The earth's thermal profile: Is there a mid-mantle thermal boundary layer?

Shock observations on melting of iron by Brown and McQueen with the inner core boundary (ICB) density contrast estimated by Masters are used with the assumption that the light ingredient of the outer core is oxygen to calculate the boundary temperature T_ICB = (5000 ± 900) K. Adiabatic extrapolation to the core-mantle boundary (CMB) gives T_ICB = (3800 ± 800) K. The temperature increment across the D″ layer is not well constrained, but is estimated to be T_D″ = (800 ± 400) K and a slightly superadiabatic extrapolation to 670 km gives T_{670 +} = (2300 ± 950) K. This is only about 300 K higher than the extrapolation to the same level from the upper mantle, T_670? = (1970 ± 150) K. The difference is far too small to make a viable mid-mantle boundary layer. Remaining unceertainties are too large to discount such a boundary layer with certainty, but agreement of our new temperature profile with temperatures deduced from equation of state studies on the lower mantle and core encourages the view that we are converging to a well-determined temperature profile for the Earth.     

Experimental reproduction of textures of chondrules

The textures of chondrules have been reproduced by crystallizing melts of three different compositions at 1 atm with cooling rates ranging from 400 to 20°C/min under 10^?9 to 10^?12 atmP_O2. A porphyritic olivine texture has been formed from a melt of olivine-rich composition (SiO₂ = 45 wt.%), a barred-olivine texture from melt of intermediate composition (SiO₂ = 47 wt.%), and radial-olivine texture from melt of pyroxene-rich composition (SiO₂ = 57 wt.%). The cooling rate for producing barred olivine is most restricted; the rate ranges from 120 to 50°C/min. Other textures can be formed with wider ranges of cooling rate. The results of the experiments indicate that some of the major types of textures of chondrules can be formed with cooling rate of about 100°C/min. With this cooling rate, the texture varies depending on the composition of melt.     

Lithium tracer-diffusion in an alkali-basaltic melt — An ion-microprobe determination

An ion-microprobe-based technique has been used to measure lithium tracer-diffusion coefficients (D_Li) in an alkali-basaltic melt at 1300, 1350 and 1400°C. The results can be expressed in the form:D_Li=7.5 ×10^?2exp(?27,600/RT)cm²S^?1The results show significantly faster diffusion rates than those previously recorded for other monovalent, divalent and trivalent cations in a tholeiitic melt. Consequently, diffusive transport of ions acting over a given time in a basaltic melt can produce a wider range of transport distance values than hitherto supposed. Hence, it is concluded that great care should be exercised when applying diffusion data to petrological problems.     

Approximate solutions for the formation of the lithosphere

The lithosphere is interpreted as a thermal boundary layer. Approximate solutions of the boundary layer cooling problem are developed which include mantle radioactivity, partial melt in the asthenosphere, a temperature gradient in the asthenosphere, and a non-zero lithospheric thickness at the ridge crests. The cooling history of oceanic lithosphere is found to be remarkably insensitive to assumptions about the amount of radioactivity in the upper mantle and the extent of melting in the asthenosphere. Determinations of the thickness of oceanic lithosphere and the depths of oceans as a function of age are in excellent agreement with boundary layer predictions which include a heat flux from the asthenosphere. However, the determinations do not resolve how much of the total asthenospheric heat flux might be caused by a temperature gradient in the asthenosphere. Simple thermal arguments indicate that the initial lithospheric thickness, L₀, at ridge crests should depend on the local half-spreading rate, V, as L₀ = 3 km/V(cm/year).     

