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Digital terrain AnalysisJohn P. Wilson and John C. Gallant1.1 PRINCIPLES AND APPLICATIONSThe development and application of the TAPES: Terrain Analysis Programs for theEnvironmental Sciences software tools described in this book was motivated by our view of the world as a stage on which a series of hierarchically scaled biophysical processes are played out (Figure 1.1). This approach is useful because it can handle the complexity of individual landscape processes and patterns as well as some of the difficulties that are encountered in delineating the appropriate spatial and temporal scales (ONeill et al. 1986, Mackey 1996, Malanson and Armstrong 1997). Many of the important biophysical processes operating at or near the earths surface are infiu- enced by both past events and contemporary controls, interactions, and thresholds (Dietrich et al. 1992, Grayson et al. 1993, Montgomery and Dietrich 1995). These interrelationships are complicated and may be best understood using a dynamic sys-terns modeling approach (Kirkby et al. 1996). The boundaries separating different spatial and temporal scales are not very clear and they may vary with individual processes and/or landscapes (cf. Sivapalan and Wood 1986, Mackey 1996, Malanson and Armstrong 1997). This state of affairs suggests that additional work is required to identify the impor-tant spatial and temporal scales and the factors that influence or control the processes and patterns operating at particular scales. The potential benefits may be substantial. Schaffer (1981), working with interacting systems of populations in community ecology, and Phillips (1986), working on examples in fluvial geomorphology, have demonstrated that the key processes operating over different timescales can be con-sidered independently of each other. Phillips (1988) has also shown how the key processes operating at different spatial scales and affecting the hydraulic gradient of a desert stream in Arizona can be considered independently of each other. Band et al.(1991) generated landscape units with low internal variance and high between-unit2DIGITAL TERRAIN ANALYSISCloud cover and C02 levels control primary energy inputs to climate and weather patterns Prevailing weather systems control long-term mean conditions;elevation-driven lapse rates control monthly climate; andgeological substrate exerts control on soil chemistrySurface morphology controls catchment hydrology;slope, aspect, horizon, and topographic shading controls surface insolationVegetation canopy controls light, heat, and water for understory plants; vegetation structure and plant physiognomy controlsFigure 1.1. Scales at which various biophysical processes dominate calculation of primary environmental regimes. Reprinted with permission from Mackey (1996) The role of GIS and environmental modeling in the conservation of biodiversity. In Proceedings of the Third Inter-national Co吵rence on Integrating GIS and Environmental Modeling, Santa Ee, New Mexico,21-25 January, 1996, edited by NCGIA. Copyright1996 by National Center for Geo-graphic Information and Analysis, University of California, Santa Barbara.variance for the importantparameters in a nonlinear, deterministic model designed to simulate carbon, water, and nitrogen cycles in a forest ecosystem using a series of hillslope and watershed templates. However, this result may not be universally applicable. Phillips (1988) warned that the key differences in spatial scales cannot be related to fundamental landscape units in numerous instances. Grayson et al. (1993) argued that we should avoid implementing at one scale models developed at a different scale because the simplifying assumptions will often undermine the validity of the original models. Kirkby et al. (1996) concluded that different processes and interactions are likely to emerge as dominant as we move from the plot scale to catchment and regional scales in soil erosion modeling applications. This state of affairs is true of other hydrological, geomorphological, and