CT dynamics
Jens Daniel Müller
27 March, 2020
Last updated: 2020-03-27
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Knit directory: BloomSail/
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library(tidyverse)
library(patchwork)
library(seacarb)
library(marelac)
library(metR)
library(scico)
library(lubridate)
library(zoo)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 represents the start date of the cruise (“YYMMDD”), not the exact mean sampling date
1.1 pCO2 profile overview
ts <-
read_csv(here::here("data/_merged_data_files",
"BloomSail_CTD_HydroC_track_RT.csv"),
col_types = cols(ID = col_character(),
pCO2_analog = col_double(),
pCO2 = col_double(),
Zero = col_character(),
Flush = col_character(),
mixing = col_character(),
Zero_ID = col_integer(),
deployment = col_integer(),
lon = col_double(),
lat = col_double(),
pCO2_RT = col_double()))
# Filter relevant rows and columns
ts_profiles <- ts %>%
filter(type == "P",
Flush == "0",
Zero == "0",
!ID %in% c("180616","180820"),
!(station %in% c("PX1", "PX2", "P14", "P13", "P01"))) %>%
select(date_time, ID, station, lat, lon, dep, sal, tem, pCO2_raw = pCO2, pCO2 = pCO2_RT_mean, duration)
# Assign meta information
ts_profiles <- ts_profiles %>%
group_by(ID, station) %>%
mutate(duration = as.numeric(date_time - min(date_time))) %>%
arrange(date_time) %>%
ungroup()
meta <- read_csv(here::here("Data/_summarized_data_files",
"Tina_V_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")))
ts_profiles <- full_join(ts_profiles, meta)
rm(meta)
# creating descriptive variables
ts_profiles <- ts_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))
ts_profiles <- ts_profiles %>%
select(-c(start, down, lift, up, end, comment, p_type, duration))
# select downcasst only
ts_profiles <- ts_profiles %>%
filter(phase == "down") %>%
select(-phase)
# ts_profiles_highres <- ts_profiles
# grid observation to 1m depth intervals
ts_profiles <- ts_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) %>%
summarise_all("mean", na.rm = TRUE) %>%
ungroup() %>%
select(-dep, dep=dep_grid)
# subset complete profiles
profiles_in <- ts_profiles %>%
filter(dep < 20) %>%
group_by(ID, station) %>%
summarise(nr = n()) %>%
mutate(select = if_else(nr > 18 | station == "P14", "in", "out")) %>%
select(-nr) %>%
ungroup()
ts_profiles <- full_join(ts_profiles, profiles_in)
rm(profiles_in)
ts_profiles %>%
arrange(date_time) %>%
ggplot(aes(pCO2, dep, col=select))+
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.
ts_profiles <- ts_profiles %>%
filter(select == "in") %>%
select(-select) %>%
filter(dep < 25)
# assign mean date_time stamp
cruise_dates <- ts_profiles %>%
group_by(ID) %>%
summarise(date_time_ID = mean(date_time)) %>%
ungroup()
# inner_join remove P14 observations lacking date_time_ID
ts_profiles <- inner_join(cruise_dates, ts_profiles)1.2 Station map
map <- read_csv(here::here("data/Maps","Bathymetry_Gotland_east_small.csv"))
# ggplot()+
# geom_contour_fill(data=map, aes(x=lon, y=lat, z=-elev), na.fill = TRUE)+
# coord_quickmap(expand = 0, xlim = c(18.7, 19.9), ylim = c(57.25,57.6))+
# theme_bw()+
# theme(legend.position="bottom")
ts_profiles %>%
group_by(station) %>%
summarise(lat = mean(lat),
lon = mean(lon)) %>%
ungroup() %>%
ggplot()+
geom_raster(data=map, aes(lon, lat, fill=-elev))+
scale_fill_scico(palette = "oslo", na.value = "grey",
name="Depth [m]", direction = -1)+
geom_label(aes(lon, lat, label=station))+
coord_quickmap(expand = 0, xlim = c(18.7, 19.9), ylim = c(57.25,57.6))+
theme_bw()
Location of stations sampled between the east coast of Gotland and Gotland deep.
