eMLR - model fitting
Jens Daniel Müller
07 December, 2020
Last updated: 2020-12-07
Checks: 7 0
Knit directory: emlr_obs_v_XXX/
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1 Required data
Required are:
- cleaned and prepared GLODAPv2_2020 file
GLODAP <-
read_csv(paste(path_version_data,
"GLODAPv2.2020_MLR_fitting_ready.csv",
sep = ""))2 Fitting all models
2.1 RMSE calculation
Individual linear regression models were fitted for C* as a function of each predictor combination. Fitting was performed separately within each basin, era, and slab. The root mean squared error (RMSE) was calculated for each fitted model.
# loops across all basins and eras
for (i_basin in unique(GLODAP$basin)) {
for (i_era in unique(GLODAP$era)) {
# i_basin <- unique(GLODAP$basin)[1]
# i_era <- unique(GLODAP$era)[1]
print(i_basin)
print(i_era )
# subset one basin and era for fitting
GLODAP_basin_era <- GLODAP %>%
filter(basin == i_basin, era == i_era)
# loop across all gamma slabs in the current basin and era
for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
# i_gamma_slab <- unique(GLODAP_basin_era$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(
params_local$MLR_full_model,
data = GLODAP_basin_era_slab)
# fit linear models for all possible predictor combinations
# unfortunately, this functions does not provide model coefficients (yet)
lm_all <- ols_step_all_possible(lm_full)
# extract diagnostics of each linear model
lm_all <- as_tibble(lm_all$result)
# add currect basin, era, and gamma values
lm_all <- lm_all %>%
mutate(basin = i_basin,
era = i_era,
gamma_slab = i_gamma_slab)
# expanding table with model diagnostics for all eras, basins, slabs
if (exists("lm_all_stats")) {
lm_all_stats <- bind_rows(lm_all_stats, lm_all)
}
if (!exists("lm_all_stats")) {
lm_all_stats <- lm_all
}
rm(lm_full, lm_all)
}
}
}
# write model diagnostics to file
lm_all_stats %>% write_csv(paste(path_version_data,
"lm_all_stats.csv",
sep = ""))
rm(i_gamma_slab, i_era, i_basin,
GLODAP_basin_era, GLODAP_basin_era_slab)RMSE was plotted against the number of predictors (limited to 2 - 5).
# lm_all_stats <- read_csv(paste(path_version_data,
# "lm_all_stats.csv",
# sep = ""))
lm_all_stats <- lm_all_stats %>%
filter(n >= params_local$predictors_min,
n <= params_local$predictors_max)
lm_all_stats %>%
ggplot(aes(n, rmse, col = basin)) +
geom_hline(yintercept = 10) +
geom_point(shape = 21) +
facet_grid(gamma_slab~era) +
scale_color_brewer(palette = "Set1")
| Version | Author | Date |
|---|---|---|
| 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 |
2.2 RMSE alternatives
AIC is an alternative criterion to RMSE to judge model quality, but not (yet) taken into account.
lm_all_stats %>%
ggplot(aes(rmse, aic, col = gamma_slab)) +
geom_point() +
scale_color_viridis_d() +
facet_grid(era~basin)
| Version | Author | Date |
|---|---|---|
| 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 |
2.3 Predictor selection
Within each basin and slab, the 10 linear regression models with lowest summed RMSE across two adjacent (ie compared) eras were selected.
# select relevant columns
lm_all_stats <- lm_all_stats %>%
select(basin, era, gamma_slab, predictors, rmse)
# calculate RMSE sum for adjacent eras
lm_all_stats_eras <- lm_all_stats %>%
arrange(era) %>%
group_by(basin, gamma_slab, predictors) %>%
mutate(rmse_sum = rmse + lag(rmse),
eras = paste(lag(era), era, sep = " --> ")) %>%
ungroup() %>%
arrange(basin, gamma_slab, predictors, era) %>%
drop_na()
# subset models with lowest RMSE sum
lm_best <- lm_all_stats_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, predictors, era)
# plot table for website
kable(lm_best) %>%
add_header_above() %>%
kable_styling() %>%
scroll_box(width = "100%", height = "400px")| basin | era | gamma_slab | predictors | rmse | rmse_sum | eras |
|---|---|---|---|---|---|---|
| Atlantic | 2012-2019 | (-Inf,26] | sal aou oxygen silicate phosphate | 3.403484 | 10.504670 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal aou oxygen silicate phosphate_star | 3.403484 | 10.504670 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal aou silicate phosphate phosphate_star | 3.403484 | 10.504670 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal tem aou oxygen phosphate | 3.387050 | 10.700824 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal tem aou oxygen phosphate_star | 3.387050 | 10.700824 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal tem aou silicate phosphate | 3.392788 | 10.554426 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal tem aou silicate phosphate_star | 3.391512 | 10.561045 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal tem oxygen silicate phosphate | 3.390411 | 10.564758 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal tem oxygen silicate phosphate_star | 3.390411 | 10.564758 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (-Inf,26] | sal tem silicate phosphate phosphate_star | 3.390411 | 10.564758 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | sal aou oxygen silicate phosphate | 4.110057 | 9.414471 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | sal aou oxygen silicate phosphate_star | 4.110057 | 9.414471 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | sal aou silicate phosphate phosphate_star | 4.110057 | 9.414471 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | sal tem aou oxygen phosphate | 4.350984 | 