Agricultural Engineering research Institute

Friction head loss equations and friction correction factors were evaluated and compared to field observations collected from thirty
center pivots with laterals made of PVCs. The friction head loss equations include Darcy-Weisbach (D-W), Hazen-Williams (H-W), and Scobey, in addition to a proposed equation valid for smooth and rough pipe types and for all turbulent flow types. The proposed equation was developed by combining the equations of D-W and H-W, along with the multiple nonlinear regression technique. The friction correction factors were computed by using the typical Christiansen, modified Christiansen, Anwar, and Alazba formulae. The evaluation has been based on statistical error techniques with observed values as a reference. With the combination of modified Christiansen, Anwar, and Alazba formulae, the results revealed that the magnitudes of friction head loss calculated by using the D-W, H-W, and proposed equations were in agreement with field observations. The root mean square deviation (RMSD) values ranged from 1.6 to 1.7 m. As expected, and when the typical Christiansen friction correction factor was used with the D-W, H-W, and proposed equations, the results showed poor agreement between observed and computed friction head loss values. This was clearly reflected by the high RMSD values that ranged from 5.4 to 5.9 m. On the other hand, agreement occurred between observed friction head loss values and those calculated by using the Scobey equation, invalid for PVC pipe type, when combined with the typical Christiansen formula. This interesting finding led to improved results of the Scobey equation through a developed Cs coefficient suitably valid for PVC pipe type through analytically mathematical derivation; accordingly, the RMSD value dropped from approximately 8.6 to 1.6 m.

A mathematical model to forecast the solar still performance under hyper arid conditions was developed using artificial neural network technique. The developed model expressed by different forms, water productivity (MD), operational recovery ratio (ORR) and thermal efficiency (gth) requires ten input parameters. The input parameters included Julian day, ambient air temperature, relative humidity, wind speed, solar radiation, ultra violet index, temperature of the feed and brine water, and total dissolved solids of feed and brine water. The developed ANN model was trained, tested and validated based on measured data. The results showed that the coefficient of determination ranged from 0.991 to 0.99 and 0.94 to 0.98 for MD, ORR and gth during training and testing process, respectively. The average values of root mean-square error for all water were 0.04 L/m2/h, 2.60% and 3.41% for MD, ORR and gth respectively. Findings revealed that the model was effective and accurate in predicting solar still performance with insignificant errors.

Artificial neural networks (ANNs) and gene expression programming (GEP) were compared to estimate daily reference evapotranspiration (ETref) under arid conditions. The daily climatic variables were collected by 13 meteorological stations from 1980 to 2010. The ANN and GEP models were trained on 65% of the climatic data and tested using the remaining 35%. The generalised Penman–Monteith (PMG) model was used as a reference target for evapotranspiration values, with hc varies from 5 to 105 cm with increment of a centimetre. The developed models were spatially validated using climatic data from 1980 to2010 taken from another six meteorological stations. The results showed that the eight ETref models developed using the ANN technique were slightly more accurate than those developed using the GEP technique. The ANN models’ determination coefficients (R2) ranged from 67.6% to 99.8% and root mean square error (RMSE) values ranged from 0.20 to 2.95 mm d-1. The GEP models’ R2 values ranged from64.4% to 95.5% and RMSE values ranged from 1.13 to 3.1 mm d-1. Although the GEP models performed slightly worse than the ANN models, the GEP models used explicit equations.

A soil box was used to investigate the water movement and soil water distribution around subsurface drip laterals with two emitters in the presence of a thin layer of polyacrylamide (PAM). Sandy soil was uniformly packed into a soil box. The PAM was applied at a rate of 29.3 kg ha-1 as a 0.01% solution by spraying it directly onto the soil surface at the required depths. With an operating pressure of 150 kPa and no PAM layer, the water consumption with a dripper line depth of 0.15 m was 12% lower than with a dripper line depth of 0.10 m. The greatest improvement in soil water-holding capacity after the addition of a PAM layer (47%) was observed when the dripper line was placed at a depth of 0.15 m under an operating pressure of 100 kPa. With a dripper line depth of 0.15 m and an operating pressure of 100 kPa, the average moisture content in the vertical planes below and above the dripper line directly increased by about 7.4 and 20%, respectively, with PAM layers at 0.25 and 0.30 m depths when compared with the moisture content with no PAM layer. The combination of a dripper line depth of 0.15 m, a PAM layer depth of 0.30 m and an operating pressure of 100 kPa will achieve optimal water management.

