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North American Journal of Fisheries Management 23:1–21, 2003q Copyright by the American Fisheries Society 2003

Designing Optimal Flow Patterns for Fall Chinook Salmon in aCentral Valley, California, River

HENRIETTE I. JAGER*Environmental Sciences Division,Oak Ridge National Laboratory,

Oak Ridge, Tennessee 37831-6036, USA

KENNETH A. ROSE

Coastal Fisheries Institute and Department of Oceanography and Coastal Sciences,Louisiana State University, Baton Rouge, Louisiana 70803-7503, USA

Abstract.—Widespread declines in stocks of Pacific salmon in the genus Oncorhynchus highlightthe need for research to find new and effective management strategies for recovery. Two recoveryobjectives are (1) to ensure that recruitment is adequate to rebuild self-sustaining populations and(2) to maintain phenotypic diversity. This study seeks to understand how seasonal flow patternsin a flow-regulated California river might be managed to attain each of these recovery objectives,specifically for the fall and late-fall runs of chinook salmon O. tshawytscha. We ask two questions:(1) Does the optimal pattern of seasonal flows change as the amount of water available is constrainedby droughts or diversions of flows? and (2) How do optimal flow regimes designed for the twoconservation objectives differ? We coupled simulated annealing with a recruitment model to findflow regimes that maximize either the number of smolt out-migrant ‘‘recruits’’ (MR) or the variationin spawning times among recruits (MV). Optimal flow regimes identified for both the MR andMV objectives changed as we increased the annual quantity of water available, allocating higherflows during the spring and fall seasons. Flow regimes that optimized the MR and MV objectiveswere different. For example, the MV flow regime with unlimited annual flow provided a pulse ofhigh flow 2 weeks before the peak spawning date of the minority late-fall run. Simulated recruitsproduced by MV flow regimes were fewer in number—and had parents that spawned later andover a wider range of dates—than recruits produced by MR flow regimes. Although these resultshave not been verified by empirical studies, they demonstrate the potential for managing specieswith special conservation status by combining state-of-the-art numerical optimization methodswith mechanistic ecological models.

Anadromous salmonids play a significant roleas keystone species in the river ecosystems drain-ing to the Pacific coast of North America (Willsonand Halupka 1995; Cederholm et al. 1999). His-torically, Pacific salmon in the genus Oncorhyn-chus permeated coastal rivers and streams fromAlaska to southern California. A tendency to re-turn to spawn in their natal river allowed salmonpopulations to adapt to local environmental con-ditions (Waples 1995) and led to an adaptive ra-diation in life history traits for chinook salmon O.tshawytscha (Healey 1994). Collectively, salmonpopulations diversified into an array of populations(also known as ‘‘runs,’’ ‘‘races,’’ or ‘‘stocks’’)with life histories distinguished by spawning timeand place. The temporal diversity and geographicdistribution of salmon populations resulted in thepresence of one life history type or another during

* Corresponding author: jagerhi@ornl.gov

Received April 26, 2001; accepted April 12, 2002

most seasons of the year in coastal rivers through-out their range. These spawning aggregations sup-port dozens of bird, mammal, and fish predators,and decomposing salmon carcasses provide a sig-nificant nutrient subsidy to the surrounding ter-restrial ecosystem (Bilby et al. 1996).

Today, the majority of Pacific salmon stockshave declined, and healthy stocks (those exceedingone-third of their historical abundances) are out-numbered by stocks that are either currently at riskor recently extirpated (Nehlsen et al. 1991;Huntington et al. 1996). Life history diversityamong salmon species has also declined becausehabitat degradation has differentially affectedsome races. This loss of life history variation isof particular concern for Pacific salmon, both froma conservation biology (i.e., single species) per-spective and from an ecosystem perspective. Froma conservation biology perspective, salmon spe-cies are defined by an evolutionary biology thatpromotes diversity in life history, and by a meta-population structure that requires diversity to per-

2 JAGER AND ROSE

sist. Homing to natal streams and infrequent stray-ing rates promote local adaptation, and thereforephenotypic diversity. This diversity of adjacentpopulations in time and space increases the like-lihood that straying adult spawners will recolonizelocally extinct runs and thereby enhance the long-term persistence of the metapopulation (Li et al.1995; Stanford et al. 1996). One might considersalmon as having a temporal, as well as a spatial,metapopulation structure supported by strayingfrom populations with different spawning times.From an ecosystem perspective, Pacific salmonrepresented a relatively stable component of eco-systems because of the temporal and spatial par-titioning of river spawning habitat among popu-lations. Efforts to restore salmon populations typ-ically focus on two recovery objectives: (1) re-building the size of salmon populations, and (2)protecting salmon populations with unique geneticand phenotypic qualities.

Flow regulation is an important policy toolavailable for meeting these two conservation ob-jectives for salmon (National Research Council1996). Salmon declines have been attributed tomany factors, including the ‘‘4Hs’’: harvesting,hydropower, habitat, and hatcheries (Lackey1999). The alteration of natural river flows, bydiverting water for hydropower and for other so-cial uses, has contributed to decreases in salmonspawning habitat, both in quality and quantity.River flow is viewed by Poff et al. (1997) as amaster variable that regulates the ecological in-tegrity of rivers. Flow manipulations will only beeffective as a tool for restoring salmon populationsif the relationship between seasonal patterns ofinstream flow and salmon recruitment is under-stood.

Flow effects differ during different life stagesand seasons. For example, elevated flows duringthe alevin life stage has been linked with reducedsurvival of salmonids (Jensen and Johnsen 1999),whereas higher spring flows may increase survivalof spring out-migrants (Kjelson and Brandes 1989;Kope and Botsford 1990; Cada et al. 1993; Speed1993; but see Williams and Matthews 1995). Re-duced temperature-related mortality and reducedpredation are two possible factors producing a pos-itive survival–flow relationship in spring. Becausejuvenile salmon have low tolerance for elevatedstream temperature, high spring flows provide anindirect benefit by slowing the rise in river tem-peratures during late spring and early summer. Pre-dation on migrating juveniles may be lower duringhigher flows for two reasons. First, predation ef-

ficiency is curbed at high river flows by higherturbidity, higher water velocities, and an increasedtendency for prey to form aggregations (Petersonand DeAngelis 1992). Second, faster downstreammigration at high flows shortens the duration ofexposure to predation risk (Berggren and Filardo1993), but it may also hasten exposure to highpredation risk in the estuary.

The effect of river flow on salmon recruitmentat times of year other than spring is less clear.Higher flows in fall attract adults waiting to mi-grate upriver to spawn (e.g., Fleming and Gross1994). Elevated flows may facilitate swimmingpast natural and artificial barriers, or they maymerely serve as a cue for migration. High fall flowsare correlated with lower temperatures that benefitfemales migrating upriver by ensuring that eggsare not damaged before spawning (IndependentScientific Group 1996). The flow level during thebuilding of redds influences later exposure to de-watering at lower flows and to scouring duringflood events, favoring stable fall and winter flows(Becker et al. 1982; Stevens and Miller 1983).Summer flows can be very critical for the juvenilelife stage of spring races because they remain inthe river over summer before migrating to sea.

In this paper, we use a numerical optimizationtechnique coupled with a recruitment model to de-sign optimal seasonal flow patterns for salmon.Our analysis builds on earlier work linking flowmanagement to chinook salmon recruitment (Bar-tholow and Waddle 1995; Jager et al. 1997). Weuse a slightly modified version of the Oak RidgeChinook Model (ORCM) to simulate the mainlinkages between salmon biology and instreamflow (Jager et al. 1997). We focus on the fall andlate-fall runs of chinook salmon at the southernextreme of their range in the lower Tuolumne Riv-er, a tributary of the San Joaquin River, California.

