Abstract--The zonal distribution of five life stage categories (egg, nauplius, early .... stages CIV-V and adults exhibit diel vertical migration (PETEXSON,. 1979) ...
~h, Vol.29, No. 6A, pp. 665 to 686, 1982. Printed tn GreatBr;taln.
0198-0149/82/0~665--22$03.00/00 © 1982PerlamonPremLtd
Interaction of currents and vertical migration in maintaining Calanus marshallae in the Oregon upwelllng zone, a simulation J.S. WROBLEWSKI* (Received 2 July 1981; in revisedform 7 January 1982; accepted 8 January 1982) Abstract--The zonal distribution of five life stage categories (egg, nauplius, early copepodites CI-III, late copepodites CIV-V, and adult) of the neritic copepod Calanus marshallac observed by PETERSON, MILLERand HUTCHINSON(Deep-Sea Research, 26, 467--494, 1979) during coastal upwelling off Oregon in August 1973 is simulated. The model uses linear formulations to express copepod developmmt and mortality and a time-dependent velocity field predicted by a numerical, upwelling circulation model to carry the copepods. Simulations demonstrate how diel vertical migration by adults can interact with upwelling currents to increase the residence time of egg-laying copepods in the nearshore zone. Diel vertical migration by late stage copepodites may enhance rather than retard their offshore transport if they enter waters sinking below the permanent pycnocline 10 to 20 km from the coast. Predicted longshore trajectories of vertically migrating copepods trapped in the region of intense upwelliag show a spiral path over the continental shelf. The extent of longshore transport for copepods seaward of this zone is strongly dependent on the structure in the flow field and on the behavior of the copepod; however, vertical migration always tends to retard longshore transport. Using the theoretical flow field, the model hindcasts the shape and location of transects needed to sample migrating and non-migrating copepods as the population moved down the coast.
INTRODUCTION
PETERSON, MILLER and HUTCHINSON(1979) presented observational evidence that the distribution of the neritic copepod Calanus marshailae in the Oregon upwelling zone is governed by interaction of the upwelling circulation with the animal's vertical migration. They suggested that an ontogenetic migration by adult females brings reproducing individuals nearshore in newly upwelled water. The females lay their eggs in the food-rich region 3 to 5 km from the coast. Developing eggs, nauplii, and early stage copepodites are carried offshore in the surface Ekman layer. P~rERSON(1979) proposed that diel vertical migration by the late stage copepodites reduces their transport out of the upwelling zone. This paper is a theoretical analysis of the field distributions presented by PErERSONet al. (1979). Laboratory studies by PET~Pa~ON(1979) have made available values for the life history parameters of the cop:pod. A detailed description of the flow that transports the life stages of C. marshallae is available in the form of a numerical, hydrodynamical model by THOMPSON (1974). This theoretical circulation is consistent with patterns of primary productivity and phytoplankton biomass observed by SMALLand M ~ z I ~ (1981) during strong upwelling. Rarely is such an extensive biological and physical data set available, making hypothesis testing by simulation analysis worthwhile. * Department of Oceanography, Dalhousie University, Halifax, NS B3H4JI, Canada. 665
666
J.s. WROBLEWSKI
TO explore the influence of ontogenetic and diel vertical migration upon the distribution of C. marshallae in the Oregon upwelling zone, a numerical (x, z, t) model was constructed. The distribution of several life cycle stages (passively drifting eggs, nauplius stages NI-VI and copepodite stages CI-III, and vertically migrating copepodite stages CIV-V and adults) are predicted for the cross-shelf, zonal plane. Simulations are conducted to enable direct comparison of model results with observations made by PETERSONet al. (1979) during the period 14-16 August, 1973. Three-dimensional trajectories of hypothetical, individual copepods that migrate and of others that do not, are computed to determine expected distances of longshore transport. The computations illustrate the degree of difficulty involved in attempting to sample both migrating and non-migrating copepods as the population moves down the coastline. The model is used to predict the location and configuration of field sampling transects that would intercept copepods exhibiting either behavior, assuming a known velocity field. MODEL DEVELOPMENT
