Lecture notes in geoinformation and cartography

Lecture Notes in Geoinformation and Cartography Series Editors: William Cartwright, Georg Gartner, Liqiu Meng, Michael P Peterson Qiming Zhou · Brian Lees · Guo-an Tang (Eds.) Advances in Digital Terrain Analysis Editors Prof Qiming Zhou Hong Kong Baptist University Department of Geography Kowlon Tong Kowlooon Hong Kong/PR China qiming@hkbu.edu.hk Prof Brian Lees The University of New South Wales at ADFA ACT 2600 Australia b.lees@adfa.edu.au Prof Guo-an Tang Nanjing Normal University Key Laboratory of Virtual Geographic Environment 210046 Nanjing China, People’s Republic tangguoan@njnu.edu.cn ISBN: 978-3-540-77799-1 e-ISBN: 978-3-540-77800-4 Lecture Notes in Geoinformation and Cartography ISSN: 1863-2246 Library of Congress Control Number: 2008921722 c 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Cover design: deblik, Berlin Printed on acid-free paper springer.com Preface The chapters in this book mostly started as presentations at the Terrain Analysis and Digital Terrain Modelling conference hosted by Nanjing Normal University in November 2006 As far as I am aware this was the first international conference devoted specifically to this area of research, and since it was also my first visit to China it was an exciting and unique experience for me The participants ranged from leaders in the field discussing visions and challenges for the future to students grappling with the possibilities and exploring new directions These papers are a selection of the many presentations at the conference and give some indication of the breadth of research on show at the meeting Digital terrain analysis has moved beyond a research tool into routine application, such as determination of catchment areas and flow pathways in hydrological analysis, supporting soil mapping through spatial prediction and the definition of landform elements, and the use of slope and other attributes for land capability analysis But there are still many areas of active research refining these methods or exploring new approaches, as this book shows One recent development explored in several of the papers in this book is the availability of global or near-global terrain data in several forms, GTOPO-30 and SRTM second data being the most significant Reliable global topographic data opens the doors for truly global analysis, consistent analysis on different continents and the generation of collective experience that is transforming the field of geomorphometry into a robust science Another theme reflected in these papers is the increasing sophistication in our understanding of issues related to scale, accuracy, uncertainty and error propagation in digital terrain analysis As these methods are increasingly used to support important decisions, information on uncertainty becomes vital for the rational use of predictions There is still some way to go before we have tools for estimating and representing uncertainties that meet the needs of our user community Other papers demonstrate the continued demand for improved methods to classify and segment the land surface into useful units for land management or mapping; showcase innovations in representing and characterising the land surface; highlight a growing focus on processes rather than statistical correlations for understanding the earth’s surface; and exemplify the ongoing development and testing of new algorithms addressing deficiencies in quality and efficiency of existing methods vi Preface At the Nanjing conference, I was astonished by the number of students from China and elsewhere training in this research area and by the variety and innovation of their work I was also impressed by their probing questions and contributions to the discussions The conference provided an opportunity to renew some old friendships, make new friends and meet for the first time some of the people whose names I knew from their published papers I greatly enjoyed the interaction with so many disciples in the field of terrain analysis and consider myself fortunate to have had the opportunity to participate in this meeting I am hopeful of many more stimulating and rewarding meetings and discussions as part of the TADTM initiative in the coming years Dr John Gallant CSIRO Land and Water, November 2007 Contents List of Contributors xi Introduction ZHOU Qiming, Brian G LEES and TANG Guo-an Advances in Digital Terrain Analysis: The TADTM Initiative Section 1: Digital Representation for Terrain