simulation of discrete-return lidar signal from conifer...

UNIVERSITY COLLEGE LONDON

DEPARTMENT OF GEOMATIC ENGINEERING

Simulation of Discrete-Return Lidar Signal from

Conifer Stands for Forestry Applications

Vasileios Kalogirou

September 2006

Supervisors: Dr. P. Lewis and Dr. M. Disney

Submitted as part requirement of the MSc in Remote Sensing

When setting out upon your way to Ithaca, wish always that your course be long,

full of adventure, full of lore. Of the Laestrygones and of the Cyclopes,

of an irate Poseidon never be afraid; such things along your way you will not find,

if lofty is your thinking, if fine sentiment in spirit and in body touches you.

Neither Laestrygones nor Cyclopes, nor wild Poseidon will you ever meet,

unless you bear them in your soul, unless your soul has raised them up in front of you.

C.P. Cavafy, Ithaka (1911)

i

ABSTRACT

Although there are many studies on the use of discrete-return lidar in forestry, only

few are dealing with the systematic assessment of the effect of lidar system

characteristics on the acquired data. In this study the potential impact of discrete-

return lidar acquisition parameters on the derived dataset was examined by using a

Monte Carlo Ray Tracing simulation approach, combined with detailed 3D models of

Scots pine (Pinus sylvestris). Moreover, processing of real lidar data from Thetford

Forest (UK) took place to examine the potential use of intensity and establish

empirical relationships for stand height and volume estimation.

The observations on intensity revealed different distributions according to the

first/last pulse targets. Generally ground hits have larger intensity values, if both of

the pulses are coming from the ground. The points whose first pulse was on the

canopy and only the last on the ground have significantly reduced intensity values.

The derived regression equations for stand height and volume gave mean difference -

between predicted and observed values- of 0.0128 m and 0,0973m3 respectively,

while the standard deviation of the differences was 2.78 m and 41,79m3.

The simulations showed that the lidar footprint is a crucial parameter which

determines the ability of the lidar system to record the top of the canopy as well as the

ground. As regards the effect of scan angle on the number of ground hits, the results

showed a general decrease with the scan angle, which is especially strong in high

needle-density stands. Not significant changes on the height of the canopy points were

reported as the scan angle increases. The maximum canopy height obtained by lidar,

which is regarded as a relatively stable metric of the canopy, showed sensitivity to

scan angle and sampling density. Particularly, the sampling density selectively affects

stronger the young stands than the older ones, where the maximum height does not

seem to vary. The experience gained through the simulations contributes to a better

understanding of the discrete-return lidar signal on forest canopies.

ii

ACKNOWLEDGEMENTS

First, I would like to thank Dr Philip Lewis and Dr Mathias Disney because except for

being my supervisors, they helped me to understand how tough is to make science and

I hope I satisfied a bit of their expectations. The discussions we had in front of the

computers will always remind me this dissertation.

Thanks also to all my Professors in the MSc course, whose doors were always

open for discussion and recommendations during this year. I’m particularly grateful

to: Dr Emmanuel Baltsavias for replying in my email, Steven Hancock for sharing his

knowledge on the computer simulations, as well as Melissa Turner from the UK

Environment Agency, who dealt with our request to use the lidar data of Thetford

Forest. Finally, I would like to thank NATO and the Greek Ministry of Foreign

Affairs for sponsoring my studies in UCL.

Particular thanks to my family for the support and love, and all of my friends

here in London and back in Greece.

iii

CONTENTS

ABSTRACT............................................................................................... i

ACKNOWLEDGEMENTS .................................................................... ii

CONTENTS............................................................................................. iii

LIST OF FIGURES ..................................................................................v

LIST OF TABLES ................................................................................ viii

ACRONYMS........................................................................................... ix

ACRONYMS........................................................................................... ix

1. INTRODUCTION..............................................................................1

1.1 PROJECT AIMS .........................................................................................1

1.2 REMOTE SENSING OF FOREST ENVIRONMENTS..........................1

1.3 LIDAR: PRINCIPLES AND INSTRUMENTS ........................................4

1.4 LIDAR IN FORESTRY ..............................................................................5

1.4.1 THE FIRST STUDIES.........................................................................5

1.4.2 NEWER STUDIES ...............................................................................6

1.5 MODELLING OF LIDAR SIGNAL .........................................................9

1.6 STUDY FRAMEWORK AND OUTLINE ..............................................11

2. DATA / MODELS AND OTHER RESOURCES.........................13

2.1 THETFORD FOREST ..............................................................................13

2.2 LIDAR DATA ............................................................................................14

2.3 FOREST MODEL .....................................................................................16

2.4 FORWARD RADIOMETRIC TRACER - FRAT..................................17

2.5 ADDITIONAL DATASETS AND OTHER RESOURCES...................17

3. PROCESSING OF LIDAR DATA.................................................19

3.1 FOREST STANDS SELECTION ............................................................19

3.2 FILTERING OF THE LIDAR POINTS .................................................22

3.2.1 RELATED LITERATURE AND IDEAS...........................................22

3.2.2 RESULTS ON FILTERING ..............................................................24

3.3 CLASSIFICATION OF THE LIDAR POINTS .....................................28

3.4 RESULTS ...................................................................................................29

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3.4.1 INTENSITY ........................................................................................29

3.4.2 REGRESSION MODELS OF STAND HEIGHT AND VOLUME .30

3.4.3 GAP PROBABILITY ..........................................................................34

4. SIMULATIONS ...............................................................................39

4.1 METHODS .................................................................................................39

4.2 RESULTS ...................................................................................................42

4.2.1 FOOTPRINT DIAMETER.................................................................42

4.2.2 SCAN ANGLE ....................................................................................45

4.2.3 SAMPLING DENSITY.......................................................................49

5. DISCUSSION ...................................................................................52

5.1 REAL LIDAR DATA PROCESSING .....................................................52

5.2 SIMULATIONS .........................................................................................55

5.3 FUTURE WORK.......................................................................................59

6. CONCLUSIONS ..............................................................................61

REFERENCES........................................................................................61

APPENDIX A1: LIST OF WRITTEN PROGRAMS.........................78

APPENDIX A2: EXAMPLES OF WRITTEN CODE........................80

APPENDIX B: NORMALIZED HEIGHT DISTRIBUTIONS .........87

APPENDIX C: ADDITIONAL FIGURES AND TABLES................91

v

LIST OF FIGURES

Figure 1: Illustration of the difference between waveform and discrete return lidar

recording (from Lefsky et al., 2002; Figure 1). ............................................................4

Figure 2: Canopy Height Model (CHM) created by small-footprint lidar (a), and the

predicted versus the actual biomass (from Bortolot and Wynne, 2005; Figures 3 and

8). ...................................................................................................................................7

Figure 3: The location of Thetford Forest. The mosaic was created using images from

EDINA Digimap (A and B, http://edina.ac.uk/digimap/ ) and Google Earth (C). ......13

Figure 4: The distribution of stand ages for the two dominating species of the

Thetford Forest (after Skinner and Luckman, 2000, Appendix A)..............................14

Figure 5: Scots pine trees for ages 10, 20, 30 and 40 (right to left). The scene

reflectance was simulated with the frat optical model at a wavelength of 1064 nm. ..16

Figure 6: Example of simulated image having a footprint of 30 cm on a 25 years-old

pine stand (left). The scene reflectance was simulated using the frat optical model at a

wavelength of 1064 nm. On the right a real Scots pine picture in black and white. ..17

Figure 7: The flowchart of the selection process. .......................................................20

Figure 8: The 31 selected stands coloured according to their age (Image by Google

Earth)............................................................................................................................21

Figure 9: Side-looking aspect of the first and last pulse points. .................................22

Figure 10: The local neighbourhood filtering process. The blue points are the local

minimums of the grid cells. The red point is the local minimum of the current tested

window. The largest slope is the one created by the green point and if its value

exceeds the threshold then the Z value of the red point is reduced. ............................24

Figure 11: The percentage of points that were modified by the slope filter, for

different window sizes and stands. ..............................................................................25

Figure 12: Non-normalized height distribution of points classified as ground by the

filtering process (example from stand #22). The effect of window size can be seen in

the maximum height and SD (More diagrams are included in the CD). .....................26

Figure 13: Distributions of the normalized height after the simple LM and the

improved LM with the slope filter. Significant differences exist in stands with high

vi

LAI, while in very young or old stands the two algorithms give similar distributions.

......................................................................................................................................27

Figure 14: No significant relationship between the stand age and the mean stand

intensity was found. However, there is a trend according to the point class. ..............29

Figure 15: The distribution of the intensities of the points on stand #20 ...................30

Figure 16: Stand age against the height of C/C lidar points. ......................................31

Figure 17: Mean stand height against the mean height of C/C points. Asterisks

represent field-measured stand height, while open circles are allometric-derived stand

height............................................................................................................................31

Figure 18: Scatterplot of observed mean stand height against estimated stand height

using cross-validation. .................................................................................................32

Figure 19: Standard deviation of the height of the lidar points (m) against stand

volume (m3). 3 stands were rejected from the calculation due to the presence of outlier

trees (red asterisks). .....................................................................................................33

Figure 20: Scatterplot of observed volume against estimated volume from lidar data,

using the regression model...........................................................................................33

Figure 21: The change in the percentage of C/C (left) and G/G (right) points as the

stand is growing. ..........................................................................................................34

Figure 22: Lidar points plotted in X,Y. The overlap areas can be seen (yellow) and

the flight line can be delineated (red). The blue points have scan angle ±5o according

to the mean flight altitude (also see Figure C1 on Appendix C). ................................36

Figure 23: In stand #9 the presence of the road in the far-range points resulted in

increased gap probability. The red line is the flight line and the colours represent the

height above ground.....................................................................................................37

Figure 24: LAI h values calculated from lidar data, for stands with different age......38

Figure 25: Generation of first and last return points on a 15 (up) and 25 (down) years

old pine with the footprint set to 30 cm. ......................................................................40

Figure 26: Footprint diameter plotted against the percentage of ground hits for

different stand ages (Up: First pulse; Down: Last pulse). ...........................................42

Figure 27: (A) Percentage of points on top, (B) maximum height and, (C) mean

height of the canopy hits plotted against footprint diameter, for different stand ages.43

Figure 28: The normalized height difference against the footprint diameter for

different stand ages: (A) Canopy points only, (B) all the first pulse points. ...............44

vii

Figure 29: Influence of scan angle on the percentage of points which hit the top of the

canopy for different stand age (stem density is 3 m). ..................................................45

Figure 30: The percentage of ground points of the first (A) and last (B) pulse, for

different scan angles and stand ages. The line on (A) is the regression model line

obtained from the real data (Figure 21-right) and the lines on (B) are showing the

value’s range. ...............................................................................................................46

Figure 31: Normalized height difference against the scan angle for different stand

ages: .............................................................................................................................47

Figure 32: Increment of mean height of all the points from nadir-view to 20 degrees

scan angle. Different stand ages and two stem densities were tested. .........................47

Figure 33: The change of maximum height from nadir to 10 (blue) and 20 (red)

degrees of scan angle for: (A) stem density of 3 m and (B) stem density of 1,5 m.....48

Figure 34: The effect of sampling density on: (A) number of first-pulse points that hit

the canopy top, (B) number of last-pulse points to hit the ground. .............................49

Figure 35: Effects of sampling density on the maximum canopy height metric. The

increment between 0.5 and 4 pts/m2 is given for different stand ages.........................50

Figure 36: The change of mean height of all (A) and canopy-only points (B).

Comments can be found on the discussion (Chapter 5)...............................................50

Figure 37: Figure from Moffiet et al. (2005). Difference on the distribution of

intensity return of ground points of C/G and ground points of G/G. The results agree

with the observations of this study. (From Moffiet et al., 2005; Figure 8)..................53

Figure 38: The waveform recorded for the same point using two different footprints.

......................................................................................................................................56

viii

LIST OF TABLES

Table 1: Technical specifications of the Optech ALTM 1210 (Baltsavias, 1999a)....14

Table 2: The selected stands with relevant information..............................................20

Table 3: An example of how the top of the canopy was defined. ...............................41

Table 4: The mean canopy height values (m) for different footprint diameters. ........55

ix

ACRONYMS

ALS Airborne Laser Scanning

AVHRR Advanced Very High Resolution Radiometer

CC Canopy first/Canopy last point

CG Canopy first/Ground last point

CHM Canopy Height Model

DSM Digital Surface Model

DTM Digital Terrain Model

fAPAR Fraction of Absorbed Photosynthetically Active Radiation

GCOS Global Climate Observing System

GTOS Global Terrestrial Observing System

FAO Food and Agriculture Organization

GG Ground first/Ground last point

IFOV Instantaneous Field Of View

LAI Leaf Area Index

LiDAR Light Detection And Ranging

LM Local Minima

MCRT Monte Carlo Ray Tracing

MODIS Moderate Resolution Imaging Spectroradiometer

NHD Normalized Height Difference (Chapter 4.1)

NPHD Normalized Predominant Height Difference

NOAA National Oceanic and Atmospheric Administration

OSGB36 Ordnance Survey Great Britain 1936 (Datum)

POG Percentage of lidar Points On Ground

POT Percentage of lidar Points On the Top of the canopy

SHAC SAR and Hyperspectral Airborne Campaign

TIN Triangulated Irregular Network

TREES Tropical Ecosystem Environment observation by Satellite

Chapter One: Introduction

1

1. INTRODUCTION

1.1 PROJECT AIMS

This study investigates the effect of discrete-return lidar acquisition parameters on the

derived dataset. The impact of footprint diameter size, scan angle and sampling

density on the dataset metrics is examined, under different stand age and density

conditions, by using simulated forest scenes.

