The vertical structure and size distributions of suspended particles off Oregon during the upwelling season

Deep-Sea Research, Vol. 25, pp. 453 to 468 © Pergamon Press Ltd. 1978. Printed in Great Britain

0011-7471/78/0501-0453 $02.00/0

The vertical structure and size distributions of suspended particles off Oregon during the upwelling season JAMES C. KITCHEN,* J. RONALD V. ZANEVELD* and HASONG PAK* (Received 5 August 1977; in revised form 31 October 1977; accepted 3 November 1977)

Abstract--A simple numerical model of the vertical distribution of two size classes of particles is developedfor situations common during the coastal upwellingseason off Oregon. The total particle concentration is assumed to be proportional to the phytoplankton population for the surface layer. The two size classes of particles are thus distinguished by their maximum specific growth rates, their half saturation constants for nitrate uptake, and their settling rates. The resulting vertical distributions and size distributions were similar in shape to the average profiles for regions inshore and offshore of a particle front during August 1974 but overestimated particle concentration by 40%. This was attributed to ignoring grazing by zooplankton. Sensitivity analyses showed the size preference was most responsive to the maximum specific growth rates and nutrient half-saturation constants. The vertical structure was highly dependent on the eddy diffusivity followedcloselyby the growth terms.

INTRODUCTION DURING the summer months, the prevailing north winds along the Oregon coast cause upwelling of cold, nutrient-rich, saline waters. The proximity of these dense waters to the warm, less saline, nutrient-poor Columbia River plume waters cause complex circulation patterns to develop (PATTULLO and DENNER, 1965 ; MOOERS, COLLINS and SMITH,1976). In response to the several circulation and nutrient patterns, the suspended matter forms various vertical distributions. The particle size distributions of the suspended matter vary greatly also (KITCHEN, MENZIES, PAK and ZANEVELD, 1975). If the mechanisms producing characteristic vertical profiles and size distributions were understood, then the circulation patterns could be determined from the distribution ofsuspended matter. The distribution of suspended matter, in turn, determines the optical properties, which can be remotely monitored via airplane or satellite (MuELLER, 1976). This paper will present a model predicting the vertical distribution of suspended matter and compare it with observations. Two different circulation patterns are described as typical of coastal upwelling off Oregon. The first is simple; onshore flow predominates over most of the water column and a fast offshore flow exists in a shallow surface layer (HuYER, 1976). The second pattern occurs when a sloping pycnocline (density front) intersects the surface near the coast. Then the offshore flow meets a much lighter water mass and is forced under it. Another upwelling cell is found offshore of the front (MOOERS, COLLINS and SMITH, 1976). STEVENSON, GARVINE and WYATT (1974) interpreted the frontal circulation pattern as a relaxation of upwelling with intense sinking of unstably stratified water at the front maintaining the upwelling at the coast by continuity restraints. There seems to be general agreement as to the magnitude of upwelling. HUYER (1976) commuted an upweUing velocity of 2 × 10 -2 cm s -1 by displacements of the isopycnals. JOHNSON (1977) achieved the same results by a mass balance calculation using a high * School of Oceanography, Oregon State University,Corvallis, OR 97331, U.S.A. 453

454

.lAMES ('. K I I ( H [ \ .

J. R o y a l I) V. Z.x',l!\ H I~ a n d H a s o ~ ,

PaK

resolution profiling current meter. Both agree that upwelling motions persist to some degree when the winds slacken after an upwelling event. An in-depth description of Oregon coastal upwelling is given by HuYEr (1974). A simple steady-state analytical solution of the relative vertical distribution of phytoplankton was given by RILEY {1963). He used a two-layer system with constant net production in the upper layer and constant negative production in the lower layer. Settling rates and mixing were uniform with depth. By varying the eddy diffusivity, Riley produced solutions qualitatively similar to the vertical distributions studied in this report. However, his assumptions of depth uniform eddy diffusivity and negligible vertical water movements make application to the coastal upwelling regime of little value. Riley's model may be more applicable to the offshore vertical maximum between the permanent and seasonal pycnoclines described by ANDERSON I 1969). Anderson believed that stability (low eddy diffusivity) plays an important role in the formation of this maximum but did not extend any of his conclusions to a similar coastal feature that he briefly ment ions. I('HIYE, BASSIN and HARRIS (1972) used a simple model where all terms of the dispersion equation except settling and vertical diffusion are lumped into one term 71z), which they later assume to be constant with depth. From this they obtain an eddy diffusivity A,(z) of the order 1 cm2s 1 EITTREIM. BISCAYE and GORDON t1973~ pointed out that constant A~ and varying T l z ) i s at least as likely. They also questioned lchiye's method (polynomial fit) of obtaining vertical profiles from sparse data. WROBLEWSKI(1976) presented an extensive numerical model of nutrient flow through two living food chain levels and detritus. The biological model is superimposed on a two-dimensional flow field determined by modeling the wind-driven upwelling circulation off the Oregon coast. The upwelling model is patterned after that of THOMPSON (1974). Wroblewski's model is complete except for one important physical process, the reduction of mixing in the seasonal and permanent pycnoclines. As a result his maxima are much deeper than those observed on the cruise that provided the data for this report. However, it is likely that we are modeling two different phenomena, as data can be found to support both models. SEMINA (1972) demonstrated a correlation between mean cell size and vertical water velocities, value of the density gradient, and phosphate concentration. A slightly more analytical approach was used by PARSONS and TAKAHASH1 (1973). They related phytoplankton growth rate la to species-specific (and therefore size-specific) light and nutrient half-saturation constants K~ and Kx, maximum specific growth rate ~tm, cell sinking rate s, upwelling velocity U and depth of the mixed layer D as follows:

la=P~[\Kt+(1)/\KN+[N]]

D

"

where ( l ) is the average light intensity in the mixed layer and IN] is the concentration of the limiting nutrient. Dominant cell size is determined by comparing the computed growth rates/~ of two different species. To be dimensionally correct the advective term should have been outside the brackets. Of the examples that Parsons and Takahashi presented, only in the estuarine case, where D is very small, does the advective term play any role at all. They presented no case of strong upwelling (i.e. U > s). In that case the validity of their advective term may fail as upwelling of 'dean' water through the thermocline and the divergence of the surface water should be a negative influence on suspended particle concentrations. The use of an average light intensity to represent an

The vertical structure and size distributions of suspended particles

455

exponentially decreasing light field also seems not reasonable. HECKY and KILHAM(1974) pointed out that half-saturation constants may be more a function of cell history than a species-specific property. In spite of the above comments, Parsons and Takahashi's method may be adequate for what they intended--to explain cell size differences among large general regions of the Pacific Ocean. Their method will not be used in its present form for explaining smaller scale variation in a coastal upwelling region. However, most of the factors used by them and by SEMINA(1972) will be included in the modeling. Seasonal changes in the ratio of nannoplankton (not retained by nets) to the net plankton were studied by MALONE (1971). He found that net plankton became abundant only during strong upwelling (as evidenced by high nutrient concentrations) and that nannoplankton exhibit less variability because of the stronger coupling of production and grazing. He postulated the stronger coupling because of the shorter life span of the protozoans that may be the primary grazers of the nannoplankton. During June and July the net plankton were selectively grazed and reduced in number in spite of relatively high nutrient concentrations. THE EQUATIONS

The vertical dispersion equation for phytoplankton, ignoring higher trophic level terms is" 0~- = 0---z 'Az

s-

[(w-

s)P] + K. + ~ '

where P is the concentration of phytoplankton, Az is the vertical eddy diffusivity of phytoplankton, w is the vertical current velocity, s is the cell sinking rate, N is the concentration of limiting nutrient, V., is the maximum specific growth rate, K. is the nutrient half-saturation constant, and L is a function of depth that corrects the equation for the light intensity. Assuming s to be constant, the advection term can be expanded as follows:

L o

OZ

OZ

The last term will be balanced by the horizontal terms in the full dispersion equation and thus should not be included in the vertical equations. For the model in this report, the effect of advection will be calculated by a translation of axes assuming a linear profile between the point in question and the next point upstream. Using a central difference gradient would create instability at the base of the pycnocline due to the large second derivative of phytoplankton with depth. Including two types of phytoplankton P1, P2 and their respective maximum specific growth rates Vml, V.,2, half saturation constants K.t, K.2, and settling rates st, s2, the total system of equations is:

OPlat -

A,

-(w-sx)

+ K.i + N"

OP2t~t --

Az

- (w - s2)

-]- K . 2 -b N "

ON

0 ( Azt~N ~ wON Vm,NP,L V.2NP2L

456

JAMES C. KITCHEN, J. RONALD V. ZANEVELD and HASONr~; PAK

The equations can be non-dimensionalized by making the following substitutions. t = t*/v.,2 z = z* (Az,,/V,,2)~', where A,,. is the maximum eddy diffusivit3,

A~ = A~* A,. N = N* No, where No is the nutrient concentration of the upwelling water

W= w*(AzmVm2) ½ P~ = P~*Po, where Po is an estimate of the maximum particulate nitrogen concen-

tration in coastal waters P2 = P2* Po ~'~ = ,"*

(Azm Vm2)~

~ 2 = l'V,.2 K . I = K , 1 * No K,.2 = K,2* No.

