D Cébron
email: cebron@irphe.univ-mrs.fr

P Maubert

M Le Bars

Tidal instability in a rotating and differentially heated ellipsoidal shell

Keywords: tides, tidal/elliptical instability, planetary cores, finite element numerical simulations, convection, stratification, Nusselt number

The stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo-and astrophysical contexts, and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows.

INTRODUCTION

The tidal or elliptical instability comes from a triadic parametric resonance between two inertial waves of a rotating fluid and an imposed elliptic deformation (see for instance the review by Kerswell 2002, and references therein). It is a generic phenomenon in turbulence (e.g. [START_REF] Widnall | The instability of short waves on a vortex ring[END_REF][START_REF] Moore | The instability of a straight vortex filament in a strain field[END_REF] and vortex dynamics (e.g. [START_REF] Leweke | Cooperative elliptic instability of a vortex pair[END_REF][START_REF] Dizès | Theoretical predictions for the elliptic instability in a two-vortex flow[END_REF][START_REF] Meunier | A merging criterion for two-dimensional co-rotating vortices[END_REF]. There, the elliptical deformation comes from interactions between adjacent vortices. But this instability is also studied in geophysical and astrophysical tidally deformed bodies: for example, its presence has been suggested (i) in binary stars [START_REF] Rieutord | Evolution of rotation in binaries: physical processes[END_REF]; Le [START_REF] Bars | Tidal instability in stellar and planetary binary system[END_REF]) and accretion disks [START_REF] Goodman | A local instability of tidally distorted accretion disks[END_REF][START_REF] Ryu | Nonlinear evolution of tidally distorted accretion disks: Two-dimensional simulations[END_REF], where they could participate in the energy and angular momentum exchanges between neighbouring systems [START_REF] Lubow | Tidal instability of accretion disks[END_REF], and (ii) in planetary cores (e.g. [START_REF] Aldridge | Elliptical instability of the Earth's fluid core[END_REF][START_REF] Cébron | A systematic numerical study of the tidal instability in a rotating ellipsoid[END_REF], where they could play an important role in the induction of a magnetic field [START_REF] Kerswell | Tidal instability as the source for Io's magnetic signature[END_REF][START_REF] Lacaze | Magnetic field induced by elliptical instability in a rotating spheroid[END_REF][START_REF] Herreman | On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids[END_REF]) and even in planetary dynamos [START_REF] Malkus | Energy sources for planetary dynamos[END_REF].

Previous studies of tidal instability have been performed for an isothermal fluid, starting from a solid body rotation or from an homogeneous isotropic turbulent rotating flow [START_REF] Fabijonas | Mean effects of turbulence on elliptic instability in fluids[END_REF]. Nevertheless, in all natural systems, temperature differences are also present, which lead either to stratification or to convection. The previous studies need then to be reinvestigated in order to quantify the impact of a temperature field on the elliptical instability. Conversely, from a thermal point of view, many studies have been performed regarding the convective flow of an incompressible homogeneous fluid in a rotating spherical shell (see for instance Aurnou 2007, and references therein). However, since most astrophysical bodies are tidally deformed, these studies have to be reinvestigated to account for the potential presence of an elliptical instability. Note that a link between tidal resonance of gravito-inertial waves and thermal effects has been proposed by Kumazawa et al. (2006) in a geophysical context. However, this study considers the resonant forcing of a given wave by tides, which is different from the elliptical instability possibly induced by parametric resonance. Then, to the best of our knowledge, the only previous work which combines thermal and elliptical effects is the theoretical study of Le [START_REF] Bars | Thermo-elliptical instability in a rotating cylindrical shell[END_REF], who considered the influence of an established diffusive temperature profile. They then interpreted the thermo-elliptical instability in terms of gravito-inertial waves resonance and determined its linear growth rate by a local approach. In order to complete this work, a guideline of our study is given by the following questions: (i) how is the growth rate of the tidal instability modified by an imposed temperature difference in the spheroidal geometry? (ii) Does the tidal instability grow over an established convective flow? (iii) Is the heat flux modified by the instability, and what are the scaling laws involved? In this paper, we tackle these questions using a systematic numerical study of the thermo-elliptical rotating flow in a fixed triaxial ellipsoidal shell. The numerical model is presented in section 2. The variations of the heat flux and the growth rate are systematically quantified and interpreted in section 3. Finally, orders of magnitude and conclusions are drawn for geo-and astrophysical flows in section 4.

NUMERICAL MODEL AND ITS VALIDATION

As sketched in figure 1, we consider the rotating flow inside a fixed triaxial ellipsoid of axes (a, b, c), with a constant tangential velocity U 1 -(z/c) 2 imposed all along the outer boundary in each plane of coordinate z perpendicular to the rotation axis (Oz), where U is the imposed boundary velocity at the equator. An homothetic ellipsoidal core, in a ratio η = 0.3, is placed at the center, with also an imposed constant tangential velocity ηU 1 -(z/c) 2 along its boundary. In the following, we use the mean equatorial radius Req = (a + b)/2 as a lengthscale and we introduce the timescale Ω -1 by writing the tangential velocity along the deformed outer boundary at the equator U = ΩReq. Then, the problem is fully described by the adimensionalized Navier-Stokes equations with four dimensionless numbers: the eccentricity ε = (b 2a 2 )/(a 2 + b 2 ), the inner to outer core ratio η, the aspect ratio c/b, and the Reynolds number Re = Ω R 2 eq /ν, or its inverse the Ekman number E k , where ν is the kinematic viscosity of the fluid. In all the computations presented here, we choose c equal to the mean equatorial radius Req = (a + b)/2, as in classical experimental setups (see e.g. [START_REF] Lacaze | Elliptical instability of the flow in a rotating shell[END_REF]). This allows us to focus on the well-known stationary spin-over mode of the tidal instability. Note that for lots of tidally deformed planetary and stellar bodies, the c-axis is the shortest axis because of the rotational flattening, whereas the longest axis is the one pointing towards the tide-raising body. In this configuration, the first selected mode of the tidal instability close to threshold may change [START_REF] Kerswell | Tidal instability as the source for Io's magnetic signature[END_REF], [START_REF] Cébron | A systematic numerical study of the tidal instability in a rotating ellipsoid[END_REF]), giving rise to oscillatory motions. Nevertheless, we expect the main physical processes described here to remain valid for these other modes.

