considerations for data series for current practices scenario november 2006 update 17 january 2007...

Considerations for Data Seriesfor Current Practices Scenario

November 2006

Update 17 January 2007

B. Contor(New stuff

will be in greenboxes or on green

slides)

Outline

• Goals

• Time series for index

• How to apply

Goals

• AVERAGE STRESS

• Variability

• Serial correlation (persistence)

• Probability distribution

Goals

• AVERAGE STRESS – correct endpoint

• Variability

• Serial correlation (persistence)

• Probability distribution

correctvariability

How to meet these goals:

• Candidate data

• Apply data– Multiple-traces paradigm– Single-trace paradigm

• Evaluation

• Reality Check

1. Candidate Data:

Candidate Time Series

• Lewis Lake SNOTEL

• White Elephant SNOTEL

• Natural flow at Heise

• Palmer Index (PDSI)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1980 1985 1990 1995 2000 2005 2010

Lew isIndex WhtEl_Index PDSI-4 Heise_NatFlow

They all are similar

Time Series

• Lewis Lake SNOTEL

• White Elephant SNOTEL

• Natural flow at Heise

• Palmer Index (PDSI)

No data before 1981

Two long-term candidates

Two Possible Indices

-1000

1000

3000

5000

7000

9000

11000

13000

1880 1900 1920 1940 1960 1980 2000 2020

cfs

-8

-6

-4

-2

0

2

4

6

8

PD

SI

Heise_Nat_Flow Avg Nat Flow PDSI (4 Div) PDSI = 1

Preference?

Also consider diversions:

Snake River Diversions

-2,000

0

2,000

4,000

6,000

8,000

10,000

12,000

1960 1970 1980 1990 2000 2010

Year

Th

ou

san

d A

cre

Fee

t

Sum

TrendLine

DeltaTrend

Avg+DeltaTrend

Also consider diversions:Snake River Diversions

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1960 1970 1980 1990 2000 2010

Year

Th

ou

san

d A

cre

Fee

t

DetrendedIndex

Two Possible Indices

-1000

1000

3000

5000

7000

9000

11000

13000

1880 1900 1920 1940 1960 1980 2000 2020

cfs

-8

-6

-4

-2

0

2

4

6

8

PD

SI

Heise_Nat_Flow Avg Nat Flow PDSI (4 Div) PDSI = 1

Increasing variability?

Two Possible Indices

-1000

1000

3000

5000

7000

9000

11000

13000

1880 1900 1920 1940 1960 1980 2000 2020

cfs

-8

-6

-4

-2

0

2

4

6

8

PD

SI

Heise_Nat_Flow Avg Nat Flow PDSI (4 Div) PDSI = 1

Change in persistence?

Year Index1992 0.5875441993 1.0279021994 0.6733241995 1.1404911996 1.3943611997 1.7094431998 1.1731361999 1.2504572000 0.8449522001 0.576585

Index, Natural Flow at Heise

0

0.5

1

1.5

2

1990 1992 1994 1996 1998 2000 2002

Average index 1.04

Candidate Years

New item: Diversions Index

• The biggest component of recharge is diversions

• Are diversions correlated to our indices?

• Remember two goals:– correct end point– correct representation of variability

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1990 1992 1994 1996 1998 2000 2002 2004 2006

PD

S &

Hei

se I

nd

ex

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Det

ren

ded

Div

esri

on

s In

dex

HeiseIndex

Detrend_Div_Indx

Correlation Between Diversionsand Lagged Natural Flow at Heise

1986 - 2005

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1 2 3 4 5 6 7 8

lag (yrs)

Co

rrel

atio

n

Yr HeiseIndex Detrend_Div_Index1992 0.588 0.9541993 1.028 0.9001994 0.673 1.0721995 1.140 0.9391996 1.394 1.0781997 1.709 1.0471998 1.173 1.0331999 1.250 1.0422000 0.845 1.1482001 0.577 0.983

1.038 1.020

Proposal: Eliminate 1997 from Candidate Pool

• Damage to infrastructure means water-use response is unique, not representative of 1997’s hydrologic condition

2. Multiple traces paradigm

• Select data to create representative series

• Use average of data to create “baseline” run– result after many periods = endpoint– trajectory from start describes how fast

adjustment will be

• Multiple traces of variable series to define probability envelope

Three methods to select from candidate years:

• Historical sequence

• Synthetic

• Stochastic

Use Historical Series to OrderCandidate Years

(Synthetic A)• Identify index of each year of record

• Associate each year of record with one candidate year

• Adjust to obtain average index ~ 1.0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1900 1920 1940 1960 1980 2000 2020

HeiseIndx Synth_A

I didn’t calculatethe diversions implications of

Synthetic A

Synthetic Series

• Identify combination of years w/ correct average

• Combine into time series– repeat “actual” order of years (Synthetic B)– adjust order (Synthetic C)

SrcYr Yr1992 11993 21994 31995 41996 51998 61999 71999 82000 92001 101992 111993 121994 131995 141996 15

Synthetic BSrcYr Yr

1992 11994 21993 31995 41996 51998 61999 71999 82000 92001 101992 111994 121993 131995 141996 15

Synthetic C

Synth_B

0

0.5

1

1.5

0 10 20 30

Synth_B

Synth_C

0

0.5

1

1.5

0 10 20 30

Synth_C

In either case:

Heise Index avg 0.992DetrendDivIndex 1.019

Stochastic Series

• Identify combination of years w/ correct average

• Combine in random order

Stochastic

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 20 40 60 80 100

I haven’t analyzed thediversions implicationsof the stochastic series

Define Variability Envelope: Repeat Series w/ Different Start

-1.5

-1

-0.5

0

0.5

1

1.5

20 25 30

Series1

Series2

Series3

Series4

Multiple-trace representation ofvariability

• Graphical: – Envelope defined by multiple traces– No matter the starting condition, envelope will

converge to range determined by water-budget

?

?

Multiple-trace representation ofvariability

• Text:

“The simulated long-term average discharge of my favorite reach is x cfs. The discharge is expected to exceed z cfs 80% of the time and y cfs 20% of the time. Within aa years, 75% of the adjustment from current discharge would be expected.”

3: Single-trace Paradigm(Repeat Representative Year)

• No pretense of predicting future time series• Run single stress to get steady-state

end point and trend of adjustment from current• Stress is a single year or average of group of

years• Groups of years are in sequential blocks to

preserve human or hydrologic serial correlation• Obtain knowledge of variability from historical

data

Yr Heise_IndxPairs Triple Quad Quint1992 0.5875441993 1.027902 0.8077231994 0.673324 0.850613 0.7629231995 1.140491 0.906908 0.947239 0.8573151996 1.394361 1.267426 1.069392 1.059019 0.9647241997 1.709443 1.551902 1.414765 1.229405 1.1891041998 1.173136 1.44129 1.425647 1.354358 1.2181511999 1.250457 1.211796 1.377679 1.381849 1.3335772000 0.844952 1.047704 1.089515 1.244497 1.274472001 0.576585 0.710768 0.890664 0.961282 1.110914

Candidate years or groups of years

All Candidate Years w/1999 repeated and 1997 omitted: 0.992

DetrendDivsYr Single Pairs Triple Quad Quint

1992 0.9541993 0.900 0.9271994 1.072 0.986 0.9751995 0.939 1.005 0.970 0.9661996 1.078 1.009 1.030 0.997 0.9891997 1.047 1.063 1.021 1.034 1.0071998 1.033 1.040 1.053 1.024 1.0341999 1.042 1.038 1.041 1.050 1.0282000 1.148 1.095 1.074 1.068 1.0702001 0.983 1.065 1.058 1.052 1.051

All candidate years with 1997 omitted and 1999repeated: Average index = 1.019

Representation of variability in single-trace paradigm:

Represent uncertainty in generating dataset by running all three best estimates

Represent hydrologic uncertainty by referringto history

(Cosgrove 2006, Draft Final Report)

(Meinzer 1923, USGS paper 489)

Proposed Presentation of Results:

Range associatedwith alternate inputdata sets

Rangeassociatedwith historicalvariability

Single-trace graphical representation of uncertainty:

Proposed Presentation,Narrative Format:

“Simulated long-term discharge of my favoritereach is x to y cfs, depending on the inputdata set used. Under average conditions and current practices, 75% of the adjustmentfrom current levels is realized within z years. Historical data and prior estimates suggest that discharge can vary by aa cfs over a single season and by bb cfs over a ten-year period.”