1.2 REMOTE SENSING OF FOREST ENVIRONMENTS

Remote sensing of forest environments goes back to the early 20s, when the first

aerial photographs started to be used for vegetation mapping (Steddom et al., 2005).

However, their development as a major tool in forestry mainly took place in the

United States since 1940 (Spurr, 1948). During the last decades, analogue processing

with photogrammetric instruments and photo-mensurational techniques has been

gradually replaced by digital airborne and satellite imagery.

The usefulness of satellite remote sensing was realised on global scale forest

assessments, where airborne data were too expensive to use. Many global projects,

especially in the tropics, made use of satellite data to assess forest resources. For

example, the TREES project (European Commission, 1997) set up by the European

Commission and the European Space Agency in 1990, used NOAA AVHRR 1km and

Landsat TM data, while the FAO Remote Sensing Survey (FAO, 1996) was based

only on Landsat TM images.

Optical or radar remote sensing data have been extensively used over the last

decades in forestry and ecology for: i) mapping forest damage (Vogelmann and Rock,

1988; Ardo et al., 1997), ii) mapping defoliation (Williams and Nelson, 1986;

Ekstrand, 1990; Radeloff et al., 1999; Hurley et al., 2002;), iii) monitoring

deforestation (Gilrouth and Hutchinson, 1990; Skole and Tucker, 1993; Alves et al.,

1999; Zhang et al., 2005), iv) burnt area mapping (Hitchcock and Hoffer, 1973;

Takeuchi, 1983; Tanaka et al., 1983; Koutsias and Karteris, 1998; Stroppiana et al.,

2002), v) assessment of forest structure and landscape dynamics (Treuhaft and

Cloude, 1999; Treuhaft and Siqueira, 2000; Peralta and Mather, 2000; Hung and Wu,


2

2005), vi) classification of species (Franklin et al., 1986; Franklin, 1994; Mickelson et

al., 1998) etc.

The derivation of forest attributes through remote sensing has been extensively

investigated during the last few years. Empirical and analytical approaches have been

used in many studies to establish relationships between forest properties (e.g. crown

diameter, forest cover etc) and the remotely-sensed signal. Empirical models are

usually site-specific, since the data are collected ‘locally’ and thus are not often

applicable when extrapolated to new areas or data (Skidmore, 2002). On the other

hand, analytical models (e.g. canopy reflectance models) first establish a physical

understanding of the remote sensing signal and give a formulated description which

can be inverted, enabling the calculation of a variable through remote sensing data.

The leaf area index (LAI – one sided leaf area per unit ground area) is

considered to be a key parameter for forest ecosystem processes, mainly due to its

connection with photosynthesis, respiration, transpiration, carbon and nutrient cycle,

and rainfall interception (Bonan, 1993). A variety of remote sensing data have been

used for LAI derivation. Recently, Soudani et al. (2006) examined empirical

relationships between IKONOS, SPOT and ETM+ data with spectral bands and

indexes. Similar study by using backscattering ratios of ENVISAT ASAR was done

by Manninen et al. (2005), while Pu and Gong (2004) utilised wavelet transform on

EO-1 Hyperion data. The above studies highlight the variety of remote sensing data

which was used for LAI estimation. However, the majority of the past attempts were

mainly based on empirical relationships between in situ-measured LAI and spectral

bands or index values, which have been proved to be limited (e.g. the relationship is

weak or saturates on high LAI values) (Gobron et al., 1997).

Today, global estimates of LAI and fAPAR (fraction of absorbed

photosynthetically active radiation) can be obtained from the NASA’s MODIS

products (MODIS website, 2006). The algorithm is using a look-up-table method to

estimate reflectance as a function of view/illumination angles and wavelength and is

based upon a six-biome land cover structural classification (6BSLCC) (see Myneni et

al., 1997, 2002). There is also the MODIS BRDF/Albedo product, based on an

algorithm which uses a semi-empirical kernel-driven BRDF model (RossThick-

LiSparse-Reciprocal) to retrieve surface BRDF and albedo (Strahler et al., 1995;


3

Schaaf et al., 2002)1. Moreover, monthly fAPAR values can be obtained from MERIS

Global Vegetation Index (ESA website, 2005). These examples illustrate that space

agencies recognise the usefulness of such products for the scientific community. Thus,

they are able to assess and satisfy the market’s need. Relevant products, like the ones

discussed above, are useful in variety of studies of terrestrial ecosystems like leaf

phenology detection (Xiao et al., 2006; Huete et al., 2006). Moreover, LAI/fAPAR

products are important for global observing systems as GCOS (climate) and GTOS

(terrestrial ecosystems) to meet the needs of their clients (FAO, 2001).

However, the forest sector’s view for biophysical parameters estimation differs

from the one described above. In forest practise, terms like LAI, fAPAR or albedo are

rarely used. Forest managers are more interested on attributes like: growing stock

(stem volume), basal area, mean tree height, diameter on breast height, canopy cover

etc2. Some of those parameters (e.g. growing stock and canopy cover) are connected

with LAI and some of them have statistical nature (e.g. basal area) and cannot be

measured straightforward on the field, but require allometric calculation. Much

remote sensing research has focused on the extraction of forest stand parameters using

optical (Franklin, 1986; Stenback and Congalton, 1990; Ardo, 1992; Curran et al.,

1992; Cohen et al., 1995; Trotter et al., 1997; Hyyppä et al., 2000; Franco-Lopez et

al., 2001; Lu et al., 2004; Muukkonen and Heiskanen, 2005) and microwave radar

data (Le Toan et al., 1992; Israelsson et al., 1994; Rauste and Hame, 1994; Fransson

and Israelsson, 1999; Santoro et al., 2001; Sun et al., 2002).

The majority of the aforementioned studies concentrated on obtaining forest

stand parameters, by relating them with spectral bands, backscatter coefficients or

indexes. As expected the results were disappointing, since the structural information

of a forest has a geometric rather than radiometric nature (St-Onge et al. 2003).

During the last decade LIDAR3 (light detection and ranging) became a common

technique to obtain canopy or individual tree information. Many published studies

agree that lidar technology provides unique view of the forest structure, which can be

used to obtain other forest variables as diameter at breast height, volume and density

(Hyyppä et al. 2001, Næsset and Bjerknes 2001, Schardt et al. 2002). The next

chapters will try to briefly review the lidar principles and applications in forestry. 1 See also the special issue of Remote Sensing of Environment [Volume 83(1-2)] on MODIS. 2 Definitions of those terms can be found on the internet (e.g. USDA Forest Service Glossary http://www.srs.fs.usda.gov/sustain/data/authors/glossary.htm ). 3 The term LIDAR will be used in small letters hereafter (lidar).


4

1.3 LIDAR: PRINCIPLES AND INSTRUMENTS

As Wagner et al. (2004) notice “Laser scanning is a direct extension of conventional

radar techniques to very short wavelengths”. The laser device of the lidar system

emits a pulse of light towards a target. The pulse travels to the target, where it gets

reflected back and the sensor captures the backscatter energy. From the round-trip

travel time and knowing the speed of light, the distance between the sensor and the

reflecting target can be calculated. Using additional information of the position and

attitude (pointing vector) of the sensor one can determine the 3D position of each

target. A variety of wavelengths can be used ranged from visible to near-infrared;

however, near-infrared is preferred in vegetation studies due to the high reflectivity of

vegetation in this part of the electromagnetic spectrum. Wehr and Lohr (1999) and

Baltsavias (1999a,b) provide details of lidar theory on a theme issue of ISPRS Journal

of Photogrammetry & Remote Sensing, dedicated to airborne laser scanning (ALS).

Figure 1: Illustration of the difference between waveform and discrete return lidar recording

(from Lefsky et al., 2002; Figure 1).

There are two distinct types of lidar systems in the commercial and research

sectors (St-Onge et al., 2003): full waveform and discrete return (see Figure 1). The

categorisation is related with the sampling density of the derived signal. In the first

case, the laser energy is densely sampled resulting in a full waveform recording. This


5

top-to-bottom information enables viewing of the vertical structure of a stand. The

waveform recording is a major advantage of full waveform lidars, due to the fact that

is connected with foliage density and structure and can be translated into a detailed

description of vertical canopy volume distribution (Lefsky et al., 1999a,b; Ni-Meister

et al., 2001). The ground sampling area (footprint) of full waveform systems varies

from 8 to 70 m (Means, 1999; Harding et al., 2000).

On the other hand, discrete return lidar systems, typically record one (e.g., first

or last), two (e.g. first and last), or a few (e.g. five) returns for each pulse (Lim et al.,

2003a). The footprint of discrete return lidar surveys varies from 0.2 to 0.9 m. as a

function of flight altitude, beam divergence and instantaneous scan angle (Baltavias,

1999b). Means (1999) provides a detailed comparison between discrete return and full

waveform lidar systems.

The majority of commercial lidar instruments utilise the discrete-return logic

and are carried aboard airplane platforms or helicopters. As already mentioned,

Baltsavias (1999a) reviews the available lidar systems across the globe; however due

to the quick development of the market, online resources can be accessed for up-to-

date information (see www.airbornelaserscanning.com for a lidar industry directory4).

At the moment, full waveform recorders are not widely available and most of them

are experimental instruments. NASA’s Goddard Space Flight Centre has developed a

series of waveform-recording laser altimeters mainly for vegetation studies including

SLICER (Scanning Lidar Imager of Canopies by Echo Recovery, Harding et al.,

1994), SLA (Shuttle Laser Altimeter, Garvin et al., 1998), VCL (Vegetation Canopy

Lidar, Dubayah et al., 1997) and its “airborne version” LVIS (Laser Vegetation

Imaging Sensor, Blair et al., 1999). The first laser altimeter to operate in a polar orbit

is the NASA’s GLAS (Geoscience Laser Altimeter System) aboard ICESat (Ice,

Cloud and land Elevation Satellite).

1.4 LIDAR IN FORESTRY

1.4.1 THE FIRST STUDIES

4 Last accessed 8th August 2006.


6

Research on lidar applications in forestry began in the former Soviet Union, Canada

and United States. According to Nelson et al. (1997) the first investigations took place

in the former Soviet Union, where researches developed the theory and hardware to

measure tree heights and stand densities using laser profilograms (Solodukhin et al.,

1977a,b; 1979; 1985; Stolyarov and Solodukhin, 1987). Even from these early

studies, Russian investigators analysed and quantified the underestimation of canopy

height by the laser pulse.

In the West, according to Lim et al. (2003a), the first studies were carried out by

the Canadian Forestry Service during the early 1980s. The potential of profiling lidar

for the estimation of stand heights, crown cover density and ground elevation was

studied by Aldred and Bonner (1985), while Arp et al. (1982) used lidar to map

tropical forests in Central America. One of the first comparative studies was done by

Krabill et al. (1980), which showed that photogrammetrically and lidar derived

contours agree within 50 cm in forested areas. Furthermore, Nelson et al. (1984,

1988a,b) have done series of evaluation studies on lidar ability to estimate forest

height, canopy density and biomass. Finally, MacLean and Krabill (1986) reported

high coefficients of determination (0.72 to 0.89) for predictive models of volume.

These early studies concluded that laser data is a promising alternative

technology for forestry applications. However, the performance and accuracy of the

measurements was strongly depended on the accurate location of the path of the laser

profile on the ground (Nelson et al., 1997). As a result the application of lidar was

limited in areas with adequate ground control. The global positioning system (GPS)

and the improvement of inertial measurement units (IMU or INS – inertial navigation

systems) enabled the development of lidar technology (Ackermann, 1999).

1.4.2 NEWER STUDIES

The research activity regarding lidar applications in forestry is mainly concentrated in

Canada, United States, Scandinavia and Central Europe (e.g. Germany). A general

demonstration of the background of the subject is given by Dubayah and Drake

(2000), while Lim et al. (2003a) provide a review of lidar applications on forests. In

addition, Hyyppä et al. (2003), Næsset (2003) and Nilson et al. (2003) review the


7

Finnish, Norwegian and Swedish experience, respectively, on laser scanning of forest

resources.

Many studies focused on the estimation of canopy and tree height, which is

logical due to their importance in operational forestry. Canopy and tree height can

also be used as predictor variables for other stand attributes, as biomass (a summary

table of lidar studies for biomass estimation can be found on Bortolot and Wynne

(2005)). On stand scale, discrete-return lidar point metrics (e.g. mean and maximum

height, quantiles etc) have been used as independent variables in regression analysis

to estimate mean and dominant height, mean diameter, basal area and other stand

variables (Nilsson, 1996; Næsset, 1997a,b,2002; Magnussen and Boudewyn, 1998;

Means et al., 2000). However, stand-level approach for mean or dominant height

prediction is influenced by the species and canopy structure (St-Onge et al., 2003).

Some models include variables which are related with the canopy density -as the

number of canopy hits divided by the total number of transmitted pulses- to optimize

the prediction (Næsset and Bjerknes, 2001).

