.7820058 1981-1999 –> 2000-2012 3.687006 16444.9557 16500.7226
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 38256.5840 38305.2295 2.8961405 1981-1999 –> 2000-2012 7.070321 60210.4709 60302.9109
mod Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 9679.5542 9714.7245 1.5574831 1981-1999 –> 2000-2012 3.219037 15348.3210 15415.2413
obs Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate_star 38424.0178 38465.7140 2.9281678 1981-1999 –> 2000-2012 7.141421 60447.6838 60526.9181
obs Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 38383.8566 38432.5022 2.9201654 1981-1999 –> 2000-2012 7.097052 60342.7364 60435.1764
mod Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + phosphate_star 10377.6599 10406.9685 1.7823172 1981-1999 –> 2000-2012 3.667686 16415.4498 16471.2167
mod Indo-Pacific (28.05,28.1] cstar_tref ~ temp + nitrate + phosphate_star 10418.0206 10447.3293 1.7962262 1981-1999 –> 2000-2012 3.659674 16421.4741 16477.2411
mod Indo-Pacific (28.05,28.1] cstar_tref ~ temp + phosphate + phosphate_star 10382.3734 10411.6821 1.7839360 1981-1999 –> 2000-2012 3.669295 16420.1488 16475.9157
mod Indo-Pacific (28.05,28.1] cstar_tref ~ temp + silicate 10493.5876 10517.0345 1.8232628 1981-1999 –> 2000-2012 3.790131 16653.6267 16698.2402
mod Indo-Pacific (28.05,28.1] cstar_tref ~ temp + silicate + phosphate_star 9997.5394 10026.8480 1.6564911 1981-1999 –> 2000-2012 3.329793 15684.9917 15740.7586
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate_star 102692.2499 102741.3695 1.6738735 1981-1999 –> 2000-2012 4.187611 179545.0500 179640.4049
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate_star 103323.3659 103372.4855 1.6938907 1981-1999 –> 2000-2012 4.189730 179941.5968 180036.9517
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + silicate + phosphate + phosphate_star 102017.6774 102066.7970 1.6527394 1981-1999 –> 2000-2012 4.164715 178847.4614 178942.8163
obs Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 48099.8315 48150.0261 2.9525389 1981-1999 –> 2000-2012 6.872030 89330.3575 89428.9168
obs Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 48921.1855 48971.3802 3.0814348 1981-1999 –> 2000-2012 7.070512 90412.1612 90510.7205
obs Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate 48395.0612 48438.0852 2.9985488 1981-1999 –> 2000-2012 6.932741 89678.9949 89763.4743
obs Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 48349.8136 48400.0083 2.9911874 1981-1999 –> 2000-2012 6.921415 89620.8232 89719.3825
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 98558.0766 98615.3827 1.5484148 1981-1999 –> 2000-2012 3.971969 174213.4913 174324.7387
obs Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 48743.7917 48793.9863 3.0531280 1981-1999 –> 2000-2012 7.056331 90287.0854 90385.6447
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 107385.8395 107434.9591 1.8285962 1981-1999 –> 2000-2012 4.161902 181793.4545 181888.8094
obs Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + phosphate_star 48979.4986 49022.5226 3.0911186 1981-1999 –> 2000-2012 7.105786 90563.1142 90647.5936
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 98781.8579 98839.1641 1.5549553 1981-1999 –> 2000-2012 3.887920 173186.6738 173297.9212
obs Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 48940.6364 48990.8311 3.0845545 1981-1999 –> 2000-2012 7.097693 90520.6161 90619.1753
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 98557.5951 98614.9013 1.5484007 1981-1999 –> 2000-2012 3.971807 174210.9983 174322.2457
mod Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + silicate + phosphate_star 98784.7772 98833.8968 1.5550994 1981-1999 –> 2000-2012 4.005121 174794.7620 174890.1170
obs Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate 48876.7753 48919.7993 3.0746436 1981-1999 –> 2000-2012 7.001614 90133.5149 90217.9943
obs Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 48708.3455 48758.5401 3.0475031 1981-1999 –> 2000-2012 6.962253 89920.9577 90019.5170
obs Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate 49371.7659 49414.7899 3.1548478 1981-1999 –> 2000-2012 7.089040 90655.6981 90740.1775
mod Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + phosphate_star 107418.0205 107458.9535 1.8297739 1981-1999 –> 2000-2012 4.173337 181967.6447 182047.1071
mod Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate_star 105321.2703 105370.3898 1.7588505 1981-1999 –> 2000-2012 4.093845 179752.6380 179847.9929

