Last updated: 2020-04-28

Checks: 7 0

Knit directory: BloomSail/

This reproducible R Markdown analysis was created with workflowr (version 1.6.1). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.


Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

The command set.seed(20191021) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version 058c709. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:


Ignored files:
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    data/Finnmaid_2018/
    Ignored:    data/GETM/
    Ignored:    data/Maps/
    Ignored:    data/Ostergarnsholm/
    Ignored:    data/TinaV/
    Ignored:    data/_merged_data_files/
    Ignored:    data/_summarized_data_files/
    Ignored:    output/Plots/Figures_publication/.tmp.drivedownload/
    Ignored:    output/Plots/Figures_publication/Appendix/

Unstaged changes:
    Modified:   output/Plots/Figures_publication/Article/Hov_abs_profiles_cum.pdf
    Modified:   output/Plots/Figures_publication/Article/data_coverage.pdf
    Modified:   output/Plots/Figures_publication/Article/profiles_all.pdf
    Modified:   output/Plots/Figures_publication/Article/station_map.pdf

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.


These are the previous versions of the repository in which changes were made to the R Markdown (analysis/Finnmaid+GETM.Rmd) and HTML (docs/Finnmaid+GETM.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File Version Author Date Message
html 66b4ba3 jens-daniel-mueller 2020-04-28 Build site.
Rmd 4f17cbb jens-daniel-mueller 2020-04-28 zeff for Finnmaid data
html 472c2b4 jens-daniel-mueller 2020-04-21 Build site.
html f8fcf50 jens-daniel-mueller 2020-04-19 created pub figures for time series
html 489ddf3 jens-daniel-mueller 2020-04-15 Build site.
Rmd ece3767 jens-daniel-mueller 2020-04-15 plot integrated temperature and surface temperature
html 2eb40f3 jens-daniel-mueller 2020-04-15 Build site.
Rmd 3aaff30 jens-daniel-mueller 2020-04-15 T penetration depth for GETM BloomSail comparison added
html 4748ea0 jens-daniel-mueller 2020-04-14 Build site.
Rmd e7c8528 jens-daniel-mueller 2020-04-14 Temp penetration depth GETM
html 48631ee jens-daniel-mueller 2020-04-09 Build site.
Rmd 4e9464f jens-daniel-mueller 2020-04-09 corrected na approx function
html 7ba778c jens-daniel-mueller 2020-04-07 Build site.
Rmd b72d86d jens-daniel-mueller 2020-04-07 included hovmoeller plots
html 7d552f7 jens-daniel-mueller 2020-04-07 Build site.
Rmd 8063869 jens-daniel-mueller 2020-04-07 corrected interpolation, referred to surface temp from getm 3d
html 3a5f620 jens-daniel-mueller 2020-04-03 Build site.
Rmd 78f88d1 jens-daniel-mueller 2020-04-03 Ploted incremental changes in temp hovmoeller
html 22e1d39 jens-daniel-mueller 2020-04-03 Build site.
Rmd 14a358c jens-daniel-mueller 2020-04-03 incremental running mean changes, error solved
html 114ccbc jens-daniel-mueller 2020-04-03 Build site.
Rmd 2c4b5b6 jens-daniel-mueller 2020-04-03 incremental changes based on smoothened timeseries
html da0e335 jens-daniel-mueller 2020-04-03 Build site.
Rmd 3a2b38f jens-daniel-mueller 2020-04-03 applied running mean to CT SST time series
html 37f88be jens-daniel-mueller 2020-04-03 Build site.
Rmd 570dcb2 jens-daniel-mueller 2020-04-03 applied running mean to CT SST time series
html 6617975 jens-daniel-mueller 2020-04-02 Build site.
Rmd ba45c29 jens-daniel-mueller 2020-04-02 ref date in delta T approach
html 415e32d jens-daniel-mueller 2020-04-02 Build site.
Rmd 093e4fd jens-daniel-mueller 2020-04-02 relabeled date_time as date_time_ID where appropiate
html 601dc73 jens-daniel-mueller 2020-04-02 Build site.
Rmd d4f6d34 jens-daniel-mueller 2020-04-02 MLD iCT: updated reference date and plot
html 9b0cb9e jens-daniel-mueller 2020-04-02 Build site.
Rmd 62fb894 jens-daniel-mueller 2020-04-02 corrected variable confusion in iCT MLD estimate
html 3e6995e jens-daniel-mueller 2020-04-02 Build site.
Rmd ee9f48e jens-daniel-mueller 2020-04-02 gt vs ts plots improved
html 6c2be48 jens-daniel-mueller 2020-04-02 Build site.
Rmd 614ab28 jens-daniel-mueller 2020-04-02 Comparison STD ts vs gt added
html cf75203 jens-daniel-mueller 2020-04-02 Build site.
Rmd b8b65b1 jens-daniel-mueller 2020-04-02 Comparison STD ts vs gt added
html 15d5bd9 jens-daniel-mueller 2020-04-02 Build site.
Rmd 7c57715 jens-daniel-mueller 2020-04-02 Windspeed plot moved to end
html e6b2f09 jens-daniel-mueller 2020-04-02 Build site.
Rmd 7ec8abc jens-daniel-mueller 2020-04-02 revised figures
html 4896558 jens-daniel-mueller 2020-04-02 Build site.
Rmd a7f8cec jens-daniel-mueller 2020-04-02 revised figures
html f322355 jens-daniel-mueller 2020-04-02 Build site.
Rmd c54fd0e jens-daniel-mueller 2020-04-02 GETM SurfaceAge included
html 624835e jens-daniel-mueller 2020-04-02 Build site.
Rmd a7ac65d jens-daniel-mueller 2020-04-02 BloomSail data 1-5m and sd in time series plots
html 26cf733 jens-daniel-mueller 2020-04-02 Build site.
Rmd 57b77af jens-daniel-mueller 2020-04-02 corrected Finnmaid lat borders and plotted fm track in map
html be5d8f5 jens-daniel-mueller 2020-04-01 Build site.
Rmd ccb509f jens-daniel-mueller 2020-04-01 Implemented delta T approach
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 a6c4c22 jens-daniel-mueller 2020-03-30 Build site.
html 80c78b3 jens-daniel-mueller 2020-03-30 Build site.
Rmd a52fa08 jens-daniel-mueller 2020-03-30 replaced gas flux page in CT dynamics, rebuild site
html 2494d0d jens-daniel-mueller 2020-03-24 Build site.
Rmd b3af732 jens-daniel-mueller 2020-03-24 cumulative changes
html 671b032 jens-daniel-mueller 2020-03-24 Build site.
Rmd 9e0c0d7 jens-daniel-mueller 2020-03-24 NCP MLD calculated
html 6d7422a jens-daniel-mueller 2020-03-24 Build site.
Rmd 5f33d21 jens-daniel-mueller 2020-03-24 NCP MLD calculated
html d0d5c9e jens-daniel-mueller 2020-03-24 Build site.
Rmd 1e2508a jens-daniel-mueller 2020-03-24 harmonized starting dates
html 487a505 jens-daniel-mueller 2020-03-23 Build site.
Rmd ca1591e jens-daniel-mueller 2020-03-23 delta CT vs delta SST
html 8029abb jens-daniel-mueller 2020-03-23 Build site.
Rmd 68cd650 jens-daniel-mueller 2020-03-23 FM CT calculation and plots
html d197f95 jens-daniel-mueller 2020-03-23 Build site.
Rmd 247cf5e jens-daniel-mueller 2020-03-23 included GETM read-in from Lara
html 247cf5e jens-daniel-mueller 2020-03-23 included GETM read-in from Lara
html 0c4d348 jens-daniel-mueller 2020-03-21 Build site.
Rmd 677a2fd jens-daniel-mueller 2020-03-21 GETM data and plots included
Rmd 0a46275 LSBurchardt 2020-03-21 #1 works if run chunk by chunk but not to knit…
html 5f8ca30 jens-daniel-mueller 2020-03-20 Build site.
html 2a20453 jens-daniel-mueller 2020-03-20 Build site.
Rmd ae57412 jens-daniel-mueller 2020-03-19 Prepared for lara to add GETM code
html 473ab25 jens-daniel-mueller 2020-03-19 Build site.
Rmd 7c712e3 jens-daniel-mueller 2020-03-19 Navbar shortened

