#' Gap-fill using EM
#'
#' This function automatically gap-fills the missing data points (marked as "NA") in the flux dataset
#' using expectation-maximization (EM) algorithm with up to 3 parallel measured reference flux time series.
#' The function is based on the algorithms in the package `mtsdi`.
#'
#' @param data a data frame that includes the flux (with NA indicating the missing data)
#' @param ref1 a data frame that includes the parallel measured reference flux time series #1,
#' does not require to have the same length as the target data to be filled
#' @param ref2 a data frame that includes the parallel measured reference flux time series #2 (optional),
#' does not require to have the same length as the target data to be filled. Default: NULL
#' @param ref3 a data frame that includes the parallel measured reference flux time series #3 (optional),
#' does not require to have the same length as the target data to be filled. Default: NULL
#' @param Flux a string indicates the column name of the flux variable to be gap-filled
#' @param Flux1 a string indicates the column name of the reference time series in ref1. Default: same as Flux
#' @param Flux2 a string indicates the column name of the reference time series in ref2. Default: same as Flux
#' @param Flux3 a string indicates the column name of the reference time series in ref3. Default: same as Flux
#' @param Date a string indicates the column name for the date in data, ref1, ref2 and ref3,
#' and it HAS to include the time information. Note that all the data frames should have the same name for the date column.
#' @param Date_form a string indicates the format of the date in data, ref1, ref2 and ref3,
#' either "ymd_hms" (default), "mdy_hms" or "dmy_hms". Note that all the data frames should have the same date format.
#' @param win a number indicates the required sampling window length around each gap (total number in two sides), unit: days (default: 5)
#' @param interval a number indicates the temporal resolution of the measurements in the dataset, unit: minutes (default: 10)
#' @param ts logical. TRUE if it is time series. Default: TRUE
#' @param method a string indicates the method for univariate time series filtering,
#' either "spline" (default),"arima", or "gam". See details in the package `mtsdi`.
#' @param sp_df an integer indicates the degrees of freedom to be used for the splines (Default: 10).
#' In case set to NULL, the degrees of freedom will be chosen by cross-validation.
#' See details in the package `mtsdi`.
#' @param fail a string or a number indicates what to do when model fails to converge:
#' 1. use the mean value in the sampling window to fill the gap ("ave", default), or
#' 2. use any value assigned here to fill the gap (e.g., 9999, NA, etc.)
#' @param ... other arguments pass to `mnimput`
#' @return A data frame that includes the original data, gap-filled data ("filled")
#' and a "mark" column that indicates the value in each row of the "filled" is either:
#' 0. original, 1. gap-filled, or 2. failed to converge
#' @examples
#' # read example data
#' df <- read.csv(file = system.file("extdata", "Soil_resp_example.csv", package = "FluxGapsR"),header = T)
#' df_ref <- read.csv(file = system.file("extdata", "Soil_resp_ref_example.csv", package = "FluxGapsR"),header = T)
#' df_filled <- Gapfill_em(data = df,ref1 = df_ref)
#' # visualize the gapfilled results
#' plot(df_filled$filled,col="red")
#' points(df_filled$Flux)
#' @export
Gapfill_em <- function(data,
ref1,
ref2 = NULL,
ref3 = NULL,
Flux = "Flux",
Flux1 = Flux,
Flux2 = Flux,
Flux3 = Flux,
Date = "Date",
Date_form = "ymd_hms",
win = 5,
interval = 10,
ts = TRUE,
method = "spline",
sp_df = 10,
fail = "ave",
...
