aerostat photogrammetry - tu delft

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Aerostat Photogrammetry

for Large Scale Hydrological Modeling

with Special Focus on Energy Balance Terms

MSc Geomatics Graduation Research Project

Athanasios Bantis

Delft, 2008

Graduation Committee:

Prof. Dr. In. Nick van de Giesen, Water Management (CiTG)

Dr. In. Kourosh Khos Elham, Optical and Laser Remote Sensing (AE)

Dr. Sisi Zlatanova, GIS technology (OTB)

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Preface

This is a graduation research project conducted as part of the study programme

of MSc Geomatics, TU Delft. The duration of the project is nine months which is

equivalent to 45 ECTS.

I would like to use this space to express my gratitude to my main supervisors:

Professor Nick van de Giesen of Water Management section of CiTG for all his

help and support during the duration of the project, and especially during the

data acquisition campaign, and Dr. Kourosh Khos Elham of Optical and Laser

Remote Sensing of AE for his invaluable help and feedback throughout the

project.

Also, I would like to thank Martijn Westhoff for his support and clarifications on

the temperature distribution model, and for his help flying the balloon at

Maisbich. Also I would like to thank Ben, and all the boys and girls of Water

Management section for their zest about the project and for their willingness to

help.

Moreover, I owe a big thank you to Bart Slot for bringing his kite during the pilot

and for his enthusiasm in the project.

Last, but most certainly not least, I would like to thank my family for their

support throughout my studies and my crazy friends Nick, Dimitris, Chryso,

Katita for cheering me up when things looked dim.

I wish you a very pleasant reading.

Thanos Bantis

Delft, August 2008

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Table of Contents

List of Acronyms .............................................................................................................................. vi

List of Figures ................................................................................................................................... vii

List of Tables ....................................................................................................................................... x

Abstract ............................................................................................................................................... xi

1. Introduction ................................................................................................................................... 1

1.1 Motivation ............................................................................................................................................... 1

1.2 Research objectives ............................................................................................................................. 1

1.3 Structure .................................................................................................................................................. 2

2. Terrain Data Acquisition for Hydrological Modeling ..................................................... 3

2.1 Overview of data acquisition techniques ................................................................................... 3

2.1.1 Land surveying .............................................................................................................................. 3

2.1.2 Photogrammetry .......................................................................................................................... 4

2.1.3 Laser scanning ............................................................................................................................... 5

2.1.4 Satellite photogrammetry ........................................................................................................ 5

2.1.5 Radargrammetry .......................................................................................................................... 6

2.1.6 SAR Interferometry ..................................................................................................................... 6

2.1.7 Trade-off .......................................................................................................................................... 6

2.2 Description of the temperature distribution model .............................................................. 7

2.2.1 Description of the energy balance terms used in the temperature model ........... 9

2.2.2 Role of Digital Elevation Model in determining energy balance terms ............... 10

3. Principles of Aerial Photogrammetry ................................................................................ 12

3.1 Concepts of analytical photogrammetry ................................................................................... 12

3.1.1. Internal geometry of a frame camera ............................................................................... 13

3.1.2 Orientation procedures in photogrammetry .................................................................. 14

3.2 Photogrammetrically derived DEM ............................................................................................ 18

4. The Maisbich Experiment ....................................................................................................... 20

4.1 Experimental setup............................................................................................................................ 20

4.1.1 Camera characteristics ............................................................................................................ 20

4.1.2 Camera triggering ...................................................................................................................... 21

4.1.3 Camera mounting ...................................................................................................................... 21

4.2 Pilot using a kite .................................................................................................................................. 22

v

4.2.1 Camera calibration .................................................................................................................... 23

4.2.2 Pilot data acquisition ................................................................................................................ 25

4.2.3 Pilot results ................................................................................................................................... 27

4.2.4 Improvement of the pilot results ........................................................................................ 31

4.3 Data acquisition over the Maisbich subcatchment ............................................................... 35

4.3.1 Site description ........................................................................................................................... 35

4.3.2 Image acquisition ....................................................................................................................... 36

4.4 Generation of DEM of Maisbich subcatchment ...................................................................... 37

4.4.1 Aerial triangulation of the upstream part of the catchment .................................... 38

4.4.2 Aerial triangulation of the downstream part of the catchment .............................. 45

4.4.3 DEM extraction ........................................................................................................................... 48

5. Analysis of Maisbich DEM ....................................................................................................... 53

5.1 DEM accuracy assessment .............................................................................................................. 53

5.2 DEM post-processing ........................................................................................................................ 56

5.3 Information extraction ..................................................................................................................... 59

5.3.1 Direct beam solar radiation and shadow ......................................................................... 59

5.3.2 Long wave (thermal) radiation and Sky View Coefficient ........................................ 60

5.3.3. Results of shadow and SVC calculation ............................................................................ 60

5.3.3.1 Shadow estimation results ................................................................................................. 61

5.3.3.2 SVC calculation results ......................................................................................................... 63

6. Temperature distribution simulations .............................................................................. 67

6.1 Temperature distribution model output .................................................................................. 67

6.2 Discussion .............................................................................................................................................. 71

7. Conclusions and recommendations .................................................................................... 72

7.1 Conclusions ........................................................................................................................................... 72

7.2 Recommendations ............................................................................................................................. 74

References......................................................................................................................................... 76

Appendix A: Tables ........................................................................................................................ 78

Appendix B: Maps ........................................................................................................................... 91

Appendix C: Graphs ....................................................................................................................... 95

vi

List of Acronyms

DEM Digital Elevation Model

SVC Sky View Coefficient

GCP Ground Control Point

GPS Global Positioning System

INS Inertial Navigation System

SAR Synthetic Aperture Radar

RMSE Root Mean Square Error

CMOS Complementary Metal Oxide Semiconductor

CCD Charged Coupled Device

LPS Leica Photogrammetry Suite

SLR Single Lens Reflex

vii

List of Figures Figure 2.1 Conceptual sketch of the temperature distribution model……………………9

Figure 2-2 The heat transfer processes influence the temperature distribution of a stream……………………………………………………………………………………………………………………..10

Figure 2-3 The 5 x 5 meter resolution DEM used by the model for the calculation of shadow influences……………………………………………………………………………………………………11

Figure 3-1 The internal geometry of a camera…………………………………………………...13

Figure 3-2 Orientation procedures in photogrammetry………….…………………………..14

Figure 3-3 The collinearity condition………………………………………………………………...15

Figure 4-1 The camera which will be used along with its technical characteristics…………………………………………………………………………………………………………18

Figure 4-2 The timer remote controller used in the experiments along with its characteristics…………………………………………………………………………………………………………19

Figure 4-3 The camera – timer – cradle system………………………………………………….20

Figure 4-4 The test site selected for the pilot……………………………………………………..20

Figure 4-5 The board that was used for calibration……………………………………………21

Figure 4-6 The point marking residuals after the calibration……………………………...22

Figure 4-7 The radial distortion curve for the 20mm lens…………………………………..22

Figure 4-8 The data acquisition using an aerostat (kite)…………………………………….24

Figure 4-9 The pilot block of images………………………………………………………………….26

Figure 4-10 The planimetric object space residual vectors of the pilot………………….27

Figure 4-11 The height object space residual vectors of the pilot………………………….27

Figure 4-12 The DEM as extracted from the pilot imagery……………………………………28

Figure 4-13 The pilot DEM residuals having the ground truth as reference…………...29

Figure 4-14 The extracted DEM from the block having converted

camera parameters…………………………………………………………………………………………………..32

Figure 4-15 Comparison of the pilot DEM’s………………………………………………………….32

Figure 4-16 Thematic map of the study site in Maisbich……………………………………….33

Figure 4-17 Snapshot of the data acquisition campaign

using a balloon as a platform……………………………………………………………………………………34

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Figure 4-18 The location of the GCP’s in the image………………………………………………36

Figure 4-19 The block now constitutes of two images………………………………………….37

Figure 4-20 The two images of the block after correcting for the initial exterior orientation parameters……………………………………………………………………………………………40

Figure 4-21 The resulting block. Only control point information is considered…..…41

Figure 4-22 The distribution of control and check points……………………………………..42

Figure 4-23 Upstream planimetric error vectors…………………………………………………43

Figure 4-24 Upstream height error vectors…………………………………………………………43

Figure 4-25 The resulted downstream block……………………………………………………….45

Figure 4-26 Planimetric error vectors of downstream…………………………………………46

Figure 4-27 Height error vectors of downstream………………………………………………...46

Figure 4-28 Different perspectives of the canopy lead to exclusion of common features…………………………………………………………………………………………………………………..48

Figure 4-29 Using seed data improves the reliability of DEM……………………………….50

Figure 4-30 The extracted upstream DEM…………………………………………………………..51

Figure 4-31 The extracted downstream DEM……………………………………………………...51

Figure 5-1 The ground truth, upstream DEM elevation values residual vectors….52

Figure 5-2 Elevation residual vectors of the downstream DEM………………………….53

Figure 5-3 Elevation residual vectors of the upstream part of Maisbich……………..54

Figure 5-4 Elevation residual vectors of the downstream part…………………………..54

Figure 5-5 The filtering procedure…………………………………………………………………...55

Figure 5-6 Final upstream DEM after editing…………………………………………………….56

Figure 5-7 Final downstream DEM after editing………………………………………………..56

Figure 5-8 The orthorectified upstream mosaic………………………………………………..57

Figure 5-9 The orthorectified downstream mosaic…………………………………………...57

Figure 5-10 The digitized stream position…………………………………………………………..59

Figure 5-11 Shadow simulations for 12:00 23/4/2006………………………………………..60

Figure 5-12 The final results of the shadow simulations……………………………………...61

Figure 5-13 An upward looking viewshed overlaid with a “fisheye” photograph……62

Figure 5-14 Determination of horizon angles……………………………………………………….63

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Figure 5-15 The locations of the samples taken for computation of SVC………………..63

Figure 5-16 Two viewshed’s of two different points on the stream……………………….64

Figure 5-17 The distribution of SVC samples………………………………………………………..64

Figure 6-1 The observed temperature values……………………………………………………..65

Figure 6-2 Temperature simulation comparison between the 5 x 5 meter DEM and the photogrammetric DEM………………………………………………………………………………………..67

Figure 6-3 The observed temperature values

for 25/04/2006, 8:00AM – 17:00PM…………………………………………………………………………68

Figure 6-4 Temperature simulation comparison for a single day………………………...68

x

List of Tables Table 2-1 Trade off table of different terrain data acquisition techniques…………….6

Table 4-1 The calibration parameters………………………………………………………………22

Table 4-2 The camera parameters seem to have converged to wrong values, having the focal length as reference……………………………………………………………………………………..25

Table 4-3 Statistics of the pilot aerotriangulation………………………………………………26

Table 4-4 The triangulation results before and after importing the converted camera parameters…………………………………………………………………………………………………..31

Table 4-5 Exterior orientation parameters after processing one image………………37

Table 4-6 Exterior orientation parameters after processing two images…………….38

Table 4-7 Exterior orientation parameters after introducing weights in the input data…………………………………………………………………………………………………………………………38

Table 4-8 Exterior orientation parameters after introducing initial values…………40

Table 4-9 Statistics of the upstream triangulation……………………………………………...44

Table 4-10 Statistics resulted from the downstream triangulation…………….…………47

xi

Abstract Knowledge of temperature distributions on streams and lakes is considered to

be a valuable source of information for a wide range of disciplines such as

ecologists, hydrologists and geochemists, as it can provide insights into the

dynamics of these water bodies (Westhoff, 2006). Modeling of surface water

temperature on the other hand is a complex process requiring coupling of spatial

and hydrological data (Boyd, Kasper, 2003).

At local scales, all influences of the landscape to the water temperature are

considered important, even those which are too difficult to quantify. High

resolution terrain data can compensate landscape influences by providing

insight in the thermal effects of direct solar radiation (by shadow modeling) and

longwave radiation (by modeling of ‘Sky View Coefficient’, SVC).

Usually, the demand on high resolution terrain data is translated into increased

costs during acquisition. As a result, scientists interested in temperature

distribution along streams are forced to make a compromise between costs and

more detailed temperature modeling.

Photogrammetry employed from an aerostat platform is proposed as an

inexpensive technique, able at providing terrain data of centimeter level

accuracy and resolution. The applicability of the proposed method was tested on

a first order stream located in Maisbich subcatchment in central Luxembourg,

where temperature modeling experiments are taking place.

A 10 x 10 cm digital elevation model (DEM) was extracted using

photogrammetric principles for the upstream and downstream part of the

subcatchment. The accuracy of the derived DEM was assessed using ground

truth points measured by a total station and points collected using the floating

mark principle. The resulted height root mean squared error was found 7cm for

the upstream and 6.44 cm for the downstream part having the ground truth

points as reference, and 8.34 cm and 23.14 cm having the floating mark points as

reference.

The DEM served as a basis for information extraction relevant to the

temperature distribution model. The influence of shadow in the stream

temperature was modeled using hillshade and viewshed algorithms. The SVC

was modeled by using upward looking viewshed algorithms. The resulted data

were imported in the temperature model. An improvement of 0.0727°C was

observed when compared to the temperature output using data from a coarser

DEM (5 x 5 meters).

Chapter 1 - Introduction

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1. Introduction

1.1 Motivation Spatial data have always been an integral part in hydrologic models for water

management applications. From the digitization of streams, rivers etc, to

analytical modeling of processes playing important role to the output of these

models, spatial data together with hydrologic parameters contributed getting

one step closer in understanding and quantifying the way natural phenomena

operate.

As these models become more complex and more localized in their spatial extent,

there is a need for minimizing assumptions and simplifications while including

as many input parameters as possible. This is to minimize output errors and

poor model performances. At such local scales, all influences are considered

important, even those which are too difficult to quantify (Boyd, 2003). High

resolution spatial data can offer such robustness as far as landscape influences

are concerned.

Nowadays, there exist many different ways of acquiring high resolution terrain

data for a specific application. Usually, the demand for very high resolution leads

to an increase of costs, as more sophisticated data acquisition equipment has to

be used. For localized hydrologic experiments, such initial investments can

compromise the available monetary budget, which results to a compromise on

the demand of high resolution.

Such a project is taking place in the Maisbich subcatchment, located in central

Luxembourg. There, TU Delft’s section of Water Management is conducting a

series of experiments aiming at modeling the distribution of water temperature

along the stream taking into consideration hydrologic and energy balance terms.

Parameters which affect the output of the model, such as shadowing and ‘Sky

view coefficient’ are either estimated using a coarse Digital Elevation Model

(DEM) that cannot compensate for the high landscape variability occurring at

such local scales, or estimated subjectively in situ. At this point, it should be

noted that in this project, when referring to DEM what is actually meant is a

digital surface representation of the area. In this definition both topography and

natural objects such as the canopy of trees, bushes etc is included.

As a result, there is a need for higher resolution landscape data, data that can

accurately and quickly chart a region in an inexpensive way.

1.2 Research objectives Primarily the objective of this graduation project is to investigate the existence of

a technique that can accurately and quickly provide very high resolution 3-

Chapter 1 - Introduction

2

dimensional terrain data for hydrologic models in a cost efficient way.

Secondarily, it is going to be tested weather these terrain data can help towards

the improvement of the developed temperature distribution model output.

The restrictions which are posed on this graduation project are:

The data acquisition technique has to be able to provide terrain data at a

centimetre level resolution. This is to ensure that all the influences that

affect the aforementioned water temperature distribution model

originating from the landscape are modelled as detailed as possible.

The spatial coverage of the data acquisition technique has to be adequate

for the specific localised hydrologic experiment.

The initial costs of obtaining and implementing the technique have to be

minimal, while ensuring cost efficiency in the repeatability of

measurements. This will help hydrologists to become independent of

costly terrain data acquisition campaigns.

1.3 Structure The structure of this graduation project is as follows:

Chapter 2 provides some background information on terrain data acquisition

techniques in relation with hydrologic experiments. The role of terrain data in

the temperature distribution model is also explained;

Chapter 3 aims at providing some theory on the chosen data acquisition

technique;

Chapter 4 deals with terrain data acquisition, data processing, and product

derivation for the temperature model;

Chapter 5 assesses the accuracy of the derived products and deals with

secondary information extraction from them;

Chapter 6 provides some information on weather the output of the temperature

model is improved with the newly derived data;

Finally, Chapter 7 provides the conclusions and recommendations of this thesis.

Chapter 2 – Terrain Data Acquisition for Hydrological Modeling

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2. Terrain Data Acquisition for Hydrological

Modeling This chapter aims at providing some background information relevant to the

objectives of this project. In the first part, a description of the present terrain

data acquisition techniques is given, along with a trade-off table, which

determines the preferred technique for hydrologic applications. In the second

part, the role of terrain data in a specific hydrologic model is described, along

with some general information about the model.