Analysis 11 George Ch MILIARESIS Quantification of Terrain Processes 13 Peter A SHARY Models of Topography 29 LI Zhilin Multi-Scale Digital Terrain Modelling and Analysis 59 ZHAO Xuesheng, BAI Jianjun and CHEN Jun A Seamless and Adaptive LOD Model of the Global Terrain Based on the QTM 85 Section 2: Morphological Terrain Analysis 105 TANG Guo-an and LI Fayuan Landform Classification of the Loess Plateau Based on Slope Spectrum from Grid DEMs 107 Josef STROBL Segmentation-based Terrain Classification 125 Lucian D DRĂGUğ and Thomas BLASCHKE Terrain Segmentation and Classification using SRTM Data 141 viii Contents LU Huaxing Modelling Terrain Complexity 159 LIU Aili DEM-based Analysis of Local Relief 177 YANG Qinke, David JUPP, LI Rui and LIANG Wei Re-Scaling Lower Resolution Slope by Histogram Matching 193 Section 3: Hydrological Terrain Analysis 211 John P WILSON, Graeme AGGETT, DENG Yongxin and Christine S LAM Water in the Landscape: A Review of Contemporary Flow Routing Algorithms Petter PILESJÖ An Integrated Raster-TIN Surface Flow Algorithm TIAN Yuan, WU Lun, GAO Yong, WANG Daming and ZHANG Yi DEM-based Modelling and Simulation of Modern Landform Evolution of Loess 213 237 257 Section 4: Uncertainty in Terrain Analysis 277 ZHOU Qiming and LIU Xuejun Assessing Uncertainties in Derived Slope and Aspect from a Grid DEM 279 LIU Xuejun and BIAN Lu Accuracy Assessment of DEM Slope Algorithms Related to Spatial Autocorrelation of DEM Errors 307 DENG Fengdong, WANG Lili, ZHUO Jing and LIU Anlin Modelling Slope Field Uncertainty Derived From DEM in the Loess Plateau 323 Contents ZHU A-Xing, James E BURT, Michael SMITH, WANG Rongxun and GAO Jing The Impact of Neighbourhood Size on Terrain Derivatives and Digital Soil Mapping ix 333 Brian G LEES, HUANG Zhi, Kimberley VAN NIEL and Shawn W LAFFAN The Impact of DEM Error on Predictive Vegetation Mapping 349 Section 5: Applications of Terrain Analysis 363 Igor V FLORINSKY Global Lineaments: Application of Digital Terrain Modelling 365 John B LINDSAY and James J ROTHWELL Modelling Channelling and Deflection of Wind by Topography 383 ZHANG Ting, LI Jun, WANG Chun and ZHAN Lei Spatial Correlation of Topographic Attributes in Loess Plateau 407 YANG Xin and XIAO Chenchao Terrain-based Revision of an Air Temperature Model in Mountain Areas 425 James R.F BARRINGER, Allan E HEWITT, Ian H LYNN and Jochen SCHMIDT National Mapping of Landform Elements in Support of S-Map, A New Zealand Soils Database 443 Concluding Remarks 459 Brian G LEES Progress in Digital Terrain Analysis 461 List of Contributors Graeme AGGETT, Riverside Technology Inc., 2290 East Prospect Road, Suite 1, Fort Collins, Colorado CO 80525 E-mail: gra@riverside.com BAI Jianjun, Department of Surveying, China University of Mining and Technology (Beijing), D11, Xueyuan Road, Beijing 100083, P.R China James R F BARRINGER, Landcare Research, PO Box 40, Lincoln 7640, New Zealand, Email: barringerj@landcareresearch.co.nz BIAN Lu, Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, Nanjing, Jiangsu 210046, P.R China Thomas BLASCHKE, Researchstudio iSPACE, ARC Austrian Research Centers, Leopoldskronstr 30, 5020 Salzburg, Austria James E BURT, Department of Geography, University of WisconsinMadison, 550 N Park St, Madison WI 53706, USA CHEN Jun, National Geometric Centre of China, No.1 Baishengcun, Zizhuyuan, Beijing 10004, P.R China Email: chenjun@nsdi.gov.cn, DENG Fengdong, Shaanxi Remote Sensing Information Centre for Agriculture, Email: phoenixlet@yahoo.com.cn DENG Yongxin, Department of Geography, Western Illinois University, Macomb, IL 61455, E-mail: y-deng2@wiu.edu Lucian D DRĂGUğ, GIS-Centre for Geoinformatics, Salzburg University, Schillerstr 30, 5020 Salzburg, Austria Email: lucian.dragut@sbg.ac.at Igor V FLORINSKY, Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region, 142290, Russia, Email: iflorinsky@yahoo.ca GAO Jing, Department of Geography, University of Wisconsin-Madison, 550 N Park St Madison WI 53706, USA Email: jgao3@wisc.edu GAO Yong, Institute of RS and GIS, Peking University, Beijing, 100871, P.R China Allan E HEWITT, Landcare Research, PO Box 40, Lincoln 7640, New Zealand HUANG Zhi, The Australian Government Department of Environment and Water Resources, Email: zhi.huang@environment.gov.au xii List of Contributors David JUPP, CSIRO Marine and Atmospheric Research, CS Christian Building, CSIRO Labs, Clunies Ross St., Black Mountain ACT, 2601, Australia Shawn W LAFFAN, School of Biological, Earth and Environmental