Figure 2: Canopy Height Model (CHM) created by small-footprint lidar (a), and the predicted

versus the actual biomass (from Bortolot and Wynne, 2005; Figures 3 and 8).

Extending the stand-scale tree height measurement, other studies concentrated

on individual tree height and crown diameter estimation (St-Onge, 1999; Lim et al.,

2001). For individual tree detection high-pulse-rate laser scanners have to be used, to

provide multiple laser pulses per square metre. Some researches used a segmentation

approach to detect individual trees and then calculate the height (Hyyppä et al., 2001;

Persson et al., 2002; Popescu et al., 2003). A normalized canopy height model (CHM

– see Figure 2) is first created by interpolating the lidar points and then image

processing algorithms (e.g. texture analysis, local maxima etc.) can be used to


8

segment the image and detect individual trees. In other words, the 3D information is

transformed in a 2D image in order to take advantage of the processing tools that

already exist.

Nevertheless, the processing step from raw lidar data to a DSM or CHM always

results in information loss. Working with raw lidar data has been increasing, although

the processing of huge lidar files on larger scales becomes difficult (Morsdorf et al.,

2004). Andersen et al. (2001, 2002) applied three-dimensional mathematical

morphology and Bayesian object recognition on the lidar cloud to reconstruct the

forest scene and extract individual tree measurements.

A similar study, based on the construction of a vector model was carried out by

Pyysalo and Hyyppä (2002), while Morsdorf et al. (2003) applied 3D-segmentation on

lidar data using K-means clustering, driven by seed points which were collected with

a typical Local Maxima algorithm. The results show that individual tree height

measurements are comparable to the field measurements, with the height error to be

less than 1.5 m for most of the cases. However, tree positioning and measurement of

crown diameter are problematic in very dense stands where several trees can be found

inside a radius of 1m. Finally, Yu et al. (2004a) applied automatic detection of

harvested trees and estimation of forest growth by using lidar data of two acquisitions,

with a time interval of two years. 61 out of 83 harvested trees were correctly detected

and growth rates for different height classes of pine and spruce were obtained.

Extending the field of lidar applications in forestry, other researches investigated

connections between the lidar signal and foliage parameters. Hinsley et al. (2002)

examined how lidar data can assist woodland structure quantification and habitat

quality analysis. Furthermore, regression analysis has been used to develop predictive

models for canopy fuel parameters estimation (Riaño et al., 2003; Andersen et al.

2005). The methodology can be used for the creation of maps that can serve as an

input into fire-behaviour models.

More recently, Solberg et al. (2006) used the Beer-Lambert Law for LAI

estimation and found a strong relationship between ground-based and lidar-derived

LAI measurements. Gap fraction was calculated as the ratio of below canopy echoes

to the total number of echoes. The final results of LAI estimations were used to

produce a defoliation map of the study area.

From the literature review it seems that small footprint discrete-return lidar

systems are used for applications more relevant to the needs of operational or


9

commercial forestry. On the other hand large footprint full waveform lidar systems

are mainly used in environmental studies which concentrate on derivation of

parameters related with the carbon cycle as LAI and gross primary production (Lefsky

et al., 1999b; Drake et al., 2002; Kotchenova et al., 2004). Since this study

concentrates on discrete return lidar the review will not be extended in large footprint

studies or terrestrial laser scanning.

Finally, it should be mentioned that lidar data can be integrated with optical or

radar data to assist the extraction of the desired information. Hudak et al. (2002) used

regression, kriging and cokriging on Landsat ETM+ data to interpolate canopy height

measurements made by lidar. Similarly, Wulder and Seemann (2003) used segmented

Landsat imagery with lidar data to update height information for forest inventory

purposes. Except Landsat, high resolution data has been used to take advantage of the

fine optical detection of crowns. For example, aerial photography has been combined

with airborne lidar data to estimate canopy and individual tree height (St-Onge and

Achaichia, 2001; Suárez et al. 2005). The fusion of lidar height points with other data

is a promising research area, mainly because it enables the combination of different

advantages, according to the nature of the data.

1.5 MODELLING OF LIDAR SIGNAL

In recent decades, particular effort has been devoted to understand the signal, which is

sensed by Earth Observation instruments. Canopy scattering models have been

developed mainly to examine how the vegetation structure and spatial distribution,

BRDF effects, or other physiological conditions, can influence the recorded signal.

Since, the lidar signal used in vegetation studies is near-infrared radiation, is expected

to obey the general framework and rules of modelling in the infrared part of

electromagnetic spectrum. However, lidar signal modelling has some characteristic

properties that should be taken into account (Disney et al., 2006; also reviewed by

Heyder, 2005):

There are no shadowing effects, since the illumination and viewing angle are the

same.

Acquisition of time resolved measurements. As a result, a sufficient description

of the canopy is needed, in contrast with traditional reflectance modelling.


10

Multiple scattering can have important influence on the distance measurements,

especially in the case of large footprint lidar.

The pulse shape and energy distribution across the footprint (spread function)

are typically Gaussian.

The sky condition and illumination (direct and diffuse) properties do not change

over the time of the lidar measurement.

One classical modelling approach is the use of radiative transfer models (Ross,

1981). Radiative transfer models, assume the canopy to be a horizontally uniform

medium, made of layers of absorbing and scattering particles (Li and Strahler, 1992).

However, for lidar modelling this approach is problematic due to the insufficient

representation of forest heterogeneity and the weakness to get time-resolved

measurements. Although adaptations can be made, the complexity of the solution is

increasing (Kotchenova et al., 2003).

Geometric optical models (GO) have been developed to model the optical

scattering behaviour of heterogeneous canopies. Geometric optical models enable the

calculation of projection and shadowing effects, while they can also be coupled with

radiative transfer models (e.g. Sun and Ranson, 2000; Ni-Meister et al., 2001).

Moreover, the three-dimensional position of the scatterers can be easily calculated, in

contrast with radiative transfer models. However, as mentioned above lidar is

operating in “hotspot” mode, which means that there are no actual shadowing effects.

During the recent decades, the rapid growth of computers led to dramatic

increase of computing power, which enabled the development of computer simulation

models. An explicit three-dimensional description of the canopy can be made using

simple objects to represent parts of the actual canopy. For example, starting from the

shape of a needle (e.g. cylinder) it is possible to define a function of phyllotaxy to

construct a shoot, which can be placed upon a branch. In this way a single artificial

tree can be represented in space. Moreover, each primary element can have a specific

description of its radiometric properties and as a result light interaction can be

simulated. Explicit 3D description of the canopy reduces the number of assumptions

as the ones related with the distribution of the vegetation or the shape of the crown

and as a result improves the accuracy and robustness of the result.

The construction of an image in the 3D computer-graphics environment involves

the use of a rendering method; in other words, the selection of the model which will

combine geometry, viewpoint, texture and lighting information to construct the final


11

image. Disney et al. (2000) group the numerical methods for the treatment of

scattering into a medium (using both the “volumetric and deterministic” definitions)

in two large categories: Radiosity and Ray Tracing methods. Radiosity methods only

deal with the global radiance transfer between objects and as a result position-

dependent effects as specular lighting or refraction cannot be simulated (Wikipedia,

2006a).

In Ray Tracing, the main idea is to trace a ray of light through a scene. This

enables path length calculation and as a result is particularly applicable in modelling

lidar acquisition (Govaerts, 1996; Roberts, 1998). A review on the use of Monte Carlo

Ray Tracing (MCRT) in optical canopy reflectance modelling can be found on Disney

et al. (2000). As concluded in the above review, the simplicity, robustness and

flexibility of MCRT methods combined with the ability to deal with explicit 3D

representations of canopy structure “has led to increasing interest in MCRT methods

over the last decade”.

1.6 STUDY FRAMEWORK AND OUTLINE

The study will try to examine relationships between lidar scan angle, footprint size

diameter and sampling density on different stands, in order to investigate if their

impact on the derived dataset can be significant. Computer simulations using MCRT

and 3D representation of forest stands are utilised for the examination. The key

questions that this study tries to address can be phrased as: Since lidar is a sampling

technology, what is the effect of sampling characteristics and forest stand properties

on the obtained results? Can these characteristics lead to bias in the results? In what

degree can the bias -if any- affect the use of the dataset for forestry applications?

The author believes that the answers of the above questions will: (i) contribute

to a better understanding of the nature of lidar, (ii) enable efficient handling of the

lidar datasets and (iii) complete our knowledge of discrete-return lidar on forest

canopies. Some recent studies, although following different methodology, try to

address these questions (Holmgren et al., 2003; Lovell et al., 2005). Moreover, other

studies on the effects of flight altitude and footprint diameter size use data from lidar

surveys to examine their impact on the dataset (Hirata, 2004; Yu et al., 2004b). The

difficulty of the above approach derives from the inability to study the impact of

individual parameters separately, because most of them are connected and cannot be


12

isolated. For example, increase of the flight altitude enables different footprint

diameters to be applied; however this affects the sampling density. In the computer

environment these parameters can be studied separately, enabling many scenarios to

be applied and of course without the cost of a flight survey.

In a recent article Næsset (2005) conclude that “Further studies are required to

assess systematically how and to what extend different system characteristics affect

the canopy properties derived for different canopy types”. This study belongs in the

framework described by Næsset.

The next Chapter provides essential description of the resources / materials that

were used in this study. The methodology and results of the processing of the “real”

lidar data can be found on Chapter 3. The Chapter explains the whole process from

the filtering of the lidar point-cloud to the calculation of empirical relationships for

stand height and volume estimation. Moreover, an attempt to derive LAI from the

lidar points is being made. Chapter 4 provides an explanation of how the simulations

were prepared and Chapter 5 discusses the obtained results.

Chapter Two: Data / Models and Other Resources

13

2. DATA / MODELS AND OTHER RESOURCES

In this chapter, essential information about the used resources can be found. Firstly,

the Thetford Forest, from where the lidar data was collected, is described. Afterwards,

information about the lidar dataset and the forest model are given, followed by a brief

discussion on the simulation programme. Finally, the last subchapter describes the

additional datasets, which were the Forestry Commission database and the ground

measurements of SHAC 2000 campaign, finishing with a small paragraph on the

software used.

2.1 THETFORD FOREST

As already mentioned, the available lidar dataset covers the area of Thetford Forest

(52o27΄Ν, 0ο40΄Ε). Thetford Forest is the largest man-made pine forest in Britain and

is located in East Anglia, UK, between the north of Suffolk and the south of Norfolk,

approximately 45 km east of Norwich (Wikipedia, 2006b). The forest was created in

1914 for timber production and is now managed by the Forestry Commission, who is

responsible for maintenance of each stand and performance of all the essential

management operations, as planting, clearing and thinning (Skinner and Luckman,

2000).

Figure 3: The location of Thetford Forest. The mosaic was created using images from EDINA

Digimap (A and B, http://edina.ac.uk/digimap/ ) and Google Earth (C).


14

The dominant tree species of the area are the Pinus nigra var. maritima

(Corsican pine) and Pinus sylvestris (Scots pine). The former has been introduced into

the British Isles, while the latter is native (Royal Forestry Society, 2006). The

majority of the forest stands are even-aged and are managed using the classical ‘forest

chain’ process for UK’s woodlands, that differs from the Continuous Cover Forestry,

which emphasises more on quality than quantity of timber (Mason et al., 1999).

Generally, the stands of Scots pine are mature to old, while the Corsican pine stands

are more evenly distributed in many age classes (Figure 4). The elevation of the area

ranges from 10m to 50m above sea level, with gentle topography.

Figure 4: The distribution of stand ages for the two dominating species of the Thetford Forest

(after Skinner and Luckman, 2000, Appendix A).

2.2 LIDAR DATA

The lidar data of the Thetford Forest were acquired on 10th of June 2000 by the UK

Environment Agency. The used airborne laser scanning (ALS) device was the

Optech’s ALTM 1210, which uses an oscillating mirror. Technical information

concerning the ALS system can be found on Table 1.

Table 1: Technical specifications of the Optech ALTM 1210 (Baltsavias, 1999a).

Operating altitude 400-1200m (2000m. optional)

Scan principle / pattern Oscillating mirror / Z-shaped

Laser wavelength 1047nm Scan angle 0o to ±20o

Scan frequency Depending on scan angle

30Hz for ±20o 50Hz for ±10o

Pulse rate 10kHz Beam divergence 0,30 mrad


15

Number of echoes per pulse First & last Intensity recording Yes

Pulse width 8ns Range accuracy 2cm

Elevation/depth accuracy <15cm (1σ)

The flying altitude varied from 850 to 990m above ground level, which resulted

in an average ground swath width of 404m (Hamdan, 2004). As regards the laser

footprint diameter, it should be noted that it varied according to the flying altitude and

the instantaneous scan angle. Taking into account that the laser beam divergence (γ)

of the ALS system is 0.30 mrad, and by using the formula 1 provided by Baltsavias

(1999b), then the range of the footprint diameter can be calculated.

