Spatial covariation of Azotobacter abundance and soil properties: A case study using the wavelet transform

The soil microflora is very heterogeneous in its spatial distribution. The origins of this heterogeneity and its significance for soil function are not well understood. A problem for understanding spatial variation better is the assumption of statistical stationarity that is made in most of the statistical methods used to assess it. These assumptions are made explicit in geostatistical methods that have been increasingly used by soil biologists in recent years. Geostatistical methods are powerful, particularly for local prediction, but they require the assumption that the variability of a property of interest is spatially uniform, which is not always plausible given what is known about the complexity of the soil microflora and the soil environment. We have used the wavelet transform, a relatively new innovation in mathematical analysis, to investigate the spatial variation of abundance of Azotobacter in the soil of a typical agricultural landscape. The wavelet transform entails no assumptions of stationarity and is well suited to the analysis of variables that show intermittent or transient features at different spatial scales.In this study, we computed cross-variograms of Azotobacter abundance with the pH, water content and loss on ignition of the soil. These revealed scale-dependent covariation in all cases. The wavelet transform also showed that the correlation of Azotobacter abundance with all three soil properties depended on spatial scale, the correlation generally increased with spatial scale and was only significantly different from zero at some scales. However, the wavelet analysis also allowed us to show how the correlation changed across the landscape. For example, at one scale Azotobacter abundance was strongly correlated with pH in part of the transect, and not with soil water content, but this was reversed elsewhere on the transect.The results show how scale-dependent variation of potentially limiting environmental factors can induce a complex spatial pattern of abundance in a soil organism. The geostatistical methods that we used here make assumptions that are not consistent with the spatial changes in the covariation of these properties that our wavelet analysis has shown. This suggests that the wavelet transform is a powerful tool for future investigation of the spatial structure and function of soil biota.     

Analysing spatially intermittent variation of nitrous oxide emissions from soil with wavelets and the implications for sampling

Emissions of gases from the soil are known to vary spatially in a complex way. In this paper we show how such data can be analysed with the wavelet transform. We analysed data on rates of N₂O emission from soil cores collected at 4‐m intervals on a 1024‐m transect across arable land at Silsoe in England. We used a thresholding procedure to represent intermittent variation in N₂O emission from the soil as a sparse wavelet process, i.e. one in which most of the wavelet coefficients are not significantly different from zero. This analysis made clear that the rate of N₂O emission varied more intermittently on this transect than did soil pH, for which many more of the wavelet coefficients had to be retained. This account of intermittent variation motivated us to consider a class of random functions, which we call wavelet random functions, for the simulation of spatially intermittent variation. A wavelet random function (WRF) is an inverse wavelet transform of a set of random wavelet coefficients with specified variance at each scale. We generated intermittent variation at a particular scale in the WRF by specifying a binormal process for the wavelet coefficients at this scale. We showed by simulation that adaptive sampling schemes are more efficient than ordinary stratified random sampling to estimate the mean of a spatial variable that is intermittent at a particular scale. This is because the sampling can be concentrated in the more variable regions. When we simulated values that emulate the intermittency of our data on N₂O we found that the gains in efficiency from simple adaptive sampling schemes were small. This was because the emission of N₂O is intermittent over several disparate scales. More sophisticated adaptive sampling is needed for these conditions, and it should embody knowledge of the relevant soil processes.     

Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transform

The magnitude of variation in soil properties can change from place to place, and this lack of stationarity can preclude conventional geostatistical and spectral analysis. In contrast, wavelets and their scaling functions, which take non‐zero values only over short intervals and are therefore local, enable us to handle such variation. Wavelets can be used to analyse scale‐dependence and spatial changes in the correlation of two variables where the linear model of coregionalization is inadmissible. We have adapted wavelet methods to analyse soil properties with non‐stationary variation and covariation in fairly small sets of data, such as we can expect in soil survey, and we have applied them to measurements of pH and the contents of clay and calcium carbonate on a 3‐km transect in Central England. Places on the transect where significant changes in the variance of the soil properties occur were identified. The scale‐dependence of the correlations of soil properties was investigated by calculating wavelet correlations for each spatial scale. We identified where the covariance of the properties appeared to change and then computed the wavelet correlations on each side of the change point and compared them. The correlation of topsoil and subsoil clay content was found to be uniform along the transect at one important scale, although there were significant changes in the variance. In contrast, carbonate content and pH of the topsoil were correlated only in parts of the transect.     