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]]

Version Author Date
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]]

Version Author Date
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]]

Version Author Date
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]]

Version Author Date
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)

Version Author Date
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)

Version Author Date
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] 4 4 7 6 10 4 10
(26,26.5] 6 5 5 6 9 6 10
(26.5,26.75] 7 5 6 6 3 6 7
(26.75,27] 6 2 5 7 6 10 8
(27,27.25] 5 2 5 8 8 8 6
(27.25,27.5] 6 3 4 6 7 2 9
(27.5,27.75] 5 2 5 7 10 6 9
(27.75,27.85] 6 4 4 5 10 9 7
(27.85,27.95] 6 2 5 6 10 7 9
(27.95,28.05] 8 NA 4 6 6 5 10
(28.05,28.1] 5 1 2 7 7 4 6
(28.1,28.15] 7 2 4 4 4 4 7
(28.15,28.2] 7 4 3 5 4 3 3
(28.2, Inf] 5 7 2 6 5 7 8
total 83.00 — 61.00 85.00 99.00 81.00 109.00
Indo-Pacific - mod
(-Inf,26] 5 5 5 7 10 5 10
(26,26.5] 4 5 4 10 6 8 10
(26.5,26.75] 4 6 3 10 4 7 10
(26.75,27] 2 8 3 10 3 6 10
(27,27.25] 3 8 3 10 3 5 10
(27.25,27.5] 3 9 4 10 7 5 7
(27.5,27.75] 3 7 5 8 10 8 5
(27.75,27.85] 4 NA 2 6 10 4 5
(27.85,27.95] 3 1 2 7 8 4 8
(27.95,28.05] 3 2 2 8 7 3 9
(28.05,28.1] 2 2 2 8 5 4 10
(28.1, Inf] 2 5 2 10 8 8 7
total 38.00 — 37.00 104.00 81.00 67.00 101.00
Atlantic - obs
(-Inf,26] 7 10 6 6 4 4 10
(26,26.5] 10 6 8 2 6 5 6
(26.5,26.75] 4 4 NA 10 4 5 6
(26.75,27] 4 4 1 10 5 6 10
(27,27.25] 4 2 3 10 6 7 10
(27.25,27.5] 6 NA 7 7 5 5 10
(27.5,27.75] 7 NA 8 5 6 8 8
(27.75,27.85] 4 NA 7 5 5 10 4
(27.85,27.95] 5 NA 7 6 7 10 6
(27.95,28.05] 6 1 6 6 10 4 4
(28.05,28.1] 4 2 4 8 10 1 6
(28.1,28.15] 2 2 2 8 5 2 5
(28.15,28.2] 2 1 2 8 5 2 6
(28.2, Inf] 8 1 5 6 6 3 9
total 73.00 — — 97.00 84.00 72.00 100.00
Indo-Pacific - obs
(-Inf,26] 7 5 4 5 10 6 10
(26,26.5] 3 4 3 10 10 4 10
(26.5,26.75] 3 8 2 10 4 5 10
(26.75,27] 4 5 4 9 3 8 5
(27,27.25] 4 3 2 10 7 9 7
(27.25,27.5] 3 2 4 9 6 9 9
(27.5,27.75] 5 1 5 8 7 6 10
(27.75,27.85] 5 2 5 8 6 6 10
(27.85,27.95] 6 2 6 6 5 8 10
(27.95,28.05] 7 4 7 4 7 7 10
(28.05,28.1] 7 4 7 4 9 8 8
(28.1, Inf] 7 7 7 4 7 4 10
total 61.00 47.00 56.00 87.00 81.00 80.00 109.00

7.4 RMSE alternatives

7.4.1 AIC

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

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

Version Author Date
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)

Version Author Date
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)

Version Author Date
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)

Version Author Date
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)

Version Author Date
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)

Version Author Date
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)

Version Author Date
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)

Version Author Date
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]]

Version Author Date
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]]

Version Author Date
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]]

Version Author Date
a79ca2c jens-daniel-mueller 2021-04-09
d3c3fde jens-daniel-mueller 2021-03-26
594d503 jens-daniel-mueller 2021-03-26 

[[4]]

Version Author Date
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]]

Version Author Date
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]]

Version Author Date
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)

Version Author Date
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)

Version Author Date
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()

Version Author Date
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 

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