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Modelling surface structure and temperature of relevance to remote sensing of cities Soux, Cristian Andres 2000

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MODELLING SURFACE STRUCTURE AND TEMPERATURE OF RELEVANCE TO REMOTE SENSING OF CITIES By Cristian Andres Soux B. Sc. (Hons.), University of British Columbia, 1996 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF GEOGRAPHY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 2000 © Cristian Andres Soux, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. 1 further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract The current increase in the use of remote sensors necessitates a closer investigation into the nature of what these sensors view. This is particularly true over urban areas where the well developed three-dimensional surface structure creates anisotropic surface radiative emissions. This study presents a numerical model to interpret and predict surface facet view factors and remotely-sensed radiative surface emissions from urban areas. The model that is developed (S3MOD) is able to create a simplified urban surface containing a repeating pattern of buildings, streets and alleys at any azimuth and geographic location. A remote sensor can then be located and oriented over a full range of possible inputs from below canopy level to near satellite height. Surface facet temperatures can be either input directly or evaluated using the Mills (1997) UCL energy balance model. S3MOD is then able to calculate surface view factors and sensor apparent temperatures. S3MOD is validated against measurements taken during a field campaign in Vancouver, B.C. The geometric validation cannot be completed using measured values due to uncertainty in the accuracy of those measurements. A theoretically based approach is employed which reveals very good agreement exists between modelled values and theory. The radiative validation is conducted using measured sensor apparent temperatures and with a sensor specific EFOV weighting function, provides good agreement between modelled and measured values. The validated model is used to investigate a number of hypothetical remote sensing scenarios. The first of these results indicates that for a specified sensor location and orientation and over a given surface structure, a critical height exists above which surface view factors do not change appreciably. In addition, it is found that sensors at different elevations but viewing the same surface area (i.e. the higher sensor has a smaller IFOV) do not have the same surface view factors. The domain size of the model must be increased to further expand the range of sensor heights over which the model works effectively. The final modelling exercise attempts to find the location and orientation where a sensor would sample surface facets in proportion to their contribution to the complete surface area for a specified urban surface type. The results of this final scenario suggest that for sensors located at five times building height, an extreme off-nadir angle is necessary to correctly sample wall facets. Further work is required to determine if this ideal sensor setup exists for some of the surface types tested. iii Table of Contents Abstract " List of Tables vii List of Figures viii List of Symbols and Abbreviations xi Acknowledgements xiv 1 INTRODUCTION 1 1.1 Research Objectives 1 1.2 Significance of Research 3 1.3 Previous Research 8 1.3.1 Thermal-Infrared Remote sensing of Urban Areas 8 1.3.2 Modelling Surface Elements 10 1.3.2.1 Vegetated Surfaces 10 1.3.2.2 Urban Surfaces 13 1.4 Summary of Obj ectives 15 2 A THREE-DIMENSIONAL SURFACE MODEL 16 2.1 Introduction 16 2.2 Model Theory 16 2.3 Model Structure 20 2.3.1 Input 20 iv 2.3.2 Building the Surface Array 22 2.3.3 SEEN Subroutine 25 2.3.4 SOLGEOM and SHADE Subroutines 26 2.3.5 View Factors 26 2.3.6 Conversion and Summation of Temperatures 28 2.3.7 Output 30 2.4 Facet Temperatures 30 3 OBSERVATION PROGRAMME 33 3.1 Introduction 33 3.2 Site Description 33 3.3 Method 36 3.3.1 Instrumentation 36 3.3.2 Sampling Methodology 39 3.4 Synoptic Conditions and Weather 40 3.5 Helicopter Flights 42 4 MODEL VALIDATION 44 4.1 Introduction 44 4.2 Geometric Validation 44 4.2.2 Image-based Geometric Validation 49 4.2.3 Theoretically-based Geometric Validation 53 4.3 Temperature Validation 55 v 4.3.1 Prescribed Temperatures 55 4.3.2 Energy Balance Modelled Temperatures 69 4.3.3 Helicopter-based Temperatures 72 5 MODEL APPLICATIONS 75 5.1 Introduction 75 5.2 Ground to Satellite 75 5.2.1 Modelling Procedure 75 5.2.2 Modelling Results 76 5.3 Theoretical Urban Zones 80 5.3.1 Modelling Procedure and Rationale 80 5.3.2 Modelling Results 83 5.4 Conclusion 86 6 CONCLUSIONS 95 6.1 Summary of Findings 95 6.2 Suggestions for Future Work 97 References 99 vi List of Tables 2.1 Inputs to S3MOD 22 3.1 Technical Specifications: A G E M A 880 LWB Tffi. system 43 4.1 Proportion of surface type 'seen', and the sensor detected surface temperature, from a range of sensor orientations 48 4.2 Results of using revised estimates of sensor orientation on model generated surface type view factors 52 4.3 Modelled and calculated values of sky view factor 54 4.4 Summary of measured and modelled surface type view factors at different times, heights and azimuths throughout the measurement period 62 5.1 Surface facet view factors for remote sensors viewing identical surface areas.... 79 5.2 Summary of surface structure characteristics for seven surface types. UTZ, urban terrain zones, based on classification of Ellefsen (1990) 82 5.3 Comparison of model input parameters and measured values of surface structure at individual sites 83 5.4 Percentage of complete surface area occupied by different surface facets for each surface type 84 vii List of Figures 1.1 Aerial view of Vancouver, B.C 2 1.2 Schematic illustration of different definitions of the urban surface 4 1.3 The components of the surface viewed by remote sensors with identical IFOV, but different viewing angles to the surface 7 2.1 A two-dimensional representation of an urban surface showing both 'seen' (single lines) and 'unseen' (double lines) portions of the surface 18 2.2 A three-dimensional urban surface with a remote sensor situated above the ground 19 2.3 Basic structure of the S3MOD program with a brief description of each subroutine 21 2.4 Plan view of an array subsection showing building, street and alley dimensions. 24 2.5 Variables used to calculate the view factor of a surface element on a plane perpendicular to the sensor viewing direction 28 3.1 Map of Vancouver, B.C. showing location of study site 34 3.2 Aerial view of False Creek South. View is to the North-West 34 3.3 Plan view of the False Creek South study site 35 3.4 Measurement site in False Creek South 36 3.5 Instrument cluster mounted on the cross-arm atop the tower 38 3.6 Pacific Weather Centre surface analysis for August 9 t h, 1997 40 3.7 Pacific Weather Centre surface analysis for August 10 th, 1997 41 viii 3.8 Meteorological variables measured at False Creek South on August 9/10, 1997 4 4.1 Photographs taken from 26 m above the surface supposedly oriented at a 45° ONA and an azimuth angle of 315°, at (a) 0720h, and (b) at 191 Oh 4< 4.2 Photos showing surface area seen by tower-based camera 5 4.3 Photos showing surface area seen by tower-based camera 5 4.4 Photo taken from the tower-based camera showing the roof top 53 4.5 Comparison between modelled and measured temperatures, at all measurement heights, using prescribed facet temperatures 58 4.6 Measured and modelled temperatures at seven times at 26 m 59 4.7 Measured and modelled temperatures at seven times at 22 m 60 4.8 Measured and modelled temperatures at seven times at 11m 61 4.9 Comparison between modelled and measured temperatures, where the measured values use prescribed facet temperatures and Everest weighting to give TEW as in (4.6) 65 4.10 Measured and modelled temperatures at seven time at 26 m 66 4.11 Measured and modelled temperatures at seven times at 22 m 67 4.12 Measured and modelled temperatures at seven times at 1 lm 68 4.13 Comparison of measured (TEW) (a) and modelled (TsBmoJ) (b) facet temperatures through the course of a day 70 4.14 Comparison between modelled and measured (TEW) temperatures using energy balance modelled facet temperatures (TEB mod) 71 ix 4.15 Measured and modelled temperatures through time using energy balance modelled facet temperatures 72 4.16 Measured and modelled sensor detected temperatures from a helicopter 74 5.1 Surface view factors from a nadir-viewing sensor moving from 100 m above the surface to 100 km above the surface 77 5.2 Surface view factors from a remote sensor, at 45° ONA and four different sensor view azimuths and being moved from 100 m to 100 km above the surface 78 5.3 Surface facet view factor from six ONA and through 90° of azimuth for surface type HDHR05 88 5.4 Surface facet view factor from six ONA and through 90° of azimuth for surface type HDAA1 89 5.5 Surface facet view factor from six ONA and through 90° of azimuth for surface type MDDH025 90 5.6 Surface facet view factor from six ONA and through 90° of azimuth for surface type MDDH05 91 5.7 Surface facet view factor from six ONA and through 90° of azimuth for surface type LDHR5 92 5.8 Surface facet view factor from six ONA and through 90° of azimuth for surface type LDHR2 93 5.9 Surface facet view factor from six ONA and through 90° of azimuth for surface typeLDLI05 94 X List of Symbols and Abbreviations ABBREVIATIONS A A Attached Apartments D H Detached Houses HD High Density HIP Heat Island Potential HR High Rise HAV building height to street width ratio IFOV Instantaneous Field of View EIRT Everest Infra-red Transducer FOV Field of View L D Low Density LI Light Industrial LUT Look-up Table M A E Mean Absolute Error M D Medium Density MSS Multi-spectral Scanner ONA Off-nadir Angle R H Row Houses R M S E Root Mean Square Error S3MOD sun-surface-sensor model sum Surface Urban Heat Island xi TIR Thermal Infra-red U B L Urban Boundary Layer U C L Urban Canopy Layer UHI Urban Heat Island UTZ Urban Terrain Zone SYMBOLS Ac complete surface area AP building plan area AT total ground level surface area Ax alley width in x direction Ay alley width in_y direction B L building length B W building width c speed of light (2.998 x 108 m s"1) d length of wall element D canyon width (Chapter 3) D Wilmott's index of agreement / fractional component h Planck's constant (6.6262 x 10"34 J s) h height of wall element (Chapter 2) H canyon height k Boltzmann's constant (1.281 x 10"23 J K L radiance (W m'2 sr"1) xii L s sensor detected radiance n counter OT observed temperature PT predicted temperature r distance to wall element r2 Pearson's coefficient of determination Sx street width in x direction Sy street width in y direction T temperature (K) TEB mod energy balance modelled facet temperature TEW sensor detected temperature with Everest weighting u sensor view vector v surface test point vector VF view factor of surface element Greek s emissivity 6 angle between two vectors X wavelength (m) Xp ratio of the building plan area to the total ground level surface area Xc ratio of the complete surface area to the total ground level surface area y/s sky view factor xiii Acknowledgements This thesis could not have been written without the support and assistance of many people. My research supervisors, Dr. T.R. Oke and Dr. J.A. Voogt, have provided me with outstanding academic support throughout the course of this project. Their patience and enthusiasm have helped me through a number of frustrating times. I am also very grateful for the personal support they have both given to me over the course of this project. Dr. D.G. Steyn has always graciously given me his time and helped me with my many view factor related questions. Dr. G. Mills was kind to provide the code and much assistance with the use of UCLMOD. R. McTaggart-Cowan provided assistance with the field programme and E. Ellis helped with lab work. Special thanks are also due to a couple of members of the department: Vincent Kujala, whose open door has allowed me to ask and have answered innumerable computing questions. Elaine Cho, for helping navigate me through the intricacies of Grad Studies, always with a smile on her face. An excellent field site was kindly provided by Polygon Metal Works Inc. in Vancouver. Funding for this research has been provided to Dr. T.R. Oke by the Natural Sciences and Engineering Research Council of Canada. Personal funding was provided through University of British Columbia Teaching and Research Assistantships in the Department of Geography. My family has always provided me with absolute love for which I cannot begin to express my thanks. To my friends, thanks for all you have taught me and all the insanity we have shared. Finally, thanks to Elena, whose love, support, and humour always make my days better. xiv Chapter 1 INTRODUCTION 1.1 Research Objectives This study was prompted by the need to develop a numerical model to interpret and predict remotely measured radiative surface emissions from urban areas. The current increase in the use of remote sensors for measuring atmospheric and surface phenomena directly, and providing input data to various numerical weather and climate prediction models, necessitates a closer investigation into the nature of what these sensors measure, especially what they 'see'. Understanding what a remote sensor is viewing is vital to the interpretation of the output signal or image generated from that sensor. Due to the uneven, three-dimensionality of urban systems the same sensor viewing from different points above may 'see' a different mix of surface elements, i.e. different parts of the complete surface are obscured from view. The complete surface is the entire area comprising the boundary between the surface and the air (Voogt and Oke, 1997) , see Figure 1.2. In Figure 1.1 we see a photograph of Vancouver, B.C. taken from the air. This perspective shows the complexity present in a typical urban surface. What is seen, and hence what area a remote sensor with a similar field-of-view (FOV) would acquire its input from, is a combination of many surface facets, both sunlit and shaded. One can imagine that viewed from a different perspective this same urban surface would contain a different combination of surface facets that would lead to a different input to the remote sensor (see Figure 1.3 for a two-dimensional illustration of this effect). This highly three-1 dimensional surface structure leads to a directional variation of the measured radiance (anisotropic radiance distribution; also referred to as anisotropy). Anisotropy is comonly reported in degrees C (i.e. the range of surface temperatures measured from different directions). The complexity found in typical urban surfaces requires that any observations or measurements acquired from that surface be analyzed and interpreted within the context of anisotropy. It is important to note that the uncertainties associated with surface emissions come from a lack of knowledge regarding three-dimensional surface structure; much of the active surface (the surface in contact with the atmosphere) lies in the vertical plane or is obscured from view. Uncertainties also arise from lack of knowledge of the surface emissivities of the viewed facets. Figure 1.1 Aerial view of Vancouver, B.C. In addition to their inherent complexity, urban surfaces exist over a wide range of latitudes, and hence experience differing solar regimes as well as varying building and 2 street orientations. Therefore, a model to predict both what portion of the surface is viewed by the sensor and what radiation is emitted from that same surface, at a given location in place and time, provides a valuable tool to scientists interested in measuring and modelling surface-atmosphere interactions. 