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

6.3 Target variable coefficients

A data frame to map the target variable is prepared.

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

eras_backward <- GLODAP_glanced %>%
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> ")) %>% 
  ungroup() %>% 
  select(era, eras) %>% 
  unique()

eras_era <- full_join(eras_backward, eras_forward) %>% 
  filter(str_detect(eras, "NA") == FALSE)

# extend best model selection from eras to era
lm_best <- full_join(
  lm_best_eras %>% select(data_source, basin, gamma_slab, model, eras),
  eras_era) %>% 
  drop_na() %>% 
  arrange(era, basin, gamma_slab, data_source)

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

rm(eras_era, eras_forward, eras_backward)

6.4 Cant coeffcients

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

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

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

6.5 Write files

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


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

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

7 Model diagnotics

7.1 Selection criterion vs predictors

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

7.1.1 All models

GLODAP_glanced %>%
  group_split(era) %>%
  map(
    ~ ggplot(data = .x,
             aes(
               as.factor(n_predictors),
               !!sym(params_local$MLR_criterion),
               col = data_source
             )) +
      geom_hline(yintercept = c(0, 10)) +
      geom_boxplot() +
      facet_grid(gamma_slab ~ basin) +
      scale_color_brewer(palette = "Set1") +
      ylim(c(0, NA)) +
      labs(x = "Number of predictors",
           title = paste("Era:", unique(.x$era)))
  )
[[1]]

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

[[2]]

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

7.1.2 Best models

left_join(lm_best_target %>% select(basin, gamma_slab, era, model),
          GLODAP_glanced) %>%
  group_split(era) %>%
  imap(
  ~ ggplot(data = .x,
         aes("",
             !!sym(params_local$MLR_criterion),
             col = data_source)) +
  geom_hline(yintercept = c(0, 10)) +
  geom_boxplot() +
  facet_grid(gamma_slab ~ basin) +
  scale_color_brewer(palette = "Set1") +
  ylim(c(0, NA)) +
  labs(x = "Number of predictors pooled",
           title = paste("Era:", unique(.x$era)))
  )
[[1]]

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

[[2]]

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

7.2 RMSE correlation between eras

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

7.2.1 All models

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

lm_all_eras %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0, max_rmse),
              ylim = c(0, max_rmse)) +
  geom_abline(slope = 1,
              col = 'red') +
  facet_grid(data_source ~ basin)

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

7.2.2 Best models

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

lm_best_eras %>%
  ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  coord_equal(xlim = c(0, max_rmse),
              ylim = c(0, max_rmse)) +
  geom_abline(slope = 1,
              col = 'red') +
  facet_grid(data_source ~ basin)

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

7.3 Predictor counts

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

# calculate cases of predictor used
lm_all_stats <- lm_best_cant %>% 
  pivot_longer(starts_with("delta_coeff_"),
               names_to = "term",
               names_prefix = "delta_coeff_",
               values_to = "delta_coeff") %>% 
  filter(term != "(Intercept)",
         delta_coeff != 0) %>% 
  group_by(data_source, basin, gamma_slab) %>% 
  count(term) %>% 
  ungroup() %>% 
  pivot_wider(values_from = n, names_from = term)

# print table
lm_all_stats %>%
  gt(rowname_col = "gamma_slab",
     groupname_col = c("basin", "data_source")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )
aou nitrate phosphate phosphate_star sal silicate temp
Atlantic - mod
(-Inf,26] 4 5 6 4 10 6 10
(26,26.5] 6 5 5 6 9 6 10
(26.5,26.75] 8 5 6 6 4 5 6
(26.75,27] 6 1 6 7 7 10 7
(27,27.25] 5 2 5 8 8 8 6
(27.25,27.5] 6 5 3 5 8 1 8
(27.5,27.75] 5 2 5 7 10 6 9
(27.75,27.85] 5 4 4 6 10 10 6
(27.85,27.95] 6 3 5 5 10 8 8
(27.95,28.05] 8 NA 4 6 6 5 10
(28.05,28.1] 5 1 2 7 7 4 6
(28.1,28.15] 7 2 4 4 4 4 7
(28.15,28.2] 7 4 3 5 4 3 3
(28.2, Inf] 5 7 2 6 5 7 8
total 83.00 — 60.00 82.00 102.00 83.00 104.00
Indo-Pacific - mod
(-Inf,26] 5 5 5 7 10 5 10
(26,26.5] 4 5 4 10 6 8 10
(26.5,26.75] 4 6 3 10 4 7 10
(26.75,27] 2 8 3 10 3 6 10
(27,27.25] 3 8 3 10 3 5 10
(27.25,27.5] 3 9 4 10 7 5 7
(27.5,27.75] 3 7 5 8 10 8 5
(27.75,27.85] 4 NA 2 6 10 4 5
(27.85,27.95] 3 1 2 7 8 4 8
(27.95,28.05] 3 1 2 7 8 4 8
(28.05,28.1] 2 2 2 9 6 4 9
(28.1, Inf] 2 5 2 10 8 8 7
total 38.00 — 37.00 104.00 83.00 68.00 99.00
Atlantic - obs
(-Inf,26] 7 10 6 6 4 4 10
(26,26.5] 10 6 8 2 6 5 6
(26.5,26.75] 4 4 NA 10 4 5 6
(26.75,27] 4 4 1 10 5 6 10
(27,27.25] 4 2 3 10 6 7 10
(27.25,27.5] 6 NA 7 7 5 5 10
(27.5,27.75] 7 NA 8 5 6 8 8
(27.75,27.85] 4 NA 7 5 5 10 4
(27.85,27.95] 5 NA 7 6 7 10 6
(27.95,28.05] 6 1 6 6 10 4 4
(28.05,28.1] 4 2 4 8 10 1 6
(28.1,28.15] 2 2 2 8 5 2 5
(28.15,28.2] 2 1 2 8 5 2 6
(28.2, Inf] 8 1 5 6 6 3 9
total 73.00 — — 97.00 84.00 72.00 100.00
Indo-Pacific - obs
(-Inf,26] 7 5 4 5 10 6 10
(26,26.5] 3 4 3 10 10 4 10
(26.5,26.75] 3 8 2 10 4 5 10
(26.75,27] 4 5 4 9 3 8 5
(27,27.25] 4 3 2 10 7 9 7
(27.25,27.5] 3 2 4 9 6 9 9
(27.5,27.75] 5 1 5 8 7 6 10
(27.75,27.85] 5 2 5 8 6 6 10
(27.85,27.95] 6 2 6 6 5 8 10
(27.95,28.05] 7 4 7 4 7 7 10
(28.05,28.1] 7 4 7 4 9 8 8
(28.1, Inf] 7 7 7 4 7 4 10
total 61.00 47.00 56.00 87.00 81.00 80.00 109.00