){
# # define the pipe from the package "magrittr"
`%>%` <- magrittr::`%>%`
### add sequence mark to the gaps -------
mt <- is.na(data[,Flux])
ind <- 1 # index for marking the gaps
mk <- vector()
for (i in 1:length(mt)) {
if (mt[i]==FALSE){
mk[i] <- 0 # non-gaps are marked as 0
} else {
if (mt[i]==TRUE){
mk[i] <- ind # gaps are marked as the value of ind
if (i != length(mt)){ # to prevent the error when loop reach the end
if (mt[i+1]==FALSE) {
ind <- ind+1 # when reached the end of a gap, change add 1 to ind
}
}
}
}
}
print(paste0(max(mk)," gaps are marked")) # display the total number of gaps
### prepare data for gapfilling -----
# the sampling window length
pt_h <- 60/interval # how many data points per hour
winID <- win/2*pt_h*24 # how many data points for the sampling window at EACH side of the gap
# create vector to save the predicted gapfilled data
gap <- rep(NA,nrow(data))
# extract the data needed for gap-filling
dft <- data[,c(Date,Flux)]
names(dft) <- c("Date","Flux")
dft <- dft %>%
dplyr::mutate(Date=switch(Date_form, # convert the date into right format depending on the input format
"ymd_hms" = lubridate::ymd_hms(Date),
"mdy_hms" = lubridate::mdy_hms(Date),
"dmy_hms" = lubridate::dmy_hms(Date),
stop("Invalid date format for data")))
# extract the data for reference1
ref1 <- ref1[,c(Date,Flux1)]
names(ref1) <- c("Date","Flux1")
ref1 <- ref1 %>%
dplyr::mutate(Date=switch(Date_form, # convert the date into right format depending on the input format
"ymd_hms" = lubridate::ymd_hms(Date),
"mdy_hms" = lubridate::mdy_hms(Date),
"dmy_hms" = lubridate::dmy_hms(Date),
stop("Invalid date format for ref1")))
dft <- dplyr::left_join(dft,ref1,by = "Date")
formula <- as.formula("~Flux+Flux1")
# if the second reference is present
if (!is.null(ref2)){
ref2 <- ref2[,c(Date,Flux2)]
names(ref2) <- c("Date","Flux2")
ref2 <- ref2 %>%
dplyr::mutate(Date=switch(Date_form, # convert the date into right format depending on the input format
"ymd_hms" = lubridate::ymd_hms(Date),
"mdy_hms" = lubridate::mdy_hms(Date),
"dmy_hms" = lubridate::dmy_hms(Date),
stop("Invalid date format for ref2")))
dft <- dplyr::left_join(dft,ref2,by = "Date")
formula <- as.formula("~Flux+Flux1+Flux2")
}
# if the third reference is present
if (!is.null(ref3)){
ref3 <- ref3[,c(Date,Flux3)]
names(ref3) <- c("Date","Flux3")
ref3 <- ref3 %>%
dplyr::mutate(Date=switch(Date_form, # convert the date into right format depending on the input format
"ymd_hms" = lubridate::ymd_hms(Date),
"mdy_hms" = lubridate::mdy_hms(Date),
"dmy_hms" = lubridate::dmy_hms(Date),
stop("Invalid date format for ref3")))
dft <- dplyr::left_join(dft,ref3,by = "Date")
formula <- as.formula("~Flux+Flux1+Flux2+Flux3")
}
# a vector for marks of each gap
mark <- rep(0,nrow(dft))
# a number to record the number of failed regression
nf <- 0
### gap filling by the marked index of each gap ----------
for (i in 1:max(mk)) {
indx <- which(mk==i) # index of the gap
# define the sampling window
wind_st <- ifelse(min(indx)-winID>=0,min(indx)-winID,1) # use the beginning of time series if not enough sample points are present
wind_ed <- ifelse(max(indx)+winID>nrow(data),nrow(data),max(indx)+winID) # use the end if not enough
# extract data to fit the model
df_em <- data.frame(dft[wind_st:wind_ed,],
mk=mk[wind_st:wind_ed])
# EM imputation
if (method=="spline"){ # use spline as default
df_out <- try(mtsdi::mnimput(formula = formula,
df_em,
ts=ts, method="spline",
sp.control=list(df=sp_df),
...
),
silent = T)
} else { # or use other methods
df_out <- try(mtsdi::mnimput(formula = formula,
df_em,
ts=ts, method=method,
...
),
silent = T)
}
# if error
if (class(df_out)=="try-error"){
if (fail == "ave"){ # use average in the sampling window
gap[indx] <- mean(dft$Flux[wind_st:wind_ed],na.rm = T)
mark[indx] <- 2 # failed to filled gap
nf <- nf+1 # add up the failed times
print(paste0("#",i," out of ",max(mk)," gaps: Failed...")) # for checking progress
} else { # or use the designated value
gap[indx] <- fail
mark[indx] <- 2 # failed to filled gap
nf <- nf+1 # add up the failed times
print(paste0("#",i," out of ",max(mk)," gaps: Failed...")) # for checking progress
}
} else { # if imputation succeed
gap[indx] <- df_out$filled.dataset$Flux[df_em$mk==i]
mark[indx] <- 1 # filled gap
print(paste0("#",i," out of ",max(mk)," gaps: succeed!!")) # for checking progress
}
} # end of the loop
df_new <- data.frame(data,
filled = gap,
tem = dft[,"Flux"],
mark) %>%
dplyr::mutate(filled = ifelse(mark==0,tem,filled)) %>%
dplyr::select(-tem) # drop the temperory column
# print a summary of the gapfilling ------------
stat <- table(mk)[-1] # number of data points in each gap
# print using "cat" for break into lines
cat(paste0("","\n",
"##### Summary #####","\n",
"","\n",
"Total gaps: ",max(mk),"\n",
"< 1 day: ",sum(stat<pt_h*24),"\n",
">= 1 & < 7 days: ",sum(stat>=pt_h*24 & stat<pt_h*24*7),"\n",
">= 7 & < 15 days: ",sum(stat>=pt_h*24*7 & stat<pt_h*24*15),"\n",
">= 15 days: ",sum(stat>=pt_h*24*15),"\n",
"Failed gaps: ",nf
))
# return the output data frame
return(df_new)
}
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