Analysis of cant estimates
Jens Daniel Müller
06 January, 2021
Last updated: 2021-01-06
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Knit directory: emlr_mod_v_XXX/
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1 Data sources
Cant estimates from this sensitivity case:
- Mean and SD per grid cell (lat, lon, depth)
- Zonal mean and SD (basin, lat, depth)
- Inventories (lat, lon)
cant_3d <-
read_csv(paste(path_version_data,
"cant_3d.csv",
sep = ""))
cant_zonal <-
read_csv(paste(path_version_data,
"cant_zonal.csv",
sep = ""))
cant_predictor_zonal <-
read_csv(paste(path_version_data,
"cant_predictor_zonal.csv",
sep = ""))
cant_inv <-
read_csv(paste(path_version_data,
"cant_inv.csv",
sep = ""))Target variable (cstar_tref) estimates from this sensitivity case:
- Mean and SD per grid cell (lat, lon, depth)
- Zonal mean and SD (basin, lat, depth)
target_3d <-
read_csv(paste(path_version_data,
"target_3d.csv",
sep = ""))
target_zonal <-
read_csv(paste(path_version_data,
"target_zonal.csv",
sep = ""))Cleaned GLODAP-based synthetic model subsetting file as used in this sensitivity case
GLODAP <-
read_csv(paste(
path_version_data,
"GLODAPv2.2020_MLR_fitting_ready_model_runA.csv",
sep = ""
))2 Cant budgets
Global Cant inventories were estimated in units of Pg C. Please note that here we added Cant (all vs postitive only) values and do not apply additional corrections for areas not covered.
cant_inv_budget <- cant_inv %>%
mutate(surface_area = earth_surf(lat, lon),
cant_inv_grid = cant_inv*surface_area,
cant_pos_inv_grid = cant_pos_inv*surface_area) %>%
group_by(basin_AIP, eras, inv_depth) %>%
summarise(cant_total = sum(cant_inv_grid)*12*1e-15,
cant_total = round(cant_total,1),
cant_pos_total = sum(cant_pos_inv_grid)*12*1e-15,
cant_pos_total = round(cant_pos_total,1)) %>%
ungroup()2.1 Standard depth
Results integrated over the upper 3000 m
cant_inv_budget %>%
filter(inv_depth == params_global$inventory_depth_standard) %>%
gt(rowname_col = "basin_AIP",
groupname_col = c("eras", "inv_depth"),
row_group.sep = " | Depth: ") %>%
summary_rows(
groups = TRUE,
fns = list(total = "sum")
)| cant_total | cant_pos_total | |
|---|---|---|
| 1982-1999 --> 2000-2012 | Depth: 3000 | ||
| Atlantic | 7.3 | 7.7 |
| Indian | 4.9 | 6.4 |
| Pacific | 17.1 | 18.4 |
| total | 29.30 | 32.50 |
| 2000-2012 --> 2013-2019 | Depth: 3000 | ||
| Atlantic | 3.5 | 4.3 |
| Indian | 3.9 | 5.5 |
| Pacific | 18.0 | 18.5 |
| total | 25.40 | 28.30 |
2.2 Other depths
Results integrated over the upper 100, 500, 1000, 3000, 10^{4} m
cant_inv_budget %>%
filter(inv_depth != params_global$inventory_depth_standard) %>%
gt(rowname_col = "basin_AIP",
groupname_col = c("eras", "inv_depth"),
row_group.sep = " | Depth: ") %>%
summary_rows(
groups = TRUE,
fns = list(total = "sum")
)| cant_total | cant_pos_total | |
|---|---|---|
| 1982-1999 --> 2000-2012 | Depth: 100 | ||
| Atlantic | 1.3 | 1.3 |
| Indian | 1.0 | 1.0 |
| Pacific | 2.4 | 2.4 |
| total | 4.70 | 4.70 |
| 1982-1999 --> 2000-2012 | Depth: 500 | ||
| Atlantic | 4.3 | 4.3 |
| Indian | 3.3 | 3.4 |
| Pacific | 7.5 | 7.6 |
| total | 15.10 | 15.30 |
| 1982-1999 --> 2000-2012 | Depth: 1000 | ||
| Atlantic | 5.5 | 5.7 |
| Indian | 3.9 | 4.4 |
| Pacific | 9.9 | 10.4 |
| total | 19.30 | 20.50 |
| 1982-1999 --> 2000-2012 | Depth: 10000 | ||
| Atlantic | 7.2 | 8.2 |
| Indian | 5.1 | 6.8 |
| Pacific | 18.7 | 20.2 |
| total | 31.00 | 35.20 |
| 2000-2012 --> 2013-2019 | Depth: 100 | ||
| Atlantic | 0.9 | 0.9 |
| Indian | 0.6 | 0.7 |
| Pacific | 1.8 | 1.9 |
| total | 3.30 | 3.50 |
| 2000-2012 --> 2013-2019 | Depth: 500 | ||
| Atlantic | 2.5 | 2.6 |
| Indian | 1.8 | 2.1 |
| Pacific | 5.7 | 5.8 |
| total | 10.00 | 10.50 |
| 2000-2012 --> 2013-2019 | Depth: 1000 | ||
| Atlantic | 3.3 | 3.5 |
| Indian | 2.5 | 3.3 |
| Pacific | 7.6 | 7.8 |
| total | 13.40 | 14.60 |
| 2000-2012 --> 2013-2019 | Depth: 10000 | ||
| Atlantic | 3.4 | 4.6 |
| Indian | 3.8 | 5.7 |
| Pacific | 22.7 | 23.2 |
| total | 29.90 | 33.50 |
rm(cant_inv_budget)The following analysis is restricted to the standard inventory depth of 3000 m.
