A Simulation of the Distribution of Acartia Clausi During Oregon Upwelling, August 1973

Journal of Plankton Research Volume 2 Number 1 1980

A simulation of the distribution of Acartia clausi during Oregon Upwelling, August 1973 J.S.Wroblewski Department of Oceanography, Dalhousie University, Halifax, Nova Scotia B3H4J1, Canada Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 (Received August 1979; revised November 1979; accepted December 1979)

Abstract. The distribution of the estuarine copepod Acartia clausi in coastal waters off Oregon during an upwelling period in August 1973 is simulated. A time dependent, two dimensional (x, z, t) model relates maximum offshore extent of the copepod's four life stages (egg, nauplius, copepodite, and adult) to intensity of the wind stress driving the upwelling circulation, stage development time, and mortality. Realistic solutions are obtained by using actual intermittent wind forcing recorded by an anemometer at Newport. Offshore transport is overestimated when the circulation model is driven by theoretical continuous winds, suggesting zooplankton may be washed out of coastal upwelling zones (e.g. off Northwest Africa) which undergo periods of prolonged upwelling. With an accurate model of offshore transport and stage development time, the mismatch between predicted and observed distributions may be used to estimate field mortality of the various stages.

Introduction Zooplankton standing stock was once believed to be greater in the slope region off Oregon than over the continental shelf during the summer upwelling season. Peterson (1972) surveyed the oceanic, slope and shelf regions but did not sample the nearshore zone when making this conclusion. In a detailed study of the Oregon upwelling zone, Peterson and Miller (1975) found high concentrations of copepods in the upper 20 m of the water column within 15 km of the coast during the 1969-71 upwelling seasons, as did Myers (1975) in August, 1973. Wroblewski (1977) simulated the abundant zooplankton seaward of the upwelling front but failed to account for the high inshore copepod populations. This research explores the question posed recently by Peterson, et al. (1979): how do high concentrations of zooplankton arise nearshore, and how are they main- tained in the face of offshore transport during coastal upwelling? This paper examines the dynamics of the estuarine species Acartia clausi.* A second paper (in preparation) deals with the coastal species Calanus marshallae and explores the con- sequences of diel and ontogenetic vertical migration in lengthening the residence time of zooplankton in the upwelling region. The first approach taken to investigate the phenomenon of high inshore zooplankton concentrations was to make order of magnitude calculations of the expected cross-shelf transport of those zooplankton whose source is the estuaries, bays and shallows along the coast. It was found that advection predicted from classical upwelling theory (Smith, 1968) with no regard for the time dependency in the winds that force the upwelling circulation, overestimates the extent of offshore transport of these zooplankton. To resolve this discrepancy and to separate the effect of

* The systematics of this species are in doubt (Bradford, 1976).

animal, both of which act to limit the cross-shelf distribution of A. clausi. Formulation of Acartia clausi dynamics To demonstrate why large inshore concentrations of copepods are not to be expected during upwelling, consider the general equation for the distribution of a nonconservative variable, Z (here, numbers of A. clausi m~3) in the sea

-^ + V uZ - V- (K,y Z) = sources and sinks (1) where t is time, u represents the horizontal and vertical water velocities, and K, is the coefficient of the eddy diffusivity in the coordinate direction i. The first term is the local change in Z, the second represents advection of Z, and the third represents turbulent mixing. Sources and sinks refer to the biological processes (e.g. recruitment and mortality) whereby Z becomes nonconservative. Let us choose a Cartesian coordinate system in which y is the longshore direction, x is positive toward the coast and z is positive downward. If we assume a nondivergent flow field and neglect diffusion for the moment, the seaward distribution of Z can be simply expressed as

The horizontal velocity u is positive towards shore. Parameter f} describes the rate 44 Model of Acartia clausi daring Oregon Up welling of change in Z with time. If there is a continual source of A. clausi at the coastal boundary to balance the advective and biological losses at sea, the steady state solution to equation (2) can be written

where Zois the concentration at the coast. If a mean value of u in the surface layer, time averaged over the two month

upwelling season, is - 10 cm sec~'(Bryden, 1978) and the lifetime of the copepod Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 is 60 days (Conover, 1956), adults could be found to the farthest seaward extent of the upwelling zone. However observations (Peterson et al., 1979) show the e-folding length scale (i.e. the distance travelled in reducing Z to Zee"1) to be at most 10 km (Figures 1 and 2). Therefore either the measured value of u is grossly in error (unlikely) or the mortality rate B is significantly higher than death by aging would allow and many animals disappear before their lifespan has elapsed. We can use a numerical circulation model to refine our estimate of u. Since the e-folding length scale is fixed from observations, the model gives an indirect estimate of the hard to measure

KILOMETERS 0 5 10 IS NAUTICAL MILES

?7 A r

FIg.l A chart of the central Oregon coast showing locations of transects sampled during August 14-16, 1973 (from Peterson et al., 1979).

45 J.S.Wroblewikl

DISTANCE FROM SHORE (KM) 25 20 15 10 5 I

45# 12' N NESTUCCA LINE Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 14 AUGUST 73

25 20 10

45*06'N . CASCADE HEAD LINE 15 AUGUST 73

25 20 15

44*40'N NEWPORT LINE* 16 AUGUST 73

Fig.2 Spatial structure and abundance (number m~3) of copepodite and adult Acartia clausi sampled during August 14-16, 1973. Dots indicate Clarke-Bumpus net sample depths (from Peterson eta!., 1979).