1.2 Significance of Research The urban surface is a complex entity that plays an important role in affecting urban climate. It does this through absorption, reflection and emission of radiation, in the transformation of energy and mass, in its interception of precipitation and pollutants and in its frictional and deflecting influence on airflow. This importance to climatic and meteorological variables requires a precise definition of what is meant by an "urban surface". Five ways of defining the surface of an urban system have been suggested by Voogt and Oke (1997). Figure 1.2 illustrates these possibilities, (a) is the "ideal" or "complete" surface where every minute part of the interface is represented. It is not possible to model or measure this surface exactly. Therefore, simplifications must be made, (b) is the perspective of a ground-based observer. This view regards the surface as the equivalent of the ground, it ignores vertical elements and therefore any urban area will be poorly represented by this view, (c) is the "roof-top" view and in an analogous way to (b) ignores the vertical depth in the interface and treats the area below roof level as a "black box" where only a mean description of the underlying surface is used, (d) is the "bird's eye" view and is the surface that a vertically-oriented remote sensor would see if 3 Figure 1.2 Schematic illustration of different definitions of the urban surface. From Voogt and Oke (1997). positioned directly above the system. This view does not take into account any surfaces that are obscured from above including vertical facets, (e) is the surface at which screen level air temperature is measured, (f) is the "zero-plane" approach which is commonly 4 used in systems with significant of vertical structure such as forest and crop canopies. It is based on a downward extrapolation of the vertical variation of atmospheric entities to some height within the canopy which is deemed to be an effective surface. It is a mathematically defined height but cannot be sensed directly. From the preceding discussion it can be seen that any measurement or modelling endeavor that ideally requires a representation or property of the complete urban surface as its goal requires a certain level of compromise. Depending on the entity being studied, the sensing system used, the accuracy required and the scale of interest, concessions to the "ideal" case must be made. Measurement of surface radiative emissions is an important aspect of the study of urban climates. Accurate knowledge of emissions can lead to a greater ability to evaluate urban surface temperatures and surface energy balances. As measurements of radiance are taken from remote sensing platforms located at varying distances and positions above the ground, definition of the surface being sensed is a requirement. What a remote sensor 'sees' (similar to its view factor) is directly linked to its output signal thereby affecting the information gleaned from that sensor. The precise definition of a view factor is "a geometric ratio that expresses the fraction of the radiation output from one surface that is intercepted by another" (Oke, 1987), where the remote sensor is the intercepting surface in this case. For satellite-based remote sensors the simplest case exists when an instrument with a relatively narrow instantaneous field of view (IFOV) or solid angle through which an instrument is sensitive to radiation, is located directly overhead (i.e. elevation angle « 90°) and at a very large distance away. This situation leads to the "birds-eye" view of the 5 surface. For the urban case this refers to roof-tops, tree-tops, roadways and any unobstructed open areas. These features do not represent the total urban surface (active area) that is in contact, and therefore interacting, with the atmosphere and this leads to exposed horizontal surfaces being preferentially sampled over other surfaces. At more densely built-up sites the complete surface area is much greater than the "birds-eye" view area. (For example, cubic buildings separated by a distance equal to their characteristic length (i.e., at a plan density of 0.25) have an active area to plan area ratio of 2. A low density suburban area with scattered trees may have a ratio of 1.5 while in downtown cores values may be up to 3) (Roth, et al. 1989, Grimmond and Oke, 1999). Any vertical surface, such as building walls and areas beneath tree canopies, therefore are not "seen" by the sensor and an inaccurate evaluation of true radiative emissions from the complete surface is obtained. For elevation angles that are less than 90° relative to the city, the amount of vertical surface viewed increases. For a given viewing angle this effect depends upon the ratio of the active: plan area of the target. If surface radiant temperature or reflected solar radiation are being measured, the position of the sun relative to the city and sensor also impacts the measured values. Figure 1.3 illustrates this anisotropy, and in conjunction with Equation 1.1 shows the importance of sensor-surface-sun geometry in evaluating reflected and emitted radiation. Sensor detected radiance ( L s ) is assumed to be a linear combination of surface component radiances weighted according to their fractional contribution (f) within the sensor IFOV: L s = 2]fi-Li (1.1) i=l 6 where i represents a component surface within the sensor IFOV and Lj is a representative surface radiance for that component (Voogt, 1995). |~~| g r o u n d v i e w e d ["J wal ls v i e w e d |~1 r oo fs v i e w e d Figure 1.3 The components of the surface viewed by remote sensors with identical IFOV, but different viewing angles to the surface. Understanding directional variations in space and time is therefore important for the interpretation of remotely-sensed measurements and identification of potential biases. It also allows the expansion of spatial and temporal coverage via off-nadir sensing, and may yield improved or additional information about the surfaces viewed (Kimes et al., 1984). 7 1.3 Previous Research This section briefly reviews two areas of previous research. Firstly, studies of thermal-infrared (TIR) remote sensing of urban surfaces are reviewed in the context of their relevance to urban climatology in general, and specifically efforts made to examine the role of anisotropy on measurements. Secondly, efforts to model surface elements of both urban and rural surfaces, with the goal of accounting for anisotropic radiative emissions, are reviewed. 1.3.1 Thermal-Infrared Remote Sensing of Urban Areas There is a great deal of interest in developing knowledge about urban temperatures, therefore much of remote sensing research of cities has focused on the thermal-infrared portion of the electromagnetic spectrum. Using this relatively easily acquired, detailed, and spatially-continuous data source has enabled study of the surface urban heat island (SUHJ). Voogt (1995) provides an excellent overview of some of the studies that have focused on TIR remote sensing of urban areas. These studies have provided greater insight into the nature of the SUFII and have shown its differences and similarities with the near-surface air temperature UHI. In addition to gaining knowledge of surface temperatures, many of these studies have attempted to relate remotely sensed surface temperatures to air temperature (Barring etal, 1985; Eliasson, 1991; Gallo and Owen, 1999; Henry et al, 1989; Lee, 1993; Stoll and Brazel, 1992). There has been a general lack of correlation between these measurements and this can attributed to three main factors (Roth et al, 1989). Firstly, lack of simple coupling between the surface and air due to advection in the urban canopy 8 layer, secondly, biased spatial sampling of surface temperatures by remote sensors which preferentially view horizontal and unobstructed surfaces, and lastly, a failure to recognize the different scales of climatic phenomena in the urban atmosphere. The ramifications of sensor view factors and anisotropy on remotely-sensed readings were not appropriately accounted for in these studies which in turn partly led to poor correlations between surface and air temperatures. This fact precipitated the need for studies into the role of anisotropic emissions in urban areas. Direct investigation, in urban areas, into the biases introduced by TIR remote sensors has only been carried out on two occasions. Roth et al. (1989) performed a qualitative appraisal of how the complex three-dimensional nature of the urban surface poses a problem for what the sensor views. This in part led to the work of Voogt (1995) and Voogt and Oke (1997, 1998), who used a unique combination of sensor platforms (helicopter and truck) to show the anisotropy and spatial distribution of surface temperatures within the city of Vancouver. This work also led to the creation of a database from which estimates of the complete urban surface temperature can be made. The importance of this work is that it was the first to quantitatively assess the magnitude of the anisotropic emissions in selected urban land use areas. The results indicate that strong anisotropy was found in all areas of study with the maximum differences ( > 9° C) occurring over the downtown study area near midday. Anisotropy varies with time and view direction depending upon the orientation of the surface and the solar geometry for that place and time of year. The importance of including a consideration of anisotropy when using thermal remotely sensed imagery over urban areas was emphasized. An attempt was also made to model these emissions, the results of which will be discussed in 9 Section 1.3.2.2. Although not a direct examination of the role of anisotropy, lino and Hoyano (1996) measured surface temperature distributions over Kawasaki, Japan with both a downward and a side-looking airborne multi-spectral scanner (MSS). This approach was taken in an attempt to accurately portray the true distribution of surface temperatures rather than those obtained solely by nadir-viewing MSS. This information was then used to calculate a sensible heat flux based index, the Heat Island Potential (HIP). It is important to note that the role of anisotropy has not only been examined in an urban context, although this is perhaps where its effects are most significant. Anisotropy also exists over natural surfaces. Lipton and Ward (1997) examined the biases observed from satellite-derived surface temperatures in mountain areas. These biases were correlated with satellite viewing angle and temperatures of the mountainsides sampled. Prata (1994), using satellite mounted infrared radiometers viewing row crop structures, found that anisotropic emission of radiation was an important effect to take into consideration when evaluating true surface temperature. Paw U (1992) also provides a review of six other studies where anisotropic emissions over plant canopies were observed to have important effects on remotely-sensed temperatures. 1.3.2 Modelling Surface Elements 1.3.2.1 Vegetated Surfaces The majority of studies to model surfaces have been interested in non-urban surfaces. The geometric description of vegetative surface elements used in radiative transfer models in plant canopies has become more advanced than those in urban areas 10 due to the greater size of the user-community involved (Voogt, 1995). To accurately model thermal emissions a realistic representation of the surface and its elements must first be obtained. This section will look at the methods that have been used to model the three-dimensional surface structure of vegetated surfaces. For the purposes of modelling, vegetated surfaces can be divided into three categories: (1) random surface elements; (2) homogeneous crop covers; (3) row-crop structures. Random surface element modelling involves placing solid three-dimensional surface elements such as cones (to represent trees) or other geometric shapes, depending on the nature of the surface elements, at random locations on the surface of choice. Li and Strahler (1985) developed a geometric-optical forest canopy model of randomly placed conifers that are illuminated at an angle on a surface. The model assumed that conifers can be modelled as cones that cast shadows on a contrasting background and therefore inter-pixel variations in radiance are due to: (1) variations in the number of trees from pixel to pixel; (2) variations in the size (height) of trees both within and between pixels; and (3) chance variation in overlapping of crowns and shadows within the pixels. The model demonstrated that the three-dimensional geometry used was able to go a long way towards explaining the bi-directional reflectance distribution function of forest canopies (essentially the change in reflectance with changing sun-sensor-surface geometry), and therefore emphasized the importance of shape, form and shadowing of objects in influencing images of real scenes. One shortcoming of the model is that it assumes nadir, or near-nadir sensor orientation. This limits its effectiveness in cases where this assumption is not met. The strength of the model lies in its ability to reproduce, relatively 11 accurately, reflected and emitted radiation from a complex three-dimensional surface. Its relevance and potential value to modelling urban surfaces rests on this ability. The second type of model of vegetated surfaces, the homogeneous crop cover model, has been used in a number of studies. In these models canopy leaves may be modelled as randomly distributed elements of a given shape, with prescribed distributions of inclination and orientation angle over a canopy volume, so that probability theory may be used to describe the field statistically (Norman, 1975). Using the total leaf area per unit soil area in the different canopy layers as the primary structural parameter, and additional information such as plant distribution and density, the probability of interception or non-interception of radiation of a given layer of vegetation can be calculated. Kimes et al. (1981) formulated a thermal infrared exitance model using these probabilities. This model was extended and refined to incorporate the variation of the probability of interception due to changes in view angle and azimuth (McGuire et al., 1989; Smith et al, 1981). This type of model, although useful over certain vegetated surfaces, is not directly transferable to the urban environment where surface structures lack the different layers present in plant canopies. A variant of the homogeneous crop cover type of model was used by Otterman et al. (1995) to infer the hemispheric thermal-infrared emission by directional measurements. The authors modelled a sparse canopy as both thin, cylindrical stalks and small spheres in an attempt to find an appropriate angle from which to measure surface hemispheric infrared emission. They found that a directional measurement at a specified zenith angle (50°) provided a very satisfactory estimate of the hemispheric emission. This 12 study is a good example of the need to recognize and account for emission temperature that varies with the view direction. The final type of model used for vegetated surfaces, and the most intuitively obvious choice for transferability to the urban case, is the row-crop structure model. These models use extended rectangular surfaces to represent the overall vegetation structure. The models, also known as "geometric projection models" , use a combination of component temperatures and canopy structure information to predict apparent sensor temperature given a remote sensor IFOV (Voogt, 1995). The models of Sutherland and Bartholic (1977), Jackson etal. (1979), Kimes etal. (1981), Kimes and Kirchener (1983) and Caselles and Sobrino (1989) have been used to consider the thermal radiance of row crops and orchards. A simplified version of the Jackson et al. (1979) model was validated by Kimes and Kirchener (1983) with good agreement between measured and modelled responses. With the use of inversion strategies these types of models are also useful in extracting row structure information and component temperatures. The apparent similarity of row crops to urban canyons has led to the attempt of Voogt (1995) to devise a model to predict urban surface temperatures (next Section). 1.3.2.2 Urban Surfaces Geometric models present a plausible solution for the estimation of anisotropy of surface radiance. Voogt (1995) uses a slightly modified version of a model, first described by Sobrino et al. (1990) and Sobrino and Caselles (1990) for use in nighttime conditions and later modified to include daytime conditions (Caselles et al., 1992). It is used to predict the contribution of various surface facets to the total radiance detected, 13 and with the inclusion of a one-dimensional energy balance model, to predict the complete urban surface temperature. Row crops are assumed to be sufficiently long to allow the simplification of what is in reality a three-dimensional entity to two-dimensions. This same simplifying assumption is used, by Voogt (1995), in the urban case where street canyons are broken at regular intervals and therefore ideally require a three-dimensional representation. The Voogt (1995) model uses as its input, the dimensions: height of buildings, widths of streets and alleys, solar azimuth and elevation, sensor height and angle and IFOV to estimate the fractional contribution of each component surface within the instrument IFOV to the total image. This geometric surface model was then coupled with a one-dimensional energy balance model developed initially by Myrup (1969) and later modified by Outcalt (1971). The energy balance model was used to evaluate the surface temperatures of individual surface facets. The results of this modelling effort show large differences exist between observed and modelled values. Voogt (1995) attributes this to the two-dimensional representation employed by the model, the simplistic representation of the surface structure (and omission of important elements such as trees from the surface model), and to biases in the image-extracted component temperatures. It is forwarded by Voogt (1995) that future work be done to create a more realistic model that incorporates three-dimensional urban surface representations and solid angle sensor geometry. 14 1.4 Summary of Objectives The objective of the present thesis is to study the role of sensor location and view angle on surface view factors and remotely sensed emissions from urban surfaces. This is accomplished through the following means: • Use a numerical model to predict the fractional components (i.e. surface facet view factors) of a three-dimensional representation of an urban surface viewed by a remote sensor and validate those results against field observations. • In conjunction with both in situ measurements and an urban canopy layer (UCL) energy balance model, predict remotely-sensed apparent surface temperatures. The validated model can then be used in hypothetical settings to further investigate the effects of surface structure and sensor position and orientation on surface view factors. 