Simplified models investigating the interaction of currents and vertical migration by plankton in the open sea have been proposed by RmEY (1976), KAMYKOWSKI(1976), EVANS, STEEI,E and KULLENBERG(1977), STEELEand MULLIN(1977), LEDBETTER(1979), and EVANS and TAYLOR(1980). The models all stem from the realization by HARDYand GUNTHER(1935) that zooplankton distributions can be dramatically affected by migration through a zone of horizontal current shear. The results indicate that patchiness can be created in the distribution of zooplankton. The present simulation study differs from the above models in the detail included in the current pattern and in the plankton dynamics. The flow field is not symmetric, i.e., the presence of the coast introduces horizontal structure in the currents and ultimately in the zooplankton distribution. The velocity field is also highly time-dependent, being driven by a fluctuating wind stress. The biological dynamics are designed to describe the life history of a particular copepod species. To some extent the model sacrifices generality to obtain realistic solutions for C. marshallae (O'CONNOR and PATTEN, 1968). In a similar approach, BROCKMANN (1979) applied the results of a numerical circulation model in an attempt to calculate drift path trajectories of the zooplankton species Euphausia krohnii in the upweiling zone off Northwest Africa. Formulation of C. marshallae dynamics The zonal distribution of five life stage categories of C. marshallae over the Oregon continental shelf was modeled by the two-dimensional (x, z, t) equation, -
0Z, 0Z, 0Z, 32Z, b2Z, + u -+ (w + w,) ------7- - - = population dynamics, Ot Ox Oz - K h 3xZ - K ~ 3z 2 -
(1)
where n = 1, 5 such that Z] represents the concentration of eggs (numbers m-3), Z2 is the concentration of nauplii, Z 3 is the concentration of copepodites in stages C I-III. Variable Z 4 represents stages glIV~V and Z5 is the concentration of adults. The total population biomass Zt = Y.Z,, n = 1,5. Thus, Z , is the fraction of the total population in the nth stage category. Parameter Z, will be used later in scaling equation (1), allowing the solution of the equation without specifying a value for Z,, which is hard to measure.
Interaction of currents and Calanus vertical migration
667
The first term in equation (1) is the loc~l ~ f i Z,, where t is time. The second and third terms represent advection of Z,. where u and w represent the horizontal and vertical water velocities, respectively. The diffusion terms represent turbulent mixing of Z , on scales smaller than can be resolved by the model. The coefficients/('h and K, have been assumed constant. This is justifiable when a detailed velocity field is available to simulate the structure in the distribution of a biological variable primarily governed by advection [see WROBLEWSKI and O'BR]F~ (1981) for a lengthy explanation]. If the details of the flow are not included, a variable diffusion coefficient must be used to parameterize the motions. As late copepodite stages CIV-V and adults exhibit diel vertical migration (PETEXSON, 1979), the vertical advection term in equation (1) has a biological component. The vertical velocity w, is the swimming speed of the nth life stage category. Eggs, nauplii, and copepodites CI-III are considered passive drifters, whereby w, -- 0, n = 1, 3. For copepodites CIV-V and adults, however, w, is assumed a function of time w, -- w, sin(2~ct), where w, is the maximum vertical migration speed of the nth stage. Based on vertical distributions of C. marshallae reported by PETF-RSON(1979), W, is assumed to be 0.1 cm s -~ for both CIV-V and adults. A higher value of K, is used for vertically migrating copepodites and adults than for passively drifting stages (see Table 1). Thus, the model has the property that only a fraction of the later stage copepodites migrate to the surface at night and not all of these leave the surface each day. The population dynamics included in equation (1) describe the development of eggs successively into nanplii, copepodites, and finally adults (Fig. 1). Mortality at each stage is also described. Development time of each life stage category is available from laboratory studies by PETERSON(1979). The model assumes C. marshallae development is not food limited in the upwelling zone and is mainly governed by temperature. PETERSON(1979) gives support for this assumption. (a)
j
z,
/I
Eggs
Nouplii
1 Copepodites / cz-"
z,
"1Copepodites /
Adults
1
(h)
- StageCI ~6do)~I StageNT t9 doysJ
Mortality
16% Idortalitv
Adult I
27%
Mortolitv
I Eventual 100% Mortality
Fig.l. (a) Schematic representation of the C. marshailae population dynamics included in the model. (b) Development times (determined by Pm'ERSON, 1979) and percent mortalities during each developmental period.
