distribution of wind generated
waves as inferred from
stereophotographic
observations of the sea
surface
L. H. Holthuijsen
TECHNISCIIE UNIVERSITET
Scheepshydromechanica
Archief
Mekelweg 2, 2628
CD Delft
Te1:015-2786873/Fax:2781836
Proefschrift
!pt. verkrijging van de graad van doctor in de technische wetenschappen aan de Technische Hogeschool Delft, op gezag van de Rector Magnificus prof. ir. B.P.Th. Veltman, voor een commissie aangewezen door het college van dekanen te verdedigen op dinsdag 26 mei 1981 te 14.00 uur
door Leonardus Henricus Holthuijsen civiel ingenieur geboren te Amsterdam
The directional energy
distribution of wind generated
waves as inferred from
stereophotographic
observations of the sea
surface
Abstract Introduction 5 Methods of observation 21 Methods of analysis 47 Results 80 Discussion 105 Conclusions 134 Acknowledgements 138 List of symbols 141 List of references 145 Appendices 151
Abstract
I. Introduction
1.1 Nature and scope
1.2 Literature review 1.3 Methodology 1.3.1 Introduction 1.3.2 Observations 1.3.3 Analysis 1.4 Results Methods of observation 2.1 Introduction
2.2 Stereophotography of wind generated waves
2.2.1 Introduction
2.2.2 Basic elements of the system 2.2.3 Operational system
2.2.4 Operational procedures 2.2.5 Photogrammetric analysis
Methods of analysis
3.1 Introduction
3.2 Description of wind generated waves
3.3 Spectral analysis
3.4 Spectral resolution and reliability
5 8 16 16 16 18 19 21 21 21 23 30 37 39 47 48 56 65 3
3.5.2 Parameter estimation 72
35.3 Goodness-of-fit between model and observation
Results
4.4 Introduction SO
4.2 Geophysical conditions, 81
4.2.1 Introduction 81
4.2.2 Topography of the sites 82
4.2.3 Meteorological conditions 83
4.3' Stereophotographic observations 87
4.4 Wavenumber spectra 89
4.5 Directional distributions 93
4.6 Directional parameters 94
4.7 Goodness-of-fit between model and
observa-tion 995 4.8 Frequency spectra 101 Discussion 5.1 Introduction 105 5.2 General discussion 105 5.3
Directionally' decoupled wave generation 114
5.4 The directional distribution 1121
The directional width 123
6. Conclusions 134 -73 4. 5. 5.5
List of symbols 141
List of references 145
Appendices I Altitude of photography 151
II The least-squares method 155
III Geophysical conditions 157
IV Overlapping stereo areas 174
V Swell and noise regions 176
VI Values of TT and s 179
VII Frequency spectra at sea level 180
VIII Testcase 183
IX Parameterized wave growth 186
van de richtingsverdeling van de energie van door wind opgewekte go-yen op basis. van waarnemingen met een.relatief hoog oplosseni vermogen.,
Ongeveer 75 waarnemingen van bovengenoemde verdeling zijn geselecteerd uit vijf spectra die verkregen zijm uit stereofotografische opnamen van het zee oppervlak. Drie van deze spectra zijn waargenomen in een situa-tie die de ideale groei situasitua-tie wordt genoemd. nit is een situasitua-tie waar een homogene, stationaire wind loodrecht vanaf een lange rechte kust waait over diep water. De twee andere spectra zijn waargenomen in soortgelijke situaties. Het verschii met de ideale situatie is voor 66n spectrum dat de windrichting schuin op de kust stond en voor het andere spectrum dat de kustlijn onregelmatig was.
lye waargenomen richtingsverdelingen zijn vergeleken met het cos2s(0/.2)-model dat geintroduceerd is door Longuet-Higgins e.a. (1963). Doordat de waarnemingen een hoog oplossend vermogen bezitten is het mogelijk de verschillen tussen de waarnemingen en het model te kwantificeren. Het
blijkt dat de overeenkomst tussen model en waarnemingen goed is voor veel praktische doeleinden in de ideale groei situatie. Het model is in ideze situatie zelfs op een hoog niveau statistisch consistent met die waarnemingen waarvoor een consistentie analyse is uitgevoerd- In de twee andere situaties blijkt de vorm van de richtingsverdeling sterk bein-vloed te zijn door de geometrie van de bovenwindse kustlijn. Dit sugge-reert een golfgroeiwaarbij de komponenten uit verschillende richtingen onafhankelijk van elkaar groeien. De resultaten van een eenvoudig para-metrisch golfvoorspellings, model steunen deze auggestie.
De vorm van het waargenomen functionele verband tussen de breedte para-meter s van het cos2s(6/2)-mode1 en het golfgetal komt redelijk goed
overeen met de vormen die voorgesteld zijn door Mitsuyasu e.a. (1975) en Hasselmann e.a. (1980). Deze waargenomen overeenkomst is opmerkelijk voor de niet-ideale groei sltuaties waar de spectra sterk beinvloed wor-den door de geometrie van de bovenwindse kustlijn. Het belangrijke ver-scbil tussen de voorstellen van Mitsuyasu e.a. (1975) en Hasselmann e.a., (1980) voor wat betreft de schaal van de breedte parameter s, kan niet beoordeeld worden aan de hand van de waarnemingen van deze studie. De reden hiervan is dat bet aantal waarnemingen van deze schaal in deze studie te klein is en dat de verschillen tussen deze waarnemingen en ieder van de voorstellen ongeveer gelijk is...
the directional energy distribution of wind generated waves on the basis of observations with a relatively high resolution.
Approximately 75 observations of the above distribution are studied. They are selected from five spectra which are determined from stereophotogra-phic observations of the sea surface. Three of these spectra were obtained in a so-called ideal generation situation. This is a situation where a homogeneous, stationary wind blows perpendicularly off a straight coast over deep water. The other two spectra were observed in similar situa-tions. The difference with the ideal situation is for one spectrum that the wind was slanting across the coastline and for the other that the coastline was irregular.
The observed distributions are compared with the cos2s(0/2)-model intro-duced by Longuet-Higgins et al. (1963). The differences between the
ob-servations and this model can be quantified due to the high resolution of the observations. It is found in the ideal situation that the model agrees well for most practical purposes with the observed distributions. In fact, the model is found to be highly consistent with those
observa-tions in the ideal situation for which a consistency analysis was carried out. In the other two situations it is found that the shape of the direc-tional energy distribution is strongly influenced by the geometry of the upwind coastline. This suggests a directionally decoupled generation of the waves. The results of a simple parametric wave hindcasting model support this suggestion.
The shape of the observed functional relationship between the width para-meter s of the cos2s(0/2)-model and the wavenumber agrees fairly well with the shapes suggested by Mitsuyasu et al. (1975) and Hasselmann et al. (1980).
