An Empirical Methodology for Estimating Entrainment ...

Transactions cf the American Fisheri£s Sociel)' 110:253-260, 1981

An Empirical Methodology for Estimating Entrainment Losses at Power Plants Sited on Estuaries JoHN BoREMAN 1 AND C. PHILLIP GooDYEAR 2

National Power Plant Team, United States Fish and Wildlife Service 2929 Plymouth Road, Room 206, Ann Arbor, Michigan 48105 SIGURD

w.

CHRISTENSEN

Environmental Sciences Division, Oak Ridge National Laboratory Oak Ridge, Tennessee 37830

Abstract A model based on empirically derived age-, time-, and space-variant entrainment susceptibility data may be used for estimating conditional entrainment mortality of aquatic organisms, particularly fish and shellfish, caused by operation of one or more power plants on an estuary. Model application requires knowledge of the morphometry of the water body, the power-plant flow rates, the probability of entrainment survival, and the duration, distribution, and abundance of en trainable age-groups. A novel feature of the model is that organism distribution and movement within the model are defined by information derived from field samples rather than by hydrodynamic principles and equations.

Section 316(b) of United States Public Law 92-500 has stimulated numerous endeavors aimed at predicting or assessing mortality of aquatic organisms due to entrainment in power-plant cooling water. Models for predicting entrainment mortality range from simple mathematical expressions, such as those proposed by Lawler (1976) and Goodyear (1977), to the linking of organism movement and complex hydrodynamic equations, such as those used by Hess et al. (1975) and Eraslan et al. (1976). Parameters common to all these models are the cooling water withdrawal rate of the power plant, the volume or rate of flow of the water body from which the cooling water is withdrawn, and one or more factors that account for susceptibility of individual organisms to withdrawal by the plant. Some models assume that all organisms in the water body are equally susceptible to withdrawal by the power plant; others may account for age-, time-, and spacevariant susceptibility. Because entrainment oc-

1 Present address: Northeast Fisheries Center, National Marine Fisheries Service, Woods Hole, Massachusetts 02543. 2 Present address: National Fisheries Center-Leetown, Route 3, Box 41, Kearneysville, West Virginia 25430.

curs over an extended period, movement of entrainable individuals is an important determining factor. Models have been used to simulate individual movement patterns through the use of hydrodynamic equations, although few models specify distribution patterns based directly on field data, and these have been developed only for site-specific situations. Mortality of aquatic organisms due to entrainment may be expressed as the fraction of the initial populations that would be killed by entrainment during a specified time period if no other causes of mortality operated. This expression, termed the conditional entrainment mortality rate, is analogous to the conditional fishing mortality rate as defined by Ricker ( 197 5). The conditional entrainment mortality rate is equivalent to the fractional reduction in year-class strength following the time period of entrainment if the other sources of mortality are density-independent. This situation exists regardless of the magnitude of the mortality due to sources other than entrainment. This paper presents a generalized mathematical equation for estimating the conditional entrainment mortality rate of aquatic organisms due to water withdrawal from an estuary by one or more power plants. This equation, termed the Empirical Transport Model (ETM), incorporates empirically derived age-, time-,

253

254

BOREMAN ET AL.

and space-variant entrainment susceptibility data. The ETM may be applied to fish or shellfish populations inhabiting water bodies containing existing or proposed power plants or other water intake structures. Two forms of the ETM are presented: one form is for situations when entrainable organisms are placed in the water body at essentially the same time (singlecohort approach), and the other form is for situations when entrainable organisms are introduced to the water body over an extended period (multiple-cohort approach). An example of how the latter form of the ETM may be applied in an estuarine situation, a sensitivity analysis of model parameters, and a listing of the associated computer code in BASIC language, can be found in Boreman et al. (1978).

