Application of Continuous Wavelet Transform in?Examining Soil Spatial Variation: A?Review

An adequate understanding of soil spatial variation as a function of space and scale is necessary in ecological modeling, environmental prediction, precision agriculture, soil quality assessment and natural resources management. Soil spatial variation can be partitioned into frequencies (scale) and positions (location) by the wavelet transform. This review focuses mainly on different applications of the continuous wavelet transform (CWT) for the identification of the scale and location dependence of soil attributes. We discussed both wavelet spectra and wavelet coherence in our analysis of soil spatial variation. Global wavelet spectra, being the sum of wavelet spectra over all spatial locations at a scale, can be used to examine the dominant scale of variation. Furthermore, some variations at a particular scale persist over all locations (termed global features), whereas others are present at only a few locations (localized features). Wavelet spectra can be used to identify both localized and global features. The combination of localized and global features provides a complete picture of the scale-location information of different processes in the field and may provide better guidance in designing efficient management practices. Wavelet coherency partitions the total correlation between two variables into correlations at different scales and locations, while also revealing the scale- and location-specific relationship between those two variables. This relationship may be helpful in developing predictive links between one property and another.     

Wavelet Analysis and Filtering to Identify Dominant Orientations of Permeability Anisotropy

An accurate representation of permeability anisotropy is needed to model the rate and direction of groundwater flow correctly. We develop a wavelet analysis technique that can be used to characterize principal directions of anisotropy in both stationary and non-stationary permeability fields. Wavelet analysis involves the integral transform of a field using a wavelet as a kernel. The wavelet is shifted, scaled, and rotated to analyze different locations, sizes, and orientations of the field. The wavelet variance is used to identify scales and orientations that dominate the field. If the field is non-stationary, such that different zones of the field are characterized by different dominant scales or orientations, the wavelet variance can identify all dominant scales and orientations if they are distinct. If the dominant scales and orientations of different zones are similar, the wavelet variance identifies only the dominant scale and orientation of the primary zone. In this paper, we present a combined wavelet analysis and filtering approach to identify all dominant scales and orientations in a non-stationary permeability field. We apply the method to permeability data obtained in the laboratory from the Massillon sandstone.     

Multiscalarity of the Nutrient–Chlorophyll Relationship in Coastal Phytoplankton

The relationship between nitrogen (N) and phytoplankton chlorophyll a (Chl) establishes a basis for understanding eutrophication in coastal marine ecosystems. A substantial literature exists on cross-ecosystem analysis of this relationship, but there is little information on cross-scale patterns. A collection of observational records in Bedford Basin (Canada) was used to construct the N–Chl relationship at four time scales: intra-day, intra-annual, interannual, and interdecadal. Additionally, a dataset of contingent observations from 16 biogeochemical ocean provinces was used to construct the N–Chl relationship at large spatial scale. In Bedford Basin, N statistically predicts Chl at time scales that are short (intra-day, intra-annual) and long (interdecadal) but not intermediate (interannual). There is an apparent stoichiometric regularity in the dependence of Chl on N that crosses time scales. Further, an apparent similitude exists between the local pattern at long time scale and the global pattern at large space scale.     

Factorial kriging of a geochemical dataset for heavy-metal spatial-variability characterization

Characterizing the spatial patterns of variability is a fundamental aspect when investigating what could be the causes behind the spatial spreading of a set of variables. In this paper, a large multivariate dataset from the southeast of Belgium has been analyzed using factorial kriging. The purpose of the study is to explore and retrieve possible scales of spatial variability of heavy metals. This is achieved by decomposing the variance-covariance matrix of the multivariate sample into coregionalization matrices, which are, in turn, decomposed into transformation matrices, which serve to decompose each regionalized variable as a sum of independent factors. Then, factorial cokriging is used to produce maps of the factors explaining most of the variance, which can be compared with maps of the underlying lithology. For the dataset analyzes, this comparison identifies a few point scale concentrations that may reflect anthropogenic contamination, and it also identifies local and regional scale anomalies clearly correlated to the underlying geology and to known mineralizations. The results from this analysis could serve to guide the authorities in identifying those areas which need remediation.     

