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1 Libraries

Loading libraries specific to the the analysis performed in this section.

library(lubridate)

2 Read files

Main data source for this project is GLODAPv2.2020_Merged_Master_File.csv downloaded from glodap.info in June 2020.

GLODAP <-
  read_csv(
    here::here(
      "data/input/GLODAPv2_2020",
      "GLODAPv2.2020_Merged_Master_File.csv"
    ),
    na = "-9999",
    col_types = cols(.default = col_double())
  )
# select relevant columns
GLODAP <- GLODAP %>%
  select(cruise:talkqc)

# create date column
GLODAP <- GLODAP %>%
  mutate(date = ymd(paste(year, month, day))) %>%
  relocate(date)

# harmonize column names
GLODAP <- GLODAP  %>%
  rename(sal = salinity,
         tem = temperature)

# harmonize coordinates
GLODAP <- GLODAP  %>%
  rename(lon = longitude,
         lat = latitude) %>%
  mutate(lon = if_else(lon < 20, lon + 360, lon))

# remove irrelevant columns
GLODAP <- GLODAP %>%
  select(-c(month:minute,
            maxsampdepth, bottle, sigma0:sigma4,
            nitrite:nitritef))

3 Data preparation

3.1 Horizontal gridding

For merging with other data sets, all observations were grouped into latitude intervals of:

  • 1° x 1°
GLODAP <- m_grid_horizontal(GLODAP)

3.2 Reference eras

Samples were assigned to following eras:

  • JGOFS_WOCE: 1981 - 1999

  • GO_SHIP: 2000 - 2012

  • new_era: > 2013

GLODAP <- GLODAP %>%
  filter(year >= parameters$year_JGOFS_start) %>% 
  mutate(era = "JGOFS_WOCE",
         era = if_else(year > parameters$year_JGOFS_end, "GO_SHIP", era),
         era = if_else(year > parameters$year_GOSHIP_end, "new_era", era))

GLODAP <- GLODAP %>% 
  mutate(era = factor(era, c("JGOFS_WOCE", "GO_SHIP", "new_era")))

3.3 Spatial boundaries

3.3.1 Depth

Observations collected shallower than:

  • minimum sampling depth: 150m

were excluded from the analysis to avoid seasonal bias.

GLODAP <- GLODAP %>% 
  filter(depth >= parameters$depth_min)

3.3.2 Bottomdepth

Following restriction was considered, but is currently not implemented:

  • minimum bottom depth: 500m
GLODAP <- GLODAP %>% 
  filter(bottomdepth >= parameters$bottomdepth_min)

3.3.3 Basin mask

The basin mask from the World Ocean Atlas was used. For details consult the data base subsection for WOA18 data.

Please note that some GLODAP observations were made outside the WOA18 basin mask (i.e. in marginal seas) and will be removed for further analysis.

# use only data inside basinmask
GLODAP <- inner_join(GLODAP, basinmask)

3.4 Flags and missing data

Only rows (samples) for which all relevant parameters are available were selected, ie NA’s were removed.

According to Olsen et al (2020), flags within the merged master file identify:

  • f:

    • 2: Acceptable
    • 0: Interpolated (nutrients/oxygen) or calculated (CO[2] parameters) value
    • 9: Data not used (so, only NA data should have this flag)

  • qc:

    • 1: Adjusted or unadjusted data
    • 0: Data appear of good quality but have not been subjected to full secondary QC
    • data with poor or uncertain quality are excluded.

Following flagging criteria were taken into account:

  • flag_f: 2, 0
  • flag_qc: 1

Summary statistics were calculated during cleaning process.

3.4.1 tco2

3.4.1.1 NA

The vast majority of rows is removed due to missing tco2 observations.

GLODAP <- GLODAP %>% 
  filter(!is.na(tco2))

##

GLODAP_stats <- GLODAP %>% 
  summarise(tco2_values = n())

##

GLODAP_obs_grid <- GLODAP %>% 
  count(lat, lon, era) %>% 
  mutate(cleaning_level = "tco2_values")
GLODAP_obs <- GLODAP %>% 
  group_by(lat, lon) %>% 
  summarise(n = n()) %>% 
  ungroup()

map +
  geom_raster(data = basinmask, aes(lon, lat, fill = basin)) +
  geom_raster(data = GLODAP_obs, aes(lon, lat)) +
  scale_fill_brewer(palette = "Dark2") +
  theme(legend.position = "top",
        legend.title = element_blank())

rm(GLODAP_obs)

3.4.1.2 f flag

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, tco2f)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era ~ tco2f) +
  theme(legend.position = "top")

rm(GLODAP_obs_grid_temp)

