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Rmd 97355fa jens-daniel-mueller 2020-03-12 CT calculations and plots 
library(tidyverse)
library(patchwork)
library(seacarb)
library(marelac)
library(metR)
library(scico)
library(lubridate)
library(zoo)
library(tibbletime)
library(sp) # check points in polygon

1 Sensor data

1.1 Data preparation

dep_grid <- 1
max_dep <- 25
max_dep_gap <- 20
max_gap <- 3
surface_dep <- 6

stations_out <- c("PX1", "PX2", "P14", "P13", "P01")
dates_out <- c("180616","180820")
phases_in <- c("down", "up")

Profile data are prepared by:

  • Ignoring those made on June 16 (pCO2 sensor not in operation)
  • Removing HydroC Flush and Zeroing periods
  • Selecting only continous downcast periods
  • Gridding profiles to 1m depth intervals
  • removing grids with pCO2 < 0 µatm (presumably RT correction artefact after zeroing)
  • Discarding profiles with 20 or more observation missing within upper 25m
  • assigning mean date_time_ID value to all profiles belonging to one cruise
  • discarding “coastal” station P01, P13, P14
  • Restricting profiles to upper 25m

Please note that:

  • The label ID representm the start date of the cruise (“YYMMDD”), not the exact mean sampling date
tm <-
 read_csv(here::here("data/_merged_data_files/response_time",
                      "tm_RT_all.csv"),
               col_types = cols(ID = col_character(),
                                pCO2_analog = col_double(),
                                pCO2_corr = col_double(),
                                Zero = col_character(),
                                Flush = col_character(),
                                mixing = col_character(),
                                Zero_counter = col_integer(),
                                deployment = col_integer(),
                                lon = col_double(),
                                lat = col_double(),
                                pCO2 = col_double()))


# Filter relevant rows and columns
tm_profiles <- tm %>% 
  filter(type == "P",
         Flush == "0",
         Zero == "0",
         !ID %in% dates_out,
         !(station %in% c("PX1", "PX2"))) %>% 
  select(date_time, ID, station, lat, lon, dep, sal, tem, pCO2_corr, pCO2, duration)

stations <- tm_profiles %>% 
  group_by(station) %>% 
  summarise(lat = mean(lat),
            lon = mean(lon)) %>% 
  ungroup()

tm_profiles <- tm_profiles %>% 
  filter(!(station %in% c("P14", "P13", "P01")))

# Assign meta information
tm_profiles <- tm_profiles %>% 
  group_by(ID, station) %>% 
  mutate(duration = as.numeric(date_time - min(date_time))) %>%
  arrange(date_time) %>% 
  ungroup()

meta <- read_csv(here::here("Data/TinaV/Sensor",
                            "Sensor_meta.csv"),
                 col_types = cols(ID = col_character()))

meta <- meta %>% 
    filter(!ID %in% dates_out,
           !(station %in% stations_out))

tm_profiles <- full_join(tm_profiles, meta)
rm(meta)


# creating descriptive variables
tm_profiles <- tm_profiles %>% 
  mutate(phase = "standby",
         phase = if_else(duration >= start & duration < down & !is.na(down) & !is.na(start),
                         "down", phase),
         phase = if_else(duration >= down  & duration < lift & !is.na(lift) & !is.na(down ),
                         "low",  phase),
         phase = if_else(duration >= lift  & duration < up   & !is.na(up  ) & !is.na(lift  ),
                         "mid",  phase),
         phase = if_else(duration >= up    & duration < end  & !is.na(end ) & !is.na(up   ),
                         "up",   phase))

tm_profiles <- tm_profiles %>% 
  select(-c(start, down, lift, up, end, comment, p_type, duration))


# select downcasst only
tm_profiles <- tm_profiles %>% 
  filter(phase %in% phases_in)

#tm_profiles_highres <- tm_profiles

# grid observation to 1m depth intervals
tm_profiles <- tm_profiles %>% 
  mutate(dep_grid = as.numeric(as.character(cut(dep, seq(0,40,1), seq(0.5,39.5,1))))) %>% 
  group_by(ID, station, dep_grid, phase) %>%
  summarise_all("mean", na.rm = TRUE) %>% 
  ungroup() %>% 
  select(-dep, dep=dep_grid)

# Remove zero pCO2 data
tm_profiles <- tm_profiles %>%
  filter(pCO2 >= 0)

# subset complete profiles
profiles_in <- tm_profiles %>% 
  filter(dep < max_dep_gap,
         phase == "down") %>% 
  group_by(ID, station) %>% 
  summarise(nr_na = max_dep_gap/dep_grid - n()) %>% 
  mutate(select = if_else(nr_na < max_gap,
                          "in", "out")) %>% 
  select(-nr_na) %>% 
  ungroup()

tm_profiles <- full_join(tm_profiles, profiles_in)
rm(profiles_in)

1.2 pCO2 profile overview

tm_profiles %>% 
  arrange(date_time) %>% 
  ggplot(aes(pCO2, dep, col=select, linetype=phase))+
  geom_hline(yintercept = 25)+
  geom_path()+
  scale_y_reverse()+
  scale_x_continuous(breaks = c(0, 600), labels = c(0, 600))+
  scale_color_brewer(palette = "Set1", direction = -1)+
  coord_cartesian(xlim = c(0,600))+
  facet_grid(ID~station)
Overview pCO~2~ profiles at stations (P02-P12) and cruise dates (ID). y-axis restricted to displayed range.

Overview pCO2 profiles at stations (P02-P12) and cruise dates (ID). y-axis restricted to displayed range.

1.3 Subset

tm_profiles <- tm_profiles %>%
  filter(select == "in",
         phase == "down") %>%
  select(-c(select, phase)) %>% 
  filter(dep < max_dep)
rm(dep_grid,max_dep_gap,max_gap,
   stations_out,dates_out,phases_in)

1.4 Cruise dates

# assign mean date_time stamp

cruise_dates <- tm_profiles %>% 
  group_by(ID) %>% 
  summarise(date_time_ID = mean(date_time),
            date_ID = format(as.Date(date_time_ID), "%b %d")) %>% 
  ungroup()

# inner_join remove P14 observations lacking date_time_ID 
tm_profiles <- inner_join(cruise_dates, tm_profiles)

1.5 Station map

# borders for fm data in BloomSail area
poly_lon <- c(18.9, 19.5, 19.5, 18.9)
poly_lat <- c(57.4, 57.2, 57.45, 57.61)

# plot area
lat_lo <- 57.25
lat_hi <- 57.6

lon_lo <- 18.6
lon_hi <- 19.7
fm <-
  read_csv(here::here("Data/_summarized_data_files",
                       "fm.csv")) %>% 
  filter(lat <= lat_hi, lat >= lat_lo, lon >= lon_lo)

fm <- fm %>% 
  mutate(Area = point.in.polygon(point.x = lon,
                                 point.y = lat,
                                 pol.x = poly_lon,
                                 pol.y = poly_lat),
         Area = as.character(Area),
         Area = if_else(Area == "1", "utilized", "sampled"))

fm %>% 
  filter(Area == "utilized") %>% 
  select(-Area) %>% 
  write_csv(here::here("Data/_summarized_data_files",
                       "fm_bloomsail.csv"))
map <- read_csv(here::here("data/Maps","Bathymetry_Gotland_east_small.csv")) %>% 
  filter(lat < lat_hi, lat > lat_lo,
         lon < lon_hi, lon > lon_lo)

map_low_res <- map %>% 
  mutate(lat = cut(lat,
                   breaks = seq(57,58,0.01),
                   labels = seq(57.005,57.995,0.01)),
         lon = cut(lon,
                   breaks = seq(18,22,0.01),
                   labels = seq(18.005,21.995,0.01))) %>% 
  group_by(lat,lon) %>% 
  summarise_all(mean, na.rm=TRUE) %>% 
  ungroup() %>% 
  mutate(lat = as.numeric(as.character(lat)),
         lon = as.numeric(as.character(lon)))

