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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)

i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
print(i_gamma_slab)

# subset one gamma slab
GLODAP_basin_era_slab <- GLODAP_basin_era %>%
  filter(gamma_slab == i_gamma_slab)

# fit the full linear model, i.e. all predictor combinations
lm_full <- lm(paste(
  params_local$MLR_target,
  paste(params_local$MLR_predictors, collapse = " + "),
  sep = " ~ "
),
data = GLODAP_basin_era_slab)

# fit linear models for all possible predictor combinations
# unfortunately, this functions does not provide model coefficients (yet)
lm_all <- ols_step_all_possible(lm_full)

# convert to tibble
lm_all <- as_tibble(lm_all)

# 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.

# GLODAP_NA <- GLODAP %>% 
#   filter_all(any_vars(is.na(.)))

# prepare nested data frame

GLODAP %>% 
  # filter(basin %in% unique(GLODAP$basin)[1],
  #        era %in% unique(GLODAP$era)[c(1,2)],
  #        gamma_slab %in% unique(GLODAP$gamma_slab)[c(5,6)]) %>%
  filter_all(any_vars(is.na(.)))

GLODAP_nested <- GLODAP %>% 
  # filter(basin %in% unique(GLODAP$basin)[1],
  #        era %in% unique(GLODAP$era)[c(1,2)],
  #        gamma_slab %in% unique(GLODAP$gamma_slab)[c(5,6)]) %>%
  drop_na() %>% 
  group_by(gamma_slab, era, basin) %>% 
  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)
  )

# 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)) %>%
  unnest(glanced) %>% 
  rename(n_predictors = n)

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

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

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

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

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


# extract input data
GLODAP_data <- GLODAP_nested_lm_fit %>%
  select(-c(fit, tidied, glanced, augmented)) %>%
  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 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  %>%
  select(basin, gamma_slab, model, era, AIC, rmse) %>% 
  arrange(era) %>% 
  group_by(basin, gamma_slab, model) %>% 
  mutate(eras = paste(lag(era), era, sep = " --> "),
         rmse_sum = rmse + lag(rmse),
         aic_sum = AIC + lag(AIC)
         ) %>% 
  ungroup() %>% 
  select(-c(era)) %>% 
  drop_na()