(Prepas and Rigler, 1978) field mortality rate, p. To simulate the offshore transport of Acartia observed during the period of field sampling, August 14-16, 1973, a numerical upwelling circulation model (Thompson, 1974) was used to predict horizontal and vertical velocities as a function of wind stress. The zonal distribution of the four life stages of A. clausi (egg, nauplius, copepodite and adult) off the Oregon coast was modeled by the two dimensional (x, z, t) equation

+ U w -K* -K. = population dynamics (3) 9t ax where n = 1, 4 such that Z, represents number of eggs m~\ Z2 is nauplii, Z3 is copepodites and Z4 is adult concentration. As A. clausi does not demonstrate any appreciable vertical migration behavior (except perhaps adult females who may vertically migrate over several meters; Landry, 1978; C.B.Miller, personal communication), w in equation (3) has no biological component. Note the horizonal and vertical coefficients of eddy diffusivity have been assumed constant. In reality Khand Kvare functions of velocity and mixing length scale. However the flow field employed here to advect the dependent variables has been predicted by a physical model which explicitly incorporates vertical mixing processes into its

46 Modd of Acartia clausi during Oregon Upwdling dynamics. Thus one need not specify the spatial structure in the eddy diffusivity. The temporal variability in the velocity field results in a turbulent flux of Zn which is a property of the flow. This implicit turbulent transport is discussed in detail by Wroblewski and O'Brien (in press). The population dynamics included in (3) describe the development of the four life stages of Acartia and the mortality at each stage. Development time of each stage as a function of seawater temperature is based on B?lehradek's equation

(McLaren, 1978) Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 D = a(T + b)c (4) where D is the development time of each stage (days) and T is temperature (°C). Parameter a (days CC~') governs the mean slope, b (°Q allows for shifts in the temperature scale and c (dimensionless) determines the curvature of the response. A basic assumption of B?lehradek's equation is that development is not limited by food availability. Chlorophyll concentrations observed in the upwelling zone tend to support this assumption, except for short periods when newly upwelled water lies close to the coast (Peterson et al., 1979). As we wish to keep the number of model parameters to a minimum, the transfer of animals from stage to stage and the mortality at each stage (Figure 3) are expressed as simple linear functions. One assumes the ages of individuals in each stage form a continuum rather than a cohort as from synchronous spawning. Thus some animals are always ready to mature to the next stage while others still require the full development time. This can be formulated as

a>Z P Z (5) (eggs) p = unit time ~ < ~ < '

2 (nauplii) g { = a, Z, - (a2 + W Z2 (6)

(copepodids) —JT— = a2Z2 -(a3 + /J3) Z3 (7)

(adults) 91* = a3 Z3 - 04 Z< (8) where the rate of development an(day"') is taken as 2/Dn. Again Dn refers to the development time of the nth stage. Because of the exponential formulation of copepod development, 87% of the individuals present at time zero will progress to the stage n +1 in the time interval Dn. The remaining 13% take longer to com- plete their development. This formulation then incorporates some recruitment which takes longer than normal. Parameter PB in equations (5) - (8) is the mortality rate (day "') at the nth stage. Mortality of each stage is constant with time, but each stage can have a different value of p according to the susceptibility of that stage to physiological death, cannibalism, predation, etc. This formulation of mortality would appear as a set of joined diagonal lines with different slopes if plotted as a survivorship curve (Hutchinson, 1978). Gehrs and Robertson (1975) found such to be the case for a population of freshwater calanoid copepods, Diaptomus clavipes.

47 J.S.WroblewskJ

A z, z2 z3 -«5 Z5 ) Z4 DEVELOPMENT Eggs Nouplii Copepodids Adults

PREDATTON ANONATURAlJ. -B.Z. I 784 z4 MORTALITY •

B Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 3.45 DAYS 14 DAYS 1023 DAYS , Egg Nauplius Copspodid Adult

80% 60% 50% KX>% MORTALITY MORTALITY MORTALITY MORTALITY

Fig.3 a) Schematic representation of the A. ctausi population dynamics included in the model, b) Development times and mortalities of eggs, nauplii, copepodids and adults assumed in the model.

Next equation (3) is scaled. This serves two purposes. First it reduces the number of parameters in the model. By normalizing time by the fastest biological rate (T = a,t), all physical and biological processes are expressed relative to the egg development time. Secondly, scaling allows one to express all offshore concentrations as a fraction of the total source population, Z, (or Z'D = Zn/Z,, n = 1,4). The total number of animals at the source may vary with geographical location along the coast, changing the absolute number of animals/m3 but not the pattern of the cross-shelf distribution. To scale the advective and diffusive terms in equation (3), let x' =x/L u' = u/U z' =z/H w' = w/W where L and H are the width and depth of the upwelling zone, U and W are typical values of the horizontal and vertical velocities respectively. Substituting these scaling relationships, equation (3) becomes, w u 2 JT La, ax' Ha, n' L a, 3X'

-n-l ~ 1 J n (9) H'a, ' JZ" a, ""-' ' a, '~ Obviously the scaled biological terms have a slightly different form for n = 1 and 4. The scaling of Zn, u, and w have been chosen such that the nondimensional quantities Z'n, u' and w' and all derivatives of Z^are order one. The magnitude U_l f^_! r-J^nH.-^ then detcrmine of the coefficients [ •].[• 1, [ 2 s La, Ha, L a, H2a, the importance of advection and diffusion relative to the biological processes

