此文为河南科技大学 12 级园林专业 毕业论文翻译，仅供参考。
Effects of topography and surface roughness in analyses of landscape structure – A proposal to modify the existing set of landscape metrics
Hoechstetter, S.*, Walz, U., Dang, L.H., Thinh, N.X.
Leibniz Institute of Ecological and Regional Development (IOER), Weberplatz 1, D-01217 Dresden, Germany E-mail: email@example.com , firstname.lastname@example.org , email@example.com , firstname.lastname@example.org * Corresponding author
Topography and relief variability play a key role in ecosystem functioning and structuring. However, the most commonly used concept to relate pattern to process in landscape ecology, the so-called patch-corridor-matrix model, perceives the landscape as a planimetric surface. As a consequence, landscape metrics, used as numerical descriptors of the spatial arrangement of landscape mosaics, generally do not allow for the examination of terrain characteristics and may even produce erroneous results, especially in mountainous areas. This brief methodological study provides basic approaches to include relief properties into large-scale landscape analyses, including the calculation of standard landscape metrics on the basis of “true” surface geometries and the application of roughness parameters derived from surface metrology. The methods are tested for their explanatory power using neutral landscapes and simulated elevation models. The results reveal that area and distance metrics possess a high sensitivity to terrain complexity, while the values of shape metrics change only slightly when surface geometries are considered for their calculation. In summary, the proposed methods prove to be a valuable extension of the existing set of metrics mainly in “rough” landscape sections, allowing for a more realistic assessment of the spatial structure Keywords: patch-corridor-matrix model, neutral landscapes, digital elevation models, relief, roughness parameters 1. Introduction –
The “3D-issue” in landscape ecology “3D” has become a frequently-used term in many fields of science, even in ecology.3D-visualisation and 3D-graphics have undergone enormous advancements in the recent years. Realistic visualisations of landscapes or cities are gaining importance in spatial planning processes, for example when the impact of construction projects is to be clarified or when the dynamics of landscape change over time are to be demonstrated. Also “3D-GIS” is beginning to emerge. However, “3D-analysis” in landscape ecology and the examination of “3D-patterns” are still somewhat neglected, even though elevation and land surface features can be regarded as key elements in many ecological processes. Thus, from a landscape ecological perspective, there is a need for 3D-analysis in terms of the examination and characterisation of the topography of landscapes and specific terrain features. Previous publications have tried to highlight the necessity to incorporate aspects of the third dimension into large-scale landscape analyses. Many authors have pointed out that topography is a factor which may play a key role in ecosystem functioning and structuring, and which in many cases is not sufficiently taken into account. The connection between surface characteristics and both the species richness and composition in vascular plants (as shown in Burnett et al. 1998; Davis & Goetz 1990; Sebastiá2004) is a well-known fact that has frequently been used for the design of biodiversity distribution models (e.g. Bolstad et al. 1998). The impact of relief on the differentiation of an ecosystem as a whole and on particular ecological functions such as soil moisture, temperature distribution, the balance of solar irradiation, or microclimate has been described in detail as well (Bailey 2004; Oke 1978; Swanson et al. 1988). Bearing these well-studied links between terrain features and ecological processes in mind, one fact appears to be noteworthy: So far, the well-established patch-corridor-matrix model – as suggested by Forman (1995) – does not explicitly consider the third dimension in its approach to describe the spatial arrangement of landscapes. It is generally accepted that the acknowledgement of the “effect of pattern on process” (Turner 1989) constitutes the self-conception of modern landscape ecology. But the established use of landscape metrics for the characterisation of geometric and spatial properties of categorical map patterns (Mc-Garigal 2002) holds a view of the land as a “planimetric” surface – aspects of three-dimensional patterns(topography, elevation) have not yet expanded into this concept (see also Blaschke & Dr?gu? 2003). A large number of landscape metrics has been described in detail and used for several purposes, including spatial planning or ecological modelling. A lot of user-friendly software products for the computation of such metrics on the basis of either vector or raster data are available,e.g. FRAGSTATS (McGarigal & Marks 1995), Leap II (Schnekenburger et al. 1997) or V-LATE (Lang & Tiede2003). But information about 3D-features like surface roughness, landform, or relief variability within landscape elements (“patches”) cannot be made accessible using these measures. Moreover, one may even yield erroneous results from the calculation of landscape metrics, since the basic geometries (area, perimeter) of patches and distances between them are generally underestimated in planimetric observations by neglecting the underlying relief. These discrepancies between the patch-corridor-matrix model and the actual conditions within landscapes can be regarded as a major drawback of the concept, especially in mountainous regions or in areas exhibiting a complex terrain. Figure 1 provides a visual representation of the effects that relief
may have on the parameter output of common groups of landscape metrics. For example, it is apparent that for area or distance metrics, a definite tendency towards higher values can be expected when surface complexity is taken into account. Geomorphology offers a large set of parameters to describe the land surface and to classify the
georelief(see Dikau & Schmidt 1999; Evans 1972; Pike 2000;Wilson & Gallant 2000). However, measures of curvature, aspect, slope, or combined parameters such as wetness indices are only of limited use when one tries to characterise the spatial pattern of landscapes using categorical maps. These measures in general relate to catchment areas and discrete landform elements, rather than to the “patches” that common landscape metrics are applied to; a compatibility between these approaches cannot be taken for granted in every case.
