Relationship between granitic soil particle-size distribution and shrinkage properties based on multifractal method

The mechanical properties of granitic residual soils vary with depth due to changes in soil type and heterogeneity caused by weathering. The purpose of this study was to relate the spatial variation of particle-size distribution (PSD) of granitic soils with soil shrinkage parameters using multifractal theory. The heterogeneity of PSD and pedogenic processes were depicted in detail by multifractal dimensions. The PSD generally increased with the increase of profile depth in accordance with the variation of single fractal dimension (D) ranging from 2.45 to 2.65. The shrinkage limit was greatly influenced by the multifractal dimension parameters, including information dimension (D₁) and capacity dimension (D₀) (Adjusted R²=0.998, P < 0.01), and the maximum linear extensibility (κ_v) was determined by spectral width (△α) and bulk density, with the latter explaining 89% of the total variance of κ_v (P < 0.01). Soil shrinkage characteristic curve was fitted by the modified logistic model (R² > 0.97, root sum of squares < 0.1), and the water variation corresponding to the maximum change rate of linear extensibility was determined by the silt content (R²=0.81, P < 0.01). Overall, the shrinkage of granitic soils was primarily influenced by PSD and soil compactness.     

陕北黄土丘陵沟壑区土壤粒径分形特征

应用MS2000激光粒度仪,获取陕北黄土高原米脂县境内10种不同土地利用类型土壤剖面4个层次40个土壤样品的粒径分布（PsD）,利用分形几何学方法分析土壤颗粒体积分形特征。结果表明：由于各土壤样品质地相同,分形维数D变化不大,在2．230～2．521之间;〈0．002mm的土壤粒径体积百分含量与D显著相关,而其余各粒径含量均通过与〈0．002mm的相关性对D产生间接影响,表明PSD的D可以充分代表土壤细化的程度与比例。土壤累积体积分数具有非线性特征,1个D值无法表征整个粒径测量范围内的土壤PSD,因此,以15脚为界,确定了2个分形域,分别计算D1和D2,存在D1〉D2的关系,且用D1和D2计算的分裂概率具有尺度依赖性。     

Fractal characterization of soil particle-size distribution under different land-use patterns in the Yellow River Delta Wetland in China

Purpose

Soil particle-size distribution (PSD) is an important soil physical property. Single- and multi-fractal models are increasingly used to characterize soil properties and may provide additional information. The Yellow River Delta is one of the best representative examples of river ecosystem wetlands in the world. In this area, different land resource development patterns strongly influence soil structure and fertility. Here, the single- and multi-fractal characterizations of soil PSD were determined based on fractal theory, and the correlations between PSD and soil organic matter (SOM) across different land-use patterns were studied.

Materials and methods

The study site was located in a typical area of the Yellow River Delta Wetland in Shandong Province in China. The tested soil samples were obtained from areas with four different land-use patterns, including integrated Robinia pseudoacacia and grass cover land (RPG), well-covered European and American poplar forestland (EAP), cropland used for growing cotton (COT), and waste grassland (WAG). Soil samples were air-dried and passed through a 2-mm screen. Based on the international system of soil size fraction, the soil PSD was described according to the percentages of clay, silt, and sand. The clay, silt, and sand fractions were determined using a laser particle size analyzer. The fractal characterizations of soil PSD were determined using the single- and multi-fractal methods.

Results and discussion

The single-fractal dimension (D) of the different land-use patterns varied greatly (between 2.4657 and 2.6789). The D values of the RPG and EAP were the greatest, which corresponded to the soils with the greatest silt content and the lowest sand content. In contrast, the D value of the WAG was the smallest, which corresponded with the lowest clay content and the greatest sand content. These results indicated that D was directly proportional to clay content and inversely proportional to sand content. The multi-fractal parameters of the soil PSD, capacity dimension (D ₀), information dimension (D ₁), and information dimension?/?capacity dimension (D ₁?/?D ₀), followed a regular trend due to different land-use patterns. These parameters decreased in the following order: RPG?>?EAP?>?COT?>?WAG. In addition, the PSD of the RPG and EAP varied widely and was more heterogeneous than the PSD of the COT and WAG. Furthermore, the single- and multi-fractal parameters were significantly correlated with SOM.

