Identifying scale specific controls of soil water storage in a hummocky landscape using wavelet coherency

High spatio-temporal variability of soil water is contributed from different ecohydrological and soil processes operating in different intensities at different scales. Traditional Pearson correlation analysis only examines linear correlation at the measurement scale. In this study, the correlation between soil water storage and its controlling factors was examined at different scales and locations in a hummocky landscape using wavelet coherency. Time domain reflectometry and neutron probe were used to measure soil water storage up to 1.4 m depth along a transect of 576 m long established in a hummocky landscape at St. Denis National Wildlife Area, Saskatchewan, Canada. In spite of visual similarity of the spatial pattern of soil water storage and elevation, the value of Pearson correlation coefficient was very small. However, wavelet coherency identified strong scale- and location-specific correlations between soil water storage and elevation. The total area of significant correlations as calculated from the total number of significant coherencies at different scales and locations was higher between soil water storage and elevation than between soil water storage and any other factors, which indicated a dominant control from elevation on soil water storage in the hummocky landscape. The largest area of significant correlation was observed at large scales (> 70 m), which can be attributed to the alternating knolls and depressions. The relationship between soil water storage and elevation at different scales was persistent at different times of the year or at different seasons with a slight reduction in the magnitude of correlation. The persistent relationship indicated the dominant control from elevation with slight change in the degree of the control. The scale-location specific correlation provides a complete picture on the controls of soil water storage, which was not possible with traditional correlation analysis.     

Wavelet analysis of soil variation at nanometre‐ to micrometre‐scales: an example of organic carbon content in a micro‐aggregate

This paper demonstrates the potential of wavelet analysis to investigate fine‐scale spatial variation in soil without statistical assumptions that are generally implausible. We analysed the optical densities of different forms of carbon which were measured at intervals of 50 nm along a 16‐µm transect on a soil micro‐aggregate using near‐edge X‐ray fine‐structure spectroscopy (NEXAFS). We found different patterns of scale‐dependent variation between the carbon forms, which could be represented by pair‐wise wavelet correlations at the different scales, and by principal components analysis of all the correlations at each scale. These results represent only one small soil micro‐aggregate and are not presented as general findings about soil carbon, but they do indicate that fine‐scale variation of soil carbon can be complex in ways that the wavelet analysis can accommodate but alternative spatial statistics such as variograms cannot. Among the patterns of variation that the analysis could identify were scale‐dependent correlations of the different forms of carbon. In some cases, positive correlations were found at coarser scales and negative at the finest scales, suggesting a multi‐scale pattern in which contrasting forms of carbon are deposited in common clumps but at finer scales either one or the other form dominates. Aromatic and carboxylic carbon varied jointly in this way. Other forms of carbon, such as carboxylic and aliphatic carbon, were strongly correlated at the finest scales but not the coarser scales. We found evidence for changes in the variance and correlation of forms of carbon along the transect, indicating that the spatial distribution of carbon at these fine scales may be very complex in ways that are inconsistent with the assumptions of geostatistics. This quantitative analysis of the spatial patterns of different soil components at micro‐scales offers a basis for formulating and testing specific hypotheses on replicated samples.     

Spatial scaling of soil salinity indices along a temporal coastal reclamation area transect in China using wavelet analysis

High spatial variability of soil salinity in coastal reclamation regions makes it difficult to obtain accurate scale-dependent information. The objectives of this study were to describe the spatial patterns of saline-sodic soil properties (using soil pH, electrical conductivity (EC_1:5) and sodium ion content (SIC) as indicators) and to gain knowledge of the scaling relationships between those variables. The soil pH, EC_1:5 and SIC data were measured at intervals of 285 m along a 13,965-m temporal transect in a coastal region of China. The spatial variability of soil pH was weak but it was strong for soil EC_1:5 and SIC at the measurement scale. There was a significant positive correlation between soil EC_1:5 and SIC, while correlations between soil pH and either EC_1:5 or SIC were weak and negative. For each saline-sodic soil parameter, the variability changed with the decomposition scales. The high-variance area at the larger scales (≥570 m) occupied less than 10% of the total area in the local wavelet spectrum, which meant that the spatial variations of the salinity indicators were insignificant at these scales. For local wavelet coherency, at a scale of 1500–2800 m and a sampling distance of 0–4500 m, the covariance was statistically significant between any two of the saline-sodic soil parameters.     

