HAL Id: hal-02880728
https://hal.archives-ouvertes.fr/hal-02880728
Submitted on 27 Jan 2021
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
changes recorded in deep-sea sediments: A
time-dependent modeling approach
S. Charbit, Christophe Rabouille, Giuseppe Siani
To cite this version:
S. Charbit, Christophe Rabouille, Giuseppe Siani. Effects of benthic transport processes on abrupt climatic changes recorded in deep-sea sediments: A time-dependent modeling approach. Journal of Geophysical Research, American Geophysical Union, 2002, 107 (C11), �10.1029/2000JC000575�. �hal-02880728�
Effects of benthic transport processes on abrupt climatic changes
recorded in deep-sea sediments:
A time-dependent modeling approach
S. Charbit, C. Rabouille, and G. Siani
Laboratoire des Sciences du Climat et de l’Environnement, UMR CNRS-CEA, Gif-sur-Yvette, France Received 27 July 2000; revised 24 July 2001; accepted 9 November 2001; published 14 November 2002.
[1] A one-dimensional time-dependent model is developed to characterize qualitatively and quantitatively the combined effects of bioturbation and burial on sedimentary signals related to abrupt climatic changes. This model is based on the widely used advection-diffusion equation and simulates rapid climatic transitions by representing the deposition flux at the sediment-water interface by a steep ramp function of time. This model is applied to both planktonic foraminifera abundance curves andd18O distributions. Output signals, obtained at the bottom of the bioturbated layer for these rapid transitions, have been generated for a broad range of sedimentation rates (5 –50 cm kyr1), biodiffusion coefficients (1031 cm2 yr1), and mixed layer thicknesses (2– 15 cm). Numerical results clearly demonstrate the importance of a dynamic description of sediment mixed layers. Properties of the
sedimentary response to fast transitions appear to be highly and nonlinearly dependent upon the sedimentation rate and the relative values of the original transition length and the time required to bury the signal below the mixed layer. Moreover, for low sedimentation rates
(10 cm kyr1) we show that signals occurring over a 50- to a 250-year timescale are
indistinguishable. To quantify the distortion of sedimentary signals, we determined the transition length of the bioturbated simulated signals and compare it to the initial transition length for given sets of bioturbation and sedimentation rates and mixed layer thicknesses. Comparison between model predictions and experimental results reveals a good agreement, showing that transition timescales are compatible with ice core-derived transitions (<100 years) for environments in which bioturbation can be approximated by a diffusive process. Tests performed ond18O distributions have illustrated the effect of bioturbation on the stratigraphic offsets between isotopic compositions of cold and warm species of
foraminifera during climatic transitions. INDEXTERMS: 3022 Marine Geology and Geophysics: Marine sediments—processes and transport; 4211 Oceanography: General: Benthic boundary layers; 4255 Oceanography: General: Numerical modeling; 4267 Oceanography: General: Paleoceanography; 4863 Oceanography: Biological and Chemical: Sedimentation; KEYWORDS: abrupt climatic changes, deep-sea sediments, bioturbation, process studies, numerical modeling
Citation: Charbit, S., C. Rabouille, and G. Siani, Effects of benthic transport processes on abrupt climatic changes recorded in deep-sea sediments: A time-dependent modeling approach, J. Geophys. Res., 107(C11), 3194, doi:10.1029/2000JC000575, 2002.
1. Introduction
[2] In the upper layers of marine sediments, recently
deposited particles are mixed by activities of benthic animals, such as crawling, burrowing, and feeding. This mixing process, known as bioturbation, enhances exchanges between new and older sediment layers and between sedi-ments, pore water, and overlying seawater. Such a process leads therefore to the modification of physical and geo-chemical properties of the sediment. For deep-sea sediments the region in which bioturbation is active, also called the mixed layer (or bioturbated layer), is restricted to the upper centimeters of the sediment [Nozaki et al., 1977; Berger and Killingley, 1982; Nittrouer et al., 1983/84; Trauth et al., 1997,
Boudreau, 1994; 1998] but may extend to several tens of centimeters in nearshore environments [Guinasso and Schink, 1975; Boudreau, 1998]. Sediment reworking also distorts the sediment record used for paleoenvironmental studies. First, stratigraphical signals may be strongly affected by particle redistribution, and as a consequence, ages of climatic events may be shifted toward older or younger values. This distortion is more pronounced for large mixing rates, large mixed layer thicknesses, and low sedimentation rates. Second, the partial or complete homogenization of the bioturbated layer alters the resolution of the sedimentary record by smoothing the input signal [McIntyre et al., 1967], eliminating high-frequency variations, and reducing the signal amplitude [Ruddiman and Glover, 1972]. As a consequence, short-term events are more heavily affected by bioturbation than long-term changes of the signal.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. C11, 3194, doi:10.1029/2000JC000575, 2002
Copyright 2002 by the American Geophysical Union. 0148-0227/02/2000JC000575
[3] Several types of models have addressed the issue of
sedimentary signal distortion. Process models are used to study the mechanisms of mixing and to predict their effects on the sedimentary record or to quantify bioturbation rates [Goldberg and Koide, 1962; Guinasso and Schink, 1975; Christensen, 1982; Lynch and Officer, 1984; DeMaster et al., 1985, 1991; Stordal et al., 1985; Christensen and Bhunia, 1986; Smith et al., 1986/87; Martin and Sayles, 1987; Kim and Burnett, 1988; Thomson et al., 1988; Smith et al., 1993; Soetaert et al., 1996]. They generally include sedimentation, bioturbation, and even physical (decay of radionuclides) or chemical (production or consumption) reactions: the purpose is to find a mathematical formulation governing the evolution of the system with given initial and boundary conditions and to deduce the relationships between input functions and the resulting output signals (bioturbated signal). An alternative approach involves the development of inverse models [Schiffelbein, 1984, 1985; Bard et al., 1987a; Trauth, 1998], which provide as an output the nonbioturbated signal. Although this approach seems to be well suited to paleoclimatic studies, complete signal restoration is strongly dependent upon the signal-to-noise ratio [Schiffelbein, 1984] or upon the steepness of the deconvolved curve [Bard et al., 1987a]. Furthermore, Bard et al. [1987a] have treated bioturbation as an instantaneous mixing, which restricts the use of their model to environ-ments where bioturbation dominates transport processes.
[4] Process models have often been developed in the
steady state mode [Goldberg and Koide, 1962; Christensen, 1982; Kim and Burnett, 1988; Soetaert et al., 1996]. However, some attempts have been made to introduce a time-dependent treatment of the signal using an impulse source of tracer (e.g., microtektites [Guinasso and Schink, 1975; Lynch and Officer, 1984], 137Cs [Christensen and
Bhunia, 1986],239, 240Pu [Smith et al., 1986/87]) deposited at the sediment-water interface, which simulates an instan-taneous geological event. Such an impulse differs from paleoclimatic signals or, more specifically, from paleocli-matic transitions from one state to another.
[5] The growing interest in the study of high-frequency
oscillations or transitions between cold and warm climatic periods requires appropriate process models to estimate the bioturbation effects on the sedimentary record. According to ice core data [Dansgaard et al., 1989; Johnsen et al., 1992; Alley et al., 1993; Taylor et al., 1993], such paleosignals last from tens to hundreds of years, which is generally less than the time required for sedimentation to bury signals below the bioturbated layer. Consequently, a dynamic description of the sediment mixed layer is clearly needed to predict and to understand the time variations of tracer concentration related to abrupt climatic or productivity changes.
[6] Therefore we have developed a one-dimensional
time-dependent model that depicts the processes (i.e., sedimenta-tion and bioturbasedimenta-tion) that modify the environmental signal contained in solid particles (i.e., foraminifera). The input flux is represented by a time-dependent function that simu-lates a rapid transition. The aim of the present study is to provide new insights about the sedimentary processes (bio-turbation and sedimentation) that lead to the distortion of the sedimentary record in the sediment mixed layer. The dis-tortion of the signal is quantitatively characterized using the parameters that control the dynamics of the mixing
mecha-nisms (mixing, sedimentation rates, and mixed layer thick-ness). The results presented in this paper indicate to what extent the transport processes will affect the preservation of rapid climatic transitions recorded in faunal signals ord18O variations. The numerical outputs are then compared to field data to show the consistency check of the model.