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

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


# print table
lm_best_eras %>% 
  kable() %>%
  add_header_above() %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "400px")
basin gamma_slab model AIC rmse eras rmse_sum aic_sum
Atlantic (-Inf,26] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 433.5759 5.060507 1982-1999 –> 2000-2012 11.063216 1006.3159
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 426.9397 4.822913 1982-1999 –> 2000-2012 10.638669 994.1743
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 429.6772 4.919542 1982-1999 –> 2000-2012 10.714379 996.2849
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 429.9839 4.930486 1982-1999 –> 2000-2012 10.721708 996.4830
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 431.6894 4.991797 1982-1999 –> 2000-2012 10.773905 997.9144
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 434.4733 5.093520 1982-1999 –> 2000-2012 10.882371 1000.9011
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 433.2529 5.048674 1982-1999 –> 2000-2012 10.999538 1004.4835
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 433.1999 5.046737 1982-1999 –> 2000-2012 10.977427 1003.8397
Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 432.8407 5.107100 1982-1999 –> 2000-2012 11.144378 1004.5799
Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 433.1747 5.045817 1982-1999 –> 2000-2012 10.939449 1002.7239
Atlantic (-Inf,26] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 264.8034 2.467771 2000-2012 –> 2013-2019 7.528278 698.3793
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 263.7707 2.444286 2000-2012 –> 2013-2019 7.267199 690.7104
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 263.7465 2.443738 2000-2012 –> 2013-2019 7.363280 693.4237
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 263.7516 2.443853 2000-2012 –> 2013-2019 7.374339 693.7355
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 263.7655 2.444167 2000-2012 –> 2013-2019 7.435965 695.4548
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 264.4908 2.460638 2000-2012 –> 2013-2019 7.554158 698.9641
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate_star 262.7366 2.466246 2000-2012 –> 2013-2019 7.560904 695.2407
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 264.6962 2.465323 2000-2012 –> 2013-2019 7.513997 697.9491
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 264.6081 2.463311 2000-2012 –> 2013-2019 7.510048 697.8080
Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 264.4925 2.460677 2000-2012 –> 2013-2019 7.506494 697.6672
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 4216.2379 5.349300 1982-1999 –> 2000-2012 10.251367 7387.2633
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4218.2375 5.349298 1982-1999 –> 2000-2012 10.227524 7386.1435
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 4215.0803 5.336876 1982-1999 –> 2000-2012 10.233900 7387.0248
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 4254.3984 5.493653 1982-1999 –> 2000-2012 10.413746 7431.2777
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4274.0663 5.573797 1982-1999 –> 2000-2012 10.520996 7456.7145
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4267.8893 5.548501 1982-1999 –> 2000-2012 10.366152 7422.6754
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate 4252.5273 5.494174 1982-1999 –> 2000-2012 10.414350 7427.4242
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4203.1163 5.290065 1982-1999 –> 2000-2012 10.116973 7359.9183
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4252.1077 5.484394 1982-1999 –> 2000-2012 10.382229 7424.2261
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4270.3605 5.558607 1982-1999 –> 2000-2012 10.483621 7448.2894
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 711.1223 2.938581 2000-2012 –> 2013-2019 8.287880 4927.3602
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 712.6200 2.933314 2000-2012 –> 2013-2019 8.282612 4930.8575
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 712.7803 2.934994 2000-2012 –> 2013-2019 8.271870 4927.8606
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 712.5692 2.932782 2000-2012 –> 2013-2019 8.426435 4966.9676
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 712.6575 2.933706 2000-2012 –> 2013-2019 8.507503 4986.7238
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate 710.8118 2.935324 2000-2012 –> 2013-2019 8.429499 4963.3391
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 712.8071 2.935275 2000-2012 –> 2013-2019 8.225340 4915.9234
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate_star 710.8439 2.935660 2000-2012 –> 2013-2019 8.509569 4982.9375
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 712.5068 2.932129 2000-2012 –> 2013-2019 8.416523 4964.6145
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 712.6199 2.933313 2000-2012 –> 2013-2019 8.491920 4982.9804
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 6295.3678 5.324324 1982-1999 –> 2000-2012 9.299431 10580.6266
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6305.2080 5.350170 1982-1999 –> 2000-2012 9.149115 10521.2961
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 6296.0631 5.326146 1982-1999 –> 2000-2012 9.288517 10576.4251
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6302.8257 5.343901 1982-1999 –> 2000-2012 9.268609 10568.6132
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6296.7858 5.328041 1982-1999 –> 2000-2012 9.293241 10578.2370
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 6304.5404 5.353680 1982-1999 –> 2000-2012 9.322087 10585.2253
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6304.1559 5.347401 1982-1999 –> 2000-2012 9.262375 10566.1541
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 6320.3404 5.390162 1982-1999 –> 2000-2012 9.219918 10548.7550
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 6318.5238 5.390649 1982-1999 –> 2000-2012 9.237930 10551.9056
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6315.8533 5.378273 1982-1999 –> 2000-2012 9.209640 10544.9098
Atlantic (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 742.4267 3.145410 2000-2012 –> 2013-2019 8.512765 7054.1511
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate 742.7777 3.149300 2000-2012 –> 2013-2019 8.480674 7040.8342
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 744.3377 3.166647 2000-2012 –> 2013-2019 8.490971 7039.7055
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 740.2960 3.121900 2000-2012 –> 2013-2019 8.472070 7045.5040
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 743.5742 3.158145 2000-2012 –> 2013-2019 8.484291 7039.6373
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 744.9560 3.173548 2000-2012 –> 2013-2019 8.517450 7047.7817
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 744.1193 3.164212 2000-2012 –> 2013-2019 8.492252 7040.9050
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 738.8201 3.105718 2000-2012 –> 2013-2019 8.495880 7059.1605
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 739.0514 3.130215 2000-2012 –> 2013-2019 8.520864 7057.5753
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 740.1362 3.120144 2000-2012 –> 2013-2019 8.498417 7055.9896
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 7189.4312 5.221245 1982-1999 –> 2000-2012 9.649750 12523.2424
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 7205.5754 5.257454 1982-1999 –> 2000-2012 9.666022 12531.1294
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7178.5605 5.197004 1982-1999 –> 2000-2012 9.605098 12503.9179
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 7181.7149 5.204026 1982-1999 –> 2000-2012 9.604609 12503.9510
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7177.7390 5.195176 1982-1999 –> 2000-2012 9.604501 12503.6071
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 7204.3618 5.254723 1982-1999 –> 2000-2012 9.688344 12540.2856
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7214.1164 5.276711 1982-1999 –> 2000-2012 9.700291 12545.8909
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7170.4959 5.179093 1982-1999 –> 2000-2012 9.630671 12513.8168
Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7214.0468 5.276554 1982-1999 –> 2000-2012 9.699708 12545.6451
Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 7212.1700 5.276833 1982-1999 –> 2000-2012 9.704473 12543.6238
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 1530.1553 3.698619 2000-2012 –> 2013-2019 8.956073 8735.7307
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1530.3716 3.700058 2000-2012 –> 2013-2019 8.897062 8708.9321
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 1532.9071 3.716969 2000-2012 –> 2013-2019 8.920996 8714.6219
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1530.4432 3.700534 2000-2012 –> 2013-2019 8.895711 8708.1822
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1532.4144 3.713677 2000-2012 –> 2013-2019 8.990389 8746.5307
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 1532.1990 3.712239 2000-2012 –> 2013-2019 8.891332 8702.6949
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate_star 1530.4894 3.714179 2000-2012 –> 2013-2019 8.992068 8743.1274
Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 1532.4660 3.714022 2000-2012 –> 2013-2019 8.990576 8746.5128
Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 1531.4068 3.720312 2000-2012 –> 2013-2019 8.997145 8743.5769
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 1530.5559 3.714622 2000-2012 –> 2013-2019 8.991234 8742.6280
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 13998.2652 5.195466 1982-1999 –> 2000-2012 10.401321 25317.4388
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 13945.7114 5.135932 1982-1999 –> 2000-2012 10.311773 25243.5833
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 13973.3431 5.167148 1982-1999 –> 2000-2012 10.322528 25256.6227
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 13950.1874 5.140976 1982-1999 –> 2000-2012 10.316097 25247.5477
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 14070.5905 5.278527 1982-1999 –> 2000-2012 10.481067 25387.4171
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 14008.8295 5.207516 1982-1999 –> 2000-2012 10.368610 25296.1903
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 13976.3552 5.170562 1982-1999 –> 2000-2012 10.392880 25307.1607