Sciences, University of New South Wales, Australia Email: shawn.laffan@unsw.edu.au Christine S LAM, GIS Research Laboratory, Department of Geography, University of Southern California, Los Angeles, CA 90089-0255, Email: csl@usc.edu Brian G LEES, The University of New South Wales at ADFA, Canberra, ACT 2600, Australia, E-mail: b.lees@adfa.edu.au LI Fayuan, Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, Nanjing, Jiangsu, 210046, P.R China LI Jun, Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, Nanjing, 210046, P.R China LI Rui, Northwest University, No 229, Northern Taibai Road, Xi’an 710069, P.R China LI Wei, Northwest University, No 229, Northern Taibai Road, Xi’an 710069, P.R China LI Zhilin, Dept of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, Email: lszlli@polyu.edu.hk LIANG Wei, Northwest University, No 229, Northern Taibai Road, Xi’an 710069, P.R China John B LINDSAY, Uplands Environments Research Unit (UpERU), School of Environment and Development, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK, Email:john.lindsay@manchester.ac.uk LIU Aili, School of Remote Sensing, Nanjing University of Information Science & Technology, Street No.114 Pancheng New, Nanjing, Jiangsu 210044, P R China Email: ailii66@126.com LIU Anlin, Shaanxi Remote Sensing Information Centre for Agriculture, Email: phoenixlet@yahoo.com.cn LIU Xuejun, Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, Nanjing, 210046, P.R China LU Huaxing, Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, No.1 WenYuan Road , Nanjing, Jiangsu, 210046, P.R China Email: huaxinglu@163.com 386 John B LINDSAY and James J ROTHWELL of the hypothetical wind flux (Antoniü and Legoviü 1999) Winstral and Marks (2002) refer to the grid cell with the maximum elevation angle in a search path as the shelter-defining cell The distance between a grid cell and its shelter-defining cell is usually small enough that Earth curvature can be ignored in estimating the horizon angle An assumption is made that large positive values of horizon angle indicate areas that are relatively sheltered from wind in a specified direction (Böhner and Antoniü in press) Locations with negative horizon angles (declinations) are located above their horizon and are therefore relatively exposed Antoniü and Legoviü (1999) recommend setting all declinations to zero, recognizing that the exposure of a site located above its horizon is often affected to a greater extent by altitude This same approach to handling declinations was also used to derive the TOPEX index Figure A 10 m resolution LiDAR digital elevation model of the Bleaklow plateau, southern Pennines, UK Contours are drawn at a 20 m interval Modelling Channelling and Deflection of Wind by Topography 387 Figure Various topographic indices of exposure/sheltering derived for the LiDAR DEM, including (A) relative terrain aspect, (B) horizon angle, (C) exposure towards the wind flux, (D) openness, (E) directional relief, and (F) fetch Each image is based on a hypothetical wind direction of 225° (i.e a wind from the southwest), except for openness (D), which is derived from data in all eight main compass directions Distance values for the fetch image (F) have been log-transformed to enhance visualization Horizon angle is frequently calculated using a maximum search distance This can significantly reduce the computational effort required to calculate the index, something that can be problematic when analysing 388 John B LINDSAY and James J ROTHWELL large DEMs There may also be sound theoretical reasons for this practice in addition to the computational benefits Böhner and Antoniü (in press) argue that whilst for solar radiation modelling an infinite search distance (implying that the ray-tracing procedure always terminates at the DEM edge) is preferred, for modelling exposure/sheltering to wind, large search distances can ignore the adaptability of airflow to terrain, i.e topographic deflection of winds In their study of snow redistribution depths in a headwater catchment in south-western Idaho, Winstral et al (2002) also concluded that a distance-limited estimation of horizon angle is preferred This results in greater weight being applied to the effects of local topography Unfortunately, a method for establishing an appropriate maximum search distance remains a challenge and it is often determined through trial-anderror optimization Furthermore, not all researchers have found the need for a maximum search distance Wörlen et al (1999), for