R/ROScalc.r

In cffdrs: Canadian Forest Fire Danger Rating System

.ROScalc <- function(FUELTYPE, ISI, BUI, FMC, SFC, PC, PDF, CC, CBH){
  #############################################################################
  # Description:
  #   Computes the Rate of Spread prediction based on fuel type and FWI
  #   conditions. Equations are from listed FCFDG (1992) and Wotton et. al. 
  #   (2009), and are marked as such.
  #
  #   All variables names are laid out in the same manner as Forestry Canada 
  #   Fire Danger Group (FCFDG) (1992). Development and Structure of the 
  #   Canadian Forest Fire Behavior Prediction System." Technical Report 
  #   ST-X-3, Forestry Canada, Ottawa, Ontario.
  #
  #   Wotton, B.M., Alexander, M.E., Taylor, S.W. 2009. Updates and revisions to
  #   the 1992 Canadian forest fire behavior prediction system. Nat. Resour. 
  #   Can., Can. For. Serv., Great Lakes For. Cent., Sault Ste. Marie, Ontario, 
  #   Canada. Information Report GLC-X-10, 45p.
  #
  # Args:
  #   FUELTYPE: The Fire Behaviour Prediction FuelType
  #        ISI: Intiial Spread Index
  #        BUI: Buildup Index
  #        FMC: Foliar Moisture Content
  #        SFC: Surface Fuel Consumption (kg/m^2)
  #         PC: Percent Conifer (%)
  #        PDF: Percent Dead Balsam Fir (%)
  #         CC: Constant
  #        CBH: Crown to base height(m)
  # Returns:
  #   ROS: Rate of spread (m/min)
  #
  #############################################################################
  #Set up some data vectors
  NoBUI <- rep(-1,length(ISI))
  d <- c("C1", "C2", "C3", "C4", "C5", "C6", "C7", "D1", "M1", "M2", "M3", "M4",
         "S1", "S2", "S3", "O1A", "O1B")
  a <- c(90, 110, 110, 110, 30, 30, 45, 30, 0, 0, 120, 100, 75, 40, 55, 190, 
         250)
  b <- c(0.0649, 0.0282, 0.0444, 0.0293, 0.0697, 0.0800, 0.0305, 0.0232, 0, 0, 
         0.0572, 0.0404, 0.0297, 0.0438, 0.0829, 0.0310, 0.0350)
  c0 <- c(4.5, 1.5, 3.0, 1.5, 4.0, 3.0, 2.0, 1.6, 0, 0, 1.4, 1.48, 1.3, 1.7, 
          3.2, 1.4, 1.7)
  names(a) <- names(b) <- names(c0) <- d

  #Calculate RSI (set up data vectors first)
  #Eq. 26 (FCFDG 1992) - Initial Rate of Spread for Conifer and Slash types
  RSI <- rep(-1,length(ISI))
  RSI <- ifelse(FUELTYPE %in% c("C1", "C2", "C3", "C4", "C5", "C7", "D1", "S1", 
                                "S2", "S3"),
          as.numeric(a[FUELTYPE] * (1 - exp(-b[FUELTYPE] * ISI))**c0[FUELTYPE]),
          RSI)
  #Eq. 27 (FCFDG 1992) - Initial Rate of Spread for M1 Mixedwood type
  RSI <- ifelse(FUELTYPE %in% c("M1"), 
            PC/100 * 
              .ROScalc(rep("C2", length(ISI)),ISI,NoBUI,FMC,SFC,PC,PDF,CC,CBH)
              + (100 - PC) / 100 *
              .ROScalc(rep("D1", length(ISI)),ISI,NoBUI,FMC,SFC,PC,PDF,CC, CBH),
            RSI)
  #Eq. 27 (FCFDG 1992) - Initial Rate of Spread for M2 Mixedwood type
  RSI <- ifelse(FUELTYPE %in% c("M2"), 
            PC/100 * 
              .ROScalc(rep("C2", length(ISI)),ISI,NoBUI,FMC,SFC,PC,PDF,CC,CBH)
              + 0.2*(100-PC)/100 *
              .ROScalc(rep("D1", length(ISI)),ISI,NoBUI,FMC,SFC,PC,PDF,CC, CBH),
            RSI)
  #Initial Rate of Spread for M3 Mixedwood
  RSI_m3 <- rep(-99,length(ISI))
  #Eq. 30 (Wotton et. al 2009)
  RSI_m3 <- 
    ifelse(FUELTYPE %in% c("M3"), 
      as.numeric(a[["M3"]] * ((1 - exp(-b[["M3"]] * ISI))**c0[["M3"]])), RSI_m3)
  #Eq. 29 (Wotton et. al 2009)
  RSI <- 
    ifelse(FUELTYPE %in% c("M3"),
      PDF/100* RSI_m3 + (1-PDF/100) * 
        .ROScalc(rep("D1", length(ISI)), ISI, NoBUI, FMC, SFC, PC, PDF, CC,CBH),
      RSI)
  #Initial Rate of Spread for M4 Mixedwood
  RSI_m4 <- rep(-99,length(ISI))
  #Eq. 30 (Wotton et. al 2009)  
  RSI_m4 <- 
    ifelse(FUELTYPE %in% c("M4"), 
      as.numeric(a[["M4"]] * ((1 - exp(-b[["M4"]] * ISI))**c0[["M4"]])), RSI_m4)
  #Eq. 33 (Wotton et. al 2009)
  RSI <- 
    ifelse(FUELTYPE %in% c("M4"),
      PDF / 100* RSI_m4 + 0.2 * (1 - PDF / 100)* 
        .ROScalc(rep("D1", length(ISI)), ISI, NoBUI, FMC, SFC, PC, PDF, CC,CBH),
      RSI)
  #Eq. 35b (Wotton et. al. 2009) - Calculate Curing function for grass
  CF <- rep(-99,length(ISI))
  CF <- 
    ifelse(FUELTYPE %in% c("O1A", "O1B"),
           ifelse(CC < 58.8, 
                  0.005 * (exp(0.061 * CC) - 1), 
                  0.176 + 0.02 * (CC - 58.8)), 
           CF)
  #Eq. 36 (FCFDG 1992) - Calculate Initial Rate of Spread for Grass
  RSI <- 
    ifelse(FUELTYPE %in% c("O1A", "O1B"),
      a[FUELTYPE] * ((1 - exp(-b[FUELTYPE] * ISI))**c0[FUELTYPE]) * CF,
    RSI)
  #Calculate C6 separately
  ROS <- 
    ifelse(FUELTYPE %in% c("C6"),
      .C6calc(FUELTYPE, ISI, BUI, FMC, SFC, CBH, option = "ROS"),
      .BEcalc(FUELTYPE, BUI) * RSI)
  #add a constraint
  ROS <- ifelse(ROS <= 0,0.000001,ROS)
  return(ROS)
}