2.1 Overview of data acquisition techniques Nowadays there exist many different techniques for obtaining accurate 3-

dimensional terrain data using various sensors onboard various platforms,

ground-based, airborne or spaceborne. Each of these techniques has their own

advantages and disadvantages. The choice for the optimal method should be

made within a specific application framework. In the context of localized

hydrologic experiments, this framework is characterized by three main factors,

namely resolution, spatial coverage, and cost of each data acquisition technique.

In the following, a description of available techniques for the acquisition of

digital terrain data is given within this framework.

2.1.1 Land surveying

Traditional land surveying includes acquiring terrain data by means of a total

station (tacheometer) or GPS. A total station uses electromagnetic signals to

measure distances and angles by means of signal reflection, with or without a

reflector. Knowing the travel time of the reflected signal and the horizontal and

vertical angles, it is possible to calculate the coordinates of any point of interest

relative to the position of the total station. A GPS on the other hand, uses the

signals acquired by satellites (a minimum of four) to compute the 3d position of

any point by means of triangulation. GPS has the disadvantage of requiring a

clear signal from space, which is usually not the case in natural environments

such as a water catchment where a lot of trees are present.

Land surveying has the potential of delivering millimeter to centimeter accuracy

level terrain data, at any desirable resolution. However, large areas are very

difficult to be covered, since each individual point is measured manually at the

field.

The cost of the technique greatly increases by the size of the area for which

terrain data is needed. For small areas, the cost is limited only by the availability

of the instruments (total station or GPS).


4

2.1.2 Photogrammetry

Photogrammetry has been defined by the American Society for Photogrammetry

and Remote Sensing as “the art, science, and technology of obtaining reliable

information about physical objects and the environment through processes of

recording, measuring, and interpreting photographic images and patterns of

recorded radiant electromagnetic energy and other phenomena” (Wolf, Dewitt,

2000). The fundamental principle of photogrammetry is making use of a stereo

pair of images to reconstruct the original 3d shape of an object or, in other

words, to form a stereo model, and then to measure the 3d coordinates of any

point of the object in the stereo model.

According to the nature of the acquisition platform, two forms of

photogrammetry can be distinguished: aerial photogrammetry and close range

photogrammetry.

Close range photogrammetry includes acquiring images taken from a short

distance to the object to be modeled. The position and orientation of the camera

usually is estimated through the use of targets on the object surface (Atkinson,

1996). Close range photogrammetry is typically used for modeling man-made

objects, such as buildings, and not the natural environment.

Aerial photogrammetry includes obtaining images from platforms such as

manned or unmanned airplanes and helicopters. Similar to close range, in aerial

photogrammetry the position and orientation of the camera is estimated by

means of points measured on the surface of the ground, known as ground

control, or a combination of GPS/INS (inertial navigation system) (Abdullah,

2004).

In both cases, photogrammetry is capable of acquiring high resolution terrain

with accuracies in the order of mm-cm. Close range photogrammetry is typically

restricted to small areas and well defined objects, while aerial photogrammetry

can cover medium to large areas. The costs in the first case are limited to the

costs of acquiring a camera and appropriate softwares. In the second case, the

costs are increased considerably as an aerial campaign has to be implemented.

An interesting approach when the topic comes to low cost aerial acquisition is

aerostat photogrammetry. Aerostats are defined as lighter-than-air crafts

(including free or tethered balloons, kites) deriving their lift from the buoyancy

of surrounding air rather than aerodynamic motion. Their advantages can be

summarized as quick in situ deploy ability, which can ensure repeatability in

observations, and reduced cost as compared to the platforms described above.

Disadvantages are the vulnerability of aerostats to wind variations, and the

difficulty to navigate the platform on a predefined path.


5

2.1.3 Laser scanning

Laser scanning is a range measurement technique based on transmitting laser

beams deflected by a mirror to a certain angle, and recording the reflected laser

beams. The distance to an object can be determined by calculating the time of

flight of the reflected laser signal, or phase shift measurements. Phase shift

measurements are more accurate, since they are independent of the flying time.

The 3d coordinates of a scan point is calculated relative to the scanner from the

measured range and the horizontal and vertical scan angles. Just like

photogrammetry, laser scanning can be employed by ground based or aerial

platforms. Using laser scanners, high point density can be achieved with cm

accuracy data.

Airborne laser scanning includes applying the technique from an aircraft. This

gives the possibility of covering medium to large areas. In airborne laser

scanning, the laser scanner is coupled with an integrated GPS/INS. The 3d

coordinates of a point on the ground is determined by the measured range, the

scan angle, and the position and attitude of the scanner measured by the

GPS/INS. The resolution of the acquired data depends on flying height and speed

as well as the laser pulse and scan frequency (Baltsavias, 1999).

Terrestrial (or ground based) laser scanning, as the name implies, is employed

from the ground. It can cover small to medium sized areas depending on the

number of scans, and is typically used in the industry sector (modeling of

pipelines, electricity cables etc).

The biggest disadvantage of the technique is the cost. Acquiring a laser scanner is

very expensive, while mounting it on an aerial platform further increases the

costs, as the platform must withstand the weight of the equipment.

2.1.4 Satellite photogrammetry

The principles of satellite photogrammetry are the same as those of aerial or

close range photogrammetry. The only difference is the fact that the images are

satellite images. Satellite photogrammetry can cover large areas, with very little

costs as the only thing that is needed is the purchase of the images. The

resolution however is very low compared to the above described platforms (up

to 1m). As a result, this technique is not suited for applications requiring great

level of detail terrain data.


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2.1.5 Radargrammetry

Radargrammetry uses the amplitude information of two overlapping Synthetic

Aperture Radar (SAR) images. Once the sensor – object stereo model is

determined, 3d terrain information can be extracted from the common points in

the SAR images using photogrammetric principles. The usage of SAR images

makes the application of the technique independent of the weather conditions.

However, the accuracy that can be achieved is in the order of meters.

2.1.6 SAR Interferometry

SAR Interferometry, contrary to Radargrammetry, is based on phase information

in two overlapping SAR images. The process of extracting 3d terrain information

using SAR Interferometry consists of a co-registering step of the SAR images,

creating a phase difference image out of them, solving the phase cycle ambiguity,

and finally determine the height of each image point from phase differences. Just

like Radargrammetry, the accuracy of the technique is at a meter level.

2.1.7 Trade-off

Following from the pros and cons of each data acquisition technique, a trade-off

can be made taking into account the three aforementioned determining factors:

resolution, spatial coverage and cost. Radargrammetry and SAR Interferometry

aren’t included in the trade off as the resolution of these techniques is too coarse

for hydrological studies. Table 2-1 summarizes an evaluation of these trade-off

criteria for each data acquisition technique.

Data acquisition techniques R

eso

luti

on

Sp

atia

l co

ver

age

Co

st

Land surveying + - -

Aerial photogrammetry + + -

Close range photogrammetry + - +

Aerostat photogrammetry + +/- +

Airborne laser scanner + + -

Terrestrial laser scanner + +/- -

Satellite photogrammetry - + +

Table 2-1: Trade off table of different terrain data acquisition techniques The ‘+’ sign

means that the criteria is an advantage for a technique, ‘-‘ means that is disadvantage,

and ‘+/-‘ means that is neither an advantage or a disadvantage.


7

As it can be concluded from the above table, photogrammetry employed from

aerostats is the only method that combines all the desired characteristics in an

optimal way. It provides a low cost solution to data acquisition over an area of

medium size with high accuracy and resolution, which makes it suitable for

hydrological studies along streams and rivers.

2.2 Description of the temperature distribution model Knowledge of temperature distribution along streams and rivers is a valuable

source of information for a wide range of disciplines, especially in the

environmental sector. This sort of information is very difficult to be obtained by

measuring the temperature at individual spots on the river - stream surface. For

instance, a hydrologist might be interested in determining the possible sources

of groundwater inflow through temperature variations. The location of these

groundwater sources is usually difficult to be distinguished without a complete

temperature profile of the stream water. For an ecologist it might be of interest

to determine the ideal spots for fish breeding. Again, a complete assessment of

the water temperature might reveal spots which are hidden, or less accessible.

The section of Water Resources Management of TU Delft has developed an

energy balance model that computes the temperature distribution along

streams, taking into account lateral inflows and primary energy flux terms

(Westhoff et al, 2007). Lateral inflows are the sources of groundwater inflow in

the stream. The energy balance terms will be briefly described in the following

section.

The model is based on a system of well mixed reservoirs (pixels) with a fixed

length of 2m. Using mass and energy balance equations, the temperature can be

estimated on a pixel by pixel basis.

The mass and energy balance for temperature transport are:

Where Q, A, and T are the discharge (m3/s), the cross sectional area (m2) and

water temperature respectively. qL is the lateral inflow per unit width (m2/s) and

TL is the temperature of the lateral inflow (°C). R is the sink/source term


8

(Boderie and Dardengo, 2003), where Φtotal is the sum of all energy fluxes per

unit area (W/m2). B is the width of the section (m), pw is the density of the water

(kg/m3) and cw is the specific heat capacity of the water. d/dt and d/dx are the

derivatives in time and space. In finite volumes equations (1) and (2) become:

Where Vi is the volume (m3) and Ai is the cross section area (m2) of section i. Ti is

the water temperature of section i. Qi - ½ and Qi + ½ are the water fluxes between

section i and the upstream and downstream section respectively. QL is the lateral

inflow (m3/s) and Ti – ½ and Ti + ½ are the upstream and downstream

temperatures of section i. For Q > 0 they are given by:

Where ΔTi and ΔTi-1 are temperature gradients between section i and upstream

and downstream section respectively.

Combining equations (4) to (7) yields:

A conceptual sketch of the model is given in the figure below (Westhoff et al,

2007).

Figure 2-1: Conceptual sketch of the model. The temperature is estimated on a pixel by

pixel basis, by considering all the discharge terms (Q) and volumes (V) of each pixel to

be taken constant over time. The temperature (T) and energy flux (R) terms are allowed

to fluctuate over time. (after Westhoff et al, 2007)


9

A major innovation of the model is that it uses very high resolution, both in space

and time, temperature measurements taken along the stream of interest, to

calibrate the model and compare the simulated to the observed temperature

values. These temperature measurements are made using a distributed

temperature sensing system employed along a multimode fiber optic cable,

which is installed on the stream of interest. This sort of system has a

temperature measurement precision of 0.01°C every meter (Westhoff et al,

2006).

The principle behind these measurements is the following. Part of the laser pulse

that is emitted from the source, is reflected back along the cable. Having timed

the return time, one could determine the distance from where the light was

reflected. Most energy will be reflected at the wavelength of the original pulse,

but part of the energy will be absorbed and re-emitted at shorter or longer

wavelengths. The reflection at longer wavelength (which is referred as Stokes

backscatter) has amplitude that is not temperature dependent. The reflection

with shorter wavelength (Anti-Stokes backscatter) has amplitude that is linearly

dependent on temperature. By measuring the Stokes/Anti-Stokes ratio, one

could determine the temperature anywhere along the cable (Westhoff et al,

2006).

2.2.1 Description of the energy balance terms used in the temperature

model

The change in the temperature of a stream can be expressed as the heat

exchange between the stream and the environment. The heat transfer processes

that influence the temperature of a stream are solar radiation (direct and

diffuse), longwave (thermal) radiation, streambed conduction, evaporation, and

stream/air convection. Figure 2-2 illustrates the heat transfer processes (Boyd

and Casper, 2003).

Figure 2-2: The heat transfer processes influence the temperature distribution of a

stream (after Boyd and Kasper, 2003)


10

The total net heat energy flux, Φtotal, is the sum of the above heat transfer

processes. Solar radiation only introduces heat energy on the stream while the

rest of the processes are capable of both delivering and removing heat from a

stream (Boyd and Kasper, 2003).

Solar radiation (both direct and diffuse) has the potential of being the main

source of energy on the stream. Stream shade on the other hand, is a factor that

affects direct solar radiation to a large extent, and can create significant

temperature variations on the stream. Therefore, it has to be estimated.

Longwave radiation includes the atmospheric longwave radiation, the back

radiation and the land cover longwave radiation. The last term depends mainly

on the vegetation present near the stream and is expressed as ‘Sky View

Coefficient’ (SVC).

Stream/air convection is the heat exchange between the stream and the air

driven by temperature differences, streambed conduction is the heat energy

conduction between the streambed and the water column, and evaporation

represents the energy that is used for evaporation (Westhoff et all, 2006).

2.2.2 Role of Digital Elevation Model in determining energy balance terms

During a sensitivity analysis that has been carried out on the estimated

parameters of the developed temperature distribution model by Westhoff et al, it

has been found that the output of the model is sensitive to parameters such as

shadow cast on the stream and SVC.

The DEM that was used initially in the model for the estimation of the shadow

influences has a resolution of 5 x 5 meters. From this DEM, critical shadow angles

were computed for each point on the stream by looking at thresholds for shading

between the critical shadow angle and the position of the sun (Boyd and Casper,

2003). The shadowing effects of vegetation were modeled by classifying the

vegetation according to its height and density (Westhoff, 2006). The SVC value

was estimated empirically at the field (Westhoff, 2006).

The above described approach has some drawbacks, mainly because of the lack

of spatial data with sufficient resolution. The resolution of the used DEM appears

to be too coarse to compensate for the high spatial variability of the landscape

(topography and vegetation) which affects the modeling of shadow to a large

degree. This is especially true considering the width of the stream (ranging from

30cm to 1m). Moreover, the vegetation height, density and SVC were estimated

subjectively on the field. The same holds for the spatial position of the

vegetation.

Having a higher resolution DEM of the area would help towards making more

objective estimates about these parameters, thus adding another source of


11

robustness to the output of the temperature model. Aerostat photogrammetry

has the potential of delivering such data quickly and in an inexpensive way.

Figure 2-3 shows the DEM that was originally used (Courtesy of Westhoff).

Figure 2-3: The 5 x 5 meter resolution DEM used by the model for the calculation of

shadow influences. This level of detail is not adequate to represent the spatial variability

which occurs at local scales near the stream (blue line). The colorbar represent the

elevation differences in meters (Courtesy of Westhoff).

Chapter 3 – Aerostat Photogrammetry: Principles & Methodology

12

3. Principles of Aerial Photogrammetry The goal of this chapter is to provide the reader a background on the theory

behind photogrammetric measurements, and explain the terminology which is

used in forthcoming chapters. The first part provides the mathematical

background of photogrammetry, while the second part gives some details on the

imagery derived DEM.

3.1 Concepts of analytical photogrammetry The basic principle of photogrammetry in general is the following: If a point

appears in two or more images, then the 3d coordinates of the point in object

space can be determined from image coordinates provided that the position and

orientation of the camera and its internal geometry is known in object space.

Figure 3-1 illustrates the basic principle.

Figure 3-1: Illustration of basic principle of photogrammetry (Source: Leica

Geosystems).

Analytical photogrammetry is a term used to define the mathematical

calculations based on the camera parameters, the measured image coordinates

and the ground truth about the object to be modeled (Wolf, Dewitt, 2000). The

final goal is to determine the 3d coordinates of any point appearing on the

images, in object space. This can be done by formulating a system of equations

having more equations than unknowns, so that it can be solved using the least

squares adjustment method. The formulation of this system is achieved through

a series of transformations (orientations) between particular coordinate

systems, namely the pixel coordinate system, the image coordinate system, and

the object coordinate system.


13

3.1.1. Internal geometry of a frame camera

The primary instrument that is used to make measurements in photogrammetry

is a camera. However, a camera is a device purposed for taking images and not

doing measurements. Therefore, calibration is necessary if one wishes to make

accurate measurements. Camera calibration (Brown, 1971) is a procedure that

defines the internal geometry of the camera.

The internal geometry of the camera is defined by the following parameters:

Position of the principal point (xo, yo);

Focal length (f);

Lens distortion (Δr);

Fiducial marks (or pixel size in the case of off-the-self digital cameras).

Figure 3-2 displays graphically the parameters associated with camera

calibration.

Figure 3-2: The internal geometry of a camera (Source: Leica Geosystems).

The principal point is defined as the point in the image plane where a

perpendicular line from the rear nodal point of the camera lens (perspective

center) intersects the image plane (Wolf, Dewitt, 2000). The length of the line

connecting the principal point to the perspective center is the focal length.

Fiducial marks are special marks placed on the margins of the frame of metric

cameras, and are used to determine the center of the image. If a digital camera is

used instead, then these marks are not necessary because the image center can

be determined from the fixed number of light sensitive elements (pixels) within

the frame of the camera.

Lens distortion is a very important parameter, as it affects greatly the accuracy of

the photogrammetric measurements. The main effect of lens distortion is the


14

deterioration of the positional accuracy of the image points on the image plane. It

can be distinguished in radial and tangential components. The radial components

can be expressed as a polynomial function of the radial distance from the

principal point, and is given by the following formula (Wolf, 1983):

Where Δr is the radial distortion, r is the radial distance from the principal point

and k are the distortion coefficients.

The tangential component is usually very small and can be neglected for

applications where very high accuracies are not needed.

All the above camera parameters are laboratory defined in the case of a metric

camera. However, if a commercial off-the-self digital camera is used, then a

calibration step is necessary.

