Last updated: 2020-05-08

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File	Version	Author	Date	Message
Rmd	7fe598e	jens-daniel-mueller	2020-05-08	map update and finnmaid subsetting in area
html	dd3bd89	jens-daniel-mueller	2020-05-07	Build site.
Rmd	ad98da2	jens-daniel-mueller	2020-05-07	harmonized parameter labeling
html	b5722a7	jens-daniel-mueller	2020-04-28	Build site.
Rmd	058c709	jens-daniel-mueller	2020-04-28	Moved nomenlacture to seperate Rmd
html	d2036b0	jens-daniel-mueller	2020-04-24	Build site.
Rmd	c28b943	jens-daniel-mueller	2020-04-24	discrete data in CT timeseries plot
html	b004af3	jens-daniel-mueller	2020-04-24	Build site.
Rmd	e07781a	jens-daniel-mueller	2020-04-24	discrete surface CT in timeseries
html	a075635	jens-daniel-mueller	2020-04-24	Build site.
Rmd	72f9a86	jens-daniel-mueller	2020-04-24	Refined depth for discrete surface time series
html	472c2b4	jens-daniel-mueller	2020-04-21	Build site.
html	69c301c	jens-daniel-mueller	2020-04-21	Build site.
html	c9549ee	jens-daniel-mueller	2020-04-19	Build site.
Rmd	f8fcf50	jens-daniel-mueller	2020-04-19	created pub figures for time series
html	f8fcf50	jens-daniel-mueller	2020-04-19	created pub figures for time series
html	6810175	jens-daniel-mueller	2020-04-17	Build site.
Rmd	864596a	jens-daniel-mueller	2020-04-17	plotted all profiles
html	4054ba1	jens-daniel-mueller	2020-04-17	Build site.
Rmd	acc1379	jens-daniel-mueller	2020-04-17	calculate AT sd
html	729b4c6	jens-daniel-mueller	2020-04-17	Build site.
Rmd	2edd18d	jens-daniel-mueller	2020-04-17	included bottle CT AT from 180723
html	bf6384a	jens-daniel-mueller	2020-04-17	Build site.
Rmd	d0eb264	jens-daniel-mueller	2020-04-17	all stations on map
html	cc2baf3	jens-daniel-mueller	2020-04-16	Build site.
Rmd	13436a3	jens-daniel-mueller	2020-04-16	worked on map
html	5e8f8e1	jens-daniel-mueller	2020-04-16	Build site.
Rmd	86b0833	jens-daniel-mueller	2020-04-16	New fixed integration depth 12m
html	4ac8782	jens-daniel-mueller	2020-04-16	Build site.
Rmd	95380d4	jens-daniel-mueller	2020-04-16	Cumulative temperature distribution on July 23
html	48631ee	jens-daniel-mueller	2020-04-09	Build site.
Rmd	4e9464f	jens-daniel-mueller	2020-04-09	corrected na approx function
html	849e990	jens-daniel-mueller	2020-04-01	Build site.
Rmd	c199200	jens-daniel-mueller	2020-04-01	included BloomSail data to Finnmaid analysis
html	f4a27b8	jens-daniel-mueller	2020-04-01	Build site.
Rmd	b1613b7	jens-daniel-mueller	2020-04-01	re-calculated MLD, renamed objects and structured site
html	6302994	jens-daniel-mueller	2020-03-31	Build site.
Rmd	50ab313	jens-daniel-mueller	2020-03-31	implemented temperature reconstruction
html	a6c4c22	jens-daniel-mueller	2020-03-30	Build site.
Rmd	d8120b3	jens-daniel-mueller	2020-03-30	reconstruction BloomSail surface started, merging MLD and DT approach
html	80c78b3	jens-daniel-mueller	2020-03-30	Build site.
html	70dbfbe	jens-daniel-mueller	2020-03-30	Build site.
Rmd	e69d1f0	jens-daniel-mueller	2020-03-30	cleaned object names
html	431a56a	jens-daniel-mueller	2020-03-30	Build site.
Rmd	9edf20d	jens-daniel-mueller	2020-03-30	flux and mixing correction revised
html	f8ad4ff	jens-daniel-mueller	2020-03-30	Build site.
Rmd	265e568	jens-daniel-mueller	2020-03-30	NCP calculation finished
html	2ade511	jens-daniel-mueller	2020-03-27	Build site.
Rmd	858e01f	jens-daniel-mueller	2020-03-27	iCT flux correction applied
html	a22daa8	jens-daniel-mueller	2020-03-27	Build site.
Rmd	9118b70	jens-daniel-mueller	2020-03-27	iCT flux correction applied
html	2d358fb	jens-daniel-mueller	2020-03-27	Build site.
Rmd	d17a2b0	jens-daniel-mueller	2020-03-27	Added air sea CO2 fluxes
html	43da055	jens-daniel-mueller	2020-03-26	Build site.
Rmd	6afdea9	jens-daniel-mueller	2020-03-26	selected iCT time series for NCP
html	1d7eebc	jens-daniel-mueller	2020-03-26	Build site.
Rmd	4d734a1	jens-daniel-mueller	2020-03-26	Started NCP estimation
html	57e3e73	jens-daniel-mueller	2020-03-26	Build site.
Rmd	275b061	jens-daniel-mueller	2020-03-26	renamed NCP correctly als iCT
