不同插值方法对成分数据空间预测结果的影响——以土壤连续分类模糊隶属度值为例

Influences of Different Interpolation Methods on Spatial Prediction of Compositional Data——A Case of Fuzzy Membership Values of Soil Continuous Classification

地球科学中成分数据(compositional data)非常普通,其在进行空间插值时必须满足4个条件:每一位置各组分之和为常数,每一组分为非负,插值结果无偏最优。本文以土壤连续分类模糊隶属度值为例,数据经对数正态变换、非对称对数比转换、对称对数比转换后进行普通克里格插值结果和成分克里格插值(compositional kriging)结果进行比较。结果表明,对原始数据和经对数正态变换后数据进行插值,每一位置预测结果隶属度之和不能满足常数1。经非对称对数比转换后,插值结果虽然满足各个位置组分之和为1,但是预测结果精度较低,且预测结果空间分布连续性不明显。数据经对称对数比转换后插值结果和成分克里格插值结果,都能满足成分数据空间插值的4个条件,但二者各有优势。相比较而言,对称对数比转换方法得到的预测结果更能体现土壤空间连续渐变特征,而成分克里格插值结果能保证隶属度本身是最优无偏估计。

Compositional data is very common in geosciences, which must meet four conditions in spatial interpolation, including ensuring positive definiteness and a constant sum of interpolated values at a given position, error minimization and lack of bias. This study took a case of fuzzy membership values of soil continuous classification, applied three methods of data transformation prior to kriging, i.e., logarithm transformation （LN）, asymmetry Logratio transformation （ALR） and symmetry Logratio transformation （SLR）. The performance of the transformed values by ordinary kriging was compared with the spatial prediction of the untransformed data using ordinary kringing （UTok）, compositional kriging （CK）. The results showed that the sum of interpolated values at a given position wasn＇t equal to constant 1 by UTok and LN. Obviously, the above predictive result was theoretically unauthentic. Contrarily, membership values of all the spatial predicted sites summed to 1 when the membership values of the known soils were transformed by asymmetry Logratio and symmetry Logratio approaches and compositional kriging. Comparatively, symmetry Logratio transform could lead to a better spatial continuous distribution pattern. Interpolation results by compositional kriging could keep membership values either unbiased predictions or minimum prediction error variances.