Ludovic Basly

Francois Cauneau

Thierry Ranchin

Lucien Wald
email: wald@cenerg.cma.fr

ERS SAR IMAGERY FOR URBAN CLIMATE STUDIES

Keywords: SAR imagery, urban microclimate, air quality, roughness

This study investigates the potentialities of ERS SAR imagery for the urban microclimate and air quality, over the city of Nantes, France. The temporal variability of the SAR signal over the city has been assessed by analyzing five images in descending mode. Beside the speckle effect, the quality of the signal is highly variable from one image to the other. Meteorological effects. make contrasts between objects and their surroundings to be more or less pronounced. Urban features are mostly present in each image, but the structures are not always well perceived within a single image. It is concluded that it is necessary to have several images. Their redundancy allows a better exploitation of the urban features. Further it decreases the level of speckle. Screening of the average SAR image clearly indicates that the perception of the roads is highly dependent on the flight direction of the spacecraft. The main factors for the perception of the morphological features are the height of the buildings, its orientation relative to the spacecraft orbit, its horizontal surface, its materials. Multiresolution analysis, by means of wavelet transform or structure function, provides a good discrimination between unbuilt areas, residential areas, industrial areas, and large groups of buildings. This preliminary study has demonstrated that urban morphological features and their typologies with relation to the air flow drag were wellperceived in SAR imagery once properly processed. Further studies are required to assess definitely the benefits and the limits of such images in urban microclimate and air quality.

INTRODUCTION

The city's compact mass of buildings and pavement constitutes a profound alteration of the natural landscape, resulting in a large number of microclimates [START_REF] Carnahan | An analysis of an urban heat sink[END_REF][START_REF] Landsberg | The Urban Climate[END_REF][START_REF] Oke | Boundary Layer Climates[END_REF]Terjung, O'Rourke, 1980). These microclimates may be revealed by the existence of the socalled urban heat islands where changes in the temperature of the atmosphere may reach several degrees compared to that of the neighbor rural area. The complex and changing mosaic of heat and cold islands influences urban ecology in a variety of ways by altering e.g., the health and physiological comfort of humans, cooling and heating requirements, vegetation, and zoological habitats. The heat islands also produce convection cells and associated air pollution diffusion patterns with increases in cloud coverage, precipitation and fog. Various scales should be taken into account in studies of urban climate, from several hundred of kilometers to the very small scales at the pedestrian level [START_REF] Landsberg | The Urban Climate[END_REF][START_REF] Oke | Boundary Layer Climates[END_REF][START_REF] Price | Assessment of the urban heat island effect through the use of satellite data[END_REF]. The present investigation aims at the assessment of the potentialities of ERS SAR imagery for the urban micro climate and air quality, namely urban morphological features and their typologies with relation to the air flow drag. The selected site is the city of Nantes, along the Loire River, west of France. The investigation has three consecutive steps. The time variability of the SAR signal is analyzed in order to check whether several images may provide an useful information over a city. That demonstrates the relevance of the SAR signal for the study of urban features. Then the mean image is visually inspected with respect to a map of the city. It clearly shows the main features, that proves the significance of the SAR signal in this purpose. Finally, a mathematical method is devised for the automatic discrimination of the districts with respect to the aerodynamic roughness of the ground.

ACQUIRED IMAGE AND PREPROCESSING

Five SAR images were provided by ESA, from October 1994 to April 1995. Radial direction is almost East West. The images were geometrically modified as follows. Six consecutive pixels belonging to the same column were averaged and replaced by their average. This reduces the number of lines and results into an approximately squared pixel of 25 m. The best image was geometrically rectified in order to fit a map with a scale of 1/100 000 in Lambert III projection by means of a bicubic interpolation, and the result constitutes the reference image. The other images were rectified with respect to this reference. The speckle was not filtered out in each image. Several tools are available which are respectful of the most pronounced structures. However we have preferred not to alter the structures any further after the geometrical rectification. The morphological features of interest are constant within the time span of our data set. The first step in our analysis is to assess the temporal variability of the SAR signal over the city. All images have been taken in descending mode, thus reducing the influence of the acquisition geometry. The whole set of images has been inspected visually and the mean image as well as the differences between the mean and each image have been constructed from the five superimposable images. The mean image is taken as the first component computed from a principal component analysis. This component comprises about 80 % of the total variance. It has been found that beside the speckle effect, the quality of the signal was highly variable from one image to another. The discrepancies in the observation of the major elements of the scene were mostly explained by meteorological effects. According to the wind vector (speed and direction), contrasts between the river and its surroundings may be more or less pronounced, due to changes in wave regime. Hence the wind has a strong influence on the detection of bridges and of natural or artificial banks. It has been found that the direction has a greater effect than the speed of the wind. Rainfall has also an effect upon the quality of the image. The dielectric constant is a function of the soil humidity: therefore contrasts between natural or vegetation areas and built areas depend also upon the quantity of rain fallen in the time period before the acquisition date. Urban features are present in each image. Each image provides a good overall description of the structures. However because of the changing quality, the structures are not always well perceived within a single image. We conclude that it is necessary to have several images. Their redundancy allows a better exploitation of the urban features. Further their averaging decreases the level of speckle without using sophisticated speckle filters which usually degrade the structures.

INTERPRETATION OF THE MEAN IMAGE

Figure 2 displays the mean image. The visual inspection demonstrates the importance of the relative direction of the target with respect to the radial direction of the radar wave. If the relative direction is perpendicular to the radial direction, then this object is clearly visible, even if it is flat such as a road or a railway track within a flat area. If the object is orientated in the same direction than the radar wave, then it is not visible. This is the case for the central station of Nantes and of the large railway complex in the western part of the Beaulieu island. However if the same object is surrounded by e.g., buildings reflecting the radar signal, it will be perceived because of the created contrast. The material of the objects is also important. For example, the group Malakoff is made of several large buildings of about 20 stores each. This group does not appear in the image because the buildings are covered of ceramics which do not reflect the radar signal. Regarding the main urban features, we conclude that • the industrial buildings are well perceived and bright (i.e. highly reflective), • the large buildings are well perceived,

• the areas comprising old buildings with more than one store are well perceived if they are mostly orientated perpendicular to the direction of propagation of the radar wave, • the residential areas are homogeneous and low reflecting • the unbuilt areas are low reflecting The morphological features are likely related to the aerodynamic roughness parameters of the ground which influence the air turbulent flow. These parameters are the roughness length (noted z 0 ) and the zeroplane displacement. They are useful to describe and quantify the turbulent way the air flows above the ground and the structure, the reduction in wind speed and accordingly in the air turbulent mixing. They depend upon the nature of the ground and of its geometry, e.g. the buildings, their shape, their height, their spacing, their orientation with respect to the air flow, É. The main factors for the perception of these morphological features are • the height of the buildings (mean and variance),

• their orientation relative to the spacecraft orbit,

• their surface onto the ground,

• their materials 5. CLASSIFICATION OF DISTRICTS WITH RESPECT TO AERODYNAMIC ROUGHNESS [START_REF] Scherer | Roughness parameters derivation from ERS1 and LandsatTM satellite data for the agglomeration of Basel / Switzerland[END_REF] have conducted a study for the classification of the city of Basel (Switzerland) with respect to aerodynamic roughness parameters. They computed the principal components of a set of three ERS SAR images. Then they performed a multiple linear regression analysis between the first two components and z 0 values taken from the literature. They concluded that SAR images may be used to map the roughness length in the city of Basel. Obviously the found relationship strongly depends upon the SAR images used for this study and maybe of the site. This prevents the relationship to be used elsewhere or with other images. In order to alleviate this shortcoming, the present study investigates some mathematical operators which are a bidimensional function of the urban structures, which provide a good discrimination of the districts with respect to the aerodynamic roughness parameters, and which can be normalized in order to render them invariant with respect to the set of images and of the site, possibly. Then, following the work of Scherer et al., a relationship may be devised by a multiple linear regression analysis, using z 0 values taken from the literature. Finally the SARderived image may be classified in terms of roughness length.

Figure 1. Mean image computed from the five SAR images. The Loire river appears in grey, crossed by several bridges in bright. In dark are the major roads, and the airport in the lower left corner. The island is the island of Beaulieu, and is part of the city of Nantes. The area is mostly comprised of urban areas, but also of some agricultural lots and woods, which are not distinguished each from the other in this image.

