Effect of spatial variation characteristics on contouring of design storm depth

The ordinary kriging method, a geostatistical interpolation technique, was applied for developing contour maps of design storm depth in northern Taiwan using intensity–duration–frequency (IDF) data. Results of variogram modelling on design storm depths indicate that the design storms can be categorized into two distinct storm types: (i) storms of short duration and high spatial variation and (ii) storms of long duration and less spatial variation. For storms of the first category, the influence range of rainfall depth decreases when the recurrence interval increases, owing to the increasing degree of their spatial independence. However, for storms of the second category, the influence range of rainfall depth does not change significantly and has an average of approximately 72 km. For very extreme events, such as events of short duration and long recurrence interval, we do not recommend usage of the established design storm contours, because most of the interstation distances exceed the influence ranges. Our study concludes that the influence range of the design storm depth is dependent on the design duration and recurrence interval and is a key factor in developing design storm contours. Copyright © 2003 John Wiley & Sons, Ltd.     

SAMPLING REMOTELY SENSED IMAGERY FOR STORAGE,RETRIEVAL, AND RECONSTRUCTION*

A major difficulty in remote sensing is handling the many data from sensors aboard aircraft and satellites. In this paper we identify an optimal procedure for sampling remotely sensed data before their storage or on their retrieval. The procedure depends on spatial correlation in the scene and uses kriging to estimate values that have been lost. An example in which data from an airborne multispectral scanner could be diminished to only about one tenth without serious loss of precision illustrates the method.     

Spatial Variability of Rock Depth in Bangalore Using Geostatistical, Neural Network and Support Vector Machine Models

Geospatial technology is increasing in demand for many applications in geosciences. Spatial variability of the bed/hard rock is vital for many applications in geotechnical and earthquake engineering problems such as design of deep foundations, site amplification, ground response studies, liquefaction, microzonation etc. In this paper, reduced level of rock at Bangalore, India is arrived from the 652 boreholes data in the area covering 220 km². In the context of prediction of reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth, Geostatistical model based on Ordinary Kriging technique, Artificial Neural Network (ANN) and Support Vector Machine (SVM) models have been developed. In Ordinary Kriging, the knowledge of the semi-variogram of the reduced level of rock from 652 points in Bangalore is used to predict the reduced level of rock at any point in the subsurface of the Bangalore, where field measurements are not available. A new type of cross-validation analysis developed proves the robustness of the Ordinary Kriging model. ANN model based on multi layer perceptrons (MLPs) that are trained with Levenberg–Marquardt backpropagation algorithm has been adopted to train the model with 90% of the data available. The SVM is a novel type of learning machine based on statistical learning theory, uses regression technique by introducing loss function has been used to predict the reduced level of rock from a large set of data. In this study, a comparative study of three numerical models to predict reduced level of rock has been presented and discussed.     

Uncertainty as the overlap of alternate conditional distributions

An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator is the overlap of alternate conditional distributions.     

Kriging with imprecise (fuzzy) variograms. I: Theory

Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.     

T -distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1

Histograms of observations from spatial phenomena are often found to be more heavy-tailed than Gaussian distributions, which makes the Gaussian random field model unsuited. A T-distributed random field model with heavy-tailed marginal probability density functions is defined. The model is a generalization of the familiar Student-T distribution, and it may be given a Bayesian interpretation. The increased variability appears cross-realizations, contrary to in-realizations, since all realizations are Gaussian-like with varying variance between realizations. The T-distributed random field model is analytically tractable and the conditional model is developed, which provides algorithms for conditional simulation and prediction, so-called T-kriging. The model compares favourably with most previously defined random field models. The Gaussian random field model appears as a special, limiting case of the T-distributed random field model. The model is particularly useful whenever multiple, sparsely sampled realizations of the random field are available, and is clearly favourable to the Gaussian model in this case. The properties of the T-distributed random field model is demonstrated on well log observations from the Gullfaks field in the North Sea. The predictions correspond to traditional kriging predictions, while the associated prediction variances are more representative, as they are layer specific and include uncertainty caused by using variance estimates.     