library(tidyverse)
library(ncdf4)
library(vroom)
library(lubridate)
library(here)
library(seacarb)
library(oce)
library(patchwork)
library(zoo)
library(metR)
# route
select_route <- "E"

# latitude limits
low_lat <- 57.3
high_lat <- 57.5

#depth range to subset GETM 3d files
d1_shallow <- 0
d1_deep <- 25

# date limits
start_date <- "2018-06-20"
end_date <- "2018-08-25"

fixed_values <- 
  read_csv(here::here("Data/_summarized_data_files", "tb_fix.csv"))

1 Approach

In order to test how (and how well) the depth-integrated CT estimates can be reproduced if only surface CO2 data from VOS Finnamaid and hydrographical GETM model date were available, two reconstruction approaches were tested:

  1. MLD: Integration of surface observation across the MLD, assuming homogenious vertical patterns
  2. Temperature: Vertical reconstruction of incremental CT changes based on profiles of incremental changes in temperature

2 GETM

The following information refer to regional mean values modeled along the Finnmaid track east and within the BloomSail field work area (57.3 - 57.5 N).

2.1 STD Profiles

Mean daily salinity and temperature profiles were extracted from 3d GETM data (vertically resolved transects).

nc <- nc_open(here::here("data/GETM", "Finnmaid.E.3d.2018.nc"))
#print(nc$var)

lat <- ncvar_get(nc, "latc")

time_units <- nc$dim$time$units %>%     #we read the time unit from the netcdf file to calibrate the time 
    substr(start = 15, stop = 33) %>%   #calculation, we take the relevant information from the string
    ymd_hms()                           # and transform it to the right format
t <- time_units + ncvar_get(nc, "time") # read time vector
rm(time_units)

d <- ncvar_get(nc, "zax") # read depths vector

for (var_3d in c("salt", "temp", "SurfaceAge")) {
  
array <- ncvar_get(nc, var_3d) # store the data in a 3-dimensional array
#dim(array) # should be 3d with dimensions: 544 coordinates, 51 depths, and number of days of month

fillvalue <- ncatt_get(nc, var_3d, "_FillValue")

# Working with the data
array[array == fillvalue$value] <- NA

    for (i in seq(1,length(t),1)){
      
      # i <- 3
      array_slice <- array[, , i] # slices data from one day
      
      array_slice_df <- as.data.frame(t(array_slice))
      array_slice_df <- as_tibble(array_slice_df)
      
      gt_3d_part <- array_slice_df %>%
        set_names(as.character(lat)) %>%
        mutate(dep = -d) %>%
        gather("lat", "value", 1:length(lat)) %>%
        mutate(lat = as.numeric(lat)) %>%
        filter(lat > low_lat, lat < high_lat,
               dep >= d1_shallow, dep <= d1_deep) %>%
        #summarise_all("value") %>%
        mutate(var = var_3d,
               date_time=t[i]) %>% 
        dplyr::select(date_time, dep, value, var) #%>% 
        #filter(date_time >= start_date, date_time <= end_date)

      
      if (exists("gt_3d")) {
        gt_3d <- bind_rows(gt_3d, gt_3d_part)
        } else {gt_3d <- gt_3d_part}
      
  rm(array_slice, array_slice_df, gt_3d_part)
      
    }
rm(array, fillvalue)

