Stochastic Streamflow Forecast Generation

1. Stochastic Streamflow Forecast Generation

2. stochastic: adj. [Gk stochastikos proceeding by guesswork] Containing a random variable; word used to describe a system that has in it an element of randomness.

3. Purpose of using synthetic streamflows instead of historical: Reduce and more appropriately reflect uncertainty of future reservoir inflows and their effect on power marketing and reservoir operating decisions

4. Uses for Stochastic Flows • Operations studies that determine inventory on probabilistic basis in support of marketing decisions • Risk management-- studies that show the risk of operating the system to meet specific criteria

5. The Problem • Produce sequences of monthly streamflows at 23 sites for forecast horizon of up to 2 years • Synthetic streamflows must behave statistically similar to historical values and be consistent with seasonal volume forecasts

6. The Solution • SAMS (Stochastic Analysis, Modeling, and Simulation) -- developed as coop effort between CSU and USBR • BPA funded enhancements to the model including the capability to generate based on initial conditions • forecasts conditioned on NWRFC final volume forecasts and antecedent flows

7. Configuration of Basin Incremental flow Total natural flow Seasonal volume forecast Mica Duncan Revelstoke Libby Kootenay Arrow Bonneville McNary Priest Rapids Albeni Falls Columbia Falls Grand Coulee Boundary Kerr The Dalles John Day Hungry Horse Lower Granite Long Lake Lookout Point Dworshak Brownlee Post Falls

8. Partitioning a time series into its various components -- deterministic and stochastic components

9. Systematic Approach to Hydrologic Time Series Modeling Identify model composition: univariate, multivariate, disaggregation? Characteristics of overall water resource system Modeler input: knowledge, experience, bias, limitations Selection of Model type: AR, ARMA, etc Characteristics of Hydrologic Physical Processes Statistical characteristics of hydrologic time series Identification of Model Form: order, periodicity? Estimation of Model Parameters: method of moments, method of maximum likelihood Testing goodness of Fit of the Model: how well do results represent history? Evaluation of Uncertainties: model uncertainty, parameter uncertainty

10. Stochastic models reproduce basic statistics and probability distributions of the historic data • assumption that variable is normally distributed

12. Approach • MPAR(3) used for 6 key sites • Spatial disaggregation of seasonal data for other 17 sites--generation of subkey sites (and subsequent sites) dependent on generated values at key sites • Used modified flows for 1929-1983 and Kuehl Moffitt synthetic seasonal volume forecasts

13. Autoregressive modelunivariate, stationary case Multivariate case and periodic case more complicated--matrix form used

14. Dissagregation models • Developed for reproducing statistics at more than one level of aggregation • General Form: Y = A X + B Z + C 

15. Stochastic Flow Forecast Generation Process antecedent flows at 24 sites Model parameter files Post processor: summarize 1000 sequences into a smaller subset that defines the distribution of flow forecasts. Output necessary files Pre-processor: facilitate input data checking and prepare formatted input file to SAMSF Seasonal volume forecasts SAMSF generate flow and seasonal volume forecasts Exogenous parameters (SOI, MEI, PDI) HYDSIM inputs: 1.flow forecasts 2. seasonal vol forecasts for VECCS Volume forecasts for VURC computations Output used to generate graphic summaries

16. Results

23. Future opportunities • gain experience using stochastic forecasts • disaggregate into daily/weekly flows • produce forecasts at more sites • use of exogenous variables • condition on new NWRFC volume forecasts • compare to ESP