Spatial and temporal variability of pore‐water pressures in residual soil slopes in a tropical climate

It is critical to understand and quantify the temporal and spatial variability in hillslope hydrological data in order to advance hillslope hydrological studies, evaluate distributed parameter hydrological models, analyse variability in hydrological response of slopes and design efficient field data sampling networks. The spatial and temporal variability of field‐measured pore‐water pressures in three residual soil slopes in Singapore was investigated using geostatistical methods. Parameters of the semivariograms, namely the range, sill and nugget effect, revealed interesting insights into the spatial structure of the temporal situation of pore‐water pressures in the slopes. While informative, mean estimates have been shown to be inadequate for modelling purposes, indicator semivariograms together with mean prediction by kriging provide a better form of model input. Results also indicate that significant temporal and spatial variability in pore‐water pressures exists in the slope profile and thereby induces variability in hydrological response of the slope. Spatial and temporal variability in pore‐water pressure decreases with increasing soil depth. The variability decreases during wet conditions as the slope approaches near saturation and the variability increases with high matric suction development following rainfall periods. Variability in pore‐water pressures is greatest at shallow depths and near the slope crest and is strongly influenced by the combined action of microclimate, vegetation and soil properties. Copyright © 2002 John Wiley & Sons, Ltd.     

Combining ordination techniques and geostatistics to determine the patterns of diatom distributions at Lake Lama, Central Siberia

The patterns of spatial variation of diatom assemblages from surface sediments in Lake Lama were quantified using a combined approach of ordination and geostatistics. The aims were (i) to estimate the amount of variation between diatom assemblages within the lake, (ii) to model the spatial variability of the diatom assemblages and their diversity, and (iii) to map the diatom distributions in the lake. A correspondence analysis (CA) separated the diatom assemblages into a planktonic and a periphytic group. Rheophilic taxa were found within the periphytic group. Variogram analysis showed that only the sample scores of the first CA axis and the Shannon diversity index were spatially structured. The range of spatial correlation was estimated to be 55 km for both variables. The diversity and, to a lesser extent, the sample scores had considerable small-scale variability of about 20 and 3%, respectively. Estimates of the first component of the CA and the Shannon index were derived using block-kriging. The maps of the estimates provided a basis for partitioning Lake Lama according to the spatial structures into an eastern and a western basin, a north–south connection between the basins, and a north–south directed tip at the far eastern end. It was shown that variation in diatom assemblages is mainly spatially structured at the catchment scale and that there is a considerable amount of variation at smaller scales. According to the modeled spatial distribution, the assemblages are most likely affected by the lake size, morphology, and the water and nutrient input introduced by rivers. This has to be taken into account when paleolimnological interpretations are drawn from records of complex lake systems like Lake Lama.     

Magnetic properties of a freshly fallen LL ordinary chondrite: the Bensour meteorite

A comprehensive rock magnetic, magnetic anisotropy and paleomagnetic study has been undertaken in the brecciated LL6 Bensour ordinary chondrite, a few months only after its fall on Earth. Microscopic observations and electronic microprobe analyses indicate the presence of Ni-rich taenite, tetrataenite and rare Co-rich kamacite. Tetrataenite is the main carrier of remanence. Magnetization and anisotropy measurements were performed on mutually oriented 125 mm³ sub-samples. A very strong coherent susceptibility and remanence anisotropy is evidenced and interpreted as due to the large impact responsible for the post-metamorphic compaction of this brecciated material and disruption of the parent body. We show that the acquisition of remanent magnetization postdates metamorphism on the parent body and predates the entering of the meteorite in Earth’s atmosphere. Three components of magnetization could be isolated. A soft coherent component is closely related to the anisotropy of the meteorite and is interpreted as a shock remanent magnetization acquired during the same large impact on the parent body. Two harder components show random directions at a few mm scale. This randomness is attributed either to the formation mechanism of tetrataenite or to post-metamorphic brecciation. All components are likely acquired in very low (≈μT) to null ambient magnetic field, as demonstrated by comparison with demagnetization behavior of isothermal remanent magnetization. Two other LL6 meteorites, Kilabo and St-Mesmin, have also been studied for comparison with Bensour.