VIPER Optimization What is optimization? How does viper’s Station and Time Period optimization...
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Transcript of VIPER Optimization What is optimization? How does viper’s Station and Time Period optimization...
VIPER Optimization
What is optimization?
How does viper’s Station and Time Period
optimization work?
How to interpret results?
What to avoid?
Tom [email protected] 503-414-3010
As used in a statistical forecasting context
TargetTomichi at Gunnison Apr-July streamflow
As used in a statistical forecasting context
TargetTomichi at Gunnison Apr-July streamflow
Data types (3)Snowpack
PrecipitationTemperature
Predictor Stations (7)Porphyry CreekSlumgullionCochetopa PassMonarch OffshootButteTaylor ParkSt Elmo
Months (4)October
NovemberDecember
January
What is the optimal combination of variables to get the best prediction?
As used in a statistical forecasting context
TargetTomichi at Gunnison Apr-July streamflow
Data types (3)Snowpack
PrecipitationTemperature
Predictor Stations (7)Porphyry CreekSlumgullionCochetopa PassMonarch OffshootButteTaylor ParkSt Elmo
Months (4)October
NovemberDecember
January
What is the optimal combination of variables to get the best prediction?
As used in a statistical forecasting context
TargetTomichi at Gunnison Apr-July streamflow
Data types (3)Snowpack
PrecipitationTemperature
Predictor Stations (7)Porphyry CreekSlumgullionCochetopa PassMonarch OffshootButteTaylor ParkSt Elmo
Months (4)October
NovemberDecember
January
What is the optimal combination of variables to get the best prediction?
As used in a statistical forecasting context
TargetTomichi at Gunnison Apr-July streamflow
Data types (3)Snowpack
PrecipitationTemperature
Predictor Stations (7)Porphyry CreekSlumgullionCochetopa PassMonarch OffshootButteTaylor ParkSt Elmo
Months (4)October
NovemberDecember
January
What is the optimal combination of variables to get the best prediction?
Too many combination to evaluate using “brute force” (at least 24,000)
As used in a statistical forecasting context
TargetTomichi at Gunnison Apr-July streamflow
Data types (3)Snowpack
PrecipitationTemperature
Predictor Stations (7)Porphyry CreekSlumgullionCochetopa PassMonarch OffshootButteTaylor ParkSt Elmo
Months (4)October
NovemberDecember
January
What is the optimal combination of variables to get the best prediction?
Too many combination to evaluate using “brute force” (at least 24,000)
Instead we could “search”,trying some combinations and
following up promising avenues.
Station optimization search algorithm, simple example
TargetTomichi at Gunnison Apr-July streamflowPredictorsA Avalanche Oct-Mar PrecipB Butte Apr 1 SWEC Cochetopa Pass Apr 1 SWED Datother Station Apr 1 SWE
Station optimization search algorithm, simple example
Build all 1 variable combinations1. A2. B3. C4. D
Station optimization search algorithm, simple example
Build all 1 variable combinations1. A2. B3. C4. D
Evaluate regression vs flow, find jackknife standard error1. A – 38 2. B – 36 3. C – 334. D – 30
Station optimization search algorithm, simple example
Build all 1 variable combinations1. A2. B3. C4. D
Evaluate regression vs flow, find jackknife standard error1. A – 38 2. B – 36 3. C – 334. D – 30
Sort equations, best to worst1. D – 30 best2. C – 333. B – 36 4. A – 38 worst
Station optimization search algorithm, simple example
Build all 1 variable combinations1. A2. B3. C4. D
Evaluate regression vs flow, find jackknife standard error1. A – 38 2. B – 36 3. C – 334. D – 30
Sort equations, best to worst1. D – 30 best2. C – 333. B – 36 4. A – 38 worst
Build 2 variable equations, regress, find jackknife standard error1. D – 30 2. C – 33 3. B – 364. A – 38
A,D - 32 B,D - 34 C,D - 29A,C - 37 B,C - 35 A,B - 39
Note: A,B is the same as B,A
Station optimization search algorithm, simple example
Re-sort results… “prune” branches, keeping top 51. C,D - 292. D - 303. A,D - 324. C - 335. B,D - 34
Station optimization search algorithm, simple example
Re-sort results… “prune” branches, keeping top 51. C,D - 292. D - 303. A,D - 324. C - 335. B,D - 34
Build all 3-variable combinations, growing from top 5 list, evaluate1. C,D - 29 A,C,D - 28 B,C,D - 362. D - 303. A,D - 32 A,B,D - 35 4. C - 335. B,D - 34
Note: A,B,C not evaluated…No “trunk” leads us there
Station optimization search algorithm, simple example
Re-sort results… “prune” branches, keeping top 51. C,D - 292. D - 303. A,D - 324. C - 335. B,D - 34
Build all 3-variable combinations, growing from top 5 list, evaluate1. C,D - 29 A,C,D - 28 B,C,D - 362. D - 303. A,D - 32 A,B,D - 35 4. C - 335. B,D - 34
Re-sort list, evaluate 4-variable combinations1. A,C,D – 28 A,B,C,D - 31 2. C,D - 29 3. D - 304. A,D - 32 5. C - 33
Note: A,B,C not evaluatedNo “trunk” leads us there
Station optimization search algorithm, simple example
Re-sort list… Optimization finished when top 5 list doesn’t change1. A,C,D - 28 2. C,D - 29 3. D - 304. A,B,C,D - 315. A,D - 32
Station optimization search algorithm, simple example
Re-sort list… Optimization finished when top 5 list doesn’t change 1. A,C,D - 28 2. C,D - 29 3. D - 304. A,B,C,D - 315. A,D - 32
Questions to ask: Which variables are “popular”?What would maintain consistency from month to month?Does the combination make physical sense? Is some data harder to get than others?
