# Register global variables
if(getRversion() >= '2.15.1') utils::globalVariables(c("destination", "study_type", "TP_identifier",
"soil_scenario_data_EFSA_2015",
"soil_scenario_data_EFSA_2017", "bottom"))
#' Calculate predicted environmental concentrations in soil
#'
#' This is a basic calculation of a contaminant concentration in bulk soil
#' based on complete, instantaneous mixing. If an interval is given, an
#' attempt is made at calculating a long term maximum concentration using
#' the concepts layed out in the PPR panel opinion (EFSA PPR panel 2012
#' and in the EFSA guidance on PEC soil calculations (EFSA, 2015, 2017).
#'
#' This assumes that the complete load to soil during the time specified by
#' 'interval' (typically 365 days) is dosed at once. As in the PPR panel
#' opinion cited below (EFSA PPR panel 2012), only temperature correction using the
#' Arrhenius equation is performed.
#'
#' Total soil and porewater PEC values for the scenarios as defined in the EFSA
#' guidance (2017, p. 14/15) can easily be calculated.
#' @note While time weighted average (TWA) concentrations given in the examples
#' from the EFSA guidance from 2015 (p. 80) are be reproduced, this is not
#' true for the TWA concentrations given for the same example in the EFSA guidance
#' from 2017 (p. 92).
#' @note According to the EFSA guidance (EFSA, 2017, p. 43), leaching should be
#' taken into account for the EFSA 2017 scenarios, using the evaluation depth
#' (here mixing depth) as the depth of the layer from which leaching takes
#' place. However, as the amount leaching below the evaluation depth
#' (often 5 cm) will partly be mixed back during tillage, the default in this function
#' is to use the tillage depth for the calculation of the leaching rate.
#' @note If temperature information is available in the selected scenarios, as
#' e.g. in the EFSA scenarios, the DT50 for groundwater modelling
#' (destination 'PECgw') is taken from the chent object, otherwise the DT50
#' with destination 'PECsoil'.
#' @importFrom methods is
#' @param rate Application rate in units specified below
#' @param rate_units Defaults to g/ha
#' @param interception The fraction of the application rate that does not reach the soil
#' @param mixing_depth Mixing depth in cm
#' @param interval Period of the deeper mixing. The default is NA, i.e. no
#' deeper mixing. For annual deeper mixing, set this to 365 when degradation
#' units are in days
#' @param n_periods Number of periods to be considered for long term PEC calculations
#' @param PEC_units Requested units for the calculated PEC. Only mg/kg currently supported
#' @param PEC_pw_units Only mg/L currently supported
#' @param tillage_depth Periodic (see interval) deeper mixing in cm
#' @param leaching_depth EFSA (2017) uses the mixing depth (ecotoxicological
#' evaluation depth) to calculate leaching for annual crops where tillage
#' takes place. By default, losses from the layer down to the tillage
#' depth are taken into account in this implementation.
#' @param cultivation Does mechanical cultivation in the sense of EFSA (2017)
#' take place, i.e. twice a year to a depth of 5 cm? Ignored for scenarios
#' other than EFSA_2017
#' @param crop Ignored for scenarios other than EFSA_2017. Only annual crops
#' are supported when these scenarios are used. Only crops with a single cropping
#' cycle per year are currently supported.
#' @param chent An optional chent object holding substance specific information. Can
#' also be a name for the substance as a character string
#' @param DT50 If specified, overrides soil DT50 endpoints from a chent object
#' If DT50 is not specified here and not available from the chent object, zero
#' degradation is assumed
#' @param FOMC If specified, it should be a named numeric vector containing
#' the FOMC parameters alpha and beta. This overrides any other degradation
#' endpoints, and the degradation during the interval and after the maximum PEC
#' is calculated using these parameters without temperature correction
#' @param Koc If specified, overrides Koc endpoints from a chent object
#' @param Kom Calculated from Koc by default, but can explicitly be specified
#' as Kom here
#' @param t_avg Averaging times for time weighted average concentrations
#' @param t_act Time series for actual concentrations
#' @param scenarios If this is 'default', the DT50 will be used without correction
#' and soil properties as specified in the REACH guidance (R.16, Table
#' R.16-9) are used for porewater PEC calculations. If this is "EFSA_2015",
#' the DT50 is taken to be a modelling half-life at 20°C and pF2 (for when
#' 'chent' is specified, the DegT50 with destination 'PECgw' will be used),
#' and corrected using an Arrhenius activation energy of 65.4 kJ/mol. Also
#' model and scenario adjustment factors from the EFSA guidance are used.
