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library(tidyverse)
library(seacarb)
library(oce)
library(marelac)
library(patchwork)
library(metR)
library(lubridate)

1 Approach

In order to test how (and how well) the depth-integrated CT estimates can be reproduced if only surface CO2 data were available, the BloomSail observations were restricted to those made in surface water and following reconstruction approaches were tested:

  • Mixed layer depth: Integration of surface observation across the MLD, assuming homogenious vertical patterns
  • CT profile reconstruction: Vertical reconstruction of incremental CT changes based on profiles of incremental changes in temperature
  • Temperature penetration depth: Integration of surface observation across the temperature penetration depth, assuming similar vertical extension as for CT drawdown.

Note: The reconstruction of CT profiles and the integration across the temperature penetration depth should produce very similar results. However, the latter avoids to create misinterpretable information about the vertical distribution of CT.

2 Data base

1m gridded, downcast profiles were used. CO2 data other than 3.5 m water depth were removed.

3 MLD approach

MLD calculation was previously described in the CT dynamics chapter.

3.1 Read data

ts_profiles_ID <-
  read_csv(here::here("Data/_merged_data_files", "ts_profiles_ID_long_cum_MLD.csv"))

ts_profiles_ID <- ts_profiles_ID %>% 
  select(ID, date_time_ID, dep, CT = value, CT_diff = value_diff, CT_cum = value_cum, sign, rho_lim, MLD)

ts_profiles_ID <- ts_profiles_ID %>% 
  mutate(rho_lim = as.factor(rho_lim))
ts_profiles_ID <- ts_profiles_ID %>% 
  mutate(CT = if_else(dep == 3.5, CT, NaN),
         rho_lim = as.factor(rho_lim))

3.2 Timeseries

ts_profiles_ID %>% 
  ggplot()+
  geom_hline(yintercept = 0)+
  geom_line(aes(date_time_ID, MLD, col=rho_lim, linetype="MLD"))+
  scale_y_reverse()+
  scale_color_viridis_d(name="Rho limit")+
  scale_linetype(name="Estimate")+
  labs(y="Depth (m)")+
  theme(axis.title.x = element_blank())

3.3 iCT calculation

Integrated CT depletion was calculated as the product of observed incremental CT changes in surface waters and the respective mixed layer depth.

ts_profiles_ID_surface <- ts_profiles_ID %>% 
  filter(dep==3.5) %>% 
  group_by(rho_lim) %>% 
  arrange(date_time_ID) %>% 
  mutate(iCT_diff = CT_diff * MLD / 1000,
         iCT_cum = cumsum(replace_na(iCT_diff, 0))) %>% 
  ungroup()

3.4 Incremental and cumulative timeseries

Total incremental and cumulative CT changes inbetween cruise dates were calculated.

p_iCT <- ts_profiles_ID_surface %>% 
  ggplot(aes(date_time_ID, iCT_diff, fill= rho_lim))+
  geom_hline(yintercept = 0)+
  geom_col(col="black", position = "dodge")+
  scale_y_continuous(breaks = seq(-100, 100, 0.2))+
  scale_fill_viridis_d()+
  labs(y="integrated CT changes [mol/m2]")+
  theme(axis.title.x = element_blank())

p_iCT_cum <- ts_profiles_ID_surface %>% 
  ggplot(aes(date_time_ID,  iCT_cum, 
             col=rho_lim))+
  geom_line()+
  geom_hline(yintercept = 0)+
  scale_color_viridis_d()+
  scale_y_continuous(breaks = seq(-100, 100, 0.2))+
  theme(strip.background = element_blank(),
        strip.text = element_blank())+
  labs(y="integrated, cumulative CT changes [mol/m2]", x="date")


(p_iCT / p_iCT_cum)+
  plot_layout(guides = 'collect')

rm(p_iCT, p_iCT_cum)

ts_profiles_ID_surface_MLD <- ts_profiles_ID_surface
rm(ts_profiles_ID, ts_profiles_ID_surface)

4 CT profile reconstruction

4.1 Read data

ts_profiles_ID <-
  read_csv(here::here("Data/_merged_data_files", "ts_profiles_ID.csv"))

ts_profiles_ID <- ts_profiles_ID %>% 
  mutate(CT = if_else(dep == 3.5, CT, NaN),
         ID = as.factor(ID)) %>% 
  select(-date_ID)

4.2 CT vs temperature

As primary production (negative changes in CT) and increase in seawater temperature have a common driver (light), the relation between both changes was investigated.