Starred variables are non-dimensional quantities. Time and space scales will be presented in dimensional form to correspond to the region of study and the choice of parameter values. It is a simple exercise, given the above equations, to make different estimates of the parameters and thus redefine the time and space scales. However. if one increases the space scale, the light functions and diffusivity function are spread out to greater depths. This is equivalent to assuming clearer water and a deeper thermocline. These changes are all compatible, because a larger space scale would imply a region further offshore where clearer water and a deeper thermocline are to be expected. Dropping the stars and simplifying gives the following non-dimensional equations. -

-

~- ~Az .~-- I--(w--s~l-~,--+

iTt

~

~N

~

~t

8z

(z /

cz

................ V,,2(K,I + N)

A~N ,

8z

V~2No(K,,1 + N)

N o ( K . 2 ~- N)

The parameters

A commonly used value of vertical eddy diffusivity of suspended matter is l cm2s (ICHIYE, BASSINand HaRmS, 1972; O'BRIEN and WROBLEWSKI,1973a), This is the value that will be assigned to Az,.. Values for the maximum specific uptake of nitrate (V,.) are usually near 10-Ss -~ (O'BRIEN and WROBLEWSKI, 1973b: MACISAAC and DUGI)ALE, 1969). In less favorable regions, MACISAAC and DUGDALE (1969) found I~, values more than an order of magnitude less. If we accept the stated values for A~,, and |'m2, then the depth increment for the model becomes 1 m and the time increment 15 rain. SMAYDA (1971) found sinking rates of about 2 × 10-4cms - ~ for healthy phytoplankton of less than 101am diameter and about 5× 10 acms -~ for healthy cells of 201am diameter. These values will be used for s~ and s2, respectively. We have not taken into account the fact that phytoplankton could increase their settling velocities without loss of viability when placed in an unfavorable environment (SMAYDA, 1974). This could, however, play a role in the creation of a maximum at the thermocline when the surface

The verticalstructureand sizedistributionsof suspendedparticles

457

waters are depleted of nutrients. The light function L has been digitized directly from Curve III, Fig. 1 in YENTSCH (1963), which was computed by combining JERLOV'S(1951) data on coastal transparency and the photosynthesis-light relationship from RYTHER(1956). Two effects that have been left out to keep the model simple are self shading and species specific light reactions. Self shading should decrease the differences in concentration from one model to the next but may enhance the differences in vertical structure. The parameter Po/No enters into the non-dimensional equation to keep both nutrients and phytoplankton (non-dimensional) of order 1. The concentration of nitrate at 20m is 20 to 30~tg at NO31-1 , which is equivalent to 280 to 420~tgN1-1 . Measurements of particulate nitrogen during a cruise off Oregon in late July 1973 indicate a maximum value of about 100 lag N 1-1. Therefore, Po/No will be assigned the value 0.3. LAws (1975) found that phytoplankton in the 500- to 10,000-1am3 cell volume range exhibited about twice the daily growth rate of cells in the 50- to 500-1xrn3 range. He demonstrated in a model that this could arise from the balance between respiration and production. Laws found cells larger than 104 ~tm3 to be controlled mainly by sinking losses. These findings are supported by studies by PAERLand MACKENZIE(1977). Differences in growth rates may also be attributed to the nutrient history of phytoplankton community. MACISAAC and DUGDALE (1969) found twice to 10 times higher growth rates in eutrophic regions than in oligotrophic regions. The region under study in this report has tremendous contrasts of nutrient concentrations, but it is also characterized by rapid changes in the order of several days. So the value 0.5 will be used for VmffVr,2. EPPLEY, ROGERS and MCCARTHY (1969) report values of Kn for nitrate of 1 to 10txg atoms1-1 for large phytoplankton and 0.1 to 1.4 for small phytoplankton. As the present study is in a nutrient-rich region, the larger values may be more appropriate. This results in non-dimensional values of 0.05 and 0.4 for Knl and Kn2, respectively. Using mixing length theory, NEUMANN and PIERSON (1966) find the eddy diffusivity A = p~zl, where cz is the vertical component of turbulent motion and I is the mixing length. They also give the work done against buoyant forces by