example, found a strong relationship between measured wind speeds and horizon angles estimated without a maximum search distance In addition to the ambiguity involved in selecting an appropriate search distance, there is also the problem that, being based on ray-tracing, horizon angle does not account for topographic deflection of wind Winstral and Marks (2002) suggest averaging horizon angle values across a range of directions (e.g every 5° over a 30° window centred on the desired wind direction) as a means of increasing the robustness of the index to deviations from the hypothetical regional wind direction Although averaging over a range of directions does improve results, it does not actually compensate for upwind channelling by topography Openness (Yokoyama et al 2002) is a topographic index of exposure/sheltering that is related to horizon angle (Figure 2C) To the authors’ knowledge, openness has never been applied as an index of exposure/sheltering to wind, although it is very similar to the field-based TOPEX index described by Wilson (1984) Openness is defined as the average zenith angle (i.e 90° minus the horizon angle) in the cardinal and diagonal directions along a distance-limited search path Therefore, unlike other DEM-derived exposure indices, openness is directionally independent This characteristic, however, means that openness, like the TOPEX index, is perhaps less suited to measuring wind exposure in areas where there is a dominant wind direction or local channelling of air (Quine and White 1994) In addition to relative terrain aspect and horizon angle, Antoniü and Legoviü (1999) and Böhner and Antoniü (in press) identify a third DEMderived topographic index for modelling wind exposure/sheltering Exposure towards the sloped wind flux (Figure 2D) combines relative terrain aspect and horizon angle in a single index This terrain attribute accounts Modelling Channelling and Deflection of Wind by Topography 389 for land-surface orientation relative to the wind and the shadowing effects of distant topographic obstacles Exposure towards the sloped wind flux (cosĮ) can be conceptualized as the angle between a plane orthogonal to the wind and a plane that represents the local topography at a grid cell (Böhner and Antoniü in press) and is calculated as follows: cos D cos P ˜ sin E  sin P ˜ cos E ˜ cosG  J (1) where μ is the terrain slope, Ȗ is the terrain aspect, į is the azimuth of the wind flux, and ȕ is the horizon angle in the wind direction (Antoniü and Legoviü 1999) Notice that cos(į - Ȗ) is equivalent to the relative terrain aspect If the horizon angle is set to zero, Equation (1) yields the exposure toward the horizontal component of the wind flux Equation (1) is commonly used for topographic solar radiation modelling (Böhner and Antoniü in press) where Į is the solar illumination angle for a given surface, defined by μ and į Exposure towards the wind flux has also been found to be one of the most useful indices for explaining spatial variability in various atmospherically-deposited contaminants (Antoniü and Legoviü 1999) In an early paper on the subject, Lapen and Martz (1993) described two DEM-derived measures of wind exposure/sheltering: directional relief and fetch Directional relief (Figure 2E), like the horizon-angle based indices described above, is a measure of the degree to which a site is located above or below its surroundings in a specified direction The main difference, however, is that directional relief is not an angular measure but rather an altitudinal difference It is calculated by subtracting the elevation of a DEM grid cell from the average elevation of the grid cells that lie between it and the edge of the DEM in a specified direction (Lapen and Martz 1993) Thus, positive values indicate that a grid cell is lower than the average elevation of the grid cells in a direction (i.e relatively sheltered) and a negative directional relief value indicates that the grid cell is higher (i.e relatively exposed) The calculation of directional relief is therefore similarly based on a ray-tracing procedure Figure 2F shows the Lapen and Martz’s (1993) measure of fetch, i.e the distance of unobstructed airflow, for the Bleaklow LiDAR DEM The Lapen and Martz (1993) fetch algorithm searches each grid cell along a ray in a specified direction until either the DEM edge is encountered or the following condition is met: Z test t Z core  D ˜ I (2) where Zcore is the elevation of the grid cell at which fetch