}

nc_close(nc)
rm(nc)

gt_3d <- gt_3d %>% 
  filter(date_time >= start_date & date_time <= end_date) %>% 
  group_by(dep,var,date_time ) %>% 
  summarise_all(list(value=~mean(.,na.rm=TRUE))) %>%
  ungroup()

gt_3d %>% 
  vroom_write((here::here("data/_summarized_data_files", file = "gt_3d_long.csv")))


rm(gt_3d, d1_deep, d1_shallow, i, lat, d, t, var_3d)

Seawater density was calculated according to TEOS-10.

gt_3d_long <- 
  read_tsv((here::here("data/_summarized_data_files", file = "gt_3d_long.csv")))

gt_3d <- gt_3d_long %>% 
  pivot_wider(values_from = value, names_from = var) %>% 
  mutate(rho = swSigma(salinity = salt, temperature = temp, pressure = dep/10))
gt_3d_long <- gt_3d %>% 
  pivot_longer(c(salt, SurfaceAge, temp, rho), values_to = "value", names_to = "var")

gt_3d_long %>% 
  ggplot(aes(value, dep,
             col=date_time,
             group=date_time))+
  geom_path()+
  scale_y_reverse(expand = c(0,0))+
  scale_color_viridis_c(name="Date", trans = "time")+
  facet_wrap(~var, scales = "free_x", ncol = 2)

2.1.1 Comparison BloomSail

Vertical, 1m-gridded BloomSail CTD profiles were used for comparison with GETM results. Merging both data sets required the BloomSail profiles to be shifted upward by 0.5m. Note that neither sampling location nor time match exactly.

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

ts_profiles_ID <- ts_profiles_ID %>% 
  mutate(rho = swSigma(salinity = sal, temperature = tem, pressure = dep/10),
         dep = dep - 0.5)

GETM results were linearly interpolated to the mean BloomSail time stamp.

ts_gt_3d <- full_join(gt_3d %>% select(date_time, dep, sal = salt, tem = temp, rho),
                      ts_profiles_ID %>% select(date_time = date_time_ID,
                                                dep, sal, tem, rho),
                      by = c("date_time", "dep"), suffix=c("_gt", "_ts"))

ts_gt_3d <- ts_gt_3d %>% 
  arrange(date_time) %>% 
  group_by(dep) %>% 
  mutate(tem_gt = approxfun(date_time, tem_gt)(date_time),
         sal_gt = approxfun(date_time, sal_gt)(date_time),
         rho_gt = approxfun(date_time, rho_gt)(date_time)) %>% 
  ungroup() %>% 
  drop_na()
ts_gt_3d_long <- ts_gt_3d %>% 
  pivot_longer(3:8, values_to = "value", names_to = c("var", "source"), names_sep = "_")

ts_gt_3d_long %>% 
  ggplot(aes(value, dep,
             col=date_time,
             group=date_time))+
  geom_path()+
  scale_y_reverse(expand = c(0,0), name="Depth (m)")+
  scale_color_viridis_c(name="Date", trans = "time")+
  facet_grid(source~var, scales = "free_x")
STD profiles modeled with GETM (upper panels, gt) and measured during BloomSail campaign (lower panels, ts)

STD profiles modeled with GETM (upper panels, gt) and measured during BloomSail campaign (lower panels, ts)

ts_gt_3d <- ts_gt_3d_long %>% 
  pivot_wider(values_from = "value", names_from = "source") %>% 
  mutate(value_diff = gt - ts)

ts_gt_3d %>% 
  ggplot(aes(value_diff, dep,
             col=date_time,
             group=date_time))+
  geom_vline(xintercept = 0, col="red")+
  geom_path()+
  scale_y_reverse(expand = c(0,0), name="Depth (m)")+
  scale_color_viridis_c(name="Date", trans = "time")+
  facet_grid(.~var, scales = "free_x")+
  labs(x="Difference GETM (gt) - Bloomsail (ts)")

2.1.2 Heat penetration depth

As an alternative approach to the integration over the MLD or the reconstruction of CT profiles, we can estimate the mean penetration depth of the warming signal, which was defined the surface change in temperature devided by the integrated change in seawater temperature across depth.

tem_diff_surface <- ts_gt_3d_long %>% 
  filter(dep < 6,
         var=="tem") %>% 
  select(date_time_ID = date_time, source, tem=value) %>% 
  group_by(date_time_ID, source) %>% 
  summarise_all(mean, na.rm=TRUE) %>% 
  ungroup() 

tem_diff_surface <- tem_diff_surface %>% 
  group_by(source) %>% 
  arrange(date_time_ID) %>% 
  mutate(tem_diff_surface = tem - lag(tem)) %>% 
  ungroup() %>% 
  select(-tem)

ts_gt_3d_long <- ts_gt_3d_long %>% 
  filter(var=="tem") %>% 
  select(date_time_ID = date_time, source, dep, tem=value) %>% 
  group_by(source, dep) %>% 
  arrange(date_time_ID) %>% 
  mutate(tem_diff = tem - lag(tem)) %>% 
  ungroup() %>% 
  select(-tem)

ts_gt_3d_long <- full_join(ts_gt_3d_long, tem_diff_surface) 
rm(tem_diff_surface)

tem_depth <- ts_gt_3d_long %>%
  filter(dep < 18) %>% 
  group_by(date_time_ID, source) %>% 
  summarise(tem_diff_int = sum(tem_diff),
            tem_diff_surface = mean(tem_diff_surface),
            tem_depth = tem_diff_int/tem_diff_surface) %>% 
  ungroup()

tem_depth %>% 
  ggplot(aes(date_time_ID, tem_diff_surface, col=source))+
  geom_hline(yintercept = 0)+
  geom_line()+
  geom_point()

tem_depth %>% 
  ggplot(aes(date_time_ID, tem_diff_int, col=source))+
  geom_hline(yintercept = 0)+
  geom_line()+
  geom_point()

tem_depth %>% 
  ggplot(aes(date_time_ID, tem_depth, col=source))+
  geom_hline(yintercept = 0)+
  geom_line()+
  geom_point()+
  scale_y_reverse()

rm(ts_gt_3d, ts_gt_3d_long, ts_profiles_ID)