48 Modd of Acartia clausi during Oregon UpweUlng governing the distribution of Z'a. Off Oregon, U often has an instantaneous value of 20 cm sec"1 (Huyer & Smith, 1978) and W is often 1 x 10"2cm sec"1 (Bryden, 1978). The width of the upwelling zone L is 50 km. Since most A. clausi individuals are found within 50 m of the surface, H is taken to be 50 m. For these length scales, appropriate 3 2 2 1 values of Khand Kvare 5x 10 cm sec~' and 1 cm sec" respectively. Choosing a, = 0.5 day"1 (see following section) and evaluating, Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 U = 0.69 —-^— = 0.003 La, Ua, W = 0.35 ... = 0.01 Ho, H2*, Thus advection and biological processes (which are scaled to be order one) are the same order of magnitude. This equal importance of advection and copepod development and mortality terms in equation (9) implies large variability can be expected in zooplankton distributions in upwelling regions. The model will demonstrate how the effect of diffusion, while initially not important, ac- cumulates over time. Estimation of parameter values for A. clausi population dynamics McLaren (1978) fitted Belehradek's equation (4) to Landry's (1975) data on egg development rate of Acartia clausi. Parameters a and b were found to be 1442 days °C"' and 10.49°C respectively. The value of c is fixed at -2.05 for each development stage. Assuming an average temperature of 8.5°C in the nearshore region of active upwelling (Peterson et al., 1979), the development time of eggs is 3.45 days. Therefore we choose a, = 0.5 day"1, which specifies an e-folding rate such that only 13% of the eggs present at time zero are unhatched four days from laying. Assuming isochronal development (Miller et al., 1977) McLaren com- puted the value of parameter a for the development of the nauplius into copepodite stage I to be 6866 days °C"'. If the temperature in the region several kilometers offshore where most nauplii develop is 10°C (Peterson et al., 1979), 1 then the development time is 14 days. Therefore we choose a2 = 0.14 day" , which gives an e-folding rate such that only 13% of the nauplii still have not developed after 14 days. Similarly from McLaren (1978), the value of development parameter a for any copepodite stage is 1288 days °C~'. If the average temperature in the region where most development occurs is 12°C, each copepodite stage develops in 2.05 days. Since there are five stages, the adult emerges after 10.89 days. Therefore we choose a} = 0.2 day "', which leaves 13% of the original number of copepodites still immature after 10 days. Landry (1978) suggests three causes of mortality of A. clausi, namely physiological or disease-caused death, cannibalism and predation by fish or larger zooplankton. It is assumed physiological causes of death can be ignored for the egg, nauplius and copepodite stages. Physiological death of adults is im- 1 portant in the absence of predation. It is specified as a /?4 value of 0.067 day" , whereby 87% of the original number of adults is lost during the 30 day final life

49 J.S.WroblewskJ stage. Predation would contribute to an increase in /?4. We will assume for now the adult copepods are not eaten. Higher values of 04 will be explored later. Mortality can be considerable in the early stages of most Crustacea and can in- clude cannibalism (Gehrs and Robertson, 1975; Hutchinson, 1978). Sekiguchi and Kato (1976) found that up to 74% of the eggs produced by A. clausi were preyed on by Noctiluca in Ise Bay, Japan in summer. Landry (1978) found similar mortality coefficients for nauplii, copepodids and adult A. clausi in a small temperate lagoon with values typically ranging from 0.1 to 0.4 day"1 during the Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 summer. Because each situation is unique, one can only guess a mortality rate and examine the model solution to see how well it fits the observations. This is called "tuning" the model. It is a valid modeling technique when all but one set of parameters is well known. How appropriate tuning the mortality parameters may be in this particular problem will be discussed in the last section. One might expect an egg mortality of 80% in the field over the total 4 day development time. Thus we initially choose /3, = 0.4 day"1. A similar mortality for nauplii of 80% over their 14 day development time would set f)2 = 0.114 day"1. If copepodites in nature have lower mortality rates than do nauplii (Steele 1 and Mullin, 1977), we can set /33 = 0.068 day" whereby only 50% of the individuals are lost over their 10 day development time. This lower mortality chosen for copepodites contradicts the hypothesis of Miller et al. (1977). They suggest A. clausi spends a proportionately shorter part of the total development time in the older stages as an adaptive response to selective predation. Indeed model simulations will later demonstrate that high mortality must be occurring at all stages. Solution of the A. clausi population dynamics model The time dependent solution of the scaled population dynamics is shown in Figure 4. The curves in Figure 4a show the successive appearance of stages where the total population develops from the egg stage. The decreasing amplitude of the curves demonstrates the effect of mortality. The population dies out as reproduction is not allowed. In the estuary, the source population maintains a steady state (Figure 4b) where egg production equals mortality,

= individuals lost to mortality unit time = p;z; + /?;z; + p'3z'3 + p4z; The severely limited distribution of A. clausi off the coast (Figure 2) does not preclude reproduction offshore. The sampling net size of 120 jim used by Peter- son et al. (1979) did not quantitatively retain Acartia eggs and nauplii. Thus they were unable to determine if reproduction was occurring at sea. However, based on the few numbers of nauplii which were caught by the nets, Peterson et al. (1979) suggest Acartia was not spawning. Moreover, by assuming no reproduction once the animals leave the estuary, the model can examine more clearly the effect of the offshore transport relative to the biological processes of development and mortality in determining the spatial position of the four life stages.

50 Model of Acartia clausi dnring Oregon UpwHIIng

Acartia clausi Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 (NO EGG LAYING BY ADULTS)

2 4 6 10

NONDIMENSIONAL TIME

Acartia clausi

(REPRODUCTION BALANCES MORTAUTY)

isl U. O O t

NONDIMENSIONAL TIME

Fig.4 Time dependent solution of the A. clausi population dynamics model, a) Development of the four life stages from eggs. Reproduaion by adults is not allowed, b) Steady state solution where reproduction balances mortality.

51 J.S.Wroblcwski

Sensitivity analysis Having formulated the population dynamics for A. clausi, one is interested in the general behavior of the model as a function of the development and mortality parameter values. Therefore an analytical sensitivity analysis of the scaled forms of equations (5) - (8) was performed using the steady state values of Z,J in the estuary. "Sensitivity" is formally defined as the displacement from equilibrium the model experiences due to a quantitative variation in an individual parameter

(Tomovic, 1963). Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 Analytical sensitivity analysis involves the derivation of partial differential equations describing the rate of change of Z,J with respect to changes in parameters a'Q and /}„, e.g. —, ——-. The scaled forms of equations (5) - (8) dPl sum to zero since we have assumed

(10)