9.454209 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | sal tem aou oxygen phosphate_star | 4.350984 | 9.454209 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | sal tem aou phosphate phosphate_star | 4.350984 | 9.454209 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | sal tem aou silicate phosphate | 4.114498 | 9.478396 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | tem aou oxygen silicate phosphate | 4.229950 | 9.323391 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | tem aou oxygen silicate phosphate_star | 4.229950 | 9.323391 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26,26.5] | tem aou silicate phosphate phosphate_star | 4.229950 | 9.323391 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | sal tem aou oxygen phosphate | 4.034562 | 8.288290 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | sal tem aou oxygen phosphate_star | 4.034562 | 8.288290 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | sal tem aou silicate phosphate | 3.901766 | 8.202575 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | sal tem aou silicate phosphate_star | 3.883341 | 8.159431 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | sal tem oxygen silicate phosphate | 3.876287 | 8.150070 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | sal tem oxygen silicate phosphate_star | 3.876287 | 8.150070 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | sal tem silicate phosphate phosphate_star | 3.876287 | 8.150070 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | tem aou oxygen silicate phosphate | 3.919468 | 8.232621 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | tem aou oxygen silicate phosphate_star | 3.919468 | 8.232621 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.5,26.75] | tem aou silicate phosphate phosphate_star | 3.919468 | 8.232621 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | sal tem aou silicate phosphate | 3.784438 | 8.358959 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | sal tem aou silicate phosphate_star | 3.763850 | 8.316361 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | sal tem oxygen silicate phosphate | 3.762644 | 8.315325 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | sal tem oxygen silicate phosphate_star | 3.762644 | 8.315325 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | sal tem silicate phosphate phosphate_star | 3.762644 | 8.315325 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | tem aou oxygen silicate phosphate | 3.773010 | 8.397167 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | tem aou oxygen silicate phosphate_star | 3.773010 | 8.397167 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | tem aou silicate phosphate phosphate_star | 3.773010 | 8.397167 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | tem oxygen silicate phosphate | 3.774724 | 8.400441 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (26.75,27] | tem oxygen silicate phosphate phosphate_star | 3.774724 | 8.400441 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | sal tem aou silicate phosphate | 4.961956 | 9.921970 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | sal tem aou silicate phosphate_star | 4.971820 | 9.834522 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | sal tem oxygen silicate phosphate | 4.971695 | 9.843107 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | sal tem oxygen silicate phosphate_star | 4.971695 | 9.843107 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | sal tem silicate phosphate phosphate_star | 4.971695 | 9.843107 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | tem aou oxygen silicate phosphate | 5.013665 | 9.818714 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | tem aou oxygen silicate phosphate_star | 5.013665 | 9.818714 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | tem aou silicate phosphate phosphate_star | 5.013665 | 9.818714 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | tem aou silicate phosphate_star | 5.040938 | 9.944515 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27,27.25] | tem silicate phosphate phosphate_star | 5.040072 | 9.952734 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | sal aou oxygen silicate phosphate | 4.333343 | 8.630122 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | sal aou silicate phosphate phosphate_star | 4.333343 | 8.630122 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | sal tem aou silicate phosphate | 4.385511 | 8.592742 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | sal tem aou silicate phosphate_star | 4.446872 | 8.604427 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | sal tem oxygen silicate phosphate | 4.427239 | 8.596783 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | sal tem oxygen silicate phosphate_star | 4.427239 | 8.596783 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | sal tem silicate phosphate phosphate_star | 4.427239 | 8.596783 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | tem aou oxygen silicate phosphate | 4.381297 | 8.616409 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | tem aou oxygen silicate phosphate_star | 4.381297 | 8.616409 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.25,27.5] | tem aou silicate phosphate phosphate_star | 4.381297 | 8.616409 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal aou oxygen silicate phosphate | 