3.1.2 Orientation procedures in photogrammetry

As mentioned earlier, orientations in photogrammetry are in essence

transformations between different coordinate systems. By performing such

procedures, one can reconstruct the 3d model of the terrain from overlapping

aerial images. The process of transforming pixel coordinates to image

coordinates is called interior orientation. Likewise, the process of transforming

image coordinates to object coordinates is defined as exterior orientation.


15

Figure 3-2: Orientation procedures in photogrammetry (Source: Khos Elham, 2008).

By using a 2d conformal (similarity) or affine transformation, the pixel

coordinates can be transformed to an image coordinate system. This practically

involves transforming the rows and columns of each pixel into a fiducial

coordinate system by utilising the fiducial marks in the case that a frame camera

is used. If a non-metric digital camera is used, then this transformation utilises

the number of pixels and the pixel size of the image. The next step is the

transformation of the fiducial coordinate system to the image coordinate system.

To do this, the camera calibration parameters, as described in the previous

section, are needed.

The transformation from image to fiducial coordinate system can be done by

(using a 2d conformal transformation):

*

+ [

] *

+ *

+

Where x2, y2 are the coordinates of a point in the fiducial coordinate system, s is a

scale factor, cos(a), sin(a), –sin(a) are the elements of a rotation between the

axes of the coordinate systems, a0, b0 are two translations and x1, y1, are the

coordinates of a point in pixel coordinate system.

The transformation of the fiducial coordinate system to the image coordinate

system is performed by subtracting the principal point coordinates xp, yp from


16

the transformed fiducial coordinates. The correction for the principal point offset

is applied in conjunction with lens distortion corrections (Wolf, Dewitt, 2000).

Where x, y are the point coordinates relative to the principal point. x2, y2 are the

fiducial coordinates of the point, and xp, yp are the coordinates of the principal

point. After the radial lens distortion value Δr is computed (eq. (11)) its

components (corrections Δx, Δy see eq. (26),(27)) are computed and subtracted

from x, and y respectively. The corrected coordinates of the point become then:

Where xc, yc are the corrected coordinates of the point, x, y are the point

coordinates relative to the principal point, and δx, δy are the corrections for the

lens distortion.

The goal of the exterior orientation procedure is to determine the spatial

position and angular orientation of the camera at the moment the image was

taken, relative to an object coordinate system. In photogrammetry, this is done

by utilising a 3d conformal transformation. This transformation is used to derive

the so-called collinearity condition equations. Collinearity is the condition

specifying that the exposure station (the camera), any object point and its

corresponding image point all lie along a straight line in a 3d space(Wolf, Dewitt,

2000). This is illustrated in the figure below where O, p, and P all lie on a straight

line.


17

Figure 3-3: The collinearity condition (Source: Leica Geosystems, 2008)

The collinearity equations consist of the coordinates of a point in the image

coordinate system (x, y, -f), the corresponding measured coordinates in the

object coordinate system (X, Y, Z) and the six exterior orientation parameters (ω,

φ, κ: three attitude parameters and Xc, Yc, Zc: three positional parameters). The

mathematical relationships are given below:

Where m11 ....m33 are the elements of a 3x3 rotation matrix M (containing ω, φ, κ),

which defines the rotation between the image coordinate system and the object

coordinate system.

In the case of a single image, the exterior orientation parameters can be

determined by utilising at least 3 object points, not lying on a straight line, whose

object space coordinates are known (ground control points, GCP’s). This method

is known as space resection. When a stereo pair of images is present, one image

can be oriented relative to the other to form a 3d model of the terrain. The

resulting 3d model can then be oriented to the object coordinate system by

utilising 3 GCP’s. The former procedure is called relative orientation, and the

latter is called absolute orientation.


18

The ultimate extension of the above described photogrammetric principles is

made using the aerial triangulation technique. This technique simultaneously

computes all six orientation parameters for each image in a block of overlapping

images. Bundle block adjustment is a method that is commonly used to perform

aerial triangulation. Parameters involved in the bundle block adjustment include

the exterior orientation parameters of each image in the block, the X, Y, Z

coordinates of tie points (points that appear in two or more images) and

adjusted GCP’s. The unknown parameters (or corrections to their initial values)

are estimated in one solution using the least squares adjustment technique. In

this work, the bundle adjustment module of the Leica Photogrammetry Suite

(LPS) software (Leica Geosystems, 2008) is used for orienting a block of images,

and carrying out photogrammetric measurements of the terrain.

3.2 Photogrammetrically derived DEM Once overlapping images are oriented, a DEM can be generated by measuring

corresponding points in images and calculating their 3d coordinates on the

ground (via collinearity equations). To automatically establish correspondence

between images, digital image matching technique is used.

Image matching refers to the automatic identification and measurement of

corresponding image points that are located on the overlapping areas of multiple

images (Leica Geosystems, 2008).

Image matching methods can be distinguished in three techniques (Atkinson,

1996):

Area based matching;

Feature based matching;

Relational based matching.

Area based matching techniques utilize the gray levels (or colour) of a template

window in one image, and a search window in a subsequent image. The matching

is done by computing the normalized cross-correlation coefficient (which takes

only radiometric differences into consideration) or by using the least squares

adjustment technique (which accounts for both radiometric and geometric

differences).

Feature based matching looks into the correspondence of common features in

the images. These features can be points, edges (linear features) or regions (area

features). Cross-correlation and least-squares technique can also be used here to

find matches between features.

Relational based matching refers to the matching made by examining both the

image features and relationships, such as proximity, parallelism, orthogonality

etc. between them.


19

The digital image matching technique that was used for DEM generation in this

work was area based matching based on cross correlation.

Once the common features have been identified in the images, the 3d

information of each feature is extracted using photogrammetric techniques as

described in the previous section.

Chapter 4 – The Maisbich Experiment

20

4. The Maisbich Experiment This chapter describes the pilot and the data acquisition over the Maisbich site. It

deals with the processing steps, and the difficulties that were encountered when

applying photogrammetric principles from an aerostat platform. This chapter is

divided in four parts. First, the experimental setup is described. Then, a pilot

using a kite as a platform is analysed. The description of the Maisbich

subcatchment comes next, along with the application of aerostat

photogrammetry in the site and the generation of a DEM.

4.1 Experimental setup In line with the project’s goal of providing a low cost terrain data acquisition

technique, a non-metric, off-the-self digital camera was used for image

acquisition. The following sections give a short description of the camera

characteristics, the camera triggering, and the camera mounting on an aerostat

platform.

4.1.1 Camera characteristics

The camera that was used throughout the experiments was a Canon EOS 350D.

This is a commercial digital single-lens reflex camera capable of providing

imagery up to 3456 x 2304 pixels resolution. It features a CMOS (Complementary

Metal Oxide Semiconductor) sensor which preserves the regularity of the light

sensitive elements found in CCD (Charged Coupled Device) sensors, with

increased power efficiency and reduced production costs. The camera can

deliver fine quality images in a JPEG and RAW format. Figure 4-1 shows the

Canon EOS 350D camera along with a summary of its specifications.

Figure 4-1: The Canon EOS 350D camera along with its technical characteristics (Source:

DP review.com).

A 20mm fixed focal length, wide angle lens was mounted on the camera to

increase the spatial coverage of each image. The horizontal, vertical and

Canon EOS 350d Sensor photo detectors 8.2 million

Sensor dimensions 22.2 x 14.8 mm (3.28 cm²)

Max resolution 3456 x 2304 pixels

Compressed format JPEG (EXIF 2.2)

Quality levels Fine, Normal

Weight (inc betteries) 540gr Dimensions 127 x 94 x 64 mm


21

diagonal angle of view obtained by this lens is 84°, 62°, and 94° respectively. The

weight of the lens is 405gr (Canon.com, 2008)

4.1.2 Camera triggering

For the triggering of the camera, a Canon TC-80N3 timer remote controller was

used. Among its functions, the most useful for the experiments are the ability to

set an interval timer, or time delay, between subsequent exposures, and the

exposure count, which is the setting up of the number of exposures. Figure 4-2

shows the Canon TC-80N3 remote controller along with a summary of its

characteristics.

Figure 4-2: The Canon TC-80N3 timer remote controller used along with its

characteristics (Source: Canon-reviews.com).

4.1.3 Camera mounting

The mounting of the camera to the aerostat platform was done using a picavet

cradle. The picavet, named after it's inventor Pierre Picavet, is comprising of a

crossbar, at the edges of which pulleys or hooks are attached, and two brackets,

each one of a single pulley, that are fixed to a single line under the platform.

Additionally, one continuous rope loops through all six pulleys, and a ring

constrains the two innermost lines as they cross. The effect is that despite the

change of the attitude of the platform, the pulleys will keep the camera in a

constant position. The complete camera – timer – cradle system is shown in the

Figure 4-3 below.

Canon TC-80N3

Interval timer 1 sec to 99 hrs, 59 min and 59 sec (in 1 sec intervals)

Self timer 1 sec. to 99 hours, 59 minutes, and 59 sec. (in 1 sec. intervals)

Long exposure timer 1 sec. to 99 hours, 59 minutes, and 59 sec. (in 1 sec. intervals)

Exposure count 1 – 99 images

Weight (incl. batteries) 85gr Dimensions 40 x 20 x 133mm


22

Figure 4-3: The camera – timer – cradle system.

4.2 Pilot using a kite In order to asses the applicability of an aerostat platform for photogrammetric

measurements, and to have an indication of the magnitude of the expected errors

(due to tilt, image blurring, effect of shadows etc.), a pilot flight was prepared.

The flight was conducted using a semi rigid Power Sled 36 kite. This sort of kite

incorporates multiple air chambers for increased lifting ability. It can fly in a

wide range of wind speed from 4 - 10 m/sec (birdseye.nl).

The test site is located in Oostduipark near Scheveningen beach in Den Haag. It

encompasses an area of about 80 x 50 meters covered with sand dunes and

vegetation. Figure 4-4 depicts the test area of the pilot.

Figure 4-4: The test site selected for the pilot (Source: Google maps, 2008).


23

4.2.1 Camera calibration

As mentioned in section 3.1.1, a calibration step has to be performed before the

camera can be used as a measuring instrument. This is especially true for a non-

metric off-the-shelf camera mounted with a wide angle lens, as the distortion of

the images increases heavily towards the edges of the image. Photomodeler

software (EOS Systems Inc, 2008) was used for camera calibration in this work.

The software features a fully automatic calibration using a 2-dimensional board,

as shown in Figure 4-5. The board is comprised of 100 points, four of which are

coded targets that serve as control points and have to be visible in all images.

The calibration model is based on the collinearity equations where the

coordinates of the target points are known in object space (since they are printed

on an A2 paper), and are automatically measured in image space using image

matching techniques. The camera calibration parameters are unknown variables

estimated in the calibration model.

Figure 4-5: The board that was used for calibration.

The board was taped to a planar surface before image acquisition. A total

number of 16 images were taken, rotated 90° with respect to each other for

precise determination of the principal point.

An indication of the calibration quality can be assessed by looking at the

residuals between the observed, and the estimated positions of the coded

targets. The Root Mean Squared Error (RMSE) is a frequently-used measure of

the differences (residuals) between values predicted by a model (in this case the

calibration model) and the values actually observed from the thing being

modeled or estimated. The RMSE aims to aggregate these residuals into a single

measure of predictive power (Wikipedia.org). The calibration resulted in a point

marking RMSE of 0.094 pixels. Figure 4-6 illustrates the point marking residuals


24

as error vectors superimposed on the calibration board. The estimated camera

calibration parameters are summarized in Table 4-1.

Figure 4-6: The point marking residuals after the calibration. The random directions of

the error vectors are an indication that no systematic error remains after the calibration

(note: the error vectors are exaggerated by a factor of 1000)

Table 4-1: The calibration parameters

Using the estimated radial distortion coefficients in the distortion model given in

equation (22) a radial distortion curve can be plotted. The radial distortion curve

provides an indication of the magnitude of the distortion of the lens as the

distance from the principle point increases. Figure 4-7 shows the obtained radial

distortion curve.

Canon EOS 350d w/ 20mm lens Focal length 20.430304 mm. Deviation: 0.003 mm

Principal point: Xo 10.852238 mm. Deviation: 0.002 mm

Principal point: Yo 7.2704020 mm. Deviation: 0.002 mm

Format width: Fw 21.918120 mm. Deviation: 3.3e-004 mm

Format height: Fh 14.611600. Deviation: 3.3e-004 mm Radial distortion coefficient: K1 2.046e-004. Deviation: 9.4e-007 Radial distortion coefficient: K2 -3.722e-007. Deviation: 6.5e-009 Radial distortion coefficient: K3 0.000. Deviation: 0.000 Tangential distortion coefficient: P1 2.674e-005. Deviation: 1.3e-006 Tangential distortion coefficient: P2 1.420e-005. Deviation: 1.3e-006


25

Figure 4-7: The radial distortion curve for the 20mm lens. The values of both x and y

axis are in pixels.

As can be seen from Figure 4-7, the magnitude of radial distortion reaches

almost 4 pixels as we approach towards the edges of the image (note: the image

resolution is 3450 x 2304 pixels). Considering that the camera is a non-metric,

commercial off-the self product, this level of distortion can be an indication that

the quality of the lens that was used is reasonably high.

4.2.2 Pilot data acquisition

The image acquisition was planned at a flying height of 40m. This was to ensure

that the accuracy of the photogrammetric products will be high enough to meet

the requirements of the temperature distribution model. However, a main

difficulty of aerostat platforms is that maintaining a constant flying height is very

difficult, and large variations (in the order of meters) from the initial plan are

inevitable. According to the planned flying height, the image scale can be

calculated as:

Where S is the image scale, f the focal length, and H the flying height.

Consequently, the area covered on the ground is 42.96 x 28.65 m, with a ground

pixel size of 12.43 mm. Assuming vertical image acquisition with a calibrated

camera, the expected accuracy on the ground can be estimated using the

following equations:


26

√

√

( )

Where σ is the accuracy of the image measurements taken as 1 pixel, ns is the

photo scale number, and B/H is the ratio of the air base (distance between two

subsequent exposure stations) to the flying height. The base to height ratio is 0.3,

if a 60% overlap between two images can be maintained.

For the ground control, a total station survey was prepared in an arbitrary

coordinate system. Artificial targets were placed on the ground in order to be

easily identifiable. The size of the targets in object space was 10 x 10 cm, colored

with a white 5cm diameter dot. In image space, the size of the targets was 12 x

12 pixels with the white dot having diameter of 6 pixels. A total number of 15

ground control points evenly distributed in the test area were measured using

the total station.

The camera – timer – cradle system was mounted 20 m below the kite line to

minimise camera movements due to sudden gust winds. The timer was

programmed to take images at 10 sec intervals. The camera was set to take

images at maximum resolution (3456 x 2304 pixels). Figure 4-8 illustrates the

data acquisition campaign.

Figure 4-8: The data acquisition using an aerostat (kite). The magnified part shows the

camera suspending from the kite line.

The image acquisition campaign lasted about 20 minutes resulting in a large

number of images. From these, 14 images were selected for processing,


27

considering their overlap and the clarity in identifying features, especially the

GCP’s.

4.2.3 Pilot results

Although a flight plan was developed prior to data acquisition, it was not

possible to follow the plan due to the nature of the data acquisition platform. In

fact, it was found that it is almost impossible to follow a predefined flight path,

making the image collection more or less ‘blindly’. As a result, from the 15

measured ground points only 11 were visible in the final dataset. From these 8

were used as control and 3 as check points. Check points are measured points in

situ whose ground coordinates do not take part in the triangulation procedure

but instead are used for comparison between the observed and the computed

coordinates. These points are considered to be a true indication of triangulation

accuracy.

The aerial triangulation procedure was the most time consuming process.

Obtaining a reliable solution with the calibration parameters as described in

section 4.2.1 was almost impossible. As a result, the camera parameters, namely

the focal length, principle point position and radial lens distortion, were included

as unknowns in the process of self-calibration block adjustment. However, the

estimates obtained from self-calibration were values that don’t correspond to

the expected camera characteristics. This can be attributed to insufficient

amount of GCP’s needed for such an initial approximation. Table 4-2 below

shows the values of the camera characteristics after self-calibration.

Table 4-2: The camera parameters seem to have converged to wrong values, having the

focal length as reference.

In order to have an initial approximation of the unknown exterior orientation

parameters, all 14 images were used. This helped in obtaining redundancy,

through the multiple measurements of the same point, in the initial solution.

After that, the images containing the largest residuals in object and image space

were removed. In the end, 8 images were included in the block. Figure 4-9 shows

the block of the images obtained for the pilot.

Camera parameters as obtained from self calibration

Focal length 31.9968 mm.

Principal point: Xo 3.8685 mm.

Principal point: Yo 5.8088 mm. Radial distortion coefficient: K1 -2.1667E-004 Radial distortion coefficient: K2 7.8459E-008


28

Figure 4-9: The pilot block of images. The red triangles represent the GCP’s, while the

red circles are the check points.

