CRiSP1.6 Theory & Calibration Manual: II.4 - Reservoir Survival INDEXTOCPREVNEXT

II.4 - Reservoir Survival

The main component of fish mortality in the reservoirs is the predation rate. The predation rate is dependent on factors such as the number and behavior of predators, size of prey, genetic disposition of prey, disease, stress from dam passage, and degree of smoltification. The theory presented below approximates the mortality processes in the reservoirs. The CRiSP.1 model incorporates some of the details of the interactions of the various factors in mortality in further modeling the predation rate. The included factors are pictured in (Fig. 28). In the model, we further partition the reservoir into forebay, tailrace and reach (also called reservoir) segments for the purpose of travel time and mortality modeling.

Fig. 28 Elements in reservoir mortality algorithm



II.4.1 - Theoretical Framework

The theoretical framework for describing reservoir mortality in the current model uses the time fish spend in a river segment and the rate of mortality in that segment. The basic equation describing the rate of mortality as a function of time is:

(54)

where

In the present model, two causes of mortality are identified: predation and gas bubble disease. CRiSP.1 assumes the rates of each are independent and this is expressed by the equation:

(55)

where

Fish enter and leave river segments every day and spend differing amounts of time in a segment as described by the migration equations. Thus, on a given day the group of fish leaving a segment may have entered on different days and thus have different residence time in the segment. To describe the number of fish that survive a river segment on a daily basis CRiSP.1 solves eq (54) for each group, identified by when they entered the segment and when they exited. The solution is:

(56)

where

Applying an elementary property of integrals, the integral is expressed:

. (57)

In general, the numerical form of the integral is:

(58)

where

The resulting equation for the number of fish passing through each river segment as a function of when it entered the segment is expressed:

. (59)

The input term S0 (tj | ti) expressing the potential number that exit on day tj given then entered the segment on day ti can be expressed:

(60)

where

II.4.2 - Predation Mortality

Predation mortality rate in CRiSP.1 is dependent on predator abundance (density), predator temperature response, and a predator activity coefficient. These factors combine to determine a predation rate r which is applied to the smolt population in each time step to determine predation mortality.

Predation occurs in three reservoir zones: forebay, tailrace, and mid-reservoir. Each zone has its own predator abundances, which vary from project to project, and predator activity coefficients, which are set system-wide via the calibration process. The predation mortality is then a function of predation rate and exposure time.

Predator abundances may vary yearly and are based on predator index studies (Beamesderfer and Rieman 1988; Rieman et al. 1991; Ward et al. 1995). The major predator is the northern pikeminnow1 (Ptychocheilus oregonensis), which accounts for approximately 78 percent of the predation mortality (Rieman et al. 1991). The abundances of other major predators--walleye and smallmouth bass--are converted into northern pikeminnow equivalents via their consumption rates. The effects of the predator removal program on pikeminnow populations have been accounted for from 1991 on.

The predator temperature response function determines maximum consumption rates as a function of temperature and is based on laboratory experiments by Vigg and Burley (1991). The parameters in the temperature response function are set during the calibration process (calibration of CRiSP.1 to NMFS survival estimates). Thus, the predator temperature response may account also for response of the prey species in the model to variation in temperature.

The predator activity coefficient scales the maximal consumption rate to represent in situ conditions where predator-prey encounters may be less frequent, alternative prey may exist, and predators may not be feeding to satiation. As stated above, this coefficient varies by reservoir zone to account for the differences in predator-prey behavior in each zone.

General Model

The predation rate is assumed to be proportional to predator abundance and consumption rate. Consumption rate is scaled by the temperature response function, with consumption increasing with higher water temperature. The general form of the predation rate in the ith zone (forebay, tailrace, or reach) for the jth project is:

(61)

where

The predation survival is determined from the predation rate in each time step as follows:

(62)

where t is time (in days).

For the temperature response function, the sigmoidal form (reparameterized) from Vigg and Burley (1991) is employed:

(63)

where

With this equation, predation rate approaches its maximal rate at higher temperatures. An example of equation (63) fit to data from Vigg and Burley (1991) is shown in Fig. 29.

Table 11 Summary of the forms of the predation mortality rate equation
Reservoir zone applied
forebay, mid-reservoir f, r per time step
tailrace t per tailrace


Fig. 29 Equation (63) fit to data from Vigg and Burley (1991) with CMAX = 8.0, T = 0.40, and TINF = 16.7. Note that each point represents the mean from 11 to 22 replicates.



The old (exponential) form of the temperature response function is also available, but it is no longer supported in the calibration. The exponential form is:

. (64)

This form may be reasonable for the spring migration period where higher temperatures are not encountered.

As formulated in equation (61), predation rate is dependent on predator abundance but not on smolt abundance. Thus with a given predator density and temperature, mean predator consumption rate is linearly related to smolt abundance. This is consistent with data provided by Vigg (1988) except at extremely high smolt abundances, which represent only a few points out of hundreds. The Vigg (1988) study was conducted in the tailrace.