15 Chapter 2 A THREE-DIMENSIONAL SURFACE MODEL 2.1 Introduction This chapter describes the theory behind, and structure of, a numerical model to predict what a remote sensor can 'see' of an urban surface as well as the apparent temperature measured by that remote sensor. The details of the model inputs and outputs and methods of necessary calculations are examined. In addition a review of an urban canopy layer energy balance model to predict facet temperatures is conducted within the context of its applicability to the surface geometric model. 2.2 Model Theory A model is an abstracted analogue of a prototype and therefore, any modelling endeavour requires a certain degree of simplification of reality. Determining the level of simplification that is necessary or appropriate is a vital component in the development of a model. The degree of simplification depends on the phenomena being modelled, the goals of the modelling exercise and the resources available to the modeller. For the case of the urban surface model described herein, the primary requirement is that the surface be represented in a three-dimensional form. There is also the desire to make the model flexible enough to portray cities at any latitude and time of year, and to allow for a range of building sizes and street orientations. The rationale for these requirements are discussed in this section, while the methods of implementing them are discussed in Section 2.3. 16 Representing the surface in three dimensions greatly increases model complexity over the previous two-dimensional case outlined in Chapter 1, because it requires a move to solid-angle geometry. The equations to calculate surface areas of different facets and 'seen' portions of the surface are far more complicated for solid-angle geometry. The three-dimensional requirement is a direct result of the finding of Voogt (1995) that modelling the urban surface as a two-dimensional structure is overly simplistic: it is not able to accurately portray viewed surface facet components and hence unable to accurately simulate remotely-sensed apparent surface temperatures. Equation (1.1) describes the relationship between sensor-detected radiance and the fractional contribution of surface component radiances. In a two-dimensional surface the viewed surface components and surface shading patterns are relatively easy to calculate using right angle trigonometry (see Figure 2.1). Extending the two-dimensional surface to three-dimensions creates a potentially irregularly-shaped viewing area as well as complex surface shading patterns (see Figure 2.2) the solution for which requires a complex set of equations. For the correct sensor detected radiance to be calculated all the surfaces 'seen' by the sensor must be accounted for in the summation and therefore they must all be included in the model. In the two-dimensional case, modelled by Voogt (1995), the lack of agreement between modelled and measured values can be attributed to the fact that not all surface components that contribute to the measured values were accounted for in the model. This fundamental problem is solved in the three-dimensional version of the model presented here. 17 sunlit surface sensor Figure 2.1 A two-dimensional representation of an urban surface showing both 'seen' (single lines) and 'unseen' (double lines) portions of the surface. The effectiveness of a model not only depends on its ability to accurately represent the specific conditions under which it has been tested but also to extend the model to physical systems with different temporal and spatial characteristics. In designing the current model the desire was to make the model flexible enough to simulate not only different urban surface morphologies (i.e. light industrial and downtown core) within the same urban area, but also to handle urban areas in different parts of the world, at different times, and from a wide range of sensing platforms. Each urban area and morphological unit (e.g. Ellefsen's (1990) urban terrain zones) has its own typical building size and street orientation that contributes to the sensor-detected radiance. These are different enough that it is unlikely that one test case is able to accurately represent them all. Therefore, a model that can be easily manipulated 18 Figure 2.2 A three-dimensional urban surface with a remote sensor situated above the ground. Sunlit, shaded and the area 'seen' by the sensor are shown. to cover as many possible surface configurations is valuable. In addition, surface radiative emissions have a strong temporal component that is directly related to the solar cycle. This leads to the necessity to include solar position, dependent on latitude, season and time of day, in a model to evaluate the presence and effects of sunlit and shaded surface facets. In addition, it is essential to be able to place the sensor at almost any potential location and orientation. Sensors can be situated, and are commonly used, at many different elevations above the surface, from below roof level to satellite height, and at many viewing angles and azimuths depending on the observational objectives. 19 The preceding discussion sets the framework for a model that is able to represent a wide range of surface types, in three-dimensional form, and view those surfaces from the point of view of a sensor situated at varying distances from the surface, at many orientations and at any given time. The next section deals with the implementation of the theoretical framework to produce a working numerical model. 2.3 Model Structure This section gives a detailed description of the methods used to produce a numerical model to predict what portion of an urban surface a remote sensor can view and to calculate the sensor detected radiance for that sensor. The structure of the model, known as S3MOD (for surface-sensor-sun model), is described in terms of its major components and the equations used. Figure 2.3 provides a graphical representation of the architecture of S3MOD divided according to the subroutines in the model. The model was written in FORTRAN and compiled on a Sun ULTRASPARC workstation. 2.3.1 Input All inputs used to describe the location of the urban area, time, surface characteristics, sensor location and orientation and facet temperatures are included in Table 2.1. Initialization of the array which stores all surface locations and their associated properties also occurs within the input portion of the program. The array is discussed in more depth in the next section. Temperatures are input to the model from either an UCL energy balance model or are otherwise prescribed by the user (e.g. are measured). The 20 INPUTS Build Array . according to input parameters Evaluate whether points are 'seen' or 'unseen' Decide if 'seen' points are sunlit or shaded Calculate view factors of 'seen' points Sum fractional radiances of'seen' points Convert radiance to apparent sensor temperature Evaluate solar position OUTPUT Convert facet temperatures to radiances. Figure 2.3 Basic structure of the S3MOD program with a brief description of each subroutine. 21 Mills (1997) model used in this study and other methods of prescribing are discussed in greater detail in Section 2.4. Table 2.1 Inputs to S3MOD. Background Surface Parameters Sensor Parameters Year Day Local Apparent Time Location (Lat, Long.) Array Size (4-D) Facet Temperatures (K) Building Width Building Length Building Height Street Width 1 Street Width 2 Alley Width 1 Alley Width 2 Street Direction Sensor Height Sensor Location (x,y) Off Nadir Angle Field Of View Sensor View Direction 2.3.2 Building The Surface Array The description of the surface is the most vital in the process of model implementation. In S3MOD the configuration of the surface (i.e. the interface between solid buildings and ground and the atmosphere) and the arrangement of all features on the surface are described by a four-dimensional array. The array contains the three spatial dimensions in an (x,y,z) coordinate system as well as a fourth dimension that assigns properties to each spatial point. A point can be thought of as having (x,y,z) coordinates but represents an area, the dimensions of which are decided upon by the user, rather than an infinitesimal point. The grid size in S3MOD determines the resolution to which individual buildings or facets can be described. For the validation described in Chapter 4 the distance between each point is considered to be equal to 1 m in the real world. This relationship can be 22 adjusted according to the needs of the user. By increasing the true distance between points the lower the resolution of the surface becomes. When changing resolution it is important to know the limits of the model and how the model differentiates between different surface types. Firstly, all points where z = 0 are considered to be either street or alleys, regardless of whether they fall at the base of a wall or not. In the same way all points on the surface where z = building height are considered to be roofs. Therefore, walls only exist below roof level and above ground level. One implication of this fact is that the smallest building height that can exist where walls are present is 3. It also means that walls will be under represented in relation to the real world. As the number of wall grid points increases this effect will tend to be minimized. The location and dimensions of buildings, streets and alleys is determined by the input parameters entered at the beginning of the program. The following is a step by step description of how S3MOD builds the surface array. The array is constructed in subsections (see Figure 2.4) that are repeated until the complete dimensions of the array are filled. Each subsection contains a building-street-building-alley combination both in the x and y directions with the possibility of street and alley widths changing between the x and y directions. This combination is repeated as many times as is necessary to fill the previously specified array size completely. The relationship between array dimensions and real world dimensions must be decided by the user based on the resolution required and the computing power available. The buildings are constrained to have the same height and are assumed to have flat roofs. 23 t • A x < Figure 2.4 Plan view of an array subsection showing building, street and alley dimensions in both x and y directions where, BL is building length, BW is building width and Sx, Sy, A x , A y are street and alley widths in the x and y directions respectively. The decision to use flat roofs was done to make the construction of the surface array easier, as well as to greatly simplify the view factor calculations (see Section 2.3.5). This assumption does limit the direct transferability of the model to areas with only flat roofs, it is believed that it can also be used as a first order approximation in areas where this criterion is not satisfied. Each location is assigned a physical parameter that determines its general nature. These include walls, roofs, streets, building interiors or air. Furthermore, each wall location is assigned the direction that it is facing. This direction is determined by the relation between each wall and the street and alley orientations. This is done so as to reduce the number of calculations necessary to determine if that wall section is visible to the sensor and whether it is shaded or sunlit. At this time it is also possible, if required, to add radiative and thermal properties to each location. These properties can include 24 emissivity, albedo, thermal diffusivity, thermal conductivity and thermal admittance. During subsequent subroutines of the program all locations are assigned further properties. These properties will be discussed as they are assigned. 2.3.3 SEEN Subroutine The array of surface elements contains points that are both within and outside the sensor's IFOV. Those within the sensor IFOV can be further subdivided into both 'seen' and 'unseen' points, where 'seen' are not blocked by buildings and 'unseen' are blocked by buildings. Points that are within the sensor IFOV and are 'seen' by the sensor must be discerned from those that are hidden. There are two ways that a point can be found to be excluded from the 'seen' points. Firstly, the line from the sensor to a point can lie at an angle from the sensor axis of view that exceeds the IFOV; all points that satisfy this criterion are immediately excluded as 'seen' points. The angle between two vectors in three-dimensional space can be evaluated using the following equation, r? = cos-1-^fT (2.1) lullvl where, 6 is the angle between vector u, that follows the sensor view direction and vector v, that extends to the point on the surface being tested. Secondly, a point can be excluded from the set of 'seen' points when although it is within the angular IFOV, it is blocked from sensor view by another building. To check for this case the model extends a ray from the location of the point towards the sensor location. If, while extending that ray either a building wall, roof or interior encountered that point will be determined to be 'unseen'. In this way all points in the array domain are tested for inclusion into the 'seen' portion of the surface. 25 2.3.4 SOLGEOM and SHADE Subroutines In much the same way that the model evaluated whether a point was within the sensor IFOV, it also decides which points are sunlit and which are shaded. The first step is to calculate the solar position. This is done using the SOLGEOM subroutine which calculates solar position based on time of day, Year day and location. For the purposes of shading, solar position is described by its elevation angle above the horizon and its compass azimuth. With the solar position known, each point on the surface is then checked to determine if it is sunlit or shaded. This determination is achieved by testing whether a point is blocked by another building, in the same way as in the SEEN subroutine and described in Section 2.3.3. Each point is then assigned either a 'sunlit' or 'shaded' status. 2.3.5 View Factors All surface elements within the sensor IFOV contribute to the sensor detected radiance. Their relative contribution is determined by the fraction of the total sensor view factor that each element occupies. To evaluate that contribution, the view factor of each surface element with respect to the sensor must be calculated. In general, to easily calculate the view factor of a surface area, that area must either lie in a plane perpendicular or parallel to the sensor viewing direction. This allows view factor estimation to occur using common techniques, such as those described by Steyn and Lyons (1984). 26 The contribution of the radiant flux at a sensor from a particular surface element of the radiating environment that is perpendicular to the sensor viewing direction can be determined by, f , / V VF = In Jd2+r2 tan - i h 2 + r2 j + h Jh2+r2 tan h + r (2.2) while the contribution of the radiant flux at a sensor with a viewing direction parallel to the surface element can be determined by , VF = 2n •tan" \ r J + yjr2+h2 tan" ylr2+h2 r (2.3) See Figure 2.5 for a description of all variables in Equations (2.2) and (2.3). This case assumes a hemispheric IFOV for the sensor. S3MOD does not have this as a requirement. Different sensor types and specifications, and any given IFOV, can be accommodated in the model. 27 Surface Element / / i r d (^Sensor Figure 2.5 Variables used to calculate the view factor of a surface element on a plane perpendicular to the sensor viewing direction. 2.3.6 Conversion and Summation of Temperatures Temperatures are entered into the model from either the Mills (1997) UCL energy balance model, or from prescribed temperatures (for a fuller description of temperatures see Section 2.4). For the model to accurately simulate sensor detected radiance, the temperature of each facet must be converted to radiance which is then intercepted by the sensor. Following this, the radiances of individual surface elements are summed to determine the total sensor detected radiance. The radiance is then converted to apparent sensor temperature. This section details the specifics of this procedure. Converting from either a prescribed or numerically modelled temperature to radiance is necessary to input data to S3MOD because a sensor doesn't detect temperature directly, it detects radiation. Therefore, to simulate the physical process that 28 occurs within the surface-sensor system and keep the model as physically accurate as possible, temperatures within the model must also be converted. The Laguerre-Gauss quadrature method of Johnson and Branstetter (1974) is used to convert temperatures to radiance. This method requires the integration of Planck's radiation equation within a given spectral band. The spectral radiance, L given by Planck's radiation equation is, where, X is the wavelength, and T is the temperature of the body, s is the surface emissivity, h is Planck's constant, c is the speed of light, k is the Boltzmann constant. Determination of the radiance in the band limits [A.i, X2] requires integration of Equation (2.4) from ^1 to X2, where Xi is considered to be less than X2. A closed form of this integration has yet to be found (except for the band limits 0 to 00) therefore a numerical technique (the Laguerre-Gauss quadrature method) is employed. The specifics of this method are given in detail by Johnson and Branstetter (1974) and therefore not repeated here. Once conversion of all temperatures is complete, the radiance of each surface element 'seen' by the sensor is summed according to Equation (1.1). The weighting given to each point is determined by its view factor from the sensor. The final step is to convert the summed radiance back to a temperature value. This is done by creating a lookup table (LUT) when initially converting temperatures to radiances. A temperature increment must be specified at this time which affects the back conversion accuracy. Accuracy is improved with greater table resolution but the cost is greater computing time. The L{A,T)=2ehc2A-5{ehc'"T -l) (2.4) (2.5) 29 radiance of the sensor will fall between some upper and lower bounds on the LUT. The temperature can then be recovered by employing a linear interpolation routine over the given bounds. 