Understanding the spatial behaviour of soil nutrients is essential for fertilizer management. Traditionally, comparison of soil testing methods has been performed using simple correlation analysis. The aims of this work were: (a) to characterize patterns of spatial variability of micronutrient concentrations obtained by two different soil testing methods, using single multifractal spectra, and (b) to compare the scale‐dependent relationship between the two datasets by joint multifractal analysis. The soil study site was located in Pernambuco state, Brazil. A 384‐m transect was marked every 3 m on an Orthic Podzol, cropped to sugar cane, in Pernambuco state, Brazil. Both, Mehlich‐3 and DTPA‐extracted micronutrients were measured in each of the 132 collected soil samples. The spatial distributions of available Fe, Mn, Cu and Zn could be fitted with multifractal models, regardless of the soil testing method. The generalized dimension, D_q versus q, and singularity spectra, f(α) versus α, showed a multifractal nature. Except for Fe, the scaling heterogeneity of the spatial distributions was higher for the Mehlich‐3 than for the DTPA datasets. Moreover, Zn exhibited the highest multifractality in both cases. Joint multifractal analysis demonstrated strong positive correlations between the scaling indices of the studied micronutrients extracted by the two methods. There were, however, different degrees of association between the scaling indices of these micronutrients, which ranked as: Zn > Cu > Fe > Mn. Except for Mn, Pearson product moment correlations between concentrations of available micronutrients extracted by the two solutions at the single or point measurement scale were weaker than those of the respective scaling indices at multiple scales. Therefore, single multifractal analysis captured a great complexity in the spatial distribution of available Fe, Mn, Cu and Zn. Knowledge of the scaling behaviour of these available nutrients could be useful for transferring information about variability from one scale to another for soil fertility management. This study suggests that correlation analysis at the single or point measurement scale may not be sufficient to fully characterize the concentrations of microelements extracted by two different methods, whereas joint multifractal analysis showed potential to improve calibration of soil micronutrient testing.

中文翻译：

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两种方法在粗糙纹理土壤中沿样带提取的土壤微量营养素的多重分形和联合多重分形分析

了解土壤养分的空间行为对于肥料管理至关重要。传统上，土壤测试方法的比较是使用简单的相关分析进行的。这项工作的目的是：（a）使用单一多重分形光谱表征通过两种不同的土壤测试方法获得的微量营养素浓度的空间变异模式，以及（b）通过联合多重分形比较两个数据集之间的比例相关关系。分析。土壤研究地点位于巴西伯南布哥州。在巴西伯南布哥州的一个种植于甘蔗的Orthic Podzol上，每3 m就会标记一个384 m的样带。在收集的132个土壤样品中分别测量了Mehlich-3和DTPA提取的微量营养素。有效铁，锰，不管土壤测试方法如何，Cu和Zn都可以使用多重分形模型进行拟合。广义维度d _q相对于q，奇点光谱f（α）相对于α，表现出多重分形的性质。除Fe以外，Mehlich-3的空间分布的尺度异质性高于DTPA数据集。此外，在两种情况下，Zn均表现出最高的多重分形性。联合多重分形分析表明，两种方法提取的研究微量营养素的定标指数之间存在很强的正相关性。但是，这些微量营养素的缩放指数之间存在不同程度的关联，排名为：Zn> Cu> Fe> Mn。除锰外，两种溶液在单一或点测量尺度下提取的可用微量营养素浓度之间的皮尔逊产物矩相关性弱于在多个尺度下的相应尺度指数。所以，单次分形分析在可用铁，锰，铜和锌的空间分布中捕获了极大的复杂性。这些可用养分的结垢行为的知识对于将有关变异性的信息从一种尺度传递到另一种尺度对于土壤肥力管理可能是有用的。这项研究表明，单点或单点测量规模的相关分析可能不足以完全表征通过两种不同方法提取的微量元素的浓度，而联合多重分形分析显示了改善土壤微量营养素测试校准的潜力。这些可用养分的结垢行为的知识对于将有关变异性的信息从一种尺度传递到另一种尺度对于土壤肥力管理可能是有用的。这项研究表明，单点或单点测量规模的相关分析可能不足以完全表征通过两种不同方法提取的微量元素的浓度，而联合多重分形分析显示了改善土壤微量营养素测试校准的潜力。这些可用养分的结垢行为的知识对于将有关变异性的信息从一种尺度传递到另一种尺度对于土壤肥力管理可能是有用的。这项研究表明，单点或单点测量规模的相关分析可能不足以完全表征通过两种不同方法提取的微量元素的浓度，而联合多重分形分析显示了改善土壤微量营养素测试校准的潜力。