In addition to these purely hydrodynamic considerations, we also solve the temperature equation with constant and uniform temperatures Ti and Te applied respectively at the inner and outer boundaries. To model the buoyancy, the density is assumed to vary linearly with the temperature and the Boussinesq approximation is used. Then, the gravity term of the Navier-Stokes equation is written: ρ g * = ρ(Te) [1α(T * -Te)] g * , where ρ is the fluid density, α the coefficient of thermal volumic expansion, g * the local gravity which depends on the position and T * the local temperature. In our model, the gravity is calculated by solving the Poisson equation for the gravitational potential φ, assuming that the outer boundary is an isopotential. Thus, the thermal part of the problem is controlled by two dimensionless numbers: the Prandtl number P r = ν/κ, where κ is the thermal diffusivity, and the Rayleigh number Ra = (α g0 (Ti -Te) d 3 )/(κ ν), where d = Req(1η) is the shell thickness and g0 is the surface gravity at the outer boundary of the corresponding sphere, i.e. g0 = 4/3 π G Req ρ(Te) with G the gravitational constant. Note that the kinematic viscosity of the fluid is assumed independent of the temperature in this work.

Finally, the problem solved is described by the following system of dimensionless equations:

∂u ∂t + u • ∇u = -∇p + 1 Re △u - Ra P r Re 2 (1 -η) 3 T g, (1)
∇ • u = 0, (2)
∂T ∂t + u • ∇T = 1 P r Re △T, (3)
△ φ = 3, (4) g = -∇φ, ( 5
)
where T is the dimensionless temperature anomaly T = (T * -Te)/(Ti -Te). All boundary conditions have been described above. This numerical setup is a simple model for a tidally deformed liquid planetary core with a solid inner core and an imposed temperature contrast. Note that in a geophysical context, because of the compressibility, the temperature difference △T = Ti -Te to consider is the superadiabatic temperature difference between the inner core boundary and the core-mantle boundary (CMB). All dimensionless numbers as well as explored numerical ranges and typical values for the Earth's and Io's cores are given in table 1. Since there is no simple symmetry in the studied configuration, the fast and precise spectral methods classically used in planetary cores studies are not relevant here. Our computations are performed with a commercial software using a finite element method, which allows to correctly reproduce the geometry and to simply impose the boundary conditions. An unstructured mesh with tetrahedral elements was created. The mesh element type employed is the standard Lagrange element P 1 -P 2, which is linear for the pressure field but quadratic for the velocity field. The temporal solver is IDA [START_REF] Hindmarsh | Suite of Nonlinear and Differential/Algebraic Equation Solvers[END_REF], based on backward differencing formulas. At each time step the system is solved with the sparse direct linear solver PARDISO † .

The numerical procedure is the same for all the computations presented in this paper: starting from a fluid at rest in a spherical shell of radius Req with a diffusive temperature profile, the shell is set in rotation at a constant angular velocity Ω and a first statistically stationary state is obtained by solving the Navier-Stokes and temperature equations; then, the spherical shell is instantaneously deformed to the chosen triaxial ellipsoidal shape and we follow the dynamics. Note that this instantaneous deformation allows to study the growth rate of the elliptical instability on a well-known conductive or convective base flow. But we have also performed computations with a gradual increase of the deformation, as well as computations starting from a deformed shell with a fluid at rest before imposing the rotation at the boundaries: the classical isothermal tidal instability then grows, which is only slightly modified by then imposing a temperature difference. In all cases, the final steady-state is the same.

Two quantities are systematically studied: (i) the growth rate σ of the tidal instability, which quantifies the feedback of the temperature field on the elliptical instability, and (ii) the Nusselt number N u, which quantifies the feedback of the elliptical instability on the thermal properties of the system. Since the elliptical instability induces a strong three-dimensional destabilization of the initial flow, the growth rate σ is determined as the time constant of the exponential growth of the mean value of the vertical velocity W = 1 V V |w| dτ , where w stands for the dimensionless vertical velocity and V for the volume of the ellipsoidal shell. The Nusselt number is calculated by dividing the measured mean heat flux at the outer boundary (once a statistically stationary state is reached) by the theoretical value of the conductive heat flux in a sphere of radius Req. It has systematically been checked that the difference between this analytically known flux and the numerically calculated flux for a purely conductive ellipsoid is below 2% for our all simulations.

The purely hydrodynamic part of the numerical simulation has already been validated in [START_REF] Cébron | A systematic numerical study of the tidal instability in a rotating ellipsoid[END_REF]. A complementary validation of the resolution of thermal effects has been done by computing the heat flux in a rotating spherical shell: in figure 2 (a), our results at Re = 344 are compared with the compilation of results given in [START_REF] Aurnou | Planetary core dynamics and convective heat transfer scaling[END_REF] for the modified Nusselt number defined by N u * = Nu E P r , where E = ν Ω d 2 is the Ekman number based on the gap width, i.e. E = ((1η) 2 Re) -1 . Note that our numerical results fill an area with few data and agree with the general trend. Besides, our results are compared in figure 2 (b) with the scaling law proposed by [START_REF] Christensen | Zonal flow driven by strongly supercritical convection in rotating spherical shells[END_REF] obtained from numerical simulations:

N u * = 0.077 (Ra * Q ) 5/9 (6)
where Ra * Q = Ra N u E 3 /P r 2 is the Rayleigh number based on the heat flux instead of the temperature contrast and which does not take into account any viscous or thermal diffusive effect. An excellent quantitative agreement is found.

INTERACTION BETWEEN THE ELLIPTICAL INSTABILITY AND THE THERMAL FIELD

In their analytical WKB analysis of the linear stability of elliptical streamlines in the presence of a diffusive temperature field, Le [START_REF] Bars | Thermo-elliptical instability in a rotating cylindrical shell[END_REF] found an analytical expression of the inviscid growth rate of the elliptical instability in the limit of small deformations as:

σ = 9 -3 Ra 16 -4 Ra ε, (7)
where Ra = η-1

ln(η) Ra E 2 P r
is a modified Rayleigh number. The expression 7 reflects the modification by thermal effects of the elliptical instability, which in this context corresponds to the parametric resonance of 2 gravito-inertial waves with the tidal deformation. Le [START_REF] Bars | Thermo-elliptical instability in a rotating cylindrical shell[END_REF] also showed that the elliptical instability cannot grow for Ra > 3 because no resonance between inertial modes is then possible. As shown in figure 3 (a), the same decreasing trend with Ra is recovered in the spherical shell, even if the results differ quantitatively from this theoretical local estimate. The first noticeable result from our complete calculations is that the growth rate of the elliptical instability is significantly enhanced by the thermal stratification (i.e. Ra < 0), as first suggested by Le [START_REF] Bars | Thermo-elliptical instability in a rotating cylindrical shell[END_REF]. It may seem at first surprising that an a priori stabilizing effect leads to an encouragment of flow destabilization, but such a behavior has already been shown for instance in a Taylor-Couette flow, where a stable configuration can be destabilized by the presence of an axial stratification, leading to the so-called strato-rotational instability (see for instance the recent experiments by Le [START_REF] Bars | Experimental analysis of the stratorotational instability in a cylindrical Couette flow[END_REF]. The second result of planetary relevance is that the tidal instability can still grow on an established convective flow. As shown in figure 4, the organization of the flow is then completely changed. Indeed, in the absence of tidal instability, the convective flow organizes in a classical columnar structure shown in figure 4 (a) (the so-called Busse columns), where motions are mainly bidimensional and vertical velocities remain small, coming only from the Ekman pumping inside the columns. On the contrary in figure 4 (b), Busse columns are completely destroyed by the tidal instability, whose velocity field is fully three-dimensional. The growth rate σ of the elliptical instability progressively decreases when the Rayleigh number increases as shown in figure 3 (a). Indeed, the thermal convective motions can be seen as a perturbation superimposed on the classical isothermal base flow of the elliptical instability, corresponding to a rotation along elliptical streamlines: when the Rayleigh number increases, the typical convective velocity increases and the ellipticity of the base flow streamlines is less and less felt by the fluid particles. The dimensionless version of this model can be quantified in defining the typical Rossby number of the flow, i.e. the ratio between the root mean square convective velocity and the typical rotating velocity ΩReq :

Ro = 1 V u • u dτ ,
where u is the dimensionless velocity in the rotating frame. One would expect to find a critical Rossby number of order 1 for the disappearance of the tidal instability. As shown in figure 3 (b), the critical value Ro ≈ 0.25, where the growth rate is zero, is indeed found for P r = 1 and Re = 344, which is near the threshold of the tidal instability. The critical Rossby number then seems to increase with the Reynolds number (see figure 3 (a) for Re = 688), if it exists at all. Indeed, when the Rayleigh number increases, the typical convective velocity also increases whereas the typical lengthscale of convection Lconv simultaneously decreases. In the limit of very large Rayleigh numbers, Lconv is very small and turbulent motions become fully tridimensional. We then expect thermal convective motions to be seen as an effective turbulent viscosity, where the results of [START_REF] Fabijonas | Mean effects of turbulence on elliptic instability in fluids[END_REF] predict an encouragement of the tidal destabilization. The extensive study of this regime is very interesting, but currently out of reach of our numerical resources. Nevertheless, our current results allow to use the critical Rossby number Roc = 0.25 determined previously for Re = 344 as a lower bound for flow at larger Reynolds numbers. This result is sufficient for the planetary applications that we are interested in, as will be shown in the next section.

When thermal and tidal instabilities are simultaneously present, heat transfers are determined by the competition between the natural thermal convection and the forced convection due to the elliptical instability. In the latter case, the flow driven by the instability can be schematically described by three distinct regions: a fully mixed and isothermal bulk, and viscous boundary layers at the outer and inner boundaries, where the temperature is purely diffusive. The advective heat flux driven by the tidal instability is then determined by the size of the viscous boundary layers δν , following N u -1 ∼ d/δν. With the classical scaling law of viscous boundary layers, we obtain N u -1 = α1/ √ E * , where α1 is a constant, E * = ν u ei d the Ekman number associated with the flow driven by the instability, and uei the fluid velocity due to the elliptical instability. As shown in [START_REF] Cébron | A systematic numerical study of the tidal instability in a rotating ellipsoid[END_REF], this velocity uei may be computed numerically in the absence of temperature gradient by subtracting to the computed flow the theoretical base flow corresponding to an imposed rotation along elliptical streamlines.

u ei Ω Req generally scales as α2 √ Re -Rec near the threshold of instability, where α2 ≈ 0.036 has been determined numerically and where Rec is the critical Reynolds number for the onset of tidal instability equal to Rec = (5.24/ε) 2 in the isothermal case for a stationary deformation. u ei Ω Req then saturates toward 1 far from the threshold. Keeping the same scaling in the presence of thermal effects, we expect the Nusselt number to vary as:

N u -1 = α1 α2 (1 -η) Re Rec -1 1/4 √ Re. ( 8
)
Our numerical results shown in figure 5 (a) validate this scaling with α1 ≈ 0.01. Far from threshold, E * = E and the scaling law becomes

N u = α1/ √ E. ( 9
)
Note that according to this model, the Nusselt number is a measure of the amplitude of the instability. Then, the agreement between our results and the scaling law confirms that the amplitude of the instability is not inhibited by a strong stratification, provided that the Reynolds number is far enough from the threshold. The systematic evolution of the Nusselt number with the Rayleigh number is shown in figure 5 (b). In the absence of tidal and convective instabilities, N u remains equal to 1. In the presence of tidal instability, the heat flux remains constant at a value larger than 1 up to a transition Rayleigh number which depends on Re, where the natural convection becomes more efficient than the forced one. Indeed, ( 8) and ( 9) describe the heat flux by the forced convection only, and are valid in particular for stably-stratified regimes and before the onset of convection Ra < Rac. But following [START_REF] King | Boundary layer control of rotating convection systems[END_REF], once Ra > Rac and convective and tidal instabilities are competing, the heat transfer is determined by the most efficient mechanism. Following scaling laws ( 6) and ( 9), the transition between the forced convection and the natural convection appears for the transition Nusselt number N u * t = Nu E P r = 0.077 (Ra * Q ) 5/9 = α1 √ E P r , which corresponds to the transition Rayleigh number: Rat ≈ 2.5 E -8/5 P r 1/5 .

(10)

For Ra > Rat, heat transfers are controlled by the natural convective motions, whereas for Ra < Rat, heat transfers are controlled by the tidal instability. For planetary applications, it is more convenient to write this result in term of flux Rayleigh number defined by Ra f = Ra N u, for which the transition appears at