GLODAP <- GLODAP %>%
  filter(tco2f %in% parameters$flag_f)

3.4.1.3 qc flag

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, tco2qc)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era ~ tco2qc) +
  theme(legend.position = "top")

##

GLODAP <- GLODAP %>%
  filter(tco2qc %in% parameters$flag_qc)

GLODAP_stats_temp <- GLODAP %>%
  summarise(tco2_flag = n())

GLODAP_stats <- cbind(GLODAP_stats, GLODAP_stats_temp)
rm(GLODAP_stats_temp)

##

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era) %>%
  mutate(cleaning_level = "tco2_flag")

GLODAP_obs_grid <-
  bind_rows(GLODAP_obs_grid, GLODAP_obs_grid_temp)

rm(GLODAP_obs_grid_temp)

3.4.2 talk

3.4.2.1 NA

Quite a few tco2 observations are discarded, due to missing talk data, in particular in the JGOFS/WOCE era. However, there seems to be a high number of observations remaining from the affected cruises, so that the coverage does not seem to be reduced drastically.

GLODAP <- GLODAP %>% 
  mutate(talkna = if_else(is.na(talk), "NA", "Value"))

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, talkna)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era ~ talkna) +
  theme(legend.position = "top")

GLODAP <- GLODAP %>% 
  select(-talkna) %>% 
  filter(!is.na(talk))

##

GLODAP_stats_temp <- GLODAP %>% 
  summarise(talk_values = n())

GLODAP_stats <- cbind(GLODAP_stats, GLODAP_stats_temp)
rm(GLODAP_stats_temp)

##

GLODAP_obs_grid_temp <- GLODAP %>% 
  count(lat, lon, era) %>% 
  mutate(cleaning_level = "talk_values")

GLODAP_obs_grid <-
  bind_rows(GLODAP_obs_grid, GLODAP_obs_grid_temp)

rm(GLODAP_obs_grid_temp)

3.4.2.2 f flag

Restricting the f flag to 2 would results in data gaps in the south-east Pacific. Interpolated or calculated data (f flag 0) are therefore included.

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, talkf)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era ~ talkf) +
  theme(legend.position = "top",
        legend.title = element_blank())

# ###

GLODAP <- GLODAP %>%
  filter(talkf %in% parameters$flag_f)

3.4.2.3 qc flag

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, talkqc)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era ~ talkqc) +
  theme(legend.position = "top",
        legend.title = element_blank())

###

GLODAP <- GLODAP %>%
  filter(talkqc %in% parameters$flag_qc)
##

GLODAP_stats_temp <- GLODAP %>%
  summarise(talk_flag = n())

GLODAP_stats <- cbind(GLODAP_stats, GLODAP_stats_temp)
rm(GLODAP_stats_temp)

##

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era) %>%
  mutate(cleaning_level = "talk_flag")

GLODAP_obs_grid <-
  bind_rows(GLODAP_obs_grid, GLODAP_obs_grid_temp)

rm(GLODAP_obs_grid_temp)

3.4.3 Phosphate

3.4.3.1 NA

Quite a few tco2/talk observations are discarded, due to missing phosphate data. However, there seems to be a high number of observations remaining from the affected cruises, so that the coverage does not seem to be reduced drastically.

GLODAP <- GLODAP %>% 
  mutate(phosphatena = if_else(is.na(phosphate), "NA", "Value"))

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, phosphatena)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
  scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era ~ phosphatena) +
  theme(legend.position = "top")

GLODAP <- GLODAP %>% 
  select(-phosphatena) %>% 
  filter(!is.na(phosphate))

##

GLODAP_stats_temp <- GLODAP %>% 
  summarise(phosphate_values = n())

GLODAP_stats <- cbind(GLODAP_stats, GLODAP_stats_temp)
rm(GLODAP_stats_temp)

##

GLODAP_obs_grid_temp <- GLODAP %>% 
  count(lat, lon, era) %>% 
  mutate(cleaning_level = "phosphate_values")

GLODAP_obs_grid <-
  bind_rows(GLODAP_obs_grid, GLODAP_obs_grid_temp)

rm(GLODAP_obs_grid_temp)

3.4.3.2 f flag

Restricting the f flag to 2 would not drastically reduce available data. Interpolated or calculated data (f flag 0) are therefore included.

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, phosphatef)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
    scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era~phosphatef) +
  theme(legend.position = "top",
        legend.title = element_blank())

###

GLODAP <- GLODAP %>%
  filter(phosphatef %in% parameters$flag_f)

3.4.3.3 qc flag

Phosphate data for which secondary quality was not applied (qc flag 0) were removed.