tm_track <- tm %>% 
  arrange(date_time) %>% 
  slice(which(row_number() %% 50 == 1))

ggplot()+
  geom_contour_fill(data = map_low_res,
                    aes(x=lon, y=lat, z=-elev),
                    na.fill = TRUE,
                    breaks = seq(0,300,30))+
  geom_raster(data=map %>% filter(is.na(elev)),
              aes(lon, lat), fill="darkgrey")+
  geom_path(data = tm_track, aes(lon, lat, group=ID, col="sampled"))+
  geom_path(data = fm, aes(lon, lat, group=ID, col=Area))+
  geom_label(data = stations %>% filter(!(station %in% c("P14", "P13", "P01"))),
             aes(lon, lat, label=station, col="utilized"))+
  geom_label(data = stations %>% filter(station %in% c("P14", "P13", "P01")),
             aes(lon, lat, label=station, col="sampled_station"))+
  coord_quickmap(expand = 0, ylim = c(lat_lo+0.01, lat_hi-0.01))+
  labs(x="Longitude (°E)", y="Latitude (°N)")+
  scale_fill_gradient(low = "lightsteelblue1", high = "dodgerblue4",
                   name="Depth (m)", breaks = seq(0,180,30),
                   guide = "colorstrip")+
  scale_color_manual(values = c("white", "darkgrey", "orangered"), guide=FALSE)
Location of stations sampled between the east coast of Gotland and Gotland deep.

Location of stations sampled between the east coast of Gotland and Gotland deep. 

ggsave(here::here("output/Plots/Figures_publication/article", "station_map.pdf"),
       width = 220, height = 150, dpi = 300, units = "mm")

rm(map, map_low_res,
   lat_hi, lat_lo, lon_hi, lon_lo, 
   poly_lat, poly_lon,
   fm, tm_track)

rm(tm)

1.6 Data coverage

cover <- tm_profiles %>% 
  group_by(ID, station) %>% 
  summarise(date = mean(date_time),
            date_time_ID = mean(date_time_ID)) %>% 
  ungroup()

cover %>% 
  ggplot(aes(date, station, fill=ID))+
  geom_vline(aes(xintercept = date_time_ID, col=ID))+
  geom_point(shape=21)+
  scale_fill_viridis_d(labels = cruise_dates$date_ID,
                       name = "Mean cruise date")+
  scale_color_viridis_d(labels = cruise_dates$date_ID,
                       name = "Mean cruise date")+
    scale_x_datetime(date_breaks = "week",
                   date_labels = "%b %d")+
  theme(axis.title.x = element_blank())
Spatio-temporal data coverage, indicated as station visits over time.

Spatio-temporal data coverage, indicated as station visits over time. 

ggsave(here::here("output/Plots/Figures_publication/article", "data_coverage.pdf"),
       width = 130, height = 65, dpi = 300, units = "mm")

rm(cover)

2 Bottle CT and AT

At stations P07 and P10 discrete samples for lab measurmentm of CT and AT were collected. Please note that - in contrast to the pCO2 profiles - samples were taken on June 16, but removed here for harmonization of results.

tb <-
  read_csv(here::here("Data/_summarized_data_files", "tb.csv"),
           col_types = cols(ID = col_character()))

tb <- tb %>% 
  filter(station %in% c("P07", "P10"),
         dep <= max_dep) %>% 
  mutate(ID = if_else(ID == "180722", "180723", ID))

tb <- inner_join(tb, cruise_dates)

2.1 Mean alkalinity

In order to derive CT from measured pCO2 profiles, the alkalinity mean + sd in the upper 25m and both stations was calculated as:

AT_mean <- tb %>% 
  filter(dep <= max_dep) %>% 
  summarise(AT = mean(AT, na.rm = TRUE)) %>%
  pull()

AT_mean
[1] 1719.706
AT_sd <- tb %>% 
  filter(dep <= 20) %>% 
  summarise(AT = sd(AT, na.rm = TRUE)) %>%
  pull()

AT_sd
[1] 26.23092

Likewise, the mean salinity amounts to:

sal_mean <- tb %>% 
  filter(dep <= 20) %>% 
  summarise(sal = mean(sal, na.rm = TRUE)) %>%
  pull()

sal_mean
[1] 6.907083
bind_cols(start = min(tm_profiles$date_time), 
          end = max(tm_profiles$date_time),
          AT = AT_mean,
          AT_sd = AT_sd,
          sal = sal_mean) %>% 
  write_csv(here::here("Data/_summarized_data_files", "tb_fix.csv"))

rm(AT_sd)

2.2 nCT calculation

The alkalinity-normalized CT, nCT, was calculated.

tb <- tb %>% 
  mutate(nCT = CT/AT * AT_mean)

2.3 Vertical profiles

tb_long <- tb %>% 
  pivot_longer(c(sal:AT, nCT), names_to = "var", values_to = "value")

tb_long %>% 
  ggplot(aes(value, dep))+
  geom_path(aes(col=ID))+
  geom_point(aes(fill=ID), shape=21)+
  scale_y_reverse()+
  scale_fill_viridis_d(labels = cruise_dates$date_ID)+
  scale_color_viridis_d(labels = cruise_dates$date_ID)+
  facet_grid(station~var, scales = "free_x")+
  theme(legend.position = "bottom",
        legend.title = element_blank())

2.4 Surface time series

tb_surface <- tb_long %>% 
  filter(dep < surface_dep) %>% 
  group_by(ID, date_time_ID, var, station) %>% 
  summarise(value = mean(value, na.rm = TRUE)) %>% 
  ungroup()

tb_surface_station_mean <- tb_long %>% 
  filter(dep < surface_dep) %>% 
  group_by(ID, date_time_ID, var) %>% 
  summarise(value_mean = mean(value, na.rm = TRUE),
            value_sd = sd(value, na.rm = TRUE)) %>% 
  ungroup()

tb_long %>%
  filter(dep<11) %>% 
  ggplot()+
  geom_line(data = tb_surface, aes(date_time_ID, value, col="Individual"))+
  geom_line(data = tb_surface_station_mean, aes(date_time_ID, value_mean, col="Both (mean)"))+
  geom_point(aes(date_time_ID, value, fill=dep), shape=21)+
  scale_fill_scico(palette = "oslo", direction = -1, name="Depth (m)")+
  scale_color_brewer(palette = "Set1", name="Station surface mean")+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  facet_grid(var~station, scales = "free_y")+
  labs(x="Mean transect date")
Time series of bottle data. Shown are mean values of samples collected at water depths < 10m (usually collected at 0 and 5 m).

Time series of bottle data. Shown are mean values of samples collected at water depths < 10m (usually collected at 0 and 5 m). 

rm(tb_long, tb_surface, tb)

Important notes: - nCT drop and temporal patterns agree well with those found in the nCT time series derived from pCO2 measurements (below).

