UNIVERSITY OF CALGARY Assessing the effect of point density and

UNIVERSITY OF CALGARY

Assessing the effect of point density and terrain complexity on the quality of LiDAR-derived DEMs in multiple resolutions

Shadan Sanii MGIS Student

Department of Geography Masters of Geographic Information Systems

September 2008

Abstract Light Detection And Ranging (LiDAR) systems are rapidly becoming the prime source for high-resolution, high-quality digital elevation models (DEM). Data density and DEM resolution are two of the main factors that affect the quality of DEMs. In addition, point density plays an important role in LiDAR mission planning and cost of a LiDAR project. The goal of this project was to assess the effect of point density and terrain complexity on the quality of LiDAR-derived DEMs in multiple resolutions. The result indicated that the quality of DEM is more affected by point density and terrain complexity than by DEM resolution. DEMs created from low-density datasets were found to be more sensitive to terrain complexity. However visual analysis of 3D DEM surfaces revealed that highresolution DEMs created from low density data contain artefacts which degrade the quality of DEM. This observation stresses the importance of an appropriate evaluation strategy when assessing the quality of DEM and other 3D surface models.

Acknowledgments The LiDAR data used for the project was kindly provided by the Terrapoint Canada Inc. I would like to thank Dr. Greg McDermid for his comments and advice through the project. Thanks also to Christopher Bater for his suggestions.

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Table of Contents Abstract ............................................................................................................................... ii Acknowledgments............................................................................................................... ii Table of Contents ............................................................................................................... iii List of Tables ..................................................................................................................... iv List of Figures ..................................................................................................................... v 1.0 Introduction ................................................................................................................... 1 2.0 Background ................................................................................................................... 3 2.1 Digital Elevation Model ............................................................................................ 3 2.2 Light Detection And Ranging ................................................................................... 6 2.2.1 Types of LiDAR ................................................................................................ 8 2.2.2 History of LiDAR .............................................................................................. 9 2.2.3 Advantages of LiDAR over other technologies ............................................... 10 2.3 LiDAR Data pre-Processing ................................................................................... 11 2.3.1 Interpolation (Constructing a model) ............................................................... 12 2.4 Quality of DEM ...................................................................................................... 15 2.5 Pervious studies ...................................................................................................... 16 3.0 Methods....................................................................................................................... 18 3.1 Study Area .............................................................................................................. 18 3.2 Dataset..................................................................................................................... 19 3.3 Analysis................................................................................................................... 22 3.4 Quality Assessment ................................................................................................. 24 4.0 Results ......................................................................................................................... 26 5.0 Discussion ................................................................................................................... 36 6.0 Conclusions ................................................................................................................. 38 References ......................................................................................................................... 40

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List of Tables Table 1: General statistics of the three study sites: Tile S1 represents the plain study area, tile S2 represents the terrain with moderate complexity and tile S3 represents terrain with extreme roughness……………………………………………………………………….22 Table 2: Root Mean Square Error, point density and mean separation across different density level in multiple resolution for plain terrain (LiDAR tile S1)………………..….27 Table 3: Root Mean Square Error, point density and mean separation across different density level in multiple resolution for terrain with moderate complexity (LiDAR tile S2)…………………………………………………………………….……………….…27 Table 4: Root Mean Square Error, point density and mean separation across different density level in multiple resolution for rough terrain (LiDAR tile S3) ……………...….27

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List of Figures Figure 1: LiDAR system components................................................................................. 7 Figure 2: Location of the study area in west-central Alberta............................................ 19 Figure 3: Three study sites (a) S1: flat terrain, (b) S2: intermediate terrain, and (c) S3: rough terrain ...................................................................................................................... 21 Figure 4: Original LiDAR point density and mean point separation distance…...….…...22 Figure 5: Flowchart describing the general analysis strategy followed in this research. . 23 Figure 6: RMSE plotted against point density…………………………………………. 28 Figure 7: RMSE plotted against point spacing ................................................................. 31 Figure 8: RMSE of three different terrain types plotted against mean point spacing....... 32 Figure 9: RMSE plotted against horizontal resolution. .................................................... 33 Figure 10: RMSE of DEM in multiple resolution for density levels of 75%, 10% and 0.1% of the original dataset. ............................................................................................. 34 Figure 11: 3D surface model of tile S3 (a) density level of 0.1% in 0.5 meter spatial resolution, (b) density level of 0.1% in 20 meter resolution, (c) density level of 5% in 0.5 meter point resolution (d) density level of 5% in 20 meter DEM resolution (e) density level of 100 % in 0.5 meter DEM resolution (f) density level of 100% in 20 meter DEM resolution........................................................................................................................... 35

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1.0 Introduction Digital elevation models (DEMs) are used to model the ground surface topography and are routinely employed in a large number of military, environmental, engineering, and GIS applications (El-Sheimy, 2005). Production of high-quality elevation models is one of the most important challenges for the scientific community and commercial market (Chaplot et al., 2006). The generation of DEMs generally consists of two main steps: (1) capturing the elevation data or the terrain data, and (2) constructing a model which defines a relation among the observed data to build DEM (El-Sheimy, 2005). There are several ways to obtain the elevation data. DEMs traditionally have been derived using photogrammetric techniques and ground surveys. The last two decades, with the growing demand for high accuracy digital elevation data and terrain information, different remote sensing technologies have been utilized to acquire high-resolution, high-accuracy elevation data (Anderson et al, 2005). One powerful technique for obtaining elevation data is Light Detection And Ranging (LiDAR). Airborne LiDAR is rapidly becoming the prime source for high density, high accuracy digital elevation data for producing high quality DEM (Lohr 1998, Wehr and Lohr 1999, Lefsky et al 2002, Anderson et al 2005, Hodgson and Bresnahan 2004, Liu 2008). LiDAR is an active Remote Sensing technology that employs laser to measure the range of a distant target. A LiDAR system produces a cloud of irregularly spaced 3D points called a point cloud. This point cloud needs to be interpolated to form a regularly spaced grid to build a DEM. Depending on the application of DEMs, they are produced in different grid size,

referred as spatial resolution, and is expressed as ground distance. The smaller the grid size, the higher the resolution representing terrain surface in more detail (Liu et al. 2008).

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Highly dense LiDAR data allows for the generation of very detailed high resolution DEM (Liu et al. 2007, 2008). However one of the problems with LiDAR data is that the file sizes are often very large, resulting in extensive computation time and large computing requirements (processor speed, RAM, mass storage, etc.) for performing even a simple statistical analysis (Anderson et al 2005, Chaplot et al. 2006, Raber at al. 2007, and Liu et al. 2008). By reducing the dataset we can considerably reduce the processing time and storage space and subsequently increase the efficiency. On the other hand data density and DEM resolution are two of the main factors that affect the quality of DEMs (Gong et al. 2000, Kienzle 2004, Li et al. 2005, Fisher and Tate 2006, Lui et al. 2008). When creating DEM from reduced LiDAR dataset in multiple resolutions, it is still important to maintain the acceptable accuracy. Data point density can also affect the choice of interpolation algorithm used to generate the DEM model from the point data. In addition, the desired point spacing and its associated point density play a significant role in LiDAR mission planning and overall LiDAR project cost (Maune 2001, Raber et al 2007). Point spacing between measurements depends on the scan angle of the laser ranging system and the airplane height over the ground (El-Sheimy et al. 2005). A higher point density generally requires a more sophisticated sensor system with a higher pulse rate, a narrower scan angle, a lower airplane height or a combination of these variables which results in the need for more flight lines (Raber et al. 2007). Because of all these reasons, determining an optimum LiDAR point density suitable for creating a DEM at a given horizontal resolution is an important issue when generating DEM from LiDAR point dataset. The objective of this study is to (i) examine the effect of LiDAR dataset point density on the quality of DEM created at multiple resolutions (ii) investigating the influence of terrain complexity on the quality of DEM when creating DEM at different data density levels in multiple resolutions.

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2.0 Background 2.1 Digital Elevation Model There are three digital structures that commonly used to represent elevation surfaces: contours, triangulated irregular networks (TINs), and regular grids (Maune 2001). Contours are lines of equal elevation at specified intervals, and are perhaps the most familiar representation of terrain surfaces (Maune, 2001, El-Sheimy et al. 2005,). TINs are a vector-based representation of the surface comprised of non-overlapping contiguous triangle facets (Peuker et al. 1978). These facets consist of planes connecting the three neighbouring points in the network (lee et al. 1992). Main advantage of TIN models is the ability to adapt to the variable surface complexity. Where there is little variation in height, small amount of storage space is required. In areas of more intense topographic variation, the data density is increased. TIN models maintain the original input data therefore they can capture abrupt changes in surface form, such as ridges, valley floors, pits and cols (Maune 2001). Grid elevation models are made up of equal-sized grid cells, each containing a value of elevation. They can be distributed as simple 2D matrices of elevations, storing the location of a single point and the grid cell size and orientation implying the horizontal locations of all other points (Kumler 2006). There are different products that considered as grid elevation models including: DEM, digital terrain model (DTM) and digital surface model (DSM). The term DTM is often used synonymously with DEM, but in reality they are different products (Petrie and Kennie, 1999, El-Sheimy et al. 2005). A DEM represents the bare earth terrain with regularly-spaced Z values. The Z value is the measurement of height above a datum and represents the absolute altitude (El-Sheimy et al. 2005).A DTM is similar to DEM but it may also include the elevation of significant topographic features such as river ridge lines, plus mass points and breaklines that are irregularly spaced. In general, DTMs represent terrain features more distinctively (Maune 2001). DSMs are similar to a DEM

