Supplemental Methods

1 Tributary detection efficiency

Detection efficiency at the in-stream PIT tag array closest to the mouth of the tributary (the confluence of the tributary with the mainstem Columbia or Snake River) was estimated for each tributary state. However, detection efficiency was not modeled for three tributaries of the Snake River (the Salmon River, the Grande Ronde River, and the Clearwater River), as these tributaries did not have a detection site on the mainstem of the tributary within 100 km of the confluence.

We modeled detection efficiency in tributaries using logistic regression based on two predictors: 1) changes in antenna configurations over time, and 2) the discharge in the tributary. Changes in antenna configurations were identified from the operational history of the site, based on antennas being installed, decommissioned, upgraded, or moved. Changes in antenna configurations are identified in Table S1. Discharge was included as a predictor based on our hypothesis that river stage would influence the antenna coverage of the river channel. Discharge data were queried from USGS by finding the station on the interactive USGS dashboard closest the river mouth array and navigating to the data page for the specific site. Discharge data were available for all tributaries except Fifteenmile Creek and the Imnaha River; detection efficiency in these tributaries was therefore only modeled as a function of antenna configurations.

Table S1: Tributary PIT tag antenna configurations used in detection efficiency estimation. Years refer to the Steelhead run years in which the site was active in a specific configuration. Site refers to the PIT tag detection site chosen for the detection efficiency estimation, based on its proximity to the mouth of the tributary. Configuration refers to the configuration of antennas at the site, where Initial is the name given to the antenna configuration at the site at the start of the time series, and any subsequent changes from the initial configuration at the site are noted in this column.

Tributary Years Site Configuration
Hood River 12/13-21/22 Hood River Mouth (HRM) Initial
Fifteenmile Creek 11/12-18/19 Fifteenmile Ck at Eighmile Ck (158) Initial
Deschutes River 13/14-18/19 Deschutes River Mouth (DRM) Initial
John Day River 12/13-21/22 John Day River, McDonald Ferry (JD1) Initial
Umatilla River 06/07-13/14 Three Mile Falls Dam (TMF) Initial
Umatilla River 14/15-21/22 Three Mile Falls Dam (TMF) Antenna installation at entrance to adult ladder
Walla Walla River 05/06-11/12 Oasis Road Bridge (ORB) Initial
Walla Walla River 12/13-14/15 Oasis Road Bridge (ORB) and Walla Walla R at Pierce RV Pk (PRV) Initial configuration where two mouth sites were operational simultaneously and their joint detection efficiency was estimated
Walla Walla River 15/16-18/19 Walla Walla R at Pierce RV Pk (PRV) Initial
Walla Walla River 19/20-21/22 Walla Walla River Barge Array (WWB) Initial
Yakima River 05/06-21/22 Prosser Diversion Dam (PRO) Initial
Wenatchee River 10/11-21/22 Lower Wenatchee River (LWE) Initial
Entiat River 07/08-21/22 Lower Entiat River (ENL) Initial
Methow River 09/10-16/17 Lower Methow River at Pateros (LMR) Initial
Methow River 17/18-21/22 Lower Methow River at Pateros (LMR) Site was moved 5 km upstream and transceivers replaced
Okanogan River 13/14-21/22 Lower Okanogan Instream Array (OKL) Initial
Tucannon River 10/11-19/20 Lower Tucannon River (LTR) Initial
Tucannon River 20/21-21/22 Lower Tucannon River (LTR) All antennas replaced, additional antenna installed
Asotin Creek 11/12-17/18 Asotin Creek Mouth (ACM) Initial
Asotin Creek 18/19-21/22 Asotin Creek Mouth (ACM) All components replaced and upgraded
Imnaha River 10/11-21/22 Lower Imnaha River ISA @ km 7 (IR1) Initial

For our model of detection efficiency, we denote \(z_i\) as the detection of fish \(i\), \(p_det\) as the probability of detection for fish \(i\), \(\alpha_{j,k}\) as the antenna configuration for tributary \(j\) under configuration \(k\), \(\beta_j\) as the slope for the effect of discharge, and \(x_{j,t}\) as the mean discharge for tributary \(j\) in year \(t\). The model for detection efficiency was as follows:

\[ z_i \sim Bernoulli(p_{det,i}) \\ logit(p_{det,i}) =\alpha_{j,k} + \beta_j x_{j,t} \]

The above model was implemented in Stan (Carpenter et al., 2017), with 3 chains run for 5,000 warmup and 5,000 sampling iterations each. Discharge values were Z-scored prior to the model being fit. The posteriors from this model for each of the \(\alpha\) (site configuration intercepts) and \(\beta\) (effect of discharge) terms were used as priors in the primary Stan model that was used to estimate movement. The resulting detection efficiency correction for each run year can be found in Fig. S1.

2 Covariate data processing

Temperature data

Due to the noise and gaps inherent to the temperature data, a series of steps were performed to clean this data. First, plots of temperature were manually inspected and sequential runs of temperature points that were outside of the range of possible values for that time of year were removed. Next, a filtering algorithm was applied to remove any temperature values that were more than four degrees outside of the interannual average temperature value for that day of the year, as well as any values that were more than two degrees outside of the 7-day moving average. To address the incomplete temporal resolution for temperature at each dam in our modeling framework, a state-space model was fit using the MARSS package (Holmes et al., 2014). The inputs for this model were the cleaned temperature data at the forebay and tailrace for the eight dams (a total of 16 temperature time series). The model was structured with only a single process (the basin-scale temperature) and 16 observations of that process. Each dam had a different offset/bias term (8 total). Model-estimated temperatures on each day for each dam were then exported by using the estimate of the basin-scale temperature plus the dam-specific offset.