Mathematical Basis The conditional entrainment mortality rate, m, during a time interval, t, for a group of organisms that is continually vulnerable to entrainment is expressed as: m = I - e-Et,

(1)

where E = the instantaneous entrainment mortality rate constant during a specified time interval t (per unit time). The instantaneous constant E is a function of the amount of water withdrawn by power plants in relation to the volume of the water body, as well as a function of the susceptibility of individual organisms to power-plant water withdrawal and of subsequent mortality due to plant passage:

E=~

V'

(2)

where P = the rate of power-plant water withdrawal during a specified time interval (volume per unit time); f = the fraction of organisms entering the power plant that eventual1y is killed by plant passage; W = the ratio of the average intake to average water body concentration of organisms; V =the volume of the water body.

group throughout their period of entrainment vulnerability (termed the "entrainment period"). The conditional entrainment mortality rate for any age-j organism during a specified time interval within the entrainment period, ml> based on Equation (1), is: (3)

where

t; =the duration of age j; EJ = the instantaneous entrainment mortality rate of age-j organisms (per unit time), defined as

£. = PjjWJ

v '

J

where

jj = the fraction of age-j organisms

entering the power-plant intake that are eventually killed by plant passage; WJ = the ratio of the average intake to average water body concentration of age-j organisms. The total conditional entrainment mortality rate for J agecgroups, m" is given as: mJ =

l - (1 - m 0 )(1 - m 1 )

•••

(l - mJ)

(4A)

J

= 1-

TI (1

- mJ)

(4B)

J=O

=

1-

J

TI e-E,t,,

(4C)

j=O

where (1 - m;) is the probability of surviving the imposition of mortality mi. If susceptibility to entrainment (f; and WJ) does not vary with age, then Equation (4C) can be reduced to a single-age model by redefining the duration of the age as the duration of the entire entrainment period. Besides varying with age, the susceptibility of an individual organism to entrainment mortality may vary with the location of that organism in the water body relative to the location of the power plant intake. If a water body has K regions, the proportion of the standing crop of age-j organisms initially occurring in region k is defined as D;k, so that: (5)

Single-Cohort Approach

Assume that spawning occurs during a short time interval so that members of the entrainable population are essentially in the same age-

When there is no interchange of age-j organisms among regions, the entrainment mortalities in the various regions are not competing

255

PREDICTION OF ENTRAINMENT LOSSES

with each other. In this case, the total conditional entrainment mortality rate is evaluated by summing over the population survival rate in each region and subtracting from 1. The ~ortality rate of age-j organisms over K regions, m;K. is given as: K

m;K = 1 - :LD;k(l - m;k)

(6A)

k~l

(6B)

where t,jk

E;k

where Pk

=

the instantaneous entrainment mortality rate of age-j organisms in region k (per unit time), defined as

where mr = the total conditional entrainment mortality rate of a population. Equation (7) may also be adapted for application in the case when vulnerable organisms are classified by life stages of unequal durations, rather than by age. The conditional entrainment mortality rate over L life stages in K regions is obtained by simply replacing parameters based on age with ones based on life stage: mr = 1 -

L

K

1~1

k~l

IJ L D1k(I

- m1k)

= P,J;kWJk

=

V,,

= =

W;k =

the rate of power plant water withdrawal from region k (volume per unit time), the volume of region k, the fraction of age-j organisms entering the power plants in region k. that eventually is killed by plant passage, and the ratio of the average intake to average regional concentration of age-j organisms in region k.

When substantial interchange of age-j organisms does occur among regions, age-j can be broken up into several subages, thereby increasing the total number of vulnerable ages (j). Since organisms are instantaneously redistributed among all regions between time intervals, this has the effect of increasing the amount of interchange among age-j organisms. If density-dependent migration occurs, Equation (6) is not applicable. Equation (6) may be collapsed to only those regions from which power plants withdraw water. However, the total number of regions, K, should initially be established to accommodate all distribution data pertaining to the organisms in question. The final step in the single-cohort approach is combining the concepts of multiple ages and multiple regions. Combining equations (4) and (6) we get: =

(SA) (SB)

vk

fjk

nvr

(7B)

(7A)

whe~e

D 1k =the average proportion of the

standing crop of life stage-l organisms initially occurring in region k; m1k = the conditional entrainment mortality rate of life stage-l organisms in region k; E1k = the instantaneous entrainment mortality rate constant of life stage-l organisms in region k (per unit time); t1 = the duration of life stage l.