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate_star 14021.3967 5.224179 1982-1999 –> 2000-2012 10.448953 25351.9343
Atlantic (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 14018.6991 5.218800 1982-1999 –> 2000-2012 10.384194 25309.1286
Atlantic (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 14026.6066 5.230151 1982-1999 –> 2000-2012 10.454694 25356.9817
Atlantic (27,27.25] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3182.3642 4.648874 2000-2012 –> 2013-2019 10.042840 17351.6047
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 3219.2737 4.811725 2000-2012 –> 2013-2019 10.007191 17217.5389
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3224.9950 4.837474 2000-2012 –> 2013-2019 9.973406 17170.7063
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3220.9256 4.819145 2000-2012 –> 2013-2019 9.986293 17194.2687
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3225.1036 4.837964 2000-2012 –> 2013-2019 9.978940 17175.2910
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3213.1008 4.784097 2000-2012 –> 2013-2019 10.004508 17233.2073
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3183.8217 4.655199 2000-2012 –> 2013-2019 9.933726 17254.4121
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3189.8172 4.681308 2000-2012 –> 2013-2019 9.888824 17198.6467
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3233.9271 4.877949 2000-2012 –> 2013-2019 10.048511 17210.2824
Atlantic (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3186.8033 4.668165 2000-2012 –> 2013-2019 9.886964 17205.5024
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 14494.4155 4.261438 1982-1999 –> 2000-2012 8.767104 27808.0152
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 14436.3401 4.212692 1982-1999 –> 2000-2012 8.702940 27734.3493
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 14429.8911 4.207314 1982-1999 –> 2000-2012 8.725569 27756.1805
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 14456.7748 4.231456 1982-1999 –> 2000-2012 8.812991 27844.3181
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 14453.5260 4.227059 1982-1999 –> 2000-2012 8.808336 27842.8139
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 14457.6698 4.230530 1982-1999 –> 2000-2012 8.810934 27846.0903
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 14460.2734 4.232712 1982-1999 –> 2000-2012 8.831390 27866.8017
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 14425.8024 4.203907 1982-1999 –> 2000-2012 8.706700 27736.5006
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 14452.5828 4.227944 1982-1999 –> 2000-2012 8.823282 27853.8076
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 14454.5194 4.227890 1982-1999 –> 2000-2012 8.820438 27854.9812
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 2957.8047 3.609736 2000-2012 –> 2013-2019 7.977174 17574.2506
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2955.8845 3.596777 2000-2012 –> 2013-2019 7.947170 17554.5900
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 2954.5051 3.592228 2000-2012 –> 2013-2019 7.853665 17448.9206
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 2955.1080 3.594215 2000-2012 –> 2013-2019 7.806908 17391.4481
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2962.7295 3.619435 2000-2012 –> 2013-2019 7.826748 17392.6206
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2957.4910 3.602082 2000-2012 –> 2013-2019 7.805989 17383.2935
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate 2961.5444 3.622142 2000-2012 –> 2013-2019 7.987186 17575.2215
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 2958.5877 3.605708 2000-2012 –> 2013-2019 7.969140 17572.4007
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 2961.6867 3.615974 2000-2012 –> 2013-2019 7.954872 17547.0364
Atlantic (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 2969.0584 3.640512 2000-2012 –> 2013-2019 7.984661 17560.5143
Atlantic (27.5,27.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 16542.1647 4.153216 1982-1999 –> 2000-2012 8.451668 29135.2541
Atlantic (27.5,27.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 16550.7344 4.160774 1982-1999 –> 2000-2012 8.495835 29178.9020
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 16517.5545 4.135673 1982-1999 –> 2000-2012 8.453426 29130.2316
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 16508.0357 4.128908 1982-1999 –> 2000-2012 8.459687 29133.8835
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 16544.2177 4.154683 1982-1999 –> 2000-2012 8.527226 29212.0243
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 16517.5032 4.135637 1982-1999 –> 2000-2012 8.489917 29167.0107
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 16541.2709 4.152578 1982-1999 –> 2000-2012 8.463300 29146.8235
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 16550.1225 4.160336 1982-1999 –> 2000-2012 8.505584 29188.5519
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 16551.4539 4.159857 1982-1999 –> 2000-2012 8.487432 29174.0648
Atlantic (27.5,27.75] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 16553.7450 4.161497 1982-1999 –> 2000-2012 8.498705 29186.0780
Atlantic (27.5,27.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 4005.9956 4.155211 2000-2012 –> 2013-2019 8.308427 20548.1604
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 4017.4319 4.189196 2000-2012 –> 2013-2019 8.436014 20689.1732
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 4068.5317 4.344473 2000-2012 –> 2013-2019 8.473381 20576.5673
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4054.6796 4.301821 2000-2012 –> 2013-2019 8.456504 20598.8973
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4061.0942 4.321520 2000-2012 –> 2013-2019 8.457157 20578.5974
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4003.9913 4.149283 2000-2012 –> 2013-2019 8.301861 20545.2621
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 4012.2841 4.173864 2000-2012 –> 2013-2019 8.360224 20600.6628
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4054.4335 4.301067 2000-2012 –> 2013-2019 8.460924 20605.8874
Atlantic (27.5,27.75] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 4004.1272 4.149685 2000-2012 –> 2013-2019 8.311182 20557.8721
Atlantic (27.5,27.75] cstar_tref ~ temp + silicate + phosphate + phosphate_star 4059.3789 4.322396 2000-2012 –> 2013-2019 8.492044 20622.4998
Atlantic (27.75,27.85] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 10874.8814 4.034012 1982-1999 –> 2000-2012 8.362141 16916.5959
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 10858.2725 4.016691 1982-1999 –> 2000-2012 8.306815 16881.5535
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 10882.7359 4.044323 1982-1999 –> 2000-2012 8.362560 16917.6679
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 10884.5370 4.044115 1982-1999 –> 2000-2012 8.362146 16921.3692
Atlantic (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 10869.0211 4.027892 1982-1999 –> 2000-2012 8.329790 16898.0306
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 10884.3038 4.043871 1982-1999 –> 2000-2012 8.360824 16920.6147
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10883.4760 4.043004 1982-1999 –> 2000-2012 8.368096 16923.7234
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 10869.1603 4.028037 1982-1999 –> 2000-2012 8.356187 16910.8848
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 10861.7672 4.020329 1982-1999 –> 2000-2012 8.356907 16907.5574
Atlantic (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 10865.2986 4.024009 1982-1999 –> 2000-2012 8.354192 16908.0046
Atlantic (27.75,27.85] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 2677.7637 6.280793 2000-2012 –> 2013-2019 10.314805 13552.6451
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 2677.7868 6.280971 2000-2012 –> 2013-2019 10.297662 13536.0593
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2675.6826 6.264835 2000-2012 –> 2013-2019 10.308950 13560.2196
Atlantic (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 2676.7575 6.273072 2000-2012 –> 2013-2019 10.300964 13545.7785
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2673.5798 6.248750 2000-2012 –> 2013-2019 10.294441 13559.6206
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 2677.8263 6.281274 2000-2012 –> 2013-2019 10.309311 13546.9866
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2674.2865 6.254151 2000-2012 –> 2013-2019 10.274481 13536.0537
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2671.5305 6.233115 2000-2012 –> 2013-2019 10.283239 13561.7984
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate_star 2672.3791 6.254859 2000-2012 –> 2013-2019 10.305306 13560.9552
Atlantic (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 2677.3291 6.277457 2000-2012 –> 2013-2019 10.301467 13542.6277
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 22935.5088 3.995860 1982-1999 –> 2000-2012 7.862768 35492.8373
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 22840.1729 3.949526 1982-1999 –> 2000-2012 7.859627 35447.7765
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate_star 22940.0225 3.999045 1982-1999 –> 2000-2012 7.910295 35546.9550
Atlantic (27.85,27.95] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 23347.2434 4.202292 1982-1999 –> 2000-2012 8.142383 35989.4275
Atlantic (27.85,27.95] cstar_tref ~ sal + silicate + phosphate + phosphate_star 23383.7706 4.222145 1982-1999 –> 2000-2012 8.189884 36055.6031
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 22911.2422 3.984015 1982-1999 –> 2000-2012 7.905914 35532.4808
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 22855.4154 3.956897 1982-1999 –> 2000-2012 7.867478 35463.5736
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 23086.2188 4.070218 1982-1999 –> 2000-2012 7.983419 35697.4090
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate 23090.0283 4.073112 1982-1999 –> 2000-2012 8.118099 35849.1312
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 22898.9595 3.978033 1982-1999 –> 2000-2012 7.895269 35514.8145
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 7125.9903 4.462957 2000-2012 –> 2013-2019 8.458817 30061.4992
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7104.7624 4.424298 2000-2012 –> 2013-2019 8.373824 29944.9353