To estimate the temperatures experienced by fish, the median residence time in each state in our model was first calculated. To do so, we calculated the difference between the date on which a fish was observed exiting a state and the date on which a fish was observed entering a state, and then computed the state-specific median across all fish. However, for the two furthest upstream states (upstream of Lower Granite Dam and upstream of Wells Dam), residence times were significantly longer and were found to be bimodal. Based on our hypothesis that movement decisions are made soon after a fish enters a state, we fit a two-component mixture model using the mixtools package in R (Benaglia et al., 2010) to residence times in these states and used the median residence time for fish in the first mode. The mean temperature experienced by the fish while in a state was estimated as the mean temperature across a window of time defined as the date a fish was observed entering a state plus the median residence time for all fish in that state.

Spill data

Daily average spill (in thousands of cubic feet per second) was queried from the Columbia Basin Conditions portal from the DART page for the eight dams that were modeled as the boundaries of states (Bonneville, McNary, Priest Rapids, Rock Island, Rocky Reach, Wells, Ice Harbor, and Lower Granite). Spill data were processed in two different ways to facilitate the inclusion of two hypothesized relationships between spill and fish fallback over dams. For en-route fallback, spill volume was processed in the same way as temperature: by taking the mean volume of spill across the residence time window. For post-overshoot fallback, spill volume was converted into days of winter spill, by counting the number of days that had nonzero spill in the months of January, February, and March for each year.

Supplemental Results

1 Sample sizes

The number of fish per run year from each combination of natal tributary and rearing type (natural or hatchery origin).
Population 05/06 06/07 07/08 08/09 09/10 10/11 11/12 12/13 13/14 14/15 15/16 16/17 17/18 18/19 19/20 20/21 21/22 22/23 23/24 Total
Fifteenmile Creek (N) 0 0 0 11 47 89 95 33 32 37 24 10 18 43 39 6 1 0 5 490
Deschutes River (N) 0 0 38 68 117 113 109 81 180 97 49 40 28 39 45 27 0 3 0 1034
John Day River (N) 68 119 114 247 347 279 287 151 261 243 217 88 80 67 113 72 50 68 113 2984
Umatilla River (H) 9 12 59 80 115 77 64 24 13 36 42 29 16 1 1 6 7 36 86 713
Umatilla River (N) 2 10 17 21 14 13 81 65 68 171 278 145 117 62 58 34 53 113 88 1410
Walla Walla River (H) 33 32 25 301 415 222 261 120 111 163 114 112 119 97 58 41 48 111 65 2448
Walla Walla River (N) 11 11 10 8 61 95 115 90 57 75 72 19 27 19 23 15 23 39 27 797
Yakima River (N) 15 12 18 16 33 23 40 18 45 78 93 38 42 46 60 50 44 40 66 777
Wenatchee River (H) 399 400 350 450 818 523 427 380 183 189 173 25 38 27 20 69 3 31 28 4533
Wenatchee River (N) 0 0 2 8 71 73 53 32 31 39 44 9 7 3 15 14 8 7 6 422
Entiat River (N) 0 3 8 7 75 74 55 26 43 66 56 34 8 15 17 12 4 5 5 513
Methow River (H) 1866 3088 478 35 128 58 319 324 292 286 289 108 126 50 31 86 92 113 139 7908
Methow River (N) 0 0 6 13 42 24 33 18 43 44 51 22 13 7 25 17 19 20 17 414
Okanogan River (H) 172 36 8 17 9 9 117 134 100 141 115 56 78 42 18 50 20 39 76 1237
Tucannon River (H) 58 83 549 423 639 259 166 83 121 141 133 76 69 51 35 20 42 100 89 3137
Tucannon River (N) 35 24 40 15 50 44 50 55 45 59 59 9 25 13 22 30 14 27 27 643
Clearwater River (H) 36 34 48 176 95 679 721 650 315 368 317 571 160 255 73 317 169 552 394 5930
Clearwater River (N) 37 29 50 79 138 200 140 111 88 285 177 82 27 23 45 111 24 53 33 1732
Asotin Creek (N) 0 1 12 23 30 27 42 45 79 107 57 28 18 15 17 32 19 37 18 607
Grande Ronde River (H) 19 102 163 149 1135 619 654 414 382 571 549 367 345 225 147 181 146 238 279 6685
Grande Ronde River (N) 35 15 35 37 65 83 86 64 63 62 68 36 19 19 28 24 9 15 13 776
Salmon River (H) 36 20 67 78 1650 1233 1471 949 965 1137 710 427 296 217 184 297 219 229 290 10475
Salmon River (N) 17 21 19 49 158 104 126 70 116 148 90 32 18 21 31 48 27 50 41 1186
Imnaha River (H) 31 36 33 33 734 442 392 161 337 408 407 156 164 103 73 95 121 181 192 4099
Imnaha River (N) 38 14 35 124 151 124 143 70 93 129 162 58 37 24 40 53 42 47 67 1451
Total 2917 4102 2184 2468 7137 5486 6047 4168 4063 5080 4346 2577 1895 1484 1218 1707 1204 2154 2164 62401

