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Deep-Sea Research I 51 (2004) 885–908
A vertical model of particle size distributions and fluxes in the midwater column that includes biological and physical processes—Part II: application to a three year survey in the NW Mediterranean Sea Lars Stemmanna,*,1, George A. Jacksona, Gabriel Gorskyb a
Department of Oceanography, Texas A&M University, College Station, TX 77843-3146, USA b Laboratoire d’Oceanographie de Villefranche, BP 28, 06234 Villefranche sur Mer, France
Received 22 November 2002; received in revised form 12 August 2003; accepted 2 March 2004
Abstract The largest decrease in the particle vertical flux occurs in the mesopelagic zone where particles are transformed by biological and physical mechanisms. Particle size distributions provide important clues into those processes affecting particle transformations in this region. We have studied them using an inter-annual data set showing the evolution of particle size distributions between 100 and 1000 m, comparing them to results from a series of size-resolved models of particle dynamics that include physical coagulation and biological remineralization. The formulation that best fits the observations consists of a combination of settling, microbial activity and zooplankton feeding. The calculated particulate organic carbon losses to microbial activity and zooplankton feeding are consistent with independent estimates of these rates. The model shows that it is possible to predict the particle size distribution at 1000 m depth knowing the particle size distribution at 100 m depth and the rates of transformation in the mesopelagic. The mesozooplankton appears to be important in decreasing the high flux of large particles in the upper midwater zone, microbes becomes more important in the deeper midwater zone as zooplankton become rarer. The results suggest that the mesozooplankton have a much greater effect on particle flux than the macrozooplankton. Their importance requires the mesozooplankton to feed preferentially on large settling particles, probably using remote detection. The present work shows that using particle size spectra is a useful way to understand the transformation of the vertical flux of element in the midwater zone. However, most of the assumptions on particle properties and processes are based on surface studies and more data from the midwater zone are needed to confirm the hypotheses. The model allows us to formulate crucial questions regarding particle dynamics in the midwater zone. r 2004 Elsevier Ltd. All rights reserved. Keywords: Marine snow; Particle flux; Midwater zone; Modeling; Mesopelagic; Coagulation; Mediterranean Sea
1. Introduction *Corresponding author. E-mail addresses:
[email protected] (L. Stemmann),
[email protected] (G.A. Jackson),
[email protected] (G. Gorsky). 1 Present address: Laboratoire d’Oceanographie de Villefranche, BP 28, 06234 Villefranche sur Mer, France. Tel.: +33(0)4-93-76-38-18; fax: +33-(0)4-93-76-38-34.
The mesopelagic zone, also known as the midwater or twilight zone, is receiving increasing attention because it is there that most of the particulate organic carbon exported from the euphotic zone is remineralized (e.g., Martin et al.,
0967-0637/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.dsr.2004.03.002
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1987). The decrease in particle flux with depth is often described with simple empirical relationships that do not include any mechanisms (e.g., Martin et al., 1987; Alldredge and Gotschalk, 1988; Armstrong et al., 2002). Because particle solubilization and remineralization processes occur at the scale of the individual particle, models of particle dynamics provide the means to estimate the depths at which the different elements carried by particles are solubilized. Recent work has shown that particle size spectra can yield information not only on the particle mass distributions but also on the interactions between particles and their environment (reviewed in Stemmann et al., 2004). In the absence of more direct measurements of the processes and their rates in the midwater zone, observations on particle size spectra and models of particle dynamics can be used to infer the relevant mechanisms. In Stemmann et al. (2004), we discussed and developed several size-dependant equations describing particle dynamics resulting from settling, coagulation, fragmentation, microbial remineralization and zooplankton consumption (Table 1). The French JGOFS time series DYFAMED site in the NW Mediterranean Sea was intensively sampled for several years. Among the measurements were particle size distributions measured between 60 and 1000 m depth, vertical particle
fluxes, hydrographic water properties, and biological distributions (phytoplankton, zooplankton, and microbe) (Stemmann et al., 2002; Marty et al., 2002). These data can be used to test models of vertical particle flux. This paper combines the different mechanisms in Stemmann et al. (2004) in a series of eight models (see Table 4) and tests them against observations from DYFAMED in order to gain an understanding of the important processes in the midwater zone. Our models are forced at 90 m depth with observed particle size spectra and throughout the water column with imposed zooplankton distributions that are constant in time but not space; they calculate the temporal evolution of resulting size spectra between 125 and 950 m depth in 10 layers. These predicted size spectra are compared to the observations.
2. Model implementation 2.1. Analysis of particle size distribution data The particle data used to evaluate the model were collected with the Underwater Video Profiler II (UVP II) during 46 cruises between January 1992 and July 1996 (Gorsky et al., 1992; Stemmann et al., 2002). All profiles were collected during daylight in order to avoid diel variations in
Table 1 The different mechanisms implemented in the model Mechanism
Results in
Depends on
1. Settling (S)
Downward particle flux
2. Coagulation (C)
Increase mean particle size
3. Fragmentation (Z3)
Split into two or many particles
4. Microbial activity (M) 5. Filter feeding (Z0) 6. Passive flux feeding (Z1)
Particle mass loss and shrinking Particle mass loss and detritus production Particle mass loss and detritus production
7. Active flux feedina (Z1 or Z2)
Particle mass loss and detritus production
Particle density and length, vertical conc. gradient Particle mass, length, concentration, as well as turbulence Local turbulence caused by large swimming zooplankton Attached bacteria and protozoa Macro- and mesozooplankton Particle size and density, macrozooplankton eating all Mesozooplankton eating all (Z1) or fixed amount (Z2), particle size
Fragmentation can occur through binary splitting (bin. split.) or through the production of a cloud of primary particles (prim. part.).