1 ~p

WB = g p e z l p 8~

and p 8z'

where y is the acceleration of gravity and p is the fluid density. Assuming the available energy to be constant we find that A is inversely proportional to the vertical density gradient. Two typical density profiles from the August 1974 cruise are shown in Fig. 1 along with the computed relative eddy diffusivities. One was observed offshore of the particle front and one was inshore. The gradients are almost identical in the two profiles although the absolute values are much different. The profile of diffusivity (which will be included in the models) consists of a broad region of low diffusivity between the high values near the surface and below the thermocline. Nutrients will be assumed to have the same eddy diffusivity coefficients as particles. There is little literature on diffusivities of nutrients, but there is some information of diffusivity of salt which is also a dissolved substance. BOWDEN (1975) gives examples of computations resulting in eddy diffusivities

458

JAMESC. KITCHEN,J. R()NAL])V, ZANEVELDand HASt)N(, PAK

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24

k J ', I0

"

-"

~

]

~ v . Inshof ~

Par/ Vol

t

l

Part. Vol. I

t 1,

~

I 2

I _

PARTICLE VOLUME

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I...... - i

otto,g,",, ",,¢, ",,

37.

ao 0

~

"~$hoce

"! .(

0..

t~ 50

26

iI

i I 4

; 0

1 0,5

__jI 1.0

(pOre)

Particulate volume (computed from light transmission values} and density tor typical stations inshore and seaward of the particle front. To the right is the derived relative eddy diffusivity.

for salt of 0.4 to 4.0cm 2 s - ~. This is compatible with the above assumption. Figure 1 also shows the relationship of the vertical particle distribution to the t h e r m o c l i n e for both cases. Stability The difference equation that will be used in the model of p h y t o p l a n k t o n is : T T Pt + 1,: = P,.: - w H(PI,=. 1 - P,,: ) - s H (Pt.z - Pt,: T + A : , : ~ ( P t . H. _ + I - P t - ). - A.~ - ~. H .2 ( P. , - -. 7 ~ -

l)

~)

V..NL + ...... ~ TPt. K.+ "with a time increment T o f 900s and a depth increment H of 100 cm. The simple method of evaluating stability given by ACTON (1970) will be used to evaluate the difference equation above. Assuming all values P,.: at time t have errors of size ct,:, the error in P t . 1,_-can be c o m p u t e d as follows: F

T

T

T ~,,NL~ #-2 + . . . . . . ) K,, + N

+C,,z-1 I TSH+Az+I~I"f~ ) + F't,z + 1

h z

-- W

.

Because the coefficients of ~,._.. e,.~ + ~ and t:,.= .~~ are always positive, the worst case occurs when et,,, et.~-~, and Ct,z+ ~ all have the same sign. Assuming the ~: values are equal and substituting the m a x i m u m value for V , . N L T / K , + N, the worst case simplifies to:

459

The vertical structure and size distributions of suspended particles

This is greater than the critical value (1.0) but the 800 iterations amplify the error by a factor of only 1.0054800 ~ 74. The best case at the depth of maximum production occurs when e~,~_~ and et,z+ ~ equal -et,z. H

H

H

~--~ K , + N

e,.z.

Choosing the most negative values for all the terms gives ~t÷ 1.~ = (1. - 0.027 - 0.009 - 0.18 - 0.08 + 0.0054) ~. . . . 0.6094 et,z. In the average case errors would be damped, thus there is reason to believe the model will be stable. A practical test of stability became apparent in developing the model. Non-stable systems produced negative values of P at the base of the pycnocline where the second derivative of P was large and P was small. In the final version, P fell smoothly to the small values at the base of pycnodine. THE MODELS

The models will cover the top 40 m of the water column. Particles and nutrients will be constrained to have a zero gradient at the bottom boundary. The top boundary condition states that there is no flux of particles or nutrients across the top surface. Values of P1, 1192, W, and N are assigned to the middle of 1-m increments. Diffusivities are given for the edges of the increments. The time increment is 15 min and the maximum duration 200 h. The first model will attempt to describe the vertical distribution of particles found offshore of the color front during cruise Y7408B. That situation was characterized by low nutrient concentrations in the surface water. From the low nutrients and high temperatures we might assume that there was only weak upwelling. This assumption is supported by the results of a later model. Thus the velocity field will be defined as follows : 10 - 3 cms-1 upwelling from 20 to 40m and linearly increasing from 0 at the surface to 10-3 cms -1 at 20m. The starting conditions and the development of the vertical structure of nutrients and the two types of phytoplankton are shown in Fig. 2. Both kinds of particles (PI will be considered to represent small particles and P2 large particles although they are defined only by settling rate and nutrient uptake dynamics) develop a maximum in the region of low eddy diffusivity. The depth of this maximum does not change significantly during its development. The maximum of the product of the light and nutrient factors for each kind of particle occurs at the same depth as the maxima of PI and P2. For P2 this is also the point where settling and advection balance. Settling and advection balance for P~ 4m above the maximum of PF Both maxima are in the upper half of the pycnocline similar to the placement of the offshore maximum (Fig. 1). Near the surface there is a slight decrease in the large particles but an increase in the numbers of small particles. The nutrient concentration has almost achieved steady state. Next, the conditions inshore of the particle front will be modeled. The distribution of parameters suggests a more vigorous upwelling especially near the shore. Nutrient concentrations are high. The assigned values of the upwelling velocities are l0 times those used in the previous profile (Fig. 3). The gradient at the surface is small, but the turbid layer is shallow with a strong gradient beneath it. The maximum has risen until it is almost at the surface. The large particles (P2) have increased in numbers the most. Again the

