Patterns of thermal convection in slowly rotating,weakly magnetic fluid shells

The effects of rotation and a toroidal magnetic field on the preferred pattern of small amplitude convection in spherical fluid shells are considered. The convective motions are described in terms of associated Legendre functions P_l^|m| (cos θ). For a given pair of Prandtl number P and magnetic Prandtl number $\text{P}$_m the physically realized solution is represented either by m = 0 or |m| = l depending on the ratio of the rotation rate Λ to the magnetic field amplitude H. The case of m = 0 is preferred if this ratio ranges below a critical value, which is a function of the shell thickness, and |m| = l otherwise.     

Modelling the peak of the ionospheric E-layer

Calculations with a full time-varying model are used to study changes in the height and density of the E-layer peak, caused by known changes in the neutral atmosphere. Agreement with mean observed values of N_mE requires an increase of 10% in calculated ion densities, and an increase of 33% in the solar-maximum EUV model at λ<150 Å. At a fixed site, changes with the solar zenith angle χ agree well with the simple Chapman theory during most of the daylight hours. Simple modifications to the Chapman equations give improved accuracy near sunrise and sunset. When corrected for changes in χ, model results for summer and equinox show a decrease in the peak density N_mE at increasing latitudes. The overall change agrees well with experimental data, as summarised in the IRI model. Known changes in the neutral atmosphere also reproduce the increase in N_mE in winter, at latitudes up to 30°. The continuing increase at higher winter latitudes, in the IRI model, requires a major reduction in NO densities in winter. A suitable compromise is suggested. Equations fitted to the model results then provide a simpler and better behaved replacement for the IRI equations. Calculations at night show that known sources of ionisation, largely from starlight, can produce observed peak densities using current chemistry. There is an appreciable change with latitude, as starlight production increases in the southern hemisphere. The improbably large solar cycle change built into the IRI model, at night, cannot be reproduced and is not found in recent data. A new, simpler model is suggested. Changes in zenith angle and atmospheric composition cause the peak height (h_mE) to vary between 105 and 120 km, as a function of time, latitude, season and solar flux. These changes are approximated by simple equations that should be definitely preferable over the single, fixed height used in the IRI models.     

Analogue model,relating Kp index to solar wind parameters

In a previous work the authors have developed a model, providing K_p as a function of the interplanetary magnetic field B_z component. They introduced a modified B_z function (denoted as B_zm), exhibiting a delayed reaction to B_z changes. The modified function B_zm was defined by using the analogy with a damping RC-circuit output voltage. The delaying reaction of B_zm to B_z was characterized by two time constants, one for rising and one for decreasing parts of B_z. The cross-correlation between K_p and B_zm has increased to 0.7, compared with −0.4 between K_p and B_z. In this paper, new dependences of K_p on solar wind velocity and dynamic pressure are included in the model to improve its accuracy. These solar wind parameters are found to correlate best with K_p. The hourly interpolated values are also added to the 3-h K_p values to increase the statistics. The new K_p data set is denoted as K_p1. The mean dependence of K_p on B_zm and dynamic pressure are approximated with parabolas, while the dependence on the velocity is linear. The constants in the model expression are obtained by using ACE data (1998–2000). The overall model error is estimated at 0.63 units K_p. The improvement over the previous simpler dependence in terms of the model error is about 30%.     

Effects of relative motion between gas and liquid on 1-dimensional steady flow in silicic volcanic conduits: 2. Origin of diversity of eruption styles

We investigate the origin of diversity of eruption styles in silicic volcanoes on the basis of a 1-dimensional steady conduit flow model that considers vertical relative motion between gas and liquid (i.e., vertical gas escape). The relationship between the assemblage of steady-state solutions in the conduit flow model and magma properties or geological conditions is expressed by a regime map in the parameter space of the ratio of liquid-wall friction force to liquid–gas interaction force (non-dimensional number ε), and a normalized conduit length Λ. The regime map developed in the companion paper shows that when ε is smaller than a critical value ε_cr, a solution of explosive eruption exists for a wide range of Λ, whereas an effusive solution exists only when Λ ~ 1. On the other hand, when ε > ε_cr, an effusive solution exists for a wide range of Λ. Diversity of eruption styles observed in nature is explained by the change in ε accompanied by the change in magma viscosity during magma ascent. As magma ascends, the magma viscosity increases because of gas exsolution and crystallization, leading to the increase in ε. For the viscosity of hydrous silicic magma at magma chamber, ε is estimated to be smaller than ε_cr, indicating that an explosive solution exists for wide ranges of geological parameters. When magma flow rate is small, the viscosity of silicic magma drastically increases because of extensive crystallization at a shallow level in the conduit. In this case, ε can be greater than ε_cr; as a result, a stable effusive solution co-exists with an explosive solution.     

