Transcript Extended Probabilistic Forecasting

National Weather Service
River Forecast System
Ensemble Streamflow Prediction
Michael Kane
Hydromet 00-3
Wednesday, 24 May 2000
2290 East Prospect Road, Suite 1
Fort Collins, Colorado 80525
Basic Statistics of Discrete Variables
n
 MEAN
X 
 Standard Deviation
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X
i 1
i
n
1 n
2
s
(
X

X
)
 i
n  1 i 1
Basic Statistics of Discrete Variables
 Salt River Near Roosevelt
– Peak Monthly Volume
– (AF x 1000) WY
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WY
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
Q
52.9
132.0
368.7
34.4
176.6
71.6
36.2
638.6
373.8
521.8
76.2
162.4
321.5
297.1
317.0
146.3
164.7
106.2
71.2
Basic Statistics of Discrete Variables
 Salt River Near Roosevelt
– Peak Monthly Volume
– (AF x 1000) WY
 Weibull Plotting Position
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WY
1978
1980
1979
1973
1983
1985
1984
1975
1987
1982
1986
1972
1988
1981
1976
1989
1971
1977
1974
Ranked Q
638.6
521.8
373.8
368.7
321.5
317.0
297.1
176.6
164.7
162.4
146.3
132.0
106.2
76.2
71.6
71.2
52.9
36.2
34.4
M/(N+1)
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
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Extended Probabilistic Forecasting
0
5
1985
10
15
20
8
7
1986
5
10
1986
5
1985
4
3
15
2
20
1
Day
0
5
10
15
20
25
Volume
Likelihood of Exceeding Flood Capacity
Exceedance Probability
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61
57
53
49
45
41
37
33
29
25
21
17
9
13
5
1
0
1987
 Frequency analysis
using “conditioned”
hydrologic time
series traces
1987
6
0
Discharge
 Hydrologic
simulation using
historic precipitation
and temperature
ESP Forecast Applications
 Spring Flood Outlooks
 Water Supply Forecasts
 Drought Analysis
 Hydropower Planning
 Fisheries Management
 Recreation
 Navigation
 Reservoir Inflow Forecasts
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Water Management Considerations
Hydropower
Water Supply
Recreation
Flood Control
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Hydropower
Navigation
Water Quality
Fisheries
Recreation
NWSRFS Software Overview
OPERATIONAL FORECAST SYSTEM
Automatic
Data Entry
Functions
Preprocessor
Functions
Observed
Data
Files
Processed
Data
Files
PreProcessor
Parameter
Files
EXTENDED STREAMFLOW
PREDICTION SYSTEM
Forecast
Functions
Manual
Preparation
Forecast
Parameter
and
Carryover
Files
ESP
Functions
ESP
Parameter
Files
ESP
Initialization
Program
CALIBRATION SYSTEM
Manual
Calibration
Program
Historical Data
Access Programs
Historical
Data
Calibration Preprocessors and
Calibration Utility
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Calibration
Data Files
Parametric
Data
Automatic
Parameter
Optimizer
ESP Time
Series
Files
ESP Procedure
CURRENT CONDITIONS
• SOIL MOISTURE
• SNOW PACK
• RESERVOIR LEVELS
• STREAMFLOW
ALL YEARS OF
RECORD
FORECAST
TIME SERIES
MEAN AREAL
TIME SERIES
PRECIPITATION
TEMPERATURE
NWSRFS
HYDROLOGIC
MODELS
POSITIONAL
CLIMATOLOGICAL
INFORMATION
STATISTICAL
ANALYSIS
WINDOW
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STREAMFLOW
HISTORICAL
TIME SERIES
PRESENT
TIME
FORECASTS AND
OUTLOOKS
• WATER SUPPLY
• OTHER WATER MGMT
INFORMATION
ESPADP Trace Ensemble Plot
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ESPADP Expected Value Plot
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ESPADP Probability Histogram
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ESPADP Analysis Variables
Number of days above
flood stage
Instantaneous Peak Flow
Mean Daily Peak
Volume of flow
Flow
Number of days until flood
stage is exceeded
Flood stage
Minimum
instantaneous
flow
Time
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ESP Computed Variables
 Variables that can be calculated for specified window:
– Maximum mean daily value and number of days to maximum mean daily
value
– Minimum mean daily value and number of days to minimum mean daily
value
– Mean daily value
– Volume
– Maximum instantaneous value and number of days to maximum
instantaneous value
– Minimum instantaneous value and number of days to minimum
instantaneous value
– Number of days until time series gets above (or below) a specified criterion
– Number of days time series remains above (or below) a specified criterion
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ESPADP Observed and Conditional
Simulation
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ESPADP Observed and Historical Simulation
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Incorporating QPF
 ESP uses blending procedure to combine forecasts of
precipitation and temperature with historical data
 Blending parameters are defined with ESPINIT
 Blending parameters can be changed using ESP
techniques
 ESPADP provides an interface for generating blend
techniques
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ESPADP Incorporating QPF
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CPC Legend
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CPC 2-Week Lead Time Forecasts
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Using CPC Forecast Information
 Manual year weighting
 Alaska year weighting procedure
 Pre-Adjustment technique
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Alaska Procedure
 Developed at Alaska RFC
 Produces year weights for use in ESP based on CPC
forecasts
 Conceptually simple, easy to implement
 Assumes independence among categories of seasonal
precipitation and temperature
 Can be used only for one season per forecast
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Alaska Year Weighting Procedure
Climatology
Normal
Above
Normal
.33
.33
.33
.33
.33
.33
Temperature Probability
Precipitation
Probability
Temperature
Probability
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Forecast
Below
Normal
Precipitation
Probability
Temperature
Probability
Below
Normal
Normal
Above
Normal
.28
.33
.38
.33
.33
.33
Precipitation Probability
Precipitation Probability
Below
Normal
.28
Normal
.33
Above
Normal
.38
Below
Normal
.09
.11
.13
.33
.33
Normal
.09
.11
.13
.33
.33
Above
Normal
.09
.11
.13
.33
Below
Normal
.33
Normal
.33
Above
Normal
.33
Below
Normal
.11
.11
.11
.33
Normal
.11
.11
.11
Above
Normal
.11
.11
.11
ESPADP Alaska Procedure
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ESPADP Pre-adjustment technique
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Bias Adjustment Procedures
 Regression Technique
 Error Model Technique
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Regression Technique
 Plot simulated vs. observed values
 Fit regression line to all points
 Apply regression equation to conditional simulation
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Regression Technique
Observed Variable
80
60
40
20
obs = a (sim) + b
adj. cond. = a(cond) + b
0
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20
40
Simulated Variable
60
80
ESPADP Bias Adjustment
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Error Model Technique
 Historical simulation is compared to observations at every
time step
 OBS = HIST_SIM + f(error)
 Error Function, f(error), from historical simulation is used to
adjust conditional simulation at every time step
 Advantages
– Adjusts for bias
– Adjustments are inherent in ESP traces
– Can build uncertainty back into the model
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ESPADP Error Model Technique
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