2. Model Description
[7] The model presented here depicts the transport
processes (sedimentation and bioturbation) in surface sedi-ment layers and describes the evolution with depth and time of a solid conservative tracer. For our purpose it has been applied to both planktonic foraminifera species and their isotopic composition. It is thus forced either by an incoming time-dependent flux of foraminifera deposited at the sediment-water interface or by the incoming isotopic composition of oxygen carried by these calcareous shells, with an initial prescribed d18O distribution. Assuming that horizontal variability is negligible, this model provides the vertical concentration profiles of foraminifera through time or their d18O content. Our simulations have been applied to the bioturbated layer only because it is the location where the signal is distorted. Several basic assumptions concerning the nature of transport processes have been used in this study: the number of parameters is reduced to minimize the complexity in the description of the system. Although there are some different forms of mixing (i.e., local and nonlocal) that have different effects on the sedimentary signals, nonlocal exchanges have been found decreasing with increasing water depth [Soetaert et al., 1996]. Therefore, in many deep-sea environments, particle mixing can be considered as a small-scale random walk process [Boudreau, 1986], which can be approximated by Fickian diffusion; mixing intensity is thus described by a (bio)diffusion coefficient Db.
[8] Although Db is likely to decrease with sediment
depth, it is assumed constant within the mixed layer and zero below. This hypothesis is justified by Boudreau [1986], who studied the influence of spatially dependent biodiffu-sion coefficients on steady state and non-steady state tracer profiles and reached the conclusion that the choice of constant diffusivity was fully reasonable for most practical cases. Second, the sedimentation rate and the mixed layer thickness remained constant throughout the simulations. The porosity gradient in the upper sediment layers has also been ignored, implying that effects of compaction in the bioturbated layer can be neglected and that the sedimenta-tion rate is constant with depth. Finally, in the absence of appropriate constraints, biodiffusion coefficient and poros-ity were considered as time-invariant. The free parameters describing the sedimentary system are thus the sedimenta-tion rate, the mixed layer thickness, and the mixing rate. 2.1. Modeling Foraminifera Abundances
[9] Taking into account the assumptions mentioned
above, the evolution of a solid conservative tracer in the mixed layer is described by the conservation equation, derived from Berner [1980]:
@Cðx; tÞ @t ¼ Db @2Cðx; tÞ @x2 w @Cðx; tÞ @x ; 0 x L; ð1Þ
where C(x, t) is the concentration of foraminifera (cm3of solid sediment); t is the time (years) spent in the sediment, i.e., the time elapsed since the beginning of the deposition of falling particles at the sediment-water interface; x is the depth relative to the sediment-water interface and increasing downward (cm); Db is the biodiffusion coefficient (cm2
yr1); w is the sedimentation rate (cm yr1); and L is the thickness of the mixed layer (cm).
[10] At the sediment-water interface (x = 0) the boundary
condition is expressed in terms of continuity of flux: the incoming tracer flux F(t), per unit of area of bulk sediment and per year, is incorporated into the sediment by bioturba-tion and burial and is therefore equal to the sum of diffusive and advective fluxes:
8t F tð Þ ¼ Dbð1 jÞ
@C x; tð Þ
@x þ w 1 jð ÞC x; tð Þ; x¼ 0; ð2Þ
wherej is the porosity, (1 j) is the solid fraction volume (dimensionless) and F(t) is the incoming flux of foramini-fera deposited at the sediment-water interface (number of shells cm2 yr1). Conversely, below the mixed layer, diffusive processes are assumed to be negligible, and the evolution of the tracer concentration is only governed by burial; the flux through the bottom of the mixing zone (x = L) is thus reduced to the advective term. The continuity of fluxes as well as the continuity of concentrations through the interface implies a null gradient between the mixed and historical layers: 8t Dbð1 jÞ @C x; tð Þ @x x¼L þ w 1 jð ÞC x; tð Þx¼L ¼ w 1 jð ÞC x; tð Þx¼Lþ)@C x; tð Þ @x x¼L¼ 0; x¼ L: ð3Þ
The time required to bury the signal below the mixed layer is defined as the ratio of the mixed layerw (i.e., L/w).
[11] The initial condition corresponds to a steady state
concentration profile through the mixed layer. Taking into account boundary condition (3), resolution of equation (1) implies at t = 0 that the tracer concentration is constant throughout the bioturbated layer and thus that the spatial derivative of C(x, t) is zero. Substituting this condition in equation (2) then yields the initial condition:
C x; tð ¼ 0Þ ¼ F 0ð Þ
w 1ð jÞ: ð4Þ
2.2. Isotopic Oxygen Signal
[12] Incoming time-variable fluxes are forcing functions
for both abundance curves of foraminifera andd18O signals. The foraminifera signal is treated as an inert solid tracer, showing no interaction with the liquid phase (dissolution and reprecipitation). As pointed out by Bard et al. [1987a], the bioturbatedd18O signal is more complex since it results from the convolution of a two-component signal: one is relative to the isotopic variations of oxygen due to climatic changes; the other arises from the variations of foraminifera,
or the stratigraphic carrier, which is also affected by bioturbation. The relation between oxygen and its solid carrier can be illustrated by
Foxyð Þ ¼ F tt ð ÞN ; ð5Þ
where Foxy(t) is the incoming oxygen flux carried by
foraminifera (mol oxygen cm2 yr1) and N is the number of oxygen moles in a 100mg foraminifera shell.
[13] The initiald18O distribution is known, and we use the
fluxes of16O and18O (in mol cm2yr1), F16(t) and F18(t),
respectively, which allows us to use mechanistic mixing. The F16(t) and F18(t) quantities are related to Foxy(t) via the
isotopic ratio IR(t) = F18(t)/F16(t):
F16ð Þ ¼t Foxyð Þt 1þIR tð Þ; F18ð Þ ¼t Foxyð ÞIR tt ð Þ 1þIR tð Þ ; ð6Þ IR tð Þ ¼ IRPDB 1þ d18O tð Þ 103 ; ð7Þ
where F16(t) and F18(t) are the incoming 16O and 18O
fluxes (mol cm2 yr1), IR(t) is the isotopic ratio (IR(t) = F16(t)/F18(t)), IRPDB represents the isotopic ratio of the
standard of reference (IRPDB = 2067.2 106 [Valley et
al., 1986]), and d18O(t) is the time variation of the d18O distribution in the deposited foraminifera.
[14] Oxygen isotope concentrations C16(x, t) and C18(x, t)
are separately affected by bioturbation and sedimentation and satisfy equation (1). The knowledge of F16(t) and F18(t)
by means of equations (4), (5), and (6) allows us to derive the same initial and boundary conditions as equations (2) and (3), with C(x, t) replaced by C16(x, t) or C18(x, t).
2.3. Model Outputs and Mass Balance
[15] The conservation equation (equation (1)) was solved
using the Crank-Nicholson method [Carnahan et al., 1969] based on a centered finite difference scheme on a 0.1 cm spatial grid size with a time step of 1.0 year. Numerical resolution of equation (1) provides non-steady state con-centration profiles. In order to compare input and output signals relative to the variations of foraminifera abundances, the flux Fout(t) passing through the bottom of the mixed
layer (x = L) is calculated. According to the boundary condition equation (3) a relationship exists between Fout(t)
and C(L, t) and is given by
Foutð Þ ¼ w 1 jt ð ÞC L; tð Þ: ð8Þ
This relation is also valid for oxygen isotopes with C(L, t) replaced by C16(L, t) and C18(L, t), and so, the output
isotopic ratio is
IRoutð Þ ¼t
C18ðL; tÞ
C16ðL; tÞ
: ð9Þ
The resulting d18O signal is then obtained by inverting equation (6): d18outð Þ ¼t IRoutð Þt IRPDB 1 103: ð10Þ
The validity of the solution is checked by calculating the mass balance for the whole sedimentary system for foraminifera as well as oxygen isotopes. Considering that any variation of tracer inventory in the mixed layer (i.e., accumulation) must be equal to input minus output fluxes, the quantity controlling mass balance is
Total Accumulation entry burialð Þ
½ = entry burialð Þ:
For tests performed in this study (see below) the mass balance deviation was smaller than 1% over the entire 12,000 year run.
