Olivier Morel
email: o.morel@iutlecreusot.u-bourgogne.fr.

Christophe Stolz

Fabrice Mériaudeau

Patrick Gorria

Fabrice Meriaudeau

Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging

come

Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging

Introduction

The three-dimensional (3D) machine-vision systems market is expanding rapidly, providing 3D-based machine vision for process control. Nevertheless, the inspection of specular metallic objects remains a delicate task, since it requires controlling the whole lighting of the scene. Extracting shape information of specular metallic surfaces from a single view is still a challenging problem, and there are currently two techniques. The first is studying the highlights of structured lightings, with multiple ring lights, [START_REF] Yun | On the fast shape recovery technique using multiple ring lights[END_REF] with a hemisphere of 127 point sources like the SHINY system, [START_REF] Nayar | Specular surface inspection using structured highlight and Gaussian images[END_REF] or with a calibrated pattern composed of lines. [START_REF] Savarese | Local analysis for 3D reconstruction of specular surfaces[END_REF][START_REF] Savarese | Local analysis for 3D reconstruction of specular surfaces: Part II[END_REF] The second technique is studying the motion of a specularly reflected pattern on the surface that is different from the real motion of the object. [START_REF] Zheng | Acquiring a complete 3D model from specular motion under the illumination of circular-shaped light sources[END_REF] Here, we propose what we believe to be a new way of reconstructing the 3D information on specular metallic objects by extending the shape-from-polarization method to metallic surfaces. Koshikawa and Shirai [START_REF] Koshikawa | A model-based recognition of glossy objects using their polarimetrical properties[END_REF] first used polarization information to determine the shape of dielectric glossy objects. Shape information was computed by analysis of the Stokes parameters of a circularly polarized light reflected by the object surface. Later, Wolff and Boult [START_REF] Wolff | Constraining object features using a polarization reflectance model[END_REF] showed how the surface normals are constrained to the polarimetric parameters of an unpolarized light reflected by the surface. This shape-from-polarization method was developed by Miyazaki et al., [START_REF] Miyazaki | Determining shapes of transparent objects from two polarization images[END_REF][START_REF] Miyazaki | Transparent surface modeling from a pair of polarization images[END_REF] Rahmann, [START_REF] Rahmann | Inferring 3D scene structure from a single polarization image[END_REF] and Rahmann and Canterakis [START_REF] Rahmann | Reconstruction of specular surfaces using polarization imaging[END_REF] especially for transparent or reflective surfaces, but of a dielectric nature. By using the complex refractive index of the surface, we found new relations between the polarization images and the surface normals. [START_REF] Morel | Application of polarimetric imaging to 3D inspection of highly reflective metallic surface[END_REF][START_REF] Morel | Polarization imaging applied to 3D inspection of specular metallic surfaces[END_REF][START_REF] Morel | Threedimensional inspection of highly-reflective metallic objects by polarization imaging[END_REF] The previous authors did not provide any robust solutions to solve the ambiguity concerning the determination of the normal azimuth angle. We propose here a new way of solving it by using an active lighting system. Once the surface normals are computed, the surface is reconstructed by integration.

The paper is organized as follows: the shape-frompolarization method extended to specular metallic surfaces is presented in Section 2. Section 3 describes the active lighting system for solving the ambiguity of the azimuth angle. The description of the whole acquisition system and the results are given in Section 4.

Shape from Polarization for Metallic Surfaces

The surface is assumed to be continuous and is described by a Cartesian expression: z ϭ f(x, y). Therefore each surface normal (Fig. 1) is given by the following nonnormalized expression:

n ជ ϭ Ϫ Ѩf ͑ x, y ͒ Ѩx Ϫ Ѩf ͑ x, y ͒ Ѩy 1 ϭ ͩ p ϭ tan r cos q ϭ tan r sin 1 ͪ . (1)
This expression establishes the relationship between the normal orientation (given by the zenith angle r and the azimuth angle ) and the partial derivatives of the surface. This section presents the two main steps of the shape-from-polarization method. First, we demonstrate how to compute the surface normals (especially the metallic one), thanks to the polarization properties of the reflected light. Second, we describe an algorithm for reconstructing the 3D shape by integrating the normals.

A. Polarization Imaging

After being reflected, an unpolarized light wave becomes partially linearly polarized, depending on the surface normal and on the refractive index of the media it impinges on. A partially linearly polarized light wave has three parameters:

Y light magnitude I, Y degree of polarization , Y angle of polarization .
The degree of polarization varies from 0 for a completely unpolarized light to 1 for a perfectly linearly polarized light. To study the polarization state of such a wave, the use of a rotating polarizer in front of a camera is enough. [START_REF] Wolff | Polarization vision: A new sensory approach to image understanding[END_REF] The relationship between the magnitude I p of the transmission of a partially linearly polarized light wave through a rotating polarizer and the angle ␣ of the polarizing filter is given by a sinusoid (Fig. 2):

I p͑ ␣ ͒ ϭ I max Ϫ I min 2 cos ͑ 2␣ Ϫ 2 ͒ ϩ I max ϩ I min 2 , (2)
where I min and I max represent, respectively, the minimum and the maximum magnitudes seen through the polarizer. Equation ( 2) can be written in the form

I p͑ ␣ ͒ ϭ I 2 ͓ cos ͑ 2␣ Ϫ 2 ͒ ϩ 1 ͔ , (3)
with

I ϭ I max ϩ I min , ϭ I max Ϫ I min I max ϩ I min . ( 4
)
The purpose of polarization imaging is to compute the three parameters, I, , and , by interpolating formula (3). There are several methods for fitting the equation to get the parameters. Because there are three parameters, at least three images, taken with different orientations of the polarizer, are required. Since the degree of polarization is low for metallic surfaces, and to improve the accuracy of the measure of the parameters, we apply the linear least-squares method by taking 18 frames with a constant step of 10°.

Relationship Between the Angle of Polarization

and the Azimuth Angle Wolff and Boult have demonstrated how to determine constraints on surface normals by using the Fresnel reflectance model. The Fresnel coefficients of reflection F Ќ and F ʈ are the ratio between the amplitude of the reflected light and the incident light according, respectively, to the plane perpendicular and the plane parallel to the plane of incidence: [START_REF] Zheng | Acquiring a complete 3D model from specular motion under the illumination of circular-shaped light sources[END_REF] where i is the angle of incidence and t is the angle of refraction. Fresnel formulas (5) show that the orthogonal component F Ќ is greater than the parallel one F ʈ . Therefore it means that an unpolarized light wave becomes partially linearly polarized according to the normal of the plane of incidence. Thus the azimuth angle can be inferred from the angle of polarization :

F Ќ ϭ ͯ sin ͑ i Ϫ t͒ sin ͑ i ϩ t͒ ͯ 2 F ʈ ϭ ͯ tan ͑ i Ϫ t͒ tan ͑ i ϩ t͒ ͯ 2 · ,
F2 ϭ Ϯ 2 . ( 6
)
A new technique to disambiguate this relation is presented in the next subsection.

Relationship Between the Degree of Polarization and the Zenith Angle r

The disparity between the components F Ќ and F ʈ brings also a new piece of information: the degree of polarization of the reflected light. Indeed, the degree of polarization can be expressed as follows:

ϭ F Ќ Ϫ F ʈ F Ќ ϩ F ʈ . ( 7
)
To find a new relationship between the degree of polarization and the zenith angle for metallic surfaces, we introduce the complex refractive index: n ˆϭ n͑1 ϩ i͒ (where is called the attenuation index). By assuming the refractive index of the air to be 1, we can write the Snell-Descartes law:

sin i ϭ n ˆsin t , (8)
where i and t are, respectively, the incident and the refractive angles. To simplify the relations, and as is usually the case in the visible region, the following approximation [START_REF] Born | Principles Of Optics[END_REF] is applied:

Խ n ˆԽ2 ϭ n 2 ͑ 1 ϩ 2 ͒ Ͼ Ͼ 1. ( 9
)
Thanks to this approximation, by substituting Eqs.

(5) into Eq. ( 7) and by writing i ϭ r with Snell-Descartes law (8), we can express the degree of polarization for metallic surfaces as follows:

͑ r͒ ϭ 2n tan r sin r tan 2 r sin 2 r ϩ Խ n ˆԽ2 . ( 10
)
Figure 3 shows that the difference between the true degree of polarization, and its approximation grows slightly only for great values of the angle r . The curve also shows that the ambiguity concerning the determination of the angle r , according to the degree of polarization , does not have to be treated for surfaces with slopes lower than 80°, is the case with the studied objects. For most metallic surfaces, the peak appears generally at a higher angle than that for dielectric surfaces. Nevertheless, the disambiguation method developed by Miyazaki et al. [START_REF] Miyazaki | Transparent surface modeling from a pair of polarization images[END_REF] for the angle r can be applied. In this case, two degrees of polarization images have to be acquired with a light rotation of the object.

B. Surface Reconstruction

Once the angles r and are determined, the normals are computed according to Eq. (1). To reconstruct the surface shape from the normals, we use the Frankot-Chellappa 17 algorithm. Denoting by f ˜, p ˜and q ˜the Fourier transforms of, respectively, the surface height and the x, y gradients, we have

∀ ͑ u, v ͒ ͑ 0, 0 ͒ , f ˜͑u, v ͒ ϭ Ϫjup ˜Ϫ jvq ũ2 ϩ v 2 . ( 11
)
We reconstruct the surface shape by taking the inverse transform of the former equation. As we can see, this algorithm is available only for surfaces with a null mean slant. Since the derivative and the Fourier transform are linear operators, the surface can be split according to:

F3 f ͑ x, y ͒ ϭ f 0͑ x, y ͒ ϩ g ͑ x, y ͒ , ( 12
)
where f 0 is the surface reconstructed from Eqs. (11) and g is the surface mean plane; g can be deduced by

g ͑ x, y ͒ ϭ xp ˜͑0, 0 ͒ ϩ yq ˜͑0, 0 ͒ ϩ cst, ( 13
)
where cst is a constant (integration constant). This algorithm based on a Fourier transform is less time consuming than the standard algorithm based on relaxation. [START_REF] Ikeuchi | Determining surface orientations of specular surfaces by using the photometric stereo method[END_REF] The shape for 1024 ϫ 1024 sized images are built in less than 1 s.