is being determined, Ztest is the elevation of the grid cell being tested as a potential topographic obstacle, D is the distance between the two grid cells in metres, 390 John B LINDSAY and James J ROTHWELL and I is the height increment in m·m-1 (notice I is effectively unitless) If the search does not identify an obstacle grid cell before the edge of the DEM is reached, the distance between the DEM edge and Zcore is entered Based on the Lapen and Martz (1993) procedure, edge distances are assigned negative values to differentiate between these artificially truncated fetch values and those for which a valid topographic obstacle is identified For the purpose of effective visualization, Figure 2F shows the logarithmtransformed, absolute fetch values rather than the original distances measured by the fetch algorithm In Equation (2), I is essentially the minimum tangent of the slope between Zcore and Ztest needed for the test grid cell to be considered a significant topographic barrier to wind Lapen and Martz (1993) suggest values for I in the range of 0.025 to 0.1 based on their study of snow distributions in low-relief agricultural landscapes of the Canadian Prairies Fetch analysis, based on Equation (2), has been applied to the study of patterns of tree species in Taiwan (Huang 2002) Most of the existing exposure/sheltering indices focus on identifying areas of wind shadow that result from topographic obstacles A common problem with these indices is their inability to incorporate the channelling/deflection of wind by topography This is a limitation of the raytracing procedure on which most of these indices are based The main drawback to using ray-tracing in wind modelling applications is that moving air and light not behave similarly Whereas a ray of light ends when it encounters a barrier (except for back-scatter), a flowline of air will be deflected around the obstacle, altering its flow direction That is, wind is capable of being deflected from its path by topographic features Evidently, the channelling and deflection of near-surface winds by topography is not adequately modelled by existing wind exposure/sheltering indices In the following section, we describe a simple topographic index that can be used to simulate channelling and deflection of winds by topography The Channelling/Deflection Index DEM-based flow routing algorithms have been used extensively to model the flow of surface and near-surface water (e.g O’Callaghan and Mark 1984, Freeman 1991, Tarboton 1997) These algorithms are used to simulate the spatial patterns of flow directions and contributing area (A), or flow accumulation, for a given surface Water and air are both fluids One of the most significant differences between these two fluids is the fact that airflow can occur in an uphill direction whilst water only flows downhill We propose a method, described below, for modelling wind Modelling Channelling and Deflection of Wind by Topography 391 channelling/deflection that is based on applying a flow routing algorithm to a surface that combines topography and information about regional wind speed and wind direction This technique effectively compensates for the downhill-only nature of DEM-based flow algorithms by altering the DEM The upwind source area that results from this analysis is the area from which the wind flux passing through a location originates The channelling/deflection index (CDI) can be calculated as follows: CDI ij Aij (C ) Aij ( P) (3) where Aij is the upwind source area for grid cell (i, j), P is a grid of a planar surface representing the wind strength and direction, and C is a grid derived by the combination of the streamlined DEM, S, and a planar surface representing the hypothetical wind characteristics C can be conceptualized as the surface that results from streamlining the DEM and tilting it downwards in the direction of the wind flux by an amount that is proportional to wind speed C and P are calculated as: C ij S ij  Pij (4) Pij tan O ˜ sin G ˜ X i  tan O ˜ cos G ˜ Y j  k (5) where Sij is the elevation of grid cell (i, j) in the streamlined DEM, Ȝ is the gradient of the plane in the wind direction į, Xi is the x co-ordinate of the ith column in the grid, Yj is the y co-ordinate of the jth row in the grid, and k is a constant It should be noted that the contributing area function, Aij, is dependent on both slope and aspect of the surface to which it is applied and not on the actual values of the surface at a specific location The