Figure 1: Common landscape metrics groups used in the patch-corridor-matrix model and the effects of underlying terrain (upper part redrawn according to Wiens et al. 1993). Other techniques to incorporate surface features into landscape analyses have been proposed. For example,Beasom (1983) has suggested a simple method for assessing land surface ruggedness based on the intersections of sample points and contour lines. More elaborate proposals to include topographic characteristics into analyses of landscape pattern and of vegetation distributions have been made by Dorner et al. (2002). Simple moving-window algorithms for estimations of the
―concavity/convexity‖ of raster pixels in digital elevation models (DEM) have been developed by McNab (1992) and Blaszczynski (1997). While an application of these approaches for special case studies and particular thematic contexts may be very valuable, integration into the patch-corridor-matrix model has not beenachieved yet. Meanwhile, the technological progress in the field of remote sensing has led to a rapid improvement in the quality of DEMs. Especially LiDAR (―light detection and ranging―) measurements provide high-resolution elevation data of the land surface. They can accurately estimate attributes of vegetation structure and should therefore be of particular interest to landscape ecologists(Lefsky et al. 2002). First attempts to derive 3Dlandscape metrics from LiDAR data have already been made earlier (e.g. Blaschke et al. 2004). All these notes on the ―3D-issue‖ in landscape ecology and the shortcomings in the analysis of important surface features mark the starting point for the study at hand. The main purpose of this paper is to present some basic principles on how to solve the problem, based on the recognition of the discrete land unit as a central concept in landscape ecological hypotheses (Zonneveld 1989). The term ―3D‖ is used in this context, even though digital elevation models actually refer to a ―2.5D‖ representation of the real world, with one z-value associated with each x,y-coordinate. In most cases, however, DEMs can be considered as sufficient to provide an approximation of the true surface conditions. This methodically oriented article attempts to reveal and quantify the effects that the variability and roughness of the land surface may have on the parameter values of common landscape metrics and tries to present a few suitable workarounds for this issue. These include modification algorithms for common landscape metrics as well as the introduction of alternative measures to capture surface roughness. These methods are mainly exemplified using neutral landscape models. 2. Methods – Considering terrain characteristics in the patch-corridor-matrix model Two basic approaches for the first steps towards 3D-analysis of landscape structure are proposed in this paper: The first one comprises different correction algorithms for standard area, shape and distance metrics. The second one is based on the aggregation of height information in the form of simple ―surface roughness‖ parameters. 2.1Adjusting standard landscape metrics The simplest and most obvious approach to incorporate the third dimension into landscape analyses is to adjust the existing set of metrics and to mitigate the source of error associated with the planimetric projection of slopes. Such techniques have been proposed earlier by Dorner et al. (2002), who suggested to compute the true surface area of each raster cell in a DEM by the quotient projected area/cos(slope) and to approximate the true distances between adjacent cells by simple application of the Pythagorean Theorem using Euclidean distance and differences in elevation. However,a systematic integration into calculation algorithms of landscape metrics was not presented.In this paper, a more detailed approach is chosen to calculate true surface area, based on the findings of Jenness (2004). The technique is based on a moving window algorithm and estimates the true surface area for each grid cell using a triangulation method (Figure2). Each of the triangles is located in three-dimensional space
and connects the focal cell with the centre points of adjacent cells. The lengths of the triangle sides and the area of each triangle can easily be calculated by means of the Pythagorean Theorem. The eight resulting triangles are summed up to produce the total surface area of the underlying cell. This method is preferred since it can be expected to provide more accurate results; in contrast to the approach mentioned above, all eight neighbours of the pixel of interest are included in the calculation, instead of only the one defining the slope angle.