Active Lighting System

The previous section showed the ambiguity about the determination of the azimuth angle from the angle of polarization . Miyazaki et al. [START_REF] Miyazaki | Transparent surface modeling from a pair of polarization images[END_REF] numerically solve this ambiguity by propagating the information at the occluding boundary to the rest of the object. It implies obtaining the whole object image and assuming that the object is geometrically closed and that all local parts of the surface are not concave toward the camera direction. To solve this ambiguity we propose a new active lighting system.

A. Description

Our lighting system is a diffuse dome light (an expanded view is presented on Fig. 4) composed of a ring with numerous LEDs and a dome whose surface is diffuse. It provides a uniform and unpolarized light onto the object to be digitized. The ring of LEDs is split into four parts that can be independently electrically controlled. The offset orientation of the dome ␤ belongs to the interval ͓0, ͞2͔.

B. Principle

Relation (6) between the angle of polarization and the azimuth angle can be expressed as

ϭ Ϫ ͞2 ϩ ͭ 0 . ( 14
)
To demonstrate ambiguity solving, a hemisphere was used because it enables us to clearly represent all the possible surface orientations. Since the azimuth angle is not linked to the refractive index, the azimuth angle image of the hemisphere can be computed nearly all over the surface. Figures 5(a) and 5(b) show the azimuth angle images of the hemisphere, from our acquisition system (without disambiguation) and from the theoretical model, respectively. As one can see, has to be added to the azimuth angle of the points whose normals are oriented to the north. The splitting of the LED ring into two parts would have been sufficient to discriminate the north and south orientations, but it requires a perfect orientation of the dome light: ␤ ϭ 0.

To disambiguate the azimuth angle , we first compute a segmented image I quad that discriminates the surface points whose normals are oriented according to the NW, NE, SW, or SE directions. Figure 6 describes the acquisition principle of the segmented image I quad for the hemispheric object. The binary image I bin1 that discriminates the east and west orientations is obtained by a comparison of the intensity images acquired with the east and west lighting. In the same way, the binary image I bin2 is obtained by a comparison of the intensity images acquired with the south and north lighting. The segmented image I quad that discriminates the four orientations is computed according to the relation I quad ϭ 2I bin1 ϩ I bin2 . Second, has to be added to the azimuth angle whose normals are oriented according to the north direction. Thus, from the azimuth image [Fig. 5(a)] and from Finally, the algorithm of the disambiguation process can be described according to these steps:

1. ϭ Ϫ ͞2, 2. Computing I quad , 3. If ͓͑I quad ϭ 0͒ ٙ ͑ Յ 0͔͒ ٚ ͓I quad ϭ 1͔ ٚ ͓͑I quad ϭ 3͒ ٙ ͑ Ն 0͒, then ϭ ϩ ,
where ٙ and ٚ represent, respectively, the logical operators AND and OR. The result of the disambiguation is presented Fig. 5(c).

Experiments

A. Experimental Setup

The acquisition system is made up of a CCD camera, a liquid-crystal polarization rotator, and an active diffuse dome light (Fig. 7). The active diffuse dome light is used both to provide an unpolarized light on the whole surface and to solve the ambiguity concerning the azimuth angle. Since the target object is highly specular, it is placed in the center of the dome to be illuminated on most of its surface. After reflection, the light that becomes partially linearly polarized is studied with the liquid-crystal polarization rotator and the camera. The liquid-crystal polarization rotator acts as a rotating polarizer, which can be electrically controlled. This device uses nematic liquid-crystal cells associated with a linear polarizer and a quarter-wave plate, which provides tunable polarization by changing the supplied voltage. Since the degree of polarization is lower for metallic sur-faces, we use a sensitive camera with a 10-bit depth. A limitation of the system is due to the hole for the camera, leading to a min value that is about 2°. Therefore the object has to be correctly oriented to respect the constraints about the angle r . Nevertheless, approximating the angle r as inferior to 2°to r ϭ 0°( optical axis orientation) does not lead to a significant error in the 3D surface reconstruction.

B. Quantitative Comparisons

The 3D reconstruction of surfaces is linked to both the acquisition system accuracy and the object shape. Thus, instead of comparing the shape reconstructed from different devices, we compared the normals. To compare the accuracy of the normals acquisition, calibrated hemispheres were used. The norm of the error defined by the following relation was used:

e ជ ϭ n ជ th Ϫ n ជ m , (15)
where the subscripts th and m indicate, respectively, the theoretical and measured data. Figure 8 shows error images taken from three different systems: our polarimetric system, the Replica 500 scanner, and the Minolta VI-910 scanner. A perfectly specular metallic hemisphere, with a refractive index equal to n ˆϭ 1.94 ϩ 5.28i, was used with our system whereas a mat hemisphere was used with the two scanners based on triangulation. The norm of the error is computed with angle r in the interval ͓0, 80°͔, meaning that not all the hemisphere surface normals are computed for the three systems in Fig. 8. The error from the polarimetric system is quite random and homogeneous on the surface except on the center, where the normals are oriented near the optical axis. It is due to both the hole in the dome and to the degree of polarization that becomes very small in this region. Indeed, in this case the reflection co- efficients are nearly the same, increasing slightly an uncertainty concerning the angle . Table 1 presents the normal mean errors with r ʦ ͓0, 80°͔ for two different sized hemispheres and shows the good accuracy of our system for computing the surface normals.

C. Qualitative Comparisons

To qualitatively compare a 3D surface obtained with our system with a 3D surface of reference, we scanned the object with the Replica 500 scanner. This scanner, based on laser ranging, takes regular points with steps of 50 m in the X and Y axes, and the precision in the Z axis is about 20 m. The material of the object being studied is stainless steel. In computing the angle from the degree of polarization, two issues are possible. The first one, presented in Section 2, is to determine directly the angle by knowing the refractive index of the object material.

The second one is to estimate a pseudorefractive index that enables the best fit of the relation between the angle and the degree of polarization measured on a known shape of the same material. To determine this index, a known shape of the same material is placed in the center of the dome and the degree of polarization is measured. Then a calibration curve, that represents the measured average degree of polarization according to the zenith angle can be created (Fig. 9). Finally, the Levenberg-Marquardt nonlinear algorithm is used to estimate a pseudorefractive index that best fits the data. This pseudore-fractive index, which has no physical meaning, enables us to compute the zenith angle image of the new object by using relation (10).

Since the Replica scanner is sensitive to the reflectivity of the surface, a thin opaque coating has to be applied onto the object. Consequently the details of the object appear clearly more marked with our method than those with the scanner [Figs. 10(b) and 10(a), respectively]. After registering the two surfaces, the mean deviation between the surfaces is about 30 m, meaning that the shape is qualitatively well reconstructed. Moreover, the cross section, presented in Fig. 11, highlights the good accuracy of the surface computed with our method. The resolutions along the X and Y axes depend on only the lenses used and on the spatial resolution of the sensor: For instance, we are able to get X and Y resolutions that are three times finer compared with those obtained with the Minolta scanner.

D. Application to Three-Dimensional Inspection

The 3D inspection of highly reflective metallic surfaces is still a delicate task in industrial vision. The aim of our system is to reveal the shape defects on decorations from metallic objects made by stamping and polishing [Fig. 12(a)]. Previous work carried out by Seulin et al. [START_REF] Seulin | Simulation of specular surface imaging based on computer graphics: application on a vision inspection system[END_REF] was efficient in discriminating geometric aspect defects thanks to dynamic lighting: when a fringe pattern was projected, defects on a smooth surface were revealed near the transition between dark fringes and bright fringes. Nevertheless, this system is not adapted for inspecting shape defects on the object's decorations. With our polarimetric system, the 3D surface of a reference object is computed [Fig. 12(b)]. The 3D surface of the objects to be inspected is computed and compared with the reference one. For instance, Fig. 13 shows the photograph and the reconstructed surface of an object with a shape defect on the left-hand-bottom bump. After the two shells are registered, the mean deviation between the surfaces is computed (Fig. 14). In this way, our system efficiently discriminates shape defects. The ambiguity problem that appears on the bumps (because normals orientations change from the south to the north) was previously manually solved. [START_REF] Morel | Application of polarimetric imaging to 3D inspection of highly reflective metallic surface[END_REF][START_REF] Morel | Polarization imaging applied to 3D inspection of specular metallic surfaces[END_REF][START_REF] Morel | Threedimensional inspection of highly-reflective metallic objects by polarization imaging[END_REF] Results shown here present automatic 3D surface reconstruction, thanks to the active lighting system.

Conclusions

In this paper, a new way of reconstructing the 3D surface of specular metallic objects has been presented. The shape-from-polarization method has been extended to specular metallic surfaces. By using a complex refractive index, and thanks to an approximation commonly used in optics, we found new relations for computing the normals. Moreover, the active lighting system we developed enables us to solve the ambiguity concerning the normal orientation. This new way of disambiguating the azimuth angle is more robust than the numerical methods. Finally, the involved process is quite simple, requiring an active diffuse dome light, a CCD camera, and a polarization rotator. The different parts are all electrically controlled, and the 3D surfaces are automatically computed in less than 5 s with the presented configuration: 18 polarization images (1024 ϫ 1024). This acquisition time can be drastically reduced by use of faster liquid-crystal polarization rotators. The efficiency of the polarimetric system for computing the 3D shape is also presented. An application for inspecting shape defects on metallic specular objects is described. The comparison between a reference surface and a three-dimensional surface to be inspected reveals shape defects. The registration between the two surfaces, required before the comparison, is not automatic yet. Therefore future works will consist of including an automatic registration in the system. [START_REF] Besl | A method for registration of 3-d shapes[END_REF][START_REF] Matabosch | Range image registration for industrial inspection[END_REF]

Fig. 1 .