2.2 Mixed layer depth

Mean mixed/mixing layer depth estimates based on sewater density and windspeed were extracted from 3h GETM surface data.

nc_2d <- nc_open(here("data/GETM", "Finnmaid.E.2d.2018.nc"))
#print(nc_2d)

lat <- ncvar_get(nc_2d, "latc")

time_units <- nc_2d$dim$time$units %>%     #we read the time unit from the netcdf file to calibrate the time 
    substr(start = 15, stop = 33) %>%   #calculation, we take the relevant information from the string
    ymd_hms()                           # and transform it to the right format
t <- time_units + ncvar_get(nc_2d, "time") # read time vector
rm(time_units)

for (var in names(nc_2d$var)[c(3,4,6:12)]) {
  
#var <- "mld_rho"

array <- ncvar_get(nc_2d, var) # store the data in a 3-dimensional array
fillvalue <- ncatt_get(nc_2d, var, "_FillValue")
array[array == fillvalue$value] <- NA

array <- as.data.frame(t(array), xy=TRUE)
array <- as_tibble(array)
      
  gt_2d_part <- array %>%
  set_names(as.character(lat)) %>%
  mutate(date_time = t) %>%
  filter(date_time >= start_date & date_time <= end_date) %>% 
  gather("lat", "value", 1:length(lat)) %>%
  mutate(lat = as.numeric(lat)) %>%
  filter(lat > low_lat, lat<high_lat) %>%
  select(-lat) %>% 
  group_by(date_time) %>% 
  summarise_all(list(value=~mean(.,na.rm=TRUE))) %>%
  ungroup() %>% 
  mutate(var = var)
     
  if (exists("gt_2d")) {
    gt_2d <- bind_rows(gt_2d, gt_2d_part)
    } else {gt_2d <- gt_2d_part} 

rm(array, fillvalue, gt_2d_part)

}

nc_close(nc_2d)
rm(nc_2d)

gt_2d <- gt_2d %>% 
  mutate(value = round(value, 3)) %>% 
  pivot_wider(values_from = value, names_from = var) %>% 
  mutate(U_10 = round(sqrt(u10^2 + v10^2), 3)) %>% 
  select(-c(u10, v10))


gt_2d %>% 
  vroom_write((here::here("data/_summarized_data_files", file = "gt_2d.csv")))

rm(t, var, gt_2d, lat)

2.2.1 Hovmoeller Plots

gt_2d <- 
  read_tsv((here::here("data/_summarized_data_files", file = "gt_2d.csv")))

gt_2d_daily <- gt_2d %>% 
  mutate(day = yday(date_time)) %>% 
  group_by(day) %>% 
  summarise_all(list(~mean(.,na.rm=TRUE))) %>%
  ungroup() %>% 
  select(-day)

p_sal <- gt_3d %>% 
  ggplot()+
  geom_raster(aes(date_time, dep, fill=salt))+
  geom_vline(data=fixed_values, aes(xintercept = start))+
  geom_vline(data=fixed_values, aes(xintercept = end))+
  scale_fill_viridis_c(name="Salinity ", direction = -1)+
  scale_y_reverse()+
  coord_cartesian(expand = 0)+
  labs(y="Depth [m]")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())+
  geom_line(data= gt_2d_daily,
            aes(x = date_time, y = mld_rho), color = "white")


p_tem <- gt_3d %>% 
  ggplot()+
  geom_raster(aes(date_time, dep, fill=temp))+
  geom_vline(data=fixed_values, aes(xintercept = start))+
  geom_vline(data=fixed_values, aes(xintercept = end))+
  scale_fill_viridis_c(name="Temperature (°C)", option = "B")+
  scale_y_reverse()+
  coord_cartesian(expand = 0)+
  labs(y="Depth [m]", x="")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())+
  geom_line(data= gt_2d_daily,
            aes(x = date_time, y = mld_rho), color = "white")

p_rho <- gt_3d %>% 
  ggplot()+
  geom_raster(aes(date_time, dep, fill=rho))+
  geom_vline(data=fixed_values, aes(xintercept = start))+
  geom_vline(data=fixed_values, aes(xintercept = end))+
  scale_fill_viridis_c(name="d Rho (kg/m^3)", direction = -1)+
  scale_y_reverse()+
  coord_cartesian(expand = 0)+
  labs(y="Depth [m]", x="")+
  theme(axis.title.x = element_blank())+
  geom_line(data= gt_2d_daily,
            aes(x = date_time, y = mld_rho), color = "white")

p_age <- gt_3d %>% 
  ggplot()+
  geom_raster(aes(date_time, dep, fill=SurfaceAge))+
  geom_vline(data=fixed_values, aes(xintercept = start))+
  geom_vline(data=fixed_values, aes(xintercept = end))+
  scale_fill_viridis_c(name="SurfaceAge (d)", direction = -1, trans = "sqrt")+
  scale_y_reverse()+
  coord_cartesian(expand = 0)+
  labs(y="Depth [m]", x="")+
  theme(axis.title.x = element_blank())+
  geom_line(data= gt_2d_daily,
            aes(x = date_time, y = mld_rho), color = "white")

p_sal / p_tem / p_rho / p_age

rm(p_sal, p_tem, p_rho)

2.2.2 Test calculation

Mean mixed layer depth estimates were also calculated for a range of density threshold criteria, Rho lim, from sewater density based on daily mean GETM STD profiles.

gt_3d_MLD <- expand_grid(gt_3d, rho_lim = seq(0.1,0.5,0.1))

gt_3d_MLD <- gt_3d_MLD %>% 
  arrange(dep) %>% 
  group_by(date_time, rho_lim) %>% 
  mutate(d_rho = rho - first(rho)) %>% 
  filter(d_rho > rho_lim) %>% 
  summarise(MLD = min(dep)) %>% 
  ungroup() %>% 
  mutate(rho_lim = as.factor(rho_lim))