Figure 2: Method to determine true surface area and true surface perimeter of patches. True surface area of the focal raster cell is obtained by adding the eight shaded triangles, true surface perimeter by summation of the eight bold line segments (figure redrawn according to Jenness 2004). Additional computation steps have to be conducted to obtain the true surface area not only for each raster pixel but for each patch in a landscape in order to include these new geometry values into the calculation of common landscape metrics. A raster file containing the patch structure of the concerning land mosaic is overlaid with the corresponding elevation model. Then surface area values of the pixels representing each patch are summed up. Equal resolution and extent of the patch file and the elevation model are presumed. Jenness’ method is also adapted in order to calculate realistic surface perimeters of each patch. This is done by simply adding up the line segments forming the surface edge of the raster pixels (see bold lines in Figure 2) in case they are part of the patch boundary. A more intricate procedure is needed for the calculation of the true surface distances between patches of the same class, that is the 3D-equivalent to the ―Euclidean Nearest Neighbour‖ measure as used in the FRAGSTATS-set of metrics (see McGarigal et al. 2002). The question can be referred to as a so-called ―shortest path problem‖, for which various solutions are described in literature, each of them having its assets and drawbacks(e.g. Cormen et al. 2001).
In the present case, a weighted graph G(V, E) is constructed,with each raster cell representing one vertex V and each connection line between the cells forming one edge E of the graph. The weight associated to every edge is calculated by using the Pythagorean Theorem to approximate the 3D-distance between centre points of adjacent raster cells. After these steps, a suitable algorithm needs to be applied to the graph in order to determine the shortest path between a border cell of the focal patch and the closest border cell of the closest patch of the same class. In the present case, a form of the Dijkstra-algorithm is chosen, as it is expected to provide good estimates for the shortest path (Chen 2003). This method is based on an undirected circular search procedure. Considering the problem,the vast computation effort becomes evident:for a 1000 x 1000 DEM, the constructed graph consists of 1*106 vertices, aggregated to form a number of ―nodes‖ (defined by the patches present), and approx.4*106 edges. This implies that a trade-off between computation time and calculation results has to be made, with the Dijkstra-method providing an acceptable compromise between these two factors. On the basis of these true surface geometries, a number of basic landscape metrics can be calculated and be compared to their planimetric 2D-equivalents. These metrics are listed in Table 1. Table 1: Selected standard metrics, calculated using both 2D- and 3D-geometries.
2.2 Characterising surface roughness As outlined in the first chapter, surface roughness may be a critical issue in assessing a number of ecological functions, notably climatic conditions or erosion processes. Therefore, simple and straightforward measures to capture roughness characteristics are needed to help improve the accuracy of landscape analyses. The most self-evident approach in this context may be to simply calculate the ratio of true surface area (as described in the previous section) and planimetric area. This may provide a first estimate of the overall deviation of the patch surface from a perfect 2D-plane. Completely plane patches consequently result in an area ratio-value of 1. Other concepts for the characterisation of surface features such as roughness are provided by surface metrology(Stout et al. 1993). This scientific field deals with the characterisation of manufactured surfaces (for example optic lenses) on a microscopic scale. When these measures are transferred to a larger scale, they may be applicable to ecological problems and analyses of landscape structure as well. The index “Average Surface Roughness” (Ra) appears to be the most-frequently used parameter from this set and at the same time the one with the least computation effort. Ra is usually calculated as the mean absolute departure of a patch’ s elevation values from the mean plane. Unlike the 3D/2Darea
ratio, this index is not dimensionless but maintains the units of the DEM. Therefore, it can be considered as an absolute measure of surface roughness. A modification of Ra is Rq, the “Root-Mean-Square Deviation of the Surface”, which is a standardised version of the former. These and other measures for the characterisation of the land surface using surface metrology-indices are given in Table 2, even though not all of them are explicitly covered in detail in this study. Ra and Rq were chosen for this study since they are widely-used in disciplines like materials science and are rather easily interpretable. The implementation of the methods described was carried out using both the MATLAB package (Math-Works 2005) and an ArcGIS-extension programmed in C# using the .NET-environment and the ArcObjects class libraries (ESRI 2005). 2.3 Case study using neutral landscape models At this point, a couple of questions may arise: Is it actually necessary to include elevation and topography respectively into analyses of landscape structure?Is there any significant difference at all between the 2D- and 3D-forms of landscape metrics? Do simple roughness parameters tell us anything about the relief variability? And, which may even be the most important one: is the additional computation effort worth being carried out? In order to help answering these questions and to make valid statements about the relevance, sensitivity and explanatory power of the proposed methods, the above mentioned indices were applied to a set of neutral landscape models and simulated DEMs. Neutral landscape models have proved to be a valuable means for therepresentation of realistic conditions or for the reflection of extreme states of landscape systems (Gardner & Urban 2007; Gardner et al. 1987; Li et al. 2004). This turned out to be useful, as neutral landscapes allow to mirror landscape sections of different structuring, whereas simulated elevation models may reflect variable heterogeneity of the underlying terrain. In the given case, the software Simmap (Saura & Martínez-Millán 2000) was used to create landscapes with an extent of 1000 x 1000 raster cells (with an assigned horizontal resolution of 1 x 1 m) and three land use classes of equal surface percentages. The initial probability p was altered to produce two different types of landscape structuring. Similarly, the programme Landserf(Wood 2005) was applied to produce elevation models of various relief variabilities. More precisely,the parameter “fractal dimension” (FD) was altered to yield three DEMs of increasing “roughness” . Details about the test landscapes and the DEMs can be derived from Figure 3. Table 2: Examples of some simple indices to derive information about surface characteristics and their calculation formulae (Precision Devices 1998).