html	30d5b10	jens-daniel-mueller	2020-03-26	Build site.
Rmd	0405651	jens-daniel-mueller	2020-03-26	Restructure MLD iCT chapter
html	90633b8	jens-daniel-mueller	2020-03-26	Build site.
Rmd	baa81d6	jens-daniel-mueller	2020-03-26	heigth surface timeseries reduced
html	f139cbd	jens-daniel-mueller	2020-03-26	Build site.
Rmd	1b8a11e	jens-daniel-mueller	2020-03-26	restructured NCP chapter, and renamed as iCT
html	c2b128e	jens-daniel-mueller	2020-03-26	Build site.
Rmd	6ec4005	jens-daniel-mueller	2020-03-26	added interpretation notes
html	63909fc	jens-daniel-mueller	2020-03-26	Build site.
Rmd	069600c	jens-daniel-mueller	2020-03-26	theme_bw
html	5011448	jens-daniel-mueller	2020-03-26	Build site.
Rmd	69ec53e	jens-daniel-mueller	2020-03-26	Comparison iCT estimates
html	b6e6117	jens-daniel-mueller	2020-03-25	Build site.
Rmd	07690b6	jens-daniel-mueller	2020-03-25	NCP MLD approach implmented
html	a667be1	jens-daniel-mueller	2020-03-25	Build site.
Rmd	93800e0	jens-daniel-mueller	2020-03-25	NCP MLD approach implmented
html	b8d7014	jens-daniel-mueller	2020-03-25	Build site.
Rmd	a13c901	jens-daniel-mueller	2020-03-25	NCP fixed depth, new variable names, ref dates introduced
html	b589daf	jens-daniel-mueller	2020-03-24	Build site.
Rmd	90979bb	jens-daniel-mueller	2020-03-24	nameing convention and NCP approaches list
html	d0d5c9e	jens-daniel-mueller	2020-03-24	Build site.
Rmd	1e2508a	jens-daniel-mueller	2020-03-24	harmonized starting dates
html	5f8ca30	jens-daniel-mueller	2020-03-20	Build site.
html	2a20453	jens-daniel-mueller	2020-03-20	Build site.
html	473ab25	jens-daniel-mueller	2020-03-19	Build site.
html	e9d33a7	jens-daniel-mueller	2020-03-19	Build site.
Rmd	ff79dbe	jens-daniel-mueller	2020-03-19	remoced errorbars in ts plot
html	4766353	jens-daniel-mueller	2020-03-19	Build site.
Rmd	0d90486	jens-daniel-mueller	2020-03-19	Hovmoeller daily changes
html	592f3b5	jens-daniel-mueller	2020-03-19	Build site.
Rmd	4103279	jens-daniel-mueller	2020-03-19	CT: removed coastal, added errorbars and hovmoeller
html	81f022e	jens-daniel-mueller	2020-03-18	Build site.
html	18a74d1	jens-daniel-mueller	2020-03-18	Build site.
Rmd	b839b18	jens-daniel-mueller	2020-03-18	CT vs tem changes implemented
html	1e39d85	jens-daniel-mueller	2020-03-18	Build site.
html	2105236	jens-daniel-mueller	2020-03-18	Build site.
html	4858097	jens-daniel-mueller	2020-03-18	Build site.
Rmd	f0233c2	jens-daniel-mueller	2020-03-18	MLD and NCP penetration depth
html	05b9bdc	jens-daniel-mueller	2020-03-17	Build site.
html	943cd6b	jens-daniel-mueller	2020-03-17	Build site.
Rmd	859c4a4	jens-daniel-mueller	2020-03-17	corrected gas exchange calculation
html	26bc407	jens-daniel-mueller	2020-03-17	Build site.
Rmd	7be14e4	jens-daniel-mueller	2020-03-17	corrected CT cum timeseries, used exact mean dates
html	cb196d8	jens-daniel-mueller	2020-03-17	Build site.
Rmd	7c10336	jens-daniel-mueller	2020-03-17	corrected CT cum timeseries, used exact mean dates
html	0202742	jens-daniel-mueller	2020-03-16	Build site.
html	7508d11	jens-daniel-mueller	2020-03-16	Build site.
Rmd	53ee423	jens-daniel-mueller	2020-03-16	gas exchange calculation completed
html	9f0c30b	jens-daniel-mueller	2020-03-16	Build site.
Rmd	1c60add	jens-daniel-mueller	2020-03-16	incremental CT changes timeseries + raw pCO2 profiles plotted
html	4150817	jens-daniel-mueller	2020-03-13	Build site.
Rmd	94e12d8	jens-daniel-mueller	2020-03-13	final cleaning
html	443d9a1	jens-daniel-mueller	2020-03-13	Build site.
Rmd	39b841d	jens-daniel-mueller	2020-03-13	all profiles pdfs included
html	ff22d6f	jens-daniel-mueller	2020-03-13	Build site.
Rmd	f49ce78	jens-daniel-mueller	2020-03-13	cumulative changes per depth
html	e404359	jens-daniel-mueller	2020-03-12	Build site.
Rmd	e9725fe	jens-daniel-mueller	2020-03-12	Clean CT dynamics
html	8e83afd	jens-daniel-mueller	2020-03-12	Build site.
Rmd	3c17c46	jens-daniel-mueller	2020-03-12	update CT cynamics
html	a3ddea4	jens-daniel-mueller	2020-03-12	Build site.
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