Partitioning resistance to overland flow on rough mobile beds

For overland flows transporting predominantly bed load over rough mobile beds without rainfall, resistance to flow f may be divided into four components: surface resistance f_s, form resistance f_f, wave resistance f_w, and bed‐mobility resistance f_m. In this study it is assumed that f = f_s + f_f + f_w + f_m, and an equation is developed for each component. The equations for f_s and f_f are borrowed from the literature, while those for f_w and f_m are developed from two series of flume experiments in which the beds are covered with various concentrations of large‐scale roughness elements. The first series consists of 65 experiments on fixed beds, while the second series contains 194 experiments on mobile beds. All experiments were performed on the same slope (S = 0·114) and with the same size of sediment (D = 0·00074 m). The equations for f_w and f_m are derived by a combination of dimensional analysis and regression analysis. The analyses reveal that the major controls of f_w and f_m are the Froude number F and the concentration of the roughness elements C_r. When the equations for f_w and f_m are summed, the C_r terms cancel out, leaving f_w+m = 0·63F^?2. An equation is developed that predicts total f, and the contributions of f_s, f_f, f_w and f_m to f are computed from the series 1 and 2 experiments. An analysis of the first series reveals that in clear‐water flows over fixed beds, f_w accounts for 52 per cent of f. A similar analysis of the second series indicates that in sediment‐laden flows over mobile beds f_w comprises 37 per cent and f_m 32 per cent of f, so that together f_w and f_m account for almost 70 per cent of f. Finally, regression analyses indicate that where F > 0·5, f_w and f_m each vary with F^?2 and f_w/f_m = 1·18. The equation developed here for predicting total f applies only to the range of hydraulic, sediment, and bed roughness conditions represented by the experimental data. With additional data from a broader range of conditions the same methodology as employed here could be used to develop a more general equation. Copyright © 2006 John Wiley & Sons, Ltd.     

Paleomagnetism of Lower Devonian volcanics and Devonian dykes from northcentral New Brunswick,Canada

Some 50 oriented samples (120 specimens) have been collected on eight sites of volcanic rocks from the Lower Devonian Dalhousie Group of northern New Brunswick and Devonian andesitic to basic dykes from central New Brunswick. Univectorial and occasional multivectorial components were extracted from the various samples. Results after AF and thermal demagnetization compare relatively well. In the volcanics and tuffs, two components of magnetization have been isolated: A (D = 33°, I = ?58°, α₉₅ = 7.3°, K = 236) for four sites and B (D = 66°, I = +53°) for three sites. The grouping of component A is improved after tilt correction but the fold test is not significantly positive at the 95% confidence level. Component A is interpreted as being primary while component B is unresolved and appears to be the resultant magnetization of a Late Paleozoic and a recent component. The pole position obtained for tilt corrected component A is 268°E, 1°S, d_p = 6.5°, d_m = 8.8°. The paleolatitude calculated for component A is 39°S. The paleopole of in situ component A is located close to those of the Early-Middle Devonian formations from Quebec, New Brunswick and New England states while the paleopole of tilt-corrected component A is similar to Lower Devonian poles of rock units from the Canadian Arctic Archipelago. If component A is primary (as we believe it to be), then the western half of the northern Appalachians had already docked onto the North American Craton by Early Devonian time. Alternatively, if component A is secondary the same conclusion applies but the juxtaposition took place in Middle Devonian time.     