Note also that the CRiSP.1 predation algorithm is very similar to the RESPRED model as described by Beamesderfer et al. (1990). One difference is that RESPRED has a type III functional response of predators on prey, i.e., consumption rate tails off at high prey abundances. Also, RESPRED uses a gamma distribution for the temperature response function instead of the sigmoidal one utilized by CRiSP.1.

Zone Specific Formulations of the Predation Model

As noted above, the predation equation (61) varies according to reservoir zone (forebay, tailrace or mid-reservoir). The forebay and mid-reservoir predation models are based on exposure time as calculated from the migration submodel. Tailrace residence times tend to be very short, so we have assumed one time step residence and have calibrated the model with that in mind.

Another type of model would incorporate exposure (travel) distance as well as exposure time. The tailrace predation model can be thought of as a travel distance based predation model.

Predator Abundance

Predator abundances (as relative predator densities) are needed for each zone of each reservoir. These abundances are based on the predator index studies performed by the Oregon Department of Fish and Wildlife and the Washington Department of Fish and Wildlife (Ward et al. 1995; Zimmerman and Parker 1995). The major piscivorous predators on juvenile salmonids are northern pikeminnow (Ptychocheilus oregonensis) formerly known as northern squawfish, smallmouth bass (Micropterus dolomieu), and walleye (Stizostedion vitreum). Abundances for these predators were based on mark-recapture studies in John Day Pool from 1983-1986 (Beamesderfer and Rieman 1991). For pikeminnow, predator index data from 1990-1991 were used as base abundances because the predator removal program had little or no effect in those years. Bass and walleye abundances were converted to pikeminnow equivalents based on their consumption rates relative to pikeminnow consumption rates (see Table 16) (Vigg et al. 1991).

The abundance data should be considered in a relative sense because abundances based on the mark-recapture studies have very broad confidence intervals (Beamesderfer and Rieman 1991), and the predator index are not intended to provide absolute abundances (Ward et al. 1995; Zimmerman and Parker 1995). The purpose of the predator index studies was to gauge relative differences in predator abundances among reservoirs and within reservoir zones. This is how this information is utilized in CRiSP.1.

In CRiSP.1, the temperature response function parameter CMAX has the effect of scaling predation rate up or down such that model-predicted survivals are consistent with observed survivals (NMFS survival estimates). See Section III.3 Predation Rate Parameter Calibration for the full explanation. This can be thought of as a scaling of the relative predator abundances to reflect the actual predator abundances.

Outline of Calculations for Predator Abundance

Outline of steps:

  1. Compute densities in John Day Pool based on 1984-1986 mark-recapture data and relative abundances in different reservoir zones (for each species).
  2. Calculate CPUE2 -> density conversion factors.
  3. Estimate densities in other reservoirs/zones based on CPUE data. For some zones, pikeminnow abundance indices must be converted to CPUE based on linear regression of CPUE vs. indices in cases where both are available.
  4. Convert smallmouth bass and walleye to "pikeminnow equivalents" based on relative consumption rates. These densities are different for spring and fall migrations due to seasonal differences in consumption rates by the predators. The CPUE is then multiplied by 1080 to convert to density (based on John Day population estimates).

Mean population abundances (1984-1986) in John Day Pool for the three predator species are provided in Table 12. Information and interim calculations are provided in Tables 13 - 21. Table 22 gives the resulting densities for spring and fall migrations. It also gives the pikeminnow percentage, which is needed when accounting for results of the pikeminnow removal program.

Table 12 Population abundance estimates for John Day Pool, 1984-1986 (Beamesderfer and Rieman 1991); the 95% confidence intervals are in parentheses.
N. Pikeminnow (>250 mm) Smallmouth Bass (>200 mm) Walleye (>250 mm)
85,316 (65,693-106,645) 34,954 (35,166-44,741) 15,168 (6,067-32,914)


Table 13 Northern pikeminnow density and distribution in John Day Pool, based on 1990-1991 CPUE data, assuming total abundance the same as 1984-1986.1
Pikeminnow Reservoir Zone Total
John Day Forebay Mid-Reservoir McNary Tailrace McNary Tailrace BRZ2
CPUE 0.69 0.25 0.76 16.33
Area 10.74 186.7 9.7 1.07 208.2
rel. abundance 0.094 0.592 0.093 0.221 1.0
abundance 8019.7 50507.1 7934.4 18854.8 85316
density 746.7 270.5 818.0 17621.3
comb. density 746.7 297.6 17621.3
1 CPUE mult factor = density/CPUE = 1080.
 2 Boat restricted zone.