Ra f t ≈ 0.025 E -21/10 P r 1/5 . ( 11
)
As explained in details by [START_REF] Sumita | Thermal interaction between the mantle, outer and inner cores, and the resulting structural evolution of the core[END_REF], a stable density stratification may have existed in the whole early Earth outer core and could even have been sufficiently large to prevent dynamo action. This initial stratification has been disrupted by some mechanism, which could have been either a gradual mechanism, including encroachment and entrainment [START_REF] Lister | Stratification of the outer core at the core-mantle boundary[END_REF], or catastrophic mechanisms driven for instance by the 1/3-annual forced nutation [START_REF] Williams | Resonances of the fluid core for a tidally decelerating Earth: Cause of increased plume activity and tectonothermal reworking events? Earth Planet[END_REF] or by tidal resonant forcing of inertial-gravity waves (Kumazawa et al. 2006). Our work suggests an alternative proposal based on a parametric triadic resonance of gravito-inertial waves. Note that since the stratification enhances the growth rate of the tidal instability and since the early Earth was already unstable from a purely hydrodynamic analysis [START_REF] Cébron | A systematic numerical study of the tidal instability in a rotating ellipsoid[END_REF], then a fortiori with a thermal stratification, the tidal instability can be a mechanism for this overturn, hence playing a role in one of the major events in geological Earth history. We can also apply the heat transfer scaling laws obtained in the previous section to the present convective state of the Earth's core. Following [START_REF] Christensen | Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields[END_REF], the typical values are E ≈ 5 • 10 -15 , Ra * Q ≈ 3 • 10 -13 and Ra f ≈ 10 29 for P r = 0.25. The first consequence that we can deduce is that Ro ∼ 10 -6 according to the scaling law Ro = 0.85 (Ra * Q ) 0.41 given by [START_REF] Christensen | Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields[END_REF], which is significantly below the lower bound for disappearance of elliptical instability Roc ≈ 0.25 found in section 3. That means that the convection does not prevent the development of the tidal instability. Besides, the scaling law (11) gives the estimate Ra f t ∼ 2 × 10 28 . The Earth's core is just above the transition between the two kind of convections considered in section 3 and its heat flux is thus controlled by natural convection. However, the closeness of the values obtained here does not preclude a tidally dominated flux in previous times or in other planetary systems, and in any case highlights the relevance of the elliptical instability as one of the major process at work in planetary cores.

To finish with, many authors have assumed that the top of the Earth core is stably stratified, this layer being the socalled ocean of the core (see for instance [START_REF] Stanley | Effects of an outer thin stably stratified layer on planetary dynamos[END_REF] for a recent review of the literature on this subject). Actually, as described in this recent work, many clues lead to the idea that several planets contain stably stratified layers in their electrically conducting regions. An opposite (but dynamically similar) situation occurs in stars under the photosphere, where the stratified radiative zone takes place under the so-called convective zone. Then, we can address the simple following questions: in such a bi-layer flow, can the elliptical instability grow? In which area, i.e. the stratified zone, the convective zone or both? And is the heat flux completely modified by the instability? A single simulation is presented in figure 6 as an illustration of the answer. In this simulation, the same temperature T = 0 is imposed at boundaries, and a temperature T = 1 is imposed at an internal neutral boundary corresponding to an homothetic ellipsoid in a ratio η2 = 0.7 : this allows to obtain a stratified inner layer and a convective outer layer, with clearly visible convective cells (figure 6 (a)). Once the tidal instability is excited, figure 6 (b) shows that the instability grows over the whole fluid and controls the heat flux. Hence in presence of the elliptical instability, a thermal stratification (i.e. a subadiabatic temperature profile) is not synonymous of thermal isolation, which is a key point from a geophysical point of view.

CONCLUSION

This paper presents the first numerical study of the interaction between the tidal instability and a thermal field. Even if the range of parameters (e.g. the Reynolds number) accessible to our numerical tool is relatively limited, we have validated general physical processes of direct relevance for planetary dynamics. We have shown that a stable temperature field encourages the tidal instability. We have demonstrated also that the tidal instability can grow on a convective flow, and may disrupt the famous Busse columns in planetary cores. Finally, we have demonstrated that the heat flux at planetary scales may be controlled by the forced convection due to this tidal instability, which in any case plays a fundamental role in the organization of fluid motions.

= α g 0 (T i -Te) d 3 κ ν -3.8 • 10 5 -10 6 10 23 -? (< Rac) Flux-based Rayleigh number Ra * Q = Ra N u E 3 /P r 2 -2.6 • 10 -5 -0.24 10 -13 -? Nusselt number N u = Q total /Q conduction 1 -5.6 10 6 -? Modified Nusselt number N u * = Nu E P r ≥ 0.002 10 -8 -? Rossby number Ro = 1 V U 2 dτ Ω R 2 eq 0 -0.4 10 -6 -?
Figure 1. Schematic representation of the considered problem. The gravity field shown here in the equatorial plane is calculated explicitly, assuming that the outer boundary is an isopotential.

Figure 2. Evolution of the modified Nusselt number in the case of a rotating spherical shell (ε = 0) for P r = 1, η = 0.3 and Re = 344. (a) Our computations are compared with a compilation of numerical and experimental results given by [START_REF] Aurnou | Planetary core dynamics and convective heat transfer scaling[END_REF]. (b) Our computations are compared with the scaling law (6) given by [START_REF] Christensen | Zonal flow driven by strongly supercritical convection in rotating spherical shells[END_REF]. 2 ) shells for P r = 1 and Re = 344 or Re = 688. Note that the classical dependance of the critical Rayleigh for the convection Rac ∝ Re 4/3 (see [START_REF] Tilgner | Finite-amplitude convection in rotating spherical fluid shells[END_REF] for instance) can be observed: the decrease of the Reynods number modifies the threshold and then, increases the convective motions.

Figure 3 .

 3 Figure 3. (a) Influence of the Rayleigh number on the growth rate of the tidal instability for ε = 0.317, c = a+b 2 , P r = 1 and Re = 344 or Re = 688. The growth rate given by equation (7) is also shown, taking into account a classical damping by a surfacic viscous term -K/ √ E k , where K is a constant of order 1[START_REF] Lacaze | Elliptical instability of the flow in a rotating shell[END_REF]. The values of K have been determined by matching the theoretical value with the numerical one at Ra = 0, giving K = 3.07 for Re = 344 and K = 2.91 for Re = 688. (b) Evolution of the growth rate of the tidal instability with the Rossby number, calculated following the scaling law given by[START_REF] Christensen | Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields[END_REF] Ro = 0.85 (Ra * Q ) 0.41 . For Re = 344, the instability disappears for Ro ≈ 0.25.

Figure 4 .

 4 Figure 4. Comparison between the convective flows in the absence of tidal instability (a, ε = 0) and in the presence of tidal instability (b, ε = 0.317) for the same values of the Reynolds number Re = 344, the Rayleigh number Ra = 18762 and the Prandtl number P r = 1. The vertical velocity is shown in three different planes. Also shown in (b) is an iso-surface of the norm of the velocity ||u|| = 0.19, which clearly exhibits the 'S' shape of the spin-over mode.

Figure 5 .

 5 Figure 5. (a) Influence of the Reynolds number on the Nusselt number for a convective flow with ε = 0.317, c = a+b 2 , P r = 1 and Ra = 18762. (b) Evolution of the Nusselt number with the Rayleigh number in spherical and ellipsoidal (ε = 0.317, c = a+b2 ) shells for P r = 1 and Re = 344 or Re = 688. Note that the classical dependance of the critical Rayleigh for the convection Rac ∝ Re 4/3 (see[START_REF] Tilgner | Finite-amplitude convection in rotating spherical fluid shells[END_REF] for instance) can be observed: the decrease of the Reynods number modifies the threshold and then, increases the convective motions.