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
Discarding profiles with 3 or more observation missing within upper 20m
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

1.1 pCO₂ profile overview

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% c("180616","180820"),
         !(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% c("180616","180820"),
           !(station %in% c("PX1", "PX2", "P14", "P13", "P01")))

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% c("down", "up"))


#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)

# subset complete profiles
profiles_in <- tm_profiles %>% 
  filter(dep < 20,
         phase == "down") %>% 
  group_by(ID, station) %>% 
  summarise(nr = n()) %>% 
  mutate(select = if_else(nr > 18 | station == "P14", "in", "out")) %>% 
  select(-nr) %>% 
  ungroup()

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

tm_profiles %>% 
  arrange(date_time) %>% 
  ggplot(aes(pCO2, dep, col=select, linetype=phase))+
  geom_hline(yintercept = 25)+
  #geom_point()+
  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 pCO2 profiles at stations (P02-P12) and cruise dates (ID). y-axis restricted to displayed range.

tm_profiles <- tm_profiles %>%
  filter(select == "in",
         phase == "down") %>%
  select(-c(select, phase)) %>% 
  filter(dep < 25)

# 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)

1.2 Station map

# fm data
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.

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)

1.3 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 visitm over time. ID (color) refers to the starting date of the cruise, except for P14, which was visited twice during each cruise.

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

rm(cover)

2 Bottle C_T and A_T

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

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")) %>% 
  mutate(CT_AT_ratio = CT/AT,
         ID = if_else(ID == "180722", "180723", ID))

tb <- inner_join(tb, cruise_dates)

2.1 Vertical profiles

tb_long <- tb %>% 
  pivot_longer(4:7, 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())

Important notes: - Spatio-temporal variation of AT is small, which jusitfies conversion of pCO₂ to C_T based on a fixed mean AT - On July 31 we see a drop in surface salinity, associated with a rise in A_T, clearly pointing at exchange of water masses, presumably later

2.2 Surface time series

tb_surface <- tb_long %>% 
  filter(dep<9) %>% 
  group_by(ID, date_time_ID, var, station) %>% 
  summarise(value = mean(value, na.rm = TRUE)) %>% 
  ungroup()

tb_surface_station_mean <- tb_long %>% 
  filter(dep<9) %>% 
  group_by(ID, date_time_ID, var) %>% 
  summarise(value = mean(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, 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")+
  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).