2.2.3 Time series

gt_2d_daily_long <- gt_2d_daily %>% 
  pivot_longer(4:8, names_to = "var", values_to = "value")

p_MLD_gt <- gt_2d_daily_long %>% 
  ggplot()+
  geom_rect(data = fixed_values, aes(xmin=start, xmax=end, ymin=-Inf, ymax=Inf), alpha=0.2)+
  geom_hline(yintercept = 0)+
  geom_line(aes(date_time, value, col=var))+
  scale_y_reverse(limits = c(25,0))+
  scale_color_brewer(palette = "Set1", name="GETM variable")+
  labs(x="", y="MLD (m)")+
  theme(axis.title.x = element_blank())

p_MLD_recalc <- gt_3d_MLD %>% 
  ggplot()+
  geom_rect(data = fixed_values, aes(xmin=start, xmax=end, ymin=-Inf, ymax=Inf), alpha=0.2)+
  geom_hline(yintercept = 0)+
  geom_line(aes(date_time, MLD, col=rho_lim))+
  scale_y_reverse(limits = c(25,0))+
  scale_color_viridis_d(name="Rho lim")+
  labs(x="", y="MLD (m)")

p_MLD_gt / p_MLD_recalc

rm(p_MLD_gt, p_MLD_recalc)

3 Finnmaid

3.1 Read data

Finnmaid data, including reconstructed data during LICOS operation failure.

fm <-
 read_csv(here::here("Data/_summarized_data_files",
                      "Finnmaid.csv"))

fm <- fm %>% 
  filter(Area == "BS",
         date > start_date,
         date < end_date) %>% 
  select(-c(Lon, Lat, patm, Teq, xCO2, route, Area)) %>% 
  mutate(ID = as.factor(ID)) %>% 
  rename(tem=Tem,
         sal=Sal,
         date_time = date)

3.2 CT calculation

Calculate based on fixed AT and salinity mean values.

fm <- fm %>% 
  mutate(CT = carb(24,
                   var1=pCO2,
                   var2=fixed_values$AT*1e-6,
                   S=fixed_values$sal,
                   T=tem,
                   k1k2="m10", kf="dg", ks="d", gas="insitu")[,16]*1e6)

3.3 Timeseries

Calculate regional mean and sd values for each crossing of the area.

fm_ID <- fm %>% 
  pivot_longer(c(pCO2, sal, tem, cO2, CT), values_to = "value", names_to = "var") %>% 
  group_by(ID) %>% 
  mutate(date_time_ID = mean(date_time)) %>%
  select(-date_time) %>% 
  ungroup() %>% 
  group_by(ID, date_time_ID, sensor, var) %>% 
  summarise_all(list(~mean(.), ~sd(.), ~min(.), ~max(.)), na.rm=TRUE) %>%
  ungroup() %>% 
  rename(value=mean)

Read BloomSail profile data from 1-5m to fill observational gap of Finnmaid date in second half of June.

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

ts_profiles_ID_long_surface <- ts_profiles_ID_long %>% 
  filter(dep > 1, dep < 5) %>% 
  mutate(ID = as.factor(ID)) %>% 
  select(-c(sign, value_cum_sign)) %>% 
  group_by(ID, date_time_ID, var) %>% 
  summarise_all(list(~mean(.)), na.rm = TRUE) %>% 
  ungroup()
fm_ID %>% 
  ggplot()+
  geom_rect(data = fixed_values, aes(xmin=start, xmax=end, ymin=-Inf, ymax=Inf), alpha=0.2)+
  geom_path(aes(x=date_time_ID, y=value))+
  #geom_ribbon(aes(x=date_time, y=value, ymax=max, ymin=min, fill="Finnmaid"), alpha=0.3)+
  geom_ribbon(aes(x=date_time_ID, y=value, ymax=value+sd, ymin=value-sd, fill="Finnmaid"), alpha=0.3)+
  geom_ribbon(data = ts_profiles_ID_long_surface,
             aes(x=date_time_ID, ymin=value-sd, ymax=value+sd, fill="BloomSail"), alpha=0.3)+
  geom_point(aes(x=date_time_ID, y=value, col=sensor))+
  geom_point(data = ts_profiles_ID_long_surface,
             aes(x=date_time_ID, y=value, col="BloomSail"))+
  geom_line(data = ts_profiles_ID_long_surface,
             aes(x=date_time_ID, y=value, col="BloomSail"))+
  facet_grid(var~., scales = "free_y")+
  scale_color_brewer(palette = "Set1")+
  scale_fill_brewer(palette = "Set1", name="+/- SD")

3.4 Missing observations

The observational gaps in the Finnmaid SST and CT time series were filled with two BloomSail observations. The time series was restricted to the period where BloomSail observations are available.

ts_gap <- ts_profiles_ID_long_surface %>% 
  filter(ID %in% c("180718", "180723"),
         var %in% c("tem", "CT")) %>% 
  select(date_time_ID, ID, var, value = value) %>% 
  mutate(sensor = "BloomSail")

fm_ts_ID <- full_join(fm_ID, ts_gap) %>% 
  arrange(date_time_ID) %>% 
  select(-sd) %>% 
  filter(var %in% c("tem", "CT")) %>% 
  mutate(period = "BloomSail",
         period = if_else(date_time_ID < fixed_values$start, "pre-BloomSail", period),
         period = if_else(date_time_ID > fixed_values$end, "post-BloomSail", period))

fm_ts_ID %>% 
  ggplot()+
  geom_rect(data = fixed_values,
            aes(xmin=start, xmax=end, ymin=-Inf, ymax=Inf), alpha=0.2)+
  geom_path(aes(date_time_ID, value, col=period))+
  geom_point(aes(date_time_ID, value, col=period))+
  facet_grid(var~., scales = "free_y")+
  scale_color_brewer(palette = "Set1")

fm_ts_ID <- fm_ts_ID %>% 
  filter(period == "BloomSail") %>% 
  select(-period)

rm(fm_ID, fm, ts_gap, ts_profiles_ID_long_surface)