4.254833 | 8.797541 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal aou oxygen silicate phosphate_star | 4.254833 | 8.797541 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal aou silicate phosphate phosphate_star | 4.254833 | 8.797541 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal tem aou silicate phosphate | 4.257281 | 8.770381 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal tem aou silicate phosphate_star | 4.279870 | 8.791175 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal tem oxygen silicate phosphate | 4.263150 | 8.770336 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal tem oxygen silicate phosphate_star | 4.263150 | 8.770336 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | sal tem silicate phosphate phosphate_star | 4.263150 | 8.770336 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | tem aou oxygen silicate phosphate | 4.254461 | 8.841584 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.5,27.75] | tem aou silicate phosphate phosphate_star | 4.254461 | 8.841584 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | sal aou oxygen silicate phosphate | 5.076845 | 10.015311 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | sal aou oxygen silicate phosphate_star | 5.076845 | 10.015311 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | sal aou silicate phosphate phosphate_star | 5.076845 | 10.015311 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | sal tem aou silicate phosphate | 5.095841 | 10.034259 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | sal tem aou silicate phosphate_star | 5.071867 | 10.017678 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | sal tem oxygen silicate phosphate_star | 5.095317 | 10.035262 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | sal tem silicate phosphate phosphate_star | 5.095317 | 10.035262 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | tem aou oxygen silicate phosphate | 5.043024 | 9.998922 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | tem aou oxygen silicate phosphate_star | 5.043024 | 9.998922 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.75,27.85] | tem aou silicate phosphate phosphate_star | 5.043024 | 9.998922 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal aou oxygen silicate phosphate | 4.399038 | 9.478116 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal aou oxygen silicate phosphate_star | 4.399038 | 9.478116 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal aou silicate phosphate phosphate_star | 4.399038 | 9.478116 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal aou silicate phosphate_star | 4.610095 | 9.717955 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal tem aou silicate phosphate | 4.434316 | 9.510629 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal tem aou silicate phosphate_star | 4.414772 | 9.491907 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal tem oxygen silicate phosphate | 4.434211 | 9.510296 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal tem oxygen silicate phosphate_star | 4.434211 | 9.510296 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal tem silicate phosphate | 4.434323 | 9.612493 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.85,27.95] | sal tem silicate phosphate phosphate_star | 4.434211 | 9.510296 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal aou oxygen silicate phosphate | 4.556534 | 10.648594 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal aou oxygen silicate phosphate_star | 4.556534 | 10.648594 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal aou silicate phosphate phosphate_star | 4.556534 | 10.648594 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal aou silicate phosphate_star | 4.636048 | 10.728109 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal tem aou phosphate phosphate_star | 4.731872 | 10.906041 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal tem aou silicate phosphate | 4.663218 | 10.780813 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal tem aou silicate phosphate_star | 4.592345 | 10.683449 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal tem oxygen silicate phosphate | 4.636499 | 10.742576 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal tem oxygen silicate phosphate_star | 4.636499 | 10.742576 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (27.95,28.05] | sal tem silicate phosphate phosphate_star | 4.636499 | 10.742576 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | sal tem aou oxygen phosphate | 4.313118 | 10.693142 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | sal tem aou oxygen phosphate_star | 4.313118 | 10.693142 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | sal tem aou phosphate phosphate_star | 4.313118 | 10.693142 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | tem aou oxygen phosphate | 4.411489 | 10.861880 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | tem aou oxygen phosphate phosphate_star | 4.411489 | 10.861880 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | tem aou oxygen phosphate_star | 4.411489 | 10.861880 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | tem aou oxygen silicate phosphate | 4.242968 | 10.616782 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | tem aou oxygen silicate phosphate_star | 4.242968 | 10.616782 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | tem