An analysis of sinking rates of natural copepod and euphausiid fecal pellets

Transcription

1 Limnol. Oceanogr., 26(l), 1981, An analysis of sinking rates of natural copepod and euphausiid fecal pellets Paul D. Komar, Alan P. Morse, and Lawrence F. Small School of Oceanography, Oregon State University, Corvallis Scott W. Fowler International Laboratory of Marine Radioactivity,2 Mu&e Oc&anographique, Principality of Monaco Ahstruct Recent investigations have demonstrated that the settling velocity, w,, of a cylinder at low Reynolds numbers (the Stokes region) is given by ws = o.0790~(p, - p)gl(# where L and D are the cylinder length and diameter, ps is the particle density, and SL. and p are the fluid viscosity and density. This relationship is compared with published data on the settling velocities of cylindrical fecal pellets produced by euphausiids and copepods. The agreement between data and the equation is very good. The analysis further permits the indirect evaluation of the fecal pellet density. A mean density fi, = 1.22 g*cm- was so determined, which corresponds almost exactly to the one reliable direct measurement of fecal pellet density (1.23 g.cm- ). A second equation is available that can be used if the fecal pellets are ellipsoidal or oval rather than cylindrical. It is well established that the settling of fecal pellets produced by copepods, euphausiids, and other organisms in the sea is important in controlling the vertical distributions in the water column of many different elements and materials (organic carbon, 0,, C02, PCBs, artificial radionuclides, etc.), and in contributing to the bottom sediments (e.g. Schrader 1971; Small and Fowler 1973; McCave 1975; Honjo 1976, 1978; Fowler 1977; Elder and Fowler 1977). As a part of improving our understanding of this process, the settling rates of fecal pellets of a range of sizes produced by various organisms have been measured. Osterberg et al. (1963) performed the earliest experiments of this type, deter- 1 Research supported by NSF/CORES, Vertical Transport and Exchange of Materials in the Upper Waters of the Ocean (VERTEX). T. Beasley, R. Holman, and H. Schrader read the manuscript and K. Komar helped in data analysis. P. Wiebe provided his original data set on fecal pellet settling. 2 The International Laboratory of Marine Radioactivity operates under a tripartite agreement between the International Atomic Agency, the Government of the Principality of Monaco, and the Oceanographic Institute at Monaco. I72 mining the settling rates of fecal pellets of Euphausia paci$ca, but the animals were given food in the laboratory which might not have been representative of their diet at sea. Fowler and Small (1972) have shown that laboratory conditions and artificial feeding can lead to anomalous light-density fecal pellets, with low- er settling rates. Smayda (1969) collected fecal pellets of unknown origin from Narragansett Bay and timed their settling rates in a laboratory settling tube. Wiebe et al. (1976) collected fecal pellets of unknown origin and age from a particle trap 2,150 m deep in the Tongue of the Ocean, Bahamas, and performed timed sinking-rate experiments. Fowler and Small (1972) measured sinking rates of natural fecal pellets from freshly collected euphausiids. Small et al. (1979) h ave two data sets for natural copepod fecal pellets, one from a collection from mixed small copepods ( mm long) and a second for pellets derived from the pontellid copepod Anomalocera patersoni (-3 mm long). Those data combined with previous data showed an increase in sinking rate with increasing fecal pellet volume and pro-

