地震动空间变化随机描述及相干函数模型研究进展

本研究主要讨论地震动空间变化的随机描述.首先给出了基于密集地震台阵记录估计相干函数的方法,并对计算中需要关注的问题给出了相应的解释;然后对现有的经验和半经验相干函数模型的建立进行了详细的梳理,并对模型在工程应用中的适用性、有效性和局限性进行了讨论;最后通过对比分析不同相干函数模型对场址地震动空间相关性的模拟结果,对相干函数模型的选择提出了建议.     

考虑堆石料空间变异性的土石坝坝坡地震稳定性随机有限元分析

本文探讨了筑坝堆石料的空间变异性对土石坝坝坡动力稳定性的影响。以新疆某在建高面板堆石坝为例,在蒙特卡洛法的框架下,采用基于局部平均细分法的随机有限元法模拟考虑筑坝堆石料空间变异性时土石坝的地震响应及坝坡滑移情况,通过对比随机有限元法和常规确定性有限元法的计算结果,提出:在地震动作用下,考虑筑坝材料空间变异性时,坝坡滑动体的数量、规模以及滑移量和滑动历时都有不同程度的增大,因而坝坡整体危险程度显著高于不考虑材料空间变异性的情况。坝坡各项动力安全性指标对筑坝材料空间变异性非常敏感;因而,考虑筑坝材料空间变异性时,各项安全性指标的离散性较大。     

空间变化的地震动功率谱的实用模型

提出了一个空间变化的地震动功率谱模型．这个模型与已有的模型比较有两个特点: ① 根据现有的多个模型多次地震的平均结果，不是某一次台阵记录提出的模型；② 考虑了测点间的自功率谱参数的变化．      

基于强度和能量控制的随机地震动模型

考虑地震动的随机性和频率与强度非平稳性,通过理论分析,提出了一般随机地震动模型,并给出了确定模型参数的原则和方法。该模型以地震动强度、地震动能量以及地震动持时等宏观指标作为控制随机地震动模型参数的指标,而对其内在的频谱组成等指标只要求满足一般地震动的特征。该模型可以用于描述平稳随机过程、强度非平稳随机过程以及强度和频率完全非平稳随机过程。通过与常用功率谱模型的比较,验证了该模型的合理性。     

考虑超随机特性的人工地震动合成

文中根据自相关函数随机噪声部分的2个重要性质提出了自相关函数随机噪声部分的迭代生成算法,并给出了以确定性自相关函数为目标函数,考虑随机噪声部分影响的人工合成地震动方法.本文的研究结果表明地震动加速度的平方和（SS）比峰值加速度（PGA）更好地量度了地震地面运动强度.文中用蒙特卡罗方法分析了自相关函数噪声项对人工合成地震动幅值和反应谱的影响：由于自相关函数的随机噪声项对地震动总功率或平方和的贡献为0,因此随机噪声项对合成地震动幅值的影响不大,但由于自相关函数随机噪声项明显改变了地震动功率谱在频域上的分布特征,使原本光滑的平均反应谱出现了明显的波动,从而在一定程度上提高了平均反应谱的峰值,使自相关函数噪声部分对平均反应谱也有一些影响.     

不同地球模型对中国陆区大气负荷位移建模的影响

目前进行质量负荷位移建模时通常使用的是全球或区域平均的一维地球模型,这类地球模型无法反映地壳结构的局部差异,如地壳厚度、地震波波速等.本文利用地表气压再分析数据产品NCEP/NCAR Reanalysis 1(NCEP R-1)和不同地球模型(Preliminary reference Earth model (PREM)、AK135、STW105和CRUST1.0)计算的负荷格林函数计算中国陆区的大气负荷垂向形变,结合GPS实测位移数据,评估基于不同地球模型计算得到的地表形变的差异.通过比较PREM与不同地球模型的建模结果发现,一维地球模型之间的建模差异较小,主要集中在气压变化较大的东部地区和西北地区,气压变化较小的青藏高原地区的建模差异则更小.相反,PREM与CRUST1.0模型在青藏高原地区的建模差异最大,在东部地区的建模差异最小.PREM与STW105、AK135和CRUST1.0在中国陆区的最大位移建模差异分别为0.05、0.34和0.44 mm.不同地球模型的建模差异是由负荷格林函数不同产生的,而负荷格林函数在近场受上地壳厚度的影响较大.对于局部地壳结构差异明显的青藏高原地区,一维地球模型AK135和STW105的建模结果对GPS残差的修正效果与PREM相当,而CRUST1.0地壳模型在修正PREM后可以使残差的WRMS最高降低0.93%.本文的研究表明,地壳结构的局部差异对负荷位移建模的影响不容忽视.

