Skip to contents

Guarantee-based sizing of rainwater harvesting systems

Source: R/sizing.R
rh_sizing.Rd

These functions find the design value that guarantees zero deficit over the whole simulation, by repeatedly calling the engine rh_simulate():

Usage

rh_guaranteed_demand(
  precip,
  area,
  capacity,
  runoff = 0.8,
  efficiency = 0.85,
  initial = capacity,
  overflow_timing = c("after_demand", "before_demand"),
  method = c("bisection", "optimize", "step"),
  tol = 0.001,
  step = NULL
)

rh_guaranteed_capacity(
  precip,
  demand,
  area,
  runoff = 0.8,
  efficiency = 0.85,
  initial = NULL,
  overflow_timing = c("after_demand", "before_demand"),
  method = c("bisection", "optimize", "step"),
  tol = 0.001,
  step = NULL,
  max_capacity = NULL
)

rh_required_area(
  precip,
  demand,
  capacity,
  runoff = 0.8,
  efficiency = 0.85,
  initial = capacity,
  overflow_timing = c("after_demand", "before_demand"),
  method = c("bisection", "optimize", "step"),
  tol = 0.001,
  step = NULL,
  max_area = NULL
)

Arguments

precip

Numeric vector of precipitation depths, in millimetres (mm). Each element is one time step (typically a day).

area

Catchment area in square metres (m2). May be a vector of per-block areas, in which case the total sum(area) is used.

capacity

Reservoir capacity V, in cubic metres (m3).

runoff

Runoff coefficient C (the coeficiente de escoamento superficial), dimensionless in [0, 1]. Scalar or vector recycled to length(precip). Default 0.8.

efficiency

System efficiency eta (dimensionless, [0, 1]), accounting for the first-flush diverter/solids-discard device. Scalar or vector recycled to length(precip). ABNT NBR 15527:2019 recommends 0.85 when no data are available (the default).

initial

Initial stored volume S(0), in cubic metres (m3). For rh_guaranteed_demand() and rh_required_area() it defaults to capacity (full reservoir). For rh_guaranteed_capacity() the default NULL makes the reservoir start full at each trial capacity, and an explicit value is clamped to the trial capacity during the search.

overflow_timing

Order of operations within a time step:

  • "after_demand" (default): inflow is added, demand is withdrawn, and only the remainder can overflow. This is the continuity-equation form S(t) = S(t-1) + Q(t) - D(t) clamped to [0, V], the YBS (yield before spillage) operating rule of the rainwater-tank literature (Jenkins et al., 1978; Fewkes and Butler, 2000), and reproduces the published case-study results.

  • "before_demand": inflow is added and the reservoir overflows before demand is withdrawn, the YAS (yield after spillage) rule. It spills more water, giving slightly conservative yields, and is provided for sensitivity analysis.

method

Solver: "bisection" (default), "optimize" (automatic optimisation with stats::optimize()) or "step" (incremental search by step).

tol

Tolerance: a deficit not greater than tol is treated as zero, and the solver stops when the search interval is narrower than tol.

step

Increment for method = "step". Defaults to one thousandth of the search upper bound.

demand

Non-potable demand per time step, in cubic metres (m3). Scalar or vector recycled to length(precip).

max_capacity

Optional upper bound for the capacity search. Defaults to the total demand (which trivially guarantees no deficit), grown if needed.

max_area

Optional upper bound for the area search. Grown automatically until a feasible area is found.

Value

A single numeric value: the guaranteed demand (m3/day), guaranteed capacity (m3) or required area (m2).

Details

  • rh_guaranteed_demand() - the largest constant daily demand that can be met with no deficit (the demanda garantia).

  • rh_guaranteed_capacity() - the smallest reservoir capacity giving no deficit (the capacidade/volume garantia). The reservoir is assumed full at the start, so initial follows the trial capacity unless set.

  • rh_required_area() - the smallest catchment area giving no deficit.

Because the total deficit is monotone in each of these variables, the default solver is an efficient bisection controlled by tol. Two alternatives are available: an automatic optimiser ("optimize", base R stats::optimize()) and a simple incremental search ("step", a for-loop advancing by step).

Examples

precip <- rep(c(0, 0, 30, 0, 0, 0, 50), 8)
rh_guaranteed_demand(precip, area = 775.53, capacity = 5)
#> [1] 1.666442
rh_guaranteed_capacity(precip, demand = 0.4, area = 775.53)
#> [1] 1.200391
rh_required_area(precip, demand = 0.4, capacity = 5)
#> [1] 42.3708