 1 Fig. 1. Light-wave reflection on a specular surface.

Fig. 2 .

 2 Fig. 2. Variation of the light intensity according to the angle of the polarizer ␣.

Fig. 3 .

 3 Fig. 3. Comparison between the approximated degree of polarization and the real degree of polarization for a metallic surface ͑n ˆϭ 1.94 ϩ 5.28i͒.

Fig. 4 .

 4 Fig. 4. (Color online) Expanded view of the active lighting system.

Fig. 5 .

 5 Fig. 5. Disambiguation of the azimuth angle: (a) without disambiguation ( is defined modulo ), (b) theoretical values ( is defined modulo 2), (c) result of the disambiguation ( is defined modulo 2).

Fig. 6 .Fig. 7 .

 67 Fig. 6. Acquisition principle of the segmented image I quad .

Fig. 8 .F4F5F6

 8 Fig. 8. Error images of the normals e ¡: (a) polarimetric system, (b) Replica scanner, (c) Minolta VI-910 scanner.

Fig. 9 .

 9 Fig. 9. Calibration curve.

Fig. 10 .

 10 Fig. 10. 3D reconstruction of a specular metallic object: (a) surface from the 3D scanner, (b) surface from our method.

Fig. 12 .

 12 Fig. 12. (a) Object reference photograph and (b) its 3D reconstructed surface.

Fig. 13 .

 13 Fig. 13. (a) Photograph of an object with a shape defect and (b) its 3D reconstructed surface (b).

Fig. 14 .

 14 Fig. 14. Mean deviation between the two reconstructed surfaces.

Table 1 . Mean Error on Normals Acquisition

 1

	Hemisphere	Polarimetric	Replica	Minolta
	Diameter (mm)	System	Scanner	Scanner
	41.275	0.0695	0.0882	0.1034
	44.450	0.0644	0.0614	0.0790

10 June 2006 ͞ Vol. 45, No. 17 ͞ APPLIED OPTICS 5 rich2/zod-osa/zod-osa/zod01706/zod3098-06z xppws Sϭ1 4/10/06 4/Color Figure(s): 4COnline: 4 Art: IP-64554 F7 F8


MD Simona Roggero
email: simona.roggero@unito.it

Paola Quarello

Tiziana Vinciguerra

Filomena Longo

Antonio Piga

Ugo Ramenghi

Roggero Simona

Quarello Paola

Vinciguerra Tiziana

Longo Filomena

Piga Antonio

Ramenghi Ugo

Severe iron overload in Diamond-Blackfan anemia: a

Keywords: Iron, Bone marrow failure, Iron-clinical iron overload Diamond-Blackfan anemia, iron overload, chelation treatment

INTRODUCTION

The consequences of iron overload in multitransfused thalassemia patients are well know, whereas the situation in other settings is poorly documented [START_REF] Piga | Survival improvement in thalassemia: who should take the credit?[END_REF]. Damage due to iron overload may be important in chronic anemias when the prospects of life are good or improve with advances in treatment. Few studies of iron overload in patients with transfusion-dependent Diamond-Blackfan anemia (DBA) have been published [START_REF] Ambruso | Effect of subcutaneous deferoxamine and oral vitamin C on iron excretion in congenital hypoplastic anemia and refractory anemia associated with the 5q-syndrome[END_REF][START_REF] Beck | Endocrine studies in Blackfan-Diamond anemia: evidence for hypothalamic-pituitary dysfunction under frequent transfusion therapy[END_REF]. DBA (OMIM 205900) is a rare congenital or early-onset pure red cell aplasia observed in 5-10 per million live births [START_REF] Campagnoli | Molecular basis of Diamond-Blackfan anemia: new findings from the Italian registry and a review of the literature[END_REF]. Corticosteroids and red cell transfusions are the mainstays of therapy.

Approximately 60-70% of patients initially respond to corticosteroids but many patients require highdose steroids, or develop resistance to therapy and require long-term transfusion or allogeneic stem cell transplantation [START_REF] Campagnoli | Molecular basis of Diamond-Blackfan anemia: new findings from the Italian registry and a review of the literature[END_REF][START_REF] Vlachos | Diagnosing and treating Diamond Blackfan anaemia: results of an international clinical consensus conference[END_REF]. In the last few years, new insights into treatment-related, long-term side effects have become apparent. For transfusion-dependent patients, secondary hemochromatosis is a major medical problem.

The overall actuarial survival at greater than 40 years of age is 75%: 100% for those in sustained remission, 86% for steroid-maintainable patients and 57% for transfusion-dependent patients. There is a statistically significant survival advantage for steroid-maintainable as compared to transfusiondependent patients [START_REF] Lipton | Improving clinical care and elucidating the pathophysiology of Diamond Blackfan anemia: an update from the Diamond Blackfan Anemia Registry[END_REF]. About 23% of all deaths reported in the DBA American Registry are related to complications due to iron overload [START_REF] Lipton | Improving clinical care and elucidating the pathophysiology of Diamond Blackfan anemia: an update from the Diamond Blackfan Anemia Registry[END_REF]. These data highlight the fact that this overload in regularly transfused DBA patients should not be underestimated, and constitutes a serious complication.

Evidence regarding the efficacy of chelation therapy for the treatment of transfusional iron overload has largely been based on experience in patients with thalassemia major [START_REF] Cappellini | Guidelines for the clinical management of thalassemia[END_REF].

The aim of our study was to quantify iron overload directly from the liver iron concentration (LIC) in a large cohort of regularly transfused DBA patients, and relate it to their transfusion and chelation history and their iron-related complications. We also match this cohort with a comparable set of thalassemia major patients.

METHODS

Patients

We retrospectively analyzed all DBA patients referred to our Institution from June 2000 to June 2008. The exclusion criteria were:

-transfusion independence due to achievement of spontaneous remission or to the response to steroid therapy; -bone marrow transplantation.

Informed consent was collected from each patient. Clinical information included gender, age at diagnosis, age at first transfusion, number of units received, amount of transfusional iron, age at start of iron chelation, drug and prescription schedule and compliance.

The following conditions were regarded as iron-related complications: IDDM, altered glucose tolerance, hypothyroidism, hypoparathyroidism, hypogonadism, cardiopathy [START_REF] Cappellini | Guidelines for the clinical management of thalassemia[END_REF]. Regarding cardiopathy we distinguished clinical from preclinical (ejection fraction within normal limits but with a decrease of >10% in more than two consecutive assessments and/or iron cardiac overload measured by cardio RMN T2* and/or prophylactic use of angiotensin converting enzyme inhibitors or angiotensin II receptor antagonists).

For SQUID evaluation, a venous blood sample was collected to measure serum ferritin.

Chelation treatment compliance

Compliance with chelation management was estimated at each follow up visit by a Centre physician from the sum of the following data:

-number of infusions prescribed, -number of infusions reported by the patient, -number of infusions recorded by the electronic pump (Crono ® , Cane s.r.l., Italy), -examination of infusion sites, -conversation with the patient.

The thresholds set for adequate DFO chelation were 20-40 mg/kg/day, as an 8-12-hour subcutaneous infusion, for a minimum of 5 days a week based on the iron input/output ratio.

Iron intake

The iron intake (mg of iron) was calculated as total amount of red blood cells (RBCs) transfused×1.08 [START_REF] Cappellini | A phase 3 study of deferasirox (ICL670), a once-daily oral iron chelator, in patients with beta-thalassemia[END_REF]. The total amount of RBCs transfused was calculated as the total amount of blood (mL) multiplied by the hematocrit of each unit (%).

The total number of transfused RBC units was available for all thalassemia and DBA patients. The hematocrit of each unit was available for all thalassemia patients and for 56% of DBA patients. For the remainders, transfused in different Italian Centers, we considered for the iron intake calculation

Evaluation of iron overload

Several parameters were employed:

-Serum ferritin Serum ferritin was determined at SQUID evaluation; ferritin values were centralized in the same laboratory by automated immunofluorescent assays (BRAHAMS Ferritin KRYPTOR).

-Liver iron concentration determination LIC was measured by noninvasive technique of magnetic liver susceptometry using SQUID biomagnetic susceptometer (Model 5700 Tristan Technology, S.Diego CA) [START_REF] Angelucci | Hepatic iron concentration and total body iron stores in thalassemia[END_REF].

All SQUID evaluations were made with the same device in Turin Centre. LIC was expressed as mg Fe/g liver dry weight (d.w.), with a wet weight/dry weight ratio of 5.83 as observed in the specific deferasirox studies [START_REF] Roper-Bouchet | Drying methods affect the wet:dry weight ratio of liver tissue samples and impact liver iron content measurements[END_REF]. Iron overload was considered severe when LIC was > 15 mg Fe/g liver d.w., moderate when it was 7-15 mg Fe/g liver d.w. and mild when it was 1.3 -7 mg Fe/g liver d.w. [START_REF] Angelucci | Hepatic iron concentration and total body iron stores in thalassemia[END_REF][START_REF] Olivieri | Survival in medically treated patients with homozygous beta-thalassemia[END_REF].

Iron overload was classified in accordance with the observations on thalassemia, where LIC values > 7 mg iron/g d.w. or > 15 mg iron/g d.w. have been associated with an increased risk of cardiac disease or death respectively [START_REF] Olivieri | Iron-chelating therapy and the treatment of thalassemia[END_REF].

-Cardiac iron concentration determination Cardiac iron loading was quantified by means of the MRI T2* technique as described by Anderson [START_REF] Anderson | Cardiovascular T2* magnetic resonance for the early diagnosis of myocardial iron overload[END_REF]. On a Philips Intera Giroscan 1,5 Tesla scanner calibrated by the authors T2* values < 20 ms were indicative of iron overload, and this was considered severe when T2* was < 10 ms according to Pennell [START_REF] Pennell | T2* magnetic resonance and myocardial iron in thalassemia[END_REF].

Control group

The DBA cohort was compared to a β-thalassemia major cohort selected from the whole series treated at our Centre. The cohort selection included the following steps:

-Inclusion criteria by transfusion-dependence, adequate iron chelation prescription and compliance.