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era, phosphateqc)

map +
  geom_raster(data = GLODAP_obs_grid_temp, aes(lon, lat, fill = n)) +
    scale_fill_viridis_c(option = "magma",
                       direction = -1,
                       trans = "log10") +
  facet_grid(era~phosphateqc) +
  theme(legend.position = "top",
        legend.title = element_blank())

###

GLODAP <- GLODAP %>%
  filter(phosphateqc %in% parameters$flag_qc)

##

GLODAP_stats_temp <- GLODAP %>%
  summarise(phosphate_flag = n())

GLODAP_stats <- cbind(GLODAP_stats, GLODAP_stats_temp)
rm(GLODAP_stats_temp)

##

GLODAP_obs_grid_temp <- GLODAP %>%
  count(lat, lon, era) %>%
  mutate(cleaning_level = "phosphate_flag")

GLODAP_obs_grid <-
  bind_rows(GLODAP_obs_grid, GLODAP_obs_grid_temp)

rm(GLODAP_obs_grid_temp)

3.4.4 eMLR variables

Rows with missing eMLR variables were removed, only the qc flag was considered.

GLODAP <- GLODAP %>% 
  filter(!is.na(tem))

##
  
GLODAP <- GLODAP %>% 
  filter(!is.na(sal))

GLODAP <- GLODAP %>%
  filter(salinityf %in% parameters$flag_f)

GLODAP <- GLODAP %>%
  filter(salinityqc %in% parameters$flag_qc)

##
  
GLODAP <- GLODAP %>% 
  filter(!is.na(silicate))

GLODAP <- GLODAP %>%
  filter(silicatef %in% parameters$flag_f)

GLODAP <- GLODAP %>%
  filter(silicateqc %in% parameters$flag_qc)
##
  
GLODAP <- GLODAP %>% 
  filter(!is.na(oxygen))

GLODAP <- GLODAP %>%
  filter(oxygenf %in% parameters$flag_f)

GLODAP <- GLODAP %>%
  filter(oxygenqc %in% parameters$flag_qc)
##

GLODAP <- GLODAP %>% 
  filter(!is.na(aou))

GLODAP <- GLODAP %>%
  filter(aouf %in% parameters$flag_f)
##
  
GLODAP <- GLODAP %>% 
  filter(!is.na(nitrate))

GLODAP <- GLODAP %>%
  filter(nitratef %in% parameters$flag_f)

GLODAP <- GLODAP %>%
  filter(nitrateqc %in% parameters$flag_qc)
##

GLODAP <- GLODAP %>% 
  filter(!is.na(depth))

GLODAP <- GLODAP %>% 
  filter(!is.na(gamma))

##

GLODAP_stats_temp <- GLODAP %>% 
  summarise(eMLR_variables = n())

GLODAP_stats <- cbind(GLODAP_stats, GLODAP_stats_temp)

rm(GLODAP_stats_temp)

##

GLODAP_obs_grid_temp <- GLODAP %>% 
  count(lat, lon, era) %>% 
  mutate(cleaning_level = "eMLR_variables")

GLODAP_obs_grid <-
  bind_rows(GLODAP_obs_grid, GLODAP_obs_grid_temp)

rm(GLODAP_obs_grid_temp)
GLODAP <- GLODAP %>% 
  select(-ends_with(c("f", "qc")))

3.4.5 Manual adjustment A16 cruise

For harmonization with Gruber et al. (2019), cruises 1041 (A16N) and 1042 (A16S) were grouped into the GO_SHIP area despite taking place in 2013/14.

GLODAP_cruises <- GLODAP %>% 
  filter(basin == "Atlantic",
         year %in% c(2013, 2014)) %>% 
  count(lat, lon, cruise)

map +
  geom_raster(data = GLODAP_cruises, aes(lon, lat, fill = as.factor(cruise))) +
  scale_fill_brewer(palette = "Dark2") +
  theme(legend.position = "top",
        legend.title = element_blank())

rm(GLODAP_cruises)
GLODAP <- GLODAP %>%
  mutate(era = as.character(era)) %>% 
  mutate(era = if_else(cruise %in% c(1041, 1042),
                      "GO_SHIP", era))

GLODAP <- GLODAP %>% 
  mutate(era = factor(era, c("JGOFS_WOCE", "GO_SHIP", "new_era")))

3.5 Create clean observations grid

GLODAP_obs_grid_clean <- GLODAP %>% 
  count(lat, lon) %>% 
  select(-n)