γϑ )(cos2

instLinst

hA = (1)

ALinst = instantaneous laser footprint diameter (m)

h = flying altitude over the ground (m)

γ = laser beam divergence or IFOV (mrad)

θinst = instantaneous scan angle (deg)

According to this calculation the footprint diameter varied from 25.5cm. (for the

minimum flying altitude and 0o scan angle) to 33.6cm. (for the maximum flying

altitude and 20o scan angle). The sampling density is depended on the specific

position of a region, in relation with the flight lines. Some forest stands felt inside the

overlap areas, while others were scanned only once. On average, one laser hit was

recorded every 3 to 8 m2. The timing and intensity of both the first and last significant

return for each laser pulse were recorded. The correction that took place to the data

and the level of initial processing are not known. The lidar points were supplied as

comma separated .txt files in the following format:

X_last , Y_last , Z_last , I_last , X_first , Y_first , Z_first , I_first

where the first/last flag states whether the field is related with the first or last pulse,

the X and Y are the coordinates into the British National Grid Eastings and Northings,

the Z field contains the height information in meters above sea level datum (OSGB36

Datum) and the I is the recorded intensity.


16

2.3 FOREST MODEL

Detailed structural information is very important particularly when simulating

radiation in the optical domain, as lidar signal (Disney et al., 2006). As already

mentioned in the introduction, Lovell et al. (2005) in a simulation study of lidar

assumed that the trees are solid objects. This approach is not suitable for lidar

simulations, since penetration through the canopy is an important property of the lidar

dataset. Holmgren et al. (2003) reported bias in their results, using a similar

simulation methodology. In this study, a detailed 3D representation of the coniferous

canopy structure was taken by the Treegrow model, developed by Leersnijder (1992).

The modelled trees are quite realistic and only some details are not incorporated, like

the effect of gravity on the needles (see Figure 6).

The model was parameterised to match the observed height and diameter growth

curves. Environmental, species-specific and tree-specific parameters are driving the

model to ‘grow’ a single tree. For construction of the pine stands5, a pseudo-random

‘cloning’ method was used to allow for some variability in the tree orientation and

position. Detailed information on the stand construction and parameterisation can be

found on Disney et al. (2006).

Figure 5: Scots pine trees for ages 10, 20, 30 and 40 (right to left). The scene reflectance was

simulated with the frat optical model at a wavelength of 1064 nm.

5 The forest stands were constructed by M. Disney and kindly provided for this study.


17

2.4 FORWARD RADIOMETRIC TRACER - FRAT

For the simulations P. Lewis’ ray tracer frat operated in lidar mode was used. The

model is driven by the 3D locations and orientations of the scattering elements

coupled with their radiometric properties (Disney et al., 2006). Frat simulates the

waveform of the lidar signal using Monte Carlo Ray Tracing by illuminating a square

footprint with uniform distribution and records the reflected direct and diffuse

illumination, as function of distance from the sensor.

Different experiments were run by changing the input parameters of frat.

Particularly, the effect of scan angle, footprint size and sampling density was tested

under different stand age and stem density conditions. Simulations are run at 1064 nm

with an imaging plane of 100*100 pixels and the vertical resolution was set equal to 5

cm. Only the direct illumination was modelled and the resulted waveform was then

processed to produce only first and last return measurements. The method is described

in the Chapter 4.

Figure 6: Example of simulated image having a footprint of 30 cm on a 25 years-old pine stand (left) 6. The scene reflectance was simulated using the frat optical model at a wavelength of 1064

nm. On the right a real Scots pine picture in black and white.

2.5 ADDITIONAL DATASETS AND OTHER RESOURCES

A UK Forestry Commission forest database of the Thetford Forest was available. The

database contained the outlines of every stand, with information of age, mean stand

height, mean volume, whether it is mixed or not etc. The values of the variables were 6 As mentioned, the software uses a square footprint, however for viewing purposes the picture was cut to give the footprint impression.


18

calculated using allometric equations and tariff tables, by the Forestry Commission

(Edwards, 1998).

In addition to the forest database, field measurements for 28 stands, which were

acquired during the SAR and Hyperspectral Airborne Campaign (SHAC) in 2000,

were available. The campaign was organised as part of the NERC/BNSC Link Project

‘CARBON’ scheme, and was carried out over a period of two weeks between 19th of

June to 1st of July 2000, which actually means that the measured bio-physical

parameters can be used for the lidar data analysis, since the time interval is only 9

days. All the methods that were used for the measurements are described by Skinner

and Luckman (2000).

A variety of software was used to complete this dissertation. AWK and C-shell

programming were used for the main processing of the ‘real’ and simulated lidar

dataset. Matlab and Stata 8 Intercooled assisted the analysis and graphical

representation of the results. Finally, ArcGIS 9 was used for overview and selection

(by location) of the points and Microsoft Excel only for creation of simple plots.

Chapter Three: Processing of Lidar Data

19

3. PROCESSING OF LIDAR DATA

The chapter describes the processing of the lidar data of Thetford Forest. First, 31

stands were selected and the lidar points falling into them were cut to assist the

individual analysis of each stand. The scan angle of each pulse and the distance

between the first and the last pulse were calculated and appended to the file.

Moreover, the local minima algorithm was written and applied, using different

window sizes. The algorithm was improved by applying a neighbourhood slope filter

to the minimum points. After that, the height Z of the points was normalized.

Empirical relationships between stand height, volume and statistical descriptions of

the lidar dataset were established using regression and cross-validation was used to

evaluate them.

3.1 FOREST STANDS SELECTION

The first task before starting the processing of the lidar points was to select a sample

of forest stands. The selection was done as follows:

i) For every chosen stand respective lidar points should exist, covering the

whole area of the stand.

ii) The final sample should cover the whole range of age classes if

possible.

iii) At least some of the stands have to be chosen from the SHAC report,

since ‘ground truth’ measurements are available for them.

31 forest stands were chosen, with ranging age from 5 to 73. The majority of

them were Corsican pine stands, since the Scots pine stands are quite old and it was

difficult to find a good representative sample. 16 of the 31 chosen stands had been

surveyed during the SHAC campaign.

A simple AWK program was used to search the large lidar files and pick up the

points that belong in the rectangular area of each stand, according to the minimum and

maximum coordinates. Then these files were imported into ArcMap to apply the

select by location function, using the stand polygons to keep only those points which


20

are inside the stands. During this process a buffer of 3m was applied to minimize side

effects. The points of each stand were exported manually into .txt files. During the

export process the ArcMap adds an additional null field to take the place of the ID for

each record. The ID fields as well as some gross errors on the intensity of some points

were deleted. The errors were possibly caused during the processing before the data

was given for this study. This first stage of the process is given in the flowchart of

Figure 7, while description of the programs can be found on Appendix A1:

Figure 7: The flowchart of the selection process.

Finishing the selection process, individual files containing lidar points for each

stand were available. Moreover, the lidar point density in hits per m2 was calculated

by dividing the total number of pulses falling inside a stand with the total area of the

stand. The point density varied from 0.138 to 0.335 hits/m2. Table 2 contains

information for all the selected stands, while the position of each stand in the area is

given in Figure 8.

Table 2: The selected stands with relevant information.

Stand ID Age Species Mean Height

(m)

Area (m2)

Lidar Point Density

(hits/m2) S02 5 CP 1,260 93863 0,323 S13 6 CP 1,880 112469 0,178 S30 7 CP 3,640 25273 0,192 S16 8 CP 21,745? 66731 0,191 S26 9 CP 4,710 50383 0,227 S28 10 CP 4,655 82675 0,216 S11 13 CP 6,040 125430 0,138 S31 13 CP 7,580 81817 0,296 S08 14 CP 6,600 130126 0,222 S09 14 CP 7,370 78744 0,187 S23 14 CP 6,870 85690 0,193 S27 15 CP 5,450 71155 0,209


21

S03 16 CP 7,710 56876 0,179 S14 16 CP 9,575 140330 0,180 S18 17 SP 9,400 116663 0,200 S25 18 CP 11,530 66397 0,201 S21 20 CP 11,175 148280 0,203 S24 23 CP 11,415 92729 0,194 S05 26 CP 11,620 81865 0,155 S06 26 CP 14,060 70033 0,335 S01 29 SP 11,710 85568 0,176 S15 30 CP 15,270 161908 0,217 S12 34 CP 19,575 58632 0,245 S19 34 CP 17,910 133186 0,188 S22 42 CP 3,800? 37938 0,176 S20 68 SP 24,890 131951 0,185 S04 72 SP 23,270 70690 0,164 S07 72 SP 23,270 109952 0,175 S10 72 SP 23,270 53832 0,222 S17 72 SP 25,640 143193 0,192 S29 73 CP 30,010 66916 0,179

Note: CP=Corsican pine, SP=Scots pine, green height value for height measured using field survey, red height value for height given by Forestry Commission database, ? = problematic

height value.

Figure 8: The 31 selected stands coloured according to their age (Image by Google Earth).

Finally, the scan angle and the distance between the first and the last pulse were

calculated, for every pulse. The calculation was based on simple geometry, using the

coordinates of the first and last pulse (Figure 9) and the equations 2 and 3, given


22

below. The information of scan angle and distance between the first and last pulse was

then appended to each point-record.

Figure 9: Side-looking aspect of the first and last pulse points.

22xyDLength +∆Ζ= (2)

⎟⎟⎠

⎞⎜⎜⎝

⎛∆Ζ

= − xyDAngleScan 1tan. (3)

3.2 FILTERING OF THE LIDAR POINTS

3.2.1 RELATED LITERATURE AND IDEAS As mentioned in chapter 2.2, the lidar files contain height information in meters above

sea level datum (OSGB36 Datum). The height value should be normalized according

to the ground, in order to convert height above sea level into height above ground.

The normalization can be made using a high accuracy Digital Terrain Model (DTM),

which in this case was not available. A usual method is to obtain the terrain

information from the lidar points. The removal of height lidar points not representing

the ground is called filtering.

The filtering of lidar points to obtain a DTM is a challenging and still active

research area. Some researchers proposed morphological operators, which use the

same principles of “erosion” and “dilation” like in the raster image processing

(Eckstein and Munkelt, 1995; Hug and Wehr, 1997; Kilian et al., 1996; Vosselman,

2000). Other, approaches start with a coarse TIN DTM and iteratively refine it using


23

distance and angle criteria, so vegetation points (or house edges) can be detected

(Axelson, 2000). Lohmann and Koch (1999), used the linear prediction method,

which relies on the correlation of neighboring points, as expressed in the covariance

function.

Moreover, Hansen and Vögtle (1999) proposed a method based on convex hull,

as reported by Krzystek (2003). Their technique assumes that the lowest lidar points

are representing the ground and creates a convex hull from the remaining point cloud.

Additional laser points, lying within a user-defined distance refine iteratively the

DTM. Finally, Wack and Wimmer (2002) proposed the use of pyramid hierarchical

gridding.

One of the simplest algorithms that has extensively used is the local minima

algorithm. The algorithm applies a grid to the lidar points and then for each grid

square, finds the minimum height value, which is likely to represent the ground. The

last return points are used, because they contain more ground points, since the last

pulse reaches the ground more frequently than the first pulse. The algorithm can be

used as a pre-processing module in a subsequent filtering process, however many

researchers use it without applying any other additional filtering, due to its simplicity.

Several tests on local minima were run using various grid sizes from 4 to 10m

for all the stands. A threshold value was added to the algorithm in order to prevent the

calculation of the local minimum when there are not enough points in the grid. Of

course, the threshold value is related with the density of the points found in a stand.

As a result, the density of each stand was used to calculate for the threshold value.

The simple decided rule was that the local minima algorithm should work only on

cells which contain at least the half of the ‘expected’ points, according to the known

point density value. When the division by 2 gave a float number, then the closest

smaller integer was taken.

In order to improve the performance of the filter, another rule regarding the local

slope of the points was included. The idea is based on the algorithms that use the

slope criterion, described by Vosselman (2000), Vosselman and Maas (2001) and

Axelson (2000). First, the algorithm calculates the threshold according to the point

density of each stand and then finds the local minimum in each cell. Afterwards, the

local neighborhood filter scans again every cell to check the local 3x3 neighbor

minimums. The slopes created by the current (center) minimum and its other 8

neighbor minimums are calculated and the maximum slope is compared with the


24

slope-threshold value. The comparison takes place only for points falling into

1.5xGrid_cell circular distance from the center point. If the largest slope is found to

be less than the threshold value, controlled by the user, then the minimum point is not

modified. In the case when the slope is found to exceed the threshold, its Z value is

reduced to reach the level of the lower neighborhood minimum (Figure 10; also the

flowchart of the algorithm can be found on the Appendix C, Figure C 4). A counter

variable was added in the program to test how often the slope criterion is used to

change a local minimum value.

This method was expected to improve the performance of the local minima

algorithm (LM hereafter), especially in very dense canopies, where the LM fails to

find ‘real’ ground points. The slope threshold was decided to be 20 degrees because,

as already mentioned, the area has gentle topography. Since the slope criterion

corrects for outlier minimums, it was decided not to use threshold value of the number

of points found in the cell.

Figure 10: The local neighbourhood filtering process. The blue points are the local minimums of the grid cells. The red point is the local minimum of the current tested window. The largest slope is the one created by the green point and if its value exceeds the threshold then the Z value of the

red point is reduced.

3.2.2 RESULTS ON FILTERING

Generally, the addition of the slope criterion, improved the results of the height

normalisation. It should be noted that the use of the slope criterion by the filter is

affected by the cell size, because small cells are more likely to have non-ground


25

points, while using large grid, the possibility to find ground points is increased. This

hypothesis was confirmed (see Figure 11). It seems that the larger the cell, the less the

need for the slope filter to be used, while the denser the stand, the times that the slope

filter is used is increased (Figure 11).