4 iCT

4.1 MLD approach

Use dCT from Finnmaid and MLD from GETM and calculate iCT as their product.

iCT_MLD <- fm_ts_ID %>%
  select(date_time_ID, var, value) %>% 
  pivot_wider(values_from = value, names_from = var) %>% 
  rename(SST = tem)

iCT_MLD <- full_join(iCT_MLD,
                     gt_2d_daily %>% 
                       select(-c(SSS, SST, U_10)) %>% 
                       rename(date_time_ID = date_time))

iCT_MLD <- iCT_MLD %>% 
  pivot_longer(cols = 4:8, values_to = "MLD", names_to = "var") %>% 
  arrange(date_time_ID) %>%
  group_by(var) %>% 
  mutate(MLD = na.approx(MLD)) %>%
  ungroup()

iCT_MLD <- iCT_MLD %>% 
  drop_na() %>% 
  group_by(var) %>% 
  arrange(date_time_ID) %>% 
  mutate(date_time_ID_diff = as.numeric(date_time_ID - lag(date_time_ID)),
         date_time_ID_ref  = date_time_ID - (date_time_ID - lag(date_time_ID))/2,
         CT_diff = CT - lag(CT),
         SST_diff = SST - lag(SST),
         CT_i_diff = CT_diff * MLD / 1000,
         CT_i_cum = cumsum(replace_na(CT_i_diff, 0))) %>% 
  ungroup()

4.1.1 Incremental and cumulative timeseries

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

iCT_MLD %>% 
  ggplot()+
  geom_hline(yintercept = 0)+
  geom_point(aes(date_time_ID,  0), shape=21)+
  geom_col(aes(date_time_ID_ref, CT_i_diff, fill= var),
           col="black", position = "dodge", alpha = 0.5)+
  geom_line(aes(date_time_ID,  CT_i_cum, 
             col= var))+
  scale_y_continuous(breaks = seq(-100, 100, 0.2))+
  scale_fill_brewer(palette = "Set1", name="Incremental")+
  scale_color_brewer(palette = "Set1", name="Cumulative")+
  labs(y="integrated CT changes [mol/m2]", x="date")

4.2 delta T appraoch

As primary production (negative changes in CT) and increase in seawater temperature have a common driver (light), the relation between both changes was investigated and will be used to reconstruct changes in CT throughout the water column.

The following analysis is restricted to the BloomSail period.

4.2.1 SST time series

fm_ts_ID %>% 
  filter(var == "tem") %>% 
  ggplot()+
  geom_rect(data = fixed_values, aes(xmin=start, xmax=end, ymin=-Inf, ymax=Inf), alpha=0.2)+
  geom_path(aes(x=date_time_ID, y=value, col="Finnmaid"))+
  geom_point(aes(x=date_time_ID, y=value, col="Finnmaid"))+
  geom_path(data = gt_2d, aes(x=date_time, y=SST, col="GETM 2d, 3h"))+
  geom_path(data = gt_2d_daily, aes(x=date_time, y=SST, col="GETM 2d, daily"))+
  geom_path(data = gt_3d %>% filter(dep == 3),
            aes(x=date_time, y=temp, col="GETM 3d, 3m"))+
  scale_color_brewer(palette = "Set1", name="")+
  labs(x="", y="SST (°C)")

4.2.2 dCT vs dSST

To investigate the change of surface CT with SST, we merge daily mean 2d GETM and Finnmaid data. GETM observations were linearly interpolated to match the time of Finnmaid observations.

fm_ts_ID_wide <- fm_ts_ID %>% 
  filter(var %in% c("CT")) %>% 
  select(date_time_ID, var, value) %>% 
  pivot_wider(values_from = value, names_from = var)

fm_gt_3d <- expand_grid(fm_ts_ID_wide, dep = unique(gt_3d$dep))
rm(fm_ts_ID_wide)

fm_gt_3d <- full_join(gt_3d %>% select(date_time_ID = date_time, dep, tem = temp), 
                      fm_gt_3d)
fm_gt_3d <- fm_gt_3d %>% 
  arrange(date_time_ID) %>% 
  group_by(dep) %>% 
  mutate(tem = approxfun(date_time_ID, tem)(date_time_ID)) %>% 
  ungroup() %>% 
  arrange(dep) %>% 
  filter(!is.na(CT))
CT_tem <- CT_tem %>% 
  arrange(date_time_ID) %>%
  mutate(CT = na.approx(CT, na.rm = FALSE),
         FM = na.approx(FM, na.rm = FALSE)) %>% 
  drop_na()

rolling_mean <- rollify(~mean(.x, na.rm = TRUE), window = 3)

CT_tem <- CT_tem %>% 
  mutate(CT_rm = rolling_mean(CT) %>% lead(n = 1),
         FM_rm = rolling_mean(FM) %>% lead(n = 1),
         gt_rm = rolling_mean(gt) %>% lead(n = 1))
p_SST <- CT_tem %>% 
  ggplot()+
  geom_rect(data = fixed_values, aes(xmin=start, xmax=end, ymin=-Inf, ymax=Inf), alpha=0.2)+
  geom_point(aes(date_time_ID, FM, col="FM"))+
  geom_path(aes(date_time_ID, FM_rm, col="FM"))+
  geom_point(aes(date_time_ID, gt, col="gt"))+
  geom_path(aes(date_time_ID, gt_rm, col="gt"))+
  scale_color_brewer(palette = "Set1", name="")+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())

p_CT <- CT_tem %>% 
  ggplot()+
  geom_rect(data = fixed_values, aes(xmin=start, xmax=end, ymin=-Inf, ymax=Inf), alpha=0.2)+
  geom_point(aes(date_time_ID, CT, col="FM"))+
  geom_path(aes(date_time_ID, CT_rm, col="FM"))+
  scale_color_brewer(palette = "Set1", name="")+
  theme(axis.title.x = element_blank())

p_SST / p_CT

CT_tem <- CT_tem %>% 
  select(-c(CT, FM, gt)) %>% 
  rename(CT = CT_rm,
         FM = FM_rm,
         gt = gt_rm)
CT_tem <- fm_gt_3d %>% 
  filter(dep == 3) %>% 
  arrange(date_time_ID) %>% 
  mutate(CT_diff = CT - lag(CT),
         SST_diff = tem - lag(tem)) %>% 
  select(-tem)