Exploring the variation in soil saturated hydraulic conductivity under a tropical rainforest using the wavelet transform

Saturated hydraulic conductivity (K_s) of the soil is a key variable in the water cycle. For the humid tropics, information about spatial scales of K_s and their relation to soil types deduced from soil map units is of interest, as soil maps are often the only available data source for modelling. We examined the influence of soil map units on the mean and variation in K_s along a transect in a tropical rainforest using undisturbed soil cores at 0–6 and 6–12 cm depth. The K_s means were estimated with a linear mixed model fitted by residual maximum likelihood (REML), and the spatial variation in K_s was investigated with the maximum overlap discrete wavelet packet transform (MODWPT). The mean values of K_s did not differ between soil map units. The best wavelet packet basis for K_s at 0–6 cm showed stationarity at high frequencies, suggesting uniform small‐scale influences such as bioturbation. There were substantial contributions to wavelet packet variance over the range of spatial frequencies and a pronounced low frequency peak corresponding approximately to the scale of soil map units. However, in the relevant frequency intervals no significant changes in wavelet packet variance were detected. We conclude that near‐surface K_s is not dominated by static, soil‐inherent properties for the examined range of soils. Several indicators from the wavelet packet analysis hint at the more dominant dynamic influence of biotic processes, which should be kept in mind when modelling soil hydraulic properties on the basis of soil maps.     

砂壤质褐土饱和导水率与物理性质的多尺度关系——小波分析法

正确估算土壤水力特性是准确了解土壤水分运动和溶质运移过程的前提。土壤水力特性具有明显的空间变异特征,由于其空间异质性是各种物理、化学和生物过程(如生物活动、耕作、地形、土壤侵蚀)在不同尺度下综合作用的产物,导致其变异     

连续小波变换在齿轮磨损估计中应用研究

通过对连续小波变换的分析研究,提出了一种提取信号在小波尺度上的能量谱的信号分析方法。该方法能有效地对不同磨损状况下的齿轮振动信号进行分析,分析结果说明信号在小波尺度上的能量谱与齿轮的磨损程度有密切的关系。求出不同磨损状况下齿轮振动信号的能量谱对尺度的积分值,并根据这些值拟合得到的曲线与齿轮磨损过程曲线非常相似,这说明可以用连续小波变换的能量谱估计齿轮磨损状况。最后提出了一种连续小波变换的齿轮磨损特征量提取方法,用于提取齿轮磨损程度的特征向量,特征量间的欧氏距离说明这些特征向量能很好地表征齿轮的磨损状况     

基于特征集成学习的四川省土壤厚度预测

以四川省土壤厚度预测为例，为农业生产与生态环境评价中土壤厚度空间分布图的编制提供方法支持。对比分析了随机森林、分位数回归森林、支持向量机、集成学习模型对连续型土壤厚度的预测精度，并提出了一种基于特征集成学习的土壤厚度类型预测算法。研究结果表明：①四川省土壤厚度具有较高的空间异质性，控制其空间变化的主要地形因子包括谷底平坦综合指数、高程与地形湿度指数；②四川省土壤厚度预测模型的决定系数为0.32~0.47，均方根误差为0.28~0.41 m；③面向连续型土壤厚度预测的集成模型具有较高的预测精度与稳健性，能够充分集成子模型的优势。特征集成学习能够有效集成并融合了连续型土壤厚度预测与离散型土壤厚度类型预测结果，通过减少方差来提高预测结果的稳健性。     

The representation of complex soil variation on wavelet packet bases

The discrete wavelet packet transform (DWPT) is an advanced wavelet technique that has distinct advantages over the discrete wavelet transform (DWT) previously used in soil science. Because the DWT divides the spatial frequencies of the data into non‐uniform intervals, it may fail to resolve features of the spatial variation that a simpler spectral analysis might identify under stationary conditions. However, the DWPT allows us to retain the advantages of the DWT (particularly the lack of stationarity assumptions) while achieving much better resolution in the spatial frequency domain. This is at the cost of poorer spatial resolution at the higher frequencies. However, by selecting a best wavelet packet basis from among the many possible, according to some appropriate criterion, we can find a compromise between frequency and spatial resolution that is best suited to the representation of our particular data set. In this paper, I describe a number of analyses based on the DWPT and apply them to two data sets on the soil. The advantages of the DWPT with best basis selection are clearly illustrated. In particular, non‐stationary behaviour of a significant periodic component of variation was identified that could not be effectively resolved by the DWT. Improved resolution in the frequency domain allowed aspects of the non‐stationary variation of soil to be resolved in a multiresolution analysis (MRA) adapted to the variation of the data.     