2 Fecal pellet sinking rates l-2 vided an improved empirical relationship for the prediction of pellet sinking rates. Such relationships can provide an estimate of the settling rate of a fecal pellet of known volume, but a shortcoming of an empirical relationship is that it does not permit correction for the variable viscosity of seawater. More important, it does not contain the fecal pellet density as a parameter, a factor that is known to be important to the resulting settling rate. Nor can we logically compare the empirical relationship to the available experimental data on the settling rates of grains of the same shape but having other densities (e.g. with the glass cylinders of the experiments described below). Komar (1980) has derived equations for the settling rates of ellipsoidal and cylindrical-shaped grains. Our present purpose is to determine whether those equations can also be applied to the evaluation and analysis of the settling rates of fecal pellets, providing an alternative approach to the empirical relationships of Small et al. (1979). A second purpose of our analysis is to determine improved estimates of fecal pellet densities, a parameter important in the evaluation of verti- cal fluxes of organic matter and elements in the oceans where particle trap data are unavailable (Bishop et al. 1977). Governing equations The settling behavior of any particle is governed in part by its Reynolds number, which for fecal pellets may be taken as Re = ~w.sdn P (1) where p and p are the water density and viscosity, w, is the pellet settling rate, and D,, is a measure of the particle - size, here taken to be its nominal diameter (the diameter of a sphere having the same volume and weight as the nonspherical pellet). Because of the small values of w,~ and D,, for the fecal pellets of usual marine plankton, values of the Reynolds number from Eq. 1 are also small. The copepod data of Small et al. (1979) give the range Re = and the eu- phausiid data of Fo\+Tler and Small (1972) yield Re = Except for a fe\\. of the very largest euphausiid pellets, the values are below the Re = 0.5 value that is usually taken as the upper limit for the application of the Stokes settling eqllation of spheres. The well known Stokes equation is w,~ = $ $(p\ - p)gd2 (2) where ps is the particle density, g is the acceleration of gravity (981 cm * s m?), and D is the sphere diameter. Smayda (1969) used the Stokes equation to estimate the settling rates of fecal pellets, taking p,< = 1.19 g*crn- from Dillon (1964) for the mean pellet density, and concluded that the results agree reasonably well \\Tith his measured pellet settling rates. Hutchinson (1967) and others discuss the problems in using the Stokes equation, the foremost being that it strictly applies only to spheres. With shapes other than spheres, the particle shape will definitely have an effect on its settling rate. Until recently it has been difficult to make satisfactory corrections for cuc~h shape effects. Komar and Reimers (1978) and Komar (1980) have derived equations that are modified forms of the Stokes relationship of Eq. 2, modified so that they apply to ellipsoidal and cylindrical particles. For circular cylinders alone, Komar (1980) deduced the semiempirical ecl~lation w,s = o.0790~(p.s - p)gl (:;i (:3) where L is the cylinder length and D i\ its diameter. L serves as a measure of the cylinder size in Eq. 3, and the ratio L:D serves to define its shape. Equation 3 is limited in application to pwsllp < 2, that is, basically to the Stokes region. All of the fecal pellet data meet this requirement so that Eq. 3 should be applicable to cylindrical fecal pellets. If ellipsoids as well as cylinders are considered, then Komar (1980) found that (4)

3 174 Komar et al. where of the shape, D,, is again the nominal diameter particle and E is a measure of defined by Janke (1966) as E = D OS2 + Di2 + D, -t s 3 1 6) where D,, Di, and D, are the smallest, intermediate, and longest axial diameters of the ellipsoid. In the case of cylinders, D, = L and D, = Di = cylinder diameter, For spheres, D, = Di = DI, and therefore E = 2.0, and Eq. 4 reduces to the Stokes relationship of Eq. 2. As with the other equations discussed here, Eq. 4 is limited in application to the Stokes region. Equations 3 and 4 are empirically based on the ellipsoid-settling experiments of Komar and Reimers (1978) and the cylinder-settling experiments of Komar (1980). In the former, regular ellipsoidal pebbles were settled in glycerine (viscosity about l,ooo-1,500 times that of water); in the latter, glass cylinders were settled in glycerine. Although both data sets are based on the settling of large particles in a fluid much more viscous than water, what is of importance are the ranges of the Reynolds numbers. As can be seen in Eq. 1, the larger values of w, and D,, for the pebbles and cylinders will be compensated by the increased value of the viscosity of glycerine (the density p of glycerine is not much higher than that of water). It turns out that the Reynolds numbers of the settling pebbles and cylinders in glycerine are also in the Stokes range (Re < O.S), just as arc the pellets settling in water. The Reynolds number is the criterion for dynamic similarity (Shapiro 1961), being used for examp1 c for scale-model wind-tunnel studies of the drag on airplanes. Because the settling pebbles and cylinders have the same Reynolds number ranges as the fecal pellets settling in water, they can be considered to be hydrodynamically equivalent. Therefore, Eq. 3 and 4 can be expected to apply to settling of cylindrical and ellipsoidal fecal pellets. Further experiments by Baba and Komar (in press) have shown that particle surface roughness and minor irregularitics have a negligible effect on the settling rate. Data comparison The euphausiid data of Fowler and Small (1972) and the copepod data of Small et al. (1979) are used here chiefly to examine the applicability of Eq. 3 and 4 to fecal pellet settling. These data were selected because they more closely rcpresent true oceanic conditions than those derived totally from laboratory studies. The data are plotted in Fig. 1 as w,~ vs. L (L:D) 1.fi(i4 from Eq. 3. It is important that the units be consistent, and the cgs system is used throughout this analysis. Being a log-log plot, for the data to follow Eq. 3 there must be a straight-line fit with a slope of 1.0. Such a straight line is shown, yielding the relationship w, = (1.21 x 103)P L -1*664 ( D ) (6) which is seen to fit the data reasonably well. The fact that a good straight line with unit slope does fit the available data can be taken as partial confirmation of the applicability of Eq. 3 to fecal pellets. Taking Eq. 3 and 6 as equivalent permits an evaluation of the pellet mean density, &, since p = g. (cm. s) 1 for the water viscosity and p = g. cm-3 for the salt water density under the conditions of the measurements (about 13 C in seawater). Equating the 1.21 x lo3 coefficient of Eq. 6 to O.O79O(p, - p)glp of Eq. 3 yields ps = 1.22 g * cm 3 for the mean density of the fecal pellets. Figure 2 shows the distributions of the ps values calculated from Eq. 3 for each of the individual pellets and their measured settling rates, assuming now that Eq. 3 is applicable on an individual basis. The data of Fig. 2 are divided into three groups: the euphausiid data of Fowlel and Small (1972), the mixed copepod, and the A. patersoni copepod data of Small et al. (1979). The euphausiids and the mixed copepods give about the same results, the mean pellet densities of the two groups being ps = 1.29 and 1.28 g. cm-3 (the distribution of the copepod fecal pellets is highly skewed toward higher densities, and the mode is closer

