Mireille Lefevre

Jan Remund

Michel Albuisson

Wald Lucien
email: lucien.wald@ensmp.fr.

STUDY OF EFFECTIVE DISTANCES FOR INTERPOLATION SCHEMES IN METEOROLOGY

Keywords: interpolation, distance, latitude, meteorology, irradiation

This work explores the possibility of integrating the geographical elements such as orography and presence of water bodies as well as the latitudinal effects into an effective distance when interpolating meteorological fields. This effective distance may then be used in any interpolation methods instead of the standard geodetic distance. Several hundreds of sites are used in Europe to assess the benefits of several effective distances. The meteorological parameters under concern are ten-years averages of monthly means of daily sum of horizontal global irradiation, daily sum of sunshine duration, daily extremes of air temperature, atmospheric pressure and water vapor pressure, and of monthly sums of precipitation. This work demonstrates that taking into account the latitudinal effects in the distance increases the accuracy in interpolation. Such effects have been seldom mentioned in previous publications.

The orographic effects may be partly corrected by adding the weighted difference in elevation to the geodetic distance. The following effective distance between the point P and each of the measuring sites X i for all parameters, is found to give better results than the others:

where d geo is the geodetic distance in km, latitudes Φ P and Φ X are expressed in degrees, δh is the difference in elevation between P and X i (expressed in km) and f oro is set to 500.

INTRODUCTION

In meteorology, as well as in other geophysical sciences, Earth surface processes are mostly known by the means of networks of ground-based instruments though increasing use is made of satellite observations. Each network is scarce and interpolation methods are necessary to assess the value V(P) of the parameter under concern for any geographical point P located between the sites of measurements X i .

There is a wealth of publications dealing with the interpolation of meteorological fields. This work does not propose a new method but focuses on the definition of the distance between sites, a distance that is used in all methods. An important aspect of our work is the ability to perform a fast interpolation using an unknown number of measuring sites, especially in the framework of the Web service SoDa, which exploits a smart network of distributed resources to deliver information relating to the solar radiation [START_REF] Rigollier | Exploitation of distributed solar radiation databases through a smart network: the project SoDa[END_REF]. Several resources necessitate estimates of meteorological fields at any point in the world [START_REF] Soda | SoDa -Integration and exploitation of networked Solar radiation Databases for environment[END_REF]. These estimates should be provided by a fast interpolation technique.

The problem of interpolation may be seen as an adjustment mathematical problem, that is what is the hyper-surface that fits best the observed values V(X i )? [START_REF] Picinbono | Remarques sur l'interpolation des signaux[END_REF]). This surface is usually defined in an analytical form but piecewise polynomials, e.g., B-splines are often very appropriate [START_REF] Hou | Cubic splines for image interpolation and digital filtering[END_REF]. Once the parameters of the model known by adjustment over the observed values, it provides a value for any geographical point P for the area under concern. Least-square fitting of surfaces of polynomial type on a global or local scale, thin plate method or Hsieh-Clough-Tocher method, are examples of such methods [START_REF] Hutchinson | Estimating monthly mean values of daily total solar radiation for Australia[END_REF][START_REF] Hulme | A 1961-1990 climatology for Europe for climate change modelling and impact applications[END_REF]. One of their advantages is the degree of continuity of the derivatives of the estimated field.

A more conventional approach consists in estimating the meteorological parameter at the single geographical point P using the nearest sites where measurements are made. The estimated value is a combination of the measurements V(X i ) weighted by a function of the distance d i between the point P and each of the measuring sites X i . The shorter the distance, the larger the influence of the site and the larger the weight of the site in the combination. The estimated value V(P) is expressed as:

V(P) = (1)
where V(X i ) is the value measured by the i th site among the nearest N measuring sites and w i is the weight for this site, with = 1.

In such a linear interpolation, there is no bias, that is that the estimated field V* takes the measured values V(X i ) at the geographical points X i located over the measuring sites. This may not be the case for the fields resulting from a method based upon adjustment mechanisms. However, the first derivative of the field resulting from a linear interpolation is not continuous. Popular methods like kriging, objective analysis, and inverse squared distance are examples of linear interpolation methods [START_REF] Journel | Mining Geostatistics[END_REF][START_REF] Thiébaux | Spatial Objective Analysis: with applications in atmospheric science[END_REF]. In the inverse squared distance method, also called gravity method, the weights w i are given by

w i = / (2)
where d i , d j are respectively the distances from respectively the site X i and the sites X j to the geographical point P:

i i PX d = and d i , d j ≠ 0 (3)
Different methods use different weights. Some methods make use of the estimated spatial structure of the field itself to compute the weights. This structure is expressed by e.g. the variogram or the correlation function.

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. Whatever the method, of adjustment type or linear type, a distance between the sites and the geographical point P is computed. It is usually the geodetic distance or the Euclidean distance if the data are located on a grid whose cells are regularly spaced. Given two sites P and X of geographical co-ordinates (Φ P , λ P ) and (Φ X , λ X ), where Φ and λ stand for latitude and longitude, the geodetic distance d geo between P and X is:

d geo = R Θ (4)
where

cos Θ = sin Φ P sin Φ X + cos Φ P cos Φ X cos(λ P -λ X ) (5)
where Θ is expressed in radians and (λ P -λ X ) is the difference in longitude. The geodetic distance is the distance at the surface of the Earth considered as a sphere of radius R (R= 6371 km). It is also called the horizontal distance. Here, the latitude is counted positive from the equatorial plane northwards and negative southwards. The longitude is counted positive eastwards from the Greenwich meridian and negative westwards.

TAKING INTO ACCOUNT NATURAL PROCESSES

The spatial structure of a meteorological field is a function, usually complex, of several natural processes. Among others are the latitudinal effects and the orography. They should be taken into account for a better estimate of the field. Some methods, like the co-kriging, offer the possibility to take into account the cross-variation or the cross-structure of the meteorological parameter under concern and of another parameter. This additional parameter should be positively correlated to the first one and sampled for a larger number of locations.

The range of values of the second parameter taken by the measuring sites should be large, too.

Finally, the set of values should represent the field under concern. This is not often the case, as shown by the example of France in the construction of the European Solar Radiation Atlas

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. (ESRA, 2000). In this case, forty-four stations were used that measure global irradiation, sunshine duration, air temperature and pressure at ground level, precipitation and water vapor.

Out of these 44 sites, only 12 have elevations greater than 200 m (27 % of the total). Out of these 12, three have elevation greater than 400 m (7 %) and three have elevation between 300 and 400 m. The range of elevation described by these sites is too narrow to establish an accurate description of the effects of the orography: approximately 40 % of the French territory exhibit elevation greater than 200 m, and more than 15 % has elevation higher than 500 m. The data set does not reproduce the distribution of the elevation values.

The use of detailed additional information may improve the results of the interpolation at the expenses of computational complexity. Co-kriging is often used in such cases, though other techniques prove as efficient [START_REF] Beyer | Assessment of the method used to construct clearness index maps for the new European solar radiation atlas (ESRA)[END_REF][START_REF] Hudson | Mapping temperature using kriging with external drift: theory and an example from Scotland[END_REF][START_REF] Lo | Estimation des précipitations à partir de l'analyse utilisant le relief pour l'hydrométéorologie (AURELHY)[END_REF][START_REF] Zelenka | Techniques for supplementing solar radiation network data[END_REF]). In the construction of the European Solar Radiation Atlas (ESRA 2000), a segmentation of Europe was performed by the means of clustering analysis before proceeding to interpolation using a gravity method. In a similar way, [START_REF] Supit | Global radiation[END_REF] proposes to combine interpolated values of the Angström coefficients, representative sunshine duration for the area under concern and a regression model to estimate the solar irradiation. In their socalled climatologically aided interpolation method, [START_REF] Willmott | Climatologically aided interpolation (CAI) of terrestrial air temperature[END_REF] make a combined use of air temperature climatology and interpolated temperature deviations at measuring sites. Typical circulation patterns may be used to guide the interpolation [START_REF] Courault | Spatial interpolation of air temperature according to atmospheric circulation patterns in southeast France[END_REF]. [START_REF] Kunz | MeteoNorm -a comprehensive meteorological database and planing tool[END_REF] used detailed models describing local relationships between orography and meteorological fields for Switzerland, a country with a very dense network of measuring stations. Some methods make use of multiple linear regression analysis of data from a set of nearby measuring sites to locally model changes in meteorological fields.

The value at the point P is predicted from these sites using the regression curve, each site X i

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. being in addition inverse-weighted by its distance to P [START_REF] Anonymous | Spatial interpolation of daily meteorological data[END_REF][START_REF] Jones | Fitting a third-order Markov rainfall model to interpolated climate surfaces[END_REF][START_REF] Nalder | Spatial interpolation of climatic normals[END_REF][START_REF] Price | A comparison of two statistical methods for spatial interpolation of Canadian monthly mean climate data[END_REF][START_REF]Spatial interpolation and estimation of solar irradiation by cumulative semivariograms[END_REF][START_REF] Van Der | Spatial interpolation of daily meteorological data for the Crop Growth Monitoring System (CGMS)[END_REF][START_REF] Van Der Voet | Spatial interpolation of daily meteorological data: a knowledge-based procedure for the region of the European Communities[END_REF].

Beside these efforts, other authors tried to integrate the natural processes into the definition of an effective distance. This process-based distance is then used in any interpolation method, instead of the geodetic distance. This is the approach selected for this work. Compared to other techniques, the use of an effective distance permits to develop fast interpolation methods that can be launched within a Web service.