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particle concentration (Lampitt et al., 1993; Graham et al., 2000; Stemmann et al., 2000). Averaging the data over the 20 to 100 m depth ranges yielded sampling volumes ranging from 28 l for the 20 m, 70 l for the 50 m, and 140 l for the 100 m thick layers. Additional descriptions of the methodology used to estimate the particle distribution during DYFAMED can be found in Stemmann et al. (2002). The UVP II provides an equivalent spherical diameter (ESD) for each particle observed. Instrument calibration results suggest that the instrument can provide diameters for particles as small as 80 mm in the laboratory, but field observations show that the instrument misses a substantial number of particles smaller than about 0.15 mm. Similarly, although the instrument could measure particles as large as 10 cm, the rarity of large particles and small volumes sampled makes the uncertainty of their concentrations unreasonably large. We increased the sample volumes by averaging over a layer 20– 100 m thick, but still had a maximum practical particle diameter of 1.5 mm for there to be at least three particles per section. The particle size spectrum is a useful description of the relationship between particle abundance and size. The number spectrum nðmÞ ¼ dN=dm can be calculated from the total number of particles per unit volume dN in a size range between m and m þ dm; where dm is a small mass increment. Here n and N are both functions of particle mass, but they can be functions of particle diameter d or any other particle property. For example, if nðdÞ and nðmÞ are particle size spectra expressed as functions of particle diameter and mass, they can be converted between each other by nðdÞ ¼ nðmÞ
dm : dd
ð1Þ
Number spectra with respect to observed diameter ðnðdÞÞ were calculated by grouping particles into size ranges (bins) and dividing the number concentration for each bin by the bin width. These values were interpolated to values of nðdÞ at the median diameters for the sections using a spline fit and then converted to nðmÞ using Eq. (1). These values of nðmÞ were used to calculate the values of Qi for the six useable sections (Table 2).
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The conversion of nðdÞ to nðmÞ requires a relationship between particle diameter and mass. Fractal scaling provides such a relationship. The three key descriptors are an initial cell diameter d1 ; a cell density rp and a fractal dimension for aggregates D3. Because the prymnesiophytes usually dominant at the DYFAMED site have a size peak at a diameter of 5 mm (Marty et al., 2002; Sciandra, pers. comm.), we use values of d1 ¼ 5 mm, rp ¼ 1:062 g cm3 and D3 ¼ 2:3 (Jackson et al., 1997). The value of rp is typical for cytoplasmic material (Mann and Lazier, 1991). Particulate organic carbon concentration (POC) is calculated from wet weight assuming that POC=0.1, dry weight=0.01 wet weight (Ruiz, 1997). This value corresponds to the annual mean of POC dry weight measured on particles collected by sediment traps at DYFAMED site at 200 m depth (Miquel et al., 1994). The estimated POC content and the settling speeds calculated using these values are similar to observed values for particles (>200 mm) (e.g., Alldredge and Gotschalk, 1989; Alldredge, 1998). Values for other parameters are shown in Table 3 and the resulting particle properties in Table 2. We simulate particle interactions over a larger size range than that for which observations exist. In Stemmann et al. (2004), we show that the lack of particle data in the size o0.02 cm does not necessarily affect coagulation rates for the larger particles if most of the particle mass is in the size range >0.01 cm. In the absence of data on the distribution over a larger size range, we have assumed that this is true for the surface forcing. However, we do allow the formation of smaller particles below the surface. The continuous particle size spectra can be approximated for computational convenience by dividing the particle size range into subranges called sections. For the ith section (Si), the mass of the smallest particle ðmi Þ is half the mass of the largest ð¼ 2mi ¼ miþ1 Þ: We use 23 such sections to span the particle size spectra between d ¼ 4:6 mm and 0.32 cm (Table 2). The mass concentration of particles in Si, Qi ; is Z 2mi nðmÞm dm: ð2Þ Qi ¼ mi
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Table 2 Particle properties in the 23 sections of the model Settling speed (m d1)
POC (mg)
Section
Apparent diameter ðdÞ (mm)
Conserved diameter (mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.0046 0.0062 0.0084 0.0120 0.0146 0.0204 0.0274 0.0370 0.0498 0.0670 0.0902 0.122 0.164 0.220
0.0057 0.0072 0.0091 0.0114 0.0144 0.0191 0.0229 0.0288 0.0363 0.0458 0.0577 0.0727 0.0916 0.115
15 16 17 18 19 20
0.297 0.400 0.538 0.724 0.975 1.31
0.145 0.183 0.231 0.291 0.367 0.462
19.0 28.2 41.8 62.1 92.3 137.0
1.72 103 3.44 102 6.88 102 0.137 0.275 0.550
21 22 23
1.77 2.38 3.21
0.582 0.733 0.923
204.0 302.0 449.0
1.10 2.20 4.40
0.074 0.110 0.164 0.244 0.363 0.539 0.800 1.19 1.77 2.62 3.90 5.79 8.60 12.8
1.05 106 2.10 106 4.20 106 8.41 106 1.68 105 3.36 105 6.72 105 1.34 104 2.69 104 5.38 104 1.07 103 2.15 103 4.30 103 8.60 103
Values in bold stress the sections with the UVP data. The settling speed increases from 0.07 to 450 m d1 and the mass from 1 106 to 4.4 mg of POC as the section number increases.
The sectional approach does assume a shape for the size spectrum over its range. More details are in Stemmann et al. (2004). 2.2. Spatial formulation We divide the water column between 100 and 1000 m into 10 layers, with the top two layers each 50 m thick and the remaining, eight layers each 100 m thick. In each layer, the change in Qi ðzj ; tÞ is f dQi X dQi ¼ ; ð3Þ dt dt o o¼1 where o is the index of the process changing the particle concentrations and f is the total number of processes. For simplification, we note that Qi ¼ Qi ðzj ; tÞ: The mechanisms are particle set-
tling, coagulation, fragmentation by swimming zooplankton, microbial degradation, and zooplankton feeding (Table 1). The average concentration over a depth range is assigned to its average depth. The differential equations for the model were numerically integrated using the ode15 s function in MATLAB (The Mathworks Inc., Natick, MA). The system is forced at the top with timevarying particle size spectra averaged between 80 and 100 m and assigned a nominal 90 m depth. This water layer at the DYFAMED site is usually located just beneath the mixed layer (Marty et al., 2002). The values of Qi ðtÞ at any time are estimated using a piecewise Hermite polynomial interpolation of the observations. We use the first vertical profile of size spectra in a time series to set the initial conditions throughout the water column for
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Table 3 List of model parameters and the range of values used in the model Symbol
Description
Units
Range
Default value
c
Clearance rate for filter feeder+,,a
m3 d1
25 106 25 103
d1 D3 mi p r R R0i;j Qi Si zj a dm e rp s
Initial cell diameter Fractal dimension Particle mass for lower bound of Si Fraction of mass unassimilated by zooplankton Microbial specific degradation rate,+ Total measure of model fit Measure of model fit for Si at zj Particle mass concentration in Si ith section Nominal depth for jth layer Stickiness+ Gut volume+ Dissipation rate of energy+ Source particle density Cross-sectional area for flux feeding+,,a
mm 1.7–3
25 105 25 103 5 2.3
0.4–0.9 0.025–0.2
0.5 0.05
0–0.8 106–105 106–105 1.068–1.108 2 107–7.8 103
0.4 105 106 1.068 1.3 105 7.8 103
d1
m cm3 cm2 s3 g cm3 m2
We only list the parameters which values are not given in Table 2 of Stemmann et al. (2004). Used in the sensitivity analysis (see Table 5). + Used to test the impact on the specific rates of change (see Fig. 4). a The lower standard value is used for mesozooplankton and the larger for macrozooplankton.
