R/Gapf_NLS.R

In junbinzhao/FluxGapsR: Gap-filling for flux data using different methods

#' Gap-fill using NLS
#'
#' This function automatically gap-fills the missing data points (marked as "NA") in the soil respiration dataset
#' using the non-linear Levenberg-Marquardt algorithm as a function of the soil temperature. A Lloyd-Taylor model is used
#' to formulate the relationship (Lloyd & Taylor, 1994). In cases when Lloyd-Taylor model yields large residuals, a basic exponential
#' function is used instead ("Flux~a*exp(b*Ts)").
#'
#' @param data a data frame that includes the flux (with NA indicating the missing data) and soil temperature
#' @param Flux a string indicates the column name for the flux variable to be gap-filled
#' @param Ts a string indicates the column name for the soil temperature
#' @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 R10 the start value for the parameter R10 in the Lloyd-Taylor model (default: 10)
#' @param E0 the start value for the parameter E0 in the Lloyd-Taylor model (default: 400)
#' @param fail a string or a number, 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.)
#' @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
#' @references
#' Lloyd J., Taylor, J.A., 1994. On the Temperature Dependence of Soil Respiration. Functional Ecology. 8, 315-323.
#' @examples
#' # read example data
#' df <- read.csv(file = system.file("extdata", "Soil_resp_example.csv", package = "FluxGapsR"),header = T)
#' df_filled <- Gapfill_nls(data = df)
#' # visualize the gapfilled results
#' plot(df_filled$filled,col="red")
#' points(df_filled$Flux)
#' @export
Gapfill_nls <- function(data,
                        Flux = "Flux",
                        Ts = "Ts",
                        win = 5,
                        interval = 10,
                        R10 = 10,
                        E0 = 400,
                        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(Flux,Ts)]
  names(dft) <- c("Flux","Ts")
  # 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

    # fit the Lloyd-Taylor model
    fit1 <- try(minpack.lm::nlsLM(Flux~a*exp(b*(1/(283.15-227.13)-1/(Ts-227.13))),
                                 start = list(a=R10,b=E0),
                                 data = dft[wind_st:wind_ed,],
                                 control=minpack.lm::nls.lm.control(maxiter = 1000)
                                 ),
               silent = TRUE)
    # fit the basic model
    fit2 <- try(minpack.lm::nlsLM(Flux~a*exp(b*Ts),
                                 start = list(a=1,b=0.1),
                                 data = dft[wind_st:wind_ed,],
                                 control=minpack.lm::nls.lm.control(maxiter = 1000)
                                 ),
                silent = TRUE)

    # choose the model
    if (class(fit1)!="try-error") {
      if (class(fit2)!="try-error"){
        if (sum(summary(fit1)$residuals) > sum(summary(fit2)$residuals)){ # both are not error, choose the one with smaller residuals
          fit <- fit2
        } else {
          fit <- fit1
        }
      } else { # if fit2 is error, fit1 is not
        fit <- fit1
      }
    } else { # if fit1 is error
      fit <- fit2
    }

    # predict the gaps
    if (class(fit)!="try-error"){ # if the fit converged
      gap[indx] <- predict(fit,newdata=dft[indx,])
      mark[indx] <- 1 # filled gap
      print(paste0("#",i," out of ",max(mk)," gaps: succeed!!")) # for checking progress
    } else {
      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
      }
    }
  } # 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)
}