-For each DBA patient, we assigned two thalassemia patients matched for sex and iron intake.

When more than two thalassemics were eligible for each DBA patient, the two with the closest iron intake were chosen.

-Each pair of assigned thalassemia patients has been randomly splitted in group A or B.

-Group A and B have been tested for homogeneity.

-Group A has been randomly taken for the comparison analysis with DBA. Bland-Altman analysis has been applied to group A and B that resulted homogeneous for iron intake and LIC. The Student's t-Test was used to assess the difference between DBA and thalassemia groups, and a p-value of 0.05 was considered as significant.

Statistics

RESULTS

DBA patients

We considered 31 Italian transfusion-dependent DBA patients. Their clinically relevant features are set out in Table 1. They were all on slow subcutaneous infusion of deferoxamine (Desferal®, DFO, Novartis Pharma AG, Basel, Switzerland); the mean chelation treatment duration was 7,4 years (SD: 6,3 years; median 5,8 years; range: 0-19,5 years); no side effects were reported.

Iron overload

No patient had a normal LIC. Mean LIC was 13,4 mg Fe/g d.w. (SD: 6,8; median 15,1; range 1,4-30,3). Mean ferritin level was 1760 ng/ml (SD: 1152 ng/ml; median: 1500 ng/ml, range: 101-4851 ng/ml); serum ferritin and LIC showed a positive relationship (r = 0,41, p = 0,02).

A severe iron overload (LIC>15 mg/Fe/g liver d.w.) was observed in 17/31 (54%) patients, of whom 10/17 (59%) were inadequately chelated (Figure 1, Table 1). Inadequate chelation was observed in 52% (16/31): 10/16 due to inappropriate prescription and 6/16 to low compliance.

All the 8 patients younger than 5 years showed a moderate (2) or severe [START_REF] Lipton | Improving clinical care and elucidating the pathophysiology of Diamond Blackfan anemia: an update from the Diamond Blackfan Anemia Registry[END_REF] iron overload, 2 to delayed onset of chelation or inadequate prescription or poor compliance. Three patients were assessed for cardiac iron by MRI. One had a T2* value of 7.7 ms, indicating a high cardiac risk. This patient was a nine-year old girl with moderate LIC and non-optimal DFO therapy (late onset and inadequate compliance). Echocardiographic parameters including left ventricular (ejection fraction) were normal. She also developed primary hypothyroidism at the age of 7 (patient no. 14, Table 1).

Complications

Seven (23%) patients presented one or more iron-related complications; a severe iron overload was observed in four (57%) patients (Table 1). On the average, clinical complications occurred 13.1 years after diagnosis and 11.2 years after the start of transfusional therapy.

Comparison between DBA and thalassemia

Clinical features of DBA patients and correlations with thalassemia patients are reported in Table 2.

A significant difference (p<0.0001) between the LIC values of the two groups (Table 2) was found.

The DBA group displayed a substantial and significantly higher LIC. Hypothyroidism (4), diabetes mellitus (2), hypoparathyroidism (1), heart disease (preclinical cardiopathy in 2 cases) were all

DISCUSSION

There are many studies on the long-term consequences of iron overload, but full reports analyzing iron overload in DBA patients are missing in the literature.

We observed a high prevalence of severe iron overload and inadequate chelation in transfusiondependent DBA patients on long-term follow-up. In our DBA cohort the iron overload was significantly higher than that of thalassemia patients with similar iron intake. Disease-specific differences may potentially exist. However, our data are not sufficient to demonstrate an intrinsically higher propensity to develop iron overload.

In our DBA cohort we found that the correlation between LIC and ferritin levels was not strong, suggesting that a single measurement of serum ferritin was a poor predictor of LIC in DBA, as previously observed in many studies of thalassemia and sickle cell disease [START_REF] Pakbaz | Serum ferritin underestimates liver iron concentration in transfusion independent thalassemia patients as compared to regularly transfused thalassemia and sickle cell patients[END_REF]. Despite the fact that transfusion dependent DBA patients are at risk of developing iron overload, chelation is not well routinely used.

We observed inadequate chelation in 52% of regularly transfused patients: 63% due to an inappropriate prescription (<20mg/kg/day and/or infusions <5 days/week), and 37% to low compliance. The time on transfusion before starting chelation treatment was longer in DBA compared to thalassemia patients (p<0.05). Our DBA patients were all on slow subcutaneous infusion of DFO.

Between the two oral chelators currently used in patients with iron overload, Deferiprone (Ferriprox®, Apotex) is potentially associated with agranulocytosis and is thus generally avoided in DBA in the absence of particularly strong clinical indications (i.e. severe cardiac iron overload) [START_REF] Henter | Fatal agranulocytosis after deferiprone therapy in a child with Diamond-Blackfan anemia[END_REF]. Deferasirox (Exjade®, ICL670, Novartis Pharma AG, Basel, Switzerland) has recently been shown to be effective and well tolerated in patients on a regular transfusion program including several DBA patients [START_REF] Tchernia | The once-daily oral iron chelator ICL670 is well tolerated and effective in treating transfusional iron overload in Diamond-Blackfan anemia patients 10th EHA Meeting[END_REF][START_REF] Porter | Relative response of patients with myelodysplastic syndromes and other transfusion-dependent anaemias to deferasirox (ICL670): a 1-yr prospective study[END_REF][START_REF] Vichinsky | Clinical application of deferasirox: practical patient management[END_REF][START_REF] Porter | Concepts and goals in the management of transfusional iron overload[END_REF], and should be useful in DBA patients. We observed a high rate iron-related complication in our DBA cohort: twenty-three per cent of our DBA patients had a clinically significant organ damage that could be attributed to iron overload. In addition, 57% of all the complications (mostly endocrinopathies) occurred in patients with severe iron overload. Two patients had evidence of preclinical heart disease. No cardiac failure or death were observed in our series. This severe picture, similar to a no chelation condition, might be explained by non-optimal chelation (late onset, type, dose, prescription and compliance). Our finding on iron cardiac load were preliminary and limited; low T2* can occur in DBA. The evidence of cardiac iron in a nine-year-old patient should be considered seriously, as in our thalassemia series no patient under eleven-year-old has a pathological T2*. A F o r P e e r R e v i e w 7 similar finding has been recently published on a large series of thalassemia major patients [START_REF] Wood | Magnetic resonance imaging assessment of excess iron in thalassemia, sickle cell disease and other iron overload diseases[END_REF] or thalassemia intermedia [START_REF] Origa | No evidence of cardiac iron in 20 never-or minimally-transfused patients with thalassemia intermedia[END_REF]. A larger study dedicated to cardiac function in these patients is warranted.

The comparison of the severity of iron overload effect in thalassemia and DBA is a complex issue.

The risk of toxicity from iron overload hinges on several factors: the magnitude of iron overload, the organ iron distribution, the duration of exposure to toxic iron levels; we can not exclude an unknown biological mechanism that leads to an early severe iron overload in DBA. As in other chronic anemias such as thalassemia syndromes, sickle cell disease, sideroblastic anemia and hereditary spherocytosis, also in DBA [START_REF] Nemeth | Iron regulation and erythropoiesis[END_REF][START_REF] Hershko | Iron loading and its clinical implications[END_REF] should be interesting to explore the expression of hepcidin and the effect of HFE gene mutations to evaluate their contributions to iron overload.

Our study shows that iron overload is a serious, relatively common and early complication in regularly transfused DBA patients and more frequent than observed in regularly chelated thalassemia patients.

Physicians must be concerned that the management of transfusional iron overload is an important component of DBA treatment. Iron concentration should be carefully evaluated and monitored and the clinical consequences of iron overload should be early considered.

Both LIC and serum ferritin should be considered before initiating iron chelation so that chelation is begun when a critical overload is reached. Moreover, they should be regularly evaluated during chelation to measure its efficacy.

Overloaded patients should be duly treated; optimal compliance must be constantly encouraged in these patients. Optimizing transfusions and regulating body iron levels by chelation will minimize the risk of iron overload, improve their quality of life, and possibly extend survival.

3 -

 3 The inclusion criteria were:-DBA diagnosis in accordance with the criteria accepted by the DBA working group of the European Society for Paediatric Haematology and Immunology, ESPHI[START_REF] Campagnoli | Molecular basis of Diamond-Blackfan anemia: new findings from the Italian registry and a review of the literature[END_REF][START_REF] Vlachos | Diagnosing and treating Diamond Blackfan anaemia: results of an international clinical consensus conference[END_REF]; transfusion dependence and one or more LIC evaluations by SQUID (Superconducting Quantum Interference Device)[START_REF] Angelucci | Hepatic iron concentration and total body iron stores in thalassemia[END_REF].

  75% that is the mean one of our blood bank and in line with the most Italian blood bank.

  Descriptive statistics were generated with Statistica v.6, StatSoft Inc.

  patients. As regards other clinical complications, hypogonadism was present in 4 DBA and 3 thalassemia patients.

Figure. 1

 1 Figure. 1 Correlation between time on regular transfusion and LIC by SQUID depending on chelation treatment. The red circles represent patients with inadequate chelation due to prescription or compliance; the blue diamonds indicate adequate chelation.

Figure. 1

 1 Figure. 1 Correlation between time on regular transfusion and LIC by SQUID depending on chelation treatment. The red circles represent patients with inadequate chelation due to prescription or compliance; the blue diamonds indicate adequate chelation. 254x190mm (96 x 96 DPI)

Table 1 .

 1 Clinical features of DBA patients

	Pt=patient; RBCs= red blood cells; FTN=ferritin; LIC=liver iron concentration; F=female; M=male;
	c=low compliance; p=inadequate prescription; HD=heart disease; HT=hypothyroidism; HG=
	hypogonadism; HP: hypoparathyroidism; DM: diabetes mellitus; HD: heart disease

Table 2 .