668
J.s. WROBLEWSKI
The developmental transfer of population numbers from stage to stage and the mortality at each stage are expressed as linear functions. KgEMV.Rand NIxoN (1978) resorted to complex formulations to model the details of age structure of copepod populations in Narragansett Bay, a complexity not necessary for our purposes. Instead assume that the ages of individuals in each stage form a continuum. Moreover, let a fixed fraction of all individuals in a stage develop into the next stage in unit time. Neglecting spatial derivatives for the moment, this can be formulated as dZ ~ eggs laid (eggs) = - a ]Z ~- 13jZ i (2) dt unit time dZ2 (nauplii) . . . . . dt
(1 I Z l - ((12 -.t- [3 2) Z 2
(3)
dZ3 (CI-III) . . . . . . dt
(12Z2- ((13 + 133)Z3
(4)
dZ4 (CIV-V) . . . . dt
(13Z3 - ((14 + ~4) Z 4
(5)
(adults)
dZ5 dt
= (14Z4 - 135Z5,
(6)
where a,(day -t) is 2/D., where D , is the development time of the nth life stage category. With this formulation of copepod development, 87% of the individuals present at time zero will progress to the stage n + 1 in the time interval D n. The remaining 13% take longer to complete their development. However, there is no preference for these individuals to mature in the next u nit of time. Peterson found enough variance in the development times to justify this level of parameterization.* Parameter 13, is the mortality rate (day-t). Each stage has a different value of 13 assigned, based on field observations reported by PETERSON(1979) or on the reported susceptibility of a particular stage to predation. Although PETERSON(1979) was able to identify cohorts in his 1977 field samples, he concluded that C, marshallae abundances remain relatively constant during the summer. Because there is no pronounced increase in the total population, one can assume dZt/dt = 0. Egg production then balances the summed mortality of the various stages, 5
eggs laid = Y- 13,Z,. unit time n=] With this assumption, the egg mortality term 13IZI cancels from the model equations and there is one less parameter to be specified in the model. The above formulation has the effect of immediate reincarnation of all mortalities back into eggs. However, as some females are always present (due to a choice of initial conditions), these females can be regarded as producing eggs at a rate which balances the local loss of all copepod stages. A more realistic formulation of egg production will be used later in modeling the zonal distribution of C. marshallae to demonstrate that the spatial patterns are relatively insensitive to the details of egg production, Indeed the more realistic formulation requires the * Parameterization is the process of representing in the model the net effects of unresolved dynamics.
Interaction of currents and Calanus vertical migration
669
specification of unknown parameters. In its p t ' e ~ f ~ , the set of equations (2) to (6) is conservative and lends itself to a useful, analytical sensitivity analysis.
Parameter values for C. marshallae population dynamics Laboratory rearing of C. marshallae by PETERSON(1979) showed the egg development time D~ to be approximately 2 days at 10°C. For colder, newly upwelled waters nearshore, egg hatching times would be longer. Parameter u, is chosen to be 0.5 day -~. With the formulation of development in the model, 63% of the eggs present at time zero will have hatched after 2 days, and 87% will have hatched after 4 days. PETERSON(1979) observed a development time from the first nauplius stage to CI of 19 clays at 10°C. Therefore, a2 -- 0.104 day -~ such that 87% of the nauplii present at time zero will have developed into the CI stage after 19 days. As the development oftbe first copepodite stage into the CIV stage takes 16 days at 10°C, parameter ct 3 =0.127 day -m. PETERSON (1979) found the development from CIV to CVI was not isochronal (MILLER,JOHNSONand HEINLE, 1977; MCLAR~N, 1978), instead taking a relatively long period. In the model parameter a4 = 0.074 day -~, whereby 87% of an initial CIV number will have matured into the adult stage within 27 days. Values for the mortality rate parameters [3, are based on observations of stage-specific abundances in the field reported by PETERSON(1979). Mortality is thought to be extremely high between the egg and NIII stage, less so for the late nauplii and copepodite stages, and high again in the adult stage. As the egg mortality term has been eliminated from the model equations, only an overall nauplius mortality need be specified. With a value of [32--0.104 day -~, 87% of the nauplii are lost during the first 19 days from hatching. Mortality is not differentiated among the six nauplius stages. PETERSON(1979) suggested that mortality during the copepodite stages is very low, only approximately I% per day. Therefore, [33 = 134= 0.01 day -~. High mortality of Calanus in the nauplius stage and near-zero mortality in the early copepodite stages is consistent with the results of a field study of C. helgolandicus (pacificus) by MULLINand BROOKS(1970). The adult stage on the other hand does not survive long in the nearshore zone, where predation by planktivorous fishes causes a high mortality, ~5 = 0.16 day -~ (PETERSON, 1979). The values of all population dynamics parameters for C. marshallae are summarized in Table 1.