S15S20 (the range sampled by UVP II). Because we have no data for other sizes or sections, we set the values of Qi to 0 throughout the water column at the start and at 90 m for all times for the other sections. We approximate the effect of particle sinking at depth zj (term 1 in Stemmann et al., 2004) by @Qi ðzj ; tÞ Qi ðzj ; tÞ Qi ðzj1 ; tÞ ¼ wi : ð4Þ @t zj zj1 1 2.3. Zooplankton forcing We estimate macrozooplankton abundances using data from the DYFAMED site obtained during the DYNAPROC cruise in May 1995. The samples were collected at 10 depths using the BIONESS multinet sampler with a mesh size of 500 mm (Andersen et al., 2001b). Because zooplankton concentrations are maximal at this time of the year, the imposed effect of zooplankton on particle flux should represent an upper limit. We have divided the macrozooplankton into different
groups by their potential behaviors (Fig. 1): euphausiids, fishes, amphipods, mysiids, and other less abundant groups (without copepods) are filter feeders; pteropods are passive flux feeders; and euphausiids are particle breakers. We consider copepods as the only mesozooplankton because they are numerically the most abundant and because small copepods (B500 mm) have been observed to colonize aggregates in swarms (Steinberg et al., 1997). Sampling them efficiently requires nets with mesh sizes o100 mm (Gallienne and Robins, 2001). Because we do not have the relevant data throughout the water column for the DYFAMED site, we use a regression relating depth and copepod abundance determined with nets with a mesh size of 250 mm in the Tyrrhenian Sea (Scotto di Carlo et al., 1984). Because the copepod concentration in the Tyrrhenian Sea is about 10 times lower than in the rest of the Western Mediterranean Sea, we have multiplied the abundances calculated using the regression by 10 (Scotto di Carlo et al., 1984). The calculated concentration range of 250
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Fig. 1. Relative abundances of the different zooplankton groups. The relative abundances have been calculated by dividing the measured abundances throughout the water column by the highest concentration in each group. The scaling of abundances for each group are 0.307 m3 (filter feeders), 0.14 m3 (particle breakers), 0.063 m3 (passive flux feeders), and 250 m3 (mesozooplankton).
individuals m3 between 100 and 200 m is within the range of 100–300 individuals m3 between 0 and 200 m estimated at the DYFAMED station during DYNAPROC cruise using a WP2 net (Andersen et al., 2001a). We assume that zooplankton encounter rates are proportional to particle concentration or flux, as appropriate. For filtration feeders we use clearance rates of c ¼ 25 106 and 5 3 1 1 25 10 m d ind for mesozooplankton and 25 104 and 25 103 m3 d1 md1 for macrozooplankton (Huntley and Boyd, 1984). For passive flux feeders, we calculate the crosssectional area of particle capture by an individual, s; using diameters of 1 and 5 cm, about half and twice the value given for pteropods (Jackson, 1993). For the active flux feeders (copepods), we calculate the cross-sectional area using radii of 200 mm and 2.5 mm. We assume that the large macrozooplankton ingest totally any particles they encounter and that the smaller mesozooplankton either engulf or mine
particles that they encounter. In the case of mining, we assume that the fraction of mass uptake, dm ; cannot be larger than the gut capacity of the animal. The gut capacity is set to a copepod’s gut volume, 106 and 105 cm3 (Harris, 1994). A fraction, p=(1assimilation efficiency), of the ingested particulate matter is discharged as fecal material. We use p ¼ 0:5; within the reported range of 0.1–0.6 reported for midwater detritivores (Steinberg et al., 1997). The diameter of the smallest fecal pellets is set to 40 mm, one-fifth of the body size of a typical mesozooplankter. For particle breakup by macrozooplankton, we use the encounter rate between euphausiids and particles of B101 m3 d1 individual1, calculated for a swimming speed of 1.1 cm s1 and an effective impact diameter of 1 cm (Dilling and Alldredge, 2000). Because of the lack of measurements of particle breakup in the midwater column, we assume that disaggregation rates are constant with particle size.
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2.4. Microbial degradation We impose the specific rate of microbial activity through the water column, but use two different formulations: fixed with depth at 0.05 d1 or decreasing linearly with depth from 0.2 to 0.05 d1 at 125 and 950 m depths. 2.5. Comparing model results to field observations We calculate for each models one global measure of model fit to the data over all depths, times and sections. The fraction of variance, R; explained by the simulation is 20 X 10 X h ðQi;p ðzj; tk Þ Qi;o ðzj; tk ÞÞ2 1 X R¼ ; ð60hÞ i¼15 j¼1 k¼2 ðQi;o ðzj; tk Þ Q% i Þ2 ð5Þ where Qi;p ðzj ; tk Þ and Qi;o ðzj ; tk Þ are the predicted and observed mass spectra in Si at depth zj of the jth layer and time tk for the kth interval, and Q% i is the mean concentration in Si over the length of the record being simulated. Because the models are tested on records of different lengths, the number of time intervals h varies with the simulation. Smaller values of R indicate better matches between observed and predicted values. We also calculate a local measure of model goodness R0i;j for depth zj for Si R0i; j ¼
h Qi;p ðzj; tk Þ 1 X : log10 h k¼2 Qi;o ðzj; tk Þ
ð6Þ
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This measure allows us to assess the relative model over- or underestimation of particle concentration in different size ranges at different locations. 2.6. Strategy We are interested in determining what the signatures of the different processes altering the particle spectra are. We are also interested in determining the importance of the different processes in explaining the observed particle size distributions. As part of the process of exploration, we build eight different models combining the different processes and we alter some parameter values (Tables 4 and 3). While the observations were made over a 3-year period, their frequency did vary. Furthermore, physical turnover of the water occurring during deep winter convection can swamp the other processes that we want to study. As a result, our simulations span different periods. First, we simulate particle dynamics over the entire 3-year period (January 1992 to July 1995). Second, we divide the data into three separate periods that exclude probable times of deep winter convection: 17 May to 10 December 1993 with eight profiles, 8 April to 3 December 1994 with eight profiles, and 3 April to 31 May 1995 with 12 profiles. Finally, we use the time period in spring 1995 to compare POC respiration by bacteria and zooplankton and POC vertical flux from the model results to independent estimates.