actual values of C and P therefore have no effect on Aij Thus, the value of k does not influence CDIij and can be set to zero or any other desired value For example, k could be set to a high positive or negative number if there were an algorithmic limitation on the range of values contained in C and P—the Xi and Yj terms in Equation (4) can otherwise yield very large positive or negative values The DEM is not directly used to model the spatial pattern of wind channelling and deflection Instead a streamlined version of the terrain model is applied This accounts for the fact that (1) a zone of reduced wind speed and turbulence extends for some distance in the leeward direction of an obstacle, and (2) air starts to rise some distance before it reaches an obstacle due to a wedge of high pressure located in the windward direction A 392 John B LINDSAY and James J ROTHWELL streamlined terrain model, S, which incorporates these wind zones, can be calculated as follows: ­°Z ij S ij E ij , I ® °¯Z cd  D ˜ I tan E ij  I tan E ij t I (6) where grid cell (c, d) is the first grid cell encountered in a ray extending from grid cell (i, j) in direction į that satisfies the condition tanȕij < I I is the same height increment described in Equation (2) and is specified by the user Equation (6) is first used to model the wind shadow in the leeward direction In a second step, horizon angle is calculated using the leeward streamlined DEM and a wind direction of į -180 Equation (6) is then used a second time to create the final streamlined DEM, i.e the terrain model that incorporates both the leeward wind shadow and the windward highpressure ‘ramp’ The leeward effects of an obstacle on airflow extend over a much greater distance than the windward effects, implying that Ileeward < Iwindward Research suggests that the effect of an obstacle on wind patterns can be observed for a distance of 10 to 40 times the obstacle height on the leeward side and approximately two times the obstacle height on the windward side (Lapen and Martz 1993, Huang 2002) This implies values of Ileeward and Iwindward of 0.025–0.1 and 0.5, respectively, although these are approximations Figure shows the effect of using Equation (6) to streamline the Bleaklow LiDAR DEM An algorithm for streamlining terrain based on Equation (6) has been implemented in TAS GIS, a freely distributed software package for spatial analysis and environmental modelling (Lindsay 2005) Figure Shaded relief images derived from (A) the Bleaklow DEM, and (B) the streamlined DEM resulting from the application of Equation (6) to the DEM (Figure 1) with a hypothetical wind direction of 225° and Ileeward and Iwindward values set to 0.067 (i.e a slope of 1:15) and 0.5, respectively Modelling Channelling and Deflection of Wind by Topography 393 Equation (4) describes the local balance between the force of gravity pulling a parcel of air downslope, and the horizontal pressure gradient force pushing the parcel in the direction of the regional wind P can be thought of as a plane describing the spatial pattern (gradient and aspect) of atmospheric pressure Thus, Ȝ is directly proportional to the horizontal pressure gradient force and therefore also to wind speed Increasing Ȝ, effectively increasing wind speed, reduces the relative influence of topography, or gravitational force, on the airflow pattern resulting from Equation (3) (Figure 4) This implies that stronger winds are deflected, in the horizontal plane, by topographic obstacles to a lesser extent than gentler winds, due to increased momentum In actuality the horizontal pressure gradient force is usually much smaller than the force of gravity In fact, if a typical value for the horizontal pressure gradient (a tangent slope of approximately 0.01 Pa·m-1) were used for Ȝ, Equation (3) would be heavily weighted towards the influence of the gravitational force The resulting modelled airflow pattern would suggest that air drained from a landscape towards the nearest downslope topographic low Clearly this is unrealistic The answer to this problem lies in the fact that Equation (4) represents the relative balance of all the forces acting on an air parcel Although the gravitational force is relatively large, it is severely dampened by the nearly equivalent, though variable, vertical pressure gradient force This can be accounted for either by including a vertical pressure gradient term in Equation (4) by the addition of a weighting parameter, or equivalently, by ensuring that