Last updated: 2019-11-08

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Knit directory: BloomSail/

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library(tidyverse)
library(seacarb)
library(data.table)
library(broom)
library(lubridate)

Sensitivity considerations

A change in DIC of 1 µmol kg-1 corresponds to a change in pCO2 of around 1 µatm, in the Central Baltic Sea at a pCO2 of around 100 µatm (summertime conditions).

df <- data.frame(cbind(
  (c(1720)),
  (c(7))))

Tem <- seq(5,25,5)
pCO2<-seq(50,500,20)

df<-merge(df, Tem)
names(df) <- c("AT", "S", "Tem")  

df<-merge(df, pCO2)
names(df) <- c("AT", "S", "Tem", "pCO2")  

df<-data.table(df)
df$AT<-df$AT*1e-6

df$DIC<-carb(flag=24, var1=df$pCO2, var2=df$AT, S=df$S, T=df$Tem, k1k2="m10", kf="dg", pHscale="T")[,16]
df$pCO2.corr<-carb(flag=15, var1=df$AT, var2=df$DIC, S=df$S, T=df$Tem, k1k2="m10", kf="dg", pHscale="T")[,9]

df$pCO2.2<-df$pCO2.corr + 25
df$DIC.2<-carb(flag=24, var1=df$pCO2.2, var2=df$AT, S=df$S, T=df$Tem, k1k2="m10", kf="dg", pHscale="T")[,16]


df$ratio<-(df$pCO2.2-df$pCO2.corr)/(df$DIC.2*1e6-df$DIC*1e6)

df %>% 
  ggplot(aes(pCO2, ratio, col=as.factor(Tem)))+
  geom_line()+
  scale_color_viridis_d(option = "C",name="Tem [°C]")+
  labs(x=expression(pCO[2]~(µatm)), y=expression(Delta~pCO[2]~"/"~Delta~DIC~(µatm~µmol^{-1}~kg)))+
  scale_y_continuous(limits = c(0,8), breaks = seq(0,10,1))
pCO~2~ sensitivity to changes in DIC.

pCO2 sensitivity to changes in DIC.

Version Author Date
33e3659 jens-daniel-mueller 2019-10-22
rm(df, Tem, pCO2)

HydroC sensor settings

The sensor was first run with a low power pump (1W), later and for most parts of the expedition with a stronger (8W) pump. Pumps were switched between recordings (data file: SD_datafile_20180718_170417CO2-0618-001.txt):

  • 2018-07-17;13:08:34
  • 2018-07-17;13:08:35

Logging frequency for all measurement modes (Measure, Zero, Flush) was set to:

10 sec for all recordings including SD_datafile_20180714_073641CO2-0618-001.txt

Increase to 2 sec in SD_datafile_20180717_121052CO2-0618-001.txt at:

  • 2018-07-14;07:52:02
  • 2018-07-14;07:52:12
  • 2018-07-14;07:52:14

Increase to 2 sec in SD_datafile_20180718_170417CO2-0618-001 at:

  • 2018-07-17;12:27:25
  • 2018-07-17;12:27:27
  • 2018-07-17;12:27:28

Response time determination

Response times were determined by fitting a nonlinear least-squares model with the nls function as described here by Douglas Watson.

  • Flush period length: variable
  • Flush period restricted to equilibration phase, avoiding initial gas mixing effects occuring at the start of each Flush period
  • only completet Flush periods (duration > 500 sec) included
# Read and prepare data

df <- read_csv(here::here("data/_merged_data_files",
                          "BloomSail_CTD_HydroC_Contros_clean.csv"),
               col_types = cols(ID = col_character(),
                                pCO2_analog = col_double(),
                                pCO2 = col_double(),
                                Zero = col_factor(),
                                Flush = col_factor(),
                                Zero_ID = col_integer(),
                                duration = col_double(),
                                mixing = col_character()))

df <- df %>%
  select(date_time, ID, dep, tem, Flush, pCO2, Zero_ID, duration, mixing)

df <- df %>%
  filter(Flush == 1, mixing == "equilibration")

df <- df %>% 
  group_by(Zero_ID) %>% 
  mutate(duration = duration- min(duration),
         max_duration = max(duration)) %>% 
  ungroup() %>% 
  filter(max_duration >= 500) %>% 
  select(-max_duration)

An example plot for a nls model fitted to pCO2 observations during a Flush phase is shown below.

