High-order Stochastic Simulation of Complex Spatially Distributed Natural Phenomena

Spatially distributed and varying natural phenomena encountered in geoscience and engineering problem solving are typically incompatible with Gaussian models, exhibiting nonlinear spatial patterns and complex, multiple-point connectivity of extreme values. Stochastic simulation of such phenomena is historically founded on second-order spatial statistical approaches, which are limited in their capacity to model complex spatial uncertainty. The newer multiple-point (MP) simulation framework addresses past limits by establishing the concept of a training image, and, arguably, has its own drawbacks. An alternative to current MP approaches is founded upon new high-order measures of spatial complexity, termed “high-order spatial cumulants.” These are combinations of moments of statistical parameters that characterize non-Gaussian random fields and can describe complex spatial information. Stochastic simulation of complex spatial processes is developed based on high-order spatial cumulants in the high-dimensional space of Legendre polynomials. Starting with discrete Legendre polynomials, a set of discrete orthogonal cumulants is introduced as a tool to characterize spatial shapes. Weighted orthonormal Legendre polynomials define the so-called Legendre cumulants that are high-order conditional spatial cumulants inferred from training images and are combined with available sparse data sets. Advantages of the high-order sequential simulation approach developed herein include the absence of any distribution-related assumptions and pre- or post-processing steps. The method is shown to generate realizations of complex spatial patterns, reproduce bimodal data distributions, data variograms, and high-order spatial cumulants of the data. In addition, it is shown that the available hard data dominate the simulation process and have a definitive effect on the simulated realizations, whereas the training images are only used to fill in high-order relations that cannot be inferred from data. Compared to the MP framework, the proposed approach is data-driven and consistently reconstructs the lower-order spatial complexity in the data used, in addition to high order.     

Evaluation of rainfall spatial correlation effect on rainfall-runoff modeling uncertainty,considering 2-copula

Lack of accuracy of rainfall-runoff simulation (RRS) remains critical for some applications. Among various sources of uncertainty, precipitation plays a particular role. Rainfall rates as the main input data of RRS are of the first factors controlling the accuracy. In addition to the depth, spatial and temporal distributions of rainfall impact the flood discharge. Most of the previous studies on RRS uncertainty have ignored rainfall spatial distribution, where in large catchments, it is necessary to be modeled explicitly. Karoon III is one most important basin of the Iran because of the Karoon III dam in the outlet. In the present work, effect of spatial correlation of rainfall on HEC-HMS (SMA) continuous RRS uncertainty is evaluated using 2variate copula (2copula). Monte Carlo simulation (MCS) approach was used to consider the rainfall spatial dependence. To reduce the computational expense, sampling efficiency and convergence for MCS, Latin hypercube sampling (LHS) was used. Copula functions consider wide range of marginal probability distribution functions (PDFs), eliminating limits of regular join PDFs. For this aim, two scenarios were investigated. In the first scenario, sub-basin rainfall was considered independent, and in the second scenario, 2copula was adopted to model spatial correlation of rainfall. Dimensionless rainfall depths were calculated for each sub-basin, and the PDFs were determined. The generated random dimensionless rainfalls were reweighted and multiplied by watershed’s mean rainfall value. Stochastic Climate Library was used to generate continuous daily rainfalls. Sampling from dimensionless rainfalls using LHS algorithm, 100 runs of calibrated model-simulated 100 flows for each day following MCS, and 80 % certainty bound was calculated. Results showed that considering dependence decreased 18 % of the maximum uncertainty bound width, so the methodology could be recommended for decreasing predicted runoff error.     

