Where: WCU = crop consumptive water use (cm) from the effective root zone (60cm), θ2 = soil moisture percentage by weight after irrigation, θ1 = soil moisture percentage by weight before the following irrigation, Bd = bulk density in (g/cm³) of the i^th soil layer, D_i = depth of the i^th layer of soil and n = number of soil layers in the root zones.

Soil moisture content from 0-20, 20-40 and 40-60 cm depths was measured by the gravimetric method for each plot before sowing, straight after harvest and just before and after irrigation event. Soil moisture measured by gravimetric method (weight basis) was converted into volumetric proportion by multiplying by bulk density.

Some physical and chemical properties of the experimental site are shown in Table (2). Chemical and physical soil analyses were conducted by the standard methods described by Tan (1996). Chemical analysis of the irrigation water indicated that electrical conductivity (EC) was 0.50 (dS/m) at 25 °C and pH value was 7.55.

Agronomic measurements were done for root and above ground biomass weight at 50 and 75 days after planting. Maximum leaf area was measured and the leaf area index (LAI) was calculated by the following equation:

Where: plant ground area is the area of land occupied by the plant (equal distance between the plant * distance between ridges).

Harvest was done on the 14^th of April during the two growing seasons. Wheat grain and biological yield were measured at harvest and harvest index was calculated. These measurements were used to check the accuracy of the CropSyst model in predicting the final wheat yield.

2.2 CropSyst model

Model description

The objective of the Crop model (Stockle et al, 1994) is to serve as an analytical tool to study the effect of cropping systems and management on crop productivity and the environment. For this purpose, Crop-Syst simulates soil water budget, soil-plant nitrogen budget, crop phenology, crop canopy and root growth, biomass production, crop yield, residue production and decomposition, soil erosion by water, and pesticide fate, which are affected by weather, soil characteristics, crop characteristics, and cropping system management options which include crop rotation, variety selection, irrigation, nitrogen fertilization, pesticide applications, soil and irrigation water salinity, tillage operations, and residue management.

The water budget in the model includes rainfall, irrigation, runoff, interception, water infiltration and redistribution in the soil profile, crop transpiration, and evaporation. The nitrogen budget in CropSyst includes nitrogen application, nitrogen transport, nitrogen transformations, ammonium absorption and crop nitrogen uptake. The calculation of daily crop growth, expressed as biomass increase per unit area, is based on a minimum of four limiting factors; namely, light, temperature, water and nitrogen. Pala et al. (1996) suggested that minor adjustments of some of these parameters, accounting for cultivar-specific differences, are desirable whenever suitable experimental information is available. Details on the technical aspects and use of the CropSyst model have been reported elsewhere (Stockle et al, 1994).

Model calibration

After each growing season, input files required by Crop-Syst model for El-Bustan location and wheat crop were prepared and used to run the model. For each treatment one management file was prepared to represent each irrigation treatment. The date of each phenological stage was used to calculate growing degree days for that stage. Total biomass, grain yield, total and seasonal evapotranspiration, computed from the soil-moisture measurements from all the treatments, were used for model calibration. The values of the crop input parameters were either taken from the CropSyst manual (Stockle et al., 1994) or set to the values observed in the experiments. The calibration consisted of slight adjustments of selected crop input parameters to reflect reasonable simulations. These adjustments were between values that were either typical for the crop species or known from previous experiences with the model.

2.3 Goodness of fit

To test the goodness of fit between the measured and predicted data, percent difference between measured and predicted values of grain yield and biological yield in each growing season was calculated, in addition to consumptive use. Furthermore, root mean square error which describes the average difference between measured and predicted value were calculated (Jamieson et al.,1998).Also, Willmott index of agreement was calculated, which take a value between 0.0-1.0 and 1.0 means perfect fit (Willmott, 1981).

