Toward a general procedure for analysis of extreme random events in the earth sciences

Engineering and scientific approaches to design magnitude estimation are briefly revisited. Some defense is offered for use of annual maxima in design as if they were variables from a common distribution. However, to assume any particular form of distribution tail beyond the largest data value is not justifiable, regardless of the degree of data support over the main body of the distribution. An alternative approach to the design problem is suggested through use of parameter-free nonparametric estimation using the kernel method. Some simulation results are presented which suggest that the parameter-free approach is worthy of further development. A particular advantage of nonparametric methods is that competing estimators can be checked against parametric distributions, leading to a progressive improvement in estimator accuracy.This paper was presented (by title) at Engineering Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

储层参数平面分布预测方法评价

利用逐步回归分析、神经网络、相关滤波、协克里金和非参数回归分析等方法,实现了由地震资料与测井资料联合应用对孔隙度参数的平面分布预测。通过实例分析比较了各自的地质效果。归纳总结出各种方法的特点及应用条件。     

气候变化对洪水频率和洪峰流量的影响

以月平均流量和月最大洪峰流量的相关关系为基础,建立了洪水频率评价模型,并用非参数方法估计各级流量的条件概率.利用月水量平衡模型求得未来不同气候变化情况下的月均流量过程,并探讨气候变化对洪峰流量及洪水频率的影响.东江和汉江部分流域的应用结果表明,降水变化对洪水频率和洪峰流量的影响要比气温变化对其的影响敏感得多,气温升高2℃,降水增加10%～20%,2年一遇的洪水频率要相应增加19.1%～47.4%;20年一遇的洪峰流量要增加10.2%～24.1%.     

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基于矢耳石形态分析的凤鲚(Coilia mystus) 群体识别研究

以长江口、胶州湾、渤海湾和辽东湾4个地理群体的凤鲚(Coilia mystus)矢耳石样本为研究对象,采用形状指数和椭圆傅里叶系数分析相结合的方法研究了该4个凤鲚群体的矢耳石形态特征及差异性。方差分析结果表明,大部分形态变量存在显著的群体差异,引入协变量(耳石长)之后除形状因子外这种差异依然显著。基于协方差校正的判别分析只保留了耳石重量及9个傅里叶系数用于群体识别,而非参数检验的判别分析则保留了耳石重量、分形维数、环状度、矩形趋近率、圆度和19个傅里叶系数用于群体识别。相应地,基于非参检验的凤鲚群体的总体识别成功率(68.2%)明显高于协方差校正的判别分析结果(46.2%),表明前者比后者更能提高耳石形态分析的群体识别能力。     

Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach

Abstract

Hydrological models are commonly used to perform real-time runoff forecasting for flood warning. Their application requires catchment characteristics and precipitation series that are not always available. An alternative approach is nonparametric modelling based only on runoff series. However, the following questions arise: Can nonparametric models show reliable forecasting? Can they perform as reliably as hydrological models? We performed probabilistic forecasting one, two and three hours ahead for a runoff series, with the aim of ascribing a probability density function to predicted discharge using time series analysis based on stochastic dynamics theory. The derived dynamic terms were compared to a hydrological model, LARSIM. Our procedure was able to forecast within 95% confidence interval 1-, 2- and 3-h ahead discharge probability functions with about 1.40 m³/s of range and relative errors (%) in the range [–30; 30]. The LARSIM model and the best nonparametric approaches gave similar results, but the range of relative errors was larger for the nonparametric approaches.

Editor D. Koutsoyiannis; Associate editor K. Hamed

Citation Costa, A.C., Bronstert, A. and Kneis, D., 2012. Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach. Hydrological Sciences Journal, 57 (1), 10–25.     

雷达高度计海况偏差估计非参数模型研究

本文基于Jason-2高度计,采用核函数估计（NW）和局部线性回归估计(LLR)两种非参数估计方法,选用高斯(Gaussian)核函数和球谐(Epanechnikov)核函数及固定带宽和局部可调带宽。对不同组合形式的模型进行优选,确定LLR估计方法的Epanechnikov核函数、局部可调带宽为最优非参数模型。通过对最优非参数模型和参数模型结果进行对比分析表明,非参数模型在北高纬度区域表现更优,而在中低纬度及南纬区域参数模型不失优势。将非参数模型应用于我国HY-2A高度计,得到与以上同样的结论。     

顾及系统误差的坐标转换方法研究

针对Bursa模型在坐标系转换时没有顾及局部变形和累积误差的问题,通过对坐标转换误差进行分析,本文提出将由此产生的系统误差看作非参数信号的半参数估计,采用半参数模型对某一区域坐标进行解算,并对检核点非参数分量进行推估,与Bursa模型进行比较,结果表明半参数模型能够有效地消除系统误差。并探讨了不同确定平滑因子α的方法对坐标转换精度影响,计算结果表明,在正则矩阵R相同情况下,不同平滑因子确定方法得到的坐标转换精度有所不同,但均优于Bursa模型转换精度。     

Summary statistics in geochemistry: A study of the performance of robust estimates

Numerical data summaries in many geochemical papers rely on arithmetic means, with or without standard deviations. Yet the mean is the worst average (estimate of location) for those extremely common geochemical data sets which are non-normally distributed or include outliers. The widely used geometric mean, although allowing for skewed distributions, is equally susceptible to outliers. The superior performance of 19 robust estimates of location (simple median, plus various combined, adaptive, trimmed, and skipped,L, M, andW estimates) is illustrated using real geochemical data sets varying in sources of error (pure analytical error to multicomponent geological variability), modality (unimodal to polymodal), size (20 to >2000 data values), and continuity (continuous to truncated in either or both tails). The arithmetic mean tends to overestimate location of many geochemical data sets because of positive skew and large outliers; robust estimates yield consistent smaller averages, although some (e.g., Hampel's and Andrew's) do perform better than others (e.g., Shorth mean, dominant cluster mode). Recommended values for international standard rocks, and for such important geochemical concepts as average chondrite, can be reproduced far more simply via robust estimation on complete interlaboratory data sets than via the rather complicated and subjective methods (e.g., laboratory ratings) so far used in the literature. Robust estimates also seem generally less affected by truncation than the mean; for example, if values below machine detection limits are alternatively treated as missing values or as real values of zero, similar averages are obtained. The standard (and mean) deviations yield consistently larger values of scale for many geochemical data sets than the hinge width (interquartile range) or median absolute deviation from the median. Therefore, summaries of geochemical data should always include at least the simple median and hinge width, to complement the often misleading mean and standard deviation.     

An empirical coverage test for the g -sample problem

A nonparametricg-sample empirical coverage test has recently been developed for univariate continuous data. It is based upon the empirical coverages which are spacings of multiple random samples. The test is capable of detecting any distributional differences which may exist among the parent populations, without additional assumptions beyond randomness and continuity. The test can be effective with the limited and/or unequal sample sizes most often encountered in geologic studies. A computer program for implementing this procedure, G-SECT 1, is available.