INTERPOLATING MEAN RAINFALL USING THIN-PLATE SMOOTHING SPLINES
INTERPOLATING MEAN RAINFALL USING THIN-PLATE SMOOTHING SPLINES
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DOI：
10.1080/02693799508902045
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发表时间：
1995-07-01
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影响因子：
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通讯作者：
HUTCHINSON, MF
中科院分区：
文献类型：
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作者：
HUTCHINSON, MF
薄板平滑样条提供了准确的，操作简单，计算效率高的解决方案的空间插值的问题的一个标准的时间段的年平均降雨量从点数据，其中包含许多短期降雨量的手段。分析依赖于开发一个统计模型的观测到的降雨量的空间变化的手段，被认为是嘈杂的估计标准周期的手段。该模型的误差结构有两个组成部分，分别考虑到观察到的短期均值与标准周期均值的强烈空间相关偏离，以及通过位置和海拔的平滑函数表示标准周期平均降雨量的不相关缺陷。薄板样条，与程度的平滑确定最小化广义交叉验证，可以估计这个光滑的功能在两个方面。首先，通过估计相应的非对角误差协方差矩阵，可以直接适应数据的空间相关误差结构。其次，可以通过使用线性回归将观察到的短期平均值标准化为标准周期平均值估计值来消除数据误差结构中的空间相关性。当应用到数据的两种方法给出了类似的插值精度，和误差估计的拟合表面是在良好的协议与保留数据的残差。简化版本的数据误差模型，它只需要在每个位置的最低限度的汇总数据，也提出。用这些模型获得的插值精度仅略低于用更完整的统计模型获得的精度。它示出，一个连续的，空间变化的，适当缩放的高程的依赖性的结合，使表面精度的主要贡献。根据数字高程模型确定的方面的依赖性，只会带来微小的进一步改进。
Thin plate smoothing splines provide accurate, operationally straight-forward and computationally efficient solutions to the problem of the spatial interpolation of annual mean rainfall for a standard period from point data which contains many short period rainfall means. The analyses depend on developing a statistical model of the spatial variation of the observed rainfall means, considered as noisy estimates of standard period means. The error structure of this model has two components which allow separately for strong spatially correlated departures of observed short term means from standard period means and for uncorrelated deficiencies in the representation of standard period mean rainfall by a smooth function of position and elevation. Thin plate splines, with the degree of smoothing determining by minimising generalised cross validation, can estimate this smooth function in two ways. First, the spatially correlated error structure of the data can be accommodated directly by estimating the corresponding non-diagonal error covariance matrix. Secondly, spatial correlation in the data error structure can be removed by standardising the observed short term means to standard period mean estimates using linear regression. When applied to data both methods give similar interpolation accuracy, and error estimates of the fitted surfaces are in good agreement with residuals from withheld data. Simplified versions of the data error model, which require only minimal summary data at each location, are also presented. The interpolation accuracy obtained with these models is only slightly inferior to that obtained with more complete statistical models. It is shown that the incorporation of a continuous, spatially varying, dependence on appropriately scaled elevation makes a dominant contribution to surface accuracy. Incorporating dependence on aspect, as determined from a digital elevation model, makes only a marginal further improvement.