THE EFFECTIVE DISTANCE

Beyer et al. (1997et al. ( ), MeteoNorm (2000) ) or [START_REF] Zelenka | Techniques for supplementing solar radiation network data[END_REF] used an effective distance:

d eff = (6)
where d geo is the geodetic distance between the measuring site X and the current location P and δh is the difference in elevation of both locations. The geodetic distance and the elevation should be expressed in the same units, e.g. in km. The parameter f controls the equivalence between horizontal and vertical distances. f is set to 100 by Zelenka et al. and to 300 by Beyer et al. The latter stress that the results are only weakly dependent upon f, for most of the elevation differences encountered in their work. This effective distance was then used in cokriging or inverse squared distance interpolation. [START_REF] Anonymous | Spatial interpolation of daily meteorological data[END_REF] and [START_REF] Van Der Voet | Spatial interpolation of daily meteorological data: a knowledge-based procedure for the region of the European Communities[END_REF] studied an effective distance taking into account the absolute difference in elevation of both locations, the possible presence of a climatic barrier between the site X and the point P and the distance to the coastline.

The present work explores various ways to take into account the orography, the effect of the latitude and the presence of the large water bodies. This exploration is possible because all

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. necessary information is now available for the whole Earth in a digital form and with a sufficient accuracy. When launching the present study, it was expected that a better representation of the orographic features and profiles would lead to a better accuracy in interpolation.

The effective distance d eff is based on the geodetic distance that is effectively increased to take into account some processes:

d eff 2 = f lat 2 f NS 2 (d geo 2 + f oro 2 d oro 2 + f sea 2 d sea 2 ) (7)
where f lat and f NS are taking into account the latitudinal effects, (f oro d oro ) is the additional distance taking into account the orography and (f sea d sea ) that induced by large water bodies.

Latitudinal effects

The meteorological fields have well-marked distributions along the latitudes. They are anisotropic: the fields tend to be homogeneous along the latitude with strong North-South gradients (see e.g., [START_REF] Anthes | Meteorology, 7th Edition[END_REF]Atlas of hydrometeorological data 1991;ESRA 2000).

The meteorological phenomena are preferentially moving along the latitudes. Their size and lifetime are related to each other and the relationship is independent from the latitude at first order. We studied the possible normalization of the geodetic distance by the perimeter of the latitude of the site P. Actually, we found out that this transformation has a negligible impact on the results. [START_REF] Price | A comparison of two statistical methods for spatial interpolation of Canadian monthly mean climate data[END_REF] reported a similar result. Accordingly, the factor f lat is set to 1.

Another factor f NS is introduced to model the anisotropy of the fields and to penalize the North-South distances:

f NS = 1 + a NS Φ P -Φ X  [1+ (sinΦ P + sinΦ X ) / 2] (8)
where a NS is an arbitrary parameter.

Orography

In the Equation [6], the orographic effects are represented by a difference in elevation. This does not reproduce the case of an orographic barrier separating two sites P and X of equal elevation. It is proposed to use instead the profile of elevation. Given an elevation profile extracted from a gridded digital elevation model (DEM), and approximating a grid cell by its center, the distance d i at the ground surface between two cells i and i+1 of elevation h i and h i+1 is:

d i 2 = d geo 2 + (h i+1 -h i ) 2 (9)
We thus define the orographic distance as:

d oro 2 (P, X i ) = (10)
where N is the number of cells comprised between P and X i , along the shortest geodetic distance. The distance d oro penalizes elevation profiles [P, X i ,] offering large elevation gradients. The digital elevation model used is the model TerrainBase (1995). The size of the grid cell is 5' of arc angle (approximately 10 km at mid-latitude) and the elevation step is 1 m.

The algorithm of [START_REF] Bresenham | Algorithm for computer control of digital plotter[END_REF] was used for computing orographic profiles. It is fast and

works in integer values.

The meteorological parameters strongly depend upon the elevation. We enforce the orographic distance d oro by multiplying it by the parameter f oro . It controls the equivalence between the horizontal and vertical distances. Setting f oro to 500 means that a difference in elevation of 100 m is equivalent to a geodetic distance of 50 km.

Other orographic distances are computed for comparison with d oro . We define the elevation difference distance: f oro δh, where δh is the difference in elevation between P and X i , like in Equation 6, and the elevation maximum difference distance: f oro ∆Η, where ∆Η is the Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. maximum difference in height that can be found in the orographic profile between P and X i : it is the absolute value of the difference between the highest point and the lowest one.

Water bodies effect

Large water bodies separating sites may create climatological barriers. The geodetic distance over such water bodies between P and X i is called d sea . Using TerrainBase in an appropriate manner, one may represent large water bodies and thus compute d sea using the same cell size than for orography. Adding a quantity equal to f sea d sea , where f sea is determined in an empirical way, penalizes the geodetic distance. The influence of the component (f sea 2 d sea 2 ) was assessed by using a selected number of sites of similar elevations, which are separated by large water bodies (e.g., sites in Azores Islands, Eire and Spain). Actually, we found that the influence of the water bodies component is negligible. Varying f sea from 0 to 10 does not lead to a noticeable change in accuracy. Accordingly, this component is disregarded.

DATABASE AND TESTS

The various components of the effective distance were assessed for an area encompassing Europe, ranging from 30° West to 70° East and from 25° to 75° North. Ten-year averages of monthly means of several parameters are available in the CD-ROM of the ESRA (2000):

• daily sums of horizontal global irradiation for 586 sites,

• daily sum of sunshine duration for 556 sites,

• daily extreme of air temperature for 435 sites,

• monthly sum of precipitation for 435 sites,

• atmospheric pressure for 266 sites,

• water vapor pressure for 274 sites.

The daily irradiations and the daily sums of sunshine duration were converted into respectively daily clearness indices KT and relative sunshine durations S/S0. For each parameter, each site is in turn assumed to be unknown and the value of the parameter is assessed by interpolation technique using the other sites for each month. The estimates are compared to the measured values and the discrepancies are computed. The set of discrepancies for all sites is then analyzed as a function of month, latitude, site, longitude and elevation. Two quantities are computed to synthesize the discrepancies: the bias and the root mean square.

Two interpolation techniques are used: the gravity method and the nearest-neighbor method.

Having two methods permit to compare the results and the conclusions reached for each of them regarding the distances. Several distances are tested and compared. For each distance and if relevant, empirical parameters were adjusted in order to decrease the errors in interpolation:

• distance D1 (geodetic): D1 = dgeo

• distance D2 (equation [6]): D2 2 = (dgeo 2 + f 2 δh 2 ).
Elevations are in km. According to MeteoNorm (2000), the quantity f is set to 300 for radiation parameters, 100 for temperature, 200 for precipitation and 100 for air pressure and water vapor pressure.

• distance D3: D3 = fNS dgeo, with fNS = 1 + aNS ΦP -ΦX [1+ (sinΦP + sinΦX) / 2]. Latitudes are expressed in degrees. The value of aNS leading to the smallest error in interpolated value was found to be 0.3. Nevertheless, the range of values [0.2, 0.4] gives similar errors.

• distance D4: D4 2 = fNS 2 (dgeo 2 + foro 2 doro 2 )

• distance D5: D5 2 = fNS 2 (dgeo 2 + foro 2 δh 2 )

• distance D6: D6 2 = fNS 2 (dgeo 2 + foro 2 ∆H 2 )
For distances D4, D5 and D6, the quantity f oro was set to 500, with elevation in km. The influence of the exact value of f oro on the error is negligible, provided f oro is approximately in the range [100,1000]. This value is the same for all meteorological parameters.

RESULTS

The results show the large influence of the parameter f NS on the error in interpolation.

Compared to the distance D1 (geodetic) and D2, the distance D3 provides better results. The Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. incorporation of the latitudinal effects in the effective distance is the major contributor to the increase in accuracy with respect to the standard distances.

The accuracy is further increased by the inclusion of the orographic effects (distances D4, D5

and D6). We were disappointed by the results obtained by the distance D4, taking into account the profile of elevation between the point P and the site X i . An improvement of accuracy was expected, which was not evidenced at all. Better results are attained by simpler formulae, such as the distances D5 and D6. The results attained for the distances D5 and D6

are similar, with a slight advantage to D5. This distance D5 has also a major advantage: it is faster to compute than D6. Finally, it should be noted that the influence of the orography correction is small compared to that of the latitudinal effects.

Table 1 gives the bias and RMSE (root mean square error) for each meteorological parameter, for the two interpolation methods (nearest neighbor and gravity) and for the distances D1, D2

and D5. In all cases the smallest bias and RMSE are observed for the distance D5. Radiation parameters are reproduced with an accuracy of approximately 10 % or better. For irradiation, these results are similar to those reported in [START_REF] Wmo | Meteorological aspects of the utilization of solar radiation as an energy source[END_REF] for geodetic distances less than 400 km. Accuracy on rainfall is poor; it is well known that rainfall is a discrete field and that such interpolation methods are not appropriate to estimate precipitation. On the contrary, climatological means of air pressure are fairly continuous fields and these interpolation methods give very good results. As for the air temperature, bias is small and RMSE amounts to approximately 2 °C. When compared to the results of [START_REF] Hulme | A 1961-1990 climatology for Europe for climate change modelling and impact applications[END_REF], based on a fitting of much more stations (approximately 800) using a thin-plate technique, covering the same area and dealing with similar types of data, our errors with distance D5 are similar for the precipitation and larger for the sunshine duration, air temperature and water vapor pressure.

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002 D5.

Figure 1 displays the bias and RMSE observed as a function of the latitude for the clearness index, for the three distances D1, D2 and D5. One may observe that the errors are constant with the latitude. The increase in bias and RMSE with the lowest and highest latitudes is due to a border effect: there is no measuring sites southwards (respectively northwards) of the point P because we are working in a limited area and not on the whole Earth. This anisotropy in the distribution of sites X i leads to an increase in error.

Ideally, the bias should be equal to zero. The distance D5 is that offering the bias that is the most constant with the latitude and the closest to zero. This distance is also that exhibiting the smallest RMSE. In addition, this RMSE is almost constant with latitude. The errors observed for the other distances are slightly larger.