3 nCT profiles

3.1 Calculation from pCO2

Alkalinity normalized CT (nCT) profiles were calculated from sensor pCO2 and T profiles, and constant salinity and alkalinity values. Note that the impact of fixed vs. measured salinity has only a negligible impact on nCT profiles.

tm_profiles <- tm_profiles %>% 
  mutate(nCT = carb(24, var1=pCO2, var2=AT_mean*1e-6,
                   S=sal_mean, T=tem, P=dep/10, k1k2="m10", kf="dg", ks="d",
                   gas="insitu")[,16]*1e6)

rm(sal_mean)

tm_profiles %>% 
  write_csv(here::here("Data/_merged_data_files/CT_dynamics", "tm_profiles.csv"))

3.2 Plot all profiles

tm_profiles <-  tm_profiles %>% 
  arrange(date_time_ID)

p_tem <- 
  tm_profiles %>% 
  ggplot(aes(tem, dep, col=ID, group = interaction(station, ID)))+
  geom_path()+
  scale_y_reverse(expand = c(0,0))+
  labs(x = "Temperature (\u00B0C)",
       y = "Depth (m)")+
  scale_color_viridis_d(guide = FALSE)

p_pCO2 <- 
  tm_profiles %>% 
  ggplot(aes(pCO2, dep, col=ID, group = interaction(station, ID)))+
  geom_path()+
  scale_y_reverse(expand = c(0,0))+
  labs(x = expression(pCO[2]~(µatm)))+
  scale_color_viridis_d(guide = FALSE)+
  theme(axis.text.y = element_blank(),
        axis.title.y = element_blank(),
        axis.ticks.y = element_blank())

p_nCT <- 
  tm_profiles %>% 
  ggplot(aes(nCT, dep, col=ID, group = interaction(station, ID)))+
  geom_path()+
  scale_y_reverse(expand = c(0,0))+
  labs(x = expression(nC[T]~(µmol~kg^{-1})))+
  scale_color_viridis_d(labels = cruise_dates$date_ID)+
  theme(legend.title = element_blank(),
        axis.text.y = element_blank(),
        axis.ticks.y = element_blank(),
        axis.title.y = element_blank())

p_tem + p_pCO2 + p_nCT

ggsave(here::here("output/Plots/Figures_publication/article", "profiles_all.pdf"),
       width = 180, height = 80, dpi = 300, units = "mm")

rm( p_tem, p_pCO2, p_nCT)

3.3 Mean profiles

Mean vertical profiles were calculated for each cruise day (ID).

tm_profiles_ID_mean <- tm_profiles %>% 
  select(-c(station,lat, lon, pCO2_corr, date_time)) %>% 
  group_by(ID, date_time_ID, dep) %>% 
  summarise_all(list(mean), na.rm=TRUE) %>% 
  ungroup()

tm_profiles_ID_sd <- tm_profiles %>% 
  select(-c(station,lat, lon, pCO2_corr, date_time)) %>% 
  group_by(ID, date_time_ID, dep) %>% 
  summarise_all(list(sd), na.rm=TRUE) %>% 
  ungroup()

tm_profiles_ID_sd_long <- tm_profiles_ID_sd %>% 
  pivot_longer(sal:nCT, names_to = "var", values_to = "sd")
  
tm_profiles_ID_mean_long <- tm_profiles_ID_mean %>% 
  pivot_longer(sal:nCT, names_to = "var", values_to = "value")
  
tm_profiles_ID_long <- inner_join(tm_profiles_ID_mean_long, tm_profiles_ID_sd_long)

tm_profiles_ID_mean %>% 
  write_csv(here::here("Data/_merged_data_files/CT_dynamics", "tm_profiles_ID.csv"))

rm(tm_profiles_ID_sd_long, tm_profiles_ID_sd, tm_profiles_ID_mean_long, tm_profiles_ID_mean)
tm_profiles_ID_long %>% 
  ggplot(aes(value, dep, col=ID))+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_d()+
  facet_wrap(~var, scales = "free_x")
Mean vertical profiles per cruise day across all stations.

Mean vertical profiles per cruise day across all stations. 

all <- tm_profiles_ID_long %>% 
  filter(var %in% c("nCT", "tem")) %>% 
  rename(group = ID)

tm_profiles_ID_long %>% 
  filter(var %in% c("nCT", "tem")) %>% 
  ggplot()+
  geom_path(data=all, aes(value, dep, group=group))+
  geom_ribbon(aes(xmin = value-sd, xmax=value+sd, y=dep, fill=ID), alpha=0.5)+
  geom_path(aes(value, dep, col=ID))+
  scale_y_reverse()+
  scale_color_viridis_d()+
  scale_fill_viridis_d()+
  facet_grid(ID~var, scales = "free_x")
Mean vertical profiles per cruise day across all stations plotted indivdually. Ribbons indicate the standard deviation observed across all profiles at each depth and transect.

Mean vertical profiles per cruise day across all stations plotted indivdually. Ribbons indicate the standard deviation observed across all profiles at each depth and transect. 

rm(all)

Important notes:

  • the standard deviation of CT in the upper 10m increases on June 30.

3.4 Individual profiles

CT, pCO2, S, and T profiles were plotted individually pdf here and grouped by ID pdf here. The later gives an idea of the differences between stations at one point in time.

# tm_profiles_highres <- tm_profiles_highres %>% 
#   filter(phase == "down")

pdf(file=here::here("output/Plots/CT_dynamics",
    "tm_profiles_pCO2_tem_sal_CT.pdf"), onefile = TRUE, width = 9, height = 5)

for(i_ID in unique(tm_profiles$ID)){
  for(i_station in unique(tm_profiles$station)){

    if (nrow(tm_profiles %>% filter(ID == i_ID, station == i_station)) > 0){
      
      
      # i_ID      <-      unique(tm_profiles$ID)[1]
      # i_station <- unique(tm_profiles$station)[1]

      p_pCO2 <- 
        tm_profiles %>%
        arrange(date_time) %>% 
        filter(ID == i_ID,
               station == i_station) %>%
        ggplot(aes(pCO2, dep, col="grid_RT"))+
        # geom_point(data = tm_profiles_highres %>% 
        #              arrange(date_time) %>% 
        #              filter(ID == i_ID, station == i_station),
        #            aes(pCO2_corr, dep, col="raw"))+
        # geom_point(data = tm_profiles_highres %>% 
        #              arrange(date_time) %>% 
        #              filter(ID == i_ID, station == i_station),
        #            aes(pCO2, dep, col="raw_RT"))+
        geom_point(aes(pCO2_corr, dep, col="grid"))+
        geom_point()+
        geom_path()+
        scale_y_reverse()+
        scale_color_brewer(palette = "Set1")+
        labs(y="Depth [m]", x="pCO2 [µatm]", title = str_c(i_ID," | ",i_station))+
        coord_cartesian(xlim = c(0,200), ylim = c(30,0))+
        theme_bw()+
        theme(legend.position = "left")
      
      p_tem <- 
        tm_profiles %>%
        arrange(date_time) %>% 
        filter(ID == i_ID,
               station == i_station) %>%
        ggplot(aes(tem, dep))+
        geom_point()+
        geom_path()+
        scale_y_reverse()+
        labs(y="Depth [m]", x="Tem [°C]")+
        coord_cartesian(xlim = c(14,26), ylim = c(30,0))+
        theme_bw()
      
      p_sal <- 
        tm_profiles %>%
        arrange(date_time) %>% 
        filter(ID == i_ID,
               station == i_station) %>%
        ggplot(aes(sal, dep))+
        geom_point()+
        geom_path()+
        scale_y_reverse()+
        labs(y="Depth [m]", x="Tem [°C]")+
        coord_cartesian(xlim = c(6.5,7.5), ylim = c(30,0))+
        theme_bw()
      
      p_nCT <- 
        tm_profiles %>%
        arrange(date_time) %>% 
        filter(ID == i_ID,
               station == i_station) %>%
        ggplot(aes(nCT, dep))+
        geom_point()+
        geom_path()+
        scale_y_reverse()+
        labs(y="Depth [m]", x="nCT* [µmol/kg]")+
        coord_cartesian(xlim = c(1400,1700), ylim = c(30,0))+
        theme_bw()
      

      print(
            p_pCO2 + p_tem + p_sal + p_nCT
            )
      
      rm(p_pCO2, p_sal, p_tem, p_nCT)