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate_star 7128.0697 4.470425 2000-2012 –> 2013-2019 8.469470 30068.0922
Atlantic (27.85,27.95] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 7252.5447 4.700544 2000-2012 –> 2013-2019 8.902835 30599.7881
Atlantic (27.85,27.95] cstar_tref ~ sal + silicate + phosphate + phosphate_star 7256.3673 4.711774 2000-2012 –> 2013-2019 8.933919 30640.1379
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 7115.2877 4.443424 2000-2012 –> 2013-2019 8.427439 30026.5299
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7108.0471 4.430258 2000-2012 –> 2013-2019 8.387155 29963.4624
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 7103.4415 4.421904 2000-2012 –> 2013-2019 8.492121 30189.6603
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate 7123.8314 4.462667 2000-2012 –> 2013-2019 8.535778 30213.8596
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7116.1552 4.445004 2000-2012 –> 2013-2019 8.423037 30015.1147
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 25073.9337 4.352777 1982-1999 –> 2000-2012 8.342483 42626.9552
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 24471.9632 4.060875 1982-1999 –> 2000-2012 7.892974 41772.7567
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 24546.8541 4.096097 1982-1999 –> 2000-2012 7.932417 41854.5387
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate_star 24546.7040 4.096971 1982-1999 –> 2000-2012 7.933342 41852.4710
Atlantic (27.95,28.05] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 24627.5619 4.134396 1982-1999 –> 2000-2012 8.018926 42013.3987
Atlantic (27.95,28.05] cstar_tref ~ sal + silicate + phosphate + phosphate_star 24703.6739 4.171804 1982-1999 –> 2000-2012 8.056574 42087.8964
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 24874.6609 4.253895 1982-1999 –> 2000-2012 8.285157 42492.5274
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 24630.5637 4.135827 1982-1999 –> 2000-2012 8.000257 41983.9342
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 24548.6424 4.096941 1982-1999 –> 2000-2012 7.932794 41855.5624
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 24594.9355 4.118870 1982-1999 –> 2000-2012 7.970281 41927.1877
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 6595.6481 5.181753 2000-2012 –> 2013-2019 9.242629 31067.6113
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6612.7826 5.223253 2000-2012 –> 2013-2019 9.319350 31159.6366
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate_star 6618.7445 5.242650 2000-2012 –> 2013-2019 9.339620 31165.4485
Atlantic (27.95,28.05] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 6661.0115 5.341857 2000-2012 –> 2013-2019 9.476253 31288.5734
Atlantic (27.95,28.05] cstar_tref ~ sal + silicate + phosphate + phosphate_star 6684.9603 5.406780 2000-2012 –> 2013-2019 9.578584 31388.6342
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6528.1046 5.021349 2000-2012 –> 2013-2019 9.275244 31402.7655
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 6655.9750 5.329346 2000-2012 –> 2013-2019 9.465174 31286.5387
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6620.5097 5.242077 2000-2012 –> 2013-2019 9.339018 31169.1521
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 6619.4521 5.239496 2000-2012 –> 2013-2019 9.666819 31840.6454
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6654.9905 5.326904 2000-2012 –> 2013-2019 9.445775 31249.9261
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 19063.9934 4.255912 1982-1999 –> 2000-2012 7.982983 30891.2971
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 18757.4801 4.064031 1982-1999 –> 2000-2012 7.694376 30471.1903
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 19064.3528 4.257424 1982-1999 –> 2000-2012 7.989946 30895.9714
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 18911.3192 4.159230 1982-1999 –> 2000-2012 7.891413 30744.5448
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 19074.2411 4.262482 1982-1999 –> 2000-2012 7.982368 30893.2095
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 18998.4975 4.214164 1982-1999 –> 2000-2012 7.943624 30828.5707
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 18993.7260 4.211138 1982-1999 –> 2000-2012 7.941534 30824.8816
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 19013.5601 4.223729 1982-1999 –> 2000-2012 7.975505 30869.4053
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 19011.6390 4.223779 1982-1999 –> 2000-2012 7.981788 30872.6558
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 18714.5925 4.037882 1982-1999 –> 2000-2012 7.781425 30560.9482
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4619.5169 5.048047 2000-2012 –> 2013-2019 9.303959 23683.5104
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4456.0461 4.532035 2000-2012 –> 2013-2019 8.596065 23213.5261
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 4619.7863 5.055609 2000-2012 –> 2013-2019 9.313033 23684.1391
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4618.4350 5.044445 2000-2012 –> 2013-2019 9.203675 23529.7542
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4624.6529 5.065178 2000-2012 –> 2013-2019 9.327659 23698.8940
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4624.9012 5.066008 2000-2012 –> 2013-2019 9.280172 23623.3988
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4633.3926 5.094463 2000-2012 –> 2013-2019 9.305601 23627.1186
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4444.9098 4.498865 2000-2012 –> 2013-2019 8.722594 23458.4699
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 4455.7473 4.537123 2000-2012 –> 2013-2019 8.760902 23467.3862
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4438.7921 4.480747 2000-2012 –> 2013-2019 8.518629 23153.3846
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 14118.3815 4.081475 1982-1999 –> 2000-2012 7.322784 21870.4207
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 14059.8454 4.033895 1982-1999 –> 2000-2012 7.273943 21810.7239
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 14116.6181 4.081668 1982-1999 –> 2000-2012 7.324553 21868.1058
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 14052.8058 4.028211 1982-1999 –> 2000-2012 7.270363 21805.6208
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 14117.3683 4.080647 1982-1999 –> 2000-2012 7.323118 21870.4765
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 14074.0477 4.045388 1982-1999 –> 2000-2012 7.286486 21825.8931
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 14115.7179 4.080932 1982-1999 –> 2000-2012 7.324163 21867.5245
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 14066.1590 4.039000 1982-1999 –> 2000-2012 7.281086 21818.9128
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate_star 14099.2932 4.067527 1982-1999 –> 2000-2012 7.309684 21850.1122
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 14052.9939 4.028362 1982-1999 –> 2000-2012 7.318169 21849.3204
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2775.5444 4.683716 2000-2012 –> 2013-2019 8.765191 16893.9259
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2757.1214 4.592042 2000-2012 –> 2013-2019 8.625937 16816.9669
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 2773.8886 4.685446 2000-2012 –> 2013-2019 8.767115 16890.5066
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2775.7588 4.684794 2000-2012 –> 2013-2019 8.713005 16828.5646
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 2777.5520 4.693816 2000-2012 –> 2013-2019 8.739204 16851.5997
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2777.0779 4.691429 2000-2012 –> 2013-2019 8.730429 16843.2369
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate_star 2775.8363 4.695249 2000-2012 –> 2013-2019 8.762776 16875.1296
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 2757.6109 4.594454 2000-2012 –> 2013-2019 8.686061 16888.3693
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + phosphate + phosphate_star 2755.6944 4.594866 2000-2012 –> 2013-2019 8.688504 16886.9304
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2756.5446 4.589201 2000-2012 –> 2013-2019 8.617563 16809.5385
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate 6221.8984 3.727801 1982-1999 –> 2000-2012 7.143492 9031.4666
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate 6220.0525 3.728054 1982-1999 –> 2000-2012 7.150645 9029.7517
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6221.1592 3.726587 1982-1999 –> 2000-2012 7.149093 9032.8322
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 6204.4215 3.699210 1982-1999 –> 2000-2012 7.121790 9016.1173
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6217.0776 3.719892 1982-1999 –> 2000-2012 7.154906 9032.6026
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 6235.8005 3.750701 1982-1999 –> 2000-2012 7.184719 9051.0196
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6211.7102 3.711107 1982-1999 –> 2000-2012 7.143123 9026.3135
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 6214.5818 3.715805 1982-1999 –> 2000-2012 7.166041 9034.7765
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate 6213.2155 3.716842 1982-1999 –> 2000-2012 7.173249 9033.2971
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6214.3560 3.715435 1982-1999 –> 2000-2012 7.170354 9035.9829
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate 1015.1912 2.781502 2000-2012 –> 2013-2019 6.509303 7237.0896
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1015.8571 2.786024 2000-2012 –> 2013-2019 6.543894 7255.9924
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate 1013.2580 2.781956 2000-2012 –> 2013-2019 6.510010 7233.3105
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 1015.1012 2.780892 2000-2012 –> 2013-2019 6.507479 7236.2604
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate_star 1014.0305 2.787202 2000-2012 –> 2013-2019 6.545394 7252.3601
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 1012.8285 2.765520 2000-2012 –> 2013-2019 6.464730 7217.2500
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1015.2607 2.781974 2000-2012 –> 2013-2019 6.501867 7232.3383
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 1014.9989 2.780198 2000-2012 –> 2013-2019 6.530899 7250.7994
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + phosphate + phosphate_star 1013.1182 2.781007 2000-2012 –> 2013-2019 6.532832 7247.5990