     

平稳随机地震地面运动过程模型及其统计特征

地震地面运动过程具有强烈的随机性,应用随机理论对实际工程结构进行地震可靠性分析和抗震设计与加固时都需要建立合理的随机地震地面运动模型,本文选择3种典型的随机地震动模型,即理想白噪声模型、金井清模型和改进的金井消模型,分析了它们的物理概念、频域特征以及适用范围。引入状态向量,建立状态方程．通过复振型叠加法分析了地震地面运动过程的时域统计特性,推导出3种随机地震动模型的相关函数的解析表达式．这些结果可为结构随机地震反应时域分析和抗震可靠性评估提供基础。     

竖向地震动强度包络函数的空间变化规律

利用SMART 1台阵三次地震记录拟合了各个测点在地震中的竖向地震动强度包络曲线及Amin 和Ang的强度包络函数中各模型参数值,分析了各模型参数的空间变化规律,建立了各模型参数随二维空间坐标及土层厚度变化的随机模型,为多点地震动合成中竖向强度包络函数的计算提供了理论依据。     

植被电磁散射的半空间模型研究

本文给出了地面植被电磁散射的半空间模型研究方法.在以往的相关文献中,均采用自由空间格林函数求解单个叶片散射体的散射场,本文利用半空间并矢格林函数求出了单个散射体的散射场,然后运用Monte Carlo方法模拟生成地面植被层,得到了在半空间下植被层的电磁散射特性,计算出了单、双站雷达散射截面,并与自由空间下的散射场做了相互对比.结果表明,在半空间格林函数下得到的散射场更为适用于描述地面植被的电磁散射特性.     

基于《电力设施抗震设计规范》的地震动随机模型参数研究

依据《电力设施抗震设计规范》（GB50260-96）中的设计反应谱,对随机地震动功率谱参数的取值进行了具体研究。首先,采用时间包络函数考虑地震的非平稳特性,给出了地震动持时的取值;然后,根据加速度峰值等效原则,迭代计算得到地面的加速度功率谱密度曲线;最后,选定Clough-Penzien修正过滤白噪声模型作为拟合函数,通过非线性拟合技术拟合了与《规范》中的地震烈度、场地类别相对应的谱参数。研究结果表明,Clough-Penzien修正过滤白噪声模型能较好地拟合其曲线形状。本文给出了相对于规范中的地面加速度功率谱参数值,可供这种模型作为地震地面运动输入时选用。     

An analysis of the impact of spatial variability in rainfall on runoff and sediment predictions from a distributed model

This paper investigates the effect of introducing spatially varying rainfall fields to a hydrological model simulating runoff and erosion. Pairs of model simulations were run using either spatially uniform (i.e. spatially averaged) or spatially varying rainfall fields on a 500‐m grid. The hydrological model used was a simplified version of Thales which enabled runoff generation processes to be isolated from hillslope averaging processes. Both saturation excess and infiltration excess generation mechanisms were considered, as simplifications of actual hillslope processes. A 5‐year average recurrence interval synthetic rainfall event typical of temperate climates (Melbourne, Australia) was used. The erosion model was based on the WEPP interrill equation, modified to allow nonlinear terms relating the erosion rate to rainfall or runoff‐squared. The model results were extracted at different scales to investigate whether the effects of spatially varying rainfall were scale dependent. A series of statistical metrics were developed to assess the variability due to introducing the spatially varying rainfall field. At the catchment (approximately 150 km²) scale, it was found that particularly for saturation excess runoff, model predictions of runoff were insensitive to the spatial resolution of the rainfall data. Generally, erosion processes at smaller sub‐catchment scales, particularly when the sediment generation equation had non linearity, were more sensitive to spatial rainfall variability. Introducing runon infiltration reduced the total runoff and sediment yield at all scales, and this process was also most sensitive to the rainfall resolution. Copyright © 2011 John Wiley & Sons, Ltd.     

Assessment of rainfall spatial variability and its influence on runoff modelling: A case study in the Brue catchment,UK

This study explores rainfall spatial variability and its influence on runoff modelling. A novel assessment scheme integrated with coefficient of variance and Moran's I is introduced to describe effective rainfall spatial variability. Coefficient of variance is widely accepted to identify rainfall variability through rainfall intensity, whereas Moran's I reflects rainfall spatial autocorrelation. This new assessment framework combines these two indicators to assess the spatial variability derived from both rainfall intensity and distribution, which are crucial in determining the time and magnitude of runoff generation. Four model structures embedded in the Variable Infiltration Capacity model are adopted for hydrological modelling in the Brue catchment of England. The models are assigned with 1, 3, 8, and 27 hydrological response units, respectively, and diverse rainfall spatial information for 236 events are extracted from 1995. This study investigates the model performance of different partitioning based on rainfall spatial variability through peak volume (Q_p) and time to peak (T_p), along with the rainfall event process. The results show that models associated with dense spatial partitioning are broadly capable of capturing more spatial information with better performance. It is unnecessary to utilize models with high spatial density for simple rainfall events, though they show distinct advantages on complex events. With additional spatial information, Q_p experiences a notable improvement over T_p. Moreover, seasonal patterns signified by the assessment scheme imply the feasibility of seasonal models.     