      
    }
  }
}

dev.off()

rm(i_ID, i_station, tm_profiles_highres)
tm_profiles_long <- tm_profiles %>%
  select(-c(lat, lon, pCO2_corr)) %>% 
  pivot_longer(sal:nCT, values_to = "value", names_to = "var")


pdf(file=here::here("output/Plots/CT_dynamics",
    "tm_profiles_ID_pCO2_tem_sal_CT.pdf"), onefile = TRUE, width = 9, height = 5)

for(i_ID in unique(tm_profiles$ID)){

  #i_ID <- unique(tm_profiles$ID)[1]
  
  sub_tm_profiles_long <- tm_profiles_long %>% 
        arrange(date_time) %>% 
        filter(ID == i_ID)
 
  print(
  
  sub_tm_profiles_long %>% 
    ggplot()+
    geom_path(data = tm_profiles_long,
              aes(value, dep, group=interaction(station, ID)), col="grey")+
    geom_path(aes(value, dep, col=station))+
    scale_y_reverse()+
    labs(y="Depth [m]", title = str_c("ID: ", i_ID))+
    theme_bw()+
    facet_wrap(~var, scales = "free_x")
   
  )  
  rm(sub_tm_profiles_long)
}

dev.off()

rm(i_ID, tm_profiles_long)

3.5 Profiles of incremental changes

Changes of seawater vars at each depth are calculated from one cruise day to the next and divided by the number of days inbetween.

tm_profiles_ID_long <- tm_profiles_ID_long %>%
    group_by(var, dep) %>%
    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 = value     - lag(value, default = first(value)),
           value_diff_daily = value_diff / date_time_ID_diff,
           value_cum = cumsum(value_diff)) %>% 
  ungroup()
tm_profiles_ID_long %>% 
  arrange(dep) %>% 
  ggplot(aes(value_diff_daily, 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")

3.6 Profiles of cumulative changes

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

tm_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()+
  facet_wrap(~var, scales = "free_x")+
  labs(x="Cumulative change of value")

Important notes:

  • Salinity in the upper 10m decreases by >0.1 on June 30, and returns to average conditions already on Aug 02.

Cumulative positive and negative changes of seawater vars were calculated separately at each depth relative to the first cruise day on July 5.

tm_profiles_ID_long <- tm_profiles_ID_long %>% 
  mutate(sign = if_else(value_diff < 0, "neg", "pos")) %>% 
  group_by(var, dep, sign) %>%
  arrange(date_time_ID) %>%
  mutate(value_cum_sign = cumsum(value_diff)) %>% 
  ungroup()
tm_profiles_ID_long %>% 
  arrange(dep) %>% 
  ggplot(aes(value_cum_sign, dep, col=ID))+
  geom_vline(xintercept = 0)+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_d()+
  scale_fill_viridis_d()+
  facet_wrap(~interaction(sign, var), scales = "free_x", ncol=4)+
  labs(x="Cumulative directional change of value")

# tm_profiles_ID_long %>%
#   write_csv(here::here("Data/_merged_data_files/CT_dynamics", "tm_profiles_ID_long_cum.csv"))

4 Timeseries

4.1 Timeseries depth intervals

Mean seawater parameters were calculated for 5m depth intervals.

tm_profiles_ID_long_grid <- tm_profiles_ID_long %>% 
  mutate(dep = cut(dep, seq(0,30,5))) %>% 
  group_by(ID, date_time_ID, dep, var)  %>% 
  summarise_all(list(mean), na.rm=TRUE) 

tm_profiles_ID_long_grid %>% 
  ggplot(aes(date_time_ID, value, col=as.factor(dep)))+
  geom_path()+
  geom_point()+
  scale_color_viridis_d(name="Depth (m)")+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  facet_wrap(~var, scales = "free_y", ncol=1)+
  theme(axis.title.x = element_blank())

rm(tm_profiles_ID_long_grid)

4.2 Hovmoeller plots

4.2.1 Absolute values

bin_nCT <- 30

p_nCT_hov <- tm_profiles_ID_long %>% 
  filter(var == "nCT") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID, y=dep, z=value),
                    breaks = MakeBreaks(bin_nCT),
                    col="black")+
  geom_point(aes(x=date_time_ID, y=c(24.5)), size=3, shape=24, fill="white")+
  scale_fill_scico(breaks = MakeBreaks(bin_nCT),
                   guide = "colorstrip",
                   name="nCT (µmol/kg)",
                   palette = "davos", direction = -1)+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        legend.position = "left")

bin_Tem <- 2

p_tem_hov <- tm_profiles_ID_long %>% 
  filter(var == "tem") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID, y=dep, z=value),
                    breaks = MakeBreaks(bin_Tem),
                    col="black")+
  geom_point(aes(x=date_time_ID, y=c(24.5)), size=3, shape=24, fill="white")+
  scale_fill_viridis_c(breaks = MakeBreaks(bin_Tem),
                       guide = "colorstrip",
                       name="Tem (°C)",
                       option = "inferno")+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        legend.position = "left")

p_nCT_hov / p_tem_hov
Hovmoeller plotm of absolute changes in C~T~ and temperature.

Hovmoeller plotm of absolute changes in CT and temperature. 

rm(p_nCT_hov, bin_nCT, p_tem_hov, bin_Tem)

4.2.2 Incremental changes

bin_nCT <- 2.5

nCT_hov <- tm_profiles_ID_long %>% 
  filter(var == "nCT") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID_ref, y=dep, z=value_diff_daily),
                    breaks = MakeBreaks(bin_nCT),
                    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_nCT),
                       guide = "colorstrip",
                       name="nCT (µmol/kg)")+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())

bin_Tem <- 0.1

Tem_hov <- tm_profiles_ID_long %>% 
  filter(var == "tem") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID_ref, y=dep, z=value_diff_daily),
                    breaks = MakeBreaks(bin_Tem),
                    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_Tem),
                       guide = "colorstrip",
                       name="Tem (°C)")+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  theme_bw()+
  labs(x="",y="Depth (m)")+
  coord_cartesian(expand = 0)

nCT_hov / Tem_hov
Hovmoeller plotm of daily changes in C~T~ and temperature. Note that calculated value of change (in contrast to absolute and cumulative values) are referred to the mean dates inbetween cruise, and are not extrapolated to the full observational period.

Hovmoeller plotm of daily changes in CT and temperature. Note that calculated value of change (in contrast to absolute and cumulative values) are referred to the mean dates inbetween cruise, and are not extrapolated to the full observational period. 

rm(nCT_hov, bin_nCT, Tem_hov, bin_Tem)

4.2.3 Cumulative changes

bin_nCT <- 20

nCT_hov <- tm_profiles_ID_long %>% 
  filter(var == "nCT") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID, y=dep, z=value_cum),
                    breaks = MakeBreaks(bin_nCT),
                    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_nCT),
                       guide = "colorstrip",
                       name="nCT (µmol/kg)")+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())

bin_Tem <- 2

Tem_hov <- tm_profiles_ID_long %>% 
  filter(var == "tem") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID, y=dep, z=value_cum),
                    breaks = MakeBreaks(bin_Tem),
                    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_Tem),
                       guide = "colorstrip",
                       name="Tem (°C)")+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  theme_bw()+
  labs(x="",y="Depth (m)")+
  coord_cartesian(expand = 0)

nCT_hov / Tem_hov
Hovmoeller plotm of cumulative changes in C~T~ and temperature.

Hovmoeller plotm of cumulative changes in CT and temperature. 

rm(nCT_hov, bin_nCT, Tem_hov, bin_Tem)

5 Depth-integration CT

A critical first step for the determination of net community production (NCP) is the integration of observed changes in nCT over depth. Two approaches were tested:

  • Integration of changes in nCT over a predefined, fixed water depth
  • Integration of changes in nCT over a mixed layer depth (MLD)

Both aproaches deliver depth-integrated, incremental changes of CT inbetween cruise dates. Those were summed up to derive a trajectory of cummulative integrated nCT changes.

