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```
#' Evaluate parameter uncertainty
#'
#' This function searches for acceptable model solutions within the uncertainty
#' parameters and long-term storage balances using Latin hypercubes.
#'
#' The function creates n parameter sets using a Latin hypercube. It runs
#' `CityWaterBalance()` with each set, accepting solutions that meet
#' user-defined criteria for storage balances. It then computes the mean of
#' flow solutions, and doubles n until the difference between the means of old
#' and new solutions is less than tol for all flows. Defaults for parameter
#' value ranges are set to reasonable values, but they should be reconsidered
#' for each application. Defaults for storage balances are set high to allow
#' for solution discovery, however, acceptable values must be determined on a
#' case-by-case basis.
#'
#' @param data xts or zoo object. See CityWaterBalance function for details.
#' @param p list of initial parameter values. See CityWaterBalance function or
#' the inputs below for descriptions.
#' @param n integer number of initial parameter sets to search
#' @param tol tolerance acceptable difference mean flow solutions
#' @param interc vector of min and max fraction of pet lost to interception
#' @param et_mult vector of min and max multiplier for et
#' @param flow_mult vector of min and max multiplier for outflow
#' @param open_wat vector of min and max fraction of area that is open water
#' @param run_mult vector of min and max multiplier for runoff
#' @param run_css vector of min and max fraction of runoff diverted to sewers
#' @param bf_mult vector of min and max multiplier for baseflow
#' @param nonrev vector of min and max fraction of potable water supply lost to
#' leaks
#' @param ind_evap vector of min and max fraction of industrial use that
#' evaporates
#' @param wast_gen vector of min and max fraction of potable use that returns to
#' sewers
#' @param pot_atm vector of min and max fraction of potable use that evaporates
#' @param npot_infilt vector of min and max fraction of nonpotable use that
#' infiltrates
#' @param slud_evap vector of min and max fraction of wastewater that evaporates
#' from sludge
#' @param leak_css vector of min and max fraction of wastewater effluent from gw
#' infiltration
#' @param dgw vector of min and max fraction of groundwater from deep, confined
#' aquifers
#' @param dgw_rep vector of min and max multiplier for deep groundwater pumping
#' replacement
#' @param global_bal vector of min and max acceptable global water balance
#' values, cumulative over model run
#' @param sw_bal vector of min and max acceptable surface water balance
#' values, cumulative over model run
#' @param css_bal vector of min and max acceptable sewer system water balance
#' values, cumulative over model run
#' @param sgw_bal vector of min and max acceptable shallow groundwater balance
#' values, cumulative over model run
#' @param dgw_bal vector of min and max acceptable deep groundwater balance
#' values, cumulative over model run
#' @return out numeric solutions
#' @importFrom tgp lhs
#' @examples
#' \dontrun{
#' data <- cwb_data
#' data$cso <- 0
#' p <- list("interc" = 0,"et_mult" = 1,"flow_mult" = 1, "open_wat" = 0.02,
#' "run_mult" = 3.378, "run_css" = 0.35, "bf_mult" = 1,
#' "nonrev" = 0.08, "ind_evap" = 0.012, "wast_gen" = 0.85,
#' "pot_atm" = 0.13, "npot_infilt" = 0.5, "slud_evap" = 0,
#' "leak_css" = 0.05, "dgw" = 0.5, "dgw_rep" = 0.5)