Figure 11: The percentage of points that were modified by the slope filter, for different window

sizes and stands.

For example, in stand #21 (age=20, green line in Figure 11) even when using a

10x10m grid to find the local minimum, 5% of the points are still lying above the

slope neighbourhood threshold. So what the filter does is to reduce their heights and

then apply the normalisation. Furthermore, in very young stands (S002 – yellow line)

the filter is working for only a few points, because the LM has already found many

ground points. The same trend can be observed in very old stands (S029 – red line)

where after a certain window size (7x7) the LM has a better performance in finding

ground points. Of course, increasing the window size is giving more accurate ground-

points dataset, but on the other hand the density of the points is reduced.

The effect of window size can be evaluated using the histograms of the heights

of assumed-to-be-ground points and the statistics derived from their distribution. One

example for stand #22 is given in Figure 12. For a window size of 5m the algorithm

gives a ground-point dataset, the height distribution of which can be plotted.

However, there are some points that clearly do not represent the ground (see the


26

arrows on Figure 12). If those points were ground-points and not outliers then the

distribution would have a different shape. The ground does not change suddenly from

33 to 45 m on a flat area. The maximum height value is a good index, of when the

outlier points have been filtered out. In this case, when using 8x8m grid the maximum

height is reduced from 46.58 to 32.47m which means that most of the non-ground

points have been excluded and the remaining variation is due to the ground.

Figure 12: Non-normalized height distribution of points classified as ground by the filtering

process (example from stand #22). The effect of window size can be seen in the maximum height and SD (More diagrams are included in the CD).


27

In addition, a comparison between the simple LM and the improved LM7 was

applied. As expected there is a significant impact on the height distribution of the

normalized stands, which could result in misleading heights if only the LM filtering

was used. When the LM finds a minimum point that does not represent the ground

and applies the normalisation according to that, then it reduces the actual height of the

points in this cell. This is the reason why the height distributions of LM seem to

contain fewer points in higher values and more points in lower values (Figure 13).

Moreover, one can conclude that the slope neighbourhood filter has more impact in

stands with high leaf area index (LAI), because in these stands (like stand #3 and #15

of Figure 13) the density of vegetation impedes the laser pulse to reach the ground, so

the LM algorithm is not finding many ground points.

Figure 13: Distributions of the normalized height after the simple LM and the improved LM with

the slope filter. Significant differences exist in stands with high LAI, while in very young or old stands the two algorithms give similar distributions.

7 As ‘improved LM’ the author means the developed algorithm of LM accompanied with the slope filter.


28

Finally, the appropriate window size was chosen for each stand by analysing

qualitatively the height distributions and the reduction of the maximum height

according to the main curve of the ground, as explained above in Figure 12. The

normalisations were applied and at the end of the finishing process, for every stand

there was a file containing the normalized-according to the ground- height.

Normalized-height distributions for all the 31 stands can be found on the Appendix B.

3.3 CLASSIFICATION OF THE LIDAR POINTS

Generally, it is desirable to classify the lidar data as ground and vegetation points, in

order to process them individually. This would also help to analyse their intensity

information and check if there is significant difference between pulses coming from

the ground and pulses coming from the vegetation. However, this classification is

limited in the sense that it does not take into account the first/last return concept, by

which the lidar data are acquired. Thinking this way, the classification of the lidar

points can be done in three categories, as follows:

i) Points of which the first pulse hits the ground and as a result the last pulse

comes from the ground as well. We could refer to them as ground/ground or G/G

points.

ii) Points of which the first pulse hits a part of the canopy (braches, leaves or

needles) and the last pulse fades in the canopy as well. We could refer to them as

canopy/canopy or C/C points.

iii) Points of which the first pulse hits a part of the canopy but the last pulse

penetrates it and hits the ground. We could refer to them as canopy/ground or C/G

points.

It should be mentioned that as ground points, were considered points within 1m

distance from the ground. In the bibliography a range of 0.5-2m is used to account for

the variation due to the lidar vertical accuracy and to exclude effects of stones, shrubs,

etc. (Nilsson, 1996; Næsset, 1997a; Næsset and Bjerknes, 2001; Næsset, 2002;

Solberg et al., 2006). An AWK program was written to apply this classification to the

lidar files and extract C/C,G/G and C/G points8.

8 As already mentioned C/C,G/G and C/G will be used hereafter to describe ‘Canopy first/Canopy last’, ‘Ground first/Ground last’ and ‘Canopy first/Ground last’ points.


29

3.4 RESULTS

3.4.1 INTENSITY First the intensity response of the three categories was tested, for the 31 stands. No

relationship between the mean stand intensity and the stand age was found. Despite

that, a trend appears in the mean value of intensity according to the point class (Figure

14). The G/G points seem to have higher values of intensity, than the C/C points. The

most possible explanation is based on the fact that the vegetation of the ground

contributes in the spectral response of the G/G points. Moreover, the needles of the

conifers have lower reflectance than the ground vegetation.

On the other hand, the mean intensity values of the C/G points are difficult to be

explained. Their ground and canopy mean values are generally quite close to each

other and lower than expected, in comparison with the C/C and G/G points. The

Figure 14 shows the three ‘layers’ of mean intensity according to their class.

Figure 14: No significant relationship between the stand age and the mean stand intensity was

found. However, there is a trend according to the point class.

Even if the trend in the mean intensity values of the three categories is easy to be

recognised, the spread of the values impedes their classification according to their

intensity. One example of two combined histograms for C/C and G/G points is shown

on Figure 15. It should be mentioned that for very young stands (less than 10 years)


30

the applied classification is not expected to be very accurate, since for low height

stands the one meter ground buffer might contain canopy points as well. Discussion

on the results of intensity examination can be found on Chapter 5.1.

Figure 15: The distribution of the intensities of the points on stand #20 (Additional figures can be found on Appendix C – Figures C2 and C3).

3.4.2 REGRESSION MODELS OF STAND HEIGHT AND VOLUME Empirical relationships were developed to relate the stand mean height and volume

with specific lidar data properties. Firstly, the relationship between stand age and lidar

mean height was established. The C/C points were used in this case, which are more

sensitive in crown increment due to the fact that they are coming only from the

canopy (Figure 16). The regression curve looks quite similar with the modelled curves

derived by Disney et al. (2006), although the reduction of increase rate is more

gradual in this case, since the thinning operations are gradually applied in Thetford

(pers. comm. of Disney et al.(2006) with Dr. Sebastien Lafont, formerly UK Forest

Research, Alice Holt, now ECMWF). The coefficient of determination (R2) was 0.86.

It should be mentioned that between the stand ages of 40 to 70 only 2 observations

were available.

In the same way the height of the C/C lidar points were plotted against the mean

stand height (Figure 17). It should be highlighted that almost the half of the stands had

their mean height measured on the field during the SHAC 2000, while the rest


31

contained allometric-measured height. Nevertheless, it was decided to use them as

‘observed’ values to increase the number of observations, knowing that this might

increase the error as well. It is well-known that lidar points underestimate the actual

stand height and this trend can be seen in Figure 17. Only for two young stands the

lidar points overestimated the stand height, due to the presence of older trees that

biased the arithmetic mean to higher values. The model explains 88.8% of the height

variation.

Figure 16: Stand age against the height of C/C lidar points.

Figure 17: Mean stand height against the mean height of C/C points. Asterisks represent field-

measured stand height, while open circles are allometric-derived stand height.


32

Independent data were not available to assess the accuracy of mean stand height

determined from the lidar data, applying the above regression model. Therefore,

cross-validation was used. One of the 28 observations9 was removed from the dataset

at a time, and the remained stands were used to calculate the model again. Then the

mean stand height of the removed observation was predicted using the model. The

result is shown in Figure 18. The mean difference between predicted and observed

stand height is 0.0128 m which is not significant in statistical sense and the standard

deviation of the differences is 2.78 m.

Figure 18: Scatterplot of observed mean stand height against estimated stand height using cross-

validation.

The same methodology was used to construct a regression model for stand

volume estimation. Many different variables and models were tested. The standard

deviation (SD) of the height of lidar points is an index of the age of the stands, since

all of them are even-aged. As the stand is growing the standard deviation of the height

of lidar points is increased because the crown layer is going away from the ground.

This direct relationship wouldn’t hold if the stand was natural with many age and

height classes; however in this case it is applicable as long as there are not outlier

trees to bias the calculation of standard deviation (Figure 19). The young stands #2,

#13 and #30 were not included in the calculation of the model, as the presence of old

9 3 of the 31 stands were rejected from the calculation due to large conflict between the SHAC and the allometric height value.


33

trees in them biased the SD. The coefficient of determination of the resulted model

was 0,94.

Figure 19: Standard deviation of the height of the lidar points (m) against stand volume (m3). 3

stands were rejected from the calculation due to the presence of outlier trees (red asterisks).

Cross-validation was used again to assess the accuracy of the regression

equation. The mean difference between predicted volume and ‘observed’ volume10 is

0,0973m3 and the standard deviation of the differences is 41,79m3.

Figure 20: Scatterplot of observed volume against estimated volume from lidar data, using the

regression model.

10 Volume is not actually ‘observed’ since it is derived from equations of basal area.


34

3.4.3 GAP PROBABILITY

It is interesting that the percentages of the three categories of points (C/C, G/G and

C/G) are changing as the stand age is increased. As the stand grows the C/C points are

increased, while the G/G points are decreased. The trend is changing when the stand

is getting older than 40, when normally gaps start to appear in the crown (Figure 21).

This gradual change might also be the effect of the thinning operations that are

applied in the stands. The percentage of C/G points show a smaller variation

beginning from very low values of young stands to ~20% for stands around 30 years

old.

Figure 21: The change in the percentage of C/C (left) and G/G (right) points as the stand is

growing.

If all the lidar measurements were acquired at nadir angle, then the inversion of

the geometry of the range-finding could provide an estimation of canopy cover

(Andersen et al., 2003). Off-nadir angle acquisition affects the probability of the laser

pulse to pass through a canopy layer. As a result, the assumption that the percentage

of C/C or G/G points is straightforward related with the gap fraction is not valid, if the

acquisition angle is not considered. Unfortunately, the acquisition angle for each pulse

is not given by the manufacturers. Even when angles are calculated by the method

described in chapter 3.1, the calculation is limited in those points for which there is

sufficient distance between the first and last recorded point in order to ensure robust

angle estimation.

Gap frequency is a very important parameter of forest ecology. According to Li

and Sthrahler (1988) ‘this frequency can be defined as the probability that a photon


35

will pass through the canopy unintercepted’. A simple model based on Beer-Lambert

law for continuous canopies is (Norman and Welles, 1983): ϑcos/kL

gap eP −= (4)

Where Pgap is the gap probability, L is the leaf area index (LAI), k is determined by

the distribution of leaf inclination angle (G-function) and ϑ is the angle of attenuation

(equal to scan angle in this case). From equation 4 and assuming a spherical leaf angle

distribution is derived:

gapPLAI ln*cos*2 ϑ−= (5)

Using lidar data the ‘horizontally projected LAI’ or LAIh can be derived. LAIh is

defined by Asner et al. (2003) as ‘the area of “shadow” that would be cast by each

leaf in the canopy with a light source at infinite distance and perpendicular to it,

summed up for all leaves in the canopy’. The gap probability should be measured

from points having similar scan angle, meaning that they attend the canopy with more

or less the same angle. In a recent paper, Solberg et al. (2006) calculated gap

probability as the ratio of below canopy echoes to the total number of echoes. In other

words the calculation of gap probability is derived from:

ALL

Ggap N

NP = (6)

Where NG is the number of ground pulses and NALL the number of all the pulses.

The difficulty of derivation of scan angle for each pulse has been explained

above. One solution would have been to interpolate the angle values using the

scanning pattern and relying only on the points whose values are accurately

calculated. In fact many ground points have their first and last pulse in close distance

and as a result the calculation of scan angle, based on the principle of Figure 9 of page

22, is not robust.

Plotting the lidar points in X,Y is easy to recognise the flight lines and the

overlap areas, due to the sudden increase in the point density. Using this pattern the

flight lines can be digitised on ArcGIS (Figure 22; next page). Then the scan angle of

each point can be calculated within certain accuracy by using the mean flight altitude

and according to its distance from the flight line. Using the above methodology two

measurements of Pgap were obtained: one using the points lying near the flight line

(scan angle = ±5o) and another for points lying in the far edge of the field of view

(scan angle between ±10 to ±20). The mean angle ϑ of the range was used in the


36

equation (5) to calculate LAIh. For the first set of points lying near the flight line, a

mean angle of 2,5o (since the angles ranged from 0 to 5 degrees) was used while for

the far-range points a mean angle of 15o was applied (since the angle ranged from 10

to 20).

Figure 22: Lidar points plotted in X,Y. The overlap areas can be seen (yellow) and the flight line can be delineated (red). The blue points have scan angle ±5o according to the mean flight altitude

(also see Figure C1 on Appendix C).

The methodology was applied in 8 stands from different age classes. Two LAIh

estimations for each stand was calculated, one for each angle-set and then the results

were averaged. For some stands only one measurement was possible since they

contained points only in one range of angles. Assuming a homogenous stand

structure, the gap probability should be affected only by the scan angle. As a result the

two LAIh measurements of a stand are expected to be similar. Indeed the

measurements were quite close to each other with minimum and maximum difference

of 0,06 and 0,76 respectively.

