VIPER Optimization What is optimization? How does viper’s Station and Time Period optimization work? How to interpret results? What to avoid? Tom Pagano

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



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?






Months (4)October

NovemberDecember

January







Months (4)October

NovemberDecember

January







Months (4)October

NovemberDecember

January


Too many combination to evaluate using “brute force” (at least 24,000)






Months (4)October

NovemberDecember

January


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


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




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


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



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


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


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


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



EQUATION SUMMARY:




tablesRecognize popular variables



EQUATION SUMMARY:





Be aware of num. obs



EQUATION SUMMARY:





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


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



3. Evaluate all combinations for NRCSStrm between Jul and Mar(e.g. Aug-Feb is a valid combo Jun-Mar is not)

Interpretation



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



Period of recordStandard error

#1 32.7#2 45.9

Streamflow

ForecastObserved


#1

#2

High error period

Which station is really “best”?

better



Period of recordStandard error

#1 32.7#2 45.9

Standard errorfor overlapping period

(1988-2006)#1 32.7#2 28.8

Streamflow

ForecastObserved


#1

#2

High error period

Which station is really “best”?

better

better

Documents

VIPER Optimization What is optimization? How does viper’s Station and Time Period optimization work? How to interpret results? What to avoid? Tom Pagano