The aerial triangulation using self calibrating block adjustment yielded a RMSE

for the 8 control points of 3.38 cm in X, 13.03 cm in Y, and 29.96 cm in Z. The

corresponding image space RMSE was 7.3168 pixels in x, and 5.1493 pixels in y.

For the three check points the corresponding RMSE in object space was 26.03 cm

in X, 37.63 cm in Y, and 51.04 cm in Z. The image space RMSE values were 0.8113

pixels in x direction, and 2.5869 pixels in y. Figures 4-10 and 4-11 below

illustrate the planimetric and height object space residuals for both control and

check points. Table 4-3 provides a summary of the aerotriangulation statistics.

Table 4-3: Statistics of the pilot aerotriangulation (all values are in meters).

GCP’s RMSE Mean error

X 0.0338 -0.0255

Y 0.1303 -0.0171

Z 0.2996 -0.1501

Check RMSE Mean error

X 0.2603 -0.2242

Y 0.3763 -0.2644

Z 0.5104 0.1658


29

Figure 4-10: The planimetric residual vectors in object space. The control points are

illustrated by the red triangles, the check points by the red circles, and the exposure

stations of the images by the blue crosses. The coordinates are in the arbitrary total

station coordinate system (in meters). The error vectors are scaled up, to an extent that

they do not overlap.

Figure 4-11: The height residual vectors in object space. The symbols are the same as

the previous figure. The direction of the arrows indicates the sign of the residuals.


30

It was immediately identified that the obtained accuracies both in image and

object space largely deviate from the expected numbers. Reasons for the poor

triangulation results as compared to the expected accuracy derived in the flight

plan can be many. After close examinations, the following were hypothesized as

possible causes for the large errors:

Errors in the camera calibration results;

Insufficient number of GCP’s;

Inadequate geometry of image acquisition.

All the above described errors compromise the quality of the DEM extracted

from imagery to a large degree, making it an unreliable source for information

that will contribute to the improvement of the hydrologic models. Nevertheless,

a DEM was extracted with the above described configuration, in order to

examine the errors with respect to the ground truth data. Figure 4-12 below

illustrates the extracted DEM.

Figure 4-12: The DEM as extracted from the pilot imagery.

As can be seen, many blunder points appear throughout the DEM surface. These

are identified as the white and black spots on the smooth gray of the DEM

surface. The RMSE over the control and check points was 4.92 m for the six

control points appearing in the overlapping area of the images, and 0.98 m for

the two check points. The corresponding mean error was 0.2532m for the GCP’s

and 0.5073m for the check points. Figure 4-13 below illustrates the vectors of

residual between the ground truth and the DEM values.


31

Figure 4-13: The pilot DEM residuals having the ground truth as reference.

4.2.4 Improvement of the pilot results

As mentioned earlier, the calibration of the sensor was identified as one of the

possible causes for the large errors. The use of the interior orientation

parameters estimated by the Photomodeler software, resulted in very poor

triangulation results and, for some images, no solution at all. Only after self

calibrating block adjustment an approximation of the interior orientation

parameters could be achieved. These approximate camera parameters, however,

not only were quite different from the Photomodeler results, but also seemed far

from the real specifications of the sensor. Therefore, a closer examination of the

calibration procedure was necessary.

The calibration module of the Photomodeler software, although very reliable in

the sense that it provides results with very small point marking residuals, is not

designed to be interoperable with other digital photogrammetric workstations

such as the LPS. The estimation of the interior orientation parameters is

performed in a different framework. For instance, in Photomodeler the principal

point is taken relative to the upper-left corner of the image. However, in LPS the

principal point is measured as an offset from the image center. Therefore, a

conversion is needed if the Photomodeler calibration parameters are to be used

in LPS.

The sensor size estimated by Photomodeler was:

Fw = 21.918120 mm

Fh = 14.612088 mm


32

The location of the principal point was:

Xo = 10.852238 mm

Yo = 7.270402 mm

To convert the Photomodeler principal point offsets to values that can be used in

LPS we have:

px = (10.852238 – (21.918120/2)) = -0.1068 mm

py = ((14.612088/2) – 7.270402) = 0.0356 mm

Therefore, the input coordinates of the principal point in LPS are -0.1068 mm in

X and 0.0356 mm in Y.

Discrepancies between the software were also identified in the measuring of the

lens distortion. The formula that is used in Photomodeler is:

Whereas in LPS the formula that is used is:

As can be seen, the formula that LPS uses is the Photomodeler’s formula divided

by the radial distance. To avoid further confusions, the corrections for the lens

distortion were included as extra parameters in the triangulation process. These

additional parameters can compensate for the systematic errors inherited from

the lens distortion. The equations used for the correction of lens distortion are:

With:

In the above equations x and y are image coordinates from the principal point, r

is the radial distance from the principal point and k1 and k2 are the radial


33

distortion coefficients. The reason for the absence of k0 term from the above

equations is that it has the same effect as focal length, and can not be self-

calibrated with focal length simultaneously (Leica Geosystems, 2008). The

accuracy of the distortion coefficients is heavily dependent on the number and

accuracy of GCP’s.

A test was carried out to verify the effect of the conversion mentioned above on

the triangulation results. Two blocks of images with the same properties except

for the interior orientation parameters were prepared. In one block, the interior

orientation parameters estimated by the LPS self calibration option were used.

In the other block, the interior orientation parameters obtained by

Photomodeler were converted and imported in LPS. The values were f = 20.4303

mm, and location of principal point xo = -0.1068 mm, yo = 0.0356 mm. With these

settings, the triangulation was performed again. Table 4-4 summarizes the new

triangulation results for the 8 GCP’s and 3 check points in both blocks.

Self calibration camera parameters Converted camera parameters

Control RMSE Check RMSE Control RMSE Check RMSE

Object X: 0.0338 m Object X: 0.2603 m Object X: 0.0166 m Object X: 0.1742 m

Object Y:0.1308 m Object Y: 0.3763 m Object Y: 0.0203 m Object Y: 0.4353 m

Object Z: 0.2996 m Object Z: 0.5104 m Object Z: 0.0625 m Object Z: 0.0499 m

Image x: 7.3168 pixels Image x: 0.8113 pixels Image x: 1.3944 pixels Image x: 0.4965 pixels

Image y: 5.1493 pixels Image y: 2.5869 pixels Image y: 1.3994 pixels Image y: 0.3793 pixels

Table 4-4: The triangulation results before and after importing the converted camera

parameters

The mean error in X, Y, Z direction for the second block was -0.0057m, -0.0087m,

and -0.0241m respectively for the GCP’s. For the check points the mean error

was -0.1113m, -0.2660m, -0.0357m in X, Y, and Z.

As can be seen, the triangulation with converted camera parameters yields

better RMSE values both in image and ground space. The exterior orientation

parameters along with their accuracies are given in the Tables A-1 to A-4, which

can be found in the Appendix A. From these tables, it can be concluded that the

converted camera parameters as obtained from Photomodeler calibration

report, have given more realistic estimates with reduced uncertainties for almost

all unknowns. However, one can notice that the results still include some

unrealistic values for the spatial position of some images. For instance, on image


34

7 the flying height (Zs) has a negative value. These images were excluded during

DEM generation.

Figure 4-14 illustrates the DEM generated from the second block of images. The

control point RMSE was 0.3317 m, and for the two check points the RMSE was

0.1305 m. The mean error was -0.1892m for the GCP’s, and 0.0883m for the

check points.

Figure 4-14: The extracted DEM from the block having converted camera parameters.

The Figure 4-15 below provides a comparison of the DEM derived from the first

block, and the DEM derived from the images with converted camera parameters,

with the ground truth data as reference. As can be seen, the deviation from the

ground truth is smaller for the latter DEM.

Figure 4-15: Comparison of the pilot DEM’s


35

4.3 Data acquisition over the Maisbich subcatchment To provide the input information for the temperature distribution model

described in section 2.2, aerostat photogrammetry was employed in the Maisbich

subcatchment, with settings similar to the pilot described in the previous section.

In the following, a description of the site as well as the data acquisition and

processing is presented.

4.3.1 Site description

The study site is located in central Luxembourg on a small first order stream that

is part of the Maisbich water catchment. The subcatchment is the eastern part of

Maisbich, located in 49°53′ N latitude and 6°02′E longitude, having elevation

ranging from 296 to 494m. Along the stream, a fiber optic cable has been

installed which provides continuous temperature measurements both in space

and time. The total length of the studied section of the stream is 580m. In Figure

4-16 below, a thematic map of the Maisbich subcatchment is shown.

Figure 4-16: Thematic map of the study site. Luxemburg is surrounded by Belgium,

Germany and France. The Maisbich catchment is located in central Luxembourg (Source:

Westhoff et al, 2007).

The stream is located inside a mixed evergreen and broadleaves forest, which

makes its accessibility difficult. The stream itself is rather small, with both

depths and cross sections ranging below 1 meter.

Large parts of the stream are completely covered by the foliage of the trees. This

prevents the application of aerostat photogrammetry as the foliage prevents the


36

field of view to the ground. As a result, the application of the method was decided

to be limited to the upstream and downstream parts.

4.3.2 Image acquisition

The setting up of the experiment was the same as described in the pilot, except

for the lifting platform. The primary parameter that affects measurements with

aerostat photogrammetry is the presence or absence, of wind. Aerostats are very

vulnerable to existing wind conditions during the acquisition since their lifting

ability is totally dependent on this factor. Wind speed information which was

obtained from a weather station installed near the subcatchment for the past two

years, indicated that the wind conditions are relatively calm (not exceeding 3

m/sec) in the period that image acquisition would take place.

The use of a kite as an aerostat was thus found inadequate for providing lift to

the camera – timer – cradle system under the above described condition, since

the lifting ability of a kite is directly proportional to wind speed. As a result, a

helium filled balloon was chosen as the aerostat platform for image acquisition.

The size of the balloon must be adequate to withstand the weight of the camera –

timer – cradle (1050 gram in total) considering also a lift safety margin. For this

reason, a 1.83 m diameter balloon was obtained. This sort of balloon has a

helium capacity of 3.7m3 and can lift up to 2.3 kg. The balloon was tethered using

three lines to the operators who control and navigate it, in order to be ‘anchored’

to the sky. Depending on the wind conditions, the number of operators can be

reduced. The Figure 4-17 below shows a snapshot of the data acquisition using a

balloon as an aerostat.

Figure 4-17: Snapshot of the data acquisition campaign using a balloon as a platform.


37

The image acquisition campaign lasted five days from 09/05/08 until 14/05/08.

During this period several attempts were made to acquire images for both

upstream and downstream parts of the subcatchment. The time of flight was

chosen during the midday so that the effects of shadows are minimized.

However, wind speed tends to pick up around midday and loss of equipment

almost occurred during the first day of acquisition due to excessive wind speed.

Luckily, the weather conditions improved the following days and image

acquisition was carried out without significant problems. The flying height was

considered to be the same as in the pilot, i.e. 40m. The resulting dataset

comprised of 89 images for the upstream and 88 images for the downstream

part. The criteria for choosing the images to be processed were the same as the

ones in the pilot.

The acquisition of ground truth was carried out using a Topcon GPT – 7000i total

station, able to provide points up to mm level accuracy, in an arbitrary

coordinate system. The GCP targets were the same as the ones used during the

pilot. This time, special attention was given to the placing and collection of GCP’s

to minimize the chance of falling outside the ground coverage area. The number

of points to be measured was increased and their placing was made intensively

denser compared to the pilot. In the end, 26 points were collected for the

upstream and 14 points for the downstream part.

4.4 Generation of DEM of Maisbich subcatchment The use of very low-cost means in aerial photogrammetry inevitably introduces

errors of increased magnitude when compared to standard aerial

photogrammetry.

Recalling from section 4.2.3, the hypothesized causes of triangulation errors as

identified in the pilot were errors due to camera calibration results, insufficient

amount of GCP’s, and errors due to the inadequate geometry of image

acquisition.

Although an improvement of the results was achieved by converting the

principal point position, the use of a non-metric camera and the lack of precisely

laboratory defined interior orientation parameters inevitably caused uncertainty

when constructing the internal geometry of the camera. This uncertainty

propagated in all subsequent measurements which are made using the sensor.

As it is already mentioned in section 4.3.2 the problem of insufficient number of

ground truth was dealt by creating a larger and denser network of GCP’s both for

the upstream and the downstream parts of the subcatchment.

Another source of uncertainty originates from the use of a highly unstable

platform such as an aerostat, which causes poor geometry of image acquisition.

Even in aircraft photogrammetry, it is impossible to keep the optical axis of the


38

camera truly vertical. However, the deviation of the optical axis in such cases

usually does not exceed 3° (Wolf, Dewitt, 2000). This condition does not hold in

aerostat photogrammetry. The lack of efficient stabilising equipment and the

vulnerability of the platform to wind cause the images to be taken from different

angles all the time, with a deviation ranging from 1° to 10° between subsequent

images in the block. Such high deviation together with the lack of initial

estimates for the spatial position and angular orientation of images introduces

many problems during the aerial triangulation process.

Moreover, modelling a natural environment, such as a water catchment,

introduces image matching errors. Most importantly, repetitive patterns,

especially in the forested parts, combined with the different orientation of the

images cause uncertainty and introduce difficulties when trying to identify

common points in both images.

All these factors affect the quality of the final photogrammetric products and at

the same time pose challenges to be tackled in the processing of the Maisbich

images.

4.4.1 Aerial triangulation of the upstream part of the catchment

After importing the images which constituted the block and the definition of the

camera model by means of the converted interior orientation parameters, the

positions of the GCP’s were identified on the images, and their image and ground

space coordinates were imported. Since the bad geometry of the images was the

reason that correct initial exterior orientation estimates could not be obtained in

the triangulation process, the following strategy was devised: The processing

begun be orienting one image. For this a minimum of 3 GCP’s and no tie points is

needed. Then, each subsequent image is added one at a time, while GCP’s and tie

points were included when appropriate. This way the triangulation can be

initiated with correct initial values, while at the same time the images were

wrong values emerged could be identified.

In line with the above, one image was oriented initially using space resection.

The technique uses the control point information to estimate the exterior

orientation parameters associated with the image in the time of exposure,

making use of the collinearity equations. In principal, three GCP’s are needed for

this task. However, having redundant GCP’s is always an advantage as it

increases the accuracy of the photogrammetric solution (Wolf, Dewitt, 2000). In

the first image of the block, 7 GCP’s were visible, providing sufficient information

for an accurate initial approximation. Figure 4-18 indicates the location of the

GCP’s in the image.


39

Figure 4-18: The location of the GCP’s in the image (red triangles). The image id is

represented as a white number on the top right corner of the image.

The triangulation resulted in the following exterior orientation parameters along

with their accuracies (coordinates in meters, angles in degrees):

Image ID Xs Ys Zs ω φ κ

1 2038.8176 85.5573 43.0369 2.1469 184.0535 341.4384

Image ID mXs mYs mZs mω mφ mκ

1 0.1226 0.0968 0.0334 0.1537 0.1753 0.0494

Table 4-5: Exterior orientation parameters after processing one image.

In the above table, Xs, Ys, Zs, are the camera position in X, Y and Z direction in

object space coordinate system, and ω, φ, κ, are rotations about the image x, y,

and z axis respectively. mXs, mYs, mZs, mω, mφ, and mκ are the corresponding

accuracies (in meters).

The residuals of the 7 GCP’s in image space were 0.6045 pixels in x and 2.7195

pixels in y.

The effects of the errors caused by bad geometry were visible already after

importing the second image in the block. The control points appearing in only

one image were removed as they decrease the redundancy of the triangulation

solution. Five GCP’s remained in the overlapping area of the two images, each

one adding four equations in the solution. The total number of unknowns at this

point is twelve (six exterior orientation parameters for each image), which

results in 8 degrees of freedom.

Performing aerotriangulation with the configuration as described above,

resulted in a RMSE for the 5 GCP’s appearing in the overlapping area of the

images of 3.16cm in X, 3.79cm in Y and 15.81cm in Z. The image RMSE errors


40

were 2.5306 in x and 3.8719 in y. Figure 4-19 shows the extent of the two images

along with the associated GCP’s.

Figure 4-19: The block of two images. The irregularity (which is caused by the tilt) on

image 2 is already visible.

Table 4-6 gives the exterior orientation parameters after triangulation. Having a

closer look at the results, one could clearly identify that the iteration converged

in a wrong value for the Zs of the second image. Moreover, the uncertainty in the

estimates increased, as it can be seen from the accuracies of the exterior

orientation parameters.


1 2038.9158 85.4496 42.9063 2.3083 184.2493 341.3813

2 2032.2838 86.3318 -31.8581 -6.8204 181.8726 201.7363


1 0.6025 0.3892 0.3721 0.5665 0.9667 0.2336

2 0.9274 0.6222 0.2787 0.9122 1.3828 0.2158 Table 4-6: Exterior orientation parameters after processing two images.