Spatial variability of rainfall on a sub‐kilometre scale

The variability of rainfall in space and time is an essential driver of many processes in nature but little is known about its extent on the sub‐kilometre scale, despite many agricultural and environmental experiments on this scale. A network of 13 tipping‐bucket rain gauges was operated on a 1·4 km² test site in southern Germany for four years to quantify spatial trends in rainfall depth, intensity, erosivity, and predicted runoff. The random measuring error ranged from 10% to 0·1% in case of 1 mm and 100 mm rainfall, respectively. The wind effects could be well described by the mean slope of the horizon at the stations. Except for one station, which was excluded from further analysis, the relative differences due to wind were in maximum ±5%. Gradients in rainfall depth representing the 1‐km² scale derived by linear regressions were much larger and ranged from 1·0 to 15·7 mm km^?1 with a mean of 4·2 mm km^?1 (median 3·3 mm km^?1). They mainly developed during short bursts of rain and thus gradients were even larger for rain intensities and caused a variation in rain erosivity of up to 255% for an individual event. The trends did not have a single primary direction and thus level out on the long term, but for short‐time periods or for single events the assumption of spatially uniform rainfall is invalid on the sub‐kilometre scale. The strength of the spatial trend increased with rain intensity. This has important implications for any hydrological or geomorphologic process sensitive to maximum rain intensities, especially when focusing on large, rare events. These sub‐kilometre scale differences are hence highly relevant for environmental processes acting on short‐time scales like flooding or erosion. They should be considered during establishing, validating and application of any event‐based runoff or erosion model. Copyright © 2009 John Wiley & Sons, Ltd.     

Influence of rainfall spatial variability on flood prediction

This paper deals with the sensitivity of distributed hydrological models to different patterns that account for the spatial distribution of rainfall: spatially averaged rainfall or rainfall field. The rainfall data come from a dense network of recording rain gauges that cover approximately 2000 km² around Mexico City. The reference rain sample accounts for the 50 most significant events, whose mean duration is about 10 h and maximal point depth 170 mm. Three models were tested using different runoff production models: storm-runoff coefficient, complete or partial interception. These models were then applied to four fictitious homogeneous basins, whose sizes range from 20 to 1500 km². For each test, the sensitivity of the model is expressed as the relative differences between the empirical distribution of the peak flows (and runoff volumes), calculated according to the two patterns of rainfall input: uniform or non-uniform. Differences in flows range from 10 to 80%, depending on the type of runoff production model used, the size of the basin and the return period of the event. The differences are generally moderate for extreme events. In the local context, this means that uniform design rainfall combining point rainfall distribution and the probabilistic concept of the areal reduction factor could be sufficient to estimate major flood probability. Differences are more significant for more frequent events. This can generate problems in calibrating the hydrological model when spatial rainfall localization is not taken into account: a bias in the estimation of parameters makes their physical interpretation difficult and leads to overestimation of extreme flows.     

A statistically based runoff‐yield model coupling infiltration excess and saturation excess mechanisms

A statistically based runoff‐yield model is proposed in this paper. The model considers spatial heterogeneities of rainfall, soil infiltration capacity and soil water storage capacity that are main factors controlling runoff‐yield process. It assumes that the spatial variation of rainfall intensity at each time step can be characterized by a probability density function, which is estimated by matching the hyetograph through goodness‐of‐fit measure, whereas the spatial heterogeneities of soil infiltration capacity and soil water storage capacity are described by parabola‐type functions. Surface runoff is calculated according to infiltration excess mechanism; the statistical distribution of surface runoff rate can be deduced with the joint distribution of rainfall intensity and soil infiltration rate, thus obtaining a quasi‐analytical solution for surface runoff. Based on saturation excess mechanism, the groundwater flow (flows below the ground are collectively referred to as groundwater flow) is calculated by infiltration and the probability distribution of soil water storage capacity. Consequently, the total runoff is composed of infiltration excess and saturation excess runoff components. As an example, this model is applied to flood event simulation in Dongwan catchment, a semi‐humid region and a tributary of Yellow River in China. It indicates that the proposed runoff‐yield model could achieve acceptable accuracy. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating the effects of spatial variability of infiltration on the output of a distributed runoff and soil erosion model using Monte Carlo methods