Multiple-Cohort Approach

The entrainment period usually is greater than the length of time an individual member of a population takes to grow through the entrainable life stages (termed its "entrainment interval") because spawning typically occurs over an extended period of time. As such, more than one age usually is present in the water body at a given moment in the entrainment period. If conditions in the water body that influence entrainment (such as power-plant flow rates) change during the entrainment period, the susceptibility of an individual organism to entrainment mortality will be dependent upon when, during the spawning period, that individual was spawned. For example, if powerplant flows are reduced in the latter part of the entrainment period, individuals spawned later in the spawning period will experience less entrainment mortality, if it is assumed all individ-

256

BOREMAN ET AL.

uals in the population develop at the same rate regardless of when they were spawned. If we define S as the duration of the spawning period and J as the entrainment interval measured in the same units of time (time steps) as the duration of the spawning period, then the length of the entrainment period is S + J time steps. The proportion of total eggs spawned during time step s in the spawning period is defined as R 8 , so that: (9)

The value of S also is equal to the total number of cohorts. If the effect of entrainment mortality on a given cohort is independent of the effect of entrainment mortality on other cohorts, the total entrainment mortality rate of the population (mr) is obtained by summing over the entrainment survival rates for all cohorts and subtracting from one. Combining Equations (7) and (9), we get: S

mr

=

1-

J

K

L Rs II L Ds+j,jkexp(-Es+j,jkt;), s=I

j=O k=l

(10)

where

=the proportion of age-j organisms in region k during time steps+ j, t; = the duration of age j, and Es+i.ik = the instantaneous entrainment mortality rate of age~j organisms in region k during time step s + j (per unit time), defined as

Ds+;,;h·

where Ps+i.k =the rate of power-plant water withdrawal from region k during time step s + j (volume per unit time), fs+;,;h· = the fraction of age~j organisms entering the power plants in region k during time step s + j that eventually is killed by plant passage, and W 8+;,;h· = the ratio of the average intake to average regional concentration of age-j organisms in region k during time step s + j.

When vulnerable organisms are classified by life stages with durations that are not equal to the s or j time step, Equation (9) must be modified. In this situation, data that define the values of D and E will not be available on an agespecific basis, but rather will be available only on a life-stage-specific basis. To accommodate temporal variation in physical parameters, such as power-plant withdrawal flows, it is necessary to retain a measure of the number of time steps from the beginning of the entrainment period (s + j) in the multiple-cohort approach. Equation (9) cannot be modified for this accommodation by simply substituting life-stage parameters for age parameters wherever they appear, as was the case in the single-cohort approach. Instead, lifestage parameters can be incorporated into Equation (9) by developing a means of relating life stages to ages. The entrainment mortality imposed on organisms of age j is equivalent to the entrainment mortality imposed on organisms in the life stage or life stages which overlap age j. This concept leads to the following equations, which are analogous to Equations (SA) and (SB): m;K

=

1-

l -

L

K

1~1

k~l

L

K

1~1

k~l

II L D1k(l

- m;zk)

II L D1kexp(-E1kC;1l;),

(l IA)

(l IB)

where m;zk = the conditional entrainment mortality rate of life stage-[ organisms in region k during agej; C;1 = the fraction of age~j organisms in life stage l; and D 1k and E 1k are as previously defined. For example, if j is measured in weeks, and eggs require 4 days to hatch and larvae last 13 days, then C 0 •1 would equal 4/ 7 , C 0 , 2 would equal 3/ 7 , and C 0 , 3 , C 0 , 4 , et cetera, would equal zero; C 1 , 1 would equal zero, C 1 , 2 would equal 1, and C 1 , 3 , C i. 4 , et cetera, would equal zero; and so on. We introduce the parameter C;1 so that all the parameters in Equation ( 11) can be varied, but life stages still can be tracked because they are usually the minimum age classification in a sampling program. Mixing of organisms then occurs at a regular interval and is no longer dependent on life-stage duration. The objective, however, is to develop an

257


equation for the conditional entrainment mortality rate for all entrainable life stages during the entrainment period. In the same manner in which Equations (7) and (9) lead to Equation (10), Equations (8) and (9) can be combined to yield: S

mr

= 1-

J

L

K

~ R,

II II

s=l

J=O l=l k=l

~ D1kexp(-Es+J,1kCJ1tJ),

(12) where Es+J,lk = the instantaneous entrainment mortality rate constant of life stage-[ organisms in region k during time step s + j (per unit time).