Obviously the roughness is a function of the scale of concern. Therefore tools for multiresolution analysis have been applied onto the mean image to extract the relevant information at various scales. Two operators have been found to be the most efficient with respect to their quality in discrimination and their easiness in use and analysis: the multiresolution analysis, coupled with a wavelet transform, and the structure function, also called variogram. It is found that the multiresolution analysis is well suited to distinguish groups of buildings, with typical scale of about 100 m. This approach provides also a good discrimination between unbuilt areas, residential areas, industrial areas, and large groups of buildings. Structure functions give very similar results. Their degree of anisotropy is a function of the density and type of buildings, and of the overall orientation of the area. It depends upon the scale. Another parameter is the variance of the sample, which is given by the value for the largest scale. The closer to the pixel size the typical size of the objects and the more homogeneous the district, the smaller the variance. Privileged directions within a district and heterogeneous district increase the variance. The last parameter of importance is the value of the structure function for the scale equal to one pixel (the nugget effect). This value is comprised of the non structured noise within the image (i.e. the speckle), which has been reduced by the averaging of the five images, and of the subpixel variance, that is of the heterogeneities having a scale smaller than, but close to, the pixel size. The more heterogeneous a district at subpixel size, the larger the nugget effect. For example, Figure 2 exhibits the structure function for a district made of spaced large buildings (West Beaulieu island). In this district, the storage buildings are located along the docks, with metallic parts, and components perpendicular to the radial direction. These components are clearly visible in the SAR signal while the radial components are not or less sensed. This induces a larger signal in the EW direction than in the NS one, which creates an anisotropy in the structure function for sizes larger than about 70 m. The structure function exhibits a finite variance for the largest pixel sizes. This means that the size of the sample (here 7 pixels, that is about 200 m) is larger than the typical size of the structures in this district. It follows that the structure function is a suitable tool to discriminate types of buildings and their organization with respect to the aerodynamic roughness parameters.

CONCLUSIONS

This study has shown that the main morphological features within a city are mostly present within a SAR image. However, the quality of the signal is highly variable from one image to the other. The discrepancies in the observation of the major elements of the scene were mostly explained by meteorological effects. Because of this change in quality, the structures are not always well perceived within a single image. It is concluded that it is necessary to have several images. Their redundancy allows a better exploitation of the urban features. Further their averaging decreases the level of speckle. The screening of the average SAR image clearly indicates that the perception of the roads is highly dependent on the flight direction of the spacecraft. The morphological features are likely related to the ground roughness. The main factors for the perception of these morphological features are the height of the buildings (mean and variance), its orientation relative to the spacecraft orbit, its surface onto the ground, its materials. Relevant processing has been performed to the mean image to extract the relevant information at various scales. Multiresolution analysis, by means of wavelet transform or structure function, provides a good discrimination between unbuilt areas, residential areas, industrial areas, and large groups of buildings. Given the importance of the orientation of the target relative to the spacecraft orbit, further investigations should be made using images taken at various orientations. Image processing techniques are to be further developed and carefully assessed for an automatic detection and classification of morphological features. Campaigns of groundmeasurements are necessary to establish quantitative relationships between the properties of these morphological features as observed in the SAR imagery and the roughness length. This preliminary study has demonstrated that urban morphological features and their typologies with relation to the air flow drag were wellperceived in SAR imagery once properly processed. It is concluded that SAR images have large potentialities in the domain of urban microclimate and air quality and that further studies are required to assess definitely the benefits and the limits of such images.

Figure 2

 2 Figure 2 Structure function for a district made of spaced large buildings. The left graph (3.a) shows the structure function in 3D, the right graph (3.b) shows its projection (in isoline) onto the xy plane. Pixel size is 25 m.


L Basly

F Cauneau

C Couvercelle

T Ranchin

L Wald

SAR IMAGERY FOR URBAN AIR QUALITY

This study focuses on the assessment of the potentialities of the Synthetic Aperture Radar imagery to study urban micro-climate and air quality. In urban area, air quality is quite dependent on the air flow drag which is influenced by the aerodynamic roughness parameters of the ground. These parameters are linked to the urban structural features and their typologies. They characterise the evolution of the vertical wind profile with the altitude. To extract structural features, the structure function (also called variogram) is processed on ERS images of the city of Nantes (France). A classification according to the structure function is done that leads to a mapping of the aerodynamic roughness by allotting a roughness parameter to each class.

INTRODUCTION

Streets network and buildings modify the aerodynamic roughness of the ground and alters the natural landscape. The urban aerodynamic roughness generates turbulence which acts on the dispersion of pollution layers and also on streets ventilation. The alteration of the natural landscape creates microclimates such as heat islands where atmospheric reactions are increased [START_REF] Oke | Boundary Layer Climates[END_REF]. Numerous studies deal with the modelling of the air flow drag in relation with the air pollutants diffusion in and above a city. These modelling of the urban climatology need the knowledge of aerodynamic roughness parameters [START_REF] Bottema | Urban roughness modelling in relation to pollutant dispersion[END_REF]. These parameters are the aerodynamic roughness length z 0 and the zero displacement height z d . They characterise the evolution of the vertical wind profile. They are related to the urban morphology which influences the turbulent air flow.

This investigation particularly aims at the assessment of the potentialities of SAR imagery for the extraction of urban features and their typologies. The studied site is the city of Nantes, along the Loire river, west of France. At first, we have assessed the time variability of the multitemporal SAR images over the city. Images are averaged for increasing the quality of information over the city. The mean image demonstrates the relevance of the SAR imagery for the study of urban features. Then the mean image is visually inspected with respect to a map of the city and aerial photographs. Main urban features of our interest are present, that proves the significance of the SAR imagery in urban detection. Structure function is used for the automatic discrimination of the districts related to the aerodynamic roughness of the ground. Indeed, in a previous study, we have shown that the structure function was a suitable tool to discriminate types of buildings and their organisation [START_REF] Basly | ERS SAR imagery for urban climate studies[END_REF]. A classification of the mean image according to the structure function is made. Finally, a map of aerodynamic roughness based on this mathematical method is made, which demonstrates the usefulness of the SAR imagery for urban air quality.

DATA USED AND TIME VARIABILITY

The data are ERS-1 and ERS-2 SAR images provided by ESA. The set of data contains seven images in Precision Image format (PRI), taken from May 1995 to October 1996. All images have been taken in descending mode. Radial direction is almost East -West. In PRI format the speckle is slightly decreased by a multilook processing. The pixel size is 12.5 meter in both directions. The images were geometrically corrected to fit a IGN map with a scale of 1:100 000 in Lambert III projection. The speckle is not filtered out in images to not alter the structures any further after the geometrical rectification.

The time variability of the SAR signal over the city is assessed. The morphological urban structures are always present in each image. We can consider that these structures are invariant in the time span of our dataset. Beside the speckle effect, meteorological conditions affect the signal quality. The wind vector (direction and velocity) mostly affects the contrast between rivers and their banks, but also between rivers and bridges. Rainfall affects the contrast between urban area and vegetation area. Urban structures are perceived in a single image, but the change in quality avoid a good interpretation. So, we have averaged multitemporal images. This average decreases the level of speckle, without using sophisticated filters, preserving the structures. It allows a better discrimination of the urban features.

PHOTOINTERPRETATION OF THE SAR MEAN IMAGE

Figure 1 displays the mean image obtained by averaging the six best images. Major roads are well perceived, they appear in dark as the rivers. Arable land and unbuilt areas appear in grey. Built-up areas appear in bright. The visual inspection demonstrates the importance of the geometry of the object because in urban area reflection backscattering prevails on diffuse backscattering [START_REF] Gouinaud | Traitement des images satellitaires pour la détection d'agglomérations[END_REF][START_REF] Dong | Radar backscatter analysis for urban environments[END_REF]. The relative orientation of the object with respect to the direction of the radar wave also affects the backscattering. If the relative orientation of the object is perpendicular to the radar wave direction then the backscattering is high, and the object is clearly visible. If the relative orientation and the wave direction are the same then the object is less visible and even not visible, except for objects with metallic elements such as railway track, bridge, roof of commercial and industrial buildings, etc. An example of the importance of the orientation is the Malakoff group which is made, in part, of eleven 20storey buildings of 20 meters wide. This group is located on the north of the Loire river and on the east of the downtown. It covers a surface of approximately 10 km 2 . The hip of the buildings face the east, so the frontages do not face the radar wave and the backscattering is very low. Indeed, the backscattering is similar to the waste ground area which is located on the north of the group. On the contrary, we can see a large imaging anisotropy situated in the south of the town of Rezé, in the south of the Loire river. This anisotropy is the result of the backscattering of a shopping market which is about 140 meters long and 80 meters wide. This anisotropy allows the determination of the relative orientation of this shopping center, and it approximately faces the radar wave.

Concerning the roads or the streets, they appear dark because of the specular reflection. However, if they are situated in a high density built-up area and if they are transversally orientated then they are not visible.

Regarding the main urban features, we conclude that :

• the industrial buildings are well perceived and highly reflective (i.e. appear in bright), • the areas comprising buildings with more than one store are well distinguished if they are mostly orientated perpendicular to the direction of propagation of the radar wave,

• the residential areas are homogeneous and low reflecting (grey tone),

• the unbuilt areas are low reflecting (dark tone).

