Analysis of Saturation Risk in Sprinkler Irrigation : Case of Cherfech Irrigation Perimeter in Tunisia

This study is targeted to the assessment of the saturation risk in sprinkler irrigation. For this purpose, in situ field trials were carried out to infer the saturated hydraulic conductivity (Ks) and sorptivity (S) using the disc infiltrometer method. Since the measured values of Ks are very close to prescribed application rate, caution is required. In a first step, the pressure head at the wetting front (hf) and the useful porosity (θs – θi) are assumed to be constant. Thus, the logarithmic derivation of the sorptivity provides a relation between relative variations of S and Ks. The ponding time (Ts) is estimated from Green and Ampt (1911) and Philip (1957b) infiltration equations. The risk of saturation is deemed to be inexistent inasmuch as simulated values of Ts are greater than the irrigation times practiced in the zone. In a second step, the values of the pressure head at the wetting front and saturated water content were assumed to be variable with soil texture. Simulations of the ponding time were carried out based on Rawls and al. (1981) data. For the recommended sprinkler spacing in the Cherfech perimeter (12 m × 12 m), the simulations show a good agreement between Ts values generated from Green and Ampt and Philip equations for Ks ranging from 1.5 to 6 mm/h. Moreover, it was established that saturation risk due to a gradual texture variation is virtually inexistent in the conditions prevailing in Cherfech perimeter.


Introduction
The fair distribution of water under sprinkler irrigation is a major concern.Irrigation network should be adapted to the soil texture, crop, available water discharge, water quality and environmental conditions.Results of Playan and Mateos (2006) show that the improvement of the irrigation efficiency depends on the appropriate choice of equipment, pedo-climatic conditions, water availability and socio-economic conditions.The assessment of sprinkler irrigation performance was widely analyzed (Merriam & Keller, 1978;Heermann et al., 1990;Keller & Bliesner, 1990;Burt et al., 1997;Pereira, 1999).Tiercelin (1998) and Keller and Bliesner (1990) emphasized that distribution uniformity is a prominent factor in the design and management of sprinkler irrigation systems.The unfair water distribution induces harmful impact on crop yield and environment.Indeed, under irrigation may induce crop yield reduction and soil salinization.Conversely, excess of irrigation may induce crop yield reduction by asphyxia as well as a leaching of fertilizers and pesticides.Solomon (1983) indicated that water stagnation and runoff has a prejudicial impact on soil and crop.Angulo-Jaramillo et al. (2000), and Trout and Kinkacid (1987) indicated that soil water characterization is of prima facie importance for designing irrigation systems and modeling water movement within the soil.Li and al. (1976) stressed that the determination of the infiltration rate is essential for designing sprinkler irrigation systems.This holds true particularly for high infiltration rates and short irrigation periods.Diamond and Thomas (2003) underlined that the determination of the infiltration rate is fundamental for accurate prediction of runoff.Physically sound formulas show that runoff occurs when rainfall intensity exceeds the saturated hydraulic conductivity.In absence of a shallow water table or an underlying substratum, no runoff is expected when rainfall intensity is very low with respect to the saturated hydraulic conductivity.It is established that the higher the rainfall intensity, the shorter the ponding time.The saturation time may be straightforwardly derived from analytical and empirical infiltration equations (Slack, 1980;Broadbridge & White, 1987;Kutilek & Nilsen, 1994;Parlange et al., 1999;Smith et al., 2002;Assouline et al., 2007).It is worthy to say that the prerequisite knowledge of the ponding time is necessary to overcome the stagnation hazard.This challenge is all the greater as sprinkler irrigation is commonly practiced on fine soils in Tunisia.
This study is devoted to (i) the estimation of the ponding time under sprinkler irrigation, (ii) the analysis of the saturation risk for gradually variable soil texture taking into account the performance of the irrigation system in Cherfech irrigation perimeter.

Material and Methods
Field trials were carried out in the experimental station of Cherfech located in the north of Tunisia (latitude 37° N, longitude 10.5° E, altitude 328 m).The irrigation perimeter of Cherfech covers 2022 ha.

Characterization of the Experimental Site
The climate of the studied zone is semi-arid.It is characterized by a hot summer and moderated and rainy winter.The mean values of annual rainfall and reference evapotranspiration are 443 mm and 1112 mm, respectively.Table 1 summarizes the values of the soil bulk density ( d ), volumetric soil water contents at the field capacity and at wilting point ( fc and  wp ) as well as granulometric fractions over 1 m soil depth.According to the United States Department of Agriculture [USDA] classification, the soil is a fine loam over the depth 0-40 cm and loamy over the remaining soil depth.The mean electrical conductivity of the water irrigation, supplied by Medjerda Channel, is equal to 2.6 dS/m.