This observed agreement is remarkable for the non-ideal situations where the spectra are influenced by the geometry of the upwind coastline. The considerable discrepancy as regards the scale of s in the suggestions of Mitsuyasu et al. (1975) and Hasselmann et al. (1980) cannot be resol-ved with the observations of the present study. The reason is that the number of observations of this scale is too small and that the discre-pancies between these observations and each of the suggestions are appro-ximately equal.
I. Introduction
Nature and scope
A considerable amount of energy is carried over the ocean surface by waves which are generated by the wind. This flux of energy can be very destructive. To assess the potential danger to man's acti-vities one needs to study such waves. One aspect of such study, the
characterization of the directionality of the waves, is the subject of this thesis.
Waves in the ocean can be described on a number of scales. On a very large (oceanic) scale one is interested in the wavefields as
they are generated and propagated on the ocean surface. It is usually sufficient in this scale to consider main characteristics of the waves. These vary slowly in place and time. One is thus able to describe the development of the sea state as generated for in-stance by an atmospheric depression crossing the North Atlantic Ocean. On a smaller scale, and this is the scale with which this
thesis is mainly concerned, one would like to describe the wavefield more in detail in a relatively small area, that is, in an area small enough
to
consider themain
characteristics to be constant. The seasurface itself varies wildly in this small area, even within a few seconds or a few meters. To remove this apparent chaos one uses an integral representation of the surface known as the energy spectrum. This spectrum, in its most general form, presents the energy of the waves as a function of frequency, wavenumber and direction.
The spectrum just mentioned is three-dimensional but it can be readily reduced to a two- or one-dimensional spectrum. The most important, or at least the one most often used, is the frequency spectrum. This spectrum has been studied fairly thoroughly by many investigators. It has been observed in a large variety of conditions,
4t.444ti.A.
ranging from controlled laboratory experiments to hurricanes on the high seas. Important results, both for practical implications and for fundamental research, have been obtained. The knowledge of this
type of spectrum can also be applied to the one-dimensional wave-number spectrum due to the close relationship between the two
spec-tra.
For engineering purposes the frequency characteristics of the spec-trum are usually more important than the directional characteris-tics. At least that is what one would conclude from the fact that most design procedures for maritime structures accept the
frequen-cy spectrum, and this spectrum alone, as boundary condition (as far as the waves are concerned). But more advanced design models con-sider the directional aspects of the spectrum as well because it is recognized that the response of the structures often depends also, and sometimes to a large degree, on the directional behaviour of the waves. Information on the directionality of waves is also required
in fundamental research. Notable examples are studies in air-sea interactions and studies
in
coastaldynamics.
Whereas the observations of frequency spectra are relatively many and detailed, the observations of the directional characteristics are few and coarse. Only very few detailed observations have been made in the past. The reason for this is probably that such obser-vations require relatively complicated techniques. Theory has not alleviated this situation so that our present knowledge of the di-rectionality of waves is rather poor.
More information on the directionality of ocean waves is required by engineers and scientists and consequently more observations are needed. These observations can in principle be carried out in the
ocean or in the laboratory but preference should go to observations in the oceanic environment. The reason for this is that it is
difficult to apply laboratory results to the ocean. There are mainly two problems. The first is one of scale: it seems physically impossi-ble to simultaneously scale the spatial dimensions, time, turbulence
etc.. This problem seriously hampers present studies of frequency spectra in laboratories. The second problem is that the wind and wave flumes in the laboratories are relatively narrow. Such geometry
is not representative for windfields over the ocean. The directional characteristics of wind and waves in a laboratory flume are therefore probably entirely different from those in realistic ocean conditions. For this reason it it not advisable to use the laboratory approach
as the prime source of information for the directionality of ocean waves.
In the present study observations were carried out in the oceanic environment, the areas of observation being located in the southern North Sea off the coasts of Holland and Germany. The geophysical conditions were chosen such that the results could be generalized to situations different from those of the observations. The windfields during the observations were fairly homogeneous and stationary, the upwind coast line was either straight or irregular and the water was relatively deep.
The techniques which have been used previously to obtain detailed in-formation of the directionality of ocean waves are based on photography, or radar, or closely spaced wave gauge arrays. The technique chosen for this study is stereophotography. Two synchronized cameras, each carried by a helicopter, were used to take a total of about six hundred stereo photo pairs during a period of three years (1973 - 1976). Each stereo photo pair provides a three-dimensional image of the sea sur-face as it was at the moment of exposure. Approximately fifty stereo
photo pairs are selected and analyzed to estimate five independently observed two-dimensional wavenumber spectra. Four of these spectra are considered sufficiently interesting for a continued evaluation.
The evaluation of the four spectra consists of two parts. In the first part conspicuous shape characteristics of the observed spectra are rela-ted to the geometry of the upwind coastline. A simple parametric wave hindcast model is used in this evaluation. The second part concerns the parameterization of the observed directional energy distributions. Approximately seventy-five of such functions can be determined from the four spectra. These are compared with suggestions from the literature on this subject.
1.2 Literature review
The literature on the directionality of ocean waves is rather limited but still too extensive to fully review here. A selection has been made of those publications most relevant
to
this study.As indicated in the preceding paragraph, theoretical formulations of directional characteristics of ocean waves are almost non-existent. There seems to be only one generally accepted theory. This theory is due to Phillips (1957) who argued that waves are initially generated by a resonance mechanism. The two-dimensional wave spectrum generated through this mechanism is distinctly bi-modal at any given frequency or wave-number (within certain limitations). Observations by Longuet-Higgins et al. (1963) and Gilchrist (1966) support this result of Phillips' theory. However, the energy in that part of the spectrum where Phillips' theory is relevant is small compared to the total energy of the spectrum and Phillips' theory is therefore almost irrelevant for engineering purposes.
Other theoretical considerations have been published which are indirect-ly related to the shape of the two-dimensional spectrum. They are origi-nally due to Hasselmann (1962, 1963). Longuet-Higgins (1976), Fox (J976), Webb (1978) and Dungey and Hui (1979) elaborate on the work of Hassel-mann and consider nonlinear wave-wave interactions for narrow spectra which are typical for young sea states. They found that the energy transfer within the spectrum is directed from the peak of the spectrum to lower and higher frequencies, mainly in directions making angles tan
-1(1/v5.)
with the mean direction. The rate of transfer to lower fre-quencies is slightly greater than that to higher frefre-quencies.The nonlinear wave-wave interactions have a shape-stabilizing effect on the one-dimensional frequency spectrum (Hasselmann et al., 1973). It is very well possible that they have a similar effect on the two-dimen-sional wavenumber spectrum. If this were true it would imply that if, for some reason, the shape of the two-dimensional spectrum differs from some standard shape, the nonlinear interactions will redistribute the energy in the spectrum such that the standard shape is attained. It should be noted that this process would only be operative during the generation phase of wave development. Unfortunately, progress in the study of these nonlinear interactions is very slow and no results have been reported in the literature (at least not to the knowledge of the author) which may indicate such stabilizing tendencies as regards the directional characteristics of the two-dimensional spectrum.