Spatial variability of rainfall trends in Iran

The main objective of this paper is to analyze the spatial variability of rainfall trends using the spatial variability methods of rainfall trend patterns in Iran. The study represents a method on the effectiveness of spatial variability for predicting rainfall trend patterns variations. In rainfall trend analysis and spatial variability methods, seven techniques were used: Mann–Kendall test, Sen’s slope method, geostatistical tools as a global polynomial interpolation and the spatial autocorrelation (Global Moran’s I), high/low clustering (Getis-Ord General G), precipitation concentration index, generate spatial weights matrix tool, and activation functions of semiliner, sigmoid, bipolar sigmoid, and hyperbolic tangent in the artificial neural network technique .For the spatial variability of monthly rainfall trends, trend tests were used in 140 stations of spatial variability of rainfall trends in the 1975–2014 period. We analyzed the long and short scale spatial variability of rainfall series in Iran. Spatial variability distribution of rainfall series was depicted using geostatistical methods (ordinary kriging). Relative nugget effect (RNE) predicted from variograms which showed weak, moderate, and strong spatial variability for seasonal and annual rainfall series. Moreover, the rainfall trends at each station were examined using the trend tests at a significance level of 0.05. The results show that temporal and spatial trend patterns are different in Iran and the monthly rainfall had a downward (decreasing) trend in most stations, and the trend was statistically significant for most of the series (73.5% of the stations demonstrated a decreasing trend with 0.5 significance level). Rainfall downward trends are generally temporal-spatial patterns in Iran. The monthly variations of rainfall decreased significantly throughout eastern and central Iran, but they increased in the west and north of Iran during the studied interval. The variability patterns of monthly rainfall were statistically significant and spatially random. Activation functions in the artificial neural network models, in annual time scale, had spatially dispersed distribution with other clustering patterns. The results of this study confirm that variability of rainfall revealing diverse patterns over Iran should be controlled mainly by trend patterns in the west and north parts and by random and dispersed patterns in the central, southern, and eastern parts.     

Spatiotemporal variations in rainfall–topographic relationships in southwestern Saudi Arabia

Spatial variations in the relationship between topography and mean annual and seasonal rainfalls in southwestern Saudi Arabia are examined using Kruskal–Wallis one-way analysis of variance. The topographic factors include physiographic features (topography), altitude, slope, proximity to a ridge or crest of mountains, and proximity to the Red Sea. There is a statistically significant effect of topographic factors on the mean annual rainfall, but the results are more significant for the mean seasonal rainfall. The largest amount of mean rainfall in the study area occurs during spring, when rainfall displays a significant relationship with topographic factors, in which more orographic rainfall patterns are associated with higher altitude, greater proximity to a ridge and steeper slopes. Higher altitudes do not necessarily receive more rain; some low altitude locations (i.e., the southern part of the study area) receive more rain during summer and fall because they are located on the windward side of the Asir Mountains and are exposed to the moist air masses brought by the southwest monsoonal system in summer and by the northwest air flow from the Mediterranean and Red Sea in the fall in addition to local convective rainfall patterns. Rainfall in winter increases in the foothills of the Asir Mountains above the coastal plain of the Red Sea. The steep western slopes (windward side) receive more rainfall than the gentle eastern slopes (leeward side): this may be due to the Asir Mountains forcing moist air masses carried by the westerly and northwest winds to rise and cool before they descend and warm on the leeward side.     

四川盆地降水日变化特征分析和个例模拟

利用台站观测降水资料,分析四川盆地及周边地区降水分布和日变化特征,得到以下结论:四川地区降水存在2个高值中心,均位于盆地周围的山地;盆地降水"夜雨"特征明显;川西高原降水峰值以午夜前降水量的贡献为主;盆中与盆地西南边缘山地的降水峰值由夜间降水量与降水频率共同作用;盆地东北边缘的山地是午前降水频率与后半夜的降水量均有贡献。其次,结合WRF模式的数值试验,对2008年9月23～24日发生在盆地的夜间暴雨过程进行模拟研究和综合分析。结果表明WRF模式较好地模拟了此次天气过程降水的空间分布和日变化规律,通过分析模拟的环流场与温湿场发现,夜雨的形成与大尺度环流场的影响和地形强迫关系密切。     

The FFT Moving Average (FFT-MA) Generator: An Efficient Numerical Method for Generating and Conditioning Gaussian Simulations

A fast Fourier transform (FFT) moving average (FFT-MA) method for generating Gaussian stochastic processes is derived. Using discrete Fourier transforms makes the calculations easy and fast so that large random fields can be produced. On the other hand, the basic moving average frame allows us to uncouple the random numbers from the structural parameters (mean, variance, correlation length, ... ), but also to draw the randomness components in spatial domain. Such features impart great flexibility to the FFT-MA generator. For instance, changing only the random numbers gives distinct realizations all having the same covariance function. Similarly, several realizations can be built from the same random number set, but from different structural parameters. Integrating the FFT-MA generator into an optimization procedure provides a tool theoretically capable to determine the random numbers identifying the Gaussian field as well as the structural parameters from dynamic data. Moreover, all or only some of the random numbers can be perturbed so that realizations produced using the FFT-MA generator can be locally updated through an optimization process.     

