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ESP Post Processor Hypothetical Test Example

ESP Post Processor Hypothetical Test Example. Objective.

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ESP Post Processor Hypothetical Test Example

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  1. ESP Post ProcessorHypothetical Test Example

  2. Objective • The objective of this test is to evaluate alternative approaches for a hydrologic post-processor to generate an ensemble prediction (simulation) of observed streamflows using calibration hydrographs and corresponding observations as input data. • The functional relationship between the observed and simulated hydrographs is prescribed as part of the test.

  3. Hypothetical Test Case • This particular test uses a hypothetical calibration hydrograph • constructed from the observed hydrograph so that the “simulated” hydrograph “leads” the observed by one day and • is equal to the observed value multiplied by a random factor with a standard deviation equal to 10% of the observed value. • This test was designed to see if two alternative processors (GLM and a statistical error model) could adjust for phase errors as well as systematic biases and random errors.

  4. Example Simulation Test Select historical data from each year from a window of N days where N = Na + Nf + Nbuffer Analysis Period Future Period Qobsf (to be predicted) Qsimf (given) Qobsa (given) Qsima (given) Time Na = 8 Nf = 45 Buffer Buffer Nw = Na + Nf “Present” (t = 0) Nbuffer = 15 Note: Nbuffer sets of Nw days of data are taken from each of NYRS years of data. This gives NOBS = NYRS * Nbuffer observations for each day

  5. Correlations between Observed and Simulated and Ensemble Means

  6. Serial Correlation Functions of Transformed Streamflow Data

  7. A-Matrix for Lag-Test Example

  8. B-Matrix for Lag-Test Example

  9. Eigenvalue Distribution of BBT for Lag-Test Example

  10. Comparison of Observed, Simulated (Lag-Test) and Adjusted Ensemble Streamflow Hydrographs (z-space)

  11. Comparison of Observed, Simulated (Lag-Test) and Adjusted Ensemble Streamflow Hydrographs

  12. Mean and Standard Deviation Statistics of Observed, Simulated and Adjusted Ensemble Members

  13. Comparison of RMS Errors

  14. Cumulative Distribution Functions of Daily Observed, Simulated and Adjusted Ensemble Streamflow Values

  15. Conclusions • The General Linear Model (GLM) was able to: • Correct the phase error • Create ensemble members that have the same climatology as the observed values • Preserved “intrinsic” skill (after phase error correction) • The Statistical Error Model of (Qobs-Qsim): • Could not distinguish between phase and random errors • Could not preserve the climatology of the observations • Gave much larger RMS errors than the GLM

  16. Thank You

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