3.6 Write summary file

GLODAP_stats_long <- GLODAP_stats %>%
  pivot_longer(1:length(GLODAP_stats),
               names_to = "parameter",
               values_to = "n")

GLODAP_stats_long  %>%  write_csv(
  here::here(
    "data/interim",
    "GLODAPv2.2020_stats.csv"
  )
)

##

GLODAP_obs_grid_clean %>% 
  write_csv(
    here::here(
      "data/interim",
      "GLODAPv2.2020_clean_obs_grid.csv"
    )
  )

##

GLODAP <- GLODAP %>% 
  select(year, date, era, basin, lat, lon, cruise,
         bottomdepth, depth, tem, sal, gamma,
         tco2, talk, phosphate,
         oxygen, aou, nitrate, silicate)

GLODAP  %>%  write_csv(
  here::here(
    "data/interim",
    "GLODAPv2.2020_clean.csv"
  )
)

4 Overview plots

4.1 Cleaning stats

Number of observations at various steps of data cleaning.

GLODAP_stats_long <- GLODAP_stats_long %>%
  mutate(parameter = fct_reorder(parameter, n))

GLODAP_stats_long %>% 
  ggplot(aes(parameter, n/1000)) +
  geom_col() +
  coord_flip() +
  labs(y = "n (1000)") +
  theme(axis.title.y = element_blank())

rm(GLODAP_stats_long)

4.2 Assign coarse spatial grid

For the following plots, the cleaned data set was re-opened and observations were gridded spatially to intervals of:

  • 5° x 5°
GLODAP <- m_grid_horizontal_coarse(GLODAP)

4.3 Histogram Zonal coverage

GLODAP_histogram_lat <- GLODAP %>%
  group_by(era, lat_grid, basin) %>%
  tally() %>%
  ungroup()

GLODAP_histogram_lat %>%
  ggplot(aes(lat_grid, n, fill = era)) +
  geom_col() +
  scale_fill_brewer(palette = "Dark2") +
  facet_wrap( ~ basin) +
  coord_flip(expand = 0) +
  theme(legend.position = "top",
        legend.title = element_blank())

rm(GLODAP_histogram_lat)

4.4 Histogram temporal coverage

GLODAP_histogram_year <- GLODAP %>%
  group_by(year, basin) %>%
  tally() %>%
  ungroup()

era_median_year <- GLODAP %>%
  group_by(era) %>%
  summarise(t_ref = median(year)) %>%
  ungroup()

era_median_year
# A tibble: 3 x 2
  era        t_ref
  <fct>      <dbl>
1 JGOFS_WOCE  1994
2 GO_SHIP     2008
3 new_era     2016
GLODAP_histogram_year %>%
  ggplot() +
  geom_vline(xintercept = c(
    parameters$year_JGOFS_end + 0.5,
    parameters$year_GOSHIP_end + 0.5
  )) +
  geom_col(aes(year, n, fill = basin)) +
  geom_point(
    data = era_median_year,
    aes(t_ref, 0, shape = "Median year"),
    size = 2,
    fill = "white"
  ) +
  scale_fill_brewer(palette = "Dark2") +
  scale_shape_manual(values = 24, name = "") +
  scale_y_continuous() +
  coord_cartesian(expand = 0) +
  theme(
    legend.position = "top",
    legend.direction = "vertical",
    legend.title = element_blank(),
    axis.title.x = element_blank()
  )

rm(GLODAP_histogram_year,
   era_median_year)

4.5 Zonal temporal coverage (Hovmoeller)

GLODAP_hovmoeller_year <- GLODAP %>%
  group_by(year, lat_grid, basin) %>%
  tally() %>%
  ungroup()

GLODAP_hovmoeller_year %>%
  ggplot(aes(year, lat_grid, fill = log10(n))) +
  geom_tile() +
  geom_vline(xintercept = c(1999.5, 2012.5)) +
  scale_fill_viridis_c(option = "magma", direction = -1) +
  facet_wrap( ~ basin, ncol = 1) +
  theme(legend.position = "top",
        axis.title.x = element_blank())

rm(GLODAP_hovmoeller_year)

