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Probabilistic seasonal water supply forecasting in

This article discusses the USDA-NRCS perspective on probabilistic seasonal water supply forecasting in an operational environment. It covers existing water supply forecasts, statistical forecasting methods, forecast coordination, and communicating uncertainty. The article also explores sources of predictability and various technical issues related to forecasting.

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Probabilistic seasonal water supply forecasting in

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  1. Probabilistic seasonal water supply forecasting in an operational environment: the USDA-NRCS Perspective Tom Pagano Tom.Pagano@por.usda.gov 503 414 3010 Natural Resources Conservation Service

  2. Existing water supply forecasts Statistical forecasting methods “Routing” and “mixed-past” forecasts Simulation modeling Forecast coordination Communicating uncertainty

  3. Location

  4. Historical Average Location Time Period

  5. Historical Average Location Time Period Error Bounds “Most Probable” Water Volume

  6. Historical Average Location Time Period Error Bounds “Most Probable” Water Volume Forecasts are coordinated with the National Weather Service (NWS). Both agencies publish identical numbers.

  7. Sources of predictability 1950-99 VIC model skill Explained variance in predicting Apr-July runoff Blue – Snowpack Green – Soil Moisture Red – El Nino Darker colors- more important (courtesy of M Dettinger, Scripps)

  8. Apr-Sept Streamflow Stehekin R at Stehekin, WA Regression equations relating point measurements vs flow: 1. Snow water equivalent 2. Antecedent precipitation 3. Antecedent streamflow 4. Climate indices (e.g. El Nino) Y-variable can be transformed for non-linear forecasting e.g. sqrt(streamflow) = a * snow + b R = 0.91 Streamflow (k ac-ft) Apr 1 Rainy Pass Snow Water (inches)

  9. Calculating forecast probabilities 1. Jackknife standard error (JSE) stdev(Fcst-Obs)/sqrt(n) 2. T-statistic : TINV(2*(1-Prob),DF) 90% non-exceedence with 30 degrees of freedom (DF) TINV(2*(1-0.9),30) = 1.31

  10. Calculating forecast probabilities 1. Jackknife standard error (JSE) stdev(Fcst-Obs)/sqrt(n) 2. T-statistic : TINV(2*(1-Prob),DF) 90% non-exceedence with 30 degrees of freedom (DF) TINV(2*(1-0.9),30) = 1.31 3. 90% non-exceed = 50% non-exceed + 1.31 * JSE 500 kac-ft + 1.31 * 76 = 600 kac-ft 10% non-exceed = 50% non-exceed – 1.31 * JSE 500 kac-ft - 1.31 * 76 = 400 kac-ft 4. Untransform if non-linear equation e.g. Y’ = exp(Y), Y2, Y3

  11. Other technical issues “Routing” How to keep downstream forecasts (and distribution widths and shapes) consistent with upstream forecasts? “Mixed-Past” How to reflect changed uncertainty when part of your target period is in the past? e.g. April-July forecast issued June 1 and Apr-May is “known” (or is it?)

  12. Simulation modeling (e.g. a watershed model forced with daily weather data producing ensemble hydrographs) Data uncertainty: Quality control, Representativeness Model uncertainty: Processes, Scales

  13. Simulation modeling (e.g. a watershed model forced with daily weather data producing ensemble hydrographs) Data uncertainty: Quality control, Representativeness Model uncertainty: Processes, Scales Calibration uncertainty: Probabilistic parameters State uncertainty: Manual adjustment, Data assimilation

  14. Simulation modeling (e.g. a watershed model forced with daily weather data producing ensemble hydrographs) Data uncertainty: Quality control, Representativeness Model uncertainty: Processes, Scales Calibration uncertainty: Probabilistic parameters State uncertainty: Manual adjustment, Data assimilation Future weather uncertainty: Historical resampling (ESP), Trace weighting, Weather model preprocessing Output uncertainty: Post processing, Bias adjustment

  15. What effect does coordination have on probability distributions? 100 90 70 50 30 10 0 Probability of non- exceedence Nrcs Nws Consensus Dry Wet Volume NRCS – raw equation output

  16. What effect does coordination have on probability distributions? 100 90 70 50 30 10 0 Probability of non- exceedence Nrcs Nws Consensus Dry Wet Volume NRCS – raw equation output NRCS – subjective assessment

  17. What effect does coordination have on probability distributions? 100 90 70 50 30 10 0 Probability of non- exceedence Nrcs Nws Consensus Dry Wet Volume NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output

  18. What effect does coordination have on probability distributions? 100 90 70 50 30 10 0 Probability of non- exceedence Nrcs Nws Consensus Dry Wet Volume NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output NWS – raw ESP NWS – bias adjusted ESP

  19. What effect does coordination have on probability distributions? 100 90 70 50 30 10 0 Probability of non- exceedence Nrcs Nws Consensus Dry Wet Volume NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output NWS – raw ESP NWS – bias adjusted ESP NWS – subjective assessment

  20. What effect does coordination have on probability distributions? 100 90 70 50 30 10 0 Probability of non- exceedence Nrcs Nws Consensus Dry Wet Volume NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output NWS – raw ESP NWS – bias adjusted ESP NWS – subjective assessment NRCS-NWS – Consensus forecast (Official forecast)

  21. What effect does coordination have on probability distributions? 100 90 70 50 30 10 0 Probability of non- exceedence Nrcs Nws Consensus Dry Wet Volume NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output NWS – raw ESP NWS – bias adjusted ESP NWS – subjective assessment NRCS-NWS – Consensus forecast (Official Forecast) Bounds shifted from objective guidance. No bound narrowing implies no skill added.

  22. Communication of forecasts Within NRCS, almost 50 years of deterministic forecasts until advent of NRCS-NWS coordination in 1980s Early NRCS bounds ambiguous, approximations at best Since 1990, probability forecasts technically sound but communication remains an issue Users seem to gravitate towards scenarios, analogues (but analogues have their own baggage) No good spatial visualizations of uncertainty have ever existed

  23. If statistical seasonal water supply forecasting is the Blue Square of communicating uncertainty Simulation Modeling is the Black Diamond, a special challenge predicted ensemble median of predicted obs

  24. If statistical seasonal water supply forecasting is the Blue Square of communicating uncertainty Simulation Modeling is the Black Diamond, a special challenge predicted ensemble Peak of median median of predicted obs

  25. If statistical seasonal water supply forecasting is the Blue Square of communicating uncertainty Simulation Modeling is the Black Diamond, a special challenge predicted ensemble Peak of median does not equal Median of peaks median of predicted obs

  26. The “cone of uncertainty” National Weather Service graph from 1949! 58 years later…

  27. A deterministic product that ignores uncertainty… But does it need to be something else?

  28. A deterministic product that ignores uncertainty… But does it need to be something else? Is it OK to give the “casual user” “incomplete” information?

  29. Is there a way to express forecast confidence better? And is that different than forecast uncertainty? Confidence V. High High Moderate High

  30. NRCS produces seasonal water supply outlooks Probabilistic aspects derived from statistical tool performance Many scientific and technical issues remain re probabilistic forecasts from simulation models Communication of uncertainty a critical but largely under-researched topic END

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