The above theories have not resulted in a formulation of main directio-nal characteristics of the wave energy spectrum; observations have pro-vided much more information.
Two. kinds of observations can be distinguished. The first kind relates to detailed observations of the directional energy distribution ,whereas
the second kind concerns only integral properties of these distributions. These two categories will be addressed separately.
At least a few dozen investigators have made observations of the first kind or claim to have done this (e.g. Cote et al., 1960; Tyler et al., 1974; Simpson, 1967;Matushevskii and Strekalov, 1963; Sugimori, 1975; Zadkornikov et al., 1972; Howard, 1969; Stilwell, 1969; Kasevich et al., 1972). It is remarkable however, that most of these investigators con-clude the analysis of their data at the moment when the spectra are fi-nally obtained from the observations. Their results (spectra) are usually reduced to a few illustrations in a publication which can hardly serve as a basis for further interpretation. Only two groups of these investigators seem to have undertaken a search for some standard shape or for some systematic dependencies.
The first group carried out a joint effort in a project called SWOP, the Stereo Wave Observation Project, and the results have been well publicized, notably in Cote et al., (1960). From stereophotographs of the sea surface taken from airplanes these investigators were able to calculate one two-dimensional wavenumber spectrum to a fair degree of detail. The pictures were taken over the North Atlantic Ocean, approxi-mately 750 km east of New York in a slowly varying windfield. An ana-lysis of this spectrum provided the directional distribution as a function of wavenumber. After subjectively fitting a number of simple analytical functions to these distributions, the following was chosen to give the best fit.
60(e)
= A1 + A2 cos2 + A3 cos40 (1.2.1)The notation is in accordance with the definitions in chapter The shape of these observed distributions can apparently be described by
how these coefficients depended on the frequency and the windspeed (al-though the dependency on the windspeed was not observed).
It appeared from the observations that the relative importance of the cos40-term in equation (1.2.1) decreases as the frequency increases. The effect of this on the directional distribution is that the width increases as the frequency increases.
The other group of investigators who analyzed the shape of the directio-nal distribution (Tyler et al., 1974) used backscatter of radio waves from the ocean surface in their observations. They obtained ten, extremely detailed, observations of the directional distribution of a wavecomponent of 7 s period on eight consecutive days around Wake Is-land in the Pacific Ocean. Tyler et al. (1974) judge the observed component to be fully or almost fully developed, that is, the energy density in the frequency spectrum of this component would not increase appreciably with higher windspeed of longer fetch or duration. The com-ponent was located on the high frequency side of the peak of the fre-quency spectrum. Several models for the directional energy distribution were tested and the most satisfactory model turned out to be the follo-wing.
150(e) = A4fa0 + (I
-
cos25(0/2)} (II,.2. 2)Tyler et al. (1974) judge the difference between the observations and this model to be small, the normalized standard deviation V2' defined in paragraph
2
3.5.3 being on the order of 0.20. The value of
a
was small so that for most engineering purposes the following model should be adequate.300) = A5cos2s(0/2) (1.2.3)
The width of the directional distributions of equations (1.2.2) and (1.2.3) is controlled by the power of the cosine-term. The width decrea-ses as the value of s increadecrea-ses. Its variation with frequency could ob-viously not be studied from the observations of Tyler et al. (1974) as only one frequency was observed. A systematic dependency of s on the windspeed (which varied from about 6 to 13 m/s) was not found. This is not in agreement with the findings of Mitsuyasu et al. (1975) and Hassel-mann et al. (1980) which will be considered later in this review.
Stewart and Teague (1980) recently published results of other observa-tions with the same radar technique. No directional distribuobserva-tions were presented in the publication but one interesting aspect concerning these functions was pointed out. It appears from their data that the growth rate of the spectral energy density (the coefficient of exponential growth in a frame moving with the group velocity of the component) in the ideal wave generation situation * is proportional to the cosine of the angle between the wind direction and the direction of wave propaga-tion. Stewart and Teague (1980) inferred from this that an initial direc-tional distribution will remain unchanged in shape during (exponential) growth with fetch. This implies that the width of the directional distri-bution function is constant during growth. Such invariance is not in agreement with the observations of Mitsuyasu et al. (1975) and Hassel-mann et al. (1980). These authors found that the width varies with the growth stage.
* The ideal wave generation situation is a situation where a homogeneous, stationary wind blows perpendicularly off a straight coast over relatively deep water.
f
f = fm
observations provides only integral properties of the directional energy distribution. Such properties are for instance a mean direction and a typical width of the directional energy distribution. The observations reported in the literature which are most relevant to the present study were made using records of the vertical motion, the slope and, in some observations, the curvature of the sea surface with a buoy. Shape ana-lysis of the directional energy distribution on the basis of this kind of observations is very limited due to the fact that the directional resolution of the observations is relatively low. But it is possible to indicate whether the observations are consistent with proposed models (Long and Hasselmann, 1979). Such investigations have not been carried out yet but Longuet-Higgins et al. (1963), using a different approach
2s
do indicate that the cos (8/2)-model of equation (1.2.3) agrees better with their observations than do three other models.
The main result of these investigations of integral properties of the directional distribution (as far as they are relevant to the present study) is the numerical value of the width parameter s of the
cos2s-(0/2)-model as a function of frequency and windspeed. Longuet-Higgins et al. (1963), Mitsuyasu et al. (1975), Tyler et al. (1974), and Hassel-mann et al. (1980) computed values of s from their observations.
One would perhaps expect systematic dependencies between s and relevant geophysical parameters to exist only in relatively simple meteorological situations such as the ideal situation described above. But referring to the shape-stabilizing influence of the nonlinear interactions in the spectrum (Hasselmann
et
al., 1973, Hasselmann et al., 1976) one may also anticipate systematic dependencies for spectra generated in slowly varying windfields. In fact, Hasselmann et al. (1976), argue that the directional distribution function can be regarded in such situations as a function of the nondimensional frequency f with the wave age as a parameter:(1.2.5)
Where U is the local windspeed and fm and cm are the frequency at the peak of the spectrum and the phase velocity (c = g/(270) at this fre-quency. The independent variables used in these expressions to normalize the frequency are fm and U (cm depends on fm). Actually Hasselmann et al. (1976) suggest U/cm as a parameter but the reciprocal, the wave age
8
(=cm is used here. There are two reasons for this. The first is
that 8 increases as the wind field develops (which seems more logical than a decreasing value of U/c ). The second reason is that 8 is a his-torically accepted parameter (e.g. Sverdrup and Munk, 1947) whereas U/cm is less so.
A number of investigators have used the above variables to normalize their data, though not always as suggested by Hasselmann et al. (1976). Instead, s was considered as a function of another dimensionless frequency by Longuet-Higgins et al. (1963),Tyler et al. (1974), Mitsuyasu et al. (1975) and Regier and Davies (1977):
2.11.