rm(map)1.3 Data coverage
cover <- ts_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_color_viridis_d()+
scale_fill_viridis_d()
Spatio-temporal data coverage, indicated as station visits over time. ID (color) refers to the starting date of the cruise, except for P14, which was visited twice during each cruise.
rm(cover)2 Bottle CT and AT
At stations P07 and P10 discrete samples for lab measurments 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", "Tina_V_Bottle_CO2_lab.csv"),
col_types = cols(ID = col_character()))
tb <- tb %>%
filter(station %in% c("P07", "P10")) %>%
select(-pH_Mosley) %>%
mutate(CT_AT_ratio = CT/AT)
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()+
scale_color_viridis_d()+
facet_grid(station~var, scales = "free_x")+
theme(legend.position = "bottom")
Important notes: - Spatio-temporal variation of AT is small, which jusitfies conversion of pCO2 to CT based on a fixed mean AT - On July 30 we see a drop in surface salinity, associated with a rise in AT, clearly pointing at exchange of water masses, presumably later
2.2 Surface time series
tb_surface <- tb_long %>%
filter(dep<10) %>%
group_by(ID, date_time_ID, var, station) %>%
summarise(value = mean(value, na.rm = TRUE)) %>%
ungroup()
rm(tb_long)
tb_surface %>%
ggplot(aes(date_time_ID, value, col=station))+
#geom_point(aes(lubridate::ymd(ID), value, col=station))+
geom_point()+
geom_path()+
scale_fill_viridis_d()+
scale_color_brewer(palette = "Set1")+
facet_grid(var~., 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).
AT_mean <- tb_surface %>%
filter(var == "AT") %>%
summarise(AT = mean(value, na.rm = TRUE)) %>%
pull()
tb_surface %>%
filter(var == "CT_AT_ratio") %>%
ggplot(aes(lubridate::ymd(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: - CT drop and temporal patterns observed in the CT/AT time series agrees well with those found in the CT time series derived from pCO2 measurements
2.3 Mean alkalinity
In order to derive CT from measured pCO2 profiles, the mean alkalinity in the upper 20 m and both stations was calculated as:
AT_mean <- tb %>%
filter(dep <= 20) %>%
summarise(AT = mean(AT, na.rm = TRUE)) %>%
pull()
AT_mean[1] 1717.08Likewise, the mean salinity amounts to:
sal_mean <- tb %>%
filter(dep <= 20) %>%
summarise(sal = mean(sal, na.rm = TRUE)) %>%
pull()
sal_mean[1] 6.894127bind_cols(start = min(ts$date_time),
end = max(ts$date_time),
AT = AT_mean,
sal = sal_mean) %>%
write_csv(here::here("Data/_summarized_data_files", "tb_fix.csv"))3 CT profiles
3.1 Calculation from pCO2
CT 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 CT profiles.
ts_profiles <- ts_profiles %>%
drop_na()
ts_profiles <- ts_profiles %>%
filter(pCO2 > 0)
ts_profiles <- ts_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, AT_mean)
ts_profiles %>%
write_csv(here::here("Data/_merged_data_files", "ts_profiles_CT.csv"))3.2 Mean profiles
Mean vertical profiles were calculated for each cruise day (ID).
ts_profiles_ID_mean <- ts_profiles %>%
select(-c(station,lat, lon, pCO2_raw, date_time)) %>%
group_by(ID, date_time_ID, dep) %>%
summarise_all(list(mean), na.rm=TRUE) %>%
ungroup()
ts_profiles_ID_sd <- ts_profiles %>%
select(-c(station,lat, lon, pCO2_raw, date_time)) %>%
group_by(ID, date_time_ID, dep) %>%
summarise_all(list(sd), na.rm=TRUE) %>%
ungroup()
ts_profiles_ID_sd_long <- ts_profiles_ID_sd %>%
pivot_longer(4:7, names_to = "var", values_to = "sd")
ts_profiles_ID_mean_long <- ts_profiles_ID_mean %>%
pivot_longer(4:7, names_to = "var", values_to = "value")
ts_profiles_ID_long <- inner_join(ts_profiles_ID_mean_long, ts_profiles_ID_sd_long)
rm(ts_profiles_ID_sd_long, ts_profiles_ID_sd, ts_profiles_ID_mean_long, ts_profiles_ID_mean)
ts_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 <- ts_profiles_ID_long %>%
filter(var %in% c("CT", "tem")) %>%
rename(group = ID)
ts_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 CT in the upper 10m increases on June 30.