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or DTM, except that a DSM incorporates the elevation of the top surface of building, tree, towers and other features above the bare earth (Maune 2001). Because of their efficient and simple data structure, ease of computer implementation (Moore et al. 1991, El-Sheimy et al. 2005), widespread availability, and relatively low cost (Maune, 2001), grid based DEMs are the most common representation of terrain surface, and are extensively used in GIS-based land characterization (Martz and Garbrecht 1992, Kienzle 2004, Chaplot et al. 2006, Willson and Glant 2000). Today, DEMs play an important role in a large number of terrain-related applications, including hydrological analyses, natural resources management (Franklin, 2000) , transportation, planning (Davis and Wang 2001) determination of the environmental impact of an activity (Desmet et al. 1999), military applications, analysis of the potential erosion of agricultural soil (Aguilar 2005) , hydraulic modeling for flood zone mapping (Kenward et al. 2000, Marks and Bates 2000, Manson et al. 2002, Omer et al. 2003, Aguilar 2005), watershed partition (Band 1986 ), extraction of drainage networks (Marks 1984), viewshed analysis (Fisher 1993), derivation of geomorphic features (Lee et al. 1992), quantification of landslide-terrain types (Pike 1988, Gao 1993, Gao, 1995) and generating ortho-images (Aguilar 2005). The generation of DEMs generally consists of two main tasks: (1) capturing the elevation data, and (2) constructing a model which defines a relation amongst the observed data to build DEM (El-Sheimy et al. 2005). There are different techniques for data acquisition for the purpose of DEM generation. Traditionally, DEMs have been derived from photogrammetric techniques and ground elevation surveys (USGS 1998, Anderson et al. 2005), though recently digital remote sensing-based techniques such as Interferometric Synthetic Aperture Radar (IFSAR) and LiDAR have become more common. Photogrammetric techniques for capturing elevation are based on the measurement of stereoscopic parallax in a series of stereo-pair aerial or satellite imageries. Stereoscopic parallax is the displacement of an object caused by taking the images of the same object from different point of observation (Tate 1998). Conventional photogrammetry involves

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the use of analytical stereoplotters, which duplicate the exact relative position and orientation of the camera at the time of photo acquisition to recreate the stereo-model. After recreating the geometry of stereo model, stereoscopic parallax of objects in stereopair images is measured. Measured parallax then is converted into object height using parallax equations (Tate 1998). The model then is related with the ground coordinate using ground control points. Once the model has been absolutely oriented it is possible to extract the DEM through sampling techniques (El-Sheimy et al. 2005). Recent technological advances in photogrammetry have made it possible to process highspatial-resolution aerial and satellite imagery in a digital format. Airborne images may be acquired by means of analog; the photos are then digitized using high-resolution scanners. It is now also possible to acquire airborne stereo imagery directly in digital format. Accurate referencing of images is performed using GPS kinematic positioning during data acquisition (Baldi et al. 2002). Today, softcopy workstations have largely replaced the analog instruments, and automated stereo-correlation has become a standard method of generating DEMs from digital stereo images (Hinaro et al. 2003). Stereo-correlation is a computational and statistical procedure utilized to derive a DEM automatically from stereo-pair registered images (Ackermann 1984, Ehlers and Welch 1987, Lang and Welch 1999, Hinaro et al. 2003). The core of stereo-correlation is automatic image matching. Although approaches may vary according to the software employed, the procedures normally include the collection of ground control points, determination of parallax values on a per-pixel basis using automatic image matching techniques and, finally, post-processing to remove anomalies from the DEMs (Kok et al. 1987). IFSAR is a new active remote sensing technology designed to make topographic measurements and can operate during day and night. Operating from either a spaceborne or an airborne platform, IFSAR employs the coherent nature of synthetic aperture radar (SAR) echoes (Jensen 2000). A SAR synthetically simulates a very long antenna using the forward movement of the aircraft (Hill et al. 2000), and images are formed from radar

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signals returned to the antennae from the terrain surface. IFSAR measures the phase difference from the two image scene from the same terrain object acquired by two antennas separated in the cross track by a known distance. An interferogram (a representation of interference of two electromagnetic waves) is produced based on the phase difference (Shepherd at al. 2002). IFSAR directly determine and georeference the elevations by using the interferometric phase difference and position of antenna determined by onboard GPS and INS (Maune, 2001). Overviews of IFSAR technology can be found in Zebker (1986), Medson et al (1999), Rosen (2000) and Maune (2005). One powerful new technique for obtaining elevation data is LiDAR. LiDAR is rapidly becoming the prime source for high density, high accuracy digital elevation data for producing quality DEMs (Lohr 1998, Wehr and Lohr 1999, Lefsky et al. 2002, Anderson et al. 2005). I will talk about LiDAR technology and its history in more details in the following sections. 2.2 Light Detection And Ranging LiDAR is an active remote sensing technology that employs an airborne laser to measure the range and/or other information of a distant target. A LiDAR system basically consists of

integration of three technologies: a laser unit, an inertial navigation system (INS) also known as inertial measurement unit (IMU) and a global positioning system (GPS) (Figure 1). The laser unit contains the laser transmitter and the receiver (El-Sheimy et al. 2005) that sends out light beam toward the target. The transmitted light interacts with the target, and a portion of this light is reflected back to the receiver. By detecting the change in the properties of the light, some of the target properties can be determined (NASA, 1999). By knowing the round-trip travel time for a pulse of laser light from aircraft to the target and the speed of light, the distance to the target can be computed as:

t=2

d c

Equation [1]

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Where t is the round-trip travel time for a pulse of laser light from aircraft to the target, c is the speed of light and d is the distance from laser instrument to target (Hofton et al. 2000, Dubayah and Drake 2000).

Figure 1: LiDAR system components. Source: deercrossingdailynews.info/photo.html

The laser instrument usually is mounted on an aircraft or a helicopter. The laser unit sends thousands of pulses per second, each pulse having duration of a few nanoseconds (109 seconds). Most commercial laser rangers operate in the 1,100 to 1,200 nm (nearinfrared). Usually aircraft fly at the speed of 200 to 250 km per hour, at heights of 300 to 1000m. A typical LiDAR system has the scan angles of generally ± 20 to ± 30, and pulse rates of 2,000 to 50,000 pulses per second (El-Sheimy et al. 2005). In order to obtain the 3D measurement from a platform, the position and attitude of the platform have to be known. These parameters are measured by GPS and INS. GPS determine the position of the platform in space and INS is used to measure any rotation of the platform in space.

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2.2.1 Types of LiDAR

A LiDAR system may use pulsed laser or continuous wave (CW) laser. Pulsed LiDARs simply use the pulsed ranging principle, measuring the traveling time between emitted and received pulse. By knowing the speed of light, the distance between the laser instrument and target can be determined as per Equation 1. CW Lasers transmit a continuous signal and measure the phase difference between the transmitted and received signal reflected from the target. By knowing the period of the signal and the fact that traveling time is directly proportional to the phase difference, travel time can be calculated (Wehr and Lohr. 1999). Pulsed LiDARs use high power during laser pulse and consequently they produce higher signal-to-noise ratios for the collected radiation which leads to higher ranging accuracy. Pulsed LiDARs are usually used for long-range remote sensing, while CW LiDARs are used when the signal can be integrated over long time periods or when the target is nearby, allowing for more sensitive measurement over a smaller span of ranges (NASA, 1999). Because of the relatively large diameter of the laser signal, only a portion of a transmitted light beam may hit a solid object and reflect back to the sensor. The rest of it may continue traveling towards the ground, and can interact with objects at lower elevations and reflect back again. Hence, each transmitting signal can have several returns. This usually occurs in morphologically complex surface such as forested areas. Most LiDAR systems record either the first return or the last return or both. There are some commercial systems that can record up to five discrete returns for each transmitted signal by identifying major peaks that represent discrete objects in the path of the laser illumination (Wehr and Lohr 1999, Lefsky et al. 2002). These types of sensors are called discrete- return LiDAR. Other types of LiDAR sensors, called waveform, fully digitize the returned signal (Wehr and Lohr 1999, Dubayah et al. 2000). Waveform recording sensors record the time-varying intensity of the returned signal for each laser pulse, and provide a record of the height distribution of the surfaces illuminated by the laser signal (Harding et al. 1994, Dubayah et al. 2000, Lefsky et al. 2002). Discrete-return systems are suitable for detailed mapping of ground due to their high resolution, which results from small diameter of the laser footprint and the high repetition rates (Flood and Gutelis 8

1997, Lefsky et al. 2002). Waveform LiDAR systems are used for characterizing canopy structure (Lefsky et al, 2002) and bathymetric surveys (Irish and Lillycrop 1999). Discrete-return LiDAR data was used to perform the research reported later in this paper. 2.2.2 History of LiDAR

The development of optical laser goes back to 1960. Townes and Schawlow first put the theory of the optical laser forward by publishing a paper in 1958. Maiman constructed the first successful optical laser – a ruby laser – in 1960 (Flood 2001). Since the late 1960s, laser altimetry has been used in many applications, including topographic mapping of the moon and the earth, atmospheric monitoring and oceanographic studies. The first spaceborne laser scanner were ruby laser systems, mounted on APOLLO 15 and 16, lunched by NASA to the moon in 1964 (Gardner 1992) . Airborne systems have been used to map regional topography around the world for a variety of geophysical purposes including volcanic hazard assessment, ice sheet elevation change, coastal erosion, and tree height derivation through the 1960s and 70s ( Garvin, 1996, Magnussen and Boudewyn 1998, Dubayah et al. 2000). In late 70s, airborne laser instruments such as NASA’s Atmospheric Oceanographic LiDAR (AOL) and Airborne Topographic Mapper (ATM) were developed primarily for research purposes. However, these custom-designed sensors had limited commercial applications. Azimuth Corporation of Westford of Massachusetts and Optech incorporated of Toronto, are two main companies that initially developed commercial LiDAR systems in early 1980s (Maun, 2001). Commercial use of LiDAR mapping has grown rapidly after 1995 due to the advancement of computer technology, positioning systems, orientation systems and availability of commercial off-the-shelf sensors. Increased awareness by end users and contracting agencies of the advantages of LiDAR technology for elevation data capturing has also been a contributing factor, establishing LiDAR systems as a commercially-valuable alternative for development of DEMs (Flood 2001, Satale and Kulkarni 2003).