27rUfVI,. 2..6)
Regier and Davies (1977) used a width parameter different from s but the results can well be interpreted in terms of the parameter s. These inves-tigators found a high correlation between s and ? for frequencies with a phase speed less than the wind speed ( > 1) but the high correlation was lost for frequencies where the phase speed was greater than the wind speed
-(f < 1). Mitsuyasu et al. (1975) found that they could maintain a fairly high correlation for this part of the spectrum by introducing the peak
frequency fm (in the wave age
al
as an independent variable.Hasselmann et al. (1980) followed the above suggestion of Hasselmann et al. (1976) and considered their observations of the width parameters s as
-a function of f. They cl-aim -a slightly sm-aller sc-atter in their d-at-a -as compared to using i as an independent variable. But the difference seems small and may not be statistically significant.
Mitsuyasu et al. (1975) and Hasselmann et al. (1980) found that the maxi-um value of s was located at or near the peak frequency and that s de-creased as simple power functions of
f.
These authors fitted such func-tions to their data and suggested that the results be universally appli-cable to young sea states (wave age 6 < 1). The agreement between the results of Mitsuyasu et al. (1975) and Hasselmann et al. (1980) is fair as far as the shape of the functional relationship between s and f is concerned. However, the absolute value of s as a function of wave age8,
is greatly different.The main conclusions from the above review are:
Present theoretical considerations in the literature do not lead to a formulation of directional characteristics of the wave spectrum. Nonlinear wave-wave interactions probably force the two-dimensional spectrum of growing sea states into a standard shape.
Observations of the directional characteristics of the wave spectrum are scarce and usually not very detailed.
Those observations which have been published indicate that in a con-stant
or
slowly varying windfield the directional spreading of the spectrum is most narrow at the peak of the spectrum.Detailed observations indicate that the shape of the directional distribution remains unchanged during the phase of exponential growth in the ideal situation. These indications do not agree with the obser-vations and suggestions which are mentioned in point g of this review. Detailed observations carried out in slowly varying wind fields, support the cos2s(0/2)-model for the directional distribution.
a.
g. Suggestions, based on observations, have been made in the literature which relate the width parameter s of the cos2s(0/2)-model to the
fre-quency, the peak frequency and the wind speed. These relationships do not agree with each other as far as the scale of s is concerned.
The main problems which are addressed in this study are more or less di-rectly related to the above conclusions. They concern, firstly, the shape of the directional distribution. It is deemed useful to verify the applica-bility of the cos2s(0/2)-model with detailed observations in ideal wave generation situations and in non-ideal situations. Secondly, the depen-dency of s on frequency, peak frequency and wind speed is inferred from such observations. In addition to this, some comments on wave generation are made on the basis of these observations.
1.3 Methodology
1.3.1 Introduction
It was indicated at the end of the literature review in the preceding paragraph that the present study requires a number of detailed
observa-tions of the directional distribution which are to be compared with the cos2s(@/2)-model. The methods of observation and analysis are briefly outlined in this paragraph. They are described in detail i n the chap-ters 2 and 3.
1.3.2 Observations
There seem to be only three practical methods to obtain detailed obser-vations of the directional distribution. The first two are based on photography and the third is based on radar techniques.
The first photographic method is basically the interpretation of a pic pic
-ture of the sea surface as the record of reflected daylight (Stilwell, 1969; Kasevich et al., 1972). The intensity of daylight reflected from the sea surface depends on the slope of the surface. One can theoretical-ly transform such a picture into a two-dimensional wavenumber spectrum. This transformation seems to be fairly simple under very special
condi-tions of skylight illumination. But in general it requires advanced photographic methods of measuring light intensity distributions both from the sea surface and from the sky. Such methods are usually not readi-ly available.
The second photographic method, stereophotogrammetry, is a conventional method. Since the required facilities were available it is the method chosen for this study. The method is standard in land survey and it is commercially feasible for that purpose. Its use for observations of waves requires some adaptations but these are only practical in nature. They do not concern the basics of the method. The method is described in detail in paragraph 2.2 where it will appear that photography from helicopters was used.
At the initiation of the present study (1972) it seemed that the radar techniques
would
notbe
practical within a short period of time. But inthe
course
of this study at least one group of investigators put one such technique at a practical level (Tyler et al., 1974). This approach might have been a feasible alternative for the stereophotogrammetric method had facilities been available.The field program to obtain the stereo pictures for this study was domi-nated by the need to perform observations only during specific
meteoro-logical and topographical conditions which follow from the scientific requirements of the study. Observations were to be carried out in the ideal situation as described in paragraph 1.2 and in situations deviating from this. These were not the only specifications for the field program.
A large number of other aspects were to be considered. Among these were the weather conditions from the points of view of the photographers and the pilots, the availability of aircraft etc.
Two campaigns were carried out, one in 1973 in the German Bight in the framework of an international project called JONSWAP (e.g. Hasselmann
et al., 1973) and one in 1976 off the coast of Holland. One campaign, in 1975, was fully prepared, also in the framework of JONSWAP, but weather conditions did not permit any meaningful observations (very low windspeeds during otherwise ideal conditions).
During the photographic missions additional observations were carried out at one or more points in the area of observation. The most impor-tant were observations of the windspeed and wind direction near sea
level and of frequency spectra of the waves.
L3.3 Analysis
Six hundred stereo picture pairs were obtained in the field program. They varied widely in quality, both as regards the scientific interest and as regards the photographic quality. The first step in the analysis is the grading of these pictures according to their scientific quality and, separately, their photographic quality.
The capacity of the department responsible for the stereophotogrammetric analysis was sufficient to analyze about fifty picture pairs (equivalent to five spectra). These pictures were divided over three observations in an ideal situation and two observations in other situations. The choice was more or less subjective and based on the grading of the pictures. In addition to these five spectra,one test case was analyzed
From these spectra (excluding the test case) it is possible to obtain about seventy-five independent directional distributions with a direc-tional resolution of typically 100 -200. The cos2s(0/2)-model, which was introduced earlier, is fitted to the observations with a least-squares technique, and a quantitative measure of the goodness-of-fit of this model to the observations is determined. The statistical consistency between the model and the observations is investigated for one spectrum with a Monte-Carlo method. This method was also used to determine the
statistical variability of the observed model parameters (the main direc-tion and the value of s).
1.4 Results
Three spectra were obtained in the ideal situation. The qualification "ideal" is used here although some swell was present. This swell caused one of the spectra to be dropped from the analysis. The locally genera-ted spectra appeared to be essentially unimodal and the directional ener-gy distribution was most narrow near the peak of the spectra. This is in agreement with the literature on this subject. Two more spectra were observed, one in a homogeneous, stationary wind field slanting across a straight coast line and one in a homogeneous, stationary wind field with an irregular upwind coast line (both situations with relatively deep water). The shapes of these two spectra are strongly influenced by the geometry of the upwind coast line. This suggests that wave com-ponents from different directions are generated independently from each other (directionally decoupled generation). The results of a simple parametric wave hindcasting model support this suggestion.
