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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 288.8293 5.496553 1982-1999 –> 2000-2010 11.499263 861.5693
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 280.4162 4.995403 1982-1999 –> 2000-2010 10.811158 847.6508
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 282.3829 5.108303 1982-1999 –> 2000-2010 10.903141 848.9906
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 282.2873 5.102754 1982-1999 –> 2000-2010 10.893976 848.7863
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 280.2768 4.987500 1982-1999 –> 2000-2010 11.392397 864.3011
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 283.5811 5.178331 1982-1999 –> 2000-2010 10.960439 849.8061
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 289.7931 5.557086 1982-1999 –> 2000-2010 11.345937 856.2209
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 288.6992 5.488437 1982-1999 –> 2000-2010 11.439301 859.9299
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 288.6760 5.486986 1982-1999 –> 2000-2010 11.417676 859.3157
Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 288.6475 5.485210 1982-1999 –> 2000-2010 11.378843 858.1966
Atlantic (-Inf,26] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 426.2550 3.287971 2000-2010 –> 2011-2019 8.784524 715.0843
Atlantic (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 413.7789 3.038329 2000-2010 –> 2011-2019 8.033732 694.1951
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 411.9823 3.003976 2000-2010 –> 2011-2019 8.112279 694.3652
Atlantic (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 411.8147 3.000791 2000-2010 –> 2011-2019 8.103545 694.1020
Atlantic (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 411.4512 2.993895 2000-2010 –> 2011-2019 8.172226 695.0322
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 411.1104 2.987445 2000-2010 –> 2011-2019 8.544531 700.9035
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 424.4422 3.250461 2000-2010 –> 2011-2019 8.738898 713.1414
Atlantic (-Inf,26] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 423.6359 3.233916 2000-2010 –> 2011-2019 8.720903 712.3119
Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + phosphate + phosphate_star 419.8646 3.197865 2000-2010 –> 2011-2019 8.755179 707.6613
Atlantic (-Inf,26] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 421.6980 3.194494 2000-2010 –> 2011-2019 8.679704 710.3455
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 3135.3105 5.396464 1982-1999 –> 2000-2010 10.298531 6306.3358
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 3131.6623 5.366250 1982-1999 –> 2000-2010 10.244475 6299.5683
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 3136.1327 5.390149 1982-1999 –> 2000-2010 10.287173 6308.0772
Atlantic (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 3179.3420 5.626709 1982-1999 –> 2000-2010 10.514504 6349.3057
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 3171.1409 5.581025 1982-1999 –> 2000-2010 10.501118 6348.0202
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3164.5037 5.544325 1982-1999 –> 2000-2010 10.361975 6319.2898
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate 3169.7579 5.584449 1982-1999 –> 2000-2010 10.504625 6344.6548
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3126.6725 5.339699 1982-1999 –> 2000-2010 10.166608 6283.4745
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 3154.4974 5.489451 1982-1999 –> 2000-2010 10.387286 6326.6158
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3168.9640 5.568962 1982-1999 –> 2000-2010 10.493975 6346.8929
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 1738.0291 3.714040 2000-2010 –> 2011-2019 9.110503 4873.3396
Atlantic (26,26.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 1711.7423 3.551474 2000-2010 –> 2011-2019 8.917723 4843.4046
Atlantic (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 1708.6100 3.533915 2000-2010 –> 2011-2019 8.924065 4844.7427
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 1721.5574 3.607059 2000-2010 –> 2011-2019 9.188084 4892.6983
Atlantic (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 1724.8058 3.625647 2000-2010 –> 2011-2019 9.312741 4914.8866
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate 1740.7240 3.729911 2000-2010 –> 2011-2019 9.314360 4910.4819
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 1739.7539 3.712423 2000-2010 –> 2011-2019 9.052122 4866.4264
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 1715.5090 3.572703 2000-2010 –> 2011-2019 9.062155 4870.0064
Atlantic (26,26.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 1718.1769 3.587817 2000-2010 –> 2011-2019 9.156779 4887.1410
Atlantic (26,26.5] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 1724.5027 3.623908 2000-2010 –> 2011-2019 9.298264 4912.3276
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 3952.5849 5.430917 1982-1999 –> 2000-2010 9.406023 8237.8437
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3952.1846 5.429200 1982-1999 –> 2000-2010 9.228145 8168.2727
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 3951.8375 5.427712 1982-1999 –> 2000-2010 9.390083 8232.1995
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3953.1019 5.433135 1982-1999 –> 2000-2010 9.357843 8218.8895
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 3953.3927 5.434384 1982-1999 –> 2000-2010 9.399584 8234.8440
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + phosphate + phosphate_star 3951.6985 5.435696 1982-1999 –> 2000-2010 9.404103 8232.3834
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3953.5905 5.435232 1982-1999 –> 2000-2010 9.350206 8215.5887
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 3956.8813 5.449379 1982-1999 –> 2000-2010 9.279135 8185.2960
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 3955.2674 5.451041 1982-1999 –> 2000-2010 9.298322 8188.6492
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3957.1520 5.450544 1982-1999 –> 2000-2010 9.281911 8186.2085
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate 2891.8172 3.750315 2000-2010 –> 2011-2019 9.184549 6845.1751
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 2888.7759 3.739468 2000-2010 –> 2011-2019 9.170385 6841.3609
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 2903.8906 3.793686 2000-2010 –> 2011-2019 9.221398 6855.7281
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2899.0903 3.776382 2000-2010 –> 2011-2019 9.209518 6852.1922
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 2882.9929 3.718929 2000-2010 –> 2011-2019 9.153312 6836.3857
Atlantic (26.5,26.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2897.2753 3.769860 2000-2010 –> 2011-2019 9.205093 6850.8658
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 2930.4432 3.890845 2000-2010 –> 2011-2019 9.340224 6887.3245
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2929.2448 3.886407 2000-2010 –> 2011-2019 9.343022 6887.8060
Atlantic (26.5,26.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2912.8918 3.826348 2000-2010 –> 2011-2019 9.276892 6870.0438
Atlantic (26.5,26.75] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 2926.5067 3.876286 2000-2010 –> 2011-2019 9.334490 6885.4367
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 4912.3246 5.920384 1982-1999 –> 2000-2010 10.343511 10243.9122
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4875.3284 5.779125 1982-1999 –> 2000-2010 10.207630 10209.1395
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 4907.9294 5.903423 1982-1999 –> 2000-2010 10.311991 10233.4834
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 4890.4792 5.836562 1982-1999 –> 2000-2010 10.244657 10215.8366
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 4911.9362 5.918883 1982-1999 –> 2000-2010 10.341706 10243.3979
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 4892.2665 5.843375 1982-1999 –> 2000-2010 10.243957 10214.5026
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4889.9929 5.834710 1982-1999 –> 2000-2010 10.244035 10215.8610
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4895.7228 5.856573 1982-1999 –> 2000-2010 10.290194 10231.6466
Atlantic (26.75,27] cstar_tref ~ temp + aou + phosphate + phosphate_star 4899.9337 5.880364 1982-1999 –> 2000-2010 10.340122 10244.6140
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4887.6858 5.825929 1982-1999 –> 2000-2010 10.277507 10231.0066
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 3831.7013 4.007609 2000-2010 –> 2011-2019 9.786734 8707.0297
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate 3758.9213 3.798780 2000-2010 –> 2011-2019 9.702203 8666.8507
Atlantic (26.75,27] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 3753.6168 3.783993 2000-2010 –> 2011-2019 9.620555 8644.0961
Atlantic (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 3758.5171 3.797652 2000-2010 –> 2011-2019 9.641026 8650.7836
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 3753.3893 3.783360 2000-2010 –> 2011-2019 9.618069 8643.3822
Atlantic (26.75,27] cstar_tref ~ sal + temp + silicate + phosphate_star 3799.7096 3.920198 2000-2010 –> 2011-2019 9.776779 8693.4347
Atlantic (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 3757.2186 3.794027 2000-2010 –> 2011-2019 9.783406 8687.2934
Atlantic (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 3757.1716 3.793896 2000-2010 –> 2011-2019 9.619825 8644.8574
Atlantic (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 3757.1238 3.793763 2000-2010 –> 2011-2019 9.785673 8687.8463
Atlantic (26.75,27] cstar_tref ~ temp + silicate + phosphate + phosphate_star 3755.2277 3.794053 2000-2010 –> 2011-2019 9.787725 8684.4005
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 9708.2287 5.485955 1982-1999 –> 2000-2010 10.691809 21027.4023
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 9669.8680 5.418617 1982-1999 –> 2000-2010 10.594458 20967.7400
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 9685.7666 5.446424 1982-1999 –> 2000-2010 10.601804 20969.0461
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 9673.5819 5.425100 1982-1999 –> 2000-2010 10.600221 20970.9421
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 9710.2433 5.489514 1982-1999 –> 2000-2010 10.776014 21086.0492
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 9726.0560 5.517532 1982-1999 –> 2000-2010 10.678626 21013.4168
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 9676.3647 5.429963 1982-1999 –> 2000-2010 10.652281 21007.1702
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate_star 9728.9255 5.526190 1982-1999 –> 2000-2010 10.750963 21059.4631
Atlantic (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 9732.7949 5.529517 1982-1999 –> 2000-2010 10.694911 21023.2245
