Uncertainty,entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d'état

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle.     

PRINCIPES FONDAMENTAUX DE LA THEORIE DU MOUVEMENT DES EAUX SOUTERRAINES

ABSTRACT

In southeastern Arizona, almost all summer rainfall results from widely-scattered high-intensity afternoon or evening thunderstorms of limited areal extent. For eleven years of record on the Walnut Gulch Experimental Watershed, Tombstone, Arizona, about 70 percent of the annual rainfall of 11 1/2 inches and over 95 percent of the annual runoff occurred in July, August, and early September. In contrast, about 5 percent of the rainfall occurred in the previous 3 months, and about 25 percent in the remaining 6 1/2 months.

Therefore, summer rainfall, although highly variable, represented the most dependable source of water to the Walnut Gulch watershed. On the average, significant rainfall was recorded on some part of the watershed on 40 percent of the days in the critical July-August period. The maximum frequency was 3 out of every 4 days in 1955, and the minimum 3 out of every 10 days in 1960.

The wettest year was 1955, with a continuous rainy period of 47 days; whereas, the driest was 1960, with the longest rainy period lasting only 5 days. The longest summer drought during the period of record occurred in 1962, when no rain fell for 17 days in August, following a 14-day rainy period in late July.

As yet, there are not enough data to determine reliable expectancies for summer rainy or drought periods.     

Rainfall estimation using raingages and radar — A Bayesian approach: 1. Derivation of estimators

Procedures for estimating rainfall from radar and raingage observations are constructed in a Bayesian framework. Given that the number of raingage measurements is typically very small, mean and variance of gage rainfall are treated as uncertain parameters. Under the assumption that log gage rainfall and log radar rainfall are jointly multivariate normal, the estimation problem is equivalent to lognormal co-kriging with uncertain mean and variance of the gage rainfall field.The posterior distribution is obtained under the assumption that the prior for the mean and inverse of the variance of log gage rainfall is normal-gamma 2. Estimate and estimation variance do not have closed-form expressions, but can be easily evaluated by numerically integrating two single integrals. To reduce computational burden associated with evaluating sufficient statistics for the likelihood function, an approximate form of parameter updating is given. Also, as a further approximation, the parameters are updated using raingage measurements only, yielding closed-form expressions for estimate and estimation variance in the Gaussian domain.With a reduction in the number of radar rainfall data in constructing covariance matrices, computational requirements for the estimation procedures are not significantly greater than those for simple co-kriging. Given their generality, the estimation procedures constructed in this work are considered to be applicable in various estimation problems involving an undersampled main variable and a densely sampled auxiliary variable.     

Binomial model on seismic risk analysis

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Probabilistic Assessment of Temperature in the Euganean Geothermal Area (Veneto Region, NE Italy)

In the geothermal Euganean area (Veneto region, NE Italy) water temperatures range from 60 to 86°C. The aquifer considered is rocky and the production wells in this study have a depth ranging from 300 to 500 m. For exploitation purposes, it is important to identify zones with a high probability that the temperature is more than 80°C and zones with a high probability that the temperature is less than 70°C. First, variographic analysis was conducted from 186 temperature data of thermal ground waters. This analysis gave results that are consistent with the main regional tectonic structure, the NW-SE trending Schio-Vicenza fault system. Then indicator variograms of the second, fifth, and eighth decile were compared to identify the spatial continuity at different thresholds. The unacceptability of a multigaussian hypothesis of the random function and the necessity to know the cumulative distribution function in any location, suggested the use of a nonparametric geostatistical procedure such as indicator kriging. Thus, indicator variograms at the cutoffs of 65, 70, 73, 75, 78, 80, 82, and 84°C were analyzed, fitted, and used during the indicator kriging procedure. Finally, probability maps were derived from postprocessing indicator kriging results. These maps identified scarcely exploited areas with a high probability of the temperature being higher than 80°C, between 70 and 80°C and areas with high probability of the temperature being below 70°C.     

火焰原子吸收光谱法测定铜精矿中银含量的测量不确定度评定

采用《测量不确定度评定与表示指南》，以火焰原子吸收光谱法测定铜精矿中的银含量为例，对测量结果进行不确定度评定。分析了不确定度的重要来源，包括称样质量、标准工作溶液、工作曲线拟合、试液定容体积及测量重复性等引入的不确定度分量组成。对各不确定度分量进行分析计算，求得标准不确定度为1．56，扩展不确定度为3．12。     

Utility Efficient Frontier: An Application in the Oil and Gas Industry

Current practice shows that the use of portfolio and utility theory is very low among petroleum companies. This article advocates the use of both portfolio theory and utility theory as decision-making tools to improve performance of oil and gas companies. We introduce a model that can be practically used and applied in the oil and gas industry. This model generates an optimized, efficient portfolio and, at the same time, enables the decision maker to incorporate his risk attitude and policy. This can only be done by combining both the portfolio theory and utility theory through an approach called the utility mean-variance model. A typical oil portfolio optimization problem is investigated by applying both portfolio and utility theories. Through the utility mean-variance model, an efficient frontier that captures decision maker risk attitude is achieved.     

Logic-tree Approach for Probabilistic Tsunami Hazard Analysis and its Applications to the Japanese Coasts

For Probabilistic Tsunami Hazard Analysis (PTHA), we propose a logic-tree approach to construct tsunami hazard curves (relationship between tsunami height and probability of exceedance) and present some examples for Japan for the purpose of quantitative assessments of tsunami risk for important coastal facilities. A hazard curve is obtained by integration over the aleatory uncertainties, and numerous hazard curves are obtained for different branches of logic-tree representing epistemic uncertainty. A PTHA consists of a tsunami source model and coastal tsunami height estimation. We developed the logic-tree models for local tsunami sources around Japan and for distant tsunami sources along the South American subduction zones. Logic-trees were made for tsunami source zones, size and frequency of tsunamigenic earthquakes, fault models, and standard error of estimated tsunami heights. Numerical simulation rather than empirical relation was used for estimating the median tsunami heights. Weights of discrete branches that represent alternative hypotheses and interpretations were determined by the questionnaire survey for tsunami and earthquake experts, whereas those representing the error of estimated value were determined on the basis of historical data. Examples of tsunami hazard curves were illustrated for the coastal sites, and uncertainty in the tsunami hazard was displayed by 5-, 16-, 50-, 84- and 95-percentile and mean hazard curves.