The reasons for these wrong values should be primary sought in the input data.

The location of GCP’s on the images was double checked for blunders. Since there

were no mistakes at this point, then uncertainty in measuring of GCP’s was

considered both in image and ground space. However, introducing weights in the

solution in the form of standard deviation values for both GCP’s coordinates in

image and object space, did not solve the unrealistic Zs value. The same was true

when changing the weights of interior orientation parameters.


41

Since the wrong convergence problem is not related to uncertainty of the input

data, one should look for reasons in the nature of the data acquisition platform.

Block triangulation algorithm used by the digital photogrammetric workstation

is designed to operate with near vertical images, meaning that the deviation of

the optical axis of the camera should not exceed 3°. Using a highly unstable

platform, such as helium-filled balloon, makes the images to be acquired with

varying tilt angles which often exceed the above convention, classifying them to

low or even high oblique.

To deal with this problem, the initial values for all exterior orientation

parameters were taken from the previously processed image. In the case of the

first two images, the initial exterior orientation values were taken from image 1

and used as input in image 2. The triangulation results are shown in Figure 4-20.

Figure 4-20: The two images of the block after correcting for the initial exterior

orientation parameters for image 2.

The RMSE of the 5 control points appearing in the overlap area is 2.75 cm in X,

3.6 cm in Y and 4.63 cm in Z. The corresponding image residuals are 0.63 pixels

in x and 2.89 pixels in y. All the input values are considered fixed at this point and

no additional parameters were added for estimation. More detailed the exterior

orientation parameters along with their accuracies are shown in Table 4-8

(values in meters, angles in degrees).


1 2038.9158 85.4496 42.9063 2.3083 184.2493 18.6187

2 2035.8010 90.4753 41.9207 0.1974 183.4659 22.3422


1 0.3521 0.2274 0.2175 0.3311 0.5650 0.1366

2 0.4376 0.2826 0.1937 0.4138 0.7026 0.1462 Table 4-8: Exterior orientation parameters after introducing initial values


42

As can be seen from the table above, the exterior orientation parameters seem to

have converged to realistic values; note especially the flying height Zs of the

second image. Also the accuracies of each parameter for both images are

improved, indicating a more rigorous solution.

This strategy was followed for all the subsequent images of the block. Regardless

of the overlap, an attempt was made to use as many images as possible, in order

to increase redundancy by increasing the number of observations. In the end, 15

images comprised the block. Again, no check or tie point was considered. Figure

4-21 shows the resulting block.

Figure 4-21: The resulting block. Only control point information is considered.

The triangulation procedure resulted in RMSE for the 27 control points of 9.4

mm in X, 1.5 cm in Y and 1.66 cm in Z. In image space, the residuals of the control

points were 0.8722 pixels in x and 1.5896 pixels in y. The resulted exterior

orientation parameters together with their accuracies are shown in the Appendix

A, tables 5 and 6.

As it can be seen from the tables, the error inherited in the observations has been

minimized and distributed evenly throughout the block, yielding better

estimates for all unknowns. However, these figures indicate that the model

adjust well in the GCP’s, since only this information was used. This does not

mean that it behaves the same for the rest of the points on the images. To verify

that the triangulation is truly representative for all points appearing on the

images, and to reveal accumulated errors throughout the block, some of the

GCP’s were converted to check points. Additionally, to increase the redundancy

image points appearing in the overlap area of the images were selected, the so-

called tie points. Tie point collection is a very labor intensive and time


43

consuming procedure, especially when the area of interest is a natural one,

having no distinct features. However, if the exterior orientation parameters are

accurate enough, it can be automated, by utilizing image matching techniques

together with constraints that limit the search space (such as searching along the

epipolar line).

Following from the above, from the 27 measured control points in the field, 6

were converted to check points. The total number of the tie points that was

collected was 108. Figure 4-21 shows the distribution of the control and check

information.

Figure 4-22: The distribution of control (red triangles) and check points (red circles)

Triangulation was performed again with the above input, resulting in a RMSE

error for the 19 control points appearing in the overlap area of 1.55 cm in X, 7.3

mm in Y and 4.8 cm in Z. The corresponding image space RMSE was 0.8053

pixels in x and 0.9245 pixels in y. For the 6 check points the RMSE was 1.55 cm in

X, 2.73 cm in Y and 3.71 cm in Z. The image residual of the check points was

0.4548 pixels in x and 0.5011 pixels in y. Table 4-9 summarize the above.


X 0.0155 0.0034

Y 0.0073 -0.0001

Z 0.0480 -0.0103


X 0.0155 -0.0006

Y 0.0273 -0.0121

Z 0.0371 -0.0165

Table 4-9: Statistics of the upstream triangulation. All values are in meters.


44

The Figures 4-23, 4-24 illustrate the planimetric and height error vectors of each

individual control and check point.

Figure 4-23: Planimetric error vectors. The red circles illustrate the check points, the red

triangles the control points, and the blue crosses the exposure stations. Coordinates are

in meters. The vectors are scaled to an extent that they do not overlap.

Figure 4-24: Height error vectors. The notation is the same as above. The arrows

pointing upwards indicate a positive sign while the ones pointing downwards indicate a

negative sign. Coordinates are in meters.


45

Although the RMSE error with this configuration was increased for the control

points, the image space error was significantly decreased. Comparing these

values with the expected accuracy as derived from parallax equations (20) and

(21) (1.7 cm planimetric, 5.8 cm in height) one could claim that the triangulation

converged to correct estimates.

The resulting exterior orientation parameters with the corresponding accuracies

can be found in Appendix A, tables 7, 8.

4.4.2 Aerial triangulation of the downstream part of the catchment

The problem of unrealistic exterior orientation values which was encountered

during the aerial triangulation of the upstream, was also present in the

processing of the downstream images. To overcome it, the strategy applied in the

upstream part was used.

However, this time there were some additional problems which affected the

triangulation results. Due to time limitations, fewer GCP’s were collected. As a

result, the estimates of the unknowns contained greater uncertainty. To

overcome this, a greater number of images were processed in combination with

increased number of tie points. This provided increased redundancy through

multiple observations of each point. Problems were also introduced by the

inconvenient geometry of the images, which was more intense in the

downstream part.

The resulting block consisted of 15 images. The number of ground control points

was 14. From these, 9 were used as GCP’s and 5 as check points. The total

number of tie points was 271.


46

Figure 4-25: The downstream block. The triangles indicate the GCP’s while the circles

the tie points

Aerial triangulation converged to the following RMSE’s of the input data. For the

9 GCP’s 4.1 mm in X, 1.17 cm in Y and 2.42 cm in Z. The corresponding image

space residuals were 0.7152 pixels in x and 1.0708 pixels in y. For the 5 check

points the error was 4.5 cm in X, 5.03 cm in Y, and 4.05 cm in Z. In image space,

the RMSE was 0.7358 pixels in x, and 0.7328 pixels in y. Compared to the

triangulation results of the upstream, these accuracies are better. However, one

should keep in mind that in this block the reduced number of control points

resulted in increased uncertainty for the triangulation results. This is reflected

by the decreased accuracy for each exterior orientation parameter as compared

to the upstream. Table 4-10 summarises the statistics of the triangulation of the

downstream images.


47


X 0.004 0.001

Y 0.0017 0.0016

Z 0.0242 0.0177


X 0.045 0.0255

Y 0.0503 0.0341

Z 0.0405 0.001

Table 4-10: Statistics resulted from the downstream triangulation (all values are in

meters).

Figures 4-26, 4-27 indicate the scaled residual vectors of each GCP and check

point.

Figure 4-26: Planimetric error vectors of downstream. The red circles illustrate the

check points, the red triangles the control points, and the blue crosses the exposure

stations. Coordinates are in meters.


48

Figure 4-27: Height error vectors. The notation is the same as above. The arrows

pointing upwards indicate a positive sign while the ones pointing downwards indicate a

negative sign. Coordinates are in meters.

The increased ground space residuals of points 37 and 34 show the effect of the

presence of shadow on the triangulation results. These two points appeared on

completely shadow-covered parts of the images, and their image coordinate

measurements were less accurate.

The resulted exterior orientation parameters along with their accuracies are

given in the tables 9, 10 of Appendix A.

4.4.3 DEM extraction

After defining the sensor model by means of interior and exterior orientation, it

is possible to extract a DEM from the overlapping area of two images.

The process of DEM extraction is influenced by the triangulation results, which in

turn is influenced by the nature of data acquisition platform. Since digital image

matching techniques are used in order to locate corresponding points in the

overlapping area of the images, inaccurate triangulation results will result in

false matches. However, the effect of the triangulation results is minor when

compared to the image matching problems introduced by repetitive patterns.

The biggest problems were identified in the forested areas. Finding

corresponding points inside the canopy was very difficult and even impossible in

some cases even after adapting the search window and correlation coefficient

limit.


49

Once the corresponding points in each stereopair are identified, their image

coordinates are recorded, and their 3D ground coordinates are computed using

collinearity equations (forward intersection procedure). The result is a point

cloud, which is then used to model the terrain surface by means of interpolation.

Reasons for weak or false matches can be many. The lack of distinct

unambiguously identifiable objects leads to finding corresponding points in

features such as leafs, branches, flowers etc. The position of these features could

change due to the presence of wind during image acquisition, especially when

considering a ten-second interval between subsequent images. This effect is

more intense in the top parts of the canopy which are directly exposed to the

wind.

Moreover, some points appeared in one image but were occluded in other

images. This fact can be attributed to the nature of the data acquisition platform.

Since the orientation of each subsequent image can differ greatly, each feature is

observed through different perspective. In forested parts of the area this could

lead in hiding corresponding points inside the canopy, preventing their visibility

in both stereopair images. Figure 4-28 shows the disappearance of a common

feature (a branch appearing on the right image) due to different perspective

views of the canopy.

Figure 4-28: Different perspectives of the canopy lead to exclusion of common features.

In addition, intense pattern repeatability inside the canopy prevented the image

matching algorithm from identifying corresponding points and contaminated the

results with false matches in some cases.

All the above described problems introduce errors in the final DEM which

manifest themselves in the form of peaks or pits, or lead in no matching at all,

leaving these areas to be interpolated from the surrounding points.


50

The effect of the errors described above was more intense in the downstream

part. This can be justified by considering the increased uncertainty, due to

reduced number of GCP’s, in the exterior orientation parameters, and in the

worst block geometry compared to the upstream.

To cope with the image matching problems, some corresponding points had to

be identified manually in a very time-consuming and labour-intensive process.

Initially, a DEM was extracted from each individual stereopair with a threshold

overlap of 40%. The stereopairs were then superimposed onto the DEMs and

inspected visually. This way the exclusion of features such as trees, or the

identification of sudden peaks or pits were flat area should be could be

identified. The images, from which the false DEM was extracted, were processed

again in the triangulation module. Common points were identified manually in

the problematic areas of the images in the form of tie points. The image space

RMSE of each new tie point was inspected in order to keep the error in the

triangulation as low as possible. These points were then used as seed points in

the image matching algorithm to improve the accuracy of the resulting DEM.

Figure 4-29 shows the results of importing the manually identified tie points as

seed data during DEM extraction. The left image shows an area of a DEM which is

covered by trees but is incorrectly mapped as flat area. The right image shows

the corresponding area after feeding the algorithm with manually selected seed

data of the canopy.

Figure 4-29: Using seed data improves the reliability of DEM. The red arrow indicates

the position of trees.


51

Search window size, correlation window size and correlation coefficient limit are

some parameters that influence the digital image matching process. These

parameters had to be modified in problematic areas to increase the accuracy of

DEM. The size of search window in X direction defines the search area along the

epipolar line, and was decreased to decrease the chance of false matching. For

the same reasons, the correlation window size was also decreased. The

correlation coefficient limit was set to 0.80. This way, it is ensured that sufficient

points are collected while minimising the chance of false matches. However, the

effect of these modifications in the problematic areas was negligible.

From a total number of 36 and 35 individual DEM files for the upstream and the

downstream part respectively, 24 were used in the final merged DEM for the

upstream and 9 for the downstream. The criterion for the selection was the

individual DEM accuracy relative to ground truth, and the correspondence with

reality by superimposing them on the stereopairs from which they were created.

The ground point spacing of the merged DEM was 12.24 cm in X and 12.20 cm in

Y for the upstream and 11.67 cm in X, 11.26 cm in Y for the downstream. Figure

4-30 shows the resulting upstream DEM, and Figure 4-31 depicts the

downstream DEM.


52

Figure 4-30: The extracted upstream DEM. Elevation values are in meters.

Figure 4-31: The extracted downstream DEM. Elevation values are in meters

Chapter 5 – Analysis of Maisbich DEM

53

5. Analysis of Maisbich DEM This chapter deals with the analysis of the photogrammetrically generated DEMs

as described in section 4.4.3. It is divided in three parts. The first part provides a

quality assessment of the upstream and downstream DEMs, the second describes

DEM editing and orthorectification, and the third part deals with information

extraction relevant to the temperature distribution model in the context of

section 2.2.2.

5.1 DEM accuracy assessment An indication of the quality of a photogrammetrically derived DEM can be

obtained by comparing the elevation values with a dataset of higher accuracy,

and calculating the discrepancies between the two datasets. In the absence of a

reference DEM of higher accuracy, the ground truth data collected by the total

station were used to assess the quality of the derived DEM. This makes sense

since the points collected by total station are assumed to have cm – mm

accuracy.

For the upstream part of the catchment, 24 points were used i.e. all the ground

truth points appearing in the overlapping area of at least two images. Their X and

Y coordinates were identified on the extracted DEM, and the Z values at that

position were compared with the Z values of the reference data. Figure 5-1 below

visualises the residuals.

Figure 5-1: The ground truth, upstream DEM elevation values residual vectors

(exaggerated to the point that they don’t overlap). The coordinates are in meters.

The corresponding RMSE was 7 cm, while the mean error was 4.03 cm.


54

The same procedure was followed for the downstream DEM of Maisbich. This

time, 11 ground truth points were used. The RMSE was 6.44 cm, while the mean

error was 5.01cm. Figure 5-2 shows the residual vectors between the two

datasets.

Figure 5-2: Elevation residual vectors (exaggerated to the point that they don’t overlap)

of the downstream DEM.

Furthermore, an additional accuracy assessment was made by measuring the

reference data in a stereo model. This method makes use of the principle of

floating mark to stereoscopically measure the apparent displacement in the

position of an object, with respect to a frame of reference, which is caused by a

shift in the position of the observation (parallax differences).

In order to view the stereo model, an anaglyphic stereo viewing technique was

applied. The technique includes projecting the stereopair of images with

different shades of colours. The first (left) image is projected with a red shade

while the second (right) image with blue shade. The operator wearing a

corresponding pair of glasses can view the left image with the left eye and the

right image with the right eye, i.e. has a stereoscopic view of the area covered by

the overlapping part of the two images.

To measure the reference elevations, the concept of floating mark and parallax

was used. Two small identical marks were placed on the images, one on the left

and one on the right. The two marks were shifted in position until they fuse

together into a single mark which appears to exist in the stereo model and to lie

at a particular elevation.

The elevation of each particular point was compared to the corresponding

elevation of the extracted DEM.


55

A total number of 50 points were selected for this task, both for the upstream

and for the downstream part of Maisbich. The points were evenly distributed

throughout the block. In addition, an attempt was made to select points inside

the tree canopy, as far as this was possible.

The resulting RMSE for the 50 upstream points was 8.34 cm. The mean error was

-2.04 cm. Figure 5-3 below illustrates the elevation residual vectors.


of the upstream part of Maisbich.

For the downstream the RMSE error for the 50 manually selected points was

23.14 cm. The mean error was found -3.17 cm. The reason for the increased

RMSE compared to the upstream, could be caused by imprecise measurement of

the elevation values in the stereo model. Since measuring height in the stereo

model requires stereoscopic measurement skills, which are obtained by

experience, the measured values may not be very precise. Figure 5-4 below,

visualises the elevation residual vectors


56


of the downstream part.

The corresponding tables for the above described accuracy assessment can be

found in Appendix A, tables A-11 to A-14.

5.2 DEM post-processing After DEM extraction from imagery, post-processing is necessary to remove

mismatch errors appearing in the form of sudden pits or peaks in the elevation.

Having the imagery as reference, these areas were identified and interpolated

from the surrounding pixels. For that reason, a 2nd order polynomial filter was

used inside a user-specified area of interest. Ten buffer points were used outside

the area of interest for the interpolation, on a pixel distance of two pixels from

the edge of the area of interest. Since interpolation methods permanently change

the pixel values, they should be applied with caution. Following from that,

interpolation was applied only to individual pixels and only when these pixels

appear unambiguously as blunder points. Figure 5-5 shows the results of the

interpolation on a ground area. The red arrow indicates the location of a blunder

point which was removed.

Figure 5-5: The filtering procedure.


57

The figures 5-6, 5-7 below illustrate the final DEM’s after editing.

Figure 5-6: Final upstream DEM after editing.