Conclusions

Our findings indicated that the single- and multi-fractal parameters adequately described the scaling properties of the soil PSD and the influences of soil structure and soil nutrients for the different land-use patterns in the Yellow River Delta Wetland of China.     

Multifractal characteristics of soil particle size distribution under different land-use types on the Loess Plateau,China

Soil particle-size distribution (PSD) is one of the most important physical attributes due to its great influence on soil properties related to water movement, productivity, and soil erosion. The multifractal measures were useful tools in characterization of PSD in soils with different taxonomies. Land-use type largely influences PSD in a soil, but information on how this occurs for different land-use types is very limited. In this paper, multifractal Rényi dimension was applied to characterize PSD in soils with the same taxonomy and different land-use types. The effects of land use on the multifractal parameters were then analyzed. The study was conducted on the hilly-gullied regions of the Loess Plateau, China. A Calcic Cambisols soil was sampled from five land-use types: woodland, shrub land, grassland, terrace farmland and abandoned slope farmland with planted trees (ASFP). The result showed that: (1) entropy dimension (D₁) and entropy dimension/capacity dimension ratio (D₁/D₀) were significantly positively correlated with finer particle content and soil organic matter. (2) D₀, D₁ and D₁/D₀ were significantly influenced by land use. Land use could explain 24.6–58.5% of variability of D₀, D₁/D₀ and D₁, which may be potential parameters to reflect soil physical properties and soil quality influenced by land use.     

Estimation of soil water retention function based on asymmetry between particle‐ and pore‐size distributions

By examining the symmetry between the distributions of particle‐size (PSD) and pore‐size (POD) in a soil, as hypothesized by early pore‐solid fractal (PSF) models, we found significant discrepancies in fractal dimensions between the PSD and the water retention curve (WRC) of a soil. Therefore, we developed an asymmetry‐based PSF model to estimate better the WRC directly from the PSD data of a soil. To do so, we adopted the concept of a microscopic arrangement of different‐sized particles to address such asymmetry, and evaluated the performance of the modified PSF model on five soil textural classes (coarse‐, moderately coarse‐, medium‐, moderately fine‐ and fine‐textured soils) using experimental PSD and WRC data from the UNSODA database (159 undisturbed soils for model calibration and 70 undisturbed soils for model validation). The fit of the symmetry‐based PSF model to the calibration dataset showed that the fractal dimension of the WRC (D_p) was slightly larger than that of cumulative mass distribution of particles (D_s) for most soils. The asymmetry‐based PSF model performed better than the symmetry‐based PSF model. In addition, the asymmetry‐based PSF model reduced the tendency to under estimate soil water content for a given matric head and the performance of the asymmetry‐based model was consistent irrespective of soil texture, indicating that the adoption of asymmetry between the PSD and the POD was adequate in predicting the WRC of a porous, particulate system such as soil.     

Assessing soil particle-size distribution on experimental plots with similar texture under different management systems using multifractal parameters

Soil particle-size distribution (PSD) is a fundamental soil physical attribute with dominant influence on many other soil properties. Laser diffraction combined with multifractal analyses have proven to be useful to obtain precise information from PSDs. The aim of this work was to assess similitude or difference of PSDs sampled on plots of an experimental field and belonging to the same textural class using multifractal parameters. The field experiment consisted of two tillage treatments and two cropping systems. It was conducted following a randomized complete split-block design with four replications on a Humic Dystrudept. Tillage treatments were conventional tillage (CT) and no tillage (NT) while crop rotations were ryegrass-sorghum (RS) and ryegrass-corn (RC). Particle-size distribution analysis by the sieve-pipette and by laser diffraction corroborate that all the samples were assigned to the same textural class. Singularity spectra f(α) and Rényi spectra, D_q, showed that multifractal distribution was a suitable model for PSDs obtained by laser diffraction. However, in the range of moments − 10 < q < 10, the r² values for the linear fits leading to a Rényi spectrum, D_q, were higher than those for the singularity spectrum, suggesting the former was better defined than the latter. No significant differences in multifractal parameters were found between plots with contrasted crop rotation, RS and RC. In contrast, Hölder exponent of order zero (α₀) and several parameters derived from the left branch of both, the f(α) and the D_q spectra, were significantly different between CT and NT treatments. No effects of mixing by cultivation were detected in our work, so that differences in PSDs between no-tilled and conventionally-tilled plots were simply attributed to patchiness and variation on the experimental field. Multifractal analysis of PSDs measured by laser diffraction provides further insight in verifying patterns of between plot soil texture variations (i.e. randomness or trends) in completely randomized block designs.     