We used optimization methods to identify theoptimal pattern of seasonal flow for two differentmanagement objectives: (1) maximizing overallrecruitment and (2) maximizing variation in runtimes among recruits. Recruitment is defined hereas the number of individuals that successfullyreach the smolt stage and emigrate from freshwaterto saltwater. The run time of a recruit is definedas the date that a recruit was spawned by its par-ents. For each of the two objectives, we determinedhow the optimal pattern of seasonal flow changesin response to changes in the annual amount ofwater available. Decision-makers can use this in-formation to adjust instream flow policies to the

3DESIGNING OPTIMAL FLOW PATTERNS

hydrologic conditions (e.g., wet versus dry) in agiven year.

Our analysis uses chinook salmon, a well-studied species, to demonstrate how optimizationmethods can be coupled with a biologically de-tailed recruitment model to identify optimal flowconditions. We recognize that our understandingof how flow affects the growth, survival, repro-duction, and movement of salmon is incomplete,and the specific recruitment model we used is oneof many possible model formulations. Despitethese limitations, our approach can yield insightsinto optimal flows for chinook salmon and illus-trate the general approach of coupling optimiza-tion methods to mechanistic models. Our methodshould be applicable to many other species forwhich environmental effects on recruitment arecomplex and for which it is important to identifyoptimal environmental conditions for recruitment.

Central Valley Chinook Salmon

The Central Valley of California historicallysupported substantial numbers of both spring- andfall-run chinook salmon (Myers et al. 1998; Yo-shiyama et al. 2000). Although spring chinooksalmon were historically more abundant than fallchinook salmon, they now represent a much small-er fraction of the fishery. Fall chinook salmon stillsupport a significant ocean fishery due, in part, tohatchery production (Moyle 1994). The spring andwinter runs have been extirpated from the San Joa-quin River. Dams blocking access to headwaterand spring-fed streams have resulted in populationdeclines and federal listing of the spring and winterruns in the Sacramento River as endangered underthe Endangered Species Act (Fisher 1994; Healey1994; Myers et al. 1998).

Fall chinook salmon actually include two runs:a fall run and a late-fall run. Genetic differencesbetween these two runs indicate that they werereproductively isolated, probably by temporal andspatial segregation of spawning (Nielsen et al.1994). Fall-run adults spawn between October andDecember, whereas late-fall adults spawn betweenJanuary and April. Historically, both fall runs oc-cupied the Sacramento and San Joaquin river ba-sins (Hatton and Clark 1942; Fisher 1994). Adultsof the late-fall run spawned in upper main-stemrivers, where summertime water temperatures re-mained low enough for juvenile growth (Fry 1961;Fisher 1994). In the Central Valley, late-fallspawners lost access to their historical spawninghabitat following construction of the Friant Damon the San Joaquin River and the Shasta Dam on

the Sacramento River. The two runs and the tworiver basins are regulated jointly as the CentralValley fall-run Evolutionarily Significant Unit(ESU; National Marine Fisheries Service 1999),which is not currently listed by the federal gov-ernment as threatened or endangered. Three linesof evidence suggest that the late-fall run has aconsiderably greater risk of extinction than the fallrun: (1) population sizes are smaller (Yoshiyamaet al. 2000), (2) population sizes are declining fast-er (Yoshiyama et al. 2000), and (3) two races(spring and winter runs) that also used spawninghabitat above dams are now listed or extirpated.Both fall runs are considerably more depressed inthe San Joaquin River basin than in the SacramentoRiver basin (Myers et al. 1998). According toHuntington et al. (1996), both the fall and late-fallruns are at risk of extirpation from the San JoaquinRiver basin.

Fall chinook salmon spend their adult lives inthe ocean. At some point between ages 2 and 5,adults migrate into rivers during the fall to spawn(Table 1). Each female digs a redd in the gravelriver bottom. During courtship, she releases hereggs into her redd. After fertilization of the eggsby one or more males, the female buries the eggs.Eggs incubate through the winter, hatch as alevins(nonfeeding larvae) into intergravel spaces, andemerge from redds as fry (defined here as presmoltjuveniles) in the spring. The emergent fry of fallchinook salmon feed on invertebrates along rivermargins for the first month or two and graduallymove downstream. Fry may exit tributaries in win-ter or spring to rear in the lower main stem andupper estuaries before becoming smolts. The pro-cess of smoltification enables them to tolerate salt-water and migrate to the ocean.

This study focuses on the Tuolumne River, atributary of the San Joaquin River. The LaGrangeDam, at 83.7 km above the confluence, blocks up-stream migration of adult salmon returning tospawn. The average natural annual flow estimatedbelow LaGrange Dam between 1897 and 1923 was2,390 hm3 (1 hm3 5 106 · m3; McBain and Trush2000). The average impaired annual flow mea-sured below LaGrange Dam between 1971 and1999 was 952 hm3 (McBain and Trush 2000; Pat-erson 1987:20–23). The difference between nat-ural and impaired flow is accounted for by up-stream water diversions.

Methods

The Oak Ridge Chinook Salmon model.—TheOak Ridge Chinook Salmon model (ORCM; Jager

4 JAGER AND ROSE

TABLE 1.—Timing of events leading to recruitment of fall-run and late-fall-run chinook salmon in the Central Valley,California, and the main factors influencing the growth, development, and survival of each early life stage simulatedby the Oak Ridge Chinook Salmon Model (FERC 1996).

Life stage Fall run Late-fall runInfluences on growth

and development Influences on survival

Egg

Alevin

Oct–Dec

Dec–Mar

Jan–Apr

Mar–May

River temperature

River temperature

TemperatureWeighted usable areaDensity of spawnersWeighted usable areaDensity of spawners

Fry Jan–Apr Apr–Jun River temperatureFish weightFish size (rank)

Fish sizePredator densityJuvenile densityTemperature

Smolt Mar–Jun Oct–May River temperatureFish weight

Size of smoltPredator densityJuvenile densityTemperature

et al. 1997) is a spatially explicit and individual-based model of fall chinook salmon recruitmentin a river below a dam. The model links a spatiallyexplicit representation of river habitat with a bioticmodel of chinook salmon reproduction, develop-ment, growth, and mortality. The river habitatchanges seasonally and includes important spatialgradients (e.g., temperature, predator densities)between upstream spawning areas and lowerreaches inhabited during out-migration. The bioticcomponent uses a daily time-step to simulate co-existing life stages, as individuals grow, developfrom one life stage to the next, move, and die(Table 1). The ORCM simulates the river phase ofchinook salmon ecology, beginning with adults en-tering the river to spawn. For each redd, we sim-ulate the daily development and mortality of eggand alevin life stages. After emerging from redds,the daily development, growth, mortality, anddownstream movement of individual juveniles(defined here as fry and smolts) is simulated, cul-minating in the migration of smolts from the river(i.e., recruitment). The values and definitions ofmodel parameters are listed in Table 2.

Habitat component.—The biotic events leadingfrom upriver migration of spawners to the out-migration of recruits are simulated in a spatiallyexplicit river habitat represented by a series ofadjacent, 1.6-km segments differing in the pro-portion of riffle and pool habitat, temperature, andflow (at confluences with tributaries or diversions).Simulated average daily water temperature in eachriver segment is determined by allowing water re-leased by the dam (about 128C year-round; FERC1996) to equilibrate to the air temperature as thewater travels downstream. The simulated rivertemperature of each segment depends on daily air

temperature, dam release temperature, and flowrate, which controls the rate of travel downstream.Daily flow in each segment is generated as part ofthe optimization procedure and used to drive theORCM.