Divergent evolution and the spatial structure of soil landscape variability

The spatial structure of soil variability at the landscape scale was examined on adjacent geomorphic surfaces dating from 80 to 200 ka in eastern North Carolina. The purpose was to determine whether there is evidence at broader scales (distances of 10²–10⁴ m) for the divergent evolution observed in the field at very detailed scales (distances of 10⁰–10² m). The state probability function (SPF), which measures spatial dependence for categorical environmental data along a transect, was applied to soil series mapped at a 1:24,000 scale. The older Talbot Terrace and younger Pamlico Terrace surfaces showed distinctly different patterns of spatial variability. The range of spatial dependence was shorter on the older surface (about 200 vs. 300 m), and the SPF was higher at any given distance, indicating more variability. The SPF for the Pamlico surface also indicates a periodicity related to fluvial dissection of the landscape, which is not readily detectable on the Talbot transect despite its greater degree of dissection. The results confirm earlier field studies which suggest that pedogenesis is marked by divergence, whereby differences in initial conditions or local perturbations persist and increase to produce a more variable soil cover.     

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.     

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.     

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.     

Scale- and location-dependent correlations of soil strength and the yield of wheat

The relationship between soil strength and crop yield may be summarized by a linear correlation coefficient (usually negative). It is likely, however, that this over-simplifies a complex situation in which the relationship between these variables depends on spatial scale and location. We used the wavelet transform to assess this scale- and location-dependence. We established a transect on an arable field in Eastern England, and studied the correlations of soil strength (top- and subsoil) with crop yield. The transect comprised 267 contiguous 0.72 m × 0.72 m plots. Measurements were taken during two consecutive growing seasons of winter wheat (harvest dates of August 2004 and 2005). Soil strength was measured with a penetrometer in the spring of each growing season. As expected, the overall correlation of soil strength with yield was negative but weak. Wavelet analysis revealed that, at fine spatial scales, topsoil and subsoil strength were correlated more or less equally with yield; however, at coarse spatial scales, topsoil strength had a stronger correlation with yield than did subsoil strength. The correlation of topsoil strength with yield at fine spatial scales (corresponding to about 1 m on the ground) was negative. A likely source of this fine-scale variation was the soil compaction associated with tractor wheelings. The correlation of topsoil strength with yield at the coarsest spatial scale (corresponding to about 50 m on the ground) was positive. This correlation was temporally stable, and might have reflected how soil strength can act as a proxy for other soil attributes. In the 2005 growing season, we found evidence that, at intermediate spatial scales, the correlation of soil strength with yield changed depending on the position on the transect. This was probably due to an interaction between the compaction associated with tractor wheelings and the local soil conditions. There was no evidence of such location-dependence in the correlation of soil strength with yield in the 2004 growing season. In summary, the effect of soil strength on crop yield was not expressed in a constant negative correlation across all spatial scales and locations: the negative correlation occurred mainly at fine spatial scales, and the correlation changed according to the position in the landscape and the prevailing local soil conditions.     

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.     

Spatial variability of selected carbon,nitrogen, and phosphorus parameters on acid and calcareous rangeland soils

Abstract

The magnitude of C, N, and P seasonal or long‐term variability in rangelands is difficult to assess because of intrinsic soil heterogeneity even in seemingly uniform areas. A need exists, therefore, to determine the minimum number of samples necessary so significant changes in C, N and P can be assessed where minimal confounding from soil types and vegetation exist. To achieve this end, laboratory and field studies of selected C, N, and P parameters were conducted to compare variability among six transect lines, radiating from a central point. Samples were taken along each transect line every 3 m to a distance of 15 m. Parameters measured were: total organic C (OC), total Kjeldahl N (TKN), NH₄‐N, NO₃‐N, NaHCO₃‐extractable inorganic P (NaHP), and total organic P (TPo). Two rangeland soils, a moderately acid Ascalon sandy loam, and a calcareous Haverson loam, were sampled at two depths to assess spatial differences. Results indicated that under the experimental conditions, OC, TKN and TPo would require at least 9, 6, and 10 replications, respectively, for 95% confidence limit for an allowable error of 10%. The smaller available mineral pools were much more variable than the total pools, and could require as many as 20 to 30 samples.     