The best agreement between the observations and the cos2s(0/2)-mode1 is found in the ideal situation. The agreement in the slanting wind situa-tion is only slightly poorer (although the main direcsitua-tions deviate con-siderably from the wind direction) and the agreement is considered to be
poor in the irregular coast situation.
The Monte-Carlo technique is applied to only one of the spectra observed in the ideal situation (for reasons of economy). It is found that the model is highly consistent with the observation (at the 0.79 fractile point). The statistical variability of the width parameter s in the same spectrum is found to be relatively large: the standard deviation of s is on the order of 30% of the observed value of s.
Approximately 75 independent values of s are compared with the sugges-tions of Mitsuyasu et al. (1975) and Hasselmann et al. (1980). The shape of the functional relationship between s and the frequency agrees
fair-ly well with the suggestions exept for the observation in the slanting wind situation. In this situation the observed value of s decreases more rapidly for increasing frequency than according to the suggestions. The observed scale of s, as a function of wave age, does not agree well with the suggestions of Mitsuyasu et al. (1975) or Hasselmann et al.
The purpose of this chapter is to describe in detail the method which was used to obtain the wave observations which are the focus of this study. The method is stereophotography from helicopters. Additional ob-servations at sea level (waves, wind and currents) are used to evaluate and interpret those observations but they are conventional and a des-cription of these methods of observation is of secondary importance. It
is given in Appendices III and VII.
The stereophotographic technique is dealt with in paragraph 2.2. Al-though this technique is also rather conventional, existing operational systems could not be used because they are designed to survey stationary objects while the sea surface is a relatively fast moving object. This necessitated the development of a new operational system, which has
been an essential effort in the realisation of the present study. The description of the system is therefore rather detailed for such a con-ventional technique. It will be addressed in paragraph 2.2.5.
2.2 Stereophotography of wind generated waves
2.2.1 Introduction
Stereophotography has a relatively tong history in the study of wind generated waves. Schumacher (1939) gives a description of a very early effort (1904) with the cameras mounted on an ocean going ship. Unfor-tunately, spectral analysis had not entered the field of wave research at that time, and the interpretation of these data, and also other early data, was very limited. Surprisingly many efforts have been made since the experiments in 1904. Platforms for the cameras were landbased
(e.g. piers), shipbased or airborne (blimps or aircraft). The best known operation is probably the Stereo Wave Observation Project (SWOP, Cote et al. 1960). In this project two aircraft were used to take stereo pictures of waves at a location in the North Atlantic Ocean.The
investigators succeeded in estimating the two-dimensional spectrum of the observed wavefield. Other investigators have followed similar pro-cedures. Simpson (1967) describes a project which may well be called SWOP II (as Simpson does) as it was an almost exact copy of the ori-ginal SWOP. More recently Sugimori (1975) describes the results of stereophotography of waves and indicates that the procedures were the same as in SWOP. Horikawa and Sasaki (1972) refer to an operational system to obtain stereo photos of waves from blimps. Investigators in Russia have used stereophotography rather extensively (relatively speaking). Matushevskii and Strekalov (1963), Davidan et al. (1974) and Krylov et al. (1968) describe or refer to stereophotographic observa-tions of wind generated waves.
The following paragraphs describe several aspects of the system used in this study, such as the basic approach, the cameras, the aircraft and the operational procedures. The basics of stereophotogrammetry are con-ventional and need not be described in detail as standard textbooks pro-provide such information. It will suffice to give a brief outline of
the principles. The other aspects of the system are more particular for the present study and they will be described more in detail.
The description in this paragraph 2.2 is almost identical to the one given in Holthuijsen (1979). A less detailed description is given in Holthuijsen et al. (1974).
to measure waves in situations different from those assumed in this study such as for instance in the surfzone, in a harbour or near break-waters. The arguments used there would probably be very similar. As a matter of fact a number of stereo pictures of breaking waves has been made over the breakwaters of Rotterdam harbour and even the spray from these breaking waves can be observed in three dimensions in these pic-tures. The system has also been successfully used to measure waves ge-aerated in a hydraulic laboratory.
2.2.2 Basic elements of the system
Some relevant aspects of stereophotogrammetry will be outlined briefly based on Thompson (1966), and some basic system requirements will be in-dicated.
Principles of stereophotogrammetry
To reduce the system to its most essential structure, it is assumed that the photographs are made looking downwards, that is, the camera axes are truly vertical during the exposure of the film. The image in
the photograph will then be
a
projection of the terrain directly under the camera. The distance between points on the ground at equal elevation can be determined fairly simply if the scale of photography is known. This scale can be expressed in terms of f and h as in equation (2.2.1) where s is the scale, defined as the ratio of corresponding distances in the terrain and in the photograph, f is the focal length of the lens and h is the altitude of photography above the horizontal terrain level ABC (fig. 2.2.1).If the values of f and h are known the positions of A, B and C can be determined relative to the camera from the images a, b and c. But if the terrain is hilly or mountainous, two photographs are needed to de-termine the geometry of that terrain.
Fig. 2.2.1. Vertical photography of plane ABC.
The situation for one stereo photo pair is illustrated in fig. 2.2.2. Consider the pictures to be taken truly vertically by two identical cameras from the same altitude.
The elevation of the cameras above the horizontal plane of reference is h1 and the distance between the cameras is 00' = b. An x-axis through the geometric centres of the pictures n and n' has been adopted in each picture. The elevation of a point A in the terrain is h2. Its image in the lefthand picture is a and in the righthand picture it is a'. The
p = na1 - n'a'
It can be shown, using similar triangles, that h2 is
bf
= h
-h2
1 p
Fig. 2.2.2. Stereo photo pair (after Thompson, 1966).
projections of a and a' on the x-axes are a1 and '
a'1 which are the images of
A1. The values of the abcissas na1 and n'al are different and
this difference is by definition the parallax (p) of A for the two pic-tures. Its value is given in the following equation:
(2.2.2)
(2.2.3)
This equation is the basis of the photogrammetric analysis to determine the elevation of points in the photographed terrain.
System requirements
The concept of parallax is central to the analysis. Note that the deri-vation of equation (2.2.3) is based on three assumptions (a) no tilt of the photographs, (b) equal camera elevation and (c) equal focal
lengths. These conditions will not be met exactly in practice and allo-wance for deviations must be made in the analysis of pictures taken during actual field operations. These corrections are described in standard textbooks such as Thompson (1966), Schwidefsky (1963) or Finsterwalder and Hofman (1968).
It appears that the corrections can be carried out most readily when the deviations from the ideal situation are small. In that case con-ventional instruments and procedures can be used to analyze the
pic-tures. Restrictions on the position and the orientation of the pictures imposed by photogrammetric instrumentation or procedures which reflect directly on the operational system are listed below.
altitude difference overlap of pictures in x-direction overlap of pictures in y-direction tilt difference in orientation 10% sly - 70% 80% 30 15°
Table 2.2.1. Limitations or camera position and orientation.