CHARACTERIZING VARIATIONS IN SOIL PARTICLE‐SIZE DISTRIBUTION ALONG A GRASS–DESERT SHRUB TRANSITION IN THE ORDOS PLATEAU OF INNER MONGOLIA,CHINA

The application of fractal geometry to describe soil degradation and dynamics is becoming a useful tool for better understanding of the performance of soil systems. In this study, four different land cover types, which represent a sequence of grass–desert shrub transition and a gradient of desertification, were selected, and soils at depths of 0–10, 10–20 and 20–40 cm were sampled in the Ordos Plateau of Inner Mongolia, PR China. The fractal theory was used to analyse the soil particle‐size distribution (PSD) and its variations. The results showed that (i) vegetation conversion and desertification significantly changed the soil PSD. During the desertification process, soil coarse fractions that ranged from 250 to 100 µm significantly increased, whereas fine fractions lower than 50 µm significantly decreased (p < 0·01); (ii) fractal model of the accumulative volume particle‐size distribution is appropriate, and fractal dimensions (D_m) of soil PSD significantly decreased along the sequence of grass–desert shrub transition; (iii) D_m is more sensitive to the desertification process, and therefore, we suggest D_m other than soil texture and soil organic carbon as a reliable parameter to reflect the soil environment change induced by desertification. Copyright © 2011 John Wiley & Sons, Ltd.     

土壤水分特征曲线的分形模拟

Many empirical models have been developed to describe the soil water retention curve （SWRC）. In this study, a fractal model for SWRC was derived with a specially constructed Menger sponge to describe the fractal scaling behavior of soil; relationships were established among the fractal dimension of SWRC, the fractal dimension of soil mass, and soil texture; and the model was used to estimate SWRC with the estimated results being compared to experimental data for verification. The derived fractal model was in a power-law form, similar to the Brooks-Corey and Campbell empirical functions. Experimental data of particle size distribution （PSD）, texture, and soil water retention for 10 soils collected at different places in China were used to estimate the fractal dimension of SWRC and the mass fractal dimension. The fractal dimension of SWRC and the mass fractal dimension were linearly related. Also, both of the fractal dimensions were dependent on soil texture, i.e., clay and sand contents. Expressions were proposed to quantify the relationships. Based on the relationships, four methods were used to determine the fractal dimension of SWRC and the model was applied to estimate soil water content at a wide range of tension values. The estimated results compared well with the measured data having relative errors less than 10% for over 60% of the measurements. Thus, this model, estimating the fractal dimension using soil textural data, offered an alternative for predicting SWRC.     

Structure and self-similarity in silty and sandy soils: the fractal approach

Soil structure was studied using the concept of fractals and related to soil texture and aggregate properties such as surface charges and aggregate stability. The mass and porosity fractal dimensions (D_m and D_p) of silty and sandy soils were determined on in situ soils using a variety of soil sections (thin, very-thin and ultra-thin), by image analysis on a continuous scale from m to 10^?9 to 10^?1m. Surface fractal dimensions (D_s) of these soils were determined on < 2 mm air-dried samples using mercury porosimetry and the fractal cube generator model. The results suggest that soils are not pore fractals but mass and surface fractals with D_m= 1.1 D_s when the dimension of the embedding Euclidean space d is 3. The soil structures could possibly be described by fractal diffusion-limited aggregation with complex interconnected aggregates or by fractal cluster–cluster aggregation models. As a preliminary conclusion, the fractal approach appears to be a potentially useful tool for understanding the underlying mechanisms in the creation or destruction of soil structure.     