Figure 3: Combinations of neutral landscape models and simulated DEMs. 3. Results – The effect of topography on selected landscape metrics The six land mosaic/elevation model-combinations were subject to 3D-landscape analysis according to the outlined techniques. The arithmetic mean of the index values was calculated for all the patches present in the landscapes in order to illustrate the effect of the underlying relief in the examined situations (planimetric conditions as well as DEMs with fractal dimension 2.1, 2.5 and 2.9 respectively). The results are displayed in the diagrams in Figure 4. Some fundamental findings can be noted. For the mean patch area and mean patch perimeter, there is a clear trend towards higher values for increasing relief variability.This holds true for both the highly fragmented landscape (p = 0.54) as well as for the mosaic dominated by fewer and larger patches (p = 0.58). The differences between the planimetric case and each of the three simulated DEMs prove to be significant when compared using a t-test for paired samples. As expected, a clear dependence of the values on the terrain variability and the ability of the applied methods to capture this effect can be demonstrated. For the distance measure “Nearest Neighbour”, a similar effect is evident. There is a clear increase for the mean distance between nearest neighbours of the same class when the relief is becoming “rougher” and more variable. For the group of the shape metrics, the findings are not as clear and not as easily interpretable. For the Fractal Dimension (FRAC), the differences between the 2D-version and its 3D-equivalent applied to the three DEMs are rather low and almost neglectable, while still slightly increasing with terrain roughness. Perimeter- Area Ratio (PARA) shows its typical size-dependency (McGarigal et al. 2002), and therefore this index has to be carefully interpreted due to the growing mean patch size with increasing terrain roughness. Thus, a definite statement about the effects of terrain on the output of this parameter can hardly be made. All in all, this parameter appears to be largely independent of terrain roughness. As the Shape Index (SHAPE) corrects for the size problem of the Perimeter-Area Ratio index, it may be the most interesting one to have a closer look at within the group of the shape metrics. The differences of the mean Shape Index for the four relief situations examined seem to be rather small for the 2D-case and the first two elevation models with an abrupt rise for the most variable elevation model. This again is the case for both of the landscape mosaics considered. Of course, this rise is up to a certain extent proportional to the increase in mean patch area (see above), as SHAPE tends to increase with growing area, even if perimeter increases for the same factor at the same time. This can be derived from the calculation formula for SHAPE. Finally, the two simple roughness parameters calculated,Average Surface Roughness (Ra) and Root-Mean-Square Deviation of the Surface (Rq), were applied to he test landscapes. The results indicate a clear dependency of the parameter outputs on the underlying relief with a very similar behaviour of the two indices and similar outputs for the two different landscape mosaics.