4 Fecal pellet sinking rcltcs 175 I I I Illll FECAL PELLET SETTLING. mixed small copepods 0 Anomolocero Paterson1 x mlxed euphausilds I I II Iii I I I 1 IO 3 L2 ( L/ D )- 664, cm2 Fig. 1. Comparison of copepod data of Small et al. ( 1979) and the C~tiplIktll4iid (IaLL 01 l o\\ ltlr ~(1 SIII~LII (1972) to relationship suggested by Eq. 3. Straight line shown y irid\ Eel. 6. to the 1.22 g-cm- value above). The mean density of the A. patersoni pellets in Fig. 2 is significantly less (1.15 g. cm :{). This difference is also apparent in the original plotting of the data in Fig. 1. As discussed by Small et al. (1979), A. patersoni was collected from very near the sea surface, where the animals concentrated to the near exclusion of other copepods; Small et al. concluded that it might be expected that the animals would ingest a large fraction of lightweight particles and subsequently produce lightweight pellets. The standard deviations and ranges of ps values in Fig. 2 are certainly large1 than actually present. The abovc~ procedure basically assumes that all of the scatter of the data obser\&le in Fig. 1 is caused by the variability in pellet dcnsities. As shown by the settling measllrclments of Turner (1977), there can I)e ;i large variability in the sclttling rates of illdividual fecal pellets; this could produce much of the scatter in Fig. 1. Therefore, the calculated standard dc\tiations and ranges of densities in Fig. 2 will 1~ too large. This shollld not significantly af f; cbt

5 Komnr et al. mlxed copepods PELLET DENSITY, ps, g/cm3 Fig. 2. Freqllcncy graph of calculated fecal pellet densities, B, obtained from Eq. 3 and the measured settling rates. Also shown are means and standard deviations of the three data groups, the mean ps values determined in the analysis, however. We carried out a similar analysis to that in Fig. 1 for the data of Wiebe et al. (1976), obtained from natural fecal pellets collected in a particle trap. Although their data are more scattered, they still clearly follow the relationship of Eq. 3, but with a different coefficient from that in Eq. 6 due to the different water temperature (and hence viscosity and density) at which Wiebe et al. measured pellet settling rates. The best fit to the trend of the data of Wiebe et al. alone also yields an estimated mean fecal pellet density bs = 1.22 g. cm-s, identical to the value obtained with the combined data of Fowlcr and Small (1972) and Small et al. (1979). Th is is somewhat coincidental, in view of the scatter of the Wiebe et al. data. In a similar fashion but using the Stokes relationship (Eq. 2), Wiebe et al. also arrived at the estimate 1.22 g* cm- 3 for mean pellet density. This shows that when the data are highly scattered, Eq. 2 and 3 can be expected to yield approximately the same results. There is little information available on measured fecal pellet densities by which we can judge the reasonableness of the above indirect determinations. Dillon ( 1964) gives a value of 1.19 g * cmp3 for the mean density of pellets collected from sediments but does not state how he arrived at this value. Recently, one of us (S.W.F.) measured 133 cylindrical pellets from the euphausiid Megunyctiphanes noruegicn. There was some uncertainty in their collective wet weight, but the results indicate an average density be- tween 1.19 and 1.27 g*cm -3, suggesting a mean of about 1.23 g. cm+, This value agrees almost exactly with our above results from Eq. 3. Additional direct measurements of fecal pellet densities are needed, but this initial comparison indicates again that Eq. 3 appears to give a consistent analysis of fecal pellet settling. It may be that the indirect use of Eq. 3 to determine fecal pellet densities is more accurate than direct measurements, which are extremely difficult. By way of summary, in Fig. 3 we plot the measured fecal pellet settling rates

