Ice‐cover variability on shallow lakes at high latitudes: model simulations and observations

A one‐dimensional thermodynamic model for simulating lake‐ice phenology is presented and evaluated. The model can be driven with observed daily or hourly atmospheric forcing of air temperature, relative humidity, wind speed, cloud amount and snowfall. In addition to computing the energy balance components, key model output includes the temperature profile at an arbitrary number of levels within the ice/snow (or the water temperature if there is no ice) and ice thickness (clear ice and snow‐ice) on a daily basis, as well as freeze‐up and break‐up dates. The lake‐ice model is used to simulate ice‐growth processes on shallow lakes in arctic, sub‐arctic, and high‐boreal forest environments. Model output is compared with field and remote sensing observations gathered over several ice seasons. Simulated ice thickness, including snow‐ice formation, compares favourably with field measurements. Ice‐on and ice‐off dates are also well simulated when compared with field and satellite observations, with a mean absolute difference of 2 days. Model simulations and observations illustrate the key role that snow cover plays on the seasonal evolution of ice thickness and the timing of spring break‐up. It is also shown that lake morphometry, depth in particular, is a determinant of ice‐off dates for shallow lakes at high latitudes. Copyright © 2003 John Wiley & Sons, Ltd.     

Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

Relationship between footwall composition,crustal contamination,and fluid–rock interaction in the Platreef,Bushveld Complex,South Africa

In the northern limb of the 2.06-Ga Bushveld Complex, the Platreef is a platinum group elements (PGE)-, Cu-, and Ni-mineralized zone of pyroxenite that developed at the intrusion margin. From north to south, the footwall rocks of the Platreef change from Archaean granite to dolomite, hornfels, and quartzite. Where the footwall is granite, the Sr-isotope system is more strongly perturbed than where the footwall is Sr-poor dolomite, in which samples show an approximate isochron relationship. The Nd-isotope system for samples of pyroxenite and hanging wall norite shows an approximate isochron relationship with an implied age of 2.17 ± 0.2 Ga and initial Nd-isotope ratio of 0.5095. Assuming an age of 2.06 Ga, the ɛNd values range from −6.2 to −9.6 (ave. −7.8, n = 17) and on average are slightly more negative than the Main Zone of the Bushveld. These data are consistent with local contamination of an already contaminated magma of Main Zone composition. The similarity in isotope composition between the Platreef pyroxenites and the hanging wall norites suggests a common origin. Where the country rock is dolomite, the Platreef has generally higher plagioclase and pyroxene δ ¹⁸O values, and this indicates assimilation of the immediate footwall. Throughout the Platreef, there is considerable petrographic evidence for sub-solidus interaction with fluids, and the Δ _{plagioclase–pyroxene} values range from −2 to +6, which indicates interaction at both high and low temperatures. Whole-rock and mineral δD values suggest that the Platreef interacted with both magmatic and meteoric water, and the lack of disturbance to the Sr-isotope system suggests that fluid–rock interaction took place soon after emplacement. Where the footwall is granite, less negative δD values suggest a greater involvement of meteoric water. Consistently higher values of Δ _{plagioclase–pyroxene} in the Platreef pyroxenites and hanging wall norites in contact with dolomite suggest prolonged interaction with CO₂-rich fluid derived from decarbonation of the footwall rocks. The overprint of post crystallization fluid–rock interaction is the probable cause of the previously documented lack of correlation between PGE and sulfide content on the small scale. The Platreef in contact with dolomite is the focus of the highest PGE grades, and this suggests that dolomite contamination played a role in PGE concentration and deposition, but the exact link remains obscure. It is a possibility that the CO₂ produced by decarbonation of assimilated dolomite enhanced the process of PGE scavenging by sulfide precipitation.     

