Statistical Models of Water Temperature in

the Delta under Climate-Change

Scenarios: A CASCaDE Project

October 24, 2008

Wayne Wagner & Mark StaceyUC-Berkeley

CASCaDE project

• Combine climate, hydrodynamic, sediment, biologic models for future scenarios

• Need quick temperature models to inform scenario choices– The Model– Results– Requirements and Limitations

2

3

4

56 9

1012

13

14

15

16

18 117

Data Sources for Model Development

o IEP- Provides water data

• Water temperature• Salinity

o CIMIS- Provides atmospheric forcing data

• Insolation• Wind• Air temperature

The Model

• Pure Statistic Model– Mulitple linear regression at each location

– Tair refers to average of daily max and min – Can be used to predict Tw,max , Tw,avg , Tw,min

• Data split for calibration/verification– Calibrate with first half for b0 , b1 , b2 , b3

– Initialize second half w/ measured data

Jan86 Dec86 Nov87 Oct88 Sep89 Sep90 Aug91 Jul92 Jun93 Jun94 May95 Apr96 Mar97

10

15

20

25

T max

[οC

]

SJ Antioch

PredictedMeasured

Apr97 Mar98 Feb99 Jan00 Dec00 Dec01 Nov02 Oct03 Sep04 Sep05 Aug06 Jul07 Jun08

10

15

20

25

T max

[οC

]

SJ Antioch

PredictedMeasured

Water Temperature Model

Verification r2 = .974

Calibration r2 = .975

• Projections at Antioch – Top panel: Calibration period (defines 4 parameters)– Bottom panel: Unconstrained calculation to test model

performance. Parameters defined in calibration period.

Jan86 Sep86 Jun87 Feb88 Oct88 Jul89 Mar90 Nov90 Aug91 Apr92 Jan93 Sep935

10

15

20

25

30

T max

[οC

]

SJ Mossdale

PredictedMeasured

May94 Jan95 Oct95 Jun96 Mar97 Nov97 Jul98 Apr99 Dec99 Sep00 May01 Jan02

10

15

20

25

T max

[οC

]

SJ Mossdale

PredictedMeasured

Water Temperature Model

Verification r2 = .952

Calibration r2 = .958

• Projections at Mossdale (SJ River) – The model displays high predictive skill, but

measurements lag model during warming periods.

• Projections at Rio Vista (Sacramento River)- The model displays high predictive skill with respect to

the yearly cycle and yearly maximums in the northern Delta.

Jan86 Sep86 May87 Feb88 Oct88 Jun89 Mar90 Nov90 Aug91 Apr92 Dec92 Sep93

10

15

20

25T m

ax [ο

C]

Sac Rio Vista

PredictedMeasured

May94 Jan95 Oct95 Jun96 Mar97 Nov97 Jul98 Apr99 Dec99 Aug00 May01 Jan02

10

15

20

25

T max

[οC

]

Sac Rio Vista

PredictedMeasured

Water Temperature Model

Verification r2 = .968

Calibration r2 = .974

• Projections at Rio Vista (Sacramento River) – The model displays high predictive skill at with respect

to the yearly cycle and yearly maximums in the northern Delta.

– Note finer scale comparisons.

Jan86 Sep86 May87 Feb88 Oct88 Jun89 Mar90 Nov90 Aug91 Apr92 Dec92 Sep93

10

15

20

25T m

ax [ο

C]

Sac Rio Vista

PredictedMeasured

May94 Jan95 Oct95 Jun96 Mar97 Nov97 Jul98 Apr99 Dec99 Aug00 May01 Jan02

10

15

20

25

T max

[οC

]

Sac Rio Vista

PredictedMeasured

Water Temperature Model

Verification r2 = .968

Calibration r2 = .974

Water Temperature Model

Feb99 May99 Sep99 Dec994

6

8

10

12

14

16

18

20

22

24T m

ax [ο

C]

Sac Rio Vista

PredictedMeasured

• Measurements lead model during cooling periods.

Water Temperature Model

Feb99 May99 Sep99 Dec994

6

8

10

12

14

16

18

20

22

24T m

ax [ο

C]

Sac Rio Vista

PredictedMeasured

• Measurements lead model during cooling periods.

• Model reproduces temperature fluctuations on weekly timescales

Variability of Predictive Skill

• Model parameters are calculated at each location in the Delta.– Model does not include flow term.

• Model performance is variable.– Performance is a function of

• Length of data record used for calibration.• Location in the Delta with respect to principal water

masses.

0 500 1000 1500 2000 2500 3000 3500 4000 45000.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Length of Calibration Period (days)

r2

Effects of Short Calibration Periods

Verification r2 vs. Length of Calibration Period

0 500 1000 1500 2000 2500 3000 3500 4000 45000.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Length of Calibration Period (days)

r2

Effects of Short Calibration Periods

• Calibration periods > 1 year greatly improve predictive skill of the model.

Spatial Variability of Model Skill

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

r2 vs. Position

0.9

0.92

0.94

0.96

0.98

1

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

r2 vs. Position

0.9

0.92

0.94

0.96

0.98

1

Tidal dominanceSan Joaquin dominance

Sacramento dominance

Spatial Variability of Model Skill

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

r2 vs. Position

0.9

0.92

0.94

0.96

0.98

1

Tidal dominanceSan Joaquin dominance

Sacramento dominance

Spatial Variability of Model Skill

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

r2 vs. Position

0.9

0.92

0.94

0.96

0.98

1

Tidal dominance

Sacramento dominance

San Joaquin dominance

Mixed Influence

Spatial Variability of Model Skill

Projections for CASCaDE Scenarios

• Statistical model– Verification r2 >.90 provided enough calibration data.– Timing off seasonally in some locations.

• Projection– Calibrate with full dataset.– Initialize with measured water temperature.– Force with downscaled climate data from Mike Dettinger

(CASCaDE) .

100 Year Water Temperature Projections

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

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10

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25

30

T max

[οC

]Sac Rio Vista

gfdl a2measured

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

5

10

15

20

25

30

T max

[οC

]Sac Rio Vista

gfdl a2measured

Smelt threshold100 Year Water Temperature Projections

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

5

10

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30

T max

[οC

]

gfdl a2

2000 2010 2020 2030 2040 2050 2060 2070 2080 20900

20

40

60

80

100

120

140

Day

s/Y

ear >

25ο C

Sac Rio Vista

• Dramatic increase in the number of days exceeding 250C under this scenario.

100 Year Water Temperature Projections

Projections (2010 - 2030)

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

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38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2010-2030) vs. Position

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl a2 forcing.

Projections (2040 - 2060)

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2040-2060) vs. Position

2040 - 20602010 - 2030

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl a2 forcing.

Projections (2070 - 2090)

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2070-2090) vs. Position

2070 - 20902010 - 2030

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl a2 forcing.

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

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38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2070-2090) vs. Position

2070 - 20902010 - 2030

Biggest change along Sacramento corridor

Projections (2070 - 2090)

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl a2 forcing.

100 Year Water Temperature Projections

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

5

10

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30T m

ax [ο

C]

Sac Rio Vista

gfdl b1measured

100 Year Water Temperature Projections

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

5

10

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20

25

30T m

ax [ο

C]

Sac Rio Vista

gfdl b1measured

Smelt threshold

100 Year Water Temperature Projections

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090

5

10

15

20

25

30T m

ax [ο

C]

gfdl b1

2000 2010 2020 2030 2040 2050 2060 2070 2080 20900

10

20

30

40

50

60

70

80

90

100

Day

s/Y

ear >

25ο C

Sac Hood

• Significant increase in the number of days exceeding 250C under this scenario.

Projections (2010 - 2030)

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2010-2030) vs. Position

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl b1 forcing.

Projections (2040 - 2060)

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

38

38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2040-2060) vs. Position

2040 - 20602010 - 2030

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl b1 forcing.

Projections (2070 - 2090)

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

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38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2070-2090) vs. Position

2070 - 20902010 - 2030

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl b1 forcing.

Biggest change along Sacramento corridor

Projections (2070 - 2090)

Dot size is proportional to the average number of days per year in exceedence of 250C at each location under gfdl b1 forcing.

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

37.9

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38.1

38.2

38.3

Longitude

Latit

ude

Days Exceedence/Year (2070-2090) vs. Position

2070 - 20902010 - 2030

Conclusions

• Simple statistical model shows high predictive skill of water temperatures at locations throughout the Delta– Model is computationally cheap.– Model requires > 1 year of calibration data.– Model does not include flow term.– Model does not work as well in central Delta due to mixing.

• When forced by climate data from CASCaDE, the model predicts much higher frequency of exceedence of 250C along Sacramento corridor.

Dependence on Air Temperature

-122.2 -122.1 -122 -121.9 -121.8 -121.7 -121.6 -121.5 -121.4 -121.3 -121.2

37.8

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38.1

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38.3

Longitude

Latit

ude

b2 (air temperature coefficient)

1

1.5

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2.5

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x 10-3