2.4 Climate change scenarios

In this work, the HadCM3, which is a coupled atmosphere-ocean general circulation model (AOGCM) developed at the Hadley Centre for Climate Prediction and Research (United Kingdom) was used (Gordon et al., 2000 and Pope et al., 2000) as it is considered more significant and more sophisticated than earlier versions. This model has a spatial resolution of 2.5 x 3.75 (latitude by longitude). HadCM3 provides information about climate change all over the entire world during the 21^st century and presents information about three times slices: 2020s, 2050s, and 2080s. In order to provide information on possible changes in the world climate, the climate change models are forced to consider future scenarios. The IPCC (Nakicenvic et al., 2000) has developed emission scenarios known as SRES (Special Report on Emission Scenarios). The four SRES scenarios combined two sets of divergent tendencies: one set varies between strong economic values and strong environmental values, while the other set varies between increasing globalization and increasing regionalization (IPCC-TGCIA, 1999). Two climate change scenarios were considered in this study: A2 and B2. These selected two scenarios take into consideration rise in global annual mean temperature by 3.09 and 2.16°C, respectively, CO₂ concentration 834 and 601 ppm, respectively and global mean sea level rise 62 and 52 cm, respectively. As the resolution of the model is very big, simple interpolation techniques of these percentages have been applied to fit the station site. Data were downloaded in GRIB format from the IPCC Data Distribution Centre web site. The GRBCONV program source code can be found at the following web site: http://cera-www.dkrz.de/IPCC_DDC/IS92a/HadleyCM3/hadcm3.html

The GRBCONV program was used to convert the data files from GRIB format to the more conventional ASCII. The download site does not offer the option to subset the data based on an area of interest. Therefore a custom program was used to extract the data for the region of interest. HadCM3 variables were monthly precipitation, solar radiation, minimum and maximum temperatures.

A2 and B2 climate change scenarios were used to run the CropSyst model to predict wheat yield and consumptive use in the year of 2050s. The effect of climate change on each of the two growing seasons will be discussed separately where each season would be a representation of the growing season of the year of 2050.

3. Results and discussion

3.1 Wheat yield, irrigation amounts and water use efficiency

Water use efficiency was the lowest under farmer irrigation, whereas the applied irrigation amount was the highest (650 mm), compared to the irrigation treatments in both growing seasons (Table3). The highest water use efficiency was obtained when irrigation was applied using 0.8 of ETc with fertigation application in 80% of application time, i.e. 16.86 and 15.90 kg/ mm for the first and second seasons respectively. The results in Table (3) showed that the highest yield was obtained under irrigation application using 1.2 of ETc with fertigation application in 80% of application time in both growing seasons.

3.2 Model calibration Wheat grain yield

CropSyst model showed good agreement between measured and predicted values of wheat grain yield (Table 4). Low percentage of difference between observed and predicted values was obtained, as well as low root mean square error. Furthermore, the value of Willmott index which was close to 1 indicated good agreement. Several publications highlighted the accuracy of the model, such as Benli et al., (2007) who indicated that the model prediction showed low RMSE. Furthermore, Benli et al., (2007) stated that high Will-mott index of agreement was obtained with a value of 0.98, which is similar to what is shown in Table (4).

Wheat biological yield

The model over-predicted the values of wheat biological yield under some irrigation treatments, where the percentage of change between observed and predicted values were between +2.61% to -2.29% in the first growing season (Table5). In the second growing season, the value ranged between -3.91% and +0.81%.

Root mean square error was 0.39 and 0.34 ton/ha for the first and the second seasons, respectively. In addition, Willmott index of agreement was close to 1, i.e. 0.97 and 0.98%. Benli et al., (2007), stated that RMSE represented 21% of the observed average, whereas Willmott index of agreement between the observed and simulated biomass was 0.76, which means that is reasonably close to 1.

Wheat Consumptive use

The obtained results from the calibration of CropSyst model for consumptive use revealed that the percentage of change between measured and predicted values was less than 1.5% in both growing seasons (Table 6). Root mean square error was 2.80 and 2.23 mm and Willmott index of agreement was close to 1. Similar results were obtained by Wang et al., (2006), where RMSE was 0.07 mm for evapotranspiration and Punnkuk et al., (1998), where it was 0.05 mm when CropSyst was used to predict evapotranspiration. Benli et al., (2007) stated that CropSyst model predicted consumptive use reasonably well. The RMSE values were 11% of the average observed ET and the Willmott index of agreement (0.91) was reasonably close to 1.