Figure 5-7: Final downstream DEM after editing.


58

Once a DEM is extracted, it can be used to remove the effects of tilt and terrain

topography from the images so that they behave as true vertical photographs.

The process is known as orthorectification, and is carried out in two steps. First,

a transformation is applied using the collinearity equations to relate the original

distorted image to the rectified image, and a digital resampling step which maps

the transformed pixels to a regular grid in the form of an image. The result is an

orthorectified image, which combines the geometric rigidity of a map and the

radiometric properties of an aerial photograph.

This map can then be used as a background layer for extracting information such

as width length and curvature of the stream, canopy extent, vegetation coverage

etc. Figures 5-8, 5-9 show the results of the process.

Figure 5-8: The orthorectified upstream mosaic.

Figure 5-9: The orthorectified downstream mosaic.


59

5.3 Information extraction The final extracted DEM served as a basis for information extraction. Recalling

from section 2.2.2, the parameters that influence the output of the temperature

distribution model are the shadowing of the stream and the SVC. The following

sections describe their influence in detail, and the processing steps towards

estimating these terms.

5.3.1 Direct beam solar radiation and shadow

Solar radiation is considered to be the most significant heat transfer process in

the stream thermal budget. Stream surface shade on the other hand, is an

important parameter controlling the heating received from solar radiation. By

definition, decreased levels of shade cast on the stream increase the amount of

radiation which in turn has a warming effect on the temperature of the stream.

Stream surface shade is influenced and controlled by two factors, namely

channel morphology and near stream vegetation. Channel morphology is defined

by topographic factors, namely stream geometry, stream gradient/sinuosity,

channel width and depth. These factors could have an increasing or decreasing

effect on the total amounts of solar radiation received. Near stream vegetation on

the other hand has a decreasing effect, since it obstructs the sun rays reaching

the stream surface, depending on the vegetation height and the timing of the

shadow (Boyd, 2003).

The temperature distribution model developed by Westhoff et al uses critical

shadow angles, calculated from the 5 x 5 meter resolution DEM for each grid cell

to estimate the shadow. These shadow angles are determined by looking at

thresholds for shading depending on topographic and vegetation angles. If the

solar altitude is greater than the topographic shade angle which is the angle

between a point on the stream and the highest topographic feature, then the

stream is not shaded from direct solar radiation. The shading from vegetation is

modeled by classifying the vegetation in six different classes by means of height

and density. The threshold angles are determined in seven directions (northeast,

north, southeast, south, southwest, west and northwest) (Westhoff et al, 2007).

The photogrammetrically derived DEM provides an overview of the topographic

features and vegetation cover throughout the stream at a very high (cm level)

resolution. This helps to simulate the shadow effects originating from the tree

canopy and from the banks of the stream. These simulations were performed

using hillshade and viewshed algorithms for each stream pixel and are described

in the forthcoming section (5.3.3). These data were then imported to the

temperature distribution model, and the results were evaluated using in situ

temperature measurements.


60

5.3.2 Long wave (thermal) radiation and Sky View Coefficient

Another important source of heating on the stream besides direct beam solar

radiation, is longwave radiation originating from the atmosphere and near

stream vegetation. Longwave radiation includes three components: atmospheric

longwave radiation, back radiation and land cover longwave radiation. The

temperature distribution model developed by Westhoff et al, calculates the above

components using equations derived from the Stefan-Boltzman law (Westhoff,

2007).

Land cover longwave radiation, is the radiation emitted by riparian vegetation

and received from the stream. The denser the vegetation, the larger the amounts

of longwave radiation received by the stream. This is expressed as “View to Sky

Coefficient” (SVC), which is a unitless indication of the obstructed versus the

visible portion of the sky from a specific position on the stream.

Traditionally, this parameter is computed by taking hemispherical (“fisheye”)

photographs from a specific position on the ground, aiming at the sky. However,

the use of this technique is very labor intensive and costly.

In the temperature distribution model developed by Westhoff et al, this

parameter was determined by calibration. The calibration procedure was

performed by varying the values of the parameter in an attempt to minimize the

RMSE of the model output. During a sensitivity analysis that has been carried out

for some parameters of the model, it was found that the model is very sensitive

to changes in the values of SVC. The sensitivity has been determined by

recomputing the RMSE using parameter values 10% above and 10% below the

optimized values (Westhoff et al, 2007) .

During the calibration performed by Wetshof et al, the value of SVC was taken

constant throughout the stream. However, this is not the case, as vegetation and

stream morphology can make the values of the parameter to vary greatly. The

high sensitivity of the SVC could be an indication that the output of the

temperature model could be improved if there was a way to have more refined

information about the parameter.

Using the photogrammetrically derived DEM it is possible to create an upward

looking viewshed for any location on the stream and determine which portion of

the sky is obstructed and which is not.

5.3.3. Results of shadow and SVC calculation

The following sections describe the processing steps and the results of the

shadow estimation and SVC calculation from the imagery extracted DEM.


61

5.3.3.1 Shadow estimation results

In order to be able to simulate the sun rays falling onto the stream, it is necessary

to have the stream position relative to the solar position. The orientation of the

sun relative to the north (solar azimuth) and the angular distance of the sun

above or below the horizon (solar altitude) are two parameters that are essential

for the simulations. These data were obtained from a nearby weather station, for

the period of 23/4/2006 – 4/5/2006 at 10 minute intervals.

The shadow calculation operations were performed only for the upstream part.

This is because a larger part of the stream is visible from the images and can be

digitized from the orthorectified mosaic. The total length of the digitized stream

is 76 m. The absolute position of the stream on the ground was determined using

control points taken from Google Earth (Google Earth, 2008), and was

considered accurate enough for simulating the sun path. Figure 5-10 below

indicates the position of the stream onto the orthorectified mosaic.

Figure 5-10: The stream position (blue polygon)

The primary principle of the simulations is simple. If a surface is not exposed to

the sun for a specific pair of solar altitude and solar azimuth angles, then it is in

the shadow. To implement the principle, hillshade in combination with viewshed

algorithms were applied.

Hillshading occurs when the source of light is away for the surface of interest.

First, the determination of the light source (considered at infinity) is needed.

This is done by the solar altitude and azimuth angles. If the incidence angle of the

sun rays is smaller than 90° relative to the surface normal, then the surface is

exposed to the sun. If the incidence angle is 90° to the surface normal, then the


62

surface is only partially exposed, due to micro-geomorphology, vegetation etc. If

the sun rays are forming an angle larger than 90° with the normal, then the

surface is in the shadow.

Hillshading provides a value for each raster cell ranging from 0 (shadowed) to

255 (exposed). The values in between are determined according to the slope and

aspect of the surface, relative to the incidence angle.

However, the use of only a hillshade algorithm is not adequate to simulate the

actual shadow cast on the stream. A topographic or vegetation feature could

obstruct the visibility of the surface from the light source, even if the incidence

angle is less than 90°. For that reason, hillshading was used in combination with

a viewshed algorithm. Viewshed algorithms identify the cells of a raster that can

be seen from one or more observation points. Viewsheds were created for the

specific solar azimuth and altitude, essentially indicating which parts of the

terrain are in the shadow of other features.

All the pixels appearing in the shadow of an obstacle are assigned a value of zero.

For all the other pixels, hillshade principles were applied. The procedure was

repeated for each solar angle pair. This resulted in 946 simulations, one for each

10 min interval of each day. Figure 5-11 below illustrates two of the simulation

maps.

Figure 5-11: Left, shadow modelling for 12:00 23/4/2006. Right, shadow modelling for

14:00 of the same day.

The digitised stream was then used as a mask on the simulated shadow maps

extracting the pixel values that appear to be on the stream. Figure 5-12 below


63

indicates the results of the simulation on the stream. The y axis represents the

distance from the stream in pixels (a pixel equals to 140cm2), while the x axis

indicates the number of simulations. The colour bar represents the hillshade

values. The values range from 0 (if the pixel is in the shadow) to 250 (the pixel is

directly exposed). Judging from Figure 5-12, it is evident that some parts of the

stream remain in the shadow throughout the day, as they are completely covered

by vegetation.

Figure 5-12: The final results of the shadow simulations. The colorbar represents the

hillshade values.

5.3.3.2 SVC calculation results

An upward looking viewshed is a raster representation of the entire sky that is

visible or obstructed when viewed from a specified location. This is similar as

taking a “fisheye” photograph aiming at the sky. To demonstrate the theory, in

Figure 5-13 below, a viewshed is shown overlaid with a hemispherical

photograph.


64

Figure 5-13: An upward looking viewshed overlaid with a “fisheye” photograph (Source:

ESRI, 2008)

For each specified raster cell, viewsheds are calculated by searching a number of

directions around the locations of interest. The maximum angle of sky

obstruction, sometimes referred to as effective horizon angle (Dozier et al.,

1990), is then determined in each direction. Figure 5-14 illustrates the

determination of horizon angles. For the angles in between interpolation is

applied. Then, the horizon angles are converted to a hemispherical coordinate

system by utilizing an equiangular hemispherical projection, representing a

three dimensional hemisphere of directions into a two dimensional grid. Each

grid cell is assigned a value, which represent the visible versus obstructed sky.

The grid cell location, row and column correspond to an angle relative to the

straight upward, and an angle relative to the north on the hemisphere of

directions (HEMI, 2000).

Figure 5-14: Determination of horizon angles (Source: HEMI, 2000)


65

For the SVC calculation, a total number of 100 samples at approximately 50 cm

intervals were selected along the stream. Figure 5-15 below shows the locations

of the selected points.

Figure 5-15: The locations of the samples taken for computation of SVC

SVCs were computed for all the above samples using the methodology described

above. The parameter ranges between two values, 0 (all sky is obstructed) and 1

(all sky is visible). Figure 5-16 below illustrates the resulting viewsheds for two

points, the first point appearing at the beginning of the digitized stream having

SVC value of 0.3089 and the second appearing at 7 m upstream from that point

having a value of 0.40.

Figure 5-16: Two viewsheds of two different points on the stream

Figure 5-17 below shows the spatial distribution of the samples taken for the

SVC calculation, along with the SVC values of each point.


66

Figure 5-17: Left: The distribution of SVC samples. The colorbar represents the SVC

values. Right: Whisker plot of the distribution. The red line represents the mean value.

Chapter 6 – Temperature distribution model simulations

67

6. Temperature distribution simulations The goal of this chapter is to compare the simulated temperatures of the

Maisbich stream as computed with the original 5 x 5 meter resolution DEM used

by Westhoff et al (2007), and the simulation temperature values as derived from

data originated from the new photogrammetrically extracted DEM. The basis for

this comparison will be the temperature values as were measured using the fiber

optic cable technique described in section 2.2.1. The chapter is divided into two

parts. The first part deals with the temperature simulation results, while the

second provides a discussion on the simulation output.

6.1 Temperature distribution model output In order to have an indication on weather the output of the developed

temperature model was improved with the newly derived data described in

section 5.3, two simulations were performed. The first one consisted of input

data derived from the 5 x 5 meter DEM, while the second with the data derived

from the photogrammetric DEM. The model was slightly modified so it can give

output only for the first 78m of the upstream part of Maisbich, i.e. the part of the

stream that was visible in the images. The simulations were performed using

data from the period of 23/04/2006 12:00 until 30/04/2006 00:00. This is

because in this period there existed measured temperature data for calibration

and comparison of the simulated temperature values. Figure 6-1 below

illustrates the reference temperature measurements using the fiber optic cable

technique.

Figure 6-1: The observed temperature values. The x axis represents the distance on the

stream (2m step) while the y axis represents the number of simulations (10sec step).

The colorbar represents the temperature values.


68

The calibration of the model during the first simulation was already performed

by Westhoff et al, (2006), so no further adjustments were necessary. The

comparison between the simulated and observed temperature values for that

period using Westhoff’s calibration resulted in a RMSE of 0.7152°C with mean

error of -0.1082°C.

Before performing any simulations with the data derived from the

photogrammetric DEM as input, a data manipulation step was necessary so that

they could be used as input in the temperature distribution model. This

primarily included selecting the time period between 23/04/2006 12:00, to

30/04/2006 00:00, i.e. the time period in which temperature observations were

evident. The output of the shadow simulations was 2 dimensional, meaning that

there was a shadow indication for each pixel appearing on the stream both in

width and length. The temperature distribution model however accepts only one

shadow value for each pixel from the starting point of the stream. Therefore, the

shadow values across the stream were averaged so that every pixel along the

stream has only one shadow value, ranging from 0 (shadowed) to 1 (exposed).

Moreover, the resulted shadow matrix had to be interpolated, so it can be in

correspondence with all the data that the temperature model is using as input.

This included interpolating the time step of the shadow simulation matrix from

10 minute intervals into 10 second intervals for the before mentioned time

period, while interpolating the distance step from 12 x 12cm, which is the

resolution of the photogrammetrically derived DEM, to 2 x 2m.

The model takes one value for the determination of SVC, so the mean value of the

SVC distribution was used as input.

The resulted RMSE after calibration with the observed temperature values was

0.6425°C with mean error of -0.09°C. Calibration was necessary to adjust the

energy balance terms, namely diffuse solar radiation, fraction of solar radiation

reaching the streambed, and depth of conduction layer, to achieve more rigorous

output. The calibration has been done by varying these parameters in order to

minimize the RMSE error.

Figure 6-2 below illustrates the simulation results in both cases.


69

Figure 6-2: Up Left: The simulation temperature values using data from the 5x 5 m DEM.

Down Left: The corresponding residuals with the fiber optic cable data. Up Right: The

simulated temperature using data from the photogrammetric DEM. Down Right: The

corresponding residuals between observed and simulated values. The RMSE error in the

first case was found 0.7152°C, while in the second 0.6425°C. The mean error in the first

case was found -0.1082°C, while in the second -0.09°C.

Additionally, an attempt was made to compare the simulated to the observed

temperature values for an individual day, in the time period where shadow is

mostly evident to occur. The date which was chosen was the 25th of April from

8:00 PM until 17:00 AM. This way the effects of the simulated shadow to the

temperature model output can be more easily distinguished. Figure 6-3 shows

the observed temperature values for the individual day while Figure 6-4 below

illustrates the simulation results along with the residual values when compared

to the observed temperatures.


70

Figure 6-3: The observed temperature values for 25/04/2006, 8:00AM – 17:00PM.

Figure 6-4: Up Left: The simulated temperature with the 5x5 m DEM. Down Left: The

corresponding residuals. Up Right: The simulated temperature with the

photogrammetric DEM. Down Right: The corresponding residuals. The RMSE error in

the first case was 0.2418°C, while in the second 0.19°C.

The RMSE in the case of data from the 5 x 5 m DEM was found 0.2418°C, while in

the case of data derived from the photogrammetric DEM was 0.19°C. The

corresponding mean error in the first case was 0.4445°C, while in the second

0.2098°C.


71

6.2 Discussion The reduced RMSE error using data from the photogrammetric DEM is an

indication that the output of the temperature model has improved when

compared to the 5 x 5m DEM. The increased residuals during the first

simulations in Figure 6-2, could be an indication of measurement blunders,

caused by a jump of the fiber optic cable out of the water for example. Observing

the figures 6-3, 6-4, it can be distinguished that the shadow values of the

photogrammetric DEM have decreased the temperature residuals considerably,

and modeled the temperature variation better, especially during the afternoon

hours of the simulations, at distances 60 – 78 meter from the starting point of the

measurements.

It was also found that the computation of SVC value using the method described

in section 5.2.2 tends to underestimate its value, with respect to the temperature

simulations output. A reason for this could be the apparent change in riparian

vegetation at the banks of the stream between the period the temperature

measurements were performed, and the period of the photogrammetric

measurements. Since the temperature measurements using the fiber optic cable

were made during late April, while the photogrammetric measurements early

May, it could be assumed that the riparian vegetation on the banks of the stream

has increased, leading to a decrease of the SVC value. In any case, it would be

interesting to have some ground truth data of the parameter, taken for instance

by hemispherical photographs, so that an indication of the accuracy of the SVC

value can be assessed.

Chapter 7 – Conclusions & Recommendations

72

7. Conclusions and recommendations The goal of final chapter of this graduation research project is to summarise the

findings of all the previous chapters in relation with the research objectives as

presented in the introduction chapter. After that, recommendations on how to

further improve the findings are presented.

7.1 Conclusions The primary research question introduced in section 1.2 was the following:

Is there a data acquisition technique that can accurately, quickly and cost

efficiently provide 3-dimensional terrain data?

Aerial photogrammetry applied from an aerostat platform was proposed as such

a data acquisition technique. It was found that the power of digital

photogrammetry together with a very low cost data acquisition platform can

provide end data of high accuracy and resolution.