Atlantic (27,27.25] cstar_tref ~ temp + silicate + phosphate + phosphate_star 9733.4287 5.534207 1982-1999 –> 2000-2010 10.758751 21063.8037
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 7602.3998 4.880163 2000-2010 –> 2011-2019 10.396461 17327.7611
Atlantic (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7663.6587 4.999960 2000-2010 –> 2011-2019 10.418577 17333.5267
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 7606.0063 4.887135 2000-2010 –> 2011-2019 10.416049 17338.4624
Atlantic (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 7658.3056 4.989375 2000-2010 –> 2011-2019 10.435799 17344.0721
Atlantic (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7663.6145 4.999873 2000-2010 –> 2011-2019 10.424972 17337.1963
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 7608.0479 4.891087 2000-2010 –> 2011-2019 10.380601 17318.2912
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7512.0275 4.708652 2000-2010 –> 2011-2019 10.307843 17283.7147
Atlantic (27,27.25] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7499.5910 4.685527 2000-2010 –> 2011-2019 10.203059 17225.6470
Atlantic (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 7679.4920 5.031399 2000-2010 –> 2011-2019 10.461362 17355.8568
Atlantic (27,27.25] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7502.3646 4.690674 2000-2010 –> 2011-2019 10.220191 17235.1595
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 9693.4847 4.306591 1982-1999 –> 2000-2010 8.812258 23007.0844
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 9664.6803 4.269852 1982-1999 –> 2000-2010 8.760099 22962.6895
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 9664.4092 4.269507 1982-1999 –> 2000-2010 8.787763 22990.6986
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate 9673.7224 4.283899 1982-1999 –> 2000-2010 8.865433 23061.2658
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 9675.0810 4.283081 1982-1999 –> 2000-2010 8.864359 23064.3690
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 9675.4408 4.283540 1982-1999 –> 2000-2010 8.863944 23063.8614
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 9681.4543 4.291209 1982-1999 –> 2000-2010 8.889886 23087.9826
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 9661.5928 4.265932 1982-1999 –> 2000-2010 8.768725 22972.2909
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + phosphate + phosphate_star 9675.6017 4.286294 1982-1999 –> 2000-2010 8.881632 23076.8265
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 9677.4595 4.286113 1982-1999 –> 2000-2010 8.878660 23077.9214
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 7987.1358 4.279983 2000-2010 –> 2011-2019 8.689659 17758.1466
Atlantic (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 7985.1341 4.273817 2000-2010 –> 2011-2019 8.669944 17747.7990
Atlantic (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 7962.3102 4.238823 2000-2010 –> 2011-2019 8.545414 17655.7949
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 7942.1338 4.208126 2000-2010 –> 2011-2019 8.477978 17606.8141
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 7953.4754 4.225354 2000-2010 –> 2011-2019 8.494862 17617.8846
Atlantic (27.25,27.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 7940.7543 4.206035 2000-2010 –> 2011-2019 8.471968 17602.3471
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate 7983.8438 4.274910 2000-2010 –> 2011-2019 8.689890 17758.8962
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 7985.1727 4.273877 2000-2010 –> 2011-2019 8.682948 17757.7222
Atlantic (27.25,27.5] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7983.9172 4.271944 2000-2010 –> 2011-2019 8.660643 17740.8966
Atlantic (27.25,27.5] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7993.8832 4.287308 2000-2010 –> 2011-2019 8.681689 17755.2128
Atlantic (27.5,27.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 11078.9044 4.278363 1982-1999 –> 2000-2010 8.576814 23671.9937
Atlantic (27.5,27.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 11079.3526 4.281083 1982-1999 –> 2000-2010 8.616144 23707.5202
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 11041.0553 4.236530 1982-1999 –> 2000-2010 8.554283 23653.7324
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 11024.9923 4.218900 1982-1999 –> 2000-2010 8.549680 23650.8401
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 11041.5152 4.237036 1982-1999 –> 2000-2010 8.609579 23709.3217
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 11027.9940 4.222189 1982-1999 –> 2000-2010 8.576469 23677.5015
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 11075.0238 4.274055 1982-1999 –> 2000-2010 8.584777 23680.5765
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 11075.4762 4.276777 1982-1999 –> 2000-2010 8.622025 23713.9056
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 11077.4655 4.276765 1982-1999 –> 2000-2010 8.604339 23700.0764
Atlantic (27.5,27.75] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 11080.7828 4.280449 1982-1999 –> 2000-2010 8.617658 23713.1158
Atlantic (27.5,27.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 9540.7965 4.101544 2000-2010 –> 2011-2019 8.379907 20619.7008
Atlantic (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 9635.5973 4.218703 2000-2010 –> 2011-2019 8.455233 20676.6526
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 9632.7334 4.215115 2000-2010 –> 2011-2019 8.434015 20657.7257
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 9642.4129 4.227254 2000-2010 –> 2011-2019 8.464289 20683.9280
Atlantic (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 9632.3560 4.214642 2000-2010 –> 2011-2019 8.436832 20660.3499
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 9542.1854 4.103237 2000-2010 –> 2011-2019 8.377291 20617.2092
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 9582.0456 4.152116 2000-2010 –> 2011-2019 8.452259 20680.5101
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate 9630.8842 4.215304 2000-2010 –> 2011-2019 8.492081 20706.3604
Atlantic (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 9631.9897 4.214184 2000-2010 –> 2011-2019 8.490949 20709.4552
Atlantic (27.5,27.75] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 9548.1734 4.110543 2000-2010 –> 2011-2019 8.390992 20628.9562
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 7334.9758 3.981827 1982-1999 –> 2000-2010 8.271951 13358.2567
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate 7335.7408 3.986041 1982-1999 –> 2000-2010 8.304278 13370.6727
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 7337.4951 3.985667 1982-1999 –> 2000-2010 8.303697 13374.3274
Atlantic (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 7347.9786 4.001683 1982-1999 –> 2000-2010 8.303582 13376.9882
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 7337.4903 3.985659 1982-1999 –> 2000-2010 8.302613 13373.8012
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 7342.3062 3.993009 1982-1999 –> 2000-2010 8.328677 13387.6577
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 7338.1796 3.986711 1982-1999 –> 2000-2010 8.311803 13378.4271
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 7345.0352 3.997180 1982-1999 –> 2000-2010 8.325330 13386.7598
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 7342.2302 3.992893 1982-1999 –> 2000-2010 8.329471 13388.0204
Atlantic (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 7342.6203 3.993489 1982-1999 –> 2000-2010 8.323672 13385.3263
Atlantic (27.75,27.85] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 6231.7232 4.921062 2000-2010 –> 2011-2019 8.924660 13580.9525
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 6228.9337 4.914415 2000-2010 –> 2011-2019 8.896242 13563.9095
Atlantic (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 6242.3285 4.946412 2000-2010 –> 2011-2019 8.932079 13579.8236
Atlantic (27.75,27.85] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 6227.1299 4.910122 2000-2010 –> 2011-2019 8.911806 13575.1086
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6236.7491 4.933059 2000-2010 –> 2011-2019 8.926068 13579.0553
Atlantic (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6244.0920 4.950640 2000-2010 –> 2011-2019 8.937351 13582.2716
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 6231.0732 4.919512 2000-2010 –> 2011-2019 8.916692 13576.1084
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6226.2686 4.908074 2000-2010 –> 2011-2019 8.900967 13568.4988
Atlantic (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6235.4368 4.929924 2000-2010 –> 2011-2019 8.927284 13580.5902
Atlantic (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 6230.4064 4.917923 2000-2010 –> 2011-2019 8.911412 13573.0267
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 16337.2277 3.859457 1982-1999 –> 2000-2010 7.726366 28894.5562
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 16293.5145 3.830939 1982-1999 –> 2000-2010 7.741041 28901.1181
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate_star 16350.4886 3.869464 1982-1999 –> 2000-2010 7.780713 28957.4211
Atlantic (27.85,27.95] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 16624.3837 4.052146 1982-1999 –> 2000-2010 7.992237 29266.5678
Atlantic (27.85,27.95] cstar_tref ~ sal + silicate + phosphate + phosphate_star 16665.1536 4.081658 1982-1999 –> 2000-2010 8.049397 29336.9861
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 16334.6766 3.857787 1982-1999 –> 2000-2010 7.779686 28955.9152
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 16301.3411 3.836030 1982-1999 –> 2000-2010 7.746611 28909.4993
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 16460.2838 3.940883 1982-1999 –> 2000-2010 7.854084 29071.4740
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate 16458.7944 3.941225 1982-1999 –> 2000-2010 7.986212 29217.8973
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 16327.7988 3.853288 1982-1999 –> 2000-2010 7.770525 28943.6538
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 13584.9254 4.289875 2000-2010 –> 2011-2019 8.149332 29922.1531
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 13495.5351 4.209395 2000-2010 –> 2011-2019 8.040334 29789.0496
Atlantic (27.85,27.95] cstar_tref ~ sal + aou + silicate + phosphate_star 13585.6566 4.292358 2000-2010 –> 2011-2019 8.161821 29936.1452
Atlantic (27.85,27.95] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 13883.9274 4.570421 2000-2010 –> 2011-2019 8.622568 30508.3112
Atlantic (27.85,27.95] cstar_tref ~ sal + silicate + phosphate + phosphate_star 13896.2389 4.584300 2000-2010 –> 2011-2019 8.665958 30561.3924
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 13536.3023 4.245909 2000-2010 –> 2011-2019 8.103697 29870.9789
