R/glover.R

In streamDepletr: Estimate Streamflow Depletion Due to Groundwater Pumping

glover <- function(t, d, S, Tr) {
  #' Streamflow depletion with fully-penetrating stream and no streambed.
  #'
  #' @param t times you want output for [T]
  #' @param d distance from well to stream [L]
  #' @param S aquifer storage coefficient (specific yield if unconfined; storativity if confined)
  #' @param Tr aquifer transmissivity [L2/T]
  #' @details This function is described in Glover & Balmer (1954) based on work by Theis (1941). It contains numerous assumptions:
  #' \itemize{
  #'   \item Horizontal flow >> vertical flow (Dupuit assumptions hold)
  #'   \item Homogeneous, isotropic aquifer
  #'   \item Constant \code{Tr}: Aquifer is confined, or if unconfined change in head is small relative to aquifer thickness
  #'   \item Stream is straight, infinitely long, and remains in hydraulic connection to aquifer
  #'   \item Constant stream stage
  #'   \item No changes in recharge due to pumping
  #'   \item No streambank storage
  #'   \item Constant pumping rate
  #'   \item Aquifer extends to infinity
  #'   \item Stream fully penetrates through aquifer (see \link{hunt} or \link{hantush} for partially penetrating stream)
  #'   \item No streambed resistance to flow (see \link{hunt} or \link{hantush} for streambed resistance)
  #' }
  #' @return A numeric of \code{Qf}, streamflow depletion as fraction of pumping rate [-].
  #' If the pumping rate of the well (\code{Qw}; [L3/T]) is known, you can calculate volumetric streamflow depletion [L3/T] as \code{Qf*Qw}
  #' @references
  #' Glover, RE, and GG Balmer (1954).River Depletion Resulting from Pumping a Well near a River.
  #' Eos, Transactions American Geophysical Union 35(3): 468-70. doi:10.1029/TR035i003p00468.
  #'
  #' Theis, CV (1941). The Effect of a Well on the Flow of a Nearby Stream.
  #' Eos, Transactions American Geophysical Union 22(3): 734-38. https://doi.org/10.1029/TR022i003p00734.
  #'
  #' @examples
  #' glover(t = 1.5777e8, d = 1000, S = 0.2, Tr = 0.1)   # Glover & Balmer (1954) Table 1, Well 1
  #' glover(t = 1.5777e8, d = 5000, S = 0.2, Tr = 0.1)   # Glover & Balmer (1954) Table 1, Well 2
  #' glover(t = 1.5777e8, d = 10000, S = 0.2, Tr = 0.1)  # Glover & Balmer (1954) Table 1, Well 3
  #' @export

  Qf <- Rmpfr::erfc(sqrt(S * d * d / (4 * Tr * t)))
  return(Qf)
}