2.3.7 Output The output given by S3MOD is relatively simple. For a given set of inputs the model provides a breakdown of view factors for each of the following surface types; roofs, sunlit and shaded walls and sunlit and shaded streets and alleys. Properties of the 'seen' and 'unseen' surface elements can also be summarized if required by the user. Finally, both the sensor detected radiance and apparent sensor temperature are output. 2.4 Facet Temperatures The temperatures of individual facets can be obtained in one of two ways. The first is to directly enter observed values into S3MOD. The second is to generate facet temperatures in an energy balance model. Both methods have been used, and the results of both are presented in Chapter 4. Measured values were obtained during a field experiment specifically designed to validate S3MOD. A review of the field experiment is given in Chapter 3. The numerical model used to generate temperatures is discussed briefly in this section. For a numerical model to be useful in the generation of facet temperatures it has to represent an urban surface at a similar scale to S3MOD and it must be possible to run it with commonly available inputs. For these reasons and its ease of use the Mills (1997) UCL model was chosen. 30 The Mills (1997) UCL model distinguishes itself from others in its attempts to simulate the exchanges of energy both within the UCL and between the UCL and the urban boundary layer (UBL). Although the UCL and UBL exist at different scales the interactions between the two are vital to the climates of both. The UCL is the region that lies below roof level and its climate is a result of complex exchanges between many surfaces within the urban canopy and exchanges of radiation, heat, moisture and momentum from the overlying UBL. The Mills (1997) UCL energy balance model attempts to characterize these interactions and generate temperatures of individual surface facets within the UCL. In the model a building group is composed of identical structures placed on a flat surface at regular intervals. Buildings are made up of five surfaces with dimensions of depth, length and height. Building locations are defined relative to each other with a pair of orthogonal separating widths. The group of buildings with this definition is assumed to be sufficiently extensive to be representative of a portion of the UCL. Inputs to the model include: 1) location and time of year, 2) meteorology, and 3) building and substrate characteristics. The UCL is made up of both closed and open volumes. The former include a building volume and its enclosing surface. The open volume, or 'canyon', shares the walls of the buildings and is bounded on the bottom by the solid canopy floor, and above by the an open canyon top interface. Interactions between the UCL and UBL occur across this open roof level interface and through rooftops. The model simulates the energy balances of the surfaces and volumes of the UCL and evaluates thermal stresses associated with different building configurations under different climates. All interactions 31 between the UCL and UBL occur through the canyon top and no horizontal exchanges occur as the building group is considered to be extensive. Bulk transfer relations for a neutral atmosphere are used for estimations of heat and momentum transfer. The momentum flux is used to simulate the canyon wind field which is used to calculate the canyon heat flux at the canyon walls and floor. Canyon air temperature is calculated using the canyon top sensible heat flux. Canyon surface and air temperatures, which are in equilibrium with each other, are evaluated using numerical methods. The roof surface temperatures are easily obtained through radiative and turbulent exchange with the atmosphere, because the roof does not interact with any other UCL surfaces. Within canopy energy balances and surface temperatures are partially dependent on each other and cannot be solved independently. Therefore, an iterative technique is used to evaluate these values at each time step. Temperatures at points on the surface of the canyon are considered to be instantly responsive to current conditions, whereas substrate temperatures are updated at each timestep and provide the 'memory' for the simulated system and contain the accumulated history of surface/substrate exchanges. Temperature profiles through the walls and substrate are updated at each timestep and integrated forward to the next simulation time. The energy budget of the building interiors depends on the updated temperature profile. The building and canyon volumes are linked through exchanges across the wall facets, and the building volume is linked to the UBL through exchanges across the roof facet. For a more complete description of the UCL energy budget model see Mills (1997). The described energy budget model satisfies the scale and input requirements necessary to produce surface facet temperatures for input to S3MOD. 32 Chapter 3 OBSERVATION PROGRAMME 3.1 Introduction In an effort to validate the model described in Chapter 2, a field observation campaign was undertaken. The observation programme occurred over a two day period during August, 1997 in Vancouver, B.C. (49° 15' N, 123° 18' W). All measurements taken were used as either inputs to the model or as comparison values to model outputs. This chapter reviews all aspects of the observation programme including a description of the physical site, the methods employed and the rationale behind measurements taken. Also included is a brief review of helicopter flights taken in 1992 over the same region of Vancouver (Voogt, 1995). Data from those flights are used to extend validation of S3MOD. 3.2 Site Description Observations for this study were conducted in the False Creek South area of Vancouver (see Figure 3.1). This area is a light industrial district containing predominantly flat roofed rectangular buildings (see Figure 3.2). The site where all measurements were taken is located near the corner of West 3rd Avenue and Alberta Street. The site contains a gated parking lot bounded on the east and west by 8 m high flat topped buildings, on the south by an alley way and 8 m high flat topped building and on the north by a 20 m wide street. The site was devoid of vegetation except for a strip of short grass that exists between the sidewalk and street (see Figures 3.3 and 3.4). The site 33 Figure 3.1 Map of Vancouver, B.C. showing location of study site (from Wynn and Oke, 1992). Figure 3.2 Aerial View of False Creek South. View is to the North-West 34 Legend . . Scale f 3 Roof Asphalt 1 cm = 2 . 5 m | Awning Q Tower gill Grass ^ Instrument Tripod I S I s'iiii s'ii = mi = mi = un = mi s mi m nn s nn = mi = nn = un = nn = mi = un = un = mi m mi = mi = mi = mi = mi = mi = un = mi = mi = MM = llll = llll = NU = UN = llll = |||| = III = Ml = III! = III! = III! = llll = llll = III! = III! = III! = III! = llll = llll = I 11  = 1 1 1 1 = IIH = | = mi = mi = mi — ml = 1 1 1 1 rim a = 1 1 1 1 = 1 1 1 1 3 Lamp Standard Q B llll \ = 11' = 1 1 1 1 = = 111 min = u. = I I I I = =iiu 3 1 1 1 1 = = M i l = llll 3 llll : = llll i llll i Fence Hoarding Gated Fence Figure 3.4 Plan view of the False Creek South study site. 35 was chosen because it offered a relatively simple canyon and building configuration, the building height was low enough so that the instruments could be positioned well above rooftop, lack of vegetation (specifically large trees and shrubs) and accessibility (for instrument placement) to both the interior and rooftop of the building adjacent to the parking lot. Figure 3.4 Measurement site in False Creek South. View is looking to the north. The pneumatic tower is in its rested position. 3.3 Method 3.3.1 Instrumentation The goal of the observation programme was to both provide inputs to and validate S3MOD. This was done by taking measurements from a number of different platforms on August 9th and 10th, 1997. For validation to be possible observations had to be taken over a range of heights above the surface, at differing viewing directions and over the course 36 of a full day. This allows the model to be tested in a wide range of conditions. Measurements were taken from an instrument package on a 26 m telescoping pneumatic tower, a roof-mounted tripod and ground-based tripods, and by hand at various points. The tower could be raised and lowered and the instrument package could be rotated through 360° of azimuth. An instrument package was mounted on a cross-arm at the top of the tower (see Figure 3.5). The instruments were divided into two sections. The first section (on the left side of Fig. 3.5) contained instruments to directly validate S3MOD. These instruments were mounted at a downward-facing 45° off-nadir angle and included a 15° IFOV infrared transducer (Everest Interscience Model 4000A, hereafter referred to as EIRT), a pyranometer with a 15° IFOV shield (Li-Cor Model 200SB) and a 35 mm single lens reflex camera (Minolta Model X700), with a 50 mm lens. The camera could be activated remotely by using an infrared shutter control. The second set of instruments (on the right side of Fig. 3.5), used to collect background data included, a 60° IFOV EIRT oriented at 30° off-nadir downward-facing, a hemispheric viewing downward-facing pyranometer (Li-Cor Model 200SB), a downward-facing pyrgeometer (Eppley Model PIR), and a net pyrradiometer (Swissteco Model SI) oriented in the horizontal. The second location where observations were taken (the roof of the adjacent building, Fig. 3.3), contained instruments mounted on a 1.5 m tripod as well as on the edge of the roof. The tripod-mounted instruments included a wind sentry (R.M. Young Model 03002-10) for wind speed and direction, a humidity and air temperature probe (Vaisala Model ITMP35C), and a downward-facing 60° IFOV EIRT oriented at 30° off-nadir. The roof based instruments included an upward-facing pyrgeometer (Eppley Model PIR) and an upward facing 37 pyranometer (Kipp and Zonen Model CM5). All measurements on both the tower and roof were recorded on a Campbell Scientific CR 2IX data logger. The final group of instruments were ground-based tripod-mounted infrared thermometers (Everest Interscience Model 4000) used to measure facet temperatures of various surfaces. These facets included streets and North, South, East and West-facing walls. These surface temperatures were recorded on HOBO data loggers. Spot measurements of facet temperatures and temperatures of various surface types (grass, Net Pvrradiometer Camera 15° EIRT \ Pyranometer ,.-x »j\ 6 0 ° E I F Pyrgeometer Figure 3.5 Instrument cluster mounted on the cross-arm atop the tower. windows, sidewalks and previously mentioned surface facets) were taken using a hand-held infrared thermometer (Minolta Model Compac 3). 38 3.3.2 Sampling Methodology All measurements can be divided into two types. Those taken for direct model validation and those used as background meteorological data for model input. This section discusses the temporal and directional nature of both types of measurements. Measurements for model validation were taken using the tower, tripod mounted and handheld infrared thermometers. To satisfy the goal of viewing the surface from a wide range of directions and times tower based measurements were taken at three heights (11 m, 22 m, 26 m) above the canyon bottom, at eight equally-spaced azimuths between 0° and 270° and at seven different times (five daytime and two nighttime). This scheme gave a total of 168 different surface scenes over the course of 24 hours. Measurements were recorded every 5 seconds for approximately 1 minute, by the data logger, at each height/azimuth position and time and a photograph was taken (only during daytime) to document which surface features were in the IFOV of the instruments. Outside each 1 minute recording period the 15° IFOV EIRT and pyranometer measurements were logged as 5 minute averages to coincide with the other tower and roof-based background observations. Tripod based surface temperature measurements were taken at 30 second intervals and averages recorded every 5 minutes. Handheld infrared thermometer surface temperature measurements were taken immediately following each set of tower observations (i.e. on seven occasions). All background observations were taken at 5 second intervals with average values recorded every 5 minutes throughout the 24 hour period. 39 3.4 Synoptic Conditions and Weather The period during which measurements were taken was characterized by fine weather under the influence of an anticyclonic system. The surface analysis charts for August 9 and 10, 1997 and measured weather variables are given in Figures 3.6 to 3.8 respectively. Figure 3.6 Pacific Weather Centre surface analysis for August 9 , 1997. 40 41 CD 01 Q. CO 1 1 1 1 1 ' 1 Wind Speed 1 1 1 ' 1 ' 1 Direction 200 ° CD a 150 Q 100 (D 26 H O 24-S ro 22 CD Q. E 20-<D f— 18 H 1 1 r - Temperature T T -50 70 » « * N S * ^ Time (PDT) Figure 3.8 Meteorological variables measured at False Creek South on August 9/10, 1997. 3.5 Helicopter Flights A series of helicopter flights were conducted over the False Creek South area of Vancouver, including the site of the 1997 observations, in August 1992. The goal of these flights was to gather detailed surface temperature information, in an effort to examine the extent of anisotropy of longwave emissions over the surface, through the acquisition of images from different view directions. An AGEMA Thermovision 800 Brut System was used as the thermal imaging system (Table 3.2). For a more detailed description of the flights and instruments used see Voogt (1995). The images obtained revealed detailed information regarding surface temperature distributions. From this information temperatures of individual surface facets could be obtained in addition to mean image 42 temperatures. These observations can be directly compared to output generated by S3MOD and are therefore a valuable additional data source for model validation. Table 3.1 Technical Specifications: AGEMA 880 LWB TIR system. Range Sensitivity Accuracy Digitization Scanning Modes -30°C to 1300°C 0.05°C at 30°C ±2% or ±2°C 12 bit (4096 levels) full scale range 12 bit (4096 levels) half FSR (GAIN = 2) 0 - 280 lines @ 6.25 Hz 1 - 140 lines @ 6.25 Hz 2 - 70 lines @ 25 Hz 3 - 140 lines @ 12.5 Hz 4 - 280 lines @ 6.25 Hz 5 - Line scanning mode 4:1 interlace 2:1 interlace non-interlaced non-interlaced non-interlaced 43 Chapter 4 MODEL VALIDATION 4.1 Introduction The performance of the model is compared with measurements taken during the field campaign described in Chapter 3. The validation of S3MOD is conducted on two fronts. Firstly, the ability of the model to estimate the surface components 'seen' by the sensor is evaluated. This is done in both a quantitative and qualitative manner and is termed the geometric validation. Secondly, model generated sensor-detected surface temperatures are compared with measured values. This is done from the perspective of a sensor mounted on two different platforms. In addition, facet temperatures generated by the Mills (1997) energy budget model for the canopy layer are compared to measured values and entered into S3MOD to calculate the temperature detected by the sensor. 4.2 Geometric Validation The geometric validation of S3MOD is perhaps the most important aspect in the evaluation of model performance. Evaluating sensor-detected radiance requires the model to generate an accurate estimate of both the facet temperatures and the surface area 'seen'. Therefore, without a proper estimate of the portions of the surface within the sensor's field of view it is impossible to try to generate realistic sensor detected temperatures. To validate S3MOD from a geometric standpoint photographs of the surface were taken from a tower to represent the sensor view (or IFOV) of the surface (see Chapter 3 for a complete description). The area on the surface 'seen' by the sensor and captured on 44 film was divided into five surface types (sunlit and shaded wall, sunlit and shaded ground and rooftop). The proportion of each surface type was calculated by digitizing the photographs and delimiting the regions occupied by surface type. The projected area of each surface type was then calculated and expressed as a percent of the total area. This calculated value is analogous to a view factor. The rationale for this assumption is that since the IFOV of the lens used is very small and no visible image distortion is apparent, there should be only negligible differences from the true value of the surface type view factors. The model calculates the view factor of each surface type 'seen' by the sensor (see Chapter 2). This should then allow direct comparison between values generated by the model and those measured. The customary method of comparing modelled versus measured values does not, however, give an accurate reading of model performance in this case. This is due to two main limitations, or sources of error. The first limitation is the reliability of the measured data." Ideally, the exact position and orientation of the sensor should be known to be able to assess the model. In the planning and execution of the field programme it was assumed that these properties would be known. In the final analysis it turns out this may not be the case and the ramifications of this are significant. Figure 4.1 shows photographs taken from what was assumed to be the same sensor position and orientation, but at two different times of day. Therefore, other than surface shading proportions, both images should be identical. This is obviously not the case. The cause is a combination of less than perfect experimental design and inherent instrument error. 