5.1 Fixed depths approach

Incremental and cumulative nCT changes inbetween cruise dates were integrated across the water colums down to predefined depth limits. This was done separately for observed positive/negative changes in CT, as well as for the total observed changes.

fixed_depths <- seq(9,13,1)

Predefined integration depth levels in metres are: 9, 10, 11, 12, 13

5.1.1 Calculate inCT

inCT_grid_sign <- tm_profiles_ID_long %>% 
  select(ID, date_time_ID, date_time_ID_ref) %>% 
  unique() %>% 
  expand_grid(sign = c("pos", "neg"))

inCT_grid_total <- tm_profiles_ID_long %>% 
  select(ID, date_time_ID, date_time_ID_ref) %>% 
  unique() %>% 
  expand_grid(sign = c("total"))

# dep_i <- 10
#rm(inCT, dep_i)

for (dep_i in fixed_depths) {


inCT_sign_temp <- tm_profiles_ID_long %>% 
  filter(var == "nCT", dep < dep_i) %>% 
  mutate(sign = if_else(ID == "180705" & dep == 0.5, "neg", sign)) %>% 
  group_by(ID, date_time_ID, date_time_ID_ref, sign) %>% 
  summarise(nCT_i_diff = sum(value_diff)/1000) %>% 
  ungroup()

inCT_sign_temp <- inCT_sign_temp %>% 
  group_by(sign) %>%
  arrange(date_time_ID) %>% 
  mutate(nCT_i_cum = cumsum(nCT_i_diff)) %>% 
  ungroup()

inCT_sign_temp <- full_join(inCT_sign_temp, inCT_grid_sign) %>% 
  arrange(sign, date_time_ID) %>% 
  fill(nCT_i_cum)


inCT_total_temp <- tm_profiles_ID_long %>% 
  filter(var == "nCT", dep < dep_i) %>% 
  group_by(ID, date_time_ID, date_time_ID_ref) %>% 
  summarise(nCT_i_diff = sum(value_diff)/1000) %>% 
  ungroup()

inCT_total_temp <- inCT_total_temp %>% 
  arrange(date_time_ID) %>% 
  mutate(nCT_i_cum = cumsum(nCT_i_diff)) %>% 
  ungroup() %>% 
  mutate(sign = "total")

inCT_total_temp <- full_join(inCT_total_temp, inCT_grid_total) %>% 
  arrange(sign, date_time_ID) %>% 
  fill(nCT_i_cum)

inCT_temp <- bind_rows(inCT_sign_temp, inCT_total_temp) %>% 
    mutate(dep_i = dep_i)


if (exists("inCT")) {
  inCT <- bind_rows(inCT, inCT_temp)
  } else {inCT <- inCT_temp}

rm(inCT_temp, inCT_sign_temp, inCT_total_temp)

}

rm(inCT_grid_sign, inCT_grid_total)

inCT <- inCT %>% 
  mutate(dep_i = as.factor(dep_i))

inCT_fixed_dep <- inCT
rm(inCT, dep_i, fixed_depths)
# inCT %>%
#   write_csv(here::here("Data/_merged_data_files", "inCT_dep_limitm.csv"))

5.1.2 Time series

inCT_fixed_dep %>% 
  ggplot()+
  geom_point(data = cruise_dates, aes(date_time_ID, 0), shape=21)+
  geom_col(aes(date_time_ID_ref, nCT_i_diff, fill=dep_i),
           position = "dodge", alpha=0.3)+
  geom_line(aes(date_time_ID, nCT_i_cum, col=dep_i))+
  scale_color_viridis_d(name="Depth limit (m)")+
  scale_fill_viridis_d(name="Depth limit (m)")+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  labs(y="inCT (mol/m2)", x="")+
  facet_grid(sign~., scales = "free_y", space = "free_y")+
  theme_bw()

5.2 MLD approach

As an alternative to fixed depth levels, vertical integration as low as the mixed layer depth was tested.

5.2.1 Density calculation

Seawater density Rho was determined from S, T, and p according to TEOS-10.

tm_profiles <- tm_profiles %>% 
  mutate(rho = swSigma(salinity = sal, temperature = tem, pressure = dep/10))

5.2.2 Density profiles

tm_profiles_ID_mean_hydro <- tm_profiles %>% 
  select(-c(station,lat, lon, pCO2_corr, pCO2, nCT, date_time)) %>% 
  group_by(ID, date_time_ID, date_ID, dep) %>% 
  summarise_all(list(mean), na.rm=TRUE) %>% 
  ungroup()

tm_profiles_ID_sd_hydro <- tm_profiles %>% 
  select(-c(station,lat, lon, pCO2_corr, pCO2, nCT, date_time)) %>% 
  group_by(ID, date_time_ID, date_ID, dep) %>% 
  summarise_all(list(sd), na.rm=TRUE) %>% 
  ungroup()


tm_profiles_ID_sd_hydro_long <- tm_profiles_ID_sd_hydro %>% 
  pivot_longer(sal:rho, names_to = "var", values_to = "sd")
  
tm_profiles_ID_mean_hydro_long <- tm_profiles_ID_mean_hydro %>% 
  pivot_longer(sal:rho, names_to = "var", values_to = "value")
  
tm_profiles_ID_hydro_long <- inner_join(tm_profiles_ID_mean_hydro_long, tm_profiles_ID_sd_hydro_long)
tm_profiles_ID_hydro <- tm_profiles_ID_mean_hydro

rm(tm_profiles_ID_mean_hydro_long,
   tm_profiles_ID_mean_hydro,
   tm_profiles_ID_sd_hydro_long,
   tm_profiles_ID_sd_hydro)
tm_profiles_ID_hydro_long %>% 
  ggplot(aes(value, dep, col=ID))+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_d()+
  facet_wrap(~var, scales = "free_x")
Mean vertical profiles per cruise day across all stations.

Mean vertical profiles per cruise day across all stations.

5.2.3 MLD calculation

Mixed layer depth (MLD) was determined based on the difference between density at the surface and at depth, for a range of density criteria

# density criterion

tm_profiles_ID_hydro <- expand_grid(tm_profiles_ID_hydro, rho_lim = c(0.1,0.2,0.5))

MLD <- tm_profiles_ID_hydro  %>% 
  arrange(dep) %>% 
  group_by(ID, date_time_ID, rho_lim) %>% 
  mutate(d_rho = rho - first(rho)) %>% 
  filter(d_rho > rho_lim) %>% 
  summarise(MLD = min(dep)) %>% 
  ungroup()

5.2.4 Daily density profiles

tm_profiles_ID_hydro <- 
  full_join(tm_profiles_ID_hydro, MLD)

tm_profiles_ID_hydro %>% 
  arrange(dep) %>% 
  ggplot(aes(rho, dep))+
  geom_hline(aes(yintercept = MLD, col=as.factor(rho_lim)))+
  geom_path()+
  scale_y_reverse()+
  scale_color_brewer(palette = "Set1", name= "Rho limit")+
  facet_wrap(~ID)+
  theme_bw()
Mean density profiles and MLD per cruise dates (ID).

Mean density profiles and MLD per cruise dates (ID).

5.2.5 MLD timeseries

MLD %>% 
  ggplot(aes(date_time_ID, MLD, col=as.factor(rho_lim)))+
  geom_hline(yintercept = 0)+
  geom_point()+
  geom_path()+
  scale_color_brewer(palette = "Set1", name= "Rho limit")+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  labs(x="")

5.2.6 inCT calculation

inCT <- tm_profiles_ID_long %>% 
  filter(var == "nCT")

inCT <- full_join(inCT, MLD)

inCT <- inCT %>% 
  filter(dep <= MLD)

inCT <- inCT %>% 
  group_by(ID, date_time_ID, date_time_ID_ref, rho_lim) %>% 
  summarise(nCT_i_diff = sum(value_diff)/1000) %>% 
  ungroup()

inCT <- inCT %>% 
  group_by(rho_lim) %>% 
  arrange(date_time_ID) %>% 
  mutate(nCT_i_cum = cumsum(nCT_i_diff)) %>% 
  ungroup()

inCT <- inCT %>% 
  mutate(rho_lim = as.factor(rho_lim))

inCT_MLD <- inCT

rm(inCT, MLD, tm_profiles_ID_hydro, tm_profiles_ID_hydro_long)

