Study of hydrological phenomena by extreme value theory

We describe and give hydrological applications of a probabilistic model based on extreme value theory which can be used to study the values of a hydrologic process that exceed a certain threshold level Q _B .This model is useful in estimating extreme events X _T of return period T based on N years of available hydrologic record. We also present easy-to-use tables which give confidence intervals for X _T .The hydrologic applications reported are a flood frequency analysis, a methodology for estimating flood damage, an estimation of precipitation probabilities, and a prediction of extreme tide levels.     

Fluid Borders: Rethinking Historical Geography and Fixed Map Boundaries in Contested Regions

This article introduces a quantitative methodology for analyzing contested map borders. The article applies the new analytical technique to a data set of thirty maps showing Bulgaria in ca. 800 CE, a disputed state and period in medieval historiography with relevance to modern national politics and territorial claims. Based on the data set, we generate a series of new maps that make explicit the fluid medieval boundaries and general disagreement among geographers and historiographers. Our analysis begins with a simple point-in-polygon procedure to create a majority map that depicts the points included within the borders of the Bulgarian polity in sixteen or more of the maps (>50 percent). The majority map is then combined with percentage maps, confidence interval map boundaries, and cluster maps. The confidence interval maps are created via a spatial bootstrapping procedure and measure the uncertainty in the majority map. The cluster maps are developed via a radial basis function and provide insight into the potential affectivity based on the cartographers' countries of origin. The final map reflects the general modern consensus of the borders of the Bulgarian polity around 800 CE. Besides its quantitative contribution to medieval and modern cartographic, historiographical, and political debates, this article has developed a widely applicable methodology for synthesizing map borders and territories in cases of cartographic disagreement.     

Confidence Intervals of Quantiles in Hydrology Computed by an Analytical Method

Fitting probability distributions to hydrologic data samples is widely used for quantile estimation purposes. The estimated quantile (X^_T) is related to a return period (T). The confidence interval associated with each of the estimates has been calculated empirically, up until now, supposing that the quantile estimator is normally distributed. In this study, it is shown that the confidence interval follows a normal distribution only in the central part of the distribution. The real confidence limits are computed analytically, by defining and integrating the probability density function of the confidence interval. The results with an important number of hydrologic samples show that the upper confidence limits are significantly underestimated towards the tail of the distribution, when determined using the normality approximation for the quantile estimator.     

Comparison between VELACS numerical ‘class A’ predictions and centrifuge experimental soil test results

The numerical ‘class A’ predictions performed within the framework of the VELACS Project are compared to the experimental results recorded in the centrifuge experiments. The comparisons are made in terms of: (1) the root mean square error of the predictions with respect to the mean of the experimental results; and (2) the size of a confidence interval centered at the predicted value which contains the estimated true value of the experimental results with a 75% probability. An assessment of the capability of various groups of constitutive soil models to predict excess pore pressures induced by dynamic loading is also presented.     

全球主要地震区的18.6年地震轮回

本文根据月球交点运动周期规律,发现全球主要地震区的浅源大地震(1897—1990,Ms≥7.0)都存在18.6年地震轮回:活跃期为12.4年,平静期为6.2年。根据最好的统计结果,13个研究区中有4个区这种轮回存在的置信水平为95%,有9个区为98%。本文给出了各研究区的范围、各活跃期的具体时间、x~2检验结果和时空分布图。本文还定义了标志震级Mm来反映各研究区不同的地震活动水平。本文的结果可以充分代表全球浅源大地震的活动图象,为认识地震轮回的机制和地震的混沌性提供了新的资料。     

Palaeoflood hydrology of the Salt river,Arizona

Geomorphic evidence along bedrock-confined reaches of the Salt River in east-central Arizona provides a record of the river's largest flood events. Fine-grained flood slackwater deposits accumulated at channel margin irregularities several metres above the low-flow channel. Discharges associated with flow events responsible for the deposits were estimated by computer flow modelling. These estimates document flood magnitudes in excess of gauged historic streamflows. Relative and radiocarbon dating suggest that a flood record in excess of 600 y is preserved in the slackwater sequences. A prominent flood scar cut into grussy hillslope soils allows the extension of the prehistoric flood record to several thousand years. A maximum discharge estimate of 4600 m³s^?1 affixed to the flood scar represents the largest flood event in the record, and is given a minimum recurrence interval of 1000–2000 y. The 1952 flood is the largest historic flow event experienced along the study reach and is estimated at 2900 m³s^?1. Two palaeoflood events preserved in the slackwater stratigraphy exceed the 1952 event, and are given recurrence intervals of 300 and 600 y. The latter flood event had an estimated discharge of 3200 m³s^?1. It is apparent that discharge estimates affixed to these infrequent, large-magnitude flood events approach a maximum with decreased probabilities (large recurrence intervals). This suggests that a physical limit on discharge may exist within the Salt River drainage basin and is perhaps directly related to drainage basin size.     

西秦岭北缘断裂带特征地震平均复发间隔的确定和地震危险性评价

时间相依的地震危险性概率评估方法是最近10a来逐渐发展起来的，是一种将已获得的定量地质资料运用于活动断裂中—长期地震潜势概率评估的方法，从而使得在缺乏历史记载或仪器记录资料，但已获得断层平均滑动速率、同震位错、古地震年代序列等资料的活动断裂段上评估未来的发震概率成为可能。在定量计算活动断裂未来地震危险性的过程中，作为输入参数之一的特征地震平均复发间隔是一个至关重要的参数，它的确定将直接影响到概率计算的结果。对研究断裂上已获得的历史地震资料(H)、地质资料(G)和古地震资料(P)，笔采用了时间可预报(T)和准周期(Q)两种模式分别计算其平均复发间隔，比单一的只假定一种复发模式计算更具有完善性和可靠性。在叙述该方法的同时，以西秦岭北缘断裂为例，详细阐述了该断裂上特征地震平均复发间隔的确定，并在此基础上对西秦岭北缘断裂未来地震潜势作了定量评估。     

Regularization of geopotential determination from satellite data by variance components

 Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large linear systems. The posterior density function for the variance components, weighting factors and regularization parameters are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach. Received: 5 June 2001 / Accepted: 28 November 2001     

Moment tensor of the 1999 Dead Sea calibration shot: limitations in the isotropic source retrieval without a detailed earth model

Records of the November 11, 1999, M_L=3.9 calibration shot observed at three broad-band (BB) stations at a distance range from 35 to 63 km from the epicenter were inverted with a simple 1-D model. Complexity due to the water–solid bedrock interface near the hypocenter effectively masks the explosive mechanism in first-motion polarities. Reverberation in the water and scattering in the crust result in the long duration of the source process if estimated with a simple structure model. Only the part with a significant non-zero isotropic (ISO) component should be considered. We selected this part on the basis of the estimate of error due to inexact modeling of the crust constructed by perturbing the thickness and velocities in individual layers by 5% of their current values. Within this interval, the isotropic process of explosive characteristics is detected. However, if we do not check the significance of the isotropic part in the formally reconstructed source process, then we might miss the information about the explosion and arrive with a spurious nearly double-couple source.