rm(tb_long, tb_surface_station_mean)

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

tb_surface %>% 
  filter(var == "CT_AT_ratio") %>% 
  ggplot(aes(date_time_ID, value*AT_mean, col=station))+
  geom_point()+
  geom_path()+
  scale_fill_viridis_d()+
  scale_color_brewer(palette = "Set1")+
  labs(x="Mean transect date", y="CT-AT-ratio * mean AT")

CT timeseries, derived by multiplying the CT-AT-ratio with mean AT

Important notes: - C_T drop and temporal patterns observed in the C_T/A_T time series agrees well with those found in the C_T time series derived from pCO₂ measurementm

2.3 Mean alkalinity

In order to derive C_T from measured pCO₂ profiles, the alkalinity mean + sd in the upper 20 m and both stations was calculated as:

AT_mean

[1] 1718.872

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

AT_sd

[1] 26.23092

rm(AT_sd)

Likewise, the mean salinity amountm 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,
          sal = sal_mean) %>% 
  write_csv(here::here("Data/_summarized_data_files", "tb_fix.csv"))

rm(tb)

3 C_T profiles

3.1 Calculation from pCO₂

C_T 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 C_T profiles.

tm_profiles <- tm_profiles %>% 
  filter(pCO2 > 0)

tm_profiles <- tm_profiles %>% 
  mutate(CT = carb(24, var1=pCO2, var2=1720*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_CT <- 
  tm_profiles %>% 
  ggplot(aes(CT, 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_CT

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_CT)

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:CT, names_to = "var", values_to = "sd")
  
tm_profiles_ID_mean_long <- tm_profiles_ID_mean %>% 
  pivot_longer(sal:CT, 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.

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

tm_profiles_ID_long %>% 
  filter(var %in% c("CT", "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.

rm(all)

Important notes:

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

3.4 Individual profiles

C_T, 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_CT <- 
        tm_profiles %>%
        arrange(date_time) %>% 
        filter(ID == i_ID,
               station == i_station) %>%
        ggplot(aes(CT, dep))+
        geom_point()+
        geom_path()+
        scale_y_reverse()+
        labs(y="Depth [m]", x="CT* [µmol/kg]")+
        coord_cartesian(xlim = c(1400,1700), ylim = c(30,0))+
        theme_bw()
      

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

      
    }
  }
}

dev.off()

rm(i_ID, i_station, tm_profiles_highres)

tm_profiles_long <- tm_profiles %>%
  select(-c(lat, lon, pCO2_corr)) %>% 
  pivot_longer(sal:CT, 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_errorbar(aes(date_time_ID, ymax=value+sd, ymin=value-sd, col=as.factor(dep)))+
  geom_point()+
  scale_color_viridis_d(name="Depth [m]")+
  facet_wrap(~var, scales = "free_y", ncol=1)

rm(tm_profiles_ID_long_grid)

4.2 Hovmoeller plotm

4.2.1 Absolute values

bin_CT <- 30

p_CT_hov <- tm_profiles_ID_long %>% 
  filter(var == "CT") %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID, y=dep, z=value),
                    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_scico(breaks = MakeBreaks(bin_CT),
                   guide = "colorstrip",
                   name="CT (µmol/kg)",
                   palette = "davos", direction = -1)+
  scale_y_reverse()+
  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()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        legend.position = "left")

p_CT_hov / p_tem_hov

Hovmoeller plotm of absolute changes in C_T and temperature.

rm(p_CT_hov, bin_CT, p_tem_hov, bin_Tem)

4.2.2 Incremental changes

bin_CT <- 2.5

CT_hov <- tm_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())

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()+
  theme_bw()+
  labs(x="",y="Depth (m)")+
  coord_cartesian(expand = 0)

CT_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.

rm(CT_hov, bin_CT, Tem_hov, bin_Tem)

4.2.3 Cumulative changes

bin_CT <- 20

CT_hov <- tm_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())

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()+
  theme_bw()+
  labs(x="",y="Depth (m)")+
  coord_cartesian(expand = 0)

CT_hov / Tem_hov

Hovmoeller plotm of cumulative changes in C_T and temperature.

rm(CT_hov, bin_CT, Tem_hov, bin_Tem)