优化光谱输入量的土壤有机质随机森林预测模型

以往的土壤有机质预测研究往往只提取一种光谱输入量,忽略了不同光谱输入量之间的互补性。为探究光谱输入量在预测土壤有机质时的最佳组合,以及不同光谱输入量在离散小波变换不同分解尺度下的变化趋势,该研究以宝清县土壤有机质为研究对象,对光谱反射率进行离散小波变换,对各个分解尺度下的特征光谱提取光谱特征参数、光谱指数以及主成分并分别组合,基于8种光谱输入量建立随机森林模型进行土壤有机质预测。结果表明：1)利用不同光谱输入量预测有机质的精度均高于直接使用光谱反射率建模的精度,将不同光谱输入量组合可以提升预测效果,单个光谱输入量中主成分的预测效果最好,组合中光谱特征参数和主成分的组合预测效果最好;2)随着分解尺度的变化,不同光谱输入量的预测精度的变化趋势也不同,并且单个光谱输入量的变化趋势也会影响该光谱输入量组合的变化趋势;3)所有预测结果中,精度最高的是分解尺度为6时光谱特征参数与主成分的组合,R²达到0.78,均方根误差达到1.32%,可以较好地预测土壤有机质。研究结果说明光谱输入量结合离散小波变换预测土壤有机质是可行的,可以为土壤有机质的预测提供可靠思路。     

Scaling analysis of soil water storage with missing measurements using the second‐generation continuous wavelet transform

Information on the spatial variability of soil water storage (SWS) at different scales is important for understanding various hydrological, ecological and biogeochemical processes in the landscape. However, various obstructions such as roads or water bodies may result in missing measurements and create an irregular spatial series. The wavelet transform can quantify spatial variability at different scales and locations but is restricted to regular measurements. The objective of this study was to analyse the spatial variability of SWS with missing measurements using the second‐generation continuous wavelet transform (SGCWT). Soil water content (converted to SWS by multiplying with depth) was measured with a neutron probe and time‐domain reflectrometry along a transect of 128 points. Because there were missing measurements, I used SGCWT to partition the total variation into different scales and locations. Whilst there were some small‐scale variations (< 20 m) along the transect, the medium scale variations (20–70 m with an average of about 30–45 m) were mainly concentrated within the depressions along the transect. The strongest variations were observed at around 90–110 m scale, representing the variations resulting from alternating knolls and depressions. Similar spatial patterns at different scales were observed during different seasons, indicating temporal stability in the spatial pattern of SWS. Among the controlling factors, the wavelet spectra of relative elevation (RE) and organic carbon (OC) were very similar to that of SWS. The wavelet covariance was also large between SWS and RE and OC at all seasons. As the OC reflects the long‐term history of water availability and might be controlled by topographic setting or elevation, it can be concluded that elevation is an important controlling factor of SWS irrespective of seasons in this type of landscape. The SGCWT provides a new way of analysing the spatial variability of regularly measured soil properties or those with missing measurements.     

Geostatistics and its application to soil science

Abstract. Geostatistics is principally the application of regionalized variable theory. The methods it embodies are applicable throughout the earth sciences for investigating the spatial variation of, and for estimating continuous random variables. The semi-variogram is the central tool of geostatistics. It can quantify the scale and intensity of spatial variation and it provides the essential spatial information for local estimation by kriging and for optimizing sample intensity. It can also be used in an exploratory manner to try to discover underlying causes of the variation. Geostatistical methods have been widely applied in the mining industry and there are many examples of their application in soil science. Their use is illustrated by a case study of soil spatial variation in the Wyre Forest of England.     

基于3S技术的地形起伏度与区域土壤侵蚀的相关性研究

地形起伏度直接影响着地面的径流变化,是导致土壤侵蚀的主要根源之一。分析两者相关性的前提是准确提取地形起伏度,而确定研究数据尺度下地形起伏度的最佳分析窗口是得出可靠结果的保障。在3S技术的支持下,运用均值变点法分析罗甸县基于DEM（空间分辨率为30 m×30 m）的最佳分析窗口,并依据2007年修正的土壤侵蚀分类分级标准估算研究区各样本单元的土壤侵蚀量,对两者进行相关性分析。结果表明:罗甸县在该尺度数据源下的最佳分析窗口为32×32,最佳统计面积为0.921 6 km²,实证了均值变点分析方法提取地形最佳分析窗口的可行性;地形起伏度与区域土壤侵蚀模数的相关系数为0.519 1,充分说明了作为宏观地形因子之一的地形起伏度是区域土壤侵蚀的主导因素之一。     

