Survival Analyses in Support of NOAA’s Draft Biological ...€¦ · NOAA’s Draft Biological...
Transcript of Survival Analyses in Support of NOAA’s Draft Biological ...€¦ · NOAA’s Draft Biological...
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Survival Analyses in Support of NOAA’s Draft Biological Opinion on
California WaterFix
Russell W. Perry, USGS, Western Fisheries Research CenterA. C. Pope, J. G. Romine, A. Blake, and J. Burau, USGS
P, Brandes, USFWS, A. Ammann and C. Michel, NMFS
23 January 2017U.S. Department of the InteriorU.S. Geological Survey
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Overview• New Bayesian Mark-Recapture Model
– Overview of methods and results– Forms basis for BiOp Analyses
• Using these models for Cal WaterFix– Simulating survival under NAA and PA– Evaluating NDD Bypass Rules– Shaping operations with survival criteria
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Acoustic Telemetry Datafor Analysis
• Data from 2 Acoustic Telemetry Studies– NOAA (CALFED) and USFWS (Delta Action 8)– Late-fall Chinook salmon– Vemco acoustic telemetry– 2,170 Acoustic tagged fish– 5 Years (2007 – 2011)– 17 unique release groups– Migrated between late Nov. and early March– Sacramento River Flows at Freeport
• ~6,000 – 77,000 ft3/s
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12 miles
12 km
Survival Reaches
1
23
45 67
8
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MultistateModel
Schematic3 types of parameters:p = Detection probabilityΨ = Routing probabilityS = Survival probability
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Estimation Framework• Time-varying individual covariates
– Covariate values based on date of reach entry
• Date of entry unknown for undetected fish– Need to integrate likelihood over missing data– Requires a model for missing data
• Model for reach-specific travel times– Estimate parameters from observed travel times– Impute missing travel times
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Strength of Bayesian Framework• Time-varying individual covariates
– Previous approaches used average values
• Single integrated model– Survival and travel time
• MCMC to integrate over missing data
• Random effects– Quantify “extra” variation among release groups
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Model for Travel Times• Assume travel times (ti, j) distributed lognormally
µj = mean of log(ti,j)σj = standard deviation of log(ti,j)exp(µj) = median travel time
• Goal is to estimate µ and σ for each reach
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Effect of Discharge on Travel Times• Relate median travel times to Delta inflows at
Freeport
αj = reach-specific slope parameters
Qi,j,d = Freeport discharge on day d when ith fish entered jth reach
I(DCCi,j,d = open) = binary indicator for reaches downstream of DCC
εg,j = deviation of gth release group, ~Normal(0, ξ)
( ), 0, 1, , , 2, , , , jDCC = openi j j j i j d j i j d gQ Iµ α α α ε= + + +
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Effect of Discharge on Survival• Relate survival to Delta inflows at Freeport
βj = reach-specific slope parameters
Qi,j,d = Freeport discharge on day d when ith fish entered jth reach
I(DCCi,j,d = open) = binary indicator for reaches downstream of DCC
εg,j = deviation of gth release group, ~Normal(0, ξ)
( ) ( ), 0, 1, , , 2, , , ,logit DCC = openi j j j i j d j i j d g jS Q Iβ β β ε= + + +
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R
R
R
R
R
R
R
R
-2 0 1 2
1Flow-0.6 -0.2 0.2
2DCC
Parameter Estimates:Travel Time
• Negative slopes for all reaches
• Except DCC (Reach 6)
• Travel time decreases with inflow in all reaches
• DCC effects less certain• Except Rio Vista – Chipps
(Reach 7)
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Parameter Estimates:Survival
-2 0 2 4
Reach 8
Reach 7
Reach 6
Reach 5
Reach 4
Reach 3
Reach 2
Reach 1
1Flow-1.5 -0.5 0.5
2DCC 12 miles
12 km
1
23
4
5 67
8
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Flow-Survival Relations
12 miles
12 km
1
2
0.0
0.4
0.8
10 30 50 70
0.0
0.4
0.8
10 30 50 70
Surv
ival
pro
babi
lity
Reach 1
Reach 2
Discharge (ft3/s x 1000)
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0.0
0.4
0.8
10 30 50 70
0.0
0.4
0.8
10 30 50 70
4
12 miles
12 km
3
5
Surv
ival
pro
babi
lity
Reach 3
Reach 4 Reach 50.0
0.4
0.8
10 30 50 70
Flow-Survival Relations
Reach 5
Discharge (ft3/s x 1000)
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0.0
0.4
0.8
10 30 50 70
Parameter Estimates:Survival
12 miles
12 km
7
8Surv
ival
pro
babi
lity
0.0
0.4
0.8
10 30 50 70
Reach 7
Reach 8
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Route-Specific Survival
Sacramento River Discharge at Freeport (ft3/s x 1000)
0.0
0.2
0.4
0.6
0.8
1.0
10 20 30 40 50 60 70 80
Surv
ival
pro
babi
lity
0.0
0.2
0.4
0.6
0.8
1.0
10 20 30 40 50 60 70 800.