3. Input Functions and Parameters
3.1. Foraminifera Abundances
[16] The incoming flux of solid materials deposited at the
sediment-water interface is represented by a function F(t) (number of foraminifera per cm2of bulk sediment per year). In order to simulate rapid climatic transitions between cold and warmer conditions, F(t) is represented by a linear steep ramp function of time and is equal to a constant before and after the transition:
F tð Þ ¼ F0; t¼ 0
F tð Þ ¼ F1; t > t ð11Þ
F tð Þ ¼ðF0 F1Þ
t tþ F0; 0 < t t
F0 and F1 are the arbitrary initial and final values of the
flux, and t is the transition duration.
[17] In our simulations the porosity is assumed to be
equal to 0.85. The initial and final values of the incoming flux of foraminifera are specified in the model (4.1 and 10.4 shells cm2yr1). For the range of sedimentation rates (5 – 50 cm kyr1) considered in this study (see below) these adopted values represent a few hundreds to a few thousands of foraminifera shells per gram, numbers commonly observed in many deep-sea sediments: for example, cores CH73-139C [Bard et al., 1987b], SU90-08 [Grousset et al., 1993], NA87-22 (H. Leclaire, unpublished data, 1995), and V27-20 and V28-14 [Ruddiman and McIntyre, 1981]. In the case studied herein (Figure 1) F(t) increases with time, and thus, for transitions between cold and warm periods it simulates approximately the abundance curve of warm species of foraminifera.
[18] To characterize and to quantify the alteration of
signals, several sets of experiments have been performed with t = 50, 100, 250, 500, and 1000 years. In the first series of tests, bioturbated signals have been generated for a range of Dbvalues (0.001, 0.005, 0.01, 0.05, 0.10, 0.50, and
1.0 cm2yr1). This is the usual range found in the literature
for deep-sea sediments [DeMaster and Cochran, 1982; Li et al., 1985; Stordal et al., 1985; Cochran, 1985; Thomson et al., 1988; Legeleux et al., 1994; Boudreau, 1994; Middel-burg et al., 1997]. These runs have been repeated for fixed values of the sedimentation rate:w = 5, 10, 20, and 50 cm kyr1. In these simulations the thickness of the mixed layer has been fixed to 8 cm, a value compatible with the worldwide mean of 9.8 ± 4.5 cm given by Boudreau [1994] and also observed in cores French-American Mid-Ocean Undersea Study (FAMOUS) 527-3 [Nozaki et al., 1977], V19-188 [Peng et al., 1977], and ERDC 92 [Peng et al., 1979]. Second, the influence of the sedimentation rate has been studied separately: cross tests have been conducted withw ranging from 5 to 60 cm kyr1for the same values of t and with Db and L fixed to 0.1 cm2 yr1 and 8 cm,
respectively. Finally, similar runs have been performed to examine the effect of the mixed layer thickness for some values of the sedimentation rate (w = 5 and 20 cm kyr1) and mixing rate (Db= 0.005, 0.05, and 0.5 cm2yr1) and
with L ranging from 2 to 15 cm, which represent the extremes of the sediment thickness undergoing bioturbation for most of the environments [Jumars and Wheatcroft, 1989; Boudreau, 1994].
3.2. Isotopic Signal
[19] Isotopic signal variation (d18O) was similarly
simu-lated by a sharply decreasing function of time:
d18O tð Þ ¼ d18 initO; t¼ 0; d18O tð Þ ¼ d18finalO; t > t; ð12Þ d18O tð Þ ¼ d 18 initO d18finalO t tþ d 18 initO; 0 < t t:
As before, initial and final values ofd18O have been taken arbitrarily and are assumed to be constant before and after the transition, equal to 4.2 and 0.8, respectively. These values are compatible withd18O values observed during the Last Glacial Maximum and the Holocene in North Atlantic cores V23-81 (E. Cortijo, unpublished data, 1995 and NA87-22 [Duplessy et al., 1992].
[20] Since thed18O signal is coupled to the solid carrier,
both warm and cold species of foraminifera have been considered in order to examine whether the nature of the carrier influences the observed d18O signal in sediments. This coupling between the oxygen signal and the abundance curve of solid carrier is expressed through equation (5). In the case of warm species (subpolar) the original (i.e., unmixed) abundance curve is represented by an increasing function F(t). For polar species a decreasing flux function was adopted. The first series of tests performed for fora-minifera (t = 50 – 1000 years, Db= 103cm2yr1, and L
= 8 cm for w = 5, 10, 20, and 50 cm kyr1) has been
Figure 1. (opposite) Examples of numerical signals resulting from an initial transition of 500 years (tr,in= 400 years),
represented as a function of sediment depth. Signals have been simulated for (a) different Dbvalues (with fixed values of
the sedimentation rate w and the mixed layer thickness), (b) different L values (with fixed values of w and Db), and (c)
differentw values (with fixed values of Dband L). These plots depict the foraminifera fluxes (number of tests per cm2of
bulk sediment and per year) obtained at the bottom of the mixed layer after advection and bioturbation. Below the mixed layer the fluxes are only governed by burial. To illustrate the effects of these transport processes on the sedimentary record, the unmixed signal has been also superimposed.
reproduced for the isotopic signal for both polar and subpolar carriers and analyzed in terms of stratigraphic offset between the polar and subpolard18O records.
4. Results and Discussion
4.1. Characterization of the Distortion
[21] Examples of simulated bioturbated signals recording
the abundance variation of foraminifera over a 500-year period are depicted as a function of time in Figure 1 for different values of the mixing rate Db (103 1.0 cm2
yr1), the mixed layer thickness L (4 – 12 cm), and the sedimentation rate w (10 – 50 cm kyr1). The undisturbed signal that would be recorded at the bottom of the mixed layer in the absence of mixing is also represented.
[22] As expected, increased bioturbation rate or mixed
layer thickness produces longer transitions in the sedimen-tary record (Figures 1a and 1b). Conversely, a better preservation of the signal is obtained for increasing sed-imentation rate (Figure 1c). For oscillatory signals (not shown) the same conclusions can be reached, and the amplitude is considerably reduced compared to the unmixed signal. Moreover, for this kind of signal the front-like structure is shifted downward, and a long tail is observed before the onset of the perturbation. For the case studied herein, highly distorted signals are characterized by long tails on both sides of the recorded transition. The compar-ison between the initial and the recorded signal has been made using the transition length redefined between 10 and 90% of the total amplitude of the signal. For convenience this new parameter will be noted tr,in(for input signals)
and tr,out (for output signals); for input signals having a
real duration of 50, 100, 250, 500, and 1000 years tr,inis
equal to 40, 80, 200, 400, and 800 years, respectively. 4.2. Sensitivity Experiments
4.2.1. Combined Effect of the Mixing and Sedimentation Rates
[23] Numerical simulations of bioturbated signals (with
tr,in values between 40 and 800 years) were run for a
broad range of mixing intensities (from 103 to 1.0 cm2 yr1) and for several values of the sedimentation rate (w = 5, 10, 20, and 50 cm kyr1) with a mixed layer thickness fixed to 8 cm. The output values tr,out are plotted on a
semi-logarithmic scale as a function of the biodiffusion coeffi-cient Dbfor foraminifera fluxes (Figure 2).
[24] Examination of these diagrams reveals, first,
extremely elevated values of the tr,outparameter for short
input transitions length (40 – 200 years) with sedimentation rates lower than 10 cm kyr1. As an example, for a sedimentation rate of 5 cm kyr1 and a mixing intensity of 1.0 cm2yr1a 40 year input signal will have an apparent duration (tr,outvalue) of 3700 years. Similarly, for a larger
sedimentation rate (10 cm kyr1) and a mixing rate of 0.1 cm2 yr1, an 80-year input signal will be recorded with a duration of about 1600 years. This indicates that in these conditions, mixing remains sufficiently high to impede quantitatively the preservation of rapid episodes. For smaller mixing rates (Db= 102cm2yr1), output transition
lengths are still much larger than the original transition duration: for the 80-year transition and a similar sedimenta-tion rate (10 cm kyr1) the output transition length is around
900 years. Second, for larger sedimentation rates (w = 20 cm kyr1) and mixing rates ranging from 0.01 to 0.1 cm2yr1 an 80-year input signal will have an apparent duration between 350 and 700 years. As expected, the difference between the tr,out and the tr,in values is reduced when
sedimentation rates increase, indicating a better signal preservation.