However, one should be aware of the fact that the stands contain access paths

and small roads, whose spatial distribution affects the measurement of gap

probability. Consequently, it is expected that the LAI will be affected and the results

sometimes might be the opposite than expected. For example, in stand #9 (Figure 23)

there is a road in the border of the stand. According to the flight line, this region was

in the far-range of scanning. One might expect the gap probability of the far-range

points to be less than the one measured in the nadir. However, the road’s presence

increased the number of points which reached the ground and as a result the LAI

measurement was far less than the one measured by the nadir points.


37

Figure 23: In stand #9 the presence of the road in the far-range points resulted in increased gap

probability. The red line is the flight line and the colours represent the height above ground.

As the stand is growing the LAIh is increased dramatically. Stands between 15 to

30 years old showed LAIh values above 4. However, it should be noted that the

selective thinning operations are affecting the LAIh, keeping its value in low levels.

Besides, the purpose of gradual thinning is to keep the LAIh in reasonable values, to

leave enough light and space for the remaining trees. Moreover, LAI is affected by the

time of the year when the measurement is done.

According to LAI measurements done by Roberts et al. (1982) in Thetford

Forest during the spring of 1977, the maximum LAI value for Corsican pine was

greater than 10. However, the accurate description of the LAI estimation method is

not given and the survey is quite old to rely, since the management operations might

have changed.

Field measurements of LAI for the stands were not available and as a result

comparison and validation is not possible. However, as newer studies suggest lidar-

derived LAI is expected to relate strongly with ground-based measurements and once

the relationship is defined by regression, then LAI estimations can be done using

discrete-return lidar data (Solberg et al., 2006).


38

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80

Stand age

Leaf

Are

a In

dex

h (b

y lid

ar)

Figure 24: LAI h values calculated from lidar data, for stands with different age.

Chapter Four: Simulations

39

4. SIMULATIONS

4.1 METHODS

As already mentioned frat simulates the waveform of the lidar signal by illuminating a

square footprint with uniform distribution and records the reflected direct and diffuse

illumination, as function of distance from the sensor. Therefore, it was assumed that

the illuminated area has a square projection and that the energy is distributed

uniformly across the pulse. The above assumption is not expected to have major

impact, since the study is comparative and the effects will be the same for all the

simulations. However, it should be considered that with equal diameter and edge the

area of the square is larger than the one illuminated by an ellipsoidal-like footprint.

The term ‘footprint diameter’ will be used to refer to the length of the square’s edge.

The simulations were run in the stand models created by M. Disney, as

described in Chapter 2.3. Different homogeneous stands, with varying age from 5 to

50 (with a step of 5 years) and four different stem densities (1.5 , 3 , 4.5 and 6 m)

were available. The effect of scan angle was examined, applying five different angles

(0, 5, 10, 15 and 20 degrees). In order to adjust the impact of the scan angle into the

real conditions, a slight increase on the footprint was included as the angle increases.

For the flight altitude of 900 m and with a beam divergence of 0.3 mrad (as the

specifications of the ALTM lidar survey), the increase of diameter is almost 3.5 cm

(from nadir to 20 degrees angle)11. It should be mentioned that the simulations were

run on random points in specific areas of the stands, with the assumption that the

random point sampling will give the same results like the ones obtained by the lidar

scanning pattern.

In addition, different footprint diameters, from 10 to 90 cm (with a step of 10

cm) were tested on specific stands (20, 25, 35 and 45 years old with 3 m stem

density). In this simulation only nadir acquisition was used. Finally, simulations

corresponding to sampling densities of 1, 2, 4, 6 and 8 points per square metre were

run on the same area of a 25 years old stand.

The results of the simulations had to be sampled in order to create a discrete-

return lidar dataset. They are many detection methods with which the laser scanner

11 Also see Table C 1 on Appendix C.


40

can determine the first and the last pulse and derive discrete, time-stamped trigger-

pulses. Wagner et al. (2004) compared different detection methods as threshold,

centre of gravity, maximum, zero crossing of the second derivative and constant

fraction. The results suggest that the performance of each methodology is depended

on several factors as the object distance and the noise level. Most of the times the

details of the detection method applied by commercial laser scanner systems are not

known, since the manufacturers do not provided relevant information (pers. comm.

Dr. E. Baltsavias, Institute of Geodesy and Photogrammetry, Swiss Federal Institute

of Technology (ETH), Zurich ).

Figure 25: Generation of first and last return points on a 15 (up) and 25 (down) years old pine

with the footprint set to 30 cm.


41

In this study we used the method of maximum which samples the waveform on

its first and last peak. A low threshold of 0.0005 (reflectance) was also added after an

examination of many waveforms. The program discrete was written to apply this

sampling and create the discrete return lidar datasets. Two graphical examples are

given in Figure 25. The program, also, calculates the height above ground of the two

pulses, giving the distance of the camera and the scan angle.

The stand metrics that were measured after the simulations were: (i) the

percentage of points -from the first and last return- that hit the ground (Points On

Ground – POG), (ii) the percentage of points -from the first return- that hit the top of

the canopy (Points On Top – POT), (iii) the arithmetic mean of all the canopy points

derived from the first return, (iv) the maximum canopy height of the first return

points, and (v) the normalized height difference (NHD). NHD is the difference

between the mean height of the model stand and the one derived by the lidar

simulation, normalized by the model stand height.

The decision of the above metrics was based on their importance to describe

penetration in the canopy (as POG) or ability to record the canopy height accurately

(as POT, mean and maximum height). Also the influence on forestry applications can

be evaluated using the above metrics. For example, the number of points that hit the

top of the canopy has major impact on the derived Digital Surface Model or on the

Canopy Height Model, while the number of ground hits affects the gap probability

measure. It should be underlined here that as “ground hit” is defined every point

whose height is less than 20 cm and the top of the canopy is assumed to be the upper 1

m part of the canopy, so 5 years-old stands were excluded (Table 3).

Table 3: An example of how the top of the canopy was defined.

Model Stand

Age Dominant Height

(m) Top of the canopy (m)

10 2.86 >1.86 15 5.57 >4.57 20 8.44 >7.44 25 11.23 >10.23 35 16.31 >15.31 45 20.39 >19.39


42

4.2 RESULTS

The results of the simulations are presented in this Chapter. Initial observations are

also briefly described, however the main discussion and analysis of the simulations

takes place in Chapter 5.2.

4.2.1 FOOTPRINT DIAMETER Simulations for small footprints ranging from 10 to 90 cm were run on a 25 years old

pine stand, which had stem density of 3 m. Effects on the POG, POT, mean and

maximum height metrics (as defined on Chapter 4.1) were examined on four different

age classes of 20, 25, 35 and 45. The constructed diagrams are shown below:

Figure 26: Footprint diameter plotted against the percentage of ground hits for different stand

ages (Up: First pulse; Down: Last pulse).


43

A

B

C

Figure 27: (A) Percentage of points on top, (B) maximum height and, (C) mean height of the canopy hits plotted against footprint diameter, for different stand ages.


44

A

B Figure 28: The normalized height difference against the footprint diameter for different stand

ages: (A) Canopy points only, (B) all the first pulse points.

Significant changes on the obtained results were revealed. Almost all the

examined metrics seem to be affected by the footprint diameter. The results suggest

that an increase of 10 cm in the footprint diameter increases the points that fall on the

top of the canopy by an average of 6% (Figure 27(A)). The impact is stronger for

changes on the range of 10 to 40 cm footprint diameters. As expected the percentage

of first-pulse ground points was decreased because larger footprints increase the

possibility of needle material to be detected as first pulse measurements (Figure 26).

On the other hand, last-pulse ground points were increased as the footprint diameter

broadens.


45

The normalized height difference was reduced as a result of the increased mean

height of lidar points, which means that the height estimation came closer to the actual

stand height (Figure 28). Again the influence was stronger on footprint increments of

10 to 30 cm while insignificant changes according to stand age were detected. The

maximum height showed a relatively stable behaviour without major changes as mean

height. Extended discussion of the results can be found on Chapter 5.2.

4.2.2 SCAN ANGLE The impact of scan angle on the stand metrics was examined. Connection between the

scan angle and the height metrics was of a particular interest, as well as effects on

penetration in the canopy. The results are shown on the following diagrams:

Figure 29: Influence of scan angle on the percentage of points which hit the top of the canopy for

different stand age (stem density is 3 m).


46

A

B

Figure 30: The percentage of ground points of the first (A) and last (B) pulse, for different scan angles and stand ages. The line on (A) is the regression model line obtained from the real data

(Figure 21-right) and the lines on (B) are showing the value’s range.


47

A

B Figure 31: Normalized height difference against the scan angle for different stand ages:

(A) Only canopy points, (B) all the first pulse points.

Figure 32: Increment of mean height of all the points from nadir-view to 20 degrees scan angle.

Different stand ages and two stem densities were tested.


48

A

B Figure 33: The change of maximum height from nadir to 10 (blue) and 20 (red) degrees of scan

angle for: (A) stem density of 3 m and (B) stem density of 1,5 m.

The scan angle proved to have a major influence on the ground hits percentage

(Figure 30), while its effect on the points reaching the top of the canopy is rather

random (Figure 29). The canopy-only height seems to be unaffected by scan angle,

showing only a random variation. This can be seen on the normalized height

difference diagram (Figure 31(A)). On the other hand, when all the points are taken

into account then the statistical descriptions are changing: The mean height of the

dataset acquired on 20 degrees angle is increased with the increment to be related with

the stand age (Figure 32).

Furthermore, the maximum height was increased for acquisitions obtained on 10

and 20 degrees, by an average of 13.39 and 19.85 cm respectively (Figure 33) in


49

forest stands with stem density of 3 m. The increment was reduced when a denser

stand was tested (stem density = 1.5 m). Further discussion can be found in Chapter

5.2.

4.2.3 SAMPLING DENSITY

The effect of sampling density was examined on an area of 20x20 m on each stand.

Different number of points was generated on this area: 200, 400, 800, 1200 and 1600,

resulting on sampling densities of 0.5, 1, 2, 3 and 4 points per square metre

respectively. Three stand ages -25, 35 and 45- were tested. The same stand metrics

were obtained and the constructed diagrams are given in the next pages:

A

B Figure 34: The effect of sampling density on: (A) number of first-pulse points that hit the canopy

top, (B) number of last-pulse points to hit the ground.


50

Figure 35: Effects of sampling density on the maximum canopy height metric. The increment

between 0.5 and 4 pts/m2 is given for different stand ages.

A

B

Figure 36: The change of mean height of all (A) and canopy-only points (B). Comments can be found on the discussion (Chapter 5).


51

As expected, the increase of the sampling density resulted in a linear increment

of the points, which hit the ground or the canopy. The “intensity” of the effect seems

to be connected with the stand age, since the three examined ages showed different

rates of increase (Figure 34). Changes in centimetre-level were obtained on the

maximum canopy height, especially for younger stands (Figure 35), while the mean

height was not affected significantly (Figure 36).

Chapter Five: Discussion

52

5. DISCUSSION

5.1 REAL LIDAR DATA PROCESSING

The filtering process proved to be an important part of the processing chain. Working

with raw lidar data, enabled the examination of two different filtering algorithms: the

simple local minima and the optimised local minima with slope criterion on the local

neighbourhood. The improved filter was particularly used in stands with high level of

needle-material density where the last pulse fades in the canopy more often, providing

wrong ground-level points (Figure 11; Chapter 3.2.2). The filtering process, as proved

by the diagrams on Figure 13, can have major impact on the height distribution of the

lidar points and therefore can affect the percentage of the intermediate parts of the

canopy, which are usually included in regression models for stand height estimation

(e.g. Næsset and Bjerknes, 2001). The improvement was weak on very young or old

stands, possibly due to the increased penetration of the last pulse, in contrast with

stand ages between 20 and 35 where the pine canopies tend to be denser.

The potential usefulness of intensity of lidar data has not been examined

sufficiently in the past (Lim et al., 2003b). The categorisation of points on C/C, G/G

and C/G classes reveals different distributions and mean values, as Figures 14 and 15

showed (another two examples can be found on Figures C2 and C3 of the Appendix).

Points whose first and last pulse hit the ground tend to give higher intensity values, in

contrast with canopy-only (or C/C) points. The first explanation of this observation is

that the ground of the study area is covered by vegetation which possibly affects the

return signal with its spectral properties. It is also known that conifers do not have

high reflectance values in the near-infrared, as broadleaves do. In addition one should

take into account the volumetric properties of these targets: the ground is a more

“compact” material when compared with the needles, which compose a more “soft”

target, with many microgaps and thus the reflected laser pulse is not that strong.

Another major finding that supports the above interpretation is the lower

intensities of C/G points, even if they come from the canopy (the first pulse) or the

ground (the last pulse). In this case the opposite trend can be observed (Figure 14;

Chapter 3.4.1): the first-pulse canopy points have slightly higher mean intensities than

the last-pulse ground values. This suggests that the signal is scattered as it travels


53

through the canopy and therefore less amount reaches the ground to return back and

enable last-pulse intensity recording. This is particularly obvious on high needle-

density canopies (20 to 35 stand age; Figure 14) where the mean values are more

clearly distinguishable. This effect also might be influenced by the position of the

point in the canopy. A lidar point on the edge of a crown will possibly give a first-

pulse canopy point with low intensity and a last-pulse ground point with higher

intensity. The opposite will happen for a lidar point on the middle of a crown, whose

travel line passes through canopy material and the signal’s power fades quicker.