Spatial heterogeneity of loess contour tilled microtopographic slope in rainfall erosion

Loess tilled surface is the geographical unit for the quantitative study of the soil erosion process. Contour tillage has been proved to be the most effictive measure for soil and water conservation in the Chinese Loess Plateau. Studies on the spatial heterogeneity of loess tilled surfaces will contribute to the understanding of the mechanism of erosion evolution. For this, a laboratory experiment was performed on contour tilled sloping surfaces where the hydrological-erosive processes were simulated. At different erosion stages, point cloud measurements were made using a terrestrial laser scanning system (TLS); then the heterogeneity depending on detrending and directionality were analysed by both the semivariogram method and the rescaled range analysis method. Results showed that: (1) the fractal dimensions D_S and D_R were equivalent when determined from either the semivariogram method or the rescaled range analysis method, although the semivariogram method appears to be more reliable in identifying the specific stage of the erosion evolution process; (2) the contour tilled microtopographies had an anisotropy behavior depending on direction; (3) the fractal dimension (either D_S or D_R) in different erosion stages was less than 1.5, which indicates that the microtopography of the sloping surface exhibits characteristics of persistent fractional Brownian motion and positive spatial autocorrelation. Irrespective of tillage measure and slope percentage, the sloping surface can be regarded as having random roughness. The results reveals a quantitative relationship between microtopography and sloping erosion. Also, it may provide guidance for further studies regarding the spatial variability and heterogeneity of various tilled slopes on the microtopographic scale.     

Evaluation of 1H NMR relaxometry for the assessment of pore‐size distribution in soil samples

¹H NMR relaxometry is used in earth science as a non‐destructive and time‐saving method to determine pore size distributions (PSD) in porous media with pore sizes ranging from nm to mm. This is a broader range than generally reported for results from X‐ray computed tomography (X‐ray CT) scanning, which is a slower method. For successful application of ¹H NMR relaxometry in soil science, it is necessary to compare PSD results with those determined from conventional methods. The PSD of six disturbed soil samples with various textures and soil organic matter (SOM) content were determined by conventional soil water retention at matric potentials between −3 and −390 kPa (pF 1.5–3.6). These PSD were compared with those estimated from transverse relaxation time (T₂) distributions of water in soil samples at pF 1.5 using two different approaches. In the first, pore sizes were estimated using a mean surface relaxivity of each soil sample determined from the specific surface area. In the second and new approach, two surface relaxivities for each soil sample, determined from the T₂ distributions of the soil samples at different matric potentials, were used. The T₂ distributions of water in the samples changed with increasing soil matric potential and consisted of two peaks at pF 1.5 and one at pF 3.6. The shape of the T₂ distributions at pF 1.5 was strongly affected by soil texture and SOM content (R² = 0.51 − 0.95). The second approach (R² = 0.98) resulted in good consistency between PSD, determined by soil water retention, and ¹H NMR relaxometry, whereas the first approach resulted in poor consistency. Pore sizes calculated from the NMR data ranged from 100 μm to 10 nm. Therefore, the new approach allows ¹H NMR relaxometry to be applied for the determination of PSD in soil samples and for studying swelling of SOM and clay and its effects on pore size in a fast and non‐destructive way. This is not, or only partly, possible by conventional soil water retention or X‐ray CT.     