Figure 6 .

 6 Figure 6. Visualization of the reduced temperature T in the case of a stratified layer under a convective zone (Re = 344, c = a+b 2 ). The inner and outer boundaries verify T = 0 and at a ratio η2 = 0.7, a temperature T = 1 is imposed such that the Rayleigh number based on the thickness of the shell is Ra = 18762, whereas the Rayleigh number based on η2 is equal to Ra2 = Ra (1-η 2 ) 3 (1-η) 3 ≈ 1512. (a) Temperature in the equatorial plane for a spherical shell of outer radius Req = c. (b) Temperature in the equatorial plane and surface of iso-value ||u|| = 0.19 at saturation of the tidal instability for the corresponding ellipsoidal shell at ε = 0.317.

Figure 2 .

 2 Figure 1.

Figure 3 .

 3 Figure 3. (a) Upper figure. (b) Lower figure.

Figure 5 .

 5 Figure 5. (a) Upper figure. (b) Lower figure.

Table 1 .

 1 List of relevant dimensionless parameters with the explored numerical ranges as well as their typical values in the Earth's and Io's cores.

	Dimensionless parameters	Definition	Numerical ranges	Earth & Io's core estimates
	Eccentricity	ε = b 2 -a 2 a 2 +b 2	0 -0.32	10 -7 -10 -4
	Core radius ratio	η	0 -0.3	0.35 -?
	Oblateness	c/b	0.86 -1	997/100 -995/100
	Reynolds number Ekman number Ekman number based on the gap	Re = Ω R 2 eq /ν E k = 1/Re E = ((1 -η) 2 Re) -1	0 ≤ 10 3 ≥ 0.001 ≥ 0.002	10 15 -10 13 10 -15 -10 -13 10 -15 -10 -13
	Prandtl number	P r = ν/κ	1	0.25 -0.25
	Rayleigh number	Ra

† www.pardiso-project.org

Figure 4. (a) Upper figure. (b) Lower figure.

Figure 6. (a) Upper figure. (b) Lower figure.


Daniele Galli
email: galli@iamb.it-danigalli@tiscali.it

Chiara Morini
email: c.morini@iamb.it

Biagio Di I Terlizzi
email: diterlizzi@iamb.it

SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS THE EXPERIENCE OF THE COOPERATION PROJECT RATIONALIZATION OF RAS EL AIN IRRIGATION SYSTEMS

Keywords: Cooperation, Agriculture, Sustainability, Syria, Herbaceous crops Coopération, Agriculture, Durabilité, Syrie, Cultures Herbacées

This paper reports the main results of an integrated initiative of international technical cooperation in agriculture financed by the Italian Ministry of Foreign Affairs and jointly implemented by the CIHEAM MAI Bari and the Syrian Ministries of Irrigation and of Agriculture and Agrarian Reform. The project entitled: "Rationalization of Ras El Ain Irrigation Systems" started in January 2005 and ended in March 2008. The project was aimed at addressing the problem of water resources scarcity in the project area of Ras El Ain, around the springs of Al Khabour, located in the Hassakeh province (North Mesopotamia) of the Syrian Arab Republic. During the project implementation, a real field experience was carried out involving national and international researchers, local officers and technicians, and local farmers as direct beneficiaries. An appropriate sustainable model concerning the crop management practice was elaborated to save both water resources and production inputs for cotton and wheat. In this paper the main results of this innovative cooperation approach in a multiethnic context are presented.

INTRODUCTION

The problems related to water resources in the Mediterranean region are quite complex and involve different countries, as shown by the frequent conflicts that have occurred through history and that are still affecting the Mashrek region.

An extremely interesting scenario concerns the water resources of one of the main transboundary catchments of the Middle East, the Euphrates river, which is formed in Turkey and runs through Syria and Iraq before flowing into the Persian Gulf. Actually it runs through the boundaries of three States, so the proper management of the water resources of Euphrates and of its tributaries is essential for the whole region for agricultural production. This strategic position is inevitably associated with territorial tensions related to the access, control and management of water resources, which necessitates special focus and the development of integrated management models and tools, especially when these water resources, which are declining due to climate changes, are shared by different economic and institutional bodies.

The Syrian national programmes have long been targeted to the support of irrigated agriculture, notably to irrigate the dry lands of the valley of Khabour stream, a tributary of Euphrates. The impressive works for the recent exploitation of water resources through the control of surface water flow (e.g. Tishreen reservoir, close to the Turkish boundary) and the pumping of groundwater resources for the cultivation of native species have strongly altered the equilibrium between human-induced activities and the resources of the natural environment. This is also associated with a progressive loss in memory of the traditional systems for the exploitation and management of surface water resources derived from rainfall (water harvesting systems). This is partly caused by massive migratory flows of different ethnic groups. In the agricultural areas crossed by the Khabour, the need to promote cropping solutions consistent with the available resources is particularly urgent to promote social stability, food security and sustainable economic growth. Promoting a sustainable crop management model appropriate to the local conditions in the Syrian areas and stimulating the cooperation of the parties concerned has shown to be essential for the economic, social and environmental sustainability of the local agricultural production.

GENERAL FRAMEWORK

Origin of the initiative

Over the last half-century the agriculture of north-eastern Syria has been transformed mostly by irrigation. This expansion of irrigated agriculture has responded to the nation's food security policy objectives to satisfy the food requirements of an increasing population that features one of the highest growth rates in the world [START_REF] Maar | Ministry of Agriculture and Agrarian Reform of Syria[END_REF]. A growing concern in Syria is the design and implementation of sustainable irrigation water policies aimed to increase the water use efficiency in agriculture and to preserve water resources by reducing future consumption. The cooperation project "Rationalization of Ras El Ain Irrigation systems", implemented between 2005 and 2008, was aimed at tackling the problem of water resources scarcity in the project area of Ras El Ain around the springs of Al Khabour River, located in the Al Hassakeh Governorate in the North of ancient "Mesopotamia", toponym for the area of the Tigris-Euphrates river system, largely corresponding to modern-day north-eastern Syria. The great importance of the initiative is the pre-condition for the renewal of the agricultural activity of the area, which has caused, over the last few years, severe economic losses and harmful social and environmental effects due to insufficient water resources and poor management resulting from the use of inappropriate and poorly efficient irrigation techniques. The major objective of the initiative is the food and income security for local farmers that might be achieved by improving agriculture and stabilizing the agricultural production through the sustainable development of irrigation techniques. The project is framed in the international cooperation programmes of the Italian Ministry of Foreign Affairs, funded by the Italian SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS. Galli D., Morini C., Di Terlizzi B. Cooperation and assigned to CIHEAM -Mediterranean Agronomic Institute of Bari (MAIB) for its implementation.