 2 Comparison of relevant clinical features of DBA and thalassemia patients 11.

		0	M	0.0	54930	5.1	5.81	Yes	2261	8.6	No
	18	11.8	M	5.9	35520	2.0	0.42	No ( c )	2003	30.3	No
	19	12.4	F	0.1	55045	0.3	11.97	Yes	836	15.3	No
	20	12.4	F	10.0	12460	2.0	0.40	No ( p )	702	3.1	No
	21	13.2	F	5.8	47360	0.4	6.99	No ( p )	839	7.9	No
	22	14.4	F	0.7	63285	1.0	12.62	Yes	101	5.1	No
	23	15.0	F	1.1	68500	1	12.90	No ( c )	3000	27	Yes (HT)
	24	16.2	F	0.1	78660	5.9	10.26	No ( p )	1338	17.2	Yes (HG, HPP)
	25	18.1	M	0.1	96970	0.4	17.64	No ( p )	1000	6.6	No
	26	17.7	M	1.1	95515	3.9	12.71	Yes	2854	15.2	Yes (DM, HT, HG, HD)
	27	20.5	F	7.9	85715	3.0	9.56	Yes	2576	10.5	No
	28	22.4	F	0.2	131790	2.7	19.51	Yes	1815	15.1	Yes (DM)
	29	22.6	M	0.4	132390	5.5	16.73	Yes	2593	6.9	Yes (HT, HG)
	30	22.7	M	0.1	133870	3.8	18.73	Yes	589	3	Yes (HT, HG)
	31	29.7	M	3.4	191975	7.0	19.28	Yes	649	1.4	No
	MEAN MEDIAN	11.5 9.2	M/F: 13/18	1.76 0.7	49976 35470	2.43 1.75	7.4 5.8	YES/NO: 15/31	1760 1500	13.4 15.1	YES/NO: 7/31
	RANGE	1.8-29.6		0-10	660-191975	0.35-7.42	0-19.5		101-4851	1.4-30.3

Page 10 of 12 John Wiley & Sons American Journal of Hematology

F o r P e e r R e v i e w

Table 2 . Comparison of relevant clinical features of DBA and thalassemia patients DBA patients Thalassemia patients

 2

	N	Mean	Range	N	Mean	Range	Student's t-Test

ACKNOWLEDGMENTS

This work was supported by grants from Banca del Piemonte to UR, and Ministero Italiano della Ricerca Scientifica e Tecnologica and Regione Piemonte to UR and AP.

F o r P e e r R e v i e w


Erik Dietzenbacher
email: e.dietzenbacher@eco.rug.nl.

Esther Velázquez

Departamento Economía

Analyzing Andalusian virtual water trade in an input-output framework

Keywords: Input-Output Models, Virtual Water, Trade and Sustainability JEL Classification: R15, Q25, Q17

Analyzing Andalusian virtual water trade in an input-output framework

Erik Dietzenbacher, Esther Velázquez

Introduction

In arid regions, water shortages not only cause serious physical problems but also hinder the social and economic development of the region (see [START_REF] Aguilera-Klink | Agua, economía y medio ambiente: interdependencias físicas y la necesidad de nuevos conceptos[END_REF].

While an appropriate allocation of water may alleviate the pressure on this scarce resource, it appears that a few production sectors account for almost all water consumption. In this paper, we focus on the destination of water in Andalusia -one of the most arid regions in Europe -after it has been embodied in the production of goods and services. Using an input-output framework, we calculate how much water consumption should be attributed to each of the final demands, distinguishing between domestic (i.e. Andalusian), other regional (i.e. Spanish) and foreign destinations. This allows us to determine the trade of water that is directly and indirectly embodied in, for example, the exported products and services.

Our approach implements the concept of virtual water within an input-output framework. Explaining the management of water demand, the concept of virtual water was introduced by [START_REF] Allan | Fortunately there are substitutes for water otherwise our hydropolitical futures would be impossible[END_REF][START_REF] Allan | Overall perspectives on countries and regions[END_REF]. It is defined as the amount of water that is "contained" in a certain product [START_REF] Allan | Virtual water: a strategic resource. Global solutions to regional deficits[END_REF]. It should be noted, however, that the term "contained" covers more than just the physical water content of a product and includes all the water that has been consumed in its production process. Input-output analysis is a suitable tool for determining the virtual water content of one euro of product i. It covers the (direct) water consumption in production process i, the water consumption to produce the amount of each good k that is used as an input in process i, the water consumption to produce the inputs necessary for producing this input of k, and so forth. Summing all the requirements gives the amount of virtual water, i.e. the total amount of water embodied in one euro of final demand for product i. The concept of virtual water is particularly relevant in connection with trade (see e.g. [START_REF] Lenzen | An input-output analysis of Australian water usage[END_REF]. 1 For example, a certain region might be able to save water by replacing some of its domestic production of water intensive goods by imports from regions that are relatively water abundant. This immediately relates to the Heckscher-Ohlin theory (Wichelns, 2001;[START_REF] Hakimian | Water scarcity and food imports: an empirical investigation of the 'virtual water' hypothesis in the MENA region[END_REF][START_REF] Sayan | H-O for H2O: can the Heckscher-Ohlin framework explain the role of free trade in distributing scarce water resources around the Middle East?[END_REF], which states that relatively water abundant regions export goods and services that are produced in a relatively water intensive way. Many of the semi-arid countries in the Middle East have approached their water problems in this way and introduced appropriate food policies and strategies. For instance, Israel and Jordan have reduced (or even abandoned) the export and the production of water intensive crops, so as to optimize the allocation of the scarce water resources (see [START_REF] Van Hofwegen | Virtual water trade -conscious choices[END_REF]. The virtual water content of imports and exports also plays an important role in determining the so-called water footprints (see e.g. [START_REF] Chapagain | Water Footprints of Nations, Value of Water Research Report Series[END_REF]). 2 The water footprint of a nation, for example, gives the total volume of water used in the production of goods and services consumed by the inhabitants of that country.

Trade matters, because inhabitants consume imported products and thus foreign virtual water, while at the same time domestic water is used in the production of export products that are consumed abroad.

The plan of the paper is as follows. Section 2 briefly discusses some of the geographical and economic characteristics of Andalusia that are relevant for our study. The input-output framework in relation to water consumption is presented in Section 3. As descriptive measures, we will discuss the direct water coefficients and the virtual water multipliers. Section 4 appropriates water consumption to the actual final demands to determine the virtual water contents. The sensitivity of product prices to water pricing and its relation to regional policy aspects are taken into 4 account in Section 5. We discuss how nullifying certain exports affects total water consumption, gross regional product, employment, and the regional trade balance.

Section 6 deals with the virtual water content of Andalusian imports and exports, and examines whether its trade pattern is in line with the Heckscher-Ohlin theory. Our conclusions are given in Section 7.

Geographical and development aspects

Apart from being a vital element for life, water is also a strategic resource for any economic activity. The extent to which water is available may condition the development of a region in a significant way. In order to determine the role that water plays in the Andalusian economy, we will discuss some geographical features of the region as well as some relevant aspects about water in Andalusia and its main uses.

Andalusia is strategically located in the south of Spain and may be described as a vast triangular plain of 87,561 Km 2 (which is 17% of the Spanish territory). This plain is bordered in the north by the Sierra Morena and the Bética mountains; in the south-west by the Atlantic Ocean; and in the east and south-east by the Mediterranean Sea. Due to this geographical situation, Andalusia has a Mediterranean climate, characterized by irregular rainfall -both over time and across space -and long hot summers with high evapotranspiration.

The hydrographical network consists of five river basins: the Guadalquivir basin, the Guadiana basin and the Guadalete-Barbate basin, each flowing into the Atlantic Ocean; and the South basin and the Segura basin flowing into the Mediterranean Sea. The data in Table 1 show the sizes of the basins and the amounts With 59%, the Guadalquivir basin is clearly the largest within Andalusia. The figures in the fourth and fifth column show how much water (in billion liters per year) is provided by each of the basins. Note that 73% of this is surface water, while 27% is from underground reservoirs.

INSERT TABLE 1

The economic development of Andalusia has induced an increase in the demand for water over time. In its turn, this has led to a stronger pressure on the scarce water resources. As we will see in more detail in the next section, the agricultural sectors absorb 90% of the available water resources due to the very large amount of irrigated land. According to Lopez-Fuster and Montoro (2002, p. 3), Spain ranks third in the world and first in Europe, in terms of irrigated land. Andalusia covers 23.3% of the Spanish irrigated land (Consejería de Agricultura y Pesca, 1999, p. 84). This is a very high percentage if we take into account that Andalusia is the most arid region in the country and the one with the most serious problems of water shortages. The problems are further aggravated because the existing irrigation systems are rather old and only few hi-tech systems that save water are used. Irrigation by gravity is still the system that is used most widely in the region (44.9%). In addition, the effects of the large number of tourists that visit the Andalusian coast should be mentioned. Tourism has become one of the important drivers of the region. Especially in the summer, tourist activities require a lot of water, which conflicts with the use in the agricultural sector. Agricultural activities and tourism together have risen the demand for water to such an extent that the coastal areas are mostly irrigated with underground water. A consequence of this is that intrusion of salty sea water takes place, which raises the problems due to overexploitation even further. Also the manufacturing sector has undergone a large expansion over time.

This occurred mainly in the Guadalquivir river basin and around the major cities and the main harbours of the region. The expansion involved in particular food processing and the agricultural products sector, both of which consume considerable amounts of water [START_REF] Velázquez | An input-output model of water consumption: analysing intersectoral water relationships in Andalusia[END_REF].

An explorative analysis of water consumption

In this section we will discuss water consumption at the sectoral level. We have used the Andalusian input-output table for 1990 (see Instituto de Estadística de Andalucía, 1995) and data on water consumption (Agencia de Medio Ambiente, 1996). The first column in Table 2 gives the vector w with sectoral water consumption (in billion liters). It shows that 90% of all the water consumption takes place in the agricultural cluster (sectors 1-6). The manufacturing cluster (sectors 7-19) and the services cluster (sectors 20-25) account each for 5% of the water consumption. The second column gives the vector x with sectoral production (in million euros). It follows that agriculture accounts for only 8% of the total output value, manufacturing for 34%, and services for 58%. So, almost all water is consumed by sectors that are responsible only for a minor share in the output value. This suggests that the prices for the agricultural prices are too low, once water is priced according to its scarcity.