cant_inv <- cant_inv %>%
filter(inv_depth == params_global$inventory_depth_standard)3 Cant - positive
In a first series of plots we explore the distribution of Cant, taking only positive estimates into account (positive here refers to the mean cant estimate across MLR model predictions available for each grid cell). Negative values were set to zero before calculating mean sections and inventories.
3.1 Zonal mean sections
# i_basin_AIP <- unique(cant_zonal$basin_AIP)[2]
# i_eras <- unique(cant_zonal$eras)[1]
for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
for (i_eras in unique(cant_zonal$eras)) {
print(
p_section_zonal(
df = cant_zonal %>%
filter(basin_AIP == i_basin_AIP,
eras == i_eras),
var = "cant_pos_mean",
subtitle_text =
paste("Basin:", i_basin_AIP, "| eras:", i_eras))
)
}
}
3.2 Isoneutral slab distribution
Mean of positive cant within each horizontal grid cell (lon x lat) per isoneutral slab.
Please note that:
- density slabs covering values >28.1 occur by definition only either in the Atlantic or Indo-Pacific basin
- gaps in the maps represent areas where (thin) density layers fit between discrete depth levels used for mapping
cant_gamma_maps <- m_cant_slab(cant_3d)
cant_gamma_maps <- cant_gamma_maps %>%
arrange(gamma_slab, eras)# i_eras <- unique(cant_gamma_maps$eras)[1]
# i_gamma_slab <- unique(cant_gamma_maps$gamma_slab)[1]
for (i_eras in unique(cant_gamma_maps$eras)) {
for (i_gamma_slab in unique(cant_gamma_maps$gamma_slab)) {
print(
p_map_cant_slab(
df = cant_gamma_maps %>%
filter(eras == i_eras,
gamma_slab == i_gamma_slab),
subtitle_text = paste(
"Eras:", i_eras,
"| Neutral density:", i_gamma_slab)
)
)
}
}
3.3 Inventory map
Column inventory of positive cant between the surface and m water depth per horizontal grid cell (lat x lon).
# i_eras <- unique(cant_inv$eras)[1]
for (i_eras in unique(cant_inv$eras)) {
print(
p_map_cant_inv(
df = cant_inv %>% filter(eras == i_eras),
var = "cant_pos_inv",
subtitle_text = paste("Eras:", i_eras))
)
}
3.4 Global sections
for (i_eras in unique(cant_3d$eras)) {
print(
p_section_global(
df = cant_3d %>% filter(eras == i_eras),
var = "cant_pos",
subtitle_text = paste("Eras:", i_eras)
)
)
}
4 Cant - all
In a second series of plots we explore the distribution of all Cant, taking positive and negative estimates into account.
4.1 Zonal mean sections
# i_eras <- unique(cant_zonal$eras)[1]
# i_basin_AIP <- unique(cant_zonal$basin_AIP)[1]
for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
for (i_eras in unique(cant_zonal$eras)) {
print(
p_section_zonal(
df = cant_zonal %>%
filter(basin_AIP == i_basin_AIP,
eras == i_eras),
var = "cant_mean",
gamma = "gamma_mean",
breaks = params_global$breaks_cant,
col = "divergent",
subtitle_text =
paste("Basin:", i_basin_AIP, "| eras:", i_eras))
)
}
}
4.2 Isoneutral slab distribution
Mean of all Cant within each horizontal grid cell (lon x lat) per isoneutral slab.
