Response time correction of Contros HydroC pCO2 data
Jens Daniel Müller
08 November, 2019
Last updated: 2019-11-08
Checks: 6 1
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))
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 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$Zero_ID)) {
for (max_duration in duration_intervals) {
df_ID <- df %>%
filter(Zero_ID == i, duration <= max_duration)
fit <-
try(
df_ID %>%
nls(pCO2 ~ SSasymp(duration, yf, y0, log_alpha), data = .),
TRUE)
if (class(fit) == "nls"){
tau <- as.numeric(exp(-tidy(fit)[3,2]))
pCO2_end <- as.numeric(tidy(fit)[1,2])
pCO2_start <- as.numeric(tidy(fit)[2,2])
dpCO2 = pCO2_end - pCO2_start
mean_abs_resid <- mean(abs(resid(fit))/pCO2_end)*100
temp <- as_tibble(bind_cols(Zero_ID = i, duration = max_duration, tau = tau, resid = mean_abs_resid))
if (exists("tau_df")){tau_df <- bind_rows(tau_df, temp)}
else {tau_df <- temp}
if (mean_abs_resid > 1){warn <- "orange"}
else {warn <- "black"}
print(
augment(fit) %>%
ggplot(aes(duration, pCO2))+
geom_point(col = warn)+
geom_line(aes(y = .fitted))+
geom_vline(xintercept = tau)+
geom_hline(yintercept = pCO2_start + 0.63 *(dpCO2))+
labs(y=expression(pCO[2]~(µatm)), x="Duration of Flush period (s)",
title = paste("Zero_ID: ", i,
"Tau: ", round(tau,1),
"Mean absolute residual (%): ", round(mean_abs_resid, 2)))+
xlim(0,600)
)
}
else {
temp <- as_tibble(bind_cols(Zero_ID = i, duration = max_duration, tau = NaN, resid = NaN))
if (exists("tau_df")){tau_df <- bind_rows(tau_df, temp)}
else {tau_df <- temp}
print(
df_ID %>%
ggplot(aes(duration, pCO2))+
geom_point(col="red")+
labs(y=expression(pCO[2]~(µatm)), x="Duration of Flush period (s)",
title = paste("Zero_ID: ", i,
"nls model failed"))+
xlim(0,600)
)
}
}
}
dev.off()
rm(df_ID, fit, i, tau, dpCO2, pCO2_end, pCO2_start, temp, max_duration, mean_abs_resid, warn)
tau_df %>%
write_csv(here::here("data/_summarized_data_files", "Tina_V_HydroC_response_times_all.csv"))
# Plot individual Flush periods with linearized response variable --------
# for (i in unique(df$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
Outcome
Estimated \(\tau\) values were only taken into account when stable environmental pCO2 levels were present. Absence of stable environmental pCO2 was assumed when the mean absolute fit residual was above 1 % of the final equilibrium pCO2, for any model fit of that flush period irrespective of the chosen fit interval length. Usually, fits with the higher duration did not meet this criterion. For some unexplained reason the first \(\tau\) determination resulted in values about twice as high as all other Flush periods and was therefore removed as an outlier.
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 groups of fits with high absolute fit residual: 296 (67.3 %)
It should be noted that all failed model fits occured in flush periods where the residual criterion was not meet by at least one other fit (i.e. fitting only failed under unstable conditions).
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.
| Version | Author | Date |
|---|---|---|
| f3277a5 | jens-daniel-mueller | 2019-11-08 |
tau_resid %>%
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 %>%
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 %>%
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.
Mean response time
Finally, the mean response times are:
max_Zero_ID <- max(unique(df[df$date_time < ymd_hms("2018-07-17;13:08:34"),]$Zero_ID))
min_Zero_ID <- min(unique(df[df$date_time > ymd_hms("2018-07-17;13:08:34"),]$Zero_ID))
# tau_df %>%
# mutate(pump_power = if_else(Zero_ID <= 20, "1W", "8W")) %>%
# group_by(pump_power) %>%
# summarise(tau = mean(tau, na.rm = TRUE))
tau_resid %>%
mutate(pump_power = if_else(Zero_ID <= max_Zero_ID, "1W", "8W")) %>%
group_by(pump_power) %>%
summarise(tau = mean(tau))# A tibble: 2 x 2
pump_power tau
<chr> <dbl>
1 1W 77.4
2 8W 56.6Pre-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)
- Check results from field response time experiment (high zeroing frequency)
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 utf8_1.1.4 rlang_0.4.1
[13] pillar_1.4.2 glue_1.3.1 withr_2.1.2
[16] modelr_0.1.5 readxl_1.3.1 lifecycle_0.1.0
[19] munsell_0.5.0 gtable_0.3.0 workflowr_1.4.0
[22] cellranger_1.1.0 rvest_0.3.4 evaluate_0.14
[25] labeling_0.3 knitr_1.25 fansi_0.4.0
[28] highr_0.8 Rcpp_1.0.2 scales_1.0.0
[31] backports_1.1.5 jsonlite_1.6 fs_1.3.1
[34] hms_0.5.1 digest_0.6.22 stringi_1.4.3
[37] grid_3.5.0 rprojroot_1.3-2 here_0.1
[40] cli_1.1.0 tools_3.5.0 magrittr_1.5
[43] lazyeval_0.2.2 crayon_1.3.4 whisker_0.4
[46] pkgconfig_2.0.3 zeallot_0.1.0 xml2_1.2.2
[49] assertthat_0.2.1 rmarkdown_1.16 httr_1.4.1
[52] rstudioapi_0.10 R6_2.4.0 nlme_3.1-137
[55] git2r_0.26.1 compiler_3.5.0