Table 14 Walleye density and distribution in John Day Pool, 1984-1986; relative densities are mean for 1984-1986 from Beamesderfer and Rieman (1988).
Walleye Reservoir Zone Total
John Day Forebay Arlington Irrigon McNary Tailrace McNary Tailrace BRZ
relative density 0.002 0.114 0.305 0.58 0.000 1.0
Area 10.74 117.1 69.6 9.7 1.07 208.2
abundance




15,168
comb. density 0.0 77.2



Table 15 Smallmouth bass density and distribution in John Day Pool, 1984-1986; relative densities are mean for 1984-1986 from Beamesderfer and Rieman (1988).1
Smallmouth Bass Reservoir Zone Total
John Day Forebay Arlington Irrigon McNary Tailrace McNary Tailrace BRZ
relative density 0.374 0.289 0.277 0.060 0.0 1.0
Area 10.74 117.1 69.6 9.7 1.07 208.2
rel. abundance 0.070 0.586 0.334 0.010
1.0
abundance 2446.8 20483.1 11674.6 349.5 0.0 34,954
comb. density 227.8 165.5

1 For final calculation, forebay and mid-reservoir were averaged (weighted by area) to give a density of 168.8.


Table 16 Mean daily salmonid consumption estimates for the major predators (salmonids predator-1 day-1) from Vigg et al. (1991); walleye and smallmouth bass estimates are for the reservoir only.
Month N. Pikeminnow Walleye Smallmouth Bass
Tailrace Mid-Reservoir Forebay
April 0.123 0.043 0.053 0.021 0.003
May 0.416 0.251 0.280 0.113 0.009
June 0.318 0.086 0.136 0.118 0.019
July 1.950 0.154 0.270 0.447 0.118
August 0.350 0.094 0.130 0.232 0.070


Table 17 Consumption rates for N. Pikeminnow, Walleye and Smallmouth Bass in John Day Pool, 1984-1986, from Vigg et al. (1991); mean for April-June.
Species Reservoir Zone
Forebay Mid-Reservoir Tailrace BRZ
N. Pikeminnow 0.1561 0.127 0.330
Walleye - 0.08 -
Smallmouth Bass 0.0102 0.010 -
1 Mean from Table 16 for April - June.
 2 Assumed to be same as reservoir consumption rate.


Table 18 Consumption rates for N. Pikeminnow, Walleye and Smallmouth Bass in John Day Pool, 1984-1986, from Vigg et al. (1991); mean for July-August.
Species Reservoir Zone
Forebay Mid-Reservoir Tailrace BRZ
N. Pikeminnow 0.201 0.124 1.21
Walleye - 0.34 -
Smallmouth Bass 0.0942 0.094 -
1 Mean from Table 16 for July - August.
 2 Assumed to be same as reservoir consumption rate.


Table 19 Pikeminnow density indices (CPUE) in all reservoir zones, 1990-1991
Reservoir Zone CPUE Ref
Bonneville tailrace 6.30 c
tailrace BRZ 16.35 c
forebay 5.71 a
mid-reservoir 2.102 a
The Dalles tailrace 0.512 a
tailrace BRZ 5.47 a
forebay 1.104 a
mid-reservoir 1.61 d
John Day tailrace 2.75 a
tailrace BRZ 21.54 a
forebay 0.69 c
mid-reservoir 0.25 c
McNary tailrace 0.76 c
tailrace BRZ 16.33 c
forebay 0.17 c
mid-reservoir 0.51 d
upper reservoir 0.89 d
Ice Harbor tailrace 0.45 d
tailrace BRZ 8.42 d
forebay 0.08 e
mid-reservoir 0.30 e
Lower Monumental tailrace 0.76 e
tailrace BRZ 1.30 e
forebay 0.67 e
mid-reservoir 0.83 e
Little Goose tailrace 1.52 b
tailrace BRZ 16.31 b
forebay 0.64 e
mid-reservoir 0.39 e
Lower Granite tailrace 1.63 b
tailrace BRZ 28.29 b
forebay 0.48 e
mid-reservoir 0.17 e
upper reservoir 1.86 b
Hanford Reach (Priest Rapids) tailrace 2.85 f
Priest Rapids tailrace BRZ 6.28 g
forebay 1.62 g
mid-reservoir 0.97 f
Wanapum tailrace BRZ 11.33 g
forebay 1.32 g
mid-reservoir 2.82 f
Rock Island tailrace BRZ 20.20 g
forebay .66 g
mid-reservoir 2.27 f
Rocky Reach tailrace BRZ 1.62 g
forebay 9.0 g
mid-reservoir 2.38 f
Wells tailrace BRZ 1.50 g
forebay 1.50 g
mid-reservoir 1.26 f
Chief Joseph tailrace BRZ 1.47 g
a. 1990 CPUE data (Zimmerman et al. 1997)
 b. 1991 CPUE data (Zimmerman et al. 1997)
 c. mean 1990 and 1991 CPUE data (Zimmerman et al. 1997)
 d. CPUE estimated from 1990 density index (Ward et al. 1993)
 e. CPUE estimated from 1991 density index (Ward et al. 1993)
 Linear regressions for estimating CPUE's from density index based on reciprocal square root zero catches: R2= 0.818 (intercept = -3.11, slope = 3.13, p < 0.001) for index < 1.6; R2 = 0.711
(intercept = -7.64, slope = 7.44, p < 0.01) for index > 1.6.
 f. 1993 CPUE (Loch et al. 1994)
 g. CPUE estimated from 1993 density index (Loch et al. 1994) using linear regression.