Evaluation of models to upscale the small scale variability of Cd sorption in a case study

Cadmium sorption, basic soil properties and water retention were jointly analyzed in an acidic sandy podzol under pine forest in the North of Germany. Samples were taken along a 10 m transect at a depth of 0.15 m with a sample-support of 0.15 m. The small-scale Cd sorption variability was upscaled in two steps. Firstly, it was simplified and, secondly, aggregated from the sample to the pedon scale. We evaluated different models to simplify Cd sorption variability at different levels of spatial aggregation. Our evaluation method was the numerical simulation of Cd transport in the topsoil where the variability of Cd sorption is the key input.We described Cd sorption with the Freundlich parameterization and tested three models to simplify its spatial variability. The reference model (model 1) had two and the simplified models only one spatially variable sorption parameter. Model 2 varied the parameter K_f of the Freundlich parameterization and set the exponent constant. Model 3 expressed only the linear variability of sorption. Each sample had a scaling factor that related to a constant sorption reference function. The Freundlich parameter K_f of the third simplification model (model 4), was derived by a local pedotransfer function. Its variability was, therefore, filtered by the available variation of a limited number of basic soil properties.The average sorption was at all aggregation levels not significantly different between the models. However, the corresponding uncertainty was smallest for model 3, intermediate for model 4 and largest for model 2. We evaluated the different sorption variability models with the simulation of Cd transport. The mean Cd concentrations in the topsoil predicted by the different models were statistically not different. However, at all support scales, the uncertainties of the predicted mean Cd concentrations and the RMSE's were smallest when model 3 was used, where the error was about 20% at the sample scale and decreased to below 10% at the pedon scale. Therefore, if measurements of sorption isotherms are available, we recommend to use model 3 to derive the mean sorption behavior with minimal uncertainty.     

基于水系改进的高分辨率DEM和GEOWEPP的流域产沙量估算及其空间尺度效应研究

基于水系改进的高分辨率DEM和GEOWEPP,从坡面、子流域和流域3种空间尺度对五桥河流域产沙量进行了估算。结果表明,从不同的空间尺度进行考察,流域的水土流失特征存在较大的差异。从坡面尺度到子流域尺度和流域尺度,研究区114.6 km2面积上的年产沙总量从3.79×105t减少至1.25×105t和0.84×105t,单位面积年产沙量从33.09 t hm-2减少至10.94 t hm-2和7.29 t hm-2,年均泥沙输移比从1.000减小至0.331和0.220。将GIS与GEOWEPP结合,既能反映流域输出终端的泥沙量,又可以刻画流域内部土壤侵蚀的强度和空间分布,能为流域水土保持措施布置提供更为科学的依据。     

Spatial variability of topsoils and vegetation in a grazed steppe ecosystem in Inner Mongolia (PR China)

It is not clear from the literature how the spatial distribution of topsoil and vegetation properties is affected by grazing cessation. Thus, the objective of this study was to elucidate if long‐term grazing exclosure increases spatial heterogeneity of topsoil and vegetation properties in a steppe ecosystem in NE China. Variograms and crossvariograms were calculated for bulk density, organic carbon (OC), total N, and total S concentration, δ¹³C, pH, Ah horizon thickness, vegetation cover, and aboveground biomass. Five sites with different grazing intensities (ungrazed since 1979, ungrazed since 1999, winter grazing, continuously grazed, heavily grazed) were sampled with two different grid sizes, allowing the exploration of scale effects. Small grids (15 m spacing, 5 m nested sampling) exhibited a different spatial structure compared to large grids (50 m spacing, 10 m nested sampling). Spatial distribution in small grids changed with grazing intensity. Generally, heterogeneity of topsoil properties increased with decreasing grazing intensity from a homogeneous to a patchy distribution. We attribute this to vegetation recovery/succession and deposition of windblown material in ungrazed areas. The plot ungrazed since 1999 showed different spatial dependencies than continuously and heavily grazed plots, but has not yet reached the high variability of the plot which was ungrazed since 1979. Large grid sampling did not detect small‐scale variability or grazing impacts, but showed spatial dependencies that were attributed to topography or soil erosion/deposition. Low OC concentration and low Ah thickness were associated with hilltop and shoulder positions, resulting in lower OC stocks at these topographic units.     