3.3 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.
pdf(file=here::here("output/Plots/CT_dynamics",
"ts_profiles_pCO2_tem_sal_CT.pdf"), onefile = TRUE, width = 9, height = 5)
for(i_ID in unique(ts_profiles$ID)){
for(i_station in unique(ts_profiles$station)){
if (nrow(ts_profiles %>% filter(ID == i_ID, station == i_station)) > 0){
# i_ID <- unique(ts_profiles$ID)[1]
# i_station <- unique(ts_profiles$station)[1]
p_pCO2 <-
ts_profiles %>%
arrange(date_time) %>%
filter(ID == i_ID,
station == i_station) %>%
ggplot(aes(pCO2, dep, col="grid_RT"))+
geom_point(data = ts_profiles_highres %>% arrange(date_time) %>% filter(ID == i_ID, station == i_station),
aes(pCO2_raw, dep, col="raw"))+
geom_point(data = ts_profiles_highres %>% arrange(date_time) %>% filter(ID == i_ID, station == i_station),
aes(pCO2, dep, col="raw_RT"))+
geom_point(aes(pCO2_raw, 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 <-
ts_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 <-
ts_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 <-
ts_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, ts_profiles_highres)ts_profiles_long <- ts_profiles %>%
select(-c(lat, lon, pCO2_raw)) %>%
pivot_longer(6:9, values_to = "value", names_to = "var")
pdf(file=here::here("output/Plots/CT_dynamics",
"ts_profiles_ID_pCO2_tem_sal_CT.pdf"), onefile = TRUE, width = 9, height = 5)
for(i_ID in unique(ts_profiles$ID)){
#i_ID <- unique(ts_profiles$ID)[1]
sub_ts_profiles_long <- ts_profiles_long %>%
arrange(date_time) %>%
filter(ID == i_ID)
print(
sub_ts_profiles_long %>%
ggplot()+
geom_path(data = ts_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_ts_profiles_long)
}
dev.off()
rm(i_ID, ts_profiles_long)3.4 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.
ts_profiles_ID_long <- ts_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()
ts_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")
3.5 Profiles of cumulative changes
Cumulative changes of seawater vars were calculated at each depth relative to the first cruise day on July 5.
ts_profiles_ID_long %>%
arrange(dep) %>%
ggplot(aes(value_cum, dep, col=ID))+
geom_vline(xintercept = 0)+
geom_point()+
geom_path()+
scale_y_reverse()+
scale_color_viridis_d()+
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.
ts_profiles_ID_long <- ts_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()
ts_profiles_ID_long %>%
write_csv(here::here("Data/_merged_data_files", "ts_profiles_ID_long_cum.csv"))
ts_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")
4 Timeseries
4.1 Timeseries depth intervals
Mean seawater parameters were calculated for 5m depth intervals.
ts_profiles_ID_long_grid <- ts_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)
ts_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(ts_profiles_ID_long_grid)4.2 Hovmoeller plots
4.2.1 Absolute values
bin_CT <- 20
CT_hov <- ts_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_viridis_c(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 <- ts_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()+
theme_bw()+
labs(x="",y="Depth (m)")+
coord_cartesian(expand = 0)
CT_hov / Tem_hov
Hovmoeller plots of absolute changes in CT and temperature.