Our results showed that CropSyst model was able to predict yield and consumptive use of wheat grown in sandy soil under the Egyptian conditions (Tables 3, 4 and 6). One of the benefits of using CropSyst model is that it can give an insight to processes that took place during wheat growth in the growing season which was difficult to be measured in the field. The good agreement between measured and predicted values of wheat grain and biological yield as well as consumptive use implied that the model worked sufficiently well to warrant the exploration of the effect of climate change scenarios.

Reduction in wheat yield under A2 climate change scenario was higher than the reduction under B2 climate change scenario (Table 7). Furthermore, the reduction in the yield was higher in the second growing season than in the first growing season.

The highest percentage of yield reduction was obtained for farmer irrigation and irrigation using 0.6 of ETc with fertigation application in 60% of application time. The farmer irrigation was associated with high applied irrigation water in both growing seasons and low water use efficiency under current climate conditions (Table 3). Moreover, the high reduction in the yield for farmer irrigation could be a result of leaching nutrients away from root zone and oxygen deficiency (Ouda et al., 2008). Similar results were obtained by Ouda et al., (2010). Irrigation using 0.6 of ETc with fertigation application in 60% of application time treatment was coupled with low applied irrigation water (Table 2). This result emphasis proper management of irrigation water under current climate conditions, which could reduce yield losses under climate change conditions.

The results in Table (7) implied that climate change altered the natural growing conditions for wheat, which resulted in biotic stress, such as heat and water stresses that wheat plants exposed to. Exposing wheat plants to high moisture stress depressed seasonal consumptive use and grain yield (El-Kalla et al., 1994 and Khater et al., 1997). During vegetative growth, phyllochron decreases in wheat under water stress and leaves become smaller, which could reduce leaf area index (Gardner, et al., 1985) and reduce the number of reproductive tillers, in addition to limit their contribution to grain yield (Mosaad et al., 1995). Furthermore, water stress occurs during grain growth could have a strong effect on final yield compared with stress occurred during other stages (Hanson and Nelson, 1980). High temperature reduces numbers of tillers and spikelet initiation and development rates (McMaster, 1997). Moreover, high temperature during flowering causes pollen sterility (Saini and Aspi-nall, 1982) and reduces number of kernels per head, if it occurred during early spike development (Kolderup, 1979). The duration of grain filling is also reduced under heat stress (Sofield et al., 1977), as well as growth rates with a net effect of lower final kernel weight (Bagga and Rawson 1977; McMaster, 1997).

The lowest percentage yield reduction was obtained for irrigation using amount of 1.0 of ETc with fertigation application in 80% of application time, i.e. 28 and 27% under A2 in the first and second season, respectively. Under B2 climate change, the percentage of yield reduction was 24 for both growing seasons, respectively (Table 7). These results implied that fertigation application increased water and fertilizer use efficiency and prevents N and K leaching in the sandy soil of the experimental site. Water and fertilizer use efficiencies increased yield under current climate conditions (Table 3) and help wheat plants to withstand the stressful conditions of climate change (Table 7). Therefore, it is recommended to irrigate wheat using amount of 1.0 of ETc with fertigation application in 80% of application time to reduce yield losses.

Water use efficiency

The anticipated climate change condition is expected not only to decrease crops yield, but also to lessen water use efficiency. Water use efficiency was reduced under both A2 and B2 climate change scenarios, compared to its corresponding values under current climate conditions (Table 8). However, the reduction was higher under A2, compared to B2. The highest water use efficiency in the first growing season was obtained with irrigation amount of 1.0 of ETc with fertigation application in 80% of application time, i.e. 10.94 and 11.70 kg/mm under both A2 and B2 scenarios, respectively (Table 8). Regarding the second growing season, irrigation with an amount of 0.8 of ETc and fertigation application in 80% of application time resulted in highest water use efficiency, i.e. 10.98 and 11.21 kg/mm under both A2 and B2 scenarios.Therefore, it is recommended to irrigate wheat grown in sandy soil with an amount of either 1.0 or 0.8 of ETc with fertigation  application in 80% of application time to reduce yield losses and increase water use efficiency. Similar results   were obtained by Khalil et al., (2009), where water use   efficiency was reduced under climate change.

