Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Using numerical modelling to evaluate tsunami hazard near the Kuril Island

A sequence of computer experiments is used to study questions concerning the tsunami problem as a quantitative estimate of tsunami danger, detailed geographical tsunami classification, determination of the parameters of critical tsunami waves, and the conditions of their development. We call a wave critical, if its impact on the coast is most hazardous.Using the Middle Kuril Island as an example, we present the results of a computer experiment which includes determining the wavefields on the shelf and estimating the effects connected with the deep-water Bussol and Diana Straits.Numerical simulation of tsunami waves of different sources permits the assessment of the extent of tsunami danger in different areas of the coastal zone of Simushir Island, depending on the location of the focus zone and their geometry.The major singularities of the wavefield arise in the zones of the deep-water straits. The distribution of the amplification factors is determined by both the global parameters of the wavefields and the local properties of individual harbours. The results obtained for a particular harbour in the northern part of Simushir Island, formed the basis for the quantitative estimate of tsunami danger for this area.     

塔里木河源区冰川系统变化趋势预测

塔里木河源区是我国冰川分布最集中的地区之一,总面积达17 745.51 km2,占全国冰川总面积的30%;同时本区又属于我国升温幅度最大的地区之一。应用冰川系统变化的功能模型,对塔里木河源区冰川系统在本世纪对气候变化的趋势进行预测。结果表明:到2050年,如气温比1961~1990年高出1.9~2.3℃,本区冰川面积将减少4%~6%,冰川径流将增加22%~34%,零平衡线将上升62~94 m;如此升温率持续到本世纪末,则本区冰川面积将减少10%~16%,冰川径流将会回落,但仍比本世纪初多11%~13%,零平衡线将上升156~233 m。     

Hydrogeology of thermal waters in Viterbo area, central Italy

A conceptual hydrogeological model of the Viterbo thermal area (central Italy) has been developed. Though numerous studies have been conducted on its geological, geochemical and geothermal features, there is no generalized picture defining the origin and yield of the hydrothermal system. These latter aspects have therefore become the objectives of this research, which is based on new hydrogeological and geochemical investigations. The geological setting results in the coexistence of overlapped interacting aquifers. The shallow volcanic aquifer, characterized by fresh waters, is fed from the area around the Cimini Mountains and is limited at its base by the semiconfining marly-calcareous-arenaceous complex and low-permeability clays. To the west of Viterbo, vertical upflows of thermal waters of the sulphate-chloride-alkaline-earth type with higher gas contents, are due to the locally uplifted carbonate reservoir, the reduced thickness of the semiconfining layer and the high local geothermal gradient. The hot waters (30–60°C) are the result of deep circulation within the carbonate rocks (0.5–1.8 km) and have the same recharge area as the volcanic aquifer. The upward flow in the Viterbo thermal area is at least 0.1 m³/s. This flow feeds springs and deep wells, also recharging the volcanic aquifer from below.     

New Generation of Probabilistic Seismic Hazard Assessment for the Area Cologne/Aachen Considering the Uncertainties of the Input Data

A new earthquake catalogue for central, northern and northwestern Europe with unified M_w magnitudes, in part derived from chi-square maximum likelihood regressions, forms the basis for seismic hazard calculations for the Lower Rhine Embayment. Uncertainties in the various input parameters are introduced, a detailed seismic zonation is performed and a recently developed technique for maximum expected magnitude estimation is adopted and quantified. Applying the logic tree algorithm, resulting hazard values with error estimates are obtained as fractile curves (median, 16% and 84% fractiles and mean) plotted for pga (peak ground acceleration; median values for Cologne 0.7 and 1.2 m/s² for probabilities of exceedence of 10% and 2%, respectively, in 50 years), 0.4 s (0.8 and 1.5 m/s²) and 1.0 s (0.3 and 0.5 m/s²) pseudoacclerations, and intensity (I₀ = 6.5 and 7.2). For the ground motion parameters, rock foundation is assumed. For the area near Cologne and Aachen, maps show the median and 84% fractile hazard for 2% probability of exceedence in 50 years based on pga (maximum median value about 1.5 m/s²), and 0.4 s (>2 m/s²) and 1.0 s (about 0.8 m/s²) pseudoaccelerations, all for rock. The pga 84% fractile map also has a maximum value above 2 m/s² and shows similarities with the median map for 0.4 s. In all maps, the maximum values fall within the area 6.2–6.3° E and 50.8–50.9° N, i.e., east of Aachen.     