rm(CT_hov, bin_CT, Tem_hov, bin_Tem)4.2.2 Incremental changes
bin_CT <- 2.5
CT_hov <- ts_profiles_ID_long %>%
filter(var == "CT") %>%
ggplot()+
geom_contour_fill(aes(x=date_time_ID_ref, y=dep, z=value_diff_daily),
breaks = MakeBreaks(bin_CT),
col="black")+
geom_point(aes(x=date_time_ID, y=c(24.5)), size=3, shape=24, fill="white")+
scale_fill_divergent(breaks = MakeBreaks(bin_CT),
guide = "colorstrip",
name="CT (µmol/kg)")+
scale_y_reverse()+
theme_bw()+
labs(y="Depth (m)")+
coord_cartesian(expand = 0)+
theme(axis.title.x = element_blank(),
axis.text.x = element_blank())
bin_Tem <- 0.1
Tem_hov <- ts_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 plots 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(CT_hov, bin_CT, Tem_hov, bin_Tem)4.2.3 Cumulative changes
bin_CT <- 20
CT_hov <- ts_profiles_ID_long %>%
filter(var == "CT") %>%
ggplot()+
geom_contour_fill(aes(x=date_time_ID, y=dep, z=value_cum),
breaks = MakeBreaks(bin_CT),
col="black")+
geom_point(aes(x=date_time_ID, y=c(24.5)), size=3, shape=24, fill="white")+
scale_fill_divergent(breaks = MakeBreaks(bin_CT),
guide = "colorstrip",
name="CT (µmol/kg)")+
scale_y_reverse()+
theme_bw()+
labs(y="Depth (m)")+
coord_cartesian(expand = 0)+
theme(axis.title.x = element_blank(),
axis.text.x = element_blank())
bin_Tem <- 2
Tem_hov <- ts_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 plots of cumulative changes in CT and temperature.
rm(CT_hov, bin_CT, 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 CT over depth to derive iCT. 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 CT inbetween cruise dates. Those were summed up to derive a trajectory of cummulative iCT changes.
5.1 Fixed depths approach
Incremental and cumulative CT 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.
iCT_grid_sign <- ts_profiles_ID_long %>%
select(ID, date_time_ID, date_time_ID_ref) %>%
unique() %>%
expand_grid(sign = c("pos", "neg"))
iCT_grid_total <- ts_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(5,20,5)) {
iCT_sign_temp <- ts_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 <- ts_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_limits.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.
ts_profiles <- ts_profiles %>%
mutate(rho = swSigma(salinity = sal, temperature = tem, pressure = dep/10))5.2.2 Density profiles
ts_profiles_ID_mean_hydro <- ts_profiles %>%
select(-c(station,lat, lon, pCO2_raw, pCO2, CT, date_time)) %>%
group_by(ID, date_time_ID, dep) %>%
summarise_all(list(mean), na.rm=TRUE) %>%
ungroup()
ts_profiles_ID_sd_hydro <- ts_profiles %>%
select(-c(station,lat, lon, pCO2_raw, pCO2, CT, date_time)) %>%
group_by(ID, date_time_ID, dep) %>%
summarise_all(list(sd), na.rm=TRUE) %>%
ungroup()
ts_profiles_ID_sd_hydro_long <- ts_profiles_ID_sd_hydro %>%
pivot_longer(4:6, names_to = "var", values_to = "sd")
ts_profiles_ID_mean_hydro_long <- ts_profiles_ID_mean_hydro %>%
pivot_longer(4:6, names_to = "var", values_to = "value")
ts_profiles_ID_hydro_long <- inner_join(ts_profiles_ID_mean_hydro_long, ts_profiles_ID_sd_hydro_long)
rm(ts_profiles_ID_sd_hydro_long,
ts_profiles_ID_sd_hydro,
ts_profiles_ID_mean_hydro_long)
ts_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
ts_profiles_ID_mean_hydro <- expand_grid(ts_profiles_ID_mean_hydro, rho_lim = c(0.1,0.2,0.5))
MLD <- ts_profiles_ID_mean_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
ts_profiles_ID_mean_hydro <-
full_join(ts_profiles_ID_mean_hydro, MLD)
ts_profiles_ID_mean_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_point()+
geom_path()+
scale_color_brewer(palette = "Set1", name= "Rho limit")+
labs(x="")
5.2.6 iCT calculation
# iCT_grid_sign <- ts_profiles_ID_long %>%
# select(ID, date_time_ID, date_time_ID_ref) %>%
# unique() %>%
# expand_grid(sign = c("pos", "neg"))
#
# iCT_grid_total <- ts_profiles_ID_long %>%
# select(ID, date_time_ID, date_time_ID_ref) %>%
# unique() %>%
# expand_grid(sign = c("total"))
iCT <- ts_profiles_ID_long %>%
filter(var == "CT")
iCT <- full_join(iCT, MLD)
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_limits.csv"))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.