INSERT TABLE 2

The third column in Table 2 gives the vector y with direct water input coefficients. They are defined as

i i i x w y / =
and describe the water consumption (in liters) per euro of production. On average this coefficient is 53, but note that there is an extreme variance across sectors. In particular citrus fruits (sector 3) and cereals and legumes (sector 1) require an enormous amount of water per euro of output. Also the other four agricultural sectors are well above average. Consequently, the manufacturing and service sectors must have coefficients much smaller than average.

We see that only three manufacturing sectors (metallurgy, 9; chemicals and plastics, 11; and paper, printing and publishing, 18) and one service sector (hotel and catering, 22) consume more than 5 liter per euro production.

Although cereals and legumes (sector 1) has a very high direct water input coefficient and absorbs more than 25% of all the water, a large part of its products are sold to the food processing sector (14). So, indirectly, the food products contain a considerable amount of water, because this sector requires cereals and legumes as its inputs. The appropriate way to take all such indirect effects into account is by using an input-output framework. Consider the input-output table (in monetary terms) as

given by Table 3. The typical element ij z of the n n × matrix Z gives the intraregional intermediate deliveries. That is, the deliveries from sector i in Andalusia to sector j in Andalusia, with i, j = 1, …, n. The element ij f of the k n × matrix F, gives the deliveries of sector i in Andalusia to the final demand category j (= 1, …, k). The final demand categories are private consumption, public consumption, investments, exports to the rest of Spain, exports to other EU countries, and exports to the rest of the world.

INSERT

The row vector v′ gives the value added in each sector (which comprises wages and salaries, depreciation, operating surplus, and indirect taxes minus subsidies). Note that the sum of this vector gives the total value added in Andalusia, which is its gross regional product (GRP, similar to GDP). The typical element ij m of the n n × matrix M gives the imports that originate in a "foreign" (i.e. either in the rest of Spain or in an other country) sector i and that are bought by the Andalusian sector j. The elements i x of vector x give the (gross) output or money value of the production in sector i in Andalusia.

Note that the sectoral outputs may be obtained by summing over the rows or the columns. Summing over the columns yields the following accounting equation;

ij j ij j i f z x Σ + Σ =
. Direct input coefficients are defined as

j ij ij x z a / =
and they indicate the (extra) input in euros from sector i in Andalusia, that is required for the (extra) production of one euro by sector j in Andalusia. Using this definition and collecting the final demand categories (i.e.

ij j i f f Σ =
), implies that the accounting equation can be rewritten as

i j ij j i f x a x + Σ =
, or as x = Ax + f in matrix notation.

If the matrix A with direct input coefficients is assumed to be constant, it is possible to evaluate how much output each sector must produce for any given (i.e. gives the total (extra) amount of virtual water that is required per (extra) euro of final demand in sector j. These virtual water multipliers (i.e.

ij i i l y Σ
) are given in the fourth column of Table 2.

Note that the average virtual water multiplier (= 74) is 38% larger than the average direct water input coefficient (= 53). The first is obtained as the total water consumption (3,365 billion liters) divided by the total final demands (45,651 million euros). 3 It thus gives the weighted average of the separate water multipliers, using sectoral final demands as weights. The average direct water input coefficient is obtained by dividing the total water consumption by total production (62,952 million euros). The average direct water input coefficient uses sectoral outputs as weights.

The results in Table 2 for the water multipliers again show the distinction between the agricultural sectors (1-6) and the other sectors. Two of these sectors that should be mentioned are food processing (sector 14) and hotel and catering trade (22). This means that relatively little water is consumed by the sectors themselves, but indirectly a fairly large amount of water is necessary for their products. The matrix A of intermediate input coefficients confirms that hotel and catering trade strongly relies on inputs from food processing, which in its turn relies heavily on inputs from the agricultural sectors that are highly water intensive.

The virtual water content of final demands

The Andalusian input-output

Σ

, respectively. The results are given in the columns ( 5)-( 8) in Table A1.

For example, the 34.6 million euros of Andalusian final demand for cereals and legumes have required, directly and indirectly, 66.3 billion liters of total water.

A summary of the detailed results in Table A1, is given in Table 4. The sectors have been aggregated into the clusters Agriculture (sectors 1-6), and Services (20-25). The results give the final demands as a percentage of the total final demands (45,650.8 million euros) and their virtual water contents as a percentage of the total water consumption (3,364.7 billion liters). It turns out that the final demands for agricultural products are only 6% of the total final demands but their production requires no less than 54% of all water consumption. Final demands for services, on the other hand, amount to 61% of the total and are responsible for only 13% of the total water consumption. Note that exports to other regions or countries are 27% of all final demands, but account for more than half (52%) of the total water consumption.

INSERT TABLE 4

The most striking result is that the exports of agricultural products are only 3%

of the total final demands, but their virtual water content is 30% of the total water consumption. Another major water using sector is food processing. From Table A1 it follows that its final demands are 11% (its exports 7%) of the total final demands, while the virtual water content is 29% (respectively 19%) of the total water consumption.

Price sensitivity and policy aspects

In this section, we will first show how the virtual water multipliers in Table 2 can be interpreted as changes in the prices of the products, resulting from a cost-push.

Assume that the price of water is set at (or increased by) 1 euro per m 3 (= 1000 liters).

In Section 3, we have obtained the accounting equation

ij j ij j i f z x Σ + Σ =
from the rows in Table 3, which led to the quantity model x = Ax + f. Using the columns in the input-output table leads to the accounting equation

j ij i ij i j v m z x + Σ + Σ =
. A common assumption (which, however, is rarely mentioned explicitly) is that the current price of each product is 1 euro. This implies that the physical unit of measurement is chosen appropriately, namely as the amount (e.g. in kilograms or meters) that can be bought for 1 euro. Dividing the accounting equation by j

x gives

+ Σ + Σ = ) / ( ) / ( 1 j ij i j ij i x m x z ) / ( ) / ( ) / ( j j j ij i ij i j j x v x m a x v + Σ + Σ =
. This equation states that the price (i.e. 1 euro) of one physical unit of product j, equals the costs involved in producing that unit. These costs consist of domestic inputs ( ij i a Σ ), imports (

j ij i x m / Σ
) and value added items ( j j x v / , including wages and salaries and the operating surplus). In matrix notation, the set of equations yields

1 1 ˆ- - ′ + ′ + ′ = ′ x v x M e A e e
, where e denotes the summation vector consisting of ones. 4 Rewriting yields

= - ′ + ′ = ′ - - - 1 1 1 ) )( ( A I x v x M e e L x v x M e ) ( 1 1 - - ′ + ′ .
Suppose that we now introduce the costs of using water and let j w ~ denote the water costs (in euros) in sector j. The price of product j will therefore change, because it also has to cover the costs of using water. Let j p denote the new price of one physical unit of product j. Equating the new price to the total costs per physical unit

L x w x v x M e p ) ( 1 1 1 - - - ′ + ′ + ′ = ′
. Subtracting the new price equation from the equation for the current prices yields

L x w e p 1 ˆ- ′ = ′ - ′
. That is, the price change for product j

equals ij i i i j l x w p ) / ( 1 Σ = -
. Recalling that the current price is set at 1, an outcome of

04 . 1 = j p
for example would indicate that the new price of product j is 4% higher than the current price.

Let us now return to The sensitivity of product prices to a cost push implies that water pricing might be used as a policy option. 5 Introducing water prices (or increasing them) may generate two effects. First, in sectors that use water directly this will decrease the spoiling of water and will stimulate to use water more efficiently. In its turn, this will lead to a decrease in the direct water coefficients

j j j x w y / =
. Second, increased prices of the products (e.g. due to water pricing) will cause a decrease in demand and consequently a decrease in the use of water. A full quantification of this effect would require demand elasticities or a CGE model and a detailed description of a policy device for water pricing. This would include information on how the receipts of water pricing are spent (e.g. redistributed through subsidies). Such an exercise, however, is beyond the scope of this paper and in the remainder of this section we will limit ourselves to sketching the beneficial effects on water saving in relation to other effects.

The results in the previous section show that 49% of the actual water consumption could have been saved, if Andalusia had stopped exporting agricultural products and food processing goods (which, together, account for only 10% of the total final demands). Of course, in considering such a drastic reduction also other effects need to be taken into account. A decrease of the exports implies a fall in production and thus also a drop in employment and value added (or gross regional product, GRP). In addition, the regional trade balance will be affected.

We will calculate the effects of a complete nullification of the "foreign" exports (i.e. to the rest of the EU and to the rest of the world). It is assumed that the A1. To derive the effect on value added, define the direct value added coefficient as

i i i x v / = µ
, indicating value added per unit of output. A full reduction of the foreign exports of sector j reduces the total value added in the region (or gross regional product, GRP) by ) ( 251

RoW j RoEU j ij i i f f l + Σ = µ
. The employment effect could have been obtained in a similar way, if the data had been available. As an approximation, we have computed the reduction in the labor costs. Define

i i i x s / = ω , with i
s the wages and salaries (including employers' contributions) paid in sector i.

Then ) ( 251

RoW j RoEU j ij i i f f l + Σ = ω
gives the reduction in labor costs due to nullifying the foreign exports of sector j. If this reduction is expressed as a percentage of the total labor costs, it equals the percentage reduction in employment if the average wage rate is the same in all sectors. Because this will not be the case, the reduction in labor costs can only be used as an approximation of the employment effect.