Please note that:
- density slabs covering values >28.1 occur by definition only either in the Atlantic or Indo-Pacific basin
- gaps in the maps represent areas where (thin) density layers fit between discrete depth levels used for mapping
# i_eras <- unique(cant_gamma_maps$eras)[1]
# i_gamma_slab <- unique(cant_gamma_maps$gamma_slab)[5]
for (i_eras in unique(cant_gamma_maps$eras)) {
for (i_gamma_slab in unique(cant_gamma_maps$gamma_slab)) {
print(
p_map_cant_slab(
df = cant_gamma_maps %>%
filter(eras == i_eras,
gamma_slab == i_gamma_slab),
var = "cant",
col = "divergent",
subtitle_text = paste(
"Eras:", i_eras,
"| Neutral density:", i_gamma_slab))
)
}
}
4.3 Inventory map
Column inventory of all Cant between the surface and 3000m water depth per horizontal grid cell (lat x lon).
# i_eras <- unique(cant_inv$eras)[1]
for (i_eras in unique(cant_inv$eras)) {
print(
p_map_cant_inv(
df = cant_inv %>% filter(eras == i_eras),
var = "cant_inv",
col = "divergent",
subtitle_text = paste("Eras:", i_eras))
)
}
5 Cant variability
5.1 Across models
Standard deviation across Cant from all MLR models was calculate for each grid cell (XYZ). The zonal mean of this standard deviation should reflect the uncertainty associated to the predictor selection within each slab and era.
# i_eras <- unique(cant_zonal$eras)[1]
# i_basin_AIP <- unique(cant_zonal$basin_AIP)[2]
for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
for (i_eras in unique(cant_zonal$eras)) {
print(
p_section_zonal(
df = cant_zonal %>%
filter(basin_AIP == i_basin_AIP,
eras == i_eras),
var = "cant_sd_mean",
gamma = "gamma_mean",
legend_title = "sd",
title_text = "Zonal mean section of SD across models",
subtitle_text =
paste("Basin:", i_basin_AIP, "| eras:", i_eras))
)
}
}
5.2 Across basins
Standard deviation of mean cant values was calculate across all longitudes. This standard deviation should reflect the zonal variability of cant within the basin and era.
# i_eras <- unique(cant_zonal$eras)[1]
# i_basin_AIP <- unique(cant_zonal$basin_AIP)[2]
for (i_basin_AIP in unique(cant_zonal$basin_AIP)) {
for (i_eras in unique(cant_zonal$eras)) {
print(
p_section_zonal(
df = cant_zonal %>%
filter(basin_AIP == i_basin_AIP,
eras == i_eras),
var = "cant_sd",
gamma = "gamma_mean",
legend_title = "sd",
title_text = "Zonal mean section of Cant SD",
subtitle_text =
paste("Basin:", i_basin_AIP, "| eras:", i_eras))
)
}
}
5.3 Correlation
5.3.1 Cant vs model SD
5.3.1.1 Era vs basin
cant_3d %>%
ggplot(aes(cant, cant_sd)) +
geom_vline(xintercept = 0) +
geom_hline(yintercept = 10) +
geom_bin2d() +
scale_fill_viridis_c(option = "magma",
direction = -1,
trans = "log10",
name = "log10(n)") +
facet_grid(basin_AIP ~ eras)
5.3.1.2 Basin vs gamma
cant_3d %>%
ggplot(aes(cant, cant_sd)) +
geom_vline(xintercept = 0) +
geom_hline(yintercept = 10) +
geom_bin2d() +
scale_fill_viridis_c(option = "magma",
direction = -1,
trans = "log10",
name = "log10(n)") +
facet_grid(gamma_slab ~ basin_AIP)
5.3.2 Cant vs regional SD
5.3.2.1 Era vs basin
cant_zonal %>%
ggplot(aes(cant_mean, cant_sd)) +
geom_vline(xintercept = 0) +
geom_hline(yintercept = 10) +
geom_bin2d() +
scale_fill_viridis_c(option = "magma",
direction = -1,
trans = "log10",
name = "log10(n)") +
facet_grid(basin_AIP ~ eras)
5.3.2.2 Era vs basin
cant_zonal %>%
ggplot(aes(cant_mean, cant_sd)) +
geom_vline(xintercept = 0) +
geom_hline(yintercept = 10) +
geom_bin2d() +
scale_fill_viridis_c(option = "magma",
direction = -1,
trans = "log10",
name = "log10(n)") +
facet_grid(gamma_slab ~ basin_AIP)
6 Cant - predictor contribution
for (i_var in paste("cant",
c("intercept", params_local$MLR_predictors),
sep = "_")) {
print(
p_section_zonal_divergent_gamma_eras_basin(df = cant_predictor_zonal,
var = i_var,
gamma = "gamma")
)
}
rm(i_var)7 Neutral density
7.1 Slab depth
The plot below shows the depths of individual gamma slabs (color) together with the synthetic subsetting available in the respective slab.
