probabilistic seasonal water supply forecasting in
DESCRIPTION
Probabilistic seasonal water supply forecasting in an operational environment: the USDA-NRCS Perspective Tom Pagano [email protected] 503 414 3010 Natural Resources Conservation Service. Existing water supply forecasts Statistical forecasting methods - PowerPoint PPT PresentationTRANSCRIPT
Probabilistic seasonal water supply forecasting in an operational environment: the USDA-NRCS Perspective
Tom Pagano [email protected] 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