5.2.7 Time series

inCT_MLD %>% 
  ggplot()+
  geom_point(data = cruise_dates, aes(date_time_ID, 0), shape=21)+
  geom_col(aes(date_time_ID_ref, nCT_i_diff, fill=rho_lim),
           position = "dodge", alpha=0.3)+
  geom_line(aes(date_time_ID, nCT_i_cum, col=rho_lim))+
  scale_color_viridis_d(name="Rho limit")+
  scale_fill_viridis_d(name="Rho limit")+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  labs(y="inCT [mol/m2]", x="")+
  theme_bw()

5.3 Comparison of approaches

In the following, all cummulative iCT trajectories are displayed. Highlighted are those obtained for the fixed depth approach with 10 m limit, and the MLD approach with a high density threshold of 0.5 kg/m3.

inCT <- full_join(inCT_fixed_dep, inCT_MLD)

inCT <- inCT %>% 
  mutate(group = paste(as.character(sign), as.character(dep_i), as.character(rho_lim)))

inCT %>% 
  arrange(date_time_ID) %>% 
  ggplot()+
  geom_hline(yintercept = 0)+
  geom_point(data = cruise_dates, aes(date_time_ID, 0), shape=21)+
  geom_line(aes(date_time_ID, nCT_i_cum,
                group=group), col="grey")+
  geom_line(data = inCT_fixed_dep %>% filter(dep_i==12, sign=="total"),
            aes(date_time_ID, nCT_i_cum, col="12m - total"))+
  geom_line(data = inCT_MLD %>% filter(rho_lim == 0.1),
            aes(date_time_ID, nCT_i_cum, col="MLD - 0.1"))+
  scale_color_brewer(palette = "Set1", name="")+
  scale_x_datetime(breaks = "week", date_labels = "%d %b")+
  labs(y="inCT [mol/m2]", x="")

rm(inCT, inCT_MLD)

6 NCP determination

In order to derive an estimate of the net community production NCP (which is equivalent to the formed organic matter that can be exported from the investigated surface layer), two steps are required:

  • decision about the most appropiate iCT trajectory
  • correction of quantifyable CO2 fluxes in and out of the investigated water volume during the period of interest, this includes:
    • Air-sea CO2 fluxes
    • CO2 fluxes due to vertical mixing
    • CO2 fluxes due to lateral transport of water masses (not corrected here)

6.1 Best iCT estimate

To determine the optimum depth for the nCT integration we investigated the vertical distribution of cumulative temperature and nCT changes on the peak of the productivity signal on June 23:

tm_profiles_ID_long_180723 <- tm_profiles_ID_long %>% 
  filter(ID == 180723,
         var == "nCT")

p_tm_profiles_ID_long <- tm_profiles_ID_long_180723 %>% 
  arrange(dep) %>% 
  ggplot(aes(value_cum, dep))+
  geom_vline(xintercept = 0)+
  geom_hline(yintercept = 12, col="red")+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  labs(x="Cumulative change of nCT on July 23 (180723)")+
  theme(legend.position = "left")

tm_profiles_ID_long_180723_dep <- tm_profiles_ID_long_180723 %>% 
  select(dep, value_cum) %>% 
  filter(value_cum < 0) %>%
  arrange(dep) %>% 
  mutate(value_cum_i = sum(value_cum),
         value_cum_dep = cumsum(value_cum),
         value_cum_i_rel = value_cum_dep/value_cum_i*100)

p_tm_profiles_ID_long_rel <- tm_profiles_ID_long_180723_dep %>% 
  ggplot(aes(value_cum_i_rel, dep))+
  geom_hline(yintercept = 12, col="red")+
  geom_vline(xintercept = 90)+
  geom_point()+
  geom_line()+
  scale_y_reverse(limits = c(25,0))+
  scale_x_continuous(breaks = seq(0,100,10))+
  labs(y = "Depth (m)", x = "Relative contribution on July 23")+
  theme_bw()

p_tm_profiles_ID_long + p_tm_profiles_ID_long_rel

rm(tm_profiles_ID_long_180723,
   tm_profiles_ID_long_180723_dep,
   p_tm_profiles_ID_long,
   p_tm_profiles_ID_long_rel)
tm_profiles_ID_long_180723 <- tm_profiles_ID_long %>% 
  filter(ID == 180723,
         var == "tem")

p_tm_profiles_ID_long <- tm_profiles_ID_long_180723 %>% 
  arrange(dep) %>% 
  ggplot(aes(value_cum, dep))+
  geom_vline(xintercept = 0)+
  geom_hline(yintercept = 12, col="red")+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  labs(x="Cumulative change of Temp on July 23")+
  theme(legend.position = "left")

tm_profiles_ID_long_180723_dep <- tm_profiles_ID_long_180723 %>% 
  select(dep, value_cum) %>% 
  filter(value_cum > 0) %>%
  arrange(dep) %>% 
  mutate(value_cum_i = sum(value_cum),
         value_cum_dep = cumsum(value_cum),
         value_cum_i_rel = value_cum_dep/value_cum_i*100)

p_tm_profiles_ID_long_rel <- tm_profiles_ID_long_180723_dep %>% 
  ggplot(aes(value_cum_i_rel, dep))+
  geom_hline(yintercept = 12, col="red")+
  geom_vline(xintercept = 90)+
  geom_point()+
  geom_line()+
  scale_y_reverse(limits = c(25,0))+
  scale_x_continuous(breaks = seq(0,100,10))+
  labs(y = "Depth (m)", x = "Relative contribution on July 23")+
  theme_bw()

p_tm_profiles_ID_long + p_tm_profiles_ID_long_rel

rm(tm_profiles_ID_long_180723,
   tm_profiles_ID_long_180723_dep,
   p_tm_profiles_ID_long,
   p_tm_profiles_ID_long_rel)

The cummulative iCT trajectory determined by integration of CT to a fixed water depth of 12 m was used for NCP calculation for the following reasons:

  • During the first productivity pulse that lasted until July 23:
    • no negative nCT changes were detected below that depth
    • cumulative nCT switch sign at that depth
    • 95% of the cumulative warming signal appears across that depth
  • MLD were too shallow to cover all observed negative CT changes

6.2 Air-Sea CO2 flux

6.2.1 Surface water data

The cruise mean pCO2 recorded in profiling-mode (stations only) and depths < 6m was used for gas exchange calcualtions.

tm_profiles_surface_long <- tm_profiles %>% 
  filter(dep < surface_dep) %>% 
  select(date_time = date_time_ID, ID, tem, pCO2 = pCO2, nCT) %>% 
  pivot_longer(tem:nCT, values_to = "value", names_to = "var")

tm_profiles_surface_long_ID <- tm_profiles_surface_long %>% 
  group_by(ID, date_time, var) %>% 
  summarise_all(list(~mean(.), ~sd(.), ~min(.), ~max(.))) %>% 
  ungroup()

rm(tm_profiles_surface_long)

p_pCO2_surf <- tm_profiles_surface_long_ID %>%
  filter(var == "pCO2") %>% 
  ggplot(aes(x=date_time))+
  geom_ribbon(aes(ymin=mean-sd, ymax=mean+sd), alpha=0.2)+
  geom_path(aes(y=mean))+
  geom_point(aes(y=mean))+
  scale_fill_discrete(guide=FALSE)+
  scale_x_datetime(date_breaks = "week",
                   sec.axis = dup_axis())+
  labs(y = expression(atop(pCO[2], (mu*atm))),
       title = "Surface water observations")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())

p_tem_surf <- tm_profiles_surface_long_ID %>%
  filter(var == "tem") %>% 
  ggplot(aes(x=date_time))+
  geom_ribbon(aes(ymin=mean-sd, ymax=mean+sd), alpha=0.2)+
  geom_path(aes(y=mean))+
  geom_point(aes(y=mean))+
  scale_fill_discrete(guide=FALSE)+
  scale_x_datetime(date_breaks = "week",
                   sec.axis = dup_axis())+
  labs(y = "temp \n (\u00B0C)")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())