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==10, sign=="total"),
aes(date_time_ID, CT_i_cum, col="10m - 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 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)
7 Best iCT estimate
The cummulative iCT trajectory determined by integration of CT 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 iCT changes were located within the upper 10m
- no positive iCT changes were located within the upper 10m
- Deeper (fixed() layers were affected by iCT changes
- MLD were too shallow to cover all observed negative CT changes
ts_profiles_ID_long_180723 <- ts_profiles_ID_long %>%
filter(ID == 180723,
var == "CT")
p_ts_profiles_ID_long <- ts_profiles_ID_long_180723 %>%
arrange(dep) %>%
ggplot(aes(value_cum, dep, col="total"))+
geom_vline(xintercept = 0)+
geom_hline(yintercept = 10, col="red")+
geom_path(aes(value_cum_sign, dep, col="directional"))+
geom_point(aes(value_cum_sign, dep, col="directional"))+
geom_point()+
geom_path()+
scale_y_reverse()+
scale_color_brewer(palette = "Set1", name="estimate")+
labs(x="Cumulative change of CT on July 23 (180723)")+
theme(legend.position = "left")
ts_profiles_ID_long_180723_dep <- ts_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_ts_profiles_ID_long_rel <- ts_profiles_ID_long_180723_dep %>%
ggplot(aes(value_cum_i_rel, dep))+
geom_hline(yintercept = 10, 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 to ts_profiles_ID_long on July 23")+
theme_bw()
p_ts_profiles_ID_long + p_ts_profiles_ID_long_rel
rm(ts_profiles_ID_long_180723,
ts_profiles_ID_long_180723_dep,
p_ts_profiles_ID_long,
p_ts_profiles_ID_long_rel)7.1 Air-Sea CO2 flux
7.1.1 pCO2 water
The cruise mean pCO2 recorded in profiling-mode (stations only) and depths < 3m was used for gas exchange calcualtions.
ts_profiles_surface <- ts_profiles %>%
filter(dep < 3) %>%
select(date_time_ID, ID, tem, pCO2_water = pCO2)
ts_profiles_surface_ID <- ts_profiles_surface %>%
group_by(ID) %>%
summarise_all(mean) %>%
ungroup() %>%
select(-ID, date_time = date_time_ID)
ts_profiles_surface_ID %>%
ggplot(aes(date_time, pCO2_water, col="Cruise mean"))+
geom_point(data=ts_profiles_surface,
aes(date_time_ID, pCO2_water, col="observed"))+
geom_path()+
geom_point()+
scale_color_brewer(palette = "Set1", name="")+
theme(axis.title.x = element_blank())
#rm(ts_profiles_surface)
start <- min(ts_profiles_surface_ID$date_time)
end <- max(ts_profiles_surface_ID$date_time)7.1.2 Wind and atm. pCO2
Metrological data were recorded on the flux tower located on Ostergarnsholm island.
og <- read_delim(here::here("Data/Ostergarnsholm/Tower", "Oes_Jens_atm_water_June_to_August_2018.csv"),
delim = ";" )
og <- og %>%
mutate(date_time = ymd_hms( paste(paste(year, month, day, sep = "/"),
paste(hour, min, sec, sep = ":")))) %>%
select("date_time",
"CO2 12m [ppm]",
"w_c [ppm m/s]",
"WS 12m [m/s]",
"WD 12m [degrees]",
"T 12m [degrees C]",
"RIS [W/m^2]"
) %>%
filter(date_time > start,
date_time < end)
rm(end, start)
og <- og %>%
mutate(freq = "30 min") %>%
select(date_time, freq, pCO2_atm = "CO2 12m [ppm]", wind = "WS 12m [m/s]")7.1.3 Time series plots
Data sets for atmospheric and seawater observations were merged and interpolated to a common time stamp.