Table 20 Relative CPUEs for smallmouth bass and walleye in the Snake and Columbia rivers (standardized to John Day Pool) based on the abundances from Zimmerman and Parker (1995). Raw data from N. Bouwes, ODFW, pers. com. Also given are CPUEs for the upper Columbia (not standardized to John Day Pool) from Loch et al. (1994).
Reservoir Smallmouth Bass Walleye
Bonneville 0.69 6.39
The Dalles 0.83 2.88
John Day 1.00 1.00
McNary 0.89 1.11
Ice Harbor 3.93 0.00
L. Monumental 3.87 0.00
Little Goose 4.92 0.00
Lower Granite 11.72 0.00
Hanford Reach (Priest Rapids Tailrace) 0.00 0.21
Priest Rapids 0.45 0.02
Wanapum 0.02 0.06
Rock Island 0.02 0.01
Rocky Reach 0.19 0.13
Wells 0.06 0.05


Table 21 River dimensions for the Snake and Columbia rivers (Ward et al. 1995) and for the upper Columbia River (Loch et al. 1994). Tailrace (at the head of the reservoir) is assumed to be 0.6 km in length; forebay is assumed to be 6.0 km in length.

length (km) avg. width (km) total S.A. (km2) S.A. tailrace (km2) S.A. forebay (km2) S.A. reservoir
Bonneville 74.3 1.37 101.79 0.82 8.22 92.75
The Dalles 38.5 1.42 54.67 0.85 8.52 45.30
John Day 122.9 1.79 219.99 1.07 10.74 208.18
McNary 52.0 1.58 82.16 0.95 9.48 71.73
Snake R. below Ice Harbor 16.0 0.61 9.76 0.37
9.76
Ice Harbor 51.3 0.61 31.29 0.37 3.66 27.26
L. Monumental 46.2 0.58 26.80 0.35 3.48 22.97
Little Goose 59.9 0.51 30.55 0.31 3.06 27.18
Lower Granite 85.3 0.64 54.59 - 3.84 50.37
Columbia R. below P.R. Dam 46.2 0.87 40.19 0.95
39.67
Priest Rapids 29.0 0.87 25.23 0.52 5.22 19.49
Wanapum 61.1 0.96 58.66 0.58 5.76 52.32
Rock Island 33.8 0.46 15.55 0.28 2.76 12.51
Rocky Reach 67.3 0.55 37.01 0.33 3.30 33.39
Wells 47.0 0.56 26.32 0.34 3.36 22.62


The predator abundance calculations above arrive at the predator densities shown in Table 22. As stated earlier, the densities are considered to be relative, that is they provide a relationship between densities from one zone to the next. They are not intended to be absolute predator densities.

The difference between spring and fall densities stems from the differences in per predator consumption rates in those periods (see Tables 17 and 18). These densities are the base densities for 1990 and prior years. For subsequent years, adjustments are made as a result of the pikeminnow removal program.

Table 22 1990 predator densities for spring (SP) and fall (FA) migrations, by reach and zone. Pikeminnow fraction (% PM) are given for Snake and lower Columbia reaches that are subjected to the pikeminnow removal program.
Reach Zone Density (SP) % PM (SP) Density (FA) % PM (FA)
Estuary mid-res. 2137.73 0.853 3314.1 0.551
Jones Beach mid-res. 2008.13 0.844 3184.5 0.532
Columbia Gorge mid-res. 1835.33 0.829 3011.7 0.506
Bonneville Tailrace mid-res. 7123.91 0.955 8244.91 0.825
Bonneville Dam tailrace 17658.0 1.0 17658.0 1.0
Bonneville Dam forebay 6173.27 0.998 6221.54 0.991
Bonneville Pool mid-res. 2458.31 0.869 3579.31 0.597
The Dalles Dam tailrace 5907.6 1.0 5907.6 1.0
The Dalles Dam forebay 1195.78 0.993 1253.84 0.947
The Dalles Pool mid-res. 2105.88 0.928 2670.63 0.731
Deschutes Confluence mid-res. 2105.88 0.928 2670.63 0.731
John Day Dam tailrace 23263.2 1.0 23263.2 1.0
John Day Dam forebay 754.57 0.987 824.53 0.903
John Day Pool mid-res. 353.52 0.824 631.23 0.461
McNary Dam tailrace 17636.4 1.0 17636.4 1
McNary Dam forebay 191.94 0.956 254.20 0.722
McNary Pool mid-res. 616.60 0.893 899.64 0.612
Lower Snake River mid-res. 894.63 0.941 1345.28 0.626
Ice Harbor Dam tailrace 9093.6 1.0 9093.6 1
Ice Harbor Dam forebay 123.25 0.701 398.19 0.216
Ice Harbor Pool mid-res. 430.23 0.878 880.88 0.429
Lower Monumental Dam tailrace 1404.0 1.0 1404.0 1
Lower Monumental Dam forebay 759.89 0.952 1030.63 0.702
Lower Monumental Pool mid-res. 1034.23 0.950 1478.01 0.664
Little Goose Dam tailrace 17614.8 1.0 17614.8 1
Little Goose Dam forebay 737.33 0.937 1081.53 0.639
Little Goose Pool mid-res. 605.39 0.891 1169.56 0.461
Lower Granite Dam tailrace 30553.2 1.0 30553.2 1
Lower Granite Dam forebay 628.30 0.825 1448.21 0.357
Lower Granite Pool mid-res. 1246.57 0.875 2590.50 0.421
Columbia above confluence mid-res. 607.8
890.8
Hanford Reach mid-res. 3078.0
3078.0
Priest Rapids Dam tailrace 6782.6
6782.6
Priest Rapids Dam forebay 1779.6
2121.7
Priest Rapids Pool mid-res. 1099.6
1335.2
Wanapum Dam tailrace 12238.6
12238.6
Wanapum Dam forebay 1422.9
1437.5
Wanapum Pool mid-res. 3088.1
3233.3
Rock Island Dam tailrace 21816.5
21816.5
Rock Island Dam forebay 719.2
734.4
Rock Island Pool mid-res. 2460.1
2491.3
Rocky Reach Dam tailrace 1752.4
1752.4
Rocky Reach Dam forebay 9727.0
9871.5
Rocky Reach Pool mid-res. 2675.1
3051.5
Wells Dam tailrace 1617.1
1617.1
Wells Dam forebay 1620.8
1666.4
Wells Pool mid-res. 1399.9
1539.2
Chief Joseph Dam tailrace 1590.1
1590.1