45 Fig 4.1 Photographs taken from 26 m above the surface supposedly oriented at a 45° ONA and an azimuth angle of 315°, at (a) 0720h, and (b) at 1910h. The tower used for this study is not completely rigid and therefore experiences a certain amount of flex. The amount of flex depends on wind speed, tower height and how secure the stays are that support the tower. Wind speed was variable throughout the period of measurements (see Figure 3.8) and therefore caused a varying amount of flex in the tower, and from slightly different directions. Since the tower was repetitively being raised and lowered it was necessary to re-secure the stays at regular intervals, this must have caused the final position of the tower to vary slightly. The tower was raised to three 46 different heights during the course of each set of measurements. Tower rigidity decreased and wind load increased on the instrument package with increasing tower height. Although no quantitative estimate of the combined effect of these factors is possible it is obvious they play a significant role in increasing potential error in estimating the exact position and orientation of the sensor package atop the tower. The second potential source of error arises from the method used to orient the cross-arm that held the instrument package atop the tower. Initially a motorized rotation system was used, and allowed for an explicit determination of the azimuth that the sensors were facing. Unfortunately this malfunctioned and instead it was necessary to manually rotate the cross-arm. At each of the eight azimuth positions the orientation of the cross-arm was lined up by eye from ground-level. This method was not as accurate as desired and made it difficult to be consistent in terms of sensor position from measurement to measurement. Therefore, this led to an estimate of sensor location and orientation that was less accurate than ideally required to validate the model properly. The sensitivity of the model to input conditions, and how lack of knowledge regarding those conditions potentially impacts assessment of model performance is demonstrated in Table 4.1. The data show the differences that exist in sensor-detected temperature, and surface types 'seen', by changing the orientation of the sensor. Modelled changes of 5° in either ONA or azimuth can alter the surface temperature sensed by over 5°C. Therefore, as demonstrated in Table 4.1, relatively small errors in the inputs (which are known to exist, e.g. Fig. 4.1) can result in significant differences in model output. This means that, using the 'measured' data to geometrically validate the 47 modelled data is fraught with difficulty. The associated problems of using the observed temperature data to validate the modelled temperatures are discussed in Section 4.3.1. Table 4.1 Proportion of surface type 'seen', and the sensor detected surface temperature, from a range of sensor orientations. Time ONA Azimuth Height Sunlit Shaded Sunlit Shaded Roof Temp. (h) (deg) (deg) (m) Wall (%) Wall (%) Ground (%) Ground (%) (%) (°C) 0730 40 315 22 32.5 3.47 0.00 0.00 64.03 21.2 0730 50 315 22 0.00 0.00 12.54 1.55 85.91 17.8 0730 45 310 22 0.00 0.00 1.67 1.82 96.51 16.6 0730 45 320 22 32.93 0.00 0.00 0.52 66.55 21.7 0730 45 315 22 0.00 0.00 1.22 1.98 96.79 16.5 The second limitation that leads to difficulty in the geometric validation of the model is that if it were possible to measure, there would probably be a negative correlation between accuracy and number of surface types present in a scene. The word 'probably' is used because there is no explicit way of measuring accuracy with the available data. Any comparison between measured and modelled data is tainted by the lack of knowledge surrounding the measurement conditions. The negative correlation is a result of choosing 'proportion of surface type' as the validation criterion. For scenes with only one surface type present it is far easier for the model to achieve accurate results. This is because the four surfaces not represented in the scene are modelled perfectly (i.e. 0% seen), whereas in scenes that contain all five surface types even small inaccuracies cause differences between modelled and measured values for all five surfaces. This means that for complex scenes (i.e. with multiple surface types present) the model performs artificially poorly. The model should perform equally well regardless of the number of surface types present in a scene. The combination of this problem, and the 48 previously discussed uncertainty in input conditions, makes conducting a quantitative appraisal of model performance in terms of geometry very difficult. Therefore, two alternate approaches to estimate the geometric accuracy of the model are taken. 4.2.2 Image-based Geometric Validation A first approach to acquiring a more accurate estimate of sensor orientation is to use the photographs taken concurrently with tower-based measurements. This can be achieved by first selecting photographs that contain a number of surface types, so as to check the model's ability to distinguish between surface types. The second step is to locate the centre of each photograph and specify its location in the real world based on an arbitrarily defined grid system. With knowledge of precisely where the centre of the photograph is (in three dimensional space) and assuming the sensor location is known, the sensor ONA and azimuth can be calculated using simple right angle trigonometry. Although there is some error associated with sensor position, using photographic evidence and ground truthing an estimate can be made. Without the assumption that the sensor position is known this method does not work. Four images were selected to test this method and acquire a more quantitative estimate of the model's ability to calculate which surface types are 'seen' and also calculate the different surface type view factors. Each of the images contained a minimum of two surface types within the sensor's IFOV. Figures 4.2 and 4.3 show the selected images as well as the surface areas contained within the Everest IRT's IFOV. Using the method described previously, the ONA and azimuth for the sensor in each of 49 the images is calculated and used as input to S3MOD. The results of running S3MOD with these new Figure 4.2 Photos (Image 1= (a), Image 2 = (b)) showing surface area seen by the tower-based camera as well as the surface region within the 15° IFOV of Everest IRT (red circle). 50 51 input values is shown in Table 4.2 along with the view factors estimated from the photographs. Table 4.2 Results of using revised estimates of sensor orientation on model generated surface type view factors. (C) indicates view factor values are calculated directly from the images while (M) indicates view factor values are modelled. Image Roof Roof Sunlit Sunlit Sh. Sh. Sunlit Sunlit Sh. Sh. # (Q (M) Wall Wall Wall Wall Ground Ground Ground Ground (C) (M) (Q (M) (C) (M) (C) (M) 1 0.69 0.86 0.00 0.00 0.31 0.14 0.00 0.00 0.00 0.00 2 0.75 0.97 0.00 0.00 0.25 0.03 0.00 0.00 0.00 0.00 3 0.66 0.34 0.00 0.00 0.21 0.10 0.10 0.47 0.03 0.08 4 0.78 0.99 0.00 0.00 0.22 0.01 0.00 0.00 0.00 0.00 The results show that there are some significant differences between model calculated view factors and those evaluated from the four images. Whether using these four photographs is a robust test of the model's ability to calculate what a remote sensor 'sees' is debatable. Firstly, the images chosen are some of the most difficult cases to model. This is due primarily to their complexity. A scene which contained only one surface type would undoubtedly be modelled much more accurately. This is because there is a much wider margin of error for the modelled sensor position. Figure 4.4 shows an image that contains only rooftop. Even by changing the sensor orientation (and hence changing what is 'seen' by the sensor) by 5° there is no difference in what the sensor 'sees' nor in what the model predicts. Secondly, as was previously mentioned, there remains an error associated with the exact position of the sensor that cannot be eliminated. In conjunction, these factors will in all likelihood lead to an exaggerated 52 estimate of the error associated with modelled view factors. Therefore, a secondary approach to the geometric validation of the model is conducted. Figure 4.4 Photo taken from the tower-based camera showing the roof top occupying the entire 24° horizontal FOV of the camera as well as the 15° IFOV of the Everest IRT (red circle). 4.2.3 Theoretically-based Geometric Validation To attempt a theoretically-based geometric validation, S3MOD was set up to replicate a simple urban canyon structure. The sensor, with a FOV of 180°, was situated above the centre of the hypothetical canyon at building height, facing downwards with its receiving surface in the horizontal (parallel with the canyon floor). In this orientation and location the sensor's view of the ground is equal to the sky view factor (ys) of an upward-looking hemispheric sensor on the ground at the mid-width of the canyon. The 53 ground view factor calculated by the model can then be compared to published values of sky view factor for given height to width (HAV) ratios of infinitely-long canyons. The model was tested with five HAV ratios and compared against values calculated by (Oke,. 1981) using y/s=cos0, (4.1) where B = tan'1 (H/D), H being the height and 2D the width of the canyon A comparison of the modelled and calculated values reveals good agreement between the calculated results and those output from the model (Table 4.3). Additional proof of the geometric validity of the model lies in the fact that, as would be expected, for all five cases each wall of the canyon is equally represented in the total view factor of the sensor. These numbers tend to confirm the geometric accuracy of the model. Discrepancies between modelled and calculated values could be due to the assumption of an infinitely-long canyon not being satisfied in the model, or that the spatial resolution of the model is not great enough. Model resolution was limited by computer memory size. Table 4.3 Modelled and calculated values of sky view factor. HAV 0.25 0.50 1.0 2.0 4.0 tysky theory 0.89 0.71 0.45 0.24 0.12 yfsky mod 0.87 0.68 0.43 0.23 0.11 To perform a more detailed and accurate geometric validation of the model probably requires a highly controlled laboratory-style experiment, where the sensor position and orientation are accurately controlled. In addition, rather than using facet type as the unit of measure, all facets on the surface could be divided into areas that 54 correspond to a location in the model's surface array. In this way direct comparison, on a 'cell-by-cell' basis, can be carried out to determine whether the model accurately classifies and calculates surface areas 'seen'. Time constraints did not allow this experiment to be conducted in the present study. 4.3 Temperature Validation After gaining a measure of the geometric accuracy of S3MOD the next step is to test its ability to simulate sensor detected temperature. This is done in three ways and from two platforms: • to assign temperatures to each surface facet using values measured during the field programme. • to estimate surface temperatures using meteorological information collected during the field programme with the Mills (1997) model. • to use measured facet temperatures and attempt to model sensor detected temperature from the point of view of instruments mounted on a helicopter flying above the surface. 4.3.1 Prescribed Temperatures To validate S3MOD from a sensor detected-temperature-standpoint a direct comparison of modelled and measured values is conducted. The sensor-detected surface temperatures are modelled using prescribed facet temperatures as measured during the field campaign (see Chapter 3). In essence, it is not a fully but a partially-modelled sensor-detected temperature. This method provides one way in which the model can be 55 used when facet temperatures are known. This allows both an assessment of how well the geometric portion of the model works, because there is less error associated with input facet temperatures, and the ability of the model to amalgamate the facet temperatures into a sensor-detected temperature. The model was run for all measured cases with the results as shown in Figures 4.5 - 4.8. Several of the figures contain summary statistics of model performance, including the mean absolute error (MAE) between predicted (PT) and observed (07) temperatures of n number of sets: MAE £PT-OT n (4.2) the root mean squared error (RMSE) '^{PT-OT)-RMSE-n (4.3) the agreement between the two sets is described using Pearson's coefficient of determination (r ): r 2 = Y^PTOT J^PT^OT n 1 YPT2-n n (4.4) and Wilmott's index of agreement, D (Willmott, 1984): n(RMSE)2 D = l PT-OT + OT-OT (4.5) 56 In general, the results show good agreement between the modelled and measured values. There are, however, a number of features of both figures that require further investigation and explanation. Firstly, visual appraisal of Figure 4.5 shows the slope is less than 1, and that the data do not pass through the origin. At low temperatures the model underpredicts the temperature, while at higher temperatures it overpredicts. This can, at least partially, be attributed to the response of the sensor used in the measurements. The stated FOV of the Everest IRT is for 80% of the total signal. Therefore, 20% of the signal comes from outside this FOV. In the case of the model, 100% of the 'signal' comes from the input sensor FOV. This leads to a discrepancy between the modelled and measured values that resembles the slope of the data in Figure 4.5. For the lowest modelled temperatures, which occur around 0100 hr (see Figures 4.6 - 4.8) the dominant 'seen' facets are roof tops which are also the coldest facets (Table 4.4 shows the view factors for all surface types from the sensor package at all measurement times). Therefore, the model will 'see' almost exclusively the coldest facets, whereas the actual Everest sensor will 'see', because of its response curve, a greater range of facets, all of which are warmer than the rooftops. This leads to the model underpredicting the measured temperature. An analogous case exists for the highest modelled and measured temperatures, except that the rooftops are then the warmest facet type, and the Everest 'sees' more cooler facets than the model, has a lower measured temperature than the model predicts. The model can be adjusted to accommodate for the difference in signal response between the Everest and the model. The nature of this 20% signal is not explicitly known, but according to manufacturer's specifications if 80% of the signal comes from 15° FOV, 57 then 100% is within ~ 25° FOV. Using this relationship as the basis, the model was updated by adding 20 % of the mean temperature of all facets occurring between 15° FOV and 25° FOV to the 80 % of the unaltered output from the 15° FOV model run, according to the equation TEW =0.8(ri5) + 0.2(r. s-25), (4.6) where TEW is the final sensor-detected temperature with Everest weighting applied, 7 i s is the sensor-detected temperature from the 15° FOV model run and, 7i5-25 is the approximated sensor-detected temperature between 15° FOV and 25° FOV. The Modelled Temperature (°C) Figure 4.5 Comparison between modelled and measured temperatures, at all measurement heights, using prescribed facet temperatures. Statistics of model performance are included. 58 £ E Prescribed Model Measured & 30 E 90 135 180 225 270 315 Azimuth (deg.) Prescribed Model Measured e « S 30. Q. E 45 90 180 225 270 315 Azimuth (deg.) • Prescribed Model • Measured O 4 0 a 90 135 225 270 315 Azimuth (deg.) • Prescribed Model Measured 135 180 225 270 315 Azimuth (deg.) • Prescribed Model • Measured 90 135 180 225 270 315 Azimuth (deg.) Prescribed Model Measured 135 180 Azimuth (deg.) 225 270 315 Prescribed Model Measured 135 180 225 270 Azimuth (deg.) Figure 4.6 Measured and modelled temperatures at seven times. These measurements were conducted from 26 m above the surface while the tower was rotated through 8 azimuth positions between 0° and 315°. 