00.
20.
40.
60.
81.
0
10 20 30 40 50 60 70 80
0.0
0.2
0.4
0.6
0.8
1.0
10 20 30 40 50 60 70 80
Sacramento R.
Georgiana Slough
Sutter and Steamboat S
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0 10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
70,000 cfs
Travel time (d)
Pro
babi
lity
dens
ity
Sacramento R. (2.1 d)Sutter and Steamboat S. (2.5 d)Georgiana S. (4.5 d)Delta Cross Channel (NA)
Route-Specific Travel Times
0 10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
25,000 cfs
Travel time (d)
Pro
babi
lity
dens
ity
Sacramento R. (6.6 d)Sutter and Steamboat S. (7.3 d)Georgiana S. (11.6 d)Delta Cross Channel (14.4 d)
0 10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
5,000 cfs
Travel time (d)
Pro
babi
lity
dens
ity
Sacramento R. (11.3 d)Sutter and Steamboat S. (11.9 d)Georgiana S. (17.9 d)Delta Cross Channel (19.7 d)
Travel time (d)
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Summary
• Inflows affect travel times in all reaches
• Inflows affect survival in some reaches– Upper reaches: high survival at all flows– Transition reaches: strongest flow-survival
relations– Tidal reaches
• no evidence of flow effect• imposes upper limit on route-specific survival
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Simulating Survival, Travel Time, and Routing for NAA and PA
1. “Release” 10,000 fish at Freeport each day.2. Reach 1 survival same for all fish.3. Draw reach 1 travel times as f(flow)
– NAA: flow = Freeport discharge– PA: flow = Bypass discharge
4. At junction of Sutter/Steamboat and Sac, draw route as f(flow).
5. Reach-specific survival f(flow) at arrival time.6. Repeat for all subsequent reaches.
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5000
1000
020
000
5000
0
DCC Closed
DCC OpenByp
assd
isch
arge
ft3
s
NAAPA
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Mea
n su
rviv
al th
roug
h D
elta
-0.2
-0.1
0.0
0.1
0.2
Oct Nov Dec Jan Feb Mar Apr May Jun Jul
Diff
eren
ce in
sur
viva
l (P
A -
NA
A)
1943 (WY type = W)
Outputs for Each Year: SurvivalNRDC-18
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Outputs for Each Year: Travel Time
5000
1000
020
000
5000
0
DCC Closed
DCC OpenByp
assd
isch
arge
ft3
s
NAAPA
24
68
1012
14
Med
ian
trave
l tim
e th
roug
h D
elta
(d)
-4-2
02
4
Oct Nov Dec Jan Feb Mar Apr May Jun Jul
Diff
eren
ce in
trav
el ti
me
(PA
- N
AA
)
1943 (WY type = W)
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Outputs for Each Year: Routing
5000
1000
020
000
5000
0DCC Closed
DCC OpenB
ypas
sd
isch
arge
ft3s
NAAPA
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Cum
ulat
ive
fract
ion
usin
g ea
ch ro
ute
(PA
)
DCCGeorgiana S.Sutter & Steamboat S.Sacramento R.
Oct 01 Nov 01 Dec 01 Jan 01 Feb 01 Mar 01 Apr 01 May 01 Jun 01
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Cum
ulat
ive
fract
ion
usin
g ea
ch ro
ute
(NA
A)
1943 (WY type = W)
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Summarizing Survival Differences
-0.2
0-0
.10
0.00
0.05
Diff
eren
ce in
sur
viva
l (P
A -
-0.2
0-0
.15
-0.1
0-0
.05
0.00
0.05
Diff
eren
ce in
sur
viva
l (L1
- N
AA
)-0
.10
-0.0
50.
000.
050.