p_nCT_surf <-
tm_profiles_surface_long_ID %>%
  filter(var == "nCT") %>% 
  ggplot()+
  geom_point(data = tb_surface_station_mean %>% 
               filter(var == "nCT"),
             aes(x = date_time_ID,
                 y = value_mean,
                 color = "discrete")) +
  geom_linerange(data = tb_surface_station_mean %>%
                   filter(var == "nCT"),
             aes(x = date_time_ID,
                 ymin = value_mean - value_sd,
                 ymax = value_mean + value_sd,
                 color = "discrete"))+
  geom_ribbon(aes(x=date_time, ymin=mean-sd, ymax=mean+sd), alpha=0.2)+
  geom_path(aes(x=date_time, y=mean))+
  geom_point(aes(x=date_time, y=mean))+
  scale_color_manual(values = "red")+
  scale_x_datetime(date_breaks = "week",
                   sec.axis = dup_axis())+
  labs(y = expression(atop(nC[T],
                           (mu*mol~kg^{-1}))))+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        legend.position = c(0.35,0.75),
        legend.title = element_blank(),
        legend.direction = "horizontal",
        legend.background = element_rect(fill = "transparent"),
        legend.key = element_rect(colour = "black", fill = "white"))


p_pCO2_surf + p_tem_surf + p_nCT_surf + 
  plot_layout(ncol = 1)

#rm(tm_profiles_surface)

start <- min(tm_profiles_surface_long_ID$date_time)
end   <- max(tm_profiles_surface_long_ID$date_time)

6.2.2 Wind and atm. pCO2

Metrological data were recorded on the flux tower located on Ostergarnsholm island.

og <- read_csv(here::here("data/_summarized_data_files",
                          "og.csv"))

og <- og %>%
  filter(date_time > start,
         date_time < end)

rm(end, start)

Data sets for atmospheric and seawater observations were merged and interpolated to a common time stamp.

tm_profiles_surface_ID <- tm_profiles_surface_long_ID %>% 
  filter(var %in% c("pCO2", "tem")) %>% 
  select(date_time:mean) %>% 
  pivot_wider(names_from = "var", values_from = "mean")

rm(tm_profiles_surface_long_ID)

tm_og <- full_join(og, tm_profiles_surface_ID) %>% 
  arrange(date_time)

tm_og <- tm_og %>% 
  mutate(pCO2 = approxfun(date_time, pCO2)(date_time),
         tem = approxfun(date_time, tem)(date_time),
         wind = approxfun(date_time, wind)(date_time)) %>% 
  filter(!is.na(pCO2_atm))

rm(tm_profiles_surface_ID, og)
rolling_mean   <- rollify(~mean(.x, na.rm = TRUE), window = 48)

tm_og <- tm_og %>% 
  mutate(wind_daily = rolling_mean(wind),
         pCO2_atm_daily = rolling_mean(pCO2_atm))
p_pCO2_atm <- tm_og %>%
  ggplot(aes(x=date_time))+
  geom_path(aes(y=pCO2_atm))+
  scale_x_datetime(date_breaks = "week",
                   sec.axis = dup_axis())+
  labs(y = expression(atop(pCO["2,atm"], (mu*atm))),
       title = "Atmospheric observations")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())

p_wind <- tm_og %>%
  ggplot(aes(x=date_time))+
  geom_path(aes(y=wind))+
  scale_x_datetime(date_breaks = "week",
                   sec.axis = dup_axis())+
  labs(y = expression(atop(windspeed, (m~s^{-1}))))+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        legend.title = element_blank())

p_pCO2_atm + p_wind +
  plot_layout(ncol = 1) + 
  plot_layout(guides = 'collect')

6.2.3 Air-sea fluxes

F = k * dCO2

with

dCO2 = K0 * dpCO2 and

k = coeff * U^2 * (660/Sc)^0.5

Unitm used here are:

  • dpCO2: µatm

  • K0: mol atm-1 kg-1

  • dCO2: µmol kg-1

  • wind speed U: m s-1

  • coeff for k calculation (eg 0.251 in W14): cm hr-1 (m s-1)-2

  • gas transfer velocities k: cm hr-1 (= 60 x 60 x 100 m s-1)

  • air sea CO2 flux F: mol m–2 d–1

  • conversion between the unit of k * dCO2 and F requires a factor of 10-5 * 24

Sc_W14 <- function(tem) {
  2116.8 - 136.25 * tem + 4.7353 * tem^2 - 0.092307 * tem^3 + 0.0007555 * tem^4
}

# Sc_W14(20)

tm_og <- tm_og %>% 
  mutate(dpCO2 = pCO2 - pCO2_atm,
         dCO2  = dpCO2 * K0(S=6.92, T=tem),
         # W92 = gas_transfer(t = tem, u10 = wind, species = "CO2",
         #                      method = "Wanninkhof1")* 60^2 * 100,
         #k_SM18 = 0.24 * wind^2 * ((1943-119.6*tem + 3.488*tem^2 - 0.0417*tem^3) / 660)^(-0.5),
         k = 0.251 * wind^2 * (Sc_W14(tem)/660)^(-0.5))
  # pivot_longer(9:10, names_to = "k_para", values_to = "k_value")

# calculate flux F [mol m–2 d–1]

tm_og <- tm_og %>% 
  mutate(flux = k*dCO2*1e-5*24)
#         flux_daily = rolling_mean(flux))

rm(Sc_W14)
p_flux_daily <- tm_og %>%
  ggplot(aes(x=date_time))+
  geom_path(aes(y=flux))+
  # geom_path(aes(y=flux_daily, col="24h"))+
  # scale_color_brewer(palette = "Set1")+
  scale_x_datetime(date_breaks = "week",
                   sec.axis = dup_axis())+
  labs(y = expression(atop(flux[daily], (mol~m^{-2}~d^{-1}))),
       title = "Air-sea fluxes")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        legend.title = element_blank())
# scale flux to time interval

tm_og <- tm_og %>% 
  mutate(scale = 24*2) %>% 
  mutate(flux_scale = flux / scale) %>% 
  arrange(date_time) %>% 
  mutate(flux_cum = cumsum(flux_scale)) %>% 
  ungroup()

p_flux_cum <- tm_og %>%
  ggplot(aes(x=date_time))+
  geom_path(aes(y=flux_cum))+
  scale_fill_discrete(guide=FALSE)+
  scale_x_datetime(date_breaks = "week",
                   sec.axis = dup_axis())+
  labs(y = expression(atop(flux[cum],
                           (mol~m^{-2}))))+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())

p_flux_daily + p_flux_cum +
  plot_layout(ncol = 1)

6.3 iCT correction

The cumulative integrated nCT (inCT) time series obtained through integration across the upper 12m of the water column was used for further calculations of NCP.

Correction of inCT for air-sea CO2 fluxes will be based on estimates derived from observation with 30min measurement interval and calculation according to Wanninkhof (2014).

To derive an integrated NCP estimated, the observed change in inCT must be corrected for the air-sea flux of CO2. inCT was determined for the upper 12m of the water column. The MLD was always shallower 12m, except for the last cruise day. Therefore:

  • Cumulative air-sea fluxes can be added completely to inCT before Aug 7.
  • Between Aug 7 and the last cruise on Aug 15 it was assumed, that the CO2 flux was homogenously mixed down to the deepend thermocline at 17m. The flux correction applied to the upper 12m can therefore be scaled with a factor 12/17.