Table 4 The eight different models Version
Symbol
Mechanism
1 2 3 4 5 6 7 8
S S+B S+Z0 S+Z1 S+Z2 S+C S+B+Z1 S+B+Z1+C
Settling Settling+microbial activity Settling+filter feeding (meso+macrozooplankton) Settling+flux feeding and total ingestion (meso+macrozooplankton) Settling+flux feeding and mining (mesozooplankton) Settling+coagulation Settling+microbial activity+flux feeding and total ingestion Settling+microbial activity+flux feeding and total ingestion +coagulation
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3. Results The average of observed number size spectra shows the typical decrease of n with increasing particle size (Fig. 2A). The relative decrease of n between 90 and 950 m is greater for particles larger than 0.075 cm than for smaller ones. Most of the mass is found in particles centered on d ¼ 0:05 cm (Fig. 2B). 3.1. 3-year simulations A comparison between the observed POC concentrations calculated using the UVP data and those predicted with the model in the same size range provides a general overview of the similarities and differences between the two. In this case, the predicted POC concentrations are the particle concentrations that were calculated over the entire 3-year period using the terms describing particle settling, microbial activity, and flux feeding on the entire particle (Version 7, Table 4, Fig. 3). The predicted POC concentrations have the same general pattern as the observed ones, but are smaller in the deeper part of the water column, especially from January to March in 1993 and
1994. A good match with the general trends but an underestimation of observed deep winter concentrations is characteristic of all the versions and parameter values that we used (not shown here). The poorer performance of the model during winter may result from intermediate and deep water formation (Gascard, 1978), which could change the vertical distribution of particles in ways we do not have the data to incorporate here (Stemmann et al., 2002). To avoid interference from deep water formation, we exclude the winter periods from further simulations, restarting simulations when density profiles indicate the beginning of seasonal stratification. 3.2. Effects of the different mechanisms on rates The effect of the different mechanisms on the particle size spectra can be seen by comparing the instantaneous specific rates of change for each section ðQ1 i ðdQi =dtÞl Þ: As an example, we examine their values at a location near the surface mixed layer where the particle concentrations are still high (175 m) and at a deeper location where the particle concentrations are low (850 m). The calculations are performed for the time when we
Fig. 2. Mean particle number spectra nðdÞ (A) and mass spectra ðmnðdÞÞ (B) for all samples collected using the UVP II data at DYFAMED station during 1992–1996 at 90 and 950 m depth. The area under a curve in (B) is the total particle mass concentration.
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Fig. 3. Time and depth distribution of POC between January 1992 and July 1995, (A) estimated by the UVP and (B) predicted by the model. The POC concentration is calculated by integration over all the particle sizes. The marks () denote the sampling dates and the arrow the beginning of the time period including the cruise DYNAPROC (May 1995).
have the best sampling resolution for the particles and the time when the zooplankton and in situ bacterial activity data were collected (10 May 1995 during the cruise DYNAPROC). Because there are no measurements for particles outside S15–S20, we use values of Qi calculated by running the full model/Version 8 (Table 4) to calculate the specific rates. The layers near the surface should be most affected by the lack of near surface data at the small and large size ranges because the model has not fully equilibrated. As they pass through the first layer, the particles in the S15S20 size range start populate the smaller and larger size ranges. By the second layer, centered at 175 m depth, there are enough particles in the overlying layer so that settling increases concentrations of particles (S15–S20) at rates that increase with particle size up to 0.4 d1 (Fig. 4A). Concentrations of smaller particles (S1–S14) and larger particles (S21S23) decrease, respectively, at low rates and very high rates (2 to 5 d1) because the system has not fully adjusted to the limited size range of the surface boundary condition (see Fig. 10C). At 850 m depth, settling increases particle concentrations for all sizes, with
rates that generally increase with particle size from almost 0 to 0.12 d1 (Fig. 5A). The greater settling speed of larger particles makes the specific rates of change greater for larger particles for a given gradient in concentrations (Eq. (4)). At both 175 and 850 m depths, microbial activity results in a mass loss for almost all particle sizes (Figs. 4B and 5B). There is a gain of mass for S1–S9 (o0.005 cm) at 175 and 850 m depth. The gain for S14 (0.02 cm) at 175 m depth is also a result of the lack of data for this size range at the surface. For S15–S20, the specific losses increase with particle size from 0.02 to 0.1 and 0.1 to 0.4 d1, with a rate depending on the microbial degradation rate r: The specific rate of change does not vary with depth or particle concentration but does with the shape of the particle size spectrum. The pattern for the mesozooplankton feeding shows rates for the unmeasured size ranges that are highly variable (Figs. 4C and 5C). For example, the rapid gain in S21–S23 (23 d1 at 175 m) results from a relatively constant mass addition from fecal pellets normalized by the low particle concentrations outside the measured range. In S15–S20, the rates range from almost
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Fig. 4. Specific rate of change, Q1 i ðdQi =dtÞl at 175 m depth for the different mechanisms as a function of apparent particle diameter. The calculation is for 10 May 1995 at 175 m depth. (A) Settling (S); (B) microbial degradation (M); (C) copepod feeding (Z0: filter feeders, Z1: flux feeders and Z2: ‘‘miners’’); (D) macrozooplankton feeding (Z0: filter feeders and Z1: flux feeders); (E) fragmentation (Z3); and (F) coagulation (C). See Table 1 for explanations. For each mechanism, the two lines represent the lower and upper limits calculated using the range of values (Table 3). Note that in some cases the lower limit is not visible on the graphs because the specific changes are very low. The dotted vertical lines correspond to the size sections (S15S20) for which we have the UVP data (all the sections are marked on the upper axis of A, B, and C). The number above C and D indicates the highest value for the rates.
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Fig. 5. (A–F) Specific rate of change, Q1 i ðdQi =dtÞl at 850 m depth for the different mechanisms as a function of apparent particle diameter. Details as in Fig. 4.
0.6 to 0.1 d1 and depend on the encounter mode and amount ingested during an encounter with a particle. For filter feeding (Z0), the specific rates vary with particle size and are less than the rates for flux feeding. Flux feeding combined with particle mining (Z2) results in loss rates that are
greatest for 0.05 cm particles (S17); flux feeding combined with total particle consumption (Z1) has loss rates that increase with particle size at both depth. Because zooplankton concentrations decrease with increasing depth, the specific loss rate to the mesozooplankton decreases with depth.