#' @param leaching Should leaching be taken into account? The default is FALSE,
#' except when the EFSA_2017 scenarios are used.
#' @param porewater Should equilibrium porewater concentrations be estimated
#' based on Kom and the organic carbon fraction of the soil instead of total
#' soil concentrations? Based on equation (7) given in the PPR panel opinion
#' (EFSA 2012, p. 24) and the scenarios specified in the EFSA guidance (2015,
#' p. 13).
#' @return The predicted concentration in soil
#' @references EFSA Panel on Plant Protection Products and their Residues (2012)
#' Scientific Opinion on the science behind the guidance for scenario
#' selection and scenario parameterisation for predicting environmental
#' concentrations of plant protection products in soil. \emph{EFSA Journal}
#' \bold{10}(2) 2562, doi:10.2903/j.efsa.2012.2562
#'
#' EFSA (European Food Safety Authority) 2017) EFSA guidance document for
#' predicting environmental concentrations of active substances of plant
#' protection products and transformation products of these active substances
#' in soil. \emph{EFSA Journal} \bold{15}(10) 4982
#' doi:10.2903/j.efsa.2017.4982
#'
#' EFSA (European Food Safety Authority) (2015) EFSA guidance document for
#' predicting environmental concentrations of active substances of plant
#' protection products and transformation products of these active substances
#' in soil. \emph{EFSA Journal} \bold{13}(4) 4093
#' doi:10.2903/j.efsa.2015.4093
#'
#' @author Johannes Ranke
#' @export
#' @examples
#' PEC_soil(100, interception = 0.25)
#'
#' # This is example 1 starting at p. 92 of the EFSA guidance (2017)
#' # Note that TWA concentrations differ from the ones given in the guidance
#' # for an unknown reason (the values from EFSA (2015) can be reproduced).
#' PEC_soil(1000, interval = 365, DT50 = 250, t_avg = c(0, 21),
#' Kom = 1000, scenarios = "EFSA_2017")
#' PEC_soil(1000, interval = 365, DT50 = 250, t_av = c(0, 21),
#' Kom = 1000, scenarios = "EFSA_2017", porewater = TRUE)
#'
#' # This is example 1 starting at p. 79 of the EFSA guidance (2015)
#' PEC_soil(1000, interval = 365, DT50 = 250, t_avg = c(0, 21),
#' scenarios = "EFSA_2015")
#' PEC_soil(1000, interval = 365, DT50 = 250, t_av = c(0, 21),
#' Kom = 1000, scenarios = "EFSA_2015", porewater = TRUE)
#'
#' # The following is from example 4 starting at p. 85 of the EFSA guidance (2015)
#' # Metabolite M2
#' # Calculate total and porewater soil concentrations for tier 1 scenarios
#' # Relative molar mass is 100/300, formation fraction is 0.7 * 1
#' results_pfm <- PEC_soil(100/300 * 0.7 * 1 * 1000, interval = 365, DT50 = 250, t_avg = c(0, 21),
#' scenarios = "EFSA_2015")
#' results_pfm_pw <- PEC_soil(100/300 * 0.7 * 1000, interval = 365, DT50 = 250, t_av = c(0, 21),
#' Kom = 100, scenarios = "EFSA_2015", porewater = TRUE)