460

JAMES C. KITCHEN, J. RONALD V. ZANEVEI,]) and HASONG PAl4

0

,.)8 I

04

i0

I

200 i

----V

I0

I

2OO

ca

2o I n

I.~

3C

P

P2

4C

o!

_•L

I

,oi

I

200

I

I

I

2C

30

Nitrate

1

40

Fig. 2~ Fhe development of the vertical structure o( the two types uf phytoplankton and nitrate {all in nondimensional units) for the low-nutrient, mild upwelling model.

nutrient concentration is near steady state but at a much higher concentration. As conditions in the upwelling region can change very quickly, a model has been included which is a combination of the previous two (i.e. high nutrients and low vertical advection) (Fig. 4). The concentrations increase rapidly and the maxima display a large increase in depth. Nutrients quickly change to a profile similar to the first model. The surface waters are dominated by small particles and the pycnocline by large particles. OBSERVED DIS1RIBtIIIONS Particle size distributions, light transmission, nutrient concentration, chlorophyll-a, and hydrographic parameters were measured off the Oregon coast during August, 1974. The methods used are similar to those of a cruise the previous year (KITCHEN, MENZIES, PAK and ZANEVELD, 1975) except that chlorophyll-a was determined by the method of STRICKLANDand PARSONS(1968) instead of by fluorimeter measurements. Transmission of red light (66Ohm) was measured by a 1-m path length nephelometer developed by the

The vertical sti'uctureand size distributionsof suspendedparticles 0.4

0

0.8 I

461

I

I0

ZO

50 40

0

"~

IO hr$

r-~

3c

Pz

4C

0

I0

ZO

30

Nitrate

I

40

Fig. 3.

The development of the vertical structure of the two types of phytoplankton and nitrate (all in nondimensional units) for the high-nutrient, strong upwelling model.

optical oceanography group at Oregon State University. The regression: In (volume)= 1.713- 5.957(Tr), where the suspended volume is in 106 I.Lrri3 cm -3 and transmission (Tr) is expressed as a fraction, was derived from samples taken no deeper than 40m. The standard errors for the intercept and slope are 0.079 and 0.173, respectively, and the correlation coefficient is 0.915. This regression will be used to take advantage of the greater resolution with respect to depth and the greater precision of the nephelometer measurements than the volume determinations. DATA

Three sections were occupied along 45°00'N latitude. Figure 5 shows transmission, log-log slope of the particle size histograms (lower values indicate a greater relative proportion of larger particles) and temperature for these sections. A nearshore minimum in transmission extends offshore in a finger-like projection along the top of the thermocline. In the first and third sections there is a lobe of low transmission extending down to 20 m. The log-log slopes of the particle size distributions show a distinct front at the same D.S.R. 25 5 C

462

JAMES C. KITCHEN, J. RONALD V. ZANEVELD and HASONG PAK

0

0.4

0.8

1.2

200

2O 3O 40

t,

IO

,--,

0

I0

~,/oo I\/oo -

~-~ 1

I

J

I

200

20

30

40

Fig. 4. The development of the vertical structure of the two types of phytoplankton and nitrate (all in nondimensional units) for the high-nutrient, mild upwellingmodel.

place the transmission shows the downward extending lobe. Beneath the front and inshore is a large homogeneous area of slope between 3.0 and 3.5. Transmission varies greatly ( ~ 4 5 to 60%) in this same area. In the clearest waters the slopes are also low ( < 3.0). The near-surface isotherms are nearly horizontal, showing a 5- to 10-m surface mixed layer with strong stratification beneath. Transects at 44055 ' and at 45°05 ' latitude had similar features. Nutrients, chlorophyll-a, and zooplankton (not shown), in the euphotic zone, are all high where the slope of the size distribution is low. Nutrients are depleted (< 1 ~tmole1-1) offshore of the particle size distribution front. A more extensive data presentation for this cruise is given by KITCHEN (1978). The vertical structure of the suspended matter is compared with the model results in Fig. 6. Figure 6(a) shows the average vertical profiles of suspended matter as determined by light transmission measurements for stations seaward and inshore o f the particle front. Models 1 and 2 are qualitatively similar to the average profiles of the offshore and inshore stations, respectively. Figures 6(c) and (d) compare the relative numbers of large and small particles. The experimental data are computed by dividing the volume concentration of