59 S Prescribed Model Measured Prescribed Model Measured E 135 180 225 270 Azimuth (deg.) 90 135 160 225 270 315 Azimuth (deg.) • Prescribed Model • Measured : s 135 180 225 270 315 Azimuth (deg.) • Prescribed Model * Measured 90 135 180 225 270 315 Azimuth (deg.) • Prescribed Model • Measured 8 « 1 30 90 135 180 225 270 315 Azimuth (deg.) • Prescribed Model * Measured 180 225 270 315 Azimuth (deg.) • Prescribed Model * Measured 45 90 270 315 Azimuth (deg.) Figure 4.7 Measured and modelled temperatures at seven times. These measurements were conducted from 22 m above the surface while the tower was rotated through 8 azimuth positions between 0° and 315°. 60 8 H 1 Q. 1 &i 30 to 30 • Prescribed Model " Measured 0 45 90 135 180 225 270 315 Azimuth (deg) • Prescribed Model • Measured i to 30 45 90 180 225 270 315 • Prescribed Model • Measured to to »4 fi so 135 180 225 270 315 Azimuth (deg.) • Prescribed Model - Measured 90 135 180 225 270 315 Azimuth (deg.) • Prescribed Model * Measured m m 135 180 225 270 315 Azimuth (deg.) • Prescribed Model • Measured 90 135 180 225 Azimuth (deg.) 270 315 • Prescribed Model • Measured 90 135 180 225 270 315 Azimuth (deg.) Figure 4.8 Measured and modelled temperatures at seven times. These measurements were conducted from 11 m above the surface while the tower was rotated through 8 azimuth positions between 0° and 315°. 61 Table 4.4 Summary of measured and modelled surface type view factors at different times, heights and azimuths throughout the measurement period. Decimal Azimuth Height Roof Sun. Wall ShWall Sun.Grn Sh.Grnd Roof Sun. Wall ShWall Sun.Grn Sh.Grnd Time (dee.) (m) (meas.) (meas.) (meas.) d (meas.) (meas.) (model) (model) (model) d (model) (model) 7.25 0 26 0.00 0.00 0.00 0.91 0.09 0.00 0.00 0.00 1.00 0.00 7.25 45 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 7.25 90 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 7.25 135 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 7.25 180 26 0.00 0.13 0.08 0.02 0.77 0.00 0.00 0.00 0.48 0.52 7.25 225 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.86 0.14 7.25 270 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 7.25 315 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 7.5 0 22 0.00 0.00 0.00 0.81 0.19 0.00 0.00 0.00 1.00 0.00 7.5 45 22 0.07 0.00 0.33 0.29 0.31 0.00 0.00 0.00 0.86 0.14 7.5 90 22 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.48 0.52 7.5 135 22 0.97 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 7.5 180 22 0.00 0.00 0.00 0.03 0.97 0.00 0.00 0.00 0.61 0.39 7.5 225 22 0.97 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.53 0.47 7.5 270 22 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 7.5 315 22 0.33 0.44 0.06 0.09 0.09 0.85 0.00 0.00 0.02 0.13 7.68 0 11 0.00 0.00 0.00 0.00 1.00 0.97 0.00 0.02 0.00 0.01 7.68 45 11 0.00 0.00 0.10 0.00 0.90 0.00 0.00 0.08 0.92 0.00 7.68 90 11 0.00 0.00 0.79 0.00 0.22 0.00 0.00 0.08 0.00 0.92 7.68 135 11 0.00 0.00 0.07 0.00 0.94 0.97 0.00 0.02 0.01 0.00 7.68 180 11 0.00 0.00 0.00 0.00 1.00 0.85 0.00 0.00 0.15 0.00 7.68 225 11 0.00 0.18 0.39 0.00 0.44 0.85 0.00 0.00 0.03 0.11 7.68 270 11 0.00 0.75 0.25 0.00 0.00 0.97 0.00 0.02 0.00 0.01 7.68 315 11 0.00 0.09 0.44 0.00 0.47 0.00 0.08 0.00 0.92 0.00 9.17 0 11 0.00 0.00 0.00 0.00 1.00 0.85 0.00 0.00 0.01 0.14 9.17 45 11 0.00 0.00 0.45 0.00 0.55 0.97 0.02 0.00 0.00 0.01 9.17 90 11 0.00 0.00 0.80 0.00 0.20 0.00 0.08 0.00 0.92 0.00 9.17 135 11 0.00 0.00 0.00 0.00 1.00 0.85 0.00 0.00 0.15 0.00 9.17 180 11 0.00 0.00 0.00 0.00 1.00 0.97 0.00 0.02 0.01 0.00 9.17 225 11 0.00 0.40 0.00 0.60 0.00 0.00 0.08 0.00 0.92 0.00 9.17 270 11 0.00 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 9.17 315 11 0.00 0.25 0.00 0.75 0.00 1.00 0.00 0.00 0.00 0.00 9.42 0 22 0.00 0.00 0.00 0.59 0.41 0.00 0.00 1.00 0.00 0.00 9.42 45 22 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 9.42 90 22 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 9.42 135 22 0.41 0.00 0.49 0.00 0.10 1.00 0.00 0.00 0.00 0.00 9.42 180 22 0.00 0.00 0.00 0.73 0.27 1.00 0.00 0.00 0.00 0.00 9.42 225 22 072 0.28 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 9.42 270 22 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 9.42 315 22 0.90 0.10 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 9.67 0 26 0.00 0.00 0.00 0.90 0.10 1.00 0.00 0.00 0.00 0.00 9.67 45 26 0.97 0.00 0.00 0.03 0.00 0.00 1.00 0.00 0.00 0.00 9.67 90 26 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 9.67 135 26 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 9.67 180 26 0.00 0.00 0.15 0.54 0.32 0.00 0.72 0.28 0.00 0.00 9.67 225 26 1.00 0.00 0.00 0.00 0.00 0.80 0.00 0.00 0.20 0.00 9.67 270 26 0.95 0.00 0.00 0.03 0.03 0.98 0.00 0.00 0.02 0.00 9.67 315 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.99 0.00 13.25 0 26 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.01 0.00 0.99 ' 13.25 45 26 0.63 0.00 0.22 0.16 0.00 0.98 0.00 0.00 0.02 0.00 13.25 90 26 1.00 0.00 0.00 0.00 0.00 0.80 0.00 0.00 0.20 0.00 13.25 135 26 1.00 0.00 0.00 0.00 0.00 0.80 0.00 0.00 0.20 0.00 13.25 180 26 0.00 0.00 0.28 0.29 0.44 0.98 0.00 0.00 0.02 0.00 13.25 225 26 1.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.99 0.00 13.25 270 26 1.00 0.00 0.00 0.00 0.00 0.80 0.00 0.00 0.20 0.00 13.25 315 26 1.00 0.00 0.00 0.00 0.00 0.98 0.00 0.00 0.02 0.00 13.5 0 22 0.00 0.00 0.00 1.00 0.00 0.00 0.01 0.00 0.99 0.00 13.5 45 22 0.93 0.07 0.00 0.00 0.00 0.80 0.00 0.00 0.14 0.06 62 13.5 90 22 1.00 0.00 0.00 0.00 0.00 0.98 0.00 0.00 0.02 0.00 13.5 135 22 0.41 0.48 0.00 0.11 0.00 0.00 0.00 0.01 0.00 0.99 13.5 180 22 0.00 0.00 0.26 0.74 0.00 0.00 0.00 0.00 1.00 0.00 13.5 225 22 0.75 0.00 0.25 0.00 0.00 0.00 0.00 0.00 1.00 0.00 13.5 270 22 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 13.5 315 22 0.69 0.00 0.31 0.00 0.00 0.00 0.00 0.00 0.00 1.00 13.75 0 11 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 13.75 45 11 0.00 0.32 0.00 0.68 0.00 0.00 0.00 0.00 1.00 0.00 13.75 90 11 0.00 0.83 0.00 0.17 0.00 0.00 0.00 0.00 1.00 0.00 13.75 135 11 0.00 0.26 0.00 0.74 0.00 0.00 0.00 0.00 1.00 0.00 13.75 180 11 0.00 0.00 0.00 0.99 0.01 0.00 0.00 0.00 1.00 0.00 13.75 225 11 0.00 0.00 0.52 0.08 0.41 0.00 0.00 0.00 1.00 0.00 13.75 270 11 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 13.75 315 11 0.00 0.00 0.00 0.80 0.20 0.00 0.00 0.00 0.00 1.00 16.3 0 26 0.00 0.00 0.00 0.71 0.29 0.00 0.00 0.00 0.47 0.53 16.3 45 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.92 16.3 90 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 16.3 135 26 1.00 0.00 0.00 0.00 0.00 0.76 0.00 0.00 0.24 0.00 16.3 180 26 0.00 0.00 0.28 0.35 0.37 0.95 0.00 0.00 0.05 0.00 16.3 225 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.24 0.00 0.76 16.3 270 26 0.95 0.00 0.00 0.04 0.01 0.00 0.24 0.00 0.76 0.00 16.3 315 26 0.66 0.00 0.21 0.10 0.03 0.95 0.00 0.00 0.05 0.00 16.5 0 22 0.00 0.00 0.00 0.37 0.63 0.76 0.00 0.00 0.24 0.00 16.5 45 22 0.71 0.23 0.06 0.00 0.00 0.76 0.00 0.00 0.24 0.00 16.5 90 22 1.00 0.00 0.00 0.00 0.00 0.95 0.00 0.00 0.05 0.00 16.5 135 22 0.79 0.00 0.21 0.00 0.00 0.00 0.00 0.24 0.00 0.76 16.5 180 22 0.00 0.00 0.00 0.63 0.37 0.76 0.00 0.00 0.24 0.00 16.5 225 22 0.89 0.00 0.11 0.00 0.00 0.95 0.00 0.00 0.05 0.00 16.5 270 22 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.24 0.00 0.76 16.5 315 22 0.78 0.00 0.22 0.00 0.00 0.76 0.00 0.00 0.00 0.24 16.75 0 11 0.00 0.00 0.00 0.00 1.00 0.95 0.00 0.00 0.00 0.05 16.75 45 11 0.00 0.00 0.00 0.94 0.06 0.00 0.00 0.24 0.00 0.76 16.75 90 11 0.00 0.28 0.52 0.10 0.09 1.00 0.00 0.00 0.00 0.00 16.75 135 11 0.00 0.00 0.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 16.75 180 11 0.00 0.00 0.00 0.00 1.00 0.00 0.40 0.60 0.00 0.00 16.75 225 11 0.00 0.00 0.38 0.00 0.62 0.00 1.00 0.00 0.00 0.00 16.75 270 11 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 16.75 315 11 0.00 0.00 0.58 0.00 0.42 1.00 0.00 0.00 0.00 0.00 19.25 0 26 0.00 0.00 0.00 0.96 0.04 1.00 0.00 0.00 0.00 0.00 19.25 45 26 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 19.25 90 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 19.25 135 26 0.96 0.04 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 19.25 180 26 0.02 0.24 0.14 0.29 0.31 1.00 0.00 0.00 0.00 0.00 19.25 225 26 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 19.25 270 26 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 19.25 315 26 0.86 0.00 0.14 0.00 0.00 1.00 0.00 0.00 0.00 0.00 19.5 0 22 0.00 0.00 0.00 0.64 0.36 0.00 0.00 1.00 0.00 0.00 19.5 45 22 0.78 0.10 0.12 0.00 0.00 0.80 0.00 0.00 0.08 0.12 19.5 90 22 1.00 0.00 0.00 0.00 0.00 0.97 0.00 0.00 0.02 0.01 19.5 135 22 0.48 0.15 0.30 0.00 0.07 0.00 0.00 0.03 0.00 0.97 19.5 180 22 0.00 0.01 0.00 0.16 0.83 0.00 0.03 0.00 0.97 0.00 19.5 225 22 0.95 0.00 0.05 0.00 0.00 0.97 0.00 0.00 0.00 0.03 19.5 270 22 1.00 0.00 0.00 0.00 0.00 0.80 0.00 0.00 0.02 0.18 19.5 315 22 0.50 0.00 0.50 0.00 0.00 0.80 0.00 0.00 0.14 0.07 19.6 0 11 0.00 0.00 0.00 0.00 1.00 0.97 0.00 0.00 0.00 0.03 19.6 45 11 0.00 0.00 0.28 0.00 0.72 0.00 0.00 0.03 0.00 0.97 19.6 90 11 0.00 0.00 0.78 0.00 0.22 0.80 0.00 0.00 0.20 0.00 19.6 135 11 0.00 0.00 0.00 0.00 1.00 0.97 0.00 0.00 0.03 0.00 19.6 180 11 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.03 0.00 0.97 19.6 225 11 0.00 0.00 0.10 0.00 0.90 0.80 0.00 0.00 0.20 0.00 19.6 270 11 0.00 0.00 0.00 0.00 1.00 0.97 0.00 0.00 0.03 0.00 19.6 315 11 0.00 0.00 0.11 0.00 0.89 0.00 0.00 0.03 0.97 0.00 63 results in Figures 4.9 - 4.12 show there is improvement over previous model runs as given by the statistics of model performance. The navigational errors discussed previously that caused uncertainty in sensor position and orientation, are still present in this version of the model, and likely contribute significantly to discrepancies between modelled and measured values. There is one other aspect to the relationship between modelled and measured temperatures that requires discussion. In both Figures 4.5 and 4.9 there is greater scatter in the data at the highest temperatures. There are probably two main reasons for this. The first is that at times of day when high sensor-detected temperatures exist there is a greater range in facet temperatures (standard deviation at 1300h = 13.2°C) than at times of day when lower surface temperatures are present (standard deviation at OlOOh = 4.8°C). Therefore, due to the wide range of facet temperatures, errors in estimating the correct proportion of surface facets 'seen' results in relatively large sensor-detected temperature errors compared to times when the range in facet temperatures is smaller. The second reason for the larger scatter is again related to the high facet (especially rooftop) temperatures seen in the middle of the day. Thermals rising from hot surface facets tend to temporarily cool those surfaces. The resulting fluctuations are averaged out of the measured facet temperatures (which are 5 minute means), whereas the sensor-detected temperature from the top of the tower is a 20 second reading and captures some of this variability. This does not necessarily apply to all readings but helps to explain some of the scatter. Overall, S3MOD performs well, especially when Everest IRT FOV weighting is applied. The model is able to capture the anisotropy of surface temperatures as exhibited 64 by Figure 4.13 and in absolute terms provides a good estimate of sensor-detected temperatures, even when it still includes geometric errors (Section 4.2). Modelled Temperature (°C) Figure 4.9 Comparison between modelled and measured temperatures, where the measured values use prescribed facet temperatures and Everest weighting to give TEw as in (4.6). Statistics of model performance are included. 65 | • Prescribed Model • Measured " Prescribed Model • Measured 75 S »4 135 180 225 270 315 Azimuth (deg.) 135 160 Azimuth (deg.) 270 315 • Prescribed Model • Measured 50 • Prescribed Model Measured l i 20 225 270 50 100 150 200 250 300 350 Azimuth (deg.) • Prescribed Model Measured E 135 180 225 270 Azimuth (deg.) • Prescribed Model • Measured 135 180 225 270 Azimuth (deg.) • Prescribed Model • Measured 180 225 270 315 Azimuth (deg.) Figure 4.10 Measured and modelled temperatures with Everest weighting (TEw) at seven times. These measurements were conducted from 26 m above the surface while the tower was rotated through 8 azimuth positions between 0° and 315°. 66 £ «-i • Prescribed Model * Measured | x 135 180 225 270 315 Azimuth (deg.) • Prescribed Model • Measured 90 135 180 225 270 315 Azimuth (deg.) £ «-n "53 fc> 30-Prescribed Model Measured £ «-l 30 • Prescribed Model Measured Azimuth (deg.) • Prescribed Model • Measured 135 180 225 270 315 Azimuth (deg.) Prescribed Model Measured - • 90 135 180 225 270 315 Azimuth (deg.) Azimuth (deg.) Prescribed Model Measured 90 135 180 225 270 315 Azimuth (deg.) Figure 4.11 Measured and modelled temperatures with Everest weighting (JEW) at seven times. These measurements were conducted from 22 m above the surface while the tower was rotated through 8 azimuth positions between 0° and 315°. 67 • Prescribed Model • Measured • Prescribed Model Measured 8 -H fe 30 H EL E 135 180 225 270 315 Azimuth (deg.) • Prescribed Model * Measured 90 135 180 225 270 315 Azimuth (deg.) • Prescribed Model " Measured 45 90 135 180 X axis title 270 315 90 135 180 Azimuth (deg.) 225 270 315 e • Prescribed Model • Measured 225 270 Azimuth (deg.) 8 *o I fe 30 D. E • Prescribed Model • Measured 45 BO 160 225 270 315 Azimuth (deg.) Prescribed Model Measured Azimuth (deg.) Figure 4.12 Measured and modelled temperatures with Everest weighting (TEW) at seven times. These measurements were conducted from 11 m above the surface while the tower was rotated through 8 azimuth positions between 0° and 315°. 68 4.3.2 Energy Balance Model Temperatures The second method to compare modelled and measured temperatures uses surface facet temperatures generated using the Mills (1997) UCL energy balance model described in Section 2.4 Using an energy balance model to acquire facet temperatures is useful because it is not always possible to have measurements of surface facet temperatures when it is desirable to run the model. Figures 4.14 and 4.15 show the performance of the model using energy balance modelled facet temperatures (TEB mod)- In addition to the sources of error that exist for the prescribed facet temperature version of the model, there are additional errors associated with the energy balance model itself. Figure 4.13 shows a comparison between the measured facet temperatures and the energy balance modelled facet temperatures over the course of one day. The most obvious feature of this figure, and probably the largest source of error in the modelled sensor-detected temperatures, is the approximate one hour offset between peak facet temperatures of the energy balance model output and measurements. The reasons for these features are not readily apparent but indicate that certain problems exist with the energy balance model when used under the conditions of this study. These errors could be a result of simplifications in the description of the surface in the energy balance model. The size of the buildings in the energy balance model was not exactly the same as those present in the study area. This was due to a restriction on building volume imposed by the energy balance model, which resulted in the modelled buildings being smaller than at the study site. In addition the model assumes a surface of regularly repeating identical structures on the surface. This was not precisely 69 the case at the study site. Although not perfect, the energy balance model provides a realistic (in terms of absolute facet temperatures and diurnal temperature range) description of a simple urban surface that can provide insight into surface facet temperature changes. Figure 4.13 Comparison of measured (TEW) and modelled (mod) (TEB mod) facet temperatures through the course of a day. Gaps indicate times when measurements are not available. The north and ground facets only have measurements at times indicated by data points. 70 60 50 MAE = 7.80 °C N* / • • o o RMSE = 8.93 °C • cu R2 = 0.78 iratur 40 D = 0.85 / • red Tempe 30 I / m / m : ' ' / m Measu - 1 . Measu 20 -/ • -.* • ! 10 • i • i • i 1 i 1 1 10 20 30 40 50 60 70 Modelled Temperature (°C) Figure 4.14 Comparison between modelled and measured (TEW) temperatures using energy balance modelled facet temperatures (TEB mod)- Statistics of model performance are included. 71 o o CD • EE <D Q. E 7 0 - , 60 H 50 H 40 H 30 H 20 A 10 h=26m h=11m h=11m h=26m h=11m h=26m h=26m, 22m 0100h • • • • • • • • • • • • •• • • • • m • • • • • • • • • • • . 1 • 1 • • • • • • 0700h 0900h 1300h 1630h 1900h 1 1 10 I 20 1 1 30 40 Measured EBModel 50 2200h ' 1 60 70 Model Run Number Figure 4.15 Measured and modelled temperatures through time using energy balance modelled facet temperatures. Each time segment (e.g. OlOOh) refers to a period when measurements were taken and energy balance model output was available. At each time segment the tower was positioned at one height above the surface (except 2200h, where two heights were used) while the tower was rotated through 8 azimuth positions between 0° and 315°. The tower height for each time segment is noted on the figure. The model run numbers are sequential but are not at regular time intervals. 