(Note that for the steady state condition, parameter 0, drops out of the dynamics.) Thus we may neglect one equation from (5)-(8) and substitute the closure relationship

z,' + z,' + z3' + z; = I in the sensitivity analysis. We arbitrarily neglect the scaled form of equation (5), i.e. (10). The final equations for the sensitivity analysis are then Z;-(ai + pi)Zi = 0 (12)

a2'Zj'-(a,' + ft')Zj' = 0 (13)

a,'Z3'-p4'Z4' = 0 (14) and equation (11). Differentiation of (11)- (14) with respect to the parameter a2' is represented in matrix form as AX = B or

az; 1 -{f*i + Pt) 0 It 0 a2 -(cr, + 0 Zj

0 0 -P* 0 3»2 sz; 1 1 1 1 0 3*2

The square coefficient matrix A is always the same upon differentiation with

52 Model of Acartia clausi daring Oregon UpweUlng respect to any parameter. However the column vector B is different for each parameter. One evaluates VZ[/ 3a'2, dZ\/ da'lt etc. by using Gaussian elimination to solve for the matrix inverse, A"1. The solution to the set of simultaneous equations is X = A~'B. The steady state values of Z,', Z'ly Zjand Z\and the values of the parameters used in the analysis are given in Table I. Table I is the result of the matrix solution for each parameter. The values in

Table I are the partial derivatives (eg. 9 Z,7 3a^) normalized by the parameter Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 and dependent variable values at equilibrium. The first quantity in Table I is then (a^/Z,') (9Z|'/0 oi). Expressed in this manner, a model sensitivity of -0.111 means for a 1% increase in a'2, the steady state value of Z{ would decrease by 0.111%. A 10% increase in ^2 would decrease Z,'by 1.11%, and soon. The results of the sensitivity analysis are easily interpreted and biologically meaningful. The most sensitive behavior of the model is the value of Z3 (copepodite abundance) in response to the parameter a, (copepodite development rate). Increases in the development rate of copepodites would of course decrease their standing stock. The next most sensitive response is in Z^ (nauplii abundance) as a function of a'2(nauplii development rate), for the same reason. As adults Z'4 develop no further, this standing stock is most sensitive to the mortality coefficient for adults, /3{. Many of the model responses illustrated in Table I are in- tuitively obvious. Some are more subtle but can be explained as indirect effects. The conclusion from all this is that our simple formulation of Acartia clausi population dynamics can give sensible predictions. We are now ready to couple the biological dynamics with the physics of upwelling. Physical dynamics in the model region The region modeled is shown in Figure 5. All biological simulations are confined to the upper 50 m of the water column within 50 km of the coast. The region is divided into a grid with dimensions 2.5 m in z and 1 km in x. The bottom topography assumed by the circulation model is a linearized version of the actual bottom slope off Oregon. A bottom depth of 50 m at the coast is assumed to simplify computations. Thus we are unable to resolve the A. clausi distribution in the shallow coastal zone and must parameterize this spatial structure with a

Table I. Sensitivity analysis of A. clausi dynamics. Partial derivative values of eggs Zj, nauplii Zj, copepodites Z3 and adults Z't differen- tiated with respect to development and mortality parameters and normalized by parameter/component ratio, e.g. (aj/Zj) (dZ[/9 atf. Steady state values Z{ = 0.144, Zi •= 0.295, Zj = 0.166, Z'A = 0.395. Parameters a{ = 0.280, aj = 0.400, Pi - 0.228, ft = 0.136, ft = 0.134.

z; Z2 Z3 z; -0.111 -0.658 0.317 0.389 "i -0.002 -0.002 -0.748 0.317 Pi 0.402 -0.063 -0.059 -0.074 Pi 0.166 0.159 -0.107 -0.134 Pi, 0.389 0.373 0.345 -0.566 53 J.S.WroblewikJ

'.•:•:•:•:+:•:•:*

A TOPOGRAPHY 45°I5'N 500 Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

1000

a. UJ 1500 Q

2000

2500 150 100 50 DISTANCE (km)

Flg.5 Bottom topography assumed in the numerical upwelling circulation model of Thompson (1974). The rectangular stippled region at the upper right delineates the region of the A. clausi model.

coastal boundary condition. The physical dynamics incorporated in the upwelling circulation model used to advect the biological variables are discussed in detail by Thompson (1974). In essence, the model simulates the time dependent response of the ocean to coastal wind stress. Explicit reconstructions of Ekman layers at the surface, bottom and seasonal pycnocline interface are developed using perturbations of velocity from the vertical average. A telescoping grid was used for high resolution of the flow in the upwelling zone. Sverdrup ocean interior dynamics were matched to the nearshore circulation. The model includes a vertical turbulent mixing whose intensity is tied to the dynamic stability of the water column, which is itself determined during model evolution. The numerical model predicts the position of the upwelling front, the localities of upwelling, convergences and divergences. A basic assumption is no longshore variation in the velocity field. The circulation model was driven by two different wind conditions: a theoretical, continuous wind stress favorable for strong upwelling, (Figure 6a); and a wind stress calculated from anemometer data recorded at Newport, Oregon during August, 1973 (Figure 6b).

54 Modd of Acartia clausi dnring Oregon Upwelling Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

I I I I I I I 5 10 15 20

TIME (DAYS)

E o (A

CO CO UJ Q:

CO o z

AUGUST 1973 Flg.6 The north-south component of the wind stress in a) the theoretical continuous upwelling case, and b) the August 1973 intermittent upwelling case. 55 J.S.Wroblewiki