Monte Carlo procedures were used to evaluate the effects of spatial variations in the values of the infiltration parameter on the results of the ANSWERS distributed runoff and erosion model. Simulation results obtained were compared with measured values. Field infiltration measurements indicated spatial correlation at much smaller distances than the size of an element. Therefore, at first only the error of the mean had to be taken into consideration for block infiltration rates. Consequently, not only single hydrographs were produced, but also error bands. Secondly, nine other hypothetical spatial correlation structures were also evaluated using Monte Carlo methods. in particular at low nugget variances, increasing spatial correlation of infiltration resulted in increasing coefficients of variation in model outputs. In general, rainstorms with low rainfall intensities were more difficult to simulate accurately than extreme events with high rainfall intensities. This is explained by the greater influence of the infiltration uncertainties at low rainfall intensities.     

Regional assimilation of in situ observed soil moisture into the VIC model considering spatial variability

ABSTRACT

In order to improve the soil moisture (SM) modelling capacity, a regional SM assimilation scheme based on an empirical approach considering spatial variability was constructed to assimilate in situ observed SM data into a hydrological model. The daily variable infiltration capacity (VIC) model was built to simulate SM in the Upper Huai River Basin, China, with a resolution of 5 km × 5 km. Through synthetic assimilation experiments and validations, the assimilated SM was evaluated, and the assimilation feedback on evapotranspiration (ET) and streamflow are analysed and discussed. The results show that the assimilation scheme improved the SM modelling capacity, both spatially and temporally. Moreover, the simulated ET was continually affected by changes in SM simulation, and the streamflow predictions were improved after applying the SM assimilation scheme. This study demonstrates the potential value of in situ observations in SM assimilation, and provides valuable ways for improving hydrological simulations.     

Propagation of uncertainty from rainfall to runoff: A case study with a stochastic rainfall generator

We explore the impact of uncertainties in the spatial–temporal distribution of rainfall on the prediction of peak discharge in a typical mountain basin. To this end, we use a stochastic generator previously developed for rainfall downscaling, and we estimate the basin response by adopting a semi-distributed hydrological model. The results of the analysis provide information on the minimum rainfall resolution needed for operational flood forecasting, and confirm the sensitivity of peak discharge estimates to errors in the determination of the power spectrum of the precipitation field.     

A model to consider the spatial variability of rainfall partitioning within deciduous canopy. I. Model description

In this first paper of two, a numerical simulation model capable of simulating the spatial variability of rainfall partitioning within a canopy is presented. The second paper details how the model is parameterized, and some testing of its capabilities. The first stage of the model is to derive the mature canopy structure. This is achieved through simplified individual tree structures and a random placement routine based on a modified Poisson distribution. Following this the spatial discretization for throughfall is attained as a series of layers of triangles with a tree trunk at every apex. The number of layers is derived from the leaf area index through a modified Poisson distribution. Seasonal variation in the deciduous canopy is simulated through a time vector routine. The rainfall partitioning section of the model is based upon the Rutter model which has been modified to each individual triangle layer. The main feature of this model is that it offers a method of simulating rainfall partitioning at a scale that is a function of the size of the elementary physical components (tree and leaf scale). This can be used to investigate soil moisture variations under a canopy, or to study the variations within the forest hydrological processes themselves. © 1997 John Wiley & Sons, Ltd.     

Functional evaluation of a simplified scaling method for assessing the spatial variability of soil hydraulic properties at the hillslope scale

Abstract

Mapping soil hydraulic parameters with traditional scaling methods that use laboratory-determined hydraulic characteristics (the LAB method) is not always feasible as it involves expensive, time-consuming and sophisticated measurements on soil samples collected in several locations of the study area. An alternative scaling method (the AP method) has been recently proposed to indirectly retrieve the soil hydraulic properties following the Arya-Paris physico-empirical pedotransfer function, which makes use of particle-size distribution and bulk density values. In this synthetic study we verify the performance of the AP method from a functional perspective, by evaluating the differences in the simulated soil water budget through a Monte Carlo approach. Notwithstanding that the AP method can provide soil hydraulic property patterns with faster experimental procedures and minor costs, we observe significant bias in the predicted spatially-averaged soil water budget due to a poor parametric calibration of the AP method and an imprecise identification of the spatial correlation structure of the AP-estimated scaling factors.

Citation Nasta, P., Romano, N., and Chirico, G.B., 2013. Functional evaluation of a simplified scaling method for assessing the spatial variability of soil hydraulic properties at the hillslope scale. Hydrological Sciences Journal, 58 (5), 1059–1071.