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2.2.3 Advantages of LiDAR over other technologies

LiDAR offers several advantages and unique commercial capabilities when compared to other traditional technologies for data collection for the purpose of DEM generation (Jensen 2000, Lefsky et al. 2002), including (i) high accuracy, (ii) high density, (iii) ability to penetrate vegetation, (iv) capability to record multiple echo, (v) and, most importantly, relatively low cost. I will briefly discuss these advantages in the following section, but will first point out the main drawbacks of alternative technologies, to better highlight the benefit of using LiDAR systems. The main disadvantage of traditional ground surveying is the extensive amount of time and labour it requires for capturing and processing the elevation data (Lefsky et al. 2002). Photogrammetric techniques also require extensive post-processing stages to be performed for obtaining the elevation data (Adams and Chandlers 2002), and require the collection of ground control points. Photogrammetric methods have some limitations in different environmental areas. They are inaccurate in forested areas, where the ground is not visible, and in areas of low relief and texture, such as wetland areas and coastal dune systems (Lefsky et al. 2002). In urban areas, high buildings cause shadow and parallax problems for areal photogrammetric imageries (Hill, et al. 2000). Because of building shadows, IFSAR systems have limitations for detail urban mapping due to issues underlying microwave reflections and interaction with manmade environments (Hodgson et al. 2003). Airborne LiDAR is capable of rapidly generating high-density, high-accuracy, digital elevation data under a variety of conditions (Flood 1999), and can achieve a vertical accuracy of 15 to 25 centimetres (El-Sheimy et al. 2005). LiDAR can penetrate forest canopy to map the ground beneath the tree canopies, accurately map the sag of electrical power lines between transmission towers or provide accurate elevation data in areas of low relief (Flood 1999). In addition, some LiDAR systems have the ability to record multiple returns, which allows for mapping bare ground, tree canopies and also providing 10

detailed information about tree density, height, canopy cover and biomass for characterizing the structure of vegetation and habitats (Hill et al. 2000). LiDAR can be used in situations where ground access is limited, prohibited or risky to field crews. LiDAR is less sensitive to environmental conditions such as weather, sun angle or leaf on/off conditions. Since LiDAR is an active sensor, it can be operated during day and night (Flood 1999). Night time data acquisition provides reduced clouds, calmer air and minimal air traffic over major urban areas. LiDAR systems directly generate georeferenced 3D coordinates of terrain points, without the need for triangulation and rectification as needed in conventional photogrammetric techniques, the production cycle is shorter than photogrammetric methods, and as a result it is relatively easy and fast to process and deliver the digital raw LiDAR data. Furthermore, large portions of the processing and post processing sequences of the data can be automated (Hill et al. 2000, El-Sheimy et al. 2005). Most importantly, LiDAR is highly cost-effective. The cost of producing the elevation data, point for point, can be significantly less than other forms of traditional data collection techniques (Flood 1999). Traditional approaches have required the acquisition and analysis of many stereo pairs of aerial photography, extensive ground surveying and noticeable post-collection analysis for the production of precise elevation data set. LiDAR technology is an affordable, flexible and manageable alternative to those old, expensive, labour-intensive and time-consuming traditional techniques (Hill et al. 2000).

2.3 LiDAR Data pre-Processing

LiDAR systems produce a three-dimensional cloud of point measurements from reflective objects scanned by the laser beneath the flight path. Therefore, raw LiDAR data can contain return signals from any target the laser beam happens to strike, including human-made objects (eg, buildings, telephone poles, and power lines), vegetation, or even birds (Barber and Shortrudge 2004, Stoker et al. 2006). In order to create a DEM,

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measurements from none-ground features such as buildings, vehicles, and vegetation have to be distinguished and removed (Zhang et al. 2003). The process of separating of ground points from non-ground points is referred as classification or filtering. Over the past years, various filtering methods and classification algorithms have been developed to extract bare earth from the point cloud produced by airborne LiDAR (Axelsson 1999, Sithole and Vosselman 2004). More information about LiDAR data filtering and classification algorithm can be found in Axelsson (1999), and Sithole and Vosselman (2004). After separating ground points from the raw point cloud, ground points needed to be interpolated in order to form a regularly spaced grid DEM (Axelsson, 1999).

2.3.1 Interpolation (Constructing a model)

Interpolation is the process of estimating the values of a certain variable in unknown locations based on the value of measured neighbouring points (Buttough and McDonnell, 1998, Li et al 2005, El-Sheimy et al. 2005, Liu 2007). There are number of spatial interpolation techniques that can be used for interpolating a surface, including inverse distance weighted (IDW), radial basis functions (RBF), trend surface analysis (TSA), polynomial regression, and kriging techniques. All these interpolation methods share the common principal that things that are closer together tend to be more alike than things that are farther apart (Tobler 1970). There are two main categories of linear interpolation: deterministic and geostatistical. Deterministic techniques create surfaces based on measured points and mathematical formulas, and do not take into account a model of the spatial structure within the data (Anderson et al. 2005). On the other hand, geostatistical methods employ the statistical properties of the measured data to improve estimates at unknown locations. Geostatistical techniques quantify the spatial autocorrelation (statistical relationships among the measured points) among measured points and account for the spatial configuration of the

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sample points around the prediction location. These techniques not only have the capability of producing prediction surfaces, but they can also provide some measure of the accuracy of these predictions (Cressie 1993). Deterministic interpolation techniques themselves can be categorized into two groups: global and local. Global techniques use the entire data set for calculating the predictions, while local techniques calculate predictions from the sample points within neighbourhoods, which are smaller spatial areas within the larger study area (Mathews 2002). Deterministic interpolators can also be divided into exact and inexact interpolators. Exact interpolators force the surface to pass through the sample data values, while inexact interpolation techniques predict a value that is different from the measured value. (Mathews 2002) One of the most commonly-used techniques for interpolation of scatter points is IDW interpolation. IDW is a local exact interpolator method, and is based on the assumption that the interpolating surface should be influenced most by the nearby points and less by the more distant points. The interpolating surface is a weighted average of the sample points. The weight assigned to each sample point is in inverse proportion to a power of distance. Points closer to the predicted location apply greater weights than those farther away (Wilson and Gallant 2000, Chaplot et al. 2005, Anderson et al. 2005). The simplest weighting function is inverse power:

W (d ) =

1 dp

Equation [2]

Where d is distance and p>0. The value of p is specified by the user. By defining a higher power, more emphasis is placed on the nearest points, resulting in a more detailed surface, but less smooth. Defining a lower power results in a higher influence of the points that are farther away, and consequently a smoother surface. A power of 2 is most 13

commonly used with IDW. The characteristics of the interpolated surface can also be controlled by defining a neighborhood size. Neighborhood size can be fixed, by identifying a distance, or it can be variable, by defining the number of points. Generally smaller neighborhood or a minimum number of points is used when the surface has great amount of variation (Shepard 1968, Fisher et al. 1987, ArcGIS 9.1 Desktop help 2005). Previous research has shown IDW to be suitable for use with dense sample data (Doucette and Beard, 2000). Radial basis functions (RBF) methods are a series of deterministic exact interpolation methods, and are based on the assumption that the interpolation function should pass the data points and at the same time should be as smooth as possible (Talmi and Gilat 1997) RBFs minimize the total curvature of the surface. There are five different basis functions: Thin-plate spline, spline with tension, completely regularized spline, multiquadric function, inverse multiquadric function. Each basis function has a different shape and results in a slightly different interpolation surface. However, the RBFs are local interpolation method capable of extrapolation (Doucette and Beard 2000). RBFs are used for calculating smooth surfaces from a large number of data points. The functions produce good results for gently varying surfaces, but are generally inappropriate when there are large changes in the surface values within a short horizontal distance, or when there is uncertainty and error with the sample data. Kriging is a geostatistical interpolation method that takes into account both the distance and the degree of variation between known data points in order to estimate the vale at an unknown point. Besides producing prediction surfaces, they can also provide some measure of the accuracy of these predictions (Davis 1986). The process of kriging is divided into two distinct tasks: (i) quantifying the spatial structure of the data and (ii) producing a prediction. Quantifying the structure, known as variography, is where a spatial autocorrelation model is fitted to the data. In the next step, kriging will use the fitted model from variography, the spatial data configuration, and the values of the measured sample points around the prediction location to make a prediction

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for an unknown value for a specific location (Cressie 1993, Kitanidis 1997). There are several types of kriging, including ordinary, simple, universal, and block kriging. Ordinary kriging and universal kriging are most commonly used. Several studies have been conducted to compare relative accuracy of different interpolation techniques. There seems to be no single interpolation method that is the best for all data sources, terrain pattern and applications (Zimmerman et al. 1999, El-Sheimy et al. 2005, Fisher and Tate 2006, Liu, 2008). While some of pervious studies are in favour of geostatistical techniques, most of them agree that simple deterministic methods such as IDW are suitable when a dense dataset, like LiDAR dataset, is available. Anderson et al. (2005) compared IDW and OK interpolation techniques for the purpose of DEM generation from LiDAR dataset. Their result indicated that simple, straightforward interpolation approaches such as IDW could be sufficient for interpolating irregularly spaced LiDAR data sets. In a similar study, Lloyd and Atkinson (2002) found that kriging was the more accurate method when point densities were low, but concluded that no advantage was gained from using the more sophisticated geostatistical approaches when large dataset were available. Su and Bork (2006) validated DEMs created using splining, IDW, and kriging algorithms, and found that IDW was the most accurate interpolator, with RMS errors 0.02 meter less than those for splining and kriging. 2.4 Quality of DEM

Several factors affect the accuracy of DEMs: (i) the source of the elevation data, including the techniques used for obtaining the elevation data, the distribution and the density of samples; (ii) the interpolation algorithm used to construct the DEM model from this elevation data; (iii) the horizontal resolution of the constructed DEM model; and (v) and the topographic complexity of the terrain being represented (Chang and Tsai 1991, Florinsky 1998, Thompson et al. 2001, Gong et al. 2000, Kienzle 2004, Anderson et al. 2005, Li et al. 2005, Fisher and Tate 2006, Lui et al. 2007). In this study, I am only concerned with the effects of DEM horizontal resolution, point density and terrain 15

complexity. A large body of literature discuses the effect of these factors on the quality of DEM in general. Among these studies, sseveral of them have been conducted more specifically to examine the effect of, grid resolution, LiDAR point density and terrain complexity on the quality of the DEMs derived from LiDAR dataset. Some of these will briefly be discussed in the next section. 2.5 Pervious studies