It appears clearly that SAR imagery is linked to the structural features of the urban area. The main factors for the perception of structural features are :

• the height and the width of the buildings (mean and variance), • the orientation relative to the spacecraft orbit,

• the surface onto the ground,

• the density of buildings (i.e. the number of buildings per area unit), • the contrast between built-up area and the surrounding,

• the materials of the buildings.

These structural and morphological features alter the roughness of the ground which influences the air turbulent flow, hence they are linked with the aerodynamic roughness parameters z 0 and z d .

AERODYNAMIC ROUGHNESS

The aerodynamic roughness length, z 0 , characterises the surface state and characterises the interaction of the air flow with the ground surface. z 0 is dependent on the irregularities of the ground [START_REF] Monin | Statistical Fluid Mechanics : Mechanics of Turbulence[END_REF]. Thus, z 0 is influenced by the local morphology.

The zero-displacement height (or zero-plane displacement), z d , represents the physical height of the obstacles on the ground surface. z d is used for method of calculation and it is not fundamental for the understanding of the phenomena happening near the ground.

Both roughness parameters take place in the description of the vertical wind profile U(z) which allows the knowledge of the evolution of the wind velocity with the altitude above the ground surface.

On the assumption of neutral conditions i.e. when having an air flow with a constant momentum above an infinite and homogeneous surface, the vertical variation of the horizontal mean velocity can be described with the formula (1) :

U  z = u K ln  z-z d z 0  (1)
where :

• z is the height above the ground,

• u * is a scaling variable representing the friction velocity, • K is the Von Karman constant. U(z) is used in modelling of the diffusion of pollutants layer above cities but also for modelling the streets ventilation [START_REF] Bottema | Urban roughness modelling in relation to pollutant dispersion[END_REF][START_REF] Mills | An urban canopy-layer climate[END_REF].

The relationships which link z 0 and the local morphology are complex, and the evaluation of z 0 is complex too.

We have demonstrated that local morphology, which is related to the aerodynamic roughness length, influences SAR imagery. Hence we have explored the possibility of using SAR images to derive aerodynamic roughness map of cities.

THE STRUCTURE FUNCTION AS AN INDICATOR OF THE LOCAL VARIABILITY

It is found that the structure function (also called variogram) is well suited to distinguish different kind of built-up area. Indeed, the structure function respect the anisotropy and the variance of the considered area. The degree of anisotropy of the structure function is a function of the density, of the type of buildings, and of the overall orientation of the area. The variance of the sample is given by the value of the larger scale. The closer to the pixel size the objects and the more homogeneous the district, the smaller the variance. We have used a bidimensional structure function in order to have information in both directions [START_REF] Basly | ERS SAR imagery for urban climate studies[END_REF].

Figures 2, 3, and4 display example of structure function processed on different urban area. Figure 2 exhibits the structure function for the Pornic bridge. This metallic bridge crosses the Loire river, south of the Beaulieu island. The bridge is north-south oriented and appears in bright. The structure function is totally anisotropic, showing very high correlation between north -south pixels (variance is about zero), and very low correlation between eastwest pixels even for short distance. Further, finite variance means that the size of the sample (here 7 pixels, that is about 120 meters) is larger than the typical size of the structures observed. Figure 3 shows the structure function for downtown. This part of the city is situated on the north of the Loire river. There is no privileged direction for small scales (here scale is taken as a distance). At larger scale the north -south direction imposed by two main streets is reinforced by large administrative buildings lining these streets. Accordingly the structure function is isotropic for small scales (up to 50 meters) and becomes anisotropic with a larger variance in the east -west direction. Further the variance is finite and the maximum value is not high, because this part of the city is homogeneous, and the typical size of the structures are close to the pixel size. In figure 4 is displayed the structure function of a residential area, the Grillaud district. This district is situated on the west part of the city, and it is made of small buildings and houses barely spaced. There is no privileged direction and no typical scale for the objects. Hence the structure function is isotropic for all scales under concern, and the variance is not finite, indeed the variance increases as the size of the sample increases.

We conclude that the structure function is a suitable tool to discriminate different types of builtup area and their structures related to the aerodynamic roughness. For the classification, in order to avoid excessive computing time, we have characterised the structure function with only nine points instead of 64. These points represent the following information :

• anisotropy,

• slope,

• orientation of the observed structure, • maximum level.

After extracting the characteristic points, nine image layers are built. Then an unsupervised hierarchical descending classification is made using hash coding processing [START_REF] Albuisson | Optimisation des traitements des images multi-sources. In 1 er Colloque international[END_REF].

Comparing the area covered by each class with the mean image, the IGN map and also with aerial photographs, we have found correspondences between classes and urban local morphology (density in built area, mean height, height variability, orientation, spacing of buildings,...). It means that this classification corresponds to a classification of the urban morphology. We have seen that this morphology is related to the aerodynamic roughness.

Hence, a mapping of the aerodynamic roughness is possible by allotting an aerodynamic roughness parameter to each class.

MAPPING OF THE AERODYNAMIC ROUGHNESS LENGTH

The z 0 values are taken from the literature [START_REF] Scherer | Roughness parameters derivation from ERS-1 and Landsat-TM satellite data for the agglomeration of Basel / Switzerland[END_REF]. z 0 is 0.01 meter for rivers, up to 3.0 meter for industrial buildings. Figure 5 displays the aerodynamic roughness length map of the city of Nantes. The brighter the grey level, the larger the z 0 .

Looking at figure 5 we recognise the shape of the Loire river and guess the Beaulieu island. The valley of the Erdre river and the airport are also visible and appear in dark, so a weak z 0 value. The boundary between urbanised area and country is not conspicuous. The result is difficult to interpret because some classes have close z 0 values, so they have close grey level. Further, the structure function gives information for a sample of 8 pixels in both directions, so for a sample of about 140 meters in both direction. This precision is sufficient to describe different districts, but their boundaries are not respected.

The accuracy of the map has not been assessed yet. A means to assess the accuracy would be to compare the results with measurements of z 0 values or to their by means of conventional methods.

CONCLUSIONS

The main urban features related to the aerodynamic roughness are mostly present within a SAR image. Averaging multitemporal data is necessary due to the high variability of the quality of the images. This average decreases the speckle and allows a better discrimination of the urban features that shows the usefulness of SAR imagery for urban studies.

The orientation and the geometry of the objects with respect to the radar wave direction play a major role for them to be perceived.

A method has been devised to map the aerodynamic roughness length z 0 over the city of Nantes that proves the relevance of SAR imagery for studies of urban air quality.

Independence of the method with respect of data used has been assessed by applying it on the set of data used in a previous study [START_REF] Basly | ERS SAR imagery for urban climate studies[END_REF].

Comparing the results we have found similarity although the formats of the data were not the same (Single Look Complex vs PRI). It demonstrates that the method used is reliable.

Accuracy of the computed maps is still to be assessed.

  STRUCTURE FUNCTIONConsidering the results obtained with the structure function, a classification of the mean image is done by computing the structure function for each point of the image.

Figure 2 .

 2 Figure 2.

Figure 3 .

 3 Figure 3.

Figure 4 .

 4 Figure 4.

L. Basly, F. Cauneau, C. Couvercelle, T. Ranchin, L. Wald

L. Basly, F. Cauneau, C. Couvercelle, T. L. Wald

ACKNOWLEDGEMENT

The authors are indebted to ESA which has provided the ERS data.


Ludovic Basly
email: ludovic.basly@cenerg.cma.fr

Lucien Wald

Remote Sensing and Air Quality in Urban Areas

This paper aims at showing the potentialities of the Earth observation (EO) data for the knowledge of the atmospheric pollutants concentration field over metropolitans areas. At present, deterministic modeling and decision support systems only use pollutants maps obtained with mathematical methods. But, given the few scattered stations measuring the pollutants concentrations, an accurate map of the spatial distribution is almost impossible with standard methods. We found a strong correlation between the black smoke (BS) concentrations and data from sensor TM6 of the Landsat satellite. The map derived from the EO data gives errors close to those obtained by standards methods. The representation is nevertheless closer to the real urban environment. In a near future, EO derived products could be treated in near real time in conjunction with pollutants measurements to provide accurate information to decision maker.

Introduction

In the western Europe more than two thirds of the population live in urban areas and urbanization is still continuing [START_REF]EEA: Europe's Environment: The Second Assessment[END_REF]. It is found that transport is the main source of atmospheric pollution in cities and the number of personal car is still growing [START_REF]EEA: Europe's Environment: The Dobris Assessment[END_REF]. Furthermore, the air pollution can be exacerbated by local weather conditions and wind patterns leading to phenomena such that heat (or cold) islands which influence the chemical transformation of pollutants. Hence the urban air pollution is a very complex phenomenon involving a lot of parameters and processes (physics, chemistry, meteorology, geography, and other environmental sciences) and links between them are not fully understood.