For most analysis procedures the stereoscopic effects are optimal if the overlap of the pictures is about 60% in x-direction. This is
illus-trated in fig. 2.2.3.
rig
1*-60*/.Rig. 2.2.3.. StereophotographiC overlap_
The format of the picture in x-direction is 1;, corresponding to a dis-tance 1x in the terrain. By considering similar triangles in fig. 2.2.3 and by equating b to 0.4 lx as required for a 60% overlap in x-direc-tion, the following relationship can be found.
h f 42.2.4)
b 0E.4
For a given set of cameras with f and 1; fixed, it appears that the ratio h/b is fixed. This leaves h, the altitude, or b, the distance between the cameras, to be chosen for the actual photographic opera,
tions.
'The altitude fora photographic' mission is chosen on the basis of two considerations. They concern the error in the measurements and the size of the area to be photographed. More information on this subject in terms of spectral parameters is given in Appendix I.
In conventional geodetic survey the stereophotographs are usually ob-tained by a camera looking vertically downward from an airplane which is flying directly over the terrain of interest. The pictures are ta-ken in sequence such that consecutive pictures cover overlapping areas
on the ground. In these areas of overlap, the stereo effects are used to determine the geometry of the terrain. Note that the two camera stations needed to produce the stereo effects are two different posi-tions of one camera and that the time interval between the pictures is irrelevant for fixed (non-moving) terrains.
The sea surface changes rapidly and if the conventional technique were used, serious distortions in the stereo effect would occur due to the change in surface geometry between two exposures. To limit these dis-tortions to an acceptable level, the time interval between the expo-sures should be at most a few ms (see below). It is not possible with conventional aircraft to position the camera at the two stations
with-in this time with-interval and consequently two cameras are needed which take the pictures more or less simultaneously. Using two cameras simul-taneously rather than one camera in sequence is the single most impor-tant difference between the systems as used in the present system and as used in conventional geodetic survey.
In the literature on this subject several investigators have indicated a maximum permissible value for the interval between the exposures. However, they do not go into detail as to how they arrived at the value. Cote et al. (1960) stated a desired value of less than 10 ms
and Cruset (1952) recommended an interval of less than 5 ms. One excep-tion to the conclusion that two synchronized cameras are needed is pro-vided by Howard (1969) who estimated that a 40 ms interval would still
produce satisfactory results. From this assumption he proceeded to imple-ment a system consisting of one high speed camera (movie camera) in a
fast flying airplane. Howard (1969) did obtain stereo effects and the pictures were analyzed to produce wave number spectra.
In the present study an effort is made to estimate the maximum permissi-ble time interval. It is difficult to state the propermissi-blem quantitatively and only an order of magnitude can be established. The measurements in
the stereo photographs are based on parallax effects in the images, that is, on horizontal displacements in the pictures. These should solely be the result of the three-dimensional geometry of the surface. But horizontal displacements are also caused by the horizontal or verti-cal movements of the surface between the two exposures. In particular the horizontal movement was considered to be important since its speed
is much greater than that of the vertical movement. It was estimated that a horizontal displacement in the surface of a decimeter, say, would result in an error of a few centimeter in determining the surface elevation from a few hundred meters altitude. This error seems to be acceptable. To correctly establish from this spatial limitation the
re-quirement for the time interval is very complicated because
of the random nature of the sea surface. The problem is reduced appre-ciably if it is assumed that the phase speed of the significant wave can be used to transform the spatial limitations into a time interval. The photographic system has been designed to be used in situations where this phase speed would not exceed 10 m/s (significant period less
than 7 s). It follows that in the most unfavourable conditions the above mentioned limit of one decimeter, and consequently the error of a few centimeter, is reached in 10 ms. For good measure the acceptable limit was set at 5 ms. These values are consistent with those mentioned by Cote et al. (1960) and Cruset (1952).
The value of 5 ms seems to be unnessecarily small when compared with the exposure time of the film which is 5 to 10 ms. But the effect of the finite exposure time is to blur the image, whereas differences in timing produce false parallax which can cause larger errors.
Other basic requirements on the system are standard for aerial photo-graphic survey and will not be discussed here.
MA'
Operational systemThe operational system consists primarily of two vertically downward looking cameras each mounted in a helicopter. The cameras, the aircraft, the camera mounting and the flight performance will be discussed next.
Cameras
The central elements in the operational system are obviously the came-ras. The task to select and synchronize the cameras was given to the Central Electronics Service Department of the Delft University of
Tech-nology. This task was performed in close cooperation with the Survey Department of the Ministry of Public Works which eventually provided the selected cameras and radio equipment.
In
the operations for normal geodetic survey, cameras are used which have been specially designed for high-quality aerial photography. The performance of these cameras is usually adequate and an investigation was started to establish whether this type of camera could besynchro-nized to the specified degree.
The cameras usually require very limited manual operation. They can be triggered electronically, that is, the command pulse to start the sequence in the camera to open and close the shutter can be given by an electrical signal. In the cameras which were investigated this sequence consisted of moving mechanical parts in the camera. It was found that the time between the triggering of the camera and the actual opening of the shutter varied randomly from exposure to exposure. In the
follo-wing this interval between triggering and shutter opening will be called camera delay. It consists of an average delay and a random variation which for the purposes of the present study is adequately described by
its standard deviation. When two of these cameras are triggered perfect-ly simultaneousperfect-ly, the film in the two cameras would still be exposed at different times due to the differences in camera delays.
When activating a camera one can conceivably anticipate the moment of exposure from mechanical or electronic indicators in the camera. When the delay in one of the cameras (the shortest delay) is electronically
increased to match the delay in the other camera one can obtain syn-chronized exposures. This approach was seriously considered for cameras with a rotary disc shutter where such an anticipation can be made for each exposure. Synchronization seemed to be attainable by
controlling the speed of the rotating discs electronically but major mechanical and electronic adaptations in the cameras would be needed and the proprietors (commercial firms) did not wish to have the came-ras adapted to such an extent. Instead a less demanding approach was
tried. If the standard deviation of the camera delay could be reduced to an acceptable value (1 or 2 ms, say) only the difference between the average camera delays of the two cameras would need compensation. This has been tried by providing each camera with an electronic unit to generate an additional delay for each camera such that the total average delay in one camera is (almost) equal to that of the other camera. The basic idea is illustrated in fig. 2.2.4 where the time diagram of the sequence is schematically indicated.
camera I
i
1
\
Fig. 2.2.4. Time diagram
of
camera triggering.electronic mechanic
delay delay
e.t
system camera exposure
If the exposure in the two cameras is to be initiated within a time lapse of 5 ms, it follows that the standard deviation of the camera delay should be at most a few ms, the variance being equal to the sum of the variances of the individual delays, and even then the 5 ms limit would sometimes be exceeded.
