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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)
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Outline
• Goals
• Time series for index
• How to apply
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Goals
• AVERAGE STRESS
• Variability
• Serial correlation (persistence)
• Probability distribution
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Goals
• AVERAGE STRESS – correct endpoint
• Variability
• Serial correlation (persistence)
• Probability distribution
correctvariability
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How to meet these goals:
• Candidate data
• Apply data– Multiple-traces paradigm– Single-trace paradigm
• Evaluation
• Reality Check
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1. Candidate Data:
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Candidate Time Series
• Lewis Lake SNOTEL
• White Elephant SNOTEL
• Natural flow at Heise
• Palmer Index (PDSI)
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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
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Time Series
• Lewis Lake SNOTEL
• White Elephant SNOTEL
• Natural flow at Heise
• Palmer Index (PDSI)
No data before 1981
Two long-term candidates
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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?
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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
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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
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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?
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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?
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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
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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
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0
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0.4
0.6
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1
1.2
1.4
1.6
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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
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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
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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
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Proposal: Eliminate 1997 from Candidate Pool
• Damage to infrastructure means water-use response is unique, not representative of 1997’s hydrologic condition
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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
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Three methods to select from candidate years:
• Historical sequence
• Synthetic
• Stochastic
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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
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0
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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
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Synthetic Series
• Identify combination of years w/ correct average
• Combine into time series– repeat “actual” order of years (Synthetic B)– adjust order (Synthetic C)
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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
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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
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Stochastic Series
• Identify combination of years w/ correct average
• Combine in random order
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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
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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
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Multiple-trace representation ofvariability
• Graphical: – Envelope defined by multiple traces– No matter the starting condition, envelope will
converge to range determined by water-budget
?
?
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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.”
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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
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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
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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
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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)
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Proposed Presentation of Results:
Range associatedwith alternate inputdata sets
Rangeassociatedwith historicalvariability
Single-trace graphical representation of uncertainty:
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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:
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4. Evaluation
• AVERAGE STRESS
• Variability– Histogram– Serial correlation (persistence)
• order of sample years
– Visual assessment of trace– Frequency distribution
• Reality Check
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•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
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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
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•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
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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
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•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
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•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
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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
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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
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(End)