5 Depth-integration C_T

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

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

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

5.1 Fixed depths approach

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

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

iCT_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(iCT, dep_i)

for (dep_i in seq(9,13,1)) {


iCT_sign_temp <- tm_profiles_ID_long %>% 
  filter(var == "CT", 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(CT_i_diff = sum(value_diff)/1000) %>% 
  ungroup()

iCT_sign_temp <- iCT_sign_temp %>% 
  group_by(sign) %>%
  arrange(date_time_ID) %>% 
  mutate(CT_i_cum = cumsum(CT_i_diff)) %>% 
  ungroup()

iCT_sign_temp <- full_join(iCT_sign_temp, iCT_grid_sign) %>% 
  arrange(sign, date_time_ID) %>% 
  fill(CT_i_cum)


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

iCT_total_temp <- iCT_total_temp %>% 
  arrange(date_time_ID) %>% 
  mutate(CT_i_cum = cumsum(CT_i_diff)) %>% 
  ungroup() %>% 
  mutate(sign = "total")

iCT_total_temp <- full_join(iCT_total_temp, iCT_grid_total) %>% 
  arrange(sign, date_time_ID) %>% 
  fill(CT_i_cum)

iCT_temp <- bind_rows(iCT_sign_temp, iCT_total_temp) %>% 
    mutate(dep_i = dep_i)


if (exists("iCT")) {
  iCT <- bind_rows(iCT, iCT_temp)
  } else {iCT <- iCT_temp}

rm(iCT_temp, iCT_sign_temp, iCT_total_temp)

}

rm(iCT_grid_sign, iCT_grid_total)

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

iCT %>% 
  ggplot()+
  geom_point(data = cruise_dates, aes(date_time_ID, 0), shape=21)+
  geom_col(aes(date_time_ID_ref, CT_i_diff, fill=dep_i),
           position = "dodge", alpha=0.3)+
  geom_line(aes(date_time_ID, CT_i_cum, col=dep_i))+
  scale_color_viridis_d(name="Depth limit (m)")+
  scale_fill_viridis_d(name="Depth limit (m)")+
  labs(y="iCT [mol/m2]", x="")+
  facet_grid(sign~., scales = "free_y", space = "free_y")+
  theme_bw()

iCT_fixed_dep <- iCT
rm(iCT, dep_i)
# iCT %>%
#   write_csv(here::here("Data/_merged_data_files", "iCT_dep_limitm.csv"))

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, CT, 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, CT, 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.

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()

Overview density profiles at stations (P01-P14) and cruise dates (ID). Horizontal lines indicate determined MLD

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()+
  labs(x="")

5.2.6 iCT calculation

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


iCT <- tm_profiles_ID_long %>% 
  filter(var == "CT")

iCT <- full_join(iCT, MLD)

# iCT %>%
#     write_csv(here::here("Data/_merged_data_files", "tm_profiles_ID_long_cum_MLD.csv"))

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

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

iCT <- iCT %>% 
  group_by(rho_lim) %>% 
  arrange(date_time_ID) %>% 
  mutate(CT_i_cum = cumsum(CT_i_diff)) %>% 
  ungroup()

# iCT_total_temp <- full_join(iCT_total_temp, iCT_grid_total) %>% 
#   arrange(sign, date_time_ID) %>% 
#   fill(CT_i_cum)

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

iCT %>% 
  ggplot()+
  geom_point(data = cruise_dates, aes(date_time_ID, 0), shape=21)+
  geom_col(aes(date_time_ID_ref, CT_i_diff, fill=rho_lim),
           position = "dodge", alpha=0.3)+
  geom_line(aes(date_time_ID, CT_i_cum, col=rho_lim))+
  scale_color_viridis_d(name="Rho limit")+
  scale_fill_viridis_d(name="Rho limit")+
  labs(y="iCT [mol/m2]", x="")+
  #facet_grid(sign~., scales = "free_y", space = "free_y")+
  theme_bw()

iCT_MLD <- iCT
rm(iCT, MLD)

# iCT %>%
#   write_csv(here::here("Data/_merged_data_files", "iCT_dep_limitm.csv"))

5.3 Comparison of approaches

In the following, all cummulative iC_T 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.

iCT <- full_join(iCT_fixed_dep, iCT_MLD)