4.6 Coverage maps by era

4.6.1 Subsetting process

GLODAP_obs_grid <- GLODAP_obs_grid %>%
  mutate(era = factor(era, c("JGOFS_WOCE", "GO_SHIP", "new_era")),
         cleaning_level = factor(
           cleaning_level,
           unique(GLODAP_obs_grid$cleaning_level)
         ))

map +
  geom_raster(data = GLODAP_obs_grid %>%
                filter(cleaning_level == "tco2_values") %>%
                select(-cleaning_level),
              aes(lon, lat, fill = "tco2_values")) +
  geom_raster(data = GLODAP_obs_grid %>%
                filter(cleaning_level != "tco2_values"),
              aes(lon, lat, fill = "subset")) +
  scale_fill_manual(values = c("red", "grey"), name = "") +
  theme(legend.position = "top",
        axis.title = element_blank())

map +
  geom_raster(data = GLODAP_obs_grid %>%
                filter(cleaning_level == "tco2_values") %>%
                select(-cleaning_level),
              aes(lon, lat, fill = "tco2_values")) +
  geom_raster(data = GLODAP_obs_grid %>%
                filter(cleaning_level != "tco2_values"),
              aes(lon, lat, fill = "subset")) +
  scale_fill_manual(values = c("red", "grey"), name = "") +
  facet_grid(cleaning_level ~ era) +
  theme(legend.position = "top",
        axis.title = element_blank())

4.6.2 eMLR variables

Grey pixels refer to sampling locations filtered for availability of tco2 data only.

GLODAP <- GLODAP %>% 
  mutate(era = factor(era, c("JGOFS_WOCE", "GO_SHIP", "new_era")))

GLODAP_tco2_grid <- GLODAP %>%
  count(lat, lon, era)

map +
  geom_raster(data = GLODAP_tco2_grid, aes(lon, lat), fill = "grey80") +
  geom_bin2d(data = GLODAP,
             aes(lon, lat),
             binwidth = c(1,1)) +
  scale_fill_viridis_c(option = "magma", direction = -1, trans = "log10",
                       name = "log10(eMLR_variables)") +
  facet_wrap(~era, ncol = 1) +
  theme(legend.position = "top",
        axis.title = element_blank())

5 Exploratory data analysis

source("code/eda.R")
eda(GLODAP, "GLODAPv2_2020_clean")
rm(eda)

The output of an automated Exploratory Data Analysis (EDA) performed with the package DataExplorer can be accessed here:

Link to EDA report of GLODAPv2_2020 raw data


sessionInfo()
R version 4.0.2 (2020-06-22)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18363)

Matrix products: default

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

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

other attached packages:
 [1] lubridate_1.7.9 metR_0.7.0      scico_1.2.0     patchwork_1.0.1
 [5] collapse_1.3.2  forcats_0.5.0   stringr_1.4.0   dplyr_1.0.0    
 [9] purrr_0.3.4     readr_1.3.1     tidyr_1.1.0     tibble_3.0.3   
[13] ggplot2_3.3.2   tidyverse_1.3.0 workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] httr_1.4.2         viridisLite_0.3.0  jsonlite_1.7.0     here_0.1          
 [5] modelr_0.1.8       Formula_1.2-3      assertthat_0.2.1   blob_1.2.1        
 [9] cellranger_1.1.0   yaml_2.2.1         pillar_1.4.6       backports_1.1.8   
[13] lattice_0.20-41    glue_1.4.1         digest_0.6.25      RColorBrewer_1.1-2
[17] promises_1.1.1     checkmate_2.0.0    rvest_0.3.6        colorspace_1.4-1  
[21] sandwich_2.5-1     htmltools_0.5.0    httpuv_1.5.4       Matrix_1.2-18     
[25] pkgconfig_2.0.3    broom_0.7.0        haven_2.3.1        xtable_1.8-4      
[29] scales_1.1.1       whisker_0.4        later_1.1.0.1      git2r_0.27.1      
[33] farver_2.0.3       generics_0.0.2     ellipsis_0.3.1     withr_2.2.0       
[37] cli_2.0.2          magrittr_1.5       crayon_1.3.4       readxl_1.3.1      
[41] evaluate_0.14      fs_1.4.2           fansi_0.4.1        xml2_1.3.2        
[45] tools_4.0.2        data.table_1.13.0  hms_0.5.3          lifecycle_0.2.0   
[49] munsell_0.5.0      reprex_0.3.0       compiler_4.0.2     lfe_2.8-5.1       
[53] rlang_0.4.7        grid_4.0.2         rstudioapi_0.11    labeling_0.3      
[57] rmarkdown_2.3      gtable_0.3.0       DBI_1.1.0          R6_2.4.1          
[61] zoo_1.8-8          knitr_1.30         utf8_1.1.4         rprojroot_1.3-2   
[65] stringi_1.4.6      parallel_4.0.2     Rcpp_1.0.5         vctrs_0.3.2       
[69] dbplyr_1.4.4       tidyselect_1.1.0   xfun_0.16