Nickel partitioning between olivine and silicate melt

Partitioning of Ni between olivine and silicate melt has been determined for compositions in the system Fo-Ab-An (1 atm) for temperatures ranging from 1250°C to 1450°C. Nickel concentrations were determined by electron microprobe; concentration levels in the liquids ranged from 0.1% to 0.5%. Platinum capsules or Pt wire loops were used as containers. Equilibrium was evaluated from kinetic considerations and by variation of run parameters; it was documented in one case by a bracketed reversal. No evidence was found for a dependence of the partition coefficient D (Ni in olivine/Ni in liquid) on Ni concentration. D is strongly dependent on melt composition, varying linearly with (1/MgO) at constant temperature. The intrinsic temperature dependence of D is small; the apparent temperature dependence reported in previous studies is largely related to the variation of melt composition with temperature. Our D values determined in the simple system Fo-An-Ab agree well with those reported by Leeman for natural (Fe-bearing) basalt systems. Overall variation of D in our system (and in natural basalts) can be expressed by the regression: D = (124/MgO) ? 0.9Our data are used to evaluate published Ni-MgO relationships in natural basalt series from Kilauea, Crozet, Cape Verde and Baffin Bay. A combination of olivine accumulation and fractional crystallization processes are sufficient to model these series. Using our data, unique “parental” liquids can be specified for each of these series; the MgO content of these liquids varies from 6% to 13%. Basalts with MgO contents greater than these “parental” liquids must be accumulative. The linear Ni-MgO trends, high absolute Ni concentrations, and large spread of Ni contents for the high-MgO basalts argue convincingly against their being “primary” liquids. Models such as those of O'Hara [6,13] and Clarke [24], based on the assertion of primary high-MgO liquids, must therefore be re-evaluated.Because of the high Si/O ratio and low MgO content of island arc andesites, the Ni partition coefficient D may be quite high. Therefore, the relatively low Ni content of such andesites may not be an argument against their derivation as direct partial melts of the mantle.     

Cumulate nodules as evidence for convective fractionation in a phonolite magma chamber

The physical mechanism by which chemical zonation develops in magma chambers has been controversial partly because unambiguous geological constraints have been lacking. The 11,000 years B.P. eruption of Laacher See Volcano produced a zoned tephra deposit and also ejected crystal-rich nodules which provide a snapshot of the materials crystallising at the magma chamber margins. New data on petrography and chemical compositions of nodules, their cumulate minerals and interstitial glasses are used to deduce the chemical evolution of the phonolite melt due to fractional crystallisation of the mineral assemblages. These data, together with those on the vertical zonation of the melt in the bulk of the chamber, are shown to be consistent with a model of stratification of the chamber by convective fractionation, in which a thin boundary layer of residual melt from fractional crystallisation ascends at the chamber side and accumulates at the roof. Crystallisation could have provided buoyancy to drive convection by enriching incompatible volatile components (mainly water) in the residual melt. Available fluid dynamic studies of single- and double-diffusive boundary layers are used to assess convection in the Laacher See chamber. The boundary layer is likely to have been: (1) laminar, which implies that the density gradient in the chamber steepened upwards; (2) in the counterflow regime, in which compositional and thermal layers flow in opposite directions; and (3) thin ( 10 cm), estimated from theory for a flat wall, suggesting that wall morphology could be important in determining boundary layer characteristics. Estimates of mass transfer rates due to this mechanism suggest that the chamber could have become stratified in a time of the order of 10³ years.     

Apatite/liquid partition coefficients for the rare earth elements and strontium

Sixteen sets of apatite/liquid partition coefficients (D^ap/liq) for the rare earth elements (REE; La, Sm, Dy, Lu) and six values for Sr were experimentally determined in natural systems ranging from basanite to granite. The apatite + melt (glass) assemblages were obtained from starting glasses artificially enriched in REE, Sr and fluorapatite components; these were run under dry and hydrous conditions of 7.5–20 kbar and 950–1120°C in a solid-media, piston-cylinder apparatus. An SEM-equipped electron microprobe was used for subsequent measurement of REE and Sr concentrations in coexisting apatites and quenched glasses. The resulting partition coefficient patterns resemble previously determined apatite phenocryst/groundmass concentration ratios in the following respects: (1) the rare earth patterns are uniformly concave downward (i.e., the middle REE are more compatible in apatite than the light and heavy REE); (2) D_REE^ap/liq is much higher for silicic melts than for basic ones; and (3) strontium (and therefore Eu²⁺) is less concentrated by apatite than are the trivalent REE. The effects of both temperature and melt composition on D_REE^ap/liq are systematic and pronounced. At 950°C, for example, a change in melt SiO₂ content from 50 to 68 wt.% causes the average REE partition coefficient to increase from ～7 to ～30. A 130°C increase in temperature, on the other hand, results in a two-fold decrease in D_REE^ap/liq. Partitioning of Sr is insenstitive to changes in melt composition and temperature, and neither the Sr nor the REE partition coefficients appear to be affected by variations in pressure or H₂O content of the melt.The experimentally determined partition coefficients can be used not only in trace element modelling, but also to distinguish apatite phenocrysts from xenocrysts in rocks. Reported apatite megacryst/host basalt REE concentration ratios [12], for example, are considerably higher than the equilibrium partition coefficients, which suggest that in this particular case the apatite is actually xenocrystic.A reversal experiment incorporated in our study yielded diffusion profiles of REE in apatite, from which we extracted a REEαCa interdiffusion coefficient of 2–4×10^?14 cm²/s at 1120°C. Extrapolated downward to crustal temperatures, this low value suggests that complete REE equilibrium between felsic partial melts and residual apatite is rarely established.     