Controls on porphyroblast size along a regional metamorphic field gradient

Garnet-bearing schists from the Waterville Formation of south-central Maine provide an opportunity to examine the factors governing porphyroblast size over a range of metamorphic grade. Three-dimensional sizes and locations for all garnet porphyroblasts were determined for three samples along the metamorphic field gradient spanning lowest garnet through sillimanite grade, using high-resolution X-ray computed tomography. Comparison of crystal size distributions to previous data sets obtained by stereological methods for the same samples reveals significant differences in mode, mean, and shape of the distributions. Quantitative textural analysis shows that the garnets in each rock crystallized in a diffusion-controlled nucleation and growth regime. In contrast to the typical observation of a correlation between porphyroblast size and position along a metamorphic field gradient, porphyroblast size of the lowest-grade specimen is intermediate between the high- and middle-grade specimens’ sizes. Mean porphyroblast size does not correlate with peak temperatures from garnet-biotite Fe-Mg exchange thermometry, nor is post-crystallization annealing (Ostwald Ripening) required to produce the observed textures, as was previously proposed for these rocks. Robust pseudosection calculations fail to reproduce the observed garnet core compositions for two specimens, suggesting that these calc-pelites experienced metasomatism. For each of these two specimens, Monte Carlo calculations suggest potential pre-metasomatism bulk compositions that replicate garnet core compositions. Pseudosection analyses allow the estimation of the critical temperatures for garnet growth: ∼481, ∼477, and ∼485°C for the lowest-garnet-zone, middle-garnet-zone, and sillimanite-zone specimens, respectively. Porphyroblast size appears to be determined in this case by a combination of the heating rate during garnet crystallization, the critical temperature for the garnet-forming reaction and the kinetics of nucleation. Numerical simulations of thermally accelerated, diffusion-controlled nucleation, and growth for the three samples closely match measured crystal size distributions. These observations and simulations suggest that previous hypotheses linking the garnet size primarily to the temperature at the onset of porphyroblast nucleation can only partially explain the observed textures. Also important in determining porphyroblast size are the heating rate and the distribution of favorable nucleation sites.     

In situ strength measurements on natural upper-mantle minerals

Using in situ strength measurements at pressures up to 10 GPa and at room temperature, 400, 600, and 700°C, we examined rheological properties of olivine, orthopyroxene, and chromian-spinel contained in a mantle-derived xenolith. Mineral strengths were estimated using widths of X-ray diffraction peaks as a function of pressure, temperature, and time. Differential stresses of all minerals increase with increasing pressure, but they decrease with increasing temperature because of elastic strain on compression and stress relaxation during heating. During compression at room temperature, all minerals deform plastically at differential stress of 4–6 GPa. During subsequent heating, thermally induced yielding is observed in olivine at 600°C. Neither orthopyroxene nor spinel shows complete stress relaxation, but both retain some stress even at 700°C. The strength of the minerals decreases in the order of chromian-spinel ≈ orthopyroxene > olivine for these conditions. This order of strength is consistent with the residual pressure of fluid inclusions in mantle xenoliths.     

Freely floating-body simulation by a 2D fully nonlinear numerical wave tank

Nonlinear interactions between large waves and freely floating bodies are investigated by a 2D fully nonlinear numerical wave tank (NWT). The fully nonlinear 2D NWT is developed based on the potential theory, MEL/material-node time-marching approach, and boundary element method (BEM). A robust and stable 4th-order Runge–Kutta fully updated time-integration scheme is used with regriding (every time step) and smoothing (every five steps). A special φ_n-η type numerical beach on the free surface is developed to minimize wave reflection from end-wall and wave maker. The acceleration-potential formulation and direct mode-decomposition method are used for calculating the time derivative of velocity potential. The indirect mode-decomposition method is also independently developed for cross-checking. The present fully nonlinear simulations for a 2D freely floating barge are compared with the corresponding linear results, Nojiri and Murayama’s (Trans. West-Jpn. Soc. Nav. Archit. 51 (1975)) experimental results, and Tanizawa and Minami’s (Abstract for the 6th Symposium on Nonlinear and Free-surface Flow, 1998) fully nonlinear simulation results. It is shown that the fully nonlinear results converge to the corresponding linear results as incident wave heights decrease. A noticeable discrepancy between linear and fully nonlinear simulations is observed near the resonance area, where the second and third harmonic sway forces are even bigger than the first harmonic component causing highly nonlinear features in sway time series. The surprisingly large second harmonic heave forces in short waves are also successfully reproduced. The fully updated time-marching scheme is found to be much more robust than the frozen-coefficient method in fully nonlinear simulations with floating bodies. To compare the role of free-surface and body-surface nonlinearities, the body-nonlinear-only case with linearized free-surface condition was separately developed and simulated.     

