Exposit runoff calculations for surface water

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+#' Runoff loss percentages as used in Exposit 3
+#'
+#' A table of the loss percentages used in Exposit 3 for the twelve different Koc classes
+#'
+#' @name perc_runoff_exposit
+#' @format A data frame with percentage values for the dissolved fraction and the fraction
+#'   bound to eroding particles, with Koc classes used as row names
+#'   \describe{
+#'     \item{dissolved}{The percentage of the applied substance transferred to an
+#'       adjacent water body in the dissolved phase}
+#'     \item{bound}{The percentage of the applied substance transferred to an
+#'       adjacent water body bound to eroding particles}
+#'   }
+#' @source Excel 3.01 spreadsheet available from
+#'   \url{https://www.bvl.bund.de/DE/04_Pflanzenschutzmittel/03_Antragsteller/04_Zulassungsverfahren/07_Naturhaushalt/psm_naturhaush_node.html#doc1400590bodyText3}
+#' @export
+#' @examples
+#' print(perc_runoff_exposit)
+Koc_breaks <- c(0, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, Inf)
+tmp <- paste(Koc_breaks[1:11], Koc_breaks[2:12], sep = "-")
+Koc_classes <- c(tmp[1], paste0(">", tmp[2:11]), ">50000")
+perc_runoff_exposit <- data.frame(
+  Koc_lower_bound = Koc_breaks[1:12],
+  dissolved = c(0.11, 0.151, 0.197, 0.248, 0.224, 0.184, 0.133, 0.084, 0.037, 0.031, 0.014, 0.001),
+  bound = c(0, 0, 0, 0.001, 0.004, 0.020, 0.042, 0.091, 0.159, 0.192, 0.291, 0.451))
+rownames(perc_runoff_exposit) <- Koc_classes
+
+#' Runoff reduction percentages as used in Exposit
+#'
+#' A table of the runoff reduction percentages used in Exposit 3 for different vegetated buffer widths
+#'
+#' @name perc_runoff_reduction_exposit
+#' @format A named list of data frames with reduction percentage values for the
+#' dissolved fraction and the fraction bound to eroding particles, with
+#' vegetated buffer widths as row names. The names of the list items are the Exposit versions
+#' from which the values were taken.
+#'   \describe{
+#'     \item{dissolved}{The reduction percentage for the dissolved phase}
+#'     \item{bound}{The reduction percentage for the particulate phase}
+#'   }
+#' @source Excel 3.01 spreadsheet available from
+#'   \url{https://www.bvl.bund.de/DE/04_Pflanzenschutzmittel/03_Antragsteller/04_Zulassungsverfahren/07_Naturhaushalt/psm_naturhaush_node.html#doc1400590bodyText3}
+#' @export
+#' @examples
+#' print(perc_runoff_reduction_exposit)
+buffers <- c("No buffer", paste(c(5, 10, 20), "m"))
+perc_runoff_reduction_exposit <- list(
+   "3.01" = data.frame(
+    dissolved = c(0, 40, 60, 80),
+    bound = c(0, 40, 85, 95),
+    row.names = buffers),
+  "2.0" = data.frame(
+    dissolved = c(0, 97.5),
+    bound = c(0, 97.5),
+    row.names = c("No buffer", "20 m"))
+)
+
+#' Calculate PEC surface water due to runoff and erosion as in Exposit 3
+#'
+#' This is a reimplementation of the calculation described in the Exposit 3.01 spreadsheet file,
+#' in the worksheet "Konzept Runoff". Calculation of sediment PEC values is not implemented.
+#'
+#' @param rate The application rate in g/ha
+#' @param Koc The sorption coefficient to soil organic carbon
+#' @param DT50 The soil half-life in days
+#' @param t_runoff The time between application and the runoff event, where degradation occurs, in days
+#' @param exposit_reduction_version The version of the reduction factors to be used
+#' @param V_ditch The volume of the ditch is assumed to be 1 m * 100 m * 30 cm = 30 m3
+#' @param V_event The unreduced runoff volume, equivalent to 10 mm precipitation on 1 ha
+#' @return A list containing the following components
+#'   \describe{
+#'     \item{Input}{A matrix containing dissolved and bound input for the different distances}
+#'     \item{PEC_sw_runoff}{A matrix containing PEC values for dissolved and bound substance
+#'       for the different distances. If the rate was given in g/ha, the PECsw are in microg/L.}
+#'   }
+#' @export
+#' @source Excel 3.01 spreadsheet available from
+#'   \url{https://www.bvl.bund.de/DE/04_Pflanzenschutzmittel/03_Antragsteller/04_Zulassungsverfahren/07_Naturhaushalt/psm_naturhaush_node.html#doc1400590bodyText3}
+#' @seealso \code{\link{perc_runoff_exposit}} for runoff loss percentages and \code{\link{perc_runoff_reduction_exposit}} for runoff reduction percentages used
+#' @examples
+#'   PEC_sw_exposit_runoff(500, 150)
+PEC_sw_exposit_runoff <- function(rate, Koc, DT50 = Inf, t_runoff = 3,
+  exposit_reduction_version = c("3.01", "2.0"),
+  V_ditch = 30, V_event = 100)
+{
+  k_deg <- log(2)/DT50
+  input <- rate * 1 * exp(-k_deg * t_runoff) # assumes 1 ha treated area
+
+  if (length(Koc) > 1) stop("Only one compound at a time supported")
+
+  exposit_reduction_version <- match.arg(exposit_reduction_version)
+  red_water <- perc_runoff_reduction_exposit[[exposit_reduction_version]]["dissolved"] / 100
+  red_bound <- perc_runoff_reduction_exposit[[exposit_reduction_version]]["bound"] / 100
+  reduction_runoff <- perc_runoff_reduction_exposit[[exposit_reduction_version]] / 100
+  transfer_runoff <- 1 - reduction_runoff
+
+  V_runoff <- V_event * (1 - reduction_runoff[["dissolved"]]) # m3
+  V_ditch_runoff <- V_ditch + V_runoff
+  V_flowing_ditch_runoff <- 2 * V_ditch_runoff
+  f_runoff_exposit <- function(Koc) {
+    Koc_breaks <- c(perc_runoff_exposit$Koc_lower_bound, Inf)
+    Koc_classes <- as.character(cut(Koc, Koc_breaks, labels = rownames(perc_runoff_exposit)))
+    perc_runoff <- perc_runoff_exposit[Koc_classes, c("dissolved", "bound")]
+    return(unlist(perc_runoff) / 100)
+  }
+  f_runoff <- f_runoff_exposit(Koc)
+  runoff_dissolved <- input * f_runoff["dissolved"] * transfer_runoff["dissolved"]
+  runoff_bound <- input * f_runoff["bound"] * transfer_runoff["bound"]
+  runoff_input <- cbind(runoff_dissolved, runoff_bound)
+  runoff_input$total <- runoff_input$dissolved + runoff_input$bound
+
+  PEC_sw_runoff <- 1000 * runoff_input / V_flowing_ditch_runoff
+
+  result <- list(Rate = rate,
+                 Koc = Koc,
+                 Input = runoff_input,
+                 PEC_sw_runoff = PEC_sw_runoff)
+  return(result)
+}