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 13508.2150 4.220718 2000-2010 –> 2011-2019 8.056748 29809.5561
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 13521.9337 4.233004 2000-2010 –> 2011-2019 8.173887 29982.2174
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate 13534.3297 4.245934 2000-2010 –> 2011-2019 8.187159 29993.1242
Atlantic (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 13536.0475 4.245680 2000-2010 –> 2011-2019 8.098968 29863.8463
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 18162.5936 4.205570 1982-1999 –> 2000-2010 8.195275 35715.6151
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 17789.1558 3.965596 1982-1999 –> 2000-2010 7.797695 35089.9492
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 17850.1721 4.003848 1982-1999 –> 2000-2010 7.840169 35157.8567
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate_star 17848.3223 4.003943 1982-1999 –> 2000-2010 7.840314 35154.0893
Atlantic (27.95,28.05] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 17886.4129 4.026743 1982-1999 –> 2000-2010 7.911273 35272.2497
Atlantic (27.95,28.05] cstar_tref ~ sal + silicate + phosphate + phosphate_star 17941.1504 4.062849 1982-1999 –> 2000-2010 7.947619 35325.3729
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 18060.9704 4.138863 1982-1999 –> 2000-2010 8.170125 35678.8369
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 17909.0742 4.041125 1982-1999 –> 2000-2010 7.905555 35262.4447
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 17846.8744 4.001771 1982-1999 –> 2000-2010 7.837624 35153.7944
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 17882.9884 4.024574 1982-1999 –> 2000-2010 7.875985 35215.2406
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 13394.7850 4.847917 2000-2010 –> 2011-2019 8.813513 31183.9407
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 13395.0461 4.848201 2000-2010 –> 2011-2019 8.852049 31245.2182
Atlantic (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate_star 13423.4135 4.881294 2000-2010 –> 2011-2019 8.885237 31271.7358
Atlantic (27.95,28.05] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 13533.6307 5.001073 2000-2010 –> 2011-2019 9.027816 31420.0436
Atlantic (27.95,28.05] cstar_tref ~ sal + silicate + phosphate + phosphate_star 13580.4243 5.056037 2000-2010 –> 2011-2019 9.118886 31521.5747
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 13422.6920 4.878319 2000-2010 –> 2011-2019 9.017183 31483.6624
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 13481.2542 4.942738 2000-2010 –> 2011-2019 8.983863 31390.3284
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 13414.9303 4.869844 2000-2010 –> 2011-2019 8.871616 31261.8047
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate 13481.2469 4.942730 2000-2010 –> 2011-2019 9.251220 31797.5137
Atlantic (27.95,28.05] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 13467.0277 4.927011 2000-2010 –> 2011-2019 8.951585 31350.0160
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 13599.7391 4.087323 1982-1999 –> 2000-2010 7.814394 25427.0428
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 13394.0384 3.916073 1982-1999 –> 2000-2010 7.546418 25107.7487
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate_star 13599.8553 4.089123 1982-1999 –> 2000-2010 7.821646 25431.4739
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 13523.8755 4.023311 1982-1999 –> 2000-2010 7.755493 25357.1011
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 13605.7518 4.092440 1982-1999 –> 2000-2010 7.812326 25424.7202
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 13567.6030 4.060084 1982-1999 –> 2000-2010 7.789544 25397.6761
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 13569.8193 4.061956 1982-1999 –> 2000-2010 7.792352 25400.9750
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 13554.9409 4.049401 1982-1999 –> 2000-2010 7.801177 25410.7861
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 13553.4525 4.049832 1982-1999 –> 2000-2010 7.807842 25414.4693
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 13395.6364 3.917376 1982-1999 –> 2000-2010 7.660919 25241.9922
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate_star 10059.3105 4.835988 2000-2010 –> 2011-2019 8.929415 23666.2211
Atlantic (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 10097.1215 4.890815 2000-2010 –> 2011-2019 8.996245 23718.1052
Atlantic (28.05,28.1] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 10088.8259 4.878733 2000-2010 –> 2011-2019 8.969258 23692.3289
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 9885.8490 4.592239 2000-2010 –> 2011-2019 8.508312 23279.8874
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10062.1179 4.840038 2000-2010 –> 2011-2019 8.863348 23585.9935
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10091.4080 4.882490 2000-2010 –> 2011-2019 8.942574 23659.0110
Atlantic (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10127.2848 4.934997 2000-2010 –> 2011-2019 8.996954 23697.1041
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 9970.7270 4.709935 2000-2010 –> 2011-2019 8.759336 23525.6679
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 9981.4731 4.727868 2000-2010 –> 2011-2019 8.777700 23534.9256
Atlantic (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 9795.9238 4.470751 2000-2010 –> 2011-2019 8.388126 23191.5602
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 10330.1445 3.998367 1982-1999 –> 2000-2010 7.239676 18082.1837
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 10284.7001 3.949268 1982-1999 –> 2000-2010 7.189316 18035.5786
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate_star 10328.6195 3.998883 1982-1999 –> 2000-2010 7.241767 18080.1073
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10297.0379 3.962538 1982-1999 –> 2000-2010 7.204691 18049.8529
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 10327.6211 3.995624 1982-1999 –> 2000-2010 7.238096 18080.7293
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10301.5818 3.967436 1982-1999 –> 2000-2010 7.208535 18053.4272
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + phosphate + phosphate_star 10328.1774 3.998403 1982-1999 –> 2000-2010 7.241633 18079.9840
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10304.9579 3.971080 1982-1999 –> 2000-2010 7.213166 18057.7117
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate_star 10320.5589 3.990129 1982-1999 –> 2000-2010 7.232286 18071.3779
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 10282.4678 3.946872 1982-1999 –> 2000-2010 7.236679 18078.7944
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 6586.8666 4.515600 2000-2010 –> 2011-2019 8.464868 16871.5667
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 6586.7214 4.515308 2000-2010 –> 2011-2019 8.477846 16883.7594
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 6622.9393 4.588710 2000-2010 –> 2011-2019 8.556147 16924.5211
Atlantic (28.1,28.15] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 6600.9253 4.543954 2000-2010 –> 2011-2019 8.515034 16905.8832
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 6604.7316 4.551661 2000-2010 –> 2011-2019 8.538706 16924.4470
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 6588.1712 4.518224 2000-2010 –> 2011-2019 8.509534 16911.8187
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 6541.2783 4.424869 2000-2010 –> 2011-2019 8.371740 16823.7462
Atlantic (28.1,28.15] cstar_tref ~ temp + aou + silicate + phosphate_star 6591.7661 4.529493 2000-2010 –> 2011-2019 8.521260 16913.8343
Atlantic (28.1,28.15] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 6605.3271 4.552868 2000-2010 –> 2011-2019 8.550304 16934.6154
Atlantic (28.1,28.15] cstar_tref ~ temp + silicate + phosphate + phosphate_star 6604.7951 4.555845 2000-2010 –> 2011-2019 8.555786 16934.3877
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + nitrate + phosphate 4918.4310 3.646214 1982-1999 –> 2000-2010 7.061905 7727.9992
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate 4917.1696 3.647703 1982-1999 –> 2000-2010 7.070294 7726.8688
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 4915.6130 3.640535 1982-1999 –> 2000-2010 7.063041 7727.2859
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 4914.5533 3.638402 1982-1999 –> 2000-2010 7.060981 7726.2490
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 4927.9207 3.665402 1982-1999 –> 2000-2010 7.097418 7742.5240
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 4916.7100 3.642744 1982-1999 –> 2000-2010 7.092926 7736.8879
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 4917.5277 3.644392 1982-1999 –> 2000-2010 7.094629 7737.7224
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + phosphate + phosphate_star 4915.2535 3.643840 1982-1999 –> 2000-2010 7.098759 7734.8806
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate 4915.6321 3.644603 1982-1999 –> 2000-2010 7.101010 7735.7137
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 4914.4446 3.638183 1982-1999 –> 2000-2010 7.093102 7736.0714
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate 2334.5648 3.463431 2000-2010 –> 2011-2019 7.101832 7249.1181
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 2308.9709 3.363254 2000-2010 –> 2011-2019 7.039058 7242.0153
Atlantic (28.15,28.2] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 2322.5095 3.415879 2000-2010 –> 2011-2019 7.081280 7250.4302
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 2344.8870 3.504672 2000-2010 –> 2011-2019 7.149064 7262.4147
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 2331.4349 3.451021 2000-2010 –> 2011-2019 7.137746 7269.8427
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate 2348.4359 3.527045 2000-2010 –> 2011-2019 7.171648 7264.0679
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 2331.6254 3.451776 2000-2010 –> 2011-2019 7.089958 7246.0700
Atlantic (28.15,28.2] cstar_tref ~ temp + aou + silicate + phosphate_star 2333.3468 3.466538 2000-2010 –> 2011-2019 7.153366 7269.8055
Atlantic (28.15,28.2] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 2337.0773 3.473424 2000-2010 –> 2011-2019 7.148280 7269.6551
Atlantic (28.15,28.2] cstar_tref ~ temp + silicate + phosphate + phosphate_star 2340.2535 3.494104 2000-2010 –> 2011-2019 7.169556 7271.1246
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 10750.1547 3.195897 1982-1999 –> 2000-2010 6.037790 16237.8492
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + phosphate + phosphate_star 10755.2490 3.201352 1982-1999 –> 2000-2010 6.054436 16249.6765
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 10757.2462 3.201350 1982-1999 –> 2000-2010 6.053806 16253.1843
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 10790.0423 3.226688 1982-1999 –> 2000-2010 6.061429 16272.1382