Numerical methods A detailed description of the numerical methods used in the simulation model can be found in Wroblewski and O'Brien (in press). The finite differencing of equation (9) consists of representing the local time derivative with a leap-frog scheme, using a quadratic-conservative scheme (Piacsek & Williams, 1970) for the advective terms and an explicit scheme for the diffusive terms. The diffusive and biological terms are lagged in time. A time step AT of 0.002 (or At = 0.1 hr) was used, which was well within the bounds for computational stability. Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 Boundary conditions The habitat of A. clausi off Oregon includes the bays, estuaries and a narrow, shallow zone within 2 km of the beach which is not directly affected by the upwelling circulation (C.B.Miller, personal communication). The coastal boundary condition for the spatial solutions is taken to be the steady state A. clausi population values of Z'B (Figure 4b) where reproduction balances mortality and advective losses to the upwelhng zone, which must be the case for a stable source population (Ketchum, 1954). Since we do not know how the actual advective addition of the copepods to the upwelling zone varies with time or longshore position, we assume a constant coastal boundary condition. The profile shown in Figure 7 specifies the concentration of A. clausi with depth at the coastal boundary. The fraction of the total population at each grid point is based on observational data (Myers, 1975). Note the total area under the curve equals one. Since at 10 m depth 12.5% of the population occurs, and since 3,000 A. clausi m"3 were observed at that depth, then Z, = 24,000 animals m"2 integrated over the water column. This total number of animals is distributed over a 50 m water column according to the profile in Figure 7 and partitioned among the four life stages as the steady state fractions (Figure 4b). The assumption of the same depth distribution for all life stages is reasonable only for some copepods. The ecology of many coastal species, e.g. Calanus marshallae_, is fundamentally tied to the differential distribution of the adult and larval stages (Peterson et al., 1979). Water upwelhng into the model region from below is devoid of animals. If water is moving out of the model region, the concentration of the biological variable Zn just inside the boundary determines the value at the boundary. No advective mass flux is allowed across the air-sea interface. No diffusive mass flux is allowed through any boundary. Initial conditions

Initial conditions are Zn = 0 everywhere except at the coastal boundary. Animals are adverted away from the coast as they are caught up by the flow. The velocity field is spun up from rest at time zero. Initial ocean stratificiation is realistic for the onset of upwelling with density values and depth of the seasonal pycnocline based on hydrographic data (Thompson, 1974). Model results a. 77ie strong upwelling case. The distribution of A. clausi during a strong upwelling event is simulated by driving the numerical circulation model with the

56 Model of Acartia clausi during Oregon Up welling

% OF TOTAL POPULATION AT DEPTH

gfO 123456789 10 II E 13 Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

c zo -

Flg.7 Coastal boundary condition for the A. clausi model. The profile specifies the fraction of Z, found at depth. wind stress shown in Figure 6a. The wind stress is specified as zero at the begin- ning of the model run, increases linearly to - 0.5 dyne cm"2 at the coast over the first model day and remains at this value until model day 11, at which time it decreases back to zero. Model integrations continue for 10 more days to study the effect of wind relaxation on the distribution of Acartia. The dimensional parameter values for the full A. clausi distribution model used in both the strong and intermittent upwelling cases are recounted in Table II. A snapshot of the velocity field on model day 4 is shown in Figure 8a. The en- circled arrow shows the magnitude of the wind stress at that time. The flow field is visualized by vectors representing the position and instantaneous velocity of tracer particles which have been adverted by the flow. Only the vectors within 25 km of the coast are shown. The vector arrows are scaled by the maximum vector occurring in the field at that time. It should be noted that the vertical scale is exaggerated relative to the horizontal scale by two orders of magnitude. After 4 days of wind forcing there exists strong onshore flow along the bottom and strong offshore flow in the surface Ekman layer. The center panel in Figure 8 shows the seaward distribution of A. clausi eggs as

57 J.S.Wrobtewild

Table II. Parameter values for the Acartia clausi model.

Parameter Value Parameter Value

3 H 5X10 cm °i 0.50 day-' 3 2 1 1 Kh 5X10 cm sec" "2 0.14 day: 2 1 Kv 1 cm sec "' °3 0.20 day" 1 L 5x10* cm Pi 0.40 day" 1 At S^xl^sec P2 0.114 day" 1 U 20 cm sec" Pi 0.068 day"' 2 1 1 Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 W lx 10" cm sec" PA 0.067 day" Ax lxl05cni Az 2.5xl02cm they are adverted away from the coast. Because most eggs hatch within 4 days, the flow field does not carry them far before they hatch into the nauplius stage. The bottom panel shows the distribution of A. clausi adults. The 30 day duration of the adult stage allows Z4' to act more as a conservative tracer, especially since we have assumed a negligible field mortality. The model solution after 10 days of strong upwelling is shown in Figure 9. The velocity trajectories (Figure 9a) show two cyclonically rotating gyres as proposed by Mooers et al. (1976). The upwelling velocities are four times larger than on model day 4 and the maximum offshore velocity is - 6 cm sec"1. Significant concentrations of eggs occur out to 10 km (Figure 9b). The 0.5 contour for adults (600 A. clausi m~3) extends out to 14 km offshore (Figure 9c). Note the strong downwelling in the region 5 to 15 km offshore (Figure 9a). This is due to cold, dense, upwelled water sinking beneath the permanent pycnocline which intersects the surface at 7 km offshore, forming a surface front. The downwelling is reflected in the plume structure of both the egg and adult distributions. Figure 10 shows the distribution of A. clausi nauplii and copepodids on model day 10. Their distribution pattern is similar to that of the adults. Absolute magnitudes of the concentrations differ, however, because of boundary values and the development process. Yet even within a ten day time scale, maturing copepods have contributed only a small fraction to the offshore adult standing stock, owing to the high mortality of nauplii and copepodids. On model day 11 the wind stress decreases to zero and the upwelling circulation relaxes. Offshore flow at the surface gradually slows, and then reverses due to the seaward pressure gradient built up during the prior ten days. There is still some residual offshore flow at 40-50 m depth on model day 20 (Figure lla). During the relaxation period, the net effect of advection is to transport A. clausi back towards the coast. The egg and adult distributions (Figure lib and c) reflect the onshore flow at the surface. The 0.5 contour of the adult distribution moves from a position of 14 km offshore on model day 10 to only 9 km offshore on model day 20. Note however that diffusion continues to move animals seaward, down the concentration gradient. M The length scale over which diffusive transport is significant is given by (Kht) . For a ten day period, this scale is 6.6 km. Indeed if the model is run for ten days without advection, the 0.5 contour is moved out to 5 km purely by the diffusion