4. Discussion – On the relevance of the proposed methods This short methodological examination is supposed to clarify the effect of topography and surface roughness on a few common landscape metrics. Moreover, some both simple and fundamental approaches to consider these effects are presented. Patch area and perimeter exhibit a strong connectedness to the variability of the underlying terrain. The effects may not be as distinct under real-world conditions. But the simulated landscape models and DEMs clearly demonstrate that a consideration of landscape mosaics as purely planimetric surfaces and their characterisation using 2D-landscape metrics may not be sufficient in every case, especially when terrain is highly variable. When one tries to characterise landscapes in these cases, the application of corrected metrics as proposed in this paper may be advisable. The same holds true for distance measures. These metrics may have a critical relevance e.g. in species-centred habitat analyses. As can be seen from the results presented here, the effect of the relief on the “true” surface distances between patches should not be neglected in rough terrain. This effect may be exaggerated by the application of the simulated landscapes, even if the purpose is to reveal the fundamental relationship between distance and topography and to provide a technique to improve the calculation of such distance measures. Statements regarding shape indices like PARA, FRAC or SHAPE are not as concise. These metrics do react to the terrain, but absolute differences between the examined relief situations tend to be low and the trend is not as obvious for all of these measures as is the case for area, perimeter and distance measures. One reason for this may be the simple fact that in the calculation algorithms for these metrics, parameters of the patch geometries appear both above and below the fraction line. Therefore, when dividing for example 3D-perimeter by 3D-area (both having larger values compared to their 2D-equivalents), the differences between the 2Dand the 3D-approach may simply level out to a certain extent. Finally, the results reveal that the analysis of surface roughness may serve as a valuable instrument to provide highly condensed information about the topographic characteristics of patches. As both Ra and Rq are closely connected to the initial roughness parameter of the respective DEMs (i.e. their fractal dimension FD), they can be regarded as a good extension of common landscape metrics towards the third spatial dimension, especially as their calculation algorithms are rather straight-forward and can be easily integrated into the patch-corridor-matrix model of landscapes. Moreover, the results from these parameters are easily interpretable. To assess the influence of landscape configuration and patch structuring on the metrics output, the two chosen mosaics with an initial probability p were supposed to serve as a representation of different structural conditions. It turns out that the general trends in index behaviour for increasing fractal dimension of the underlying relief are generally the same. The distance to the nearest neighbour in the same class tends to be larger for p = 0.58, because on average larger patches of other classes have to be crossed. This indicates that the application of the correction algorithm for distance calculations may be particularly valuable in coarse-grained landscapes with large relief variability. Aside from these findings, preliminary studies carried out applying the proposed methods to real-world data have