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 10731.3487 3.181482 1982-1999 –> 2000-2010 6.060807 16248.1191
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 10728.7370 3.179486 1982-1999 –> 2000-2010 6.023418 16218.0259
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10731.0986 3.181291 1982-1999 –> 2000-2010 6.053994 16242.7529
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 10744.1035 3.191252 1982-1999 –> 2000-2010 6.060164 16252.8239
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + phosphate + phosphate_star 10748.0965 3.195853 1982-1999 –> 2000-2010 6.073061 16261.2329
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10750.0516 3.195818 1982-1999 –> 2000-2010 6.052061 16248.9378
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 5149.7745 3.397095 2000-2010 –> 2011-2019 6.592993 15899.9291
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 5110.9188 3.329870 2000-2010 –> 2011-2019 6.600185 15956.8299
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + phosphate + phosphate_star 5148.0960 3.397657 2000-2010 –> 2011-2019 6.599009 15903.3450
Atlantic (28.2, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 5107.7700 3.324481 2000-2010 –> 2011-2019 6.525831 15865.0161
Atlantic (28.2, Inf] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 5136.1313 3.373338 2000-2010 –> 2011-2019 6.568755 15885.6616
Atlantic (28.2, Inf] cstar_tref ~ sal + silicate + phosphate + phosphate_star 5140.2175 3.383915 2000-2010 –> 2011-2019 6.585412 15895.6541
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 5149.0059 3.395753 2000-2010 –> 2011-2019 6.575238 15877.7429
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate 5111.0241 3.330051 2000-2010 –> 2011-2019 6.564791 15911.4345
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 5101.6502 3.314032 2000-2010 –> 2011-2019 6.495323 15832.7488
Atlantic (28.2, Inf] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 5096.3574 3.305021 2000-2010 –> 2011-2019 6.500839 15846.4090
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 22961.4289 6.046591 1982-1999 –> 2000-2010 14.236288 31977.1892
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 23304.7553 6.344873 1982-1999 –> 2000-2010 14.597031 32339.9356
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 23126.3147 6.189788 1982-1999 –> 2000-2010 14.387600 32142.6063
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 22976.8754 6.059705 1982-1999 –> 2000-2010 14.104247 31946.9264
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 22986.7044 6.068064 1982-1999 –> 2000-2010 14.106606 31954.8483
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 23125.4654 6.187315 1982-1999 –> 2000-2010 14.316187 32122.1714
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 23409.4149 6.438695 1982-1999 –> 2000-2010 14.547965 32399.9501
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 23448.2206 6.473833 1982-1999 –> 2000-2010 14.569690 32434.5241
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 23036.5127 6.110602 1982-1999 –> 2000-2010 14.137054 32000.8094
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 23464.3603 6.488504 1982-1999 –> 2000-2010 14.582292 32450.0108
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 22455.5956 4.607565 2000-2010 –> 2011-2019 10.654156 45417.0244
Indo-Pacific (-Inf,26] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 23646.0865 5.387137 2000-2010 –> 2011-2019 11.732009 46950.8417
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate 22954.8055 4.920990 2000-2010 –> 2011-2019 11.110778 46081.1201
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate 22846.8547 4.850457 2000-2010 –> 2011-2019 10.910161 45823.7300
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 22875.9744 4.869038 2000-2010 –> 2011-2019 10.937102 45862.6787
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + nitrate + silicate 22949.6472 4.916367 2000-2010 –> 2011-2019 11.103682 46075.1126
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate 23959.1150 5.613169 2000-2010 –> 2011-2019 12.051864 47368.5299
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 24048.5769 5.679493 2000-2010 –> 2011-2019 12.153327 47496.7975
Indo-Pacific (-Inf,26] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 23070.0181 4.994687 2000-2010 –> 2011-2019 11.105290 46106.5308
Indo-Pacific (-Inf,26] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 23714.4483 5.435710 2000-2010 –> 2011-2019 12.123788 47394.8082
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 16278.6346 4.758499 1982-1999 –> 2000-2010 11.733905 26316.1177
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 16326.3244 4.800244 1982-1999 –> 2000-2010 11.733395 26345.6887
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 16214.9873 4.703351 1982-1999 –> 2000-2010 11.693842 26258.9124
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 16229.3888 4.715773 1982-1999 –> 2000-2010 11.726174 26281.7950
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 16352.8769 4.823645 1982-1999 –> 2000-2010 11.807644 26394.0318
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 16390.2402 4.856766 1982-1999 –> 2000-2010 11.868495 26443.2113
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 16234.4699 4.720164 1982-1999 –> 2000-2010 11.734573 26288.5805
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 16377.6840 4.845610 1982-1999 –> 2000-2010 11.859460 26431.5570
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 16391.9135 4.858255 1982-1999 –> 2000-2010 11.871070 26445.3464
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 16408.2533 4.874601 1982-1999 –> 2000-2010 11.897042 26463.7768
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 10825.9734 4.041757 2000-2010 –> 2011-2019 8.800256 27104.6080
Indo-Pacific (26,26.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 10782.4235 3.996178 2000-2010 –> 2011-2019 8.796422 27108.7479
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate 10896.5545 4.116734 2000-2010 –> 2011-2019 8.820085 27111.5418
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 10931.9794 4.154887 2000-2010 –> 2011-2019 8.870660 27161.3682
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 10877.6390 4.096505 2000-2010 –> 2011-2019 8.920149 27230.5160
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 10923.6380 4.145872 2000-2010 –> 2011-2019 9.002638 27313.8782
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 10939.5339 4.163069 2000-2010 –> 2011-2019 8.883233 27174.0038
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10895.0448 4.115115 2000-2010 –> 2011-2019 8.960726 27272.7288
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 10924.4452 4.146743 2000-2010 –> 2011-2019 9.004998 27316.3587
Indo-Pacific (26,26.5] cstar_tref ~ sal + temp + silicate + phosphate_star 10924.3283 4.148777 2000-2010 –> 2011-2019 9.023378 27332.5816
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 18108.2897 5.515598 1982-1999 –> 2000-2010 10.847566 28109.5779
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 18101.5040 5.507232 1982-1999 –> 2000-2010 10.833499 28101.3368
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 17622.8233 5.070097 1982-1999 –> 2000-2010 10.085528 27428.4323
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 18041.2827 5.450229 1982-1999 –> 2000-2010 10.866399 28095.1800
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate 17727.2908 5.162438 1982-1999 –> 2000-2010 10.260131 27585.4478
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 17792.6666 5.221078 1982-1999 –> 2000-2010 10.365647 27680.3893
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 17802.8631 5.230284 1982-1999 –> 2000-2010 10.386866 27698.1195
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 17916.4183 5.335754 1982-1999 –> 2000-2010 10.782319 27986.3916
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 17828.4324 5.253441 1982-1999 –> 2000-2010 10.697963 27899.1943
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 18072.9574 5.480137 1982-1999 –> 2000-2010 10.798293 28067.8681
Indo-Pacific (26.5,26.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 10253.8653 4.848552 2000-2010 –> 2011-2019 10.355784 28355.3692
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 10212.3644 4.790004 2000-2010 –> 2011-2019 9.860100 27835.1877
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 10291.1466 4.901758 2000-2010 –> 2011-2019 10.351987 28332.4293
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate 10232.1991 4.817897 2000-2010 –> 2011-2019 9.980335 27959.4900
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 10252.9895 4.847309 2000-2010 –> 2011-2019 10.068387 28045.6561
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 10317.0223 4.939029 2000-2010 –> 2011-2019 10.436552 28408.3139
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate + phosphate_star 10254.9756 4.850128 2000-2010 –> 2011-2019 10.080412 28057.8388
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + phosphate_star 10272.5625 4.878018 2000-2010 –> 2011-2019 10.213772 28188.9808
Indo-Pacific (26.5,26.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 10249.7820 4.842760 2000-2010 –> 2011-2019 10.096201 28078.2144
Indo-Pacific (26.5,26.75] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 10287.1328 4.896001 2000-2010 –> 2011-2019 10.434333 28421.2301
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 26548.6370 5.015004 1982-1999 –> 2000-2010 10.446224 43951.6992
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 26479.5872 4.974466 1982-1999 –> 2000-2010 10.364884 43842.4958
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 26440.5342 4.952323 1982-1999 –> 2000-2010 10.379156 43841.0792
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 26675.5767 5.087093 1982-1999 –> 2000-2010 10.567073 44130.6004
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 26391.0780 4.924424 1982-1999 –> 2000-2010 10.313134 43752.2156
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 26609.1855 5.048658 1982-1999 –> 2000-2010 10.471774 44005.9003
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 26728.1053 5.117710 1982-1999 –> 2000-2010 10.576339 44161.3073
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 26622.6444 5.056426 1982-1999 –> 2000-2010 10.582280 44124.2683
Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 26730.7658 5.119265 1982-1999 –> 2000-2010 10.582158 44168.3320
Indo-Pacific (26.75,27] cstar_tref ~ temp + nitrate + silicate + phosphate_star 26729.3465 5.119605 1982-1999 –> 2000-2010 10.604272 44187.1487
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 16483.1695 4.428586 2000-2010 –> 2011-2019 9.443590 43031.8066
Indo-Pacific (26.75,27] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 16463.8316 4.411940 2000-2010 –> 2011-2019 9.386406 42943.4188