CT_tem %>% 
  ggplot()+
  geom_hline(yintercept = 0)+
  geom_vline(xintercept = 0)+
  geom_smooth(aes(SST_diff, CT_diff), method = "lm", se=FALSE)+
  geom_point(aes(SST_diff, CT_diff, fill=date_time_ID), shape=21)+
  scale_fill_viridis_c(trans = "time", name="Date")

CT_tem <- CT_tem %>% 
  mutate(factor = CT_diff/SST_diff,
         factor = if_else(is.na(factor), 0, factor))

Time series of incremental changes in CT and SST help to identify measurement days during which changes in both parameters deviate from the expected correlation (factor).

CT_tem_long <- CT_tem %>% 
  pivot_longer(c(CT_diff, SST_diff, factor), values_to = "value", names_to = "var")#

CT_tem_long %>% 
  ggplot(aes(date_time_ID, value))+
  geom_hline(yintercept = 0)+
  geom_point()+
  geom_line()+
  scale_color_brewer(palette = "Set1")+
  facet_grid(var~., scales = "free_y")+
  theme(axis.title.x = element_blank())

The ratio of surface changes in CT with SST based on GETM SST was used.

CT_tem <- expand_grid(CT_tem %>% select(date_time_ID, factor),
                      dep = unique(fm_gt_3d$dep))

fm_gt_3d <- full_join(fm_gt_3d %>% select(date_time_ID, dep, tem), 
                      CT_tem %>%  select(date_time_ID, dep, factor))
fm_gt_3d <- fm_gt_3d %>% 
  group_by(dep) %>% 
  arrange(date_time_ID) %>% 
  mutate(tem_diff = tem - lag(tem)) %>% 
  ungroup() %>% 
  mutate(CT_diff = tem_diff * factor) %>% 
  select(-factor)

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

fm_gt_3d <- fm_gt_3d %>% 
  group_by(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,
         CT_diff_daily = CT_diff / date_time_ID_diff,
         CT_cum = cumsum(replace_na(CT_diff, 0))) %>% 
  ungroup()

4.2.3 Profiles of incremental changes

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

fm_gt_3d %>% 
  arrange(dep) %>% 
  ggplot(aes(CT_diff_daily, dep, col=date_time_ID, group=date_time_ID))+
  geom_vline(xintercept = 0)+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_c(trans = "time")+
  labs(x="Change of CT inbetween cruises per day")

fm_gt_3d %>% 
  arrange(dep) %>% 
  ggplot(aes(tem_diff, dep, col=date_time_ID, group=date_time_ID))+
  geom_vline(xintercept = 0)+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_c(trans = "time")+
  labs(x="Change of temperature inbetween cruises per day")

4.2.4 Profiles of cumulative changes

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

fm_gt_3d %>% 
  arrange(dep) %>% 
  ggplot(aes(CT_cum, dep, col=date_time_ID, group=date_time_ID))+
  geom_vline(xintercept = 0)+
  geom_point()+
  geom_path()+
  scale_y_reverse()+
  scale_color_viridis_c(trans = "time")+
  labs(x="Cumulative change of CT")

4.2.5 Hovmoeller daily changes

Hoevmoeller plots were generated for the reconstructed daily and cumulative changes in CT. Absolute values are not reproducible with this approach.

bin_tem <- 0.25

fm_gt_3d %>%
  filter(dep < 26) %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID_ref, y=dep, z=tem_diff),
                    breaks = MakeBreaks(bin_tem),
                    col="black")+
  geom_point(aes(x=date_time_ID, y=c(25)), size=3, shape=24, fill="white")+
  scale_fill_divergent(breaks = MakeBreaks(bin_tem),
                       guide = "colorstrip",
                       name="Tem (°C)")+
  scale_y_reverse()+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())
Hovmoeller plots of modelled daily changes in temperature.

Hovmoeller plots of modelled daily changes in temperature.

rm(bin_tem)
bin_CT <- 10

fm_gt_3d %>%
  filter(dep < 15) %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID_ref, y=dep, z=CT_diff_daily),
                    breaks = MakeBreaks(bin_CT),
                    col="black")+
  geom_point(aes(x=date_time_ID, y=c(14)), size=3, shape=24, fill="white")+
  scale_fill_divergent(breaks = MakeBreaks(bin_CT),
                       guide = "colorstrip",
                       name="CT (µmol/kg)")+
  scale_y_reverse()+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())
Hovmoeller plots of daily reconstructed changes in C~T~.

Hovmoeller plots of daily reconstructed changes in CT.

rm(bin_CT)

4.2.6 Hovmoeller cumulative changes

bin_CT <- 30

fm_gt_3d %>%
  filter(dep < 15) %>% 
  ggplot()+
  geom_contour_fill(aes(x=date_time_ID, y=dep, z=CT_cum),
                    breaks = MakeBreaks(bin_CT),
                    col="black")+
  geom_point(aes(x=date_time_ID, y=c(14)), size=3, shape=24, fill="white")+
  scale_fill_divergent(breaks = MakeBreaks(bin_CT),
                       guide = "colorstrip",
                       name="CT (µmol/kg)")+
  scale_y_reverse()+
  theme_bw()+
  labs(y="Depth (m)")+
  coord_cartesian(expand = 0)+
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank())
Hovmoeller plots of cumulative reconstructed changes in C~T~.