Project area

The project area is located in the Al Hassakeh Governorate (fig. 1) in the district of Ras El Ain, which means in the local language «origin of water resources». The project area is flat, slightly undulated and quite homogeneous; its altitude is in the range of 350 to 370 m a.s.l.

Figure 1. Map of Syria and project area

This area is the ancient land where an agricultural and urban civilization was developed around 7,000 years ago and has been strongly influenced by the climate changes over the last millenniums. The main drainage arteries Khabour River and its left tributary, the Jirjib River. The recent works for the exploitation of water resources that involves the control of surface water (dikes) and the pumping of ground water used to irrigate local crops, has strongly altered the equilibrium between man and natural resources.

The climate is classified as transitional between the Mediterranean and desert climate, with a medium yearly rainfall of 250 mm. Rainfall is mostly concentrated in winter, whereas summer is characterized by the nearly total lack of precipitation for about six months. The maximum temperatures (43 C°) are recorded between July and August; the minimum ones (2 C°) in December. The rain season starts in October, peaks in January and ends in May. The period from June to September is nearly completely dry.

Existing Problems

The use of inappropriate irrigation techniques associated with a water policy that was not calibrated on the actual requirements and availability in the area, has led in a relatively short period of time, to severe economic losses and harmful social and environmental effects.

Agriculture is made possible by groundwater pumping systems (fig. 3); only in the early '2000s the Authorities started to tighten the regulations on the indiscriminate use of groundwater, with a view to limit the permissive policy that has prevailed since the '50s.

In the project area, the non-sustainable management of water resources has jeopardized the economic sustainability of agriculture in the medium to the long run, and has accentuated the hydro-geological risks of the area where some portions of land have collapsed by subsidence due to the drawdown of ground water level (fig. 2). The occurrence of such phenomena seems to be related to the over-exploitation of underlying groundwater and it might constitute the future scenario of the area in the absence of a sustainable management with the current trend to climate change. The flow of the Al Kebrit springs, which supply the Al Khabour River, has sharply dropped, over the last few years, from 50 m 3 /s to nearly zero. This has made the water balance of the river negative, with subsequent effects on the two water reservoirs (with a Galli D., Morini C., Di Terlizzi B. capacity of 230 and 92 million m 3 , respectively), which are partly supplied by it and used for multiple purposes (irrigation, drinking water, energy). To preserve groundwater and spring flow, irrigation by wells has been forbidden during summer in an area of 34,000 ha. In this area there are as many as 1,652 privately owned authorised wells with a mean depth of 100-200 m. Water is usually lifted by vertical axis pumps (driven by a diesel engine) and applied by furrow irrigation. Water losses are estimated to about 40 -50%. The Syrian Government has recently authorised cotton cultivation over 20% of the area in summertime, provided farmers use modern water saving irrigation techniques. Actually poorly efficient and water-demanding irrigation techniques have been used so far and the techniques used to irrigate the major crops (wheat and cotton) do not seem actually suitable for the local conditions (Fig. 4). Sprinkler and drip irrigation are not very efficient due to the high salt content of irrigation water that often causes soil salinization and silting.

SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS.
For achieving a sustainable use of water resources it is essential to carefully monitor these resources, but this has never been done so far, and the consumptive uses have been calculated on an empirical rather than scientific basis. Another problem is also that in the agricultural research station of Hassakeh they have only the recorded values of water used for irrigation.

Due to the poor attention to the water use, wrong national water policies have been adopted that have not assessed the actual cost of consumed water. This has caused waste of water resources and has encouraged farmers to mostly cultivate wheat and cotton, which are not sustainable in the long run.

SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS. Galli D., Morini C., Di Terlizzi B.
Furthermore, food and income security policies have been implemented by a strong national support to agriculture through subsidised prices on production and aid to farmers. Recent reforms in the sector seem to indicate that in the future there will be less public involvement in the agriculture, and more freedom to farmers in the production and marketing-related decisions. However, farmers are used to a strong public control over agriculture and are not ready to such a change.

FEATURES OF THE COOPERATION APPROACH

Institutional synergies and participatory approach

The general objective of the initiative was the food and income security for local farmers, obtained by improving and stabilizing the agricultural production through the sustainable development of irrigation techniques. To achieve this objective, the work plan of the project has involved the analysis of traditional farming systems in the project area, in order to promote improved crop management practices and introduce new annual crops in the rotations, thus breaking continuous cereal cropping and increasing water use efficiency.

A

Increase Yields

The increase in crop yields was one of the main project's objectives, as it could allow local farmers to increase their income. The action carried out may be summarized by three main steps: studies, on-field experimentation and dissemination activities. The studies were aimed to prepare an overview of the agricultural sector in that area. The applied methodologies included the following: identification of the target group in agreement with the project beneficiaries; fieldwork to collect the data through questionnaires and semi-structured interviews with farmers; 4 Participatory Rural Appraisal sessions in the project area to have a preliminary feedback of the collected data; Data interpolation through the use of a suitable electronic spreadsheet set up for the farms of that area; analytical comparison of the data according to the local statistics from MAAR and NAPC.

Another part of studies concerned the completion of the local marketing analysis: it concerns a detailed study on the costs, benefits, sale channels and market trends of "alternative crops" such as cumin, sesame, lentil, watermelon seeds, chickpea, cucumber, soy-bean, sorghum and tomato. The NAPC was also involved to prepare a study on the national and international markets for cumin, sesame, soy-bean, organic cotton, sorghum and lentil crops. Trials on crops and technologies were carried out by participatory methodologies with the aim to transfer knowledge and techniques and convince farmers to introduce innovations and compare their old techniques and crops with the new tested ones. For this reason, the project implemented, on a voluntary basis and with the help of Farmers' Union, 22 demo fields, involving local farmers. To better monitor these fields and to fully compare the new with the traditional techniques, the project defined "cropping data sheets", in which all daily agricultural activities and economic data are reported, requiring farmers' involvement.

The demo fields were cultivated mainly with the strategic crops as Wheat and Cotton but also with Chickpea, Maize Sunflower, Soybean, Sorghum. An innovative tested crop, "Brassica Carinata" could be used to produce "Bio Diesel", as it is drought tolerant (Tab. 1).

Save water resources

The second objective of the project was to reduce the use of ground water resources in the project area, through well mapping so as to create GIS maps. To map the water quality in the project area, a database on the chemical-physical properties of water and soil for 1,392 wells was set up for establishing the first Territorial Information System (TIS) of the area. The planned activities involved two steps: office and field works.

