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Daily water-balance simulation of a rainwater harvesting reservoir

Source: R/simulate.R
rh_simulate.Rd

Simulates the daily operation of a finite rainwater reservoir using the method of simulation of ABNT NBR 15527:2007 (Annex A.2), with the available-volume equation of NBR 15527:2019 (see rh_available_volume()). The mass-balance (continuity) equation for a finite reservoir is

Usage

rh_simulate(
  precip,
  demand,
  area,
  capacity,
  runoff = 0.8,
  efficiency = 0.85,
  initial = capacity,
  overflow_timing = c("after_demand", "before_demand")
)

Arguments

precip

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

demand

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

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). Defaults to capacity (a full reservoir, per the NBR 15527:2007 A.2 hypothesis). Must not exceed capacity.

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  • "after_demand" (default): inflow is added, demand is withdrawn, and only the remainder can overflow.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  • "before_demand": inflow is added and the reservoir overflows before demand is withdrawn, the YAS (yield after spillage) rule.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.

Value

An object of class rharv_sim: a list with elements series (a data frame with one row per time step and columns step, captured, overflow, supplied, deficit, storage), inputs (the parameters used) and summary (the metrics returned by rh_metrics()). The print() and summary() methods give a quick overview.

Details

$$S(t) = Q(t) + S(t-1) - D(t), \quad 0 \le S(t) \le V$$

where Q(t) is the captured volume, D(t) the demand and V the reservoir capacity. Evaporation is not considered. Following the standard, the reservoir is assumed full at the start (initial = capacity by default).

Examples

precip <- c(0, 0, 25, 0, 40, 0, 0)
sim <- rh_simulate(precip, demand = 0.5, area = 775.53, capacity = 5)
sim
#> <rharv_sim>
#>   steps: 7 | area: 775.53 m2 | capacity: 5 m3 | timing: after_demand
#>   attendance: 100.0% | reliability: 100.0% | days unmet: 0
#>   totals (m3): deficit 0.00 | overflow 31.78 | usable 2.50
rh_metrics(sim)
#>   n captured_total overflow_total supplied_total deficit_total demand_total
#> 1 7       34.27843       31.77843            3.5             0          3.5
#>   usable_volume final_storage days_unmet reliability_pct attendance_pct
#> 1           2.5             4          0             100            100
#>   attendance_pct_legacy
#> 1                   100