The main problems that were encountered during implementing the proposed

method were:

Inconsistencies between different software used to perform different

tasks, namely camera calibration and aerotriangulation;

The highly unstable nature of the data acquisition platform together with

lack of initial estimates for the exterior orientation parameters forced the

bundle block adjustment procedure to converge to unreasonable

estimates for the spatial position and angular orientation of the camera;

The inability of following a predefined flight plan resulted in a significant

loss of ground truth information, as a number of control points were not

visible in the image dataset;

Occlusion problems, caused by different perspective views of common

features, together with the apparent shift in the position of specific

features due to wind, caused image matching problems during DEM

extraction. These problems were more evident inside the canopy of trees.

A conversion of the interior orientation parameters of Photomodeler software

was necessary if they were to be used in aerotriangulation performed by LPS

software. This conversion was performed by adjusting the principal point offset

from the top left corner of an image, to an offset from the centre of the image.

The validity of the above was tested on the pilot dataset and resulted in a

significant improvement in the image and ground space RMSE errors.

The wrong convergence problem was dealt by processing and adding in one

image at a time in a block of images. The estimates obtained from the images

having sufficient ground truth information were used as input for the


73

problematic images. This provided the aerotriangulation algorithm with

sufficient information to reach in more reasonable and accurate estimates.

The inability of following a predefined flight path was dealt by acquiring as many

images as possible, so that the chances of missing ground truth data is

minimised. The advent of off-the-self digital cameras with large memory helped

in this task. Obtaining multiple images, despite their overlap, helped towards

introducing redundancy in the input data by increasing the number of

observations of each single point appearing on the images.

The occlusion problems during DEM extraction was dealt by manually

introducing seed points to the image matching algorithm. These seed data were

tie points measured manually in the problematic areas of tree canopy. This

helped minimising the loss of information occurring by insufficient mass points

in these areas.

For the upstream part of Maisbich, the aerotriangulation procedure resulted in a

planimetric RMSE of 1.5 and 2.7cm in X, Y, and 3.7cm in Z, having the check

points as reference. For the downstream part, the corresponding RMSE’s were

4.5cm in X, 5.03cm in Y and 4.05cm in Z direction. All these values are very close

to the expected accuracy as derived from parallax equations (1.7 planimetric 5.8

height) for 40m flight height.

The final end product was a photogrammetrically extracted DEM of very high

accuracy and resolution. The resulted upstream DEM has a resolution of 12 x

12cm, and height accuracy of 7cm, as assessed by the ground truth data, and

8.34cm as assessed by points selected using the floating mark principle. The

downstream Maisbich DEM has a resolution of 11 x 11cm and accuracy of

6.44cm using the ground truth data and 23.14cm using the floating mark

method. The increased error in the later case could be an indication of increased

uncertainty of the aerotriangulation procedure caused by reduced number of

control points, together with the lack of experience of the operator when

measuring height using the principle of floating mark.

The secondary research objective posed in the introduction chapter of this

graduation project was the following:

How can high resolution terrain data help towards the improvement of the output

of the developed temperature distribution model?

The photogrammetrically derived DEM served as a basis for all information

extraction relevant to the temperature distribution model. Hillshade and

viewshed algorithms were applied in order to model the shadow casted on the

Maisbich stream. The simulations were performed for a time span of 23/4/2006

– 4/5/2006 at 10 minute intervals. The resulted shadow matrix was


74

manipulated so it can be in accordance with all the data the temperature model

is using. The manipulation included interpolation of the time step, and distance

step, and scaling the hillshade values to a nominal scale (shadow, no shadow).

The SVC was estimated by taking samples along the digitized stream and

computing upward looking viewsheds from these points. The viewsheds were

created by searching in a specified number of horizon angles, and converting

them in a hemispherical coordinate system.

These secondary data were used as input in the temperature distribution model.

The shadow calculation helped towards modeling the effects of direct solar

radiation better, while the SVC helped towards estimating the effects of

longwave radiation. The simulations resulted in a temperature RMSE of

0.6425°C, which is an improvement of 0.0727°C compared to the data derived

from the 5 x 5 meter resolution DEM. The comparison was also performed for an

individual day (25/04/2006, 8:00AM – 17:00PM) so that the effects of the shadow

can more easily be distinguished. The resulted RMSE in the latter case was

0.19°C which is an improvement of 0.05°C over the previous available data.

It was also found that the proposed estimation method of SVC tends to

underestimate its value with respect to the temperature simulation output.

Reasons for this could be the change in vegetation caused from the time span

between the photogrammetric and the fiber optic cable measurements.

7.2 Recommendations A number of recommendations can be though of for further research, so that the

findings of this project can be fully exploited.

The accuracy assessment of the photogrammetrically derived DEM was

done using the ground truth data, and the data obtained by the floating

mark principle. Although this assessment can be considered adequate, its

representativeness in areas where ground truth is impossible to be

collected (inside the tree canopy) diminishes. It would be beneficial to

have a dataset of higher accuracy and resolution, collected by laser

scanning for instance. This way a more robust accuracy indication could

be achieved.

Since the main problem during triangulation was the lack of initial

estimates, theoretically it would be beneficial to mount a GPS receiver and

an INS instrument on the aerostat platform so that such estimates can be

directly obtained. This way the number of ground truth can be reduced

and used only for accuracy assessment.

The collection of ground truth in this project was performed using a total

station. One way to further reduce the associated costs of the project is to

build a network of ground control by measuring the relative distance of


75

the points and the angles of the network. This can be done by a metro

tape and a protractor. This makes sense since in this project the spatial

information could be in an arbitrary coordinate system.

The measurements were made using a digital SLR camera. In principle,

any off-the-self digital camera can be used, as long as a trade off between

the final costs and the accuracy – resolution fits the application

requirements.

Although almost all the steps towards reaching triangulation results

required manual intervention, it has been proven that the problems

described in section 7.1 can be overcome by performing specific tasks.

This fact makes the fully automation of aerotriangulation procedure

feasible. This could allow scientists from different background requiring

high resolution terrain data to use this technique without

photogrammetric knowledge.

Aerostat photogrammetry requires a clear view of the object to be

modelled from the images. This was not the case for some parts of the

stream, as a clear view of the stream was obstructed by the tree canopy in

the time period the measurements took place. In order to model the

whole studied stream, repeating the measurements when the tree canopy

does not block the view to the ground is necessary. This could be during

the autumn or during spring before the new germination period.

As far as the derived data are concerned, it would be beneficial to have

some reference data about the SVC and the shadow casted on the stream.

This way an accuracy indication can be attached along with the derived

products.

References

76

References Abdullah, Q.A., 2004. Photogrammetric platforms. In: J.C. McGlone (Editor),

Manual of Photogrammetry. American Society for Photogrammetry and Remote Sensing, Bethesda, Maryland, pp. 1151.

Atkinson, K.B., 1996. Close Range Photogrammetry and Machine Vision. Whittles

Publishing, Caithness, 371 pp. Baltsavias, E., 1999. Airborne laser scanning: basic relations and formulas. ISPRS

Journal of Photogrammetry and Remote Sensing, 54(1999): 199-214. Boyd, M., Kasper, B., 2003. Analytical Methods for Dynamic Open Channel Heat

and Mass Transfer. Available at http://www.heatsource.info. Burrough, P., McDonnel R., 2000. Principles of Geographical Information

Systems. Oxford University Press. EOS Systems Inc, 2008. Photomodeler Pro 5.

Dozier, J. and J. Frew. 1990. Rapid calculation of terrain parameters for radiation modeling from digital elevation model data. IEEE Transactions on Geoscience and Remote Sensing 28:963–969.

ESRI, 2008. ArcGIS v9x. Germroth, M., Cartensen, L., 2005. GIS and Satellite Visibility: Viewsheds from

Space. ESRI International User Conference. Helios Environmental Modelling Institute, 2000. The Solar Analyst User Manual.

Available at: http://www.fs.fed.us/. Koh, A., Graham, R., 2002. Digital Aerial Survey: Theory and Practice. Whittles

Publicing. Leica Geosystems, 2006. Leica Photogrammetric Suite Project Manager. Selker, G., van de Giesen, N., Westhoff, M., Luxemburg, W., Parlange, M. B., 2006.

Fiber Optics Opens Window in Stream Dynamics. Geophysical research letters vol 33.

Westhoff, M., Savenije, H., Luxemburg, W., Stelling, G., van de Giesen, N., Selker, J.

Pfister, L., Ulhenbrook, S., 2007. A Distributed Stream Temperature Model Using High Resolution Temperature Observations. Hydrology and Earth Systems Science.

Wolf, P. R., Dewitt B. A., 2000. Elements of Photogrammetry with Applications in

GIS. McGraw Hill.

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References

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Brown, D.C., 1971. Close-range camera calibration. Photogrammetric Engineering, 37(8): 855-866Brown, D.C., 1971. Close-range camera calibration. Photogrammetric Engineering, 37(8): 855-866.

Mikhail, E. M., Bethel J. S., McGlone J. C., 2001. Introduction to Modern

Photogrammetry. John Willey and sons. DPreview.com. Visited on December 2008. Canon.com. Visited on December 2008. Canon-reviews.com. Visited on May 2008. Birdseye.nl. Visited on March 2008. Kapshop.nl. Visited on April 2008. Maps.google.com. Visited on March 2008. Wikipedia.org. Visited on July 2008. Google Earth.com. Visited on July 2008.

Appendix A: Tables

78

Appendix A: Tables


1 1936.3613 98.4896 60.6801 172.224 -16.7463 -57.3292 2 1941.3292 100.3487 61.1082 173.546 -12.8447 -50.996 3 1960.9149 103.569 59.314 232.4419 195.7405 117.3171 6 2001.6874 102.2222 -60.0222 8.0421 -209.2626 293.4552 7 1976.8028 96.4502 -63.0229 180.7292 -342.9966 -276.2711 8 1969.9828 114.5084 63.3644 342.3927 -174.8729 89.9362 9 1970.8697 113.2927 72.9435 173.1531 -10.9971 -73.1876

12 1954.7404 105.56 57.2267 355.2519 -157.6301 -247.5421 Table A-1: Exterior orientation parameters of the pilot dataset with self-calibration block adjustment.


1 1.2662 0.7027 0.2065 0.6191 1.1135 0.186 2 0.8555 0.5759 0.1831 0.5006 0.7439 0.113 3 0.414 0.4658 0.1875 0.4164 0.3778 0.0775 6 0.5478 0.4702 0.3354 0.4818 0.5464 0.1491 7 0.8099 0.7217 0.1981 0.6733 0.7642 0.1139 8 0.5437 0.4702 0.217 0.4069 0.4493 0.1339 9 0.6425 0.5589 0.2208 0.4169 0.4831 0.0715

12 0.4716 0.426 0.223 0.3959 0.4459 0.0865 Table A-2: Accuracies of the exterior orientation parameters of the pilot dataset with self-calibration block adjustment.

Appendix A: Tables

79

Image ID Xs Ys Zs ω φ Κ

1 1938.6853 94.1002 36.6839 174.4437 -9.8776 -57.3808 2 1943.9758 95.5002 36.9391 174.9479 -4.1668 -51.213 3 1960.9923 100.531 35.6672 174.7866 -5.2264 -62.4899 6 1989.9094 100.2436 35.9272 174.5027 -8.8583 -64.7767 7 1975.4216 102.8119 -40.9505 178.1522 -350.9573 -273.4866 8 1974.0362 109.2331 39.4644 350.7499 -182.9332 89.4667 9 1973.3972 112.1159 44.7694 176.5676 -1.3878 -73.4237

12 1951.998 103.6678 34.3923 359.3017 191.7737 113.301 Table A-3: Exterior orientation parameters of the pilot dataset with converted camera parameters.

Image ID mXs mYs mZs mω mφ Mκ

1 0.187 0.1285 0.0386 0.176 0.2583 0.0483 2 0.1088 0.0984 0.0332 0.1328 0.1469 0.0304 3 0.0637 0.0749 0.0358 0.1039 0.0877 0.0196 6 0.0972 0.0778 0.0454 0.1132 0.1373 0.026 7 0.1412 0.0843 0.0405 0.1143 0.2097 0.0298 8 0.0889 0.0735 0.0403 0.0919 0.1164 0.0216 9 0.0945 0.1035 0.0448 0.1184 0.1101 0.0208

12 0.0722 0.0685 0.0403 0.096 0.1042 0.024 Table A-4: Accuracies of the exterior orientation parameters of the pilot dataset with converted camera parameters.

Appendix A: Tables

80

Image ID Xs Ys Zs ω φ Κ

1 2038.8384 85.5590 43.0439 2.1430 184.0864 18.5642 2 2035.7422 90.7849 42.0347 359.7578 183.3555 22.1906 3 2024.9556 86.5148 33.3809 2.0860 176.0606 17.3497 4 2021.4279 95.1002 38.1617 356.3269 189.3692 14.9084 5 2018.2758 97.9300 40.0984 0.5654 182.7336 13.9649 6 2004.7719 91.9097 36.0390 359.0745 185.2976 37.6129 7 2001.0568 96.5944 38.1496 356.9432 180.3951 17.8734 8 2006.3236 106.3932 37.0960 348.8900 191.2889 4.8006 9 2002.3326 110.8760 37.6085 7.6750 185.5136 18.2461

10 1993.7110 104.4327 34.5456 2.4571 181.9766 16.5728 11 1986.3783 107.3898 42.5248 358.2553 176.9886 15.7831 12 1971.7784 110.1490 40.9596 356.6687 182.0068 14.2227 13 1968.6509 118.8444 43.4190 359.6444 183.1827 357.3781 14 1969.5218 106.5912 40.3306 357.6791 188.9399 34.6694 15 1972.6225 115.3925 46.0397 356.2301 186.1055 354.6328

Table A-5: Exterior orientation parameters of the upstream part of Maisbich. Only GCP information is considered.

Appendix A: Tables

81


1 0.0801 0.0591 0.0283 0.0937 0.1160 0.0302 2 0.0748 0.0845 0.0429 0.1272 0.1170 0.0329 3 0.0657 0.0682 0.0288 0.1373 0.1261 0.0350 4 0.0674 0.1373 0.0304 0.2205 0.1093 0.0328 5 0.1080 0.2172 0.0369 0.3308 0.1593 0.0515 6 0.1294 0.1981 0.0845 0.3217 0.2028 0.0836 7 0.0819 0.1577 0.0426 0.2367 0.1193 0.0508 8 0.0622 0.1236 0.0390 0.1904 0.0935 0.0293 9 0.1362 0.1675 0.1243 0.2411 0.2134 0.0759

10 0.0919 0.0969 0.0430 0.1527 0.1418 0.0339 11 0.0898 0.1643 0.0328 0.2099 0.1140 0.0361 12 0.1298 0.3002 0.0546 0.3713 0.1629 0.0628 13 0.1998 0.3257 0.0607 0.3805 0.2250 0.0836 14 0.2577 0.3825 0.1677 0.4734 0.3128 0.1005 15 0.1503 0.2956 0.0445 0.3290 0.1677 0.0537

Table A-6: Accuracies of exterior orientation parameters of the upstream part of Maisbich. Only GCP information is considered.

Appendix A: Tables

82


1 2038.9220 85.6233 43.0127 2.0256 184.1899 18.5598 2 2035.9747 90.8067 41.9185 359.6874 183.7026 22.2598 3 2024.9720 86.5988 33.4003 1.8985 176.0952 17.3489 4 2021.3367 95.1164 38.1695 356.2973 189.2376 14.9414 5 2018.2464 97.9665 40.0835 0.5070 182.6887 13.9443 6 2004.8530 91.6209 35.8836 359.5445 185.3818 37.4808 7 2001.1297 96.3099 38.0748 357.3614 180.4655 27.7751 8 2006.2905 106.3774 37.1029 348.9089 191.2400 4.7827 9 2002.1645 111.0175 37.7489 7.4723 185.2591 18.2176

10 1993.5963 104.4539 34.6089 2.4132 181.7960 16.5833 11 1986.3497 107.3559 42.5323 358.2950 176.9523 5.7906 12 1971.6602 110.0531 40.9697 356.7867 181.8591 14.2101 13 1968.5228 119.0162 43.4497 359.4490 183.0381 357.3811 14 1969.4481 106.6462 40.3571 357.6042 188.8647 34.6884 15 1972.7153 115.5491 46.0096 356.0516 186.2130 354.6503

Table A-7: Exterior orientation parameters of the upstream part of Maisbich.

Appendix A: Tables

83


1 0.0462 0.0465 0.0166 0.0759 0.0631 0.0194 2 0.0506 0.0459 0.0226 0.0712 0.0733 0.0235 3 0.0529 0.0508 0.0335 0.1013 0.1056 0.0274 4 0.0488 0.0897 0.0188 0.1447 0.0775 0.0207 5 0.0603 0.1127 0.0187 0.1719 0.0883 0.0285 6 0.0368 0.0646 0.0269 0.1054 0.0605 0.0289 7 0.0321 0.0613 0.0164 0.0928 0.0482 0.0202 8 0.0308 0.0614 0.0194 0.0951 0.0471 0.0143 9 0.0910 0.1229 0.0798 0.1769 0.1393 0.0468

10 0.0398 0.0476 0.0175 0.0751 0.0608 0.0164 11 0.0394 0.0583 0.0154 0.0749 0.0490 0.0149 12 0.0380 0.0882 0.0187 0.1094 0.0481 0.0192 13 0.0569 0.0897 0.0205 0.1048 0.0640 0.0227 14 0.0472 0.0988 0.0252 0.1204 0.0619 0.0244 15 0.0472 0.0940 0.0184 0.1047 0.0530 0.0185

Table A-8: Accuracies of exterior orientation parameters of the upstream part of Maisbich.