A framework for spatio-temporal scales and concepts from different disciplines: the ‘vulnerability cube’

The concept of vulnerability is increasingly used in the fields of disaster risk reduction and climate change adaptation, as well as socioeconomic studies. This paper reviews research inputs into the concept of vulnerability and highlights the challenges of resolving its spatial and temporal variability with building resilience and adaptation. We hypothesise that a clear understanding of scale is key to integrating these related issues, by differentiating three dimensions of scale when analysing relationships between the observed and the intrinsic scale of a given phenomenon, namely space, time and dimensional level. The paper analyses 20 vulnerability assessment approaches, ranging from the global down to the local scale, and positions them with regard to their integration of the spatial component. We then develop a vulnerability cube as a framework to position existing approaches and to map them in a three-dimensional space. The three axes represent space, time and dimension and provide a structure for the different notions of scales and ultimately for a spatial analysis workflow. The vulnerability cube framework helps us to position different vulnerability assessments and to identify overlaps, differences and specific characteristics. Additionally, this three-dimensional conceptualisation allows the identification and discussion of appropriate scaling issues.     

Spatial scale and measuring segregation: illustrated by the formation of Chicago’s ghetto

Few studies of residential segregation in cities have directly addressed the issue of spatial scale, apart from noting that the traditional indices of segregation tend to be larger when calculated for small rather than large spatial units. That observation however ignores Duncan et al.’s (Statistical geography: problems in analyzing areal data. Free Press, Glencoe, 1961) explication that any measure of segregation at a fine-grained scale necessarily incorporates, to an unknown extent, segregation at a larger scale within which the finer-grained units are nested. To avoid that problem, a multi-level modelling perspective is introduced that identifies the intensity of segregation at each scale net of its intensity at any larger scale included in the analysis. It is applied to an analysis of the emergence of Chicago’s Black ghetto over the twentieth century’s first three decades, using data at the ward and ED scales. It shows that across Chicago as a whole segregation was equally as intense at the two scales, with statistically significant increases in that intensity at both scales across the three decades. At the finer scale, however, segregation was much more intense across the EDs within those wards that formed the core of the emerging ghetto than it was in the remainder of the city.     

Generalized Coarse Graining Procedures for Flow in Porous Media

This paper focuses on heterogeneous soil conductivities and on the impact their resolution has on a solution of the piezometric head equation: owing to spatial variations of the conductivity, the flow properties at larger scales differ from those found for experiments performed at smaller scales. The method of coarse graining is proposed in order to upscale the piezometric head equation on arbitrary intermediate scales. At intermediate scales large scale fluctuations of the conductivities are resolved, whereas small scale fluctuations are smoothed by a partialy spatial filtering procedure. The filtering procedure is performed in Fourier space with the aid of a low-frequency cut-off function. We derive the partially upscaled head equations. In these equations, the impact of the small scale variability is modeled by scale dependent effective conductivities which are determined by additional differential equations. Explicit results for the scale dependent conductivity values are presented in lowest order perturbation theory. The perturbation theory contributions are summed up with using a renormalisation group analysis yielding explicit results for the effective conductivity in isotropic media. Therefore, the results are also valid for highly heterogeneous media. The results are compared with numerical simulations performed by Dykaar and Kitanidis (1992). The method of coarse graining combined by a renormalisation group analysis offers a tool to derive exact and explicit expressions for resolution dependent conductivity values. It is, e.g., relevant for the interpretation of measurement data on different scales and for reduction of grid-block resolution in numerical modeling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Upscaled modeling of well singularity for simulating flow in heterogeneous formations

Subsurface flows are affected by geological variability over a range of length scales. The modeling of well singularity in heterogeneous formations is important for simulating flow in aquifers and petroleum reservoirs. In this paper, two approaches in calculating the upscaled well index to capture the effects of fine scale heterogeneity in near-well regions are presented and applied. We first develop a flow-based near-well upscaling procedure for geometrically flexible grids. This approach entails solving local well-driven flows and requires the treatment of geometric effects due to the nonalignment between fine and coarse scale grids. An approximate coarse scale well model based on a well singularity analysis is also proposed. This model, referred to as near-well arithmetic averaging, uses only the fine scale permeabilities at well locations to compute the coarse scale well index; it does not require solving any flow problems. These two methods are systematically tested on three-dimensional models with a variety of permeability distributions. It is shown that both approaches provide considerable improvement over a simple (arithmetic) averaging approach to compute the coarse scale well index. The flow-based approach shows close agreement to the fine scale reference model, and the near-well arithmetic averaging also offers accuracy for an appropriate range of parameters. The interaction between global flow and near-well upscaling is also investigated through the use of global fine scale solutions in near-well scale-up calculations.     