Chaplot et al. (2006) evaluated the effects of landform types, data density, and interpolation techniques on the accuracy of DEM over a large range of scales. They used five interpolation techniques: IDW, OK, UK, multiquadratic radial basis function (MRBF), and regularized spline with tension (RST). They conducted their analysis using a data form total of six sites, three in the mountainous region of northern Laos and three in the more gentle landscape of western France, with various surface areas from microplots, hillslopes, and catchments. They used the mean error (ME) and the root mean square error (RMSE) as the measure of accuracy to assess the quality of DEM, and compared each DEM produced with different LiDAR data density at a given horizontal resolution to a reference DEM produced from the original LiDAR data with the highest density. Their study showed that irrespective of the spatial scales and spatial structure of altitude, there are few differences between the interpolation techniques when the sampling density is high. The result is in accordance with those of Borga and Vizzaccaro (1997), Loyd and Atkinson (2002), and Lazzaro and Montefusco (2002).They also concluded that higher-resolution DEMs were more sensitive to data density than lowerresolution DEMs. In a similar study, Anderson et al. (2005) evaluated the effects of LiDAR data density on the statistical validity of the IDW and OK interpolators. They performed their analysis in a forested, low-relief landscape using a series of ten 1000-ha LiDAR tiles. Tile data were sequentially reduced through random selection of a predetermined percentage of the original LiDAR data set, resulting in data sets with 50%, 25%, 10%, 5% and 1% of their original densities. They used cross-validation and independent validation procedures to compare the root mean square error (RMSE) and standard error (SE) between 16

interpolators and across density sequences. Their statistical analysis indicated that LiDAR data sets could withstand substantial data reductions while maintaining adequate accuracy for elevation predictions. Liu et al (2007) also examined the effects of LiDAR point density on the accuracy of DEMs. They attempted to explore to what extent a set of LiDAR data could be reduced for improving storage and processing efficiency. Their main objective was investigating the relationship between data density, data file size, and processing time. They carried out their study in a moderate complex terrain area, and the original data were subsequently reduced to produce a series of datasets with varying data densities: 100%, 75%, 50%, 25%, 10%, 5%, and 1% of the original dataset. Reduced datasets were used to create a series of DEMs at 5 m resolution. To assess the accuracy of DEMs across different data density level, an independent validation procedure was used. RMSE and standard deviation for each DEM was calculated to evaluate the overall accuracy of the DEM. The study showed that LiDAR data can be reduced to a certain level without significantly decreasing the accuracy of the output DEM. For a moderate complex terrain, LiDAR dataset with an average spacing of 2.4 m could be reduced to 50% of its original data density without degradation of the quality of the DEM. Such data reduction resulted in significant decrease of both data file size and processing time for DEM generation, without sacrificing the DEM quality (Lui, 2007). Despite the pervious studies, as Anderson et al. (2005) noted, still there is a need for more investigation to determine the effects of data reduction of LiDAR datasets on the creation of grid DEM at multiple resolutions in relation to terrain complexity. The specific objective of this research was to create a series of DEM at different spatial resolution for different LiDAR data density in three different terrain complexity, then compare each DEM in order to examine the effect of DEM grid size and LiDAR point density on the quality of DEM in different terrain type.

17

3.0 Methods 3.1 Study Area

The study area for this research is located about 75 kilometers south of Grande Prairie, Alberta, and 143 Kilometres’ west of Fox Creek (Figure 2). The study area is part of the lower foothills natural subregion (Government of Canada, 2006): a landscape characterized by undulating to strongly rolling dissected plateaus at the western edge of the interior plains with some inclusions of the undulating Alberta plains. The area is not suitable for producing agricultural crops, as it has few growing degree-days and a short growing season. But forest productivity tends to be high compared to other forested natural subregions. Excess moisture in lower elevation areas combined with nutrient-rich groundwater can support very productive and diverse forests. Aspen, balsam poplar, white birch, lodgepole pine, black spruce, white spruce, balsam fir and tamarack grow as pure stands or as mixtures on a variety of slopes and aspects; stands with three or four tree species are common. Pure deciduous stands can be found at lower elevations. Shrubby grasslands are more common on the driest sites, and poor to rich fens dominated by black spruce, tamarack, shrubs and herbs occur on low, wet sites (Government of Canada, 2006).

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Figure 2: Location of the study area in west-central Alberta. Three study sites (a) S1: flat terrain, (b) S2: intermediate terrain, and (c) S3: rough terrain

3.2 Dataset

The LiDAR data used in this project was acquired from Terrapoint Canada Inc, and is part of larger dataset acquired to provide the Government of Alberta with an accurate digital elevation database for the projects related to mountain pine beetle infestations in various forested areas around the province of Alberta. The original dataset was collected over the period of October 20th to November 6th of 2003 at 990 meters flying height. The LiDAR system had the pulse rate of 20 KHz and

19

the Laser beam wavelength of 1064 nm. GPS unit used in this fight project is Trimble 4700. The accuracy of the LiDAR data was estimated as 25 cm vertically and 45 cm horizontally. The data set was reported to have the nominal single-swath pulse density of 0.49m2, nominal aggregate pulse density of 0.98 pts m2, and nominal swath width of 643 m. All horizontal coordinates were collected and referenced to NAD83 (CSRS) and projected in UTM Zone 11. The Vertical datum was CGVD28 and geoid model was HT2.0. coordinate system. Before releasing the LiDAR data sets, Terrapoint Canada Inc. processed the data using proprietary TerraScan software. Ground and non-ground returns were separated, and the artifacts – vegetation and manmade objects – were removed. The resulting end product was an irregularly-spaced bare earth elevation datasets. The data was delivered in ASCII xyz txt format. Three study sites were chosen from the larger dataset: each covering an area of one square kilometre. This smaller data size allows the computer to process the highly dense LiDAR dataset in a reasonable time. To study the effect of terrain complexity on the accuracy of the DEM, the selection criteria was focused on covering different terrain structures: flat terrain (S1), terrain with intermediate complexity (S2), and rough terrain (S3). Figure 3 depicts the 3D representation of selected LiDAR tiles for this study. Elevation ranges from 860 to 936 m in the flat study site (S1), from 954m to 1035m in the moderate study site (S2), and from 888m to 1030m in the rough study site (S3). General statistics of the original LiDAR datasets (not reduced) for the three study sites is presented in Table 1. Figure 4 shows point density and mean point separation distance estimated for the original (not reduced) LiDAR data set for three study sites.

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(a)

(b)

(c) Figure 3: Three study sites (a) S1: flat terrain, (b) S2: intermediate terrain, and (c) S3: rough terrain

21

Table 5: General statistics of the three study sites: Tile S1 represents the plain study area, tile S2 represents the terrain with moderate complexity and tile S3 represents terrain with extreme roughness

LiDAR data tile

Number of points

Minimum Height

Maximum height

Elevation range

Average height

S1

259054

860.41

936.53

76.12

893.52

1.2300

0.2513

S2

368484

954.46

1035.91

81.45

999.71

1.0537

0.3685

S3

436467

888.76

1030.09

141.33

974.86

1.0105

0.4508

Point Separation Distance of the original LiDAR dataset 1.4

0.45 0.4 0.35 0.3 0.25 0.2 0.15

1.2 1

Meter

Point per Square meter

Point Density of the original LiDAR dataset

Mean Separation (m) Point Density*

0.8 0.6 0.4

0.1 0.05 0

0.2 0

S1

S2

S3

S1

S2

S3

Figure 4: Original LiDAR point density and mean point separation distance.

3.3 Analysis

The general analysis strategy used to study the effect of point density and DEM horizontal resolution in LiDAR data from three different levels of terrain complexity is summarized in Figure 5. I will discuss each these steps in more detail below.

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Extracting three study sites

Breaking the datasets into validation and training dataset

Reducing the training dataset to 75%, 50%. 25%, 10%, 5% , 1% and 0.5%

Determining the point density and point spacing of the reduced datasets

Creating DEM grids in multiple resolutions

Performing independent validation using the validation dataset

Calculating the Root Mean Square Error

Creating 3D surface model

Figure 5: Flowchart describing the general analysis strategy followed in this research.

From the initial dataset, three tiles that cover the area of one square kilometre were extracted using ArcGIS 9.2 (Environmental Systems Research Institute (ESRI), 2006). Golden Software Surfer 8 was used to obtain some general statistics about each dataset. The initial step was to break each dataset into two random subsets using Hawth’s tool module in ArcGIS 9.2: one for training (97%) and one for validation (3%). The training dataset was later reduced to 75%, 50%, 25%, 10%, 5%, 1%, 0.5% and 0.1% of the original dataset through random selection. Data reduction was performed using the Hawth’s Analysis tools of ArcGIS 9.2 (Environmental Systems Research Institute

23

[ESRI], 2006). Surfer Golden Software was used to estimate point density, elevation range, maximum and minimum elevation of each density level. Average point density was estimated as:

λ=

N ( Range( x))( Range( y ))

Equation [3]

Where N is the number of point, x is the easting and y is the northing coordinates. LiDAR datasets are often characterized on the basis of point spacing. Therefore, I estimated the associated point spacing for each point density level. To establish a measure of point spacing, I used the “Near” tool from Spatial Analyst toolbox. This tool determines the distance between each point and its closest neighboring point. Mean average of near distance was calculated for each tile across different density level. Next, each reduced density level was interpolated to form regularly spaced grids. Grid DEMs were created in multiple spatial resolutions of 0.5, 1, 1.5, 2, 5, 10, 15, 20, 25 and 30 meter in each density level resulting is total of 80 DEMs. I used IDW interpolation based on the previous studies which identified IDW as a fast, simple and efficient interpolator suitable for use with high-density LiDAR data. Surfer 8.05 (Golden Software Inc., 2004) was used to perform the interpolation, with the power parameter set to a value of 2. The search radius was flexible in that it always allowed for a neighborhood including at least 16 elevation points. 3.4 Quality Assessment

Since there was no ground truth dataset available in this study, absolute geodetic accuracy of the DEM could not be evaluated. As a result, I conducted a relative quality assessment of the DEM using validation and predication dataset extracted from the same source. To evaluate the relative quality of DEMs, an independent validation approach was used.

