1. Water Resources Planning and Management Daene C. McKinney River Basin Modeling

2. Water Resources Water at: – Wrong place, wrong quantity, wrong time What to do? Manipulate the hydrologic cycle – Build facilities? Remove facilities? Reoperate facilities? Reservoirs Canals Levees Other infrastructure

3. Scales Time Scales Water management plans – Consider average conditions within discrete time periods Weekly, monthly or seasonal – Over a long time horizon Year, decade, century – Shortest time period No less than travel time from the upper basin to mouth For shorter time periods some kind of flow routing required Flood management – Conditions over much shorter periods Hours, Days, Week

4. Processes Processes we need to describe: – Precipitation – Runoff – Infiltration – Percolation – Evapotranspiration – Chemical concentration – Groundwater

5. Data Measurement Data sources Flow conditions – Natural – Present – Unregulated – Regulated – Future Reservoir losses Missing data –Precipitation-runoff models –Stochastic streamflow models –Extending and filling in historic records

6. Yield Yield - amount of water that can be supplied during some time interval Firm yield - amount of water that can be supplied in a critical period – Without storage: firm yield is lowest streamflow on record, – With storage: firm yield can be increased to approximately the mean annual flow of stream

7. Regulation and Storage Critical period - period of lowest flow on record – “ having observed an event in past, it is possible to experience it again in future ” Storage must be provided to deliver additional water over total streamflow record Given target yield, required capacity depends on risk that yield will not be delivered, i.e., the reliability of the system

8. Hydrologic Frequency Analysis Flow duration curves – Percent of time during which specified flow rates are equaled or exceeded at a given location Pr{ Q > q }

9. Central Asia Naryn River Syr Darya

10. Naryn River Annual Flows Glacier melt Min. flow Median flow

11. Naryn River Annual Flows

12. Quantiles X is a continuous RV p-th quantile is x p Median: x 50 – equally likely to be above as below that value Examples – Floodplain management - the 100-year flood x 0.99 – Water quality management minimum 7-day-average low flow expected once in 10 years 10th percentile of the distribution of the annual minima of the 7-day average flows p xpxp X F X (x)

13. Quantiles Observed values, sample of size n Order statistics (observations ordered by magnitude Sample estimates of quantiles can be obtained by using

14. Flow Duration Curve P(X>x)= Ranked YearFlowRank 1-i/(n+1)= Flow xi 1-p x (i) 19111081710.996525 19121112620.987478 19131150330.978014 19141142840.968161 19151023350.958378 … 199710343870.0615062 199814511880.0515242 199914557890.0416504 200012614900.0316675 200112615910.0218754 20021667592=n0.0120725

15. Flow Duration Curve  Flow duration curve - Discharge vs % of time flow is equaled or exceeded.  Firm yield is flow that is equaled or exceeded 100% of the time

16. Increase Firm Yield - Add storage To increase the firm yield of a stream, impoundments are built. Need to develop the storage-yield relationship for a river Simplified methods – Mass curve (Rippl) method – Sequent peak method More complex methods – Optimization – Simulation

17. Simplified Methods Mass curve (Rippl) method – Graphical estimate of storage required to supply given yield – Constructed by summing inflows over period of record and plotting these versus time and comparing to demands Time interval includes “critical period” – Time over which flows reached a minimum – Causes the greatest drawdown of reservoir

18. Rippl method

19. Rippl Method QtQt RtRt Capacity K Accumulated Releases,  R Accumulated Inflows,  Q

20. Sequent Peak Method