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. from that of the measuring site contained within the cell. We observed that the larger the difference in these elevations, the larger the errors in interpolation. This mostly occurs for sites with elevation circa 1500 m and thus partly explains the increase of errors for this elevation. The bias is equal to zero for all distances, except around 1500 m. The differences in errors between the distances are very small. Nevertheless, the distance D5 offers the best results.

Interpolation Error as a function of Latitude

Figure 3 displays the bias and RMSE that are expected as a function of the effective distance D5 for each parameter. These curves may serve to provide an approximate RMSE together with an assessment of the meteorological parameter at any geographical point. They have been obtained in the following way. For each point P and each meteorological parameter, the monthly values are estimated using measuring sites located within a ring at a given effective distance D5 from P, given a tolerance of ±30 % on the distance. This distance was set to various values in an iterative way. For each distance, the errors are computed and synthesized into bias and RMSE. Finally, the curves of the bias and RMSE as a function of the effective distance are displayed. The effective distance reported in the figure 3 is the mean effective distance of the sites located within the ring. The interpolation method is the gravity method.

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429.

CONCLUSION

This work demonstrates that taking into account the latitudinal effects in the distance brings an increase in the accuracy in interpolation. Such effects have been seldom mentioned in previous publications. The orographic effects may be partly corrected by adding the weighted difference in elevation to the geodetic distance.

We recommend the use of the following effective distance between the point P and each of the measuring sites X i for all parameters:

d eff 2 = f NS 2 (d geo 2 + f oro 2 δh 2 ) (11) with f NS = 1 + 0.3 Φ P -Φ X  [1+ (sinΦ P + sinΦ X ) / 2],
where d geo is the geodetic distance in km, latitudes Φ P and Φ X are expressed in degrees, δh is the difference in elevation between P and X i (expressed in km) and f oro is set to 500.

This distance is identical to the geodetic distance if sites are on the same latitudes and have the same elevation. If the difference in latitude between the point P and a site X i is 10° at 45°N, then the effective distance is equal to 6 times the geodetic distance. As for the difference in elevation, assuming no difference in latitude between the point P and a site X i and assuming that the geodetic distance is much larger than (500 δh), the effective distance may be approximated by:

d eff ≈ d geo [1 + (f oro 2 δh 2 / d geo 2 )/2] (12)
For a difference in elevation of 200 m and a geodetic distance of 200 km, then the effective distance is equal to 1.1 times the geodetic distance. The larger the geodetic distance, the smaller the influence of the difference in elevation.

An implementation of this distance was performed within the SoDa service on the Web (SoDa 2001). This prototype service delivers information on solar radiation and related quantities [START_REF] Rigollier | Exploitation of distributed solar radiation databases through a smart network: the project SoDa[END_REF]. The implemented resource serves climatological values of monthly

Presented to the XXVII Annual Assembly, European Geophysical Society, Nice, April 2002, Geophysical Research Abstracts, vol. 4, April 2002, EGS02-A-03429. global irradiation and ambient temperature for any point on Earth within a cell of 5' of arc angle. The already available gridded climatological databases are used for Europe: ESRA (2000) and MeteoNorm (2000) for irradiation and MeteoNorm for temperature. Otherwise, a gravity technique integrating the proposed effective distance is applied. This technique was selected as a good trade-off between fast answer and accuracy. Meteorological inputs are taken from the databases of long-term means held in the product MeteoNorm [START_REF] Remund | Generation of hourly shortwave radiation data on tilted surfaces at any desired location[END_REF], originating from the database CliNo of the World Meteorological Organization (WMO 1998), the Global Energy Balance Archive [START_REF] Gilgen | Means and trends of shortwave incoming radiation at the surface estimated from Global Energy Balance Archive data[END_REF], http://bsrn.ethz.ch/gebastatus/)

and the USA National Solar Radiation Data Base (http://rredc.nrel.gov/solar/old_data/nsrdb/).

There are 1124 stations for the irradiation and 2559 for temperature. The digital elevation model is the TerrainBase database.

To permit real time answer, the search for stations is limited to a region of 2000 km in radius (geodetic distance). If no station is present (e.g. ocean parts), the zonal mean value is computed over a band of 10° in width and is allotted to the site of interest. The quality of the retrieval is given by previous works as well as the present one. For monthly means of the temperature, the mean bias error is about 0.1 °C and the RMSE 1.9 °C. For regions with denser networks like Europe, the RMSE is smaller: about 1 °C [START_REF] Remund | Worldwide interpolation of meteorological data[END_REF]. For monthly irradiation, the error depends on the source. The gridded data for Switzerland and Europe were constructed using a dense network and a combination of ground measurements and satellite data. For Switzerland, the relative RMSE is about 6 % [START_REF] Remund | Generation of hourly shortwave radiation data on tilted surfaces at any desired location[END_REF] and for Europe, it ranges from 6 % (summer) to 10-15 % (winter) [START_REF] Beyer | Assessment of the method used to construct clearness index maps for the new European solar radiation atlas (ESRA)[END_REF]. Outside

Europe, where interpolation is called upon, the relative RMSE is about 10 -15 %.

Figure 1 .Figure 2 .

 12 Figure1. Interpolation errors (bias, RMSE) as a function of the latitude (in degrees) for the clearness index, using three different distances D1, D2 and D5 and the gravity method. The mean value of the measured clearness index is also given.

Figure 2

 2 Figure 2 displays the bias and RMSE observed as a function of the elevation of the point P for the clearness index, for the three distances D1, D2 and D5. The errors are more or less constant with the altitude, except for sites with an elevation of approximately 1500 m. The DEM TerrainBase gives the elevation of the center of the grid cell. This elevation may differ

Figure 3 .

 3 Figure 3. Interpolation errors as a function of the effective distance D5 (in km) for several meteorological parameters. Bias is in thick line, RMSE in dotted line. The gravity method is used.

Table 1 .

 1 , EGS02-A-03429. Bias and RMSE (root mean square error) for each meteorological parameter, for the two interpolation methods (nearest neighbor and gravity) and for the distances D1, D2 and

				Clearness index	Relative sunshine duration	Rainfall (mm)	Air pressure (0.1 hPa)	Water vapor pressure (0.1 hPa)	Air temp. max. (°C)	Air temp. min. (°C)
			Number
			of	6778	6521	4981	3166	3240	5220	5220
			samples
			Mean value	0.44	0.41	58	10154	99	14.4	6.5
			Bias	0.001	0.000	0.8	0.4	-1.2	-0.4	-0.2
		D1	RMSE	0.046 (11 %)	0.058 (14 %)	27.9 (48 %)	17.8 (0.17 %)	19.4 (20 %)	4.0	2.8
	Nearest-neighbor	D2	Bias RMSE	-0.001 0.040 (9 %)	-0.002 0.054 (13 %)	-1.3 24.6 (42 %)	0.4 17.8 (0.17 %)	-0.6 18.6 (19 %)	0.0 3.2	0.1 2.1
			Bias	-0.001	-0.001	-2.0	0.5	-1.0	0.0	0.0
		D5	RMSE	0.040 (9 %)	0.052 (10 %)	23.9 (41 %)	17.1 (0.17 %)	15.4 (16 %)	2.7	2.0
			Bias	-0.004	-0.008	3.3	1.4	0.2	-0.4	-0.2
		D1	RMSE	0.041 (9 %)	0.063 (15 %)	23.2 (40 %)	20.4 (0.20 %)	19.6 (20 %)	3.6	2.8
			Bias	-0.007	-0.009	1.9	1.4	0.4	-0.3	-0.1
	Gravity	D2	RMSE	0.041 (9 %)	0.062 (15 %)	23.2 (40 %)	20.4 (0.20 %)	19.5 (20 %)	3.5	1.9
			Bias	-0.003	-0.004	0.3	-0.4	0.4	0.1	0.1
		D5	RMSE	0.034 (8 %)	0.046 (11 %)	21.7 (37 %)	14.8 (0.15 %)	14.9 (15 %)	2.5	1.9

Copyright Ecole des Mines de Paris -Armines -Meteotest

ACKNOWLEDGEMENTS

The Commission of the European Communities under Contract Number IST-1999-12245 supported this work. Discussions with Hans-Georg Beyer, Tamas Prager and Aniko Rimoczi-Paal are gratefully acknowledged.


Christelle Rigollier

Mireille Lefèvre

Sylvain Cros

Lucien Wald

Heliosat 2: an improved method for the mapping of the solar radiation from Meteosat imagery

Solar irradiance at the ground level can be determinated from Meteosat images by the means of several methods. The purpose of this work is to present the method Heliosat 2, an improved version of the well known Heliosat 1 method. Heliosat 1 converts observations made by geostationary meteorological satellites into estimates of the global irradiation at ground level. It was implemented in many places and is routinely used to produce maps. It suffers from some drawbacks, which come from several empirically defined parameters inside the method. The accuracy of the estimates is very sensitive to their tuning during the implementation phase. This method cannot cope with changes in spaceborne radiometers. Consequently, parameters have to be tuned at each change. Four points of improvements were identified. Values in images were calibrated, hence large time-series spanning over several changes of sensors and satellite may be processed. It also permits to adopt known models of the physical processes in atmospheric optics; thus removing the need of empirically defined parameters. A new model of clear sky irradiation was used for a better accuracy of the estimates performed by the method. The computation of the ground albedo and the cloud albedo makes use of recognised models of the radiance and the atmospheric transmittance. The relationship between the cloud index and the hourly global irradiation was modified to better represent the cloudy skies. This new method Heliosat 2 exhibits results that are more accurate than those provided by the method Heliosat 1 by approximately 30 %. Comparisons were made with ground measurements obtained at 35 sites in Europe. For daily irradiation we observed a relative mean square error of less than 200 J. cm -2 and 110 J.cm -2 for the monthly mean of daily irradiation.

INTRODUCTION

Mapping solar radiation at the ground level is an important issue for several applications. The solar energy technologies as the photovoltaic system, thermal solar power plant or optimisation of daylight usage in building need accurate information in solar radiation earth surface repartition. This knowledge is also essential for primary production forecast, photo chemical, meteorological and climatological studies.