PEC_soil <- function(rate, rate_units = "g/ha", interception = 0,
mixing_depth = 5,
PEC_units = "mg/kg", PEC_pw_units = "mg/L",
interval = NA, n_periods = Inf,
tillage_depth = 20,
leaching_depth = tillage_depth,
crop = "annual",
cultivation = FALSE,
chent = NA,
DT50 = NA,
FOMC = NA,
Koc = NA, Kom = Koc / 1.724,
t_avg = 0,
t_act = NULL,
scenarios = c("default", "EFSA_2017", "EFSA_2015"),
leaching = scenarios == "EFSA_2017",
porewater = FALSE)
{
# Comments with equation numbers in parentheses refer to
# the numbering in the EFSA guidance from 2017, appendix A
rate_to_soil = (1 - interception) * rate
rate_units = match.arg(rate_units)
PEC_units = match.arg(PEC_units)
scenarios = match.arg(scenarios)
if (scenarios == "EFSA_2017") {
if (crop != "annual") stop("Only annual crops are currently supported")
if (cultivation) stop("Permanent crops with mechanical cultivation are currently not supported")
}
sce <- switch(scenarios,
default = data.frame(rho = 1.5, T_arr = NA, theta_fc = 0.2, f_om = 1.724 * 0.02,
f_sce = 1, f_mod = 1, row.names = "default"),
EFSA_2015 = if (porewater) soil_scenario_data_EFSA_2015[4:6, ]
else soil_scenario_data_EFSA_2015[1:3, ],
EFSA_2017 = if (porewater) soil_scenario_data_EFSA_2017[4:6, ]
else soil_scenario_data_EFSA_2017[1:3, ]
)
n_sce = nrow(sce)
soil_volume = 100 * 100 * (mixing_depth/100) # in m3
soil_mass = soil_volume * sce$rho * 1000 # in kg
# In EFSA (2017), f_om is depth dependent for permanent crops
# For annual crops, the correction factor is 1 (uniform f_om is
# assumed)
mixing_depth_string <- paste(mixing_depth, "cm")
tillage_depth_string <- paste(tillage_depth, "cm")
if (scenarios == "EFSA_2017" & crop != "annual") {
# Correction factors f_f_om with depth according to EFSA 2017, p. 15
f_f_om_depth = data.frame(
depth = c("0-5", "5-10", "10-20", "20-30"),
bottom = c(5, 10, 20, 30),
thickness = c(5, 5, 10, 10),
f_f_om_no_cultivation = c(1.95, 1.30, 0.76, 0.62),
f_f_om_cultivation = c(1.50, 1.20, 0.90, 0.75))
# Averages for the 0-5 cm and 0-20 cm layers
f_f_om_layer = data.frame(
layer = c("0-5", "0-20"),
f_f_om_no_cultivation = c(1.95, (5 * 1.95 + 5 * 1.3 + 10 * 0.76)/20),
f_f_om_cultivation = c(1.50, (5 * 1.5 + 5 * 1.2 + 10 * 0.9)/20))
# The resulting mean value for 0-20 cm and no cultivation of 1.1925 is
# consistent with the value of 1.19 given in Table B.4 on p. 54 of the
# 2017 EFSA guidance
f_f_om_average <- function(depth, cultivation) {
rownames(f_f_om_layer) = paste(f_f_om_layer$layer, "cm")
if (depth %in% c(5, 20)) {
if (cultivation) {
return(f_f_om_layer[paste0("0-", depth, " cm"), "f_f_om_cultivation"])
} else {
return(f_f_om_layer[paste0("0-", depth, " cm"), "f_f_om_no_cultivation"])
}
} else {
stop("Depths other than 5 and 20 cm are not supported when using EFSA 2017 scenarios for permanent crops")