For reservoir zones in the model for which no CPUE or predator index information was available, the following assumptions were made about predator density:

Predator Removal Adjustments

The predator density estimates in Table 22 are for the years up to and including 1990. For subsequent years, the densities must be adjusted for the predator (pikeminnow) removal program. Table 23 shows the percent reduction in predation due to pikeminnows at each project for each year. Note, this does not directly give the reduction in predator numbers.

To calculate the change in predator numbers due to the estimated change in predation, we use the fact that when . Recall from equation eq (62) that survival in a specific reservoir zone is given by:

and that predator density P is a factor in r. Since rt is on the order of 0.05 and predation , the percent change in predation is approximately equal to the percent change in predator density:

. (65)

So, to calculate adjusted predator densities, reduce the pikeminnow portion of the predator density from Table 22 by the amount of predation reduction shown in Table 23.

Table 23 Pikeminnow reduction program on the Snake and lower Columbia rivers. Percent reduction in predation due to pikeminnows as a result of the pikeminnow removal program at each reservoir for each year (Peters et al. 1999, 113). Estimates of predation reduction for 2001-2006 are included in Peters et al. (1999, 113).
Reach 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Estuary 0.000 0.029 0.076 0.078 0.120 0.155 0.160 0.141 0.129 0.136
Jones Beach 0.000 0.029 0.076 0.078 0.120 0.155 0.160 0.141 0.129 0.136
Columbia Gorge 0.000 0.029 0.076 0.078 0.120 0.155 0.160 0.141 0.129 0.136
Bonneville Tailrace 0.006 0.029 0.076 0.078 0.120 0.155 0.160 0.141 0.129 0.136
Bonneville Pool 0.006 0.100 0.271 0.185 0.173 0.154 0.148 0.149 0.152 0.151
The Dalles Pool 0.065 0.272 0.274 0.274 0.283 0.309 0.329 0.298 0.305 0.306
Deschutes Confluence 0.065 0.272 0.274 0.274 0.283 0.309 0.329 0.298 0.305 0.306
John Day Pool 0.009 0.125 0.181 0.198 0.186 0.140 0.136 0.099 0.068 0.074
McNary Pool 0.000 0.020 0.016 0.013 0.009 0.007 0.004 0.003 0.001 0.001
Lower Snake 0.000 0.020 0.016 0.013 0.009 0.007 0.004 0.003 0.001 0.001
Ice Harbor Pool 0.000 0.137 0.107 0.080 0.058 0.041 0.027 0.017 0.009 0.004
Lower Mon. Pool 0.000 0.083 0.105 0.099 0.084 0.078 0.054 0.036 0.023 0.031
Little Goose Pool 0.000 0.057 0.129 0.122 0.128 0.115 0.124 0.088 0.061 0.064
Lower Granite Pool 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000


Predator Density / Reservoir Volume Interaction

Predators may become concentrated in the forebay or tailrace when the depth of the region is decreased by lowering the reservoir. It is possible that concentrating predators increases the encounter rate between predators and prey, and thus effectively increases the mortality rate in the forebay and tailrace.

This mortality increase can be included in CRiSP.1 runs by selecting predator density/volume interaction in the Runtime Settings window opened from the Run menu. When selected, predator density is a function of pool elevation for reservoir, forebay and tailrace regions. Predator density adjustments to the forebay and tailrace (Fig. 30) are given by3:

(66)

where

Fig. 30 Predator concentration function at dam



II.4.3 - Supersaturation Mortality

High levels of total dissolved gas in the river lead to the development of gas bubble disease (GBD) in smolts, as well as other aquatic life. This condition involves the formation of bubbles in the organs, tissues, and vascular system of the fish. GBD is also suspected of compromising the fish's vitality by increasing its susceptibility to predators, bacteria, and disease (U.S. Army Corps of Engineers 1994a). Because of the varied symptoms and effects of total dissolved gas, GBD will be considered an independent force of mortality.