Indo-Pacific (26.75,27] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 16428.4950 4.384510 2000-2010 –> 2011-2019 9.336833 42869.0292
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + nitrate + phosphate 16551.9213 4.481069 2000-2010 –> 2011-2019 9.614471 43306.8286
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 16694.8478 4.595543 2000-2010 –> 2011-2019 9.679548 43365.1100
Indo-Pacific (26.75,27] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 16688.9743 4.590781 2000-2010 –> 2011-2019 9.677874 43364.5510
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate 16585.8757 4.509594 2000-2010 –> 2011-2019 9.670673 43385.8521
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 16461.5367 4.410153 2000-2010 –> 2011-2019 9.334577 42852.6147
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 16579.5856 4.503001 2000-2010 –> 2011-2019 9.551659 43188.7711
Indo-Pacific (26.75,27] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 16699.4864 4.599306 2000-2010 –> 2011-2019 9.655732 43322.1308
Indo-Pacific (27,27.25] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 35670.0603 4.974370 1982-1999 –> 2000-2010 10.608943 57341.3366
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 35309.5480 4.824617 1982-1999 –> 2000-2010 10.444095 56962.3681
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 35308.5742 4.825037 1982-1999 –> 2000-2010 10.591578 57137.1300
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 35284.8459 4.814522 1982-1999 –> 2000-2010 10.566343 57097.8167
Indo-Pacific (27,27.25] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 35474.6985 4.892651 1982-1999 –> 2000-2010 10.628761 57268.8515
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 35231.4757 4.792785 1982-1999 –> 2000-2010 10.404049 56874.2321
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 35310.1065 4.824845 1982-1999 –> 2000-2010 10.586820 57135.2123
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 35510.4214 4.907493 1982-1999 –> 2000-2010 10.603724 57256.5760
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 35303.9350 4.822321 1982-1999 –> 2000-2010 10.455265 56973.2222
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 35173.8071 4.769407 1982-1999 –> 2000-2010 10.379146 56814.6937
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 21818.7859 4.156484 2000-2010 –> 2011-2019 9.086054 57382.1476
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 21829.0519 4.162052 2000-2010 –> 2011-2019 8.986669 57138.5999
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate 21852.8010 4.176052 2000-2010 –> 2011-2019 9.001088 57161.3753
Indo-Pacific (27,27.25] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 21748.6218 4.118624 2000-2010 –> 2011-2019 8.933147 57033.4678
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 21776.6548 4.133709 2000-2010 –> 2011-2019 8.926494 57008.1305
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate 21790.9111 4.141401 2000-2010 –> 2011-2019 8.966247 57101.0177
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 21857.3829 4.177458 2000-2010 –> 2011-2019 9.057590 57301.8644
Indo-Pacific (27,27.25] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 21848.5346 4.172640 2000-2010 –> 2011-2019 9.042079 57267.1450
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 21760.3106 4.124907 2000-2010 –> 2011-2019 8.947228 57064.2456
Indo-Pacific (27,27.25] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 21709.3642 4.097592 2000-2010 –> 2011-2019 8.866999 56883.1712
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 35490.2196 4.527821 1982-1999 –> 2000-2010 9.529209 57859.7438
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 35268.1904 4.444842 1982-1999 –> 2000-2010 9.430180 57615.9867
Indo-Pacific (27.25,27.5] cstar_tref ~ aou + silicate + phosphate + phosphate_star 35417.7023 4.500793 1982-1999 –> 2000-2010 9.570596 57887.5221
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 35268.3069 4.444885 1982-1999 –> 2000-2010 9.442561 57634.3501
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 34790.6996 4.273022 1982-1999 –> 2000-2010 9.340352 57258.9176
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 34993.4022 4.345136 1982-1999 –> 2000-2010 9.110538 57008.1285
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 34882.2957 4.305459 1982-1999 –> 2000-2010 9.598910 57672.7848
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 34769.1797 4.265437 1982-1999 –> 2000-2010 9.020252 56767.4865
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + phosphate + phosphate_star 35103.4606 4.385523 1982-1999 –> 2000-2010 9.177101 57156.6244
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 34416.6766 4.143086 1982-1999 –> 2000-2010 8.865441 56364.4154
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 23672.7042 3.394415 2000-2010 –> 2011-2019 7.742852 58675.3055
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate 23788.8206 3.439468 2000-2010 –> 2011-2019 7.791026 58798.1111
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 23606.4332 3.369396 2000-2010 –> 2011-2019 7.642418 58397.1328
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + nitrate + silicate + phosphate + phosphate_star 23817.3716 3.449678 2000-2010 –> 2011-2019 7.900315 59101.3422
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate 23620.9549 3.374862 2000-2010 –> 2011-2019 7.680321 58503.2506
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 23643.5537 3.383387 2000-2010 –> 2011-2019 7.737249 58661.2558
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 23742.7748 3.421070 2000-2010 –> 2011-2019 7.771864 58751.9371
Indo-Pacific (27.25,27.5] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 23640.0614 3.382068 2000-2010 –> 2011-2019 7.726709 58632.0839
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 24377.2710 3.672173 2000-2010 –> 2011-2019 7.937610 59146.4508
Indo-Pacific (27.25,27.5] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 24127.5050 3.571200 2000-2010 –> 2011-2019 7.714286 58544.1816
Indo-Pacific (27.5,27.75] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 37411.4844 3.798735 1982-1999 –> 2000-2010 8.395065 60782.7417
Indo-Pacific (27.5,27.75] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 37329.1664 3.775225 1982-1999 –> 2000-2010 8.364257 60689.8157
Indo-Pacific (27.5,27.75] cstar_tref ~ aou + silicate + phosphate + phosphate_star 37424.9994 3.802517 1982-1999 –> 2000-2010 8.395891 60791.1534
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 37160.4366 3.728615 1982-1999 –> 2000-2010 8.316642 60519.3477
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + phosphate + phosphate_star 37439.2685 3.806513 1982-1999 –> 2000-2010 8.399806 60805.2797
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 36877.1435 3.651649 1982-1999 –> 2000-2010 8.237501 60232.2915
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 37407.1093 3.796952 1982-1999 –> 2000-2010 8.167875 60381.4132
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 37370.5001 3.786732 1982-1999 –> 2000-2010 8.157635 60344.7676
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + phosphate + phosphate_star 37545.1263 3.836297 1982-1999 –> 2000-2010 8.207287 60517.5503
Indo-Pacific (27.5,27.75] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 37323.2376 3.773577 1982-1999 –> 2000-2010 8.117956 60249.2110
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 26426.9090 3.287086 2000-2010 –> 2011-2019 7.251045 64418.6502
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate 26781.3598 3.404881 2000-2010 –> 2011-2019 7.374287 64789.7531
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 26569.2213 3.333619 2000-2010 –> 2011-2019 6.985268 63446.3647
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + nitrate + phosphate_star 27497.7682 3.653830 2000-2010 –> 2011-2019 7.439450 64864.2829
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 27347.5437 3.600013 2000-2010 –> 2011-2019 7.396965 64754.6530
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate 26503.2206 3.311957 2000-2010 –> 2011-2019 6.988743 63473.5369
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 26421.4788 3.285324 2000-2010 –> 2011-2019 6.994600 63511.2864
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 26564.3461 3.332014 2000-2010 –> 2011-2019 7.022177 63583.9871
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 26431.6349 3.288621 2000-2010 –> 2011-2019 6.996176 63515.1393
Indo-Pacific (27.5,27.75] cstar_tref ~ sal + temp + silicate + phosphate_star 26668.9420 3.367282 2000-2010 –> 2011-2019 7.090629 63808.1753
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 17704.3157 3.213514 1982-1999 –> 2000-2010 7.240497 28156.2970
Indo-Pacific (27.75,27.85] cstar_tref ~ aou + silicate + phosphate + phosphate_star 17703.3629 3.214006 1982-1999 –> 2000-2010 7.253794 28165.1283
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 17758.2469 3.238951 1982-1999 –> 2000-2010 7.240365 28186.5833
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 17705.0336 3.213851 1982-1999 –> 2000-2010 7.242544 28158.5899
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + nitrate + phosphate 17749.1350 3.234639 1982-1999 –> 2000-2010 7.270347 28209.1493
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 17758.7886 3.239208 1982-1999 –> 2000-2010 7.266514 28211.0673
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 17685.1866 3.204539 1982-1999 –> 2000-2010 7.257858 28161.3640
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 17753.4811 3.236695 1982-1999 –> 2000-2010 7.252665 28195.2959
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 17683.3143 3.203662 1982-1999 –> 2000-2010 7.262376 28164.4294
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 17684.1423 3.204050 1982-1999 –> 2000-2010 7.238697 28143.1807
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate 13946.1878 3.274557 2000-2010 –> 2011-2019 6.479096 31631.3744
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 13890.0732 3.240378 2000-2010 –> 2011-2019 6.444047 31573.4036
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 13872.8989 3.229989 2000-2010 –> 2011-2019 6.445734 31581.9640
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 13889.6845 3.240142 2000-2010 –> 2011-2019 6.443882 31573.1654
Indo-Pacific (27.75,27.85] cstar_tref ~ sal + temp + silicate + phosphate_star 13888.2407 3.240479 2000-2010 –> 2011-2019 6.473591 31632.1442
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 13909.2389 3.252011 2000-2010 –> 2011-2019 6.455673 31592.5532
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 13865.8640 3.225743 2000-2010 –> 2011-2019 6.428552 31547.3576
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 13835.6430 3.207566 2000-2010 –> 2011-2019 6.411615 31519.7852