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The specific rates for the macrozooplankton show a similar pattern as the mesozooplankton but the rates are lower (Figs. 4D and 5D). For S15–S20 at 175 m depth, the effect of macrozooplankton feeding changes depending on the encounter mode. The specific rates for filter feeding (Z0) are constant with particle size; those for flux feeding (Z1) increase for larger particle because of their faster settling speeds. Increasing the collection cross-section significantly increased the effect of flux feeding. Both sets of specific rates also decrease with depth or become null as the macrozooplankton abundances decrease to zero (Z1 at 850 m, Fig. 5D). At 175 m depth, the rates associated with fragmentation by macrozooplankton have different patterns depending on the way the aggregate is fragmented (Fig. 4E): fragmentation into many small particles yields specific loss rates that are similar for all sizes except at the section of the primary particles where they accumulate while splitting into two yields a gain in particle concentration for small particles and a loss for large particles. The relative importance of macrozooplankton fragmentation, as well as feeding, are small relative to the mechanisms mediated by the mesozooplankton (o0.01 d1), even if larger values are used for the encounter rates (Table 3). At both depths, coagulation by both shear and differential sedimentation increases the concentration of particles larger than S17 (0.054 cm) at the expense of the smaller particles (Figs. 4F and 5F). The rates in S21–S23 are greater than in S15–S20 because of the normalization by the low particle concentrations outside the measured range. In S15–S20, the specific rates for shear tend to be smaller than those for differential sedimentation, even at a relatively high turbulence rate (e ¼ 105 cm2 s3). The smaller particle concentration with greater depth decreases the specific rate of this process. The processes having the greatest potential impact on the particle size spectrum are settling, coagulation, microbial activity and mesozooplankton feeding. The two processes involving macrozooplankton (fragmentation and feeding) have rates almost 2 orders of magnitude smaller than those of the dominant processes. As a result of
these calculations, we will focus on eight versions of the model having different combinations of the dominant mechanisms (Table 4). They will not include fragmentation and have macrozooplankton feeding incorporated into the effect of the mesozooplankton. The different parameters values important for settling, bacterial and zooplankton activities will be used in the sensitivity analysis. The other parameters will be kept constant at the value given in Table 3. 3.3. Seasonal simulations The eight versions of the model are simulated with the standard parameters and compared with the observations using R0i;j (Eq. (6)), which measures the average ratio between prediction and observation at each depth and size. Version 1 (settling only) overestimates the particle concentrations in each depth layer. The error increases with particle size (specially in 1995 while in 1993 and 1994, there is a peak around S18) and depth throughout (Figs. 6A, 7A and 8A). The overestimation is particularly marked in spring 1995. The addition of any process to particle settling improves the results. Adding microbial activity (Version 2) or filter feeding (Version 3) to the settling reduces the overestimation but the residuals increase with size and depth (Fig. 6B and C, Fig. 7B and C, and Fig. 8B and C). Adding zooplankton flux feeding and total ingestion (Version 4) to settling causes a marked decline in the overestimation (with a marked underestimation in 1993) and the ratios are more constant with size for each years (Figs. 6D, 7D and 8D). Adding zooplankton flux feeding and mining (Version 5) to settling causes an underestimation of concentrations for particles smaller than 0.05 cm (S17) and an overestimation for the larger particles (Figs. 6E, 7E and 8E). Adding coagulation (Version 6) increases the ratios for the larger particles and decreases the ratios for the smaller particles (Figs. 6F, 7F and 8F). Thus, adding any one of the particle transformation mechanisms to particle settling from above tends to improve the fit but introduces an additional bias.
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Fig. 6. Spring–fall 1993: Ratio of predicted and observed particle number spectra R0i; j (Eq. (6)) as a function of apparent particle diameter. Each plot corresponds to one model. Each line curve is the average over time of the ratio for one layer. Results for the first (125 m) and last (950 m) layer are highlighted by the heavy continuous and dash lines. (A) Version 1; (B) Version 2; (C) Version 3; (D) Version 4; (E) Version 5; (F) Version 6; (G) Version 7; and (H) Version 8. See Table 4 for explanations.
Using more than two mechanisms produces mixed results. The combination of settling, microbial activity and zooplankton flux feeding with total ingestion (Version 7) greatly improves the predictions for 1995 (Fig. 8G) but worsens the predictions for spring 1993 and 1994 (Figs. 6G and 7G). Adding coagulation to Version 7 (Version 8) does not improve the results (Figs. 6H, 7H and 8H). The global measure R (Eq. (5)) can be used to make a systematic comparison of model results using different parameter values for the three seasons (Table 5). The variations that best fit the data are 4, 7, and 8 for 1993, 8 in 1994, and 7 and 8 for 1995. Version 2 calculated using rp ¼ 1:08 g cm3 or calculated using a constant r ¼ 0:2 d1 or r varying with depth increases the fit
compared to the standard simulation. Flux feeding with total ingestion in addition to settling yields the best fit, especially for high values of the cross sectional surface area of particle capture, s. 3.4. Flux Version 7 with the standard parameters provides a test of the model’s ability to predict the daily particle numerical and mass flux at 200 and 1000 m depth, at the high and low ends of the particle concentration range. The calculated POC fluxes are of the same order of magnitude and have a similar trend as the daily POC fluxes in sediment traps at 200 m for May 1995 (Fig. 9). The calculated fluxes are about 2.5 times greater and
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Fig. 7. (A–H) Spring–fall 1994: Ratio of predicted and observed particle number spectra R0i; j as a function of apparent particle diameter. Details as in Fig. 6.
the daily variations smaller than the values measured with the sediment traps at 1000 m (Fig. 9A). The observed flux at 1000 m is approximately 10% of the flux at 200 m. The calculated flux of particles is almost 100 times higher than the observed flux of fecal pellets measured in the traps at both depths, suggesting that most of the collected particles are not pellets (Fig. 9B).