Crystallization calculations for a binary melt cooling at constant rates of heat removal: implications for the crystallization of magma bodies

We report on thermodynamic non-equilibrium crystallization calculations for a unit volume of a binary melt subject to a constant, prescribed rate of heat loss. Crystallization histories and crystal size distributions for both melt components were calculated by accounting for the nucleation and growth of crystals. The crystal sizes were found to decrease with increasing rates of heat loss. The crystallization time defined as the time to crystallize 99% of the unit volume also decreased strongly with increasing rates of heat loss up to a critical rate. The critical rate was found to be somewhat smaller than the heat loss rate for the beginning of glass formation. At larger than critical rates, crystallization time increased again and for rates larger than the glass formation rate, crystallization time became infinite. The residual melt composition was found to increasingly deviate from the equilibrium composition with increasing rates of heat loss. But as long as the loss rate was less than the critical rate the crystallization path reverted to the eutectic composition during the final crystallization. For supercritical rates, no such reversion was observed. We compared the critical rate with estimates of the rates of heat loss in magmatic intrusions based on the Stefan solution for a freezing half space. It was found that rates of heat loss should be supercritical at distances of up to 0.5 m from the margin of an intrusion. In this region, non-equilibrium effects are expected to dominate and the texture of the crystallized rock should be characterized by small crystals and by glass. The glass and the crystals should be of non-equilibrium composition. Non-equilibrium effects should be negligible only at distances of more than 5 m from the margin where the rates of heat loss are less than 10⁻² times critical. At these distances, the crystallized rock should have an equigranular texture and an equilibrium composition.     

Amino acid racemization in four species of ostracodes: Taxonomic,environmental, and microstructural controls

Here we quantified the aspartic acid and glutamic acid racemization rates of the four main ostracode species (Herpetocypris reptans, Candona neglecta, Ilyocypris gibba and Cyprideis torosa) present in several Iberian Peninsula localities covering a wide chronological range (ca. 1 Ma to present). At low D/L values (at Asp D/L < 0.40; and Glu D/L = 0.09–0.18), H. reptans racemized at higher rates than C. neglecta, C. torosa and I. gibba. In contrast, for Asp D/L > 0.4 and Glu D/L > 0.18, H. reptans, C. neglecta and C. torosa showed similar racemization rates. I. gibba exhibited the lowest D/L values in old samples (Middle and Lower Pleistocene). We attribute these differences in amino acid racemization rates mainly to variations in valve protein composition. We found that the microstructure of the valves of each species (size, morphology, and arrangement of crystals) differed, but did not appear to change over time (at least for the last ca. 1 Ma). Such differences may also be linked to the type of proteins involved in the respective calcification processes of these organisms. On the basis of our results, and given that other studies have demonstrated that the majority of inter-crystalline proteins are leached early after death (a few centuries or millennia), we propose that the degradation rates of the most resistant inter- and intra-crystalline proteins in each species differ depending on the protein composition of the valves. Although further research is required, we suggest that amino acid racemization in each ostracode species might be related to valve microstructure.     