Single-trace text representation of uncertainty:

4. Evaluation

• AVERAGE STRESS

• Variability– Histogram– Serial correlation (persistence)

• order of sample years

– Visual assessment of trace– Frequency distribution

• Reality Check

•AVERAGE STRESS = Average Index?

1.0000 0.999 0.992 0.992 0.9991.028 1.048

0.961 0.964

0.000

0.200

0.400

0.600

0.800

1.000

mean

Data

Historic Index

Synth_B

Synth_C

Stochastic

1993

99-00

98-01

92-96

I haven’t analyzed thediversions implicationsof all the options

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

min 5th 25th median 75th 95th max

Data

Historic Index

Synth_B

Synth_C

Stochastic

•Variability

I haven’t analyzed thediversions implicationsof all the options

Histogram

•Serial Correlation – Order of Sample Yrs

No of Years in "Natural" Order in Series

12%

70%

40%

15%

0%

10%

20%

30%

40%

50%

60%

70%

80%

Historical Synthetic B Synthetic C Stochastic

Stochastic

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 20 40 60 80 100

Synth_B

0

0.5

1

1.5

0 20 40 60 80 100

Synth_C

0

0.5

1

1.5

0 20 40 60 80 100

Historical Index

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1900 1920 1940 1960 1980 2000 2020

Data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1900 1920 1940 1960 1980 2000 2020

HeiseIndx

•Serial Correlation –Visual Assessment

I haven’t analyzed thediversions implicationsof all the options

•Probability Frequency DistributionMay be important for both diversions and

natural recharge components?

0

5

10

15

20

25

30

35

0.5

0.6

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Mor

e

Data

Historic Index

0

5

10

15

20

25

30

35

0.5

0.6

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Mor

e

Data

Synthetic_B

0

5

10

15

20

25

30

35

0.5

0.6

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Mor

e

Data

Stochastic

0

5

10

15

20

25

30

35

0.5

0.6

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Mor

e

Data

Synthetic_C

I haven’t analyzed thediversions implicationsof all the options

•Summary TableCriteria Historical

IndexSynthetic B Synthetic C Stochastic Sample

Years, Pairs, Etc

Avg of Candidate

Period

Average Stress Good Good Good Good Med Good

Variability Med Med Med Med N/A N/A

Serial Correlation:

Years in Natural Order

Bad Good Med Bad N/A N/A

Serial Correlation:

Visual Assessment

Good Bad Med Med N/A N/A

Probability Distribution

Bad Bad Bad Bad N/A N/A

I haven’t analyzed thediversions implicationsof all the options

Frequency

Reality Check

• Correct Average is vital– What if stress is not

correlated to indices?– What about climate change?

• Other characteristics relate to variability– What if the variability has

been changing?– What if we can’t match

distribution?– What if we get

autocorrelation wrong?– What about persistence?

Two Possible Indices

-1000

1000

3000

5000

7000

9000

11000

13000

1880 1900 1920 1940 1960 1980 2000 2020

cfs

-8

-6

-4

-2

0

2

4

6

8

PD

SI

Heise_Nat_Flow Avg Nat Flow PDSI (4 Div) PDSI = 1

Two Possible Indices

-1000

1000

3000

5000

7000

9000

11000

13000

1880 1900 1920 1940 1960 1980 2000 2020

cfs

-8

-6

-4

-2

0

2

4

6

8

PD

SI

Heise_Nat_Flow Avg Nat Flow PDSI (4 Div) PDSI = 1

Reality Check

• Every time-series option has at least one “BAD” entry!

• We have another way to deal with variability

Criteria Historical Index

Synthetic B Synthetic C Stochastic Sample Years,

Pairs, Etc

Avg of Candidate

Period

Average Stress Good Good Good Good Med Good

Variability Med Med Med Med N/A N/A

Serial Correlation:

Years in Natural Order

Bad Good Med Bad N/A N/A

Serial Correlation:

Visual Assessment

Good Bad Med Med N/A N/A

Probability Distribution

Bad Bad Bad Bad N/A N/A

(End)