ts_og <- full_join(og, ts_profiles_surface_ID) %>%
arrange(date_time)
ts_og <- ts_og %>%
mutate(pCO2_water = na.approx(pCO2_water, rule = 2),
tem = na.approx(tem, rule = 2),
wind = na.approx(wind, rule = 2)) %>%
filter(!is.na(pCO2_atm))
ts_og_daily <- ts_og %>%
mutate(day = yday(date_time)) %>%
group_by(day) %>%
summarise_all(mean, na.rm = TRUE) %>%
ungroup() %>%
select(-day) %>%
mutate(freq = "daily")
ts_og <- bind_rows(ts_og, ts_og_daily)
rm(ts_profiles_surface, ts_profiles_surface_ID, og, ts_og_daily)ts_og_long <- ts_og %>%
gather("parameter", "value", 3:6)
ts_og_long %>%
ggplot(aes(date_time, value, col=freq))+
geom_line()+
facet_grid(parameter~., scales = "free_y")+
scale_color_brewer(palette = "Set1", direction = -1)+
theme(axis.title.x = element_blank())
7.1.4 Flux calculation
F = k * dCO2
with
dCO2 = K0 * dpCO2 and
k = coeff * U^2 * (660/Sc)^0.5
Units 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 (= 6060100 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)
ts_og <- ts_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),
W14 = 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]
ts_og <- ts_og %>%
mutate(flux_daily = k_value*dCO2*1e-5*24)
rm(Sc_W14)7.1.5 Daily fluxes
ts_og %>%
ggplot(aes(date_time, flux_daily, col=k_para))+
geom_line()+
labs(y="F (mol m-2 d-1)")+
scale_color_brewer(palette = "Set1")+
facet_wrap(~freq)+
theme(axis.title.x = element_blank())
7.1.6 Cumulative Fluxes
# scale flux to time interval
ts_og <- ts_og %>%
mutate(scale = if_else(freq == "daily", 1, 24*2)) %>%
mutate(flux_scale = flux_daily / scale) %>%
group_by(freq, k_para) %>%
arrange(date_time) %>%
mutate(flux_cum = cumsum(flux_scale)) %>%
ungroup()
ts_og %>%
ggplot(aes(date_time, flux_cum, col=k_para, linetype=freq))+
geom_line()+
labs(y="F (mol m-2)")+
scale_color_brewer(palette = "Set1")+
theme(axis.title.x = element_blank())
7.1.7 iCT 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.
iCT_10 <- iCT_fixed_dep %>%
filter(dep_i == 10, sign=="total") %>%
select(-c(sign, dep_i))
rm(iCT_fixed_dep)
iCT_10_flux <- iCT_10 %>%
select(date_time = date_time_ID, CT_i_cum)
date_180806 <- unique(iCT_10_flux$date_time)[7]
ts_og_flux <- ts_og %>%
mutate(flux_scale = if_else(date_time > date_180806,
10/17 * flux_scale,
flux_scale)) %>%
group_by(freq, k_para) %>%
arrange(date_time) %>%
mutate(flux_cum = cumsum(flux_scale)) %>%
ungroup() %>%
filter(k_para == "W14", freq =="30 min") %>%
select(date_time, flux_cum)
iCT_10_flux <- full_join(iCT_10_flux, ts_og_flux) %>%
arrange(date_time)
rm(ts_og_flux)
iCT_10_flux <- iCT_10_flux %>%
mutate(CT_i_cum = na.approx(CT_i_cum, rule = 2),
flux_cum = na.approx(flux_cum, rule = 2),
CT_i_cum_total = CT_i_cum + flux_cum)
iCT_10_flux %>%
arrange(date_time) %>%
ggplot()+
geom_hline(yintercept = 0)+
geom_line(aes(date_time, CT_i_cum, col="observed"))+
geom_line(aes(date_time, CT_i_cum_total, col="flux corrected"))+
geom_ribbon(aes(date_time, ymin = CT_i_cum, ymax = CT_i_cum_total,
fill="Air-sea flux"), alpha=0.2)+
scale_fill_brewer(palette = "Set1", name="")+
scale_color_brewer(palette = "Set1", name="")+
labs(y="integrated, cumulative CT [mol/m2]")+
theme(axis.title.x = element_blank())
8 Nomenclature of objectes
Should be identical for stored files and objectes in R environment
- source
- ts: tina 5 sensor
- tb: tina 5 bottle
- fm: finnmaid
- og: ostergarnsholm tower
- mp: bathymetric map
- subsetting and modification levels