Coupling within Fluvial Geomorphic Systems:Spatial and Temporal Implications

INTRODUCTIONHow fluvial systems respond to environmental changedepends on how rapidly the effects of changes in sediment loadsupplied from upstream or changes in base level affectingdownstream zones are propagated through the system.Thisproperty has been defined as the coupling of the system(Harvey,2 0 0 0 a,1997a;Brunsden,1993;Brunsden andThornes,1979) .Coupling therefore relates to connectivity between thedifferent zones of the fluvial system,defined by Schumm(1977) as source areas,tra…     

Scale and the other: Levinas and geography

This paper seeks to contribute to Geography's recent conversation of identity, landscape, scale and difference. It brings into dialogue previously divergent discussions about space, place and difference and proposes an approach that treats time, space, place and scale as co-equal conceptual and/or analytical elements of cultural landscapes. It argues that many philosophical debates about embodiment, emplacement and difference abstract a universalized notion of `place', `body' and `self' which confounds and conflates scale issues and consequently confuses the dialectical interplay of `time', `space', `being' and `culture' across scales. The paper takes the work of Emmanuel Levinas (1906-1995) and the discursive communities around it as a philosophical entry point into these debates.     

小波变换在饶阳凹陷层序地层格架建立中的应用

小波变换提供了一种研究层序地层格架的新方法,它将测井信号从一维深度域转换到二维深度—尺度域,从多尺度识别不同级次的地层旋回界面。根据小波变换的原理,确定了测井数据小波变换在层序地层划分中的地质意义,建立了四种小波变换中的地层旋回模型。在饶阳凹陷的实际应用中,选取自然伽马曲线进行小波变换,应用时频色谱图分析和快速傅里叶变换多种方法选取尺度因子。通过对时频色谱图和不同尺度下小波系数曲线的综合分析,对饶阳凹陷古近系G104井层序地层进行了划分,并以2 198.625m位置为突变界面,划分出两个较大尺度旋回,以2142.375m、2 163.875m、2 198.625m、2 238.625m位置为界面,划分出5个较小尺度旋回。实际结果应用表明,小波多尺度变换划分层序地层的结果和传统方法划分基本一致。     

A Review of Damage Intensity Scales

A wide range of scales and indices are used to describe natural hazards and theirimpacts. Some scales infer damage levels from hazard characteristics while othersuse damage levels to estimate a physical characteristic. Damage scales may relyon raw dollar values, percent loss estimates, damage states, normalized values ormacrodamage categories. Whatever the basis of the scale it should tell the truth.However, scales are compromises between the need for detailed information andbeing simple enough to use.Damage scales may be nominal (categorical), ordinal, interval or ratio scales. Frequencywords such as ``few', ``many' can be dealt with in a range of ways to produce contiguous,widely separated, broadly overlapping or narrow overlapping values. Most scales rely onmaximum values but some focus on minimum or threshold values. The number of levelson damage scales commonly ranges from five to 13. Some long-lived damage scales haveevolved through several editions, changing to reflect the new or additional uses to whichthey have been put and as buildings and the nature of damage to those structures has changed.Few scales state precisely the purpose of the scale, deal clearly with ambiguities or provideguidelines for the use of qualitative information.     

Application of the self-calibrated palmer drought severity index and standardized precipitation index for estimation of drought impact on maize grain yield in Pannonian part of Croatia

Recent global warming and more frequent droughts are causing significant damage to maize production. A reliable estimate of drought intensity and duration is essential for testing maize hybrids to drought tolerance. For this purpose, the self-calibrating 10-day palmer drought severity index (scPDSI) and standardized precipitation index (SPI) for 1, 2, 3, 6, 9, 18, 27, and 36 10-day scales were used to estimate the effects of drought on grain yield of 32 maize hybrids evaluated in 2017 and 2018 at eight experimental locations in the Pannonian part of Croatia. Time series of observed 10-day mean air temperature, relative humidity, and precipitation totals for a set of “reference” weather stations of the croatian meteorological and hydrological service (DHMZ) for the period 1981–2018 were used to calculate the scPDSI and SPI indices. According to the 10-day scPDSI and SPI for different time scales, 2018 proved to be a “normal year,” while 2017 experienced a “mild to moderate drought,” which resulted in a 13% reduction in maize grain yield at eight experimental locations compared to 2018. The correlation between grain yield and drought indices for summer months was the highest for the 10-day scPDSI. To some extent, correlations between summer months’ SPI for the 3 10-day time scale and maize grain yield were comparable to the corresponding correlations for the 10-day scPDSI. However, for other SPI time scales considered, the corresponding correlations were weaker and less informative. The dependence of grain yield on scPDSI values was not the same for all hybrids, indicating their different tolerance to drought. The reduction in grain yield due to drought was primarily caused by insufficient grain filling (lower 1000-grain weight) and, to some extent, by a reduction in the number of grains. In this study, application of 10-day scPDSI data proved to be more relevant in detecting effects of drought on agronomic traits than application of SPI data for the most time scales.