4. Discussion 4.1. Environmental conditions at DYFAMED The study site is located at 43 250 N, 07 520 E in the Ligurian Sea, 52 km off Nice, France in water 2350 m deep. The continental shelf is narrow and
the slope is steep there, with the 1000 m isobath only 9 km from Nice. There is a permanent geostrophic front separating the sampling site from coastal water (Sournia et al., 1990). During only one of the 46 cruises did the coastal water associated nepheloid layer extend to the DYFAMED station (Stemmann, 1998). Stemmann et al. (2002) argued that the observed particle variability at DYFAMED site results predominantly from local forcing rather than from advective inputs. They suggested that temporal evolution of particle concentration and size distribution results from seasonal climatic forcing and is driven by the phytoplankton production near the surface. High phytoplankton biomass, in the form of diatoms and prymnesiophytes, enhances particle accumulation and sedimentation during winter and spring while stratification and
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Fig. 8. (A–H) Spring–fall 1995: Ratio of predicted and observed number spectra R0i;j as a function of apparent diameter. Each plot corresponds to one model. Details as in Fig. 6.
low biomass in the form of picophytoplankton lead to particle depletion in summer and autumn. These observations suggest that considering the site as one dimensional is a reasonable assumption for the three time periods simulated in this work. This assumption is further developed in the next section. In addition, deep water convection may also redistribute particles in the water column during winter (Stemmann et al., 2002). Because most of the particle mass and variations are observed in winter (Fig. 3), future development of the model should point toward the inclusion of vertical convection in the model. 4.2. Inter-annual variability If there were no particle degradation or consumption in the water column, the deeper particle
concentrations would be higher than those observed, particularly of the larger particles in 1995 (Fig. 8A). This common difference clearly indicates that particle removal occurs in the water column and that it is greater for large particles. The different combination of mechanisms for modifying particle distributions that we have used here provide a way to test the best candidates to explain the removal. Our results show clearly that the best combinations for all the years include zooplankton flux feeding and/or microbial activity (Versions 4, 7, and 8), although the best parameter values are different for the three cases. The combination of microbial activity and flux feeding provides a good fit to the data for 1995. The addition of coagulation to this former combination does not have much of an effect on the fit (Fig. 8G and H). In contrast, the same
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Table 5 Sensitivity analysis: values of R for each simulation with different parameter values Year
Version
Std
1993 1993 1993 1993 1993 1993 1993 1993
1 2 3 4 5 6 7 8
3.18 1.41 1.85 0.79 1.70 2.63 1.25 1.27
1994 1994 1994 1994 1994 1994 1994 1994
1 2 3 4 5 6 7 8
5.39 2.59 2.55 2.37 1.65 1.42 1.76 1.50
1995 1995 1995 1995 1995 1995 1995 1995
1 2 3 4 5 6 7 8
7.49 2.05 3.50 0.53 1.23 3.81 0.35 0.38
A
B
C
D
1.50 1.63
3.69 2.22 2.78 0.86 1.78 3.87 1.10 1.13
3.20 1.26
6.04 4.17 4.02 2.58 1.80 1.52 1.96 1.46
3.01 2.13
6.67 3.52 4.55 0.52 1.36 3.74 0.38 0.39
1.79 2.52 3.07 1.04 1.07
1.27 1.43
3.60 4.87 5.34 1.78 1.36
2.36 1.29
3.81 6.02 7.31 0.33 0.34
1.63 1.49
E
F
1.45
2.76
1.59 1.60
0.99 1.02
2.13
5.04
2.01 1.81
2.11 1.43
1.01
4.82
0.55 0.59
0.40 0.38
Missing values indicate that the parameter change had no impact on the mechanism for that version. The best results (closest to zero) for each column are in bold. Std: standard simulation; A: r ¼ 0:025 d1; B: s ¼ 1:3 105 m2; C: r ¼ 0:025 d1, s ¼ 1:3 105 m2; D: rp ¼ 0:08 g cm3; E: r=0.2 d1; F: r ¼ f ðzÞ:
combination of mechanisms greatly underestimates the concentrations for 1993 and 1994 with an error that increases with depth (Figs. 6, 7G, H). A possible reason for this underestimation would be if there is a greater particle consumption by the midwater community as a result of slower particle settling than we have calculated. Such a variation of settling speed could result if the properties of the particle source changes. Observations of the phytoplankton which are the particle source at DYFAMED site show that, although prymnesiophytes usually dominate, the spring of 1994 was dominated by diatoms (Marty et al., 2002). Aggregates composed predominantly of diatoms could have higher settling speeds because their primary particles are denser. In such a case, particle density would be increased from 1.062 to
a value more typical of diatoms, 1.108 g cm3 (e.g., Azetsu-Scott and Johnson, 1992). Using this higher density does increase the settling speed but does not improve the fit for any combination of mechanisms (Table 5, column D). Another possible reason for the underestimation of deep particle concentrations is that activity rate for the microbes or the zooplankton is too high for 1993 and 1994. This possibility can be tested using lower values for r and s: The lower values of r yield a slightly better fit for Versions 7 and 8 in 1993 and 1995, but offer no significant improvement in 1994 (Table 5). Reducing only s worsens the fit for the 3 years. The fact that changes in zooplankton and microbial activity can increase the fit suggests that their variations on interannual scales be responsible for changes in particle
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Fig. 9. Vertical fluxes of total POC and fecal pellets calculated using Version 7 for spring 1995. (A) Vertical POC flux measured in sediment traps and calculated using the model. (B) Vertical flux of fecal pellets measured in the sediment traps and particles numerical flux calculated using the model.