- profiles vs surface: operation mode tina 5
- ID: mean values for cruise (reduced temporal resolution)
- daily: daily mean values
- long: data stored in long format (all observations in only 2 columns “var” and “value”)
- fix: constant, unique values such as long-term means, starting dates, etc
- iCT: includes cumulative numbers as iCT estimates
- NCP: includes cumulative numbers as NCP estimates
- CT_tem: data subset to analyse changes of CT with tem
- 3d vs 2d: surface vs depth resolved GETM data
9 Nomenclature of variables
- Descriptive variables
- date
- date_time
- date_time_ID: mean date of cruise
- date_time_ID_diff: time differences in between cruises
- date_time_ID_ref: mean date in between cruises corresponding to observed incremental changes
- station
- ID: character identifying starting date of cruise as YYMMDD
- dep: 1m depth intervals
- lat
- lon
- Observed variables: column names, or identifier in column “var” for long-format tables
- pCO2
- sal
- tem
- CT
- U10: wind speed at 10m
- mld: mixed or mixing layer depth
- Variable name extension
- mean
- sd
- min
- max
- int: interpolated value
- grid: value gridded to a coarser resolution
- diff: difference to previous value
- diff_daily: difference to previous value divided by number of days
- i: intergrated over depth
- cum: cumulative value over time
- sign: identifier for pos. or neg. differences
- p_XXX: ggplot object
10 Open tasks / questions
- clean and harmonize chunk labeling (label: plot, 1 plot per chunk, etc)
- included removed stations in map and coverage plot
- Significance of changes in AT for calculated CT changes
- Harmonize selection of profiles for tau optimization and BGC interpretation (how many missing discrete depth intervals are allowed?)
sessionInfo()R version 3.5.0 (2018-04-23)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18363)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] zoo_1.8-6 lubridate_1.7.4 scico_1.1.0 metR_0.5.0
[5] marelac_2.1.9 shape_1.4.4 seacarb_3.2.12 oce_1.2-0
[9] gsw_1.0-5 testthat_2.3.1 patchwork_1.0.0 forcats_0.4.0
[13] stringr_1.4.0 dplyr_0.8.3 purrr_0.3.3 readr_1.3.1
[17] tidyr_1.0.0 tibble_2.1.3 ggplot2_3.3.0 tidyverse_1.3.0
loaded via a namespace (and not attached):
[1] nlme_3.1-137 bitops_1.0-6 fs_1.3.1
[4] RColorBrewer_1.1-2 httr_1.4.1 rprojroot_1.3-2
[7] tools_3.5.0 backports_1.1.5 R6_2.4.0
[10] DBI_1.0.0 colorspace_1.4-1 withr_2.1.2
[13] sp_1.3-2 tidyselect_0.2.5 gridExtra_2.3
[16] compiler_3.5.0 git2r_0.26.1 cli_1.1.0
[19] rvest_0.3.5 xml2_1.2.2 labeling_0.3
[22] scales_1.0.0 checkmate_1.9.4 digest_0.6.22
[25] foreign_0.8-70 rmarkdown_2.0 pkgconfig_2.0.3
[28] htmltools_0.4.0 highr_0.8 dbplyr_1.4.2
[31] maps_3.3.0 rlang_0.4.5 readxl_1.3.1
[34] rstudioapi_0.10 generics_0.0.2 jsonlite_1.6
[37] RCurl_1.95-4.12 magrittr_1.5 Formula_1.2-3
[40] dotCall64_1.0-0 Matrix_1.2-14 Rcpp_1.0.2
[43] munsell_0.5.0 lifecycle_0.1.0 stringi_1.4.3
[46] yaml_2.2.0 plyr_1.8.4 grid_3.5.0
[49] maptools_0.9-8 formula.tools_1.7.1 promises_1.1.0
[52] crayon_1.3.4 lattice_0.20-35 haven_2.2.0
[55] hms_0.5.2 zeallot_0.1.0 knitr_1.26
[58] pillar_1.4.2 reprex_0.3.0 glue_1.3.1
[61] evaluate_0.14 data.table_1.12.6 modelr_0.1.5
[64] operator.tools_1.6.3 vctrs_0.2.0 spam_2.3-0.2
[67] httpuv_1.5.2 cellranger_1.1.0 gtable_0.3.0
[70] assertthat_0.2.1 xfun_0.10 broom_0.5.3
[73] later_1.0.0 viridisLite_0.3.0 memoise_1.1.0
[76] fields_9.9 workflowr_1.6.0 ellipsis_0.3.0
[79] here_0.1