# Plot example Flush period with exponential fit ----------------------

i <- 95

df_ID <- df %>%
  filter(Zero_ID == i, duration <= 300)

fit <-
df_ID %>%
  nls(pCO2 ~ SSasymp(duration, yf, y0, log_alpha), data = .)

tau <- as.numeric(exp(-tidy(fit)[3,2]))
pCO2_end <- as.numeric(tidy(fit)[1,2])
pCO2_start <- as.numeric(tidy(fit)[2,2])
dpCO2 = pCO2_end - pCO2_start
mean_abs_resid <- mean(abs(resid(fit)))

augment(fit) %>%
  ggplot(aes(duration, pCO2))+
  geom_point()+
  geom_line(aes(y = .fitted))+
  geom_vline(xintercept = tau)+
  geom_hline(yintercept = pCO2_start + 0.63 *(dpCO2))+
  labs(y=expression(pCO[2]~(µatm)), x="Duration of Flush period (s)")
Example response time determination by non-linear least squares fit to the pCO~2~ recovery signal after zeroing. The vertical line indicates the determined response time tau.

Example response time determination by non-linear least squares fit to the pCO2 recovery signal after zeroing. The vertical line indicates the determined response time tau.

Version Author Date
74212a6 jens-daniel-mueller 2019-11-08
rm(df_ID, fit, i, tau, dpCO2, pCO2_end, pCO2_start)
duration_intervals <- seq(150,500,50)

In the following we determine the response time tau for all zeroings and for total durations of:
150, 200, 250, 300, 350, 400, 450, 500 secs

# Plot all individual Flush periods with exponential fit ----------------------

pdf(file=here::here("output/Plots/response_time",
    "RT_determination.pdf"), onefile = TRUE, width = 7, height = 4)

for (i in unique(df$Zero_ID)) {
  for (max_duration in duration_intervals) {
    
    df_ID <- df %>%
      filter(Zero_ID == i, duration <= max_duration)
    
    fit <- 
      try(
      df_ID %>%
          nls(pCO2 ~ SSasymp(duration, yf, y0, log_alpha), data = .),
      TRUE)
    
    if (class(fit) == "nls"){
    
      tau <- as.numeric(exp(-tidy(fit)[3,2]))
      pCO2_end <- as.numeric(tidy(fit)[1,2])
      pCO2_start <- as.numeric(tidy(fit)[2,2])
      dpCO2 = pCO2_end - pCO2_start
      mean_abs_resid <- mean(abs(resid(fit))/pCO2_end)*100
      
      temp <- as_tibble(bind_cols(Zero_ID = i, duration = max_duration, tau = tau, resid = mean_abs_resid))
      
      if (exists("tau_df")){tau_df <- bind_rows(tau_df, temp)}
        else {tau_df <- temp}
      
      print(
      augment(fit) %>%
        ggplot(aes(duration, pCO2))+
        geom_point()+
        geom_line(aes(y = .fitted))+
        geom_vline(xintercept = tau)+
        geom_hline(yintercept = pCO2_start + 0.63 *(dpCO2))+
        labs(y=expression(pCO[2]~(µatm)), x="Duration of Flush period (s)",
             title = paste("Zero_ID: ", i, "Mean absolute residual (%): ", round(mean_abs_resid*100, 2)))+
        xlim(0,600)
      )
      
    }
  }
}

dev.off()
png 
  2 
rm(df_ID, fit, i, tau, dpCO2, pCO2_end, pCO2_start, temp, max_duration, mean_abs_resid)

# Plot individual Flush periods with linearized response variable  --------


# for (i in unique(df$Zero_ID)) {
# 
# #i <- 50
# df_ID <- df %>%
#   filter(Zero_ID == i,
#          mixing == "equilibration")
# 
# mean_pCO2 <- df_ID %>% 
#   slice((n()-4) : n()) %>% 
#   summarise(mean_pCO2 = mean(pCO2))
# 
# df_ID <- full_join(df_ID, mean_pCO2) %>% 
#   mutate(dpCO2 = max(pCO2) - pCO2,
#          ln_dpCO2 = log(dpCO2))
# 
# 
# df_ID %>%
#   ggplot(aes(duration_equi, ln_dpCO2))+
#   geom_point()+
#   geom_smooth(method = "lm")+
#   theme_bw()
# 
# # augment(fit) %>%
# #   ggplot(aes(duration_equi, pCO2))+
# #   geom_point()+
# #   geom_line(aes(y = .fitted))+
# #   geom_vline(xintercept = tau)
# 
# ggsave(here::here("/Plots/TinaV/Sensor/HydroC_diagnostics/Response_time_fits",
#                   paste(i,"_Zero_ID_HydroC_RT_linear.jpg", sep="")),
#          width = 10, height = 4)
# }