Constraining the origin and evolution of confined turbidite systems: southern Cretan margin,Eastern Mediterranean Sea (34°30–36°N)

Bathymetric, 9.5-kHz long-range sidescan sonar (OKEAN), seismic reflection and sediment-core data are used in the analysis of two tectonic troughs south of Crete, Eastern Mediterranean Sea. Here, up to 1.2 s two-way travel time (TWTT) of strata have accumulated since the Middle Miocene in association with extension in the South Aegean region. The study area comprises >100-km- long by >25-km-wide basins filled by sediments subdivided into two seismic units: (1) an upper Unit 1 deposited in sub-basins which follow the present-day configuration of the southern Cretan margin; (2) a basal Unit 2, more than 500 ms (TWTT) thick, accumulated in deeper half-graben/grabens distinct from the present-day depocentres. Both units overlap a locally stratified Unit 3 comprising the pre-Neogene core complex of Crete and Gavdos. In this work, the interpreted seismic units are correlated with the onshore stratigraphy, demonstrating that denudation processes occurring on Crete and Gavdos in response to major tectonic events have been responsible for high sedimentation rates along the proximal southern Cretan margin. Consequently, topographically confined sedimentary units have been deposited south of Crete in the last 12 Ma, including turbidites and other mass-flow deposits fed by evolving transverse and axial channel systems. Surface processes controlling facies distribution include the direct inflow of sediment from alluvial-fan systems and incising mountain rivers onto the Cretan slope, where significant sediment instability processes occur at present. In this setting, seismic profiles reveal eight different types of stratigraphic contacts on basin-margin highs, and basinal areas show evidence of halokinesis and/or fluid escape. The acquired data also show that significant changes to the margin’s configuration occurred in association with the post-Alpine tectonic and eustatic episodes affecting the Eastern Mediterranean.     

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

Sedimentology of a subtidal,tide-dominated sand body in the Yellow Sea,southwest Korea

Odanam Satoe, a subtidal, tide-dominated sand body in the Yellow Sea, Korea, is linear in plan and asymmetrical in cross-section. It consists of fine- to medium-grained, well-sorted subangular sand. Bedforms consist of high-amplitude (1–2 m) sandwaves on the lower flanks of the gentler-sloping bar surface, and medium-amplitude (0.5-1 m) sandwaves on the sand body trough adjoining the steeper face, the bar crest and shallower parts of the gently sloping bar surface. Bedforms are absent on the relatively steeper bar surface, which is characterized by 2° slopes. Bedform orientation on the gentler slope is oblique by 30° to the bar crest, parallel to the sand-body crest on the crest itself, and opposite to the steeper sand-body face in the trough below the steeper slope of the bar.Bottom current velocity data show that tidal currents are semi-rotary with a flood time—velocity asymmetry over the gentler slope, and ebb time—velocity asymmetry over the steeper slope during most of the tidal cycle. Tidal-current flow parallels bar elongation over the steeper slope, whereas over the gentler slope, tidal-current flow is directed at 30° to the bar crest and changes to normal to the crest one hour prior to low tide. Bedform orientation mapped with side-scan sonar shows agreement with these flow directions.Sand dispersal around the sand body is controlled by time—velocity asymmetry and partial rotary flow directions of tidal currents. This circulation causes not only a trapezoidal mode of grain dispersal, but also westerly migration of the sand body documented from comparative bathymetric surveys in 1964 and 1980.     

Geomorphological evidence for upslope canyon-forming processes on the northern KwaZulu-Natal shelf,SW Indian Ocean,South Africa

A geomorphological and statistical analysis of slope canyons from the northern KwaZulu-Natal continental margin is documented and compared with submarine canyons from the Atlantic margin of the USA. The northern KwaZulu-Natal margin is characterized by increasing upslope relief, concave slope-gradient profiles and features related to upslope growth of the canyon forms. Discounting slope-gradient profile, this morphology is strikingly similar to canyon systems of the New Jersey slope. Several phases of canyon incision indicate that downslope erosion is also an important factor in the evolution of the northern KwaZulu-Natal canyon systems. Despite the strong similarities between the northern KwaZulu-Natal and New Jersey slope-canyon systems, key differences are evident: (1) the concavity of the northern KwaZulu-Natal slope, contrasting with the ∼linear New Jersey slope; (2) the relative isolation of the northern KwaZulu-Natal canyons, rather than the dense clustering of the New Jersey canyons; and (3) the absence of strongly shelf-breaching canyons along the northern KwaZulu-Natal margin. In comparison with the New Jersey margin, we surmise a more youthful stage of canyon evolution, a result of either the canyons themselves being younger or the formative processes being less active. Less complicated patterns of erosion resulting from reduced sediment availability have developed in northern KwaZulu-Natal. The reduction in slope concavity on the New Jersey margin may be the result of grading of the upper slope by intensive headward erosion, a process more subdued—or less evident—on the KwaZulu-Natal margin.