库布齐沙地滴灌人工林土壤水分运移及其与土壤分形特征的关系

【目的】探究库布齐沙地人工林滴灌下土壤水分运移规律以及其与土壤分形特征的关系,以期为人工林滴灌策略制定提供参考。【方法】以典型人工林为研究对象,基于激光粒度衍射法测得土壤粒径分布并计算单重及多重分形维数,通过大田试验明确灌水及水分再分布过程湿润锋动态变化规律,并采用通径和冗余分析等手段探究湿润锋运移与分形特征的联系。【结果】1)库布齐沙地滴灌人工林湿润锋水平及垂向运移可分别用对数函数(R2=0.941~0.990)和幂函数(R2=0.958~0.996)描述；2)砂粒含量高于70%、黏粒低于2.5%土壤条件下,利用粉粒、黏粒含量构建的多元回归模型能较好地计算停灌后二维水分运移距离(R²=0.839~1.0),但对停灌前适用性较差(R2=0.243~0.403)；3)单重分形维数D和信息维数D1、信息维数/容量维数D1/D0、关联维数D2均与砂粉比呈负相关,而滴灌形成的湿润体体积与砂粉比正相关,且D较D0、D1、D1/D0、D2更能解释土壤砂粉比差异对湿润锋运移的影响。【结论】滴灌下人工林水分运移满足函数定量关系,砂粒占比高于70%且黏粒低于2.5%时,土壤质地越粗则湿润体体积越大,可在灌溉策略制定时进行土壤粒径分析,节约决策成本。与库布齐沙地相似环境条件下,滴灌时长6h流量3.0L.h-1时,速生杨和榆树林在停灌后48h需启动下次灌溉,沙柳和旱柳林则不需要。     

不同风沙土壤颗粒的分形特征

应用土壤颗粒的重量与粒径分布原理来描述了古尔班通古特沙漠地风沙土壤颗粒的分形特征。通过对10种样品颗粒的机械组成进行分析,分别计算出了它们的分形维数(D=2.3237～2.9347),并分析了其与流动风沙土、半固定风沙土和固定风沙土之间的关系。分析结果表明,风沙土壤结构具有明显的分形特征,其粒径分布分形维数为2～3。土粒表面分形维数与2～0.2mm间的土粒含量存在显著的负相关;而与0.02～0.002mm和<0.002mm的颗粒含量存在显著的正相关,表现为随着土壤质地从流动风沙土、半固定风沙土到固定风沙土的变化,其土粒表面的平均分形维数呈依次增高。土粒表面分形维数与三种典型风沙土壤有机质含量为极显著正相关,而与其硬度为显著负相关。     

Variability in soil properties at different spatial scales (1 m-1 km) in a deciduous forest ecosystem

The purpose of this research was to test the hypothesis that variability in 11 soil properties, related to soil texture and soil C and N, would increase from small (1 m) to large (1 km) spatial scales in a temperate, mixed-hardwood forest ecosystem in east Tennessee, USA. The results were somewhat surprising and indicated that a fundamental assumption in geospatial analysis, namely that variability increases with increasing spatial scale, did not apply for at least five of the 11 soil properties measured over a 0.5-km² area. Composite mineral soil samples (15 cm deep) were collected at 1, 5, 10, 50, 250, and 500 m distances from a center point along transects in a north, south, east, and westerly direction. A null hypothesis of equal variance at different spatial scales was rejected (P?0.05) for mineral soil C concentration, silt content, and the C-to-N ratios in particulate organic matter (POM), mineral-associated organic matter (MOM), and whole surface soil. Results from different tests of spatial variation, based on coefficients of variation or a Mantel test, led to similar conclusions about measurement variability and geographic distance for eight of the 11 variables examined. Measurements of mineral soil C and N concentrations, C concentrations in MOM, extractable soil NH₄-N, and clay contents were just as variable at smaller scales (1-10 m) as they were at larger scales (50-500 m). On the other hand, measurement variation in mineral soil C-to-N ratios, MOM C-to-N ratios, and the fraction of soil C in POM clearly increased from smaller to larger spatial scales. With the exception of extractable soil NH₄-N, measured soil properties in the forest ecosystem could be estimated (with 95% confidence) to within 15% of their true mean with a relatively modest number of sampling points (n?25). For some variables, scaling up variation from smaller to larger spatial domains within the ecosystem could be relatively easy because small-scale variation may be indicative of variation at larger scales.     

