reservoir: reservoir: Tools for Analysis, Design, and Operation of Water...

In reservoir: Tools for Analysis, Design, and Operation of Water Supply Storages

Description

Measure single reservoir performance using resilience, reliability, and vulnerability metrics; compute storage-yield-reliability relationships; determine no-fail Rippl storage with sequent peak analysis; optimize release decisions for water supply, hydropower, and multi-objective reservoirs using deterministic and stochastic dynamic programming; evaluate inflow characteristics.

Analysis and design functions

The Rippl function executes the sequent peak algorithm [Thomas and Burden, 1963] to determine the no-fail storage [Rippl, 1883] for given inflow and release time series. The storage function gives the design storage for a specified time-based reliability and yield. Similarly, the yield function computes the reliability yield given the storage capacity. The simRes function simulates a reservoir under standard operating policy, or using an optimised policy produced by sdp_supply. The rrv function returns three reliability measures, resilience, and dimensionless vulnerability for given storage, inflow time series, and target release [McMahon et al, 2006]. Users can assume Standard Operating Policy, or can apply the output of sdp_supply to determine the RRV metrics under different operating objectives. The Hurst function estimates the Hurst coefficient [Hurst, 1951] for an annualized inflow time series, using the method proposed by Pfaff [2008].

Optimization functions

The Dynamic Programming functions find the optimal sequence of releases for a given reservoir. The Stochastic Dynamic Programming functions find the optimal release policy for a given reservoir, based on storage, within-year time period and, optionally, current-period inflow. For single-objective water supply reservoirs, users may specify a loss exponent parameter for supply deficits and then optimize reservoir release decisions to minimize summed penalty costs over the operating horizon. This can be done using dp_supply or sdp_supply. There is also an option to simulate the output of sdp_supply using the rrv function to validate the policy under alternative inflows or analyze reservoir performance under different operating objectives. The optimal operating policy for hydropower operations can be found using dp_hydro or sdp_hydro. The operating target is to maximise total energy output over the duration of the input time series of inflows. The dp_multi and sdp_multi functions allow users to optimize for three weighted objectives representing water supply deficit, flood control, and amenity.

Storage-depth-area relationships

All reservoir analysis and optimization functions, with the exception of Rippl, storage, and yield, allow the user to account for evaporation losses from the reservoir surface. The package incorporates two storage-depth-area relationships for adjusting the surface area (and therefore evaporation potential) with storage. The simplest is based on the half-pyramid method [Liebe et al, 2005], requiring the user to input the surface area of the reservoir at full capacity via the surface_area parameter. A more nuanced relationship [Kaveh et al., 2013] is implemeted if the user also provides the maximum depth of the reservoir at full capacity via the max_depth parameter. Users must use the recommended units when implementing evaporation losses.

Stochastic generation of synthetic streamflow replicates

The dirtyreps function provides quick and dirty generation of stochastic streamflow replicates (seasonal input data, such as monthly or quarterly, only). Two methods are available: the non-parametric kNN bootstrap [Lall and Sharma, 1996] and the parametric periodic Autoregressive Moving Average (PARMA). The PARMA is fitted for p = 1 and q = 1, or PARMA(1,1). Fitting is done numerically by the least-squares method [Salas and Fernandez, 1993]. When using the PARMA model, users do not need to transform or deseasonalize the input data as this is done automatically within the algorithm. The kNN bootstrap is non-parametric, so no intial data preparation is required here either.

References

Hurst, H.E. (1951) Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers 116, 770-808.

Kaveh, K., H. Hosseinjanzadeh, and K. Hosseini. (2013) A new equation for calculation of reservoir's area-capacity curves, KSCE Journal of Civil Engineering 17(5), 1149-1156.

Liebe, J., N. Van De Giesen, and Marc Andreini. (2005) Estimation of small reservoir storage capacities in a semi-arid environment: A case study in the Upper East Region of Ghana, Physics and Chemistry of the Earth, 30(6), 448-454.