Table 1. Parameter valuesfor the Calanus marshallae model Physical parameter H Kh Kv L At U W Ax Az
Value 5 x 103cm 5 × 105¢m2s -I 1 cm 2 s-I(for Z13 ) 10 cm 2 s -1 (for ~4,5) 5 × 10%m 3.6 × 102s 20 cm s -t I X 10-2cm s -I I x 105cm 2.5 × 102cm
Biological parameter
Value (day - | )
aI a2 a3 a4 [32 ~3
0.500 0.104 0.127 0.074 0.104 0.010 0.010 0.160
[34
[35
670
J.s. WROBLEWSKI
Scaring, solution, and sensitivity analysis of the population dynamics model Already one parameter, namely 13i, has been eliminated from the set of equations (2) to (6). By scaling these equations the number of parameters in the model can be further reduced. If one normalizes time by the fastest biological rate tt ~(x = a it) and normalizes each concentration by Z t (Z'. = Z . / Z t ) , the model solutions become independent of these two parameter values, The scaled forms of equations (2) to (6) are
dZ'~ dx
= ~'2z'2 + ~'3z'3 + ~'~z'~ + ~'sz'~ - z ' ,
- - = ct'n_lZ',_l -(ct" + [3") Z" dx
(7)
for n = 2, 4
(8)-(10)
and I
I
(l l)
"~- 0 . 4 Z 4 -- p ~ Z t s ,
dx
where primed parameters denote original values normalized by a l and primed variables denote scaling by Z r The time-dependent numerical solution of the scaled population dynamics model is shown in Fig. 2. Peak concentrations of eggs, nauplii, copepodites CI-III, and finally copepodites CIV-V appear successively from an initial abundance of adults. The population achieves a steady-state partition among the five life stage categories after 50 days. Because
1.0-~ Co~onus morsholloe 0.81 ~UX~-TS (reproductionboloncesmortolity}
I\
P, 0.4 Lz.
ol
z2,.
......
.....
..... .... " v
!
0
!
I
5
I
I
tO
I
,. I
15
I
20
NONDIMENSIONAL TIME ~" Fig. 2. Time-delmndent solution of the C. marshailae population dynamzcs model, where ¢88s, nauplii, early and late copcpod~ develop sequentially from an initial number of adults, Concentrations of each stage are express¢¢las a fraction of Z t, the total population (all stages m-l). Each nondimensional
unitof timerepresents2 days,
Interaction of currents and Ca/anus vertical migration
671
¢, = 0.5 day -I, each non-dimensional unit of time in Fig. 2 represents 2 days. The steadystate concentrations obtained by the numerical solution of equations (7) to (11) agree to within a negligible error with the analytical solution of these linear equations. One can use these steady-state values in a sensitivity analysis of the biological model. To determine the general behavior of the model as a function of the development and mortality parameters, an analytical sensitivity analysis was performed. 'Sensitivity' is formally defined as the displacement from equilibrium the model experiences due to a quantitative change in an individual parameter (ToMovlc, 1963). The derivation of this sensitivity analysis is similar to that presented by WROnLEWSKI(1980) and will not be described here. The results of the analysis are summarized in Table 2. Overall, the most sensitive behavior of the model is the variation of Z~ (adult numbers) in response to the parameter 13~ (adult mortality rate). The sign of this sensitivity is negative, indicating that a decrease in adults results from increased mortality. The second-most sensitive dependent variable is Z~ (copepodite CI-III numbers), which responds to ct'3 (early copepodite development rate). The faster the development into the next stage, the lower the numbers in that life stage category. The next two highest sensitivities, ~Z'2/~¢'2 and ~Z'c/~a'4, are explained by the same argument. The fifth-largest sensitivity is positive in sign, and indicates that increases in ~ (mortality rate of nauplii) would result in higher egg numbers Z'~. This is a consequence of the assumption that egg production in the model is balanced by the summed mortalities of the various life stage categories. The results of the sensitivity analysis are not surprising in view of the linearity of the population model dynamics. The quantity in each model compartment increases or decreases with changes in the parameters, analogous to speeding up or slowing down the processing along an assembly line. The worth of the sensitivity analysis lies in identifying the most important parameters. These parameter values must be accurately determined in the field or laboratory. It is somewhat distressing that the most important parameter lYs (adult mortality rate) is very difficult to estimate in the ocean (MULLISand BROOKS, 1970; PETERSON, 1979). The development rate parameters ¢2, ¢x3, and a4 can be measured more easily at sea or in the Iaboratory.