Laboratory investigations of two types of conventional aerial survey cameras showed that the variation of the camera delay was too large and that reducing it could only be achieved by major alterations in the cameras. This would have been prohibitively expensive and two other types of cameras were considered. The first type was Hasselblad 500 EL, which is a fine camera but which has not been designed as a survey camera. The geometric stability and the lens distortions are not up to the usual standards for survey photography. However, it was found that
the standard deviation of the camera delay could be reduced to approxi-mately 0.3 ms with only minor alterations in the camera. In view of this it was decided to use these cameras and to improve on or correct for metric shortcomings. The second type of camera was the UMK camera of Jenoptik (Jena,GDR) which came available one year after
the
implementation of the Hasselblads. The metric qualities of this cameraare good and the standard deviation of the camera delay was found to be approximately 1.5 ms. This camera too has not been designed for
aerial survey photography. The focal length f and the image format are 5.0 cm and 5.0 x 5.0 cm2 for the Hasselblad cameras and 10.0 cm and 17.0 x 12.0 cm for the UMK cameras. The nominal format size in x-direc-tion and y-direcx-direc-tion for both types of cameras is 1.0 cm larger but the edges of the pictures were not used due to reduction of photographic quality at these edges.
For both types of cameras electronic control units were built. These units were built in larger units which were totally self-contained for
equipment as a radio receiver (to trigger the cameras), suction pump (for flattening the film during exposure) and power supply. Each unit provides support for each of the cameras but a second camera can also be plugged in. It can be triggered simultaneously with the other cameras. The function of this additional camera will be explained later when the problem of determining the scale of photography will be addressed. For a detailed description reference is made to v.d. Vliet (1972,1974).
The equipment was tested extensively both in the laboratory and during testflights (5 flights in all, each with approximately 60 exposures). During the first flight with the Hasselblads, the cameras were mounted outside the aircraft. This mounting proved to be unsatisfactory be-cause the camera delays grew to unacceptable values during the flight. These delays could be measured during the flights through the use of a flash gun contact on the cameras which closed at the initiation of the exposure. To find the cause of the unstable character of the camera delays, the cameras were tested in the laboratory and it was found that the camera delays were sensitive to changes in temperature and humidity. To avoid this problem, the cameras were mounted inside the aircraft and sealed from the outside air by a window pane of optical glass. The Hasselblad cameras have performed perfectly ever since. The
same type of mounting was used for the UMK cameras. These cameras,
how-ever, failed to perform from time to time due to failures of
electro-nical or mechaelectro-nical parts inside the cameras. These failures could not always be traced or repaired during the photographic missions and some
missions have had to be abandoned. It should perhaps be restated in this context that the cameras have not been specifically designed for survey photography from aircraft and that they have been subject to conditions which are probably far outside the manufacturer's specifi-cations (e.g. excessive vibrations, see the third section of this para-graph on camera mounting).
Aircraft
Other major components in the system are the camera carriers and from the outset it was decided to use aircraft for this purpose. Blimps, which have been used by other investigators (e.g. Horikawa and Sasaki,
1972) were not seriously considered because of availability and ope-rational problems. In consultation with experts several types of air-craft were checked and both military and commercial institutions were visited. It does not seem relevant to relate the findings here and it may suffice to state that the Royal Netherlands Air Force was able and willing to provide assistance far superior to alternative options
available.
The aircraft chosen were helicopters which were operated by the Search and Rescue team of Soesterberg airbase (now at Leeuwarden air base). Two of these helicopters were assigned to the study for a total of
120 flying hours over a period of three years. The primary peace-time task of this team is to perform search and rescue operations at sea and a secondary peace-time task is to carry out photographic missions. Obviously this was a very fortunate combination of capabilities and technical facilities.
The helicopters were of the type Alouette III with a transportation capacity of six persons. These helicopters, as used by the Search and Rescue team, did not carry sophisticated equipment to aid in navigation. Only magnetic compass and speedometer were used. This seems to be
ade-quate since the requirements for the accuracy of navigation are not very severe as the primary purpose of the study is to investigate the directional characteristics of the waves without necessarily relating these to the position of observation. The latter was a secondary objec-tive at best. For the purpose of the study it is considered acceptable
to know the position with an accuracy consistent with the variations of characteristic parameters of the wave field. The orientation of the helicopters is needed to determine the orientation of the pictures relative to the wind direction. An average deviation of 50 and a stan-dard deviation of 50 in thE 1-elicopter orientation seems to be
accep-table for this purpose.
Camera mounting
The helicopters were accomodated with drop doors. These were open during the photographic missions and the cameras were mounted over these doors on a wooden plank. As noted before, a window pane of optical glass sealed the cameras from the outside air. It was found during the test flights that the floor of the helicopter tilted approximately 7° (head down) at a forward speed of about 70 knots which was a typical speed for all operations. For convenience in the analysis of the pictures this tilt was removed from the cameras by tilting the mountings. The cameras were secured with bolts and nuts to the wooden plank which in turn was bolted down to the helicopter floor. A consequence of this construction was that the motion of the helicopter, including
vibra-tions, were transmitted directly to the cameras. A gyro-stabilized and vibration-damping construction was considered but the cost was prohibitive.
In addition to the two downward looking cameras (one in each helicop-ter), a third camera was introduced. This camera was used for two pur-poses both related to estimating the distance between the helicop-ters: maintaining the helicopter formation and determining the scale of photography.
In conventional aerial survey the scale of photography is usually determined from known distances in the photographs between points in
the terrain. The equivalent situation at sea would be to have a ship or other structure with known dimensions in the area of photography. This is very well possible and in SWOP (Cote et al., 1960) a ship was used which towed a buoy. The distance between the ship and the buoy was continuously monitored and provided the required distance in the pictures. A major drawback of this approach is that the area
of operation is restricted to the immediate vicinity of such structures. To avoid this restriction another method was adopted here which is based on determining the distance between the cameras (or the helicopters) photographically. The third camera (also a Hasselblad 500 EL) was used for this. It was mounted in one of the helicopters with the other heli-copter in the field of view through an open window. The image of that helicopter was projected on the film and since the geometry of that helicopter is known the distance can be computed. The accuracy of this method was estimated by testing the method with the helicopters on the
ground and it was found to be better than 3%.
This third camera was also used as a range-finder during the flight to maintain the relative position of the helicopters. A number of
calibra-tion lines was super-imposed on the viewer of the camera which helped an observer to estimate the distance between the helicopters.
Flight performance
The performance of the helicopters has been evaluated through an exten-sive test flight over sea and it was found that all of the requirements listed in table 2.2.1 could be met. The windspeed during the flight was approximately 10 m/s and the atmospheric conditions were rather turbu-lent. The altitude varied from 200m to 500m. The observed values of ca-mera position and orientation are listed below.
Table 2.2.2. Observation of camera position and orientation (see also table 2.2.1).
The numbers in this table are based on approximately thirty observations except those for the difference in orientation which are based on ten ob-servations. The average deviation of the helicopter orientation relative to its desired orientation was 1.5o. The standard deviation of the heli-copter yaw was 3.30
(0-yaw = 0.06 radians). These values were based on ten observations over a fixed platform at sea with known orientation.