Efficient irrigation techniques

The third objective has been the introduction of innovative and sustainable irrigation systems: sprinkler and drip irrigation and mainly the "Improved surface irrigation System", a system developed in collaboration by the MAIB, the Syrian researchers and the project management unit, based on local farmers' needs.

SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS. Galli D., Morini C., Di Terlizzi B.
The philosophy of these systems is based on the three dimensions (environmental, social, economic) of sustainability and can be summarized as follows:

-Flexible and adaptable to different farms and different crops for saving water resources (environmental sustainability) ; -Easy to be used by farmers because they are conceptually close to farmer's knowledge (social sustainability); -Economically viable both in terms of investment and running costs (economic sustainability).

The project developed an innovative system: "improved surface irrigation system", based on local background and farmers' needs, which allows the farmer to use less seeds and to save in terms of cropping practices, water, labour and energy (fig. 15). The project also introduced in the area a new sprinkler irrigation system. This system, less expensive than the local one, enabled saving more water than the improved surface irrigation system. Both systems had no depressing effect on production. Usually, crop yields in the plots irrigated by these systems were higher than in the plots irrigated by the traditional system. The new system was extended to farmers by a fully participatory approach. In addition, the demo fields for irrigation involved farmers' participation, also from an economic point of view. Extension service and training on the use of the new systems have also been provided to farmers.

Figure 9. Schematic structure of the improved surface irrigation system 3.5.

New irrigation system: sowing and furrowing combined

During the project implementation, an innovative system to combine good sowing and good preparation of furrows has been planned. It makes use of a modern seeding while digging furrows for surface irrigation (mainly for the improved surface system). In this way the farmer can use less seeds (from 450 -500 Kg/Ha to 200 -250 Kg/Ha with this system). At the same time the machine makes two regular furrows much better than the traditional furrow system. The system is made up of a seeder with two furrowers and two rollers that provide a light compaction of the soil. This system allows planting also inside the furrow without losing any cultivated surface. By this system it is not necessary to pass again in the field to make the furrow (reduction of soil compaction). Indeed you can decrease the usual cost of cultivation. The system has shown good results in demo fields. (fig. 16 and17).

RESULTS

The project has been implemented with the active involvement of local stakeholders, through the spreading of technologies, the dissemination of the main project outcome by different media, and the participation in national events and local fairs.

As to the technical management, the project operated to optimize crop yields (for cotton and wheat) in 22 demo fields, over a total area of 21 hectares. The proposed new irrigation systems have been tested and enabled using lower amounts of water than those traditionally applied by farmers. The reduction of water for irrigation use, achieved by the proposed improved methods, did not involve any decrease in income; it resulted instead in a reduction of running costs and working time. As compared to the fields cultivated with traditional methods, the introduction of new irrigation and cropping techniques resulted in considerable yield increases both for wheat (11% for improved irrigation systems and 13.6% for sprinkler system) and cotton (9.6% using the improved system). The abovementioned yields were obtained applying lower water amounts lower than those normally applied by farmers. Specifically, the average water saving in the 2 years for wheat was 35% in improved irrigation and 59% in sprinkler systems; for cotton the improved system allowed 36% water saving (Tab. 5 and 6). For wheat, the Project applied two irrigation systems: sprinkler and improved surface irrigation. Moreover, new agricultural machines such as mechanical seeding, cultivator and ripper were also used. Thanks to the new applied technologies, the wheat cultivated by improved surface irrigation systems resulted in a 43% rise in income. The wheat cultivated by sprinkler irrigation led to a 23% income increase (fig. 18). As to cotton cultivation, the Project applied the improved surface irrigation system, whereas the new machinery such as the pneumatic seeding, the weeding cultivator and the ripper were not present in the area. The new applications (agricultural machinery and Improved surface irrigation system) used by the Project resulted in a 45% increase in the operating margin (fig. 19 and20).

From the social point of view, this result allowed farmers to save manpower and time and carry out additional rural activities and alternative crops (e.g. lentil, cumin, sorghum…) to be sold on the local markets for increasing their income. Through the dissemination of project results, about 100 hectares cultivated for the "replication activities" based on farmers' initiatives allowed local farmers to understand and familiarize with the proposed irrigation systems and test a sustainable water resources management.

ISDA 2010, Montpellier, June 28-30, 2010 knowledge heritage with the modern technologies. Constant attention has been paid to the participatory approach and to the involvement of farmers in the sustainable management of irrigation systems, made possible through on-going training and information activities: the capacity building of the local technicians will contribute to the sustainability of the actions beyond the end of the project. Anyway, significant extension service in terms of marketing strategies, quality control and farm management analysis would be therefore required. In addition to an integrated regional water management plan for agriculture making use of modern methodologies and technologies, it is necessary to widespread modern irrigation techniques while still recovering and optimizing the traditional water management systems on the farm scale, improved and made more efficient and sustainable. The increased man-made pressure on the availability and distribution of local resources necessitates innovative technical solutions by the agricultural sector to prevent social conflicts, but it also requires specified governance skills by the institutions and the decision-makers, and above all medium and long-term policies, aimed at orienting over time the economic and productive models and the individual and social life and consumption models to emphasize the value of resources and their best use. In conclusion, providing innovative technical solutions to favour the proper water management has enabled achieving a good level of efficiency in the use of water resources and an improved performance of irrigation systems by reducing the applied water volumes but keeping at the same time good crop productivity in the medium -long run. The available technical knowledge, embodied in the sustainable cropping practices and techniques adjusted to the local conditions, has enabled achieving significant results; however this know how should become a diffuse and shared heritage, notably for the protection of resources. Within this framework, the technological innovation is to be promoted and favoured by further developing integrated management policies, models and tools, which are a priority to face the above issues effectively. To this purpose, it will be essential from an institutional point of view to work synergically with the National Irrigation project (N.I.P), which will enable the further dissemination of the proposed model and its sustainability over time, also during the "second phase" of the project in other Syrian governorates, financed from the Italian Cooperation in 2009: the continuity of this collaboration between the Italian and Syrian communities is the sign of the concrete willingness of the Syrian Institutions to the modernization and to the integration toward the international community.

Fig. 2 .Figure 4 .

 24 Fig. 2. Collapses in project area (2005) Fig. 3. Groundwater abstraction (2005)

  The experimentations were run in the experimental farm (which covers 37 Hectares) in 24 plots with different crops and different irrigation systems. The dissemination of the results involved three sectors: Extension Service, Training for local farmers and technicians, Demo plots and Field days (fig. 9 and 10). It was essential to suggest to farmers new technologies and new crops and varieties, to be tested and compared with the local ones. For this reason, an experimental farm was set up in the Research centre in Ras El Ain within Arnan Shemaly District, covering a total area of 31.7 Hectares. SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS. Galli D., Morini C., Di Terlizzi B.