Zircon saturation revisited: temperature and composition effects in a variety of crustal magma types

Hydrothermal experiments in the temperature range 750–1020°C have defined the saturation behavior of zircon in crustal anatectic melts as a function of both temperature and composition. The results provide a model of zircon solubility given by: In D_Zr^zircon/melt= ?3.80?[0.85(M?1)]+12900/T where D_Zr^zircon/melt is the concentration ratio of Zr in the stoichiometric zircon to that in the melt, T is the absolute temperature, and M is the cation ratio (Na + K + 2Ca)/(Al · Si). This solubility model is based principally upon experiments at 860°, 930°, and 1020°C, but has also been confirmed at temperatures up to 1500°C for M = 1.3. The lowest temperature experiments (750° and 800°C) yielded relatively imprecise, low solubilities, but the measured values (with assigned errors) are nevertheless in agreement with the predictions of the model.For M = 1.3 (a normal peraluminous granite), these results predict zircon solubilities ranging from ～ 100 ppm dissolved Zr at 750°C to 1330 ppm at 1020°C. Thus, in view of the substantial range of bulk Zr concentrations observed in crustal granitoids (～ 50–350 ppm), it is clear that anatectic magmas can show contrasting behavior toward zircon in the source rock. Those melts containing insufficient Zr for saturation in zircon during melting can have achieved that condition only by consuming all zircon in the source. On the other hand, melts with higher Zr contents (appropriate to saturation in zircon) must be regarded as incapable of dissolving additional zircon, whether it be located in the residual rocks or as crystals entrained in the departing melt fraction. This latter possibility is particularly interesting, inasmuch as the inability of a melt to consume zircon means that critical geochemical “indicators” contained in the undissolved zircon (e.g. heavy rare earths, Hf, U, Th, and radiogenic Pb) can equilibrate with the contacting melt only by solid-state diffusion, which may be slow relative to the time scale of the melting event.     

Potassium partitioning into molten iron alloys at high-pressure: Implications for Earth's core

The partition coefficients of potassium, D_K, between molten sanidine, KAlSi₃O₈, and molten roedderite, K₂Mg₅Si₁₂O₃₀, with FeS-rich alloy and pure Fe metal liquids have been investigated in a multi-anvil press, between 5 and 15 GPa, at a temperature of 2173 K, and at an oxygen fugacity between 0.5 and 3 log units below the iron-wüstite (IW) buffer. No pressure dependence of the D_K coefficients in sulphur-free and sulphur-bearing systems was found within the investigated pressure range. We also observed minor effect of the silicate melt composition for an nbo/t (non-bridging oxygen to tetrahedral cation ratio) higher than 0.8 ± 0.4. In contrast, the partitioning of potassium varies strongly with the metallic phase composition, with an increase of K-solubility in the metallic liquid for high sulphur and oxygen contents.We review all available high-pressure data to obtain reliable D_K coefficients for the interaction between molten silicates and Fe-alloy liquids at pressures and temperatures relevant to those of core formation in a terrestrial magma ocean. The dominant controlling parameters appear to be the temperature and the chemical composition of the metallic phase, with D_K coefficients significantly increased with temperature, and with the sulphur and oxygen contents of the Fe-alloy liquid. Our considerations distinguish two extreme cases, with an S-free or S-bearing iron core, which yield K contents of ∼25 or ∼250 ppm, respectively. These two extreme values have very different consequences for thermal budget models of the Earth's core since its formation.     

Pressure dependence of nickel partitioning between forsterite and aluminous silicate melts

Nickel partitioning between forsterite and aluminosilicate melt of fixed bulk composition has been determined at 1300°C to 20 kbar pressure. The value of the forsterite-liquid nickel partition coefficient is lowered from >20 at pressures equal to or less than 15 kbar to <10 at pressures above 15 kbar.Published data indicate that melts on the join Na₂O-Al₂O₃-SiO₂ become depolymerized in the pressure range 10–20 kbar as a result of Al shifting from four-coordination at low pressure to higher coordination as the pressure is increased. This coordination shift results in a decreasing number of bridging oxygens in the melt. It is suggested that the activity coefficient of nickel decreases with this decrease in the number of bridging oxygens. As a result, the nickel partition coefficient for olivine and liquid is lowered.Magma genesis in the upper mantle occurs in the pressure range where the suggested change in aluminum coordination occurs in silicate melts. It is suggested, therefore, that data on nickel partitioning obtained at low pressure are not applicable to calculation of the nickel distribution between crystals and melts during partial melting in the upper mantle. Application of high-pressure experimental data determined here for Al-rich melts to the partial melting process indicates that the melts would contain about twice as much nickel as indicated by the data for the low-pressure experiments. If, as suggested here, the polymerization with pressure is related to the Al content of the melt, the difference in the crystal-liquid partition coefficient for nickel at low and high pressure is reduced with decreasing Al content of the melt. Consequently, the change ofD_Ni^{ol-andesite melt} is greater than that ofD_Ni^{ol-basalt melt}, for example.     