There is uncertainty as to the significance of GBD-induced mortality at low levels of supersaturation (<110%); however, it is clear in all studies that as the amount of supersaturation increases (>110%) the rate of mortality increases significantly. The transition between low levels of generally sublethal effects to the higher level lethal condition involves a shift in the bubble-related mechanisms that lead to death. Specifically, at levels of supersaturation below the threshold fish are more susceptible to death related to infection and stress while above the threshold fish experience death from large intravascular bubbles (White et al. 1991).

Theory

In CRiSP.1, the level of total dissolved gas (TDG) is represented by percent of total dissolved gas saturated in the water above equilibrium (100%). TDG is generated by spill at the dams and then dissipated as the water moves downstream. In the model, the effects of both lethal and sublethal levels of TDG are considered as well as the changes in the effective TDG concentration resulting from depth and distance downstream.

Fig. 31 Factors in gas bubble disease model





The relationship between migration factors and gas bubble disease is illustrated in Fig. 31. TDG supersaturation can be defined with any of the submodels selected from the TDG Saturation Equations windows opened from the Dam menu.

Gas Mortality Equation

To incorporate both the lethal and sublethal effects of gas bubble disease, the model uses a piecewise linear function that expresses the rate of mortality Mtdg as a function of Gs, the level of total dissolved gas above equilibrium (see Fig. 32). This piecewise linear characteristic is accomplished by using the Heaviside function H(), which switches from 0 to 1 as its argument changes from negative to positive. This allows the model to assume a moderate linear increase in mortality (slope a) at low levels of dissolved gas supersaturation. When the lethal threshold of saturation Gc is reached, the Heaviside function turns on and the mortality curve increases linearly with a higher rate (slope a + b). Using the work of Dawley et al. (1976), the empirical gas mortality rate equation is:

(67)

where

Fig. 32 Illustration of eq (81), the dissolved gas mortality equation



Vertical Distribution

A population of fish from a given species will spread out vertically. A number of distribution functions have been hypothesized (Zabel 1994). For simplicity, CRiSP.1 uses an isosceles triangular distribution given by:

(68)

where

Fig. 33 Illustration of fish depth distribution of fish



The work of Zabel (1994) shows that fish of a given species tend to seek specific depths that are correlated to the level of illumination.

Size / Mortality Relationship

Although no mechanism has been developed justifying a linear relationship, qualitatively the ability of a fish to establish gas equilibrium within its environment should be related to its volume to surface area ratio, which is proportional to fish length. Thus on physical principles of gas exchange, a length relationship should be involved with TDG supersaturation mortality. For a first order estimate of the length relationship to mortality, the regression (illustrated in Fig. 36) is forced through the intercept:

(69)

where

From eq (69), the TDG mortality rate can be corrected for fish length using:

(70)

where

Downstream Dissipation

As fish move downstream in a reservoir their mortality rate due to TDG supersaturation generally decreases because dissolved gas levels are highest at the upstream end and dissipate as the water moves downstream. Using the reservoir gas distribution model (see Section II.5 Total Dissolved Gas), the saturation level is expressed differently for each side of the river:

(71)

(72)

where

The dissipation parameter k is defined with respect to time. To express this time-dependent process in spatial coordinates, the time coordinate was transformed to distance downstream using the average velocity in the pool:

(73)

where

Transforming time to downstream distance using eq (73) defines a new dissipation parameter:

. (74)

The surface supersaturation for each side of the river takes on the general form:

(75)

which leads to:

(76)

where

Based on work by Fidler and Miller (1994) demonstrating that the critical supersaturation concentration Gc is depth dependent, with Gc increasing as depth increases; CRiSP.1 utilizes a linear relationship to relate Gc to fish depth. Then the rate of mortality as a function of fish depth and distance downstream can be expressed as:

(77)

where

Thus, there is a different mortality rate on each side of the river.

Integrate for Average Rate through Pool

For each side of the river the mortality rate is first averaged over the depth and length of the pool, and then an average mortality rate per day for the pool is created by calculating the flow weighted average over the two sides of the river. Thus, the average mortality rate for a fish while it is in a pool is given by the equation:

(78)

where

(79)

and

Parameter Determination

Gas Mortality Equation

Recall from equation (67), there are two gas mortality rate coefficients:

Determination of the gas mortality equation parameters begins with fitting mortality rates of fish exposed to various TDG levels for various lengths of time. The TDG mortality rate equation is given by setting the predator mortality to zero in eq (55). The resulting survival equation is:

(80)

where

Then the rate of mortality due to supersaturation as a function of time and TDG level can be expressed as:

. (81)

The survival curves provided by Dawley et al. (1976) yielded pairs of (t,S) for varying levels of dissolved gas. Pairs of (G,Mtdg) were obtained using each of the data points determined from the graphs. This data and the mortality rate Mtdg calculated from (81) are shown in Table 24 and Table 25.

When the mortality rates are known, the a and b parameters follow from simple linear regressions of the mortality rate on the dissolved gas level, allowing for different slopes between the a and b values.