High-pressure silicate liquidus data: Retrieval of partial molar enthalpy and partial molar entropy of mixing,a test of the regular solution formulation,and comments on theP-T modelling of ascending magmas

The activity of a silicate liquid component in a melt at an elevated liquidus temperature and pressure may be expressed analytically in terms of the 1-bar liquidus temperature activity and functions of the partial molar volume and partial molar enthalpy of mixing. Alternatively, the activity of the elevated (i.e. higherP-T) liquidus may be expressed in terms of the difference of heat content, heat capacity, entropy and volume of the component in the crystalline form and in the melt. Equating these two expressions, the partial molar enthalpy of mixing and there-from the partial molar entropy of mixing may be determined, provided the liquidus temperatures of the phase in question at both 1 bar and higher pressure and at a constant melt composition are known. Several such retrievals for CaMgSi₂O₆, Mg₂SiO₄, NaAlSi₃O₈, and TiO₂ from experimental phase equilibrium data are presented. It is argued that as the partial molar enthalpy of mixing generally has large values, the regular solution formulation on the basis of a constant function of the activity coefficient would lead to erroneousP-T estimates for ascending magmas.     

Oscillations of the Earth with periods of 9–57 min in the background seismic process and the energy flux direction in the range of the free oscillation 0 S 2

Retrospective data of monitoring under conditions of low seismic activity are used to identify free oscillations of the Earth, including the fundamental mode, the oscillation with a central period of 54 min (₀ S ₂ ^m multiplet), split into five lines with azimuthal numbers m = ?2, ?1, 0, 1, 2. It is shown that some lines of this oscillation are also recorded in atmospheric pressure variation spectra and group in ensembles of observations around frequencies predicted by the ₀ S ₂ ^m splitting theory. This phenomenon is discovered in data recorded both synchronously and in different time intervals. A causal relationship involved in the oscillation under study is determined on the basis of the examination of the direction of the acoustic energy flux. The energy flux in the region of the ₀ S ₂ ^m multiplet is shown to be directed from the Earth toward the atmosphere. This suggests that deep processes in the Earth are capable of exciting its upper shells.     

The distribution of bomb-produced tritium and radiocarbon at GEOSECS station 347 in the eastern North Pacific

Following Roether et al. [1] an upwelling model has been tested to explain the distribution of bomb-produced tritium at the GEOSECS I test station off Baja, California. We have extended their treatment to include the time histories for tritium and for bomb radiocarbon now available for this station. If the CO₂ gas exchange rate at this station is similar to the ocean average value of 20 moles/m² yr, then the upwelling rate must be quite small (<3 m/yr). However, a satisfactory match to the time histories of¹⁴C and of³H is achieved only if an upwelling rate of 40 m/yr is used. In this case, however, a CO₂ exchange rate of 70 moles/m² yr would be required to match the observed surface water¹⁴C/C ratios and a tritium input 4 times the expected value would be needed. The inconsistency in the bomb¹⁴C time history obtained using the accepted CO₂ exchange rate is likely the result of horizontal effects which void the validity of one dimensional modeling in this region of the ocean.     

Magnetic instabilities in rapidly rotating spherical geometries. III. The effect of differential rotation

Abstract

We investigate the influence of differential rotation on magnetic instabilities for an electrically conducting fluid in the presence of a toroidal basic state of magnetic field B ₀ = B_MB₀(r, θ)1 _φ and flow U₀ = U_MU₀ (r, θ)1_φ, [(r, θ, φ) are spherical polar coordinates]. The fluid is confined in a rapidly rotating, electrically insulating, rigid spherical container. In the first instance the influence of differential rotation on established magnetic instabilities is studied. These can belong to either the ideal or the resistive class, both of which have been the subject of extensive research in parts I and II of this series. It was found there, that in the absence of differential rotation, ideal modes (driven by gradients of B ₀) become unstable for A_c ? 200 whereas resistive instabilities (generated by magnetic reconnection processes near critical levels, i.e. zeros of B₀) require A_c ? 50. Here, Λ is the Elsasser number, a measure of the magnetic field strength and Λ_c is its critical value at marginal stability. Both types of instability can be stabilised by adding differential rotation into the system. For the resistive modes the exact form of the differential rotation is not important whereas for the ideal modes only a rotation rate which increases outward from the rotation axis has a stabilising effect. We found that in all cases which we investigated Λ_c increased rapidly and the modes disappeared when R_m ≈ O(Λ_C), where the magnetic Reynolds number R_m is a measure of the strength of differential rotation. The main emphasis, however, is on instabilities which are driven by unstable gradients of the differential rotation itself, i.e. an otherwise stable fluid system is destabilised by a suitable differential rotation once the magnetic Reynolds number exceeds a certain critical value (R_m )_c. Earlier work in the cylindrical geometry has shown that the differential rotation can generate an instability if R_m ) ?O(Λ). Those results, obtained for a fixed value of Λ = 100 are extended in two ways: to a spherical geometry and to an analysis of the effect of the magnetic field strength Λ on these modes of instability. Calculations confirm that modes driven by unstable gradients of the differential rotation can exist in a sphere and they are in good agreement with the local analysis and the predictions inferred from the cylindrical geometry. For Λ = O(100), the critical value of the magnetic Reynolds number (R_m )_c Λ 100, depending on the choice of flow U₀ . Modes corresponding to azimuthal wavenumber m = 1 are the most unstable ones. Although the magnetic field B ₀ is itself a stable one, the field strength plays an important role for this instability. For all modes investigated, both for cylindrical and spherical geometries, (R_m )_c reaches a minimum value for 50 ≈ Λ ≈ 100. If Λ is increased, (R_m )_c ∝ Λ, whereas a decrease of Λ leads to a rapid increase of (R_m )_c, i.e. a stabilisation of the system. No instability was found for Λ ≈ 10 — 30. Optimum conditions for instability driven by unstable gradients of the differential rotation are therefore achieved for ≈ Λ 50 — 100, R_m ? 100. These values lead to the conclusion that the instabilities can play an important role in the dynamics of the Earth's core.     