Processed with an appropriate method, images from meteorological geosynchronous satellite can produce maps of solar radiation, which are more accurate than those obtained from interpolation of measurements of radiation made at ground level [START_REF] Perez R | Comparing satellite remote sensing and ground network measurements for the production of site/time specific irradiance data[END_REF]). Among the existing irradiance calculation schemes, the Heliosat algorithm can estimate solar radiation from Meteosat satellite image with satisfactory results [START_REF] Cano | A method for the determination of the global solar radiation from meteorological satellite data[END_REF], Diabaté et al. 1989, Heidt et al. 1998). This method was simple enough to be widely disseminated in the world (Diabaté et al. 1988(Diabaté et al. , 1989;;[START_REF] Moussu | A technical note on a low-cost high-quality system for the acquisition and digital processing of images of WEFAX type provided by meteorological geostationary satellites[END_REF]). Nevertheless, this method Heliosat 1 suffers from several drawbacks, which come from several empirically defined parameters inside the method.

Moreover, it cannot cope with changes in spaceborne radiometers, which occur periodically in operational meteorological programmes. Consequently, parameters have to be tuned at each change. To overcome these drawbacks, we developed a new method called Heliosat 2. This method is based on the same physical principles with the possibilities of using known models of the physical processes in atmospheric optics.

First, this paper presents the method Heliosat 1 in its general principles and its potential improvements. It then describes the several developed improvements, which define the method Heliosat 2. Finally, it presents comparisons with ground measurements, which quantify the accuracy of these satellite estimations.

THE METHOD HELIOSAT 1

The principle of the method Heliosat 1 is the construction of a "cloud index" resulting from a comparison of what is observed by the sensor to what should be observed over that pixel if the sky were clear, which is related to the "clearness" of the atmosphere. Actually, this principle is that commonly adopted when the only inputs are images taken in the visible broad range. It is the one used by several method of proven quality [START_REF] Pastre | D †veloppement d'une m †thode de d †termination du rayonnement solaire global ‡ partir des donn †es Meteosat[END_REF]Möser, Raschke, 1983[START_REF] Esra | Second and Extended Edition, Vols I et II[END_REF][START_REF] Cano | A method for the determination of the global solar radiation from meteorological satellite data[END_REF][START_REF] Stuhlmann R | An improvement of the IGMK model to derive total and diffuse solar radiation at the surface from satellite data[END_REF][START_REF] Delorme | Quick use of Wefax images from Meteosat to determine daily solar radiation in France[END_REF][START_REF] Colle | Distribution of solar irradiation in Brazil derived from geostationary satellite data[END_REF]. At each pixel (i, j) of the current image at time t, a normalised count CN* t (i,j) is computed as:

CN* t (i,j) = (CN t (i,j) -CN0 t ) / [I 0 (t) (sin  S (i,j)) (sin  S (i,j)) 0,15 ]
Where  CN t (i,j) is the numerical count observed by the sensor at time t for this pixel (i, j), CN0 t being what can be called the sensor zero (the numerical counts are not necessarily calibrated),  (sin  S ) 0,15 is the clear sky transmittance (model of Perrin de Brichambaut, Vauge 1982).

This normalised count CN* t (i,j) is related to the apparent albedo  t (i,j) observed by the spaceborne sensor. In preparation to the determination of the cloud index n t (i,j), a reference map of the normalised count for clear sky is constructed [START_REF] Diabat€ | Description of an operational tool for determining global solar radiation at ground using geostationary satellite images[END_REF]. It is also called the normalised count for ground, CN* g (i,j). Given a time-series of images, it is evaluated at each pixel in a recursive fashion by minimising the variance between the digital counts and those resulting from the clear sky model, the cloudy cases being eliminated at each step [START_REF] Cano | A method for the determination of the global solar radiation from meteorological satellite data[END_REF]). The cloud index is defined as a function of CN* g (i,j), CN* t (i,j), and the typical normalised count of the brightest cloud tops CN* cloud :

n t (i,j) = [CN* t (i,j) -CN* g (i,j) ] / [CN* cloud -CN* g (i,j)) ]
The computation of CN* cloud is performed using the inverse of the algorithm used for determining the reference albedo map and retaining only the cloudy areas. The histogram of this "only cloud" image provides an estimation of CN* cloud .. The clearness index KT h (i,j) may be defined for the hour h centred on t as: (i,j) where G 0h (i,j) is approximated by I 0 t sin  S , where  S is for the middle t of the hour. Care should be taken of the sunset and sunrise. Several previous studies did show a linear relationship between the cloud index and the clearness index, where the parameters A and B are positive and have been determined once for ever (Diabaté et al. 1988, Diabaté 1989):

KT h (i,j) = G h (i,j) / G 0h
KT h (i,j) = -A n t (i,j) + B
This relationship between KT h (i,j) and n t (i,j) leads to the computation of the global hourly irradiation G h (i,j).

The global daily irradiation G d (i,j) is computed from the set of hourly irradiations available for that day. The larger the number of images used per day, the lower the level of error. A model has been proposed by Diabaté (1989), using an analytical law fitted onto climatological hourly values. However most users adopted the following model. Let denote the horizontal daily irradiation outside the atmosphere by G 0d (i,j) and the daily clearness index by KT d (i,j). G d (i,j) is then computed from the N assessments of the hourly irradiation G h (i,j) made during the day:

G d (i,j) = KT d (i,j) G 0d (i,j) = G 0d (i,j) Erreur ! where w h = Erreur !, it comes: G d (i,j) = G 0d (i,j) Erreur !
The method Heliosat 1 is currently used by several institutes in Europe and elsewhere with geostationary satellites like Meteosat (Europe), GOES (USA) or GMS (Japan). This method contains several empirical parameters, especially in the computation of the apparent albedoes of the ground and the clouds. The clear sky model the atmosphere is also expressed by the sole exponent wherever the location. The parameters A and B in the relationship between KT h (i,j) and n t (i,j) may be adjusted by comparison with measurements made at meteorological stations. These parameters were well tuned during the construction of the method or of its varieties and this explains the good results attained by the authors when performing a comparison with ground observations. For example, according to Diabaté (1989), Diabaté et al. (1988) or Grüter et al. (1986), the typical relative error (RMSE) is about 7-18 percent for the assessment of the hourly irradiation and 10-15 percent for the assessment of the daily irradiation,

THE METHOD HELIOSAT 2 DESIGN

The empirically defined parameters in Heliosat 1 should be expressed using physical laws. We propose a new version of this method by introducing external knowledge on the optical state of the atmosphere for each location as supplementary inputs, given the fact the inputs should still be images taken in the visible range of the radiometer. This new version, called Heliosat 2 should improve the capabilities of the method in order to process any type of data from geostationary meteorological satellites, including large time-series of images taken by different sensors. Its implementation should be improved and applicable in real-time or archived data and its accuracy should be improved. Given the good fundamentals of the method Heliosat 1 with respect to the objectives, it was decided to keep its principles, that is the computation of a cloud index n from the apparent albedo, the albedo of the ground (i.e. without clouds or minimal albedo) and the albedo of the very bright clouds (or maximum albedo). Four points of improvements were identified, in order to meet the objectives expressed above. They are detailed as in the following paragraph. The efforts were aiming at a better quality on a global sense, which means that operational aspects and accuracy of the assessed irradiation were equally treated.

Images calibration

An operational method has been developed, tested and validated for the calibration of the visible channel of the series of satellites of the Meteosat Operational Programme [START_REF] Rigollier | The operational calibration of images taken in the visible channel of the Meteosat-series of satellites[END_REF]. It performs on an automatic basis and is well suited for the processing of large volume of data. It is based upon the analysis of the content of the satellite images. It can likely be used for the calibration of other geostationary satellites having spectral bands similar to Meteosat, such as GOMS, GMS, Insat, and the first GOES series. Daily sets of calibration coefficients are obtained by this method and are used to convert Meteosat digital counts in to radiances.

Modelling the clear sky irradiation

Studies of several clear sky models were performed. Of particular interest are the models of the European Solar Radiation Atlas (ESRA). [START_REF] Rigollier | On the clear sky model of the 4th European Solar Radiation Atlas with respect to the Heliosat method[END_REF] demonstrate that these models could be used in the framework of the Heliosat method. The accuracies of these models are among the best, and the constancy of their performances with respect to different conditions are a clear advantage with the aim of producing a robust method. The accuracy (RMSE) in the assessment of the diffuse hourly irradiation ranges from 11 Wh m -2 to 35 Wh m -2 for diffuse irradiations up to 250 Wh m -2 . The accuracy in the ESRA model is mostly gained by the introduction of the Linke turbidity factor. This factor provides a reasonable estimation for the water vapour and aerosols optical effects. From an operational point of view, the use of the ESRA model implies the knowledge at each pixel of the image, of the Linke turbidity factor and of the ground elevation. Both data can be found on line at http://www.soda-is.org.