2 Covariate correlations

All dams

Correlation between spill and flow across all run years in the dataset, by dam.
Dam Mean Flow Mean Spill R-squared
Bonneville Dam 177.04 46.73 0.61
McNary Dam 168.59 52.07 0.80
Priest Rapids Dam 117.07 20.84 0.72
Rock Island Dam 113.00 12.22 0.60
Rocky Reach Dam 109.27 8.12 0.61
Wells Dam 109.43 8.80 0.65
Ice Harbor Dam 45.87 18.17 0.82
Lower Granite Dam 45.33 12.23 0.71
Correlation between spill and temperature across all run years in the dataset, by dam.
Dam Mean temp Mean Spill R-squared
Bonneville Dam 13.11 46.73 0.08
McNary Dam 12.32 52.07 0.04
Priest Rapids Dam 11.45 20.84 0.03
Rock Island Dam 11.07 12.22 0.04
Rocky Reach Dam 11.06 8.12 0.01
Wells Dam 10.87 8.80 0.01
Ice Harbor Dam 12.42 18.17 0.00
Lower Granite Dam 11.52 12.23 0.02

Bonneville Dam

Correlation between spill and flow for each year, for Bonneville Dam
Run Year Mean Flow Mean Spill R-squared
05/06 180.17 41.81 0.53
06/07 181.43 41.00 0.50
07/08 158.63 42.10 0.63
08/09 176.30 43.57 0.72
09/10 140.96 36.58 0.61
10/11 202.42 51.84 0.63
11/12 226.12 65.71 0.89
12/13 200.28 47.16 0.80
13/14 179.49 43.32 0.62
14/15 179.59 42.42 0.17
15/16 165.34 39.32 0.23
16/17 213.67 71.28 0.74
17/18 211.81 59.17 0.70
18/19 167.99 42.83 0.63
19/20 157.30 43.00 0.46
20/21 169.73 43.06 0.55
21/22 162.99 42.98 0.27
22/23 180.03 51.71 0.86
23/24 137.09 43.82 0.64
Correlation between spill and temperature for each year, for Bonneville Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 12.60 41.81 0.15
06/07 12.70 41.00 0.18
07/08 12.34 42.10 0.16
08/09 12.14 43.57 0.13
09/10 12.80 36.58 0.19
10/11 12.36 51.84 0.05
11/12 12.18 65.71 0.07
12/13 12.81 47.16 0.14
13/14 12.92 43.32 0.12
14/15 13.72 42.42 0.13
15/16 14.02 39.32 0.21
16/17 13.08 71.28 0.00
17/18 13.29 59.17 0.06
18/19 13.24 42.83 0.14
19/20 13.25 43.00 0.14
20/21 13.15 43.06 0.09
21/22 13.18 42.98 0.08
22/23 12.88 51.71 0.05
23/24 13.90 43.82 0.08

McNary Dam

Correlation between spill and flow for each year, for McNary Dam
Run Year Mean Flow Mean Spill R-squared
05/06 171.49 48.98 0.70
06/07 170.81 44.03 0.74
07/08 149.40 37.95 0.81
08/09 164.91 45.81 0.86
09/10 132.37 32.68 0.82
10/11 190.75 65.60 0.87
11/12 215.33 82.03 0.97
12/13 192.16 64.59 0.92
13/14 171.66 51.86 0.86
14/15 174.30 46.22 0.61
15/16 156.69 35.75 0.55
16/17 204.29 74.21 0.85
17/18 204.60 69.46 0.82
18/19 159.08 49.98 0.86
19/20 150.22 49.63 0.78
20/21 162.52 49.52 0.81
21/22 155.80 47.77 0.55
22/23 173.80 65.12 0.91
23/24 129.43 38.14 0.74
Correlation between spill and temperature for each year, for McNary Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 11.81 48.98 0.11
06/07 11.91 44.03 0.14
07/08 11.55 37.95 0.15
08/09 11.35 45.81 0.10
09/10 12.01 32.68 0.18
10/11 11.58 65.60 0.00
11/12 11.39 82.03 0.05
12/13 12.02 64.59 0.14
13/14 12.13 51.86 0.06
14/15 12.93 46.22 0.06
15/16 13.23 35.75 0.13
16/17 12.30 74.21 0.00
17/18 12.50 69.46 0.02
18/19 12.45 49.98 0.06
19/20 12.46 49.63 0.07
20/21 12.36 49.52 0.08
21/22 12.39 47.77 0.02
22/23 12.09 65.12 0.04
23/24 13.11 38.14 0.07

