Probabilistic seasonal water supply forecasting in an operational environment: the USDA-NRCS Perspective Tom Pagano Natural Resources Conservation Service

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

Location

Time Period Historical Average

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

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

Sources of predictability 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)

Apr-Sept Streamflow Stehekin R at Stehekin, WA Apr 1 Rainy Pass Snow Water (inches) R = 0.91 Streamflow (k ac-ft) 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

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

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) = % non-exceed = 50% non-exceed * JSE 500 kac-ft * 76 = 600 kac-ft 10% non-exceed = 50% non-exceed – 1.31 * JSE 500 kac-ft * 76 = 400 kac-ft 4. Untransform if non-linear equation e.g. Y’ = exp(Y), Y 2, Y 3

“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?) Other technical issues

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

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

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

What effect does coordination have on probability distributions? Volume Probability of non- exceedence NRCS – raw equation output Dry Wet Nrcs Nws Consensus

What effect does coordination have on probability distributions? Volume Probability of non- exceedence NRCS – raw equation output NRCS – subjective assessment Dry Wet Nrcs Nws Consensus

What effect does coordination have on probability distributions? Volume Probability of non- exceedence NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output Dry Wet Nrcs Nws Consensus

What effect does coordination have on probability distributions? Volume Probability of non- exceedence NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output NWS – raw ESP NWS – bias adjusted ESP Dry Wet Nrcs Nws Consensus

What effect does coordination have on probability distributions? Volume Probability of non- exceedence NRCS – raw equation output NRCS – subjective assessment NWS – raw equation output NWS – raw ESP NWS – bias adjusted ESP NWS – subjective assessment Dry Wet Nrcs Nws Consensus

What effect does coordination have on probability distributions? Volume Probability of non- exceedence 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) Dry Wet Nrcs Nws Consensus

What effect does coordination have on probability distributions? Volume Probability of non- exceedence 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) Dry Wet Nrcs Nws Consensus Bounds shifted from objective guidance. No bound narrowing implies no skill added.

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

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

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

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

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

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

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

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

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