[25] More interesting is the relationship between the
preservation and the duration of input signals. For low sedimentation rate (5 cm kyr1) all transitions are recorded with the same duration, which is generally much larger than the initial transition. When sedimentation rate increases, some transition durations can be distinguished from the others (800 years for w = 10 cm kyr1 and 400 and 800 years for w = 20 cm kyr1). Moreover, the distinction between recorded transitions is rather independent of the bioturbation rate. Actually, these plots reveal that for most frequently observed bioturbation rates (0.01 – 0.1 cm2yr1) the distinction between those transitions is strongly linked to the transit time in the mixed layer (i.e., L/w): the transitions having an initial duration larger than the transit time can be differentiated. This is illustrated in Figure 3, where the tr,outparameter corresponding to the bioturbated
foraminifera abundances, has been plotted as a function of the sedimentation rate w, ranging from 5 to 60 cm kyr1, with L fixed to 8 cm and Db = 0.1 cm2 yr1, a value
classically found in deep-sea sediments. Subsequently, the transit times corresponding to these numerical data range from 130 to 1600 years. This plot allows a rough identification of a critical sedimentation rate value and thus of a critical value of the transit time, from which the transitions can be differentiated. An 800 year input signal may be identified if the transit time does not exceed 800 years (sedimentation rates larger than 10 cm kyr1for L = 8 cm), while 400- and 200-year transitions will be distin-guished ifw values are roughly greater than 20 and 40 cm kyr1, respectively. Shorter signals (40 and 80 years) cannot be distinguished, even for sedimentation rates as large as 60 cm kyr1. At the same time, results obtained forw = 50 cm kyr1 (Figure 2) show that curves corresponding to these
short transitions remain very poorly separated for the same Db value (0.1 cm2 yr1). Other simulations (not shown),
performed with different values of the mixed layer thickness (6 and 10 cm) and the bioturbation rate (0.005, 0.05, and 0.5 cm2yr1) lead to the same conclusions: correct identifica-tion of shorter signals is not significantly improved with lower Dbvalues but appears to be strongly dependent upon
the relative values of the transit time and the initial transition length.
4.2.2. Effect of the Mixed Layer Thickness
[26] To investigate the influence of the mixed layer
thickness on the alteration of sedimentary signals, addi-tional tests, relative to foraminifera signals, were carried out with L ranging from 2 to 15 cm and with several values of the sedimentation rate (w = 5 and 20 cm kyr1) and the biodiffusion coefficient (Db= 0.005, 0.05, and 0.5
cm2 yr1). The output transition length is plotted as a function of L (Figure 4). As expected, for a given sedimentation rate value the distortion of the signal increases with L (already observed in Figure 1) and thus with the transit time. Moreover, the slope of the tr,out
rate Db. This underlines the constant influence of
biotur-bation in the competition between mixing and sedimenta-tion processes. For large sedimentasedimenta-tion rates (20 cm kyr1), and thus low values of the transit time, this slope is lower. Therefore the effect of mixing produced by an increasing mixed layer thickness is weaker when the w value is high: the signal is then less altered (Figures 4d – 4f ). As an example, for w = 20 cm kyr1 and Db= 0.005
cm2 yr1 (Figure 4d), tr,out is almost independent of the
mixed layer thickness, which means that the signal is almost totally preserved. Moreover, as already observed in Figures 2 and 3, the link between the distinction of rapid signals and the relative values of the transit time and the initial transition length is confirmed by these plots. Recorded signals are less distinguishable as L increases. However, this effect is less pronounced for large sedimen-tation rates. As an example, forw = 5 cm kyr1a 200-year
input signal cannot be differentiated from the others, Figure 2. Output transition lengths (in years) redefined between 10 and 90% of the total amplitude of
the signal and resulting from input signals occurring over timescales ranging from 40 to 800 years. Results are plotted on a semilogarithmic scale as a function of Db(in cm2yr1) and refer to foraminifera
fluxes. These plots have been set up for a fixed value of the mixed layer thickness (L = 8 cm) and for (a)w = 5 cm kyr1, (b)w = 10 cm kyr1, (c)w = 20 cm kyr1, and (d)w = 50 cm kyr1. Values of the transit time (= L/w) through the mixed layer (tr) are also indicated in each plot.
whereas forw = 20 cm kyr1it will be differentiated for L lower than 4 cm (i.e., a transit time equal to 200 years). 4.3. Processes Governing the Alteration
of the Sedimentary Record
[27] Our sensitivity experiments indicate to what extent
the buried signals are altered for different values of Db,w,
and L and for different initial transition lengths. In particular, the evolution of signals as a function of Db
and L (Figures 2 and 4) has been shown to be strongly dependent upon the sedimentation rate w. This clearly demonstrates the multiple dependence of the preservation of the sedimentary record upon various parameters.
[28] Moreover, we have previously proposed (Figures 2
and 4) that the distinction of rapid signals was linked to the ratio of the transit time to the initial transition duration. This can also be illustrated by observing the shape of foraminifera concentration profiles throughout time. Figures 5 and 6 dis-play the evolution of the foraminifera concentration within the mixed layer resulting from burial (10 cm kyr1) and low mixing intensity (103 cm2 yr1) for two different input signals (80 and 800 years) at different steps of the transition (10, 50, and 100% of the total transition duration and 400 years after the beginning of the transition). When the tracer is deposited at the sediment-water interface during short time intervals compared to the transit time, the spatial extension of the initial distribution is reduced to a thin layer of sediment (e.g., 1 cm for a transition of 100 years and a sedimentation rate of 10 cm kyr1). As bioturbation is efficient over short distances, the signal is not advected through the mixed layer before being mixed, implying that short transitions are poorly preserved. Conversely, for a longer transition (or a lower transit time) a part of the signal will be buried below the mixed
layer before the end of the transition, and before significant mixing take place, even for high mixing rates. Therefore longer transitions will be better preserved in the sedimentary record. After the end of the transition the system should return to a steady state characterized by a flat concentration profile (no gradient) through the mixed layer. The corre-sponding concentration value is given by inverting equation ((8)) (in our case, C(L, t) = Fout(t)/[w(1 j)] = 10.4/(0.01
0.15) 6930 cm3). Figures 5d and 6d indicate that concentrations at the bottom of the mixed layer are lower, implying that the steady state will be reached on a longer timescale.
[29] Thus, to the first order the signal alteration due to
sedimentary processes (mixing and sedimentation rates in a given mixed layer thickness) is related to the competition between the transit time in the mixed layer and the original transition duration. To provide further insights into these interactions, we plotted the output transition length as a function of both the sedimentation rate and the mixed layer thickness (Figure 7) for different Dbvalues at fixed values of
the transit time. It first appears that bioturbation exerts a strong control on the duration of the recorded transition. Second, the tr,outcurves display negative slopes (Figure 7),
indicating that the effect of an increasing sedimentation rate slightly dominates the transit time effect. This emphasizes the interaction of processes demonstrated in Figures 5 and 6 where thin deposition thickness (equal to the sedimentation rate times the original transition duration) promotes mixing of the signal and produces large tr,outvalues. Therefore an
increasing sedimentation ratew with a constant transit time leads to a better preservation. In conclusion, the preservation of signals is strongly controlled by the bioturbation and the transit time. However, the sedimentation rate remains a Figure 3. Output transition lengths (in years) of the foraminifera signal represented as a function of the
sedimentation ratew (in cm kyr1) for Db= 0.10 cm2yr1and L = 8 cm and resulting from different
master variable that modulates the effect of all the other parameters.