}
}
# For the loss via leaching, the equilibrium and therefore the f_om at the
# bottom of the layer is probably most relevant. Unfortunately this is not
# clarified in the guidance.
f_f_om_bottom <- function(depth, cultivation) {
bottom_depth <- depth # rename to avoid confusion when subsetting
if (cultivation) {
f_f_om <- subset(f_f_om_depth, bottom == bottom_depth)$f_f_om_cultivation
} else {
f_f_om <- subset(f_f_om_depth, bottom == bottom_depth)$f_f_om_no_cultivation
}
return(f_f_om)
}
} else {
f_f_om_average <- f_f_om_bottom <- function(depth, cultivation) 1
}
# The following is C_T,ini from EFSA 2012, p. 22, but potentially with interception > 0
PEC_soil_ini = rate_to_soil * 1000 / soil_mass # in mg/kg (A1)
# Decide which DT50 to take, or set degradation to zero if no DT50 available
if (is.na(DT50) & is(chent, "chent")) {
if (all(is.na(sce$T_arr))) { # No temperature correction
DT50 <- subset(chent$soil_degradation_endpoints, destination == "PECsoil")$DT50
} else {
DT50 <- subset(chent$soil_degradation_endpoints, destination == "PECgw")$DT50
}
if (length(DT50) > 1) stop("More than one PECsoil DT50 in chent object")
if (length(DT50) == 0) DT50 <- Inf
}
k_ref = log(2)/DT50 # (A5)
# Temperature correction of degradation (accumulation)
if (all(is.na(sce$T_arr))) { # No temperature correction
f_T = 1
} else {
# Temperature correction as in EFSA 2012 p. 23
f_T = ifelse(sce$T_arr == 0,
0, # (A4b)
exp(- (65.4 / 0.008314) * (1/(sce$T_arr + 273.15) - 1/293.15))) # (A4a)
}
# Define Kom if needed
if (leaching | porewater) {
# If Kom is not specified, try to get K(f)oc
if (is.na(Kom)) {
# If Koc not specified, try to get K(f)oc from chent
if (is.na(Koc) & is(chent, "chent")) {
Koc <- soil_Kfoc(chent)
} else {
stop("No Kom information specified")
}
Kom <- Koc / 1.724
}
}
if (leaching) {
leaching_depth_string <- paste(leaching_depth, "cm")
f_q <- c("1 cm" = 0.8, "2.5 cm" = 0.75, "5 cm" = 0.7, "20 cm" = 0.5) # EFSA 2017 p. 54
if (leaching_depth_string %in% names(f_q)) {
q_mm_year = f_q[leaching_depth_string] * sce$prec # Irrigation at tier 1? I have not found values for Tier 1
q_dm_day = q_mm_year / (100 * 365)
leaching_depth_dm <- leaching_depth / 10
k_leach = q_dm_day/(leaching_depth_dm * (sce$theta_fc + sce$rho * f_f_om_average(leaching_depth, cultivation) * sce$f_om * Kom))
} else {
stop("Leaching can not be calculated, because f_q for this leaching depth is undefined")
}
} else {
k_leach = 0
}
# X is the fraction left after one period (EFSA 2017 guidance p. 23)
X = exp(- (k_ref * f_T + k_leach) * interval) # (A3)
# f_accu is the fraction left after n periods (X + X^2 + ...)
f_accu = 0
if (!is.na(interval)) {
if (n_periods == Inf) {
if (!is.na(FOMC[1])) {
f_accu = get_vertex(x = 8:10, y = PEC_FOMC_accu_rel(n = 10, interval, FOMC)[8:10])$yv
warning("The long term calculation is based on a pseudo-plateau constructed\n ",
"by fitting a parabola through the residues after 8, 9 and 10 years.\n ",
"This is the method used by the ESCAPE software tool for separate consideration of residues.\n ",
"Please check the validity by specifying e.g. n_periods = 20 or 50.")