Computation of the cloud index

The computation of n t is pending to the determination of the reflectances or albedoes  t g and  t cloud . In turn, these reflectances are computed from the analysis of a time-series of the reflectance observed by the sensor  t . The reflectance observed by the sensor  t under clear skies is a function of the reflectance of the ground,  t g , the sun zenithal angle,  S , the viewing angle, v , and the difference, , of the sun and satellite azimuth angles. At the first order, given the large size of the pixel, the multiple reflection and scattering effects are negligible. Assuming a Lambertian ground, the reflectance observed by the sensor is (Tanré et al. 1990):

 t (i,j) =  t atm ( S , v ,) +  t g (i,j) T t ( S ) T t ( v ) where  t atm ( S , v ,)
is the intrinsic reflectance of the atmosphere, caused by the scattering of the incident and upward radiation towards the sensor. The parameters T t ( S ) and T t ( v ) are the global transmittances of the atmosphere for the incident and upward radiation. The principle of reciprocity implies that the same formulation applies to both transmittances. Numerous works show that the ground is not exactly of Lambertian nature. [START_REF] Vermote | Second Simulation of the Satellite Signal in the Solar Spectrum (6S), 6S User Guide[END_REF] propose several bi-directional models to consider these effects in the simulation of  t (i,j). From an operational point of view, the method Heliosat 2 cannot consider these effects by lack of information. In particular, it would imply the knowledge of the landuse for each pixel of the field of view of the satellite Meteosat and of the associated model. The present approach is based upon the modelling of the intrinsic reflectance of the atmosphere, also called the path reflectance, and the atmospheric transmittance. Each term,  t atm and T t ( S ) or T t ( V ) is modelled, resulting into the explicit formulation of  t as a function of  S ,  V ,  and  t g . Inversely, this permits to compute  t g and  t cloud . Assuming that the scattering by the atmosphere is isotropic, it is conceivable that the path radiance L atm reaching the sensor is proportional to the path radiance reaching the ground. Taking account the results, [START_REF] Beyer | Modifications of the Heliosat procedure for irradiance estimates from satellite images[END_REF], the path radiance can be expressed using the expression of the diffuse irradiance under clear sky at ground level, D c :

L atm = (D c / ) (I 0met / I 0 ) (<cos V > / cos V ) 0,8
Various tests show that the approach is satisfactory, provided it is restricted to zenithal angles and viewing angles less than 75°, as was the case with the method Heliosat 1 (Diabaté 1989;Bauer 1996). It follows that the method Heliosat 2 will be unable in principle to accurately estimate the irradiation north of the latitude 65° N, and south of the latitude 65° S.

Computation of the ground albedo

The ground albedo  g (i,j) may be assessed from a time-series of Meteosat observations converted into radiances L t (i,j). The analysis of several years of images from Meteosat shows that it happens that some pixels exhibit very low radiances, similar to those observed during the night, while the sun is well above the horizon. A constraint is imposed on radiances to avoid such cases; they should be greater than 3 percent of the maximal radiance that can be observed by the sensor:

L t (i,j)  0,03 Erreur !+ b(t)
where b(t) is the calibration coefficient, and more exactly the radiance measured when viewing darkness. Knowing the Linke turbidity factor and the site elevation, the path radiance is computed:

L t atm (i,j) = Erreur ! and  t atm ( S , v ,) = Erreur !
Finally, we get a quantity * t (i,j) that is a ground albedo if the sky were clear at the instant t.

* t (i,j) = t (i,j) - atm ( S , v ,)] / T( S ) T( v )
This operation is performed for several images. For each pixel, a time series of * t (i,j) is obtained. To eliminate artefacts in assessing the ground albedo, the time series is restricted to the instants for which the sun zenithal angle  S is less than the maximum of 50° and (2  S noon / 3), where  S noon is the angle observed at noon, remembering that  S is less than 75° in any case. The second minimum of the series of retained reflectances is the ground albedo  g (i,j) for this period. The period of the time-series should be the shortest as possible in order to take into account the rapid variations of the ground albedo. Compared to the method Heliosat 1, the accurate correction of the effects of the sun and satellite angles permits to merge all the slots into the time-series. Thus, the period may be shortened. In an operational mode, especially when real time is at stake, a moving period may be adopted. This possibility to have only one albedo map for a period permits to create a background map that allows overcoming the case where at a pixel, no cloudless instant is observed. In that case, the smallest reflectance is that of a cloud and should not be considered as the ground albedo. Prior being declared a ground albedo, the second minimum is compared to the background value. It cannot be less to half this value and cannot be greater than twice this value. If it is the case, it is set to one of these limits. The result is the ground albedo.

Computation of the cloud albedo

The albedo of the clouds  cloud has been defined by Cano (1982) as the typical value for the brightest clouds. The histogram of cloud albedoes is flat and it is very difficult to characterise this parameter  cloud by a statistical quantity, such as a mode or a percentile. [START_REF] Costanzo | Bestimmung der solaren Einstrahlung am Boden aus Meteosat-Daten-Untersuchung und Erweiterung einer empirischen Methode[END_REF] or Hammer et al. (1997a, b) compute the mean value of the brightest albedoes observed in a time-series of images. The results may depend upon the length of the time-series and of the selected threshold. It should be added that some sites exhibit clear skies during several months (e.g. the Mediterranean basin), making it difficult to find very bright clouds.

The above-mentioned difficulties disappear if one is using calibrated radiances. In this case, we may adopt an actual albedo of the brightest clouds. [START_REF] Rigollier | On the clear sky model of the 4th European Solar Radiation Atlas with respect to the Heliosat method[END_REF] refers to the maximum value given by Grüter et al. (1986) that is 0.9. The effective cloud albedo depends upon the sun zenithal angle. We follow the model proposed by Taylor, Stowe (1984a):

 eff (i,j) = 0.78 -0.13 -expcos S ) 5 ]
However, the parameter  cloud is to be compared to the quantities * t (i,j) that derive from the observed radiances to compute the cloud index n. For * t (i,j) =  t cloud (i,j), the cloud index n should be equal to unity. It follows that the same equation should apply to the effective cloud albedo, leading to the apparent cloud albedo  t cloud (i,j):  t cloud (i,j) = eff (i,j) - atm ( S , v ,)] / T( S ) T( v ) Two constraints are added, gained from experience:  t cloud (i,j) > 0.2, otherwise  t cloud (i,j) = 0.2 and  t cloud (i,j) < 2.24  eff (i,j), otherwise  t cloud (i,j) = 2.24  eff (i,j) The value 2.24 is the largest anisotropy factor observed by Taylor, Stowe (1984b) for the present geometrical configuration sun-pixel-sensor and thick water cloud.

Relationship between the cloud index and the hourly global irradiation

A linear relationship was assumed between the clearness index KT h and the cloud index in the method Heliosat 1 (Grüter et al., 1986;[START_REF] Michaud-Regas N | Mise en oeuvre et validation d'une m †thode op †rationnelle et automatique pour l' †valuation d'atlas solaires en Europe ‡ l'aide de mesures satellitaires Meteosat[END_REF]) and others (Raschke et al., 1991). The hourly irradiation is computed as: (i,j) According to Diabaté (1989), the coefficients A and B do not depend upon the geographical location but on the time of the day. Three sets of values were defined: one for the morning, one for mid-day and one for the afternoon. Though satisfactory results are obtained, Diabaté (1989) stresses that there is no explanation of the variability of the parameters A and B during the day while their variability along the year or with the latitude is negligible, and questions the validity of this relationship. [START_REF] Beyer | Modifications of the Heliosat procedure for irradiance estimates from satellite images[END_REF] underline that the parameter KT h is not well describing the optical state of the atmosphere: a cloudy sky may have the same KT h than a turbid clear sky though the radiative flux reaching the spaceborne sensor may be different because of the higher albedo of the cloud or the backscattering effects. They propose to use instead the clear-sky index K ch , which is equal to the ratio of the hourly global irradiation at ground on an horizontal surface G h to the same quantity but for clear skies G ch : [START_REF] Beyer | Modifications of the Heliosat procedure for irradiance estimates from satellite images[END_REF] show that the relationship may be simply written as: K ch = 1 -n with a negligible loss in accuracy. The gain in terms of operating the method is large since it is not necessary to use ground measurements to establish or correct the parameters A and B of the relationship. However, this relationship has some drawbacks that need to be corrected. First, since the apparent albedo of the ground,  g , is not the smallest value that can be observed, it happens that the cloud index n is negative. The relationship predicts a value of K ch greater than 1, which is physically sound up to a limit of approximately 1.2 according to the observations. Secondly, the apparent albedo of the cloud,  cloud , is not the greatest value that can be observed and the cloud index n may be larger than 1. It also predicts a value of K ch negative, which is impossible. Actually, observations of the smallest clearness index in Europe for several years show that the minimal value is approximately 0.04 [START_REF] Esra | Second and Extended Edition, Vols I et II[END_REF]2000). Since

G h (i,j) = KT h (i,j) G 0h (i,j) = (-A n t (i,j) + B) G 0h
K ch = G h / G ch Furthermore,
K ch = KT h (I 0  sin  S / G ch )
Using the model for clear skies of Perrin de [START_REF] Perrin De | Le gisement solaire : Evaluation de la ressource énergétique[END_REF], we find the minimal value of the clear-sky index, K ch , of approximately 0.05, with an error of approximately 0.01. A careful analysis of many comparisons between measured global hourly irradiations and cloud indices n made in the framework of the project Satel-Light [START_REF] Fontoynont | Satel-Light, Processing of Meteosat data for the production of high quality daylight and solar radiation data available on a World Wide Web Internet server, Mid-term progress report[END_REF] show that for overcast skies (n  0.8), a linear relationship is inappropriate and underestimates K ch . It is therefore proposed to use instead a quadratic relationship up to n>1.1 where the minimal value of K ch of 0.04 is reached. Taking into account these remarks and constraining the relationship and its first derivative to be continuous everywhere, except in n = 0.2, the new relationship is the following:

n t < -0.2 K ch = 1.2 -0,2 < n t < 0.8 K ch = 1 -n 0,8 < n t < 1.1 K ch = 2.0667 -3.6667 n t + 1.6667(n t )• n t > 1.1 K ch = 0.05 Figure 4
.1 exhibits this relationship, which is made of four parts. The continuity is ensured as well as that of the derivative, except in n = -0.2.

The University of Oldenburg adopted this model in their current version of the method Heliosat 1. Compared to the standard method Heliosat 1, it provides better results (Olseth and Skarveit 1998). However, though this relationship is more satisfactory than the previous one, the limitation of the cloud index n to characterise the optical state of the atmosphere remains. The principle of the method Heliosat 1 is that a difference in global radiation perceived by the method is only due to a change in apparent albedo, which is itself due to an increase of the radiation emitted by the atmosphere towards the sensor. This principle is not always verified. Other parameters may intervene, such as multiple cloud layers and dramatic changes in the ground albedo due to the snowfall or the shadow created by a neighbouring cloud.