塔里木河上游典型绿洲土壤水盐空间分异特征

结合传统统计学与地统计学方法,以塔里木河上游典型绿洲阿拉尔垦区为研究区,根据64个样点的试验数据,分析样区表层(0-10cm)和亚表层(10-20cm)土壤水盐空间分异特征。结果表明,土壤水分、pH值、电导率和全盐具有明显的空间变异性。样区土壤盐碱化程度较高,土壤水分表现为中等变异性,pH值为弱变异性,电导率、全盐及大部分离子含量为强变异性,盐分呈现强烈的表聚性特性。土壤水分和表层pH值的半方差理论模型较符合指数模型,亚表层pH值、电导率和全盐较符合球状模型。各指标块金值/基台值在0.122～0.316之间,且表层小于亚表层,空间自相关性较高,变异更多受结构性因素影响,空间结构较为复杂。指标的空间分布与区域环境密切相关,各层土壤水分、电导率和全盐均为西北高于东南,即沿河岸-绿洲-荒漠方向递减,而pH值表现为相反的规律。研究区棉田的长期连作,使得水盐运动在多年耕作棉区较为活跃,中小尺度下水盐空间分布的异质性增强。     

温室土壤含水率与导热率空间分布及相关性

为探究土壤含水率与导热率的空间分布特征和相关性,选取温室中8 m×8 m供试地块,以1 m×1 m网格间距布设采样点,测定0～40 cm土壤含水率,并同步获取0～20 cm土层的导热率。基于经典统计学、地统计学、回归分析和谱分析等理论,对土壤含水率与导热率的空间分布特征和相关性进行研究。结果表明,土壤含水率在0～40 cm土层呈现先升高后降低的趋势,且在20～30 cm土层均值最大。10～20 cm土层土壤导热率比0～10 cm土层高15.60%。各深度土层中土壤含水率及导热率存在着较强的空间相关性（块金系数<0.192）,而试验中随机因素引起的空间变异程度较低（块金值<0.540）,最小变程大于采样间距,说明网格布设满足空间分析要求。在供水均匀条件下,不同深度土层的蒸发强度与邻域地块的土壤水分含量亦会影响含水率空间分布。在含水率范围为17%～28%时,0～20 cm土层土壤含水率与导热率呈线性正相关（R2=0.837）,谱分析结果显示导热率在含水率序列上呈现长程负相关。     

Scale‐ and location‐dependent correlation of nitrous oxide emissions with soil properties: an analysis using wavelets

This paper shows how the wavelet transform can be used to analyse the complex spatial covariation of the rate of nitrous oxide (N₂O) emissions from the soil with soil properties that are expected to control the evolution of N₂O. We use data on N₂O emission rates from soil cores collected at 4‐m intervals on a 1024‐m transect across arable land at Silsoe in England. Various soil properties, particularly those expected to influence N₂O production in the soil, were also determined on these cores. We used the adapted maximal overlap discrete wavelet transform (AMODWT) coefficients for the N₂O emissions and soil variables to compute their wavelet covariances and correlations. These showed that, over the transect as a whole, some soil properties were significantly correlated with N₂O emissions at fine spatial scales (soil carbon content), others at intermediate scales (soil water content) and others at coarse spatial scales (soil pH). Ammonium did not appear to be correlated with N₂O emissions at any scale, suggesting that nitrification was not a significant source of N₂O from these soils in the conditions that pertained at sampling. We used a procedure to detect changes in the wavelet correlations at several spatial scales. This showed that certain soil properties were correlated with N₂O emissions only under certain conditions of topography or parent material. This is not unexpected given that N₂O is generated by biological processes in the soil, so the rate of emission may be subject to one limiting factor in one environment and a different factor elsewhere. Such changes in the relationship between variables from one part of the landscape to another is not consistent with the geostatistical assumption that our data are realizations of coregionalized random variables.     