Each river segment is assigned a habitat capacityfor each life stage (numbers/m2) that depends onempirical relationships between the amount ofsuitable habitat (weighted usable area or WUA)and daily average flow. The WUA relationshipswere estimated from results of an instream-flowstudy conducted in the Tuolumne River for eachlife stage and for two mesohabitats: riffle habitatand run–pool habitats, where runs and pools aretreated as one mesohabitat (EAEST 1992b). Thetotal capacity of each segment is a weighted sumof that provided by its riffles and that provided byits runs and pools.

Upriver migration and spawning.—Simulationsbegin with the migration upstream of 5,000 adults(4,673 fall run and 327 late-fall run) to the trib-utary represented by the model. This is roughlythe average annual number of spawners countedbetween 1971 and 1988 in the Tuolumne River(EAEST 1992a). Individual spawner sizes aredrawn from a normal distribution. The initial dis-tribution of spawning times of migrating adultspawners follows a triangular distribution with astart date, peak date, and end date for each run.However, model spawners delay upstream migra-tion if the water temperature at the mouth of thetributary or discharge from the tributary is belowa threshold. The number of migrants on each dayincludes the proportion calculated from this dis-tribution, plus those unable to migrate on previousdays.

On the day of spawning, each female spawner

5DESIGNING OPTIMAL FLOW PATTERNS

TABLE 2.—Parameter values used in the Oak Ridge Chinook Salmon Model simulations for the Tuolumne River,California. Parameter sensitivity is measured by the standardized regression coefficient, which varies from 21 to 11and reveals both the direction and magnitude of a parameter’s effect. We present sensitivities to two model predictionsseparated by commas: the simulated number of out-migrants and the peak date of out-migration. Those parametersexcluded from the Jager et al. (1997) analysis are indicated by a blank, and those with a coefficient smaller than 0.05are shown as zeroes.

Name Value Sensitivity Parameter definition

afecalamoveamoveArat

3,200.20.00050.250.16

250

10.05, 00, 00, 0

Intercept of fecundity relationship with fish lengthIntercept of relationship between fry length and weightMovement rate at zero flow for fry (d/km)Movement rate at zero flow for smolts (d/km)Scaling ratio for river size against Columbia River

AreddAterrBterrbfecbl

2160.001482.61

109.42.136

0, 00, 00, 20.13

Average defended redd area (43 actual redd area; m22)Coefficient in relationship between territory and fish lengthExponent in relationship between territory and fish lengthSlope of fecundity versus fish length (cm)Exponent of relationship between length and weight for fry

bqtempcmoveDDalvDDeggs

0.526.0 3 1026

395.8500

0, 00, 0

Power function exponent relating velocity to flowSlope between travel time (d/km) and flow (m3/s)Degree-days required from hatching to emergence (8C)Degree-days required from egg laying to hatching (8C)

DDsmoFspawnKtempLminLspavg

1,0820.5

20.000670

688

0, 10.150, 00, 0

Degree-days required to develop into a smolt (8C)Minimum flow needed to upmigrate and spawn (m3/s)Temperature equilibration rate coefficient (s21)Minimum size required to develop into a smolt (mm)Average length of adult spawners (mm)

LspsdLspminLspmaxLsegspNesc

74400

1,40040.5

5,000 10.05, 0

Standard deviation of spawner lengths (mm)Minimum length of spawning adults (mm)Maximum length of spawning adults (mm)Stream distance below dam used for spawning (km)Fall-run escapement (number of adults)

PcapPlatePpockPsmoPup

0.00010.070.1250.60.4

0, 00, 00, 0

Maximum probability of successful prey captureFraction of total chinook spawners in late-fall runAverage fraction of egg pockets superimposedFraction of maximum intake obtained by smoltsProbability of upstream movement at low temperatures

PminPmaxSminSrat

0.080.60.99970.44

0, 00, 010.85, 20.340, 0

Minimum fraction of maximum ration at feeding stationMaximum daily ration (obtained by largest juveniles)Daily survival rate in marginal habitatFraction of adult spawners that are female

SwaittavgTavgTavoidTmax

14Apr 4162230

0, 0

Period from egg laying to female departure (d)First date that air temperature reaches TavgAverage annual air temperature (8C)Lower threshold for behavioral avoidance (8C)Maximum annual air temperature (8C)

TspawnTULTUPmaxUPmax

17.825

Apr 20Dec 22

0, 010.12, 20.34

10.16, 10.70

Upper temperature threshold for chinook salmon spawning (8C)Upper lethal temperature for chinook salmon (8C)Latest date of late-fall spawning migrationLatest date of fall spawning migration

UPminUPminUPpeakUPpeak

Jan 1Oct 1Mar 1Oct 27

10.11, 10.16

0, 0

Earliest date of late-fall spawning migrationEarliest date of fall spawning migrationPeak date of late-fall spawning migrationPeak date of fall spawning migration

is assigned to a spawning location that is identifiedby its river segment and its site within the segment.The river segment is chosen at random from atriangular probability distribution that imposes apreference for segments closer to the dam. Seg-ments with a larger proportion of riffle habitat con-tain more habitat suitable for spawning and in-cubation, as measured by the weighted usable areaon day t (WUAt; EAEST 1992a). The site within

the segment points to a randomly selected entryin a ranked list of potential redd sites, where thetotal number of suitable sites varies daily in re-sponse to changing flows. Each river segment hasa maximum number of suitable spawning sitesavailable under optimal flow conditions. The mod-el assigns sequential habitat quality ranks to thesesites. On a given date, the number of suitablespawning sites, Ns , may be less than the number

6 JAGER AND ROSE

available under optimal flow conditions, causingsites with higher ranks to become unsuitable (Fig-ure 1).

WUAtN 5 , (1)s average quality 3 Aredd

where average quality is estimated as the midpointof minimum and maximum suitability index as-signed to suitable redd sites in the model, and Aredd

is average redd area. This approach captures theeffects of changing flow on survival of eggs andalevins at both ends of the spectrum (i.e., scouringduring high flows and dewatering during lowflows).

Survival and development of eggs and alevins.—The model tracks the number of eggs in each reddover time. At the time of spawning, the femaledeposits her eggs; the number of eggs increaseslinearly with female length, with intercept afec andslope bfec. Daily flow-related survival of eggs andalevins is 0 at sites with rank values exceeding thenumber of suitable sites. Daily survival amongsuitable sites increases from Smin at the lowestquality site (site with rank Ns) to 1 at the highestquality site (the site with rank 1; Figure 1C). Twoother sources of mortality of early life stages aresuperimposition and temperature-related mortali-ty. When a later spawner in the model selects thesame site as a previous spawner with offspring thathave not yet emerged, superimposition causes abinomial fraction of older eggs to be killed. Su-perimposition of previous redds occurs most oftenwhen redd densities are high and spawning habitatis scarce. Temperature-related survival is highestat moderate temperatures (88C for eggs; 58C foralevins) and drops to zero at extremes tempera-tures (below 08C or above 17.28C; Murray andMcPhail 1988).

Incubation and development of eggs takes placeover the period required to accumulate a fixednumber of degree-days (Murray and McPhail1988). The duration of the alevin stage is deter-mined by the number of posthatching degree-daysrequired to achieve the alevin stage (Murray andMcPhail 1988). For both these life stages, we dis-count degree-days accrued at temperatures below58C by 50%.

Growth and development of fry and smolts.—Alevins emerge from redds at 30–40 mm in length(Murray and McPhail 1988; EBMUD 1992). Themodel simulates each juvenile chinook salmon asan individual after it emerges from the redd. Eachmodel fry develops into a smolt when it has ac-

cumulated sufficient degree-days after emergenceand has reached a minimum length (Jager et al.1997).