2.2.4 Operational procedures
The operational procedures were of two kinds: those related to the pre-parations for the photographic mission and those related to the actual flight. As regards the preparations it may suffice to indicate that the logistics were mostly arranged through military channels. Details on these arrangements, including transportation, housing, licences etc. (areas of operation in Holland and Germany) do not seem to be relevant
here. The preparation of the photographic equipment was limited to setting the instrumentation on stand-by with a film type depending on anticipated weather conditions. During the actual flight attention was concentrated on the second kind of procedures which will be discussed
next.
Average Standard
deviation
altitude difference 10.6% 1.6% (of altitude)
overlap of pictures in x-direction 60% 9.5% overlap of pictures in y-directions 79% 6.5% tilt
1.90
2.10
o o difference in orientation 5.6 4.7 IfRi
The crew of the two helicopters consisted usually of seven people but in later operations, when the MIK cameras failed from time to time, an extra crew member was introduced. Before and after each flight the crew was briefed and debriefed, the pattern for a typical flight being of the following nature.
During a flight, observations were to be carried out at a number of locations. The large scale procedure was to fly from the airport (not necessarily the home base of the helicopters but the airport where the
different groups assembled) to a pre-arranged area of observation and to hop from one point of observation to the other. During the legs of the flight to and from and between the points of observation the usual flight procedures in air traffic were observed.
At a point of observation the procedures were concentrated on obtaining a sequence of stereo photographs of non-overlapping sea surface areas,
see fig. 2.2.5. This sequence consisted typically of ten photo pairs. Such an action to obtain the sequence was called a sortie.
Fig. 2.2.5. Sequence of non-overlapping stereo photo pairs (sortie).
The pilots found it convenient to agree on the following procedure: one helicopter (the "leader") would keep to a steady course at a specified altitude, direction and speed. The other (the "follower") would take its position relative to the leader such that the two helicopters were
fly-ing side by side at a specified distance. Findfly-ing this position was based to a large extent on the information from the viewer of the third camera which acted as a range finder. The choice of the altitude for a
given set of cameras depended on several considerations related to the wave field. These considerations and the results thereof are discussed
in Appendix
When the required helicopter formation was achieved, the photographer started the photographic sequence by operating the radio transmitter. Careful timing located the pictures within al few hundred meter of the specified postion. But the operational procedures were often frustrated
by camera failures, atmospheric disturbances clouds, rain etc. and sor-ties have had to be relocated, flown again or abandoned.
2.2.5 Photogrammetric analysis
To quantify the information of the stereo photo pairs, equation (2.2.3) is evaluated for each point of interest of the sea surface. In this equation the values of b (the camera distance) and f (the focal length of the lens) are known, h (the altitude) can be chosen arbitrarily as
elevations are taken relative to an arbitrary level of references. The parallax p is determined from the pictures.
Determining the parallax of a point requires the identification of two
images of one point, one image in the lefthand picture and one in the righthand picture. These two points in the pictures are called homolo-gous points. In conventional stereophotographic survey (land terrain)
the identification of the homologous points is relatively easy through visual inspection of the pictures separately. If homologous points are not so easy to identify or if the number of points of interest is great,
some degree of automation is called for. The identification is then basi-cally carried out by a correlation technique.
Two processes can be used to carry out the correlation. The first
study. It is a fully automated process in the sense that human inter-ference is very limited. It is based on fairly recent developments in the analysis of stereo pictures and it does not seem to be fully opera-tional in the sense that it can be used succesfully in a large variety of terrain types. The pictures are scanned to digitize the optical density of the film and the position of a large number of homologous points is calculated through a numerical correlation procedure (e.g. Crawley, 1975, Brnjac et al. 1976). Various modes of operation are possi-ble such as finding the position of contourlines in the terrain at a spe-cified elevation,or finding the elevation of points on a regular grid. This process is very promising and it was seriously considered for use
in this study. A commercial firm was committed but during a test phase of the analysis procedure it was found that the firm could not fulfill the commitment because the equipment for the analysis was not available.
The second process is conventional in stereophotogrammetry. It is based on the human interpretation of the stereo pair which in a sense, may also be considered as a correlation technique. The human interpretation is much more sophisticated than that of the computer since a human being uses additional information in the perception of depth (color, size, tex-ture etc.).
When each of the two pictures of a stereo pair is presented to each of the eyes these two pictures are perceived as one image of a three-dimen-sional space. The analysis of the pictures is based on observations in this fictitious space with the aid of fairly complicated stereoscopic viewing devices. On each picture of the pair a small dot is projected. When the pictures are observed through the viewing device the two dots
seem to create one "floating" point in the fictitious space created by the stereo photo pair. A human operator can move the floating point by varying the positions of the dots in the pictures. He is thus able to
Having made the identification, the positions of the dots in the pic-tures determine the parallax, and the coordinates of the point in the three-dimensional space are recorded.
A cartesian system of x, y and z coordinates was defined in the three-dimensional space created in the stereoscopic viewing device. The x-and y-axes defined the horizontal plane x-and the z-axis was pointing
up-ward. The operator was asked to determine the sea surface elevation on a square grid in a region as large as possible. In the pictures of the
UMK cameras the region of overlap is usually a square due to the over-lap percentage and the format size of the pictures. In the pictures of the Hasselblad cameras the region was oblong for the same reasons and the operator was asked to analyze only the largest possible square from the total region available.
The mode of operation was a profiling method: the sea surface was scanned along the gridlines parallel to the y-axis (which pointed into the flight direction). While the x- and y-position was controlled automatically, the operator controlled the vertical position of the floating point which followed the sea surface as closely as possible. Every time the horizontal position of the floating point crossed a gridpoint the three coordinates of that point were recorded on tape.
In some instances the surface could not be percieved with any accuracy (loss of stereoscopy due to photo quality, sun-glitter etc.). The grid-points concerned were either labelled or skipped.
The analysis of each picture resulted in a set of observations of the elevation of the sea surface relative to an arbitrary frame of
referen-ce. This set is given symbolically as
wherei:l'istheobservedsurfaceelevation,x.and yj.are the
coordi-natesoftheridpoints,wherex.--(i-I) Ax and Y3.--(j-1) 4,,and
and
ay
are the mesh size. The general idea is illustrated in fig. 2.2.6. The symbol - is introduced to distinguish the observation from the true value of the surface elevation which will be indicated by n(x). The symbol ' is used to indicate that the plane of reference is chosen arbitrarily.loss of stereoscopy
di ection
of light
Fig. 2.2.6. Area of analysis in stereo photo pair.
The information from the analysis just described was not in a format suitable for the spectral analysis needed to obtain the two-dimensional spectrum (see paragraph 3.3). The surface information was adapted so
as to meet the specifications listed below which follow from the method which was used to Fourier transform the data (based on an FFT method,
Singleton, 1969, see paragraph 3.3):
a. The region of surface information should be square and of specified size. This size is determined from spectral requirements (Appendix I). The position of the square is chosen such that the square covers data
of the highest quality available in the total region. In some cases the limits of the square exceed the limits of the region in which