ts_profiles_ID_diff <- ts_profiles_ID %>% 
  drop_na() %>% 
  arrange(date_time_ID) %>%
  mutate(CT_diff = CT - lag(CT, default = first(CT)),
         tem_diff = tem - lag(tem, default = first(tem)),
         factor = CT_diff / tem_diff,
         factor = if_else(is.na(factor), 0, factor))

ts_profiles_ID_diff %>% 
  ggplot(aes(tem_diff, CT_diff))+
  geom_hline(yintercept = 0)+
  geom_vline(xintercept = 0)+
  geom_path()+
  geom_point()

4.3 Reconstruction of CT dynamics

The ratio of the incremental change of CT with temperature at the seasurface was applied to calculate the CT in other water depth based on the known change in temperature.

ts_profiles_ID_diff <- ts_profiles_ID_diff %>% 
  select(ID, factor)

ts_profiles_ID <- full_join(ts_profiles_ID, ts_profiles_ID_diff)
rm(ts_profiles_ID_diff)

ts_profiles_ID <- ts_profiles_ID %>%
  arrange(date_time_ID) %>%
  group_by(dep) %>% 
  mutate(tem_diff = tem - lag(tem, default = first(tem))) %>% 
  ungroup()

ts_profiles_ID <- ts_profiles_ID %>% 
  mutate(CT_diff = tem_diff * factor) %>% 
  select(-factor)

The reconstructed incremental changes are added up to derive cummulative CT changes throughout the water column.

ts_profiles_ID_long <- ts_profiles_ID %>% 
  select(ID, date_time_ID, dep, tem = tem_diff, CT = CT_diff) %>% 
  pivot_longer(4:5, names_to = "var", values_to = "value_diff") %>% 
  group_by(dep, var) %>% 
  arrange(date_time_ID) %>% 
  mutate(date_time_ID_diff = as.numeric(date_time_ID - lag(date_time_ID)),
         date_time_ID_ref  = date_time_ID - (date_time_ID - lag(date_time_ID))/2,
         value_diff_daily = value_diff / date_time_ID_diff,
         value_cum = cumsum(value_diff)) %>% 
  ungroup()

4.4 Profiles of incremental changes

Changes of seawater parameters at each depth were reconstructed from one cruise day to the next and divided by the number of days inbetween.

ts_profiles_ID_long %>% 
  arrange(dep) %>% 
  ggplot(aes(value_diff, dep, col=ID))+
  geom_vline(xintercept = 0)+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_d()+
  facet_wrap(~var, scales = "free_x")+
  labs(x="Change of value inbetween cruises per day")

4.5 Profiles of cumulative changes

Cumulative changes of seawater parameters were calculated at each depth relative to the first cruise day on July 5.

ts_profiles_ID_long %>% 
  arrange(dep) %>% 
  ggplot(aes(value_cum, dep, col=ID))+
  geom_vline(xintercept = 0)+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_d()+
  labs(x="Cumulative change of value")+
  facet_wrap(~var, scales = "free_x")

4.6 Hovmoeller plots

Hoevmoeller plots were generated for the reconstructed daily and cumulative changes in CT. Absolute values are not reproducible with this approach. Furthermore, it meets our expectations

4.6.1 Daily changes

bin_CT <- 2.5

ts_profiles_ID_long %>%
  filter(var == "CT") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID_ref, y=dep, z=value_diff_daily),
                    breaks = MakeBreaks(bin_CT),
                    col="black")+
  geom_point(aes(x=date_time_ID, y=c(24.5)), size=3, shape=24, fill="white")+
  scale_fill_divergent(breaks = MakeBreaks(bin_CT),
                       guide = "colorstrip",
                       name="CT (µmol/kg)")+
  scale_y_reverse()+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())
Hovmoeller plots of daily reconstructed changes in C~T~ and temperature.

Hovmoeller plots of daily reconstructed changes in CT and temperature.

rm(bin_CT)

4.6.2 Cumulative changes

bin_CT <- 20

ts_profiles_ID_long %>%
  filter(var == "CT") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID, y=dep, z=value_cum),
                    breaks = MakeBreaks(bin_CT),
                    col="black")+
  geom_point(aes(x=date_time_ID, y=c(24.5)), size=3, shape=24, fill="white")+
  scale_fill_divergent(breaks = MakeBreaks(bin_CT),
                       guide = "colorstrip",
                       name="CT (µmol/kg)")+
  scale_y_reverse()+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())
Hovmoeller plots of daily reconstructed changes in C~T~.