58 Model of Acartia clausi daring Oregon Upwelling

u-w Ytere* rum • *J n»ti Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

"(km)10

DISTANCE FROM SHORE (km) 20 15 10 5 I

Flg.8 The continuous upwelling case on model day 4: a) The zonal circulation, bottom topography and wind stress at that time. The maximum u and w velocities in the field are -2.9 cm sec"1 and 1.4x I0"2 cm sec"1, respectively, b) The zonal distribution of A. clausi eggs, c) The zonal distribution of A. clausi adults. Multiply nondimensional contour levels in (b) and (c) by 2,000 to obtain numbers m"3. process. Therefore the diffusive terms in equation (3) become important over long time scales. If we wish the model to remain valid for periods greater than 10 days, a more complex parameterization of diffusive transport would have to be included in equation (3). In summary these solutions indicate the offshore extent of A. clausi populations would be maximal during strong upwelling and minimal during relaxation periods. The model predicts that a sizable fraction (0.1 contour or 100 adults m"3) of the A. clausi population extends out to 25 km during strong upwelling

59 J.S.WroUcwtkl

tuns) THE -1O0 MYI Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

Radliu I/I Djrcw

20 15 ,, , 10 (km)

DISTANCE FROM SHORE (km) 20 15 10 5

Flf.9 Same ai Figure 8 but on model day 10. The maximum u and w velocities in (a) are -6.1 an sec"1 and 5.2x 10"2 cm sec"1, respectively.

periods (Figure 9c). However field data (Figure 2c) indicates few animals (< 100 animals m"3) are found further offshore than 12 km. To improve the simulation, the upwelling circulation model was next driven by more realistic wind conditions. b. The intermittent upwelling case. The assumption of a constant wind stress driving the upwelling circulation has led to an overestimate of the offshore transport of A. clausi away from the coast. As upwelling off Oregon is character- istically intermittent with wind events of 2-7 days duration (Huyer, 1976), the model was rerun using a wind stress calculated from anemometer data for the period August 1 - 10, 1973 (Figure 6b). After 10 days of intermittent upwelling the offshore extent of A. clausi adults (Figure 12b) is considerably less than 60 Modd of Acartia dausi daring Oregon Upwdllng

DAY 10 DISTANCE FROM SHORE (km) 25 20 15 K> 5 Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 -<0.05

-A

- <0.05

Fig. 10 The zonal distribution of A. dausi nauplii (a) and copepodids (b) on model day 10. Multiply nondimensional contour levels by 2,000 to obtain numbers m~3.

during 10 days of continuous winds (Figure 12a) even though the wind stress is often greater than -0.5 dynes cm"2. The significantly better simulation indicates that a realistic wind forcing is essential in modeling the distribution of plankton in upwelling regions. However the model results can still be improved. Evidently the mortality of A. dausi adults has been underestimated. To determine the effect of increased mortality (possibly caused by ctenophores, chaetognaths or zooplanktivorous fishes schooling nearshore; W.T.Peterson, personal communication) on the adult distribution, the model was rerun assuming that 90% of the adults were removed within 10 days of entering the nearshore zone from the estuary. The result of increasing p4 from 0.067 to 0.23 is to limit the offshore extent of the 0.1 contour to 14 km (Figure 12c) rather than 18 km (Figure 12b). Based on our confidence in modeling offshore transport and development time correctly, the discrepancy between simulated and observed distributions can be further adjusted, resulting in an estimate of field mortality. But we must first determine the accuracy of the model in predicting the cross-shelf transport of A. dausi on short time scales « 10 days). c. Comparison with observations. To check the ability of the model to predict the observed distribution of A. dausi off Oregon, the model was run for the period

61 J.S.Wroblewski

r nena pun uno ma -axo oat Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

DISTANCE FROM SHORE (km) 20 15 |0_

Fig. 11 Same as Figure 8 but on model day 20. The wind" stress has been zero since model day 10. The maximum u and w velocities in (a) are -2.8 cm sec"1 and 7.9x 10"3 cm sec"1, respectively.

August 6-16 and the model solutions compared to field data taken on August 14, 15 and 16 (Figure 2). Note that a strong upwelling event occurred during this 3 day period (Figure 6b). Although we cannot dismiss longshore variation in the A. clausi fields, it appears these animals occurred further offshore on August 16 after the ocean responded to the enhanced wind stress by increasing the offshore velocities in the surface Ekman layer. This is predicted by the model (Figure 13). The same water parcel may not have been sampled by the second transect as it moved down the coast from Nestucca line on August 14 to Cascade Head line on August 15 (a separation of 12 km) with a longshore velocity of -25 cm sec"1 (Johnson et al., 1976). But the Newport transect on August 16 may well have sampled that water parcel observed 60 km to the north on August 14. As the

62 Model of Acartia dausi during Oregon UpweHiiig

DAY tO CONSTANT WIND STRESS, fi4 ' O.O67 Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 x

40 O

AUGUST 10 INTERMITTENT WIND STRESS.04*0.067 25

AUGUST 10 INTERMITTENT WIND STRESS, /34 '0.23 25 20 15 P S — i i I' I I i i I / i I I I / I I I I 1/ I 1 I I I T -c

Fig.12 The predicted adult A. dausi distribution a) after 10 days of continuous upwelling and b) after 10 days of intermittent upwelling during August 1973. The lowest panel (c) is the same as (b) except the mortality coefficient f)t has been increased. alongshore flow closely follows the bathymetry (Huyer and Smith, 1978), the A. dausi concentrations off Newport may just reflect the shallower depths (Figure 1). If indeed we wish to place our confidence in predicting the offshore transport of A. dausi during this period, the numerical circulation model must be validated by comparison to current meter measurements. Seldom does one have both physical and biological measurements in detail in the same water parcel. However, Thompson (1978) was able to compare his model predictions for a 64 hour period from August 27-30, 1973 with profiles of horizontal velocity recorded by an array of three Cyclesondes (automatic profiling current meters)