It is obvious that good air is a prerequisite for the health and the well-being of human. Several studies demonstrated that in France the atmospheric pollution leads to an increase of 4% in the risk of anticipated deaths, and that 265 deaths/year may be directly attributable to air pollution [START_REF] Ecoiffier | L'air pollué est certifié mortel[END_REF]. A survey conducted by the World Health Organization (WHO) shown that, in the world, transport pollution would cause 80 000 anticipated deaths/year [START_REF] Perez | Les villes européennes asphyxiées par la voiture[END_REF]. We can also mention that WHO has estimated, for a European standard city, that life expectancy decreases in one year, and that 14 millions of Europeans have a decrease in the vital capacity of 5% [START_REF] Zappi | Une étude de l'APPA précise l'impact de la pollution sur la mortalité et la morbidité[END_REF]. Medical studies tend to demonstrate that breathing diseases may be linked to pollution peaks and that elderly people and young children are the most affected [START_REF]ERPURS: Trois analyses pour approfondir l'étude des liens entre la pollution atmosphérique et santé[END_REF], [START_REF]WHO: Climate change and human health[END_REF], [START_REF] Nevalainen | The effect of particulate air pollution on life expectancy[END_REF]. But the links that might exist between atmospheric pollution and increasing of allergy troubles are still misunderstood and further studies requiring more measurements of pollutants concentrations are needed [START_REF] Petitnicolas | L'explosion des allergies respiratoires[END_REF]. Consequently the study of atmospheric pollution problems in metropolitans areas is gaining more and more interest, and is a growing issue among the scientific and medical community in Europe. Moreover urban air pollution becomes a critical question which rightly concerns the citizens.

Urban planners and public policy makers need tools for a comprehensive knowledge of the urban environment, for the forecasting of the air pollution and for the population information. Since 1996, in France, mayors in charge of large cities of over 100 000 inhabitants must install a measuring network. This network is managed by local organization and it is composed of several static measuring stations linked to a central computer via the phone lines thus pollution data are collected in near real time (Fig. 1 shows an example of a network structure). Recently, some network have been equipped with a laboratory van which can measure the pollution in area without stations or around static stations in order to study the representiveness of the measurement. Collected data are then used to compute an atmospheric pollution indicator (ATMO) aiming at informing the local authorities as well as inform the population of atmospheric air quality. This indicator is calculated from the NO2, SO2, O3, and particulates concentrations. The air quality network is very useful because it allows an accurate knowledge of pollutants concentration in a specific point of the town, and it is therefore a good means to warn the population of pollution danger. At present, the alert system consist in a board with a map of the area under concern showing the station location with light. If pollution data measured by a station exceed a threshold then the light turn to red indicating the place where a pollution peak happen. But given the few measuring stations which are scarcely distributed, an accurate knowledge of the spatial distribution of the atmospheric pollutants is currently impossible. However air quality organizations strongly stress that the mapping of the atmospheric pollution over a city is sorely needed.

After presenting the study area and discussing what is currently done with pollutants data for obtaining map of concentration field, we will propose a new method making use of Earth Observation data.

The Study Area and Dataset

The city of Nantes is located in Western France at 54 km from the Atlantic ocean. Air Pays de la Loire (formerly Loirestu'Air) is the local organization in charge of the air quality network in the city of Nantes and vicinity. Having an image taken by the satellite Landsat the 05/20/92 at 10:17 UT, we have used pollution data corresponding to the overpass of the satellite. In May 1992, fourteen stations were located within the urban area, twelve of which were inside the city. It has been shown that the higher the air pollution, the higher the aerosols concentration [START_REF] Renoux | L'aérosol atmosphérique : ses origines ; quelques notions sur les principales propriétés physiques des aérosols[END_REF]. So we have focused the study on that pollutant. The day of May 20 was a sunny day with clear sky and light wind from North-East. The pollution level was below the critical levels.

The Current Mapping of BS

People working with air quality networks use interpolation/extrapolation techniques in order to evaluate the pollutant spatial distribution. Some scientists use the kriging method [START_REF] Frangi | Suivi spatio-temporel de la concentration en NO x en île de France[END_REF], some others recommend the use of the thin plates interpolation method [START_REF] Ionescu | Méthodes mathématiques pour estimer le champ de concentration d'un polluant gazeux à partir des valeurs mesurées aux points dispersés[END_REF] (Fig. 2 displays an example of a BS map obtained with the thin plates method). Concerning the accuracy of the map obtained, firstly it depends on the accuracy of the measuring stations, secondly it depends on the representativeness of the measurement in its neighborhood. In fact, concentration value can highly vary depending on the side of the street it had been measured [START_REF] Croxford | Siting consideration for Urban Pollution Monitors[END_REF]. Thirdly, according to Sifakis [START_REF] Sifakis | Potentialités de l'imagerie à haute résolution spatiale pour le suivi de la réparti-tion de pollutions atmosphériques dans la basse tro-posphère. Etude du cas d'Athènes, thèse de doctorat, chimie de la pollution atmosphérique & physique de l'environnement[END_REF], for a reasonable accuracy, that is an error probability of 5%, a conventional air quality network ought to have 4 stations per 2,5 km² to find concentration values with an error of 20%. In our case the city of Nantes and vicinity should have 65 stations! The cost of a station is very expensive, so quality network use passive tubes to increase the number of data but not all the pollutants can be measured with this means.

Air quality organizations point out that an accurate mapping will allow:

• the monitoring of the whole urban area periodically, • the localisation of the main pollution sources as well as their extension,

• the indication of areas where anti-pollution efforts have to be carried out,

• the establishing of the links between the distribution of the pollution and the local morphology as well as the street network,

• the optimisation of the sitting of the measuring-stations, • the validation of the numerical models dealing with the local/regional pollution,

• the integration of pollution maps into a GIS which will allow the assessment and the prediction of environmental policies, as well as the simulation of scenarios. In order to enhance the mapping of air pollutants we propose a new method making use of EO data.

Conclusions

This first attempt of mapping BS with Landsat TM6 data encourages us to continue our investigations. The results are promising, errors are similar to that found with standard methods, but the map derived with EO data provide further information concerning the urban features and morphology.

Further studies are needed to fully understand the links between the pollutants measurements and satellite data. Next investigations will focus on the establishment of more elaborated relationships by looking for areas which are similar in many aspects to the measuring sites. These aspects include the geographical and physical properties of the site and its neighborhood, which may be expressed by the spectral signature sensed by the satellite. Then we will be able to build a library of models linking the EO and pollution data as a function of several parameters including the meteorological conditions. Problem of very cloudy or rainy days, during which the satellite cannot observe the ground, are to be solved. This library models the spatial distribution of the pollutants. In an operational phase, measurements are collected by the processing center. An analysis is made of these data and external parameters. A spatial distribution model is constructed from the library and fused with measurements to produce in near real time an accurate map of concentration field of the pollutants.

The future urban network will operationally integrate external data such as satellite and aerial images or even drone images (Fig. 1). All the available satellite images taken over the area will be used (Landsat, SPOT, ENVISAT, etc.). The lack in data will be completed by campaign making use of airplane, and also drone if needed (e.g. when pollution peaks occur). All these data will be used in conjunction with pollution data collected by measuring stations, laboratory van, Sodar, Lidar (laser detection of pollutants), and even pedestrians volunteers, in order to increase the accuracy of the spatial distribution of pollutants. EO derived products, such as 2-D and 3-D maps, will also serve as input to numerical model of pollutants dispersion. The whole data will be managed through a SIG which will allow the pollution risk assessment, the simulation of scenarios in near real time. What could be, in a near future, the structure of an air quality network integrating remote sensing data from satellites, airplanes or even from drones. At this time of integration, modeling and mapping system will be fully operational as well as fully integrated in a GIS.

Fig. 1 .

 1 Fig. 1. Structure of a current (minimal) air quality networks. In dotted line are the non-fully operational tasks.

Fig. 2 .

 2 Fig. 2. BS concentration field obtained with the thin plate interpolation method making use of the 12 available measurements.

Fig. 3 .

 3 Fig. 3. Spatial distribution of BS over Nantes and vicinity derived from Landsat TM6 data on 20 May 1992 10:17 UT. The six points denote the sites used in combination with EO data.

  Fig. 4. What could be, in a near future, the structure of an air quality network integrating

The Mapping of BS Using EO Data

The expected benefits of using EO data relative to current practices have also economic and social dimensions.

Acknowledgments

The authors are indebted to Eurimage which has provided the Landsat TM data. The authors also thank Air Pays de la Loire for providing the pollution data.

