基于F-范数的不确定性平差模型的解算方法

为提高基于F-范数的不确定性平差模型的解算效率,给出直接迭代算法进行参数估计。该算法无需SVD,解算过程简单且易于编程计算,同时给出迭代不收敛时的SVD-解方程算法。二元线性拟合及沉降观测AR模型的算例结果表明,这2种算法正确可行,与SVD-迭代算法具有等价性。当迭代收敛时,宜使用直接迭代算法,收敛速度更快,解算效率更高;当迭代不收敛时,可釆用SVD-解方程算法。     

地表组合粗糙度不确定性引起的SAR反演土壤水分的不确定性分析

地表粗糙度的不确定性是引起SAR土壤水分反演结果不确定性的主要因素,现有研究大多着重于研究单个粗糙度参数（主要是相关长度）的不确定性,直接研究地表组合粗糙度不确定性的较少。本文使用偏度、峰度和四分位距3个指标来量化不确定性,通过在组合粗糙度中加入不同量级高斯噪声进行随机扰动的方法,研究组合粗糙度不确定性在反演过程中的传递,并对反演土壤水分的不确定性进行定量分析。进一步研究反演土壤水分的均方根误差对组合粗糙度不同比例误差范围的响应特征,得到满足反演精度要求的组合粗糙度误差控制范围。样区的实验分析结果表明：组合粗糙度高斯噪声标准差在0-0.045之间时,峰度取值从-0.1984到1.2501,偏度取值从0.0191到0.6791,四分位距取值从0.0018到0.0167,3个量化指标都随组合粗糙度高斯噪声量级的增大而增大,土壤水分反演值有集中在众数附近的趋势,土壤水分低估倾向比高估倾向更明显;本文提出的组合粗糙度误差控制范围可满足反演精度要求,误差控制范围与入射角负相关。     

Assessing uncertainties in a conceptual water balance model using Bayesian methodology / Estimation bayésienne des incertitudes au sein d’une modélisation conceptuelle de bilan hydrologique

Abstract

Abstract The aim of this study was to estimate the uncertainties in the streamflow simulated by a rainfall–runoff model. Two sources of uncertainties in hydrological modelling were considered: the uncertainties in model parameters and those in model structure. The uncertainties were calculated by Bayesian statistics, and the Metropolis-Hastings algorithm was used to simulate the posterior parameter distribution. The parameter uncertainty calculated by the Metropolis-Hastings algorithm was compared to maximum likelihood estimates which assume that both the parameters and model residuals are normally distributed. The study was performed using the model WASMOD on 25 basins in central Sweden. Confidence intervals in the simulated discharge due to the parameter uncertainty and the total uncertainty were calculated. The results indicate that (a) the Metropolis-Hastings algorithm and the maximum likelihood method give almost identical estimates concerning the parameter uncertainty, and (b) the uncertainties in the simulated streamflow due to the parameter uncertainty are less important than uncertainties originating from other sources for this simple model with fewer parameters.     

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.