Please note that:
- density slabs covering values >28.1 occur by definition only either in the Atlantic or Indo-Pacific basin
GLODAP_obs_coverage <- GLODAP %>%
count(lat, lon, gamma_slab, era)
map +
geom_raster(data = cant_gamma_maps,
aes(lon, lat, fill = depth_max)) +
geom_raster(data = GLODAP_obs_coverage,
aes(lon, lat), fill = "red") +
facet_grid(gamma_slab ~ era) +
scale_fill_viridis_c(direction = -1) +
theme(axis.ticks = element_blank(),
axis.text = element_blank(),
legend.position = "top")
rm(GLODAP_obs_coverage)8 Target variable
The predicted target variable (cstar_tref in this sensitivity case) is based on fitted MLRs and climatological fields of predictor variables, and calculated for each era.
8.1 Zonal mean sections
slab_breaks <- c(params_local$slabs_Atl[1:12], Inf)
for (i_basin_AIP in unique(target_zonal$basin_AIP)) {
print(
target_zonal %>%
filter(basin_AIP == i_basin_AIP) %>%
ggplot(aes(lat, depth,
z = !!sym(
paste(params_local$MLR_target, "mean", sep = "_")
))) +
geom_contour_filled(bins = 11) +
scale_fill_viridis_d(name = params_local$MLR_target) +
geom_contour(aes(lat, depth, z = gamma_mean),
breaks = slab_breaks,
col = "white") +
geom_text_contour(
aes(lat, depth, z = gamma_mean),
breaks = slab_breaks,
col = "white",
skip = 1
) +
scale_y_reverse() +
coord_cartesian(expand = 0,
ylim = c(params_global$plotting_depth, 0)) +
scale_x_continuous(breaks = seq(-100, 100, 20)) +
guides(fill = guide_colorsteps(barheight = unit(10, "cm"))) +
facet_grid(era ~ eras,
labeller = labeller(.default = label_both)) +
labs(title = i_basin_AIP)
)
}
rm(slab_breaks)
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 kableExtra_1.3.1 marelac_2.1.10 shape_1.4.5
[5] scales_1.1.1 metR_0.9.0 scico_1.2.0 patchwork_1.1.1
[9] collapse_1.5.0 forcats_0.5.0 stringr_1.4.0 dplyr_1.0.2
[13] purrr_0.3.4 readr_1.4.0 tidyr_1.1.2 tibble_3.0.4
[17] ggplot2_3.3.2 tidyverse_1.3.0 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] fs_1.5.0 lubridate_1.7.9 gsw_1.0-5
[4] webshot_0.5.2 httr_1.4.2 rprojroot_2.0.2
[7] tools_4.0.3 backports_1.1.10 R6_2.5.0
[10] DBI_1.1.0 colorspace_1.4-1 withr_2.3.0
[13] tidyselect_1.1.0 compiler_4.0.3 git2r_0.27.1
[16] cli_2.1.0 rvest_0.3.6 xml2_1.3.2
[19] isoband_0.2.2 labeling_0.4.2 sass_0.2.0
[22] checkmate_2.0.0 digest_0.6.27 rmarkdown_2.5
[25] oce_1.2-0 pkgconfig_2.0.3 htmltools_0.5.0
[28] dbplyr_1.4.4 rlang_0.4.9 readxl_1.3.1
[31] rstudioapi_0.13 farver_2.0.3 generics_0.0.2
[34] jsonlite_1.7.1 magrittr_1.5 Matrix_1.2-18
[37] Rcpp_1.0.5 munsell_0.5.0 fansi_0.4.1
[40] lifecycle_0.2.0 stringi_1.5.3 whisker_0.4
[43] yaml_2.2.1 plyr_1.8.6 grid_4.0.3
[46] blob_1.2.1 parallel_4.0.3 promises_1.1.1
[49] crayon_1.3.4 lattice_0.20-41 haven_2.3.1
[52] hms_0.5.3 seacarb_3.2.14 knitr_1.30
[55] pillar_1.4.7 reprex_0.3.0 glue_1.4.2
[58] evaluate_0.14 RcppArmadillo_0.10.1.2.0 data.table_1.13.2
[61] modelr_0.1.8 vctrs_0.3.5 httpuv_1.5.4
[64] testthat_2.3.2 cellranger_1.1.0 gtable_0.3.0
[67] assertthat_0.2.1 xfun_0.18 broom_0.7.2
[70] RcppEigen_0.3.3.7.0 later_1.1.0.1 viridisLite_0.3.0
[73] memoise_1.1.0 ellipsis_0.3.1 here_0.1