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The vertical difference between each validation point and the correspondent predicted point of the DEM was determined using the “Residual” command in Surfer8 (Golden Software Inc., 2004) for each DEM grid. The vertical difference was estimated for every validation point using the equation: E ( si ) = P( si ) − M ( si )

Equation [4]

Where E ( si ) is the error at location si , P( si ) is the predicted value of the DEM at location si , and M ( si ) is the measured value from the validation LiDAR data at location si . In order to compare the overall accuracy of the DEMs across different density levels, RMSE was calculated for each DEM as:

RMSE=

E ( si ) 2 n

Equation [5]

Where n is the total number of points, and E ( si ) is the error at location si . Li (1988), Yang and Hodler (2000) and Aguilar (2004), refer to RSME as the most widely used global accuracy measure for evaluating the DEM quality. In order to better compare the results across different density levels and resolutions, RMSE was plotted against point density, pixel size, and point spacing in separate graphs. In addition to the analytical comparison discussed above, I analyzed the quality of DEM visually, using 3D surface models created in Surfer.

25

4.0 Results RMSE across different density level in multiple resolutions for the three study sites are presented in Table 2 through 4, which show the mean point separation distance and point density estimates for each density level. In general, the results presented acceptable accuracies for each of the generated DEMs in multiple resolutions over all data density levels. The greatest RMSE was less than 4.3 m and occurred at the lowest density (0.1% of the original dataset) in the rough terrain. The flat terrain had RMSEs ranging from 0.02m to 0.2m. As terrain becomes more undulating in S2, the range of RMSE increased substantially to between 0.13m and 2.3m. The overall range of error was greatest for the terrain with the rough complexity (tile S3), where RMSE varied from 0.13m to 4.27m. Figure 6 shows RMSE mapped against point density in multiple resolutions. The trend of change was similar for three different terrain types; only the rate of the change varies for each study sites. The results indicate that point density affects the prediction error negatively; in the other worlds, RMSE increases as data density decreases. Lower density means larger point spacing. Consequently, prediction error increases as point spacing increases. Over flat terrain, RMSE was found to change very slightly from 0.25 to 0.01 po int/ m 2 ; RMSE changes from 0.0294 to 0.2097 in 0.5m DEM. From point density 0.01 po int/ m 2 RMSE starts changing more rapidly; it changes up to 1.2 in 0.5m DEM. It can be seen that the trend of RSME growth is linear up to point density of 0.06 po int/ m 2 . From this point density the trend of change is exponential. Terrain with intermediate complexity and the rough terrain yielded nearly similar results. RMSE increased only slightly from point density of 0.35 po int/ m 2 to 0.03 po int/ m 2 (RMSE changes from 0.13 to 0.31 in 0.5m DEM) but it increase more rapidly as point density gets smaller than 0.03 po int/ m 2 . The trend of change is linear up to point density of 0.1 po int/ m 2 . From this point, RMSE change has exponential growth.

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Table 6: Root Mean Square Error , point density and mean separation across different density level in multiple resolution for plain terrain ( LiDAR tile S1) Density Level

100% 75% 50% 25% 10% 5% 1% 0.50% 0.10%

Mean Separation

Point Density

0.5m

1m

1.5m

2m

5m

10m

15m

20m

25m

30m

1.2300 1.3560 1.5698 2.0739 3.1575 4.4039 10.2685 14.3670 32.5182

0.2513 0.1885 0.1256 0.0628 0.0251 0.0126 0.0025 0.0013 0.0003

0.0294 0.0584 0.0829 0.1110 0.1625 0.2097 0.4109 0.5693 1.1999

0.0530

0.0674

0.0777

0.0686 0.0868 0.1118 0.1622 0.2094 0.4107 0.5693 1.1999

0.0778 0.0912 0.1133 0.1613 0.2082 0.4089 0.5666 1.1997

0.0851 0.0961 0.1150 0.1620 0.2085 0.4090 0.5689 1.1971

0.1038 0.1067 0.1130 0.1247 0.1643 0.2071 0.4073 0.5650 1.1898

0.1283 0.1283 0.1318 0.1397 0.1724 0.2064 0.4042 0.5602 1.1933

0.1464 0.1464 0.1519 0.1577 0.1848 0.2111 0.3918 0.5360 1.1683

0.1721 0.1721 0.1735 0.1772 0.2026 0.2319 0.4113 0.5591 1.1390

0.1924 0.1924 0.1937 0.1981 0.2200 0.2487 0.4234 0.5703 1.1729

0.2123 0.2123 0.2159 0.2276 0.2418 0.2578 0.4088 0.5749 1.1473

Table 7: Root Mean Square Error, point density and mean separation across different density level in multiple resolution for terrain with moderate complexity (LiDAR tile S2). Density Level 100% 75% 50% 25% 10% 5% 1% 0.50% 0.10%

Mean Separation Point Density 1.0537 1.1693 1.3543 1.7708 2.6617 3.7562 8.2200 11.6846 25.3296

0.3574 0.2681 0.1787 0.0894 0.0357 0.0179 0.0036 0.0018 0.0004

0.5m

1m

1.5m

2m

5m

10m

15m

20m

25m

30m

0.1323 0.1451 0.1662 0.2143 0.3107 0.3985 0.7140 0.9493 2.3108

0.1317 0.1442 0.1648 0.2132 0.3097 0.3978 0.7136 0.9490 2.3106

0.1322 0.1437 0.1635 0.2118 0.3083 0.3961 0.7092 0.9483 2.3074

0.1335 0.1447 0.1640 0.2113 0.3078 0.4213 0.7129 0.9422 2.3089

0.1608 0.1704 0.1859 0.2273 0.3145 0.3996 0.7097 0.9542 2.2915

0.2401 0.2462 0.2557 0.2845 0.3602

0.3321 0.3345 0.3461 0.3655 0.4206 0.4773

0.4297 0.4294 0.4303 0.4389 0.4777 0.5242

0.7103 0.9096 2.1945

0.7584 0.9604 2.2521

0.5035 0.5033 0.5008 0.5024 0.5278 0.5691 0.7846 0.9759

0.5766 0.5757 0.5795 0.5849 0.5812 0.6182 0.7909 1.0157 2.2502

0.4294 0.7134 0.9467 2.2850

2.3315

Table 8: Root Mean Square Error, point density and mean separation across different density level in multiple resolution for rough terrain ( LiDAR tile S3) . Density Level

100% 75% 50% 25% 10% 5% 1% 0.50% 0.10%

Mean Separation

Point Density

0.5m

1m

1.5m

2m

5m

10m

15m

20m

25m

30m

1.0105 1.1134 1.2759 1.6533 2.4736 3.4333 7.6307 10.5753 23.9235

0.4234 0.3175 0.2117 0.1058 0.0423 0.0212 0.0042 0.0021 0.0004

0.1307 0.1473 0.1770 0.2470 0.3916 0.5489 1.1696 1.7604 4.2745

0.1294 0.1436 0.1745 0.2444 0.3894 0.5474 1.1687 1.7598 4.2742

0.1281 0.1453 0.1440 0.2411 0.3859 0.5425 1.1678 1.7593 4.2716

0.1286 0.1434 0.1716 0.2398 0.3851 0.5428 1.1631 1.7534 4.2733

0.1677 0.1802 0.2035 0.2600 0.3931 0.5445 1.1592 1.7366 4.2649

0.2869 0.2944 0.3084 0.3496 0.4566 0.5937 1.1695 1.7519 4.2543

0.4297 0.4322 0.4369 0.4657 0.5500 0.6663 1.1941 1.7299 4.2314

0.5660 0.5672 0.5705 0.5888 0.6502 0.7495 1.2642 1.7883 4.2579

0.7153 0.7153 0.7154 0.7254 0.7718 0.8637 1.3222 1.8448 4.2354

0.8625 0.8604 0.8635 0.8580 0.8942 0.9727 1.3906 1.8224 4.2125

27

RMSE vs Point Density S1

RMSE (m)

0.5m 1m 1.5m 2m 5m 10m 15m 20m 25m 30m

RMSE (m)

1.4

0.5m 1m 1.5m 2m 5m 10m 15m 20m 25m 30m

1.2 1 0.8 0.6 0.4 0.2 0 0.3

0.25

0.2

0.15

0.1

0.05

0

point per square meter

RMSE vs Point Density S2 2.5 2 1.5 1 0.5 0 0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

Point per square meter

RMSE vs Point Density S3

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0.5m 1m RMSE (m)

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

1.5m 2m 5m 10m 15m 20m 25m

0

point per square meter

Figure 6: RMSE plotted against point density.

28

To examine the effect of LiDAR point spacing directly, RMSE was mapped against mean point spacing in multiple resolutions for different terrain types in Figure 7. In this graph, RMSE is shown to grow linearly as point spacing increases, regardless of terrain complexity. However the rate of change varies for different terrain types. In flat terrain point spacing changes from 1.3 to 32.5 m and RMSE increases from 0.03 to 1.2 for 0.5m DEM and from 0.2 to 1.4 for 30m DEM. In the terrain with intermediate complexity point spacing changes from 1.05 to 25.3 and RMSE increases form 1.13 to 2.3 in 0.5m DEM and from 0.5 to 2.3 in 30m DEM. In the rough terrain point spacing ranges from 1.0 to 24m and RMSE ranges from 0.12 to 4.27 in 0.5m DEM. To better compare the trend of change in different terrain types, RMSE of different terrain type was mapped against point spacing in a single graph for 3 different DEM resolutions (1, 5 and 25 meter) as shown in Figure 8. Prediction error changes more dramatically in the rough area (tile S3). The change trend line has the steepest slope for tile S3. Figure 9 shows the effect of horizontal resolution of the DEM accuracy across density levels for three terrain types. In the flat study area RMSE increase as the spatial resolution decrease for high density levels (100%, 75%, 50% 25% corresponding to point spacing of 1.23, 1.35, 1.56 and 2.07 meter). As density decrease this trend changes. For the dataset reduced to 10% of the original dataset (corresponding to point spacing of 3.15 m and point density of 0.025 po int/ m 2 ), RMSE decreases from 1.625m to 1613m as grid size changes from 0.5 m to 1.5 m. RMSE then starts increasing. 30m DEM has the RSME of 0.24m. Same trend is observed for the lower density levels. First, RMSE decreases in finer resolution and then starts increasing as resolution become coarser. For the data reduced to 5 % of the original dataset RMSE decrease from 0.2097 in 0.5m DEM to 0.2064 in 10m DEM then it increase to 0.2578 in 30m DEM. For 1% density level and 0.5% density level RMSE decreases from 0.5 to 15m resolution and starts increasing from 15m to 30 m resolution. For the data reduced to 0.1% of the original dataset (corresponding to point spacing of 32.51 m and point density of 0.0003 po int/ m 2 ) RMSE start increasing from 25 m spatial resolution. 29

