Last updated: 2019-11-08

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File	Version	Author	Date	Message
Rmd	7f52e66	jens-daniel-mueller	2019-11-08	response_time pdf updated
html	72687ee	jens-daniel-mueller	2019-11-08	Build site.
Rmd	74632d6	jens-daniel-mueller	2019-11-08	response_time pdf updated
html	74212a6	jens-daniel-mueller	2019-11-08	Build site.
Rmd	6cb1935	jens-daniel-mueller	2019-11-08	response_time updated
html	33e3659	jens-daniel-mueller	2019-10-22	Build site.
Rmd	efcafd1	jens-daniel-mueller	2019-10-22	Added data base, merging, and RT determination
html	1595fe9	jens-daniel-mueller	2019-10-21	Build site.
html	a059c41	jens-daniel-mueller	2019-10-21	Build site.
Rmd	eff54ce	jens-daniel-mueller	2019-10-21	Added CTD read-in
html	32ec4f7	jens-daniel-mueller	2019-10-21	Build site.
Rmd	b2d2bbb	jens-daniel-mueller	2019-10-21	Structured data base and response time Rmd
html	bafa88f	jens-daniel-mueller	2019-10-21	Build site.
Rmd	53ad162	jens-daniel-mueller	2019-10-21	Structured data base and response time Rmd
html	076a36b	jens-daniel-mueller	2019-10-21	Build site.
Rmd	3e8a32e	jens-daniel-mueller	2019-10-21	Structured data base and response time Rmd
html	b2d0164	jens-daniel-mueller	2019-10-21	Build site.
Rmd	53ae361	jens-daniel-mueller	2019-10-21	Added data base and response time Rmd

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))

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

Response time correction of Contros HydroC pCO₂ data

Jens Daniel Müller

08 November, 2019

Sensitivity considerations

HydroC sensor settings

Response time determination

Outcome

This approach

Contros in-house

Comparison

Pre-smoothing

Response time correction

Post-smoothing

Response time optimization

Open tasks / questions

Response time correction of Contros HydroC pCO2 data

Jens Daniel Müller

08 November, 2019

Sensitivity considerations

HydroC sensor settings

Response time determination

Outcome

This approach

Contros in-house

Comparison

Pre-smoothing

Response time correction

Post-smoothing

Response time optimization

Open tasks / questions

Response time correction of Contros HydroC pCO₂ data