The obtained observations on intensity trends agree with the results of Moffiet et

al. (2005) (see Figure 37). In one of the few studies on lidar intensity, Moffiet et al.

(2005) examined the potential use of lidar points’ intensity for individual tree

classification. The distinction of White Cypress Pine (Callitris glaucophylla) and

Poplar Box (Eucalyptus populnea) was not always obvious because of extraneous

sources of variation in the dataset. Finally, according to Moffiet et al. (2005) (pers.

comm with Optech): “the power of the laser can vary slightly depending on ambient

temperature of the diodes and decreasing with age (i.e. hours of operation)”.

Figure 37: Figure from Moffiet et al. (2005). Difference on the distribution of intensity return of ground points of C/G and ground points of G/G. The results agree with the observations of this

study. (From Moffiet et al., 2005; Figure 8).

Based on the analysis it seems that intensity values cannot be used directly to

separate canopy and ground hits, even if the mean values show significant separation.

Nevertheless their values’ range produces fuzzy distributions obstructing

straightforward classification. Moreover, effects caused by the mechanical parts of the

lidar device might result in significant intensity variations, which were not realised in


54

this study but have been reported by Moffiet et al. (2005). Inevitably, the discussion

of classification of lidar points according to their intensity, involves the consideration

of the footprint diameter. The smaller the footprint the more the possibility of the

pulse to hit “pure” objects -like needles or branches- and as a result the spectral

response might be more representative of the target. Evidence for this hypothesis was

not found on this part of the study but examined on the footprint simulations (see

below for Discussion).

The linear empirical model for stand height estimation included as independent

variable the mean height of C/C points, which eliminates possible stem density

effects. The plot of lidar mean height and observed mean predominant height showed

that the underestimation of the stand height is increased on higher trees (Figure 17;

Chapter 3.4.2). This might be caused by the presence of trees whose age does not

correspond to the actual stand age. Foresters are used to leave older trees (also called

reserves) in young stands for ecological reasons. These trees influence the calculation

of the mean height on young stands by increasing its magnitude. This shows how

case-sensitive are the empirical methods for stand height estimation.

The same sensitivity can be seen on the regression model of volume, which is

based on the standard deviation of the ground-normalized height. This relationship

wouldn’t hold if the stand was not even-aged. In order to establish a good model three

young stands were eliminated from the sample due to the outlier-effect described

above, which influenced the calculation of standard deviation. Nevertheless, the

calculated equations can be used in the specific area for mean stand height and

volume estimation, with the accuracy estimation provided by the cross-validation

process.

In addition, a simple model based on Beer-Lambert law was used to estimate

LAI from the discrete-return lidar points. According to the experience gained by

Solberg et al. (2006) laser and ground-based LAI measurements relate strongly, with

the strongest relationship obtained when LAI calculation takes place within a 30 m

window. Therefore it is important to consider the area within which the estimation

will be made. As shown in Figure 23 (Chapter 3.4.3) the spatial arrangement of gaps -

especially gaps caused by paths or roads- affects the stand LAI calculation. LAI

strongly varies within a stand, making the stand-level calculation a general estimation

rather than an accurate measurement. In any case, the lack of field measurements did

not allow validation of the calculated values.


55

5.2 SIMULATIONS

The examination of the effect of lidar footprint on the dataset was of a particular

interest. In the past, Persson et al. (2002) reported not significant influence on tree

height estimates from diameters of 0.26 to 2.08 m. When larger footprint was used

(3.68 m) then the underestimation of the tree height was increased. In another study

Næsset (2004) reported relatively stable first pulse measurements in the limited range

of 16 to 26 cm. However, the examination is surely affected by the decreased pulse

density, because in order to increase the footprint the platform has to fly in higher

altitudes (noted by Yu et al., 2004b). The only way to study the footprint effect

without major changes in pulse density is to use lidar systems with adjustable beam

divergence or by using simulations, as this study suggests.

The results, as given in Chapter 4.2.1., suggest that the increase of footprint

diameter reduces the normalized height difference, due to the fact that the illuminated

area becomes larger and thus the apexes of the pine trees can be detected easier.

Therefore it is logical that higher mean canopy values are obtained. The average

increase of the mean canopy height from a footprint of 10 cm to a footprint of 90 cm

was 1 m. The step changes seem to be larger for increases between the diameters of

10 and 40 cm. A numerical example is given in Table 4.

Table 4: The mean canopy height values (m) for different footprint diameters.

Footprint diameter (cm) Stand

Age 10 20 30 40 50 60 70 80 90

20 5,81 6,22 6,35 6,51 6,64 6,59 6,74 6,8 6,87

35 13,42 13,74 13,97 14,19 14,25 14,27 14,35 14,45 14,55

Footprint diameter can vary slightly in an airborne lidar survey due to flight

altitude variations, the scan angle or platform’s attitudes (like roll). In the lidar data of

Thetford Forest the calculation of the footprint diameter for the extreme cases (lower

altitude-nadir view and high altitude-20 degrees scan) gave a difference of 8.1 cm on

the footprint diameter. This variation of the footprint -in the same survey- is

remarkable if someone considers the simulation’s results: First-pulse lidar points


56

acquired using larger footprint will have the potential to give significantly larger

height values.

Figure 38: The waveform recorded for the same point using two different footprints.

A better understanding of the footprint effect can be obtained with the analysis

of the lidar waveform, whose sampling provides first/last measurements. Figure 38

shows an example of a point whose first pulse is coming from the canopy. The

footprint of 20 cm (blue dotted line) gives a clear first-pulse response (square). On the

other hand the 80 cm footprint has a weaker reflectance, even though it is still above

the threshold (circle). Consequently the first pulse of the 80 cm footprint is coming

from a higher point of the canopy. As regards the last pulse, both of the footprints

recorded it correctly although in the case of the broad footprint the reflectance is

decreased.

It seems that when the footprint diameter is increased the laser power is spread

over a larger area and as result canopy points return weaker signal (Figure 38; also

discussed by Lovell et al., 2005). This means that the apexes of the pine trees might

not return sufficient power above the lidar system’s noise threshold. Thus, the

selection of the threshold value is crucial for whether the increase of the footprint will


58

difference) in this study. They reported a slight increase of the NPHD as the

maximum scan angle was increased. However, the results might be affected by the

change of the spatial point density, because fixed pulse frequency was used (Lovel et

al., 2005). This means that as the angle was increased less points were obtained by the

simulator, so it seems logical that the NPHD was increased. In this study, every

examined case had a fixed number of 100 created points, except on the sampling

density simulations where the number of points was adjusted to obtain different

densities.

It is also interesting that the maximum canopy height -which is regarded as a

relatively stable stand metric on lidar datasets- is increased with the scan angle

(Figure 33). However, the increment does not seem to be connected with the stand age

and is higher for open canopies (stem density of 3 m). When a 20-degrees scan angle

was used the average increment of the maximum height was almost 20 cm. The

increase might be connected with the adjustment of the footprint from 27 cm (nadir)

to 30.5 cm, although this is a slight increase. Possibly the “perspective” scan of the

pine’s apex gives stronger responses than the one acquired at nadir; as a result higher

maximum values can be obtained. This possible explanation has not been proved in

this study and further analysis using simulations on pines’ apexes is needed.

Finally, the effect of sampling density proved to have major impact on the

number of points which hit the top of the canopy. Therefore a better representation of

the canopy can be achieved. It should be underlined that statistical descriptors like the

ones chosen are limited to assess the influence of sampling density. A more complete

study on the specific parameter could include the creation of DSM and CHM, which

incorporate spatial information (e.g. Hirata, 2004).

Interestingly the increase rate of the 35 years old stand for the last-pulse points

that hit the ground was lower than the one of the two other stands (25 and 45). This

difference might be due to the dense needle material (Figure 34(B)). On the other

hand the mean height of the first pulse hits (even all the points or canopy-only) is not

affected by the sampling density. The ground-hits are increasing the same way the

canopy points do and as result the arithmetic mean is not affected. However, this

might not be the case in very close canopies, where most of the first pulse points are

falling on the canopy. It should be noted that Lovel et al. (2005) reported a weak

decrease of 0.05-0.06 on the NPHD, for densities of 0.5 pts/m2 to 4 pts/m2.


59

The maximum canopy height showed a centimetre-level increase with the

sampling density. The increment of the younger stand (25) was larger than the one of

older stands and the 45 years old stand did not show any variation at all (Figure 35).

The apexes of young pines are generally thinner; therefore the maximum canopy

height might not be sensed by a particular sampling density. As the density is

increased, the more pulses per area increase the possibility to obtain the maximum

canopy height of the thin canopy tops. On the other hand, older stands have broader

tops that can be sensed by the lidar pulses easier. As a result the effect of sampling

density on the maximum canopy height is more noticeable on young stands.

5.3 FUTURE WORK

This study used computer simulation models to assess and describe the impact of

three acquisition parameters on the discrete-return lidar dataset. The calculation of

stand metrics as points-on-top (POT), points-on-ground (POG), mean height and

maximum height were used for the evaluation. Future study should concentrate on the

actual effect on the forestry applications, examining their impact not only on the

dataset, but also on the derived results. However, some indications has been already

shown: since sampling density affects the maximum height it is expected that in

overlapping areas -where the pulses are denser- the maximum height will be higher,

especially in younger stands. Consequently, it would be interesting to examine the

statistical differences of the overlapping areas and how they can affect the empirical

regression models. Maximum height is believed to be a relatively stable lidar metric,

quite close to the actual predominant canopy height and is used in regression models.

The variations revealed in this study suggest correlative impact on the regression

equations, which have not been examined here.

Another topic of future research will be the evaluation of these parameters with

regard to the tree-level information. Hir7 T (2004) has already shown that the number

of extractive trees and the mean tree height (of extractive trees) are affected by the

sampling density of laser beams. It would be interesting to extend the above study

including other parameters as the ones studied here: scan angle and footprint diameter.

The examination of these impacts on practical variables (e.g. number of trees, crown

diameter etc) will enable the determination of optimum configurations for airborne


60

lidar missions, under various forest stand characteristics. Moreover, the scan pattern

can be simulated in contrast with the random sampling, which was utilised here.

Different scan patterns (e.g. oscillating mirror, palmer scanner, rotating polygon and

fiber scanner) can be examined to determine the optimum pattern for different forestry

applications. Relevant studies are expected in the future because optimisation of lidar

operational parameters will reduce the cost of acquisition.

Chapter Six: Conclusions

61

6. CONCLUSIONS

The impact of three discrete-return lidar system characteristics was examined using

statistical metrics, which are crucial for forestry applications. After the analysis and

discussion it is possible to summarize the major findings which answer the key

questions:

The footprint diameter is a crucial parameter which determines the

ability of the lidar system to record the top of the canopy as well as the

ground. Small footprints increase the penetration of the first-pulse

while larger footprints increase the penetration of the last-pulse.

However, the noise-threshold value of the system plays major role in

this relationship.

Centimetre-level variations of the footprint -like the ones exist on a

lidar survey- might result in increased mean height values in far range

areas, while the maximum height is not seriously affected by this

parameter.

The scan angle influences the number of points that hit the ground and

this relationship is affected by the stem density. Effects on the

maximum canopy height were reported, which might influence

regression models based on this variable.

The effect of sampling density was stronger on young stands. It is

expected that a better representation of the height variation of the

canopy can be obtained by high sampling density; however, the mean

height value is not affected. Future work is needed on the effect of

sampling density, using spatial evaluation with DSMs and CHMs.

The conclusions suggest that the information of such parameters -as the scan

angle and the instantaneous footprint diameter- is crucial for every recorded point and

might affect the statistical measures of the dataset. Therefore, future discrete-return

lidar missions on forests have to take into account these effects and include their

measurement for every recorded point, in order to improve the interpretation and

analysis.

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Appendix

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APPENDIX A1: LIST OF WRITTEN PROGRAMS

Filename Description

AWK programs

allAngles.awk Calculates the scan angle of each point, using the

coordinates of the first and last pulse.

classifyMe.awk Classifies the lidar points into C/C, G/G and C/G (see

Acronyms) according to their normalized height values.

clearMe.awk Deletes some errors of lidar data. Some records had

extreme intensity values (e.g. 50000).

delFID.awk Deletes the ID field, created by ArcMap during the table

export process.

discreteIt.awk Samples the waveform to derive only the first and the

last pulse. It searches for the first and last peak of the

signal above a specified threshold. When these are

found it calculates their above-ground height and stores

them on new file.

minimaNew.awk Applies the Local Minimum Neighbourhood Filtering. It

is controlled by the shell script minima.

ptsINcells.awk Calculates how many points should be expected in a

cell, according to the point density of each stand and

then proposes a threshold value for the Local Minima.

selectMe.awk Selects points from the original lidar files, that belong in

a specified rectangular area.

C-Shell

createPoints Creates a specified number of random points inside a

specified area centred at (0,0). It is used to derive a

random lidar point sample.

discrete Executable for the discrete (first/last) sampling of the

waveform. It works with discreteIt.awk.

minima Works with ptsINcells.awk and minimaNew.awk to

apply the Local Minimum algorithm.