The vertical structure and size distributions of suspended particles

463

Slotio~

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I_'"/i ~" Cumuli. Size Dill. ~ LO~ Slope

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t.AT: 4~-oo'N_ ~ooo 8,zo/7,,o8~o a , z , , 7 , ] iO

I 5

Fig. 5. Transmission, log-log slopes of the particle size histograms and temperature for three consecutive sections at 45°00'H latitude off the Oregon coast.

O

464

JAMES C. KITCHEN, J. RONA[,I)

0

~

IC

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30

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Fig. 6. A comparison of the observed and the obtained vertical distributions. (a) l-he average suspended particle volume(ppm) computedfrom fight transmissionmeasurementsinshoreand offshore of the particle front. (b) The sum of P1 and P2 for the three models (non-dimensional}. (c) The average and the 95% confidence intervals for the average of the ratio of large to small particles by volume. (d) The ratios of Pz to Pt for the three models.

particles between 16 and 60 pm diameter by the volume of particles between 3.5 and 16 ~m diameter. Only a qualitative agreement was expected because the size separations are somewhat arbitrary. However, there is also quantitative agreement. DISCUSSION

The drastic change in the concentration of the large particles (one to two orders of magnitude) across the particle front as well as the distribution of the other parameters indicate that the near-surface flow does not cross the front. Thus, even though a temperature front is not evident, the flow may be qualitatively similar to that reported by STEVENSON,GARVINEand WYATT(1974), i.e. a two-cell circulation pattern. Thus, there is no evidence that the subsurface maximum is affected in any way by advection of particulate matter from near-shore. This gives some justification (besides cost) for looking at onedimensional models. Because of the high correlation between chlorophyll-a and particle

The verticalstructureand sizedistributionsof suspendedparticles

465

volume as reported by KITCHEN, MENZIES, PAK and ZANEVELD (1975), the suspended particles are assumed to be predominantly phytoplankton and their by-products. The large gradients of temperature and transmission below the surface mixed layer indicate upward vertical advection and low vertical eddy diffusivities (ZANEVELD,1972). There is little debate over the hypothesis of low diffusivity in the thermocline, but the role of settling needs further discussion. The solution of the vertical dispersion equation:

02S~S (wz) A~2 = W~z=OisS = Clexp --~ +C2, where S is the concentration of suspended particles (a function of size), A is the vertical eddy diffusivity, w is combined settling and advection, and C1, C2 are undetermined constants. If w is a function of the size of the particles, then one end of the size distribution will show greater relative changes with depth, thus changing the slopes of the size distributions. The region beneath the surface mixed layer is characterized by large changes in transmission but the log-log slopes are homogeneous. We conclude that settling is relatively unimportant compared with advection of water masses. The gradient of turbidity beneath the thermocline appears to be neutral (not a function of size) dilution by the upwelling, deep, 'clean' offshore water. The results of the models (Fig. 6b) are shown in non-dimensional units. The dimensional units are determined by the parameters N O and Po/No. Po/No was assigned the value 0.3 to make P0 = 1.0 equivalent (in units ~tgNl -~) to the maximum particle concentration found inshore of the front when N o was 301xmolesl-1. Model 2 overestimates the surface concentrations by 40~. Seaward of the front, the nitrate concentrations at 20 m are about 10 ~tmolesl-1, Po/N° is the same, so a P0 of 1.0 is equivalent to 1.3 ppm by volume and the model overestimates by 40~o. The model curves have the correct shape and are in the right proportion to each other when the dimensionalizing factors are taken into account. The lack of a grazing term may account for the overestimation. Changing N o from model to model also changes the nutrient half-saturation constants. In this way, allowance is made not only for species difference but to differences arising from conditioning. Sensitivity analysis was carried out by varying the parameters by 30~o and observing the change in the model results. Model 1 was used because it had the most vertical structure and thus should be the most sensitive. The results were normalized so that if a 30~o change in a parameter produced a 30~ change in the model, the resultant statistic would be 1.0. The sensitivity was calculated at 1, 20, and 40 m and at the particle maximum which was at 7 to 9 m for the small particles and at 9 to 11 m for the large particles. The results are shown in Table 1. The eddy diffusivity has the most effect at the surface and at 40 m. The maximum specific growth rates have a large effect at the particle maximum and at 20 m, which was chosen to characterize the base of the pycnocline. The effect on the size distribution can be determined by taking the difference of the sensivity coefficients for Px and P2. The maximum specific growth rates and the half-saturation constants have a large effect while the diffusivity has a significant effect on the particle size distribution only at 40m. The sensitivity of the relative vertical structure can be determined by the difference between the coefficients at 1 m and at the maximum. The vertical structure of P I and P2 are most affected by their respective growth rates followed by the eddy diffusivity, but the change of the total suspended mass P~+P2 is most affected by the eddy diffusivity. Thus the magnitude of the features and the particle size distribution is most