biological settings as well. Most of the hydrological, geomorphological, and ecological research of the past century has been conducted at the global and nano- or microscales identified in Figure 1.1 (Mackey 1996). The meso- and toposcales have received much less attention,and yet these scales are important because many of the solutions to environmental problems, such as accelerated soil erosion and non-point-source pollution, will require changes in management strategies at these landscape scales (Moore and Hutchinson 1991). The influence of geologic substrate on soil chemistry (e.g., Likens et al. 1977) and impact of prevailing weather systems and elevation-driven lapse rates on long-term average monthly climate (e.g., Daly et al. 1994, Hutchinson 1995) exemplify some of the controls operating at the mesoscale. The influence of surface morphology on catchment hydrology and the impact of slope, aspect, and horizon shading on insolation probably represent the most important controls operating at toposcales. Numerous studies have shown how the shape of the land surface can affect the lateral migration and accumulation of water, sediments, and other constituents (e.g., Moore et al. 1988a). These variables, in turn, influence soil development (e.g., Kreznor et al. 1989) and exert a strong influence on the spatial and temporal distributions of the light, heat, water, and mineral nutrients required by photosynthesizing plants (Mackey 1996). The increased popularity of work at these two intermediate scales during the past decade has capitalized on the increasing availability of high-resolution, continuous, digital elevation data and the development of new computerized terrain-analysis tools (Wilson 1996, Burrough and McDonnell 1998, Wilson and Burrough 1999).1.1.1 Digital Elevation Data Sources and Structures Most of the currently available digital elevation data sets are the product of photogrammetric data capture (I. D. Moore et al. 1991). These sources rely on the stereoscopic interpretation of aerial photographs or satellite imagery using manual or automatic stereoplotters (Carter 1988,Weibel and Heller 1991). Additional elevation data sets can be acquired by digitizing the contour lines on topographic maps and conducting ground surveys. The advent and widespread use of Global Positioning Systems (GPS) in agriculture and other settings provides many new and affordable opportunities for the collection of large numbers of special-purpose, one-of-a-kind elevation data sets (Fix and Burt 1995, Twigg 1998, Wilson 1999a). These digital elevation data are usually organized into one of three data structares-(1) regular grids, (2) triangulated irregular networks, and (3) contours depending on the source and/or preferred method of analysis (Figure 1.2). Square-grid digital elevation models (DEMs) have emerged as the most widely used data structure during the past decade because of their simplicity (i.e., simple elevation matrices that record topological relations between data points implicitly) and ease of computer implementation (I. D. Moore et al. 1991, 1993f, Wise 1998). These advantages offset at least three disadvantages. First, the size of the grid mesh will often affect the storage requirements, computational efficiency, and the quality of the results (Collins and Moon 1981, I. D. Moore et al. 1991). Second, square grids can not handle abrupt changes in elevation easily and they will often skip important details of the land surface in flat areas (Carter 1988). However, it is worth noting that many of the problems in flat areas occur because the U.S. Geological Survey (USGS) and others persist in recording elevations in whole meters. Third, the computed upslope flow paths will tend to zigzag across the landscape and increase the difficulty of calculating specific catchment areas accurately (Zevenbergen and Thorne 1987, I. D. Moore et al. 1991). Several of these obstacles have been overcome in recent years. For example, there is no generic reason why regular DEMs cannot represent shape well in flat areas, so long as