On each day, t, the model simulates juvenilegrowth (weight gain is DW in g wet weight) usingthe bioenergetic model developed by Stewart et al.(1983):

W 5 W 1 DW,t11 t (2)

where wet weight gain, DW, equals consumptionminus energetic costs (egestion, excretion, specificdynamic action, and respiration).

The length, Lt11, of a juvenile chinook salmonincreases only when it is in good physiologicalcondition and experiences a positive weight gain:

1/blWtL 5 max L , . (3)t11 t 1 2[ ]al

Daily consumption is modeled by calculatingration as a proportion of maximum daily intake,which depends on water temperature and fishweight. The ration obtained by an individual de-pends on its rank (i.e., the number of larger, com-peting juveniles in its river segment). Energeticcosts depend on temperature and fish weight.

Growth rates vary among individuals becauseof differences in their locations and sizes. We sim-ulate variability among individual fry growth ratesby assigning higher quality feeding stations tolarger fish. Each day, fry living in a segment areranked by size. Feeding stations are reassigneddaily, such that the larger fry receive the higherquality stations that provide a higher rate of preyintake (Figure 1C). If there are more fry than sta-tions, those fry lacking a suitable feeding stationdo not grow. A resident fry may be shifted to alower- or higher-ranked feeding station as largeror smaller fry immigrate into the segment, as newfry emerge, or as resident fry die or leave.

We assume that a site with quality X (Pmin # X# Pmax) provides a fish with fraction P 5 X of itsmaximum daily feeding ration. The same proce-dure used to define the number of spawning sitesfrom spawning habitat capacity, WUAs, is used todefine the number of feeding sites based on ju-venile habitat capacity, WUAjuv. The number ofsuitable feeding sites is the current WUAjuv divid-ed by the average size of feeding ‘‘territories’’ forindividuals in the segment (Figure 1A). Feedingstations are allocated to individual fry in inverseorder of size (larger individuals first) until the totalarea of stations reaches WUAfry for the river seg-

7DESIGNING OPTIMAL FLOW PATTERNS

ment. Territory size, Tsize (m2), is derived for eachfry from a relationship with fish length, L (mm)from Grant and Kramer (1990):

B terrT 5 A L , (4)size terr

We assume that each smolt obtains a fixed pro-portion of maximum ration and does not competefor a feeding station, focusing instead on down-stream migration.

Juvenile movement.—The ORCM allows eachjuvenile to disperse from the river segment of birthto other river segments and, eventually, out of theriver. We assume different motivations for move-ments by fry and smolts. Smolt movements aredirected toward migration out of the river, whichprogresses each day. Fry are motivated by thesearch for unoccupied rearing habitat with low pre-dation risk and good conditions for growth, whichcan result in continued occupation of a single site.Simulated fry movement depends on fry density,habitat availability, and river flow and has a ten-dency to progress downstream. The probability ofupstream movement was calibrated so that pre-dicted rate of downstream movement matched theobserved rate of downstream movement at differ-ent locations in the Tuolumne River. At tempera-tures above Tavoid, model fry tend to move up-stream to avoid lethal temperatures (EPA 1971).The probability of upstream movement increasesfrom Pup at temperature Tavoid to 1.0 at TULT.

Once a simulated juvenile decides to move, itsmovement occurs at a rate that depends weakly onriver flow in the segment, Q (m3/s). The model usesa linear relationship between mean travel time (d/km) during downstream movement and Q:

travel time 5 a 1 c · A · Q,move move rat (5)

where cmove is the flow coefficient fitted to datareported by Berggren and Filardo (1993) for sub-yearling chinook in the Columbia River and Arat

accounts for differences in river size between theColumbia and the Tuolumne rivers. To adapt thisrelationship for fry in the Tuolumne River, amove

was adjusted so that a maximum of 30 d was re-quired for fry to travel 122 km (Berggren and Fi-lardo 1993). For upstream movement of fry, thesign of cmove is reversed.

To simulate out-migration, the ORCM assumesthat environmental influences indirectly act on mi-gration times by hastening or delaying develop-ment into smolts. For smolts, a variety of cues(e.g., flow, change in flow, water temperature, pre-cipitation, turbidity, photoperiod, smolt density,

the phase of the moon) can produce pulses of em-igration (EBMUD 1992). The ORCM assumes thatthe necessary cues are present and that out-mi-gration begins when fry become smolts. The dailydistance traveled by a given smolt depends on flow(equation 5) and is always in a downstream direc-tion.

Juvenile mortality.—The ORCM simulates mor-tality resulting from exposure to extreme watertemperatures, premature emigration, and preda-tion. Juveniles that remain in a segment with watertemperatures above TULT (Brett 1952) die after 1 dof exposure. The model allows juveniles to avoidhigh, sublethal temperatures by increasing thelikelihood of upstream movement.

Mortality may occur when fry leave the spawn-ing tributary before smolting. Premature emigra-tion is a more significant source of mortality whenfry densities exceed the number of feeding stationsbecause slower growth causes individuals to movedownstream more frequently.

Fish predators, including smallmouth bass Mi-cropterus dolomieu, largemouth bass M. salmoides,and Sacramento pikeminnow Ptychocheilus gran-dis, forage on chinook juveniles. Predator densitiesare specified for each of three river reaches definedby tributary confluences. Within each reach, pred-ator densities are lower in segments with a highproportion of riffle habitat.

The original version of the ORCM simulatedindividual predator–prey encounters (Jager et al.1997). This approach was computationally inten-sive, and sensitivity analysis indicated that ORCMmodel results were insensitive to the predation-related parameters (Jager et al. 1997). In the anal-yses here, we used a computationally more effi-cient option to simulate predation by replacing theindividual encounters simulated between juvenilesalmon (X 5 number of prey) and their predators(Y 5 number of predators) with the type II func-tional response (Holling 1959) shown in equation(6). We calibrated the probability of capture toobtain the same average level of predation as inthe simulations that used individual encounters:

P · XYcapPredation risk 5 . (6)1 1 P · XYcap

Testing and sensitivity analysis of the ORCM.—Jager et al. (1997) reported on the results of cor-roboration and sensitivity analysis of the ORCM.We summarize the results here. Corroboration con-sisted of comparing model predictions of juvenilegrowth and population size to field data collected

8 JAGER AND ROSE

FIGURE 1.—Model representation of habitat effects on survival in redds and juvenile foraging. The model (A)represents habitat capacity as a function of river flow; (B) specifies a proportional relationship between the numberof suitable sites and habitat capacity; and (C) specifies an inverse relationship between daily habitat-related survivalin redds (ration) and the rank of the redd site (feeding station). To determine survival (ration) at a flow of 5 m3/s, followthe arrows in panel A to calculate habitat capacity from stream flow, then calculate the number of suitable sites

9DESIGNING OPTIMAL FLOW PATTERNS

←

from habitat capacity in panel B, and finally calculate the survival (ration) at the site from its rank in panel C.Sites with a rank exceeding the number of suitable sites (e.g., 10) have zero survival (ration).

in the Tuolumne River. Jager et al. (1997) com-pared the length distribution of simulated fry tothe observed average, minimum, and maximumsizes from weekly seining catches in the TuolumneRiver from January to May 1987. The average pre-dicted and measured juvenile lengths had a max-imum difference of 6 mm. Both the model pre-dictions and the field data showed a great deal ofvariation among individuals. Although the maxi-mum length increased as spring progressed, theminimum length remained constant at around 30mm, suggesting the continual appearance of newlyemerged fry. A second comparison was made be-tween simulated population size at one date and atemporal and spatial snapshot of population sizeobtained using mark–recapture in early May 1987.An estimated 3,341 6 935 (95% confidence limits)juvenile chinook salmon inhabited the 360-mstretch of river included in this study. We extrap-olated that estimate to 14,920 6 4,174 for our1,609-m-long river segment. This extrapolatedfield estimate was similar to ORCM’s predictionof 15,443 juveniles in segment 3 on May 4, 1987.Although model predictions were deemed suffi-ciently similar to observed values, there is ex-tremely high variability in population size duringthis period when juveniles are leaving the system.Direct corroboration of the predicted number ofout-migrants was not possible because emigratingsmolts were not counted.