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

iCT %>% 
  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, CT_i_cum,
                group=group), col="grey")+
  geom_line(data = iCT_fixed_dep %>% filter(dep_i==12, sign=="total"),
            aes(date_time_ID, CT_i_cum, col="12m - total"))+
  geom_line(data = iCT_MLD %>% filter(rho_lim == 0.1),
            aes(date_time_ID, CT_i_cum, col="MLD - 0.1"))+
  scale_color_brewer(palette = "Set1", name="")+
  labs(y="iCT [mol/m2]", x="")

rm(iCT, iCT_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 iC_T 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 iC_T estimate

The cummulative iC_T trajectory determined by integration of C_T to a fixed water depth of 10 m was used for NCP calculation for the following reasons:

During the first productivity pulse that lasted until July 23:
- more than 90% of iC_T changes were located within the upper 10m
- no positive iC_T changes were located within the upper 10m
Deeper (fixed() layers were affected by iC_T changes
MLD were too shallow to cover all observed negative C_T changes

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

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 CT 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)

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.

dep_lim <- 6

tm_profiles_surface_long <- tm_profiles %>% 
  filter(dep < dep_lim) %>% 
  select(date_time = date_time_ID, ID, tem, pCO2_water = pCO2, CT) %>% 
  pivot_longer(tem:CT, 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()

p_pCO2_surf <- tm_profiles_surface_long_ID %>%
  filter(var == "pCO2_water") %>% 
  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_CT_surf <-
tm_profiles_surface_long_ID %>%
  filter(var == "CT") %>% 
  ggplot()+
  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))+
  geom_point(data = tb_surface %>% filter(var == "CT_AT_ratio"),
             aes(date_time_ID, value*AT_mean, col=station)) +
  scale_color_brewer(palette = "Set1")+
  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(0.35,0.8),
        legend.title = element_blank(),
        legend.direction = "horizontal",
        legend.background = element_rect(fill = "transparent"),
        legend.key = element_rect(fill = "transparent"))


p_pCO2_surf + p_tem_surf + p_CT_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)

6.2.3 Time series plots

Data setm 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_water", "tem")) %>% 
  select(date_time:mean) %>% 
  pivot_wider(names_from = "var", values_from = "mean")

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

tm_og <- tm_og %>% 
  mutate(pCO2_water = approxfun(date_time, pCO2_water)(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))

# tm_og_long <- tm_og %>% 
#   pivot_longer("pCO2_atm":"tem",
#                names_to = "var",
#                values_to = "value")

p_pCO2_atm <- tm_og %>%
  ggplot(aes(x=date_time))+
  geom_path(aes(y=pCO2_atm))+
  # geom_path(aes(y=pCO2_atm_daily, col="24h"))+
  # scale_color_manual(values = c("red", "black"),
  #                    guide = FALSE)+
  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))+
  # geom_path(aes(y=wind_daily, col="24h"))+
  # scale_color_brewer(palette = "Set1")+
  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')

6.2.4 Flux calculation

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_water - 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)

6.2.5 Daily fluxes

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())

6.2.6 Cumulative Fluxes

# scale flux to time interval

tm_og <- tm_og %>% 
  mutate(scale = 24*2) %>% 
  mutate(flux_scale = flux / scale) %>% 
  #group_by(freq, k_para) %>% 
  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())

6.3 iC_T correction

The cumulative iCT time series obtained through integration across the upper 10m of the water column was used for further calculations of NCP.

Correction of iCT 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 iCT must be corrected for the air-sea flux of CO2. iCT was determined for the upper 10m of the water column. The MLD was always shallower 10m, except for the last cruise day. Therefore:

Cumulative air-sea fluxes can be added completely to iCT 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 MLD. The flux correction applied to the upper 10m can therefore be scaled with a factor 10m/MLD

During the last cruise, deeper mixing up to 17m water depth was observed, resulting in increased CT values at 0-10 m and a decrease of CT in 10-17m. The loss of CT in 10-17m can be assumed to be entirely cause by mixing with low-CT surface water. Some CT loss is balanced through CT input attributable to the air-sea flux. Therefore, the observed loss, corrected for 7m/MLD-share of the air-sea-flux, was added to the integrated CT changes in 0-10m.

i_dep_lim <- 12

# extract CT data for fixed depth approach, depth limit 10m
iCT_10 <- iCT_fixed_dep %>% 
  filter(dep_i == i_dep_lim, sign=="total") %>% 
  select(-c(sign, dep_i))

rm(iCT_fixed_dep)

iCT_10 <- iCT_10 %>%
  select(ID, date_time = date_time_ID, date_time_ID_ref, CT_i_diff, CT_i_cum)