4.4. Application to the Younger Dryas – Holocene Transition
[30] Simulated bioturbated signals were compared to
experimental data observed in faunal records of two high sedimentation rate cores: SU81-18 (polar species:
Neoglo-boquadrina pachyderma sin.) and MD90-917 (subpolar species: N. pachyderma dex.), recovered near the coast of South Portugal (37460N, 10110W, 3135 m water depth) and in the deep southern Adriatic Sea (41170N, 17370E, 1010 m water depth), respectively. The N. pachyderma abundance curves are displayed in Figures 8a and 9a. The comparison between faunal abundance and sea surface temperature records as well as detailed radiocarbon chro-Figure 4. Output transition lengths (in years) resulting from input signals occurring over timescales
ranging from 40 to 800 years. Results are plotted as a function of the mixed layer thickness L (in centimeters) and refer to foraminifera fluxes. These plots have been set up for different values of the mixing rate (Db= 0.005, 0.05, and 0.5 cm2yr1) and different values of the sedimentation rate (w = 5 and
20 cm kyr1).
nologies (see Bard et al. [1987b, 1989] and Duplessy et al. [1992] for SU81-18, and Siani et al. [2002] for MD90-917) allowed us to identify the sharp increase occurring between core depths 160 and 170 cm in SU81-18 and between 275 and 285 cm in MD90-917 as the Younger Dryas – Holocene transition. The main characteristics of these transitions have been summarized in Table 1: sedimentation rate values
derived from the relation depth-radiocarbon ages (for the core section containing the transition), depth extension of the transition, duration of the observed transition, and the corresponding truncated value. According to ice core data [Alley et al., 1993; Taylor et al., 1993] the transitions between cold and warm intervals occurring during the last deglaciation lasted a few tens of years. In order to check the Figure 5. Concentration profiles at different time steps of the transition (10, 50, and 100% of the total
transition duration and 400 years after the beginning of the transition) resulting from the deposition of an increasing flux of foraminifera over a 100-year (tr,in= 80 years) period after bioturbation (Db= 103
model predictions concerning the apparent duration of a bioturbated signal we performed simulations with an input signal having a 40-year tr,invalue, using the sedimentation
rate as reported in Table 1. The purpose is to examine whether the output transition length of simulated signals is consistent with the one measured in the sediment. In our simulations the initial and final states of the forcing flux functions (i.e., the foraminifera fluxes) correspond to the average of several foraminifera concentrations, specified for each core in Table 1.
[31] For SU81-18 we had no specific knowledge of the
intensity and depth extension of mixing processes, and hence both the biodiffusion coefficient and the mixed layer thickness are considered as free parameters. We thus per-formed iterative simulations with different Dband L values
until the best agreement between the calculated tr,out
parameter and the truncated transition length observed in the sediment (tr,obs) was obtained. Numerical results
providing tr,outvalues, consistent with experimental data,
are reported in Table 1; the combinations of L and Db
Figure 6. Same as Figure 5 but for a signal having an initial duration of 1000 years (tr,in= 800 years).
parameters that yield the most compatible results with experimental data are indicated. As an example, for L = 8 cm we plotted on the same graph (see Figure 8b) the foraminifera flux computed from experimental data (squares) and the simulated signal (solid line) obtained for Db= 0.025 cm2yr1. Figure 8b illustrates the good
agree-ment between the observed sediagree-mentary record and the numerical signal.
[32] The advantage of core MD90-917 is that several
marine ash layers have been identified [Siani et al., 2002] by the abundance of glass shards found from sampling the core every 5 cm (Figure 9b). In each abundance peak, glass shards were picked and chemically analyzed to identify the origin of the eruption by a comparison with the major elemental contents of individual glass shards of marine and land deposits [Paterne et al., 1986]. Since marine ash Figure 7. Output transition lengths (in years) resulting from an initial transition of 250 years (tr,in=
200 years) and represented as a function of both the sedimentation ratew (in cm kyr1) and the mixed layer thickness (in cm) for different values of the transit time (i.e., time required to bury the signal below the mixed layer): (a) 200, (b) 400, and (c) 800 years.
layers can be considered as markers of instantaneous geo-logic events, the estimation of their dispersal in the sediment provides an appropriate tool to estimate the intensity of mixing processes [Guinasso and Schink, 1975; Ruddiman and Glover, 1972; Glass, 1969]. Assuming that the spread-ing of an impulse source follows a Gaussian distribution [Guinasso and Schink, 1975], the biodiffusion coefficient can be calculated by the relation [Crank, 1975]:
Db¼
s2
2t) DbL¼ s2
2w; ð13Þ
wheres is the standard deviation of the distribution and t is the time during which the signal has been mixed (i.e., L/w for our schematic representation of the system). Our working assumption is that the actual mixing intensity is that of the nearest glass shard abundance peak, recording a single eruptive event. For the Younger Dryas – Holocene
transition it is located between levels 295 and 330 cm and centered at 304 cm. The estimation of its dispersal yields a subsequent DbL value equal to 0.24 ± 0.03. By constraining
in this way the L and Dbvalues in our numerical simulations
we obtained tr,out values very close to the observed
transition length (see Table 1 and Figure 9c for a visual illustration with L = 8 cm).
[33] The numerous sensitivity tests performed in the
present study have demonstrated that transitions having an initial duration shorter than 200 years cannot be differ-entiated for a sedimentation rate of 40 cm kyr1(Figure 3). However, these results show that the predicted distortion of very rapid sedimentary signals (i.e., a few tens of years) is consistent with the signals recorded in the sediment. The best agreement between experimental data and model sim-ulation has been obtained for realistic values of L and Dbfor
both SU81-18 and MD90-917 cores. Therefore the main conclusion drawn from this model-data comparison is that our model is able to reproduce the extent of bioturbation effects on rapid sedimentary signals. However, in the absence of any constraint on Db and L values the model
cannot provide a unique solution of the initial transition length (see SU81-18 core). In contrast, results relative to core MD90-917 show that the number of reasonable sol-utions is considerably reduced with the use of a relation between Dband L deduced, for example, from the measured
abundance of glass shard peaks. In some cases, empirical relationships between parameters governing the sedimen-tary system could also be used to provide additional con-strains [Boudreau, 1994, 1998; Middelburg et al., 1997]. In that case the initial transition lengths could be predicted more accurately, and our model could also be used to assist in the interpretation of experimental data.
4.5. Interpretations ofD18O Modeling Results
[34] The sensitivity experiments carried out for
foramin-ifera signals allowed us to derive the master parameters responsible for the preservation (or the distortion) of sedi-mentary signals. To complete this study, we now examine the main features of the distortion ofd18O signals coupled
either to polar or subpolar species of foraminifera. For a glacial-interglacial transition the evolution of the original (i.e., unmixed) abundance curve of warm (cold) species is represented by an increasing (decreasing) function F(t), namely, by a decreasing (increasing) flux represented as a function of sediment depth (Figures 10a and 10b). As already mentioned in Section 3, the coupling between the solid carrier (i.e., foraminifera) and the isotopic signal is expressed through, equation (5). The resultingd18O distri-butions are displayed in Figure 10c. Figure 10c illustrates the existence of stratigraphic offsets between isotopic com-positions of warm and cold species, observed in Indian Ocean cores [Be´ and Duplessy, 1976; Duplessy, 1978] and confirmed later by modeling works of Hutson [1980], Schiffelbein [1985], Bard et al. [1987a], and Trauth [1998]. These results can be interpreted as follows. For a glacial-interglacial transition the cold species abundance decreases with time together with its isotopic signal. Since cold foraminifera species become less abundant in the sediment, a significant proportion of individuals of heavy isotopic composition is present at depth (Figure 10a) and will be mixed with a smaller quantity of foraminifera of Figure 8. (a) Abundance curve of N. pachyderma sin. of
core SU81-18. The arrow indicates the Younger Dryas – Holocene transition observed between 160 and 170 cm. (b) Comparison between the simulated signal (tr,in= 40 years)
represented for Db= 0.025 cm2 yr1 and L = 8 cm (solid
line) and the flux of foraminifera computed from experi-mental data (squares).
lighter isotopic composition deposited during and after the transition. In the buried signal the decrease of d18O and polar foraminifera will thus be delayed with respect to the time at which the climatic warming really occurred because of the large pool of cold foraminifera with high d18O. In contrast, for warm species (Figure 10b) a small number of individuals are initially present in the sediment, whereas a large number of foraminifera of low d18O are deposited during the transition. These foraminifera are transferred by bioturbation to depth. This implies that the measured iso-topic composition of warm species indicates a climatic warming before its actual occurrence. This different behav-ior with respect to mixing implies that for a
glacial-inter-glacial transition the isotopic signal carried by a polar species appears to be more distorted than a signal coupled to a warm species.