To evaluate parameter sensitivities of theORCM, model parameters were varied and usedto simulate recruitment under flow and tempera-ture conditions for the 1986–1987 year. Jager etal. (1997) identified a subset of important param-eters by excluding those with a strong basis in fielddata, and therefore low uncertainty, and those re-dundant in their effects with other parameters. Ja-ger et al. generated 5,000 parameter combinationsdrawn by Latin-hypercube sampling from trun-cated Gaussian distributions with specified meanvalues, a coefficient of variation of 1%, and nocorrelations among parameters. For each set of pa-rameter values, ORCM predicted a number of re-sponses, from which we have selected the twomost relevant to this optimization: number of re-cruits and the peak date of emigration. The stan-dardized regression coefficient obtained by re-gression between 5,000 model predictions and the

parameter values that produced them provided anindex of sensitivity. The same parameters tendedto influence both predictions (Table 2); redd mor-tality in marginal habitat had the largest effect onthe number of recruits, and the final date of up-stream migration had the largest effect on the peakdate of out-migration. The earliest date of up-stream migration by spawners and the upper lethaltemperature for juveniles also had important ef-fects on both the number of recruits and the peakdate of out-migration.

Seasonal flows that maximize recruitment.—Weused simulated annealing (Metropolis et al. 1953)to find a seasonal flow regime that maximizedmodel-predicted salmon recruitment in hydrologicyears ranging from wet to dry. Our first objectivewas to maximize the predicted number of out-mi-grating smolts (i.e., recruitment). The freshwaterportion of the chinook salmon life cycle betweenupstream migration in the fall and out-migrationin the spring was divided into 20 periods, each 2weeks, characterized by a fixed average daily riverflow. The flow assigned to each period is one valuein a vector, Q, of 20 decision variables manipu-lated to maximize the simulated number of emi-grating smolts. The optimization program foundthe flow vector that maximized Z 5 F(Q), whereZ is the number of predicted recruits and F denotesORCM’s prediction of the objective function (i.e.,recruitment).

This optimization problem is of limited practicalinterest because it assumes that the annual quantityof river flow is unlimited. Therefore, we alsosought optimal flow regimes that maximized Z,subject to a constraint on the total amount of wateravailable annually, Qtot. We repeated the optimi-zation for Qtot values that increased geometrically:122, 245, 489, and 979 hm3. The threshold valuesabove correspond to the 20th, 45th, 60th, and 78thpercentiles of distribution of historical annualflows (e.g., 20% of years had annual flows of 122hm3 or less and 60% of years had annual flows of489 hm3 or less). In addition, we assumed thatflows within each 2-week period were only con-strained by the annual total and not by short-termconstraints, such as daily demands by irrigators,that might restrict daily flows. Summer flows be-tween July 8 and September 30 were not consid-ered relevant for fall chinook salmon because most

10 JAGER AND ROSE

juveniles emigrate by then and water temperaturesare too high for survival of those remaining.Therefore, we set daily average flows for July 8through September 30 to be 1.42 m3/s for the pur-pose of calculating an annual total flow.

All optimizations assumed 5,000 adult spawn-ers, which is roughly the average historical numberof returning adults in the Tuolumne River. Thisassumption is more likely to be a concern in ex-trapolating to higher abundances that are influ-enced by density-dependent effects, than for lowerabundances (Jager 2000).

Seasonal flows that maximize spawning-time var-iation.—In addition to the objective of maximizingsmolt recruitment for the combined fall and late-fall chinook salmon runs, we also used simulatedannealing to find flow regimes that maximized var-iation in spawning times. We calculated the stan-dard deviation (SD) in the parental spawning datesof recruits for each simulation. The parentalspawning time is the integer number of days afterOctober 1 that a given smolt emigrant wasspawned by its parents. For the optimization ofvariation in spawning-run times, we consideredtwo cases: unlimited annual flow and annual flowsof 489 hm3 or less. The optimization programfound the vector Q of daily flows, during the 202-week time periods, that maximized the objectivefunction, Zv 5 Fv(Q). For a given flow regime Q,Zv is the standard deviation in spawning run timesof out-migrating smolts predicted by the ORCMmodel, Fv.

Simulated annealing.—We used simulated an-nealing (SA) as our solution method because it isflexible and has a high probability of finding theoptimal or a near-optimal solution for a wide rangeof optimization problems (Kirkpatrick et al. 1983).Simulated annealing has theoretical assurance offinding a globally optimal solution for problemswith finite solution spaces (Geman and Geman1984). Simulated annealing performed better thanother methods in at least one comparison of heu-ristic algorithms for an optimal reserve designproblem (Pressey et al. 1997). However, the so-lution method that works best for one problem isnot guaranteed to work best for another.

Simulated annealing is an ad hoc search pro-cedure that gives good results although we lack amathematical understanding of its success in find-ing optimal solutions. Such heuristic algorithmsdo not guarantee finding a globally optimal solu-tion and have no way of measuring the distanceof individual solutions from the global optimum.However, these algorithms have at least two ad-

vantages over optimization methods that havemathematical guarantees: (1) they are feasible forlarge problems, and (2) they are completely gen-eral and can be used with any (ecological) simu-lation model. This frees the ecological model todescribe relationships between organisms, theirenvironment, and potential management policieswith whatever degree of complexity is needed. Be-cause the ecological model is separate from theoptimization, the model does not have to be sim-plified or otherwise tailored to meet the assump-tions of a particular optimization method.

Simulated annealing has three possible disad-vantages. First, SA is not the best choice for op-timization problems with a structure that is suit-able for nonheuristic methods, such as linear pro-gramming. Simulated annealing would not takefull advantage of such a problem’s structure andwould therefore be slower to reach a solution. Sec-ond, SA is inherently a sequential algorithm thatdoes not lend itself to parallelization, althoughfinding hybrid parallel algorithms is an active areaof research. Third, SA is very slow compared withother heuristic methods.

Metropolis et al. (1953) first introduced SA afterobserving an optimizing process in physical sys-tems whereby thermodynamic systems minimizefree energy during cooling (e.g., annealing of met-als). At high temperatures, molecules of a liquidmove freely. If the liquid cools slowly, its atomsare able to line themselves up to form a pure crys-tal. If the liquid is cooled too quickly (quenched),it solidifies in a higher energy state and does notreach the crystal state that has the lowest free en-ergy. In terms of a mathematical optimizationproblem, the crystal is the global optimum, andthe quenched solution is one of many locally op-timal solutions. The ability of SA to find globaloptima derives from its ability to avoid becomingtrapped in local minima by permitting ‘‘uphill’’movements.

We used the SIMANN program developed byGoffe et al. (1994) to optimize each of our twoobjectives under the ORCM model. As initial con-ditions, we constructed a flow regime, Q, by set-ting the daily flows for each period to 4.248m3/s. We ensured reasonably large initial step siz-es. During the SA search, SIMANN used ORCMto evaluate its objective function (i.e., calculatethe number of recruits or the variation in spawningtimes for each new trial flow regime). As the searchprogressed, changes in flow depended on V, a vec-tor of step sizes having a value for each of the 20periods. Step sizes were adjusted as the search

11DESIGNING OPTIMAL FLOW PATTERNS

progressed to ensure acceptance of roughly halfthe trial flow vectors evaluated. In each subsequentstep of the search, a new vector of seasonal flowsQ9 was chosen by varying the average daily flowduring one 2-week period, i. If we let qi representthe ith element of vector Q, then the updated flowat the next step was

q 9 5 q 1 (U · v ),i i i (7)

where U represents a uniformly distributed randomnumber between 21 and 1, and vi is the ith elementof V. The updated flow vector was provided to theORCM model, which then calculated the new val-ue of the objective function, Z9. If Z9 was greaterthan Z, flow regime Q9 was always accepted as anew starting point for the search. If Z9 was lessthan Z, acceptance became less likely as the sizeof the difference and the duration of the searchincreased.