466

.IAMBSC. KITCHEN,J. RONALDV. ZANEVELDand HASONG PAg

Table 1. Sensitivity coeJ~cientsfor the parameters in model 1 determined by varying the parameters by 30% and rerunning the model. Depth "

As 3Pl Pl ~Az

AS ~P2 P2 ~Az

VmJ. 3Pl PI

~Vml

Vml ~P2 P2 ~Vml

Vl2 ~P2 ~Vm2

Pl

Vm2 ~P2 P2 ~Vm2

v ~Pl Pl ~

w ~P2 P2 ~,l

1

.45

.43

.20

-.28

-.20

.33

.30

.26

Particle max

-.09

-.12

.85

-.20

-.13

.90

.09

.16

20

.Ii

-.02

.54

-.02

0.0

.67

-.54

-.43

40

.95

.77

.08

0.0

0.0

.07

-.56

-.58

l n l 8Pl

Knl 8P2

Kn2 ~Pl

gn2 ~P2

P1

P2

PI

¢2

Depth

3gnl

gnl

3Kn2

~gn2

1

-.16

.17

.21

-.36

Particle max

-.27

.06

.12

-.64

20

-.07

0.0

0.0

-.34

40

0.0

0.0

0.0

0.0

sensitive to the biological terms while the shape of the features is largely a function of the vertical structure of the eddy diffusivity. The three models reveal the trends that may occur when upwelling of a given intensity is maintained for several days. Under mild upwelling, a sharp maximum in suspended volume will form at or move to the top of the thermocline. This is the result of a rapidly decreasing light function and a rapidly increasing nutrient concentration producing maximum growth in this region. The depth at which the sinking and advection rates balance also occurs in this region but not necessarily at the same depth as the maximum. There may also be adaptations (SMAYDA, 1970, 1974)by the phytoplankton to make their sinking rates balance advection at these desirable depths. This would accentuate the maximum. Relative particle size decreases at the surface under mild upwelling conditions but the concentration may increase or decrease depending on the nutrient concentrations at the start. Nutrients are soon depleted in the surface waters. In the case of strong upwelling, nutrients become plentiful in the surface region and the maximum particle concentration moves to the surface. Larger phytoplankton become prevalent. The upwelling of 'clean' water decreases the thickness of the turbid layer. The surface concentrations would be even higher if the surface waters were not being constantly diluted by the upwelled water. If the upwelling velocities were 2.0 to 2.5 times the 10 -z cms- ~ used in model 2 as reported by HUYER(1976) and JOHNSON(1977), the surface concentration might even decrease with time. Ignored as a consequence of using a one-dimensional model is the effect of horizontal fluxes of nutrients and particles. In a two-celled circulation, a downwelling region must exist adjacent to the upwelling region. It is easy. to imagine that the nutrient-rich upwelled water is advected to a place where there is no upwelling and the consequent growth is not obscured by dilution. Thus, one cannot take the results of these few onedimensional models and apply them independently to various locations. However, if one keeps in mind the concept of conservation of matter, these models may help make sense of two-dimensional distributions.