兴国县红壤颗粒分形及其与环境因子的关系

以土壤颗粒组成数据为基础，运用分形模型，分析了红壤丘陵山区林地土壤颗粒的分形维数。结果表明：84个耕层土壤颗粒的分形维数D为2．568～2．828，其中紫色土2．722，红壤2．700，棕红壤2．693，黄红壤2．670，黄壤2．713。D随土壤质地的变细而增大。从空间分布上看，研究区域的西部和东南部D值较大，而西南部和北部D值较小，D在2．7～2．8的面积最大，为1171km^2，占总面积的47．0％，D在2．8以上的面积最小，为48km。，占总面积的1．9％。土壤分维数和坡向、海拔之间呈显著正相关关系，而与坡度、平面曲率、剖面曲率之间无明显的相关关系。     

Uncertainties in up-scaling N2O flux from field to 1°×1° scale: A case study for Inner Mongolian grasslands in China

Since N₂O emissions cannot be measured easily at large scales, global emission estimates inevitably involve problems with scaling. To date, up-scaling processes depend highly on the models and database. Because of the limitation in resolution of the databases, which provide input parameters to drive the model's regional simulations, the uncertainties generated from the up-scaling processes must be quantified. In this paper, the uncertainties in up-scaling N₂O emissions from the field scale (∼1 km²) to 1°×1° scale (∼10,000 km²) were quantified in a case study from the Xilin River basin of Inner Mongolia, China. A revised process-based DNDC model was applied in the study for quantifying N₂O fluxes with a high-resolution (1 km²) soil database constructed with remote sensing data and GIS technique. The results showed that the uncertainties coming from spatial scaling effect is 63.6%, and from the partitioning of sensitive model parameter (SOC) is 86.4%. We found that inclusion of spatial heterogeneity of soil factors resulted in lower regional N₂O emission estimates. Utilization of the spatial structural information based on soil type was more effective for reducing the spatial scaling effect in comparison with the variability information calculated from Monte Carlo method.     

我国水蚀区坡耕地土壤分离能力的空间分布与影响因素

我国水蚀区不同区域自然地理环境和土壤理化性质存在巨大差异,可能会引起土壤分离能力(Dc)的差异。然而目前大尺度上(如水蚀区)Dc的空间分布及其影响因素的研究尚未见报道。在水蚀区依据土壤类型和土壤质地不同布设了36个采样点,用扰动土(代表新耕坡耕地)测定其Dc并分析其影响因素。结果表明,水蚀区沙漠风沙土Dc最大,红壤Dc最小,Dc呈强度空间变异。西北黄土高原地区和南方山地丘陵区Dc最大。黏粒和砂粒含量适中的土壤质地Dc最大。水流剪切力与水流功率在模拟Dc方面无显著差异。Dc与粉粒、土壤粒径参数、阳离子交换量和土壤有机质存在显著的负相关关系,与砂粒、中值粒径、平均几何粒径和交换性纳百分比存在显著的正相关关系。水蚀区Dc可用水流剪切力、粉粒、阳离子交换量和土壤有机质很好地模拟(R^2=0.71,NSE=0.71)。     

Prediction of Spatial Variability of Phosphorous Over the St-Esprit Watershed

Spatial data analysis tools for predicting the variability of non-point source pollutants minimize the time, effort and cost involved in extensive and exhaustive real field data measurements. In this study, exploratory data analysis, fitting of semivariogram models, and kriging techniques of geostatistics were used to develop the spatial variability map of soil phosphorous saturation (P _sat) percentage over the St-Espirit watershed (2610 ha), located in Quebec, Canada. The P _sat measured values for the 281 geo referenced land parcel units (LPU) within the watershed were interpreted and analyzed using the ArcGIS^® tool. The geostatistical extension module of ArcGIS^® was used for exploratory data analysis, semivariogram model fitting, and development of a P _sat prediction map using the ordinary kriging technique. Using these geostatistical procedures and adjustment of lag sizes and lag intervals representing the data sets, it was estimated that the spherical semivariogram model fitted well to represent the P _sat variability with residual sum square (RSS) of 0.0003 and coefficient of determination (R ²) of 0.98. Further, the developed model was used to predict the P _sat variability over the St. Esprit watershed using the 1605 geo-referenced LPU locations. The generated spatial variability map was geo-spatially processed with the natural drainage network and land use feature classes of the watershed to ascertain the phosphorous loading and locate vulnerable LPUs for phosphorous management. It was observed that the P _sat levels were higher at the up stream locations and near the drainage channels than the locations close to watershed outlet. Also, the land pockets with more than 60% agricultural land use resulted in supra-optimal P _sat values (10% > P _sat < 20%), out of which 8.5 to 16.3 ha agricultural land of the St. Esprit watershed exhibited critical agro-environmental threshold P _sat values (P _sat > 20%). It was also revealed that, around 23.5% of the watersheds cropped area has reached these threshold levels which necessitate judicious P input management.     