     

火山活动的气候影响及其冰芯记录研究进展

系统地总结了不同时间尺度内火山活动影响气候的机理,回顾了不同区域冰芯记录火山喷发物质沉积信号的研究历史,阐述了不同气候模式对火山活动影响气候的数值模拟结果,并指出了相关研究中存在的不确定性.结果表明:火山活动通过释放大量的火山物质气溶胶影响气候波动,在年际至年代际时间尺度上,这种影响是显著的;然而,在更长的时间尺度上这种影响是否仍然存在,尚需更多研究的证实.冰芯中火山喷发物质沉积记录为研究历史时期火山活动及其气候影响提供了必要的参考资料,相关的气候模式利用该沉积记录较好地模拟了火山活动对区域乃至全球尺度气候的影响,为我们认识火山活动影响气候变化的机理提供了重要的理论支持,同时也为研究未来火山活动对气候的可能影响提供了参照.但是,冰芯中火山喷发物质沉积记录研究及数值模式模拟结果中尚存在诸多的问题和不确定性.     

The angle measure technique: A new method for characterizing the complexity of geomorphic lines

A new method for characterizing the complexity of geomorphic phenomena is presented. This method, termed the angle measure technique, involves measuring the angularity of a digitized line for a wide range of scales. In this manner, the technique is capable of delineating changes in the complexity of geomorphic lines with scale, from which the characteristic scale(s) of the lines can be identified. Unlike fractal analysis, values produced by the angle measure technique correspond to single scales. Therefore, no assumptions are made concerning the relationship between complexity and scale, and the technique can resolve variations in complexity over small ranges of scale. The technique is illustrated using both computer-generated curves and natural lines, including the trace of a river channel, and is compared to fractal analysis on a contour line crossing two lava flows.     

Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping

Fractional Brownian surfaces have been widely discussed as an appropriate model for the statistical behavior of topographic surfaces. The fractals model proposes that topographic surfaces are statistically self-similar, and that a single parameter, the fractal dimension, applies at all scales. This paper presents the results of empirical examinations of 17 topographic samples. Only one of these samples shows the statistical behavior predicted by the fractals model; however, in 15 of the 17 samples, the surfaces' variograms could be adequately described by ranges of scales having constant fractal dimension, separated by distinct scale breaks. For scale ranges between adjacent breaks, surface behavior should be that predicted by the fractals model; the breaks represent characteristic horizontal scales, at which surface behavior changes substantially. These scale breaks are especially important for cartographic representations and digital elevation models, since they represent scales at which there is a distinct change in the relation between sampling interval and the associated error.     

Investigating origin of the inadequate medium range predictability of the lower tropospheric ultra-long waves in tropics

The predictability of planetary or ultra-long scale waves is limited by the large growth of errors in these scales in almost all the medium range forecast models. Understanding the cause for the enormous build up of error is, therefore, a necessary task for improving the prediction of planetary waves. A diagnostic analysis of the systematic error energetics has been performed in the Global Forecast System model to investigate the reasons for poor predictability of the lower tropospheric ultra-long waves (wavenumber bands 1–4) in tropics using the analysis-forecast system of horizontal wind field at 850 hPa level during the boreal summer period. For this purpose, systematic error energy is computed in spatial as well as in wavenumber domain. Non-linear inter-scale transfer of error has been formulated and evaluated through energy exchanges among participating triads. The study reveals that the error is generated in the prognostic model initially with a small magnitude at the different locations around tropical convergence zone (TCZ) attributed to the inaccuracy in representing different physical processes like cumulus convection applied in the model. At subsequent evolution of forecasts, error increases and spreads along the TCZ due to its non-linear advection to the higher scales and eventually to the ultra-long scales attributed to the inherent dynamics of the model evaluated through the process of wave-wave exchange of error energy in terms of the triad interactions. The continuous generation and then, non-linear propagation of error up to the planetary scales in the course of prediction increase the uncertainty in ultra-long scales which actually inhibit to predict accurately the planetary scale waves in tropics during medium range forecasts. This work suggests caveats to the modeler’s community in the predictability study of tropical ultra-long waves.     

