Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

Sampling Fauna in Stream Sediments as well as Groundwater Using One Net Sampler

Groundwater bores act as traps. Net samplers are regularly used for sampling this type of trap for fauna. To enable direct comparisons of faunal communities in groundwater bores and stream sediments, stream sediment tubes were built similar to groundwater bores and were sampled with net samplers for fauna. These stream sediment tubes consisted of a tube anchored in the stream sediment, also called interstitial space. To test the efficacy of this trap method in stream sediments, it was compared to another type of trap, Hahn's trap. Faunal communities sampled by a net in the stream sediment tubes did not differ hugely from fauna in Hahn's trap samples. Physical and chemical factors of sampled water in both the stream sediment tubes, the surrounding interstitial sediments and the second type of traps, Hahn's traps, showed that water in both the tubes and Hahn's traps was closely related to interstitial water. The net sampler is inexpensive and easy to handle. It is suggested that sampling stream tubes with nets may be an appropriate method for long‐term monitoring studies.     

Modelling transverse dunes

Transverse dunes appear in regions of mainly unidirectional wind and high sand availability. A dune model is extended to two‐dimensional calculation of the shear stress. It is applied to simulate dynamics and morphology of three‐dimensional transverse dunes. In the simulations they seem to reach translational invariance and do not stop growing. Hence, simulations of two‐dimensional dune ?elds have been performed. Characteristic laws were found for the time evolution of transverse dunes. Bagnold's law of the dune velocity is modi?ed and reproduced. The interaction between transverse dunes led to the interesting conclusion that small dunes can travel over bigger ones. Copyright © 2004 John Wiley & Sons, Ltd.     

Kinetic energy–rainfall intensity relationship for Central Cebu, Philippines for soil erosion studies

In the study of soil erosion, specifically on detachment of soil particles by raindrop impact, kinetic energy is a commonly suggested indicator of the raindrop's ability to detach soil particles from the soil mass. Since direct measurement of kinetic energy requires sophisticated and costly instruments, the alternative approach is to estimate it from rainfall intensity. The present study aims at establishing a relationship between rainfall intensity and kinetic energy for rainfalls in Central Cebu, Philippines as a preface of a wider regional investigation.

Drop size distributions of rainfalls were measured using the disdrometer RD-80. There are two forms of kinetic energy considered here. One is kinetic energy per unit area per unit time (KE_R, J m⁻² h⁻¹) and the other is kinetic energy per unit area per unit depth (KE, J m⁻² mm⁻¹). Relationships between kinetic energy per unit area per unit time (KE_R) and rainfall intensity (I) were obtained using linear and power relations. The exponential model and the logarithmic model were fitted to the KE–I data to obtain corresponding relationships between kinetic energy per unit area per unit depth of rainfall (KE) and rainfall intensity (I). The equation obtained from the exponential model produced smaller standard error of estimates than the logarithmic model.     

Denitrification rates measured along a salinity gradient in the eutrophic Neuse River estuary, North Carolina, USA

Denitrification rates along a salinity gradient in the eutrophic Neuse River Estuary, North Carolina, were quantified using membrane inlet mass spectrometry (MIMS) within short-term batch incubations. Denitrification rates within the system were highly variable, ranging from 0 to 275 μmol N m⁻² h⁻¹. Intrasite variability increased with salinity, but no significant differences were observed across the salinity gradient. Denitrification rates were positively correlated with sediment oxygen demand at the upstream sampling site where sediment organic carbon levels were lowest. This relationship was not observed in the more saline sampling sites. Denitrification rates were highest during winter. On an annual basis, denitrification accounted for 26% of the dissolved inorganic nitrogen and 12% of the total nitrogen supplied to the system.     

Tetrahedral Plots of the Phase Relations for Basalts

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.     

Importance of climate,forest fires and human population size in the Holocene boreal forest composition change in northern Europe

The relative importance of climate, forest fires and human population size on long‐term boreal forest composition were statistically investigated at regional and local scales in Fennoscandia. We employ pollen data from lakes, reflecting regional vegetation, and small forest hollows, reflecting local vegetation, from Russia, Finland and Sweden to reconstruct the long‐term forest composition. As potential drivers of the Holocene forest dynamics we consider climate, generated from a climate model and oxygen isotope data, past forest fires generated from sedimentary charcoal data and human population size derived from radiocarbon dated archaeological findings. We apply the statistical method of variation partitioning to assess the relative importance of these environmental variables on long‐term boreal forest composition. The results show that climate is the main driver of the changes in Holocene boreal forest composition at the regional scale. However, at the local scale the role of climate is relatively small. In general, the importance of forest fires is low both at regional and local scales. The fact that both climate and forest fires explain relatively small proportions of variation in long‐term boreal vegetation in small forest hollow records demonstrates the complexity of factors affecting stand‐scale forest dynamics. The relative importance of human population size was low in both the prehistorical and the historical time periods. However, this is the first time that this type of data has been used to statistically assess the importance of human population size on boreal vegetation and the spatial representativeness of the data may cause bias to the analysis.