Role of solar activity in formation of the anomalous El Nin’o current

Monthly indices of Southern Atmospheric Oscillation (SOI) and corresponding Wolf numbers, geoeffective solar flares, magnetic AE indices as well as daily average values of the southward component of the interplanetary magnetic field (IMF B _z) and data on the wind characteristics at Antarctic stations Vostok, Leningradskaya, and Russkaya are analyzed. It is shown that a sharp decrease in the SOI indices, which corresponds to the beginning of El Nin’o (ENSO), is preceded one or two months before by a 20% increase in the monthly average Wolf numbers. In warm years of Southern Atmospheric Oscillation a linear relationship is observed between the SOI indices and the number of geoeffective solar flares with correlation coefficients p < ?0.5. It is shown that in warm years a change in the general direction of the surface wind to anomalous at the above stations is preceded one or two days before by an increase in the daily average values of IMF B _z. An increase in the SOI indices is preceded one or two months before by a considerable increase in the monthly average values of the magnetic AE indices.     

Determination of the thermal conductivity of opalinus clay via simulations of experiments performed at the Mont Terri underground laboratory

Storage in deep geological formations is a potential solution for the management of high-level radioactive wastes. In this context, different types of rocks such as argillite are extensively studied. In the Mont Terri underground laboratory (Switzerland), several experiments have been performed in order to characterize the properties of the opalinus clay. One of these experiments, called HE-C, has consisted in measuring in situ the time evolution of the rock temperature submitted to a heating source. Experimental measurements have shown that the thermal behaviour of the clay was not homogeneous around the borehole where the heater was installed. Furthermore, 3D direct numerical simulations of this experiment performed with the code Cast3M have proved that it was necessary to introduce a new parameter α to model the amount of electric power lost in cables and by air convection inside the metallic tube containing the heater. A numerical simulation–optimization technique has been used to estimate the thermal longitudinal and transverse conductivities (λ_// and λ_⊥) of the host rock. It consists in minimizing an objective function that is the sum of the squared differences between measured and calculated temperatures. But this method induced a lot of Cast3M simulations. In order to drastically reduce the CPU time, we used a neural network approximation built from a sample training of 1100 Cast3M simulations. It allowed us to calculate the objective function for 500 000 different values of the triplet (λ_//,λ_⊥,α).Finally, we obtained the following values for the thermal conductivities

• –on one side of the borehole, λ_// = 1.84 ± 0.04 W m^− 1 K^− 1 and λ_⊥ = 0.55 ± 0.03 W m^− 1 K^− 1;
• –on the other side, λ_// = 1.90 ± 0.07 W m^− 1 K^− 1 and λ_⊥ = 1.07 ± 0.09 W m^− 1 K^− 1.

The estimated thermal conductivities λ_⊥ perpendicular to the bedding plane are quite different. It is perhaps caused by the presence of an intensive fractured zone on one side of the borehole, due to bentonite swelling. It can also be due to the presence of a bed of carbonated rock.     