#' out <- getSolutions(data, p, 10, 0.1)
#' }
#' @export
getSolutions <- function(data, p, n, tol = 0.01, interc = c(0,0.05),
et_mult = c(1,1.1), flow_mult = c(1,1.1),
open_wat = c(0.01,0.1), run_mult = c(1,5),
run_css = c(0.1,1), bf_mult = c(0.5,1.5),
nonrev = c(0.05,0.2), ind_evap = c(0.01,0.02),
wast_gen = c(0.75,0.9), pot_atm = c(0.10,0.15),
npot_infilt = c(0.25,0.75), slud_evap = c(0,0),
leak_css = c(0.05,0.25), dgw = c(0.5,0.5),
dgw_rep = c(0,1), global_bal = c(-500,500),
sw_bal =c(-500,500), css_bal = c(-500,500),
sgw_bal = c(-500,500), dgw_bal = c(-500,500)){
# initialize vectors
old <- rep(0,35)
new <- rep(tol*2,35)
# initialize solutions list
sols <- list()
sols[[1]] <- rep(NA,35)
j <- 1
k <- 1
# establish iteration criteria
crit <- max(abs(new-old))
# search until mean flow solution is below tol for all flows
while (crit == 0 | crit > tol | is.na(max(new-old))){
# create Latin hypercube for sampling parameter values
params <- lhs(n, rbind(interc,et_mult,flow_mult,open_wat,run_mult,run_css,
bf_mult,nonrev,ind_evap,wast_gen,pot_atm,npot_infilt,
slud_evap,leak_css,dgw,dgw_rep))
# run each parameter set through CityWaterBalance model
for (i in 1:nrow(params)){
p$interc <- params[i,1]
p$et_mult <- params[i,2]
p$flow_mult <- params[i,3]
p$open_wat <- params[i,4]
p$run_mult <- params[i,5]
p$run_css <- params[i,6]
p$bf_mult <- params[i,7]
p$nonrev <- params[i,8]
p$ind_evap <- params[i,9]
p$wast_gen <- params[i,10]
p$pot_atm <- params[i,11]
p$npot_infilt <- params[i,12]
p$slud_evap <- params[i,13]
p$leak_css <- params[i,14]
p$dgw <- params[i,15]
p$dgw_rep <- params[i,16]
# run model
m <- CityWaterBalance(data,p,FALSE)
g <- sum(m$global_balance)
# summarize model results
a <- colSums(m$state_vars)[1]
b <- colSums(m$state_vars)[2]
c <- colSums(m$state_vars)[3]
d <- colSums(m$state_vars)[4]
f <- colSums(m$all_flows)
# test if solution conditions are met and if so, save results
if (g >= global_bal[1] && g<= global_bal[2] && a >= sw_bal[1] &&
a <= sw_bal[2] && b >= css_bal[1] && b <= css_bal[2] &&
c >= sgw_bal[1] && c <= sgw_bal[2] && d >= dgw_bal[1] &&
d <= dgw_bal[2] ){
sols[[j]] <- f
j <- j+1
}
}
# aggregate results
old <- new
flows <- do.call(rbind,sols)
new <- apply(flows,2,mean)
crit <- max(abs(new-old))
if (is.na(max(new))){
print("No solutions found")
} else {
print(paste("Number of solutions: ", nrow(flows)))
print(paste("Max change between runs: ", crit))
}
k <- k+1
print(paste("------- Run ",k,"--------"))
}
colnames(flows) <- c("Interception", "Runoff", "Runoff to sewers",
"Infiltration","River inflow",
"Imports to surface waters","Imports for potable use",
"Surface water evaporation",
"Industrial use (SW)","Potable withdrawals (SW)",
"Non-potable withdrawals (SW)","Sewer infiltration",
"Baseflow","Industrial use (SGW)",
"Potable withdrawals (SGW)","Evapotranspiration",
"Non-potable withdrawals (SGW)",
"Recharge of deep groundwater",
"Industrial use (DGW)",
"Potable withdrawals (DGW)",
"Non-potable withdrawals (DGW)",
"Evaporation of industrial water",
"Discharge of industrial water",
"Conveyance of potable water","Leakage of potable water",
"Evaporation of potable water","Wastewater generation",
"Infiltration of potable water",
"Evaporation of non-potable water",
"Conveyance of wastewater","Evaporation of sludge",
"Wastewater discharge",
"Infiltration of non-potable water",
"Combined sewer overflows","River outflow")
return(flows)
}
```

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