shown that large patches in general lead to some mitigation of terrain effects on landscape metrics, as often landscape elements comprise both“flat”and“rough”areas. This circumstance is not reflected to the same degree by the relatively homogeneous simulated elevation models used in this study, where the quantification of terrain roughness rather than general landscape configuration was the main focus. The results suggest that the proposed methods may exhibit a large potential for many ecological problems. Since especially measures for habitat area and habitat isolation or fragmentation are key variables in many species-centred analyses, the usage of correction algorithms for these geometries appears to offer the possibility of improved results (for examples dealing with these measures see Bennett 2003; Fahrig 1997; Krauss et al. 2005; van Dorp & Opdam 1987).
Figure 4: Diagrams displaying the arithmetic means and 95 %-confidence intervals around the mean value for the selected indices; each index was calculated for the two test landscapes (displayed in blue and green respectively)combined with each of the three elevation models as well as the planimetric case. 5. Conclusions and outlook The findings presented in this paper indicate that the patch-corridor-matrix model as the prevailing concept to perceive and describe landscapes may not suffice in cases where topographic and morphologic features of the land surface need to be taken into account. As topography plays a crucial role in many ecological processes, simple methods and techniques for its assessment are needed. We propose some straightforward approaches that enable landscape ecologists to account for the effects of relief and landform in their analyses. The suggested framework for the adjustment of standard landscape metrics, thus converting them to 3D-metrics, may be applied to all indices using the basic geometries of patches (i.e. their area and perimeter as well as the distances between them) as input parameters. In this way, more realistic results can be achieved. This may especially hold true for examinations where habitat area or isolation play an important role. The presented indices derived from surface metrology can serve as analysis tools for the overall variability of altitude values within patches, as one has to keep in mind that patches in reality cannot be regarded as spatially homogeneous, but rather possess their specific “within-patch-heterogeneity” . Future work has to concentrate on the refinement and improvement of the methods as well as on their testing under real-world conditions in order to gain more insight in their applicability and sensitivity. Especially the specific impacts of different topographic regions (high mountains/low mountain ranges/lowland etc.) have to be examined. In this regard, potential fields of application have been compiled by Walz et al. (2007). From our point of view, the search for alternative landscape concepts should also be emphasised in future theoretical and methodological work. McGarigal & Cushman(2005) have coined the term “gradient concept” in this context, pointing out that the patch-corridormatrix model can be regarded as an oversimplification of realistic conditions, as