If the foreign exports of sector j are nullified, the regional trade balance (defined as Andalusian exports minus imports) deteriorates by

RoW j RoEU j f f + .
Because the production is reduced as a consequence of the decline in exports, less imports (from the rest of Spain, the rest of the EU and the rest of the world) are required. The decrease in imports amounts to ) ( 251

RoW j RoEU j ij i i f f l + Σ = η
, with

i i i
x m / = η the direct import coefficients, where i m denotes the total imports of sector i. Hence, the total deterioration of the regional trade balance due to the nullification of the foreign exports of sector j yields ) )( 1 ( 251

RoW j RoEU j ij i i f f l + Σ -= η .
A summary of the results is given in Table 5. The first six rows report the effects of the nullification of each agricultural sector separately. The row "Total Agriculture" shows the effects if the foreign exports are nullified in all agricultural sectors. In the same way, the findings in the row "Total Manufacturing" give the effects of a complete export reduction in all manufacturing sectors (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). Given its importance, the results for the food processing sector ( 14) are also shown separately.

The row "Total Services" gives the effects of nullifying the foreign exports in all service sectors (20-25) and the final row "Total" shows the effects for the case in which all foreign exports are abolished.

INSERT TABLE 5

The findings in Table 5 indicate that substantial savings in water consumption may be obtained at relatively low costs (in terms of a reduction in GRP, a decline in employment and a deterioration of the regional trade balance). Consider the nullification of the foreign exports by the agricultural sectors and the food processing sector. Their foreign exports amount to 1,341.1 million euros, which is 3% of the total final demands (and 11% of the total Andalusian exports, including those to the rest of Spain). The water consumption reduces by 16% while the decrease in GRP is only 3%. The 5% fall in labor costs (which may be used as a rough approximation of the reduction in employment) is somewhat higher but still modest. The export reduction implies that also the imports are reduced (by 295.1 million euros) so that the Andalusian trade balance deteriorates by 1,046.0 million euros.

The assumptions that underlie our exercise may seem to be fairly heroic. First, it should be emphasized that we have used a linear model to calculate the effects of a nullification of the foreign exports in a set of sectors. This implies that the results in , while the GRP falls by 0.84% and the labor costs by 1.84%. Second, if the effects are triggered by using water pricing as a policy option, it may seem awkward to assume that domestic demand is not affected by the price changes. It should be emphasized that the payments for the virtual water embodied in domestic final demands exactly equal the extra value of these demands due to increased prices. In other words, the government could, in principle, use the receipts from water pricing to ensure that domestic consumers do not have to face price increases. For example, this could be done by leaving the prices unchanged and introducing export tariffs that are equal to the price increases resulting from the last column in Table 2.

The virtual water content of trade

The results in the previous sections have shown that the goods produced by the agricultural sectors and by food processing are highly water intensive (accounting for 82.6% of the total amount of water consumption). At the same time, only 38.3% of these products are destined for the domestic Andalusian final demands. We could say that Andalusia exports a major part of its available water, although it is one of the most arid areas in Europe. The question, however, is whether it is a net exporter of virtual water. It might be the case that it imports even more water than it exports.

According to the well known Heckscher-Ohlin (HO) theory of trade, a country exports the products in which it has a comparative advantage. These are the products that intensively use those factors, which are relatively abundant in the country. The first empirical test of the HO theory was by [START_REF] Leontief | Domestic production and foreign trade; the American capital position re-examined[END_REF]Leontief ( , 1956)). He calculated the extra -direct and indirect -labor and capital requirements necessary to satisfy $1 million of extra exports. In the same way, the decreases in requirements were calculated for the case where a reduction of domestic output was replaced by extra imports (to the amount of $1 million). The US was found to export labor intensive goods and to import capital intensive goods, whereas it was commonly believed to be the most capital abundant country at that time. This result has become known as the Leontief paradox and still continues to trigger ample scientific research.

In this section we will calculate the virtual water content of the exports and imports. It is assumed that the exports, for example those to the rest of Spain, are increased by one million euros using the product mix of the current exports. Hence, we construct a vector RoS f that has the same distribution as RoS f , but its elements sum to one million. That is,

RoS i i RoS j RoS j f f f Σ × = / 000 , 000 , 1
. The water requirements (or virtual water content) of the extra exports of product j are then obtained as

RoS j ij i i f l y 25 1 = Σ
. Leaving the regional trade balance unaffected, it is assumed that also the imports (in this case from the rest of Spain) increase by one million euros. This implies that these products do not need to be produced in Andalusia anymore, so that the regional water requirements decrease. Denote the vector of imports by RoS m , then a one million euro increase of the imports implies that the imports of product j are raised by

RoS i i RoS j RoS j m m m Σ × = / 000 , 000 , 1
. The water requirements then decrease by , respectively.) According to the HO theory, a region that is scarce in water would be expected to save water by increasing trade. That is,

RoS RoS f L y m L y ′ > ′
. In other words, the virtual water content of its imports should be larger than the virtual water content of its exports.

We have calculated the virtual water content for trade with the rest of Spain, with the rest of the EU, with the rest of the world, and total trade. The results are given in Table 6. It should be mentioned that the import vectors we had to use only covered imports by production sectors. For trade with the rest of Spain and for trade with the rest of the EU, Table 6 reports that the virtual water content of Andalusian exports is approximately twice as large as the virtual water content of its imports. For trade with the rest of the world, the exports contain "only" 25% more virtual water than the imports. The results in the total trade case are weighted averages of the separate results, using the actual imports and exports as weights. The imports -in million euros-are 6898 with the rest of Spain; 804 with the rest of the EU; and 2013 with the rest of the world. The corresponding exports are 8930, 1995, and 1466 million euros.

INSERT TABLE 6

In explaining why the exports have a substantially higher virtual water content than the imports have, two aspects stand out. First, the share of agricultural products (which are extremely water intensive) in Andalusian exports is much larger than their share in imports, except for trade with the rest of the world. Second, although the shares of manufacturing in exports and in imports are very similar, it turns out that the share of (relatively water intensive) food processing in exports is a multitude of its share in imports.

Conclusions

Andalusia has a considerable water shortage, but at the same time 90% of its water consumption is localized in the agricultural sectors (which generate only 8% of the total production value, 6% of all final demands and 8% of GRP). Therefore, water is a strategic factor in the development of the region. In order to cope with the increasing problems due to the water shortages, an expanded and more effective regulation of water consumption seems necessary. Also a serious reconsideration of the production processes in which the region chooses to specialize in seems appropriate.

Our findings indicated that only 48% of the water consumption should be attributed to regional (i.e. Andalusian) final demands. Hence, no less than 52% of all water consumption appears to be necessary for producing goods and services that are exported to other Spanish regions or other countries. Our calculations have shown that substantial savings in water consumption may be obtained at relatively low costs, in terms of a reduced GRP, a loss of employment and a deterioration of the regional trade balance. For example, stopping the exports to other countries by the agricultural sectors and the food processing sector would reduce water consumption by 16%, while GRP falls only by 3%. Andalusia is found to be a net exporter of products that intensively use its scarce factor water. Although the agricultural sectors generate only a small part of the Andalusian production and although the agricultural exports are only 15% of all exports, these products contain so much water that the virtual water content of an average million euros of exports is substantially larger than the virtual water content of an average million euros of imports. This finding seems to be in sharp contrast to the HO theory of trade. At the same time, however, it should be mentioned that the Andalusian climate is such that it has a comparative advantage in producing several agricultural products (such as citrus fruits) that require a large amount of sunshine and high temperatures. These "sun intensive" products, however, constitute only a relatively small part of the Andalusian production and exports. No matter whether the results contradict the HO theory or not, the fact remains that one of the most arid regions in Europe is a net exporter of virtual water.

Our central conclusion is that it is necessary to pay attention to cases like water consumption in Andalusia, where a relatively small part of the regional production structure depends heavily on a very limited resource. If policy makers aim at changing this situation in order to arrive at a more sustainable economy that uses the scarce resource less intensively, there seem to be several options. The first is the one that is usually brought to the fore, i.e. technological change. By investing in R&D, new techniques might be developed (e.g. irrigation systems) that reduce the direct water coefficients and additional investments would enable their implementation. The second option is the one that is typically not even taken into consideration. That is, restructuring the production structure, for example by reducing exports that require large amounts of water and stimulating exports of products that are less water intensive. The findings in this paper have shown that the benefits may water pricing (or increase the current price of water). On the one hand, this will save water because producers are stimulated to use water more efficiently, e.g. by reducing the spoiling of water. On the other hand, this will increase the prices of the products and, in particular, the prices of the water intensive products will be raised the most. In its turn, this will reduce the demand for these products and thus induce a saving of water. The receipts from water pricing may be used by the government to subsidize certain sectors or to offset the price increases for some groups (e.g. domestic consumers [START_REF] Antweiler | The pollution terms of trade[END_REF][START_REF] Kainuma | Estimation of embodied CO 2 emissions by general equilibrium model[END_REF][START_REF] Munksgaard | CO2 accounts for open economies: producer or consumer responsibility?[END_REF][START_REF] Machado | Energy and carbon embodied in the international trade of Brazil: an input-output approach[END_REF][START_REF] Atkinson | International trade and the 'ecological balance of payments[END_REF][START_REF] Murudian | Embodied pollution in trade: estimating the 'environmental load displacement' of industrialised countries[END_REF][START_REF] Sanchez-Chóliz | CO 2 emissions embodied in international trade: evidence for Spain[END_REF]).

2 See also the website of the UNESCO-IHE Institute for Water Education (http://www.waterfootprint.org).

3 The final demands per category are given in the first four columns of Table A1 in the Appendix. Adding the column sums gives the total final demands. 6 As far as water is concerned, the last column in

  figures in the second column give the size of each basin within Andalusia, and those

  e. the jth unit vector, provides the interpretation of the elements of the Leontief inverse. That is, ij l gives the (extra) output in sector i that is necessary for one (extra) euro of final demand in sector j. These elements of L take all direct and indirect effects into consideration. Taking the column sums of the Leontief inverse gives the so-called output multipliers. That is, ij i l Σ indicates the total (extra) output that must be produced for one (extra) euro of final demand in sector j. Multiplying the elements ij l by the direct water input coefficient i y (i.e. many (extra) liters of water are (directly and indirectly) consumed by sector i for generating one (extra) euro of final demand in sector j. Summing over i

  multipliers but only modest direct water input coefficients.