Relationship between northeast monsoon rainfall and near-surface atmospheric wind convergence over the North Indian Ocean using multisatellite data

The northeast monsoon rainfall (NEMR) contributes about 20–40 % of annual rainfall over the North Indian Ocean (NIO). In the present study, the relationship between the NEMR and near-surface atmospheric wind convergence (NSAWC) over the NIO is demonstrated using high-resolution multisatellite data. The rainfall product from the Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis and near-surface wind product from the Cross-Calibration Multi-Platform available at 0.25° × 0.25° spatial resolution are used for the study. Large-scale NSAWC and divergence maps over the tropical Indian Ocean are generated at monthly scale from the wind product for the period of 1988–2010. A preliminary analysis is carried out for two consecutive anomalous Indian Ocean Dipole (IOD) years 2005 (negative) and 2006 (positive). The distinct spatial patterns of rainfall rate and NSAWC fields over the NIO clearly show the evolution of the anomalous IOD events in the south eastern equatorial Indian Ocean (EEIO). The spatially averaged time-series of pentad NSAWC over the south EEIO box suggests that the variability occurs in phase with rainfall rate during both the northeast monsoon years. Furthermore, the scatter plot between area-averaged pentad rainfall and convergence over the south EEIO box for the period of 1998–2010 shows statistically significant linear correlation which reveals that NSAWC plays a key role in regulating the NEMR.     

Regional modelling of rainfall-induced runoff using hydrological model by incorporating plant cover effects: case study in Kelantan,Malaysia

The objective of this paper is to develop a spatial temporal runoff modelling of local rainfall patterns effect on the plant cover hilly lands in Kelantan River Basin. Rainfall interception loss based on leaf area index, loss/infiltration on the ground surface, and runoff calculation were considered as the main plant cover effects on the runoff volume. In this regard, a hydrological and geotechnical grid-based regional model (integrated model) was performed using Microsoft Excel^® and GIS framework system for deterministic modelling of rainfall-induced runoff by incorporating plant cover effects. The infiltration process of the current model was integrated with the precipitation distribution method and rainfall interception approach while the runoff analysis of integrated model was employed based on loss/infiltration water on the ground surface with consideration of water interception loss by canopy and the remaining surface water. In the following, the spatial temporal analysis of rainfall-induced runoff was performed using 10 days of hourly rainfall events at the end of December 2014 in Kelantan River Basin. The corresponding changes in pressure head and consequent rate of infiltration were calculated during rainfall events. Subsequently, flood volume is computed using local rainfall patterns, along with water interception loss and the remaining surface water in the study area. The results showed the land cover changes caused significant differences in hydrological response to surface water. The increase in runoff volume of the Kelantan River Basin is as a function of deforestation and urbanization, especially converting the forest area to agricultural land (i.e. rubber and mixed agriculture).     

广东省1960～2007年降雨侵蚀力变化趋势分析

降雨侵蚀力反映由降雨引起的土壤侵蚀的潜在能力.本文利用广东省25个站点48年(1960～2007)的日雨量资料计算了各站的降雨侵蚀力,并用Mann-Kendall(M-K)非参数检验和克里格空间插值法分析了降雨侵蚀力的时空变化规律.结果表明:广东省降雨侵蚀力的空间分布呈沿海向内陆逐渐递减的趋势.全省大部分地区的年降雨侵蚀力呈现不明显上升趋势,且存在较明显的年代际和年际变化.降雨侵蚀力的年内分布特征和降雨量分布类似,呈"双峰型",主要集中在4～9月的雨季.对于季节序列,冬季、春季和夏季大部分地区的降雨侵蚀力有不同程度的上升,秋季全省几乎所有地区呈下降趋势.汛期的降雨侵蚀力变化特征与年降雨侵蚀力相似.     

Trends in extreme rainfall over ecologically sensitive Western Ghats and coastal regions of Karnataka: an observational assessment