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 1013.5425 2.770340 2000-2012 –> 2013-2019 6.481447 7225.2527
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 13924.3551 3.293214 1982-1999 –> 2000-2012 6.135107 19412.0497
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + phosphate + phosphate_star 13927.2209 3.296222 1982-1999 –> 2000-2012 6.149306 19421.6483
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 13914.0557 3.286854 1982-1999 –> 2000-2012 6.139310 19409.9938
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 13947.1694 3.307345 1982-1999 –> 2000-2012 6.142087 19429.2653
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate 13953.2408 3.312359 1982-1999 –> 2000-2012 6.156696 19440.8450
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 13921.9575 3.291732 1982-1999 –> 2000-2012 6.135665 19411.2464
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 13949.7038 3.308919 1982-1999 –> 2000-2012 6.147366 19434.7023
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 13894.0345 3.274526 1982-1999 –> 2000-2012 6.147228 19405.6887
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 13919.3350 3.290112 1982-1999 –> 2000-2012 6.159024 19428.0554
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 13900.2273 3.278334 1982-1999 –> 2000-2012 6.134577 19399.1134
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 2017.7709 3.200287 2000-2012 –> 2013-2019 6.487141 15931.8266
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 2022.2780 3.218929 2000-2012 –> 2013-2019 6.506342 15937.2403
Atlantic (28.2, Inf] cstar_tref ~ sal + silicate + phosphate + phosphate_star 2021.0618 3.222182 2000-2012 –> 2013-2019 6.516407 15945.0530
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2005.9330 3.151837 2000-2012 –> 2013-2019 6.445815 15931.5248
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 2003.8191 3.143263 2000-2012 –> 2013-2019 6.434995 15925.7767
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate_star 2003.9511 3.151911 2000-2012 –> 2013-2019 6.447143 15929.5712
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 1999.9462 3.127614 2000-2012 –> 2013-2019 6.402140 15893.9807
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2012.4504 3.178420 2000-2012 –> 2013-2019 6.468532 15931.7854
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + phosphate + phosphate_star 2010.5849 3.178971 2000-2012 –> 2013-2019 6.470769 15930.6496
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2005.5741 3.150379 2000-2012 –> 2013-2019 6.428713 15905.8013
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 28544.2040 5.838801 1982-1999 –> 2000-2012 14.028498 37559.9643
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 29046.7941 6.175597 1982-1999 –> 2000-2012 14.427755 38081.9744
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 28762.4548 5.984073 1982-1999 –> 2000-2012 14.181885 37778.7465
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 28614.9786 5.885093 1982-1999 –> 2000-2012 13.929635 37585.0297
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 28629.0482 5.894340 1982-1999 –> 2000-2012 13.932881 37597.1922
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 28762.0241 5.982451 1982-1999 –> 2000-2012 14.111323 37758.7302
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 29222.6374 6.297965 1982-1999 –> 2000-2012 14.407236 38213.1726
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 29279.3852 6.337970 1982-1999 –> 2000-2012 14.433827 38265.6887
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 28706.9044 5.945769 1982-1999 –> 2000-2012 13.972221 37671.2011
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 29305.3767 6.356378 1982-1999 –> 2000-2012 14.450166 38291.0272
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 16970.8773 4.539189 2000-2012 –> 2013-2019 10.377990 45515.0813
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 18063.3551 5.482865 2000-2012 –> 2013-2019 11.658462 47110.1492
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 17395.7162 4.886835 2000-2012 –> 2013-2019 10.870909 46158.1711
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 17277.2166 4.786080 2000-2012 –> 2013-2019 10.671173 45892.1952
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 17302.6985 4.807212 2000-2012 –> 2013-2019 10.701552 45931.7467
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 17389.6738 4.880045 2000-2012 –> 2013-2019 10.862496 46151.6979
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 18304.2074 5.715998 2000-2012 –> 2013-2019 12.013962 47526.8448
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 17465.0495 4.944057 2000-2012 –> 2013-2019 10.889826 46171.9539
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 18021.7319 5.443550 2000-2012 –> 2013-2019 11.943917 47527.8555
Indo-Pacific (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 17973.3321 5.398189 2000-2012 –> 2013-2019 11.958233 47561.3566
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 18295.1417 4.692153 1982-1999 –> 2000-2012 11.667558 28332.6248
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 18346.5253 4.731417 1982-1999 –> 2000-2012 11.664569 28365.8896
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 18237.9972 4.648868 1982-1999 –> 2000-2012 11.639359 28281.9223
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 18256.4609 4.662810 1982-1999 –> 2000-2012 11.673210 28308.8670
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 18380.2337 4.757354 1982-1999 –> 2000-2012 11.741354 28421.3885
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 18423.0025 4.790467 1982-1999 –> 2000-2012 11.802196 28475.9736
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 18262.7106 4.667538 1982-1999 –> 2000-2012 11.681947 28316.8212
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 18416.2646 4.785235 1982-1999 –> 2000-2012 11.799085 28470.1375
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 18424.9106 4.791950 1982-1999 –> 2000-2012 11.804764 28478.3434
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 18443.7971 4.808209 1982-1999 –> 2000-2012 11.830650 28499.3205
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 8903.6476 4.127119 2000-2012 –> 2013-2019 8.819271 27198.7893
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 8821.9498 4.020922 2000-2012 –> 2013-2019 8.752340 27168.4751
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 8960.0859 4.202115 2000-2012 –> 2013-2019 8.850983 27198.0831
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 8988.7131 4.240674 2000-2012 –> 2013-2019 8.903484 27245.1740
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 8908.9778 4.134144 2000-2012 –> 2013-2019 8.891498 27289.2115
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 8949.5390 4.187997 2000-2012 –> 2013-2019 8.978464 27372.5416
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 8994.2014 4.248107 2000-2012 –> 2013-2019 8.915645 27256.9120
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 8907.0176 4.131559 2000-2012 –> 2013-2019 8.916794 27323.2822
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 8949.7645 4.188298 2000-2012 –> 2013-2019 8.980248 27374.6751
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 8947.8499 4.188413 2000-2012 –> 2013-2019 8.996622 27391.6470
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 20213.8979 5.498208 1982-1999 –> 2000-2012 10.830176 30215.1861
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 20212.9354 5.495691 1982-1999 –> 2000-2012 10.821957 30212.7682
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 19666.6993 5.050626 1982-1999 –> 2000-2012 10.066057 29472.3083
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 20109.6083 5.408594 1982-1999 –> 2000-2012 10.824763 30163.5056
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate 19771.4287 5.133071 1982-1999 –> 2000-2012 10.230764 29629.5857
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 19841.2536 5.188785 1982-1999 –> 2000-2012 10.333354 29728.9763
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 19852.6972 5.197973 1982-1999 –> 2000-2012 10.354556 29747.9536
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 19982.7717 5.305205 1982-1999 –> 2000-2012 10.751770 30052.7450
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 19908.3613 5.242901 1982-1999 –> 2000-2012 10.687423 29979.1232
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 20164.2268 5.454460 1982-1999 –> 2000-2012 10.772616 30159.1374
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 8273.8381 4.953073 2000-2012 –> 2013-2019 10.448764 28486.7735
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 8238.3748 4.889287 2000-2012 –> 2013-2019 9.939913 27905.0741
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 8362.7109 5.120345 2000-2012 –> 2013-2019 10.528975 28470.3623
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 8313.4642 5.025331 2000-2012 –> 2013-2019 10.433925 28423.0725
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate 8259.3789 4.926966 2000-2012 –> 2013-2019 10.060037 28030.8076
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 8277.8280 4.960301 2000-2012 –> 2013-2019 10.149086 28119.0816
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 8361.9789 5.115235 2000-2012 –> 2013-2019 10.521628 28468.9551
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 8278.8799 4.962209 2000-2012 –> 2013-2019 10.160182 28131.5771
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 8282.6829 4.972745 2000-2012 –> 2013-2019 10.277950 28265.4546
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 8259.8746 4.927859 2000-2012 –> 2013-2019 10.170759 28168.2359
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 29651.7034 5.030046 1982-1999 –> 2000-2012 10.461266 47054.7656
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 29591.2103 4.997968 1982-1999 –> 2000-2012 10.388386 46954.1189
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 29515.2075 4.959231 1982-1999 –> 2000-2012 10.386064 46915.7524
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 29803.1046 5.107572 1982-1999 –> 2000-2012 10.634249 47305.5611
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 29813.2618 5.112886 1982-1999 –> 2000-2012 10.592866 47268.2855
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 29499.9299 4.951480 1982-1999 –> 2000-2012 10.340191 46861.0674
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 29746.9389 5.078288 1982-1999 –> 2000-2012 10.501404 47143.6536