!.-Spatial distributions of striped bass eggs and larvae in the Potomac River during 1974. a

TABLE

Region volume Transect (x 10-• m 3 )

5 6 7 8 9 10

200 200 200 200 150 100 100

11

Eggs (%)

Yolk-sac larvae (%)

Fin-fold larvae (%)

3.10 0.90 74.80 8.00 9.70 3.10 0.5

0 0.35 20.5 36.2 8.3 32.8 1.9

0 33.5 3.3 33.5 15.9 11.2 2.7

•Source: Polgar et al. (1976).

The average estimated incubation period for striped bass eggs in the Potomac River during 1974 was approximately 2 days (Polgar et al. 1975). Average durations for the yolk-sac and fin-fold larval life stages were estimated by Polgar et al. (1976) as approximately 12 and 11 days, respectively. The resultant conversion of weekly age-groups to life stages is presented in Table 2. The values used to represent the proportion of the total striped bass eggs spawned during each week in 1974 (R, in Equation (12]) is listed in Table 3. The proportions in this table were derived by multiplying the observed weekly densities of eggs at each transect (Polgar et al. 1975) by the volume of the region surrounding Application of the ETM each transect"(Table 1), then summing over all A nuclear-fueled electric generating station regions and dividing by the analogous sum takwas proposed for Douglas Point, at river kilo- en over all regions over all weeks. meter 98 on the east side of the Potomac River. The proposed plant was designed to have We used the ETM to estimate the conditional closed-cycle cooling. Therefore the mortality entrainment mortality that the proposed plant due to plant passage would have equaled 1.0. would have imposed on early life stages of Furthermore, the ratio of the intake to the avstriped bass (Morone saxatilis) based on biologi- erage regional concentration of each life stage cal data collected by the Chesapeake Biological (W) is assumed equal to 1.0 becauSe of the Laboratory during 1974 (Polgar et al. 1975). strong influence of currents in controlling movement during this part of the striped bass Biological Input Data

In practice, the Equation-(12) version of the ETM is most likely to be used. The parameter D in Equation (12) is defined in terms of average life-stage distributions over the entire entrainment period. If sampling error during each time interval is not too large, the parameter D also may be defined for each time interval by adding the s + j subscript (Ds+J.lk). The s + j subscript for the parameter E allows the instantaneous entrainment mortality rate constant for each life stage to change with each time step within the entrainment period, which is the principal reason for adopting the multiple-cohort approach.

The l 974 distributions of the egg and larval life stages (through 25 days of age) of striped bass in the Potomac River (D1k in Equation 02]) are listed in Table 1. These distributions are based on time-integrated absolute abundance estimates for geographical regions centered on each of seven transects (Polgar et al. 1976). For purposes of ETM application we assume that the reported distributions represent the entire population of striped bass during the egg and larval life stages.

2 .~Life-;iage-to-age conversion matrix for striped _bass in the Potumdc River during 1974.

TABLE

;

.

.

Life stage Age (weeks) l

2 3 4

Egg

0.2857 0 0 0

Yolk-sac larva

0:7143

Fin-fold larva

0

l

•o

0 0

.I

0,5714

258

BOREMAN ET AL.

3.-Temporal distribution of striped bass egg production in the Potomac River during 1974.

TABLE

Observed standing cropa Week

10-16 17-23 24-30 1-7 8-14 15-21 22-28

Apr Apr Apr May May May May

(X JQ-6)

%

13.389 210.507 71,135 1,287,890 32,579 23,876 4,661

0.81 12.80 4.33 78.34 1.98 1.45 0.28

a Source: Polgar et al. ( 1975).

life history and lack of data to reject this hypothesis.

