1. WATER TEMPERATURE MODEL FOR BRANCHED RIVER SYSTEMS

2. 1-Dimensional, Time Dependent 1-Dimensional, Time Dependent – Advection only – Daily or Hourly Simulations – Energy Budget Method Mixed Lagrangian-Eulerian solution technique “Reverse Particle Tracking” Mixed Lagrangian-Eulerian solution technique “Reverse Particle Tracking” – Reduces error due to numerical dispersion – Reduces problems of numerical instability – Scaleable in time and space FORTRAN (plain vanilla) FORTRAN (plain vanilla) RBM10 Model

3. dT dt = q surf A r C p + e CHANGE IN ENERGY SURFACE ENERGY EXCHANGE ONE-DIMENSIONAL ENERGY BUDGET MATHEMATICAL MODEL MODEL ERROR

5. REVERSE PARTICLE TRACKING

6. Elements of RBM10 Framework Boundaries of Simulated System Boundaries of Simulated System System Topology System Topology Geometry/Hydrodynamics Geometry/Hydrodynamics Boundary Inputs (Flow and Temperature) Boundary Inputs (Flow and Temperature) Heat Budget Inputs based on Meteorology Heat Budget Inputs based on Meteorology

8. Dworshak

9. Geometry/Hydrodynamics Mainstem Geometry for Impounded Reaches Mainstem Geometry for Impounded Reaches - Storage reservoirs with variable elevation - Volume-elevation relationships are used to vary geometry of model elements Velocity Velocity -Continuity: V = Flow / X-Area

10. Geometry/Hydrodynamics Mainstem Geometry for Free-Flowing Reaches Varies Depending on Flow Mainstem Geometry for Free-Flowing Reaches Varies Depending on Flow – Need cross-sectional profiles of the river bottom – Open channel hydraulics relationships – HEC-RAS model gradually varied flow is assumed gradually varied flow is assumed provides cross-sectional area and top width over the range of observed flows provides cross-sectional area and top width over the range of observed flows area used to estimate velocity, width used to estimate surface area for heat exchange area used to estimate velocity, width used to estimate surface area for heat exchange

11. Meteorological Data Needed to Compute Heat Budget Air Temperature Dew Point Wind Speed Atmospheric Pressure Cloud Cover

12. Issues Issues – Mainstem Temperature Monitoring Monitoring at Dams Not Designed for Assessment of River Temperature Monitoring at Dams Not Designed for Assessment of River Temperature Limited Quality Control/Quality Assurance Limited Quality Control/Quality Assurance – Tributary Temperature Monitoring Discontinuous Record Discontinuous Record Unknown Quality Control/Quality Assurance Unknown Quality Control/Quality Assurance – Meteorology Limited Geographical Coverage Limited Geographical Coverage Data Limitations

13. SOME SOURCES OF UNCERTAINTY

14. Meteorology Meteorology – Described by five regional weather stations Mainstem Flow Mainstem Flow – Leopold equations developed from gradually-varied flow methods for un-impounded reaches Tributary Temperatures Tributary Temperatures – Non-linear regressions developed from local air temperature and weekly/monthly river temperatures – Numerical Scheme Some numerical dispersion Some numerical dispersion Conservation of mass/energy (?) Conservation of mass/energy (?)

15. PARAMETER ESTIMATION

16. Parameters Parameters ­ evaporation rates – assignment of area covered by 5 meteorological stations – Model uncertainty PARAMETER ESTIMATION

17. MODEL EVALUATION AND TESTING

21. Columbia River Statistics (1995-1999)) Mean Difference Standard Deviation Location Snake @ Ice Harbor -0.18 1.07 Columbia @ Bonneville -0.391.33

22. Mean Difference Standard Deviation Location Fraser River @ Hells Gate -0.02 0.49 Fraser River Statistics (1998)

23. SOME APPLICATION OUTSIDE THE ENVELOPE

24. DISPERSI VE

25. TWO-DIMENSIONAL

26. MODEL APPLICATION

27. Impact of Dams on Natural Condition Two scenarios are run using identical boundary inputs (weather, tributary flows/temperatures, etc.) Two scenarios are run using identical boundary inputs (weather, tributary flows/temperatures, etc.) –1. Existing Condition –2. Un-impounded Condition Dams are “mathematically removed” – altered geometry Dams are “mathematically removed” – altered geometry Corroboration not feasible – no observations Corroboration not feasible – no observations Un-impounded Condition is not the “natural condition” – model domain does not reach to headwaters Un-impounded Condition is not the “natural condition” – model domain does not reach to headwaters

30. Impact of Individual Dams on Daily Cross Sectional Average Temperature in the Columbia River

31. PREDICTED AND OBSERVED TEMPERATURES IN THE SNAKE AND COLUMBIA RIVERS USING METEOROLOGY GENERATED FOR VIC

34. SIMULATED TEMPERATURES IN THE SNAKE AND COLUMBIA RIVERS FOR THREE CLIMATE CHANGE SCENARIOS

37. The End

38. Impact of Point Sources on Mainstem Temperatures Simulated Increases in Temperature at River Mile 42 in the Columbia River due to the Existing Point Sources