Optimization is not a substitute for thinking!
Viper station optimization
Output
Output
Input data:Year Y1 X91979 99.40 24.801980 93.10 25.801981 17.40 13.801982 63.30 23.801983 129.00 25.101984 269.60 30.001985 135.70 24.601986 92.80 21.001987 127.50 22.60
DETAILED OUTPUT
RANKED REGRESSION EQUATIONS:
***** RANK 1
coef var ---- ---- 0.20602 X9 701,OCT-MAY,PRCP,SNTL,CO,AWDB,Porphyry Creek -0.28128 Constant
#obs= 22 #pc = 1 Jr = 0.873 JStdErr = 0.448JStdErrSS = 0.500 r = 0.896 StdErr = 0.407 StdErrSS = 0.546
JCK REG JCK REG STD REG STD REG YEAR OBSERVED COMPUTED ERROR COMPUTED ERROR
1979 4.63 4.84 0.21 4.83 0.20 1980 4.53 5.08 0.55 5.03 0.50 1981 2.59 2.55 -0.04 2.56 -0.03 1982 3.99 4.66 0.67 4.62 0.64 1983 5.05 4.88 -0.18 4.89 -0.16
SUMMARY OUTPUT
Name of this file: 09119000_optimization.txtNumber of combinations evaluated = 1Created on 6/13/2007 3:36:56 PM by tpagano
Transformation type: CubertAnalysis type: Principal Components
VARIABLES:
Y1 09119000,APR-JUL,SRVO,USGS,CO,AWDB,Tomichi Creek At Gunnison, Co
X9 701,OCT-MAY,PRCP,SNTL,CO,AWDB,Porphyry Creek
EQUATION SUMMARY:
RANK VARIABLES JACKKNIFE JACK. NUM. 1 STANDARD CORR. OBS. NUM. 1 2 3 4 5 6 7 8 9 0 ERROR COEF. USED PC'S X 0.448 0.873 22 1
Y1 09119000,APR-JUL,SRVO,USGS,CO,AWDB,Tomichi Creek At Gunnison, Co
X1 06L03,MAY,WTEQ,SNOW,CO,AWDB,Porphyry Creek X2 762,MAY,WTEQ,SNTL,CO,AWDB,Slumgullion X3 06L06,MAY,WTEQ,SNOW,CO,AWDB,Cochetopa Pass X4 06L09,MAY,WTEQ,SNOW,CO,AWDB,Monarch Offshoot X5 06L04,MAY,WTEQ,SNOW,CO,AWDB,Monarch Pass X6 701,MAY,WTEQ,SNTL,CO,AWDB,Porphyry Creek X7 701,OCT-MAY,PRCP,SNTL,CO,AWDB,Porphyry Creek X8 762,OCT-MAY,PRCP,SNTL,CO,AWDB,Slumgullion X12 380,OCT-MAY,PRCP,SNTL,CO,AWDB,Butte
EQUATION SUMMARY:
RANK VARIABLES JACKKNIFE JACK. NUM. 1 1 1 STANDARD CORR. OBS. NUM. 1 2 3 4 5 6 7 8 9 0 1 2 ERROR COEF. USED PC'S
1 X X 0.232 0.969 9 1 2 X X X 0.243 0.966 9 1 3 X X X X 0.251 0.964 9 1 4 X X X X 0.255 0.963 9 1 5 X X X X 0.256 0.966 8 1 6 X X X X 0.263 0.950 8 1 7 X X X X X 0.266 0.960 9 1 8 X X X X X 0.269 0.968 8 2 9 X X X X X 0.270 0.947 8 1 10 X X X X X 0.270 0.947 8 1 11 X X X 0.271 0.963 9 2 12 X X X X 0.272 0.896 19 1 13 X X X X X X 0.272 0.967 8 2 14 X X X 0.274 0.894 19 1 15 X X X 0.275 0.956 9 1
Interpreting variable
tables
Y1 09119000,APR-JUL,SRVO,USGS,CO,AWDB,Tomichi Creek At Gunnison, Co
X1 06L03,MAY,WTEQ,SNOW,CO,AWDB,Porphyry Creek X2 762,MAY,WTEQ,SNTL,CO,AWDB,Slumgullion X3 06L06,MAY,WTEQ,SNOW,CO,AWDB,Cochetopa Pass X4 06L09,MAY,WTEQ,SNOW,CO,AWDB,Monarch Offshoot X5 06L04,MAY,WTEQ,SNOW,CO,AWDB,Monarch Pass X6 701,MAY,WTEQ,SNTL,CO,AWDB,Porphyry Creek X7 701,OCT-MAY,PRCP,SNTL,CO,AWDB,Porphyry Creek X8 762,OCT-MAY,PRCP,SNTL,CO,AWDB,Slumgullion X12 380,OCT-MAY,PRCP,SNTL,CO,AWDB,Butte
EQUATION SUMMARY:
RANK VARIABLES JACKKNIFE JACK. NUM. 1 1 1 STANDARD CORR. OBS. NUM. 1 2 3 4 5 6 7 8 9 0 1 2 ERROR COEF. USED PC'S
1 X X 0.232 0.969 9 1 2 X X X 0.243 0.966 9 1 3 X X X X 0.251 0.964 9 1 4 X X X X 0.255 0.963 9 1 5 X X X X 0.256 0.966 8 1 6 X X X X 0.263 0.950 8 1 7 X X X X X 0.266 0.960 9 1 8 X X X X X 0.269 0.968 8 2 9 X X X X X 0.270 0.947 8 1 10 X X X X X 0.270 0.947 8 1 11 X X X 0.271 0.963 9 2 12 X X X X 0.272 0.896 19 1 13 X X X X X X 0.272 0.967 8 2 14 X X X 0.274 0.894 19 1 15 X X X 0.275 0.956 9 1
Interpreting variable
tablesRecognize popular variables
Y1 09119000,APR-JUL,SRVO,USGS,CO,AWDB,Tomichi Creek At Gunnison, Co
X1 06L03,MAY,WTEQ,SNOW,CO,AWDB,Porphyry Creek X2 762,MAY,WTEQ,SNTL,CO,AWDB,Slumgullion X3 06L06,MAY,WTEQ,SNOW,CO,AWDB,Cochetopa Pass X4 06L09,MAY,WTEQ,SNOW,CO,AWDB,Monarch Offshoot X5 06L04,MAY,WTEQ,SNOW,CO,AWDB,Monarch Pass X6 701,MAY,WTEQ,SNTL,CO,AWDB,Porphyry Creek X7 701,OCT-MAY,PRCP,SNTL,CO,AWDB,Porphyry Creek X8 762,OCT-MAY,PRCP,SNTL,CO,AWDB,Slumgullion X12 380,OCT-MAY,PRCP,SNTL,CO,AWDB,Butte
EQUATION SUMMARY:
RANK VARIABLES JACKKNIFE JACK. NUM. 1 1 1 STANDARD CORR. OBS. NUM. 1 2 3 4 5 6 7 8 9 0 1 2 ERROR COEF. USED PC'S
1 X X 0.232 0.969 9 1 2 X X X 0.243 0.966 9 1 3 X X X X 0.251 0.964 9 1 4 X X X X 0.255 0.963 9 1 5 X X X X 0.256 0.966 8 1 6 X X X X 0.263 0.950 8 1 7 X X X X X 0.266 0.960 9 1 8 X X X X X 0.269 0.968 8 2 9 X X X X X 0.270 0.947 8 1 10 X X X X X 0.270 0.947 8 1 11 X X X 0.271 0.963 9 2 12 X X X X 0.272 0.896 19 1 13 X X X X X X 0.272 0.967 8 2 14 X X X 0.274 0.894 19 1 15 X X X 0.275 0.956 9 1
Interpreting variable
tablesRecognize popular variables
Be aware of num. obs
Y1 09119000,APR-JUL,SRVO,USGS,CO,AWDB,Tomichi Creek At Gunnison, Co
X1 06L03,MAY,WTEQ,SNOW,CO,AWDB,Porphyry Creek X2 762,MAY,WTEQ,SNTL,CO,AWDB,Slumgullion X3 06L06,MAY,WTEQ,SNOW,CO,AWDB,Cochetopa Pass X4 06L09,MAY,WTEQ,SNOW,CO,AWDB,Monarch Offshoot X5 06L04,MAY,WTEQ,SNOW,CO,AWDB,Monarch Pass X6 701,MAY,WTEQ,SNTL,CO,AWDB,Porphyry Creek X7 701,OCT-MAY,PRCP,SNTL,CO,AWDB,Porphyry Creek X8 762,OCT-MAY,PRCP,SNTL,CO,AWDB,Slumgullion X12 380,OCT-MAY,PRCP,SNTL,CO,AWDB,Butte
EQUATION SUMMARY:
RANK VARIABLES JACKKNIFE JACK. NUM. 1 1 1 STANDARD CORR. OBS. NUM. 1 2 3 4 5 6 7 8 9 0 1 2 ERROR COEF. USED PC'S
1 X X 0.232 0.969 9 1 2 X X X 0.243 0.966 9 1 3 X X X X 0.251 0.964 9 1 4 X X X X 0.255 0.963 9 1 5 X X X X 0.256 0.966 8 1 6 X X X X 0.263 0.950 8 1 7 X X X X X 0.266 0.960 9 1 8 X X X X X 0.269 0.968 8 2 9 X X X X X 0.270 0.947 8 1 10 X X X X X 0.270 0.947 8 1 11 X X X 0.271 0.963 9 2 12 X X X X 0.272 0.896 19 1 13 X X X X X X 0.272 0.967 8 2 14 X X X 0.274 0.894 19 1 15 X X X 0.275 0.956 9 1
Interpreting variable
tablesRecognize popular variables
Be aware of num. obsMeaningful interpretations
Viper time period optimization