7.4 RMSE alternatives

7.4.1 AIC

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

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

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

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

7.4.2 AIC vs BIC

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

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

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

7.5 RMSE vs VIF

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

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

7.6 Residual patterns

7.6.1 Fitted vs actual models

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

GLODAP_augmented_best <- left_join(
  lm_best_target %>% select(data_source, basin, gamma_slab, era, model),
  GLODAP_augmented
)
# calculate equal axis limits and binwidth
axis_lims <- GLODAP_augmented %>%
  summarise(
    max_value = max(
      c(max(.fitted, max(!!sym(params_local$MLR_target))))
      ),
    min_value = min(
      c(min(.fitted, min(!!sym(params_local$MLR_target))))
    )
  )

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

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

Version Author Date
594d503 jens-daniel-mueller 2021-03-26
2eb881a jens-daniel-mueller 2021-03-26
03b6009 jens-daniel-mueller 2021-03-23
de6256b jens-daniel-mueller 2021-03-23
33b385b jens-daniel-mueller 2021-03-20
108d6b2 jens-daniel-mueller 2021-03-20
83a13de jens-daniel-mueller 2021-03-20
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
27ae473 jens-daniel-mueller 2021-02-24
4bc00ea jens-daniel-mueller 2021-02-24 
GLODAP_augmented_best %>%
  ggplot(aes(cstar_tref, .fitted)) +
  geom_bin2d(binwidth = i_binwidth) +
  scale_fill_viridis_c() +
  geom_abline(slope = 1,
              col = 'red') +
  coord_equal(xlim = axis_lims,
              ylim = axis_lims) +
  labs(title = "Selected models") +
  facet_wrap(~data_source)

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

7.6.2 Pooled

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

i_ylim <- c(-30,30)

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

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

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

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

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

7.6.3 By model domain

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

GLODAP_augmented_best %>% 
  group_split(basin, era) %>% 
  map(~ ggplot(data = .x, aes(lat, .resid)) +
      geom_bin2d(binwidth = i_binwidth) +
      geom_hline(yintercept = 0, col = "black") +
      scale_fill_viridis_c() +
      facet_grid(gamma_slab ~ data_source) +
      coord_cartesian(ylim = i_ylim) +
      labs(
        title = paste(
          "Target:",
          params_local$MLR_target,
          "| best models | basin:",
          unique(.x$basin),
          "| era:",
          unique(.x$era)
        )
      ))
[[1]]

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

[[2]]

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

[[3]]

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

[[4]]

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

7.6.4 Latitudinal mean

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

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

lat_residual %>%
  group_split(basin) %>% 
  map(
  ~ggplot(data = .x,
          aes(lat_grid, .resid_mean, col=era)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 0, col = "black") +
  facet_grid(gamma_slab ~ data_source) +
    labs(title = paste("Basin:", unique(.x$basin)))
  )
[[1]]

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

[[2]]

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

7.6.5 Latitudinal offset

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

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

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

8 VIF

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

Version Author Date
594d503 jens-daniel-mueller 2021-03-26
2eb881a jens-daniel-mueller 2021-03-26
03b6009 jens-daniel-mueller 2021-03-23
de6256b jens-daniel-mueller 2021-03-23
380d215 jens-daniel-mueller 2021-03-21
33b385b jens-daniel-mueller 2021-03-20
108d6b2 jens-daniel-mueller 2021-03-20
330dcd0 jens-daniel-mueller 2021-03-20 
GLODAP_glanced_vif %>% 
  ggplot(aes(Variables,
             log10(VIF),
             col = data_source)) + 
  geom_hline(yintercept = log10(params_local$vif_max)) +
  geom_violin() +
  scale_color_brewer(palette = "Set1") +
  facet_grid(gamma_slab~basin) +
  coord_flip()

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

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