# date of the second last cruise
date_180806 <- unique(iCT_10$date_time)[7]

# calculate cumulative air-sea fluxes affecting 0-10m
tm_og_flux <- tm_og %>% 
  mutate(flux_scale = if_else(date_time > date_180806,
                              12/17 * flux_scale,
                              flux_scale)) %>%
  arrange(date_time) %>% 
  mutate(flux_cum = cumsum(flux_scale)) %>% 
  select(date_time, flux_cum)

# calculate cumulative air-sea fluxes affecting 10-17m
tm_og_flux_dep <- tm_og %>% 
  filter(date_time > date_180806) %>% 
  mutate(flux_scale = 5/17 * flux_scale) %>%
  arrange(date_time) %>% 
  mutate(flux_cum = cumsum(flux_scale)) %>% 
  select(date_time, flux_cum)

iCT_10_flux <- full_join(iCT_10, tm_og_flux) %>% 
  arrange(date_time)

rm(tm_og_flux, iCT_10, tm_og)


# linear interpolation of cumulative changes to frequency of the flux estimates estimates 
iCT_10_flux <- iCT_10_flux %>% 
  mutate(CT_i_cum = approxfun(date_time, CT_i_cum)(date_time),
         flux_cum = approxfun(date_time, flux_cum)(date_time)) %>% 
    fill(flux_cum) %>% 
  mutate(CT_i_flux_cum = CT_i_cum + flux_cum)


# calculate cumulative fluxes inbetween cruises 
iCT_10_flux_diff <- iCT_10_flux %>% 
  filter(!is.na(date_time_ID_ref)) %>% 
  mutate(flux_diff = flux_cum - lag(flux_cum, default = 0)) %>% 
  select(date_time_ID_ref, observed=CT_i_diff, flux=flux_diff) %>% 
  pivot_longer(cols = 2:3, names_to = "var", values_to = "value_diff")


# calculate mixing with deep waters, corrected for air sea fluxes
iCT_10_mix <- tm_profiles_ID_long %>% 
  filter(ID == "180815",
         var == "CT",
         dep < 17,
         dep > 12) %>% 
  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)

iCT_10_mix_diff <- iCT_10_mix %>% 
  select(date_time_ID_ref, value_diff) %>% 
  mutate(var="mixing")

iCT_10_flux_mix_diff <- 
  full_join(iCT_10_flux_diff, iCT_10_mix_diff)

iCT_10_flux_mix <-
  full_join(iCT_10_flux,
            iCT_10_mix %>% rename(mix_cum = value_diff))

rm(iCT_10_mix, iCT_10_mix_diff, iCT_10_flux, iCT_10_flux_diff, date_180806)

iCT_10_flux_mix <- iCT_10_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),
         CT_i_flux_mix_cum = CT_i_flux_cum + mix_cum)

  
p_iCT <- iCT_10_flux_mix %>% 
  arrange(date_time) %>% 
  ggplot()+
  geom_col(data = iCT_10_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, CT_i_cum, col="observed"))+
  geom_line(aes(date_time, CT_i_flux_mix_cum, col="mixing + flux corrected"))+
  geom_line(aes(date_time, CT_i_flux_cum, col="flux corrected"))+
  scale_x_datetime(date_breaks = "week",
                   date_labels = "%b %d",
                   sec.axis = dup_axis())+
  scale_fill_brewer(palette = "Set1", name="incremental changes")+
  scale_color_brewer(palette = "Set1", 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_iCT

iCT_10_flux_mix %>%
  write_csv(here::here("Data/_merged_data_files", "tm_NCP_cum.csv"))

iCT_10_flux_mix_diff %>%
  write_csv(here::here("Data/_merged_data_files", "tm_NCP_inc.csv"))

p_pCO2_surf + p_tem_surf + p_CT_surf + 
  p_pCO2_atm + p_wind + p_flux_daily + p_flux_cum + 
  p_iCT +
  plot_layout(ncol = 1,
              heights = c(rep(1,7), 4))

ggsave(here::here("output/Plots/Figures_publication/article", "atm_water_timeseries.pdf"),
       width = 140, height = 270, dpi = 300, units = "mm")

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 CT changes
- Calculate AT-S ratios, reconstruct AT profiles, calculate true CT profiles, normalize CT 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

CT dynamics

Jens Daniel Müller

08 May, 2020