黄土丘陵区小流域土壤有效水空间变异及其季节性特征

基于213个样点土壤有效水数据,从流域、坡面和沟道三个尺度分析了黄土丘陵区典型小流域土壤有效水在春、夏、秋三个季节的空间变异特征。结果表明,土壤有效水均呈较强空间变异性,其中沟道土壤有效水均值和空间变异强度(标准差和变异系数)均显著高于坡面,坡面和沟道土壤有效水正态性明显好于流域尺度。不同尺度土壤有效水空间变异程度随均值发生变化,变异系数随均值增加呈指数递减趋势。流域和坡面尺度土壤有效水与坡向呈显著正相关关系且相关系数高于其与坡度和高程,而沟道尺度与各地形因子相关关系均较弱。土壤有效水空间变异呈现明显的季节性特征,秋季土壤有效水均值最高而空间变异性最低,夏季土壤有效水均值最低但变异系数最大。流域尺度夏季土壤有效水与高程相关系数显著高于春秋两季,而坡面尺度则相反。此外,土壤有效水抽样不确定性和估算误差随样点数量增加呈非线性递减变化趋势,当样点数超过20个时,增加样点数量的作用有限。     

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     

Estimation of spatial variability of soil water storage along the south–north transect on China’s Loess Plateau using the state-space approach

Purpose

Soil water is a critical variable for hydrological and biological processes in arid and semi-arid ecosystems. Information on regional spatial pattern of soil water storage (SWS) and its relationship with environmental factors is important for optimal water management and vegetation restoration in China’s Loess Plateau (CLP) region. State-space approach and artificial neural network (ANN) were used to analyze spatial variability of SWS in the CLP region.

Materials and methods

SWS in the 0–1, 1–2, 2–3, 3–4, and 4–5 m soil layers was measured during the period from June 2013 to September 2015 at 86 locations along a 860 km long south–north transect of CLP.

Results and discussion

The analysis showed that SWS in the 5 m soil profile generally decreased with increasing latitude, driven by decreasing precipitation and soil–water holding capacity. Using various combinations of variables, the state-space model gave a better spatial pattern of SWS than the ANN approach. The best state-space approach, which included clay content, mean annual precipitation, and slope gradient, explained 96.0% of the total variation in SWS. Then, the best ANN approach explained only 76.2% of the variation. Clay content, mean annual precipitation, and slope gradient was the most effective combination for large-scale estimation of SWS under the state-space approach.

Conclusions

The state-space model was recommended as an effective method for analyzing large-scale spatial patterns of soil water using soil, climatic, and topographic properties in the CLP region.

     

Cotton lint yield variability in a heterogeneous soil at a landscape scale

Landscape variability associated with topographic features affects the spatial pattern of soil water and N redistribution, and thus N uptake and crop yield. A landscape-scale study was conducted in a center pivot irrigated field on the southern High Plains of Texas in 1999 to assess soil water, soil NO₃-N, cotton (Gossypium hirsutum L.) lint yield, and N uptake variability in the landscape, and to determine the spatial correlation between these landscape variables using a state-space approach. The treatments were irrigation at 50 and 75% cotton potential evapotranspiration (ET). Neutron access tubes were placed at a 15-m interval along a 710 m (50% ET) and 820 m (75% ET) transect across the field. Soil NO₃-N in early spring was autocorrelated at a distance varying between 60 and 80 m. Measured soil volumetric water content (WC), total N uptake, and lint yield were generally higher on lower landscape positions. Cotton lint yield was significantly correlated to soil WC (r=0.76), soil NO₃-N (r=0.35), and site elevation (r=−0.54). Differences of site elevation between local neighboring points explained the soil water, NO₃-N and lint yield variability at the micro-scale level in the landscape. Soil WC, cotton lint yield, N uptake, and clay content were crosscorrelated with site elevation across a lag distance of ±30–40 m. The state-space analysis showed that cotton lint yield was positively weighted on soil WC availability and negatively weighted on site elevation. Cotton lint yield state-space models give insights on the association of soil physical and chemical properties, lint yield, and landscape processes, and have the potential to improve water and N management at the landscape-scale.     

