River Basin Modeling

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

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

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 Syr Darya Naryn River

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

11. Naryn River Annual Flows

12. Random Variables • Function (X) whose value (x) depends on the outcome of a chance event • Discrete RV • Takes on values from a discrete set # of years until a certain flood stage returns # of times reservoir storage drops below a level • Continuous RV • Takes on values from a continuous set e.g., Rainfall, Streamflow, Temperature, Concentration

13. Cumulative Distribution Function Continuous RV Discrete RV

14. Probability Density (Mass) Functions Probability density function Probability mass function Continuous RV Discrete RV

15. Multiple RVs • The joint distribution of two RVs, X and Y: • For example, joint distribution of current streamflow and previous streamflow

16. Independent RVs • If the distribution of RV X is not influenced by the value taken by RV Y, and vice versa, the RVs are independent • For two independent RVs, the joint probability is the product of the separate probabilities.

17. Marginal Distributions • Two RVs X and Y can have a joint distribution • The marginal distribution of Xis the distribution of X ignoring Y

18. Conditional Distributions • Conditional distribution of Xgiven that Y has taken on a particular value

19. Discrete RVs • Conditional Distribution • Joint Distribution • Marginal Distribution

20. Expectation Note (expected value of X – Mean of X)

21. Variance

22. Principle • Replacement of uncertain quantities by either expected, median or worst-case values can grossly affect the evaluation of project performance when important parameters are highly variable.

23. Qt K St Rt Example • Elevation of reservoir water surface varies from year to year depending on the inflow and demand for water.

24. Example • Average pool level • Average Visitation Rate

25. FX(x) p xp X Quantiles • X is a continuous RV • p-thquantile is xp • Median: x50 • equally likely to be above as below that value • Interquartile range: [x0.25, x0.75] • range of values that the random variable might assume • Examples • Floodplain management - the 100-year flood x0.99 • 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

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

27. Flow Duration Curve

28. 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

29. 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

30. 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

31. Rippl method

32. Qt Rt Rippl Method Accumulated Inflows, Q Capacity K Accumulated Releases, R

33. Sequent Peak Method