In the terrain with intermediate complexity (tile S2), at high density levels (100%, 75%, 50%, and 25% of the original dataset), RMSE decreases first for finer resolution and then starts increasing as resolution gets coarser. Again the gird cell size which RMSE starts rising at, varies for different density level. As density decrease RMSE start increasing at a coarser resolution. At lower data density levels (10%, 5%, 1%, 0.5% and 0.1% of the original dataset), RMSE fluctuate only slightly at finer resolution and then start increasing at some point. In the rough (tile S3) terrain at higher density levels (100%, 75%, 50 % density level) RMSE decreases first for finer resolution and starts increasing as resolution get coarser. At lower density levels, RMSE fluctuate slightly in finer resolution. It should be noted that in all cases, the rate decline in RMSE is very slow. RMSE changes only in millimetre scale when it decreases. In some cases the amount of decline is so small that it can be ignored. Although increase in the RMSE in coarser resolution is more noticeable, still RMSE changes only slightly even when the density is high. Figure 10 shows the RMSE of DEM in multiple resolutions for three different density levels (75 %, 10 % and 0.1% of the original data set). As it can be seen in lower density (0.1 %) the difference in RSME across different resolution is very small for all three terrain types, confirming the fact that in lower densities, the dataset in not sensitive to changes of DEM resolution. Figure 11 illustrates the 3D DEM surface model created for tile S3 in very fine resolution (0.5 meter) and low resolution (20 meter) for the density levels of 0.1 %, 5% and 100% of the original data set. High resolution DEM models created from low density data point Figure 11 (a) and (b) exhibit large amounts of artifacts. Visually there is not a big difference among low resolution DEMs created form different density levels (Figure 11 (b), (d) and (f).

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RMSE vs Point Spacing S1 1.4

0.5m 1m 1.5m 2m 5m 10m 15m 20m 25m 30m

RMSE (m)

1.2 1 0.8 0.6 0.4 0.2 0 0

5

10

15

20

25

30

35

Point Spacing (m)

RMSE vs Point Spacing S2 2.5

0.5m 1m 1.5m 2m 5m 10m 15m 20m 25m 30m

RMSE (m)

2 1.5 1 0.5 0 0

5

10

15

20

25

30

Point spacing (m)

RMSE

RMSE vs Point Spacing S3 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

0.5m 1m 1.5m 2m 5m 10m 15m 20m 25m 30m 0

5

10

15

20

25

30

Point Spacing (m)

Figure 7: RMSE plotted against point spacing

31

RMSE vs Point Separation 1 meter DEM 4.5 4 3.5 RMSE

3

S1

2.5 2

S2 S3

1.5 1 0.5 0 0

5

10

15

20

25

30

35

Mean Point Spacing (m)

RMSE vs Point Separation 5 meter DEM 4.5 4 RMSE (m)

3.5 3

S1

2.5 2

S2 S3

1.5 1 0.5 0 0

5

10

15

20

25

30

35

Mean Point spacing (m)

RMSE vs Point Separation 25 meter DEM 4.5 4 RMSE (m)

3.5 3

S1

2.5

S2

2

S3

1.5 1 0.5 0 0

5

10

15

20

25

30

35

Mean Point Spacing (m)

Figure 8: RMSE of three different terrain types plotted against mean point spacing.

32

RMSE (m)

RMSE vs Horizontal Resolution S1 1.4

100%

1.2

75%

1

50% 25%

0.8

10%

0.6

5%

0.4

1%

0.2

0.50% 0.10%

0 0

5

10

15

20

25

30

Horizontal Resolution (m)

RSME vs Horizontal Resolution S2 2.5

100% 75%

2 RMSE (m)

50% 25%

1.5

10%

1

5% 1%

0.5

0.50% 0.10%

0 0

5

10

15

20

25

30

Horizontal Resolution (m)

RMSE vs Horizontal Resolution S3 4.5

100%

4

75%

RMSE (m)

3.5

50%

3

25%

2.5

10%

2

5%

1.5

1%

1

0.50%

0.5

0.10%

0 0

5

10

15

20

25

30

Horizontal Resolution (m)

Figure 9: RMSE plotted against horizontal resolution.

33

RMSE in multiple resolutions 75 % density level 1

0.5m

0.9

1m

0.8

1.5m

0.7

2m

0.6

5m

0.5

10m

0.4

15m

0.3

20m

0.2

25m

0.1

30m

0 S1

S2

S3

RMSE in multiple resolutions 10% density level 1

0.5m

0.9

1m

0.8

1.5m

0.7

2m

0.6

5m

0.5

10m

0.4

15m

0.3

20m

0.2

25m

0.1

30m

0 S1

S2

S3

RMSE in multiple resolutions 0.1% density level 4.5

0.5m

4

1m

3.5

1.5m

3

2m

2.5

5m

2

10m

1.5

15m

1

20m

0.5

25m

0

30m S1

S2

S3

Figure 10: RMSE of DEM in multiple resolution for density levels of 75%, 10% and 0.1% of the original dataset.

34

(a) Density level: 0.1% Resolution: 0.5 m

(b) Density level: 0.1% Resolution: 20 m

(c) Density level: 5% Resolution: 0.5 m

(d) Density level: 5% Resolution: 20 m

(e) Density level: 100% Resolution: 0.5 m

(f) ) Density level: 100% Resolution: 20 m

Figure 11: 3D surface model of tile S3 (a) density level of 0.1% in 0.5 meter spatial resolution, (b) density level of 0.1% in 20 meter resolution, (c) density level of 5% in 0.5 meter point resolution (d) density level of 5% in 20 meter DEM resolution (e) density level of 100 % in 0.5 meter DEM resolution (f) density level of 100% in 20 meter DEM resolution.

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5.0 Discussion As expected, data density reduction influences DEM accuracy. Errors were found to increase as data density decreased. The effects of LiDAR data reduction on RMSE were similar for each DEM resolution for all three terrain types. This result is in accordance with those of Makarovic (1979), Li (1992) and Gao (1995, 1997). This trend of change in RMSE was expected because reducing density means increasing LiDAR point spacing. The larger separation distance between neighbouring points negatively affects the IDW interpolator ability to estimate the height for a given location. IDW assign weights to neighbouring sample point based on the distance to the prediction location. As the name suggests, the weight is inversely related to the distance. Points which are closer to the unknown point have stronger influence than those farther away (Wilson and Gallant 2000, Anderson et al. 2005, Chaplot et al. 2006). I found the rate of RMSE increase as a function of point spacing to occur more rapidly in rough terrain, implying that DEM accuracy is more sensitive to data reduction in complex terrain than a simple terrain. In the other words, the effect of terrain complexity becomes stronger as point spacing increases. This result confirms previous observations by Gao (1997) who indicated that the accuracy of a DEM is inversely associated with terrain complexity. A complex terrain is less accurately predicted than a simple terrain by a DEM of the same resolution and same point density (Gao, 1997). The studies carried out by of Chou et al. (1999), Kyriakidis and Goodchild (2006), Liu (2008) led to the same conclusion as well. They demonstrated that the effects of data density and DEM resolution on the accuracy of DEM are related to terrain complexity. As Liu (2008) mentioned different complex terrains require different data density and spatial resolution to produce DEMs to predict the terrain elevation at a certain level of accuracy.

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My results indicate that resolution does not have a strong effect on the RMSE, especially in lower density. It can be seen that change in RMSE across different resolution has very similar trends for different density level. The prediction error increases only slightly with the increase in grid cell size. When grid size gets coarser than 5 m, RMSE changes more rapidly. It can be seen that resolution has relatively a stronger influence on higher density levels. In higher density levels, first RMSE decrease slightly as gird cell size increase, then it starts to increase as spatial resolution gets coarser. In lower densities, RMSE fluctuates at finer resolution and then it increase with the increase of grid cell size. The decrease in the RMSE in higher resolution at low density levels affirms the statements of Florinsky (2002), Albani et al. (2004) and Liu (2008), who asserted that it is inappropriate to generate a high resolution DEM with very sparse terrain data. In this case, the generated surface would contain abundant interpolation artifacts and will more likely represent the shape of the interpolator than the shape of the terrain (Florinsky 2002, Albani et al. 2004). My findings found that in higher point density, RMSE is more sensitive to the change of spatial resolution. As data reduction goes beyond 15% of the original data, the influence of spatial resolution diminishes. When the data is reduced to 0.1% of its original density, spatial resolution has little effect on the quality of the DEM for all three terrain types. Results show that RMSE is very consistent between spatial resolutions and varies more between density levels. All these results signify that horizontal resolution does not have a strong effect on the accuracy of DEM. RMSE is more intensely affected by point density and terrain complexity than by DEM resolution. These findings are consistent with those of Aguilar (2005) who indicated that the factor with the greatest influence on the quality of the interpolation was terrain structure, followed by sampling point density and interpolation method. However my

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results are in contrast with those of Chaplet at al (2006), who found that DEM horizontal resolution significantly influenced the quality of the DEM produced from reduced datasets. By creating 3D surface DEM models, I was better able to visually analyze the quality of generated DEMs. At lower density level, 3D DEM models showed abundant interpolation artifacts in fine resolutions (Figure 11). My visual analysis confirms the observations of Florinsky (2002) and Albani et al. (2004). The presence of interpolation artifacts in spite of the good accuracy obtained through independent RMSE validation suggests that our evaluation strategy was not efficient enough. In this study I only used 3% of the original dataset as validation dataset. Independent validation might have performed more efficiently if I had used a larger validation dataset.

