1

Return Flow Discussion

ESHMC Meeting6 March 2008

Presented by Stacey Taylor

2

Overview

• Bryce Contor’s slides• Historical data analysis:

– IESW007 (Big and Little Wood Rivers)– IESW054 (Richfield)

• Ongoing Snake River return data (groups)• General conclusions

3

Current Calculation Method

Diversions

Retu

rns

Returns = b1 * Diversions(one equation for each entity)

4

Alternate Methods

Diversions

Retu

rns

Returns = bo

(one equation for each entity)

Diversions

Retu

rns

Returns = bo + b1 * Diversions(one equation for each entity)

Diversions

Retu

rns

Returns = -bo + b1 * Diversions)(one equation for each entity)

Diversions

Retu

rns

Returns = logarithmic function(one equation for each entity)

Returns = exponential

function(one equation for

each entity)

OR

Alternate Method (1) Alternate Method (2)

Alternate Method (3) Alternate Methods (4) and (5)

5

Raster Graphics

• Created several raster graphics to represent returns and diversions for IESW007 and IESW054

• Different colors represent different diversions/returns.

6

Example Raster (1)W

ater

Yea

r

MonthOct. Sept.

0

5

10

15

20

Diversion1,000 ac-ft

1928

2004

7

Example Raster (2)W

ater

Yea

r

MonthOct. Sept.

0

5

10

15

20

Diversion1,000 ac-ft

1928

2004

8

Example Raster (3)W

ater

Yea

r

MonthOct. Sept.

0

5

10

15

20

Diversion1,000 ac-ft

1928

2004

9

IESW007 Total Diversions(Big and Little Wood Rivers)

Total Diversions0

1

3

4

5

6

7

9

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Water Year1928

1940

1950

1960

1970

1980

1990

2004

Month10 11 12 1 2 3 4 5 6 7 8 9

Diversion(1,000 ac-ft)

0

10

20

30

40

50

60

70

80

90

10

Return(1,000 ac-ft)

00.10.20.30.40.50.60.70.8

1.6

Water Year1928

1940

1950

1960

1970

1980

1990

2004

Month10 11 12 1 2 3 4 5 6 7 8 9

Total Returns<VALUE>

0

0 - 0

0 - 0.1

0.1 - 0.2

0.2 - 0.3

0.3 - 0.4

0.4 - 0.5

0.5 - 0.6

0.6 - 0.7

0.7 - 0.8

0.8 - 0.9

0.9 - 1.0

1.0 - 1.1

1.1 - 1.2

1.2 - 1.3

1.3 - 1.4

1.4 - 1.5

1.5 - 1.6

1.6 - 1.7

0.91.01.11.21.31.41.5

1.7

IESW007 Total Returns(Big and Little Wood Rivers)

11

IESW054 Total Diversions(Richfield) Diversion

(1,000 ac-ft)Water Year1928

1940

1950

1960

1970

1980

1990

2004

Month10 11 12 1 2 3 4 5 6 7 8 9

0

10

20

30

0

1

2

3

4

5

6

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30

12

IESW054 Total Returns(Richfield) Return

(1,000 ac-ft)0

5

20

Water Year1928

1940

1950

1960

1970

1980

1990

2004

Month10 11 12 1 2 3 4 5 6 7 8 9

Total ReturnsValue

0

1

2

3

4

5

6

8

9

13

14

16

18

10

13

200 250 300 350 400 450 5000

1

2

3

4

5

6

7

8

f(x) = 0.0246887721910913 x − 6.65388487462722R² = 0.687215377959056

f(x) = NaN x + NaNR² = 0f(x) = NaN x + NaNR² = 0f(x) = NaN x + NaNR² = 0

Returns vs. Diversions for IESW007 (Wood Rivers)

1928-1950Linear (1928-1950)1951-1970Linear (1951-1970)1971-1980Linear (1971-1980)1981-2004Linear (1981-2004)

Diversion (1000 ac-ft)

Retu

rn (1

000

ac-ft

)

14

0 20 40 60 80 100 120 1400

5

10

15

20

25

f(x) = 0.207242892482694 x − 6.30837644666079R² = 0.858000134321785

f(x) = NaN x + NaNR² = 0f(x) = NaN x + NaNR² = 0f(x) = NaN x + NaNR² = 0 Returns vs. Diversions for