COMPARISON BETWEEN RETRIEVED VALUES AND STATION MEASUREMENTS

A comparison between irradiation values retrieved by the processing of Meteosat images and measured by ground stations is performed. It permits to measure the accuracy of the method Heliosat 2 Thirty-five stations from Europe were selected for the comparison. They were selected in flat areas, in order to avoid the specific errors encountered in mountainous areas. These countries are Belgium, France, Germany, Hungary, Norway, Spain and United Kingdom. The meteorological offices provided global hourly irradiation values. These offices perform a screening for quality check. The formats and units were unified before comparison. Measurements are performed in mean solar time or true solar time. The time of the meteorological measurements is that of the end of the measure. For example, the hourly irradiation at 11 hours is the integral of the irradiance from 10 to 11 hours. The satellite observations are performed in universal time coordinated (UTC). Consequently, the initial time series of measurements are converted into other time series expressed in universal time. The time for the satellite observation depends upon the position of the site within the field of view; it can be computed exactly knowing the characteristics of the observing system and is expressed in UTC. For each meteorological station, knowing its longitude, the UTC of the satellite observation T sat is converted into local time t sat . By weighting the two consecutive irradiation values centred on this local time t sat and by assuming that the irradiance is constant within the hour, the estimated hourly value in universal time, G* h meas (T sat ), was computed:

G* h meas (T sat ) = G* h meas (t sat ) = (t 1 -t sat + 0.5) G h (t 1 ) + (t sat -t 1 + 0.5) G h (t 1 + 1)
where t 1 and t sat are local time expressed in hours, t 1 = Round(t sat ), and Round is the rounding operator such as (Round(10.4)=10; Round(10.5)=11 etc.).

The time series of estimated measurements G* h meas (T sat ) are hereafter considered as actual measurements. Only were used the measurements of hourly irradiation greater than 10 Wh m -2 . This value corresponds to the level of diffuse hourly irradiation for the sunset and sunrise under clear-sky at 60° N in Norway. For these hours of very low solar elevation, the measured irradiation is mainly of diffuse nature and is influenced by local conditions, including orography and the presence of nearby obstacles. By removing these values, we ensure better conditions for the validation process.

The satellite data are high-resolution images covering Europe and brought to the infrared resolution, that is 5 km at nadir. They are available every half-hour, from July 1994 to June 1995. We used only the images acquired for even slots. The satellite data were processed using the method Heliosat 2 Estimates of the global hourly irradiation were thus obtained. Only the estimates, for which the solar zenithal angle is lower than 78°, were kept for the comparison, as it has been said that the description of the physical processes is not valid below that limit. Three months were used for the comparison: January 1995, April 1995 and July 1994. From each data set of hourly irradiation, and for a given month, the daily irradiation was computed as follows. For the station measurements, we sum up all the hourly irradiations greater than 10 Wh m -2 . The estimate is said valid if at least N hourly irradiations are used in the computation. N is equal to 6 in January and April and to 12 in July. For the high-resolution images, we use the above-described algorithm. The estimate is said valid if at least N hourly irradiations are used in the computation. For each hourly irradiation, the mean solar elevation should be greater than 12°. N is equal to 5 in January and April and to 8 in July. Given the two time-series, and for all stations together, we compute the difference (measured -estimated). For each parameter, the differences have been computed and are summarised in the table 5.1. The bias is usually useful for assessing the accuracy. For example, it ranges from 23 Wh m -2 in July 1994 to -10 in January 1995. However, it strongly depends upon the selected stations and the selected period and has no great statistical significance in this context because the field is not stationary. Consequently, only the RMSE is dealt with in the following. This parameter is more stable. The results are good compared to the expected accuracy for the Heliosat-II method The correlation coefficient is high in all cases. The relative increase in accuracy is approximately 30 % compared to that observed with the Heliosat 1 method.

Figure 4

 4 Figure 4.1. Relationship between the clear-sky index K ch and the cloud index n

CONCLUSION

We developed a new version of the Heliosat algorithm. It presents results that are more accurate than the previous method. The method Heliosat 2 has the capabilities to process any type of data from geostationary meteorological satellites, including large time-series of images taken by different sensors. It is applicable in real-time or on archives of images. By suppressing empirically defined parameters, the implementation is the same for all cases and the gain in operation is important. Only one map of the ground albedo will be necessary, instead of having one map per slot as presently in the most advanced versions of the method Heliosat 1. The parameterisations of the cloud and ground albedoes request the knowledge of the Linke turbidity factor and the elevation for each pixel of the Meteosat image to be processed. This constraint is not an additional one, since the model of the clear sky irradiation also requests these information. The development of this method did not use any ground measurement contrary to the method Heliosat 1 and others. This ensures a worldwide application of the method Heliosat 2. It is currently operative on the series of Meteosat images in B2 format, spanning from 1985 awards and covering Europe, Africa and Atlantic Ocean (Lefèvre et al. 2002). The times series are available on line at http://www.soda-is.org.

The method Heliosat 2 may be improved in several points. Similarly to the method Heliosat-I, the assessments are satisfactorily for sun zenithal angles larger than 75 -78°. Though applicable, it produces larger errors. The clear sky model does take into account the diffuse part of the radiation that has been reflected by the ground before impinging on the site under concern. This knowledge could help in solving the problem of low sun elevation. Another major point of improvement is the relationship between the clear sky index and the cloud index. Gains will be reached if superimposed cloud layers may be identified. Determination of ground albedo creates problem when the snow covers periodically a site as well as a permanent cloud coverage. Areas where the scales of variability are really smaller than the pixel size like mountainous areas cannot be treated accurately. The gains in accuracy obtained relative to the method Heliosat 1 are not coming from an increase of the dimensionality of the inputs originating from the satellite images. They come from external knowledge, that is the elevation and the Linke turbidity factor for each pixel.


S Cros

M Albuisson

M Lefèvre

C Rigollier

L Wald

HelioClim: a long-term database on solar radiation for Europe and Africa

An information system, called HelioClim, is available for answering the needs for long-term time-series of solar radiation data. Daily irradiation values are available over Europe, Africa and Atlantic Ocean, from 1985 onwards. This database is accessible through the Soda Web service (http://www.soda-is.com) on a free basis. Meteosat satellites images are used to produce this climatological database. The method Heliosat-2 converts these images into maps of the global irradiation at ground level. A comparison was performed between irradiation values available in HelioClim and those measured by ground stations in Europe. A measuring station is not necessarily contained within a B2 pixel and an interpolation method is needed. The root mean square error (RMSE) increases as the irradiation increases and is less than 850 Wh/m², that is a relative error of 20 %, a satisfactory result compared to what can be achieved using sparse pyranometric stations only.

INTRODUCTION

Time series of solar radiation at ground level open the way to many applications for different users. Biomass production and crop forecast, oceanography and limnology applications, urban air quality studies, sizing of space borne sensors, solar energy engineering or even the optimization of daylight use in building applications, are among the various domains needing solar radiation information. Researchers and engineers are facing the problem of solar radiation data retrieving on various parts of the world. Several studies assessed the user needs for solar radiation data (ESRA 2000). These needs consist generally in values of hourly or daily global irradiation and their derived quantities (diffuse component, spectral distribution, spatial structure of the radiation) for various part of the world. Accordingly, databases should be available that cover the whole earth surface for several years. These data should be available at high spatial resolution (about 10 km in size) with a relative accuracy less than 20 % in root mean square error (RMSE) for the daily irradiation. The data should present a convenient and low cost access. Even if several initiatives have been made to answer these requirements [START_REF] Fontoynont | Satel-Light: a WWW server which provides high quality daylight and solar radiation data for Western and Central Europe[END_REF][START_REF] Heidt | Satellite-based solar radiation data go Internet[END_REF]Cros and Wald, 2003), there is still a discrepancy between users needs requirements and availability of solar radiation data [START_REF] Cros | The availability of irradiation data, presented at Energy International Agency, Task II -Operational Performances of PV systems[END_REF].

We propose an answer by building an integrated information system called HelioClim. It contains a database of global irradiation routinely estimated from a times-series of Meteosat images from 1985 onwards and software to exploit it. This paper presents briefly the Heliosat-2 method, which converts satellite images into global irradiation maps. The method is applied to satellite images for the construction of a database of global irradiations. Comparisons are performed with ground measurements.