During the last cruise, deeper mixing up to 17m water depth was observed, resulting in increased inCT at 0-12 m and a decrease of inCT in 12-17m. The loss of nCT in 12-17m can be assumed to be entirely cause by mixing with low-nCT surface water. However, some of the observed nCT loss is balanced through nCT input attributable to the air-sea flux. Therefore, the observed loss, corrected for 5/17 of the air-sea-flux, was added to the integrated nCT changes in 0-12m.

i_dep_lim <- 12
i_dep_mix_lim <- 17
# extract CT data for fixed depth approach, depth limit 10m
NCP <- inCT_fixed_dep %>% 
  filter(dep_i == i_dep_lim, sign=="total") %>% 
  select(-c(sign, dep_i))

rm(inCT_fixed_dep)

NCP <- NCP %>%
  select(ID, date_time = date_time_ID, date_time_ID_ref, nCT_i_diff, nCT_i_cum)

# date of the second last cruise
date_180806 <- unique(NCP$date_time)[7]

6.3.1 Air-sea fluxes

# calculate cumulative air-sea fluxes affecting surface water column
tm_og_flux <- tm_og %>% 
  mutate(flux_scale = if_else(date_time > date_180806,
                              i_dep_lim/i_dep_mix_lim * flux_scale,
                              flux_scale)) %>%
  arrange(date_time) %>% 
  mutate(flux_cum = cumsum(flux_scale)) %>% 
  select(date_time, flux_cum)

# calculate cumulative air-sea fluxes affecting deepened mixed layer
tm_og_flux_dep <- tm_og %>% 
  filter(date_time > date_180806) %>% 
  mutate(flux_scale = 
           (i_dep_mix_lim - i_dep_lim)/i_dep_mix_lim * flux_scale) %>%
  arrange(date_time) %>% 
  mutate(flux_cum = cumsum(flux_scale)) %>% 
  select(date_time, flux_cum)

NCP_flux <- full_join(NCP, tm_og_flux) %>% 
  arrange(date_time)

rm(tm_og_flux, NCP, tm_og)


# linear interpolation of cumulative changes to frequency of the flux estimates estimates 
NCP_flux <- NCP_flux %>% 
  mutate(nCT_i_cum = approxfun(date_time, nCT_i_cum)(date_time),
         flux_cum = approxfun(date_time, flux_cum)(date_time)) %>% 
    fill(flux_cum) %>% 
  mutate(nCT_i_flux_cum = nCT_i_cum + flux_cum)


# calculate cumulative fluxes inbetween cruises 
NCP_flux_diff <- NCP_flux %>% 
  filter(!is.na(date_time_ID_ref)) %>% 
  mutate(flux_diff = flux_cum - lag(flux_cum, default = 0)) %>% 
  select(date_time_ID_ref, observed=nCT_i_diff, flux=flux_diff) %>% 
  pivot_longer(cols = 2:3, names_to = "var", values_to = "value_diff")

6.3.2 Vertical mixing

# calculate mixing with deep waters, corrected for air sea fluxes
NCP_mix <- tm_profiles_ID_long %>% 
  filter(ID == "180815",
         var == "nCT",
         dep < i_dep_mix_lim,
         dep > i_dep_lim) %>% 
  group_by(ID, date_time_ID, date_time_ID_ref) %>% 
  summarise(value_diff = 
              sum(value_diff)/1000 + min(tm_og_flux_dep$flux_cum)) %>% 
  ungroup()

rm(tm_og_flux_dep)

NCP_mix_diff <- NCP_mix %>% 
  select(date_time_ID_ref, value_diff) %>% 
  mutate(var="mixing")

NCP_flux_mix_diff <- 
  full_join(NCP_flux_diff, NCP_mix_diff)

NCP_flux_mix <-
  full_join(NCP_flux,
            NCP_mix %>% rename(mix_cum = value_diff))

rm(NCP_mix, NCP_mix_diff, NCP_flux, NCP_flux_diff, date_180806)

NCP_flux_mix <- NCP_flux_mix %>% 
  arrange(date_time) %>% 
  fill(ID) %>% 
  mutate(mix_cum = if_else(ID %in% c("180806", 180815), mix_cum, 0),
         mix_cum = na.approx(mix_cum),
         nCT_i_flux_mix_cum = nCT_i_flux_cum + mix_cum)

# reorder factors for plotting
NCP_flux_mix_diff <- NCP_flux_mix_diff %>% 
  mutate(var = factor(var, c("observed", "flux", "mixing")))

NCP_flux_mix_long <- NCP_flux_mix %>% 
  select(date_time, nCT_i_cum, nCT_i_flux_cum, nCT_i_flux_mix_cum) %>% 
  pivot_longer(nCT_i_cum:nCT_i_flux_mix_cum,
               values_to = "value",
               names_to = "var") %>% 
  mutate(var = fct_recode(var, 
                          observed = "nCT_i_cum",
                          `flux corrected` = "nCT_i_flux_cum",
                          `flux + mixing corrected (NCP)` = "nCT_i_flux_mix_cum"))


p_inCT <- NCP_flux_mix_long %>% 
  arrange(date_time) %>% 
  ggplot()+
  geom_col(data = NCP_flux_mix_diff,
           aes(date_time_ID_ref, value_diff, fill=var),
           position = position_dodge2(preserve = "single"),
           alpha=0.5)+
  geom_hline(yintercept = 0)+
  geom_point(data = cruise_dates, aes(date_time_ID, 0), shape=21)+
  geom_line(aes(date_time, value, col=var))+
  scale_x_datetime(date_breaks = "week",
                   date_labels = "%b %d",
                   sec.axis = dup_axis())+
  scale_fill_brewer(palette = "Dark2", name="incremental changes")+
  scale_color_brewer(palette = "Dark2", name="cumulative changes")+
  labs(y=expression(atop(integrated~nC[T], (mol~m^{-2}))),
       title = "Water column inventory changes")+
  guides(guide_colourbar(order = 1))+
  theme(axis.title.x = element_blank(),
        axis.text.x.top = element_blank(),
        legend.position = "bottom",
        legend.direction = "vertical")

p_inCT

NCP_flux_mix %>%
  write_csv(here::here("Data/_merged_data_files/CT_dynamics",
                       "tm_NCP_cum.csv"))

NCP_flux_mix_diff %>%
  write_csv(here::here("Data/_merged_data_files/CT_dynamics",
                       "tm_NCP_inc.csv"))

7 Open tasks / questions

  • clean and harmonize chunk labeling (label: plot, 1 plot per chunk, etc)
  • included removed stations in coverage plot
  • Significance of changes in AT for calculated nCT changes
    • Calculate AT-S ratios, reconstruct AT profiles, calculate true nCT profiles, normalize nCT profiles to mean AT
  • demostrate strong permanent thermocline at around 25 m

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] sp_1.4-1         tibbletime_0.1.3 zoo_1.8-7        lubridate_1.7.4 
 [5] scico_1.1.0      metR_0.6.0       marelac_2.1.10   shape_1.4.4     
 [9] seacarb_3.2.13   oce_1.2-0        gsw_1.0-5        testthat_2.3.2  
[13] patchwork_1.0.0  forcats_0.5.0    stringr_1.4.0    dplyr_0.8.5     
[17] purrr_0.3.3      readr_1.3.1      tidyr_1.0.2      tibble_3.0.0    
[21] 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      compiler_3.6.3     cellranger_1.1.0   pillar_1.4.3      
[33] scales_1.1.0       backports_1.1.5    generics_0.0.2     jsonlite_1.6.1    
[37] httpuv_1.5.2       pkgconfig_2.0.3    rstudioapi_0.11    munsell_0.5.0     
[41] plyr_1.8.6         highr_0.8          httr_1.4.1         tools_3.6.3       
[45] grid_3.6.3         nlme_3.1-145       data.table_1.12.8  gtable_0.3.0      
[49] checkmate_2.0.0    DBI_1.1.0          cli_2.0.2          readxl_1.3.1      
[53] yaml_2.2.1         crayon_1.3.4       farver_2.0.3       RColorBrewer_1.1-2
[57] later_1.0.0        promises_1.1.0     fs_1.4.0           vctrs_0.2.4       
[61] memoise_1.1.0      glue_1.3.2         evaluate_0.14      labeling_0.3      
[65] reprex_0.3.0       stringi_1.4.6