6.0 Conclusions The results obtained in this study indicate that terrain complexity and point density of LiDAR data considerably affect the accuracy of LiDAR-based DEMs. Terrain complexity was the factor with the strongest influence on the quality of the DEM in this study. DEMs created from low-density datasets are more sensitive to terrain complexity. However, it should be noted that a thorough exploratory analysis of the terrain structure was not carried out. In order to study the influence of the terrain complexity more thoroughly, further statistical analysis of the terrain structure is required. The result of independent validation shows that LiDAR datasets can be reduced noticeably and still maintain the acceptable accuracy of elevation estimates, providing the original point density is high. Comparison of RSME across different spatial resolution at each density level indicted that change in grid cell size does not considerably affect the DEM accuracy, especially in lower density levels. In general, my statistical analysis revealed an acceptable DEM accuracy across different resolutions for all the reduced density levels. However visual analysis of 3D DEM surfaces revealed that high resolution DEMs created from low density data contain 38

abundant number of artifacts which degrade the quality of DEM. This observation stresses the importance of an appropriate evaluation strategy when assessing the quality of DEM and other 3D surface models. It is not always sufficient to only rely on the result of statistical analysis. It is recommended to carry out visual analysis alongside statistical analysis. In order to profoundly evaluate the quality of a 3D surface, close attention should be paid to the choice of evaluation strategy.

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References Ackermann, F., 1984, Digital image correlation: performance and potential application in photogrammetry. Photogrammetric Record, 11 (64): 429–439. Adams, J.C., and Chandler, J.H., 2002, Evaluation of lidar and medium scale photogrammetry for detecting soft-cliff coastal change, Photogrammetric Record, 17(99): 405–418. Aguilar, F. J., Agüera, F., Aguilar, M. A., and Carvajal, F., 2005, Effects of terrain morphology, sampling density and interpolation methods on grid DEM accuracy, Photogrammetric Engineering and Remote Sensing, 71 (7): 805–816. Albani, M., Klinkenberg, B., Andison, D. W., and Kimmins, J. P., 2004,The choice of window size in approximating topographic surfaces from digital elevation models, International Journal of Geographical Information Science, 18(6): 577-593. Anderson, E. S., Thompson, J. A., and Austin, R.E., 2005, LIDAR density and linear interpolator effects on elevation estimates, International Journal of Remote Sensing, 26(18)(20): 3889-3900. ArcGIS 9.1 Desktop Help, 2005, ESRI. Axelsson, P., 1999, Processing of laser scanner data Algorithms and applications, ISPRS Journal of Photogrammetry and Remote Sensing, 54: 138-147. Baldi, P., Bonvalot, S., Briole, P., Coltelli, M., Gwinner, K., Marsella, M., Puglisi, G., and Remy, D., 2002, Validation and comparison of different techniques for the derivation of digital elevation models and volcanic monitoring (Vulcano Island, Italy), International Journal of Remote Sensing, 23(22): 4783–4800. Band, L.E., 1986, Topographic partition of watersheds with digital elevation models, Water Resources Research, 22(1): 15–24. Barber, C. P. and Shortrudge, A. M., 2004, Light Detection and Ranging (LiDAR) – Derived Elevation Data for Surface Hydrology Applications, Institute of Water Research, Michigan State University. Borga, M. and Vizzaccaro,A., 1997, On the interpolation of hydrologic variables: formal equivalence of multiquadratic surface fitting and kriging, Journal of Hydrology, 195: 160–171.

40

Burrough, P.A., and McDonnell, R.A., 1998, Principles of Geographical Information Systems, Oxford University Press, New York, 333 p. Chang, K.T., and Tsai, B.W., 1991, The effect of DEM resolution on slope and aspect mapping, Cartographic Geography Information Systems, 18: 69–77. Chaplot, V., Darboux, F., Bourennane, H., Leguedois, S., Silvera, N., and Phachomphon, K., 2006, Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density, Geomorphology, 77(1–2): 126–141. Chou, Y. H., Liu P. S., and Dezzani,R. J., 999, Terrain complexity and reduction of topographic data, Geographical Systems, 1(2): 179-197. Cowen, D. J., Jensen, J. R., Hendrix, C., Hodgson, M. E., and Schill, S. R., 2000, A GISassisted rail construction econometric model that incorporates LIDAR data, Photogrammetric Engineering and Remote Sensing, 66(11): 1323–1326. Cressie, N., 1993, Statistics for spatial data, John Wiley & Sons, New York, 900 p. Davis, C.H., and Wang, X., 2001, High-Resolution DEMS for urban applications from NAPP photography, Photogrammetric,Engineering & Remote Sensing, 67(5): 585–592. Davis, J. C., 1986, Statistics and data analysis in Geology, Second Edition, John Wiley & Sons, Inc., 646p. Desmet, P.J., Poesen, J., Govers G., and Vandeale, K., 1999, Importance of slope gradient and contributing area for optimal prediction of the initiation and trajectory of ephemeral gullies, Catena, 37(3–4):377–392. Doucette, P., and Beard, K., 2000, Exploring the capability of some GIS surface interpolators for DEM gap fill, Photogrammetric Engineering and Remote Sensing, 66: 881–888. Dubayah, R., and Drake, J., 2000, Lidar remote sensing for forestry, Journal of Forestry, 98: 44–46. Dubayah, R., Knox, R., Hofton, M., Blair, J. and Drake, J., 2000, Land surface characterization using lidar remote sensing, in Hill, M., Aspinall R., Spatial

41

Information for Land Use Management. Singapore:International Publishers Direct:25-38. El-Sheimy, N., Valeo, C., and Habib, A., 2005, Digital terrain modeling: acquisition, manipulation, and application, Boston, MA: Artech House, 257p. Ehlers, M., and Welch, R., 1987, Stereocorrelation of landsat TM images, Photogrammetric Engineering and Remote Sensing 53 (9): 1231–1237. Fisher, P. F., and Tate, N. J., 2006, Causes and consequences of error in digital elevation models, Progress in Physical Geography, 30(4): 467-489. Fisher, N.I., Lewis, T., and Embleton, B.J., 1987, Statistical Analysis of Spherical Data, Cambridge University Press, Cambridge, 329 p. Fisher, P. F., 1993, Algorithm and implementation uncertainty in viewshed analysis, International Journal of Geographic Information Science, 7: 331–47 Flood, M., and Gutelis, B., 1997, Commercial implications of topographic terrain mapping using scanning airborne laser radar, Photogrammetric Engineering and Remote Sensing 63: 327–366. Flood, M., 1999, Commercial development of airborne laser altimetry: a review of the commercial instrument market and its projected growth, International Archives of Photogrammetry and Remote Sensing, Volume XXXII-3/W14, online at < http://www.isprs.org/commission3/lajolla/pdf/p13.pdf > accessed on 5 April , 2007. Flood, M., 2001, Laser altimetry: from science to commercial LIDAR mapping, Photogrammetric Engineering & Remote Sensing, 67(11):1209–1217. Florinsky, I.V., 1998. Accuracy of local topographic variables derived from digital elevation models, International. Journal of Geographical Information Science, 12 (1): 47–61. Florinsky, I. V., 2002, Errors of signal processing in digital terrain modeling, International Journal of Geographical Information Science, 16(5): 475-501. Franklin, W.R., 2000, Applications of analytical cartography, Cartography and Geographic Information Science, 27(3): 225–237.

42

Gao, J., 1993, Identification of topographic settings conducive to landsliding from DEMs in Nelson County, Virginia, U.S.A., Earth Surface Processes and Landforms, 18: 579–591 Gao, J., 1995, Comparison of sampling schemes in constructing DTMs from topographic maps, ITC Journal, 1:18–22. Gao, J., 1997, Resolution and accuracy of terrain representation by grid DEMs at a micro-scale, International Journal of Geographical Information Science, 11: 199– 212. Gardner, C. S., 1992, Rangigng Performance of Satellite Laser Altimeters, Geoscience and Remote Sensing, IEEE Transactions, 30(5): 1061 – 1072. Garvin, J., Bufton, J., Blair, J., Harding, D., Luthcke, S., Frawley, J. and Rowlands, D., 1998, Observations of the Earth’s topography from the Shuttle Laser Altimeter (SLA): Laser-pulse echo-recovery measurements of terrestrial surfaces, Physics and Chemistry of the Earth, 23: 1053–1068. Gong, J., Li, Z., Zhu, Q., Shu. H., and Zhou, Y., 2000, Effects of various factors on the accuracy of DEMs, an intensive experimental investigation, Photogrammetric Engineering and Remote Sensing, 66(9): 1113-1117. Government of Alberta, 2006, Natural regions and subregions of Alberta. accessed online at accessed on 15 July 2008. Harding, D.J., Blair J.B., Garvin J.B. and Lawrence, W.T., 1994, Laser altimetry waveform measurement of vegetation canopy structure, Proceedings of the International Remote Sensing Symposium 1994. Pasadena (CA): California Institute of Technology, 1251–1253. Hill, J. M., Graham, L. A., and Henry, R. J., 2000, Wide-area topographic mapping and applications using airborne light detection and ranging (LIDAR) technology, Photogrammetric Engineering and Remote Sensing, 66(8): 908-909, 911-914, 927, 960.