Geostatistical method to delineate anomalies of multi-scale spatial variation in hydrogeological changes due to the ChiChi earthquake in the ChouShui River alluvial fan in Taiwan

This study uses Ordinary Kriging (OK), Sequential Gaussian Simulation (SGS) and Simulated Annealing Simulation (SAS) to relocate the completely heterotopic dataset from the locations of the Standardized Satellite Oriented Control Point System (SSOCPS) stations to the Groundwater Monitoring Networks (GMNS) stations and factorial kriging to analyze and map relationships among seven variables, including the hydraulic conductivities of three aquifers, the vertical displacements of the ground and groundwater level changes in the wells of three aquifers, and also to delineate the anomalies of multi-scale spatial variation of hydrogeological properties associated with the ChiChi earthquake, measuring 7.3 on the Richter scale, in the ChouShui River alluvial fan in Taiwan. In this study, the anomalies of spatial variation of hydrogeological properties associated with the earthquake are illustrated at micro, local and regional scales of 9, 12 and 36 km, respectively. In the study area, regionalization components associated with variation at local and regional scales are obtained and mapped by factorial kriging. Factorial Kriging Analysis (FKA) also demonstrated that the main effects of the ChiChi earthquake on the spatial variations of groundwater hydrological changes include porous media compression at micro scale, hydrogeological heterogeneousness of the sediments within the aquifer at local scale and the cyclic loading of deviatoric stress at regional scale. Finally, maps of spatial variations of regional components fully depicted all of the anomalies of spatial variation of hydrogeological changes due to the ChiChi earthquake and can be used to identify, confirm and monitor the hydrogeological properties in this study area.     

考虑页岩纹层与裂缝网络的延长组页岩多尺度三维地质结构模型

现场调查表明,砂质纹层、凝灰质纹层和天然裂缝广泛地存在于陆相页岩储层中。本文对鄂尔多斯盆地页岩储层中的纹层和天然裂缝进行了多尺度研究,并构建了三维地质结构模型。首先,基于二维裂缝现场调查,利用蒙特卡罗模拟方法建立了研究区域的三维裂缝网络模型。然后通过多种观测手段获得由宏观尺度到微观尺度的纹层结构特征。对多尺度纹层厚度的统计分析表明,米级、分米级、厘米级、毫米级和10微米级等不同研究尺度下的纹层平均厚度分别为2.26 m,2.09 dm,1.70 cm,1.48 mm和11.7 μm,呈现出分形特征,分形维数为1.06;不同研究尺度下的单层厚度均服从负指数分布规律,即各研究尺度下厚度越大的纹层,其层数越少,反之越薄的纹层其数量越多。最后,根据上述纹层平均厚度及概率分布函数特征,建立了页岩的多尺度纹层结构模型,并将其叠加在裂缝网络模型上,生成不同尺度下的页岩三维地质结构模型。模型输出的裂缝、纹层参数与研究区域的真实地质参数有着较好的对比验证。这项研究工作可为页岩气储层的水力压裂数值模拟和物理模型试验提供更可靠的地质模型。     

Suitability of fish scales as archives of temporal variations in ambient mercury levels in estuaries

To examine the suitability of fish scales as a historical archive, of environmental mercury (Hg) contamination, we analyzed a collection of scales taken from striped bass (Morone saxatilis) captured in the St. Lawrence Estuary between 1994 and 1962. The total mass of Hg in individual scales increases linearly with the weight of the scale, suggesting that Hg is well preserved in the scale tissue. Age, length, and sex of specimens captured during the same year did not significantly influence the concentration of Hg in the scales. The average Hg concentrations in scales of specimens captured in 1956 (53.2 ±9.1 ng g⁻¹) and 1962 (58.6±7.7 ng g⁻¹) are nearly twice as high as in scales from 1951 (30.2±3.0 ng g⁻¹). These results follow the trend revealed in sediment cores from the St. Lawrence Estuary. A high level of Hg in scales from 1945 (68.7±18.4 ng g⁻¹) could have been caused by an episode of Hg contamination around 1945 not recorded in the sediment or by a diet-related change in Hg exposure.