In optimizations constrained by the amount offlow available, we constructed an initial flow re-gime by dividing total annual flow evenly acrossthe 20 periods. We imposed constraints by reject-ing solutions if the sum of the 2-week flows andsummer flows exceeded the specified upper limiton annual flow.

Model predictions.—We first present the optimalflow regimes for the maximize-recruitment objec-tive for five total annual flow scenarios (four sce-narios with different constraints on total annualflow and one scenario with no limit on annualflow). We also compare these SA-derived optimalflow regimes with historical flows. Next, we pre-sent the number of ORCM-simulated recruits pro-duced by each of the annual flow scenarios. Tounderstand how increasing the limit on annual flowinfluenced differences in recruitment among sce-narios, we then present average egg-to-fry and fry-to-smolt mortality rates and the duration of suc-cessful spawning for each scenario. To explain thedifferences in mortality rates among annual-flowscenarios, we show river temperatures at two lo-cations in the river for the scenario with no limitand the scenario with annual flows of 122 hm3 orless.

We present the optimization results designed tomaximize variation in spawning times and com-pare these with results from optimizations de-signed to maximize recruitment for two annualflow scenarios (no limit and #489 hm3). We com-pare predictions for the two objectives, includingthe optimal flow regimes, the predicted number ofrecruits, the mean and standard deviation of

spawning times of successful recruits, and the con-tribution of the late-fall run.

Finally, we present average results for historicalflow regimes for water years 1980–1989. Thesevalues were predicted by ORCM by assuming5,000 spawners for each year and historical dailyflows and temperatures. Comparisons of resultsunder optimal flow regimes with results under his-torical flows and temperatures measure how muchimprovement would have been realized by follow-ing an optimal flow regime.

Results

Seasonal Flows that Maximize Recruitment

The SA search reached our stopping criteria af-ter very long periods of computation (on the orderof months). Progress for several of the maximizerecruitment optimizations was marked by long pe-riods with no improvement, punctuated by inter-mittent bursts of improvement (Figure 2).

The predicted optimal pattern for allocating sea-sonal flows among the 20 periods changed as thetotal amount of annual flow increased (Figure 3A–E). When we simulated dry hydrologic conditions(i.e., a low limit on total annual flow), the optimalflow regime allocated water more evenly acrossmonths, but it allocated more water in winter thanin fall or spring (Figure 3A). This was the onlyscenario that did not provide elevated spring flows.As total annual flow increased (Figure 3B–E), theamount of flow allocated during spring months in-creased dramatically. We observed that high springflows remained optimal in all hydrologic-yeartypes, except for the very driest. As total annualflow increased, flows provided during wintermonths did not increase very much (Figure 3A–E). When we simulated an unlimited supply ofwater, the optimal flow regime allocated high flowsduring fall months, in addition to the high flowsduring spring (Figure 3E). As annual flow con-straints tightened, we found that elevated fall flowswere the first to disappear (Figure 3D) and elevatedspring flows were the last to disappear (Figure 3D,A). These results suggest that providing a mini-mum level of winter flow is critical but that valuesabove this minimum level are not particularly ben-eficial for maximizing fall chinook salmon re-cruitment.

Once winter needs are met, additional flows dur-ing spring are more beneficial to recruitment. Re-cruitment increased sharply for total annual flowsup to 489 hm3 (Figure 4). Increasing annual flowbeyond 489 hm3 led to progressively smaller in-

12 JAGER AND ROSE

FIGURE 2.—Progress during the course of a simulatedannealing search. The maximum value of the objective(i.e., the number of out-migrants) increases with thenumber of model evaluations of trial flow regimes. Re-sults are shown for three optimizations with differentconstraints on total annual flow (#122, #245, and #489hm3, where 1 hm3 5 106 · m3/year).

creases in the numbers of recruits. This relation-ship suggests that, even when water is released inan optimal manner for salmon, a trade-off existsin drier years between allocating water to instreamflow or diverting water for other purposes.

Overall, as the annual flow increased, egg-to-fry mortality increased and fry-to-smolt mortalitydecreased (Figure 5A). Temperature was a mainfactor controlling this apparent tradeoff betweenegg-to-fry and fry-to-smolt mortality (Figure 5B).The decrease in fry-to-smolt mortality with in-creasing annual flow was caused by elevated flowduring the spring. The flow regimes optimizedwith higher annual flows provided higher flow dur-ing spring. These elevated spring flows carried thecooler water released from the dam farther down-stream before it reached equilibrium with the airtemperature. As a result, juveniles in simulationswith optimal flow regimes with higher annualflows were not exposed to lethal (high) spring tem-peratures. Forty km below the dam, water tem-peratures were higher under optimal flow regimeswith lower annual flow (e.g., the 40-km, #122-hm3 line in Figure 5B) than under optimal flowregimes with higher annual flow (e.g., the 40-km,no-limit line in Figure 5B). Consequently, juvenilemortality was lower in simulations with higher an-nual flow.

The pattern of increasing egg-to-fry mortalitywith increasing annual flow was due to elevatedflow effects on temperature during the fall. Sim-ulations of optimal flow regimes with higher an-

nual flows were characterized by higher egg-to-fry mortality because higher fall flows producedmore extreme downstream temperatures. Egg sur-vival during incubation is optimal at 88C (Figure5B); warmer and colder temperatures are stressful(Murray and McPhail 1988). In fall, water releasedfrom upstream storage reservoirs is typicallywarmer than the air (Petts 1984), which exposesredds concentrated below the dam to higher tem-peratures (e.g., the 16-km, no-limit line in Figure5B) than those farther downstream (e.g., the 40-km, no-limit line in Figure 5B). In years havingelevated fall flows, redds farther downstream ex-perience elevated temperatures because faster-moving water travels farther before reaching equi-librium with colder air temperatures.

Successful spawning occurred over a longer pe-riod under flow regimes with higher annual flow(Figure 6). The earliest successful redds were builtin early October for all hydrologic years, but thelast successful redds (those that produced off-spring that survived to emigrate as smolts) wereconstructed in mid-November in simulations withlow annual flow and as late as mid-February insimulations with high annual flow.

Seasonal Flows That Maximize Spawning TimeVariation

The flow regime that maximized the variationin run times (MV) differed from the flow regimethat maximized recruitment (MR) for both the un-limited annual flow and the flow of 489 hm3 orless. Under unlimited annual flow, the MV flowregime was characterized by higher flows than theMR flow regime during first 2-week period in Oc-tober and then for an extended period in springbetween February 4 and May 26 (Figure 7A). Oneinteresting feature of the MV flow regime is thelarge pulse of high flow between February 4 and17, just before the March 1 peak in spawning forthe late-fall run (Figure 7A). The two managementobjectives also produced different optimal flow re-gimes when annual flows were constrained to 489hm3 or less. Between October 1 and the end ofDecember, except for 2 weeks between October 29and November 11, the MV flow regime providedhigher flows than the MR flow regime. The MVflow regime provided higher flows than the MRflow regime in April, but lower flows in the sur-rounding months of March and May.