aou phosphate phosphate_star | 4.411489 | 10.861880 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.05,28.1] | tem aou silicate phosphate phosphate_star | 4.242968 | 10.616782 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | sal tem aou oxygen phosphate | 4.121460 | 11.364135 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | sal tem aou oxygen phosphate_star | 4.121460 | 11.364135 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | sal tem aou phosphate phosphate_star | 4.121460 | 11.364135 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | sal tem aou silicate phosphate_star | 4.159900 | 11.408450 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | sal tem oxygen silicate phosphate | 4.159743 | 11.409090 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | sal tem oxygen silicate phosphate_star | 4.159743 | 11.409090 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | sal tem silicate phosphate phosphate_star | 4.159743 | 11.409090 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | tem aou oxygen silicate phosphate | 4.114907 | 11.402602 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | tem aou oxygen silicate phosphate_star | 4.114907 | 11.402602 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.1,28.15] | tem aou silicate phosphate phosphate_star | 4.114907 | 11.402602 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal aou oxygen silicate phosphate | 2.842743 | 6.391368 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal aou oxygen silicate phosphate_star | 2.842743 | 6.391368 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal aou silicate phosphate phosphate_star | 2.842743 | 6.391368 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal tem aou oxygen phosphate | 2.789444 | 6.336877 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal tem aou oxygen phosphate_star | 2.789444 | 6.336877 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal tem aou phosphate | 2.790727 | 6.372110 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal tem aou phosphate phosphate_star | 2.789444 | 6.336877 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal tem aou silicate phosphate | 2.788296 | 6.353332 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal tem oxygen silicate phosphate | 2.790384 | 6.394371 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.15,28.2] | sal tem silicate phosphate phosphate_star | 2.790384 | 6.394371 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal aou oxygen phosphate | 2.990938 | 5.977066 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal aou oxygen phosphate phosphate_star | 2.990938 | 5.977066 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal aou oxygen phosphate_star | 2.990938 | 5.977066 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal aou oxygen silicate phosphate | 2.988295 | 5.974420 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal aou oxygen silicate phosphate_star | 2.988295 | 5.974420 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal aou phosphate phosphate_star | 2.990938 | 5.977066 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal aou silicate phosphate phosphate_star | 2.988295 | 5.974420 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal tem aou oxygen phosphate | 2.986378 | 5.972168 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal tem aou oxygen phosphate_star | 2.986378 | 5.972168 | 2000-2011 –> 2012-2019 |
| Atlantic | 2012-2019 | (28.2, Inf] | sal tem aou phosphate phosphate_star | 2.986378 | 5.972168 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal aou oxygen silicate phosphate | 5.401470 | 11.862149 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal aou oxygen silicate phosphate_star | 5.401470 | 11.862149 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal aou silicate phosphate phosphate_star | 5.401470 | 11.862149 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal tem aou oxygen phosphate | 5.753969 | 12.604734 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal tem aou phosphate phosphate_star | 5.753969 | 12.604734 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal tem aou silicate phosphate | 5.640435 | 12.202132 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal tem aou silicate phosphate_star | 5.711341 | 12.309447 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal tem oxygen silicate phosphate | 5.756181 | 12.369298 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal tem oxygen silicate phosphate_star | 5.756181 | 12.369298 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (-Inf,26] | sal tem silicate phosphate phosphate_star | 5.756181 | 12.369298 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal aou oxygen silicate phosphate | 3.863550 | 8.649393 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal aou oxygen silicate phosphate_star | 3.863550 | 8.649393 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal aou silicate phosphate phosphate_star | 3.863550 | 8.649393 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal tem aou oxygen phosphate_star | 4.207868 | 9.190518 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal tem aou silicate phosphate | 3.961173 | 8.756385 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal tem aou silicate phosphate_star | 4.010558 | 8.833338 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal tem oxygen silicate phosphate | 4.011190 | 8.835378 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal tem oxygen silicate phosphate_star | 4.011190 | 8.835378 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal tem silicate phosphate phosphate_star | 4.011190 | 8.835378 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26,26.5] | sal tem silicate phosphate_star | 4.012265 | 8.857148 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal aou oxygen phosphate | 4.540230 | 9.883482 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal aou oxygen phosphate phosphate_star | 4.540230 | 9.883482 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal aou oxygen phosphate_star | 4.540230 | 9.883482 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal aou oxygen silicate phosphate | 4.479259 | 9.821024 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal aou oxygen silicate phosphate_star | 4.479259 | 9.821024 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal aou phosphate phosphate_star | 4.540230 | 9.883482 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal aou silicate phosphate phosphate_star | 4.479259 | 9.821024 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal tem aou oxygen phosphate | 4.532117 | 9.874118 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal tem aou oxygen phosphate_star | 4.532117 | 9.874118 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.5,26.75] | sal tem aou phosphate phosphate_star | 4.532117 | 9.874118 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | sal tem aou oxygen phosphate | 4.228709 | 9.173889 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | sal tem aou oxygen phosphate_star | 4.228709 | 9.173889 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | sal tem aou phosphate phosphate_star | 4.228709 | 9.173889 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | tem aou oxygen phosphate | 4.253487 | 9.202065 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | tem aou oxygen phosphate phosphate_star | 4.253487 | 9.202065 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | tem aou oxygen phosphate_star | 4.253487 | 9.202065 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | tem aou oxygen silicate phosphate | 4.243043 | 9.162853 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | tem aou oxygen silicate phosphate_star | 4.243043 | 9.162853 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | tem aou phosphate phosphate_star | 4.253487 | 9.202065 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (26.75,27] | tem aou silicate phosphate phosphate_star | 4.243043 | 9.162853 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | sal aou oxygen silicate phosphate | 4.049755 | 8.751922 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | sal aou oxygen silicate phosphate_star | 4.049755 | 8.751922 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | sal aou silicate phosphate phosphate_star | 4.049755 | 8.751922 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | sal tem aou oxygen phosphate | 4.060442 | 8.751250 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | sal tem aou oxygen phosphate_star | 4.060442 | 8.751250 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | sal tem aou phosphate phosphate_star | 4.060442 | 8.751250 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | sal tem aou silicate phosphate | 4.069790 | 8.777056 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | tem aou oxygen silicate phosphate | 3.983696 | 8.633135 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | tem aou oxygen silicate phosphate_star | 3.983696 | 8.633135 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27,27.25] | tem aou silicate phosphate phosphate_star | 3.983696 | 8.633135 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal aou oxygen silicate phosphate | 3.253905 | 7.451890 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal aou oxygen silicate phosphate_star | 3.253905 | 7.451890 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal aou silicate phosphate | 3.299334 | 7.560463 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal aou silicate phosphate phosphate_star | 3.253905 | 7.451890 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal tem aou silicate phosphate | 3.257781 | 7.485243 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal tem aou silicate phosphate_star | 3.265190 | 7.540092 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal tem oxygen silicate phosphate | 3.263814 | 7.529337 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal tem oxygen silicate phosphate_star | 3.263814 | 7.529337 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | sal tem silicate phosphate phosphate_star | 3.263814 | 7.529337 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.25,27.5] | tem aou silicate phosphate phosphate_star | 3.523081 | 7.590607 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal aou oxygen silicate phosphate | 3.049164 | 6.793925 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal aou oxygen silicate phosphate_star | 3.049164 | 6.793925 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal aou silicate phosphate | 3.192178 | 7.121087 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal aou silicate phosphate phosphate_star | 3.049164 | 6.793925 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal tem aou silicate phosphate | 3.048297 | 6.791454 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal tem aou silicate phosphate_star | 3.048326 | 6.801608 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal tem oxygen silicate phosphate | 3.048268 | 6.800439 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal tem oxygen silicate phosphate_star | 3.048268 | 6.800439 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal tem silicate phosphate phosphate_star | 3.048268 | 6.800439 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.5,27.75] | sal tem silicate phosphate_star | 3.135370 | 6.916235 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | sal tem aou silicate phosphate | 2.918801 | 6.190708 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | sal tem aou silicate phosphate_star | 2.910646 | 6.162704 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | sal tem oxygen silicate phosphate | 2.910739 | 6.161407 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | sal tem oxygen silicate phosphate_star | 2.910739 | 6.161407 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | sal tem silicate phosphate phosphate_star | 2.910739 | 6.161407 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | sal tem silicate phosphate_star | 2.911220 | 6.191703 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | tem aou oxygen silicate phosphate | 2.964698 | 6.196344 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | tem aou oxygen silicate phosphate_star | 2.964698 | 6.196344 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | tem aou silicate phosphate phosphate_star | 2.964698 | 6.196344 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.75,27.85] | tem oxygen silicate phosphate | 2.968270 | 6.221983 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | sal aou oxygen silicate phosphate | 2.935395 | 5.877770 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | sal aou oxygen silicate phosphate_star | 2.935395 | 5.877770 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | sal tem aou silicate phosphate | 2.917082 | 5.861625 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | sal tem aou silicate phosphate_star | 2.908722 | 5.863722 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | sal tem oxygen silicate phosphate | 2.908676 | 5.864860 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | sal tem oxygen silicate phosphate_star | 2.908676 | 5.864860 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | sal tem silicate phosphate phosphate_star | 2.908676 | 5.864860 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | tem aou oxygen silicate phosphate | 2.934154 | 5.875776 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | tem aou oxygen silicate phosphate_star | 2.934154 | 5.875776 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.85,27.95] | tem aou silicate phosphate phosphate_star | 2.934154 | 5.875776 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | sal aou oxygen silicate phosphate | 3.078737 | 5.898810 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | sal aou oxygen silicate phosphate_star | 3.078737 | 5.898810 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | sal aou silicate phosphate phosphate_star | 3.078737 | 5.898810 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | sal tem aou oxygen phosphate | 3.105644 | 5.938887 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | sal tem aou oxygen phosphate_star | 3.105644 | 5.938887 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | sal tem aou phosphate phosphate_star | 3.105644 | 5.938887 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | sal tem aou silicate phosphate | 3.066183 | 5.918373 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | tem aou oxygen silicate phosphate | 3.107979 | 5.935595 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | tem aou oxygen silicate phosphate_star | 3.107979 | 5.935595 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (27.95,28.05] | tem aou silicate phosphate phosphate_star | 3.107979 | 5.935595 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal aou oxygen phosphate | 2.895669 | 5.632681 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal aou oxygen phosphate phosphate_star | 2.895669 | 5.632681 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal aou oxygen phosphate_star | 2.895669 | 5.632681 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal aou oxygen silicate phosphate | 2.892647 | 5.611336 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal aou oxygen silicate phosphate_star | 2.892647 | 5.611336 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal aou silicate phosphate phosphate_star | 2.892647 | 5.611336 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal tem aou oxygen phosphate | 2.886269 | 5.622329 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal tem aou oxygen phosphate_star | 2.886269 | 5.622329 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal tem aou phosphate phosphate_star | 2.886269 | 5.622329 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.05,28.1] | sal tem aou silicate phosphate | 2.899626 | 5.625053 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | aou oxygen silicate phosphate | 2.723831 | 5.826521 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | aou oxygen silicate phosphate phosphate_star | 2.723831 | 5.826521 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | aou oxygen silicate phosphate_star | 2.723831 | 5.826521 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | aou silicate phosphate phosphate_star | 2.723831 | 5.826521 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | sal aou oxygen silicate phosphate | 2.629551 | 5.728254 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | sal aou oxygen silicate phosphate_star | 2.629551 | 5.728254 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | sal aou silicate phosphate phosphate_star | 2.629551 | 5.728254 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | tem aou oxygen silicate phosphate | 2.685645 | 5.729464 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | tem aou oxygen silicate phosphate_star | 2.685645 | 5.729464 | 2000-2011 –> 2012-2019 |
| Indo-Pacific | 2012-2019 | (28.1, Inf] | tem aou silicate phosphate phosphate_star | 2.685645 | 5.729464 | 2000-2011 –> 2012-2019 |
2.4 Correlations RMSE between eras
2.4.1 All models
max_rmse <-
max(c(lm_all_stats_eras$rmse,
lm_all_stats_eras$rmse_sum - lm_all_stats_eras$rmse))
lm_all_stats_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)) +
facet_grid(eras ~ basin)
| Version | Author | Date |
|---|---|---|
| 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)2.4.2 Best models
max_rmse <-
max(c(lm_best$rmse,
lm_best$rmse_sum - lm_best$rmse))
lm_best %>%
ggplot(aes(rmse, rmse_sum - rmse, col = gamma_slab)) +
geom_point() +
scale_color_viridis_d() +
coord_equal(xlim = c(0,max_rmse),
ylim = c(0,max_rmse)) +
facet_grid(eras ~ basin)
| Version | Author | Date |
|---|---|---|
| 70bf1a5 | jens-daniel-mueller | 2020-12-07 |
| 7555355 | jens-daniel-mueller | 2020-12-07 |
| 143d6fa | jens-daniel-mueller | 2020-12-07 |
| 090e4d5 | jens-daniel-mueller | 2020-12-02 |
| 7c25f7a | jens-daniel-mueller | 2020-12-02 |
| b03ddb8 | jens-daniel-mueller | 2020-12-02 |
| 91435ae | jens-daniel-mueller | 2020-12-01 |
| 196be51 | jens-daniel-mueller | 2020-11-30 |
rm(max_rmse)# this code tests the rmse output of the ols_step_all_possible() function used
lm_1 <- GLODAP %>%
filter(basin == "Atlantic",
gamma_slab == "(-Inf,26]",
era == "new_era") %>%
lm(cstar ~ sal + tem + aou + oxygen + phosphate_star, data = .)
lm_2 <- GLODAP %>%
filter(basin == "Atlantic",
gamma_slab == "(-Inf,26]",
era == "new_era") %>%
lm(cstar ~ sal + tem + aou + oxygen + phosphate, data = .)
lm_1
lm_2
sqrt(mean(lm_1$residuals^2))
sqrt(mean(lm_2$residuals^2))3 Fitting best models
After selecting 10 linear regression models with lowest summed RMSE across all eras, models are fitted again and model coefficients are saved to file.
# format model formula
lm_best <- lm_best %>%
mutate(lm_coeff = str_replace_all(predictors, " ", " + "),
lm_coeff = paste("cstar ~", lm_coeff))
# create table with two era belonging to one eras
eras_forward <- lm_all_stats %>%
arrange(era) %>%
group_by(basin, gamma_slab, predictors) %>%
mutate(eras = paste(era, lead(era), sep = " --> ")) %>%
ungroup() %>%
select(era, eras) %>%
unique()
eras_backward <- lm_all_stats %>%
arrange(era) %>%
group_by(basin, gamma_slab, predictors) %>%
mutate(eras = paste(lag(era), era, sep = " --> ")) %>%
ungroup() %>%
select(era, eras) %>%
unique()
eras_era <- full_join(eras_backward, eras_forward) %>%
filter(str_detect(eras, "NA") == FALSE)
# extend best model selection from eras to era
lm_best <- lm_best %>%
select(-era)
lm_best <- full_join(lm_best, eras_era)
rm(eras_era, eras_forward, eras_backward, lm_all_stats, lm_all_stats_eras)# select required columns
lm_best <- lm_best %>%
select(basin, gamma_slab, era, eras, predictors, lm_coeff, rmse_sum)
# run similar loop as for rmse calculation
# to get model coefficients for 10 best models
for (i_basin in unique(GLODAP$basin)) {
for (i_era in unique(GLODAP$era)) {
# i_basin <- unique(GLODAP$basin)[1]
# i_era <- unique(GLODAP$era)[1]
print(i_basin)
print(i_era)
GLODAP_basin_era <- GLODAP %>%
filter(basin == i_basin, era == i_era)
lm_best_basin_era <- lm_best %>%
filter(basin == i_basin, era == i_era)
for (i_gamma_slab in unique(GLODAP_basin_era$gamma_slab)) {
# i_gamma_slab <- unique(GLODAP_basin_era$gamma_slab)[1]
print(i_gamma_slab)
GLODAP_basin_era_slab <- GLODAP_basin_era %>%
filter(gamma_slab == i_gamma_slab)
lm_best_basin_era_slab <- lm_best_basin_era %>%
filter(gamma_slab == i_gamma_slab)
for (i_eras in unique(lm_best_basin_era_slab$eras)) {
# i_eras <- unique(lm_best_basin_era_slab$eras)[1]
lm_best_basin_era_slab_eras <- lm_best_basin_era_slab %>%
filter(eras == i_eras)
for (i_predictors in unique(lm_best_basin_era_slab_eras$predictors)) {
# i_predictors <- unique(lm_best_basin_era_slab_eras$predictors)[2]
print(i_predictors)
lm_best_single <- lm_best_basin_era_slab_eras %>%
filter(predictors == i_predictors) %>%
select(lm_coeff) %>%
pull()
i_rmse_sum <- lm_best_basin_era_slab_eras %>%
filter(predictors == i_predictors) %>%
select(rmse_sum) %>%
pull()
lm_best_single_formula <- as.formula(lm_best_single)
lm_fit_single <- lm(lm_best_single_formula,
data = GLODAP_basin_era_slab)
# plotting model diagnostics
if (params_local$plot_all_figures == "y") {
p_model <- ggnostic(
lm_fit_single,
columnsY = c("cstar", ".fitted", ".resid"),
title = paste("eras:", i_eras,
"| era:", i_era,
"| basin:", i_basin,
"| gamma slab:", i_gamma_slab,
"| predictors:", i_predictors)
)
ggsave(
plot = p_model,