THE METHOD HELIOSAT-2 FOR THE MAPPING OF THE SOLAR RADIATION

The Heliosat method converts observations made by meteorological satellites into estimates of the global irradiation at ground level. The principle of the method, as well as most current methods, is that a difference in global radiation perceived by the sensor aboard the satellite is only due to a change in apparent albedo, which is itself due to an increase of the radiation emitted by the atmosphere towards the sensor. A key parameter is the cloud index n, resulting from a comparison of what is observed by the sensor to what should be observed over that pixel if the sky were clear, which is related to the "clearness" of the atmosphere. In principle, it can be written as: n t (i,j) = [ρ t (i,j) -ρ t g (i,j) ] / [ρ t cloud -ρ t g (i,j)) ] where • ρ t (i,j) is the reflectance, or apparent albedo, observed by the spaceborne sensor for the time t and the pixel (i, j): ρ t (i,j) = p L t (i,j) I 0met e(t) cos q S (t,i,j) , where L t (i,j) is the observed radiance, • ρ t cloud (i,j) is the apparent albedo over the brightest clouds, • and ρ t g (i,j) is the apparent albedo over the ground under clear skies. If the sky is clear, the apparent albedo ρ t (i,j) is close to the apparent albedo over the ground and the cloud index n is close to 0 (possibly negative). If the sky is overcast, the cloud index n is close to 1 (possibly larger). In brief, the cloud index n may be considered as describing the attenuation of the atmosphere (1 minus the transmittance). Thus, the cloud index n is a very convenient tool to exploit satellite images. The basic principle is not always verified. Other parameters may intervene, such as multiple cloud layers and dramatic changes in the ground albedo due to the snowfall or the shadow created by a neighboring cloud. The change in sensor outputs is not necessarily linked to a change in the optical state of the atmosphere or a change in the optical state does not necessarily translate into a change in the cloud index. The albedoes used in the above equation are constructed from a time-series of satellite images. The optical state of the clear sky is given by the clear-sky models of the European Solar Radiation Atlas (ESRA, 2000;[START_REF] Rigollier | On the clear sky model of the 4th European Solar Radiation Atlas with respect to the Heliosat method[END_REF], in t he form of the global irradiation and irradiance and its direct and diffuse components and the beam and diffuse transmittances. A key input to the ESRA models is the Linke turbidity factor. This factor provides a reasonable estimation for the water vapor and aerosols optical effects. The cloud index n is related to the global irradiation on an hourly basis by the means of the clear-sky index (the ratio of the observed irradiation to the irradiation that should be observed if the sky were clear for the same day) [START_REF] Rigollier | Towards operational mapping of solar radiation from Meteosat images[END_REF]. From these hourly irradiations, the daily irradiation can be constructed [START_REF] Raschke | Solar Radiation Atlas of Africa[END_REF]. Contrary to the original Heliosat method [START_REF] Cano | A method for the determination of the global solar radiation from meteorological satellite data[END_REF]), the approach adopted for the assessment of the cloud index and, further, of the quantities ρ g and ρ cloud , is based upon explicit formulations of the radiance and the transmittance. These formulations make use of the modeling of the clear sky radiation, thus offering a strong consistency. This explicit approach offers several advantages. It removes many empirical parameters, compared to the versions of the original method. It makes use of recognized expressions of the radiance and the transmittance. It permits to use known values of the albedo of specific objects, or to estimate such albedoes. Similarly to the method Heliosat-1, the approach does not behave satisfactorily for sun zenithal angles larger than 75 -78°. Though applicable, it produces larger errors. From an operational point of view, the method Heliosat-II requests the knowledge of the Linke turbidity factor and the elevation for each pixel of the Meteosat image to be processed. This study demonstrates a posteriori that the Linke turbidity factor is sufficient to describe the optical state of the clear atmosphere in the broadband of the satellites Meteosat.

COMPARISON BETWEEN RETRIEVED VALUES AND STATION MEASUREMENTS

High resolution satellite images are not used for the construction of the solar climatology because of their high cost at the beginning of the project; they are less expensive or free now. Reduced resolution data in the ISCCP-B2 format are used instead. This format was set up in the framework of the International Satellite Cloud Climatology Project (ISCCP) [START_REF] Schiffer | The International Satellite Cloud Climatology Project (ISCCP): The first project of the World Climate Research Programme[END_REF][START_REF] Schiffer | ISCCP global radiance data set: A new resource for climate research[END_REF] part of the World Climate Research. This set is derived from the operational Meteosat images, in both visible and thermal infrared bands. The B2 reduced resolution set is produced according to the following steps:

• first, a time sampling of geostationnary images reduces the frequency of observation to synoptic three hours intervals, starting at 0000 Universal Time (UT),

• second, the higher resolution visible channel data (images of 5000*5000 pixels) are averaged to match the lower resolution of infrared channel data. This gives an image of 2500*2500 pixels instead with a resolution of 5 km, • third, overlapping image pixels are removed, • fourth, spatial sampling of images is performed to reduce the apparent resolution to approximately 30 km at nadir by taking 1 pixel over 6 in each direction. The value of the corresponding B2 pixel is given by the radiance of the southeastern most pixel in a 6*6 pixels square. The images B2 are formed by pixels that are effectively pixels of original size (i. e. 5 km) but with a sub-sampling of 6 in each direction. This means that a B2 pixel is not an average of say, 30 * 30 km 2 , but is a pixel of 5 km in size, which represents an area of 30 km x 30 km (figure 4.1). A comparison between irradiation values retrieved by the processing of Meteosat B2 images and measured by ground stations is performed. Thirty-five stations from Europe were selected for the comparison, located in flat areas, in order to avoid the specific errors encountered in mountainous areas. These countries are Belgium, France, Germany, Hungary, Norway, Spain and United Kingdom. The meteorological offices provided global hourly irradiation values. These offices perform a screening for quality check. The formats and units were unified before comparison. Only were used the measurements of hourly irradiation greater than 10 Wh m -2 . This value corresponds to the level of diffuse hourly irradiation for the sunset and sunrise under clearsky at 60° N. For these hours of very low solar elevation, the measured irradiation is mainly of diffuse nature and is influenced by local conditions, including orography and the presence of nearby obstacles. By removing these values, we ensure better conditions for the validation process. The satellite data are available every 3-hours, from July 1994 to June 1995. The satellite data were processed using the method Heliosat-2. Estimates of the global hourly irradiation were thus obtained. Only the estimates, for which the solar zenithal angle is lower than 78°, were kept for the comparison, as it has been said that the description of the physical processes is not valid below that limit. Three months were used for the comparison: January 1995, April 1995 and July 1994. From each data set of hourly irradiation, and for a given month, the daily irradiation was computed. The estimate is said valid if at least 2 hourly irradiations are used in the computation in January and April and 3 in July. The comparisons present in this case an additional problem: a measuring station is not necessarily contained within a B2 pixel. An interpolation method is requested to estimate locally the irradiation from irradiations computed at the surrounding B2 pixels. A comparison between several methods was performed by Iehle et al. (1997) and they recommended the nearest-neighbor technique. The results strongly depend upon the relevance of the selected technique to the local spatial properties of the irradiation. The smoother the field, the better the assessment by the nearest-neighbor technique. In case of high spatial variations, the technique will be inappropriate as most of the standard ones. Given the properties of the areas under concern this work, the results should be regarded as the typical accuracy that can be achieved. Lower accuracy will be find in cases of large variations in orography or juxtaposition of local climate. Given the two time-series, and for all stations together, we compute the difference (measured -estimated) in several ways for daily irradiation for a given month, for all the days, and for the monthly mean of daily irradiation. For each parameter, the differences have been computed and are summarized in the The correlation coefficient is high in all cases, from 0.85 to 0.92. The bias is negative (overestimation) in January and positive for April and July (underestimation). It is less than 250 Whm -² in absolute value, i.e. less than 7% in relative value. The high relative value of the bias for the monthly mean of daily irradiation for January is believed to be caused by the low number of samples ( 19), since by definition, the bias should be equal for daily irradiation and for the monthly mean. The RMSE (root mean square error) increases as the irradiation increases. It is larger for the daily irradiation than for the monthly mean. For daily values, it amounts to 852 Wh m -² in July, i.e. 15% of the mean daily irradiation. The RMSE for monthly mean is smaller and the maximum is 399 Wh m -² in July, i.e. 7%.

CONCLUSION

These results demonstrate clearly that the method Heliosat-2 may apply to the images in B2 format with a satisfactory accuracy. The B2 images may even be used to assess the hourly irradiation. However, given the poor sampling in time of these images, it may be recommended to limit their use to the assessment of daily irradiation or to the irradiation for larger periods. Even with their low resolution in time and in space, B2 images are able to provide useful information to create a solar climatological database. The HelioClim project has already produced more than eighteen years time series of solar irradiation maps of Europe, Africa and Atlantic ocean, starting from 1985. This constitutes a unique database in that type of solar information. The database can be accessed through the SoDa web service: http://www.soda-is.com.

Figure 1 .

 1 Figure 1. Scheme showing the sub-sampling in the B2 format.

Table 1 .

 1 Differences between measured and estimated values in Wh m -2 for B2 images.

	Information type	Month	Mean value	Bias	RMSE	Correlation coefficient	Nb. of obs.
	Daily irradiation	Jan 95 Apr 95 Jul 94	984 3401 5797	-7 (-1%) 245 (7%) 237 (4%)	291 (30%) 730 (21%) 852 (15%)	0.89 0.91 0.86	345 1044 954
	Monthly mean	Jan 95	892	-99 (-11%) 225 (25%)	0.85	19
	of daily	Apr 95	3402	241 (7%)	350 (10%)	0.92	35
	irradiation	Jul 94	5792	250 (4%)	399 (7%)	0.86	34
	Table 1


INTRODUCTION

Data fusion is a recent term. It means an approach to information extraction spontaneously adopted in several domains before this was expressed as "data fusion". This approach is based upon the exploitation of the synergy offered by the information originating from various sources. Combination of additional independent and/or redundant data usually results into an improvement of the results. The example of human vision is often given to illustrate the advantages and benefits of data fusion. Because they have slightly different viewing angle, the two eyes of a man make possible stereo vision and hence depth perception, thus extending the capability of a single eye. Another advantage of having two eyes is redundancy; if one is disabled, we can still see.

Using recent words such as "data fusion", or "information fusion" translates the recent understanding that whatever the application domain, these synergistic approaches share common problems and common properties. The objective of data fusion is to express these problems and properties. Hence the properties of the data and their interactions will be better described and analysed; it will be easier to develop the most appropriate methods and algorithms, to monitor the quality throughout a process etc.

Data fusion is exploited by a large number of biological systems. An illustration is given by the human system, which calls upon its different senses to perceive its environment. Human sensors acquire information on view, smell, touch, sound, and taste. The acquired data are processed within the brain. To do so, the brain will use other sources of information: its memory, its experience and its a priori knowledge. Calling upon its reasoning capabilities, the brain "fuses" all this available information to perform deductions, produce a representation of the environment and order action.

Data fusion is not limited to biology. It originates in Defence activities, and such applications are still very vivid. Nevertheless, fusion applies to many other domains.

