# 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) }