it acts on the assumption of the landscape as a composite of flat and homogeneous “puzzle pieces” , divided by sharp and clearly defined boundaries. Obviously, this cannot be taken for granted in every case. This notion was also formulated by Blaschke & Dr?gu? (2003) or Ernoult et al. (2003). Fuzzy approaches (Dr?gu? & Blaschke 2006) or spectral and wavelet analysis (Couteron et al. 2006; Saunders et al. 2005) have been proposed as attempts at a solution. Further techniques to resolve the shortcomings of the patch-corridor-matrix model are needed, with the paper at hand as one approach to the problem. Acknowledgements This project (Landschaftsstrukturma? e zur Analyse der raum-zeitlichen Dimensionen (4-D-Indizes)) is funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG). References
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地形和地表景观结构粗糙度的影响分析—修改景观指数的现有 设置的建议 摘要
地形地貌的变化在生态系统功能和结构中发挥了关键的作用。然而，涉及图案 在景观生态过程中最常用的概念，所谓的“斑块—廊道—基质”模型，把景观作为 一个平面表面。因此，景观指数，作为景观镶嵌的空间布局的数值描述符，一般不 允许对地形特征的检查，甚至可能产生错误的结果，尤其是在山区。这个简单的方 法论研究为包括地势性质为大型景观的分析提供了基本的方法，包括标准景观指数 在“真”表面几何形状的基础上，与从表面测量而得粗糙度参数的应用程序的计算。 该方法是测试它们在使用中性的景观和数值高程模型是的阐释力。结果表明，面积 和距离指数对地形的复杂性具有较高的灵敏度，而当表面几何形状被考虑用作计算 时形状指数值仅稍有改变。总之，所提出的方法被证明在现有的设置主要是在“粗 糙”的景观部分方面是一个宝贵延伸，允许对空间结构的更现实的评估。 关键词：斑块—廊道—基质模式，中性景观，数字高程模型，地势，粗糙度参数
“3D”已成为许多科学领域一个经常使用的术语，即使在社会生态学上。在最 近几年，3D 可视化和 3D 图形经历巨大的进步。景观或城市的现实可视化在空间规 划过程中越来越重要，例如，当建设项目的影响需要澄清或需要证明在一段时间内 景观变化的动态。同时“3D-GIS”开始出现。然而，在景观生态学和“三维模式” 的考试方面， “3D 分析”仍有些被忽略，尽管高程和地表特征可以被视为许多生态 过程的关键元素。因此，从景观生态学的角度看，有必要在检查和鉴定景观和特殊 地形特征的方面进行三维分析。
以前的出版物试图强调在大型景观分析中纳入第三维度问题的必要性。许多学 者曾指出，地形是一个能发挥生态系统功能和结构的重要作用的因素，而在许多情 况下这是不充分的考虑。表面特性以及维管束植物的物种丰富度和群体成之间的联 系（如 Burnett 等人 1998 年，Davis 和 Goetz1990 年;Sebastiá2004 年所展示的） 提供了经常被用于生物多样性分布的模型设计是众所周知的事实例如 Bolstad 等 人， 1998） 。 地势的影响在作为一个生态系统整体， 和特定的生态功能， 如土壤湿度， 温度分布，太阳辐射的平衡，或气候的差异上进行了详细的描述（如 Bailey,2004 年; Oke ,1978 年; Swanson 等人,1988 年） 。 承载地形特征和心中生态过程之间的这些充分研究的环节，有一个事实似乎是 值得关注的：到目前为止，行之有效的斑块—廊道—基质模式—福尔曼（1995 年） 所建议的—没有明确考虑第三个维度在描述景观空间布局的方法。人们普遍认为的 “工艺图案效应” （1989 年特纳）的应答构成了现代景观生态学的自我概念。但建 立利用景观指数为分类地图图案的几何和空间属性的表征（MC-Garigal，2002 年） 持有土地的观点作为“地上物”表面—三维模式方面（地形，海拔）还没有扩展到 这个概念（另见 Blaschke 和 Dr?gu?，2003 年） 。 大量的景观指数被详细地描述，并用于多种用途，包括空间规划和生态模型。 很多人性化的软件产品对指数在矢量或栅格数据的基础上的计算是可用的，如 FRAGSTATS（McGarigal 与 Marks ，1995 年） ，飞跃 II（Schnekenburger 等，1997 年）或 V-LATE（ang 和 Tiede，2003 年） 。但关于 3D 功能的信息，如表面粗糙度， 地形，或景观元素中地势的可变性（ “斑块” ） ，不能使用这些措施进行访问。而且， 人们甚至可能在景观指数的计算中，通过忽略底层地势而产生错误的结果，由于基 本几何（面积，周长）的斑块和它们之间的距离通常低估了地上物的观察。在斑块 —廊道—基质模式和景观中的实际情况之间的这些差异可以看作是这一概念的主要 缺点，尤其是在山区或者地区表现出的复杂地形。图 1 提供的是地势可能对景观指 数共同群体参数输出的效果的直观表示。例如，显而易见的是，对于区域或距离指 数，可当考虑到表面复杂性时，预计会出现一个向较高的值的倾向。 地貌提供了一大群体参数来描述陆地表面和 georelief 分类（见 Dikau 和 Schmidt ，1999 年; Evans ，1972 年; Pike ，2000 年;Wilson 和 Gallant ，2000 年） 。然而，当一个人试图用分类图描述景观的空间格局时，曲率，坡向，或群体合 参数的措施，如湿度指数，只有有限的使用。一般来说，这些措施涉及集水区和离 散地貌元素，而不是将普通的景观指数应用到“斑块”;这些方法之间，不可能在每 一种情况下都是理所当然地兼容。 图 1：在斑块—廊道—基质模式中常用的景观指数群体和下方地形（上部重绘 根据威恩斯等，1993 年）的影响。
其它技术已经提出将表面特征融入景观分析。例如，Beasom（1983 年）已建议 用于评估基于采样点和轮廓线的交点的陆地表面耐用性的简单方法。 更详细的建议， 包括将地形特性融入景观格局和植被分布的分析，都已经由多纳等人（2002 年）提 出。简单移动窗算法在数字高程模型（数字高程模型）栅格像素的“凹/凸”的估计 已经由 McNab（1992 年）和 Blaszczynski（1997 年）开发。虽然针对特殊情况的研 究和特定专题环境的一些方法的应用程序可能是非常有价值的，但融入斑块—廊道 —基质模式还没有实现呢。 同时，在遥感领域的技术进步已导致数字高程模型的质量的迅速提高。特别是 激光雷达（ “光探测和测距” ）的测量提供了土地表面的高分辨率的高程数据。他们 可以准确地估计植被结构的属性， 因此应被景观生态学家特别关注 （如 Lefsky 等人， 2002 年） 。 首次尝试从雷达数据获得三维景观指数早已经成功 （如 Blaschke 等， 2004 年） 。 所有这些“3D 问题”的笔记在景观生态学和分析重要的表面特性的缺陷方面标 志着研究的起点。本文的主要目的是呈现出在基于离散单位土地作为景观生态假设 中的一个核心概念的认识上，就如何解决问题提出的一些基本原则（如 Zonneveld， 1989 年） 。术语“3D”是用在这种情况下，即使数字高程模型实际上是指真实世界 的“2.5D”表示形式，每个 x，y 坐标都对应一个 z 值。在大多数情况下，但是，数 字高程模型可以被认为是足够用来提供一个真正的表面条件的近似值。 本文面向有条不紊地试图揭示和量化，地表的可变性和粗糙度可能对共同景观指标 的参数值的影响，并尝试提出一些适合这个问题的解决方法。这些措施包括常见景 观指数算法的修改，以及出台其他措施来获得表面粗糙度。这些方法主要是通过中 性景观模型来举例说明。