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 13873.1643 3.230149 2000-2010 –> 2011-2019 6.433072 31554.9012
Indo-Pacific (27.75,27.85] cstar_tref ~ temp + nitrate + silicate + phosphate_star 13911.7260 3.254741 2000-2010 –> 2011-2019 6.472033 31622.0796
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 23458.7128 2.891195 1982-1999 –> 2000-2010 6.933172 38123.4718
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 23388.5950 2.869220 1982-1999 –> 2000-2010 6.910043 38053.8680
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 23426.0533 2.880613 1982-1999 –> 2000-2010 6.915152 38083.2274
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + nitrate + phosphate 23454.0281 2.889152 1982-1999 –> 2000-2010 6.937623 38129.1422
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate 23490.5449 2.900949 1982-1999 –> 2000-2010 6.957221 38173.6762
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 23460.2389 2.891051 1982-1999 –> 2000-2010 6.933002 38126.9655
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 23381.0773 2.866939 1982-1999 –> 2000-2010 6.922452 38065.2358
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 23405.0802 2.874229 1982-1999 –> 2000-2010 6.946856 38111.1530
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 23376.6622 2.865600 1982-1999 –> 2000-2010 6.961046 38111.8115
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 23408.7498 2.875345 1982-1999 –> 2000-2010 6.949573 38116.8679
Indo-Pacific (27.85,27.95] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 20084.9753 3.099919 2000-2010 –> 2011-2019 5.969139 43473.5703
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate 20098.7765 3.105360 2000-2010 –> 2011-2019 5.971894 43478.5189
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + aou + silicate + phosphate_star 20078.1636 3.097237 2000-2010 –> 2011-2019 5.971313 43482.7418
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 20066.6977 3.092728 2000-2010 –> 2011-2019 5.979143 43511.7676
Indo-Pacific (27.85,27.95] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 20078.2442 3.097269 2000-2010 –> 2011-2019 5.972495 43486.6038
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 20057.0137 3.088925 2000-2010 –> 2011-2019 5.955864 43438.0911
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + nitrate + silicate + phosphate_star 20049.8487 3.086114 2000-2010 –> 2011-2019 5.960342 43454.9289
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate 20132.3381 3.119424 2000-2010 –> 2011-2019 5.986365 43511.4238
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 20126.7301 3.116410 2000-2010 –> 2011-2019 5.982010 43503.3922
Indo-Pacific (27.85,27.95] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 20050.0225 3.086182 2000-2010 –> 2011-2019 5.961527 43458.7723
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 40311.3322 2.840684 1982-1999 –> 2000-2010 6.738397 68761.4222
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 40262.4033 2.831855 1982-1999 –> 2000-2010 6.711073 68665.8242
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + silicate + phosphate + phosphate_star 40280.2050 2.835285 1982-1999 –> 2000-2010 6.762495 68807.4383
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 40312.9605 2.840619 1982-1999 –> 2000-2010 6.717811 68711.0367
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + phosphate + phosphate_star 40314.5711 2.841246 1982-1999 –> 2000-2010 6.739890 68767.1035
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 40223.2178 2.825081 1982-1999 –> 2000-2010 6.723270 68676.5558
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 40314.1488 2.840825 1982-1999 –> 2000-2010 6.727381 68736.9066
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 40312.6635 2.840568 1982-1999 –> 2000-2010 6.735407 68757.2060
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + phosphate + phosphate_star 40315.0642 2.841332 1982-1999 –> 2000-2010 6.782980 68879.8455
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 40278.5337 2.834649 1982-1999 –> 2000-2010 6.740287 68751.4084
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 34259.8936 3.118200 2000-2010 –> 2011-2019 5.958884 74571.2258
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 34224.2058 3.109441 2000-2010 –> 2011-2019 5.941296 74486.6091
Indo-Pacific (27.95,28.05] cstar_tref ~ aou + silicate + phosphate + phosphate_star 34375.4048 3.145200 2000-2010 –> 2011-2019 5.980485 74655.6098
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 34261.7734 3.118172 2000-2010 –> 2011-2019 5.958791 74574.7340
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 34250.4602 3.115540 2000-2010 –> 2011-2019 5.940622 74473.6779
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + aou + silicate + phosphate 34236.4965 3.112295 2000-2010 –> 2011-2019 5.952792 74548.7558
Indo-Pacific (27.95,28.05] cstar_tref ~ sal + temp + nitrate + silicate + phosphate_star 34278.1438 3.121984 2000-2010 –> 2011-2019 5.981323 74698.5775
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 34258.1893 3.117338 2000-2010 –> 2011-2019 5.957906 74570.8527
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 34225.1108 3.109651 2000-2010 –> 2011-2019 5.952092 74548.5601
Indo-Pacific (27.95,28.05] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 34376.7606 3.145049 2000-2010 –> 2011-2019 5.979697 74655.2943
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 29524.9390 2.706447 1982-1999 –> 2000-2010 6.684016 49102.6083
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + silicate + phosphate + phosphate_star 29541.7982 2.710627 1982-1999 –> 2000-2010 6.701221 49140.3144
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 29470.2120 2.694355 1982-1999 –> 2000-2010 6.662013 49030.4473
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 29476.1827 2.696113 1982-1999 –> 2000-2010 6.663828 49034.5186
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 29448.5325 2.689580 1982-1999 –> 2000-2010 6.646498 48989.8265
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 29454.1074 2.690808 1982-1999 –> 2000-2010 6.648125 48996.1075
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 29412.0778 2.681570 1982-1999 –> 2000-2010 6.652237 48977.6122
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 29454.8249 2.690965 1982-1999 –> 2000-2010 6.681217 49054.7411
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + phosphate + phosphate_star 29476.0879 2.696092 1982-1999 –> 2000-2010 6.694802 49088.8009
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 29455.3638 2.691084 1982-1999 –> 2000-2010 6.680235 49053.3526
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + nitrate + phosphate + phosphate_star 35192.7171 2.961631 2000-2010 –> 2011-2019 5.668078 64715.6570
Indo-Pacific (28.05,28.1] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 35173.8549 2.957235 2000-2010 –> 2011-2019 5.663683 64698.7939
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 35030.5646 2.927221 2000-2010 –> 2011-2019 5.621576 64500.7766
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 34976.0727 2.915886 2000-2010 –> 2011-2019 5.652040 64634.4312
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + phosphate + phosphate_star 35211.3124 2.965555 2000-2010 –> 2011-2019 5.661668 64687.4951
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 35125.9547 2.947168 2000-2010 –> 2011-2019 5.636748 64574.4873
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 35089.3057 2.939488 2000-2010 –> 2011-2019 5.630296 64543.4131
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + aou + silicate + phosphate 35115.2984 2.944933 2000-2010 –> 2011-2019 5.626503 64527.3761
Indo-Pacific (28.05,28.1] cstar_tref ~ sal + temp + silicate + phosphate + phosphate_star 35176.3869 2.957769 2000-2010 –> 2011-2019 5.665762 64708.3082
Indo-Pacific (28.05,28.1] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 35193.8707 2.961453 2000-2010 –> 2011-2019 5.652418 64648.6956
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 39943.1941 3.095167 1982-1999 –> 2000-2010 7.022166 79975.8427
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + silicate + phosphate + phosphate_star 40345.3847 3.176063 1982-1999 –> 2000-2010 7.118553 80432.5698
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 41401.9773 3.397228 1982-1999 –> 2000-2010 7.369553 81599.4258
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 40246.0015 3.155575 1982-1999 –> 2000-2010 7.094079 80320.6587
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 41607.2888 3.442043 1982-1999 –> 2000-2010 7.303353 81397.6997
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate 41672.9863 3.456949 1982-1999 –> 2000-2010 7.328579 81499.7234
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + phosphate + phosphate_star 41468.4418 3.411671 1982-1999 –> 2000-2010 7.279663 81283.6817
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 41094.0597 3.331107 1982-1999 –> 2000-2010 7.190571 80877.6059
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 40145.4433 3.135385 1982-1999 –> 2000-2010 7.001291 79952.9361
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + nitrate + silicate + phosphate + phosphate_star 41556.4978 3.430902 1982-1999 –> 2000-2010 7.354405 81576.3583
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + nitrate + silicate + phosphate + phosphate_star 32015.7104 2.690536 2000-2010 –> 2011-2019 5.785703 71958.9044
Indo-Pacific (28.1, Inf] cstar_tref ~ aou + silicate + phosphate + phosphate_star 32351.2854 2.759774 2000-2010 –> 2011-2019 5.935837 72696.6701
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + phosphate + phosphate_star 31722.2050 2.631750 2000-2010 –> 2011-2019 6.028978 73124.1824
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + nitrate + silicate + phosphate 31878.5023 2.662893 2000-2010 –> 2011-2019 6.130084 73599.8301
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + phosphate + phosphate_star 31786.8244 2.644980 2000-2010 –> 2011-2019 6.151227 73681.6383
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + aou + silicate + phosphate + phosphate_star 31737.2943 2.634741 2000-2010 –> 2011-2019 5.790317 71983.2958
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + nitrate + phosphate 31873.3300 2.661857 2000-2010 –> 2011-2019 6.103900 73480.6188
Indo-Pacific (28.1, Inf] cstar_tref ~ sal + temp + aou + phosphate + phosphate_star 31645.2256 2.616546 2000-2010 –> 2011-2019 6.122316 73539.9053
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + nitrate + silicate + phosphate 32611.5835 2.813953 2000-2010 –> 2011-2019 6.145060 73705.6432
Indo-Pacific (28.1, Inf] cstar_tref ~ temp + aou + silicate + phosphate + phosphate_star 31974.4244 2.682189 2000-2010 –> 2011-2019 5.817573 72119.8677