Upscaling of saturated conductivity for Hortonian runoff modelling

Stochastic and deterministic upscaling techniques are developed that upscale saturated conductivity at the support of 0.04 m² to representative actual infiltration (I_b) for support units (blocks) of 10¹–10⁴ m², as a function of steady state rainfall and runon to the block, under Hortonian runoff (infiltration excess overland flow). Parameters in the upscaling techniques represent the surface runoff flow pattern and the spatial probability distribution of saturated conductivity within the 10¹–10⁴ m² block. The stochastic upscaling technique represents the spatial process of infiltration and runoff using a simple process-imitating model, estimating I_b using Monte Carlo simulation. The deterministic upscaling technique aggregates these processes by a deterministic function relating rainfall and runon to I_b. The stochastic upscaling technique is shown to be capable to upscale saturated conductivity derived from ring infiltrometers to I_b values of plots (1 m²) corresponding to measured I_b values using rainfall simulators. It is shown that both upscaling techniques can be used to estimate I_b for each time step and each block in transient rainfall–runoff models, giving better estimates of cumulative runoff from a hillslope and a small catchment than model runs that do not use upscaling techniques.     

Rates of dissolution of aluminosilicates in seawater

Dissolution of eight clay minerals, four zeolites, and quartz in seawater has been monitored for81/2 years. For most of the minerals, dissolution can be described as a first-order reaction in which dissolved silica approaches from undersaturation steady concentration values with time. Characteristic reaction rate constants (k₁) are of the order of 10^?7 sec^?1. One of the zeolites, clinoptilolite, shows a different dissolution behavior: SiO₂ concentration in solution reaches a high value within one year, followed by a decline to a lower value, suggestive of precipitation of another silicate phase (possibly sepiolite).A mathematical solution is given for a kinetic equation combining the parabolic-rate and first-order rate processes. It is shown that in a wide range of silicate dissolution reactions taking place over long periods of time, the presence of the parabolic-rate dissolution processes cannot be detected, thereby making its inclusion in the kinetic equations unnecessary. The experimental rates of dissolution are comparable to the SiO₂^? dissolution rates in oceanic sediments near the sediment/water interface. But deeper in the sediment, the calculated dissolution rates are significantly lower than the near-interface and experimental values.     

Melting of forsterite Mg2SiO4 up to 15 GPa

The melting curve of forsterite has been studied by static experiment up to a pressure of 15 GPa. Forsterite melts congruently at least up to 12.7 GPa. The congruent melting temperature is expressed by the Kraut-Kennedy equation in the following form: T_m(K)=2163 (1+3.0(V₀ ? V)/V₀), where the volume change with pressure was calculated by the Birch-Managhan equation of state with the isothermal bulk modulus K₀ = 125.4 GPa and its pressure derivative K′ = 5.33. The triple point of forsterite-β-Mg₂SiO₄-liquid will be located at about 2600°C and 20 GPa, assuming that congruent melting persists up to the limit of the stability field of forsterite. The extrapolation of the previous melting data on enstatite and periclase indicates that the eutectic composition of the forsterite-enstatite system should shift toward the forsterite component with increasing pressure, and there is a possibility of incongruent melting of forsterite into periclase and liquid at higher pressure, although no evidence on incongruent melting has been obtained in the present experiment.     

Non-axisymmetric α2Ω-dynamo waves in thin stellar shells

Linear α²Ω-dynamo waves are investigated in a thin turbulent, differentially rotating convective stellar shell. A simplified one-dimensional model is considered and an asymptotic solution constructed based on the small aspect ratio of the shell. In a previous paper Griffiths et al. (Griffiths, G.L., Bassom, A.P., Soward, A.M. and Kuzanyan, K.M., Nonlinear α²Ω-dynamo waves in stellar shells, Geophys. Astrophys. Fluid Dynam., 2001, 94, 85–133) considered the modulation of dynamo waves, linked to a latitudinal-dependent local α-effect and radial gradient of the zonal shear flow. These effects are measured at latitude θ by the magnetic Reynolds numbers R _α f(θ) and R _Ω g(θ). The modulated Parker wave, which propagates towards the equator, is localised at some mid-latitude θ_p under a Gaussian envelope. In this article, we include the influence of a latitudinal-dependent zonal flow possessing angular velocity Ω_*(θ) and consider the possibility of non-axisymmetric dynamo waves with azimuthal wave number m. We find that the critical dynamo number D _c?=?R _α R _Ω is minimised by axisymmetric modes in the αΩ-limit (Rα→0). On the other hand, when Rα?≠?0 there may exist a band of wave numbers 0?m?m ^? for which the non-axisymmetric modes have a smaller D _c than in the axisymmetric case. Here m ^? is regarded as a continuous function of R _α with the property m?→0 as R _α→0 and the band is only non-empty when m??>1, which happens for sufficiently large R _α. The preference for non-axisymmetric modes is possible because the wind-up of the non-axisymmetric structures can be compensated by phase mixing inherent to the α²Ω-dynamo. For parameter values resembling solar conditions, the Parker wave of maximum dynamo activity at latitude θ_p not only propagates equatorwards but also westwards relative to the local angular velocity Ω_*(θ _p ). Since the critical dynamo number D _c?=?R _α R _Ω is O (1) for small R _α, the condition m ^??>?1 for non-axisymmetric mode preference imposes an upper limit on the size of |dΩ_*/dθ|.     

