A linear mixed model, with non-stationary mean and covariance, for soil potassium based on gamma radiometry
A linear mixed model, with non-stationary mean and covariance, for soil potassium based on gamma radiometry
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DOI：
10.5194/bg-7-2081-2010
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发表时间：
2010-07
期刊：
影响因子：
4.9
通讯作者：
K. Haskard;B. Rawlins;R. Lark
中科院分区：
文献类型：
--
作者：
K. Haskard;B. Rawlins;R. Lark
抽象的。在本文中，我们提出了英格兰东部大片地区土壤钾含量的线性混合模型，其中平均值被建模为通常与钾衰变相关的能量区间内地球表面被动伽马射线发射的线性函数。针对随机效应提出了非平稳模型，即该回归未捕获的变化。具体来说，我们假设标准化随机效应的局部频谱可以通过调节公共（固定）频谱来获得，也就是说将其值提高到幂，即调节参数，其本身被建模为辐射数据的线性函数。这允许随机效应的“平滑度”局部变化。此外，局部空间相关方差和“块金”方差（考虑到采样分辨率，显然不相关）也可以建模为辐射数据的函数。使用辐射信号作为协变量可以提高验证地点土壤钾预测的精度。此外，有证据表明，随机效应的非平稳模型比平稳模型更适合数据，并且这种差异具有统计显着性。非平稳模型似乎也能更好地描述验证站点预测的误差方差。在选择替代非平稳模型方面需要进一步的工作，因为这里使用的简单程序基于比较嵌套模型的对数似然比和非嵌套模型的 Akaike 信息标准，没有识别出最能说明验证站点预测误差方差的模型。
Abstract. In this paper we present a linear mixed model for the potassium content of soil across a large region of eastern England in which the mean is modelled as a linear function of the passive gamma-ray emissions of the earth surface in the energy interval commonly associated with potassium decay. Non-stationary models are proposed for the random effect, which is the variation not captured by this regression. Specifically, we assume that the local spectrum of the standardized random effect can be obtained by tempering a common (stationary) spectrum, that is to say raising its values to a power, the tempering parameter, which is itself modelled as a linear function of the radiometric data. This allows the "smoothness" of the random effect to vary locally. In addition the local spatially correlated variance and "nugget" variance (apparently uncorrelated given the resolution of the sampling) can also be modelled as a function of the radiometric data. Using the radiometric signal as a covariate gave some improvement in the precision of predictions of soil potassium at validation sites. In addition, there was evidence that non-stationary models for the random effect fitted the data better than stationary models, and this difference was statistically significant. Non-stationary models also appeared to describe the error variance of predictions at the validation sites better. Further work is needed on selection among alternative non-stationary models, since simple procedures used here, based on comparing log-likelihood ratios of nested models and the Akaike information criterion for non-nested models, did not identify the model which gave the best account of the prediction error variances at validation sites.