Hovmoeller plots of daily reconstructed changes in CT.

rm(bin_CT)

4.7 iCT time series

Total incremental and cumulative CT changes inbetween cruise dates were calculated for the upper 10 m of the water body.

iCT_10 <- ts_profiles_ID_long %>%
  filter(dep < 17, 
         var == "CT") %>% 
  select(ID, date_time_ID, date_time_ID_ref, CT_diff=value_diff, CT_cum=value_cum) %>% 
  group_by(ID, date_time_ID, date_time_ID_ref) %>% 
  summarise(CT_i_diff = sum(CT_diff)/1000,
            CT_i_cum = sum(CT_cum)/1000) %>% 
  ungroup()

iCT_10 %>% 
  ggplot()+
  #geom_point(data = cruise_dates, aes(date_time_ID, 0), shape=21)+
  geom_col(aes(date_time_ID_ref, CT_i_diff),
           position = "dodge", alpha=0.3)+
  geom_line(aes(date_time_ID, CT_i_cum))+
  scale_color_viridis_d(name="Depth limit (m)")+
  scale_fill_viridis_d(name="Depth limit (m)")+
  labs(y="iCT [mol/m2]", x="")+
  theme_bw()

rm(ts_profiles_ID, ts_profiles_ID_long)

5 Heat penetration depth

To investigate the link between temperature rise and CT drawdown, we estimated the mean penetration depth of both parameters, which was defined as the surface change (0-6m) devided by the integrated change across depth. To derive the integrated values, we summed up all negative changes in CT and temperature. For temperature we limited the integration to the depth at which the cummulative signal on July 23 was below 5% of the surface signal.

5.1 Read data

ts_profiles_ID_long_cum <-
  read_csv(here::here("Data/_merged_data_files", "ts_profiles_ID_long_cum.csv"))

ts_profiles_ID_long_cum <- ts_profiles_ID_long_cum %>% 
  filter(var %in% c("CT", "tem")) %>% 
  mutate(ID = as.factor(ID)) %>% 
  select(-date_ID)
ts_profiles_ID <-
  read_csv(here::here("Data/_merged_data_files", "ts_profiles_ID_long_cum_MLD.csv"))

ts_profiles_ID <- ts_profiles_ID %>% 
  filter(rho_lim == 0.1) %>% 
  select(ID, date_time_ID, dep, CT = value, CT_diff = value_diff, CT_cum = value_cum) %>% 
  mutate(ID = as.factor(ID))
# surface values

diff_surface <- ts_profiles_ID_long_cum %>% 
  filter(dep < 6) %>% 
  group_by(ID, var) %>% 
  summarise(value_diff_surface = mean(value_diff, na.rm = TRUE),
            value_cum_surface  =mean(value_cum, na.rm = TRUE)) %>% 
  ungroup()

ts_profiles_ID_long_cum <- full_join(ts_profiles_ID_long_cum, diff_surface) 
rm(diff_surface)

# directional changes in CT and tem

penetration_depth_CT <- ts_profiles_ID_long_cum %>%
  filter(var == "CT") %>% 
  mutate(value_diff = if_else(value_diff<=0, value_diff, NaN),
         value_cum = if_else(value_cum  <=0, value_cum, NaN))

penetration_depth_tem <- ts_profiles_ID_long_cum %>%
  filter(var == "tem") %>% 
  mutate(value_diff = if_else(value_diff>=0, value_diff, NaN),
         value_cum = if_else(value_cum  >=0, value_cum, NaN))

penetration_depth <- full_join(penetration_depth_CT,
                                  penetration_depth_tem)

# define integration depth

integration_depth_tem <- penetration_depth_tem %>% 
  filter(ID == "180723") %>% 
  mutate(value_cum_rel = 100*value_cum/value_cum_surface)

integration_depth_tem %>% 
  ggplot(aes(value_cum_rel, dep))+
  geom_vline(xintercept = c(5))+
  geom_point()+
  geom_path()+
  scale_y_reverse(name = "Depth (m)")+
  scale_x_continuous(breaks = seq(0,100,10),
                     name = "Cumulative temperature change relative to surface (%)")

integration_depth_tem <- integration_depth_tem %>% 
  filter(value_cum_rel < 5) %>% 
  pull(dep) %>% 
  min()