A pdf with plots of all individual response time fits can be accessed here

tau_high <- 120
tau_low <- 20
resid_limit <- 1

tau_df_sub <- tau_df %>% 
  filter(resid < resid_limit, tau > tau_low, tau < tau_high)

tau_total <- nrow(tau_df)
tau_sub <- nrow(tau_df_sub)

Outcome

Response times were determined sucessfully determined by nls in a total number of 417 cases.
Restriction of the determined tau values to those falling between 20 and 120 seconds and corresponding to a fit with a mean absolute residual below 1 % of the final equilibrium pCO2, results in 365 remaining tau values (87.5 %).

tau_df_sub %>% 
  ggplot(aes(resid))+
  geom_histogram()+
  facet_wrap(~duration)

Version Author Date
74212a6 jens-daniel-mueller 2019-11-08
tau_df_sub %>% 
  ggplot(aes(Zero_ID, tau, col=duration))+
  geom_point()+
  scale_color_viridis_c()

Version Author Date
74212a6 jens-daniel-mueller 2019-11-08
tau_df_sub %>% 
  group_by(Zero_ID) %>% 
  mutate(d_tau = tau - mean(tau)) %>% 
  ggplot(aes(duration, d_tau))+
  geom_violin(aes(group=duration))+
  geom_point()

Version Author Date
74212a6 jens-daniel-mueller 2019-11-08
tau_df_sub %>% 
  group_by(Zero_ID) %>% 
  mutate(d_tau = tau - mean(tau)) %>% 
  ggplot(aes(duration, d_tau))+
  geom_smooth()+
  geom_point()+
  facet_wrap(~Zero_ID)

Version Author Date
74212a6 jens-daniel-mueller 2019-11-08
tau_df_sub %>% 
  group_by(duration) %>% 
  mutate(n_tau = n()) %>% 
  ggplot(aes(duration, n_tau))+
  geom_point()

Version Author Date
74212a6 jens-daniel-mueller 2019-11-08

This approach

Contros in-house

Comparison

Pre-smoothing

Response time correction

Post-smoothing

Response time optimization

Open tasks / questions

  • Compare Contros and own response time estimates
  • Compare differnt response time correction methods (Bittig vs. Fiedler, Miloshevich, Fietzek)
  • Test impact of duration for response time estimation on final mean response time
  • Test impact of selection criterion for “good” response time estimates on final mean response time
  • Check results from field response time experiment (high zeroing frequency)
  • Why does nls model failure increase with higher fit duration

sessionInfo()
R version 3.5.0 (2018-04-23)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 17763)

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] lubridate_1.7.4   broom_0.5.2       data.table_1.12.6
 [4] seacarb_3.2.12    oce_1.1-1         gsw_1.0-5        
 [7] testthat_2.2.1    forcats_0.4.0     stringr_1.4.0    
[10] dplyr_0.8.3       purrr_0.3.3       readr_1.3.1      
[13] tidyr_1.0.0       tibble_2.1.3      ggplot2_3.2.1    
[16] tidyverse_1.2.1  

loaded via a namespace (and not attached):
 [1] tidyselect_0.2.5  xfun_0.10         haven_2.1.1      
 [4] lattice_0.20-35   colorspace_1.4-1  vctrs_0.2.0      
 [7] generics_0.0.2    viridisLite_0.3.0 htmltools_0.4.0  
[10] yaml_2.2.0        rlang_0.4.1       pillar_1.4.2     
[13] glue_1.3.1        withr_2.1.2       modelr_0.1.5     
[16] readxl_1.3.1      lifecycle_0.1.0   munsell_0.5.0    
[19] gtable_0.3.0      workflowr_1.4.0   cellranger_1.1.0 
[22] rvest_0.3.4       evaluate_0.14     labeling_0.3     
[25] knitr_1.25        highr_0.8         Rcpp_1.0.2       
[28] scales_1.0.0      backports_1.1.5   jsonlite_1.6     
[31] fs_1.3.1          hms_0.5.1         digest_0.6.22    
[34] stringi_1.4.3     grid_3.5.0        rprojroot_1.3-2  
[37] here_0.1          cli_1.1.0         tools_3.5.0      
[40] magrittr_1.5      lazyeval_0.2.2    crayon_1.3.4     
[43] whisker_0.4       pkgconfig_2.0.3   zeallot_0.1.0    
[46] xml2_1.2.2        assertthat_0.2.1  rmarkdown_1.16   
[49] httr_1.4.1        rstudioapi_0.10   R6_2.4.0         
[52] nlme_3.1-137      git2r_0.26.1      compiler_3.5.0