Concerning the economic dimension: establishing maps will be cost-saving; making use of maps for the sizing, the design and the implementation of the monitoring network will be cost-efficient; furthermore, the fighting against pollution will be improved by pin-pointing the most polluted areas with some impacts on costsaving in preventing health troubles.

Concerning the social dimension: maps will serve to assess the efficiency of political measures for the prevention of pollution and mitigation of its effects, and as a consequence, maps will help to preserve a better quality of life for the citizen.

Several studies have shown the possible relationships between satellite data and air pollution [START_REF] Sifakis | Potentialités de l'imagerie à haute résolution spatiale pour le suivi de la réparti-tion de pollutions atmosphériques dans la basse tro-posphère. Etude du cas d'Athènes, thèse de doctorat, chimie de la pollution atmosphérique & physique de l'environnement[END_REF], [START_REF] Basly | Satellite Data for the Air Pollution Mapping[END_REF], [START_REF] Finzi | Landsat images of urban air pollution in stable meteorological conditions[END_REF], [START_REF] Brivio | Atmospheric pollution and satellite remotely sensed surface temperature in metropolitan areas[END_REF], [START_REF] Sifakis | Quantitative Mapping of Air Pollution Density Using Earth Observations : a New Processing Method and Application to an Urban Area[END_REF], [START_REF] Retalis | Assessment of the distribution of aerosols in the area of Athens with the use of Landsat Thematic Mapper data[END_REF], [START_REF] Wald | Observing Air Quality over the City of Nantes by Means of Landsat Thermal IR Data[END_REF]. We propose the use of the thermal infrared image (Landsat TM6) for which a strong correlation was found with some pollutants and more particularly with BS. After a least-squares regression, a linear relationship was found between 6 of the 12 pollution data and the corresponding digital count (radiance) of the TM6 image. The 6 remaining pollution data have served to evaluate the accuracy of the map. The relative rms error is about 80% which is fairly high but less than interpolation rmse. This relation was applied to each pixel of the image in order to derive a spatial distribution of BS over Nantes and vicinity (Fig. 3 shows a BS map obtained with EO data).

The authors are aware of the limitations of such a map and stress that not only the aerosols in the atmosphere influence the satellite measurement but also the nature of the landscape.


Ludovic Basly

François Cauneau

Thierry Ranchin

Lucien Wald

SAR imagery in urban area

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

Almost 70% of the Europe's population live in cities, and urbanization is still continuing (EEA 1998). That is why urban planners and decision makers need tools for a comprehensive assessment of the urban environment. A means for a better understanding of urban areas are remote sensing techniques [START_REF] Bonn | Précis de Télédétection[END_REF]. Satellite imagery can significantly improve the monitoring of cities in a wide range of applications, e.g., the detec tion of urban changing, mapping roads and streets [START_REF] Couloignier | Benefit of the future SPOT5 and of data fusion to urban roads mapping[END_REF], Tupin et al. 1996), mapping ur ban demarcation (Weber 1995), mapping urban air pollution [START_REF] Basly | Satellite Data for the Air Pollution Mapping[END_REF]Basly et al. 1999). Nevertheless the number of studies using SAR data is much lower than that using optical ones (visible and infrared) notably concerning investigations on urban areas (Henderson & Xia 1997, Guerre 1995), though these studies brought to the fore the advan tages of using radar images. Indeed, radar signal is sensitive to the geometry of urban fabrics, and is used for detecting builtup area as manmade fea tures [START_REF] Fellah | Multitemporal ERS1 SAR data in environmental studies : researching a quantita tive approach for soil moisture retrieval[END_REF][START_REF] Carlotto | Detecting ManMade Features in SAR Imagery[END_REF][START_REF] Dousset B | Interpretation of ERSSAR Images over Urban Surfaces[END_REF], Xia & Henderson, 1997[START_REF] Lortic | Abidjan 5 étoiles. L'image radar, un luxe inutile ou un recours nécessaire?[END_REF]. In addition, radar imagery may provide the third dimensional information [START_REF] Dong | Radar backscatter analysis for urban environments[END_REF]). Hence, SAR imaging techniques are relevant tools to analyze urban land use patterns. In that perspective, this paper examines the major factors influencing the detection of the urban fabrics, that is the orientation, the buildings materials, the meteorology, the SAR image format, and the quality of the data.

SAR DATA AND STUDY SITE

Data and Preprocessing

Two sets of images were used. One set of 5 ERS SAR images in Single Look Complex (SLC) format, and one set of 7 ERSSAR images in Precision Im age (PRI) format. That represents 12 images span ning a time of almost 2 years, from October 1994 to October 1996. All data were taken in descending pass: radial direction is almost EastWest. It is worth noting that SLC data strongly differ from PRI data. On the one hand, SLC data are complex data, in slant range geometry (i.e. the range resolu tion varies with the incidence angle), and on the oth er hand, PRI data are system corrected, multilook processed (in order to reduce speckle noise), and in ground range geometry. Furthermore, the pixel size is also different (ESA 1993). After reducing the SLC data to magnitude images, they were remapped to a PRI image taken as a reference. The speckle was not filtered out in each image. Sev eral tools are available which are respectful of the most pronounced structures (see e.g. Ranchin & Cauneau 1994[START_REF] Mathieu | Speckle Reduction with Edge Preserving[END_REF]). However we have preferred not to alter the struc tures any further after the geometrical rectification, and decided to reduce the noise by making a multi temporal average for each kind of dataset. Further more, averaging the images decreases the level of Basly L., Cauneau F., Ranchin T., Wald L., 2000. SAR imagery in urban area. In : Proceedings, EARSeL Symposium 1999 "remote sensing in the 21st Century: economic and environmental applications", Valladol id, Spain, Casanova J.L., Vaughan R. eds, Balkema, Rotterdam, pp 563568.

SAR Imagery in Urban Area

L. Basly, F. Cauneau, T. Ranchin and L. Wald

Groupe Télédétection & Modélisation

Ecole des Mines de Paris BP 207,F 06904 Sophia Antipolis Tel.: 33.4.93.95.75.75,Fax: 33.4.93.95.75.35,email: ludovic.basly@cenerg.cma.fr ABSTRACT: This paper deals with the major factors influencing the detection of urban fabrics in ERSSAR images. Data, in SLC and PRI format, were acquired over the city of Nantes (West of France). The analysis of the data was performed in conjunction with aerial photographs, maps, meteorological data, as well as a field survey. The way urban fabrics and its environment, the data processing techniques, and the weather condi tions affect the radar signal was examined and discussed. It was found that large effects originate from the ge ometry of urban features, as well as their orientation relative to the spacecraft orbit. This investigation adds evidence of the fact that the specular scattering prevails over the diffuse scattering in urban area. Practical conclusions concerning the capabilities and the limitations of ERSSAR imagery are drawn. speckle preserving the structures, and this simple processing decreases the effects of the variability of the multitemporal SAR images [START_REF] Stroobants | Une approche pragmatique de la fu sion multitemporelle des images ERS1[END_REF][START_REF] Basly | ERS SAR imagery for urban climate studies[END_REF], 1999).

The Study Area

The city of Nantes is located in Western France at 54 km from the Atlantic ocean. Geographical coordi nates are 47.23 N and 1.55 W. That location explains the oceanic climate which is quiet mildly. The city is crossed by the Loire river, and a natural island, the socalled "Beaulieu Island", is part of the city. Nantes comprises about 470 000 inhabitants, and was a very active harbor some centuries ago with many exchanges with America and Africa.

INTERPRETATION OF THE ERSSAR MEAN IMAGES

Screening the two mean images, we notice that the PRI one (Fig. 1) is smoother than the SLC one, due to the multilook processing of the PRI which reduces the speckle noise. In both images, we observe a high variability of the backscatter due to the complexity of the urban landscape. Indeed, a town contains a wide variety of length scales. Large scales are pro vided by the ground and buildings themselves, while the small scales by the roughness of the surfaces (Taket et al. 1991). In urban areas, the specular reflection prevails over the diffuse scattering because of the geometrical properties of the objects [START_REF] Dong | Radar backscatter analysis for urban environments[END_REF]. Three mechanisms of specular scattering dominate:

• the simple bounce from tilted roof,

• the double bounce from wallground,

• the triple bounce from wallwallground.