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.     

Projecting land-use change processes in the Sierra Norte of Oaxaca, Mexico

The objective of study was to explore short-term trends of processes that determine land-use change in Sierra Norte of Oaxaca (SNO), Mexico. Land use and land cover changes (LULCC) were estimated in a complex mosaic of vegetation in the SNO from 1980 to 2000, and projected them to 2020 through a Markovian model. SNO is highly vulnerable to climatic change according to a 2050 GCM scenario. However, 3% annual rate of tropical and temperate forest deforestation from agriculture and livestock encroachment, suggest the threat from land-use change is higher than that from climatic change for this study site. Productive land-use strategies are needed to reduce such high deforestation rates for tropical regions. Controlling deforestation would also reduce short-term effects of CO₂ emissions to the atmosphere. Because of the necessity to evaluate anthropogenic ecosystem changes, it is imperative to separate short-term influences such as deforestation, from long-term influences such as climatic change.     

Centennial to millennial geomagnetic secular variation

A time-varying spherical harmonic model of the palaeomagnetic field for 0–7 ka is used to investigate large-scale global geomagnetic secular variation on centennial to millennial scales. We study dipole moment evolution over the past 7 kyr, and estimate its rate of change using the Gauss coefficients of degree 1 (dipole coefficients) from the CALS7K.2 field model and by two alternative methods that confirm the robustness of the predicted variations. All methods show substantial dipole moment variation on timescales ranging from centennial to millennial. The dipole moment from CALS7K.2 has the best resolution and is able to resolve the general decrease in dipole moment seen in historical observations since about 1830. The currently observed rate of dipole decay is underestimated by CALS7K.2, but is still not extraordinarily strong in comparison to the rates of change shown by the model over the whole 7 kyr interval. Truly continuous phases of dipole decrease or increase are decadal to centennial in length rather than longer-term features. The general large-scale secular variation shows substantial changes in power in higher spherical harmonic degrees on similar timescales to the dipole. Comparisons are made between statistical variations calculated directly from CALS7K.2 and longer-term palaeosecular variation models: CALS7K.2 has lower overall variance in the dipole and quadrupole terms, but exhibits an imbalance between dispersion in   g ¹₂  and   h ¹₂  , suggestive of long-term non-zonal structure in the secular variations.     

Effects of fracture lineaments and in-situ rock stresses on groundwater flow in hard rocks: a case study from Sunnfjord, western Norway

Systematic field mapping of fracture lineaments observed on aerial photographs shows that almost all of these structures are positively correlated with zones of high macroscopic and mesoscopic fracture frequencies compared with the surroundings. The lineaments are subdivided into zones with different characteristics: (1) a central zone with fault rocks, high fracture frequency and connectivity but commonly with mineral sealed fractures, and (2) a damage zone divided into a proximal zone with a high fracture frequency of lineament parallel, non-mineralized and interconnected fractures, grading into a distal zone with lower fracture frequencies and which is transitional to the surrounding areas with general background fracturing. To examine the possible relations between lineament architecture and in-situ rock stress on groundwater flow, the geological fieldwork was followed up by in-situ stress measurements and test boreholes at selected sites. Geophysical well logging added valuable information about fracture distribution and fracture flow at depths. Based on the studies of in-situ stresses as well as the lineaments and associated fracture systems presented above, two working hypotheses for groundwater flow were formulated: (i) In areas with a general background fracturing and in the distal zone of lineaments, groundwater flow will mainly occur along fractures parallel with the largest in-situ rock stress, unless fractures are critically loaded or reactivated as shear fractures at angles around 30° to σ_H; (ii) In the influence area of lineaments, the largest potential for groundwater abstraction is in the proximal zone, where there is a high fracture frequency and connectivity with negligible fracture fillings. The testing of the two hypotheses does not give a clear and unequivocal answer in support of the two assumptions about groundwater flow in the study area. But most of the observed data are in agreement with the predictions from the models, and can be explained by the action of the present stress field on pre-existing fractures.