4.3.3 Helicopter-based Temperatures The final set of measured results to compare against modelled values come from a pair of helicopter flights conducted over the same area as that of the field programme (for a complete description see Section 3.5). Comparison between modelled sensor-detected temperature, and measured output from the helicopter-mounted AGEMA sensor at two different times, is presented in Figure 4.16. The model requires a precise input of sensor position to accurately model temperatures (see Section 4.2). Using a moving sensor 72 platform, such as a helicopter, it is almost impossible to know the exact position of the sensor at a given time. The orientation (ONA and azimuth) is more stable but does vary slightly during the flight. Therefore, knowledge of the exact portion of the surface that is being viewed is limited. To attempt to compensate for this the model was run for a range of possible sensor locations (the orientation remained constant at 45° ONA and either South or North-viewing azimuth). The modelled temperatures given in Figure 4.16 are mean values of all model runs, but include the range of values found. The modelled values are similar to the measured results. As may be expected North-viewing (i.e. seeing many South-facing walls) model runs are warmer than South-viewing runs, with the greatest difference existing later in the day when the difference between North and South-facing facets is the largest. It is important to note that it was also found that East and West-facing facets are 'seen' and can play a significant role in sensor-detected temperature depending on sensor location. The results again show the importance of knowing the details of sensor position and orientation. Small differences in these important properties can result in very different model results. In general, however, the model performs well. 73 36-34-32 30-1 O 2 8 H o £ 26-1 13 05 <D Q . E cu Flight 1 I I It 10.0 44 -I Flight 2 42-40 38-36-34-10.2 10.4 10.6 10.8 11.0 —I 13.85 — MeasuredT — North — South — - Northmax Northmin Southmax Southmin 13.90 13.95 Time (decimal hours PDT) —i 1 1 — 14.00 14.05 Figure 4.16 Measured and modelled sensor detected temperatures from a helicopter. Solid lines indicate mean modelled temperature in the direction indicated while dashed lines show the range in modelled temperatures. Measured temperatures are from alternating eastward and westward flights over the study area. Gaps in measured temperatures indicate times when the AGEMA sensor was turned off. 74 Chapter 5 MODEL APPLICATIONS 5.1 Introduction A validated version of S3MOD is able to simulate sensor view factors of the surface (Chapter 4). This provides the user with a valuable tool for examining the role of surface structure and sensor position on remotely-sensed radiative measurements. This chapter presents the results of using S3MOD in a number of hypothetical settings. 5.2 View Factors and Sensor Elevation 5.2.1 Modelling Procedure One of the goals of this project is to examine the effects of moving a sensor from the top of the urban canopy layer to near satellite height. Establishing a relationship between sensor height and surface view factor could help to interpret measurements from remote sensors and set measurement protocols for remote sensor-based studies. Depending on the goals of a study and the resources available, an investigator has to decide the type of platform from which measurements are to be made. The availability of S3MOD allows a user to examine the effects of different sensor and surface parameters on sensor-detected radiance. A case study is undertaken to investigate these effects. The scenario selected is to set up S3MOD to simulate the movement of a sensor, with a given IFOV (5°) and two ONAs (0° and 45°), from an elevation of 100 m to 100 km above an urban surface. An IFOV of 5° was chosen because it is a value that allowed a range of elevations to be tested without altering surface resolution more than once. The surface structure is the same as that used in model validation (see Chapter 4) although it 75 is necessary to scale the surface for some of the model runs due to the size of the surface area covered by the sensor IFOV at high elevations. This results in a decrease in surface resolution and potentially an increase in error. The transition between the two scales shows only a small discontinuity indicating this error is likely quite small (see Figure 5.1). The range of elevations used in this simulation begin well above the top of the UCL (approx. = 10 m) because it was determined from model validation that sensor azimuth would play a greater role on surface view factors than sensor height at low elevations (see Table 4.3). The validation was undertaken with a 15° IFOV modelled sensor whereas this modelling exercise uses a 5° IFOV modelled sensor and therefore the effect is more pronounced. The effects of low sensor elevation on sensor-detected radiance and view factors was demonstrated during the model validation and is not repeated here. An extension of this modelling exercise is to examine whether any surface view factor differences exist between a number of sensors 'seeing' identical areas on the surface but placed at different elevations. To achieve the requirement that sensors at each elevation view the same surface features, the sensor IFOV must decrease with increasing sensor height. Answering this relatively simple question is important to those involved in remote sensing studies because it determines whether substituting a change in sensor elevation with a change in IFOV is a valid procedure. 5.2.2 Modelling Results The first results of this modelling exercise are shown in Figures 5.1 and 5.2. When the sensor is nadir viewing, it can be seen that above 1000 m there is very little 76 1-0-. 0.8 H 0.6 4 Wall Ground Roof o o CO — 0.0 100 1000 10000 T 1—I—I I | 100000 Elevation (m) Figure 5.1 Surface view factors from a nadir-viewing sensor moving from 100 m above the surface to 100 km above the surface. change in view factor fractions of the major surface components (Figure 5.1). Between 500 m and 1000 m there is a small change and between 100 m and 500 m there is a more marked change. It should be noted that walls take up a very small portion of the sensor IFOV. This is due to the fact that the sensor is viewing at nadir. The results are due to the orientation of the sensor and the fact that as the area on the surface that is "seen" by the sensor becomes large (i.e. the sensor moves farther from the surface), that area becomes more representative of the entire surface, for this sensor orientation and surface structure, than a small area would be (which occurs when the sensor is closer to the ground). As the sensor is moved upward a continuum is created between small sampling area (less representative of the whole) and large sampling area (more representative of the whole). 77 o o CD LL > 0.50 -j 0.25 A 0.00 z=100000m 0.50 0.25 4 0.00 T 0 z=50000m 0.50 -n 0.25 A 0.00 0 z= 10000m 0.50 0.25 H 0.00 0.50 0.25 -1 0.00 1 ' 0 z=2000m 0.50 - i 0.25 0.00 T 0 z=1000m 0.50 0.25 -1 0.00 1 0 z=500m 0.50 -J 0.25 H 0.00 1 r 0 z=100m I 50 50 T 1 r 0 50 z=5000m "T" 50 "T" 50 50 50 i i 100 150 I 200 i i 100 I 150 200 100 150 I 200 I 100 I 150 I 200 S I 100 I 150 200 100 I 150 I 200 i - I -100 150 200 I 1 1 r 50 T 100 150 Azimuth (deg.) 200 • Wall • Ground • Roof 250 ~r— 250 250 250 I 250 I 250 250 250 Figure 5.2 Surface view factors from a remote sensor, at 45° ONA and four different sensor view azimuths and being moved from 100 m to 100 km above the surface. As there is very little change occurring above 1000 m it suggests that the sensor has reached a height of "constant" view factor. Most of the change in view factors occurs 78 below 500 m and is due to the smaller area being sampled. The previously mentioned scale change occurs at 10,000 m and appears to have little impact on view factor values. Figure 5.2 illustrates view factor changes from a sensor at a 45° ONA, from four directions and eight elevations. The figure again shows that at heights > 1000 m there is little change in view factor with increasing elevation. This assumes no change in view direction. The same factors discussed in relation to Figure 5.1 continue to operate in the model runs displayed in Figure 5.2. The majority of change in view factors occurs due to changes in sensor view direction. This result is not surprising considering the anisotropic nature of surface radiative emissions from urban areas. The results of the second portion of the initial modelling exercise are presented in Table 5.1. The data indicate that altering IFOV as a surrogate for a change in sensor elevation would result in false sensor-detected-radiance values. This is due to the fact that, although the identical area on the surface is within the sensor's IFOV, the surface facet view factors are different at each elevation. This occurs because as the sensor moves higher the angle between the surface facet and the sensor becomes smaller, hence a change in its view factor. Table 5.1 Surface facet view factors for remote sensors viewing identical surface areas. The sensor heights and IFOV values are specified for each case. Sensor Sensor IFOV Wall View Ground View Roof View Elevation (m) (deg.) Factor Factor Factor 100 106.7 .1214 .4878 .3908 200 68.0 .0631 .5528 .3842 500 30.0 .0156 .6049 .3795 1000 15.4 .0054 .6216 .3730 10000 1.54 .0001 .6329 .3670 79 5.3 Theoretical Urban Zones 5.3.1 Modelling Procedure and Rationale The second modelling exercise is to examine the role of surface structure on sensor view factors of the surface. The goal of this exercise is to use S3MOD to predict the location and orientation of a sensor that would sample facets of the surface in proportion to their contribution to the complete surface area (if such a position exists) and thus obtain a representative sample of the urban surface. Knowledge of this location and orientation is important because it could be directly linked to the notion of a possible estimation of the complete surface temperature using only one sensor-based measurement. The first step in this use of S3MOD is to decide upon a set of surface types that represent realistic and distinct urban zones. The identification of these surface types is governed by the goals of this modelling exercise. It therefore creates a set of requirements that differ from previous studies of surface morphology (e.g. for roughness estimation, Grimmond and Oke, 1999). Ellefsen's (1990) inventory of urban terrain zones (UTZ) in conjunction with estimates of surface morphology from a range of cities (Grimmond and Oke, 1999) form the basis for developing this new set of urban surface types. Ellefsen (1990) identifies seventeen urban terrain zones that provide a physical, rather than functional, description of urban areas. The specific criteria used to identify different zones are: street pattern, lot configuration, building placement on the lot, building density, building construction type, and age of construction (Ellefsen, 1990). It 80 is obvious that not all of these criteria are relevant to all studies of the urban surface, therefore, the number of zones relevant to any one study is likely to be less than seventeen. The stated goal of the present modelling exercise is to use S3MOD to find a location and orientation for a remote sensor that allows that sensor to have, within its IFOV, a proportionally representative sample of the complete surface area. The requirement of the surface representation is that its structure be a realistic facsimile of a real urban surface. The factors deemed important are: building size (both in the vertical and horizontal), building density (i.e. the number of structures per unit area), and street widths. These three factors are not independent of each other and therefore each affects the other two. With these factors in mind, Ellefsen's (1990) urban terrain zones were used to create a subset of surface types that take into account the relevant criteria for this exercise. The result is a group of seven surface types. Table 5.2 shows the structural measures for each of the surface types, the new name given to each, and their classification according to Ellefsen (1990). The nomenclature used for the surface types is as follows. The first two letters indicate the building density of the area (i.e. HD - high density, MD - medium density, LD - low density). The determination of density is done in a qualitative sense and is based on images provided by both Ellefsen (1990) and Grimmond and Oke (1999). The third and fourth letters refer to a colloquial description of an area and includes row houses (RH), attached apartments (AA), detached houses (DH), high-rise (HR), and light industrial (LI). The final numbers refer to the height to width ratio of the buildings and 81 their streets. If the height-to-width ratio contains a 0 as its first number this indicates that the ratio is less than 1 (i.e. 025 - height to width = 0.25). Some of the values (such as a building length of 400 m) in Table 5.2 may appear unrealistic. This is done because of the manner in which the building-street-alley combination is constructed within S3MOD (see Chapter 2) and to replicate the surface as accurately as possible . To simulate row houses or tightly packed apartments, where little or no space exists between individual structures, an entire length of houses is represented by one structure. For the MDDH05 case a building length of 50 m was used because no provision exists within S3MOD to create small distances between buildings that are not streets or alleys. Therefore, by making the buildings longer than is reasonable for this type of surface the total ground area is preserved, all be it at a small loss in wall cover. As with any modelling endeavour certain approximations to the real world are necessary. Table 5.2 Summary of surface structure characteristics for seven surface types. UTZ, urban terrain zones, based on classification of Ellefsen (1990). Surface UTZ Building Building Building Street Alley Type Height Length Width Width Width (m) (m) (m) (m) (m) HDRH05 A3 7 400 10 15 15 HDAA1 A2 10 400 10 10 10 MDDH025 Do3 5 15 15 20 10 MDDH05 Dc3 10 50 15 20 10 LDHR5 Del 100 40 40 20 8 LDHR2 Dc2 40 40 40 20 10 LDLI05 Do4 10 40 20 20 10 To confirm that the chosen surface types contain realistic measures of urban morphology they are compared with the results of Grimmond and Oke (1999). The Grimmond and Oke (1999) study was undertaken to determine aerodynamic 82 characteristics of an urban site through analysis of surface form. Although their objectives are different to those here, a number of the measures of surface form are relevant to the present modelling exercise. These include building height, and two non-dimensional surface area ratios Xp = Ap/Ax (the ratio of the building plan area to the total ground-level surface area) and Xc = Ac/AT (the ratio of the complete surface area to the total ground-level surface area). Table 5.3 provides a comparison between measured values and those used as inputs to the model for cases where measurements are available. It should be noted that the measured values are from individual sites within a UTZ and it must be assumed that there is variability from site-to-site. With this in mind the input parameters appear to be relatively close in value to the measured cases and therefore should provide a reasonable basis for modelling sensor view factors. Table 5.3 Comparison of model input parameters and measured values of surface structure at individual sites. Measured values are from Grimmond and Oke (1999). Surface Input Measured Input Measured Input Measured Type Building Building Xp Xp Xc Xc Height (m) Height (m) HDAA1 10 18.4 ±6.6 0.49 0.47 1.99 1.73 MDSU025 5 5.2 + 0.8 0.25 0.33 0.58 1.45 MDSU05 10 5.9 ± 1.3 0.38 0.38 1.05 1.74 LDHR2 40 34.3 0.53 0.39 2.64 2.20 LDLI05 10 5.8 + 0.1 0.42 0.46 1.04 1.39 5.3.2 Modelling Results The results from the model runs, using the seven described surface types, are presented in Figures 5.3 - 5.9. Each figure contains six plots of surface view factors 83 through 90° of azimuth and from six off-nadir angles. The sensor, with an IFOV of 15° was placed at five times the building height for all cases. Only azimuth angles of 0° to 90° are used because the surface structure is symmetric about both the North-South and East-West directions. An IFOV of 15° results in a significantly larger viewed area compared to the 5° case discussed in Section 5.2. Therefore it is assumed that the sensor height represents a height where view factors change only slightly with increasing distance from the surface. This is important because it eliminates sensor height as a significant factor in determining surface view factors. Therefore sensor azimuth and ONA are the largest contributors to changing surface view factors. Since the goal of this modelling exercise is to ascertain which orientation of sensor is closest to sampling surface facets in proportion to their contributions to the complete surface area, Table 5.3 was constructed to illustrate the surface fractional percentages of the complete surface area for each surface type. The data in Table 5.4 are to be compared with Figures 5.3 to 5.9 to find the ideal sensor location for the stated goal. Table 5.4 Percentage of complete surface area occupied by different surface facets for each surface type. Surface Type Wall (%) Ground (%) Roof(%) HDRH05 35.6 39.6 24.8 HDAA1 60.0 20.5 19.5 MDDH025 25.0 56.3 18.7 MDDH05 40.0 36.9 23.1 LDHR5 84.6 7.0 8.4 LDHR2 67.9 15.1 17.0 LDLI05 38.4 36.0 25.6 84 Comparing the values in Table 5.3 against the data presented in Figures 5.3-5.9 it is obvious that wall view factors are very low for all ONAs, and only at 55° and 60° ONA do they approach the true values. In addition, since the street orientation is North -South and East - West the highest values for wall view factors are with sensor azimuths closer to 45°. In general, this is the case for all of the surface types used. The implication is that for a sensor to sample correctly (i.e. in proportion to the complete surface area) it must be oriented at an extreme off-nadir angle otherwise wall portions will be undersampled. It is also important that the sensor not be aligned parallel to the street canyons because this exacerbates the problem of undersampling of walls. To solve the problem of viewing too little wall surface area it could be argued that the sensor should be placed closer to the ground and at a high ONA. From the validation presented in Chapter 4 (where sensor height is much lower) it can be seen that there are situations that exist where the sensor sees only walls (see Table 4.3). This implies, in conjunction with the present set of results, that a continuum exists between seeing only walls and seeing no walls. It is likely, although not definite, that at some given height and orientation all three surface components should be able to be sampled in accordance with their contribution to the complete surface area. Conversely, the correct proportion of walls seen might only be reached when the sensor is placed below roof level. This means that no roofs would be seen and therefore no sensor position and orientation would exist that satisfies the goal of sampling the surface representatively. The information contained in Figures 5.3-5.9 is not comprehensive and not meant to illustrate all the possible sensor orientations and locations. They are only a small subset of all possible combinations of ONA, IFOV, sensor azimuth, sensor location, and 85 surface structure. All of these factors, which play a role in determining surface view factors, are simultaneously contributing to the model output shown in these figures. S3MOD could be setup to test many more combinations of these variables and at greater spatial resolution. This would be computationally expensive but nonetheless quite possible. Therefore, these figures are to be used only as an example of the potential of S3MOD not as a final solution to the question posed. 