The Figure 1 shows the values of the backscatter magnitude according to different type of areas. Both images were analyzed in detail conjointly with aerial photographs, maps, meteorological data, as well as a field survey, in order to assess the influ ence of the factors abovecited. 3.1 Artificial Areas

Downtown and Dense Urban

The center town mainly comprises tall buildings with flat and tilted roofs. It is the ancient part of the city, and the density of buildings is large (Fig. 2 area (A)). The backscatter is large in average, but highly variable. The variability is due to the changes in street orientation and in building density. A strong backscatteringecho come from two groups of buildings located on the both sides of a green park (Fig. 2 (B)), enhanced by the low backscattering of the park. Nevertheless, one cannot conclude neither on the major orientation of the buildings, nor on the number of buildings. Large anisotropic backscattering may occur when particular conditions are combined (Fig. 2 (C)). If a street is aligned with the flight direction of the satel lite (i.e. when the illumination azimuth is orthogonal to the street direction), and if the ratio building height/street width satisfies a condition relative to the incidence angle, favorable multiple reflections occur, resulting in a high backscatter return (Gouin aud 1996). The street direction may be thus deter mined. Metal elements on the roofs generate enhanced dif fuse backscattering. But, this is an isotropic backscattering, and the major building orientation cannot be deduced. When the density is large, some buildings may be hidden from the radar illumination by the other buildings. This shading effect results into a weak backscatter. In addition, on flat roofs, the radar signal is specu lary reflected, so there is no return to the satellite.

Residential and Mean Urban

Most of the residential houses are single or two storeybuildings with tilted roof (Fig. 2 (D)). Like downtown there is no major orientation. In average the backscattering is lower than downtown. High backscattering may arise from tilted roof fac ing the radar wave. The roof can be considered as a rectangular smooth surface (i.e. a mirror, by analogy with the optical physic). Such a surface gives very low radar return except in specular condition at near vertical incidence (i.e. when the incidence angle is close to 0°) (Simonett & Davis 1983). In low density area, if a wall faces the illumination azimuth, a double bounce mechanism can occur re sulting in a high return signal. In that case, the resi dential house can be compared to a dihedral corner reflector. The backscatteringecho of the double bounce mechanism is lower than single bounce from tilted roof, because there is a loss of energy for each reflection. In both cases, the orientation and the bulk size of the buildings greatly affect the return of the backscat tered energy. For example, a residential area made of eleven buildings with twenty stores, covering a sur face of approximately 13 km², has a weak return (Fig. 2 (E), Fig. 2). The low return is mainly due to the orientation of the buildings: firstly the frontages are perpendicular to the ground with a wave incident angle far from 0°, secondly they cover a large sur face and do not face the radar beam. Accordingly, neither the single bounce mechanism nor the double bounce one can occur.

Industrial and Commercial

In those areas, buildings are often large, tall, with flat metal roof, and density is low (Fig. 2 (F)). For such building specular reflection occurs on the flat roof, and double or triple bounce mechanisms occur on the walls. Large returns occur if buildings face the illumination azimuth. In this case, they are well detected and their orientation and length (only one dimension) can be measured (Fig. 3). Otherwise, the buildings may be not detected or their dimensions remain unknown.

Other Urban Features

3.1.4.1Bridges

All the bridges crossing the Loire river are visible. The radar return is large, because bridges are transversally oriented according to the radar wave. In addition, bridges are in contrast with their envi ronment i.e. the Loire river. We note that two bridges built after the aerial photographs were taken (1993), appear on the ERSSAR images (Fig. 4). Nevertheless, most of the bridges crossing the Erdre and the Sèvre river are longitudinally oriented, so they do not appear unless they are made of metal.

3.1.4.2Roads, Streets and Railway Tracks Roads and streets are smooth surfaces, and the backscatter return is always low. They appear in dark in the images when oriented along the wave vector (Fig. 2 (G)). Otherwise, they can be detected if their width is large enough, the critical width be ing a function of the height of the lining buildings through the shading effect, the type of building, the density of buildings, and the presence of vegetation, water bodies, carpark ... Railway tracks appear in bright because large diffuse backscatter arise from electrical wiring and rail made of metal (Fig. 2 (I)). The detection of railway tracks is subjected to their neighborhood whatever their orientation. If the backscatter return of the neighborhood is equal or larger than that of the rail ways, the latter be undetected. Otherwise, the rail ways may be shaded by high buildings.

3.1.4.3Airport

The airport appears clearly in the image (Fig. 2 (J)). The runway and taxiway are visible, and ap pear in dark because of the specular reflection.

Natural areas

Inland Water

Rivers appear in dark in the image because of the specular reflection on smooth surface (Fig. 2 (K)). However, by analyzing several multitemporal im ages, we noticed a strong variability in the backscat ter of the Loire river, both in time and space. We found that this variability varies according to the wave regime that modified the roughness of the riv er, and that the wind direction has a greater effect than speed.

Vegetation

Parks, sport fields and grass areas, have a very low diffuse backscatter return (Fig. 2 (L)). On the contrary, areas with trees, small shrubs, and tall veg etation may cause considerable isotropic backscat teringecho (Fig. 2 (M)). Though the intensity of this diffuse backscatter is lower than for builtup area, vegetation can preclude the detection of small urban fabrics. We can note that stadium are well detected when rounding by terraces. The contrast between the ter races and the field helps in determining the major orientation (Fig. 2 (N)). The cemeteries are also well detected by contrast with the builtup neighborhood which is brighter(Fig. 2 (O)).

CONCLUSIONS AND PERSPECTIVES

Different type of urban areas can be detected in SAR images once properly processed. In high density builtup areas (downtown) the backscatteringecho is large and rarely anisotropic except in case of favorable multiple reflections. In low density area (residential area, industrial area), the backscatteringecho may be large but is inferior, in average, to high density area. Anisotropic backscattering especially occur in industrial area where building are largesized. Though, the diffuse backscattering is not a dominant mechanism in urban area, that kind of backscatter can be larger than the triplebounce mechanism, no tably when metal elements are encountered. Areas with vegetation are generally well distin guished (parks, field), but the presence of tall vege tation within urban fabrics can lead to misinterpreta tion. The street, highways and rail networks are incom pletely detected. It is worth noting that the orientation of the urban fabrics greatly affect the backscatter return. Hence, making use of ascending and descending pass con jointly will be useful to determine the orientation of observed objects. This study adds evidence on the complexity of the interpretation of SAR data over urban areas. SAR images can not be analyzed at the pixel level as in optical imagery. Each pixel has to be analyzed with in its environment by a statistical or textural ap proach [START_REF] Carlotto | Detecting ManMade Features in SAR Imagery[END_REF][START_REF] Basly | ERS SAR imagery for urban climate studies[END_REF]. As in optical imagery, urban fabrics should be stud ied by means of multisources SAR imagery. For ex ample, future studies making use of multiincidence angles, multipolarization and multipass orbiting will be more powerful in extracting valuable urban information from SAR data. That will be performed with the Advanced Synthetic Aperture Radar of the ENVISAT satellite (ESA 1998). © IGN (c) Figure 3. The Malakoff group. Figure 2a, detail of the SAR image. The Loire river appears in dark. The Vendée bridge is clearly visible on the right. Figure 2b, photograph taken from the Beaulieu island. We have estimated the height of the higher buildings, and we have found 20 stores, so about 60 meters. Figure 2c, aerial photograph enables the estimation of the sur face covered and also the buildings count. We find approxi mately 13 km 2 of covered surface, eleven 20storey buildings, five long buildings and some other buildings. 5a is a detail of the SAR image, the size of the pixel is about 13m. Figure 5b is an aerial photograph taken in 1993 by IGN, the spatial resolu tion is about 0,7 meter. Although the shopping center don't ex actly face the radar wave, the backscattering is very large. In deed, the frontage has a considerable surface, and the carpark, in front of it, enable double bounce reflection. The detail of the SAR image features an anisotropy that allows the knowledge of the orientation of the building. The building on the left of the shopping center is not well perceived because of the shadowing effect, so the backscattering is caused by the diffuse backscat tering of the roof which is certainly a metal one.

Figure 1 .

 1 Figure1. The return is large and highly variable in downtown and industrial area. The backscatteringecho is very low for the vegetation areas and water bodies. Concerning the residential areas, the values of the backscatter return are slightly larger and less variable than that of the vegetation areas.

  TUPIN F., GOUINAUD C., MAITRE H. & CRETTEZ J.P. 1996. Détection du réseau routier sur des images radar ERS 1, RFIA AFCET 96 (Rennes), 4352. WALD L. & BALEYNAUD J.M. 1999. Observing Air Quality over the City of Nantes by Means of Landsat Thermal IR Data, Int. J. Remote Sensing, 20 (5): 947959. WEBER C. 1995, Images satellitaires et milieu urbain, Paris : Hermès, 185 p.

Figure 2 .

 2 Figure 2. The city of Nantes viewed by ERSSAR system imaging. This is a mean image derived from 7 PRI images. All the images were acquired in descending pass. The Loire river appears in dark. The airport is located to the South of the river. The island is part of the city.

Figure 4 .