Maybe you know “slumgullion precip” should be a predictor, but don’t know if it should be oct-mar or nov-mar or ?
Time optimization varies stations with in groups one at a time, looking for the optimal combination.
Viper time period optimization
Maybe you know “slumgullion precip” should be a predictor, but don’t know if it should be oct-mar or nov-mar or ?
Time optimization varies stations with in groups one at a time, looking for the optimal combination.
It does not have a fancy search algorithm, it tries all combinations.
Time optimization available for Z-score or PCA… Station optimization only available in PCA for now.
Interpretation
1. Adjust only SnotelPRCP and NRCSStrm. Leave others alone.
Interpretation
1. Adjust only SnotelPRCP and NRCSStrm. Leave others alone.
2. Evaluate all combinations for SnotelPrcp between Oct and Mar that end with March(e.g. Oct-Mar, Nov-Mar, Dec-Mar, Jan-Mar, Feb-Mar, Mar-Mar)
Interpretation
1. Adjust only SnotelPRCP and NRCSStrm. Leave others alone.
2. Evaluate all combinations for SnotelPrcp between Oct and Mar that end with March(e.g. Oct-Mar, Nov-Mar, Dec-Mar, Jan-Mar, Feb-Mar, Mar-Mar)
3. Evaluate all combinations for NRCSStrm between Jul and Mar(e.g. Aug-Feb is a valid combo Jun-Mar is not)
Interpretation
1. Adjust only SnotelPRCP and NRCSStrm. Leave others alone.
2. Evaluate all combinations for SnotelPrcp between Oct and Mar that end with March(e.g. Oct-Mar, Nov-Mar, Dec-Mar, Jan-Mar, Feb-Mar, Mar-Mar)
3. Evaluate all combinations for NRCSStrm between Jul and Mar(e.g. Aug-Feb is a valid combo Jun-Mar is not)
4. Return best combination to interface
Recent additions
Don’t allow the “best” month for a group be one that eliminates that group.
e.g. Oct-Jan precipitation + August swe = “best”
But there is no august SWE.Really it just wants precip alone.
Optimize Groups in OrderOptimize Groups DependentlyOptimize Groups Independently
When optimizing one group do you leave the others on or off?
Do you want each group to try to do its best on its own, or let groups cooperate?
A word of caution about optimization!
A station is not graded on the exams that it skips
Streamflow
ForecastObserved
Station availability
#1
#2
High error period
A word of caution about optimization!
A station is not graded on the exams that it skips
Period of recordStandard error
#1 32.7#2 45.9
Streamflow
ForecastObserved
Station availability
#1
#2
High error period
Which station is really “best”?
better
A word of caution about optimization!
A station is not graded on the exams that it skips
Period of recordStandard error
#1 32.7#2 45.9
Standard errorfor overlapping period
(1988-2006)#1 32.7#2 28.8
Streamflow
ForecastObserved
Station availability
#1
#2
High error period
Which station is really “best”?
better
better