The exploitation of satellite images and more generally of observations of the Earth and our environment is presently one of the most productive in data fusion. Observation of the Earth is performed by means of satellites, planes, ships, and ground based instruments. It results into a great variety of measurements, partly redundant, partly complementary. These measurements may be punctual and timeintegrated, bidimensional and instantaneous (images), vertical profiles with time integration or not, threedimensional information (oceanic / atmospheric profiler / sounder at ground level, or satelliteborne, or shipborne). Adding the large amount of archives and numerical models representing the geophysical / biological processes, one should conclude that the quantity of information available to describe and model the Earth and our Wald L., 2001. The present achievements of the EARSeL SIG "data fusion". In : Proceedings, EARSeL Symposium 2000 "a decade of transEuropean remote sensing cooperation", Dresden, Germany, Buchroithner M. ed., Balkema, Rotterdam, pp 263266 The present achievements of the EARSeL SIG "Data Fusion" L. Wald

Centre d'Energétique Groupe Télédétection & Modélisation, Ecole des Mines de Paris, BP 207, 06904 Sophia Antipolis cedex, France

ABSTRACT: Data fusion is becoming of paramount importance in Earth observation. A Special Interest Group "data fusion" has been created within EARSeL and SEE to better understand data fusion for a better exploitation of the synergy between all instruments observing and measuring our environment. The SIG also intends to make recommendations to agencies, industries and the scientific community. The communication presents the SIG and its objectives. The achievements already accomplished are: i) statement of the importance of data fusion in Earth observation, ii) dissemination of the fundamentals and properties of data fusion, iii) concept, definition and terms of reference, and iv) assessment of methods for the synthesis of images at higher spatial resolution. Further tracks are indicated. Several publications have been made, resulting from the SIG meetings. The SIG has a wide audience worldwide, benefiting from the use of Internet. It has also launched a series of highquality international conferences in Côte d'Azur. environment increases rapidly. Data fusion is a subject becoming increasingly relevant because it efficiently helps scientists to extract increasingly precise and relevant knowledge from the available information.

The operation of data fusion by itself is not new in environment. For example, meteorologists predict weather for several tens of years. In remote sensing (i.e. Earth observation from spacecraft or aircraft), classification procedures are performed since long and are obviously relevant to data fusion. Data fusion allows formalising the combination of these measurements, as well as to monitor the quality of information in the course of the fusion process.

The European Association of Remote Sensing Laboratories (EARSeL) and the French society for Electricity and Electronics (SEE, the French affiliate of the IEEE) are fully aware of the importance of data fusion in remote sensing. They jointly organised a conference in 1996, called 'Fusion of Earth Data merging point measurements, raster maps and remotely sensed images', which was the first of a series with a venue every 2 years. During the round table of that initial meeting, the need for a working group, called special interest group (SIG) in the EARSeL jargon, was expressed, and it was created later this year.

OBJECTIVES

The SIG 'data fusion' contributes to a better understanding and use of data fusion by tackling the fundamentals in remote sensing underlying data fusion. Further the SIG will certainly be helpful in designing and engineering tools and methods for assessing a priori or a posteriori the quality of a fusion product, that is answering the following questions: is it worth performing a fusion process ? was it worth doing it ?

It has been proposed to restrict the SIG to the so called radiometric aspects. The socalled geometrical aspects are already tackled by several working groups at national and international levels. The exact meaning of these words (radiometric, geometrical) is delicate to define precisely but every one can understand this share in problems. In other words, the present SIG does not handle matter related to any pure geometrical use of the data, e.g. image matching for georeferencing, or geo referencing, accurate positioning, assessment of digital terrain models, ... unless it appears necessary for the wealth of the studies and if information cannot be obtained from elsewhere.

All applications are accepted, none is excluded. The work tasks initially set are:

list and better understand the fundamentals in data fusion list and better understand tools and methods in data fusion, develop new ones develop and provide instruments for the assessment of the quality of the fusion prepare application cases exhibiting several processes and levels of fusion. These cases will help in illustrating data fusion and in students training. Several domains (urban domain, meteorology, ...) should be handled. prepare sets of data for welldocumented sites which may be useful for testing algorithms. This should be performed with the help of the space agencies and other data providers. The SIG also makes recommendations to agencies, industries and the scientific community.

MEANS OF COMMUNICATION AND DISSEMINATION

The activities of the SIG are organised around the organisation of the series of international conferences "Fusion of Earth Data", coorganised every 2 years jointly with SEE and the Ecole des Mines de Paris. These conferences are conceived as a forum and intend to help in understanding what "data fusion" means by providing a clear description of concepts, applications, tools and benefits of data fusion. This series is characterised by a strong interactivity between participants, authors and exhibitors in a warm and friendly atmosphere. The Scientific Committee selects the communications on an anonymous basis and only keeps extended abstracts of good to excellent quality. Accordingly the presentations given during each Conference represent the latest methodologies and advanced applications. They are all of high quality, contributing to lively discussions and to the success of the conference. The "Fusion of Earth Data" Prize of 200 euros is awarded by the Scientific Committee and rewards the best paper appearing in the Proceedings.

An average of approximately 60 scientists attended each of the three Conferences. During each Conference, a plenary debate is organised on a major subject. After the closing of the Conference, half a day is devoted to an indepth discussion of this subject. The outcomes are the inputs of the following working meeting and Conference. Usually, there is one working meeting per year. Once a consensus reached and most of the hot questions answered, the outcomes are published, and a new subject is proposed.

The SIG has a wide audience worldwide, benefiting from the use of Internet. Approximately 400 persons are registered in the mailing list. A web site has been established: http://wwwdatafusion.cma.fr. It contains information on the fundamentals in data fusion, the series of Conferences and the other meetings. Together with the mailing list, it is an efficient way to disseminate the outcomes of the SIG, or to launch a discussion on a particular topic.

Nevertheless, traditional means of dissemination are not neglected such as the EARSeL Newsletter and reports to the general assemblies of EARSeL and SEE.

Several publications have been made in ISPRS meetings or in IEEE journals. These publications result from the outcomes of the SIG meetings.

DEFINITIONS, TERMS OF REFERENCE

The concept of data fusion is easy to understand. However, its exact meaning varies from one scientist to another. Several words have appeared, such as merging, combination, synergy, integration, ... All of them appeal more or less to the same concept but are however felt differently. There is also a fashion. Several times, the word « fusion » is used while « classification » would be more appropriate, given the contents of the publication.

During several meetings, the debate focused on the formalisation of the data fusion in remote sensing which is sorely needed and would shape the domain. The main outcomes of the debate were on definitions and terms of reference. The following definitions were finally agreed upon in January 1998.

Data fusion: data fusion is a formal framework in which are expressed means and tools for the alliance of data originating from different sources. It aims at obtaining information of greater quality; the exact definition of 'greater quality' will depend upon the application. Here quality has not a very specific meaning. It is a generic word denoting that the resulting information is more satisfactory for the "customer" when performing the fusion process than without it. For example, a better quality may be an increase in accuracy, or in the production of a more relevant information. In this definition, spectral channels of a same sensor are to be considered as different sources, as well as images taken at different instants.

It then has been suggested to use the terms merging, combination in a much broader sense than fusion, with combination being even broader than merging. These two terms define any process that implies a mathematical operation performed on at least two sets of information. These definitions are very loose intentionally and offer space for various interpretations. Merging or combination are not defined with an opposition to fusion. They are simply more general, also because we often need such terms to describe processes and methods in a general way, without entering details. Integration may play a similar role though it implicitly refers more to concatenation (i.e. increasing the state vector) than to the extraction of relevant information.

Other definitions were accepted, such as attributes, features, rules, decisions, etc., which actually follow international standards and terms of reference (information science, ISO/DIS 12651).

More information is available on the Data Fusion Web server.

FUTURE TRACKS

Quality is of paramount importance nowadays. There is no discussion of this point. This is especially critical for fusion processes given the amount of additional work to be performed for fusing different sources. Accordingly, ways of answering simple questions such as: what is the benefit of fusing this source and this one, are greatly welcome.

Some debates were already hold on the particular problem of the assessment of the quality of fused products, which are a synthesis of multispectral images but at a higher spatial resolution. Typical examples are the fusion of SPOT multispectral images XS with a resolution of 20 m with panchromatic images P having a 10 m resolution. The objectives of such processes are to obtain synthesised XS images having a resolution of 10 m, and close to what should be observed by a SPOT multispectral sensor having this resolution.

Beyond the arguments about methods, the protocol proposed by [START_REF] Ranchin | Fusion of satellite images of different spatial resolutions: assessing the quality of resulting images[END_REF] seems to be accepted. Parameters to quantify the quality are various. Their use depends upon the application.

A more general discussion on quality in data fusion was the subject of the last Conference and of the following working meeting. The European (CEN) and international (ISO) standards in geographical data quality were discussed with respect to the fusion aspects and were proposed as a basis for further work. Some progress has been made that will be presented on the data fusion Web server, and will be further discussed.

CONCLUSION

Needs expressed by the remote sensing community in Europe have led to the creation of a SIG on data fusion. The SIG has issued statements that identify the degree of importance of data fusion in Earth observation. It has tackled the problems of terms of reference. A new definition of the data fusion is now proposed which emphasises the concepts and the fundamentals in remote sensing.

Several other terms are also proposed which for most of them are already widely used in the scientific community, especially that dealing with information. These terms of reference are published on the Web site of the SIG. They foster exchanges within and between scientific and application communities.

The SIG is contributing to establish a sound understanding of data fusion fundamentals. Means have been set up to disseminate the outcomes of the SIG for the benefit of the Earth observation community and others. These outcomes are regularly reported to the spatial agencies, the European Commission, EARSeL and SEE. A series of high quality Conferences is the flagship of the SIG. They permit to present the latest methodologies and advanced applications, but also to discuss a major topic, which will be debated indepth during the following SIG meetings.

The SIG has now undertaken an inventory of methods, tools, and instruments for the assessment of the quality in data fusion.