The parents of recruits spawned later and overa longer period when incubated and reared underMV flow regimes than they did under MR flowregimes (Table 3). For annual flows of 489 hm3 or

13DESIGNING OPTIMAL FLOW PATTERNS

FIGURE 3.—Optimal flow regimes that maximize the simulated recruitment of chinook salmon smolt out-migrantsfor five scenarios representing a range of constraints on annual river flow: (A) #122 hm3 (1 hm3 5 106 · m3/year),(B) #245 hm3, (C) #489 hm3, (D) #979 hm3, and (E) an unconstrained scenario. These can be compared with(F) the 2-week averages of natural flows above the Don Pedro and LaGrange dams between 1919 and 1992.

less, the mean spawning date for the parents ofrecruits shifted from October 27 under the MRflow regime to November 8 under the MV flowregime. No progeny of the late-fall run were pre-dicted to survive to recruitment. For unlimited an-

nual flows, the mean spawning date shifted fromOctober 31 under MR flow regime to November7 under the MV flow regime. For unlimited annualflows, this shift toward later spawning under theMV flow regime corresponded to increased sur-

14 JAGER AND ROSE

FIGURE 4.—Simulated recruitment of chinook salmonsmolt out-migrants under flows designed to maximizerecruitment of smolt out-migrants for each of five annuallimits on flow.

vival of late-fall progeny (Table 3). Not surpris-ingly, variation in successful spawning time, asmeasured by the standard deviation of spawningdates, was greater under the MV flow regimes thanunder the MR flow regimes for both annual flowscenarios. For annual flows of 489 hm3 or less, theSD of spawning times of offspring surviving tothe recruit stage increased from 11 d under the MRflow regime to 21 d under the MV flow regime.Under unlimited annual flow, the SD of spawningdates increased from 15 d under the MR flow re-gime to 19 d under the MV flow regime. The samepattern of later mean spawning time and higherstandard deviations under MV flow regime wasalso observed when survival to the fry stage wasconsidered (Table 3).

The number of late-fall-run recruits was highestfor the optimal flow regime designed for the MVobjective under unlimited annual flows. However,the total number of recruits was substantiallysmaller in MV flow regimes than in MR flow re-gimes. For annual flows of 489 hm3 or less, totalrecruitment decreased from 1,780,889 under theMR flow regime to 664,300 under the MV flowregime and neither the MR or MV flow regimeproduced any late-fall-run emigrants. For unlim-ited annual flow, total recruitment decreased from1,960,200 under the MR flow regime to 1,369,200under the MV flow regime. For unlimited annualflow, the MR flow regime produced 3,900 late-fall-run recruits, but the MV flow regime produced12,500 late-fall-run recruits.

Optimal versus Historical Flow Regimes

According to ORCM predictions, fewer re-cruits were produced under historical flows (av-

erage 5 647,800, SD 5 218,095) than under theMR flow regime for annual flows of 489 hm3 orless (1,780,889) or for unlimited annual flows(1,960,200). The variation in spawning times pro-duced under historical flows (average 5 15.0 d,SD 5 5.0 d) was also less than the variation inspawning times produced under the MV flow re-gime for annual flows of 489 hm3 or less (21.2d) and the MV flow regime for unlimited annualflow (18.9 d).

Discussion

Seasonal Flows That Maximize Recruitment

The seasonal flow patterns that maximized pre-dicted recruitment changed with the total amountof water available annually. This suggests thatmanagement of flows to recover salmon stocks re-quires different regimes in dry hydrologic yearsthan in wet hydrologic years. Fall flows increasedin scenarios exceeding 900 hm3; a relatively lowminimum winter flow was always optimal, andspring flows increased as the availability of waterincreased. These patterns suggest the followingpriorities for flow management aimed at increasingrecruitment of fall chinook salmon: (1) provide awinter minimum flow in all hydrologic years, (2)obtain additional flows to provide high springflows in all but the driest years, and (3) providefall attraction flows in very wet years.

The importance of the high fall and spring flowsthat characterized optimal seasonal flow regimesdeveloped with unlimited annual flow depends onthe management objectives for the river. A flowregime with lower fall flows and more moderatespring flows (e.g., Figure 3C) did almost as wellin maximizing overall recruitment as the unlimitedoptimal flow, which maximized recruitment bysupplying much more water (Figure 3E). Althoughthe flow regimes using more water produced morerecruits, the incremental benefits of higher annualflows decreased as annual flow increased. The im-portance of the extra water should be evaluated interms of whether the increment in recruitment isneeded to sustain the population.

An extended period of successful spawning andsurvival of the late-fall run contributed to higherrecruitment in wetter years. Only the two optimalflow regimes designed for the wettest conditions(Figures 3D and 3E) successfully reared late-fall-run smolts (Figure 6). The latest date that an in-dividual out-migrant was spawned shifted by 3months as constraints on annual flow were relaxed,probably because of the extended block of high

15DESIGNING OPTIMAL FLOW PATTERNS

FIGURE 5.—(A) Simulated proportion of chinook salmon eggs killed before reaching the fry stage (egg-to-frymortality) and the proportion of simulated fry killed before migrating as smolts (fry-to-smolt mortality); the linesummarizes the total fraction of eggs killed (egg-to-smolt mortality). (B) Seasonal changes in river temperaturesat two distances below the dam and under two optimal flow regimes: annual flow constrained to be #122 hm3 (1hm3 5 106 · m3/year) and no limit on annual flow. Simulated air temperature, upper lethal temperature for juvenilechinook salmon, and optimal temperature for eggs are shown for reference.

spring flow. Because late-fall adults are not in thesystem during fall, one might be tempted to con-clude that the high fall flows provided in these twowetter regimes could be reduced without affecting

the late-fall run. However, it is possible that highfall flows reduce fall-run survival of eggs and al-evins in redds and thus reduce competition withlater-emerging and smaller offspring of late-fall

16 JAGER AND ROSE

FIGURE 6.—The duration of simulated chinook salmonspawning dates used by parents of successful smolt out-migrants under optimal flow regimes designed to maxi-mize recruitment under different limits on annual flow (1hm3 5 106 · m3/year). Data labels indicate the final datesof successful spawning.

spawners. The two flow regimes that require themost water may be important to consider if re-storing the late-fall run is a management priority.

One approach to designing flow patterns is toassume that we cannot understand all of the com-plex influences of flow on salmon and that the bestpolicy is, therefore, to mimic the natural flow pat-terns under which salmon life histories evolved(National Research Council 1996). Our model-based results, like those of Bartholow and Waddle(1995), support the notion that seasonal flowsshaped with a peak during spring are best for chi-nook salmon. The shape of the optimal regime forannual flows of 489 hm3 or less (Figure 3C) issimilar to the shape of the 2-week average naturalflow regime (Figure 3F). Natural flows in the SanJoaquin basin are dominated by spring snowmelt,with 60% of discharge occurring between Apriland June (Lettenmaier and Gan 1990). Accordingto Moyle and Yoshiyama (1997), the highest sur-vival of chinook salmon in the San Joaquin Riveroccurs when naturally high flow events coincidewith times of smolt emigration.

Seasonal Flows That Maximize Spawning TimeVariation

Smith et al. (1995) recommend that conserva-tion efforts focus on genetic differences along theprimary axes that permit reproductive isolationand thereby define species and races. In salmon,distinct races are defined by temporal partitioningof spawning times as well as by geographic par-titioning (e.g., Utter et al. 1995). In the specific

case of the Central Valley, J. L. Nielsen (U.S. For-est Service, personal communication) determinedthat the two late-fall populations of chinook salm-on (Sacramento and San Joaquin) are more similarto each other than to any other spawning run inthe basin. However, some stakeholders in the Cen-tral Valley question the historical importance ofthe late-fall run in the San Joaquin and Tuolumnerivers and argue that restoration is not warranted.The results of this study suggest that regulatingflows in a manner that would conserve a widerrange of run times would produce fewer total re-cruits than would regulating flows in a manner thatmaximizes total recruitment.