The Campania-Lucania (southern Italy) earthquake of 23 November 1980

We present the main seismological results of our study of the Campania-Lucania earthquake of 23 November 1980. A complete set of far field and local data has been analysed. From long-period body waves data we determine the fault plane solution (φ₁ = 140°,δ₁ = 60°,φ₂ = 75°,δ₂ = 54°), a depth of 15 km and calculate a seismic moment of 6 × 10²⁵ dyne cm and a source duration of 6 s. From data of a local network deployed immediately after the event we determine aftershock locations: they are aligned in a direction NW-SE that fit extremely well with the focal solution determined above. We can choose as fault plane the plane striking 140° and dipping at 60° and the event is a normal event with a large component of left-lateral strike slip. The source area evaluated from this aftershock distribution 14 km × 40 km is quite suitable for an earthquake of a seismic moment of 6 × 10²⁵ dyne cm.     

On the boundary integral equations in the theory of elastic vibrations

Forward seismic problems are solved for elastic media by rigorous methods (i.e., methods with controllable accuracy). Analysis of the current state of research on this subject suggests that the most promising methods are based on integral and integro-differential equations, notwithstanding the rather modest results of their application to solving forward problems in the theory of elastic vibrations. The second Green integral theorem for seismic waves, formulated and proven in the paper, yields a system of two boundary (surface) integral equations for the displacement vector u(M ₀) and the normal (to the boundary surface) vector component of the stress tensor t_n(M ₀). The integrands of the surface integrals in terms of which the function t_n(M ₀) is expressed on both sides of the interface between the medium and the heterogeneity contain the second derivatives of the Green’s tensor functions ? ^e (M ₀, M) and ? ⁱ (M ₀, M), respectively, which are responsible for a cubic singularity (third-order singularity) if the integration point M coincides with the observation point M ₀. An original method of eliminating the cubic singularity proposed in the paper involves special tensor normalization of the integrals on the outer and inner sides of the interface and subsequent subtraction of one integral from another in order to construct the second integral equation.     

The ionospheric response to the acoustic signal from submarine earthquakes according to the GPS data

The ionospheric response to the transit of acoustic waves from a number of the strongest submarine earthquakes with magnitudes M _w ≥ 7.7, which occurred during the past few years, is analyzed. The amplitude of the response in the detrended TEC is studied as a function of the magnitude and vertical component of the surface deformation. It is shown that the geomagnetic field can significantly modulate the shape of the ionospheric response, depending on whether the perturbation propagates equatorward or polarward.     

Elimination of fine suspensoids in the oceanic water column

Fine suspended materials in the particle-size range1 < r < 6 μm (r, equivalent sphere radius) from the equatorial North Atlantic, between the ocean surface and greater depths (30–5100 m), can be consistently described by a size-distribution relationshipdN/dr = Ar^?b, where the parametersA andb are independent ofr. The shape of the particle-size distribution is essentially constant and independent of depth, as reflected in the values of the logarithmic slope of the size distributionb = 4.0 ± 0.3. The particle-number and mass concentration, however, decrease strongly with depth, most of the decrease taking place in the surface layer 200 m deep. In the surface layer, mass concentration decreases exponentially with the half-concentration depthz_1/2 ? 60m; in the deep layer (200–5000 m),z_1/2 ? 1000m. The computed removal half-lives of the particulate material are0.8 ± 0.6yr in the surface layer, and60 ± 20yr in the deep layer, both half-lives being considerably shorter than Stokes settling residence times. The fast turnover or removal rate in the surface layer is compatible with the rates of zooplankton growth and carbon assimilation.