  Spanish regions remain as they are. The effects on water consumption can be readily obtained from summing the elements in the columns (7) and (8) of Table

  import products that intensively use factors which are relatively scarce in the country. Taking water into account as a production factor, Andalusia has anything but a comparative advantage in producing water intensive goods.6

  increased imports of product j.

  the negative effects are modest. The third option is to introduce

4

  Vectors are columns by definition and a row vector is obtained by transposition, indicated by a prime. A circumflex (or "hat") is used to indicate a diagonal matrix.5 The role of water pricing has been extensively discussed in the literature, albeit not in an input-output framework. Recent contributions include[START_REF] Albiac | The economic unsustainability of the Spanish national hydrological plan[END_REF];[START_REF] Arbués | Price impact on urban residential water demand: a dynamic panel data approach[END_REF];[START_REF] Brookshire | Market prices for water in the semiarid West of the United States[END_REF]; Gómez-Limón and Riesgo (2004); Mejías et al. (2004); Embid-Irujo (2005); Garrido (2005); International Journal of Water Resources Development (2005); Marques et al. (2005); and Reynaud et al. (2005).

TABLE 3

 3

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

  Table 2 and consider sector 1 (cereal and legumes), which has an output value 1x of 482 million euros and which uses 883 billion liters of water. For sector 1, for example, this implies that the current price of the product in this sector is increased by 192.7% if the price of water is increased by 1 euro per 1000 liters. It should be emphasized that the results for another initial price increase for water can easily be derived. For instance, if the price of water is raised by 0.3 euro per 1000 liters, the price in sector 1 would increase by 0.3×192.7 = 57.8%. The same methodology can also be applied straightforwardly if the increase in the price of water differs per sector. ) to 313.6% for citrus fruits (sector 3). The prices for products from the manufacturing and services sectors all increase by less than 10%, except for the price of food processing products (sector 14) which is raised by 19.0%.

	products (sector 6
	i w ~, with i i w × = 001 . 0 w the water use in Table 2. ij i l x ) ) are thus readily obtained from dividing the ij l with i i i x w y / = ) in the last column of Table 2 by e i i w / ( Σ virtual water multipliers (i.e. The price increases (i.e. i i y Σ o r P e r R e v i e 1000. F w
	O n l
	y
	14

Introducing a water price of 1 euro per 1000 liters (or increasing the current water price by that amount) implies that the water costs 1 w in this sector yield (or increase by) 883 million euros. Note that

The results in Table

2

show that introducing a water price of 1 euro per 1000 liters (or increasing the current water price by that amount) leads to huge increases in the prices of the agricultural products. They range from 25.8% for other agricultural

Table 5

 5 can be used for any other reduction. For example, reducing the foreign

	exports in vegetables and fruits by 60% and those in food processing by 20% would
	result in a saving of water by	0	.	6	×	6	.	86	+	0	.	2	×	4	.	99	=	5	.	11	%
	F o r
	P
	e
	e r
					R
								e
									v i e
															w
																		O n l
																					y

  ). The results in this paper indicate the potential size of the positive effects of water pricing (in terms of water saving) in relation to the negative effects (in terms of a loss in GRP, employment and the trade balance).

	emissions) and natural resources have been extensively investigated. The input-
	output framework appears to be a very useful framework, because it takes the
	interdependent nature of production into full account (see, for example,
	F o r F o r F o r F o r F o r
	P P P P P
	e e e e e
	e r e r e r e r e r
	R R R R R
	e e e e e
	v i e v i e v i e v i e v i e
	w w w w w
	O n l O n l O n l O n l O n l
	y y y y y

Table 2

 2

	shows that Andalusia might

Table 1 .

 1 Water resources

			Basin surface		Resources
			(in Km 2 )		(in billion liters per
					year)
	Basin	Total	In	Percentage	Surface	Sub
			Andalusia		terranean
	Guadalquivir	57,104	51,477	59	2,255	437
	Guadalete/Barbate	6,365	6,365	7	358	85
	South	17,820	17,820	20	414	630
	Guadiana I	53,067	3,248	4	1	6
	Guadiana II	6,871	6,871	8	275	60
	Segura	18,870	1,780	2	1	5
	Total	160,097	87,561	100	3,304	1,223
	Source: Consejería de Medio Ambiente (2004).

Table 2 .

 2 Aspects of water use at the sectoral level

	j Sector	Water use	Output				Direct	Virtual
						Coefficients	water
														multipliers
		w	j	x	j	y	j	=	w	j	/	x	j	Σ	i	y	i	l	ij
	1 Cereal and legumes	883	482					1,833	1,927
	2 Vegetables and fruits	906	1,326						683			693
	3 Citrus fruits	321	103					3,129	3,136
	4 Industrial plants	183	383						478			505
	5 Olive groves	465	836						556			560
	6 Other agricultural products	279	1,907						146			258
	Agriculture total	3,037	5,037								-						-
	average		-		-						603			682
	7 Extractive industry	16	4,705								3						6
	8 Water		0	151								0						4
	9 Metallurgy	25	1,683							15				19
	10 Construction materials		6	1,256								5						9
	11 Chemicals and plastics	41	1,727							24				31
	12 Machinery		1	1,080								1						4
	13 Transportation materials		3	1,542								2						5
	14 Food processing	30	6,350								5			190
	15 Textiles and apparel		5	1,132								4				41
	16 Footwear and leather																		7
	products		0	99								3
	17 Wood products		3	823								4						9
	18 Paper, printing and publishing	24	629							38				57
	19 Miscellaneous manufacturing		1	499								2						5
	Manufacturing total	155	21,676								-						-
	average		-		-								7				74
	20 Construction	17	7,308								2						7
	21 Trade	17	6,107								3						6
	22 Hotel and catering trade	71	4,073							17				80
	23 Transportation,																		6
	communications	12	3,748								3
	24 Sales related services	33	9,188								4						8
	25 Non-sales related services	23	5,816								4						8
	Services total	173	36,240								-						-
	average		-		-								5				15
	Total	3,365	62,952								-						-
	Average		-		-							53				74

Table 3 .

 3 The input-output table

	Z	F	x
	v′
	M
	x′

Table 4 .

 4 Aggregated results for the final demands and the virtual water contents

			Final demand categories
		Andalusia	Exports to	Exports to	Exports to	Total
			the Rest of	the Rest of	the Rest of
			Spain	the EU	the World
		Final demands (as % of total final demands)
	Agriculture	2.7	2.1	0.9	0.1	5.8
	Manufacturing	11.2	15.7	3.4	3.1	33.4
	Services	59.0	1.8	0.0	0.0	60.8
	Total	72.9	19.6	4.3	3.2	100.0
		Virtual water content (as % of total water consumption)
	Agriculture	23.5	19.0	10.0	1.2	53.7
	Manufacturing	11.7	16.2	3.5	2.3	33.7
	Services	12.5	0.1	0.0	0.0	12.6
	Total	47.7	35.3	13.5	3.5	100.0

Table 5 .

 5 The effects of the nullification of "foreign" exports Exports as percentage of the total final demands. 2) Reduction in water use (value added, labour costs) as percentage of the actual water use (resp. value added, labour costs). 3) Deterioration of the Andalusian trade balance in million euros.

		Exports 1	Water	Value	Labor	Trade
			Use 2	added 2	Costs 2	Balance 3
	Cereal and legumes	0.10	2.51	0.10	0.14	34.7
	Vegetables and fruits	0.73	6.86	0.79	2.17	290.0
	Citrus fruits	0.02	1.17	0.03	0.19	11.3
	Industrial plants	0.03	0.19	0.02	0.09	8.2
	Olive groves	0.00	0.01	0.00	0.01	0.6
	Other agricultural products	0.12	0.42	0.12	0.18	46.0
	Total Agriculture	1.00	11.17	1.07	2.80	383.8
	Food processing	1.94	4.99	1.84	2.67	662.2
	Total Manufacturing	6.52	5.83	5.41	9.56 1,942.6
	Total Services	0.05	0.00	0.06	0.02	23.4
	Total	7.57	17.00	6.54	12.38 2,349.7
	1)

Table 6 .

 6 Virtual water content of one million euros of imports and exports

		Import	Virtual	Export	Virtual
		distribution	water	distribution	water
		(as	content	(as	content
		percentage)	(in million	percentage)	(in million
			liters)		liters)
	Trade with the rest of Spain
	Agriculture	5.3	39.3	10.8	71.6
	Manufacturing	76.0	31.7	80.1	60.9
	(of which food processing)	(10.2)	(19.4)	(27.8)	(52.8)
	Services	18.8	1.1	9.0	0.5
	Total	100.0	72.2	100.0	133.1
	Trade with the rest of the EU
	Agriculture	13.7	80.7	20.3	168.8
	Manufacturing	86.0	21.6	78.9	58.8
	(of which food processing)	(3.6)	(6.8)	(26.9)	(51.1)
	Services	0.3	0.0	0.8	0.1
	Total	100.0	102.3	100.0	227.6
	Trade with the rest of the world
	Agriculture	7.4	52.3	3.6	26.6
	Manufacturing	92.4	12.6	95.8	53.6
	(of which food processing)	(2.6)	(4.9)	(23.7)	(44.9)
	Services	0.1	0.0	0.7	0.0
	Total	100.0	64.9	100.0	80.3
	All trade
	Agriculture	6.4	45.4	11.5	82.0
	Manufacturing	80.2	26.9	81.8	59.7
	(of which food processing)	(8.1)	(15.4)	(27.2)	(51.6)
	Services	13.4	0.8	6.7	0.4
	Total	100.0	73.2	100.0	142.1

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In a similar fashion, international flows of pollutants (such as CO

, SO 2 , and NO x

Acknowledgement:

We would like to thank the two anonymous referees for their valuable comments and suggestions.

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F o r P e e r R e v i e w

O n l y 7 Table A1. Detailed results for the final demands and the virtual water contents j AND j f

(1)