Thermochemical convection in the mantle with oceanic crust recirculation

Basalts of mid-ocean ridges are depleted in incompatible elements that have passed into the continental crust. Basalts of hot spots (oceanic islands and igneous provinces) have a chemical composition close to the primary uniform mantle and are even somewhat enriched in incompatible elements. At present, for explaining the reason for this difference, there are different qualitative schemes of differentiation and mixing of substance in the mantle. In the present work, the results of numerical modeling of the two-component thermochemical convection in the mantle are given. They quantitatively demonstrate with which parameters in the mantle the layers of different chemical composition can remain unchanged. Models with different density contrasts and with variable viscosity are examined. The times of the partial mixing of layers depending on the values of these parameters are calculated. For retaining the stratified mantle for two Ga, the density contrast must be more than 2%. If the layer D″ contains a substance of the primary composition, then, its upper boundary can be the place of origin of the plumes that feed the hot spots of the Earth. The enrichment in the incompatible elements and the variety of the chemical composition of hot spots can be explained by the mixing of the substance of the slowly eroded D″ layer and the oceanic crust accumulated in it.     

Co2+ as a chemical analogue for Fe2+ in high-temperature experiments in basaltic systems

High-temperature experiments on ferromagnesian compositions have been hampered by the rapid absorption of up to 95% of the original iron by platinum and 40% by silver-palladium capsules. Molybdenum or iron capsule materials can decrease or alleviate iron loss, but restrict oxygen fugacities to values near the iron-wustite buffer. Because Co²⁺ is stable at f_O2 =HM and because the solubility of Co in platinum in this range of f_O2 is ～0.05% at temperatures to 1350°C, its use as an analogue for Fe²⁺ is possible. In addition, experiments simulating various Fe²⁺ ratios can be easily performed by choosing appropriate Co²⁺/Fe³⁺ ratios. The cobalt phases produced possess brilliant and distinctive colors which are valuable aids in optical identification of minute phases. The cobalt analogue hypothesis was tested with atmospheric pressure experiments in air on the cobalt analogue of the 1921 Kilauea basalt at three simulated Fe²⁺/Fe³⁺ ratios. The results were compared with those of R.E.T. Hill (1969) for the natural 1921 basalt. The phase relations were the same, with the cobalt system stability fields systematically shifted by about +50°C. Microprobe analysis of olivines and the coexisting glasses indicate that the distribution of Co²⁺ between olivine and melt is independent of temperature and liquid composition. Although the analogue liquid composition differs from the equilibrium composition of the natural system, it may be corrected be employing distribution coefficients (K_D = 0.61 for the Co system; K_D = 0.33 for the Fe system) to closely approximate what the natural system would yield if iron loss did not occur.     

Empirical model of Skeletonema costatum photosynthetic rate,with applications in the San Francisco Bay estuary

An empirical model of Skeletonema costatum photosynthetic rate is developed and fit to measurements of photosynthesis selected from the literature. Because the model acknowledges existence of: 1) a light-temperature interaction (by allowing optimum irradiance to vary with temperature), 2) light inhibition, 3) temperature inhibition, and 4) a salinity effect, it accurately estimates photosynthetic rates measured over a wide range of temperature, light intensity, and salinity. Integration of predicted instantaneous rate of photosynthesis with time and depth yields daily net carbon assimilation (pg C cell^?1 day^?1) in a mixed layer of specified depth, when salinity, temperature, daily irradiance and extinction coefficient are known. The assumption of constant carbon quota (pg C cell^?1) allows for prediction of mean specific growth rate (day^?1), which can be used in numerical models of Skeletonema costatum population dynamics.Application of the model to northern San Francisco Bay clearly demonstrates the limitation of growth by low light availability, and suggests that large population densities of S. costatum observed during summer months are not the result of active growth in the central deep channels (where growth rates are consistently predicted to be negative). But predicted growth rates in the lateral shallows are positive during summer and fall, thus offering a testable hypothesis that shoals are the only sites of active population growth by S. costatum (and perhaps other neritic diatoms) in the northern reach of San Francisco Bay.     