 4 Figure 4. Here is a shopping center in the South of Rezé, a town on the South of the Loire river. Its dimension are approximately 150 meters long and 80 meters wide. Figure 5a is a detail of the SAR image, the size of the pixel is about 13m. Figure 5b is an aerial photograph taken in 1993 by IGN, the spatial resolu tion is about 0,7 meter. Although the shopping center don't ex

  Figure 4. Here is a shopping center in the South of Rezé, a town on the South of the Loire river. Its dimension are approximately 150 meters long and 80 meters wide. Figure 5a is a detail of the SAR image, the size of the pixel is about 13m. Figure 5b is an aerial photograph taken in 1993 by IGN, the spatial resolu tion is about 0,7 meter. Although the shopping center don't ex

Figure 5 .

 5 Figure 5. View of the Beaulieu island which is part of the city of Nantes. Detail of the PRISAR mean image showing the eleven bridges crossing the Loire river. The brighter one is made of metal. We notice that the pillars of one bridge in the Northern of the island are visible, that bridge is also made of metal (right arrow). The bridges showed with the right arrows are not visible on the aerial photographs (not shown here).

SAR Imagery in Urban Area

ACKNOWLEDGMENTS

The authors are indebted to the European Space Agency which has provided the ERS data under the investigation of the AO2.F113 project. The authors also thank MétéoFrance for providing the meteoro logical data.


Bruno Fornet

Guillaume Dufour

François Rogier

Interactions of a plasma and an incoming flow at Mach 3

est destinée au dépôt

Introduction

A central question in aeronautics is to improve the ight conditions of an aircraft. Among the dierent ways to go, various mechanisms of ow control have been investigated, both experimentally and numerically, during the last decades [9]. We are interested here in simulating the eects of a plasma actuator on a supersonic ow. In the studied device, a "virtual spike" appears as energy is deposited into the ow by a dense plasma coming from an electrodeless laser-guided discharge. This work is a rst step towards a better understanding of the mechanisms at hand as well as the assertion of the expectable drag reduction.

Works on similar topics have been conducted for instance in [4], [6] and [7]. The authors of [4] propose a very detailed model in order to account for the eects of a Nd:YAG laser energy deposition in air for supersonic ow control. The process was modelled from the plasma generation by the laser to its interaction with the uid ahead of a sphere. In [6], the authors study the eects of instantaneous energy deposition taken into account as uid heating on a supersonic ow ahead of a cone. Parametric studies were led depending on the upstream ow velocity as well as the cone angle using a multi-domain WENO scheme to simulate 2-D axisymmetric Euler equations. The authors of [7] investigate the possibility of creating steering moments by o-axis plasma heat addition ahead of a cone. They use a 3-D uid solver in order to do so for dierent kinds of heating processes and look at the eects of dierent parameters on the observed results.

Due to the specicities of the envisioned device, based on involved time scales, we assume as a rst approximation that plasma generation is decoupled from its eects on the uid. Under this assumption, one natural question is then to look at the eects of the introduction of a plasma of determined energy on the uid. Answering this question would give us a good idea of what is needed to be done during plasma generation.

Another aspect would be to get a better understanding of the underlying mechanisms. The previous question is of central interest considering that the device we investigate should be used in a pulsed way. The specicities of our discharge allow us to propose a simplied, numerically cost-friendly model, aimed at answering the above questions. In order to do so, important coupling mechanisms between uid and plasma have been investigated. This model is also intended for being the basis of a larger one integrating to some degree more accurate physics concerning the plasma-uid interactions as well as the mechanisms behind plasma generation.

After explaining our modelling assumptions, we will comment the qualitative results they yield. In the asymptotics of small Debye length, we consider a two-uid model with two temperatures [1]. This 2D-axisymmetric model couples the physics governing the plasma with compressible Euler type equations accounting for the uid dynamics. Several time and space scales are involved in this problem as the plasma is by several orders of magnitude thinner and more reactive than the uid as far as the densities are concerned.

The modelling assumptions.

We will detail here the assumptions made in order to obtain a simplied model, the one our simulations are actually based upon. Air chemistry is an intricate topic and in our case air will be seen as a ctive matter : to this end, we introduce a ctive air molecule (denoted A in what follows). The considered species are then the neutrals A, the rst ionized state A + and the electrons e -. The underlying kinetics are the ionization reaction:

A + e -→ A + + 2e -, and the three-body recombinations:

A + + e -+ e -→ A + e -, (1)
A + + e -+ A → A + A.
(2)

The reactions (1) and (2) are used to describe the kinetics of plasma degradation. Or course, a much more detailed model could be considered for air kinetics (see [5] for instance). We choose to consider this simple kinetics since our focus lies on the numerical simulation of multiphysics coupling. Considering more elaborate kinetics also means complexifying the coupling mechanisms, hence, in the absence of preliminary studies, the understanding of phenomena occuring for the whole coupled system may be greatly impeded.

Moreover it has been proven in [1] that, for the kind of plasma currently investigated, such a simplied model leads to satisfying numerical results as far as the eects on the ow are concerned. Describing accurately the plasma dynamics remains beyond the scope of this paper.

The reaction frequencies associated to these reactions, given in s -1 , are respectively denoted ν i , ν rc,n and ν rc,e . Their expressions are detailed in the appendix.

Consequently the conservation of mass for the dierent species can be expressed as:

∂ t n e + ∇.(n e v e ) = n e (ν i -ν rc,n -ν rc,e ), ∂ t n + + ∇.(n + v + ) = n + (ν i -ν rc,n -ν rc,e ), ∂ t n n + ∇.(n n v) = -n n (ν i -ν rc,n -ν rc,e ).
We are interested in a dense plasma, which implies it has a small Debye length. We opt then for a quasi-neutral model, which is valid in the limit of small enough Debye length. Practically we assume that, at the scale of every considered volume, the local density of positive charge equilibrates the density of negative ones: n e = n + .

Due to elastic collisions with the neutrals, we have v + v n . We choose to take

v + = v n .
Moreover the ux of charged particles Γ := -e(n e v e -n + v + ) is assumed to be divergence free in order to ensure the conservation of the charge.

As commonly assumed as a rst approximation (congruence assumption [8]), the electronic ux Γ is close to zero which leads in turn to the velocity v e being close to the velocity of the neutrals v n , modulo a diusive correction (ambipolar diusion assumption):

v e = v n -D a ∇n e n e .
Concerning the temperature of ionic molecules, we assume that T + = T n . Hence no equation relative the state of the ions needs to be computed. More precisely, the quantities whose evolution needs to be computed are: (n, v, T ) for the uid, where n := n n + n + is the density of heavy particles, v := v n = v + is the velocity of heavy particles and T := T n = T + their temperature. For the electromagnetic eld, we are in a case where magnetic eects are negligible. The electric eld will not be solved here but considered as a parameter acting as a source of energy for the electrons. We get then the following system of equations, where p := nk B T denotes the uid pressure and p e := n e k B T e the electronic pressure. The source term accounting for the momentum transfer from the plasma to the uid is:

     ∂ t n + ∇.(nv) = 0, ∂ t (nv) + ∇.(nv ⊗ v) = S mov , ∂ t (5/2p) + ∇.
S mov = n e ν e (v e -v),
the energy transferred from the plasma to the uid is described by:

S N RJ = 2
m e m air k B n e ν e (T e -T ) + n e eν rc,n W i , the plasma kinetics are taken into account through:

S chem e = n e (ν i -ν rc,n -ν rc,e ),
and the plasma energy balance is expressed by:

S N RJ = -2 m e m air k B n e ν e (T e -T ) + n e e(ν rc,n -ν i )W i .
3. Numerical aspects.

2-D axisymmetric simulations were performed using a compressible uid solver coupled with a plasma solver. For time iteration in our uid solver, we use the block inversion spatially split approximate factorization scheme. As a limiter, Venkatakrishan's is used. The chosen structured uid solver allows to solve Navier-Stokes as well as Euler equations. As presented above we will consider here a non-viscous model for the uid. The grid we use is rened on the Mach cone as well as on the axial area containing the plasma. Globally, the method chosen is based on Finite Volumes and the integration in time is implicit for the uid and explicit for the plasma. For the plasma, the MUSCL scheme is used for the computation of the convection terms. The source terms describing the interactions between uid and plasma are treated explicitly. Finally, due to the strong multiscale feature of the problem at hand, the behaviors of the plasma and the uid are solved on dierent time and space scales.

We use subcycling for the time integration and a ner, precisely localized grid to solve the plasma behavior. These results are then averaged on a rougher grid used for the computation of the uid behavior.