10
Oct Nov Dec Jan Feb Mar Apr May Jun Jul
Diff
eren
ce in
sur
viva
l (L1
- P
A)
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Evaluating NDD Bypass Rules
• Apply rule sets under “equilibrium” conditions– Assume constant inflows and operations for
cohort
• Calculate survival with and without diversion
• Evaluate survival differences for each rule set
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Oct.-Nov. Bypass Rules
Dis
char
ge f
t3s
1000
Bypass flowDiversion flow
010
2030
4050
600.
10.
20.
30.
40.
50.
60.
7
SD
elta w
ith D
CC
clo
sed
7
0.00
0.05
0.10
0.15
Diff
eren
ce in
sur
vi
Oct. - Nov. Bypass Rules
5 15 25 35 45 55
5 15 25 35 45 55
Sacramento River discharge at Freeport ft3 s 1000
0.00
0.05
0.10
0.15
0.20
10 20 30 40 50 60
Without diversionWith diversion
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Constant Low-Level Pumping
5 15 25 35 45 55
5 15 25 35 45 55
Sacramento River discharge at Freeport ft3 s 1000
Dis
char
ge f
t3s
1000
Bypass flowDiversion flow
010
2030
4050
600.
10.
20.
30.
40.
50.
60.
7
SD
elta w
ith D
CC
clo
sed
0.00
0.05
0.10
0.15
Diff
eren
ce in
sur
vi
Constant Low-Level Pumping (Dec-Jun)
0.00
0.05
0.10
0.15
0.20
10 20 30 40 50 60
Without diversionWith diversion
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Level 1 Post-Pulse Operations
5 15 25 35 45 55
5 15 25 35 45 55
Sacramento River discharge at Freeport ft3 s 1000
Dis
char
ge f
t3s
1000
Bypass flowDiversion flow
010
2030
4050
600.
10.
20.
30.
40.
50.
60.
7
SD
elta w
ith D
CC
clo
sed
0.00
0.05
0.10
0.15
Diff
eren
ce in
sur
vi
Level 1 Post-Pulse Operations (Dec-Apr)
0.00
0.05
0.10
0.15
0.20
10 20 30 40 50 60
Without diversionWith diversion
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Summary: NDD Bypass Rules• Some large survival differences
– Depends on • Bypass flows• Rule set
• In CalSim simulations– Highlights why larger differences in Oct., Nov.,
Jun.
• How else might operations be structured?
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Determining Operations based on Maximum Allowable “Take”
• Example criteria– No more than a 0.03 decrease in mean survival– 90% probability that survival is decreased by no
more than 0.03
• Use survival model to identify diversions that satisfy criteria– Find by optimization routine
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Diversions Based on Median Survival
0 20000 40000 60000 80000
020
0040
0060
0080
0010
000
Direct NDD mortality = 0
DischargeatFreeportft3 s
North
Del
taD
ivers
ionf
t3s
Median survival reduction0.0050.010.020.030.040.05
DCC closedDCC open
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Diversions Based on Full Posterior Distributionfor 0.03 survival reduction
Median
90% probabilityof <0.03 difference
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Survival Difference Based on10th percentile of NDD flowsfor 0.03 survival reduction
Median
90th Percentile
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Summary• Survival model can help identify operations
that meet specific survival criteria• Variability in survival can explicitly play a
role in setting criteria• New set of operations can be assessed with
other models– CVLCM, DPM, etc.– More robust inferences
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Acknowledgments
Delta Stewardship CouncilNOAADWRUC Davis
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Important Assumptions• Extending inferences:
– Late Fall Chinook = Winter Run?– Nov. – Mar. = Apr. – Jun.?– Hatchery = Naturally produced?– Current system state = future system state?– Predicting outside range of observed data?
• Relative vs. Absolute comparisons– Relative more robust
• NAA vs. PA• Shape of driving relationships similar
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Diversions Based on Median Survival
0 20000 40000 60000 80000
020
0040
0060
0080
0010
000
Direct NDD mortality = 0.03
DischargeatFreeportft3 s
North
Del
taD
ivers
ionf
t3s
Median survival reduction0.0050.010.020.030.040.05
DCC closedDCC open
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0 20000 40000 60000 800000.
00.
10.
20.
30.
40.
5
DischargeatFreeportft3 s
Ent
rain
men
t pro
babi
lity
Georgiana Slough, DCC closedGeorgiana Slough, DCC openDCC
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