This study investigates the ability of gene expression programming (GEP) in modeling of the infiltrated water volume (Z) under furrow irrigation. Field data were collected in the literature study for modeling Z covering wide range of opportunity time. Five variables were used as input parameters; inflow rate (Q o), furrow length (L), waterfront advance time at the end of the furrow (T L), infiltration opportunity time (T o) and cross-sectional area of the inflow (A o). The following statistical parameters that coefficient of determination (R 2), overall index of the model performance (OI), root mean square errors (RMSE) and mean absolute errors (MAE) are used as comparing criteria for the evaluation of the models' performances. The best value of the statistical parameters which range in training, testing and validation processes as the following (R 2 = 95–97%; OI = 94–97%; RMSE = 0.013–0.009 m 3 m À1 ; and MAE = 0.011–0.007 m 3 m À1) implies that the GEP model provides an excellent fit for the measured data. A comparison is made between the estimates provided by the GEP and the two-point method. The comparison results reveal that the GEP models are superior to two-point method. Furthermore, the remarkable advantage of GEP was that it resulted in an explicit equation for the estimation of the Z under furrow irrigation.

Accurate estimations of reference evapotranspira-tion (ET ref) are extremely important for maximizing the beneficial use of water and hydrologic applications, particularly in arid and semiarid regions where water sources are so limited. The aim of this study is to develop mathematical models to calculate the daily ET ref using a gene expression programming (GEP) technique. Eight GEP models (GEP-MOD1–8) were developed from combinations of climatic variables. The Penman-Monteith equation was considered the reference method, with the reference plant height varying from 5 to 105 cm in 5-cm increments. Daily climatic variables collected from 13 meteorological stations, one station from every region within the Kingdom of Saudi Arabia, covered the 1980 to 2010 period. Of the available climatic data, 65 % was used in the training process for the eight developed GEP models, and 35 % was used in the testing process. The accuracy of the eight developed GEP models to estimate ET ref varied in significance depending on the climatic variables that were included. As more climatic parameters were input, the accuracy of the GEP model increased. For the testing process, the coefficient of determination (R 2) ranged from a low of 63.4 % for GEP-MOD1 to a high of 95.4 % for GEP-MOD8, and the root mean square error (RMSE) values ranged from 3.19 mm day −1 for GEP-MOD1 to 1.14 mm day −1 for GEP-MOD8. From the spatial evaluation, the values of RMSE ranged from 3.27 mm day − 1 for GEP-MOD1 to 1.21 mm day −1 for GEP-MOD8. In addition, the respective RMSE values resulting from GEP-MOD8 for plant heights of 50 and 12 cm were 0.75 and 0.96 cm. This implies that the developed GEP-MOD8 can be used for any value of the reference plant height ranging from 5 to 105 cm with insignificant errors. Interestingly, solar radiation had an almost insignificant effect on ET ref in the hyper-arid conditions. In contrast , wind speed and plant height had a large positive effect on increasing the accuracy of calculating ET ref .

Gene Expression Programming (GEP) was used to develop new mathematical equations for estimating daily reference evapotranspiration (ETref) for the Kingdom of Saudi Arabia. The daily climatic variables were collected by 13 meteorological stations from 1980 to 2010. The GEP models were trained on 65% of the climatic data and tested using the remaining 35%. The generalised PenmanMonteith model was used as a reference target for evapotranspiration (ET) values, with hc varies from 5 to 105 cm with increment of a centimetre. Eight GEP models have been compared with four locally calibrated traditional models (HargreavesSamani, Irmak, JensenHaise and KimberlyPenman). The results showed that the statistical performance criteria values such as determination coefficients (R2) ranged from as low as 64.4% for GEPMOD1, where the only parameters included (maximum, minimum, and mean temperature and crop height), to as high as 95.5% for GEPMOD8 with which all climatic parameters included (maximum, minimum and mean temperature; maximum, minimum and mean humidity; solar radiation; wind speed; and crop height). More over, an interesting founded result is that the solar radiation has almost no effect on ETref under the hyper arid conditions. In contrast, the wind speed and plant height have a great positive impact in increasing the accuracy of calculating ETref. Furthermore, eight GEP models have obtained better results than the locally calibrated traditional ETref equations.