Priest Rapids Dam

Correlation between spill and flow for each year, for Priest Rapids Dam
Run Year Mean Flow Mean Spill R-squared
05/06 114.99 22.65 0.41
06/07 122.40 13.77 0.51
07/08 106.20 8.24 0.58
08/09 106.28 10.91 0.69
09/10 88.09 8.55 0.50
10/11 125.87 22.67 0.68
11/12 147.35 43.37 0.93
12/13 147.75 41.49 0.86
13/14 123.81 21.70 0.78
14/15 126.11 19.42 0.52
15/16 111.21 14.26 0.49
16/17 138.56 35.89 0.85
17/18 138.43 35.61 0.85
18/19 104.91 14.60 0.75
19/20 101.01 13.27 0.58
20/21 117.17 19.19 0.74
21/22 115.20 15.57 0.34
22/23 120.31 30.36 0.89
23/24 84.08 10.31 0.36
Correlation between spill and temperature for each year, for Priest Rapids Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 10.93 22.65 0.15
06/07 11.03 13.77 0.03
07/08 10.67 8.24 0.14
08/09 10.47 10.91 0.09
09/10 11.13 8.55 0.16
10/11 10.70 22.67 0.02
11/12 10.52 43.37 0.04
12/13 11.14 41.49 0.14
13/14 11.26 21.70 0.06
14/15 12.06 19.42 0.00
15/16 12.35 14.26 0.04
16/17 11.42 35.89 0.01
17/18 11.62 35.61 0.01
18/19 11.57 14.60 0.06
19/20 11.59 13.27 0.08
20/21 11.49 19.19 0.08
21/22 11.52 15.57 0.04
22/23 11.21 30.36 0.07
23/24 12.23 10.31 0.09

Rock Island Dam

Correlation between spill and flow for each year, for Rock Island Dam
Run Year Mean Flow Mean Spill R-squared
05/06 110.06 9.17 0.61
06/07 117.21 8.11 0.48
07/08 102.50 8.01 0.59
08/09 103.16 7.92 0.66
09/10 85.63 5.91 0.50
10/11 120.70 11.34 0.60
11/12 139.25 18.61 0.84
12/13 140.42 16.55 0.78
13/14 118.38 15.52 0.49
14/15 121.38 13.09 0.00
15/16 106.98 7.67 0.38
16/17 131.33 20.11 0.80
17/18 131.02 24.07 0.82
18/19 101.78 8.49 0.69
19/20 99.23 9.74 0.54
20/21 113.29 14.76 0.69
21/22 112.32 9.05 0.19
22/23 118.21 20.68 0.82
23/24 86.04 5.97 0.26
Correlation between spill and temperature for each year, for Rock Island Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 10.55 9.17 0.10
06/07 10.66 8.11 0.16
07/08 10.29 8.01 0.26
08/09 10.10 7.92 0.13
09/10 10.75 5.91 0.20
10/11 10.32 11.34 0.03
11/12 10.14 18.61 0.08
12/13 10.77 16.55 0.12
13/14 10.88 15.52 0.00
14/15 11.68 13.09 0.50
15/16 11.98 7.67 0.08
16/17 11.04 20.11 0.00
17/18 11.25 24.07 0.00
18/19 11.19 8.49 0.11
19/20 11.21 9.74 0.05
20/21 11.11 14.76 0.09
21/22 11.14 9.05 0.16
22/23 10.83 20.68 0.05
23/24 11.86 5.97 0.12

Rocky Reach Dam

Correlation between spill and flow for each year, for Rocky Reach Dam
Run Year Mean Flow Mean Spill R-squared
05/06 108.94 5.45 0.50
06/07 114.19 5.14 0.48
07/08 100.63 3.82 0.55
08/09 100.67 4.99 0.62
09/10 83.22 2.01 0.23
10/11 116.85 7.73 0.56
11/12 136.80 18.67 0.81
12/13 136.59 18.44 0.73
13/14 114.24 6.61 0.63
14/15 114.86 5.14 0.50
15/16 100.19 3.48 0.41
16/17 128.59 19.61 0.85
17/18 126.77 18.67 0.78
18/19 96.54 5.45 0.62
19/20 93.93 6.19 0.65
20/21 107.89 10.09 0.63
21/22 106.24 3.11 0.11
22/23 114.82 11.20 0.71
23/24 84.06 1.58 0.12
Correlation between spill and temperature for each year, for Rocky Reach Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 10.54 5.45 0.04
06/07 10.64 5.14 0.04
07/08 10.28 3.82 0.12
08/09 10.09 4.99 0.10
09/10 10.74 2.01 0.24
10/11 10.31 7.73 0.02
11/12 10.13 18.67 0.03
12/13 10.75 18.44 0.09
13/14 10.87 6.61 0.10
14/15 11.67 5.14 0.04
15/16 11.96 3.48 0.03
16/17 11.03 19.61 0.03
17/18 11.23 18.67 0.00
18/19 11.18 5.45 0.04
19/20 11.20 6.19 0.00
20/21 11.10 10.09 0.08
21/22 11.13 3.11 0.22
22/23 10.82 11.20 0.03
23/24 11.85 1.58 0.15