Sensitivity analysis of temperature‐index melt simulations to near‐surface lapse rates and degree‐day factors at Vestari‐Hagafellsjökull,Langjökull,Iceland

The performance of temperature‐index melt models is particularly affected by the choice of near‐surface lapse rate used to determine the sum of positive daily temperatures at different elevations, and by the choice of factor used to relate this sum to the rate of melting. Data from the Langjökull ice cap are used in this study to quantify the influence of lapse‐rate and degree‐day factor variation on temperature‐index melt simulations. The lapse rate was significantly lower during summer than in spring or autumn, as a result of diabatic cooling, reducing boundary‐layer sensitivity to free‐air temperature change. The summer lapse rate was also significantly lower than the saturated adiabatic lapse rate. A sensitivity of approximately 600 mm water equivalent (w.e.) cumulative June–August melt per 0.1 °C 100 m^–1 change in lapse rate was found across a 500‐m altitude range. The sensitivity to a 1‐mm w.e. °C^–1 day^–1 change in degree‐day factors varied more: from approximately 500 mm w.e. cumulative summer melt at low elevation to approximately 200 mm w.e. at high elevation, reflecting the decline in melt rates associated with the greater persistence of snow with increasing altitude. The determination of a degree‐day factor for snow is complicated by the densification of the ageing snowpack, but the application of a parameterization for near‐surface density on the basis of albedo helped account for the development of snow water equivalence. Lapse rate was parameterized as a function of standardized anomalies in 750 hPa reanalysis temperature and significantly improved the simulation of cumulative summer melt compared with models applying the saturated adiabatic lapse rate. Copyright © 2012 John Wiley & Sons, Ltd.     

High-magnesium primary magmas from Haleakala Volcano, east Maui, Hawaii: petrography, nickel, and major-element constraints

For any given volcanic field the compositions of primary melts provide important constraints on models of magmatic processes and volcanic eruptions. In this paper, based on petrography, olivine and bulk rock compositions, two tholeiitic picrites (samples C122 and C123) from Haleakala Volcano, east Maui are evaluated as possible primary melts. Sample C122 (bulk rock MgO = 16.6%) has a high apparent Mg-Fe exchange coefficient, K_D, between olivine phenocrysts and bulk rock (0.6). However, major-elements and Ni mass-balance calculations show that the olivines in C122 are in equilibrium with the residual melt (matrix) after closed-system equilibrium fractionation of 25 wt.% olivine. Therefore, the Mg/Fe ratio, Ca content, and Ni content of C122 are consistent with the hypothesis that the bulk composition of C122 is close to a primary melt formed by partial melting of a mantle containing olivine with composition around Fo₈₉ to Fo₉₁. The uniform composition and small size (mostly 0.2–0.3 mm) of the olivine, and the glass patches in the matrix suggest fast ascent, and rapid cooling at shallow depth for C122. On the contrary, sample C123, which has an apparent K_D (between the most mafic olivine megacrysts and the bulk rock) close to the equilibrium value (0.27), the multiple planar subgrain boundaries in most of the olivine crystals indicate that it may not be a primary melt unless the deformed olivines are generated at magmatic condition as phenocrysts. If the deformed subgrain boundary texture in olivine could indeed be generated at magmatic condition, then the wide compositional range of olivine crystals in C123 (Fo₇₄ to Fo₉₁) suggests multi-stage crystallization over a wide range of cooling temperatures.The compositions of the two picrites, and a differentiated basalt which does not contain xenocrysts suggest that the Haleakala tholeiites are derived from primary melts with at least 16–17 wt.% MgO. Lavas with such high MgO content are rare in Haleakala and other Hawaiian volcanoes; therefore, most Hawaiian tholeiites must have undergone extensive fractionation histories.     