distributions in the midwater zone. Even changes in zooplankton concentrations are not incorporated into these calculations. It is also possible that a methodological bias during 1993 and 1994 relative to 1995 skewed the data. The mean time interval between sampling was much higher in 1993 and 1994 (C40 days on average) than in 1995 (C5 days on average). Short phytoplankton blooms and lateral advection that affect the deeper particle distributions may have been missed by the longer sampling intervals during the earlier 2 years (Marty et al., 2002; Stemmann et al., 2002). Because the most frequent sampling was during 1995 (12 profiles in 62 days), a period for which we also have other data from the DYNAPROC cruise (see Andersen and Prieur, 1999), we use this period to study the model properties in greater detail and to test additional hypothesis about the effects of microbes and zooplankton (see next section). 4.3. What causes POC losses with depth? 4.3.1. Processes through the water column Two of these processes, settling and coagulation, do not actually consume particles but shift
material around in space and in particle size. The biological activity does consume material, with each mechanism having its own signature. Microbial activity does not remove enough material by itself, particularly from large particles, to account for the observed changes; flux feeding cannot remove enough small particles (Fig. 8D). The best explanation combines microbial activity and flux feeding to work across the particle size spectrum. Large particles are preferentially removed or transformed into smaller particles by the flux feeders that are present shallower (Fig. 8G and H); smaller particles sink at slower rates and are degraded by the microbes. In this interpretation, the major role of the mesozooplankton is to stop the flux of the rare large particles in the upper water column. This behavior has been proposed for the efficient removal of fast settling fecal pellets by copepods (Bathmann et al., 1987; Peinert et al., 1987; Lampitt et al., 1990; Gonzales and Smetacek, 1994; Riser et al., 2001). Our results suggest that this mechanism can be extended to all aggregates. It is interesting to note that the best results have low values for the rate of microbial degradation of particles, ro0:05 d1. At the higher rate of 0.2 d1
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Table 6 Minimium/maximum POC gains and losses estimated by the model in two layers (mg C m3 d1) Depth (m)
Vertical flux
Microbes
Flux feeders
175 850
12.9 102 0.9 102
2.2 102/18.6 102 3.7 103/3 102
6.8 104/9.8 102 1.2 105/1.8 103
the Version 2 of the model does not fit the data for 1993 and 1994, but does for 1995 (but not as well as Version 7, Table 5), regardless of other mechanism included. We tested the hypothesis that the rate of microbial activity decreases with depth by decreasing r with depth, from 0.2 at 125 m to 0.05 d1 at 950 m depth (column F, Table 5), but were unable to really improve the fit to the data. We model microbial activity in a simple manner which does not include any resulting fragmentation. Such a process has been experimentally observed and could be important for particle transformation (Biddanda and Pomeroy, 1988; Ploug and Grossart, 2000). However, too little is known to describe it mathematically at present.
and Legendre, 2001), then this is equivalent to remineralization (respiration) rates of 0.6 102– 1.4 102 mg C m3 d1. These values are within the model estimates at 175 m depth (Table 6). The calculated losses for zooplankton correspond to the assimilated fraction of the ingested particles. If 50% of it is respired (Steinberg et al., 1997), then the model respiration for flux feeding ranges from 3.4 104 to 4.54 102 mg C ind1 d1 at 175 m depth. The in situ zooplankton respiration can be estimated from the organisms number concentration and the individual metabolic rate. The oxygen consumption rate of an epipelagic copepod can be estimated as (Ikeda et al., 2001):
4.3.2. Comparison of POC losses with independent estimates of respiration These estimates for POC loss due to microbial and zooplankton activity can be compared with field and laboratory measurements of organism metabolism. Microbial degradation of the particles results from either microbial respiration on the particles or microbially mediated release of DOC which sustains suspended free living microbes. The gain or loss of POC (dQ/dt) at 175 and 850 m depth due to settling and microbial and zooplankton respiration can be estimated from the specific changes given in Fig. 4. If this mass loss splits equally between respiration and DOC release then the estimated respiration on particles varies from 1.1 102 to 9.3 102 mg C m3 d1 at 175 m depth. In comparison, Turley and Stutt (2000) estimated production of bacteria attached particles using leucine incorporation in the NW Mediterranean Sea during April 1995. They measured rates of 2.4 102–2.8 102 mg C m3 d1 between 100 and 380 m. If we consider that bacterial growth efficiency range from 0.25 to 0.5 (Rivkin
where B is the copepod mass (mg C) and T is the temperature ( C). If we assume B ¼ 1:5 mg for a copepod colonizing an aggregate (Kiørboe, 2000), T ¼ 13 C (a typical value for 175 m), and a population density of 250 copepods m3, then the population respiration is 6 102 mg C m3 d1, a value only slightly higher than the maximum estimated using the model. These estimates of POC respiration are crude, considering the numerous poorly known factors involved in their calculations. However, it is promising to note that the model predictions and independent estimates from bacterial and zooplankton respiration measurements are similar despite the very different modes of calculation.
Respiration ðml O2 h1 Þ ¼ 1:132 B0:780 e0:073T ;
4.3.3. Transfer of mass within a size spectrum Coagulation transfers particle mass from small sizes to larger ones while microbial and zooplankton activity transfer mass toward small particles sizes. This transfer of POC can be followed during a simulation (Fig. 10). For example, the mass in particles with do0:029 cm (S1–S14) increases
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Fig. 10. Summed POC concentrations for different size ranges using Version 7 for spring 1995: (A) POC in S1–S14; (B) POC in S15–S20; and (C) POC in S21–S23.
between days 2 and 30 during spring 1995 because small particles accumulate faster than they are removed by sedimentation and consumption. After day 30, the input from the overlying surface layer decreases and the small particles are progressively removed. By contrast, particles with d > 0:13 cm (S21–S23) do not accumulate in the midwater zone because they fall rapidly. The number concentrations in the three last sections (outside the range actually observed) never exceed
the concentrations observed in the largest size section sampled by the UVP II. That is, the model does not predict more large particles than have been detected by the UVP II. These simulations suggest that coagulation is not rapid enough to increase the size of particles and thereby to counterbalance the removal of the large particles. This relative unimportance for coagulation in the mesopelagic realm could result from the slow coagulation rates expected for the
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low particle concentrations and the low turbulent energy dissipation there, but it could also result from limitations in our calculations. Although these simulations were for particles ranging in size from 5 mm to 3 mm, the results were tested against the small size range available from field measurements. The smaller particles should be less susceptible to settling, zooplankton grazing, disaggregation, and possibly microbial degradation. Coagulation could be important in determining their concentrations in ways that we have not been able to test. The high variability observed in the specific rates of change for S1–S14 and S21–S23 emphasize the need for data over the complete size range before coagulation can be ruled out (Figs. 4 and 5). 4.4. Differences between zooplankton feeding types The model predicts that particle fragmentation by macrozooplankton has a small effect on particle distributions because the large organism concentrations are very low at DYFAMED. In the study describing extensive fragmentation of marine snow by euphausiids (Dilling and Alldredge, 2000), the animal concentrations within the upper 100 m off California were 100 times greater than those at the DYFAMED site. The DYFAMED site shows characteristics more typical of central oceanic gyres (Marty et al., 2002) rather than eutrophic conditions of coastal California. Although we have presented the specific rate of change for only one depth and date in spring 1995, the same pattern is observed in all cases because the zooplankton concentrations are kept constant. The macrozooplankton concentrations that we use in the model were for spring, the period of maximum animal concentration (Nival et al., 1975). Therefore, the rates that we have calculated for fragmentation by zooplankton are probably upper limits for the region. Among the different zooplankton feeding mechanisms only flux feeding fits the data well. The model calculated that filter feeding is not fast enough to be important in particle removal and that it does not specifically remove the large particles. This result is consistent with previous works that have questioned how animals could