Wells Dam

Correlation between spill and flow for each year, for Wells Dam
Run Year Mean Flow Mean Spill R-squared
05/06 109.27 6.93 0.55
06/07 113.57 9.49 0.62
07/08 101.25 4.60 0.56
08/09 101.33 6.90 0.67
09/10 83.73 2.86 0.52
10/11 116.28 8.77 0.59
11/12 135.89 21.32 0.82
12/13 136.07 17.36 0.75
13/14 114.37 7.12 0.70
14/15 116.89 4.86 0.43
15/16 101.79 4.63 0.60
16/17 127.72 12.14 0.76
17/18 125.75 17.40 0.79
18/19 97.89 6.87 0.66
19/20 95.25 5.36 0.56
20/21 109.59 10.14 0.69
21/22 105.17 6.65 0.32
22/23 114.67 14.26 0.80
23/24 82.86 2.68 0.23
Correlation between spill and temperature for each year, for Wells Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 10.36 6.93 0.01
06/07 10.46 9.49 0.02
07/08 10.10 4.60 0.05
08/09 9.90 6.90 0.06
09/10 10.56 2.86 0.18
10/11 10.13 8.77 0.00
11/12 9.94 21.32 0.03
12/13 10.57 17.36 0.09
13/14 10.68 7.12 0.02
14/15 11.49 4.86 0.04
15/16 11.78 4.63 0.02
16/17 10.85 12.14 0.01
17/18 11.05 17.40 0.00
18/19 11.00 6.87 0.07
19/20 11.01 5.36 0.02
20/21 10.91 10.14 0.07
21/22 10.94 6.65 0.02
22/23 10.64 14.26 0.03
23/24 11.66 2.68 0.04

Ice Harbor Dam

Correlation between spill and flow for each year, for Ice Harbor Dam
Run Year Mean Flow Mean Spill R-squared
05/06 50.14 16.50 0.76
06/07 40.76 13.98 0.65
07/08 36.80 13.54 0.83
08/09 52.24 20.56 0.83
09/10 38.52 14.49 0.76
10/11 59.71 22.48 0.82
11/12 65.12 27.35 0.89
12/13 40.98 16.08 0.77
13/14 42.29 15.22 0.69
14/15 41.15 13.89 0.50
15/16 39.07 12.97 0.68
16/17 59.80 29.43 0.95
17/18 60.97 27.93 0.84
18/19 48.72 23.44 0.93
19/20 42.16 16.00 0.93
20/21 40.35 14.71 0.88
21/22 33.88 12.65 0.84
22/23 46.97 21.91 0.93
23/24 40.87 16.60 0.86
Correlation between spill and temperature for each year, for Ice Harbor Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 11.90 16.50 0.01
06/07 12.00 13.98 0.06
07/08 11.64 13.54 0.01
08/09 11.44 20.56 0.04
09/10 12.10 14.49 0.12
10/11 11.67 22.48 0.00
11/12 11.49 27.35 0.03
12/13 12.11 16.08 0.04
13/14 12.23 15.22 0.00
14/15 13.03 13.89 0.06
15/16 13.32 12.97 0.01
16/17 12.39 29.43 0.06
17/18 12.59 27.93 0.00
18/19 12.54 23.44 0.00
19/20 12.56 16.00 0.00
20/21 12.46 14.71 0.01
21/22 12.49 12.65 0.00
22/23 12.18 21.91 0.00
23/24 13.20 16.60 0.00

Lower Granite Dam

Correlation between spill and flow for each year, for Lower Granite Dam
Run Year Mean Flow Mean Spill R-squared
05/06 49.31 12.10 0.73
06/07 40.13 8.91 0.59
07/08 36.57 9.87 0.85
08/09 51.32 12.31 0.81
09/10 38.75 8.67 0.70
10/11 58.88 14.32 0.79
11/12 64.01 15.30 0.82
12/13 40.20 9.08 0.66
13/14 41.63 8.78 0.55
14/15 40.86 7.98 0.39
15/16 39.24 6.92 0.49
16/17 58.95 19.21 0.87
17/18 59.50 14.83 0.71
18/19 47.94 12.87 0.81
19/20 41.78 13.87 0.80
20/21 39.78 13.45 0.82
21/22 33.49 10.96 0.77
22/23 46.82 16.43 0.86
23/24 40.60 17.13 0.85
Correlation between spill and temperature for each year, for Lower Granite Dam
Run Year Mean Temperature Mean Spill R-squared
05/06 11.01 12.10 0.02
06/07 11.11 8.91 0.12
07/08 10.75 9.87 0.03
08/09 10.55 12.31 0.06
09/10 11.21 8.67 0.14
10/11 10.78 14.32 0.01
11/12 10.59 15.30 0.05
12/13 11.22 9.08 0.08
13/14 11.33 8.78 0.05
14/15 12.13 7.98 0.11
15/16 12.43 6.92 0.09
16/17 11.50 19.21 0.03
17/18 11.70 14.83 0.03
18/19 11.65 12.87 0.01
19/20 11.66 13.87 0.02
20/21 11.56 13.45 0.02
21/22 11.59 10.96 0.00
22/23 11.29 16.43 0.00
23/24 12.31 17.13 0.00

3 Post-overshoot fallback timing

These figures show the timing of observations of overshoot (first point) and first observation following post-overshoot fallback (second point) for each fish from a given population. Red points indicate terminal overshoot observations (where fish were not seen again below an overshoot dam following overshoot). Lines connecting overshoot observations with post-overshoot fallback observations indicate that time period in which a fallback event must have occurred. Dashed green lines indicate the winter months (January, February, and March) that were used to characterize the likely spill conditions encountered by fish in overshoot states. In our model, any fish that was last observed overshooting (red dots) or where based on their detection history, may have fallen back during January, February, or March (any black lines that are at least partially between the two dashed green lines) are affected by the winter spill days covariate.