Appendix

79

runMe Runs the BRDF.com.

Matlab code

distr_normal.m For extraction of all the height distribution of the

normalized lidar files.

Foot_Mean.m

Foot_MAX.m

To create diagrams of footprint against mean height or

maximum height of simulated canopy points.

Plot_POT.m

Plot_POG.m

To create diagrams of the percentage of the ground/top

points, against age for different angles.

Validation.m

Validation2.m

Run the cross-validation process for the regression

models of height and volume (Chapter 3.4.2).

NHD_ANGLE.m

NHDall_ANGLE.m

To create diagram of Normalized Height Difference (of

canopy or all points) against angle for different stand

ages.

Appendix

80

APPENDIX A2: EXAMPLES OF WRITTEN CODE

C-SHELL SCRIPTS a) runMe (runs BRDF.com) #!/bin/csh -f set arch = `uname -m` set path = ($path /home/plewis/bpms/bin/csh /home/plewis/bpms/bin/$arch) ###Get the random points from .dat files### set x = (`gawk < randompoint.dat '{print $2}'`) set y = (`gawk < randompoint.dat '{print $3}'`) ###Apply different stand age or footprint (or angle if angle variable will be added)### foreach age (25) foreach footprint (300) set forest = forest.$age.3000.needle.obj @ i = 1 while ( $i <= $#x ) BRDF.com -lidar 15000 63000 50 -x $x[$i] -y $y[$i] -z 0 -boom 30000 -vza 0 -vaz 0 -orthographic -ideal $footprint -object $forest -blacksky -image -size 100 -a 1 -v 0 -rtd 1 -outName result.$i.$age -bands wavebands.dat -nice 19 @ i++ end end end b) createPoints #!/bin/csh -f ###grep plant forest.5.3000.needle.obj | grep -v g | grep -v matlib | gawk '{of="plant."$NF; print $2, $3 > of;}'### to check the extend of the forest set N = 400 set minmax = 10000 ###How many points do you want? & size limits +/- ### echo $N $minmax | gawk 'BEGIN{srand();} {n=$1;size=$2;for(i=0;i<n;i++){print i+1,size*((rand()*2)-1),size*((rand()*2)-1)}}' > randompoint.dat

Appendix

81

c) discrete (works with discreteIt.awk) #!/bin/csh -f foreach angle (0) foreach age (25) ##foreach foot (700) foreach record (`cat p1000`) ####Instead of writing 1,2…100…1000#### gawk < density.$record.$age.$angle.0.0.0.0.direct_contributions -f discreteIt.awk angle=$angle >> discrete.density.1000 end ##end end end d) minima (works with minimaNew.awk and ptsINcells.awk) #!/bin/csh -f set stands = `ls -l ang_*.txt | gawk '{print $NF;}' | gawk -F. '{print substr($1,6);}' | sort -n` foreach s ( $stands ) foreach c ( 4 5 6 7 8 9 10 ) set th = `gawk < ang_s$s.txt -F, -f ptsINcells.awk -v standID=$s cellsize=$c |& grep Proposed | gawk '{print $3;}'` echo $th gawk < ang_s$s.txt -F, -f minimaNew.awk stand=$s cellsize=$c nThresh=$th > ground.stand.$s.c.$c.th.$th.txt gawk < ground.stand.$s.c.$c.th.$th.txt -F, '{print $1","$2","$3;}' > splot.ground.stand.$s.c.$c.th.$th.txt # generate_graph -splot -noline splot.New.stand.$s.c.$c.th.$th.txt end end AWK CODE a) discreteIt.awk BEGIN { M_PI = 3.14159265358979323846; RTOD = 180./M_PI; cut=0; ping=0; nrgThresh=0.0005; } { if (NR>1){ dist[NR-1]=$2; nrg[NR-1]=$3; } }

Appendix

82

END { for(i=1;i<=NR-1;i++){ ##Starts from the beginning to find the FIRST PEAK above the threshold if (nrg[i]>nrg[i+1] && cut==0 && nrg[i]>nrgThresh) { cut=1; ##Calculates the height above ground with respect to the scan angle first = (30000-dist[i]/2)*cos(angle/RTOD); firstInt = nrg[i]; } } for(i=NR-1;i>=1;i--){ ##Starts from the end to find the LAST PEAK above the threshold if (nrg[i]>nrg[i+1] && cut==1 && nrg[i]>nrgThresh) { cut=2; ##Calculates the height above ground with respect to the scan angle last = (30000-dist[i]/2)*cos(angle/RTOD); lastInt = nrg[i]; } } ###Prints the height and reflectance of first and last pulse print first","firstInt","last","lastInt } b) minimaNew.awk BEGIN { FS = ","; nSamples=0; M_PI = 3.14159265358979323846; DTOR = M_PI/180.; RTOD = 180./M_PI; # initialise variables # (stand,cellsize & threshold from the minima shell script) verbose=1; boundFlag=1; test=0; angle=30; say=0; } { for(i=1;i<=4;i++){ lastReturn[i,nSamples]=$i; } for(i=5;i<=10;i++){ firstReturn[i-4,nSamples]=$i; } if(isok(lastReturn,firstReturn,nSamples)){ if(nSamples == 0){ # first time through xMin=lastReturn[1,0];

Appendix

83

xMax=lastReturn[1,0]; yMin=lastReturn[2,0]; yMax=lastReturn[2,0]; }else{ xMin=MIN(xMin,lastReturn[1,nSamples]); xMax=MAX(xMax,lastReturn[1,nSamples]); yMin=MIN(yMin,lastReturn[2,nSamples]); yMax=MAX(yMax,lastReturn[2,nSamples]); } nSamples++; } } END { angleINrad=angle*DTOR; print "For angle=",angle > "/dev/stderr"; nxcells = int((xMax - xMin)/(1.*cellsize) + 0.999); nycells = int((yMax - yMin)/(1.*cellsize) + 0.999); if(verbose){ print "I found",nSamples,"points" > "/dev/stderr"; print "{",xMin,xMax,"}","{",yMin,yMax,"}" > "/dev/stderr"; print "nCells: x:",nxcells,"y:",nycells,"of size",cellsize > "/dev/stderr"; } # loop over all samples & assign to a cell for(i=0;i<nSamples;i++){ xCell=whichCell(lastReturn[1,i],xMin,cellsize,nxcells,boundFlag); yCell=whichCell(lastReturn[2,i],yMin,cellsize,nycells,boundFlag); zPoint=lastReturn[3,i]; # how many points so far in that cell? n = nPoints[xCell,yCell]*1; cellStore[xCell,yCell,n] = i; if(n==0){ minZpoint[xCell,yCell]=zPoint; }else{ minZpoint[xCell,yCell] = MIN(minZpoint[xCell,yCell],zPoint); } if(minZpoint[xCell,yCell]==lastReturn[3,i]){minIDs[xCell,yCell]=i;} nPoints[xCell,yCell]++; } ### Local Neighbour Testing ### If there is at least one z local minimum smaller than the current ### then it changes the value of z!!! Neighbour Distance=1.5*Cellsize for(i=0;i<nycells;i++){ for(j=0;j<nxcells;j++){ n=nPoints[j,i]; for(k=0;k<n;k++){

Appendix

84

p=cellStore[j,i,k]; maxValueOld = -1e9; if(minZpoint[j,i]==lastReturn[3,p]){ # check 8 cells, closest to cell j, i for(jj=j-1;jj<=j+1;jj++){ for(ii=i-1;ii<=i+1;ii++){ if((jj!=j && ii!=i)){ maxDvalueSoFar=compareCells(minZpoint[j,i],minZpoint[jj,ii]); point2=minIDs[jj,ii]; distan=sqrt((lastReturn[1,p]-lastReturn[1,point2])^2 + (lastReturn[2,p]-lastReturn[2,point2])^2); if (maxDvalueSoFar>maxValueOld && distan<=1.5*cellsize){ maxValueOld=maxDvalueSoFar; II = ii; JJ = jj; } } } } p2=minIDs[JJ,II]; pdist=sqrt((lastReturn[1,p]-lastReturn[1,p2])^2 + (lastReturn[2,p]-lastReturn[2,p2])^2); if(maxValueOld>0){ pslope=atan2(maxValueOld,pdist)*RTOD; print lastReturn[1,p],lastReturn[1,p2],lastReturn[2,p],lastReturn[2,p2],pslope > "/dev/stderr"; # change value only if the slope is high enough if(pslope>angle){ lastReturn[3,p]=minZpoint[JJ,II]; say++ } } } } } } ###Loop again to update the minimums### for(i=0;i<nSamples;i++){ xCell=whichCell(lastReturn[1,i],xMin,cellsize,nxcells,boundFlag); yCell=whichCell(lastReturn[2,i],yMin,cellsize,nycells,boundFlag); zPoint=lastReturn[3,i]; # how many points so far in that cell? n = nPoints[xCell,yCell]; cellStore[xCell,yCell,n] = i; if(n==0){ minZpoint[xCell,yCell]=zPoint; }else{ minZpoint[xCell,yCell] = MIN(minZpoint[xCell,yCell],zPoint); }

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nPoints[xCell,yCell]++; } # Loop and print the records which have the lowest z for(i=0;i<nSamples;i++){ xCell=whichCell(lastReturn[1,i],xMin,cellsize,nxcells,boundFlag); yCell=whichCell(lastReturn[2,i],yMin,cellsize,nycells,boundFlag); # In case first return is in a different cell than the last return. This can happen due to the scan angle!!!# xFirst=whichCell(firstReturn[1,i],xMin,cellsize,nxcells,boundFlag); yFirst=whichCell(firstReturn[2,i],yMin,cellsize,nycells,boundFlag); zPoint=lastReturn[3,i]; # Create a file with normalized heights print lastReturn[1,i]","lastReturn[2,i]","lastReturn[3,i]-minZpoint[xCell,yCell]","lastReturn[4,i]","firstReturn[1,i]","firstReturn[2,i]","firstReturn[3,i]-minZpoint[xFirst,yFirst]","firstReturn[4,i]","firstReturn[5,i]","firstReturn[6,i] > "normal.stand."stand".c."cellsize".th."nThresh".txt"; # Print record with lowest z with regard to the threshold stated if(zPoint == minZpoint[xCell,yCell] && nPoints[xCell,yCell] >= nThresh && lastReturn[3,i]!=""){ doMe++; print lastReturn[1,i]","lastReturn[2,i]","lastReturn[3,i]","lastReturn[4,i]","firstReturn[1,i]","firstReturn[2,i]","firstReturn[3,i]","firstReturn[4,i]","firstReturn[5,i]","firstReturn[6,i]; }else{ if(zPoint == minZpoint[xCell,yCell] && nPoints[xCell,yCell] < nThresh) test++; } } print "Threshold used # ",test," times" > "/dev/stderr"; print "nSamples, doMe: ", nSamples, doMe > "/dev/stderr"; print "Filtering Used: ", say > "/dev/stderr"; } #In case we want the output to be printed in an image file (.pbm) #writeImage(minZpoint,nxcells,nycells,zmin,zmax,"something.pbm",0); #########################FUNCTIONS########################## func writeImage(array,nx,ny,zmin,zmax,name,nullvalue, i,j,count){ # open image file print "P2" > name; print "# CREATOR: somename.awk scaled:",zmin,zmax >> name; print nx,ny >> name; print 255 >> name; count=0; for(i=0;i<ny;i++){ for(j=0;j<nx;j++){ count++; if(count==NCOLS_IMAGE)printf("\n") >> name;

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if(array[j,i] == nullvalue){ printf("%3d ",255) >> name; }else{ printf("%3d ",int(0.5+(array[j,i]-zmin)*254/(zmax-zmin))) >> name; } } } printf("\n") >> name; close(name); } func isok(lastReturn,firstReturn,nSamples){ # placeholder for a filter on quality return(1); } func MIN(a,b){ return(a<b ? a : b); } func MAX(a,b){ return(a>b ? a : b); } func whichCell(x,xmin,xcellsize,nxcells,boundFlag, xcell){ # x is (real) coordinate # xmin : (real) min x # xcellsize : (real) cellsize # nxcells, boundflag, return: which cell were in # zero-based counting xcell = int((x - xmin)/xcellsize); if(boundFlag){ if(xcell>nxcells-1)xcell=nxcells-1; if(xcell<0)xcell=0; } return(xcell); } func compareCells(z1,z2) { return(z1-z2); } func tan(an) { if(cos(an)!=0){return sin(an)/cos(an);} else{ print "WRONG ANGLE!!!" > "/dev/stderr"; exit; } }

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APPENDIX B: NORMALIZED HEIGHT DISTRIBUTIONS

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APPENDIX C: ADDITIONAL FIGURES AND TABLES

Scan angle (degrees) Used footprint (cm)

0 (nadir) 27

5 27.2

10 27.8

15 28.9

20 30.5

Table C 1: The adjustment of the footprint according to the scan angle.

Figure C 1: Digitised flight lines (red lines) overlaid on the stands' polygons.

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Figure C 2: The distribution of the intensities of the points on stand #3.

Figure C 3: The distribution of the intensities of the points on stand #12.

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Figure C 4: The flowchart of the algorithm used to filter the lidar points.

simulation of discrete-return lidar signal from conifer...

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