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A spline kernel based smoothing algorithm: A comparison of methods with a spatiotemporal application to global climate fluctuations.

机译：基于样条核的平滑算法：时空应用方法对全球气候波动的比较。

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摘要

In statistics, smoothing is a technique that attempts to capture the key patterns or trends in data while leaving out the noise that is obscuring them. Nonparametric techniques are well-suited for smoothing as they do not rely on assumptions that the data arise from a given probability distribution.A common smoothing technique is Gaussian smoothing. Though common, the Gaussian kernel possesses infinite support, meaning that, in theory, every data point will be brought into consideration for each estimate thus, exact implementation is not possible. As an alternative, the truncated Gaussian kernel may be used. Here, the support of the kernel is truncated to some finite interval on the real line however, there is a discontinuity at the point of truncation, thereby leaking noise.To overcome these issues, a spatial smoothing algorithm (KZS), based on convolutions with the constant B-spline, that is, the uniform kernel, is introduced. This is an iterative algorithm corresponding to repeated applications of a moving average, in which the kernel approximates the Gaussian kernel having finite support.When applied in environments containing high levels of random noise and missing values, KZS achieved excellent recoveries of intricate signals and surfaces, having small relative errors. Based on several such illustrations, the KZS can be considered a comparable alternative to other commonly used smoothing methods.In a spatiotemporal application, using smoothing parameters determined from spectral information found in regional temperature, two global signals, 2-5 year periods and beyond 13 year periods, have been identified. Within monthly global temperature records, a long-term average temperature profile along latitude has been identified and parametrically approximated with great accuracy. A movie based on four-dimensional data of deviations from long-term local averages has been constructed to illustrate global warming. Maps of 2-5 year scales display deviations similarly to those observed during an El Nino event and provide the opportunity for explanation and prediction of weather anomalies in various global regions.In summary, the KZS smoothing algorithm is an effective tool for univariate and/or spatial analysis that is applicable to various areas of modern day research.Keywords: KZS, KZ filter, spline kernel, smoothing, moving average, B-spline, time series, global warming, El Nino.
机译：在统计中，平滑是一种尝试捕获关键模式或数据趋势，同时又消除了使它们模糊的噪声的技术。非参数技术非常适合平滑，因为它们不依赖于数据来自给定概率分布的假设。一种常见的平滑技术是高斯平滑。尽管很常见，但高斯核拥有无限的支持，这意味着，从理论上讲，每个估计都将考虑每个数据点，因此不可能实现精确。作为替代，可以使用截断的高斯核。在这里，内核的支持在实线上被截断到某个有限间隔，但是在截断点存在不连续性，从而泄漏了噪声。为了克服这些问题，基于卷积的空间平滑算法（KZS）引入了恒定的B样条曲线，即均匀核。这是一种迭代算法，对应于移动平均线的重复应用，其中内核近似具有有限支持的高斯内核。当在包含高水平随机噪声和缺失值的环境中使用时，KZS可以实现复杂信号和表面的出色恢复，相对误差较小。根据几个这样的图示，可以将KZS视为其他常用平滑方法的可比替代方案。在时空应用中，使用根据区域温度，两个全球信号，2-5年周期以及13年以上的频谱信息中确定的平滑参数确定的平滑参数年期间，已经确定。在每月的全球温度记录中，已经确定了沿纬度的长期平均温度分布，并以极高的精度进行了参数估算。已制作了一部电影，该电影基于与长期本地平均值的偏差的二维数据，来说明全球变暖。 2-5年尺度的地图显示的偏差与厄尔尼诺事件期间观察到的相似，并为解释和预测全球各个地区的天气异常提供了机会。总之，KZS平滑算法是单变量和/或关键词：KZS，KZ滤波器，样条核，平滑，移动平均，B样条，时间序列，全球变暖，厄尔尼诺现象。

著录项

  • 作者

    Cyr, Derek D.;

  • 作者单位

    State University of New York at Albany.;

  • 授予单位 State University of New York at Albany.;
  • 学科 Climate Change.Statistics.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 220 p.
  • 总页数 220
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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