Spatial analysis of categorical soil variables with the wavelet transform

This paper describes a wavelet transform for the analysis of categorical (multistate) soil variables, i.e. ones (such as profile classes) that have two or more discrete states. The states are transformed to a continuous variable by a mapping which is optimized by scale and location to highlight local variation. The method is illustrated with data from a transect across a gilgai landscape in Australia. A categorical variable on relief, with three states, was recorded from the sample sites, from which soil cores had also been collected and analysed. The wavelet analysis showed a transient feature of the variation at scales up to 32 m. There was an interval where the characteristic alternation of depressions with the level plain was interrupted. The variation at scale 64 m appeared to be non-stationary. The relief was more variable on one side of a change point than it was on the other. This complex variation of relief was matched by that of the electrical conductivity of the soil, most strongly at the 64-m scale. The periodicity of conductivity, and the strength of its correlation with relief, were also different either side of the change point identified in the analysis of relief alone. Conductivity also showed similar transient features to relief. Evidently the wavelet transform can be used to elucidate the variation of categorical soil variables. The information from such an analysis is likely to be useful for planning surveys of the soil to measure continuous variables by sampling and laboratory analysis.     

土壤水力特性的空间尺度效应研究进展

研究土壤水力特性的空间尺度效应,在生态水文模拟和农业水肥精准管理方面具有重大意义。水力特性空间变异研究方法主要有统计法、随机模拟法、土壤转换函数法和分形理论法;由于土壤中物理、化学和生物等过程作用的尺度不同,导致其空间变异方式亦不相同,当前主要采用地统计学、谱分析、多重分形和小波分析等方法研究水力特性的尺度效应。研究过程中仍有一些问题需解决,其中尺度转换始终是非常重要的问题,并且要与GIS等技术相结合。     

Variabilität der Sulfatsorption in einem Gley-Podsol aus Sand unter Kiefernforst

Variability of sulfate sorption in a sandy Gleyic Podzol under a pine stand In acid forest soils sulfate can be stored by sorption processes. We studied the vertical heterogeneity and the horizontal variability of sulfate sorption in a sandy forest soil under a pine stand. Disturbed soil samples were taken from the horizons of a Gleyic Podzol (vertical heterogeneity). From a 120-m transect, 25 soil samples were taken from depth increment 35—50 cm and 65—80 cm at 5-m intervals by means of a hand auger (horizontal variability). In batch experiments, sulfate sorption isotherms were measured for all profile and transect samples. The Freundlich equation is suitable to describe the individual isotherms. The sulfate sorption isotherms show considerable differences in the horizons of the profile, systematic relations between the isotherm parameters and soil properties are not obvious. In order to quantify the spatial variability of the sulfate sorption isotherms, a scaling technique is used. The spatial distribution of scale factors for depth 35—50 cm along the transect reveals a periodicity of about 17 m length. The same recurrent pattern is also identified in the spatial distribution of the cumulative sulfate deposition by canopy throughfall along the transect, and in the spatial distribution of contents of iron and aluminium oxides soluble in oxalic acid at depth level 35—50 cm. This does, however, not refer to organic carbon content and pH at this depth. From these results it is concluded that in this soil at depth 35—50 cm oxide contents are related to the amount of sulfate deposition by throughfall. In spatial ranges with high sulfate and thus acid deposition, oxide contents of the soil are decreased by accelerated podzolization, and therefore, also the sulfate sorption of the soil is low in these ranges. The period length of this recurrent pattern of about 17 m is probably only an apparent period length that results from aliasing, because a very probably real periodicity of 3—4 m length, related to the canopy edge distribution of the pine trees along the transect, is sampled at an interval of 5 m. In the subsoil (65—80 cm depth) such relations could not be detected.