Tabs 2. SensM~ analys~ of C. marshallaepopu~tion dynamics zl a(, a~ a~
[3~
z;
z;
z:
-0.184 -0.685 0.314 0.315 0.150 0.151 -0.777 0.224 0.245 0 . 2 4 6 0.245 -0.636 0.444
-0.054
z; 0.316 0.225 0.365
- 0 . 0 5 4 -01054 -0.054
[3~
0.046
0.046 -0.027 -0.027 -0.027
[~
0.052
0.052
0.052
[3~
0.137
0.137
0.137
-0.067
--0.067
0.137 -0.863
Partial derivative values of eggs Z~, nanplii Z~, CI-III copepodites Z|, CIV-V copepodites Z~, and adults Z~, differentiated with respect to the development and mortality parameters and normalized by the parameter:steady-state value ratio, e.g. (a~/Z~/aZ~/ao~).Expressed in this manner, a model sensitivity of -0.184 means for a 1% increasein e~, the steady-state value of Z~ would decrease by O. 184%.
672
J.s. WROBLEWSKI
Modeling the zonal distribution of C. marshallae
The numerical circulation model by THOMPSON(1974) was used to predict the advection of the five life stage categories of C. marshallae in the Oregon upwelling zone. The zonal distribution of Z , was predicted for a region extending 50 km from the coast down to a depth of 50 m (Fig. 3). Observations by PETERSONet aL (1979) and P~rERSON (1979) show most eggs, nauplii, and copepodites occur within this region. The zone was divided into a grid with spacings 2.5 m in depth and 1 km in the horizontal. All biological simulations were confined to the area. Thompson's circulation model predicts the flow not only within the model region but continuously from the coast out to 3500 km from shore, and from the surface down to the bottom of the water column. A telescoping grid was used for high resolution of the flow in the upwelling zone. The bottom topography assumed was a iinearized version of the actual bottom slope off Oregon. A bottom depth of 50 m at the coast was assumed to simplify computations. Thus, the shallow coastal zone is not resolved in the model. This is unfortunate, as it was the anomalously high concentrations of copepods in this region that PETE~ON et aL (1979) found most intriguing. Model solutions in the nearshore zone are an idealized account, and causes for the observed anomalous concentrations near the beach can only be suggested. The physics incorporated in the upwelling circulation model have been discussed in detail by THOMPSON(1974, 1978). Simply, the model simulates the time-dependent response of the ocean to winds favorable for coastal upwelling. To achieve the proper initial conditions in both the physical and biological fields prior to the period of observations, the model was driven for 20 days by a constant wind stress o f - 0 . 5 dyne cm -2. During this spin-up period the density field achieves a state of upwdling and the basic pattern in the zonal distribution of the various stages of C. marshallae develops. The model was then driven by a time-dependent wind stress calculated from anemometer data recorded at Newport, Oregon to simulate the upwelling circulation and distribution of C. marshallae from 6 to 16 August, 1973. Thus, the last three days of the model run predict the distribution of the five life stage categories for the period 14 to 16 August, when PETERSONet aL (1979) made their observations. The u and w velocities computed by Thompson's model were used in a scaled version of equation (1). To ensure that the physical and biological dynamics were properly coupled, time
DISTANCE OFFSHORE (kin) 5O I0
20~--o
Fig. 3.