6 Fecal pellet sinking mtcs 177 x FECAL PELLET SETTLING mixed small copepods 0 Anomolocero poterson ~ ~ Small et 01 ( 1979). l. x mixed euphausltds) Fowler and Small (1972). t portlcle trap sample 1 Wlebe et al ( / / I I I Illll I I I lllll lo- I 2 w, = ( ps-p 1 gl2 (by4, cmisec Fig. 3. Measured settling velocity of fecal pellets v\. calculated valr~e from Eel. 3. vs. u;, calculated with Eq. 3 from the mean pellet densities for the various data sets. Figure 3 differs from Fig. 1 mainly in the inclusion of the different pellet densities, which results in better alignment between the data sets. The data of Wiebe et al. (1976) are also included in the plot of Fig. 3 and they agree well with the other data sets; they were not plotted in Fig. 1 because the measurements were made at different water temperatures than those in the other studies. We performed the same type of analysis using Eq. 4 rather than Eq. 3. The fecal pellets are generally cylindrical, but with tapered or rounded ends so that they are also approximately elongated ellipsoids (Fowler and Small 1972; Small et al. 1979; Wiebe et al. 1976). A plot of measured u;,~ vs. D,, )EO. ~XO from Eq. 4 looks almost exactly the same as Fig. 1 and so has not been reproduced here. Again the best fit to the data is a straight line with unit slope, yielding a mean pellet density of & = 1.23 g*ccm-:, the same as that obtained from the analysis using Eq. 3 and Fig. 1 and from the one direct measurement by S. W. Fowler. These results indicate that Eq. 4 as well as Eq. 3 is applicable to the analysis of fecal pellet settling. It might actually be preferable for pellets that are more ellipsoidal or oval than cylindrical. The data necessary to examine this are not at present available. Equation 4 permits us to place the set-

7 178 Komar et al. W, q ( ps -p 1 g Eo3BoV2 3 FECAL PELLET SETTLING l mixed small copepods o Anomolocero potersonl x mlxed euphousllds PELLET VOLUME, V = 9 D*L, cm3 Fig. 4. Data comparison with Eq. 7, a modified form of Eq. 4. Graph is comparable to that of Small et al. (1979: fig. 6) except that it accounts for differences in fecal pellet densities and changes in water viscosity and density. tling velocity into a relationship where it is directly dependent on the pellet volume V, similar to the empirical relationship and graph of Small et al. (1979: fig. 6). From the definition of the nominal diameter D,, (diameter of a sphere with the same volume as the pellet), we have D,, = (6V/7r) 13. Substituting this in Eq. 4 for D,, yields, after some algebraic manipulation, the relationship 1~PWws (ps - p)ge * *o = kv2/ (7) where k is the proportionality coefficient to be determined from the data comparison. The data are plotted in Fig. 4 as the left side of Eq. 7 vs. the pellet volume V, calculated with the equation for a circular cylinder [v = (n/4)d2l]. The mean pellet densities determined in the above anal- yses were used in calculating the left side of Eq. 7. The straight-line fit to the data, shown in Fig. 4, yields k = 1.25 as the proportionality factor in Eq. 7. If the pellets had been perfect cylinders, we would have expected k = 1.54; if they were perfect ellipsoids, k = The best fit to the data thus yields a value that falls between the values based on perfect cylindrical and ellipsoidal shapes, an expected result from the actual shapes of the pellets. But perhaps unexpectedly, the k = 1.25 value is somewhat closer to that for the ellipsoids than for the cylinders-unexpected in that the pellets look more like cylinders. The differences in the k values are small, however, and a small error in the evaluation of the water viscosity or some other parameter could alter the results. Equation 7 with k =