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 29885.7399 5.150964 1982-1999 –> 2000-2012 10.609594 47318.9419
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 29751.6554 5.080740 1982-1999 –> 2000-2012 10.606594 47253.2793
Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 29891.0109 5.153744 1982-1999 –> 2000-2012 10.616637 47328.5770
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 13484.6841 4.380519 2000-2012 –> 2013-2019 9.410565 43136.3875
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 13455.5572 4.351307 2000-2012 –> 2013-2019 9.349274 43046.7676
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 13442.2849 4.338910 2000-2012 –> 2013-2019 9.298140 42957.4924
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate 13588.4835 4.477434 2000-2012 –> 2013-2019 9.609901 43439.0835
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 13665.1172 4.551803 2000-2012 –> 2013-2019 9.659375 43468.2218
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate 13606.2094 4.496460 2000-2012 –> 2013-2019 9.667838 43528.5839
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 13431.3651 4.328737 2000-2012 –> 2013-2019 9.280217 42931.2950
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 13598.6368 4.487217 2000-2012 –> 2013-2019 9.565505 43345.5757
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 13664.2094 4.552872 2000-2012 –> 2013-2019 9.664679 43473.4100
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 13666.1535 4.552817 2000-2012 –> 2013-2019 9.633558 43417.8089
Indo-Pacific (27,27.25] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 39455.7178 4.928826 1982-1999 –> 2000-2012 10.563399 61126.9941
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 39375.1571 4.898576 1982-1999 –> 2000-2012 10.602417 61130.4967
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 39136.4172 4.810017 1982-1999 –> 2000-2012 10.429495 60789.2373
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 39134.6601 4.810106 1982-1999 –> 2000-2012 10.576647 60963.2159
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 39080.5239 4.789516 1982-1999 –> 2000-2012 10.541337 60893.4946
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 39061.9206 4.782712 1982-1999 –> 2000-2012 10.393976 60704.6769
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 39128.4318 4.807082 1982-1999 –> 2000-2012 10.569058 60953.5376
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 39353.0682 4.890314 1982-1999 –> 2000-2012 10.586546 61099.2228
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 39085.8785 4.791476 1982-1999 –> 2000-2012 10.424420 60755.1657
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 38909.9063 4.727475 1982-1999 –> 2000-2012 10.337214 60550.7930
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 18163.3939 4.168594 2000-2012 –> 2013-2019 9.067169 57538.5510
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 18141.5860 4.154360 2000-2012 –> 2013-2019 8.964377 57278.0033
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 18148.8701 4.160414 2000-2012 –> 2013-2019 8.970520 57283.5302
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 18098.4574 4.126354 2000-2012 –> 2013-2019 8.915870 57178.9813
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 18121.6865 4.141414 2000-2012 –> 2013-2019 8.924126 57183.6071
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 18124.8240 4.143453 2000-2012 –> 2013-2019 8.950535 57253.2558
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 18180.2852 4.179652 2000-2012 –> 2013-2019 9.042842 57460.5722
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 18172.0150 4.174234 2000-2012 –> 2013-2019 9.027040 57424.3294
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 18141.3754 4.154223 2000-2012 –> 2013-2019 8.945699 57227.2539
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 18077.2400 4.112646 2000-2012 –> 2013-2019 8.840120 56987.1464
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 40387.4975 4.510456 1982-1999 –> 2000-2012 9.511844 62757.0218
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 40103.3197 4.417897 1982-1999 –> 2000-2012 9.403235 62451.1161
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 40242.1135 4.463194 1982-1999 –> 2000-2012 9.532997 62711.9333
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 40141.3932 4.430100 1982-1999 –> 2000-2012 9.427777 62507.4365
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 39511.9924 4.232615 1982-1999 –> 2000-2012 9.299946 61980.2104
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 39867.0442 4.342911 1982-1999 –> 2000-2012 9.108313 61881.7706
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 39608.9016 4.262439 1982-1999 –> 2000-2012 9.555890 62399.3907
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 39648.3702 4.274645 1982-1999 –> 2000-2012 9.029460 61646.6770
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + phosphate + phosphate_star 39975.0369 4.377659 1982-1999 –> 2000-2012 9.169237 62028.2007
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 39157.2437 4.125212 1982-1999 –> 2000-2012 8.847567 61104.9826
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 19017.5303 3.306024 2000-2012 –> 2013-2019 7.609563 58758.8781
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 19088.7821 3.339513 2000-2012 –> 2013-2019 7.649397 58848.4636
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 18972.2639 3.285498 2000-2012 –> 2013-2019 7.518113 58484.2563
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 19131.6224 3.358332 2000-2012 –> 2013-2019 7.757329 59175.7741
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + silicate + phosphate + phosphate_star 19286.2541 3.431492 2000-2012 –> 2013-2019 7.861920 59426.6685
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 18982.6299 3.290187 2000-2012 –> 2013-2019 7.552626 58591.5315
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 19001.1483 3.298581 2000-2012 –> 2013-2019 7.605263 58752.5719
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 19097.9199 3.342795 2000-2012 –> 2013-2019 7.655454 58868.4891
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 18997.8178 3.297070 2000-2012 –> 2013-2019 7.595461 58722.6472
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 19560.0172 3.562231 2000-2012 –> 2013-2019 7.687442 58717.2609
Indo-Pacific (27.5,27.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 43164.1217 3.995635 1982-1999 –> 2000-2012 8.584667 66524.7711
Indo-Pacific (27.5,27.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 43168.5383 3.997301 1982-1999 –> 2000-2012 8.590676 66534.6923
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 43112.0251 3.982130 1982-1999 –> 2000-2012 8.570157 66470.9363
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 43223.5732 4.011623 1982-1999 –> 2000-2012 8.604915 66589.5845
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 42408.1126 3.804074 1982-1999 –> 2000-2012 8.389926 65763.2606
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 43200.4659 4.005083 1982-1999 –> 2000-2012 8.376006 66174.7698
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 42409.0515 3.804306 1982-1999 –> 2000-2012 8.570161 66069.6681
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 43360.9516 4.047072 1982-1999 –> 2000-2012 8.417975 66335.2192
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 43433.4648 4.066716 1982-1999 –> 2000-2012 8.437706 66405.8889
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 43169.6726 3.997076 1982-1999 –> 2000-2012 8.341455 66095.6461
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 21154.0122 3.072646 2000-2012 –> 2013-2019 7.088715 64396.6267
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 21380.3174 3.158150 2000-2012 –> 2013-2019 7.186987 64669.7804
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 20953.1878 2.999351 2000-2012 –> 2013-2019 6.803425 63361.3004
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate 21849.2962 3.340522 2000-2012 –> 2013-2019 7.307154 64901.3157
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 20949.8236 2.998138 2000-2012 –> 2013-2019 6.802445 63358.8750
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 20949.1880 2.997909 2000-2012 –> 2013-2019 6.814107 63406.2645
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 21021.5683 3.024110 2000-2012 –> 2013-2019 6.832790 63448.3021
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 20949.1226 2.997885 2000-2012 –> 2013-2019 6.812991 63401.7954
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 21174.1768 3.080845 2000-2012 –> 2013-2019 6.920956 63725.3754
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 21750.9178 3.301246 2000-2012 –> 2013-2019 7.298322 64920.5904
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 21338.0259 3.508736 1982-1999 –> 2000-2012 7.535720 31790.0072
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 21353.0238 3.515341 1982-1999 –> 2000-2012 7.544034 31806.5801
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 21279.2805 3.482982 1982-1999 –> 2000-2012 7.536300 31755.4579
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 21237.2138 3.464656 1982-1999 –> 2000-2012 7.536156 31730.0047
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 21222.0645 3.458080 1982-1999 –> 2000-2012 7.537645 31722.2010
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 21235.0696 3.463724 1982-1999 –> 2000-2012 7.540236 31732.4269
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 21370.2560 3.522947 1982-1999 –> 2000-2012 7.538916 31812.0708
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 21269.5039 3.478714 1982-1999 –> 2000-2012 7.537428 31750.6190
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 21234.1810 3.463338 1982-1999 –> 2000-2012 7.544848 31736.0860
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 21206.7330 3.451437 1982-1999 –> 2000-2012 7.486084 31665.7714
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 10486.0157 2.904075 2000-2012 –> 2013-2019 6.387057 31765.2963
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10470.5016 2.893403 2000-2012 –> 2013-2019 6.358059 31707.7154
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10471.7962 2.894292 2000-2012 –> 2013-2019 6.352372 31693.8607
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10470.7163 2.893551 2000-2012 –> 2013-2019 6.357275 31705.7860