rm(penetration_depth_CT, penetration_depth_tem)
# calculate penetration depths

penetration_depth <- penetration_depth %>% 
  filter(dep < integration_depth_tem) %>% 
  group_by(var, ID, date_time_ID) %>% 
  summarise(value_diff_int = sum(value_diff, na.rm = TRUE),
            value_cum_int = sum(value_cum, na.rm = TRUE),
            value_diff_surface = mean(value_diff_surface, na.rm = TRUE),
            value_cum_surface = mean(value_cum_surface, na.rm = TRUE),
            penetration_depth_diff = value_diff_int/value_diff_surface,
            penetration_depth_cum = value_cum_int/value_cum_surface) %>% 
  ungroup() %>% 
  filter(penetration_depth_diff > 0)

penetration_depth_mean <- penetration_depth %>% 
  group_by(var) %>% 
  summarise(penetration_depth_diff_mean = mean(penetration_depth_diff, na.rm=TRUE),
            penetration_depth_cum_mean = mean(penetration_depth_cum, na.rm=TRUE),
            penetration_depth_diff_sd = sd(penetration_depth_diff, na.rm=TRUE),
            penetration_depth_cum_sd = sd(penetration_depth_cum, na.rm=TRUE)) %>% 
  ungroup()

penetration_depth_mean
# A tibble: 2 x 5
  var   penetration_depth~ penetration_dept~ penetration_dept~ penetration_dept~
  <chr>              <dbl>             <dbl>             <dbl>             <dbl>
1 CT                  10.2              10.4              1.01             0.393
2 tem                 11.3              10.6              2.43             0.608
p_pene_diff <- penetration_depth %>% 
  ggplot(aes(date_time_ID, penetration_depth_diff, col=var))+
  geom_hline(yintercept = 0)+
  geom_hline(data = penetration_depth_mean,
             aes(yintercept = penetration_depth_diff_mean,
                 col=var, linetype = "mean"))+
  geom_line(aes(linetype="cruise"))+
  geom_point()+
  scale_y_reverse(name = "Penetration depth (m)", breaks = seq(0,20,5))+
  scale_color_brewer(palette = "Set1", direction = -1)+
  labs(title = "Incremental CT and temperature changes")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        legend.title = element_blank())

p_pene_cum <- penetration_depth %>% 
  ggplot(aes(date_time_ID, penetration_depth_cum, col=var))+
  geom_hline(yintercept = 0)+
  geom_hline(data = penetration_depth_mean,
             aes(yintercept = penetration_depth_cum_mean,
                 col=var, linetype = "mean"))+
  geom_line(aes(linetype="cruise"))+
  geom_point()+
  scale_y_reverse(name = "Penetration depth (m)", breaks = seq(0,20,5))+
  scale_color_brewer(palette = "Set1", direction = -1)+
  labs(title = "Cumulative CT and temperature changes")+
  theme(axis.title.x = element_blank(),
        legend.title = element_blank())

p_pene_diff / p_pene_cum +
  plot_layout(guides = "collect")

rm(p_pene_cum, p_pene_diff)

5.2 iCT calculation

Integrated CT depletion was calculated as the product of observed incremental CT changes in surface waters and the respective mixed layer depth.

penetration_depth <- penetration_depth %>% 
  filter(var == "tem") %>% 
  select(ID, penetration_depth_diff)

ts_profiles_ID_zeff <- full_join(ts_profiles_ID, penetration_depth) 
  
ts_profiles_ID_zeff_surface <- ts_profiles_ID_zeff %>% 
  filter(dep==3.5) %>% 
  arrange(date_time_ID) %>% 
  mutate(iCT_diff = CT_diff * 11.3 / 1000,
         iCT_cum = cumsum(replace_na(iCT_diff, 0))) %>% 
  ungroup()
p_iCT <- ts_profiles_ID_zeff_surface %>% 
  ggplot(aes(date_time_ID, iCT_diff))+
  geom_hline(yintercept = 0)+
  geom_col(col="black", position = "dodge")+
  scale_y_continuous(breaks = seq(-100, 100, 0.2))+
  #scale_fill_viridis_d()+
  labs(y="integrated CT changes [mol/m2]")+
  theme(axis.title.x = element_blank())

p_iCT_cum <- ts_profiles_ID_zeff_surface %>% 
  ggplot(aes(date_time_ID,  iCT_cum))+
  geom_line()+
  geom_hline(yintercept = 0)+
  scale_color_viridis_d()+
  scale_y_continuous(breaks = seq(-100, 100, 0.2))+
  theme(strip.background = element_blank(),
        strip.text = element_blank())+
  labs(y="integrated, cumulative CT changes [mol/m2]", x="date")