Controls of temporal and spatial variability of methane uptake in soils of a temperate deciduous forest with different abundance of European beech (Fagus sylvatica L.)

Aerated forest soils are a significant sink for atmospheric methane (CH₄). Soil properties, local climate and tree species can affect the soil CH₄ sink. A two-year field study was conducted in a deciduous mixed forest in the Hainich National Park in Germany to quantify the sink strength of this forest for atmospheric CH₄ and to determine the key factors that control the seasonal, annual and spatial variability of CH₄ uptake by soils in this forest. Net exchange of CH₄ was measured using closed chambers on 18 plots in three stands exhibiting different beech (Fagus sylvatica L.) abundance and which differed in soil acidity, soil texture, and organic layer thickness. The annual CH₄ uptake ranged from 2.0 to 3.4 kg CH₄-C ha⁻¹. The variation of CH₄ uptake over time could be explained to a large extent (R² = 0.71, P < 0.001) by changes in soil moisture in the upper 5 cm of the mineral soil. Differences of the annual CH₄ uptake between sites were primarily caused by the spatial variability of the soil clay content at a depth of 0-5 cm (R² = 0.5, P < 0.01). The CH₄ uptake during the main growing period (May-September) increased considerably with decreasing precipitation rate. Low CH₄ uptake activity during winter was further reduced by periods with soil frost and snow cover. There was no evidence of a significant effect of soil acidity, soil nutrient availability, thickness of the humus layer or abundance of beech on net-CH₄ uptake in soils in this deciduous forest. The results show that detailed information on the spatial distribution of the clay content in the upper mineral soil is necessary for a reliable larger scale estimate of the CH₄ sink strength in this mixed deciduous forest. The results suggest that climate change will result in increasing CH₄ uptake rates in this region because of the trend to drier summers and warmer winters.     

A universal grain-size distribution of soil with scaling invariance

Soils are composed of wide-ranged grains and grain size distribution (GSD) is the fundamental characteristic determining the physical and hydraulic properties. Previously we have proposed a GSD function for various soils. However, the remarkable discrepancy in the distribution occurs in some soils, which not only limits the applicability of the function but also raises doubt as to the possibility of a universal GSD function. In this study we modify the GSD function to a general form of P(D) ~ D^−μexp(−D/D_c)ⁿ, which introduces a new exponent n for the grain size scale. It turns out that this modification has eliminated the discrepancies and universally applies to a great variety of soils from around the world (hence to be a universal GSD function, UGSD). The exponent n is proved to be a scaling factor of grain size in log-scale and divides soils into three categories of n < 1 n > 1, and n = 1. Furthermore, soils of surface processes (e.g., erosion, tillage, desertification, landslides, avalanches, deposition, and sediment transportation) remain in the same category and preserve the UGSD function. Thus, the UGSD not only provides parameters μ and D_c as synthetic indices for soil properties (e.g., as indices for spatial heterogeneity or variables for pedotransfer functions), but also describes texture changes in dynamic processes. The UGSD function represents a ‘conservative law’ underlying soil genesis and processes, which fills the knowledge gaps related to the lack of universally applicable indices for soil properties, and thus has universal applications in soil classification, spatial variability, as well as dynamical processes.