5.4 Conclusions The modelling scenarios shown in this chapter are an attempt to use S3MOD in hypothetical settings. This allows the user to investigate the effects of a range of sensor-surface orientations. The two modelling exercises described in this chapter illustrated, firstly, the effects of moving a sensor from near ground level to satellite height and secondly, an attempt to identify a sensor location and orientation where surface facets are sampled proportional to their contribution to the complete surface area. The results of the first modelling exercise show that at a certain elevation above the surface, increasing sensor height has no impact on surface facet view factors. This holds only if the sensor is nadir viewing. The height at which this effect happens is dependent on surface structure and sensor IFOV. In the case described herein only one surface type and IFOV is used and therefore an extension to this modelling exercise would be to use a range of surface structures and sensor parameters to try to generate more general results. It was also determined that attempting to use sensor-detected-radiance measurements, at a specified elevation as a proxy for measurements at another elevation 86 solely by adjusting the sensor IFOV and thus preserving the area on the surface within the sensor IFOV, results in inaccurate readings. This is because of the changes that occur in surface view factor related to sensor elevation differences. The results of the second modelling exercise show that at a set elevation above a given urban surface type there may not be a sensor location and orientation that provides the correct proportion of 'seen' surface facets. The main problem found was that wall facets tend to be undersampled for all but the largest ONA values. It would be valuable to explore the effects of moving a sensor to different heights above the surface in an effort to sample more representatively. The natural extension of this second modelling exercise is to attempt to predict complete surface temperatures from an individual measurement of temperature using a remote sensor. This goal is not easily achieved. Obtaining the correct percentage of walls, ground and roof is only a first step to predicting the complete surface temperature. It is necessary to obtain a sample of all the facets that contains their complete range of temperatures. For walls this must include each wall orientation, and for the ground it must include the correct amount of shaded and unshaded portions. This assumes that building materials, and hence thermal properties, are uniform for all buildings and ground cover. The final complication is that the facet temperatures and shading patterns are changing continuously throughout the period of a day and over the seasons. All of these factors make the task of predicting complete surface temperature exceedingly difficult. Finally, as has already been mentioned in this thesis and is again quite apparent, the model (and hence a remote sensor) is very sensitive to even small changes in 87 orientation and surface structure. It is, therefore, vital that these parameters are properly accounted for in any remote sensing study. o CO Ll_ > -Wall - Ground Roof 60°ONA P I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 55 ONA 1 i 1 i 1 i 1 i * i 1 i * n 1 i 1 i ' i 1 i 1 i 1 i 1 i ' i 1 i 1 i 1 i 1 i 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0.6 0.4 0.2 0.0 50 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 M l 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 45 ONA I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I'M 1 I ' I 1 I 1 I ^ T 1 I 1 I 1 I 1 I 1 1 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 • 0.8 • 0.6 • 0.4 • 0.2 • 0.0 • 40 ONA I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I '"I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0.6 0.4 0.2 0.0 35 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I '"I 1 I 1 I 1 I 1 I 1 I ' I 1 I ' I ' I ' I ' I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Azimuth (deg.) Figure 5.3 Surface facet view factor from six ONA and through 90° of azimuth for surface type HDHR05. The model performs best (see Table 5.3) with ONA of 55° and azimuth of 55° and ONA of 60° and azimuth of 40°. 88 Wall 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Azimuth (deg.) Figure 5.4 Surface facet view factor from six ONA and through 90° of azimuth for surface type HDAA1. The model performs best (see Table 5.3) with ONA of 60° and azimuth of 35°. 89 o CD LL > 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 • 0.8 -0.6 -0.4 -0.2 -0.0 55 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0.6 0.4 0.2 0.0 50 ONA 1 I 1 I 1 I 1 I T 1 f 1 I ' I 1 I 1 I "H 1 P I 1 I 1 I 1 I ' I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 • 0.8 • 0.6 • 0.4 • 0.2 • 0.0 • 1.0 0.8 0.6 0.4 0.2 0.0 45 ONA I 1 I 1 I 1 I 1 I 1 I 1 T 1 I 1 I i ^ ^ r T 1 ! 1 i 1 i 1 T~' i 1 i 1 i 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 40 ONA I 1 I ' I 1 I 1 I 1 I r T ~ 1 r ' I 1 I ' I 1 I 1 I ' I 1 P " ! •' I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0.6 0.4 0.2 0.0 35 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I H ' I "i I 1 I ' I 1 I 1 I ' I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Azimuth (deg.) Figure 5.5 Surface facet view factor from six ONA and through 90° of azimuth for surface type MDDH025. The model performs best (see Table 5.3) with ONA of 60° and azimuth of 50° but in general the modelled values do not match the correct values for any sensor orientation. 90 Wall 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Azimuth (deg.) Figure 5.6 Surface facet view factor from six ONA and through 90° of azimuth for surface type MDDH05. For the orientations presented her the model does not get close to matching the true values presented in Table 5.3, even at ONA of 60°. 91 o o CD Ll_ CD 1.0 0.8 0.6 0.4 0.2 0.0 -Wall - Ground Roof 60 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 55 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 50 ONA I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 45 ONA I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 40 ONA ' I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 35 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Azimuth (deg.) Figure 5.7 Surface facet view factor from six ONA and through 90° of azimuth for surface type LDHR5. The model performs best (see Table 5.3) with ONA of 60° and azimuth of 35° but at all orientations the proportion of roofs seen is much too high. 92 60 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 O co 3 CD o.o -3 55 ONA 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 50 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 45°0NA I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 1 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 0.0 40 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 -j 0.8 -0.6 -0.4 -0.2 -0.0 -35°0NA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Azimuth (deg.) Figure 5.8 Surface facet view factor from six ONA and through 90° of azimuth for surface type LDHR2. The model performs best (see Table 5.3) with ONA of 60° and azimuth of 35° but as in Figure 5.7 roof view factor values are consistently too high for all orientations. 93 1.0 0.8 0.6 0.4 0.2 0.0 -Wall - Ground Roof 60 ONA 1 l 1 l 1 r 1 l 1 l 1 I 1 l 1 l 1 I ' I 1 I 1 I 1 I 1 I 1 I 1 1 1 I H 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 O CD CO 55 ONA 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I ' I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0.6 0.4 0.2 0.0 50°ONA 1 I 1 I ' I ' I ' I 1 I ' I 1 I 1 I 1 I H 1 ! 1 I 1 I 1 I ' I ' I ' I ' I ' I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0 6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 45 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 T T I 1 I 1 I 1 I "M 1 I 1 I 1 T ' I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 40 ONA 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.0 0.8 0.6 0.4 0.2 0.0 35°ONA 1 1 1 1 1 1 1 i 1 i 1 1 1 m 1 1 1 1 1 i n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Azimuth (deg.) Figure 5.9 Surface facet view factor from six ONA and through 90° of azimuth for surface type LDLI05. The model performs best (see Table 5.3) with ONA of 55° and azimuth of 25° and ONA of 60° and azimuth of 30°. 94 Chapter 6 CONCLUSIONS 6.1 Summary of Findings The objective of this thesis was to develop a numerical model to interpret and predict remotely-sensed radiative surface emissions from urban areas. This was done to create a tool to better understand and identify anisotropic radiance distribution from urban surfaces. By achieving this aim a researcher would be better able to evaluate the impacts of anisotropy. The numerical model that has been created is able to simulate the heterogeneous nature of urban surfaces and what a remote sensor 'sees' of such systems when it is positioned at a range of locations and orientations above ground level. The model was validated against geometric and thermal measurements taken over a real urban area. It was then used to examine a number of hypothetical remote sensing scenarios. The main conclusions of this thesis are: • A validated model (S3MOD) has been developed to predict what a remote sensor 'views' of an urban surface. The measured values of surface view factors were found to be inadequate for geometric validation due to uncertainties in field measurements. The geometric validation therefore is conducted using image-calculated and theoretically-derived surface view factors. The image-based validation shows siginificant differences exist between view factors calculated from a set of images and modelled values. It is likely that these differences are exagerated by the method used and uncertainty in sensor position. The theoretically-based validation gave very good agreement between calculated and modelled view factors. 95 S3M0D was also validated from a radiative perspective. The radiative validation was conducted using measured surface temperatures and in general shows good agreement between modelled and measured values, particularly when a sensor specific IFOV modification is applied. S3MOD, and hence a real remote sensor, is extremely sensitive to its assigned location, orientation, IFOV, and the structure of the surface that it measures. This finding is borne out in all uses of S3MOD. The validation and theoretical modelling exercise results show that small changes in model input parameters can have large impacts on surface view factors and hence sensor detected radiance. This fact is of critical importance to those using S3MOD and real world based remote sensing studies because it requires the investigator to fully appreciate the impacts of experimental design decisions. A test of the impact of moving a remote sensor from near ground level to 100 km above the surface reveals little change in surface view factors above a critical elevation. This exercise shows that for a given IFOV and surface structure there is an elevation above which an increase in height results in little or no change in surface view factors. This only applies to nadir-viewing remote sensors. The elevation where this occurs is about 1000 m for the case described in Chapter 5, where the sensor EFOV is 5°. It is likely, although still untested, that over an urban area with the same structure, but a remote sensor with a larger IFOV, the height at which the view factor would become approximately constant would be lower, due to the greater surface area seen by the sensor. • A simple test is conducted to determine if decreasing a sensor's IFOV while increasing its elevation, so as to preserve the area on the surface within the sensor IFOV, would lead to similar surface view factors. The results indicate that such a scheme would fail to conserve surface view factors and therefore is a poor remote sensing strategy. • S3MOD was configured to predict the location where a remote sensor would sample surface facets in proportion to their contribution to the complete surface area, for a constructed set of urban surface types. This exercise illustrates the ability of S3MOD to test the impacts of changing surface structure and sensor position on surface view factors. The results reveal that to accurately sample walls, a remote sensor, located at five times building height, needs to be oriented at an extreme off-nadir angle. It is postulated that decreasing the elevation of the sensor, while maintaining the same IFOV, will result in a lower off-nadir angle requirement. In addition it is found that orienting a remote sensor so that it not directed at an angle parallel to street direction increases the amount of walls sampled. 6.2 Suggestions for Future Work The results of this thesis lead to a number of avenues for further research in this area and with S3 MOD. The most obvious and necessary work is to continue to run S3MOD in as many different situations as possible. Efforts should be directed in the following areas: 97 Revalidate the geometric portion of the model with more rigorously conducted field measurements. This will allow the accuracy of a wider range of view factor calculations to be verified and thereby further increase confidence in the model. Attempt to increase the domain size of the surface array within S3MOD so as to allow the model to accurately portray satellite height-based sensors. Attempt more exhaustively to find whether there is a sensor location and orientation where surface facets are sampled according to their contribution to the complete surface area for the urban surface types described in Chapter 5. Interface S3MOD with other available data and software. For example, different energy balance models could be used to evaluate their effectiveness at simulating urban surface facet temperatures thereby allowing S3MOD to be used to evaluate sensor-detected-temperatures from a range of sensor elevations and orientations over locations where facet temperatures have not been previously measured. It may be valuable to use digital elevation models to input real urban surface characteristics into S3MOD, rather than the current simple repeating surface structure. Depending on the complexity of these digital elevation models, climatically important features such as trees may be included. 98 References Barring, L., Mattsson, J.O. and Linqvist, S., 1985. Canyon geometry, street temperatures and the urban heat island in Malmo, Sweden. Journal of Climatology, 5: 433-444. Caselles,-V. and Sobrino,LA- 1989.-Determination of frost in orange groves from NOAA-9 AVHRR data. Rem. Sens. Environ., 29: 135-146. Caselles, V., Sobrino, J.A. and Coll, C , 1992. A physical model for interpreting the land surface temperature obtained by remote sensors over incomplete canopies. Rem. Sens. Environ., 39: 203-211. Eliasson, I., 1991. Urban geometry, surface temperature and air temperature. Energy and Build., 15-16: 141-145. Ellefsen, R., 1990. Mapping and measuring buildings in the canopy boundary layer in ten U.S. cities. Energy and Build, 15-16: 1025-1049. Gallo, K.P. and Owen, T.W., 1999. Satellite-Based adjustments for the urban heat island temperature bias. J. Appl. Meteor., 38(6): 806-813. Grimmond, C.S.B. and Oke, T.R., 1999. Aerodynamic properties of urban areas derived from analysis of surface form. J. Appl. Meteor., 38: 1262-1292. 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