Figure 5 .

 5 Figure 5. Field day with local farmers (2006) Figure 6. Training with local farmers (2007)

  Office works included: preparation of detailed program, updating of technicians' knowledge and supply of all materials required (PS devices, maps, district schemes for the area under study, instruments, tools and documentation). Training courses for technicians on the instructions and indications have been provided by MAIB experts. The Ministry of Irrigation has been actively involved in this activity, supplying 8 technicians and covered most expenses for the water analyses carried out in the Al Hassakeh laboratory.Field surveys were run by three teams, consisting each of three technicians, to take the coordinates of wells using GPS instrument; to analyse the well water quality directly for the following parameters: EC, pH, temperature, smell and colour (based on the measurement of the three first parameters by means of portable instruments, and on the evaluation of the others), collecting a water sample for the chemical analysis in the laboratory, and to assess the characteristics of the engine, pump, well and of the related irrigated area. In the end the technician painted a number in each well that might be identified in the database. This procedure also involved the owner of the wells (farmer). These analyses on water and soils are very important to evaluate the environmental aspect of the project area and the possible use and management of water for irrigation. The local technicians became able to plan the best irrigation solution for the local area, based on water and soil quality. These data have been collected in databases and developed in GIS maps and Territorial Information System (TIS), available on-line. The maps (fig.21 and 22) extracted from the T.I.S aims to stimulate the local and national Authorities and Institutions towards a strategic planning of local and national water resource management in the medium and long period.

Figure 7

 7 Figure 7 and 8. Thematic maps for temperature (C°) and electro-conductivity (EC)

  SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS.Galli D.,Morini C., Di Terlizzi B.

Figure 10 .

 10 Figure 10. Furrow applied in front of Figure 11. Rollers applied behind the seeder the seeder machine for wheat and other crops machine

Table 1 .

 1 Distribution of demo plots by crops(2006)(2007)

	Farm n.	District	Fields n.	Season	Crop	Variety	Plots area (ha)
			1	winter	Wheat	Cham-6	0.70
			2	winter	Brassica	Carinata	0.50
			3	winter	Chikpea	Ghab-3	0.65
			4	summer	Cotton	T.ST-453	1.96
	1	Tewmeh	5	summer	Cotton	Alepo-90	0.47
			6	summer	Maize	Ghouta-82	0.39
			7	summer	Maize	T.Konsur	0.50
			8	summer	Sun flower	T.Sirena	0.48
			9	summer	Sun flower	It.-Tuscania	0.42
	2	Tewmeh	10	winter	Brassica	Carinata	0.85
	3	Halabia	11	winter	Wheat	Cham-6	4.60
			12	summer	Cotton	Alepo-90+T.	1.00
			13	summer	Cotton	Alepo-90	0.25
	4	Tel Snan Garby	14	summer	Cotton	T.ST-453	1.70
			15	summer	Soybean	local	0.50
			16	summer	Cotton	T.ST-453	1.60
	5	Halabia	17	summer	Sorghum	T. SNOW	0.30
			18	summer	Soybean	T. Nova	0.45
	6	Tal Gazira	19	summer	Cotton	T.ST-453	1.80
			20	summer	Cotton	T.ST-453	0.73
	7	Tal Magdal	21	summer	Cotton	Alepo-90	0.27
			22	summer	Soybean	Local	0.27
		Total	22				20.4

Table 2 -

 2 Wheat Yields in 2006 and[START_REF] Fiorentino | The last Millennia Climate Changes in the Khabur Basin (Syria), inferred from natural data and historical sources. Atti del Convegno[END_REF] comparing the traditional irrigation system to the sprinkler and improved irrigation system

	Crop	Irrigation		Year 2006		Year 2007
		system
	Wheat		Yield (t/ha)	Applied water (m 3 /ha)	Yield (t/ha)	Applied water (m 3 /ha)
		Sprinkler	4,9	2.027	3,9	2.224
		Improved	5,1	3.920	3,5	2.910
		Traditional	4,3	5.530	3,2	5.000

Table 3 -

 3 Cotton Yields in 2006 and[START_REF] Fiorentino | The last Millennia Climate Changes in the Khabur Basin (Syria), inferred from natural data and historical sources. Atti del Convegno[END_REF] comparing the traditional irrigation system to the improved irrigation system

	Crop	Irrigation		Year 2006		Year 2007
		system
	Cotton		Yield (t/ha)	Applied water (m 3 /ha)	Yield (t/ha)	Applied water (m 3 /ha)
		Improved	3,7	11.200	4,6	8.106
		Traditional	3,6	16.125	4,0	14.054

Table 4 .

 4 Saving of water resources -Wheat

	Saving

Table 5 .

 5 Saving of water resources -Cotton

	Saving

Economical Comparison between Traditional & Improved

  SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS.Galli D.,Morini C., Di Terlizzi B.

	Figure 12. Economic comparison between traditional and improved irrigation systems
			Economical comparison between Traditional & Impruved
							irrigation systems
		40.000				33.600	37.013
	Value in SYP	5.000 10.000 15.000 20.000 25.000 30.000 35.000	26.211 14.600			7.389	22.413	1 Ha of Traditional 1 Ha Improved
			0
				Total Cost	Gross Output	Operation Operating
				(SYP/Ha)	Production	Margin
							(SYP/Ha.)	(SYP/Ha)
	Figure 13. Economic comparison between traditional sprinkler irrigation system
			Economical Comparison between Trational & Sprinkler
			45.000						41.055
	Value in SYP	10.000 15.000 20.000 25.000 30.000 35.000 40.000	26.211	24.263	33.600	7.389	16.792	1 Ha Traditional 1 Ha Sprinkler
			5.000
			0
				Total Cost	Gross Output	Operation Operating
				(SYP/Ha)	Production	Margin Margin
							(SYP/Ha.)	(SYP/Ha)
	Figure 14. Economic comparison between traditional and improved irrigation systems
		120.000 140.000			106.400	119.747
	Value in SYP	40.000 60.000 80.000 100.000	77.496	56.902			28.904 62.844	1 Ha Traditional 1 Ha Improved
			20.000
			0
				Total Cost (SYP/Ha)	Gross Output Production	Operating Operation Margin Margin
							(SYP/Ha.)	(SYP/Ha)

CONCLUSION

The case study proposes a sustainable crop management model and provides indications and helpful information for the future planning of the available resources, to balance the traditional

SUSTAINABLE CROP MANAGEMENT MODEL IN SYRIAN STRATEGIC CROPS.

Galli D., Morini C., Di Terlizzi B.

ISDA 2010, Montpellier, June[28][29][30] 2010