the terrain attributes are calculated by a method 4DIGITAL TERRAIN ANALYSISthat respects surface drainage. ANUDEM (Hutchinson 1988, 1989b) is one such method and is described in more detail in Chapter 2. Similarly, the advent of several new compression techniques have reduced the storage requirements and improved computational efficiency in recent years (e.g., Kidner and Smith 1992, Smith and Lewis 1994). DEMs with grid sizes of 500, 100, 30, 10, and even 1 m are increasingly available for different parts of the globe (see U.S. Geological Survey 1993,Ordinance Survey 1993, and Hutchinson et al. 1996 for examples). Triangulated irregular networks (TINS) have also found widespread use (e.g.,Tajchman 1981, Jones et al. 1990, Yu et al. 1997). TINS are based on triangular elemenu (facets) with vertices at the sample points (I. D. Moore et al. 1991). These facets consist of planes joining the three adjacent points in the network and are usually constructed using Delauney triangulation(Weibel and Heller 1991). Lee (1991) compared several methods for building TINS from gridded DEMs. However, the best TINS sample surface-specific points, such as peaks, ridges, and breaks in slope, and form an irregular network of points stored as a set of x, y, and z values together with pointers to their neighbors in the net (I. D. Moore et al. 1991). TINS can easily incorporate discontinuities and may constitute efficient data structures because the density of the triangles can be varied to match the roughness of the terrain (I. D. Moore et al. 1991). This arrangement may cancel out the additional storage that is incurred when the topological relations are computed and recorded explicitly (Kumler 1994). The third structure incorporates the stream tube concept first proposed by Onstad and Brakensiek (1968) and divides landscapes into small, irregularly shaped polygons (elements) based on contour lines and their orthogonals (Figure 1.2) (OLoughlin 1986, I. D. Moore et al. 1988a). This structure is used most frequently in hydrological applications because it can reduce complex three-dimensional flow equations into a series of coupled one-dimensional equations in areas of complex terrain (e.g., Moore and Foster 1990, Moore and Grayson 1991, Grayson et al. 1994).Excellent reviews of digital elevation data sources and data structures are presented by Carter (1988), Weibel and Heller (1991), and I. D. Moore et al. (1991).Figure 1.2. Methods of structuring an elevation data network: (a) square-grid network showing a moving 3 by 3 submatrix centered on node 5; (b) triangulated irregular network; and (c) contour-based network. Reprinted with permission from Moore, Grayson, and Ladson (1991) Digital terrain modeling: A review of hydrological, geomorphological, and ecological applicanons.hydrological Processes 5: 3-30. Copyright1991 by John Wiley and Sons Ltd.1.1 PRINCIPLES AND APPLICATIONS The proliferation of digital elevation sources and preprocessing tools means that the initial choice of data structure is not as critical as it once was (Kemp 1997a, b). Numerous methods have been proposed to convert digital elevation data from one structure to another, although care must be exercised with each of these methods to minimize unwanted artifacts (e.g., Krajewski and Gibbs 1994). In addition, larger quantities of data do not necessarily produce better results: Eklundh and Martensson (1995), for example, used ANUDEM (Hutchinson 1988, 1989b) to derive square grids from contours and demonstrated that point sampling produces faster and more accurate square-grid DEMs than the digitizing of contours. Similarly, Wilson et al. (1998) used ANUDEM to derive square grids from irregular point samples and showed that many of the x, y, z data points acquired with a truck-mounted GPS were not required to produce satisfactory square-grid DEMs. ANUDEM calculates ridge and streamlines from points of maximum local curvature on contour lines and incorporates a drainage enforcement algorithm that automatically removes spurious sinks or pits in the fitted elevation surface (Hutchinson 1988, 1989b). ANUDEM is one of several programs of this type and an early version has been implemented in the ARC/INFO (Environmental Systems Research Institute, Redlands, CA) geographical information system (GIS) with the TOPOGRID command. Qian et al. (1990) describe an alternative approach that utilizes local operators and global reasoning to automatically extract drainage networks and ridge lines from digital elevation data. Similarly, Smith et al. (1990) proposed a two-step, knowledge-based procedure for extracting channel networks from noisy DEM data. Kumler (1994) described the method used by the U.S. Geological Survey to generate square-grid DEMs from digital contour lines. Carrara et al. (1997) compared several methods for generating DEMs from contour lines; however, the range of terrain types, sample structures, and modeling routines is so great that attempts to make generalizations about best models is tremendously difficult (Burrough and McDonnell 1998, Dixon et al. 1998, Wilson 1999b). In addition, some of the interpolation methods that have been proposed are difficult to use and Eklundh and Martensson (1995) recommended that less experienced users focus on the quality of the input data instead of learning sophisticated interpolation methods. Simpler interpolation methods will give satisfactory results so long as the input data are well sampled and sophisticated algorithms are likely to produce unsatisfactory results if applied to poor data (e.g., Wilson et al. 1998).数字地形分析约翰P威尔逊和约翰C浩1.1原理与应用磁带:环境科学的软件工具,在这本书中所描述的地形分析程序的开发和应用是出于我们对世界的看法,作为一个上发挥出了一系列层次缩放的生物物理过程的阶段(图1.1)。这种方法是有用的,因为它可以处理个别景观过程和格局的复杂性,以及一些在划定适当的时间和空间尺度(奥尼尔等人,1986年,麦基Malanson和1996年,阿姆斯特朗1997年遇到的困难)。许多重要的生物物理过程达到或接近地球表面的经营infiu enced无论是过去的事件和当代的控制,互动,和阈值(Dietrich等人,1992年,格雷森等。1993年,蒙哥马利和Dietrich,1995)。这些相互关系是复杂的,可以更好地理解使用一个动态系统模式的建模方法(柯比等1996)。分离不同的时间和空间尺度的边界也不是很清楚,他们可能会随个别过程和/或景观(参见Sivapalan和木材1986,麦基Malanson和1996年,阿姆斯特朗1997年)。这种状况表明,额外的工作需要确定的重要空间和时间尺度的因素影响或控制的流程和模式,特别是规模经营。可能是巨大的潜在好处。谢弗(1981年),与群落生态学种群相互作用的系统,和Phillips(1986),工作在河流地貌的例子,已经证明可以考虑彼此独立经营的关键工序在不同的时间尺度。菲利普斯(1988)也表明如何可视为相互独立的工作在不同的空间尺度和影响,在亚利桑那州的沙漠流的水力梯度的关键工序。乐队等。(1991)产生内部低方差和高单位间的景观单位方差在非线性,确定性模型设计模拟使用一系列坡面和流域模板在森林生态系统碳,水和氮循环的重要参数。然而,这一结果未必普遍适用的。菲利普斯(1988)警告说,在空间尺度上的主要差异可以基本地貌单元,在许多情况下不相关的。格雷森等人。 (1993)认为,我们应该避免在一个规模模型,在不同规模的开发实施,因为简化的假设,往往会破坏原始模型的有效性。柯比等人。 (1996)得出的结论是不同的过程和相互作用,可能会出现为主导,我们从小区规模,在流域和区域尺度的土壤侵蚀模型应用。这种状况是真实的水文,地貌,生物设置以及。云层和二氧化碳水平控制天气和气候模式的初级能源的投入当时的天气系统的控制条件下长期平均海拔驱动的退保率控制每月气候和地质基板施加控制土壤化学表面形貌控制流域水文,坡度,坡向,地平线,地形阴影控制表面的太阳辐射植被冠层控制光,热,林下植物和水,植被结构和植物地貌控制养分利用土壤中的微生物控制养分循环 图1.1。各种生物物理过程占主导地位的主要环境制度计算的尺度。重印从麦基(1996)环境地理信息系统和生物多样性保护中的建模的角色权限。在第三国家间合作的法律程序吵rence整合GIS和新墨西哥州圣EE,环境建模,1月,21-25日,1996年,由NCGIA编辑。国家地理图形信息和分析中心,美国加州大学圣巴巴拉分校1996版权所有。 大多数在过去一个世纪的水文,地貌,生态的研究已在全球和纳米或在图1.1(麦基1996年)确定的微尺度下进行。细观toposcales已收到的关注要少得多,但这些量表是重要的,因为许多解决环境问题,如加速土壤侵蚀和非点源污染,将需要在管理战略的变化,在这些景观尺度(摩尔和Hutchinson,1991)。影响土壤化学,地质基板(例如,比喻等,1977)和当时的天气系统和海拔驱动退保率长期平均每月气候的影响(例如,达利等人1995年1994年,哈金森)的一些例证经营中尺度的控制。表面形态对流域水文的影响,坡度,坡向,与地平线上的太阳辐射阴影的影响,可能代表了最重要的控制在toposcales经营。许多研究表明,地表的形状如何影响侧向运移和聚集的水,沉积物和其他成分(例如,摩尔等。1988a)。这些变量,反过来影响发展的土壤(如中,Kreznor等,1989)和施加的光,热,水时空分布上的强大影响力,并通过光合作用植物(麦基1996年)所需的矿质营养。工作在这两个中等规模的日益普及,在过去十年中已资本化,高分辨率,连续,数字高程数据的日益普及和发展新的计算机化地形分析工具(威尔逊1996年,伯勒和麦克唐纳1998年,威尔逊伯勒1999年)。1.1.1数字高程数据的来源和结构目前可用的数字高程数据集的大部分是摄影测量数据采集产品(编号摩尔等人,1991)。这些来源依靠空中拍摄的照片或使用手动或自动立体绘图(卡特1988年,威贝尔和海勒1991)卫星影像的立体诠释。获得额外的高程数据集可以通过数字化地形图上的等高线和进行地面调查。的出现和广泛使用的全球定位系统(GPS)的农业和其他设置提供了许多新的和负担得起的机会,收集大量的特殊的目的,一个一类高程数据集(修复和Burt 1995特威格1998年,威尔逊1999年a)。 这些数字高程数据通常被组织成三个数据structares(1)定期电网,(2)不规则三角网,并根据源和/或分析的首选方法(图1.2)(3)轮廓。已成为最广泛使用的数据结构(即,简单的高程矩阵,纪录隐式数据点之间的拓扑关系),便于计算机实现(编号摩尔等,因为它们简单,在过去十年中广场网的数字高程模型(DEM) 1993f,1991年,怀斯1998年)。抵销这些优势至少有三个缺点。首先,网格网眼的大小常常会影响的存储要求,计算效率和质量的结果(Collins和月球1981年,摩尔等人编号1991)。二,方电网无法处理海拔急剧的变化很容易,他们往往会跳过在平坦地区的地表(卡特1988年)的重要细节。然而,这是值得注意的,在平板领域的许多问题的发生,因为美国地质调查局(USGS)和其他记录整个米的海拔坚持。第三,计算上坡流动路径将倾向于在景观曲折,计算准确具体的集水区(泽文伯根和索恩编号摩尔等1987年,1991年)增加了困难。近年来已经克服这些障碍的几个。 例如,有没有通用的理由为什么正规的DEM不能代表形状以及在平坦地区,只要地形属性计算方法尊重地面排水。 ANUDEM的(哈钦森1988年,1989年b)是一个这样

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