Water Resources Planning and Management Daene C. McKinney System Performance Indicators

Reservoir Management Important task for water managers around the world. Models used to – simulate or optimize reservoir performance – design reservoirs or associated facilities (spillways, etc.).

Operating Rules Allocate releases among purposes, reservoirs, and time intervals In operation (as opposed to design), certain system components are fixed: – Active and dead storage volume – Power plant and stream channel capacities – Reservoir head-capacity functions – Levee heights and flood plain areas – Monthly target outputs for irrigation, energy, water supply, etc Others are variable: Allocation of – stored water among reservoirs – stored and released water among purposes – stored and released water among time intervals

Standard Operating Policy QtQt X2 t K StSt RtRt X1 t DtDt RtRt DtDt DtDt D t +KS t + Q t Release available water & deficits occur Release demand spill excess Sufficient water to meet demands Reservoir fills and demand met Release demand & demand met Demand Reservoir operating policy - release as function of storage volume and inflow R t = R t (S t,Q t )

Hedging Rule Reduce releases in times of drought (hedging) to save water for future releases in case of an extended period of low inflows. hedging D K

Done? No System Simulation Loucks (Chapter 7, Section 9) Create network representation of system Need inflows for each period for each node For each period:  Perform mass balance calculations for each node  Determine releases from reservoirs  Allocate water to users Start t = 0 S t = S 0 S t+1 = S t +Q t -R t Stop Yes t = t + 1 Read Q t File Compute R t, Xi t, i=1,…n Data Storage QtQt X3 t K StSt R X2 t X1 t Operating PolicyAllocation Policy

Example Using unregulated river for irrigation Proposed Reservoir Capacity: K = 40 million m 3 (active) Demand: D = 30  40  45 million m 3 Winter instream flow: 5 mil. m 3 min. 45 year historic flow record available Evaluate system performance for a 20 year period Simulate Two seasons/year, winter (1) summer(2) Continuity constraints Operating policy QtQt X2 t K StSt R X1 t Flow statistics

R 2,t DtDt DtDt D t +KS 2,t + Q 2,t K Release available water Release demand + excess Summer Operating Policy Storage at beginning of summer

Performance Evaluation How well will the system perform? – Define performance criteria Indices related to the ability to meet targets and the seriousness of missing targets – Simulate the system to evaluate the criteria – Interpret results Should design or policies be modified?

Performance Criteria - Reliability Reliability – Frequency with which demand was satisfied – Define a deficit as: Then reliability is: where n is the total number of simulation periods

Performance Criteria - Resilience Resilience = probability that once the system is in a period of deficit, the next period is not a deficit. How quickly does system recover from failure?

Performance Criteria - Vulnerability Vulnerability = average magnitude of deficits How bad are the consequences of failure?

Simulate the System System Policies Input Output x g(x) y h(y) Reservoir operating policy Allocation policy Hydrologic time series Model output Model

Uncertainty Deterministic process – Inputs assumed known. – Ignore variability – Assume inputs are well represented by average values. – Over estimates benefits and underestimates losses Stochastic process – Explicitly account for variability and uncertainty – Inputs are stochastic processes – Historic record is one realization of process.

F Y (y) Simulate the System Policies Simulate each Input sequence X F X (x) x g(x) y h(y) y Compute statistics of outputs System Generate multiple input sequences x g(x) Get multiple output sequences Reservoir operating policy Allocation policy Model Distribution of inputs

The Simulation Simulate reservoir operation – Perform 23 equally likely simulations – Each simulation is 20 years long – Each simulation uses a different sequence of inflows (realization)

Example – Realization 1 Rmin0.5K4 Realizatio n1 WinterSummer YearS1yQ1yS+QR1yS2yQ2yS+QD2yR2yDeficit Deficit Number2.000 %0.100

Results Average failure frequency = Average reliability = = = 83.5% Actual failure frequency  [0, 0.40] Actual Reliability  [100%, 60%]