Last updated: 2019-11-08

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Rmd	aa27fd4	jens-daniel-mueller	2019-11-08	Finalized RT determination
html	4256bcf	jens-daniel-mueller	2019-11-08	Build site.
Rmd	7f52e66	jens-daniel-mueller	2019-11-08	response_time pdf updated
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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
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Rmd	b2d2bbb	jens-daniel-mueller	2019-10-21	Structured data base and response time Rmd
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Rmd	53ad162	jens-daniel-mueller	2019-10-21	Structured data base and response time Rmd
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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)

Response time determination

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

Model fitting

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

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.

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)

As there was some speculation about the dependence of determined response times (\(\tau\)) on the chosen duration of the fit interval, \(\tau\) was determined 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()

rm(df_ID, fit, i, tau, dpCO2, pCO2_end, pCO2_start, temp, max_duration, mean_abs_resid)

tau_df %>% 
  write_csv(here::here("data/_summarized_data_files", "Tina_V_HydroC_response_times_all.csv"))

# 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_df <- read_csv(here::here("data/_summarized_data_files", "Tina_V_HydroC_response_times_all.csv"))

# define subsetting parameters
tau_high <- 120
tau_low <- 20
resid_limit <- 1

# subset determined tau values
tau_resid <- tau_df %>% 
  filter(resid < resid_limit)

tau_resid_min_max <- tau_resid %>% 
  filter(tau > tau_low, tau < tau_high)

# calculate some metrics for the subsetting
n_Zero_IDs <- df %>% 
  group_by(Zero_ID) %>% 
  n_groups()
n_duration_intervals <- length(duration_intervals)
n_tau_max <- n_Zero_IDs * length(duration_intervals)
n_tau_total <- nrow(tau_df)
n_tau_resid <- nrow(tau_resid)
n_tau_resid_min_max <- nrow(tau_resid_min_max)

Outcome

Estimated \(\tau\) values were restricted to * mean absolute fit residual above 1 % of the final equilibrium pCO₂ * \(\tau\) falling between 20 and 120 seconds

Metrics to characterize the fitting procedure include the number of:

Flush periods: 55
Duration intervals: 8
Exercised response time fits: 440
Succesful response times determinations: 417 (94.8)%
\(\tau\)’s after removing fits with high absolute fit residual: 375 (89.9 %)
\(\tau\)’s after restriction to \(\tau\) thresholds: 365 (87.5 %)

tau_df %>% 
  ggplot(aes(resid))+
  geom_histogram()+
  facet_wrap(~duration, labeller = label_both)+
  geom_vline(xintercept = resid_limit)+
  labs(x=expression(Mean~absolute~residuals~("%"~of~equilibrium~pCO[2])))

Histogram of residuals from fit displayed for the investigate durations of the fit interval. Vertical line represents the chosen threshold.

tau_resid %>% 
  group_by(duration) %>% 
  mutate(n_tau = n()) %>% 
  ggplot(aes(duration, n_tau))+
  geom_point()+
  labs(x="Fit interval duration (sec)", y="Number of tau values")

Number of determined tau values as a function of the fit interval length, after applying a fit residual threshold

tau_resid_min_max %>% 
  ggplot(aes(Zero_ID, tau, col=duration))+
  geom_point()+
  scale_color_viridis_c(name="Duration (sec)")+
  labs(y="Tau (sec)")

Tau for all Zeroings with color representing the fit interval duration.

tau_resid_min_max %>% 
  group_by(Zero_ID) %>% 
  mutate(d_tau = tau - mean(tau)) %>% 
  ggplot(aes(duration, d_tau))+
  geom_hline(yintercept = 0)+
  geom_smooth()+
  geom_point()+
  facet_wrap(~Zero_ID, ncol = 4, labeller = label_both)+
  labs(x="Duration (sec)", y="Deviation from mean tau (sec)")

Determined tau values as a function of the fit interval duration, displayed individually for each flush period.

tau_resid_min_max %>% 
  group_by(Zero_ID) %>% 
  mutate(d_tau = tau - mean(tau)) %>% 
  ggplot(aes(duration, d_tau))+
  geom_violin(aes(group=duration))+
  geom_point()+
  labs(x="Duration (sec)", y="Deviation from mean tau (sec)")

Determined tau values as a function of the fit interval duration, pooled for all flush period.

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

Response time determination

HydroC sensor settings

Model fitting

Outcome

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

Response time determination

HydroC sensor settings

Model fitting

Outcome

Pre-smoothing

Response time correction

Post-smoothing

Response time optimization

Open tasks / questions

Response time correction of Contros HydroC pCO₂ data