Ȝ is sufficiently large to give the necessary relative weighting to the horizontal pressure gradient We prefer the latter approach because it provides a simpler model (recalling that the actual values of P need not represent realistic values of atmospheric pressure), and because in most applications we are less concerned with the airflow pattern at a specific wind speed than we are with the pattern resulting from a range of typical wind speeds This can be achieved by averaging CDIij over a range of Ȝ values (Ȝmin to Ȝmax), yielding the pattern of wind channelling/deflection over a range of wind speeds As guidance, it is reasonable that tanȜmin • Iwindward, implying that air is capable of flowing over obstacles to an extent At very steep gradients (e.g Ȝ > 80°) the effective wind speed is so high that the pathways of individual flowlines are hardly influenced by topography Thus the value of Ȝmax can be set accordingly 394 John B LINDSAY and James J ROTHWELL Figure The implications of increasing the plane gradient, Ȝ, (i.e increasing wind speed) on the modelled pattern of the topographic deflection index (CDI) The regional wind direction is constant for each simulation and assumed to be 225° (i.e a wind from the south-west) It may not be readily apparent why Aij(C) is normalized by Aij(P) in Equation (3) Edge effects are not usually problematic for surface water applications of flow routing algorithms so long as the DEM edges not intersect significant catchment divides However, in the airflow model Modelling Channelling and Deflection of Wind by Topography 395 described above, all flowlines continue without terminating from one edge of the DEM to the opposite edge; it is impossible to define meaningful flow boundaries from the monotonic surfaces C and P Therefore, estimates of Aij are severely impacted by edge contamination and the pattern of upwind source area is heavily influenced by the extent of the DEM Dividing Aij(C) by Aij(P) normalizes the pattern of upwind source area, effectively removing much of the edge contamination (Figure 5) Normalization compensates for the fact that individual flowlines not have start points, or rather their start points are unlikely to coincide with the windward edges of the DEM Even after normalisation, however, locations nearest the edge in the windward direction will suffer from a degree of edge contamination As such, in estimating the pattern of the CDI for a site, it would be advisable to buffer the area with digital elevation data in the upwind direction The sensitivity of the CDI to edge contamination is examined further in Section The normalization of the upwind source area (Equation (3)) also provides a convenient interpretation of the CDI: grid cells with CDI values less than unity are predicted to experience sheltering by upwind topography due to deflection and values greater than unity experience upwind channelling, i.e relative exposure (Figure 5C) CDIij can therefore be conceptualized as a measure of how much larger or smaller the upwind source area is for a location as a result of the influence of topography Also note that the CDI is a unitless index Because the CDI is intended to be an index of near-surface exposure/sheltering, it is useful to modify Equation (3) to account for areas where the streamlined DEM and the original DEM are not equal (i.e wind shadows in Figure 6), such that: CDI ij ­0 ° ® Aij C ° A P ¯ ij S ij z Z ij S ij Z ij (7) 396 John B LINDSAY and James J ROTHWELL Figure (A) The spatial pattern of upwind contributing area derived from a surface combining the LiDAR DEM and regional wind characteristics, (B) the pattern of upwind contributing area derived from a plane describing wind characteristics, and (C) the pattern of the topographic deflection index (CDI) resulting from the ratio of (A) to (B) The regional wind direction is assumed to be 225° (i.e a wind from the south-west) ... continued demand for improved methods to classify and segment the land surface into useful units for land management or mapping; showcase innovations in representing and characterising the land... participate in this meeting I am hopeful of many more stimulating and rewarding meetings and discussions as part of the TADTM initiative in the coming years Dr John Gallant CSIRO Land and Water,... Modelling and Simulation of Modern Landform Evolution of Loess 213 237 257 Section 4: Uncertainty in Terrain Analysis 277 ZHOU Qiming and LIU Xuejun Assessing Uncertainties in Derived Slope and