Hovmoeller plots of cumulative reconstructed changes in CT.

rm(bin_CT)

4.2.7 iCT time series

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

iCT_dT <- fm_gt_3d %>% 
  filter(dep < 10) %>% 
  group_by(date_time_ID, date_time_ID_ref) %>%
  summarise(CT_i_diff = sum(CT_diff)/1000,
            CT_i_cum = sum(CT_cum)/1000) %>% 
  ungroup()


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

4.3 Heat penetration depth

As an alternative approach to the integration over the MLD or the reconstruction of CT profiles, we can estimate the mean penetration depth of the warming signal, which was defined the surface change in temperature devided by the integrated change in seawater temperature across depth.

tem_diff_surface <- fm_gt_3d %>% 
  filter(dep < 6) %>% 
  select(date_time_ID, tem_diff_surface=tem_diff) %>% 
  group_by(date_time_ID) %>% 
  summarise_all(mean, na.rm=TRUE) %>% 
  ungroup()

fm_gt_3d <- full_join(fm_gt_3d, tem_diff_surface) 
rm(tem_diff_surface)

max_date_time_ID <- fm_ts_ID %>%
  filter(var == "CT") %>% 
  slice(which.min(value)) %>% 
  pull(date_time_ID)

tem_depth <- fm_gt_3d %>%
  filter(dep < 18) %>% 
  group_by(date_time_ID) %>% 
  summarise(tem_diff_int = sum(tem_diff),
            tem_diff_surface = mean(tem_diff_surface),
            tem_depth = tem_diff_int/tem_diff_surface) %>% 
  ungroup()

mean_heat_pen_depth <- tem_depth %>% 
  filter(date_time_ID <= max_date_time_ID) %>% 
  summarise(mean(tem_depth, na.rm = TRUE)) %>% 
  pull()

tem_depth %>% 
  ggplot(aes(date_time_ID, tem_depth))+
  geom_hline(yintercept = 0)+
  geom_hline(yintercept = mean_heat_pen_depth)+
  geom_vline(xintercept = max_date_time_ID)+
  geom_line()+
  geom_point()+
  scale_y_reverse()+
  scale_x_datetime(breaks = "week",
                   date_labels = "%b %d")

iCT_zeff <- fm_ts_ID %>%
  select(date_time_ID, var, value) %>% 
  pivot_wider(values_from = value, names_from = var) %>% 
  rename(SST = tem)

iCT_zeff <- iCT_zeff %>% 
  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,
         CT_diff = CT - lag(CT),
         SST_diff = SST - lag(SST),
         CT_i_diff = CT_diff * mean_heat_pen_depth / 1000,
         CT_i_cum = cumsum(replace_na(CT_i_diff, 0)))
iCT_zeff %>% 
  ggplot()+
  geom_hline(yintercept = 0)+
  geom_point(aes(date_time_ID,  0), shape=21)+
  geom_col(aes(date_time_ID_ref, CT_i_diff),
           position = "dodge", alpha=0.3)+
  geom_line(aes(date_time_ID, CT_i_cum))+
  scale_color_viridis_d(name="Depth limit (m)")+
  scale_fill_viridis_d(name="Depth limit (m)")+
  labs(y="iCT [mol/m2]", x="")+
  theme_bw()

5 Open tasks / questions

  • Can delta T approach be improved by:
    • Using a mean CT/SST factor -> not meaningful, because it assumes steady relation between dCT and dT
    • Using the cumulative values at iCT min
  • Plot cumulative changes in GETM temperature: Profile + Hovmoeller

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] metR_0.6.0      zoo_1.8-7       patchwork_1.0.0 seacarb_3.2.13 
 [5] oce_1.2-0       gsw_1.0-5       testthat_2.3.2  here_0.1       
 [9] lubridate_1.7.4 vroom_1.2.0     ncdf4_1.17      forcats_0.5.0  
[13] stringr_1.4.0   dplyr_0.8.5     purrr_0.3.3     readr_1.3.1    
[17] tidyr_1.0.2     tibble_3.0.0    ggplot2_3.3.0   tidyverse_1.3.0
[21] 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       splines_3.6.3      hms_0.5.3          rvest_0.3.5       
 [9] tidyselect_1.0.0   bit_1.1-15.2       viridisLite_0.3.0  colorspace_1.4-1  
[13] lattice_0.20-41    R6_2.4.1           rlang_0.4.5        fansi_0.4.1       
[17] broom_0.5.5        xfun_0.12          dbplyr_1.4.2       modelr_0.1.6      
[21] withr_2.1.2        git2r_0.26.1       ellipsis_0.3.0     htmltools_0.4.0   
[25] assertthat_0.2.1   bit64_0.9-7        rprojroot_1.3-2    digest_0.6.25     
[29] lifecycle_0.2.0    Matrix_1.2-18      haven_2.2.0        rmarkdown_2.1     
[33] sp_1.4-1           compiler_3.6.3     cellranger_1.1.0   pillar_1.4.3      
[37] scales_1.1.0       backports_1.1.5    generics_0.0.2     jsonlite_1.6.1    
[41] httpuv_1.5.2       pkgconfig_2.0.3    rstudioapi_0.11    munsell_0.5.0     
[45] plyr_1.8.6         highr_0.8          httr_1.4.1         tools_3.6.3       
[49] grid_3.6.3         nlme_3.1-145       data.table_1.12.8  gtable_0.3.0      
[53] checkmate_2.0.0    mgcv_1.8-31        DBI_1.1.0          cli_2.0.2         
[57] readxl_1.3.1       yaml_2.2.1         crayon_1.3.4       RColorBrewer_1.1-2
[61] farver_2.0.3       later_1.0.0        promises_1.1.0     fs_1.4.0          
[65] vctrs_0.2.4        memoise_1.1.0      glue_1.3.2         evaluate_0.14     
[69] labeling_0.3       reprex_0.3.0       stringi_1.4.6