4. Conclusion

This study was conducted in Egypt to assess the effect of using different fertigation treatments on wheat grown in sandy soil and under sprinkler irrigation, and to simulate the effect of climate change on wheat yield. The real challenge under climate change conditions is to use adaptation strategies, which are improved agricultural management practices, to reduce the damage caused by climate change on the yield of the growing crops. Plant breeders could use the results of the application of the simulation models to help in the development of new varieties adapted to climate change. Wheat breeders will need to focus on overcoming heat stress rather than improving drought tolerance as a result of climate change. Moreover, breeding wheat varieties with high water use efficiency is also a very important goal to be achieved.

References

Allen, R.G., Pereira, L.S., Raes, D. Smith, M. 1998. Crop evapotranspiration: Guideline for computing crop water requirements. FAO, N^o56.

Bagga, A., Rawson, I.M. 1977. Contracting responses of morphologically similar wheat varieties to temperature appropriate to warm temperature climates with hot summers: A study in controlled environment. Aust. J. Agric. Res. 40 ,965-980.

Benli, B., Pala, M., Stockle, C.,Oweis, T. 2007. Assessment of winter wheat production under early sowing with supplemental irrigation in a cold highland environment using CropSyst simulation model. Agric. Water Mang. 3:45-54.

Church, J.A., White, N.J. 2006. A 20^thcentury acceleration in global sea-level rise. Geophysical Research Letters. 33, L01602.

Eid, H.M., Anton, N.A., Tarrad, A.M. 1994. Comparative study on Egyptian wheat varieties and their response to high temperatures. Annals of Agric. Sci. Moshtohor. 32 (1) 143-154.

El-Kalla, S.E., Leilah, A.A., Basiony, A.H., Hussien S.M. 1994. Effect of Irrigation and foliar nutrition treatments on growth and yield of some wheat cultivars under El-Arish area condition. 6^th conf. Agron., Fac. Agric., Al-Azhar Uni., Egypt.

Gardner, F.P., Pearce, R.B., Mitchell, R.L. 1985. Physiology of crop plants. Iowa State University Press. Ames.

Gordon, C., Cooper, C.A., Senior, H., Banks, J., Gregory, M., Johns, T.C., Mitchell, F.B., Wood, R.A. 2000. The simulation of sea surface temperature, sea ice extents and ocean heat transports in a version of the Hadley Centre coupled model without flux adjustments. Climate Dynamics. (16):147- 168.

Hanson, A.D., Nelson E.C. 1980. The biology of crop production. New York Academic Press.

Hoffman, G. J., Howell T.A.,Solomon K.H. 1992. Management of farm irrigation system. ASAE Monograph No. 9. ASAE, USA. p. 1040.

IPCC. 2001: Summary for Policymakers: Climate Change 2001: The Scientific Basis, Contribution of Working Group I to the 3^rd Assessment Report of the Intergovernmental Panel on Climate Change. J.T. Houghton, Y. Ding, D.J. Griggs, M. Noguer, P.J. Van Der Linden, and D. Xioaosu, Cambridge University Press, Cambridge, 944pp.

IPCC-TGCIA. 1999. Guidelines on the use of Scenario Data for Climate Impact and Adaptation Assessment, Version 1. Prepared by Carter, T.R., Hulme M., and Lal. M. Intergovernmental Panel on Climate Change, task Group on Scenarios for Climate Impact Assessment. Cambridge University Press, Cambridge, 944p.

Jamieson, P.D., Porter, J.R., Goudriaan, J., Ritchie, J.T., Van Keulen, H., Stol, W. 1998. A comparison of the models AFRCWHEAT2, CERES-Wheat, Sirius, SUCROS2 and SWHEAT with measurements from wheat grown under drought. Field Crops Res. 55: 23-4.

Khalil, F.A., Farag, H., Afandi, G. El., Ouda, S.A., 2009. Vulnerability and adaptation of wheat to climate change in Middle Egypt. 13^th Conference on Water Technology. Hurghada, Egypt. 12-15 March.