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 10469.8303 2.894316 2000-2012 –> 2013-2019 6.372906 31737.0508
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 10541.4067 2.942500 2000-2012 –> 2013-2019 6.405838 31775.5877
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 10535.6450 2.938480 2000-2012 –> 2013-2019 6.389917 31742.3780
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 10541.9163 2.942856 2000-2012 –> 2013-2019 6.406267 31776.2660
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate_star 10542.3572 2.944561 2000-2012 –> 2013-2019 6.407980 31774.7247
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + silicate + phosphate + phosphate_star 10550.1520 2.950013 2000-2012 –> 2013-2019 6.421442 31800.9403
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 29032.6056 3.164474 1982-1999 –> 2000-2012 7.206451 43697.3646
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 28874.1296 3.119804 1982-1999 –> 2000-2012 7.160627 43539.4026
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 28979.9410 3.149186 1982-1999 –> 2000-2012 7.183725 43637.1150
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate 29047.2932 3.168033 1982-1999 –> 2000-2012 7.216504 43722.4072
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 28902.1512 3.127559 1982-1999 –> 2000-2012 7.204330 43613.5162
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 29030.0985 3.163211 1982-1999 –> 2000-2012 7.205162 43696.8252
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 28872.1959 3.119270 1982-1999 –> 2000-2012 7.174784 43556.3544
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 28903.0337 3.127803 1982-1999 –> 2000-2012 7.200431 43609.1066
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 28903.1826 3.127845 1982-1999 –> 2000-2012 7.202073 43611.3007
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 28901.1839 3.127845 1982-1999 –> 2000-2012 7.209971 43617.3794
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 15048.0646 2.923028 2000-2012 –> 2013-2019 6.042832 43922.1941
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 14996.2710 2.898045 2000-2012 –> 2013-2019 6.025397 43897.6745
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 14979.0913 2.889806 2000-2012 –> 2013-2019 6.023637 43903.8585
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 14975.9219 2.888288 2000-2012 –> 2013-2019 6.015847 43878.0731
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 14979.1268 2.889823 2000-2012 –> 2013-2019 6.024325 43906.3097
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate_star 14977.1495 2.889834 2000-2012 –> 2013-2019 6.036581 43946.3436
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 15019.1903 2.909074 2000-2012 –> 2013-2019 6.028344 43891.3862
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 15012.4160 2.905810 2000-2012 –> 2013-2019 6.033613 43915.4497
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 15012.5878 2.905893 2000-2012 –> 2013-2019 6.033737 43915.7704
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate_star 15018.3533 2.909635 2000-2012 –> 2013-2019 6.037480 43919.5372
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 47904.7366 2.969919 1982-1999 –> 2000-2012 6.867632 76354.8266
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 47780.9294 2.950421 1982-1999 –> 2000-2012 6.829638 76184.3502
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + silicate + phosphate + phosphate_star 47848.4212 2.961175 1982-1999 –> 2000-2012 6.888386 76375.6545
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 47903.1667 2.969364 1982-1999 –> 2000-2012 6.846556 76301.2429
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 47930.9607 2.973999 1982-1999 –> 2000-2012 6.872643 76383.4931
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 47770.3131 2.948781 1982-1999 –> 2000-2012 6.846970 76223.6511
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 47878.2409 2.965491 1982-1999 –> 2000-2012 6.852047 76300.9987
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 47862.4943 2.963047 1982-1999 –> 2000-2012 6.857887 76307.0369
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 47882.2289 2.966421 1982-1999 –> 2000-2012 6.908070 76447.0102
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 47842.3969 2.959931 1982-1999 –> 2000-2012 6.865570 76315.2717
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 27048.7232 3.056711 2000-2012 –> 2013-2019 6.026630 74953.4598
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 27050.1172 3.056537 2000-2012 –> 2013-2019 6.006958 74831.0466
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 27034.4729 3.052055 2000-2012 –> 2013-2019 6.021418 74937.6395
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 27049.0867 3.056242 2000-2012 –> 2013-2019 6.005023 74819.3998
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 27137.2607 3.081626 2000-2012 –> 2013-2019 6.047117 75015.5016
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 27007.9834 3.044480 2000-2012 –> 2013-2019 6.018294 74939.7549
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 27007.5136 3.044346 2000-2012 –> 2013-2019 6.044003 75104.5553
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 27031.2780 3.051140 2000-2012 –> 2013-2019 6.014187 74893.7723
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 27008.7941 3.044711 2000-2012 –> 2013-2019 6.017747 74935.5654
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 27148.1331 3.084771 2000-2012 –> 2013-2019 6.044702 74990.5300
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 38406.5588 2.922015 1982-1999 –> 2000-2012 6.926091 58028.6428
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 38395.9442 2.919624 1982-1999 –> 2000-2012 6.897193 57973.6135
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 38460.6636 2.932291 1982-1999 –> 2000-2012 6.922885 58059.1798
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 38354.6133 2.911805 1982-1999 –> 2000-2012 6.879462 57914.8486
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 38389.6225 2.918806 1982-1999 –> 2000-2012 6.886520 57947.9584
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 38295.4017 2.900640 1982-1999 –> 2000-2012 6.857557 57836.6956
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 38378.1269 2.916251 1982-1999 –> 2000-2012 6.873568 57920.1270
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 38350.2705 2.910985 1982-1999 –> 2000-2012 6.881652 57915.8049
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 38407.4632 2.921807 1982-1999 –> 2000-2012 6.912059 58007.3794
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 38455.3384 2.930897 1982-1999 –> 2000-2012 6.920049 58053.3273
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 26775.4943 2.847324 2000-2012 –> 2013-2019 5.769339 65182.0531
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 26675.5369 2.820708 2000-2012 –> 2013-2019 5.740332 65071.4811
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 26583.3993 2.796869 2000-2012 –> 2013-2019 5.708674 64938.0126
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 26602.2725 2.801736 2000-2012 –> 2013-2019 5.716885 64974.5743
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 26701.5915 2.828007 2000-2012 –> 2013-2019 5.746812 65091.2141
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate 26728.4312 2.835007 2000-2012 –> 2013-2019 5.769902 65202.7735
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 26696.2625 2.826098 2000-2012 –> 2013-2019 5.726738 64991.6642
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 26665.3009 2.818049 2000-2012 –> 2013-2019 5.734300 65043.4278
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 26730.4299 2.835007 2000-2012 –> 2013-2019 5.745991 65080.7004
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 26744.7300 2.838744 2000-2012 –> 2013-2019 5.760551 65152.1933
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 49656.6076 3.063464 1982-1999 –> 2000-2012 6.990462 89689.2561
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + silicate + phosphate + phosphate_star 50385.5241 3.180129 1982-1999 –> 2000-2012 7.122619 90472.7092
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 51157.2958 3.307803 1982-1999 –> 2000-2012 7.280129 91354.7443
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 50382.8882 3.179375 1982-1999 –> 2000-2012 7.117879 90457.5453
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 51371.3395 3.344206 1982-1999 –> 2000-2012 7.205516 91161.7504
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate 51620.4122 3.387418 1982-1999 –> 2000-2012 7.259048 91447.1493
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 51381.9416 3.346020 1982-1999 –> 2000-2012 7.214012 91197.1814
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 50910.7514 3.266363 1982-1999 –> 2000-2012 7.125827 90694.2976
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 50010.9368 3.119476 1982-1999 –> 2000-2012 6.985382 89818.4296
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 51414.8685 3.351658 1982-1999 –> 2000-2012 7.275161 91434.7290
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 22649.5510 2.691568 2000-2012 –> 2013-2019 5.755032 72306.1585
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + silicate + phosphate + phosphate_star 22683.4061 2.701859 2000-2012 –> 2013-2019 5.881988 73068.9302
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + phosphate 22668.9722 2.697711 2000-2012 –> 2013-2019 6.067069 74184.8397
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 22504.4311 2.650317 2000-2012 –> 2013-2019 5.958119 73661.7270
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 22670.9520 2.697706 2000-2012 –> 2013-2019 6.032091 73984.7777
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + phosphate + phosphate_star 22504.4038 2.650873 2000-2012 –> 2013-2019 6.090541 74424.1605
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 22393.4883 2.619207 2000-2012 –> 2013-2019 5.798582 72776.3765
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 22660.9150 2.694825 2000-2012 –> 2013-2019 6.039032 74032.2545
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 22476.4124 2.642425 2000-2012 –> 2013-2019 6.073219 74347.6458
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 22530.1758 2.657588 2000-2012 –> 2013-2019 5.777064 72541.1127