Let us detail our interpolation procedure. In a conical area around the axisymmetric axis r = 0, the 2-D plasma mesh and the 2-D uid mesh are the same in the axial direction, while, in the radial direction the plasma mesh is much thinner and covers only a small part of the uid mesh (r ≤ 600µm). We use then linear interpolation in the radial direction. By testing dierent meshes, we checked that enough points were taken for the uid grid in the plasma channel in order to get accurate results. We underline that the same mesh is used to search for a steady state and to test the plasma eects. Due to the local renement needed near the plasma column, studying properly convergence towards a steady state is already an issue.

As both the time step and mesh are dierent for uid and plasma we use the prime superscript for the plasma. For instance n k e,(i ,j ) denotes the electronic density on the cell whose center is (r i , z j ) at time t k . t k is the physical time reached after k time iterations on the uid. Schematic presentation of the dierent steps of our algorithm.

• Plasma initialization 1. Read uid mesh. 2. Generation of plasma mesh. 3. Initialization of plasma variables: n 0 e,(i ,j ) , v 0 e,(i ,j ) , T 0 e,(i ,j ) .

• Fluid initialization 1. Read uid mesh. 2. Initialization of uid variables: n 0 (i,j) , v 0 (i,j) , T 0 (i,j) .

3. Read boundary conditions. 4. Read initial time step. 5. Read total iteration number.

• Plasma time iteration

t k → t k +1 on grid (r i , z j ) 1. Interpolation of n k (i,j) , v k (i,j) , T k (i,j) on n k (i ,j ) , v k (i ,j ) , T k (i ,j ) .

Evaluation of v k

e,(i ,j ) .

Computation of δt

= t k +1 -t k . 4. Computation of v k +1
e,(i ,j ) and T k +1 e,(i ,j ) .

• Fluid time iteration t k → t k+1 on grid (r i , z j )

1. Resolution of uid equations without source term.

2. Test of plasma activity: if plasma still active do steps 3/ through 6/.

Plasma time iteration gives

n k e,(i ,j ) , v k e,(i ,j ) , T k e,(i ,j ) .

By interpolation we get n k

e,(i,j) , v k e,(i,j) , T k e,(i,j) .

Explicit time iteration:

Sources * δt added to solution obtained at step 1/. 6. If |Sources * δt| is small enough, choose δt k+1 > δt k .

The simulated experiment.

In this work we are interested in the eects of energy and momentum deposition on a ow. We choose to focus on commenting qualitatively the observed eects. The considered dimensions of our prole are analogous to ones we could choose for a physical experiment. We rst perform an aerodynamic simulation that converges towards a steady state.

As we assume that a dense plasma appears instantaneously, the mechanisms of creation and sustainment of the plasma are not investigated. We assume that the created plasma has properties similar to the one observed in thunder. Namely, we take:

n e = 10 24 m -3 , T e = 30000K.
As described above, the electronic velocity is deduced from the other quantities.

The structure of the plasma is assumed cylindrical, the values of the plasma densities are given as an analytic function with a smooth transition to the natural electronic density of air assumed to be 10 10 m -3 . The approximate length of the diuse plasma column is 25cm for a radius under 200µm. The plasma domain covers the range r ≤ 600µm.

The observed eects.

Table 1 Some order of magnitude. F luid heating by plasma (s)

10 -7
Density remains unchanged (s) These numbers illustrate that the considered phenomena occur on disparate time scales.

The initial uid state

We compute a steady state for a truncated quasi-realisatic prole put under an incoming uid at Mach 3. The plane prole is constructed analytically, which proves to be useful during mesh generation. The uid is considered as an ideal gas with a specic heat ratio γ = 1.4. For the presented results, the temperature of the incoming ow is taken as 260K while its molecular density is 2.10 25 m -3 . The computed steady state is the uid state prior to the instantaneous plasma appearance.

The plasma/uid behavior during the rst moments

We describe here the phenomena observed in the time window 0 < t < 3µs. The density of the uid does not change signicantly during this period. The plasma recombines very fast until it reaches a state where it is not dense and hot enough to produce any signicant eect on the uid anymore. During the rst microsecond the uid remains almost steady. The evolution of the plasma depends on the uid properties. We have a localized strong heterogeneity of the uid characteristics due to the bow shock. On one hand, in the zone of high density and pressure behind the central part of the shock, the plasma decay is faster, while it is slower ahead of it. On the other hand, as the density of the uid is higher behind the shock, for a same plasma state, the energy transmitted to the uid is higher. Indeed, while the energy deposition by elastic collisions is weaker, since proportional to T e -T, the global increase in energy is due to the three body recombination with a neutral. As a result of these two conicting eects, we observe in Figure 2 the variations of uid pressure and temperature near the shock after 3µs.

In all our graphical representations, except for the pressure P expressed in bar, the other state quantities will be given in SI units. Contrary to what happened in the initial state, in the very thin channel heated by the plasma the temperature becomes higher ahead of the shock than behind it. Let us remark that one microsecond after the introduction of the plasma, as the density remains unchanged in the heated region, the pressure shock prole is changed, as a "spike" is added to it. Let us also note that the observed eects of momentum transfer between the uid and the plasma are not very strong. The radius of the obtained heated channel is less than half a millimeter. Due to the short life time of the introduced plasma, most of the gas temperature increase occurs during the rst twenty nanoseconds.

The resulting aerodynamic eects

The resulting aerodynamic eects of the gas heating occur on a far larger time scale. After the gas heating, the overpressure in the heated central channel disappears in less than thirty microseconds. This is accompanied by the formation of a low density channel expanding radially over time.

The radius of the obtained low density channel is far from being large enough to observe any real improvement of the ight conditions due to its existence. However, the existence of this channel leads, by conservation of momentum, to a high velocity uid income.

This thin column of uid aects the structure of the velocity shock by locally pushing it inside. The reected wave makes the uid ow back. The interesting eects we obtain are a result of this phenomenon. The localization of the central part of the shock front is pushed ahead. The changes occur spatially on a scale of the same order of magnitude as the one of our truncated prole, which has a radius equal to two centimeters. The front is localized at the frontier between the two uids owing with opposite radial directions. This new shock front travels ahead of the plane nose before being pushed back into initial position. Let us remark that heating locally occurs on the axis as the two uids with opposite owing direction meet.

As shown by Figure 3, positive eects begin to appear on the ight conditions about 15 ms after the plasma was introduced. The eects cease to be signicant over 200 ms after the plasma introduction.

Although we can observe a peak in the temperature shock prole, these numerical results suggest that the corresponding velocity jump along the spike results in an almost continuous Mach number distribution.

We obtain a drag reduction up to about 21%. These eects were produced by an energy deposited into the the uid of about 10 mJ. As 2-D axisymmetric computations were conducted, the lower parts in Figure 4 were reconstructed by symmetry. We choose to show the uid state at 50 ms, since the drag coecient is reaching a minimum around this time.

Conclusion and perspectives

Due to our simulations, we observe that although the created non-equilibrium plasma column is very thin and short-lived, it can have long lasting positive eects over the uid. In order to improve the quantitativity of our results, we have to continue to investigate the dominant physical eects governing the energetic transfer between uid and plasma. In parallel, modelling and simulating the mechanisms hiddened for now in our initial state would be very interesting as it would allow a good estimation of energy eeciency. This extension is not so straigthforward as it would need to analyze the interaction of electromagnetism and optics with the physics presently taken into account. Finally, as the device has to be used in a pulsed fashion, we can use the proposed model, with further description of the physics if necessary, in order to test through numerical simulations how the device should be operated.

  (7/2pv) = S N RJ . ∂ t n e + ∇.(n e v) -∇.(D a ∇n e ) = S chem e , ∂ t (3/2p e ) + ∇. (5/2p e u e ) -∇.(λ e ∇T e ) = S N RJ e .

10 - 6 P 5 F 5 2 P

 6552 ressure equilibrates (s) 10 -ormation of low density channel (s) 10 -Expansion of the bow shock (s) 10 -ositive ef f ects on the f luid (s) 10 -1

Figure 1 .

 1 Figure 1. Scheme of the computed geometry. The units on the axis are specied in meters.

Figure 2 .

 2 Figure2. Prole of the shock after plasma heating at time 3µs. We see that the ow conditions inside the bow shock impedes the uid heating in this area.

Figure 3 .

 3 Figure 3. Variation of the drag coecient over time.

  Fluid density(m -3 ) at t = 0 Fluid density(m -3 ) at t = 50 ms Mach number at t = 0 Mach number at t = 50 ms Temperature(K) at t = 0 Temperature(K) at t = 50 ms

Figure 4 .

 4 Figure 4. We see both the deformation of the bow shock and the decrease in the Mach number around the nose of the aircraft. We remark positive axial velocities as well as heating localized on the meeting zone of two uid ow of opposite directions.

research funded by RTRA STAE/PLASMAX. ν rc,n =

Appendix

The ionization rate ( [3]) is given by:

For the three body recombination with a neutral particle as the third body ( [5]) we take: