Implementing quality control on a random number stream to improve a stochastic weather generator

For decades, stochastic modellers have used computerized random number generators to produce random numeric sequences fitting a specified statistical distribution. Unfortunately, none of the random number generators we tested satisfactorily produced the target distribution. The result is generated distributions whose mean even diverges from the mean used to generate them, regardless of the length of run. Non‐uniform distributions from short sequences of random numbers are a major problem in stochastic climate generation, because truly uniform distributions are required to produce the intended climate parameter distributions. In order to ensure generation of a representative climate with the stochastic weather generator CLIGEN within a 30‐year run, we tested the climate output resulting from various random number generators. The resulting distributions of climate parameters showed significant departures from the target distributions in all cases. We traced this failure back to the uniform random number generators themselves. This paper proposes a quality control approach to select only those numbers that conform to the expected distribution being retained for subsequent use. The approach is based on goodness‐of‐fit analysis applied to the random numbers generated. Normally distributed deviates are further tested with confidence interval tests on their means and standard deviations. The positive effect of the new approach on the climate characteristics generated and the subsequent deterministic process‐based hydrology and soil erosion modelling are illustrated for four climatologically diverse sites. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluating the effect of non-uniform and deficient irrigation—Part I

A method for evaluating the effect of non-uniform and deficient irrigation is presented. The method is based on a deterministic mathematical model that evaluates the effect of the soil water fluctuation in the root zone during the irrigation season on the crop yield.The problem is viewed in conjunction with the management strategy of irrigation water application under the assumption that only shortage of water causes a reduction in yield. The parameters describing the deficit zone of the application pattern, the soil-crop-atmosphere system and the crop response are incorporated in the model. Crop yield predictions are made through the relative water use and a multiplicative and an additive yield functions.A numerical example is used to illustrate the use of the model in sprinkler irrigation practice. The results agree well with those derived from the mathematical model evaluating the irrigation regime and the yield on each square of the irrigated area separately.     

A method to solve the paleotectonic analysis problem

The method to determine the rates of tectonic movements is based on the use of dynamic models of sedimentary basins. A standard dataset should be provided as input information: the present-day position of sedimentary layer interfaces (chronostratigraphic boundaries), land surface and basement, the layer ages, and the uncertainty limits within which the depth of sedimentation of each layer may have differed. In terms of dynamic models, the paleotectonic analysis problem is reduced to the determination of such tectonic rates that, at prescribed reference times, the model surface topography within the assumed limits would be constrained. At the final moment, the interfaces would be brought into agreement with the contemporary geologic cross-section. The analysis the problem of tectonic rates determination has shown that it has no unique solution. One of the ways to obtain the unique solution is to seek it within a prescribed class of functions, for example, the Fourier series. This method differs from the paleotectonic analysis methodology in that it treats the tectonic rates of motion as functions of time and spatial variables. Under certain conditions, it proves feasible to reconstruct the rates of tectonic movements not only within the time intervals represented in the deposited strata, but within periods of erosion as well. It also is possible to take into account the deformation-induced changes in thickness of the layers. The method's application is illustrated with an example of the Terek-Caspian Trough. As follows from the computation, the tectonic movements since the Middle Jurassic may be presented as a sum of two components: an overall slowing-down subsidence whose rate is proportional to the square root of the age, and local movements which follow a regular oscillatory time pattern with a period of 60–70 MY. The character of the local movements is such that the profile appears to break into a northern and southern segment. When one was being uplifted, the other segment was sinking, andvice versa. These two segments are separated by a deep-seated fault. This may have been a result of an external compression on the trough.     

Multifractal and Chaotic Analysis of Vrancea (Romania) Intermediate-depth Earthquakes: Investigation of the Temporal Distribution of Events

The Vrancea seismic region contains an isolated cluster of events beneath the Carpathian Arc Bend in Romania, dipping to about 200 km depth. Seismic activity mainly occurs at intermediate depths (h > 60 km). The main goal of the paper is to perform an in-depth, complex analysis of the occurrence times of these intermediate-depth events. We also try to show the versatility of the methods used to characterize different aspects of the seismicity evolution and to offer a user-friendly software toolbox to do most of the related computations. The earthquake catalog used in this study spans from 1974 to 2002 and includes only the intermediate-depth events. In the first part of the paper, we analyze the multifractal characteristics of the temporal distribution of earthquakes. The study reveals two distinct scaling regimes. At small scales we found a clear nonhomogeneous, multifractal pattern, while at large scales the temporal distribution of events shows a monofractal, and close to Poissonian (random), behavior. The multifractal behavior at small scales (minutes-hours) is shown to be clearly an effect of the short aftershock sequences that occurred after some major Vrancea earthquakes. In the second part of the paper we analyze whether our temporal series shows a persistent (or anti-persistent) long-term behavior, by using the Detrended Fluctuation Analysis (DFA) method. The results suggest that the analyzed temporal series of Vrancea earthquakes is a non-correlated process. In part three of the paper we seek to determine whether the dynamics of our earthquake system (described by the occurrence time of Vrancea earthquakes) is deterministically chaotic, deriving from a rather simple evolution law, or whether it is stochastic and is generated by a system that possesses many degrees of freedom. The results suggest that our signal is stochastic (probably does not possess an attractor). The limited time-span of the catalog and the analysis performed in this paper cannot rule out the emergence of an interesting, quasi-deterministic and low-dimensional structure in the case of major Vrancea earthquakes.Acknowledgement One of the authors (BE) is grateful to the Japanese Ministry of Education for providing him a Monbusho scholarship for studying in DPRI, Kyoto University. We thank Z.R. Struzik, M Holschneider, J. Mori and D. Kaplan for their useful comments, and acknowledge the support of the staff of DPRI, Kyoto University and the National Inst. for Earth Physics, Bucharest. We thank the two reviewers, M.B. Geilikman and M. Anghel, for their useful suggestions which improved the quality of this work.     

Coherence of dispersed synthetic strong earthquake ground motion at small separation distances

It is shown that the observed loss of coherency of synthetic strong motion on ground surface for separation distances less than about 100 m can be described in terms of the dispersion of strong motion waves. Additional contributions to the loss of coherency from variations of material properties in the soil and from geometrical departures from perfectly flat ground surface and irregular layer geometries are not considered in this paper. It is also shown that the synthetic surface displacements over a large rectangular area (100×100 m) on ground surface can be described well by a flat surface undergoing translations and rotations only, and with only minor departures from the plane flat surface.     

储层建模研究进展及发展趋势

油气田开发的后期进入高含水阶段,为了更加经济准确地进行油气开发,有必要采用储层地质建模的方法对老油气田进行储层研究。详细阐述了国内外储层地质建模的发展史,对储层地质建模的方法进行了细致的分类及论述。方法分类包括确定性建模方法和随机性建模方法。每一种建模方法又有多种子方法。提出了目前储层地质建模研究尚未很好解决的一些问题,如建模的对象局限于常规的碎屑岩储层。虽然有学者对火成岩、裂缝碳酸盐岩进行了相关的探究工作,但目前对非常规储层涉及较少,储层建模的精度也有待提高。     

Missing precipitation data estimation using optimal proximity metric-based imputation,nearest-neighbour classification and cluster-based interpolation methods

Abstract

New optimal proximity-based imputation, K-nearest neighbour (K-NN) classification and K-means clustering methods are proposed and developed for estimation of missing daily precipitation records. Mathematical programming formulations are developed to optimize the weighting, classification and clustering schemes used in these methods. Ten different binary and real-valued distance metrics are used as proximity measures. Two climatic regions, Kentucky and Florida, (temperate and tropical) in the USA, with different gauge density and network structure, are used as case studies to evaluate the new methods. A comprehensive exercise is undertaken to compare the performances of the new methods with those of several deterministic and stochastic spatial interpolation methods. The results from these comparisons indicate that the proposed methods performed better than existing methods. Use of optimal proximity metrics as weights, spatial clustering of observation sites and classification of precipitation data resulted in improvement of missing data estimates.

Editor D. Koutsoyiannis; Associate editor C. Onof     

On the criteria for the initiation of motion in tidal inlets,deterministic and stochastic approaches

Details are given herein of the refinement and application of a three-dimensional layer integrated numerical model to predict morphological changes in tidal basins. The solution of governing differential equations, which consist of the conservation of mass and momentum for the hydrodynamics, the transport equation for the suspended sediment fluxes and the sediment mass conservation equation for the bed level changes are carried out by the use of Alternating Direction Implicit (ADI) Finite Difference Method (FDM). The model includes different criteria for the initiation of motion namely Shields (1936, Application of Similarity Principles and Turbulence Research to Bed load Movement, Hydrodynamics Laboratory, California Institute of Technology, Pub. No. 167), Kolahdoozan (1999, Numerical Modelling of Geomorphological Processes in Estuarine Waters, PhD Thesis, Department of Civil and Environmental Engineering, University of Bradford, Bradford, UK, 288) and Zanke (2003, On the Influence of Turbulence on the Initiation of Sediment Motion, International Journal of Sediment Research, 18(1), 17–31), to compare different aspects of flow conditions. As the flow is highly turbulent with the random nature of its components, many researchers have tried to express sediment transport processes by using stochastic approaches. In the current study both deterministic and stochastic methods are included in the numerical model to evaluate their accuracy and efficiency. To validate the numerical model results, laboratory measurements are used, with these being obtained from an earlier experimental program undertaken by the authors. Results of a short term bed level changes in a laboratory model harbor are included for the model verification purposes. Comparisons are undertaken using different criteria for the initiation of motion, with the results highlighting that the unsteadiness in the flow parameters included in the numerical model has a major effect on the bed level changes inside the harbor, in compare with the turbulence structure of the flow. The model is then applied to a real case study of the Humber Estuary, located in the UK, with comparisons being undertaken for different criteria for the initiation of motion, using both deterministic and stochastic approaches for the long term bed level predictions.     

Stochastic modeling based on deterministic formulation: An example

In the context of seismology, an example of stochastic modeling on the basis of an established deterministic formulation is presented. The advantages of this approach to modeling over those based solely on statistical fit are discussed. It is demonstrated that the result of applying this procedure is a model whose main parameter has a physical interpretation, and therefore a validation based on criteria other than statistical goodness of fit is also possible. Statistical inference together with some demonstrating examples are also included.     

Strange seismic attractor?

Different time series were constructed from the data set containing all the seismic events recorded by the Parkfield network between 1969 and 1987. These series were analyzed to determine whether there exists an attractor in the phase space of the dynamical system characterizing seismic activity and to tentatively establish its dimension. The study has yielded ambiguous results. For all the time series analyzed, the dimension of the attractor appears higher than 12 and the correlation function of the seismic time series is undistinguishable from that of a series of random numbers of the same length. The lack of difference between the scaling parameters of two series suggests that, for all practical purposes, the seismic time series cannot be discriminated from a random series.