为实现 3D 分析景观结构的第一步， 本文中的两种基本方法都提出了： 第一个包 含不同的修正算法标准面积， 形状和距离指数。 第二个是基于高度信息在简单的 “表 面粗糙度”参数的形式上的聚集。
最简单和最直接的方法将第三个维度纳入景观分析是为了调整指数的现有设 置，并减少与斜坡地上物投影相关的误差源。这样的技术已在早些时候被 Dorner 等人（2002）提出，并建议利用数字高程模型的商数投影面积/余弦来计算每个栅格 单元的真实表面积。并使用由勾股定理的简单应用得到的近似欧氏距离和高度差相 邻单元之间的距离来计算真正的距离。然而，一个融入景观指数的系统的计算算法 并没有被提出。在本文中，更详细的方法是，在 Jenness（2004 年）的调查结果的 基础上选择计算真实表面面积。该技术是基于移动窗口算法，并使用三角测量方法 （图 2）来估计每个网格单元的真实的表面积。每个三角形都是位于三维空间，并 通过邻近单元的中心点与焦点单元连接。每个三角形的边长和三角形的面积可以容 易地通过勾股定理的手段来计算。八个所得三角形总结，以产生底层单元的总表面 积。此方法优选的是，因为它可以预期提供更准确的结果;在与上面提到的方法中， 所有八个相邻的感兴趣的像素被包括在计算中，而不是只用一个来限定倾斜角。 图 2：来确定斑块的真正的表面积和周长方法。焦点栅格单元的真实表面积通 过（根据 2004 年的 Jenness 图重绘）添加八个阴影三角形获得，真表面周长由 8 粗体的线段总和获得。
克斑块结构的光栅文件覆盖有相应的高程模型。然后，像素的表面积值代表每个斑 块的累计。斑块文件和高程模型的分辨率平等和程度被推定。Jenness 的方法也适 于以计算每个斑块的现实表面周长。在它们是斑块边界的一部分情况下，这是通过 简单地增加线段以形成栅格像素的表面边界来进行的（参见图 2 中的粗线） 。 对同一类的斑块之间的真实表面距离的计算，需要一个更复杂的过程，也就是 相当于 “欧几里德最近邻” 的 3D 被作为在 FRAGSTATS 中的量度集合 （参见 McGarigal 等，2002 年） 。这个问题可以称为所谓的“最短路径问题” ，在文献中各种解决方案 都有描述，其中每一个具有其价值和缺点（例如 Cormen 等人，2001 年） 。 在目前的情况下，加权图 G（V，E）被创造了出来，每个栅格单元表示一个顶 点 V 和单元之间形成的该图的一个边界 E 中的每个连接线。相关联的每一个边界的 权重是通过使用勾股定理来计算近似相邻栅格单元的中心点之间的 3D 距离。 在这些 步骤之后，适当的算法需要被应用到图形中，以确定焦点斑块的边界小区和相同类 的最相近斑块的最近边界小区之间的最短路径。在目前的情况下，Dijkstra 算法的 形式被选择，因为它可望为最短路径提供良好估计（2003 年，陈） 。此方法是基于 无向圆形搜索过程。考虑到其中困难，广阔的计算的效果变得明显：为一个 1000× 1000 的数字高程模型， 所构建的图包含 1×106 个顶点， 聚集以形成多个 “节点” （由 现在的斑块定义） ，和大约 4 * 106 的边界。这意味着，计算时间和计算结果之间的 折衷已经被提出， 用 Dijkstra 的方法提供这两个因素之间可接受的方案。 在这些真 正的表面几何形状的基础上，一些基本的景观指数可以对它们的地上物的 2D-当量 进行计算和比较。这些指数列于表 1。
如第一章所述，在评估一些生态功能，特别是气候条件或侵蚀过程，表面粗糙 度可能是一个关键问题。因此，用简单而直接的措施来捕获粗糙度特性是十分必要 的，它可以帮助改善景观分析的准确性。在次背景下，最简单明了的方法大概就是 是简单地计算真正的表面面积（如前一节中所述）和地上物面积的比例。这可以从 一个完美的 2D 平面提供的斑块表面的整体平面的直观评估。 完全的平面斑块因而导 致了表 1 的面积比率值。 通过表面测量一些其它的用于的表面特性的概念被提出，如粗糙度表征 （Stout 等人， 1993 年） 。 这个科学领域在微观尺度上涉及表面加工 （例如光学镜头） 的表征。当这些措施被转向大尺度时，它们也可以很好地适用于生态问题和景观结 构的分析。从该群体中索引出的指数“平均表面粗糙度” （Ra）似乎是使用最频繁的
参数，并且在同一时间内具有较少的计算工作量。Ra 通常是被作为从平均平面的平 均绝对距离的一个斑块的高程值计算的。不像 3D / 2D 的面积比，该指数是无量纲 的但是保持了数字高程模型的单元。 因此， 它可以被认为是表面粗糙度的绝对指数。 Ra 的修正是 RQ，后者是前者的一个标准化版本的“表面的开平方的绝对偏差” 。陆 地表面的特征的这些和其他措施，使用表面测量指数列于表 2，尽管在这项研究中 不是明确详细地介绍了所有的措施。 Ra 和 RQ 被选为这项研究服务，因为它们都比 较容易解释，并被广泛地使用在诸如材料科学学科。 所描述的方法的安装启用是，执行使用在网络环境中使用 C＃编程和 ArcObjects 类库 （ ESRI， 2005 年） 的 MATLAB 软件包 （数学工程， 2005 年） 和 ArcGIS 扩展。
此时，可能会出现一些问题， ：实际上，在景观结构的分析中分别包括高程和地 形地貌是有必要的吗？在所有的二维和三维形式的景观指数中是否有任何显著差 异？简单的粗糙度参数确实能告诉我们任何地形变异的任何事吗？而且，这甚至可 能是最重要的：额外的计算工作量值得开展吗？ 为了帮助回答这些问题并作出有关上述提出的方法的相关性，敏感性和解释力 的有效的声明，上面提到的指数分别适用于一系列中性景观模型和模拟数字高程模 型。中性景观模型已被证明是一个对现实条件的表示或景观系统的极端状态的反映 的有价值的方法（Gardner 和 Urban，2007 年，Gardner 等人，1987; Li 等人，2004 年） 。事实证明，这是有用的，就像中性景观模型允许反映不同结构的景观组成，而 模拟的高程模型可能反映了潜在地形的可变的异质性。 在给定的情况下，软件 Simmap（Saura 和 Martínez-MILLAN，2000 年）被用来 创造具有 1000×1000 长度的栅格单元的景观 （以 1×1μ m 的分配水平分辨率） 和三 个表面的百分比相等的土地使用等级。初始概率 p 被改变，以产生两种不同类型的 景观结构。类似地，程序 Landserf（Wood，2005 年）被应用，以产生各种地势变异 的高程模型。更精确地说，将参数“分形维数” （FD）改变以产生三个增长“粗糙度” 的数字高程模型。关于测试的景观和多个数字高程模型的细节可以从图 3 中得到。 表 2：一些得出有关表面特征和它们的计算公式（精密器件，1998 年）的信息 的简单的指数例子。
译自：Hoechstetter, S.*, Walz, etc, Effects of topography and surface roughness in analyses of landscape structure—A proposal to modify the existing set of landscape metrics[J]. Landscape Online, 2008, 03: 1-14.