40
50
20
I0
0
INITIAL CONDITIONS .....
, .........
, .........
":
i:'~
....
Grid spacing, boundary conditions, and initial conditions for the spatial population dynamics model.
Interaction of curreats and Calanusvertical migration
, in equation (I) was again scaled by the test: bioiogioal rate. sion terms in equation (1) were scaled using the relationships, x" = x l L
u' = u l U
z'=zlH
w'=wlW
and
673
advection
diffu-
w'=w,IW,
where L and H are the width and depth of the model region and U and W are typical values of the horizontal and vertical water velocities. Substituting these scaling relationships, equation (I) becomes
Or
+
(w' +
3x'
-
3 2 Z~i ~)X I 2
~z,------Y = scaled population dynamics.
(12)
The magnitude of the coefficients of the scaled advection and diffusion terms determines the importance of these physical processes relative to the population dynamics in determining the distribution of Z'~. Evaluating the coefficients using the parameter values given in Table 1, one finds that advection and population dynamics share equal importance in determining the zonal pattern of copepod distribution. SMn-ri, BRI~K, S^NT^t~DER,COWLmand HuYF..g(1981) found the ocean circulation to be significant in explaining copepod distributions in the upwelling zone off Peru. This equal importance of the physics and biology in governing the distribution of plankton probably holds true for most upwelling regions (O'BRIENand WROSLEWSKI, 1973). For numerical solution, equation (12) was finite-differenced using a leap-frog scheme for the local time derivative, a quadratic-conservative scheme (PIACSEKand WILLIAMS, 1970) for the advection terms, and an explicit scheme for the diffusion terms. The diffusion and biological terms were lagged behind the advective terms by one time step. A time step A~ = 0.002 (or At = 0.1 h) was used, which was well within the bounds for computational stability. As for biological boundary conditions, no advective flux of copepods was allowed through the coastal wall or across the air-sea interface. At the 50-m depth of the water column, the direction of the flow determined the advective boundary condition. Water upwelling into the model region from below is devoid of all C. marshallae stages except adults (Fig. 3). If water is moving out of the model region, the concentration of the variable Z" just inside the boundary determines the value at the boundary. The offshore boundary was treated such that the horizontal flux of Z" is zero. No diffusive flux was allowed across any boundary. Initial conditions in the biological fields at the start of model spin-up were Z~, equals zero everywhere within the model region (Fig. 3). The population develops as adults are carried through the bottom boundary near the coast. As adults are lost to mortality, eggs are produced to replace them. Eggs develop into nauplii, and so on. As stated above, the model was run for a total of thirty days. By the 30th day, enough CIV-V copepodites have developed to determine clearly the distribution of that particular life stage category and all previous stages. The length of the model run is not unlimited, however. The effect of diffusion on the distribution of the biological variables increases with time. For example, the influence of horizontal diffusion on the spatial pattern of Z" is significant on length scales of the order
674
J. S. WROBLEWSKI
(Kht)~. For a model run of 1 day, this length scale is 2 km, but for a run of 30 days, diffusion contributes significantly to the copepod numbers distributed on scales of 10 km. This is the scale of zooplankton patchiness we are attempting to resolve in this study. Thus, one month is the largest time scale over which the model is valid. Integrating the model beyond 30 days would require a more sophisticated parameterization of turbulent diffusion. MODEL RESULTS
Comparison of observed and predicted zonal distributions of C. marshallae Predicted zonal distributions of the five life stage categories are shown in Figs 4 to 6. Model solutions for vertically migrating adults at noon on 15 August and at midnight on 16 August are shown in Fig. 4. Adult copepods enter from below the 50-m boundary near the coast with water upweiling into the model region. This only happens when the wind stress driving the circulation model is favorable for upwelling. Once adults appear in the model region, they undergo did vertical migration, are carried by advection, diffused with the circulation, and increase or decrease according to the population dynamics in equation (12). The great majority of adults shown in Fig. 4 have been carried by advection into the region rather than having arisen from developing stages. The predicted distribution for noon on 15 August (Fig. 4a) should be compared to Fig. 13c in PETERSONet al. (1979), if the reader wishes to make his own conclusions regarding the accuracy of the model solutions. Vertical migration is important in achieving a realistic distribution of adult C. marshallae numbers. Without migration, adults and all life stages that subsequently arise are carried too far seaward. Figure 7 shows the trajectory of a hypothetical copepod that migrates between 3 DISTANCE 40
50 --
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Simulated distribution C, marshalloe adults 15 August noon
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Simulated dia.tri . C. m a r s h a l l a e
i
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.
