sdp_multi {reservoir}

Stochastic Dynamic Programming with multiple objectives (supply, flood control, amenity)

Description

Determines the optimal sequence of releases from the reservoir to minimise a penalty cost function based on water supply, spill, and water level. For water supply: Cost[t] = ((target - release[t]) / target) ^ loss_exp[1]). For flood control: Cost[t] = (Spill[t] / quantile(Q, spill_targ)) ^ loss_exp[2]. For amenity: Cost[t] = abs(((storage[t] - (vol_targ * capacity)) / (vol_targ * capacity))) ^ loss_exp[3].

Usage

sdp_multi(Q, capacity, target, surface_area, max_depth, evap, R_max = 2 *
  target, spill_targ = 0.95, vol_targ = 0.75, Markov = FALSE,
  weights = c(0.7, 0.2, 0.1), S_disc = 1000, R_disc = 10, Q_disc = c(0,
  0.2375, 0.475, 0.7125, 0.95, 1), loss_exp = c(2, 2, 2), S_initial = 1,
  plot = TRUE, tol = 0.99, rep_rrv = FALSE)

Arguments

Q

time series object. Net inflow to the reservoir.

capacity

numerical. The reservoir storage capacity (must be the same volumetric unit as Q and the target release).

target

numerical. The target release constant. Recommended units: Mm^3 (Million cubic meters).

surface_area

numerical. The reservoir water surface area at maximum capacity. Recommended units: km^2 (square kilometers).

max_depth

numerical. The maximum water depth of the reservoir at maximum capacity. If omitted, the depth-storage-area relationship will be estimated from surface area and capacity only. Recommended units: meters.

evap

vector or time series object of length Q, or a numerical constant. Evaporation from losses from reservoir surface. Varies with level if depth and surface_area parameters are specified. Recommended units: meters, or kg/m2 * 10 ^ -3.

R_max

numerical. The maximum controlled release.

spill_targ

numerical. The quantile of the inflow time series used to standardise the "minimise spill" objective.

vol_targ

numerical. The target storage volume constant (as proportion of capacity).

Markov

logical. If TRUE the current period inflow is used as a hydrological state variable and inflow persistence is incorporated using a first-order, periodic Markov chain. The default is FALSE.

weights

vector of length 3 indicating weighting to be applied to release, spill and water level objectives respectively.

S_disc

integer. Storage discretization–the number of equally-sized storage states. Default = 1000.

R_disc

integer. Release discretization. Default = 10 divisions.

Q_disc

vector. Inflow discretization bounding quantiles. Defaults to five inflow classes bounded by quantile vector c(0.0, 0.2375, 0.4750, 0.7125, 0.95, 1.0).

loss_exp

vector of length 3 indicating the exponents on release, spill and water level deviations from target. Default exponents are c(2,2,2).

S_initial

numeric. The initial storage as a ratio of capacity (0 <= S_initial <= 1). The default value is 1.

plot

logical. If TRUE (the default) the storage behavior diagram and release time series are plotted.

tol

numerical. The tolerance for policy convergence. The default value is 0.990.

rep_rrv

logical. If TRUE then reliability, resilience and vulnerability metrics are computed and returned.

Value

Returns a list that includes: the optimal policy as an array of release decisions dependent on storage state, month/season, and current-period inflow class; the Bellman cost function based on storage state, month/season, and inflow class; the optimized release and storage time series through the training inflow data; the flow discretization (which is required if the output is to be implemented in the rrv function); and, if requested, the reliability, resilience, and vulnerability of the system under the optimized policy.

See Also

dp_multi for deterministic Dynamic Programming.

Examples

layout(1:3)
sdp_multi(resX$Q_Mm3, cap = resX$cap_Mm3, target = 0.2 * mean(resX$Q_Mm3))