8 does provide another relationship for predicting fecal pellet settling rates, in this case from their determined volumes. The graph of Fig. 4 is similar to that of Small et al. (1979: fig. 6). However, their plot empirically yielded w, av. 13 whereas Eq. 7 indicates that w,av ~6fi7. The plot of data in Fig. 4 demonstrates that the 2/3-power dependence of V is much better than the dependence of the Small et al. relationship. The reason for the difference is that Eq. 7 and the graph of Fig. 4 account for the density differences in fecal pellets between the data sets whereas their graph did not. The lower value they obtained resulted from the lowered plotting position of the A. patersoni data, much as seen in Fig. 1. When the 1o;wer densities of the A. patersoni fecal ptillets are accounted for as in Fig. 4, they align better with the other data sets and agree with the V dependence according to Eq. 7. Discussion Equation 3, based on the cylinder-settling cxperimcnts of Komar (1980), seems to be applicable to the settling of cylindrical fecal pellets produced by copepods and euphausiids. The fecal pellet data show the same trend as Eq. 3 when the measured settling rate w, is compared to L (L:D)-.(jCi4(Figs. 1 and 3). The analysis permits the calculation of a mean pellet density, fis = 1.22 g. cm-3, which corresponds almost exactly to the one reliable direct measurement of mean fecal pellet density (1.23 g-cm - ), Equation 4 similarly provides a consistent analysis of fecal pellet settling, yielding the same estimate of the mean fecal pellet density. Equation 4 can also be modified to a form1 where the settling velocity is related directly to the fecal pellet volume (Eq. 7 and Fig. 4). Equations 3 and 4 :should be used in the analysis of fecal pellet settling rather than the Stokes relationship of Eq. 2, which strictly applies only to spheres. Within the present scatter of the data, Eq. 3 and 4 give basically the same results. Equation 3 is somewhat simpler to USC: Fecal pellet sinking rates 179 since it depends directly on length (L) and diameter (II) measurements of the fecal pellet. Equation 4 and its aiternate form, Eq. 7, should be used if the fecal pellets are ellipsoidal or oval rather than cylindrical, as Eq. 3 is not applicable to those shapes. References BABA, J., AND P. D. KOMAH. In press. Settling velocities of irregulnr grains at low Reynolds numbers. J. Sediment. Petrol. BISIIOP, J. K.,J. M. EDMOND, D. R. KETTEN, M. I. BACON, AND W. B. S~LKER The chemistry, biology and vertical flux of pwticulnte matter from the upper 400 m of the eqllntori;d Atlantic Ocezm. Deep-Sea Rcs. 24: DILLON, W. P Flotation technique for separating fecal pellets and small marine organisms from sand. Limnol. Oceanogr. 9: ELDER, L>. I,., AND S. W. FOWLER Polychlorinntcd biphenyls: Penetration into the deep occ:m by zooplzmkton fecnl pcllct transport. Science 197: FOWTZR, S. W Trace elements in zooplankton pzwticulate products. Natwe 269: > AND L. F. WALT, Sinking rates of euphausiid fecal pellets. Limnol. Oceanogr. 17: HONJO, S Coccoliths: Production, tmnsportation and sedimentntion. Mar. Micropaleontol. 1: Sedimentation of materials in the Sargasso Sea at 5,367 m deep st:ltion. J. Mar. Res. 36: IIUTCIITNSON, G. E A treatise on limnology, v. 2. Wiley. JANKE, N. C Effect of shape upon the scttling velocity of regular convex geometric particles. J. Sediment. Petrol. 36: KOMAR, P. D Settling velocities of circlllar cylinders at low Reynolds numbers. J, Geol. 88: AND C. E. REIMERS GIxin shape cffccts on settling rates. J. Geol. 86: M(:CAVE, I. N Vertical flux of pnrticles in the ocean. Deep-Sea Res. 22: OSTERBERG, C., A. G. CAREY, AND II. CUHL Accelerntion of sinking rates of radionlwlidcs in the ocean. Nature 200: SCIIRADER, II. J Fecal pcllcts: Role in sedimentation of pelagic diatoms. Science 174 : STIAPTHO, A. H Shape and flow. Anchor. SMALI,, L. F., AND S. W. FOWLEII Turnover :md vertical transport of zinc by the euphausiid Megnnyctiphanes norvegicn in the Ligurian Sea. Mar. Biol. 18: AND M. Y. UNLU Sinking rates of naturnl copepod fecal pellets. Mar. Riol. 51: SMAYDA, T. J Some mcasuremcnts of the

9 180 &mar et al. sinking rate of fecal pellets. Limnol. Oceanogr. 14: TURNER, J. T Sinking rates of focal pellets from the marine copepod Fontella mea&i. Mar. Biol. 40: WIEBE, P. H., S. II. BOYD, AND C. WINGET Particulate matter sinking to the deep-sea floor at 2000 m in the Tongue of the Ocean, Bahamas, with a description of a new sedimentation trap. J. Mar. Res. 34: Submitted: 14 March 1980 Accepted: 15 July 1980