Deschutes (N)

John Day (N)

Fifteenmile (N)

Umatilla (N)

Umatilla (H)

Yakima (N)

Walla Walla (N)

Walla Walla (H)

Entiat (N)

Wenatchee (N)

Wenatchee (H)

Tucannon (N)

Tucannon (H)

4 Detection efficiency estimation

Fifteenmile Creek

Fifteenmile Creek, estimated detection efficiency.
Fifteenmile Creek, estimated detection efficiency.

Deschutes River

Deschutes River, estimated detection efficiency.
Deschutes River, estimated detection efficiency.

John Day River

John Day River, estimated detection efficiency.
John Day River, estimated detection efficiency.

Umatilla River

Umatilla River, estimated detection efficiency in time period 1.
Umatilla River, estimated detection efficiency in time period 1.
Umatilla River, estimated detection efficiency in time period 2.
Umatilla River, estimated detection efficiency in time period 2.

Walla Walla River

Walla Walla River, estimated detection efficiency in time period 1.
Walla Walla River, estimated detection efficiency in time period 1.
Walla Walla River, estimated detection efficiency in time period 2.
Walla Walla River, estimated detection efficiency in time period 2.
Walla Walla River, estimated detection efficiency in time period 3.
Walla Walla River, estimated detection efficiency in time period 3.
Walla Walla River, estimated detection efficiency in time period 4.
Walla Walla River, estimated detection efficiency in time period 4.

Yakima River

Yakima River, estimated detection efficiency.
Yakima River, estimated detection efficiency.

Wenatchee River

Wenatchee River, estimated detection efficiency.
Wenatchee River, estimated detection efficiency.

Entiat River

Entiat River, estimated detection efficiency.
Entiat River, estimated detection efficiency.

Methow River

Methow River, estimated detection efficiency in time period 1.
Methow River, estimated detection efficiency in time period 1.
Methow River, estimated detection efficiency in time period 2.
Methow River, estimated detection efficiency in time period 2.

Okanogan River

Okanogan River, estimated detection efficiency.
Okanogan River, estimated detection efficiency.

Tucannon River

Tucannon River, estimated detection efficiency in time period 1.
Tucannon River, estimated detection efficiency in time period 1.
Tucannon River, estimated detection efficiency in time period 2.
Tucannon River, estimated detection efficiency in time period 2.

Asotin Creek

Asotin Creek, estimated detection efficiency in time period 1.
Asotin Creek, estimated detection efficiency in time period 1.
Asotin Creek, estimated detection efficiency in time period 2.
Asotin Creek, estimated detection efficiency in time period 2.

Imnaha River

Imnaha River, estimated detection efficiency.
Imnaha River, estimated detection efficiency.

5 Model diagnostic figures

The R-hat convergence diagnostic for each of the six models run. The R-hat convergence diagnostic compares the between- and within-chain estimates for model parameters and other univariate quantities of interest. If chains have not mixed well (i.e., the between- and within-chain estimates don’t agree), R-hat is larger than 1. We recommend running at least four chains by default and only using the sample if R-hat is less than 1.05. Stan reports R-hat which is the maximum of rank normalized split-R-hat and rank normalized folded-split-R-hat, which works for thick tailed distributions and is sensitive also to differences in scale.
The R-hat convergence diagnostic for each of the six models run. The R-hat convergence diagnostic compares the between- and within-chain estimates for model parameters and other univariate quantities of interest. If chains have not mixed well (i.e., the between- and within-chain estimates don’t agree), R-hat is larger than 1. We recommend running at least four chains by default and only using the sample if R-hat is less than 1.05. Stan reports R-hat which is the maximum of rank normalized split-R-hat and rank normalized folded-split-R-hat, which works for thick tailed distributions and is sensitive also to differences in scale.


Bulk Effective Sample Size (bulk-ESS) using rank normalized draws, for each of the six models run. Bulk-ESS is useful measure for sampling efficiency in the bulk of the distribution (related to efficiency of mean and median estimates), and is well defined even if the chains do not have finite mean or variance. Both bulk-ESS and tail-ESS should be at least 100 (approximately) per Markov Chain in order to be reliable and indicate that estimates of respective posterior quantiles are reliable.
Bulk Effective Sample Size (bulk-ESS) using rank normalized draws, for each of the six models run. Bulk-ESS is useful measure for sampling efficiency in the bulk of the distribution (related to efficiency of mean and median estimates), and is well defined even if the chains do not have finite mean or variance. Both bulk-ESS and tail-ESS should be at least 100 (approximately) per Markov Chain in order to be reliable and indicate that estimates of respective posterior quantiles are reliable.


Tail Effective Sample Size (tail-ESS) using rank normalized draws, for each of the six models run. Tail-ESS is produces by computing the minimum of effective sample sizes for 5% and 95% quantiles. Tail-ESS is useful measure for sampling efficiency in the tails of the distribution (related to efficiency of variance and tail quantile estimates). Both bulk-ESS and tail-ESS should be at least 100 (approximately) per Markov Chain in order to be reliable and indicate that estimates of respective posterior quantiles are reliable.
Tail Effective Sample Size (tail-ESS) using rank normalized draws, for each of the six models run. Tail-ESS is produces by computing the minimum of effective sample sizes for 5% and 95% quantiles. Tail-ESS is useful measure for sampling efficiency in the tails of the distribution (related to efficiency of variance and tail quantile estimates). Both bulk-ESS and tail-ESS should be at least 100 (approximately) per Markov Chain in order to be reliable and indicate that estimates of respective posterior quantiles are reliable.