4.5.1. Stratigraphic Offsets Versus Mixing Rate [35] Stratigraphic offsets s between polar and subpolar
species, calculated at the midamplitude of the signal, are represented in a semilogarithmic scale as a function of Db
for different sedimentation rate values (w = 5, 10, 20, and 50 cm kyr1) and for a mixed layer thickness fixed to 8 cm (Figure 11). The s values first increase with decreasing sedimentation rates and low initial transition lengths and with an increasing mixing intensity. For conditions of high distortion (w = 5 cm kyr1, tr,in= 40 years, and Db= 1.0
Table 1. Main Characteristics of the Younger Dryas (YD) – Holocene Transition Observed in Cores SU81-18 and MD90-917: Core Section in Which the Transition is Observed, Mean Sedimentation Ratew Relative to This Core Section, Duration of the Observed Transitions tobsand Corresponding Truncated Transition Length tr,obs(in years), and Initial and Final Foraminifera Fluxes F0and F1
(Number of Foraminifera Per cm2and Per Year)a Core YD-Holocene Core Section w, cm kyr1 tobs, years tr,obs, years F0, cm2yr1 F1, cm2yr1 tr,in, years L, cm Db, cm2yr1 tyearsr,out, SU81-18 170 – 160 cm 35 286 229b 0.3006 0.0276 40 4 0.10 211 (190 – 170 cm) (160 cm) 0.20b 231b 0.30 239 5 0.05 213b 0.06b 224b 0.07b 233b 0.08 240 6 0.03 205 0.04b 225b 0.05 241 7 0.02 192 0.03b 224b 0.04 248 8 0.02 207 0.025b 226b 0.03 243 9 0.02 221 0.025 243 0.03 261 10 0.015 207 0.02 235 11 0.015 218 0.02 247 12 0.015b 228b 0.02 260 MD90-917 285 – 275 cm 41 244 195b 0.4524 0.0035 40 7 0.03 181 (295 – 285 cm) (275 – 260 cm) [0.25]b 0.035b 191b 8 0.03b 196b [0.24]b 9 0.025b 195b [0.23]b 0.03 209 11 0.02b 197b [0.22]b a
For the comparison between the simulated signal and experimental data, levels before and after the transition have been averaged (indicated in parentheses). For core SU81-18, simulations have been performed with a mixing depth between 4 and 12 cm. For core MD90-917 the L and Dbvalues are
constrained by the relation DbL = 0.24 ± 0.03. bThe most compatible output transition length t
r,outwith the observed sedimentary record as well as the corresponding Dbvalue (SU81-18) or DbL
value, given in brackets (MD90-917).
Figure 10. (opposite) (a) Simulated bioturbated signal (w = 10 cm kyr1, Db= 0.05 cm2yr1, and L = 8 cm) resulting
from an initial transition of 250 years (tr,in= 200 years). This plots displays the flux of a cold species of foraminifera
(dashed line) during a glacial-interglacial transition as a function of sediment depth (solid line). (b) Same as Figure 10a but for a warm species of foraminifera (dash-dotted line). (c) Example of numericald18O signal (tr,in= 200 years;w = 10 cm
kyr1, Db= 0.05 cm2yr1, and L = 8 cm) coupled to both polar (dashed line) and subpolar (dash-dotted line) foraminifera.
The originald18O distribution is also represented (solid line). This plots exhibits the stratigraphic offset occurring between isotopic signals coupled to different foraminifera species and resulting from mixing.
cm2 yr1) the stratigraphic offset between warm and cold species is close to 1500 years, but it is completely negligible (i.e., 1 year) for conditions of high potential preservation (w = 50 cm kyr1, tr,in= 800 years, and Db= 103cm2yr1).
4.5.2. Comparison With Experimental Data
[36] On the basis of the observations of Be´ and Duplessy
[1976] for core RC17-69 (3130S, 32360E), Hutson [1980] reported a stratigraphic offset of 8.3 cm between two planktonic foraminifera species recording the transition between stages 5 and 6. Assuming a mean sedimentation rate of 1.8 cm kyr1, this represents a discrepancy of about 4500 years. In the same way, Duplessy [1978] noted an
Figure 9. (a) Abundance curve of N. pachyderma dex. of core MD90-917. The arrow indicates the Younger Dryas – Holocene transition observed between 275 and 285 cm. (b) Glass shards distribution; the arrow indicates the nearest abundance glass shard peak we used to derive from its dispersal an estimation of the biodiffusion coefficient, i.e., Db= 0.03 cm2yr1. (c) Comparison between the simulated
signal (tr,in= 40 years) represented for Db= 0.03 cm2yr1
and L = 8 cm (solid line) and the flux of foraminifera computed from experimental data (squares).
offset of 6000 years in core RC9-150 (31170S, 114360E), corresponding to a deviation of about 12 cm (w = 2 cm kyr1). Assuming that climatic transitions occurred in a few tens of years [Alley et al., 1993], simulations were per-formed with tr,in= 40 years with Dbranging from 103to
1.0 cm2yr1and L ranging from 4 to 15 cm to check the compatibility between the predicted and the observed strati-graphic offset. Results of these simulations are reported in Table 2. For cores RC17-69 (w = 1.8 cm kyr1) and
RC9-150 (w = 2 cm kyr1) a good agreement between exper-imental data and model simulations was found for L = 9 and 10 cm for core RC17-69 and for 13 and 14 cm for RC9-150. These values are compatible with the present worldwide average of 9.8 ± 4.5 cm given by Boudreau [1994].
[37] To find the L and Db values compatible with the
observed stratigraphic offsets, Schiffelbein [1985] used an optimization routine to minimize an error function related to the stratigraphic offset between the isotopic signal of two Figure 11. Stratigraphic offsets (in years) occurring between isotopic signals derived from polar and
subpolar species of foraminifera and represented on a semilogarithmic scale as a function of the mixing rate Db (in cm
2
yr1) for a fixed value of the mixed layer thickness (L = 8 cm) and for different sedimentation rate values.
planktonic foraminifera species. In core ERDC-84P (1250N, 157150E), stratigraphic offsets are about 4 cm along the entire core section, which is equivalent to a deviation of 2500 years. Applying the optimization routine, Schiffelbein [1985] found an optimum for L = 4.6 to 5.0 cm and Db= 6.8 103to 7.2 103cm2yr1. Using these
values, our model reproduces offsets ranging from 2270 (L = 4.6 cm) to 2450 years (L = 5.0 cm) for tr,in= 40 years. A
better agreement with experimental data has been obtained for Dbbetween 0.015 and 0.02 cm2yr1(L = 4.6 cm) and
around 8 103cm2yr1 (L = 5.0 cm). However, in both cases these Db values are close to those arising from
Schiffelbein’s [1985] method.
[38] Results reported in Table 2 quantitatively illustrate
the high nonlinearity of the system behavior. As for the examples presented in section 4.4, we cannot provide a unique solution with the present approach because of the absence of appropriate constraints on mixed layer thickness and mixing rate values. However, our results outline the compatibility between model predictions and experimental data obtained for reasonable values of both the mixing depth and the biodiffusion coefficient. Therefore the model can be used to quantify the stratigraphic discrepancies between isotopic signals coupled to different planktonic foraminifera species.
5. Conclusions
[39] The dynamic description of the transport processes
occurring in the mixed layer and acting on conservative tracers allowed us to identify the master parameters respon-sible for the distortion of rapid sedimentary signals and to quantify such a distortion. The simulations performed in the
present study have illustrated the high nonlinearity of the sedimentary response to sedimentation and mixing pro-cesses. First, it has been shown that the distinction of rapid signals occurring over a 50 – 100 year timescale (i.e., tr,in=
40 – 80 years) depends upon the transit time through the mixed layer and the initial transition length. The sedimen-tary response is equivalent for all signals having an initial transition duration much less than the transit time. Second, although the bioturbation exerts a strong control on the duration of the recorded transition we have demonstrated that the preservation of the input signal is primarily driven by the sedimentation rate. These results are both linked to the deposition thickness, i.e., the spatial extension of the signal at the time of deposition (i.e.,w t, with t being the nontruncated transition duration). As bioturbation is efficient over short distances, a thin deposition thickness (i.e., a short initial transition length or a low sedimentation rate) promotes mixing and large recorded transitions. Con-sequently, short transitions are poorly preserved.