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T
30 o. W CD 40 50
Fig. 4. The simulated zonal distribution of C. marshaUae adults at noon on 15 August and at midnight on 16 August, 1973. Concentrations are expressed as a fraction of the total population (all stages m-3).
675
Interaction of currents and Calanus vertical migration
DISTANCE OFFSHORE
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50
Fig. 5. The simulated zonal distribution of C. marshailae (a) eggs, (b) nauplii, and (c) early copepodites at noon on 15 August. Concentrations of each stage are expressed as a fraction of the total population (all stages m-3).
and 44-m depth as it is carried by the flow predicted for 6 to 16 August. In Fig. 7a the copepod is initially l km from the coast. Only the trajectory for the last 2 days is shown. The asymmetric cycles reflect the offshore flow near the surface and the onshore upwelling flow at depth. The net offshore transport of the copepod in this nearshore region is near zero. If the copepod does not migrate vertically, it is carried much further offshore, especially if it does not reside near the surface where offshore transport is minimal (Fig. 8). Once past the influence of onshore flowing currents, vertical migration may actually contribute to a net offshore transport of the copepod. Figure 7b shows the trajectory of a hypothetical copepod initially located 6 km from the coast. Looped paths near the surface reflect intermittency in the wind stress driving the ocean circulation. Relaxation of the wind stress is followed quickly by onshore flow at the surface. Beyond a distance of 7 km from shore, all flow at depth is offshore, with the strongest velocities below 20 m (Fig. 8). Vertical migration into this region enhances offshore transport of the copepod.
676
J.
S,
WROBLEWSK1
DISTANCE OFFSHORE 50
40 i
: (a)
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i
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i
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i
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distribution
" C. m o r s h o l l o e staqes
15 August
i
(km)
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C. m a r s h a l l o e stoqes 16 August i i i i
midnight I I I
a
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i
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40 11
I
l
I
I
I
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I
,
i
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Fig. 6. The simulated zonal distribution of C. marshal!ae late stage co~podites at noon on 15 August and at midnight on 16 August. Concentrations are _cxpr~sed as a fraction of the total population (all stages m-3).
The zonal distributions of the egg, nauplius, and early copepodite stages predicted for noon on 15 August arc shown in Fig. 5. The center of highest concentration is further offshore with each successive stage. The distributions should be compared to Figs 14c and 15c in PETERSON et al. (1979) and Fig. 21 in PLrrEssON(1979). The highest concentration of eggs found on 15 August along the Cascade Head transect (45°06rN) occurred in a plume extending from shore out to 10 km and down to a depth of 30 m. The plume structure is reproduced in the simulation (Fig. 5a). Nauplii found along the Cascade Head transect were also distributed in a plume, with significant numbers extending out to 20 km from shore. The model solution (Fig. 5b) features a plume but differs from the data in predicting the transport of nauplii to depths greater than observed. P~EgSON et aL (1979) observed an anomolously high concentration of nauplii in the shallow region close to shore that the model does not reproduce. The model solution for the distribution of CI-III ~ s at noon on 15 August (Fig. 5c) shows a maximum conc~mtration near the surface 10 km from shore. The Cascade Head transect data presented in Fig. 21 of P~r~gsos (1979) shows two patches of early copcpodites, one near the beach and one 13 km from shore. The Newport transect occupied 48 km to the south on 16 August (Fig. 22 in P~T~,~ON, 1979), showed most CHI Col~Podites occurred between 6 and 9 km from shore. Few early copepodites were found seaward of 20 km. However, the continental shelf is wider off Newport than in the model bottom topography, so the Newport transect data and model remflts are not directly comparable. The mortality rate of 0.01 day -t used for early copepodites in the model may be an underestimate. If a higher value were used, concentrations of Z~ would be reduced and the leading edge of
677
Interaction of currents and Calanus vertical migration
DISTANCE OFFSHORE (km) 2
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~
-- 4 0
50
15
IO
'0
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IO 20 I--
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40 '5o Fig. 7. Zonal plane trajectories predicted for a hypothetical copepod performing a did migration between 3 and 44 m. (a) The trajectory begins on 6 August at a distance 1 km from the coast. Only the path between 14 and 16 August is shown. (b) The trajectory begins on 6 August at a distance 6 km from the coast. DISTANCE OFFSHORE 5O
I
25
I
20
I
15
I
(kin) I0
I
5
I
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o
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L-5o Fig. 8. Zonal plane trajectories predicted for passive panicles initially located at selected depths and distances from the coast. Trajectories are for the period 6 to 16 August, 1973, unless the particle is carded out of the model region.