6 Final fates, under median conditions

Fifteenmile Creek

Fifteenmile Creek, estimated final fates under median conditions from 2005-2024.
Fifteenmile Creek, estimated final fates under median conditions from 2005-2024.

Deschutes River

Deschutes River, estimated final fates under median conditions from 2005-2024.
Deschutes River, estimated final fates under median conditions from 2005-2024.

John Day River

John Day River, estimated final fates under median conditions from 2005-2024.
John Day River, estimated final fates under median conditions from 2005-2024.

Umatilla River

Umatilla River, estimated final fates under median conditions from 2005-2024.
Umatilla River, estimated final fates under median conditions from 2005-2024.

Walla Walla River

Walla Walla River, estimated final fates under median conditions from 2005-2024.
Walla Walla River, estimated final fates under median conditions from 2005-2024.

Yakima River

Yakima River, estimated final fates under median conditions from 2005-2024.
Yakima River, estimated final fates under median conditions from 2005-2024.

Wenatchee River

Wenatchee River, estimated final fates under median conditions from 2005-2024.
Wenatchee River, estimated final fates under median conditions from 2005-2024.

Entiat River

Entiat River, estimated final fates under median conditions from 2005-2024.
Entiat River, estimated final fates under median conditions from 2005-2024.

Methow River

Methow River, estimated final fates under median conditions from 2005-2024.
Methow River, estimated final fates under median conditions from 2005-2024.

Okanogan River

Okanogan River, estimated final fates under median conditions from 2005-2024.
Okanogan River, estimated final fates under median conditions from 2005-2024.

Tucannon River

Tucannon River, estimated final fates under median conditions from 2005-2024.
Tucannon River, estimated final fates under median conditions from 2005-2024.

Clearwater River

NOTE: Detection efficiency could not be estimated for the Clearwater River, because of the lack of a site close to the confluence with the Snake River. Therefore, the estimate of final fate in the Clearwater River is biased low, while the estimate of final fate in the mainstem state that connects to the Clearwater river (mainstem, upstream of LGR) is biased high.


Clearwater River, estimated final fates under median conditions from 2005-2024.
Clearwater River, estimated final fates under median conditions from 2005-2024.

Asotin Creek

Asotin Creek, estimated final fates under median conditions from 2005-2024.
Asotin Creek, estimated final fates under median conditions from 2005-2024.

Grande Ronde River

NOTE: Detection efficiency could not be estimated for the Clearwater River, because of the lack of a site close to the confluence with the Snake River. Therefore, the estimate of final fate in the Clearwater River is biased low, while the estimate of final fate in the mainstem state that connects to the Clearwater river (mainstem, upstream of LGR) is biased high.


Grande Ronde River, estimated final fates under median conditions from 2005-2024.
Grande Ronde River, estimated final fates under median conditions from 2005-2024.

Salmon River

NOTE: Detection efficiency could not be estimated for the Clearwater River, because of the lack of a site close to the confluence with the Snake River. Therefore, the estimate of final fate in the Clearwater River is biased low, while the estimate of final fate in the mainstem state that connects to the Clearwater river (mainstem, upstream of LGR) is biased high.


Salmon River, estimated final fates under median conditions from 2005-2024.
Salmon River, estimated final fates under median conditions from 2005-2024.

Imnaha River

Imnaha River, estimated final fates under median conditions from 2005-2024.
Imnaha River, estimated final fates under median conditions from 2005-2024.

7 Deschutes River movement

Probability of movement into the Deschutes River by temperature, conditional on being in the reach of the mainstem Columbia between Bonneville and McNary Dam. Histograms on the plot margins indicate the temperature experiences of individual fish. Because this movement occurs within the Middle Columbia DPS, those populations have separate probabilities of movement, and are shown in panels A-F, while fish from the Upper Columbia DPS and the Snake River DPS have shared movement probabilities for this movement and are shown in panels G and H.
Probability of movement into the Deschutes River by temperature, conditional on being in the reach of the mainstem Columbia between Bonneville and McNary Dam. Histograms on the plot margins indicate the temperature experiences of individual fish. Because this movement occurs within the Middle Columbia DPS, those populations have separate probabilities of movement, and are shown in panels A-F, while fish from the Upper Columbia DPS and the Snake River DPS have shared movement probabilities for this movement and are shown in panels G and H.

8 En-route fallback as a function of spill volume

Bonneville Dam

Probability of fallback at Bonneville Dam, by volume of spill. Because this movement occurs within the Middle Columbia DPS, those populations have separate probabilities of movement, and are shown in panels A-H, while fish from the Upper Columbia DPS and the Snake River DPS have shared movement probabilities for this movement and are shown in panels I-L. Histograms on the plot margins indicate the spill experiences of individual fish.
Probability of fallback at Bonneville Dam, by volume of spill. Because this movement occurs within the Middle Columbia DPS, those populations have separate probabilities of movement, and are shown in panels A-H, while fish from the Upper Columbia DPS and the Snake River DPS have shared movement probabilities for this movement and are shown in panels I-L. Histograms on the plot margins indicate the spill experiences of individual fish.