Physical Input Data Water volumes of the seven geographical regions (V) are listed in Table 1. Transects were spaced to have equal water volumes between each transect pair and separations greater than the distance of a tidal excursion (Polgar et al. 1976). The maximum daily average water withdrawal rate (P) of the proposed plant would have been 190.8 x 10 6 m 3 per day from July through October, and 245.3 x 10 6 m 3 per day from November through January (Kohlenstein 1976). Because the Douglas Point site is at transect 7, all of the cooling water would have been withdrawn from the region surrounding this transect. Results

The available data enable use of Equation ( 12) to estimate the conditional entrainment mortality that will be imposed on the egg and larval life stages of striped bass. The conditional entrainment mortality rates for individual life stages are 0.142% for eggs, 0.234% for yolk-sac larvae, and 0.022% for fincfold larvae. The total conditional entrainment mortality rate through the fin-fold larval life stage is estimated to be 0.398%. This value, which accounts for entrainment only through 25 days of age, is consistent with the 0.6% estimated by Kohlenstein (1976) for striped bass through 90 days of age. Discussion

Violation of assumptions of the ETM may reduce the accuracy of the estimate of the conditional entrainment mortality rate significantly. Often the direction of the bias (whether the

estimate is an overestimate or underestimate of the true conditional entrainment mortality rate) will be known, but the degree of bias will not be known. The first assumption, and probably the most critical one, is that the data used to establish the spatial and temporal distributions of organisms are accurate. Problems associated with sampling gear biases, species and life-stage identifications, sampling design, and data interpretation reduce overall accuracy of the ETM estimate. However, such problems also reduce accuracy in estimates from any other methodology that relies on distribution and vulnerability data derived from field samples for computation and verification. A second assumption in the application of the ETM is that organisms redistribute instantaneously among regions of the water body between age-groups, but do not move among regions within each age-group. As such, nearfield depletion of organisms in the model due to entrainment mortality within one region is not offset by movement of other organisms of the same age into the depleted region during a given time interval. If the organism distribution data are collected during power-plant operation, the data bases for both the riverwide distribwtion and the W-factors inherently reflect the near-field depletion and the degree to which it is offset by organism movement during the time interval. If power-plant effects are large enough in relation to organism movement during the period of data collection to have substantially altered the distribution patterns of the organisms (through localized reduction in standing crops), the ETM estimates will be biased low. In addition, if the ETM is used to estimate conditional mortality rates for projected power-plant flow conditions that are different from those conditions corresponding to the period of data collection, further biases can be expected. The direction of these further biases will depend on many factors and can be controlled, to some extent, by making judicious choices for region size and length of the time intervals used in the model. Another salient aspect of the ETM methodology is the assumption that the organism distribution parameters are. being estimated from field measurements of the entire standing crop of each entrainable age-group. If.some mem-

259


bers of an entrainable age-group are located outside the area of sampling, then the ETM will overestimate the conditional entrainment mortality rate for the entire population. A final assumption concerns the uniformity of natural mortality within the modeled system. It is implicitly assumed in the ETM that the natural mortality rate of a given age or life stage is the same in all regions of the water body during the entire time that age or life stage is present within the entrainment period; that is, no differential natural mortality occurs among regions of the water body. If differential mortality occurs, and it is measurable, then a more generalized version of the ETM (Equation [5) in Boreman et al. 1978) can be used that incorporates age-, time-, and region-specific natural mortality rates. The probability of obtaining such information, however, is extremely low because of the problem of separating changes in abundance due to differential mortality from those due to movement. The conditional entrainment mortality rate should not be considered the sole measure of entrainment impact on a fish population. Density-dependent natural mortality may act to reduce or magnify the reduction in year-class strength caused by entrainment. Density-dependent natural mortality could be combined with conditional entrainment mortality in several ways. For example, in the ETM version that incorporates natural mortality (Equation [5) in Boreman et al. l 978), the natural mortality rate during a given time interval could be made a function of the standing crop of entrainable organisms at the beginning of the time interval, or the final ETM estimate of conditional entrainment mortality could be multiplied by a coefficient that accounts for compensatory capability of the organisms during the entrainment period. Due to the complexity and uncertainty of compensatory responses of fish populations, density-dependent mortality generally should be considered extrinsic to the estimate of the conditional entrainment mortality rate. We recommend use of the ETM whenever data describing the spatial and temporal distributions of entrainable organisms are available. Attempts to simulate these distributions in entrainment models by incorporating hydrodynamic transport equations have been criticized because the biological parameters used in these