Table 24 Chinook mortality rates based on survival data from Dawley et al. (1976) shallow (0.25m) and deep (2.5m) tank experiments.
%TDG Days (t) Chinook 0.25 meters Chinook 2.5 meters
Survival (S) Mortality rate (Mtdg) Survival (S) Mortality rate (Mtdg)
105 20 0.99 0.0005 1 0
40 0.98 0.00051 1 0
60 0.97 0.00051 0.99 0.00017
80 0.9 0.0013 0.97 0.00038
100 0.88 0.0013 0.97 0.0003
120 0.87 0.0012 0.96 0.00034
110 20 0.97 0.0015 1 0
40 0.95 0.0013 1 0
60 0.84 0.0029 0.99 0.00017
80 0.63 0.0058 0.97 0.00038
100 0.52 0.0065 0.95 0.00051
120

0.9 0.00088
115 10 0.95 0.0051

20 0.84 0.0087 1 0
30 0.72 0.011

40 0.62 0.012 1 0
50 0.49 0.014

60 0.22 0.025 0.97 0.00051
70 0.12 0.03

80 0.08 0.032 0.88 0.0016
100 0.05 0.03 0.83 0.0019
120

0.78 0.0021
120 10 0.77 0.026

20 0.57 0.028 1 0
30 0.32 0.038

40 0.22 0.038 1 0
50 0.1 0.046

60 0.03 0.058 0.95 0.00085
70 0.02 0.056

80 0.01 0.058 0.71 0.0043
100

0.64 0.0045
120

0.58 0.0045
127 10

0.97 0.003
20

0.88 0.0064
30

0.7 0.012
40

0.52 0.016
60

0.38 0.016
80

0.1 0.029
100

0.07 0.027


Table 25 Steelhead mortality rates based on survival data and mortality rates from Dawley et al. (1976) shallow (0.25m) and deep (2.5m) tank experiments.
%TDG Days (t) Steelhead 0.25m Steelhead 2.5m
Survival (S) Mortality rate (Mtdg) Survival (S) Mortality rate (Mtdg)
105 1 1 0 1 0
2 1 0 1 0
3

1 0
4

1 0
5 0.96 0.0082 1 0
6

1 0
7 0.95 0.0073

110 1 1 0 1 0
2 1 0 1 0
7 0.97 0.0044 0.99 0.0014
115 1 1 0 1 0
2 0.95 0.026

3 0.7 0.12 1 0
4 0.58 0.14

5 0.48 0.15

6 0.41 0.15

7 0.37 0.14 0.97 0.0044
120 0.8 0.76 0.34

1 0.67 0.4

1.2 0.42 0.72

1.9 0.060 1.5

2

0.99 0.005
3

0.96 0.014
7

0.94 0.0088
127 2

0.92 0.042
3

0.87 0.046
4

0.82 0.05
5

0.8 0.045
6

0.77 0.044
7

0.75 0.041


Fig. 34 Chinook and steelhead cumulative mortality from gas bubble disease at different levels of TDG supersaturation. Data points from Dawley et al. (1976).



Depth Dependent Critical Values

Fidler and Miller (1994) and Dawley et al. (1976) demonstrated that the critical supersaturation concentration is depth dependent and increases as depth increases. In other words, fish at lower depths are less susceptible to dissolved gas supersaturation. Based on the mechanisms controlling partial pressures of gas bubbles, the partial pressure increases approximately 10% per meter below the surface (Richards 1965). Fidler and Miller noticed a linear change in the threshold depth for gas bubble trauma symptoms. The slope of this linear relationship is 73.89 mmHg m-1, and given the relationship of TDG to pressure (.1316 %/mmHg), this equivalent to 9.72 m-1 or 2.96 ft-1.

CRiSP.1 utilizes a linear relationship to relate Geff (the effective gas concentration) to fish depth:

(82)

where

(83)

When the model is run to obtain a Geff for a stock, eq (82) is multiplied by fish density as a function of depth, and then this term is integrated over the reservoir depth. Effective gas pressures used for the regressions to determine a and b (see eq (67)) were therefore corrected for the depth of the fish in the experimental tanks.

Table 26 Depths of fish in the deep water tanks and gcorrection used to determine mortality rate coefficients
species Depth gcorrection
chinook 1.0m 9.7
steelhead 1.5m 14.6


Size-Mortality Relationship

Experiments conducted by Dawley et al. (1976) demonstrated that large fish have higher levels of mortality. The experiments exposed fall chinook of various sizes to 112% supersaturation in shallow tanks; they determined cumulative mortality curves were significantly different (Dawley et al. 1976, Fig. 10). These data can be used to infer the effect of fish length on TDG mortality in reservoirs since the study also demonstrated that shallow tank mortality curves had the same pattern as deep tank mortalities with higher TDG supersaturation levels. The experiments indicated that mortality curves in shallow tanks at 112% saturation were equivalent to mortality curves in a deep tank with 122% supersaturation.

The resulting mortality-length relationship can be used to extrapolate experimental results to field conditions where the fish are larger. The first step is to determine an empirical relationship relating TDG supersaturation mortality to fish length. This is done by regressing the mortality rates against fish length for the fish in the 112% TDG experiments. Given this relationship, the results of the Dawley fall chinook experiments are extrapolated to fall and spring chinook in the Lower Granite reservoir using different average fish lengths for each stock. The steelhead in the Lower Granite reservoir are treated similarly.