IESW054(Richfield) 1928-

1950Linear (1928-1950)

Diversion (1000 ac-ft)

Retu

rn (1

000

ac-ft

)

15

0 5000 10000 15000 20000 25000 30000 35000 400000

1000

2000

3000

4000

5000

6000

7000

-500

-400

-300

-200

-100

0

100

200

300

f(x) = 0.164689038436237 x − 152.034585725503R² = 0.989096451839597

CumulativeLinear (Cumulative)Departure from Linear

Cumulative Diversion (1000 ac-ft)

Cum

ulati

ve R

etur

n (1

000

ac-ft

)

Depa

rtur

es fr

om Li

near

1972 1975

Cumulative Return vs. Cumulative DiversionIESW007 (Wood Rivers)

16

Cumulative Return vs. Cumulative DiversionIESW054 (Richfield)

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

200

400

600

800

1000

1200

-60

-40

-20

0

20

40

60

f(x) = 0.116999148341379 x + 99.9176635440656R² = 0.99615611942521

CumulativeLinear (Cumulative)Departure from Linear

Cumulative Diversion (1000 ac-ft)

Cum

ulati

ve R

etur

n (1

000

ac-ft

)

1954 1958

1974 1981

1986

Dep

artu

re fr

om L

inea

r

17

What Caused the Change?

• Change in slope of cumulative plots– Possibly related to conversion to sprinklers– Calibration data shows percentage these increases:

• IESW007 – May 1980 to May 2002 sprinkler % increased from 14.7% to 28.0% (13% increase)

• IESW054 – May 1980 to May 2002 sprinkler % increased from 31.9% to 59.7% (28% increase)

• Aerial photography covering the area encompassed by both entities has been requested for 1969 and 1977

18

Regression Analysis

• A regression analysis was performed on each set of data (1928-1950, 1951-1970, etc)

• P-values were found for each intercept and slope (95% confidence interval)

• Given shared ranges between each set of data, a general equation may describe both entities (IESW007 and IESW054)

19

IESW007 Intercepts and Slopes(Based on 95% CI)

-15.000 -13.000 -11.000 -9.000 -7.000 -5.000 -3.000 -1.000 1.000 3.000

IESW007 Intercept Ranges1928-19501951-19701971-19801981-2004

0.005 0.010 0.015 0.020 0.025 0.030 0.035

IESW007 Slope ranges1928-19501951-19701971-19801981-2004

Shared intercept range: -3.76 to -3.67 Shared slope range: 0.0173 to 0.0235

y = 0.02x – 3.70

20

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

IESW054 Slope Ranges

1928-19501951-19701971-19801981-2004

-20 -10 0 10 20 30 40

IESW054 Intercept Ranges1928-19501951-19701971-19801981-2004

IESW054 Intercepts and Slopes(Based on 95% CI)

No shared slope range between all sets; 1981-2004 slope is negative

Shared slope range: 0.170 to 0.177

y = 0.17x - ???

21

Ongoing Snake River Return Data

• Group data for 2002-2006 were compared to IESW007 and IESW054

• Plotted returns vs. diversions • Plotted returns vs. normalized diversion

(Normalized diversion = diversion/max diversion of single entity)

• Plotted normalized returns vs. normalized diversions

22

Returns vs. Diversions for Separate Entities

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

11000000

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000 IESW002IESW010IESW011IESW016IESW028IESW031IESW032IESW036IESW041Linear (IESW041)Linear (IESW041)

Diversion (ac-ft)

Retu

rn (a

c-ft)

23

Returns vs. Normalized Diversion

0.7 0.75 0.8 0.85 0.9 0.95 10.000

0.100

0.200

0.300

0.400

0.500

0.600IESW002Linear (IESW002)IESW010Linear (IESW010)IESW011Linear (IESW011)IESW016

Diversion (each point divided by max diversion of the entity)

Retu

rn P

erce

nt o

f Div

ersi

on

24

Conclusions

• Current technique of assuming straight line plot with zero intercept may still be best(Returns = b1*Diversions)

• Slope (b1) based on historical data OR lag factors (depends on which is available)

• Slope may be better estimated with inclusion of latest data

25

Discussion