survive in a poor environment by filtering water (Durbin et al., 1983; Dagg, 1991) and have proposed alternative feeding modes. Jackson (1993) proposed that animals such as pteropods may preferentially feed on falling particles and termed this behavior flux feeding. Dagg (1993) proposed the same behavior for the midwater copepod Calanus cristatus. More recently, Kiørboe and Thygesen (2001) have shown that falling aggregates leave a chemical plume in their wake that is tens of centimeters long which may be detected by cruising copepods. Our calculations suggest that the macrozooplankton passive flux feeders (pteropods) are unable to change the particle size distribution alone because they are present in abundances at this location that are too low (o60 individuals/ 1000 m3) compared to the situations where they have been argued to be important (>105 individuals/1000 m3; Jackson, 1993). Active flux feeding (or plume finding) by mesozooplankton (essentially copepods) has a greater effect, but only if the capture cross-section is large, corresponding to a radius of 2.5 mm. If we assume that the minimum size of the copepod is 200 mm; then this radius is more than 10 times larger than the body length. The fact that the required capture distance is so much larger than the animals suggests that midwater mesozooplankton use remote detection to increase the distance of perception. For example, they are able to sense at a short distance the biochemical queue left by falling particles. The importance of active flux feeding suggests that the fast settling particles are the main food source for the animals. For mesozooplankton flux feeders, total ingestion of each particle encountered yields the best fit to the data. The encounter rates for mining are similar to those for total ingestion, but the effect of mining on the size spectra is not consistent with the removal rates for large particles (Fig. 4C). It may be that it is not appropriate to describe the interactions with the particles used here. Mining has been described as occurring on aggregates many times the size of copepods (Steinberg et al., 1997). In this work, the modeled particle diameters range from a few mm to a maximum of 0.32 cm, while the mesozooplankton are larger than
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200 mm: These copepods are almost the size of the particles, suggesting that total ingestion is more appropriate than mining here. Because of the model sensitivity to different zooplankton behavior in the midwater zone, more data on the whole particle size spectra, on the state of particle colonization by zooplankton and on zooplankton feeding behavior are needed. The midwater temporal variability of colonizing organisms is also almost unknown and future works should point in that direction because it may be important to explain temporal variations in the flux.
905
traps (e.g., Turner, 2002) and supports our hypothesis that fecal pellets should not influence the simple size spectral approach to describing particle distributions. The results of our work strongly suggest that observations on particle spectra just below the mixed layer would be useful in the future to predict the vertical flux in the deeper layers. Because the acquisition of information on particle size spectra is rapid and can cover a large spatial scale (typically the same as any CTD survey) or a long-term survey (when moored on a point), they can provide an additional way to estimate the vertical flux.
4.5. Comparison with sediment trap data 4.6. Data limitation The POC flux at 200 depth calculated by the model and estimated using sediment trap data have similar amplitudes and trends. At 1000 m depth, the modeled POC fluxes are about 2.5 times higher than the ones measured with the sediment trap. The overestimation in the deeper location may be result from the use of a constant POC/DW ratio with depth. The measured ratio decreases with depth from 0.1 to 0.05 at DYFAMED (Miquel et al., 1994). In addition, the model is not able to reproduce the daily variations observed in the sediment traps. This variability may not be real but be the result of sampling error in the collection by sediment traps of rare settling particles in a short time interval. The current version of the model does not describe the change in the biogeochemical composition of an aggregate submitted to the different processes. Future development should point in that direction because particles carry many elements (nutrients, biominerals, and trace metals) and models of particle dynamics can help to predict the depth at which they are released in the water column. An interesting result of the comparison between sediment traps and the model is that the numerical flux of fecal pellets is two orders of magnitude smaller than the flux of particles. The lower flux of fecal pellets suggest that they are highly transformed into aggregate-type particles in the midwater zone. This observation of lower fecal pellets agrees with many observations from sediment
The ability of this model to make reasonable predictions of the particle size distributions, particularly deeper, despite the limited size range we use to add particles at the top suggests that particle size distributions are extremely dynamic, being determined by processes through the water column rather than by surface inputs. However, the size dependence of the rates of change at 175 m show that there is an effect to at least that depth. Data sets with particle distributions over a greater range of sizes would improve the predictions and the tests. Also desirable are studies of the mechanisms we have assumed here. For example, observations of how microbial degradation affects particle diameter and strength as well as mass loss would allow a better description of the effect of microbes on particles. Similarly, measurements of the rates and size dependence of particle disaggregation would allow the use of more sophisticated models.
5. Conclusion The vertical distribution of particle concentration and flux in the mesopelagic region is inherently linked to the particle distributions. By combining descriptions of how the physical and biological processes affect particle size distributions in a model, we have been able to test the effect of different combinations of the processes.
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Observations of particle size distributions through the water column have allowed us to test the models results. Several combinations of processes are consistent with these observations. The mechanisms have to be able to stop the high flux of large particles in the upper midwater zone. This effect requires the mesozooplankton to feed preferentially on large settling particles using remote detection, totally ingesting the particles. Microbial activity alone does not remove enough large particles even if the degradation rate is high. Below 500 m depth microbial activity becomes more important because the zooplankton are rarer. The results also suggest that mesozooplankton have a much greater effect on particle flux than macrozooplankton. The calculated POC loss due to microbial activity and zooplankton feeding is consistent with independent measurements of these rates. These calculations show that it is possible to predict the flux at 200 m depth knowing the particle size distribution at 100 m, but that a model predicting to 1000 m depth needs to include biogeochemical transformations as well. This work is a first attempt to relate the particle size spectra in midwater to the physical and biological processes. The assumptions on particle properties and processes are based on studies in the surface mixed layer and more information is needed to confirm the hypothesis. In addition, particle size distributions need to be measured over a larger size range to fully test the results. Recent technologies for in situ sampling and in situ experiments by ROV and imaging systems should be able to provide information on particle size and transformation rates that are particularly adapted to address these questions. The model that we have developed provides a framework for future experiments in order to answer important questions on particle dynamics.
Acknowledgements This work was supported by Grants OCE9986765 and OCE9981424 from US-JGOFS program in the Ocean Sciences Division of NSF. We are grateful to V. Andersen for the data on
zooplankton and J.-C. Miquel for the sediment trap data. We also want to thank three anonymous reviewers who provided useful comments and observations on the manuscript.
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