The vertical structure and size distributions of suspended particles

467

Acknowledgements---This investigation was supported by the National Aeronautics and Space Administration under contract No. NAS 5-22319 and by the Office of Naval Research contract N00014-76-C-0067 under project NR 083-102. The support of these agencies is gratefully acknowledged. We thank the personnel of t h e OSU Marine Phytoplankton group headed by L. F. SMALLfor making available the pigment and nutrient data. REFERENCES ACTON F. S. (1970) Numerical methods that work. Harper & Row, 541 pp. ANDERSON G. C. (1969) Subsurface chlorophyll maximum in the northeast Pacific Ocean. Limnolooy and Oceanography, 14, 386-391. BOWOEN K. F. (1975) Currents and mixing in the ocean. In: Chemical oceanography, Vol. 1. J. P. RILEY and G. SKIRROW,editors, Academic Press. EITTREIM S., P. E. BISCAYE and A. L. GORDON (1973) Comments on paper by T. Ichiye, N. J. Bassin and J. E. Harris, 'Diffusivity of suspended matter in the Caribbean Sea'. Journal of Geophysical Research, 78, 6401-6403. EPPLEV R. W., J. N. ROGERS and J. J. MCCARTHY (1969) Half-saturation constants for uptake in nitrate and ammonium by marine phytoplankton. Limnology and Oceanography, 14, 912-920. HECKEY R. E. and P. KILHAM (1974) Comment on 'Environmental control of phytoplankton cell size'. Limnolofly and Oceanography, 19, 361-365. HUYER A. (1974) Observations of the coastal upwelling region off Oregon during 1972. Ph.D. Thesis, Oregon State University, Corvallis, 149 pp. HOVER A. (1976) A comparison of upwelling events in two locations: Oregon and northwest Africa. Journal of Marine Research, 34, 531-546. ICHIYE T., N. J. BASSIN and J. E. HARRIS (1972) Diffusivity of suspended matter in the Caribbean Sea. Journal of Geophysical Research, 77, 6576-6588. JERLOV N. G. (1951) Optical studies of ocean waters. Reports of the Swedish Deep-Sea Expedition, 3, 1-59. JOHNSON D. R. (1977) Determining vertical velocities during upwelling off the Oregon coast. Deep-Sea Research, 24, 171-180. KITCHEN J. C. (1978) Particle size distributions and the vertical distribution of suspended matter in the upwelling region off Oregon. M.S. Thesis, Oregon State University, Corvallis, 118 pp. KITCHEN J. C., D. MENZn~S, H. PAK and J. R. V. ZANEVELD (1975) Particle size distributions in a region of coastal upwelling analyzed by characteristic vectors. Limnology and Oceanography, 211,775-783. LAWSE. A. (1975) The importance of respiration losses in controlling the size distribution of marine phytoplankton. Ecology, 56, 419-426. MACISAACJ. J. and R. C. DUGDALE(1969) The kinetics of nitrate and ammonia uptake by natural populations of marine phytoplankton. Deep-Sea Research, 16, 45-57. MALONE T. C. (1971) The relative importance of nannoplankton and netplankton as primary producers in the California current system. Fisheries Bulletin U.S. Department of Commerce, 69, 799-820. MOOERS C. N. K., C. A. COLLINS and R. L. SMITH (1976) The dynamic structure of the frontal zone in the coastal upwelling region off Oregon. Journal of Physical Oceanography, 6, 3-21. MUELLER J. L. (1976) Ocean color spectra measured off the Oregon coast: characteristic vectors. Applied Optics, 15, 394-402. NEUMANN G. and W. J. PIERSON,JR. (1966) Principles of physical oceanography. Prentice-Hall, 545 pp. O'BRIEN J. J. and J. S. WROBLEWSKI (1973a) On advection in phytoplankton models. Journal of Theoretical Biology, 311, 197-202. O'BRIEN J. J. and J. S. WROBLEWSKI(1973b) A simulation of the mesoscale distribution of the lower marine trophic levels off west Florida. lnvestigatirn pesquera, 37, 193-244. PAERL H. W. and L. A. MACKENZIE (1977) A comparative study of the diurnal carbon fixation patterns of nannoplankton and net plankton. Limnology and Oceanography, 22, 732-738. PARSONS T. R. and M. TAKAHASHI (1973) Environmental control of phytoplankton cell size. Limnology and Oceanography, 18, 511-515. PATTULLO J. and W. DENNER 0965) Processes affecting seawater characteristics along the Oregon coast. Limnology and Oceanography, 10, 443-450. RILEY G. A. (1963) Theory of food-chain relations in the ocean. In: The sea, Vol. 2. M. N. Hill, editor, Interscience. RYTHER J. H. (1956) Photosynthesis in the ocean as a function of light intensity. Limnology and Oceanography, l, 61-70. SEMINA H. J. (1972) The size of phytoplankton cells in the Pacific Ocean. Internationale Revue der gesamten H ydrobiologie und Hydrographie, 57, 177-205. SMAYDA T. J. (1970) The suspension and sinking of phytoplankton in the sea. Oceanooraphy and Marine Biology Annual Review, 8, 353-414. SMAYDAT. J. (1971) Normal and accelerated sinking of phytoplankton in the sea. Marine Geology, l l , 105-122.

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