[40] The comparison between model predictions and
experimental data has revealed a good agreement for environments in which bioturbation can be approximated by a diffusive process and for reasonable values of the free parameters. This indicates that the model can be used to predict the bioturbation effects on sedimentary records and can provide estimates of the transition duration. To apply the model to field data, volumetric counting of individual foraminifera species are required together with estimates of Db and L values in the past. The product of the mixing
coefficient times the mixed layer thickness can be inferred from the redistribution of inert materials resulting from instantaneous depositions, such as microtektites or volcanic ash falls. Glass shard distributions can be analyzed for
Table 2. Comparison between Observed Stratigraphic Offsets s in Cores RC17-69, RC9-150, and ERDC-84P and Simulated Stratigraphic Offsets s Occurring Between Isotopic Signals of Two Different Planktonic Foraminifera Speciesa
Core Observed s [References] w, cm kyr1 tr,in years L, cm Db, cm2yr1 Simulated s,years RC17-69 8.3 cm (4500 years) [Be´ and Duplessy, 1976;
Hutson, 1980] 1.8 40 8 1.0 4185 9b 0.07 4495 0.08b 4500b 0.09 4530 10b 0.01 3990 0.02b 4490b 0.025 4580 RC9-150 12 cm (6000 years) [Duplessy, 1978] 2 40 12 1.0 5850 13b 0.45 5760 0.50b 5990b 0.55 6400 14b 0.04 5810 0.05b 6000b 0.06 6310 ERDC-84P 4 cm (2500 years) [Schiffelbein, 1985] 1.6 40 4.6 6.8 103 2270 7.2 103 2270 0.01 2400 0.015b 2480b 0.02 2530 6.8 103 2440 5.0 7.2 103 2450 8.1 103b 2490b 8.2 103 2510b a
Simulations have been performed for a 40-year input signal. Mean sedimentation ratesw are also indicated. In these simulations both the biodiffusion coefficient Dband the thickness L of the mixed layer have been considered as free parameters.
bThe most compatible results (i.e., simulated s values) between model predictions and experimental data as well as the corresponding D
bvalue or L
value.
particles with a size close to that of foraminifera. Thus the estimate of DbL is based upon the assumptions that mixing
is a diffusive process and that the ash falls are spread following a Gaussian distribution. If ash layers are observed along the entire core section, this method allows one to take into account time-dependent mixing.
[41] The simulations performed in this study for various
input signals and environmental conditions have demon-strated how mixing processes may lead to great inaccuracies in the interpretation of paleoclimatic records and in the stratigraphic correlation of deep-sea cores. The model-data comparison presented in this study illustrates how a rapid signal may be distorted and appear considerably longer than it actually is.
[42] Various authors have established a chronology based
on 14C measurements without accounting for bioturbation processes. For climatic events lasting a few tens of years and recorded in high sedimentation rate cores (>50 cm kyr1) this may not lead to dramatic misinterpretations. At the opposite the problem becomes crucial for rapid events, such as the Younger Dryas – Holocene transition, or other ones that punctuated the Last Deglaciation period. There-fore, in some cases, previously published chronologies may be biased. However, the purpose of the present study is not to discredit previous works but rather to draw paleoceanog-raphers’ attention to possible overinterpretation of their data, even in low mixing (0.005 cm2
yr1) or midsedi-mentation rate environments (20 – 50 cm kyr1). Moreover, we outlined the necessity of measuring sedimentary con-ditions (mixed layer thickness, mixing intensity, and sed-imentation rate). In that case the model can provide a useful tool to quantify the uncertainties associated to paleoceanog-raphy studies and can be used to assist in the interpretation of real data. Finally, although this study has focused on rapid signals, the model can also be applied to predict the particle redistribution resulting from an input flux specified as any arbitrary function of time.
[43] Acknowledgments. This work has been supported by the BEN-GAL program (contract MAS3 CT950018) and by the French Atomic Commission (CEA) and the Centre National de la Recherche Scientifique (CNRS). Kind encouragement by L. Labeyrie and M. Paterne was partic-ularly appreciated. We are also very grateful to J.-C. Duplessy and M. Gehlen for fruitful discussions and constructive comments on the manu-script. C. Smith helped us to improve the writing of this paper. E. Cortijo and H. Leclaire are also thanked for providing us unpublished data. This is an LSCE contribution number 0577.
References
Alley, R. B., et al., Abrupt increase in Greenland snow accumulation at the end of the Younger Dryas event, Nature, 362, 527 – 529, 1993. Bard, E., M. Arnold, J. Duprat, J. Moyes, and J.-C. Duplessy,
Reconstruc-tion of the last deglaciaReconstruc-tion: Deconvolved records ofd18O profiles,
mi-cropaleontological variations and accelerator mass spectrometric14C dating, Clim. Dyn., 1, 101 – 112, 1987a.
Bard, E., M. Arnold, P. Maurice, J. Duprat, J. Moyes, and J.-C. Duplessy, Retreat velocity of the North Atlantic polar front during the last deglacia-tion determined by14C accelerator mass spectrometry, Nature, 328, 791 – 794, 1987b.
Bard, E., R. Fairbanks, M. Arnold, P. Maurice, J. Duprat, J. Moyes, and J.-C. Duplessy, Sea-level estimates during the last deglaciation based on d18
O and accelerator mass spectrometry14C ages measured in Globiger-ina bulloides, Quat. Res., 31, 381 – 391, 1989.
Be´, A. W. H., and J.-C. Duplessy, Subtropical convergences fluctuations and Quaternary climates in the middle latitudes of the Indian Ocean, Science, 194, 419 – 422, 1976.
Berger, W. H., and J. S. Killingley, Box cores from the Equatorial Pacific:
14
C sedimentation rates and benthic mixing, Mar. Geol., 45, 93 – 125, 1982.
Berner, R. A., Early Diagenesis—A Theoretical Approach, Princeton Univ. Press, Princeton, N. J., 1980.
Boudreau, B. P., Mathematics of tracer mixing in sediments, I, Spatially dependent, diffusive mixing, Am. J. Sci., 286, 161 – 198, 1986. Boudreau, B. P., Is burial velocity a master parameter for bioturbation?,
Geochim. Cosmochim. Acta, 58, 1243 – 1249, 1994.
Boudreau, B. P., Mean mixed depth of sediments: The wherefore and the why, Limnol. Oceanogr., 43, 524 – 526, 1998.
Carnahan, B., H. A. Luther, and J. O. Wilkes, Applied Numerical Methods, John Wiley, New York, 1969.
Christensen, E. R., A model for radionuclides in sediments influenced by mixing and compaction, J. Geophys. Res., 87, 566 – 572, 1982. Christensen, E. R., and P. K. Bhunia, Modeling radiotracers in sediments:
Comparison with observations in Lakes Huron and Michigan, J. Geo-phys. Res., 91, 8559 – 8571, 1986.
Cochran, J. K., Particle mixing rates in sediments of the eastern equatorial Pacific: Evidence from210Pb,239,240Pu and137Cs distributions at Manop
site, Geochim. Cosmochim. Acta, 49, 1195 – 1210, 1985.
Crank, J., The Mathematics of Diffusion, Clarendon, Oxford, U.K., 1975. Dansgaard, W., J. W. C. White, and S. J. Johnsen, The abrupt termination of
the Younger Dryas climate event, Nature, 339, 532 – 534, 1989. DeMaster, D. J., and J. K. Cochran, Particle mixing rates in deep-sea
sedi-ments determined from excess210Pb and32Si profiles, Earth Planet. Sci.
Lett., 61, 257 – 271, 1982.
DeMaster, D. J., B. A. McKee, C. A. Nittrouer, D. C. Brewster, and P. E. Biscaye, Rates of sediment reworking et the HEBBLE site based on measurements of Th-234, Cs-137 and Pb-210, Mar. Geol., 66, 133 – 148, 1985.
DeMaster, D. J., D. C Brewster, B. A. McKee, and C. A. Nittrouer, Rates of particle scavenging, sediment reworking, and longitudinal ripple forma-tion ate the HEBBLE site based on measurements of234Th and210Pb, Mar. Geol, 99, 423 – 444, 1991.
Duplessy, J.-C., Isotopic studies, in Climatic Change, edited by J. Gribbin, Cambridge Univ. Press, New York, 1978.
Duplessy, J.-C., L. Labeyrie, M. Arnold, M. Paterne, J. Duprat, and T. C. E. van Weering, Changes in surface salinity of the North Atlantic during the last deglaciation, Nature, 358, 485 – 487, 1992.