Loucks, D.P., van Beek, E., Stedinger, J.R., Dijkman, J.P.M. and Villars, M.T. (2005) Water resources systems planning and management: An introduction to methods, models and applications. Unesco publishing, Paris, France.

McMahon, T.A., Adeloye, A.J., Zhou, S.L. (2006) Understanding performance measures of reservoirs, Journal of Hydrology 324 (359-382)

Nicholas E. Graham and Konstantine P. Georgakakos, 2010: Toward Understanding the Value of Climate Information for Multiobjective Reservoir Management under Present and Future Climate and Demand Scenarios. J. Appl. Meteor. Climatol., 49, 557-573.

Pfaff, B. (2008) Analysis of integrated and cointegrated time series with R, Springer, New York. [p.68]

Rippl, W. (1883) The capacity of storage reservoirs for water supply, In Proceedings of the Institute of Civil Engineers, 71, 270-278.

Thomas H.A., Burden R.P. (1963) Operations research in water quality management. Harvard Water Resources Group, Cambridge

kNN Bootstrap method: Lall, U. and Sharma, A. (1996). A nearest neighbor bootstrap for resampling hydrologic time series. Water Resources Research, 32(3), pp.679-693.

PARMA method: Salas, J.D. and Fernandez, B. (1993). Models for data generation in hydrology: univariate techniques. In Stochastic Hydrology and its Use in Water Resources Systems Simulation and Optimization (pp. 47-73). Springer Netherlands.

Examples

# 1. Express the distribution of Rippl storage for a known inflow process...
layout(1:4)
# a) Assume the inflow process follows a lognormal distribution
# (meanlog = 0, sdlog = 1):
x <- rlnorm(1200)

# b) Convert to a 100-year, monthly time series object beginning Jan 1900
x <- ts(x, start = c(1900, 1), frequency = 12)

# c) Begin reservoir analysis... e.g., compute the Rippl storage
x_Rippl <- Rippl(x, target = mean(x) * 0.9)
no_fail_storage <- x_Rippl$Rippl_storage

# d) Resample x and loop the procedure multiple times to get the
# distribution of no-failure storage for the inflow process assuming
# constant release (R) equal to 90 percent of the mean inflow.
no_fail_storage <- vector("numeric", 100)
for (i in 1:length(no_fail_storage)){
  x <- ts(rlnorm(1200), start = c(1900, 1), frequency = 12)
  no_fail_storage[i] <- Rippl(x, target = mean(x) * 0.9 ,plot = FALSE)$No_fail_storage
}
hist(no_fail_storage)


# 2. Trade off between annual reliability and vulnerability for a given system...
layout(1:1)
# a) Define the system: inflow time series, storage, and target release.
inflow_ts <- resX$Q_Mm3
storage_cap <- resX$cap_Mm3
demand <- 0.3 * mean(resX$Q_Mm3)

# b) define range of loss exponents to control preference of high reliability
# (low loss exponent) or low vulnerability (high loss exponent).
loss_exponents <- c(1.0, 1.5, 2)

# c) set up results table
pareto_results <- data.frame(matrix(ncol = 2, nrow = length(loss_exponents)))
names(pareto_results) <- c("reliability", "vulnerability")
row.names(pareto_results) <- loss_exponents

# d) loop the sdp function through all loss exponents and plot results
for (loss_f in loss_exponents){
 sdp_temp <- sdp_supply(inflow_ts, capacity = storage_cap, target = demand, rep_rrv = TRUE,
 S_disc = 100, R_disc = 10, plot = FALSE, loss_exp = loss_f, Markov = TRUE)
 pareto_results$reliability[which(row.names(pareto_results)==loss_f)] <- sdp_temp$annual_reliability
 pareto_results$vulnerability[which(row.names(pareto_results)==loss_f)] <- sdp_temp$vulnerability
 }
plot (pareto_results$reliability,pareto_results$vulnerability, type = "b", lty = 3)

Example output

policy converging... (>0.99)
0
0.99983498349835
policy converging... (>0.99)
0
1
policy converging... (>0.99)
0
0.998844884488449

reservoir documentation built on May 2, 2019, 5:52 a.m.