path = paste(path_version_figures, "eMLR_diagnostics/", sep = ""),
filename = paste(
"MLR_residuals",
i_eras,
i_era,
i_basin,
i_gamma_slab,
i_predictors,
"predictors.png",
sep = "_"
),
width = 14,
height = 8
)
rm(p_model)
}
# collect model coefficients in data frame
coefficients <- tidy(lm_fit_single)
coefficients <- coefficients %>%
mutate(
basin = i_basin,
era = i_era,
eras = i_eras,
gamma_slab = i_gamma_slab,
model = lm_best_single,
rmse = i_rmse_sum
)
if (exists("lm_all")) {
lm_all <- bind_rows(lm_all, coefficients)
}
if (!exists("lm_all")) {
lm_all <- coefficients
}
}
}
}
}
}
rm(lm_fit_single, coefficients, i_rmse_sum,
GLODAP_basin_era, GLODAP_basin_era_slab,
lm_best, lm_best_basin_era, lm_best_basin_era_slab, lm_best_basin_era_slab_eras,
lm_best_single, lm_best_single_formula,
i_basin, i_era, i_gamma_slab, i_predictors)3.1 Predictor counts
The number of models where a particular predictor was included were counted for each basin, density slab and compared eras
lm_all_stats <- lm_all %>%
filter(term != "(Intercept)") %>%
group_by(basin, eras, gamma_slab) %>%
count(term) %>%
ungroup() %>%
pivot_wider(values_from = n, names_from = term)
lm_all_stats %>%
gt(rowname_col = "gamma_slab",
groupname_col = c("basin", "eras")) %>%
summary_rows(
groups = TRUE,
fns = list(total = "sum")
)| aou | oxygen | phosphate | phosphate_star | sal | silicate | tem | |
|---|---|---|---|---|---|---|---|
| Atlantic - 2000-2011 --> 2012-2019 | |||||||
| (-Inf,26] | 14 | 12 | 12 | 12 | 20 | 16 | 14 |
| (26,26.5] | 20 | 12 | 14 | 12 | 14 | 14 | 14 |
| (26.5,26.75] | 14 | 12 | 12 | 12 | 14 | 16 | 20 |
| (26.75,27] | 10 | 12 | 14 | 12 | 10 | 20 | 20 |
| (27,27.25] | 12 | 8 | 12 | 14 | 10 | 20 | 20 |
| (27.25,27.5] | 14 | 10 | 14 | 12 | 14 | 20 | 16 |
| (27.5,27.75] | 14 | 10 | 14 | 12 | 16 | 20 | 14 |
| (27.75,27.85] | 16 | 10 | 12 | 14 | 14 | 20 | 14 |
| (27.85,27.95] | 12 | 8 | 12 | 12 | 20 | 20 | 12 |
| (27.95,28.05] | 14 | 8 | 12 | 14 | 20 | 18 | 12 |
| (28.05,28.1] | 20 | 14 | 14 | 14 | 6 | 6 | 20 |
| (28.1,28.15] | 14 | 12 | 12 | 14 | 14 | 14 | 20 |
| (28.15,28.2] | 16 | 10 | 16 | 10 | 20 | 12 | 14 |
| (28.2, Inf] | 20 | 14 | 14 | 14 | 20 | 6 | 6 |
| total | 210.00 | 152.00 | 184.00 | 178.00 | 212.00 | 222.00 | 216.00 |
| Indo-Pacific - 2000-2011 --> 2012-2019 | |||||||
| (-Inf,26] | 14 | 10 | 14 | 12 | 20 | 16 | 14 |
| (26,26.5] | 12 | 10 | 10 | 14 | 20 | 18 | 14 |
| (26.5,26.75] | 20 | 14 | 14 | 14 | 20 | 6 | 6 |
| (26.75,27] | 20 | 14 | 14 | 14 | 6 | 6 | 20 |
| (27,27.25] | 20 | 12 | 14 | 12 | 14 | 14 | 14 |
| (27.25,27.5] | 14 | 8 | 14 | 12 | 18 | 20 | 12 |
| (27.5,27.75] | 12 | 8 | 12 | 12 | 20 | 20 | 12 |
| (27.75,27.85] | 10 | 10 | 12 | 12 | 12 | 20 | 20 |
| (27.85,27.95] | 14 | 12 | 12 | 12 | 14 | 20 | 16 |
| (27.95,28.05] | 20 | 12 | 14 | 12 | 14 | 14 | 14 |
| (28.05,28.1] | 20 | 14 | 14 | 12 | 20 | 8 | 8 |
| (28.1, Inf] | 20 | 14 | 14 | 14 | 6 | 20 | 6 |
| total | 196.00 | 138.00 | 158.00 | 152.00 | 184.00 | 182.00 | 156.00 |
3.2 Prepare coeffcients
Coefficients are prepared for the mapping of cstar and cant.
# select relevant columns
lm_all <- lm_all %>%
select(basin, gamma_slab, era, eras, model, term, estimate)
# set coefficient to zero if not fitted (=NA)
lm_all <- lm_all %>%
mutate(estimate = if_else(is.na(estimate), 0, estimate))
# Prepare model coefficients for mapping of cstar
lm_all_cstar <- lm_all %>%
pivot_wider(values_from = estimate,
names_from = term,
names_prefix = "coeff_",
values_fill = 0)
# Prepare model coefficients differences for mapping of cant
# this requires to subtract coefficients of adjacent era
lm_all_long <- lm_all %>%
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))
lm_all_cant <- lm_all_long %>%
pivot_wider(values_from = delta_coeff,
names_from = term,
names_prefix = "delta_coeff_",
values_fill = 0)3.3 Write files
lm_all_cstar %>% write_csv(paste(path_version_data,
"lm_all_cstar.csv",
sep = ""))
lm_all_cant %>% write_csv(paste(path_version_data,
"lm_all_cant.csv",
sep = ""))
sessionInfo()R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: openSUSE Leap 15.1
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_0.5.3.9000 GGally_2.0.0 lubridate_1.7.9
[9] metR_0.9.0 scico_1.2.0 patchwork_1.1.0 collapse_1.4.2
[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 R6_2.5.0 nortest_1.0-4
[10] DBI_1.1.0 colorspace_2.0-0 withr_2.3.0
[13] gridExtra_2.3 tidyselect_1.1.0 curl_4.3
[16] compiler_4.0.3 git2r_0.27.1 cli_2.2.0
[19] rvest_0.3.6 xml2_1.3.2 sass_0.2.0
[22] labeling_0.4.2 scales_1.1.1 checkmate_2.0.0
[25] goftest_1.2-2 digest_0.6.27 foreign_0.8-80
[28] rmarkdown_2.5 rio_0.5.16 pkgconfig_2.0.3
[31] htmltools_0.5.0 highr_0.8 dbplyr_1.4.4
[34] rlang_0.4.9 readxl_1.3.1 rstudioapi_0.13
[37] farver_2.0.3 generics_0.0.2 jsonlite_1.7.1
[40] zip_2.1.1 car_3.0-10 magrittr_2.0.1
[43] Matrix_1.2-18 Rcpp_1.0.5 munsell_0.5.0
[46] fansi_0.4.1 abind_1.4-5 lifecycle_0.2.0
[49] stringi_1.5.3 whisker_0.4 yaml_2.2.1
[52] carData_3.0-4 plyr_1.8.6 grid_4.0.3
[55] blob_1.2.1 parallel_4.0.3 promises_1.1.1
[58] crayon_1.3.4 lattice_0.20-41 haven_2.3.1
[61] hms_0.5.3 pillar_1.4.7 reprex_0.3.0
[64] glue_1.4.2 evaluate_0.14 RcppArmadillo_0.10.1.2.0
[67] data.table_1.13.2 modelr_0.1.8 vctrs_0.3.5
[70] httpuv_1.5.4 cellranger_1.1.0 gtable_0.3.0
[73] reshape_0.8.8 assertthat_0.2.1 xfun_0.18
[76] openxlsx_4.2.3 RcppEigen_0.3.3.7.0 later_1.1.0.1
[79] viridisLite_0.3.0 ellipsis_0.3.1 here_0.1