基于连续小波变换的潮土有机质含量高光谱估算

土壤有机质含量快速估算对于土壤肥力评价、土壤信息化管理和精准施肥具有重要意义。该文通过对北京顺义地区64个土壤样品高光谱曲线进行连续小波变换,估算了该地区潮土有机质质量分数,并与4种常用光谱变换方法进行了比较。结果表明,潮土具有与其他类型土壤类似的光谱曲线,经过去包络线处理后,在可见与近红波段都出现了明显吸收峰;采用连续小波变换方法所确定的潮土有机质估算的敏感波段为1194、486和866nm,对应小波分解尺度为2,3和4;利用小波能量系数与有机质质量分数所构建的多元线性回归模型的决定系数R2为0.67,模型实测值与预测值的检验精度R2为0.75,RMSE为0.21;而采用4种常用光谱变换方法建立的潮土有机质估测模型的R2最高只有0.09,说明连续小波变换方法更适合于潮土有机质质量分数估测。Kringing插值分析表明,应在顺义地区东南部增加取样点,以提高模型估算精度。该研究可为潮土土壤肥力的快速测定提供参考。     

Estimation and analysis of soil hydraulic properties through infiltration experiments: comparison of BEST and DL fitting methods

The BEST method (Beerkan estimation of soil transfer parameters through infiltration experiments) appears promising and easy to estimate not only saturated hydraulic conductivity but also water retention and hydraulic characteristics. However, few tests have been conducted to test the methodology. This study involved field BEST infiltration experiments for three layers (surface, 15 and 30 cm) for each of three soils with different soil textures under grassland. By comparing BEST with DL (differentiated linearization method), we found that the DL method did not produce a good estimate of the soil hydraulic properties and neither did it identify the transient flow state. The BEST method resulted in reasonable results and is therefore promising. However, with BEST we encountered some anomalies when calculating hydraulic properties in some cases with too few data points under the transient flow state. We show that the application of BEST field experiments requires a wide range of soil water content from initial to saturated states so as to include sufficient transient flow. The soil hydraulic properties determined using the BEST method showed contrasting characteristics between different soil textures with higher saturated hydraulic conductivity under coarse texture and lower values under loam textures, especially with highly compacted soils. Vertical variation in soil hydraulic properties was significant, and the surface layer had a lower saturated hydraulic conductivity partly caused by compaction (high bulk density) or by remnants of grass plants. Further research on the effects of compaction and grass plants on soil hydraulic properties is needed.     

类别辅助变量参与下的土壤无偏采样布局优化方法

为了提高采样点在地理空间和辅助变量特征空间中的代表性,该文提出特征空间偏离指数用以测度采样点在特征空间中的无偏性,采用类别型辅助变量参与下的多维特征空间构建方法,融合地理空间和特征空间均匀分布的多目标优化目标函数,并利用空间模拟退火的方法实现采样点布局优化。以北京顺义区农田土壤重金属采样为例,选取土地利用类型、土壤质地和母质为辅助变量进行样点布局优化,并与特征空间均匀和地理空间均匀采样方法比较,结果表明:用于区域变量总体估计时,地理空间均匀采样估计精度最低,在采样尺度大于0.275时以特征空间均匀采样估计精度最好,而在采样尺度小于0.275时,无偏采样能获得更好的估计结果;在特征空间代表性方面,采样尺度较大时特征空间均匀采样样点代表性最好,采样尺度小于0.302时,无偏采样与特征空间均匀采样的代表性基本一致,地理空间采样点的代表性最差;用于空间制图时,无偏采样总体上比其他2种方法具有更好的制图精度。可见,在辅助变量支持的采样优化中,当采样尺度大且样点数较少时,适合采用特征空间均匀方法,且只能用于总体估计;采样尺度较小,样点数多时,适合采用无偏采样方法。该研究为利用辅助变量设计区域采样布局提供参考。     

Spectroscopic Determination of Soil Organic Carbon and Total Nitrogen Content in Pasture Soils

To explore a convenient and efficient approach for determining the content of soil organic carbon (SOC) and total nitrogen (TN), this study focused on capturing the features value of SOC and TN by applying the method of wavelet analysis and wavelet transformation. The soil used in the study was sampled from the pastures in Fukang City of Xinjiang Uygur Autonomous Region, China. The soil samples were tested by using a combined approach of chemical analysis and spectroscopy measurements. It was found that reflectance at 400–2500 nm was more strongly correlated to SOC than to TN. The maximum negative r values between reflectance and SOC + TN at 2309 nm was –0.81 (P < 0.01), and SOC/TN at 1693 was –0.48 (P < 0.05). The maximum correlation coefficient between SOC, TN, and wavelet coefficient was more than 0.96 compared to the relationship among SOC, TN, and spectral reflectance. By using continuous wavelet transformation (CWT), it was found that the maximum correlation coefficients were 0.981 at 2328 nm of scale 13 for SOC and 0.968 at 1741 nm of scale 6 for TN. These results also suggested that wavelet analysis was a better method for capturing the absorption features of soil properties and determining SOC and TN content.