6.2 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(basin, gamma_slab, model, eras),
  eras_era)

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

rm(eras_era, eras_forward, eras_backward)

6.3 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(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)

6.4 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 %>%
  ggplot(aes(as.factor(n_predictors),
             !!sym(params_local$MLR_criterion),
             col = basin)) +
  geom_hline(yintercept = c(0,10)) +
  geom_boxplot() +
  facet_grid(gamma_slab~era) +
  scale_color_brewer(palette = "Set1") +
  ylim(c(0,NA)) +
  labs(x="Number of predictors")

Version Author Date
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

7.1.2 Best models

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

Version Author Date
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

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(eras ~ basin)

Version Author Date
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(eras ~ basin)

Version Author Date
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(basin, eras, 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", "eras")) %>% 
  summary_rows(
    groups = TRUE,
    fns = list(total = "sum")
  )
aou nitrate phosphate phosphate_star sal silicate temp
Atlantic - 1982-1999 --> 2000-2012
(-Inf,26] 7 10 8 8 4 4 8
(26,26.5] 10 9 8 7 4 3 7
(26.5,26.75] 7 3 8 9 7 4 10
(26.75,27] 6 5 6 9 5 8 10
(27,27.25] 6 4 6 8 4 10 10
(27.25,27.5] 7 4 8 7 10 3 9
(27.5,27.75] 8 3 9 7 4 10 7
(27.75,27.85] 7 6 9 6 6 10 5
(27.85,27.95] 5 3 7 7 10 10 5
(27.95,28.05] 7 3 7 8 10 9 4
(28.05,28.1] 7 4 6 10 7 4 10
(28.1,28.15] 5 3 5 10 9 5 10
(28.15,28.2] 8 3 9 5 7 6 10
(28.2, Inf] 8 3 9 7 10 4 7
total 98.00 63.00 105.00 108.00 97.00 90.00 112.00
Atlantic - 2000-2012 --> 2013-2019
(-Inf,26] 8 10 7 8 4 4 8
(26,26.5] 10 10 7 7 3 3 7
(26.5,26.75] 9 4 8 8 7 4 9
(26.75,27] 5 4 5 9 4 10 10
(27,27.25] 7 6 7 8 4 9 9
(27.25,27.5] 8 10 9 7 4 3 7
(27.5,27.75] 7 5 8 7 4 10 8
(27.75,27.85] 8 6 7 8 4 10 6
(27.85,27.95] 5 3 7 7 10 10 5
(27.95,28.05] 6 3 7 8 10 9 5
(28.05,28.1] 7 4 6 10 7 4 10
(28.1,28.15] 7 3 5 10 7 5 10
(28.15,28.2] 7 3 7 7 10 3 10
(28.2, Inf] 5 3 7 10 10 5 7
total 99.00 74.00 97.00 114.00 88.00 89.00 111.00
Indo-Pacific - 1982-1999 --> 2000-2012
(-Inf,26] 8 6 6 6 10 5 8
(26,26.5] 6 5 6 8 10 6 8
(26.5,26.75] 7 9 7 9 7 3 6
(26.75,27] 8 8 8 9 3 6 7
(27,27.25] 9 5 9 7 7 7 5
(27.25,27.5] 10 4 10 9 4 5 5
(27.5,27.75] 10 3 10 9 5 5 5
(27.75,27.85] 8 5 7 8 5 9 8
(27.85,27.95] 7 10 7 8 3 6 7
(27.95,28.05] 10 4 10 10 4 4 4
(28.05,28.1] 10 4 10 9 5 5 4
(28.1, Inf] 9 7 10 7 3 6 6
total 102.00 70.00 100.00 99.00 66.00 67.00 73.00
Indo-Pacific - 2000-2012 --> 2013-2019
(-Inf,26] 8 8 7 6 8 4 8
(26,26.5] 6 5 6 8 10 6 8
(26.5,26.75] 7 7 7 9 9 3 6
(26.75,27] 10 7 10 7 3 3 7
(27,27.25] 9 3 9 7 8 7 6
(27.25,27.5] 6 3 8 7 9 10 5
(27.5,27.75] 7 3 7 6 9 9 7
(27.75,27.85] 4 4 5 9 5 10 10
(27.85,27.95] 5 6 5 8 5 10 9
(27.95,28.05] 9 6 9 8 5 6 6
(28.05,28.1] 10 5 10 7 7 5 3
(28.1, Inf] 10 5 10 7 7 5 3
total 91.00 62.00 93.00 89.00 85.00 78.00 78.00

7.4 RMSE alternatives

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(eras~basin)

Version Author Date
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(eras~basin)

Version Author Date
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

7.5 Residual patterns

7.5.1 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(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")

Version Author Date
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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")

Version Author Date
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)

7.5.2 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"
    )
  )

Version Author Date
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"
    )
  )

Version Author Date
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

7.5.3 By model domain

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

p_residuals <- function(df){
    ggplot(data = df, aes(lat, .resid)) +
      geom_bin2d(binwidth = i_binwidth) +
      geom_hline(yintercept = 0, col = "black") +
      scale_fill_viridis_c() +
      facet_grid(gamma_slab ~ era) +
      coord_cartesian(ylim = i_ylim) +
      labs(
        title = paste(
          "Target variable:",
          params_local$MLR_target,
          "| selected best models | basin:",
          unique(df$basin)
        )
      )
}

GLODAP_augmented_best %>% 
  group_split(basin) %>% 
  map(p_residuals)
[[1]]

Version Author Date
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6c0bec6 jens-daniel-mueller 2021-03-05
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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
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

7.5.4 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(basin, gamma_slab, era, lat_grid) %>% 
  summarise(.resid_mean = mean(.resid)) %>% 
  ungroup()

lat_residual %>%
  ggplot(aes(lat_grid, .resid_mean, col=era)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 0, col = "black") +
  facet_grid(gamma_slab ~ basin)

Version Author Date
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

7.5.5 Latitudinal offset

# calculate residual offset for adjacent eras
lat_residual_offset <- lat_residual  %>%
  select(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
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 

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_0.7.2      kableExtra_1.3.1
 [5] knitr_1.30       olsrr_0.5.3      GGally_2.0.0     lubridate_1.7.9 
 [9] metR_0.9.0       scico_1.2.0      patchwork_1.1.1  collapse_1.5.0  
[13] forcats_0.5.0    stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4     
[17] readr_1.4.0      tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.2   
[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_0.4.9              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_0.2.0          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