Optimal versus Historical Flow Regimes

Optimal flow regimes produced considerablymore recruits and greater variation in spawningtimes than did average values during the historicalperiod, especially for the MR objective. The sig-nificance of these increases, like all differencespredicted here, depends on both the uncertainty ofORCM predictions and the sensitivity of the chi-nook stocks to flow-related differences in recruit-ment or variation in spawning time.

Caveats and Future Directions

Designing seasonal flow patterns that providehigher flows when salmon need it most can helpto guide conservation and restoration efforts.Three caveats limit the applicability of the resultspresented here. First, some salmon stocks may belimited by factors other than flow regime. Second,the optimal flow regimes identified here dependon the assumptions about the effects of flow onsurvival, growth, reproduction, and movement inthe ORCM model. There are many possible floweffects that are not explicitly simulated in the mod-el, and predictions about the effects of changes inflow regime should always be verified in the field.Third, the water required by an optimal flow re-gime might not be available when it is needed.

An important caveat to our results is that flowmanagement alone may not be capable of solvingthe problems that salmon face. Any conservationeffort that fails to focus on restoring access toupstream river habitat will probably fail for certainraces, such as spring and winter chinook salmon,that historically relied on these areas for spawning(Healey and Prince 1995). For these stocks, flowmanagement should be seen as a second-tier so-lution following the first-tier solution of providingpassage around dams and removal of other barriersto migration. In general, the first step should be

17DESIGNING OPTIMAL FLOW PATTERNS

FIGURE 7.—A comparison of optimal flow regimes designed to maximize recruitment (solid bars) and variationin spawning times (hatched bars). Results are shown for (A) unlimited annual flow and (B) annual flow #489 hm3

(1 hm3 5 106 · m3/year).

to identify improvements that are most likely toeffect recovery, which might not always empha-size providing a flow regime that is beneficial forsalmon.

Although the ORCM goes farther than otherpopulation models for salmon in its attempt to rep-resent mechanistic linkages between salmon bi-ology and flow, it has its limitations. Despite itscomplexity, ORCM selectively articulates keyecological relationships affected by flow. There are

many numerous indirect effects of flow thatORCM does not represent (e.g., benthic inverte-brate production, effects of predation risk on for-aging time, debris flow, gravel redistribution).

The ORCM focuses on the scale of daily chang-es in flow and does not represent the effects oflonger- or shorter-term variations in flow. At oneextreme, long-term drought cycles require a fulllife-stage model that incorporates the ocean phaseand simulations spanning decades. At the other

18 JAGER AND ROSE

TABLE 3.—Model predictions for flow regimes designed to maximize the variation in chinook salmon spawning timesand for flow regimes designed to maximize recruitment in the Tuolumne River, California. We report total recruitment,late-fall-run recruitment, and spawning-date statistics (average and SD) for parents of offspring that survived to the frystage and for those whose offspring survived to leave the river as smolts. The results for optimal flow regimes restrictedto an annual flow of #489 km3 (1 hm3 5 106·m3/year) and optimal flow regimes with unlimited annual flow arecompared.

Model predictions

Annual flow #489 hm3

Maximizerecruitment

Maximizevariation

Unlimited annual flow

Maximizerecruitment

Maximizevariation

Total number of emigrantsLate-fall-run emigrantsAverage parental spawning date for frySD of spawning dates (d) for survivors to fry stageAverage parental spawn date for emigrantsSD of spawning dates (d) for survivors to emigration

1,780,8890

Nov 921.0

Oct 2711.1

664,3000

Nov 1830.5

Nov 821.2

1,960,2003,900

Nov 1125.6

Oct 3115.4

1,369,60012,500Nov 17

29.3Nov 7

18.9

extreme, with its daily time-step and 2-week op-timization intervals, ORCM did not represent theeffects of within-day variation in flow. Natural var-iation in flow regimes shape the disturbance re-gime in rivers in much the same way that fireshapes grassland ecosystems (Reeves et al. 1995;Poff et al. 1997). Unwin (1997) found that flowvariability during spring out-migration showed thestrongest and most consistent positive relationshipwith fry-to-adult survival of chinook salmon. Ex-perimental pulse flows in the Stanislaus River, Cal-ifornia, stimulated out-migrations in the short-term (2 d) but little additional benefit resulted fromprolonged high flows (Cramer 1997). These resultssuggest that the ability of high flows to speed em-igration may be less important than the short-termbenefits provided by pulse flows. Pulse flows mayserve as a behavioral cue to synchronize down-stream movement, allowing smolts to overwhelmpotential predators. Increased turbidity associatedwith pulse flows is also a short-term event (onethat may not occur in regulated rivers). Becauseour study used 2-week periods, our optimal flowregimes are less variable than natural flow regimes.Also, the ORCM does not at present include thefine distinctions between short-term and longer-term benefits of flow. A next step in our analysiswould be to introduce processes that operate atdifferent time scales in the ORCM model and toevaluate the effects of including realistic short-and long-term variability in flow without substan-tially increasing the number of decision variables.

Limitations in flow availability can restrict theability to manage flows according to an optimalflow regime. Droughts, combined with limits onstorage capacity and competing demands for water,can make it difficult to follow a specified regime.Such competing water needs could be incorporated

as constraints into an optimization analysis likeours. Likewise, economic considerations could beadded in future to address both the benefits to fishand costs to society.

The optimization approach described here couldbe used to design instream flows for conservationobjectives involving different rivers and salmonruns as well as for other species. Applications tochinook salmon that spawn in different riverswould merely require changing values for site-specific model parameters. Applications to differ-ent salmon species might require structural chang-es to ORCM to reflect a more complex life history.For example, chinook salmon show a much widervariation in life history patterns in rivers farthernorth than in the California river used in our study,including runs that remain in the river much longerand exit as yearlings. Although the specific quan-titative results presented here are specific to a par-ticular stock, the qualitative recommendations pre-sented for designing flows that benefit salmon indifferent hydrologic years and in situations withmultiple runs should have wider application.

In this study, we compared the optimal flow re-gimes designed to independently address two dif-ferent conservation objectives. It is also possiblefor optimization to address multiple objectives.With many more optimizations, one could con-struct a Pareto frontier of flow regimes that assignweights to the two objectives that we considered(maximizing the recruitment and maximizing var-iation in the spawning times). In our analysis, man-aging flows to conserve a variety of runs requiredcompromising overall recruitment. This impliesthat the relative weight assigned to the two objec-tives should depend on the conservation status ofthe runs. If the larger runs are stable or increasing,then diversity-enhancing flows may be favored,

19DESIGNING OPTIMAL FLOW PATTERNS

whereas a dominant run that is declining may re-quire sacrificing smaller runs. If the temporalmetapopulation structure of the runs resembles acore satellite structure, with one dominant run thatrecolonizes the others by temporal straying, thenthere is a danger that managing flows for run-timediversity would create temporal sinks, analogousto the spatial sinks described by Pulliam (1988).In contrast, managing for run-time diversity wouldbe important for classic metapopulations that de-pend on recolonization by temporal strays for per-sistence.

Acknowledgments

We appreciate discussions with Hal Cardwelland Steve Bao for sharing their expertise in op-timization theory. Mac Post provided helpful sug-gestions on efficiency, and Forrest Hoffman helpedto transport the optimizations to various UNIX andLINUX platforms. Reviews were provided byWebb Van Winkle, Chuck Coutant, Lou Gross,Barry Smith, and Paul Higgins.

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