Glass, B. P., Reworking of deep-sea sediments as indicated by the vertical dispersion of the Australasian and Ivory Coast microtektite horizons, Earth Planet. Sci. Lett., 6, 409 – 415, 1969.
Goldberg, E. D., and M. Koide, Geochronological studies of deep-sea sediments by the thorium-ionium method, Geochim. Cosmochim. Acta, 26, 417 – 450, 1962.
Grousset, F. E., L. Labeyrie, J. A. Sinko, M. Cremer, G. Bond, J. Duprat, E. Cortijo, and S. Huon, Patterns of ice-rafted detritus in the glacial North Atlantic, Paleoceanography, 8, 175 – 192, 1993.
Guinasso, N. L., and D. R. Schink, Quantitative estimates of biological mixing rates in abyssal sediments, J. Geophys. Res., 80, 3032 – 3043, 1975.
Hutson, W. H., Bioturbation of deep-sea sediments: Oxygen isotopes and stratigraphic uncertainty, Geology, 8, 127 – 130, 1980.
Johnsen, S. J., H. B. Clausen, W. Dansgaard, K. Fuhrer, N. Gundestrup, C. U. Hammer, P. Iversen, J. Jouzel, B. Stauffer, and J. P. Steffensen, Irregular glacial interstadials recorded in a new Greenland ice core, Nat-ure, 359, 311 – 313, 1992.
Jones, G. A., and L. D. Keigwin, Evidence from Fram Strait (78N) for early deglaciation, Nature, 336, 56 – 59, 1988.
Jumars, P. A., and R. A. Wheatcroft, Responses of benthos to changing food quality and quantity, with a focus on deposit feeding and bioturba-tion, in Productivity of the Ocean: Present and Past, edited by W. H. Berger, V. S. Smetacek, and G. Wefer, pp. 235 – 253, 1989.
Kim, K. H., and W. C. Burnett, Accumulation and biological mixing of Peru margin sediments, Mar. Geol., 80, 181 – 184, 1988.
Legeleux, F., J.-L. Reyss, and S. Schmidt, Particle mixing rates in sediments of the northeast tropical Atlantic: Evidence from210Pbxs,137Cs,228Thxs downcore distributions, Earth Planet. Sci. Lett., 128, 545 – 562, 1994. Li, W. Q., N. L. Guinasso, K. H. Cole, M. D. Richardson, J. W.
John-son, and D. R. Schink, Radionuclides as indicators of sedimentary processes in abyssal Caribbean sediments, Mar. Geol., 68, 187 – 204, 1985.
Lynch, D. R., and C. B. Officer, Nonlinear parameter estimation for sedi-ment cores, Chem. Geol., 44, 203 – 225, 1984.
Martin, W. R., and F. L. Sayles, Seasonal cycles of particle and solute transport processes in nearshore sediments:222Rn/226Ra and234Th/238U
disequilibrium at a site in Buzzards Bay, MA., Geochim. Cosmochim. Acta, 51, 927 – 943, 1987.
McIntyre, A., A. W. H. Be´, and R. Preikstas, Coccoliths and Plio-Pleisto-cene boundary, Prog. Oceanogr., 4, 3 – 25, 1967.
Middelburg, J. J., K. Soetaert, and P. M. J. Herman, Empirical relationships for use in global diagenetic models, Deep Sea Res. Part I, 44, 327 – 344, 1997.
Nittrouer, C. A., D. J. DeMaster, B. A. McKee, N. H. Cutshall, and I. L. Larsen, The effect of sediment mixing on Pb-210 accumulation rates for the Washington continental shelf, Mar. Geol., 54, 201 – 221, 1983. Nozaki, Y., J. K. Cochran, K. K. Turekian, and G. Keller, Radiocarbon and
210
Pb distribution in submersible-taken deep-sea cores from project FA-MOUS, Earth Planet. Sci. Lett., 34, 167 – 173, 1977.
Paterne, M., F. Guichard, J. Labeyrie, P.-Y. Gillot, and J.-C. Duplessy, Tyrrhenian Sea tephrochronology of the oxygen isotope record for the past 60,000 years, Mar. Geol., 72, 259 – 285, 1986.
Peng, T. H., W. S. Broecker, G. Kipphut, and N. Schackleton, Benthic mixing in deep sea cores as determined by14C dating and its implications
regarding climate stratigraphy and the fate of fossil fuel CO2, in The Fate
of Fossil Fuel CO2 in the Oceans, edited by N. R. Andersen and
A. Malahoff, pp. 355 – 373, Plenum, New York, 1977.
Peng, T. H., W. S. Broecker, and W. H. Berger, Rates of benthic mixing in deep-sea sediments as determined by radioactive tracers, Quat. Res., 11, 141 – 149, 1979.
Ruddiman, W. F., and L. K. Glover, Vertical mixing of ice-rafted volcanic ash in North-Atlantic sediments, Geol. Soc. Am. Bull., 83, 2817 – 2836, 1972.
Ruddiman, W. F., and A. McIntyre, The North Atlantic Ocean during the last deglaciation, Palaeogeogr. Palaeoclimatol. Palaeoecol., 35, 145 – 214, 1981.
Schiffelbein, P., Effect of benthic mixing on the information content of deep-sea stratigraphical signals, Nature, 311, 651 – 653, 1984. Schiffelbein, P., Extracting the benthic mixing impulse response function: A
constrained deconvolution technique, Mar. Geol., 64, 313 – 336, 1985. Siani, G., R. Sulpizio, M. Paterne, and A. Sbrana, Detailed
tephrochronol-ogy for the last 18,000 years in the South Adriatic deep sea sediments: Correlations with terrestrial deposits, Bull. Volcanol., in press, 2002. Smith, C. R., R. H. Pope, D. J. DeMaster, and L. Magaard, Age-dependent
mixing of deep-sea sediments, Geochim. Cosmochim. Acta., 57, 1473 – 1488, 1993.
Smith, J. N., B. P. Boudreau, and V. Noshkin, Plutonium and210Pb dis-tributions in northeast Atlantic sediments: Subsurface anomalies caused by non-local mixing, Earth Planet. Sci. Lett., 81, 15 – 28, 1986. Soetaert, K., P. M. J. Herman, J. J. Middelburg, H. S. deStigter, T. C. E. Van
Weering, and E. Epping, Modelling210Pb-derived mixing activity in ocean margin sediments: Diffusive versus non local mixing, J. Mar. Res., 54, 1207 – 1227, 1996.
Stordal, M. C., J. W. Johnson, N. L. Guinasso, and D. R Schink, Quanti-tative evaluation of bioturbation rates in deep ocean sediments, II, Com-parison of rates determined by210Pb and239,240Pu, Mar. Chem., 17, 99 –
114, 1985.
Taylor, K. C., G. W. Lamorey, G. A. Doyle, R. B. Alley, P. M. Grootes, P. A. Mayewski, J. C. W. White, and L. K. Barlow, The ‘‘flickering switch’’ of late Pleistocene climate change, Nature, 361, 432 – 436, 1993. Thomson, J., S. Colley, and P. P. E. Weaver, Bioturbation into a recently emplaced deep-sea turbidite surface as revealed by210Pbexcess,230 Thex-cess and planktonic foraminifera distributions, Earth Planet. Sci. Lett., 90, 157 – 173, 1988.
Trauth, M. H., TURBO: A dynamic probabilistic simulation to study the effects of bioturbation on paleoceanographic time series, Comput. Geos-ci., 24, 433 – 441, 1998.
Trauth, M. H., M. Sarnthein, and M. Arnold, Bioturbational mixing depth and carbon flux at the seafloor, Paleoceanography, 12, 517 – 526, 1997. Valley, J. W., H. P. Taylor, and J. R. O’Neil, in Reviews in Mineralogy, vol. 16, Stable Isotopes in High Temperature Geological Processes, Mineral. Soc. of Am., Washington, D. C., 1986.
S. Charbit, C. Rabouille, and G. Siani, Laboratoire des Sciences du Climat et de l’Environnement, UMR CNRS-CEA, CE Saclay, Orme des Merisiers, Baˆt. 709, 91191 Gif-sur-Yvette cedex, France. (charbit@ Isce.saclay.cea.fr)
![[PDF] Cours QtCreator pour débutant en pdf | Formation informatique](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)