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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
ac1a836 jens-daniel-mueller 2021-02-24
b03fbd3 jens-daniel-mueller 2021-02-24
3d3b4cc jens-daniel-mueller 2021-02-23
7b672f7 jens-daniel-mueller 2021-01-11
33ba23c jens-daniel-mueller 2021-01-07
318609d jens-daniel-mueller 2020-12-23
9d0b2d0 jens-daniel-mueller 2020-12-23
0aa2b50 jens-daniel-mueller 2020-12-23
2886da0 jens-daniel-mueller 2020-12-19
02f0ee9 jens-daniel-mueller 2020-12-18
7bcb4eb jens-daniel-mueller 2020-12-18
7131186 jens-daniel-mueller 2020-12-17
5b48ef5 jens-daniel-mueller 2020-12-17
f3a708f jens-daniel-mueller 2020-12-17

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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
ac1a836 jens-daniel-mueller 2021-02-24
b03fbd3 jens-daniel-mueller 2021-02-24
3d3b4cc jens-daniel-mueller 2021-02-23
7b672f7 jens-daniel-mueller 2021-01-11
33ba23c jens-daniel-mueller 2021-01-07
318609d jens-daniel-mueller 2020-12-23
9d0b2d0 jens-daniel-mueller 2020-12-23
0aa2b50 jens-daniel-mueller 2020-12-23
2886da0 jens-daniel-mueller 2020-12-19
02f0ee9 jens-daniel-mueller 2020-12-18
7bcb4eb jens-daniel-mueller 2020-12-18
7131186 jens-daniel-mueller 2020-12-17
5b48ef5 jens-daniel-mueller 2020-12-17
f3a708f jens-daniel-mueller 2020-12-17