McNary Dam

Probability of fallback at McNary Dam, by volume of spill. Because this movement at the juncture between the Middle Columbia, Upper Columbia, and Snake River DPS boundaries, every population has a unique probability of movement. All populations that are downstream of McNary Dam (the Fifteenmile Creek, Deschutes River, John Day River, and Umatilla River) are affected by winter spill days rather than spill volume for this movement, as it is a post-overshoot fallback movement. Histograms on the plot margins indicate the spill experiences of individual fish.
Probability of fallback at McNary Dam, by volume of spill. Because this movement at the juncture between the Middle Columbia, Upper Columbia, and Snake River DPS boundaries, every population has a unique probability of movement. All populations that are downstream of McNary Dam (the Fifteenmile Creek, Deschutes River, John Day River, and Umatilla River) are affected by winter spill days rather than spill volume for this movement, as it is a post-overshoot fallback movement. Histograms on the plot margins indicate the spill experiences of individual fish.

Ice Harbor Dam

Probability of fallback at Ice Harbor Dam, by volume of spill. Only Snake River populations are shown because an ascent of Ice Harbor Dam by any populations from the Middle or Upper Columbia would be overshoot and therefore the probability of fallback is affected by winter spill days rather than spill volume. Histograms on the plot margins indicate the spill experiences of individual fish.
Probability of fallback at Ice Harbor Dam, by volume of spill. Only Snake River populations are shown because an ascent of Ice Harbor Dam by any populations from the Middle or Upper Columbia would be overshoot and therefore the probability of fallback is affected by winter spill days rather than spill volume. Histograms on the plot margins indicate the spill experiences of individual fish.

Lower Granite Dam

Probability of fallback at Lower Granite Dam, by volume of spill. Only Snake River populations are shown because an ascent of Lower Granite Dam by any populations from the Middle or Upper Columbia would be overshoot and therefore the probability of fallback is affected by winter spill days rather than spill volume. The Tucannon River is also not shown because Lower Granite Dam is an overshoot for that population. Histograms on the plot margins indicate the spill experiences of individual fish.
Probability of fallback at Lower Granite Dam, by volume of spill. Only Snake River populations are shown because an ascent of Lower Granite Dam by any populations from the Middle or Upper Columbia would be overshoot and therefore the probability of fallback is affected by winter spill days rather than spill volume. The Tucannon River is also not shown because Lower Granite Dam is an overshoot for that population. Histograms on the plot margins indicate the spill experiences of individual fish.

9 Post-overshoot fallback as a function of March spill

This section presents the results of the same model, but run where only days of spill in March are used as a covariate instead of days of spill in January, February, and March (as is used in the base model).

The effect of March spill days on movement probabilities out of the mainstem state directly upstream of the mainstem state that connects to the natal tributary for (A) John Day River natural origin Steelhead, (B) Umatilla River natural origin Steelhead, (C) Umatilla River hatchery origin Steelhead, (D) Yakima River natural origin Steelhead, (E) Walla Walla River natural origin Steelhead, (F) Walla Walla River hatchery origin Steelhead, (G) Wenatchee River natural origin Steelhead, (H) Wenatchee River hatchery origin Steelhead, (I) Entiat River natural origin Steelhead, (J) Tucannon River natural origin Steelhead, and (K) Tucannon River hatchery origin Steelhead. Histograms on the plot margins indicate the temperature experiences of individual fish.
The effect of March spill days on movement probabilities out of the mainstem state directly upstream of the mainstem state that connects to the natal tributary for (A) John Day River natural origin Steelhead, (B) Umatilla River natural origin Steelhead, (C) Umatilla River hatchery origin Steelhead, (D) Yakima River natural origin Steelhead, (E) Walla Walla River natural origin Steelhead, (F) Walla Walla River hatchery origin Steelhead, (G) Wenatchee River natural origin Steelhead, (H) Wenatchee River hatchery origin Steelhead, (I) Entiat River natural origin Steelhead, (J) Tucannon River natural origin Steelhead, and (K) Tucannon River hatchery origin Steelhead. Histograms on the plot margins indicate the temperature experiences of individual fish.


The homing probability for (A) John Day River, (B) Umatilla River, (C) Walla Walla River, (D) Wenatchee River, (E) Tucannon River, (F) Entiat River, and (G) Yakima River Steelhead under different scenarios for basin-wide temperature and March spill days (0, 10, 20, or 30 days) at the overshoot dam. The temperature scenarios are specific run years from the dataset, with the coldest year being the 2011/2012 run year, the average year being the 2005/2006 run year, and the warmest year being the 2015/2016 run year.
The homing probability for (A) John Day River, (B) Umatilla River, (C) Walla Walla River, (D) Wenatchee River, (E) Tucannon River, (F) Entiat River, and (G) Yakima River Steelhead under different scenarios for basin-wide temperature and March spill days (0, 10, 20, or 30 days) at the overshoot dam. The temperature scenarios are specific run years from the dataset, with the coldest year being the 2011/2012 run year, the average year being the 2005/2006 run year, and the warmest year being the 2015/2016 run year.