63 J.S.WroWewsld

AUGUST 14 DISTANCE FROM SHORE (km) 25 20 15 10 5 1 Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

AUGUST 16 25 20

0.05

<0.05

Flg.13 The adult A. clausi distribution predicted foV the upwelling event August 14-16, 1973. Multiply nondimensional contour levels by 2,000 to obtain numbers m"3. Compare these distri butions to the observational data for the same period shown in Figure 2.

positioned 15 km off the Oregon coast near the Nestucca transect. The predicted u velocities averaged over the 64 hour period showed good agreement with the data in the upper 30 m of the water column (Figure 14). While similarity in the observed and predicted velocity profiles does not constitute validation of the physical model (current meter measurements near the surface of the ocean are often contaminated by inertial motions and surface waves), it does suggest the flow field used to advect A. clausi is reasonably accurate. The feature of importance in Figure 14 is not the fit of the two profiles, but the fact that both the measured and predicted magnitude of u is of the order 1 cm sec "'. The value of u is much less than instantaneous horizontal velocities which are order 10 cm sec"1.

64 Modd of Acartia dausi daring Oregon UpweUIng Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019

LU Q

100

Fig. 14 Comparison of the time averaged u velocity profile predicted by the numerical upwelling model with Cyclesonde observations for the period August 27-30, 1976. Solid lines represent observed values, dashed lines represent model prediction (from Thompson, 1978).

Predictions of time-integrated offshore transport appear to be correct. Conclusions and critique Acartia clausi is an estuarine copepod species with a severely limited offshore distribution during the summer upwelling season off Oregon. Those individuals present in the upwelling region appear to have been adverted into the sea from estuaries, bays, and shallows along the coast. Based on an ability to simulate the spatial structure of an A. clausi population in the upwelling zone during August 1973, it can be concluded that the factors governing the offshore distribution of the four life stages are 1) the magnitude and intermittency of the wind driven offshore transport, 2) the duration of each stage and 3) field mortality. The copepods are not adverted as far offshore during periods of intermittent upwelling as they are during prolonged periods of continuous upwelling. The relaxation phase of intermittent upwelling carries A. clausi back towards shore, reducing the cross-shelf transport of the copepod. This implies that plankton may be washed out of the upwelling ecosystem by steady winds. The steady wind effect has been suggested as the cause for the lower biological productivity of the Northwest Africa upwelling ecosystem compared to the Oregon system (Walsh, 1977). A second conclusion to be drawn from the simulations is that high mortality of A. clausi must be occurring at all stages. Otherwise the offshore transport of- 1 to 10 km day"1 would carry the animals far to sea within their 60 day lifespan.

65 J.S.Wroblewiki

High mortality and intermittent upwelling together can explain the limited offshore distribution of A. clausi in the Oregon upwelling zone. The clockwise rotating gyre hypothesized by Peterson et al. (1979) to explain the maintenance of high inshore copepod populations may indeed exist during the spin up phase of active upwelling (Hagen, 1974). But the gyre may be too ephemeral to affect the overall transport of zooplankton across the shelf. The alternation of active upwelling and relaxation periods characteristic of the Oregon coast in summer

(Huyer, 1976) may have a greater influence on the distribution of coastal zoo- Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 plankton populations. There is yet another hypothesis which the model explores indirectly. As part of its behavior A. clausi may seek a depth which by coincidence is also a region of minimum offshore transport. Figure 14 suggests depths of 10 to 15 m may en- compass such a region. While the model does not consider active migration by A. clausi, the concentration maximum at the coastal boundary is situated at 11 m in all simulations. Our conclusions would not differ significantly if this behavior actually occurred. The simulation model presented here reproduced the observed A. clausi distributions using simple formulations for biological development and mortality. Only seven biological parameter values were needed, three of which (the development rate parameters) are well known. However a very complex numerical circulation model driven by actual wind forcing was, necessary to predict the offshore transport of A. clausi accurately. Since A. clausi distributions are just as sensitive to the physical dynamics as to rates of development and mortality, even more sophisticated upwelling models are required before fine tuning of the simulation can assign a correct field mortality rate. Acknowledgements This work was supported by the Natural Sciences and Engineering Research Council Canada. The National Center for Atmospheric Research, Boulder, Colorado awarded the author a Computing Facilities Grant in support of this research. NCAR is sponsored by the U.S. National Science Foundation. Com- putations were also performed on the CDC 6400 at Dalhousie University. I wish to thank Dr. J.D.Thompson who provided the physical component of the model, Drs. C.B.Miller and W.T.Peterson who provided the observational data and stimulus for this research, and Drs. A.J.Bowen, C.M.Boyd, C.J.R.Garrett, J.J.O'Brien, G.A.Riley and J.R.Strickler for many valuable discussions.

66 Model of Acartia clausi during Oregon Upwelling

Appendix Definition of symbols and scaling relationships. Dimensional Scaling Non-dimensional Quantity Definition Factor Quantity H Characteristic vertical length scale — — Kh Horizontal eddy diffusivity Kv Vertical eddy diffusivity — — L Characteristic horizontal length scale — — Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 t Time to, T u x-directed velocity component u/U u' U Typical horizontal velocity — — w z-directed velocity component w/W w' W Typical vertical velocity — — X Tangent-plane Cartesian coordinate: x positive toward the coast x/L x' z Tangent-plane Cartesian coordinate: z positive upwards z/H z' Concentration (number m~3) of copepods of life stage n Zi 3 zD/z, z, Total number of copepods (all stages) peT m for population at steady state — — "n Development time coefficient of copepod stage n < Pn Mortality coefficient of copepod stage n K