} else {
f_accu = X/(1 - X) # part of (A2)
}
} else {
for (i in 1:n_periods) {
if (!is.na(FOMC[1])) {
f_accu = f_accu + 1 / (((i * interval)/FOMC[["beta"]]) + 1)^FOMC[["alpha"]]
} else {
f_accu = f_accu + X^i
}
}
}
}
f_tillage = mixing_depth / tillage_depth
PEC_background = f_accu * f_tillage * PEC_soil_ini # (A2)
PEC_soil = PEC_soil_ini + PEC_background # (A6)
# Get porewater PEC if requested
if (porewater) {
PEC_soil = PEC_soil/((sce$theta_fc/sce$rho) + f_f_om_average(mixing_depth, cultivation) * sce$f_om * Kom) # (A7)
}
# Scenario adjustment factors
PEC_soil_sce = PEC_soil * sce$f_sce
# Model adjustment factors
PEC_soil_sce_mod = PEC_soil_sce * sce$f_mod
if (is.null(t_act)) {
result <- matrix(NA, ncol = n_sce, nrow = length(t_avg),
dimnames = list(t_avg = t_avg, scenario = rownames(sce)))
result[1, ] <- PEC_soil_sce_mod
for (i in seq_along(t_avg)) {
t_av_i <- t_avg[i]
k_avg <- f_T * k_ref # Leaching not taken into account, EFSA 2017 p. 43
if (t_av_i > 0) {
# Equation 10 from p. 24 (EFSA 2015)
if (!is.na(FOMC[1])) {
result[i, ] <- PEC_soil_sce_mod * (FOMC[["beta"]])/(t_av_i * (1 - FOMC[["alpha"]])) *
((t_av_i/FOMC[["beta"]] + 1)^(1 - FOMC[["alpha"]]) - 1)
} else {
result[i, ] <- PEC_soil_sce_mod/(t_av_i * k_avg) * (1 - exp(- k_avg * t_av_i)) # (A8)
}
}
}
} else {
if (!identical(t_avg, 0)) stop("Either t_act or t_avg can be specified")
result <- matrix(NA, ncol = n_sce, nrow = length(t_act),
dimnames = list(t_act = t_act, scenario = rownames(sce)))
result[1, ] <- PEC_soil_sce_mod
for (i in seq_along(t_act)) {
t_ac_i <- t_act[i]
k_act <- f_T * k_ref # Leaching not taken into account
if (t_ac_i > 0) {
# Equation 10 from p. 24 (EFSA 2015)
if (!is.na(FOMC[1])) {
result[i, ] <-
PEC_soil_sce_mod / ((t_ac_i/FOMC[["beta"]] + 1)^(FOMC[["alpha"]]))
} else {
result[i, ] <- PEC_soil_sce_mod * exp(- k_act * t_ac_i)
}
}
}
}
return(result)
}
#' Get the relative accumulation of an FOMC model over multiples of an interval
#' @param n number of applications
#' @param interval Time between applications
#' @param FOMC Named numeric vector containing the FOMC parameters alpha and beta
#' @return A numeric vector containing all n accumulation factors for the n applications
#' @export
PEC_FOMC_accu_rel <- function(n, interval, FOMC) {
PEC_accu_rel <- 0
for (i in 1:(n - 1)) {
PEC_accu_rel[i + 1] <- PEC_accu_rel[i] + mkin::FOMC.solution(i * interval, 1,
FOMC[["alpha"]], FOMC[["beta"]])
}
return(PEC_accu_rel)
}
#' Fit a parabola through three points
#'
#' This was inspired by an answer on stackoverflow
#' https://stackoverflow.com/a/717791
#' @param x Three x coordinates
#' @param y Three y coordinates
get_vertex <- function(x, y) {
m <- cbind(x^2, x, 1)
m_inv <- solve(m)
res <- m_inv %*% y
A <- res[1]
B <- res[2]
C <- res[3]
xv = -B / (2*A)
yv = C - B**2 / (4*A)
return(list(xv = xv, yv = yv, A = A, B = B, C = C))
}
#' Calculate initial and accumulation PEC soil for a set of metabolites
#'
#' @param rate Application rate in units specified below
#' @param mw_parent The molecular weight of the parent compound
#' @param mets A dataframe with metabolite identifiers as rownames
#' and columns "mw", "occ" and "DT50" holding their molecular weight,
#' maximum occurrence in soil and their soil DT50
#' @param interval The interval for accumulation calculations
#' @param ... Further arguments are passed to PEC_soil
#' @export
PEC_soil_mets <- function(rate, mw_parent, mets, interval = 365, ...)
{
result <- matrix(NA, nrow = nrow(mets), ncol = 3,
dimnames = list(mets = rownames(mets),
PECs = c("Initial",
"Plateau",
"Accumulation")))
result[, "Initial"] <- sapply(rownames(mets),
function(x) {
PEC_soil(mets[x, "occ"] * (mets[x, "mw"] / mw_parent) * rate,
interval = NA, ...)
}
)
result[, "Accumulation"] <- sapply(rownames(mets),
function(x) {
PEC_soil(mets[x, "occ"] * (mets[x, "mw"] / mw_parent) * rate,
DT50 = mets[x, "DT50"],
interval = interval, ...)
}
)
result[, "Plateau"] <- result[, "Accumulation"] -
result[, "Initial"]
return(result)
}