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

7.2.2 Best models

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

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

Version Author Date
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
ac1a836 jens-daniel-mueller 2021-02-24
b03fbd3 jens-daniel-mueller 2021-02-24
3d3b4cc jens-daniel-mueller 2021-02-23
7b672f7 jens-daniel-mueller 2021-01-11
33ba23c jens-daniel-mueller 2021-01-07
318609d jens-daniel-mueller 2020-12-23
9d0b2d0 jens-daniel-mueller 2020-12-23
0aa2b50 jens-daniel-mueller 2020-12-23
2886da0 jens-daniel-mueller 2020-12-19
02f0ee9 jens-daniel-mueller 2020-12-18
7bcb4eb jens-daniel-mueller 2020-12-18
7131186 jens-daniel-mueller 2020-12-17
a84ff3c jens-daniel-mueller 2020-12-17 
rm(max_rmse)

7.3 Predictor counts

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

# calculate cases of predictor used
lm_all_stats <- lm_best_cant %>% 
  pivot_longer(starts_with("delta_coeff_"),
               names_to = "term",
               names_prefix = "delta_coeff_",
               values_to = "delta_coeff") %>% 
  filter(term != "(Intercept)",
         delta_coeff != 0) %>% 
  group_by(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 --> 2000-2010
(-Inf,26] 8 10 7 7 5 5 8
(26,26.5] 10 8 9 7 4 4 6
(26.5,26.75] 7 3 8 9 7 4 10
(26.75,27] 7 4 7 9 7 5 10
(27,27.25] 6 4 6 9 4 9 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 5 8 6 7 10 6
(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] 9 3 10 5 5 5 10
(28.2, Inf] 7 4 8 9 10 3 7
total 100.00 61.00 105.00 110.00 99.00 86.00 112.00
Atlantic - 2000-2010 --> 2011-2019
(-Inf,26] 7 10 8 8 4 4 8
(26,26.5] 9 10 8 7 3 4 7
(26.5,26.75] 7 6 7 8 6 6 10
(26.75,27] 5 3 6 9 6 9 10
(27,27.25] 6 7 6 9 5 7 10
(27.25,27.5] 8 10 9 7 4 3 7
(27.5,27.75] 8 4 8 7 4 10 8
(27.75,27.85] 7 6 8 8 5 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 7 10 7 7 7
(28.1,28.15] 6 4 6 10 4 8 10
(28.15,28.2] 7 3 7 7 3 10 10
(28.2, Inf] 7 3 9 8 10 7 4
total 95.00 76.00 103.00 113.00 81.00 104.00 107.00
Indo-Pacific - 1982-1999 --> 2000-2010
(-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] 7 9 7 9 2 7 7
(27,27.25] 8 5 9 7 7 8 5
(27.25,27.5] 10 4 10 9 4 5 5
(27.5,27.75] 10 4 10 10 4 4 4
(27.75,27.85] 10 5 10 7 5 6 6
(27.85,27.95] 9 9 9 7 2 5 7
(27.95,28.05] 10 4 10 10 4 4 4
(28.05,28.1] 10 3 10 9 5 5 5
(28.1, Inf] 9 7 10 7 3 6 6
total 104.00 70.00 104.00 98.00 63.00 64.00 71.00
Indo-Pacific - 2000-2010 --> 2011-2019
(-Inf,26] 9 7 6 6 9 4 8
(26,26.5] 6 5 6 8 10 6 8
(26.5,26.75] 7 8 7 7 8 5 7
(26.75,27] 9 8 9 7 4 4 7
(27,27.25] 9 3 9 7 8 7 6
(27.25,27.5] 7 4 8 7 8 9 6
(27.5,27.75] 7 3 6 7 10 8 7
(27.75,27.85] 5 5 5 8 5 10 10
(27.85,27.95] 7 5 7 7 4 10 9
(27.95,28.05] 9 6 9 8 4 7 5
(28.05,28.1] 9 5 10 8 7 5 4
(28.1, Inf] 10 5 10 7 6 6 4
total 94.00 64.00 92.00 87.00 83.00 81.00 81.00

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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
ac1a836 jens-daniel-mueller 2021-02-24
b03fbd3 jens-daniel-mueller 2021-02-24
3d3b4cc jens-daniel-mueller 2021-02-23
7b672f7 jens-daniel-mueller 2021-01-11
33ba23c jens-daniel-mueller 2021-01-07
318609d jens-daniel-mueller 2020-12-23
9d0b2d0 jens-daniel-mueller 2020-12-23
0aa2b50 jens-daniel-mueller 2020-12-23
2886da0 jens-daniel-mueller 2020-12-19
02f0ee9 jens-daniel-mueller 2020-12-18
7bcb4eb jens-daniel-mueller 2020-12-18
7131186 jens-daniel-mueller 2020-12-17
5b48ef5 jens-daniel-mueller 2020-12-17 
lm_best_eras %>% 
  ggplot(aes(rmse, AIC, col = gamma_slab)) +
  geom_point() +
  scale_color_viridis_d() +
  facet_grid(eras~basin)

Version Author Date
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
ac1a836 jens-daniel-mueller 2021-02-24
b03fbd3 jens-daniel-mueller 2021-02-24
3d3b4cc jens-daniel-mueller 2021-02-23
7b672f7 jens-daniel-mueller 2021-01-11
33ba23c jens-daniel-mueller 2021-01-07
318609d jens-daniel-mueller 2020-12-23
9d0b2d0 jens-daniel-mueller 2020-12-23
0aa2b50 jens-daniel-mueller 2020-12-23
2886da0 jens-daniel-mueller 2020-12-19
02f0ee9 jens-daniel-mueller 2020-12-18
7bcb4eb jens-daniel-mueller 2020-12-18
7131186 jens-daniel-mueller 2020-12-17
5b48ef5 jens-daniel-mueller 2020-12-17

7.5 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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
27ae473 jens-daniel-mueller 2021-02-24
4bc00ea jens-daniel-mueller 2021-02-24 
GLODAP_augmented_best %>%
  ggplot(aes(cstar_tref, .fitted)) +
  geom_bin2d(binwidth = i_binwidth) +
  scale_fill_viridis_c() +
  geom_abline(slope = 1,
              col = 'red') +
  coord_equal(xlim = axis_lims,
              ylim = axis_lims) +
  labs(title = "Selected models")

Version Author Date
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
27ae473 jens-daniel-mueller 2021-02-24
4bc00ea jens-daniel-mueller 2021-02-24 
rm(binwidth_value, axis_lims)

7.5.2 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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
27ae473 jens-daniel-mueller 2021-02-24
4bc00ea jens-daniel-mueller 2021-02-24

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

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

Version Author Date
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
27ae473 jens-daniel-mueller 2021-02-24
4bc00ea jens-daniel-mueller 2021-02-24

7.5.3 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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
27ae473 jens-daniel-mueller 2021-02-24
a1ba577 jens-daniel-mueller 2021-02-24
071743d jens-daniel-mueller 2021-02-24 

[[2]]

Version Author Date
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
27ae473 jens-daniel-mueller 2021-02-24
a1ba577 jens-daniel-mueller 2021-02-24

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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
fec3558 jens-daniel-mueller 2021-02-24

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
cf98c6d jens-daniel-mueller 2021-03-16
a1d52ff jens-daniel-mueller 2021-03-15
0bade3b jens-daniel-mueller 2021-03-15
27c1f4b jens-daniel-mueller 2021-03-14
af75ebf jens-daniel-mueller 2021-03-14
5017709 jens-daniel-mueller 2021-03-11
585b07f jens-daniel-mueller 2021-03-11
85a5ed2 jens-daniel-mueller 2021-03-10
6c0bec6 jens-daniel-mueller 2021-03-05
3c2ec33 jens-daniel-mueller 2021-03-05
af70b94 jens-daniel-mueller 2021-03-04
fec3558 jens-daniel-mueller 2021-02-24 

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