Probabilistic seasonal water supply forecasting in

Probabilistic seasonal water supply forecasting in an operational environment: the USDA-NRCS Perspective

Tom Pagano Tom.Pagano@por.usda.gov 503 414 3010Natural Resources Conservation Service

Existing water supply forecasts

Statistical forecasting methods

“Routing” and “mixed-past” forecasts

Simulation modeling

Forecast coordination

Communicating uncertainty

Location

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 1950-99 VIC model skillExplained variance in predicting Apr-July runoff

Blue – SnowpackGreen – Soil MoistureRed – El Nino

Darker colors- more important

(courtesy of M Dettinger, Scripps)

Apr-Sept StreamflowStehekin R at Stehekin, WA

Apr 1 Rainy Pass Snow Water (inches)

R = 0.91

Str

eam

flo

w (

k ac

-ft)

Regression equations relating point measurements vs flow:

1. Snow water equivalent2. Antecedent precipitation3. Antecedent streamflow

4. Climate indices (e.g. El Nino)

Y-variable can be transformedfor 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) = 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

“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

Probabilityof non-

exceedence

10090

70

50

30

100

NRCS – raw equation output

Dry Wet

NrcsNwsConsensus

What effect does coordination have on probability distributions?

Volume

Probabilityof non-

exceedence

10090

70

50

30

100

NRCS – raw equation outputNRCS – subjective assessment

Dry Wet

NrcsNwsConsensus

What effect does coordination have on probability distributions?

Volume

Probabilityof non-

exceedence

10090

70

50

30

100

NRCS – raw equation outputNRCS – subjective assessmentNWS – raw equation output

Dry Wet

NrcsNwsConsensus

What effect does coordination have on probability distributions?

Volume

Probabilityof non-

exceedence

10090

70

50

30

100

NRCS – raw equation outputNRCS – subjective assessmentNWS – raw equation outputNWS – raw ESPNWS – bias adjusted ESP

Dry Wet

NrcsNwsConsensus

What effect does coordination have on probability distributions?

Volume

Probabilityof non-

exceedence

10090

70

50

30

100

NRCS – raw equation outputNRCS – subjective assessmentNWS – raw equation outputNWS – raw ESPNWS – bias adjusted ESPNWS – subjective assessment

Dry Wet

NrcsNwsConsensus

What effect does coordination have on probability distributions?

Volume

Probabilityof non-

exceedence

10090

70

50

30

100

NRCS – raw equation outputNRCS – subjective assessmentNWS – raw equation outputNWS – raw ESPNWS – bias adjusted ESPNWS – subjective assessmentNRCS-NWS – Consensus forecast (Official forecast)

Dry Wet

NrcsNwsConsensus

What effect does coordination have on probability distributions?

Volume

Probabilityof non-

exceedence

10090

70

50

30

100

NRCS – raw equation outputNRCS – subjective assessmentNWS – raw equation outputNWS – raw ESPNWS – bias adjusted ESPNWS – subjective assessmentNRCS-NWS – Consensus forecast (Official Forecast)

Dry Wet

NrcsNwsConsensus

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 soundbut 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

predictedensemble

median ofpredicted

If statistical seasonal water supply forecasting is the Blue Square of communicating uncertainty

Simulation Modeling is the Black Diamond, a special challenge

obs

predictedensemble

median ofpredicted

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

predictedensemble

median ofpredicted

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 criticalbut largely under-researched topic

END