To determine the relationship between fish size and TDG supersaturation mortality, the mortality rate is estimated by fitting eq (69) to cumulative mortality vs. exposure time for different sized fall chinook (Fig. 35). The estimated rates are given in Table 27.

Table 27 Total dissolved gas mortality rates and fish length in shallow tank experiments (Dawley et al. 1976). Plotting symbols refer to Fig. 35.
Species Plotting Symbols Length (mm) Average Mortality Rate
fall chinook 40 0.00364
+ 53 0.0327
67 0.0374


Fig. 35 Cumulative mortality vs. exposure time to TDG supersaturation for different fish lengths.



The resulting mean mortality rates are plotted against fish length in Fig. 36. The slope of the line relating mean mortality rate to length is 0.00126. The regression was not confined to go through zero because Dawley et al. (1976) and Jensen (1986) both report that there is a sensitivity threshold for size.

Fig. 36 Mean mortality rate due to TDG supersaturation vs. fish length



Exposure Time Limits

In addition to a threshold for size, there appears to be a threshold for time as well. This suggests that compensatory mechanisms are functional for a period of time and then begin to break down. As a result, fish exposed to high levels of dissolved gas (for up to 2 months or more as in the Dawley experiments) are susceptible to mortality at a higher rate than fish exposed for a short period of time. We restrict the mortality rate data to fish exposed for 40 days or less, on the order of time that the fish are exposed in the river system. This subset of the mortality data is used to determine the TDG mortality coefficients.

Vertical Distribution

The gas bubble disease rate depends on fish depth which is characterized by a mode depth and bottom depth. Fish depths vary continuously over day and night, fish age, and position in the river. For the current model a representative depth is required for each species. The species-specific depth values were selected after reviewing the data on fish vertical distributions. The essential elements and references are given in Table 28.

Table 28 Fish vertical distributions and references
Species Location Time Mode depth Reference CRiSP.1 values
spring chinook Forebay Day 39 ft 5 ft Johnson et al. 1985 Ebel and Raymond 1976

mode=12 maximum = 36


Reservoir		 Day 12-24 ft 27-36 ft Smith 1974 Dauble et al. 1989
Night 0-12 ft 27-36 ft Smith 1974 Dauble et al. 1989
fall chinook Forebay Day


mode=12 maximum = 36

Reservoir		 Day 12-20 ft Dauble et al. 1989
Night 12-20 ft Dauble et al. 1989
steelhead
Forebay		 Day 13 ft 4 ft Johnson et al. 1985 Ebel and Raymond 1976

mode=12 maximum = 36
Night


Reservoir		 Day 0-12 ft Smith 1974
Night 12-24 ft Smith 1974


Mortality Coefficients

Using eq (67) and the Dawley survival data for fish exposed under 40 days (Table 24); the parameters a and b were fit using linear regression. Regression results are summarized in Table 29 and shown in Fig. 37.

Table 29 TDG mortality coefficients
Parameter Fall Chinook Spring Chinook Steelhead
a 0.000018 0.000021 0.000594
b 0.005150 0.005980 0.004820
gc 10.9 10.9 12.7


Fig. 37 Fits of mortality rate parameters to mortality rate data corrected for depth and fish length. Data points from Dawley et al. (1976); curve from fit of eq (67). There are extreme points not shown on the steelhead graph.



II.4.4 - Simple Mortality

A number of simple hydrosystem reservoir mortality functions can be selected to represent the equations used the FLUSH spring chinook smolt passage model as part of the Plan for Analyzing and Testing Hypotheses (PATH) (Marmorek et al. 1996). Four models are provided for spring chinook reservoir survival through the hydrosystem.

Simple Mortality

Used in FLUSH up through 1996 for model smolt reservoir survival, which excludes dam passage survival. The model was calibrated with survival studies from Little Goose Dam to The Dalles Dam over the years 1970 and 1973 through 1980. To estimate reservoir survival the dam passage survival was removed by assuming turbine mortality was 15% and bypass and spill mortalities were 2% at all projects. Spill efficiency was assumed to be 1:1 at all projects except at The Dalles Dam where it was 2:1. The equation is:

(84)

where

Simple TURBx Mortality

The FLUSH spring chinook smolt reservoir survival was changed for PATH analysis from 1997 through 2000. Three different forms of the model were developed depending on assumptions on dam passage mortality in the 1970 through 1980 period. These were designated TURB1, TURB 4, and TURB5 (Marmorek and Peters 1998). The model calibration is undocumented, but the model equation and parameters were provided by H. Schaller (pers. com.). The equation is:

(85)

where

Note: Recent PIT tag survival studies have invalidated these FLUSH reservoir mortality equations and we recommend against using them for model analysis. They are presented to document use in the FLUSH model in PATH.

1 Northern pikeminnow were formerly known as northern squawfish.
 2 Catch per unit effort
 3 The limit h/H < 0.05 is arbitrary and required to prevent divide by zero errors. The limit equates to a river depth just over the head of most managers.
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web@cbr.washington.edu
Columbia Basin Research,
School of Aquatic & Fishery Sciences,
University of Washington