678
J.S. WROBLEWSKI
the distribution would not reach so far offshore. Unfortunately there is no way to determine a better value for 133 from the limited observations. Figure 6 shows the predicted zonal distribution of CIV-V copepodites at noon at 15 August and at midnight on 16 August. The distribution of late copepodites differs markedly from the distribution pattern of the earlier stages. The highest concentrations occur far from shore and most contours do not extend to the coast. The pattern of the distribution is shaped by vertical migration of the late copepodites through shears in the horizontal currents (Fig. 8). Figure 21 in PETERSON(1979) provides data on the distribution of stages CIV-V along the Cascade Head transect on 15 August. Although the transect was too short to resolve the seaward limit of the distribution, it appears the highest concentrations occurred seaward of 10 km. The Newport transect data (Fig. 22 in PErERSON, 1979)match model predictions for noon on 16 August (not shown), but the change in bottom topography off Newport makes any verification tenuous.
Predictions of longshore transport of C. marshallae PETERSON et al. (1979) sampled C. marshallae along transects perpendicular to the coastline. Spacing of the transects was chosen to intercept the same water parcel as it moved along the coast (Fig. 3 in PETEaSON et aL, 1979). The model can be used to determine the efficiency of this experimental design in sampling a hypothetical population of C. marshailae as it is carried along the coast and offshore by the upweUing circulation. Three-dimensional trajectories were computed for hypothetical individual copepods for the 10-day period 6 to 16 August, 1973. Thompson's model was used to predict the longshore velocities as well as the zonal velocities used in the last section. The numerical circulation model assumes no longshore variation in the bottom topography, so the analysis neglects the changes in the width of the continental shelf off Newport. Figure 9a displays the trajectory of a non-migrating nauplius or early stage copepodite initially positioned 10 km from the coast at 10-m depth. The position of the copepod at the end of each day is marked by an arrowhead. Arrows are placed head to tail to indicate the trajectory over the 10-day period. Dashed vertical lines are dropped to a false floor at 50-m depth to depict horizontal movement more clearly. On 14 August after 8 days of advective transport, the hypothetical copepod finds itself at a depth of 6.8 m, still only 10.9 km from shore but 163 km further along the coast from where it began (Fig. 9a). Over the next 48 h it moves 45 km further south. Its depth remains near 6 m and its net offshore transport is minimal, the copepod finally resting 11.2 km offshore from an initial position 10 km from the coast. Vertical migration by the copepod radically changes the trajectory path. Figure 9b shows the trajectory of a late stage copepodite or adult copepod that migrates vertically between 3 and 44 m. Its initial offshore position is the same as in Fig. 9a, but the copepod begins and ends its diel migration at mid-depth. By 14 August it has moved only 100 km along the coast. OVer the next 48 h it moves only 25 km, roughly half as far south as the non-migrating copepod. While the longshore transport is lessened, the offshore transport is enhanced by migration. The final offshore position of the copepod is 20 km from the coast. However, as we saw in the zonal simulation of adult C. marshallae distribution, vertical migration helps retain copepods in the nearshore upwelling zone. Figure 10a shows the 10day trajectory path of a passively drifting copepod initially positioned 1 km from the coast at a depth of 10 m. The non-migrating copepod is carried out to 9 km from shore by 16 August.
679
Interaction of currents and Calanus vertical migration /:,,, ,,~'i,'i ~,,
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