“Amount effect” of water isotopes and quantitative analysis of post‐condensation processes

A numerical model is proposed that describes the interaction between raindrops and water vapour near the planetary boundary layer to explain the “amount effect”. This model relates the intensity to the isotopic composition of precipitation. The model resolves raindrop sizes, and explicitly includes: (1) the isotopic equilibration time of raindrops that is drop‐size dependent; (2) raindrop transit times through the atmosphere; and (3) the evolution of the isotopic composition of vapour at various rain rates. At high rain rate, the precipitation through a layer is less equilibrated with the vapour because the isotopic equilibration time is long compared to the fast transit time, and there is a preponderance of large drops, which take longer to equilibrate. The δ¹⁸O of vapour in the lower atmosphere becomes lower as a result of the interaction with these raindrops of low δ¹⁸O, and the degree of depletion of ¹⁸O is higher when precipitation rates are high. The model reproduces time‐series observations of isotopic composition of precipitation in Japan, and a vapour replenishment rate is inferred by either advection or evaporation of about 5% of the precipitation rate. The results could be the basis for a new parameterization of the isotopic equilibration for different precipitation types and rates in General Circulation Models (GCMs). When the model is applied to a GCM, this parameterization is important for places where precipitation occurs at cold temperatures (<15 °C). Copyright © 2007 John Wiley & Sons, Ltd.     

Hydrodynamic dispersion during absorption of water by soil: 1. Model soil-moisture profiles

Solute mixing during sorption of water is analysed for three model soil-water profiles: a step-function profile, an error function complement profile and a curvilinear profile.An analytical solution to the step-function profile was obtained and it was shown that the plane about which salt dispersion occurs is coincident with the plane of separation which assumes that all of the water initially present is pushed ahead by the infiltrating water. Similar results were obtained for the two other model profiles, using numerical analysis. A simplified approach for calculating these planes, based on the delta-function model, is presented for both horizontal and vertical infiltration.Proof is given that the estimate for the plane about which salt dispersion occurs should be made with λ⁰ (defined in the text) rather than with either λ′_c or λ′_θc (also defined in the text). It was also shown that the solute balance is maintained for all values of the dispersion coefficient for the flux-related boundary condition only.     

Modeling nitrogen–carbon cycling and oxygen consumption in bottom sediments

A model framework is presented for simulating nitrogen and carbon cycling at the sediment–water interface, and predicting oxygen consumption by oxidation reactions inside the sediments. Based on conservation of mass and invoking simplifying assumptions, a coupled system of diffusive–reactive partial differential equations is formulated for two-layer conceptual model of aerobic–anaerobic sediments. Oxidation reactions are modeled as first-order rate processes and nitrate is assumed to be consumed entirely in the anoxic portion of the sediments. The sediments are delineated into a thin oxygenated surface layer whose thickness is equal to the oxygen penetration depth, and a lower, but much thicker anoxic layer. The sediments are separated from the overlying water column by a relatively thin boundary layer through which mass transfer is diffusion controlled. Transient solutions are derived using the method of Laplace transform and Green’s function, which relate pore-water concentrations of the constituents to their concentrations in the bulk water and to the flux of decomposable settling organic matter. Steady-state pore-water concentrations are also obtained including expressions for the extent of methane saturation zone and methane gas flux. A relationship relating the sediment oxygen demand (SOD) to bulk water oxygen is derived using the two-film concept, which in combination with the depth-integrated solutions forms the basis for predicting the extent of oxygen penetration in the sediment. Iterative procedure and simplification thereof are proposed to estimate the extent of methane saturation zone and thickness of the aerobic layer as functions of time. Sensitivity of steady-state solutions to key parameters illustrates sediment processes interactions and synergistic effects. Simulations indicate that for a relatively thin diffusive boundary layer, d, oxygen uptake is limited by biochemical processes inside the sediments, whereas for a thick boundary layer oxygen transfer through the diffusive boundary layer is limiting. The results show an almost linear relationship between steady-state sediment oxygen demand and bulk water oxygen. For small d methane and nitrogen fluxes are sediment controlled, whereas for large d they are controlled by diffusional transfer through the boundary layer. It is shown that the two-layer model solution converges to the one-layer model (anaerobic layer) solution as the thickness of the oxygenated layer approaches zero, and that the transient solutions approach asymptotically their corresponding steady-state solutions.