models are too important, too vaguely known, and too simple to mesh with the hydrodynamic detail necessary to describe the systems (Swartzman et al. l 978). Entrainment equations that are simpler than the ETM can be used. However, because it is incumbent upon the investigator to incorporate as much information as possible in assessing or predicting entrainment impacts of power plants, use of the ETM should be advantageous in many, if not most, cases. Acknowledgments

L. W. Barnthouse, P. Kanciruk, and P. Rago critically reviewed the manuscript and provided many useful suggestions. Sigurd W. Christensen's contribution was supported by the United States Nuclear Regulatory Commission under Interagency Agreement DOE 40-550-75 with the United States Department of Energy under contract W-7405-eng-26 with Union Carbide Corporation. Publication 163 l, Environmental Sciences Division, Oak Ridge National Laboratory. References BOREMAN, j., C. P. GOODYEAR, AND S. W. CHRISTENSEN. 1978. An empirical transport model for evaluating entrainment of aquatic organisms by power plants. United States Fish and Wildlife Service, FWS/OBS-78/90, Ann Arbor, Michigan, USA. ERASLAN, A.H., w. VAN WINKLE, R. D. SHARP, S. w. CHRISTENSEN, C. P. GooDYEAR, R. M. RusH, AND W. FULKERSON. 1976. A computer simulation model for the striped bass young-of-the-year population in the Hudson River. Oak Ridge National Laboratory, Environmental Sciences Division Publication 766, ORNL/NUREG-8, Oak Ridge, Tennessee, USA. GooDYEAR, C. P. 1977. Mathematical methods to evaluate entrainment of aquatic organisms by power plants. United States Fish and Wildlife Service, FWS/OBS-76/20.3, Ann Arbor, Michigan, USA. HESS, K. W., M. P. S1SSENWINE, AND s. B. SAILA. 1975. Simulating the impact of the entrainment of winter flounder larvae. Pages 1-29 in S. B. Saila, editor. Fisheries and energy production. Lexington Books, D. C. Heath and Company, Lexington, Massachusetts, USA. KoHLENSTEIN, L. C. 1976. Power plant site evaluation final report-Douglas Point site. Maryland Power Plant Siting Program, JHU PPSE 4-2, volume 1, part 1, Annapolis, Maryland, USA. LAWLER, J. P. 1976. Physical measurements: their significance in the prediction of entrainment effects. Pages 59~91 in L D. Jensen, editor. Third

260

BOREMAN ET AL.

national workshop on entrainment and impingement. Ecological Analysts, Melville, New York, USA. PoLGAR, T. T.,]. A. M1HURSKY, R. E. ULANow1cz, R. P. MoRGAN, II, AND]. S. WILSON. 1976. An analysis of 1974 striped bass spawning success in the Potomac Estuary. Pages 151-165 in M. Wiley, editor. Estuarine processes, volume 1. Academic Press, New York, New York, USA. PoLGAR, T. T., R. E. ULANow1cz, D. A. PYNE, AND G. M. KRAJNIK. 1975. Investigations of the role of physical transport processes in determining ichthyoplankton distributions in the Potomac River.

Maryland Power Plant Siting Program, PPRP-11/ PPMP-14, Annapolis, Maryland, USA. RICKER, W. E. 1975. Computation and interpretation of biological statistics of fish populations. Fisheries Research Board of Canada Bulletin 191. SWARTZMAN, G. L., R. B. DERISO, AND C. COWAN. 1978. Comparison of simulation models used in assessing the effects of power-plant-induced mortality on fish populations. United States Nuclear Regulatory Commission, NUREG/CR-0474, Washington, District of Columbia, USA.