References Bradford, J.M.: 1976, 'Partial revision of the Acartia subgenus Acartiura (Copepoda: Calanoida: Acartiidae)'. New Zealand Journal of Marine and Freshwater Research 10, 159-202. Bryden, H.L.: 1978, 'Mean upwelling velocities on the Oregon continental shelf during summer 1973'. Estuarine and Coastal Marine Science 7, 311-327. Conover, R.J.: 1956, 'Oceanography of Long Island Sound, 1952-1954. VI. Biology of/4 cartia clausi and A. tohsa1. Bulletin Bingham Oceanographic Collection 15, 156-233. Gehrs, C.W. and Robertson, A.: 1975, 'Use of life tables in analyzing the dynamics of copepod populations' . Ecology 56, 665-672. Hagen, E.: 1974, 'Ein einfaches Schema der Entwicklung von Kaltwasserauftriebszellen vor der nord- westafrikanischen KQste'. BeitrUge zur Meereskunde 33, 115-125. Hutchinson, G.E.: 1978, An Introduction to Population Ecology. Yale University Press, New Haven. 260 pp. Huyer, A.: 1976, 'A comparison of upwelling events in two locations: Oregon and Northwest Africa'. Journal of Marine Research 34, 531-546. Huyer, A. and Smith, R.L.: 1978, 'Physical characteristics of Pacific Northwestern coastal waters'. In The Marine Plant Biomass of the Pacific Northwest Coast (Krauss, R. ed). Oregon State Uni- versity Press, pp. 37-55. Johnson, W.R., Van Leer, J.C. and Mooers, C.N.K.: 1976, 'A cyclesonde view of coastal upwelling'. Journal of Physical Oceanography 6, 556-574. Ketchum, B.H.: 1954, 'Relation between circulation and planktonic populations in estuaries'. Ecology 35, 191-200. Landry, M.R.: 1975, 'The relationship between temperature and the development of life stages of the marine copepod Acartia clausi Giesbr. Limnology and Oceanography 20, 854-857. Landry, M.R.: 1978, 'Population dynamics and production of a planktonic marine copepod, Acartia clausi, in a small temperate lagoon on San Juan Island, Washington. Internationale Revue der gesamten Hydrobiologie 63, 77-119.

67 J.S.WroblewskJ

McLaren, I.A.: 1978, 'Generation lengths of some temperate marine copepods: estimation, prediction, and implications'. Journal Fisheries Research Board Canada 35, 1330-1342. Miller, C.B., Johnson, J.K. and Heinle, D.R.: 1977, 'Growth rules in the marine copepod genus Acartia. Limnology and Oceanography 22, 326-334. Mooers, C.N.K., Collins, C.A. and Smith, R.L.: 1976, 'The dynamic structure of the frontal zone in the coastal upwelling region off Oregon'. Journal Physical Oceanography 6, 3-21. Myers, A.: 1975, 'Vertical distribution of zooplankton in Oregon coastal zone during an upwelling event'. M.Sc. Thesis, School of Oceanography, Oregon State University, Corvallis, 60 pp. Peterson, W.K.: 1972, 'Distribution of pelagic copepods off the coast of Washington and Oregon

during 1961 and 1962'. In The Columbia River Estuary and Adjacent Waters (Pruter, A.T. and Downloaded from https://academic.oup.com/plankt/article-abstract/2/1/43/1463810 by Old Dominion University user on 08 July 2019 Alverson, D.L., eds). University of Washington Press, Seattle, pp. 313-343. Peterson, W.T. and Miller, C.B.: 1975, 'Year-to-year variations in the planktology of the Oregon upwelling zone". Fishery Bulletin 73, 642-653. Peterson, W.T., Miller, C.B. and Myers, A.H.: 1979, 'Zonation and maintenance of copepod populations in the Oregon upwelling zone'. Deep-Sea Research 26, 467-494. Piacsek, S.A. and Williams, G.P.: 1970, 'Conservation properties of convection difference schemes'. Journal Computational Physics 6, 392-405. Prepas, E. and Rigler, F.H.: 1978, 'The enigma of Daphnia death rates'. Limnology and Oceano- graphy 23, 970-988. Sekiguchi, H. and Kato, T.: 1976, 'Influence of Noctiluca's predation on the Acartia population in Ise Bay, Central Japan'. Journal Oceanographic Society of Japan 32, 195-198. Smith, R.L.: 1968, 'Upwelling'. Oceanography and Marine Biology Annual Review 6, 11-46. Steele, J.H. and Mullin, M.M.: 1977, 'Zooplankton dynamics'. In The Sea, Vol. 6 (Goldberg, E.D., McCave, I.N., O'Brien, J.J. and Steele, J.H., eds). John Wiley & Sons, New York, pp. 857-890. Thompson, J.D.: 1974, 'The coastal upwelling cycle on a betaplane: hydrodynamics and thermo- dynamics', Ph.D. Thesis, Department of Oceanography, Florida State University, Tallahassee, 141 pp. Thompson, J.D.: 1978, 'Role of mixing in the dynamics of upwelling systems'. In Upwelling Eco- systems (Boje, R. and Tomczak, M., eds). Springer-Verlag, New York, pp. 203-222. Tomovic, R.: 1963, Sensitivity Analyses of Dynamic Systems (Tornquist, D. trans.). McGraw-Hill, New York. 142 pp. Walsh, J.J.: 1977, 'A biological sketchbook for an eastern boundary current'. In The Sea, Vol. 6 (Goldberg, E.D., McCave, I.N., O'Brien, J.J. and Steele, J.H. eds). John Wiley & Sons, New York, pp. 923-968. Wroblewski, J.S.: 1977, 'A model of phytoplankton plume formation during variable Oregon upwelling'. Journal of Marine Research 35, 357-394. Wroblewski, J.S.: 'Interaction of currents and vertical migration in maintaining Calanus marshallae in the Oregon upwelling zone'. Dalhousie University (in preparation). Wroblewski, J.S. and O'Brien, J.J.: 'The role of modeling in biological oceanography'. In Ocean Handbook (Home, R.A. and Hood, D.W., eds.). Marcel Dekker Press, New York (in press). Wroblewski, J.S. and O'Brien, J.J.: 'On modeling the turbulent transport of passive biological variables in aquatic ecosystems'. Submitted to Ecological Modelling.