Appendix A: Tables

84


1 2046.6873 150.7444 40.7524 354.2411 194.2154 174.4356 2 2037.4529 132.4373 46.1787 353.5733 175.6879 117.956 3 2036.6051 150.8644 40.6745 0.4496 182.3774 131.9865 4 2030.7272 130.3812 46.2973 3.5308 181.5014 130.7365 5 2027.3955 134.3649 39.6366 356.6577 185.6054 100.1141 6 2020.0535 132.9965 37.3694 7.1298 176.719 127.3106 7 2015.6492 133.9992 34.9178 359.8098 179.5118 140.0329 8 2011.7726 120.5447 37.8429 0.4086 179.1541 133.0061 9 2014.7414 117.536 37.7136 359.9685 181.5723 133.7165

10 2003.5794 112.4829 35.5727 1.0469 177.5314 110.5423 11 2003.0289 103.2622 34.9175 357.1328 179.7128 85.4108 12 1997.6006 107.2651 34.6564 358.0281 180.301 46.0745 13 2009.9949 108.5345 32.0706 358.9565 182.6421 67.387 14 1997.8887 91.4959 34.4578 2.2956 181.0464 43.9911 15 2006.7091 89.1575 28.8141 3.5076 183.9156 43.5189

Table A-9: Exterior orientation parameters of the downstream part of Maisbich.

Appendix A: Tables

85


1 0.7208 0.4484 0.1818 0.7588 1.2438 0.2503 2 0.3923 0.2143 0.0963 0.3217 0.543 0.1585 3 0.3449 0.441 0.1529 0.7483 0.613 0.1263 4 0.2694 0.2286 0.0527 0.3239 0.3799 0.0484 5 0.2184 0.1867 0.0238 0.3035 0.3652 0.0889 6 0.2419 0.1874 0.0555 0.3215 0.4382 0.0375 7 0.1968 0.1736 0.0784 0.3114 0.3758 0.0733 8 0.1949 0.2037 0.0354 0.3288 0.3185 0.0733 9 0.1974 0.2001 0.0271 0.326 0.3169 0.0747

10 0.1086 0.1376 0.0383 0.2223 0.1779 0.044 11 0.0852 0.0701 0.0225 0.1108 0.1388 0.0282 12 0.097 0.0849 0.0356 0.1373 0.16 0.0354 13 0.1635 0.1831 0.049 0.3339 0.2932 0.079 14 0.1479 0.0825 0.0396 0.1341 0.2371 0.0411 15 0.097 0.058 0.0599 0.1124 0.2019 0.0506

Table A-10: Accuracies of exterior orientation parameters of the downstream part of Maisbich.

Appendix A: Tables

86

Point ID X Y Z DEM Z residual

2 2035.5004 86.8236 6.6634 6.6471 -0.0163 5 2029.261 95.8642 4.4552 4.4024 -0.0528

21 2018.2906 85.5014 5.947 5.9856 0.0386 7 2016.2562 100.122 3.048 3.135 0.087 6 2013.0448 90.3522 4.0946 4.1441 0.0495 9 2001.3466 105.134 1.1 1.1015 0.0015

11 1991.094 102.2148 -1.944 -1.8501 0.0939 12 1993.149 107.9834 -0.8794 -0.8609 0.0185 13 1983.5138 105.608 -3.1818 -2.9581 0.2237 15 1975.905 108.8424 -4.0716 -3.9429 0.1287 14 1983.1446 118.6992 -1.1494 -1.1391 0.0103 8 2009.2976 96.1402 1.575 1.6307 0.0557

16 1966.6314 113.7762 -5.8466 -5.81 0.0366 17 1975.7552 116.4264 -4.065 -4.0293 0.0357 18 1968.3642 120.7964 -4.7894 -4.7603 0.0291 23 1960.0302 121.5568 -7.0384 -7.0363 0.0021 26 1952.608 123.2832 -8.1204 -8.0745 0.0459 25 1949.0452 119.2602 -8.6628 -8.6255 0.0373 1 2025.3874 82.8218 7.2906 7.2878 -0.0028

20 2023.7546 102.825 4.528 4.5644 0.0364 28 2000 100 0 0.0171 0.0171 24 1988.3228 112.3446 -1.2884 -1.1667 0.1217 10 1978.8132 119.3962 -2.1442 -2.13 0.0142 19 1955.5718 117.3856 -7.5332 -7.5099 0.0233

Table A-11: Ground truth versus DEM values for the upstream part of Maisbich.

Appendix A: Tables

87

Point ID X Y Z DEM Z residual

31 2034.5496 146.273 7.3712 7.3102 -0.061 38 2031.27 137.1874 6.4472 6.509 0.0618 40 2025.0702 127.946 5.319 5.3813 0.0623 42 2012.555 117.7942 2.2046 2.2479 0.0433 39 2003.9938 110.3376 0.2806 0.3401 0.0595 41 1999.2176 104.3632 -0.766 -0.7129 0.0531 44 2001.7946 93.5492 1.1092 1.1378 0.0286 37 2038.3726 140.2522 7.7862 7.8685 0.0823 35 2019.539 127.5076 3.855 3.9653 0.1103 56 2007.4576 105.4226 1.8556 1.9602 0.1046 45 1990.0438 97.0018 -2.9642 -2.9183 0.0459

Table A-12: Ground truth versus DEM values for the downstream part of Maisbich.

Appendix A: Tables

88

Point ID X Y Z DEM Z residuals 1 2021.548 84.6164 6.575 6.5344 -0.0406 2 2023.135 84.7328 6.6072 6.6415 0.0343 3 2043.431 79.2517 11.3627 11.3383 -0.0243 4 2022.935 89.2589 4.7406 4.7724 0.0318 5 2039.387 84.3893 8.1119 8.1432 0.0313 6 2023.156 94.6915 3.765 3.8019 0.137 7 2029.984 92.076 4.812 4.8278 0.0158 8 2029.363 92.495 4.8723 4.8157 -0.0566 9 2045.95 85.9278 9.4162 9.3904 -0.1258

10 2025.979 83.1894 7.1641 7.1641 -0.0001 11 2001.154 99.5134 0.2053 0.2042 -0.0011 12 2002.496 99.3888 0.407 0.4341 0.0271 13 2004.49 99.9985 1.1196 1.1338 0.0142 14 2012.264 91.4164 3.8537 3.918 0.0643 15 2017.145 90.7952 4.4189 4.4722 0.0533 16 1994.598 98.7252 6.2956 6.336 0.0404 17 1994.653 98.8782 6.2664 6.1786 -0.0878 18 2010.827 101.01 2.5825 2.623 0.0405 19 2007.421 104.0833 3.4948 3.4325 -0.1623 20 2001.992 99.4657 0.6448 0.6017 -0.0432 21 1981.729 114.2554 -2.735 -2.8284 -0.0934 22 1997.588 95.009 8.4748 8.4397 -0.0351 23 2001.623 96.2596 8.7209 8.632 -0.1889 24 1979.207 102.8227 6.0184 5.8702 -0.1481 25 2000.1 99.302 0.0807 0.0885 0.0078 26 1999.734 100.8096 -0.0285 0.0091 0.0376 27 1974.451 109.7715 -4.9433 -4.8441 0.0991 28 1978.465 119.4259 -2.2159 -2.199 0.0169 29 1968.863 107.3995 0.2592 0.1939 -0.0654 30 1971.615 110.7411 -5.5778 -5.4796 0.0982 31 1950.713 117.8993 -8.0722 -8.082 -0.0099 32 1970.966 118.0006 -4.6017 -4.6614 -0.0597 33 1984.678 117.9578 -0.8737 -0.8793 -0.0057 34 1967.499 99.3713 7.4493 7.487 0.0377 35 1973.711 101.9312 6.4367 6.2793 -0.1575 36 1977.361 103.4264 5.9048 5.8772 -0.1276 37 1981.609 102.9257 4.6305 4.6821 0.0517 38 1951.873 116.2574 -7.5604 -7.5667 -0.0063 39 1969.157 116.8801 -4.8838 -4.8926 -0.0088 40 1963.048 121.1141 -5.9568 -6.0016 -0.0448 41 1967.865 98.971 7.4005 7.4198 0.0193 42 1967.567 101.6867 5.7676 5.816 0.0485 43 1961.811 124.3346 -1.9089 -1.9423 -0.0334 44 1941.241 124.2218 -7.4931 -7.471 0.0222 45 1981.09 124.2874 4.337 4.3235 -0.0135 46 1942.771 125.7391 -5.399 -5.6307 -0.2317 47 1947.911 125.5787 -3.1061 -3.1856 -0.1795 48 1952.985 126.8436 -3.165 -3.2364 -0.0714 49 1969.499 125.6549 0.9858 0.9351 -0.0507 50 1957.43 109.8462 -2.0501 -2.0282 0.1219

Table A-13: The points selected by the method of floating mark versus DEM

values of upstream.

Appendix A: Tables

89

Point ID X Y Z DEM Z residuals 1 2017.718 127.5017 4.0258 3.954 -0.0718 2 2020.993 127.8447 4.6613 4.5513 -0.11 3 2019.583 125.4585 4.2179 4.1729 -0.0449 4 2028.98 133.9305 6.4114 6.3327 -0.0787 5 2025.7 131.0376 5.6914 5.667 -0.0245 6 2031.015 135.5724 6.4787 6.5137 0.035 7 2011.813 130.3323 6.4061 6.4265 0.0204 8 2011.991 129.7283 6.4704 6.4767 0.0064 9 2004.797 121.5563 10.3468 10.2937 -0.0531

10 2004.009 120.2712 8.6682 8.7347 0.0665 11 1999.262 115.1206 10.2269 10.3371 0.1102 12 1997.45 113.158 11.4114 11.3204 -0.091 13 1997.726 113.2438 11.2024 11.222 0.0197 14 1999.155 113.2534 9.6575 10.3992 0.7416 15 1992.854 99.0523 -2.2541 -2.2689 -0.0148 16 1994.084 100.0351 -1.8838 -1.8912 -0.0074 17 1996.672 92.2733 -0.6726 -0.644 0.0286 18 2005.802 94.0718 5.671 5.3077 -0.3633 19 2000.963 84.7607 0.6757 0.5208 -0.1549 20 2002.113 86.9335 1.3388 1.3244 -0.0143 21 2000.777 109.0969 0.184 -0.2954 -0.4794 22 1996.795 99.1492 -0.3473 -0.9455 -0.5982 23 1995.195 104.9915 -1.1367 -1.4719 -0.3353 24 2008.433 105.8337 2.6243 2.4796 -0.1447 25 2005.418 102.729 1.8165 1.7458 -0.0707 26 2030.799 126.4382 6.9127 7.0123 0.0997 27 2019.32 124.9482 4.1348 4.1628 0.028 28 2036.16 138.1289 7.5269 7.7011 0.1742 29 2022.512 124.8188 5.1118 4.9886 -0.1231 30 2014.39 114.3178 3.5873 3.549 -0.0383 31 2004.116 102.6161 1.2308 1.2474 0.0166 32 2039.909 131.5934 17.6826 17.6526 -0.03 33 2039.035 131.4437 18.8535 18.2627 -0.5907 34 1990.383 94.2845 -2.8057 -2.8408 -0.0351 35 1997.388 88.4611 -0.5126 -0.4971 0.0154 36 1994.603 97.9654 -1.7601 -1.7185 0.0416 37 2002.611 91.219 1.5665 1.5712 0.0047 38 2002.871 90.9688 1.6505 1.6807 0.0302 39 1995.354 104.2382 -1.7073 -1.6689 0.0384 40 2012.296 114.538 3.044 2.7713 -0.2727 41 2009.002 121.4682 4.372 4.3719 -0.0001 42 2003.105 117.9704 8.7522 9.2249 0.4726 43 2000.33 113.601 7.8681 7.8743 0.0062 44 2000.773 114.3703 8.3177 8.7129 0.3952

Table A-14: The points selected by the method of floating mark versus DEM

values of downstream

Appendix A: Tables

90

ID SVC ID SVC ID SVC ID SVC

1 0.4559 26 0.1316 51 0.4067 76 0.4396

2 0.455 27 0.1231 52 0.3956 77 0.4098

3 0.4289 28 0.2164 53 0.3845 78 0.3587

4 0.4077 29 0.2997 54 0.3717 79 0.4379

5 0.4447 30 0.2 55 0.4598 80 0.3565

6 0.4527 31 0.3525 56 0.299 81 0.3545

7 0.359 32 0.4821 57 0.3 82 0.3688

8 0.4176 33 0.3247 58 0.406 83 0.21

9 0.3853 34 0.2376 59 0.459 84 0.2251

10 0.3589 35 0.2487 60 0.2043 85 0.2741

11 0.1979 36 0.2067 61 0.159 86 0.2729

12 0.1816 37 0.2376 62 0.1734 87 0.2492

13 0.1928 38 0.2076 63 0.3745 88 0.3956

14 0.3304 39 0.2265 64 0.2598 89 0.3478

15 0.244 40 0.2327 65 0.1731 90 0.3376

16 0.3469 41 0.2545 66 0.3487 91 0.3554

17 0.2663 42 0.3712 67 0.2845 92 0.3078

18 0.1611 43 0.3175 68 0.2067 93 0.2984

19 0.3061 44 0.2851 69 0.18 94 0.2578

20 0.3358 45 0.3067 70 0.3 95 0.4396

21 0.2807 46 0.2789 71 0.3598 96 0.4098

22 0.2045 47 0.3397 72 0.617 97 0.3587

23 0.173 48 0.1815 73 0.3578 98 0.4379

24 0.3344 49 0.2031 74 0.3845 99 0.3565

25 0.1845 50 0.4856 75 0.3559 100 0.3545

Table A-15: SVC values.

Appendix B: Maps

91

Appendix B: Maps

Figure B-1: Upstream DEM of Maisbich.

Appendix B: Maps

92

Figure B-2: Downstream DEM of Maisbich.

Appendix B: Maps

93

Figure B-3: Upstream mosaic.

Appendix B: Maps

94

Figure B-4: Downstream mosaic.

Appendix C: Graphs

95

Appendix C: Graphs

Figure C-1: The radial distortion curve for the 20mm lens. The values of both x and y axis are in

pixels.

Figure C-2: Pilot planimetric residual vectors. Both x, y axes are in meters. The vectors are

exaggerated to the point that they don’t overlap.

Appendix C: Graphs

96

Figure C-3: Pilot height residual vectors. Both x, y axes are in meters. The vectors are


Figure C-4: Comparison of the Pilot DEMs

Appendix C: Graphs

97

Figure C-5: Upstream planimetric residual vectors. Both x, y axes are in meters. Vectors are


Figure C-6: Upstream height residual vectors. Both x, y axes are in meters. Vectors are


Appendix C: Graphs

98

Figure C-7: Downstream planimetric residual vectors. Both x, y axes are in meters. Vectors are


Figure C-8: Downstream height residual vectors. Both x, y axes are in meters. Vectors are


Appendix C: Graphs

99

Figure C-9: Height residual vectors of upstream DEM versus ground truth. Both x, y axes are in

meters. Vectors are exaggerated to the point that they don’t overlap.

Figure C-10: Height residual vectors of downstream DEM versus ground truth. Both x, y axes are

in meters. Vectors are exaggerated to the point that they don’t overlap.

Appendix C: Graphs

100

Figure C-11: Height residual vectors of upstream DEM versus points collected from reference

imagery. Both x, y axes are in meters. Vectors are exaggerated to the point that they don’t

overlap.

Figure C-12: Height residual vectors of downstream DEM versus points collected from reference

imagery. Both x, y axes are in meters. Vectors are exaggerated to the point that they don’t

overlap.

Appendix C: Graphs

101

Figure C-13: The final results of the shadow simulations. The colorbar represents the hillshade

values.

Figure C-12: Left: The distribution of SVC samples. The colorbar represents the SVC values.

Right: Whisker plot of the distribution. The red line represents the mean value.

Appendix C: Graphs

102

Figure C-13: Up Left: The simulation temperature values using data from the 5x 5 m DEM. Down

Left: The corresponding residuals with the fiber optic cable data. Up Right: The simulated

temperature using data from the photogrammetric DEM. Down Right: The corresponding

residuals between observed and simulated values. The colorbar represent the temperature.

Figure C-14: Up Left: The simulated temperature with the 5x5 m DEM. Down Left: The

corresponding residuals. Up Right: The simulated temperature with the photogrammetric DEM.

Down Right: The corresponding residuals. The colorbar represents the temperature.

aerostat photogrammetry - tu delft

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