Khater, A.N, Abdel Maksoud, H.H., Eid, H.M. 1997. Response of some wheat cultivars and their water relations to different irrigation level in Middle Delta. Egypt , J. Appl. Sci. 11(2): 15-29.

Kolderup, I. 1979. Application of different temperatures in three growth phases of wheat. II. Effects on ear size and seed setting. Acta. Agric. Scand. 29:11-116.

Majumdar, D.K. 2002. Irrigation Water Management: Principles and Practice. 2^nd ed. Prentice-Hall of India, New Delhi- 110001.487p.

MALR. 2009. Study of Important Indicators of Agricultural Statistics. Ministry of Agriculture and Land Reclamation, Egypt: Winter Crops Volume (1), N^o1170.

McMaster, G.S. 1997. Phonology, development, and growth of wheat (Triticum aestivum L.) shoot apex: A review. Advaces in Agron. 59, 63-118.

Mosaad, M.G., Ortiz-Ferrara, G., Mahalak-Shmi, V. 1995. Tiller development and contribution to yield under different moisture regimes in two Triticum species. J. Agron. 174: 173-180.

Nakicenovic, N,; Alcamo, J., Davis, G., de Vries B.; Fenhann, J., Gaffin, S., Gregory, K., Grubler, A., Jung, T.Y., Kram, T., La Rovere, E.L., Michaelis, L.; Mori, S.; Morita, T.; Pepper, W.; Pitcher, H., Price, L, Raihi, K, Roehrl, A., Rogner, H., Sankovski, A., Schlesingger, M., Shukla, P., Smith, S., Swart, R, van Rooijen, S., N Victor and Z. Dadi. 2000. IPCC Special Report on Emission Scenarios Cambridge University Press, 599 P.

Ouda, S. A., Sayed, M., El Afandi G., Khalil, F. A. 2010. Developing an adaptation strategy to reduce climate change risks on wheat grown in sandy soil in Egypt. 10^th International Conference on Development of Dry lands. 12-15 December. Cairo, Egypt.

Ouda, S.A., Khalil, F.A., Abou Elenin, R., Shreif, M., Benli, B., Qadir, M. 2008. Using Yield-Stress model in irrigation management for wheat grown in Egypt. J. Appl. Bio. Sci. 2 (1) :57-65.

Pala, M., Stockle, C.S., Harris, H.C. 1996. Simulation of durum wheat (Triticum turgidum ssp Durum) growth under different water and nitrogen regimes in a Mediterranean environment using CropSyst. Agric. Sys. 51(2) 147-163.

Pannkuk, C.D., Stockle, C.O., Papendick, R. I.1998. Evaluating CropSyst simulations of wheat management in a wheat-fallow region of the US Pacific Northwest. Agric. Syst. 57 (2): 121-133.

Pope, V.D., Gallani, M.L., Rowntree, P.R., Stratton, R.A. 2000. The impact of new physical parametrization in the Hadley Centre Climate Model-HadCM3. Climate Dynamics. (16): 123-146.

Richter, G.M., Semenov, M.A. 2005. Modelling impacts of climate change on wheat yields in England and Wales: Assessing drought risks. Agricultural Systems. 84 (1): 77-97.

Saini, H.S., Aspinall, D. 1982. Sterility in wheat (Triticum aestivum L.) induced by water stress or high temperature: Possible mediation by abscisic acid. Aust. J. Plant Physio. 9: 529-537.

Sofield, I L., Evans, T. Wardlaw, I.F. 1977. The effect of temperature and light on grain filling in wheat. R. Soc. N. Z. Bull. 12, 909-915.

Stockle, C.O., Martin, S., Campbell, S. 1994. Crop-Syst, a cropping systems model: water/nitrogen budgets and crop yield. Agricultural Systems. 46, 335-359.

Tan K.H. 1996. Soil Sampling, Preparation and Analysis. Marcel Dekker, Inc. New York, p.391.

Wang, Z., Zhang, B., Xiao-yan, L., Song, K., Liu, D. Zhang. S. 2006. Using CropSyst to simulate spring wheat growth in Black Soil Zone of Northeast China. Pedoshere. 16 (2):121-134.

Willmott, C.J. 1981. On the validation of models. Phys. Geogr. 2: 184-194.