43

Hirano, A., Welch, R. and Lang, H., 2003, Mapping from ASTER stereo image data: DEM validation and accuracy assessment, Photogrammetry and Remote Sensing 57: 356–370. Hodgson, M.E., Jensen,J. R., Schmidt, L., Schill, S. and Davis, B., 2003, An evaluation of lidar- and IFSAR-derived digital elevation models in leaf-on conditions with USGS Level 1 and Level 2 DEMs, Remote Sensing of Environment, 84: 295–308. Hodgson, M.E., and Bresnahan, P., 2004, Accuracy of Airborne Lidar-Derived Elevation: Empirical Assessment and Error Budget, Photogrammetric Engineering & Remote Sensing, 70 (3): 331–339. Hofton, M. A., Blair, J.B., Minster, J.B., Minister J. B., Ridgway, J.R., Williams, N.P., Bufton, J.L., and Rabine, D. L., 2000, An airborne scanning laser altimetry survey of Long Valley, California, International Journal of remote sensing, 21( 12): 2413-2437. Irish, J. L., and Lillycrop, W. J., 1999, Scanning laser mapping of the coastal zone: The SHOALS system, ISPRS Journal of Photogrammetry and Remote Sensing, 54:123−129. Jensen, J. R., 2000, Active and passive microwave and LIDAR remote Sensing, Remote sensing of the environment: an earth resource perspective NJ: Prentice-Hall, Chap, 9: 285– 332. Kenward,T., Lettenmaier, D. P., Wood, E. F., and Fielding, E., 2000, Effects of digital elevation model accuracy on hydrologic predictions, Remote Sensing of Environment, 74: 432–444. Kienzle, S., 2004, The effect of DEM raster resolution on first order, second order and compound terrain derivatives, Transactions in GIS, 8(1): 83-111. Kitanidis, P. K., 1997, Introduction to Geostatistics: Applications in Hydrogeology, Cambridge University Press, 249 p. Kok, A.L., Blais, J.A.R., and Rangayyan, R.M., 1987, Filtering of digitally correlated Gestalt elevation data, Photogrammetric Engineering and Remote Sensing, 53(5): 535–538. Kumler, M.P., 1994, An intensive comparison of triangulated irregular networks (TINs) and digital elevation modes, Cartographica, 31:1-99.

44

Kyriakidis, P.C., and Goodchild, M.F., 2006, On the prediction error variance of three common spatial interpolation schemes, International Journal of Geographical Information Science 20: 823–55. Lang, H., Welch, R., Miyazaki, Y., Bailey, B., and Kelly, G., 1996, The ASTER alongtrack stereo experiment—a potential source of global DEM data in the late 1990's. In: Proceedings of SPIE 2817, The International Society for Optical Engineering, 95–97. Lazzaro, D., and Montefusco, L.B., 2002, Radial basis functions for the multivariate interpolation of large scattered data sets, Journal of Computational and Applied Mathematics, 140: 521–536. Lee, J., Snyder, P. K., and Fisher, P. F., 1992, Modeling the effect of data errors on feature extraction from digital elevation models, Photogrammetric Engineering and Remote Sensing, 58: 1461–1467. Lefsky, M.A., Cohen, W. B., Parker, G. G., and Harding D.J., 2002, LiDAR remote sensing for ecosystem studies, Bioscience, 52:19-30. Li, Z., 1988, On the measure of digital terrain model accuracy, The Photogrammetric Record, 12(72):873–877. Li, Z., 1992, Variation of the accuracy of digital terrain models with sampling interval, The Photogrammetric Record, 14(79):113–128. Li, Z., Zhu, Q., and Gold, C., 2005, Digital terrain modeling: principles and methodology, Boca Raton, FL: CRC Press. Liu, X., Zhang, Z., Peterson, J., and Chandra, S., 2007a: The effect of LiDAR data density on DEM accuracy. In Proceedings of International Congress on Modeling and Simulation (MODSIM07), Christchurch, New Zealand, 1363–69. — 2007b: LiDAR-derived high quality ground control information and DEM for image orthorectifi cation, GeoInformatica, 11: 37–53. Liu, X., Peterson, J., and Zhang, Z., 2008, High-Resolution DEM Generated from LiDAR Data for Water Resource Management, Center for GIS, school of Geography and Envoironment Science Monash University, Wellington Road, Clayton, Vic 3800,

45

Australia, online at < http://www.mssanz.org.au/modsim05/papers/liu_x.pdf> accessed on 28 May 2008. Lloyd, C..D., and Atkinson, P.M., 2002, Deriving DSMs from LIDAR data with kriging, International Journal of Remote Sensing, 23(12): 2519–2524. Lohr, U., 1998, Digital elevation models by laser scanning, Photogrammetric Record, 16:105–109. Madsen, S.N., Zebker, H.A., 1999, Synthetic Aperture Radar Interferometry : Principals and applications, Manual of Remote Sensing, Boston, MA: Artech House, vol. 3 ch. 6. Magnussen, S., and Boudewyn, P., 1998, Derivations of stand heights from airborne laser scanner data with canopy-based quantile estimators, Canadian Journal of Forestry Research, 28: 1016–1031. Makarovic, B., 1979, From progressive to composite sampling for digital terrain models, Geo-Processing, 1:145–166. Manson, S.M., Ratick, S.J., and Solow, A.R., 2002, Decision making and uncertainty, Bayesian analysis of potential flood heights, Geographical Analysis, 34(2):112– 129. Matthews,S. A., 2002, ArcGIS Geostatistical Analyst, GIS Resource Document 02-19 (GIS_RD_02-19), online at < http://www.pop.psu.edu/gia-core/pdfs/gis_rd_0219.pdf> accessed on 17 July 2008. Marks, D., Dozier, J., and Frew, J., 1984, Automated basin delineation from digital elevation data, GeoProcessing, 2: 229- 311. Marks, K., and Bates, P., 2000, Integration of high-resolution topographic data with flood plain flow models, Hydrological Processes 14: 2109-2122. Martz, L.W., and Garberecht, J., 1992, Numerical definition of drainage network and subcatchment areas from digital elevation models, Computers and Geosciences, 18:747–761. Maune, D.F., Digital Elevation Model Technologies and applications: the DEM Users Manual (D.F. Maune, editor), American Society for Photogrammetry and Remote Sensing, Bethesda, Maryland, 539p.

46

Moore, I. D., Grayson, R. B., and Ladson, A. R., 1991, Digital terrain modelling: A review of hydrological, geomorphological and biological applications, Hydrological Processes,, 5(1), 3-30. NASA, 1999, LIDAR tutorial, online at < http://www.ghcc.msfc.nasa.gov/sparcle/sparcle_tutorial.html> accessed on 18 March 2007. Omer, C.R., Nelson, E.J., and. Zundel, A.K., 2003, Impact of varied data resolution on hydraulic modeling and floodplain delineation, Journal of the American Water Resources Association, 39(2):467–475. Petrie, G., and Kennie, J. M., 1987, Terrain modeling in surveying and civil engineering, Computer Aided Design 19(4): 171-187. Peuker, T.K., Fowler, R.J., Little, J.J., and Mark, D.M., 1978, The triangulated irregular network, In: Proceedings of the DTM Symposium. American Society of Photogrammetry - American Congress on Survey and Mapping, St. Louis, Missouri: 24–31. Pike, R.J., 1988, The geometric signature: quantifying landslide-terrain types from digital elevation models, Mathmatical Geology, 20: 491–511. Raber, G.T., Jensen, J.R., Hodgson, M.E., Tullis, J.A., Davis, B.A., and Berglend, J., 2007, Impact of LiDAR nominal post-spacing on DEM accuracy and flood zone delineation, Photogrammetric Engineering and Remote Sensing, 73: 793–804. Rosen, P. A., Hensley, S., Joughin, I. R., Li, F. K., Madsen, S. N., Rodriguez, E., and Goldstein, R. M., 2000, Synthetic Aperture Radar Interferometry, Proc. IEEE: 333-382. Satale, D., and Kulkarni, M., 2003, LIDAR in Mapping, Map India Poster Session, Map India Conference, 2003, GISdevelopment.net, online at accessed on 10 December 2006. Shepard, D., 1968, A two-dimensional interpolation function for irregularly-spaced data, Proceedings Twenty-third National Conference, Association for Computing Machinery, 517-24.

47

Shepherd. A., Rath, K., and Lawrenee,G., 2002, IFSAR for High-Resolution Elevation Mapping, Geospatial Solutions, online at < http://www.geospatialsolutions.com/geospatialsolutions/article/articleDetail.jsp?id=10242> accessed on 15 July 2008. Sithole, G., and Vosselman, G., 2004, Experimental comparison of filter algorithms for bare—Earth extraction from airborne laser scanning point clouds, ISPRS Journal of Photogrammetry and Remote Sensing, 59:85−101. Stoker, J.M., Greenlee, S.K., Gesch, D.B., and Menig, J.C., 2006, CLICK, the new USGS center for LiDAR information coordination and knowledge, Photogrammetric Engineering and Remote Sensing, 72: 613–16. Su, J.G., Bork E.W., 2006, Influence of vegetation, slope and LiDAR sampling angle on DEM accuracy, Photogrammetric Engineering and Remote Sensing, 72: 1265– 1274. Talmi, A., and Gilat, G., 1977, Method for smooth approximation of data, Journal of Computational Physics, 23: 93–123. Tate, E., 1998, Photogrammetry applications in digital terrain modelling and floodplain mapping, GRG 394: Research in Remote Sensing, online at < http://www.ce.utexas.edu/prof/maidment/grad/tate/study/remote/TermProj.html> accessed on 7 July 2008. Thompson, J.A., Bell, J. C., and Butler, C. A., 2001, Digital elevation model resolution: effects on terrain attribute calculation and quantitative soil–landscape modeling, Geoderma, 100: 67–89. Tobler, W.R., 1970, A computer movie simulating urban growth in the Detroit region, Economic Geography, 46(2): 234-240. United States Geological Survey (USGS), 1998, Standards for Digital Elevation Models, Reston, VA: USGS National Mapping Program. Wehr, A. and Lohr, U., 1999, Airborne laser scanning: an introduction and overview, ISPRS Journal of Photogrammetry, 54: 68–82. Wilson, J. P. and Gallant, C.J., 2000, Terrain Analysis: Principles and Applications, John Wiley and Sons, New York, 479 p.

48

Yang, X., and Hodler, T., 2000, Visual and statistical comparisons of surface modelling techniques for point-based environmental data, Cartography and Geographic Information Science, 27:165–175. Zhang, K. Q., Chen, S. C., Whitman, D., Shyu, M.L., Yan, J. H., and Zhang, C. C. ,2003, A Prograssive Morphological Filter for Removing Nonground Measearements from Airborne LiDAR Data, IEEE Transactions on Geoscience and Remote Sensing, 41(4): 872-882. Zebker, H. A., and Goldstein R.M., 1986, Topographic Mapping from Interferometric SAR Observations, Journal of Geophysical Research, 91(5): 4993-4999. Zimmerman, D., Pavlik, C., Ruggles, A., and Armstrong, M.P., 1999, An experimental comparison of ordinary and universal kriging and inverse distance weighting, Mathematical Geology, 31(4):375–390.

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