Rainfall is one of the pivotal climatic variables, which influence spatio-temporal patterns of water availability. In this study, we have attempted to understand the interannual long-term trend analysis of the daily rainfall events of ≥?2.5 mm and rainfall events of extreme threshold, over the Western Ghats and coastal region of Karnataka. High spatial resolution (0.25°?×?0.25°) daily gridded rainfall data set of Indian Meteorological Department was used for this study. Thirty-eight grid points in the study area was selected to analyze the daily precipitation for 113 years (1901–2013). Grid points were divided into two zones: low land (exposed to the sea and low elevated area/coastal region) and high land (interior from the sea and high elevated area/Western Ghats). The indices were selected from the list of climate change indices recommended by ETCCDI and are based on annual rainfall total (RR), yearly 1-day maximum rainfall, consecutive wet days (≥?2.5 mm), Simple Daily Intensity Index (SDII), annual frequency of very heavy rainfall (≥?100 mm), frequency of very heavy rainfall (≥?65–100 mm), moderate rainfall (≥?2.5–65 mm), frequency of medium rainfall (≥?40–65 mm), and frequency of low rainfall (≥?20–40 mm). Mann-Kendall test was applied to the nine rainfall indices, and Theil-Sen estimator perceived the nature and the magnitude of slope in rainfall indices. The results show contrasting trends in the extreme rainfall indices in low land and high land regions. The changes in daily rainfall events in the low land region primarily indicate statistically significant positive trends in the annual total rainfall, yearly 1-day maximum rainfall, SDII, frequency of very heavy rainfall, and heavy rainfall as well as medium rainfall events. Furthermore, the overall annual rainfall strongly correlated with all the rainfall indices in both regions, especially with indices that represent heavy rainfall events which is responsible for the total increase of rainfall.     

Hydrologic behavior and flood probability for selected arid basins in Makkah area, western Saudi Arabia

In arid regions, flash floods often occur as a consequence of excessive rainfall. Occasionally causing major loss of property and life, floods are large events of relatively short duration. Makkah area in western Saudi Arabia is characterized by high rainfall intensity that leads to flash floods. This study quantifies the hydrological characteristics and flood probability of some major wadis in western Saudi Arabia, including Na’man, Fatimah, and Usfan. Flood responses in these wadis vary due to the nature and rainfall distribution within these wadis. Rainfall frequency analysis was performed using selected annual maximums of 24-h rainfall from eight stations located in the area. Two of the most applied methods of statistical distribution, Gumbel’s extreme value distribution and log Pearson type III distribution, were applied to maximum daily rainfall data over 26 to 40 years. The Gumbel’s model was found to be the best fitting model for identifying and predicting future rainfall occurrence. Rainfall estimations from different return periods were identified. Probable maximum floods of the major wadis studied were also estimated for different return periods, which were extrapolated from the probable maximum precipitation.     

RegCM3模式在西北地区的应用研究Ⅱ:区域选择及参数化方案的敏感性

通过数值模拟方法,研究了降水对区域尺度、积云对流参数化等的敏感性.结果表明:由于较小区域尺度的模式内部场和大尺度分析场激发的外强迫之间有更强的束缚,这种束缚使得内外强迫更容易达到一致.小区域尺度模拟的降水型比大的区域尺度的模拟更好,但同时,大的区域尺度消弱了由于模式侧边界效应产生的虚假动力效应,模拟的降水在量值上更加接近于观测值.因此,进行区域气候模拟时,须根据需要对模式区域进行仔细的选择.结果同时表明,由于Grell方案倾向于模拟更多的对流降水,因此Kuo-Anthes方案对西北地区降水型和量值的模拟比Grell方案更接近于实际.由于地形对于降水的重要意义,在复杂地形下进行区域气候模拟时有必要在模式中仔细描述地形.     

我国西南山区降雨侵蚀力时空变化趋势研究

降雨是我国西南山区土壤侵蚀的主要动力因素,降雨侵蚀力反映了降雨对土壤侵蚀的潜在能力,研究降雨侵蚀力的时空变化趋势对我国西南山区土壤侵蚀的监测、评估、预报和治理具有重要意义。利用1960—2009年129个气象站逐日降雨量资料,计算出西南山区各气象站逐年降雨侵蚀力。采用趋势系数、气候倾向率和克吕格插值等方法对西南山区降雨侵蚀力50年来的时空变化趋势进行了探讨。结果表明:西南山区降雨侵蚀力空间分布特征与年降水量的空间分布特征一致;西南山区西北部的青藏高原区域降雨侵蚀力年际变化明显,变差系数Cv一般高于0.40;西南山区大部地区降雨侵蚀力呈上升趋势,说明由降雨侵蚀力引起的土壤侵蚀风险在增加,但在成都平原附近降雨侵蚀力在明显下降;降雨侵蚀力变化趋势系数随海拔高度升高而不断增加,在海拔2 500 m以上地区尤为明显,西南山区西北部的高海拔地区海拔高度对降雨侵蚀力增加具有放大效应。     

