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

2. 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.).

3. 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

4. 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 )

5. 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

6. 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

7. 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

8. 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

9. 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?

10. 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

11. 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?

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

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

14. 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.

15. 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

16. 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)

17. Example – Realization 1 Rmin0.5K4 Realizatio n1 WinterSummer YearS1yQ1yS+QR1yS2yQ2yS+QD2yR2yDeficit 10.0004.740 0.7404.0001.8055.8053.000 0.000 22.8052.9185.7231.7234.0001.4995.4993.200 0.000 32.2992.7475.0451.0454.0001.5485.5483.400 0.000 42.1482.8194.9660.9664.0001.7535.7533.600 0.000 52.1533.8716.0232.0234.0002.2296.2293.800 0.000 62.4293.5856.0152.0154.0002.2356.2354.000 0.000 72.2354.7366.9712.9714.0002.9846.9844.100 0.000 82.8843.2756.1592.1594.0002.2126.2124.200 0.000 92.0123.1885.2001.2004.0002.6666.6664.300 0.000 102.3663.4015.7671.7674.0001.2405.2404.300 0.000 110.9403.8114.7500.7504.0002.3716.3714.400 0.000 121.9713.4355.4071.4074.0002.4216.4214.400 0.000 132.0212.4604.4810.5003.9811.3175.2984.400 0.000 140.8982.3773.2750.5002.7751.8964.6714.400 0.000 150.2713.6923.9630.5003.4631.8315.2934.500 0.000 160.7933.3024.0950.5003.5951.3004.8954.500 0.000 170.3952.5482.9440.5002.4442.0474.4914.5004.491-0.009 180.0002.454 0.5001.9541.6583.6124.5003.612-0.888 190.0003.139 0.5002.6392.7685.4074.500 0.000 200.9072.9103.8160.5003.3161.4454.7624.500 0.000 Deficit-0.897 Number2.000 %0.100

18. Results Average failure frequency = 0.165 Average reliability = 1- 0.165 = 0.835 = 83.5% Actual failure frequency  [0, 0.40] Actual Reliability  [100%, 60%]