Determination of the Soil Infiltrability
The infiltration law was established using the infiltrometer disc method (Peroux & White, 1988).Contrariwise to the double ring method of Muntz (Maheshwari, 1996), the disc infiltrometer method has the merit to provide hydraulic conductivity at the saturation and also hydraulic conductivities for very low soil water pressure heads (Coquet et al., 2000).The estimation of K s by the disc infiltrometer is based on the Wooding (1968) equation: where, q ∞ , h 0 , K,  and r refer to the infiltration density rate [LT -1 ], imposed potential at the soil surface [L], soil water conductivity [LT -1 ], Kirchhoff potential [L 2 T -1 ] and the radius of the infiltrometer disc [L].
Equation ( 1) was derived from steady state regime under axisymmetric flow from a surface point source.
Assuming that soil water conductivity varies exponentially with soil water pressure head (Gardner, 1958, K(h) = K s e h ), the infiltration density rate may be written as: The approach of multi-potential disc infiltrometer developed by Reynolds and Elrick (1991) and by Ankeny et al. (1991) allow the inference of the parameters of K(h) law from the knowledge of two pairs of discharge-soil water pressure head.
The sorptive number  (L -1 ) is straightforwardly derived from solving the above equation system.
The know mono-pote pair of em where, S, θ The param the value o The soil s derived fro when wate where, I a conductivi where, the

Experi
Three infil was used suctions eq suction (-1 soil surfac Initial and displays t infiltromet Philip: In the sam 3 bars at th m/s.Unde

Infiltra
Recorded illustrates surface and the depth indepen The high value of the correlation coefficient R indicate a very good agreement between fitted and observed results.The value of A provides a saturated hydraulic conductivity equal to 11.3 mm/h.Subsequently, application rates should be fixed less than this threshold to prevent ponding and runoff.Table 2 summarizes the values of S and K s measured by the mono-potential (2a) and multi-potential methods (2b).
Table 2. Soil water characteristics using the disc infiltrometer 2a.mono-potential method h 0 (cm) θ i (cm 3 /cm 3 ) θ s (cm 3 /cm 3 ) S (cm/s It should be emphasized that the two trials were performed in different points.According to Nielsen et al. (1973) and Vauclin et al. (1994), the saturated hydraulic conductivity is widely affected by the spatial soil variability.Therefore, we can assume that K s values presented in tables (2a) and ( 2b) are virtually of the same order of magnitude.These values are in a good agreement with K s values reported by Hillel (1974) for loamy textured soils (K s ranging from 5 to 10 mm/h).

Saturation Risk Analysis for on Sprinkler Spacing of 12 m × 12 m
For a given pressure head at the sprinkler nozzle, the discharge is constant.Therefore, the decrease of the sprinkler spacing induce an increase of the application rate.Consequently, caution is required to avoid saturation and runoff hazards when sprinklers are close to each other.The narrow gap between saturated hydraulic conductivity (11.3 mm/h) and suitable application rate (9 mm/h) incited us to investigate the risk of soil saturation.Assuming that (h 0 -h f ) (θ s -θ i ) is constant, the logarithmic derivation of Equation ( 11) leads to the following expression: It should be stressed that Green and Ampt (1911) and Philip (1957b) equations assume a uniform soil texture and constant initial water content all over the soil depth.It is obvious that perfect uniformity is an idyllic schematization of the reality.This is why we investigated the impact of an eventual texture change on the ponding time.Hereinafter, we assumed that soil texture varies from clay loam to silt loam.For these soil types, K s varies from 1.5 to 7.6 mm/h according to the National Engineering Handbook (1991).The sorptivity values were calculated using an incremental approach based on Equation ( 16).The derived ponding times were determined for a constant application rate of 9 mm/h.Values of (h f -h 0 ), ( s -θ i ), K s , S and T s are expressed in mm, cm 3 /cm 3 , mm/h, mm/h 1/2 and h, respectively.Table 3 indicated that ponding times are of the same magnitude than those depicted in Figure 3. Definitively, Figure 3 and Table 3 show that the risk of soil saturation generated by a gradual soil texture variation is virtually inexistent for the practical irrigation times in the study region.Referring to the pedology map of the zone, one can claim that it is unlikely that saturated soil hydraulic conductivity varies from 3 to 11.3 mm/h.

Conclusion
Field trials showed that optimal application rate is equal to 9 mm/h for a sprinkler spacing of 12 m × 12 m.This application rate is so close to the saturated hydraulic conductivity (11.3 mm/h).To assess the soil saturation hazard due to the spatial soil variability, we compared the calculated ponding times to the irrigation times operated in the study region.It was established that Green and Ampt (1911) and Philip (1957b) methods produce similar results for K s ranging within 1.5 to 6 mm/h.The estimated ponding times are greater than operated irrigation times in the region.Therefore, one can conclude that the saturation risk is virtually inexistent in the study area.Consequently, farmers can use the prescribed application rate without saturation hazard.This application rate is the best compromise between energy cost and water distribution uniformity.

Figure 3
Figure3displays the evolution of the ponding time with respect to K s for the two aforementioned equations.
Figure 3 sh 1.5 to 6 m saturation higher tha results sho The comp between G Figure 4 sh

Table 1 .
Soil water characteristics and granulometry in Cherfech station

Table 3 .
Ponding time for three soil texture based onRawls et al. (1981) data