基于随机雨型的山洪灾害预警模式

针对雨型随机性所导致山洪灾害预警预报空报、漏报率过高问题,为提升山洪灾害预警精度,依据概率分布传递扩散原理,以雨型特征参数为控制条件,提出了基于参数控制的随机雨型生成法,建立了基于随机雨型的山洪灾害临界雨量计算模型及考虑决策者风险偏好的预警模式。以裴河流域为例,对不同雨型集下的临界雨量进行对比分析,并确定研究区6h临界雨量阈值空间。结果表明:雨峰位置、峰值倍比、前期土壤含水量对临界雨量的影响范围分别为32%~34%、33%~34%、15%~22%;雨型较前期影响雨量对临界雨量影响幅度更大;由雨峰位置系数和峰值倍比(r,bmax)双因子雨型集所确定的6h临界雨量阈值空间为98~185mm;考虑决策者不同风险偏好的临界雨量预警模式合理可靠,对更合理地开展山洪灾害预警工作具有指导意义。     

Evaluation of TRMM rainfall for soil moisture prediction in a subtropical climate

The Tropical Rainfall Measuring Mission (TRMM) is a joint space mission between NASA and the Japan Aerospace Exploration Agency (JAXA) designed to monitor and study tropical rainfall. In this study, the daily rainfall from TRMM has been utilized to simulate the soil moisture content up to 30 cm vertical soil profile of at an interval depth of 15 cm by using the HYDRUS 1D numerical model for the three plots. The simulated soil moisture content using ground-based rainfall and TRMM-derived rainfall measurements indicate an agreeable goodness of fit between the both. The Nash–Sutcliffe efficiency using ground-based and TRMM-derived rainfall was found in the range of 0.90–0.68 and 0.70–0.40, respectively. The input data sensitivity analysis of precipitation combined with different irrigation treatment indicates a high dependency of soil moisture content with rainfall input. The overall analysis reveals that TRMM rainfall is promising for soil moisture prediction in absence of ground-based measurements of soil moisture.     

Gradual Deformation and Iterative Calibration of Gaussian-Related Stochastic Models

This paper describes a new method for gradually deforming realizations of Gaussian-related stochastic models while preserving their spatial variability. This method consists in building a stochastic process whose state space is the ensemble of the realizations of a spatial stochastic model. In particular, a stochastic process, built by combining independent Gaussian random functions, is proposed to perform the gradual deformation of realizations. Then, the gradual deformation algorithm is coupled with an optimization algorithm to calibrate realizations of stochastic models to nonlinear data. The method is applied to calibrate a continuous and a discrete synthetic permeability fields to well-test pressure data. The examples illustrate the efficiency of the proposed method. Furthermore, we present some extensions of this method (multidimensional gradual deformation, gradual deformation with respect to structural parameters, and local gradual deformation) that are useful in practice. Although the method described in this paper is operational only in the Gaussian framework (e.g., lognormal model, truncated Gaussian model, etc.), the idea of gradually deforming realizations through a stochastic process remains general and therefore promising even for calibrating non-Gaussian models.     

全球大气季节内振荡对长江流域持续暴雨影响的研究进展

在引证论述大气季节内振荡(ISO)对暴雨(强降水)重要作用的基础上,概括性地回顾影响长江流域持续暴雨的大气ISO基本特征及其形成机制的主要成果。重点针对全球热带内外不同时间尺度的大气ISO的空间变化和年际变化与长江流域持续暴雨之间联系的研究工作进行总结评述,较为完整地总结长江流域夏季降水季节内变化的气候特征和全球不同空间和时间尺度的ISO对东亚副热带地区持续暴雨影响的已有认识,并结合2个半球的ISO与长江流域持续暴雨关系的研究现状,对未来暴雨(强降水)与不同时尺度ISO相互作用及其在10～30 d延伸期预报中的应用中有价值的科学问题和研究热点进行探讨,以期强调南半球ISO变化在全球和东亚副热带气候系统中的重要地位,提高夏季长江流域持续暴雨10～30 d延伸期预报和旱涝气候预测准确率。     

Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging

Conditioning realizations of stationary Gaussian random fields to a set of data is traditionally based on simple kriging. In practice, this approach may be demanding as it does not account for the uncertainty in the spatial average of the random field. In this paper, an alternative model is presented, in which the Gaussian field is decomposed into a random mean, constant over space but variable over the realizations, and an independent residual. It is shown that, when the prior variance of the random mean is infinitely large (reflecting prior ignorance on the actual spatial average), the realizations of the Gaussian random field are made conditional by substituting ordinary kriging for simple kriging. The proposed approach can be extended to models with random drifts that are polynomials in the spatial coordinates, by using universal or intrinsic kriging for conditioning the realizations, and also to multivariate situations by using cokriging instead of kriging.