(p_iCT / p_iCT_cum)+
  plot_layout(guides = 'collect')

rm(p_iCT, p_iCT_cum)

#rm(ts_profiles_ID, ts_profiles_ID_surface)

6 Comparison of approaches

iCT_10_flux_mix <-
  read_csv(here::here("Data/_merged_data_files", "ts_NCP_cum.csv"))

iCT_10_flux_mix <- iCT_10_flux_mix %>% 
  filter(!is.na(CT_i_diff))
ggplot()+
  geom_line(data = ts_profiles_ID_zeff_surface,
            aes(date_time_ID,  iCT_cum, col="zeff"))+
  geom_line(data = ts_profiles_ID_surface_MLD %>% filter(rho_lim == 0.1),
            aes(date_time_ID,  iCT_cum, col="Rho 0.1"))+
  geom_line(data = iCT_10,
            aes(date_time_ID,  CT_i_cum, col="CT recon"))+
  geom_line(data = iCT_10_flux_mix,
            aes(date_time,  CT_i_cum, col="best guess"))+
  geom_hline(yintercept = 0)+
  scale_color_brewer(palette = "Set1", name="Estimate")+
  scale_y_continuous(breaks = seq(-100, 100, 0.2))+
  scale_x_datetime(breaks = "week",
                   date_labels = "%b %d")+
  theme(axis.title.x = element_blank())+
  labs(y="integrated, cumulative CT changes [mol/m2]")


sessionInfo()
R version 3.6.3 (2020-02-29)
Platform: i386-w64-mingw32/i386 (32-bit)
Running under: Windows 10 x64 (build 18363)

Matrix products: default

locale:
[1] LC_COLLATE=English_Germany.1252  LC_CTYPE=English_Germany.1252   
[3] LC_MONETARY=English_Germany.1252 LC_NUMERIC=C                    
[5] LC_TIME=English_Germany.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] lubridate_1.7.4 metR_0.6.0      patchwork_1.0.0 marelac_2.1.10 
 [5] shape_1.4.4     seacarb_3.2.13  oce_1.2-0       gsw_1.0-5      
 [9] testthat_2.3.2  forcats_0.5.0   stringr_1.4.0   dplyr_0.8.5    
[13] purrr_0.3.3     readr_1.3.1     tidyr_1.0.2     tibble_3.0.0   
[17] ggplot2_3.3.0   tidyverse_1.3.0 workflowr_1.6.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.4         whisker_0.4        knitr_1.28         xml2_1.3.0        
 [5] magrittr_1.5       hms_0.5.3          rvest_0.3.5        tidyselect_1.0.0  
 [9] viridisLite_0.3.0  here_0.1           colorspace_1.4-1   lattice_0.20-41   
[13] R6_2.4.1           rlang_0.4.5        fansi_0.4.1        broom_0.5.5       
[17] xfun_0.12          dbplyr_1.4.2       modelr_0.1.6       withr_2.1.2       
[21] git2r_0.26.1       ellipsis_0.3.0     htmltools_0.4.0    assertthat_0.2.1  
[25] rprojroot_1.3-2    digest_0.6.25      lifecycle_0.2.0    haven_2.2.0       
[29] rmarkdown_2.1      sp_1.4-1           compiler_3.6.3     cellranger_1.1.0  
[33] pillar_1.4.3       scales_1.1.0       backports_1.1.5    generics_0.0.2    
[37] jsonlite_1.6.1     httpuv_1.5.2       pkgconfig_2.0.3    rstudioapi_0.11   
[41] munsell_0.5.0      highr_0.8          plyr_1.8.6         httr_1.4.1        
[45] tools_3.6.3        grid_3.6.3         nlme_3.1-145       data.table_1.12.8 
[49] gtable_0.3.0       checkmate_2.0.0    utf8_1.1.4         DBI_1.1.0         
[53] cli_2.0.2          readxl_1.3.1       yaml_2.2.1         crayon_1.3.4      
[57] RColorBrewer_1.1-2 farver_2.0.3       later_1.0.0        promises_1.1.0    
[61] fs_1.4.0           vctrs_0.2.4        memoise_1.1.0      glue_1.3.2        
[65] evaluate_0.14      labeling_0.3       reprex_0.3.0       stringi_1.4.6