aerostat photogrammetry - tu delft
TRANSCRIPT
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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
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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
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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
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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
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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
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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
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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).
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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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.
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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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.
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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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.
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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)
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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)
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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
Chapter 2 – Terrain Data Acquisition for Hydrological Modeling
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.
Chapter 3 – Aerostat Photogrammetry: Principles & Methodology
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
Chapter 3 – Aerostat Photogrammetry: Principles & Methodology
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.
Chapter 3 – Aerostat Photogrammetry: Principles & Methodology
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
Chapter 3 – Aerostat Photogrammetry: Principles & Methodology
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.
Chapter 3 – Aerostat Photogrammetry: Principles & Methodology
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.
Chapter 3 – Aerostat Photogrammetry: Principles & Methodology
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.
Chapter 3 – Aerostat Photogrammetry: Principles & Methodology
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
Chapter 4 – The Maisbich Experiment
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
Chapter 4 – The Maisbich Experiment
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).
Chapter 4 – The Maisbich Experiment
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
Chapter 4 – The Maisbich Experiment
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
Chapter 4 – The Maisbich Experiment
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:
Chapter 4 – The Maisbich Experiment
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,
Chapter 4 – The Maisbich Experiment
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
Chapter 4 – The Maisbich Experiment
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
Chapter 4 – The Maisbich Experiment
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.
Chapter 4 – The Maisbich Experiment
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.
Chapter 4 – The Maisbich Experiment
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
Chapter 4 – The Maisbich Experiment
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
Chapter 4 – The Maisbich Experiment
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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
Chapter 4 – The Maisbich Experiment
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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
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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
Chapter 4 – The Maisbich Experiment
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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.
Chapter 4 – The Maisbich Experiment
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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
Chapter 4 – The Maisbich Experiment
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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.
Chapter 4 – The Maisbich Experiment
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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
Chapter 4 – The Maisbich Experiment
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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.
Image ID Xs Ys Zs ω φ κ
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
Image ID mXs mYs mZs mω mφ mκ
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.
Chapter 4 – The Maisbich Experiment
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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).
Image ID Xs Ys Zs ω φ κ
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
Image ID mXs mYs mZs mω mφ mκ
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
Chapter 4 – The Maisbich Experiment
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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
Chapter 4 – The Maisbich Experiment
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.
GCP’s RMSE Mean error
X 0.0155 0.0034
Y 0.0073 -0.0001
Z 0.0480 -0.0103
Check RMSE Mean error
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.
Chapter 4 – The Maisbich Experiment
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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.
Chapter 4 – The Maisbich Experiment
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.
Chapter 4 – The Maisbich Experiment
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.
Chapter 4 – The Maisbich Experiment
47
GCP’s RMSE Mean error
X 0.004 0.001
Y 0.0017 0.0016
Z 0.0242 0.0177
Check RMSE Mean error
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.
Chapter 4 – The Maisbich Experiment
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.
Chapter 4 – The Maisbich Experiment
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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.
Chapter 4 – The Maisbich Experiment
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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.
Chapter 4 – The Maisbich Experiment
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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.
Chapter 4 – The Maisbich Experiment
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.
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 5 – Analysis of Maisbich 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.
Figure 5-3: Elevation residual vectors (exaggerated to the point that they don’t overlap)
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
Chapter 5 – Analysis of Maisbich DEM
56
Figure 5-4: Elevation residual vectors (exaggerated to the point that they don’t overlap)
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.
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 5 – Analysis of Maisbich 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
Chapter 5 – Analysis of Maisbich DEM
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
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 5 – Analysis of Maisbich DEM
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)
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 5 – Analysis of Maisbich DEM
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.
Chapter 6 – Temperature distribution model simulations
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.
Chapter 6 – Temperature distribution model simulations
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.
Chapter 6 – Temperature distribution model simulations
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.
Chapter 6 – Temperature distribution model simulations
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
Chapter 7 – Conclusions & Recommendations
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
Chapter 7 – Conclusions & Recommendations
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
Chapter 7 – Conclusions & Recommendations
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
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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
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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
Image ID Xs Ys Zs ω φ κ
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.
Image ID mXs mYs mZs mω mφ mκ
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
Image ID mXs mYs mZs mω mφ mκ
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
Image ID Xs Ys Zs ω φ κ
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
Image ID mXs mYs mZs mω mφ mκ
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
Image ID Xs Ys Zs ω φ κ
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
Image ID mXs mYs mZs mω mφ mκ
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
exaggerated to the point that they don’t overlap.
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
exaggerated to the point that they don’t overlap.
Figure C-6: Upstream height residual vectors. Both x, y axes are in meters. Vectors are
exaggerated to the point that they don’t overlap.
Appendix C: Graphs
98
Figure C-7: Downstream planimetric residual vectors. Both x, y axes are in meters. Vectors are
exaggerated to the point that they don’t overlap.
Figure C-8: Downstream height residual vectors. Both x, y axes are in meters. Vectors are
exaggerated to the point that they don’t overlap.
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.
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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.