Evaluation and comparison of empirical seepage estimation models for irrigation canals (Case study Darab Plain)

Water is a valuable asset for agriculture in arid and semi arid regions, worldwide. Reducing water leaks from the irrigation canals will save more water and leads to economic agriculture. Previous studies showed the importance of seepage assessmemt in irrigation canals. Assessment of seepage can be done by practical, theoritical and empirical methods. The review of literature reveals that the direct or practical methods can be more trustable comparing to theoretical or empirical methods or models. Ponding and inflow-outflow methods were widely used as direct or practical methods for seepage evaluation in irrigation canals. Use of empirical seepage formulas needs less cost and time comparing to other type of methods. However, the empirical models have different estimation accuracy and needs to be evaluated more. It is recommended in literature that the empirical models should be calibrated for a specific region before use. Simple empirical models have an estimation error about 15 percent due to direct measured values.

In present study, seepage was measured and compared in three irrigation earth canals in Darab plain using inflow-outflow method and various empirical formulas. These three canals named Hasanabad Canal, Mansuriyeh Canal, and Janatshahr Canal. The soil texture class of these three canals is Loam, Clay Loam and Sandy Loam, respectively. The canal flow velocity was measured using Valeport flow meter in the beginning and the end of three distances of 200 meters along each canal. The discharges were computed by multiplying the mean velocities and flow areas. Difference between the inflow and outflow discharge shows the canal seepage in the selected reaches. The Ingham, Davis-Wilson, Molesworth-Yennidumia, Affengendon, Moritz, Misra, Garg, Indian Punjab, Egyptian Irrigation Department empirical models were used for the study. Mean absolute error, root mean square error, normalized root mean square error, coefficient of variation of root mean square error, and χ2 test were used for the comparison of estimated and measured values. These empirical formulas were calibrated and validated due to the inflow-outflow method.

Results showed that the Moritz and Affengendon formulas with mean absolute error of 49% and 1445% percent had the least and most difference with inflow-outflow method before calibration. The error of estimation of the other formulas was about 125%. The highest estimated seepage was in the Affengendon formula, while the lowest was in the Ingham and Indian Punjab formulas. Comparison of estimated seepage values using t-test shows that the difference between the empirical seepage formulas is significant at 95% confidence probability. However, the difference between Moritz and inflow-outflow methods, Ingham and Molesworth-Yennidumia, Ingham and Indian Punjab, Molesworth-Yennidumia and Indian Punjab formula, Garg and Davis-Wilson formula was not significant at 95% confidence probability. The seepage estimation error of uncalibrated Ingham formula was about 95%, while for calibrated formula was less than 11 percent. The error of seepage estimation using uncalibrated Moritz and Molesworth-Yennidumia formulas were about 52 and 96 percent. This error for the uncalibrated Indian Punjab, Affengendon, Egyptian irrigation department, Garg and Misra formulas were about 95, 1220, 90, 92 and 68 percent, respectively. Results also showed that the error of calibrated Ingham, Molesworth-Yenidumia, Moritz, Davis-Wilson and Affengendon models, was about 7, 8, 9, 10, 10 percent comparing to inflow-outflow method, respectively. After these five formulas, the error of estimation of Garg, Egyptian, Misra, and Indian formulas were 17, 18, 20 and 20 percent, respectively. In order to validate the evaluated empirical formulas, some statistical parameters such as root mean square error, normalized root mean square error, coefficient of variation of root mean square error, and χ2 test were used. Results shows that the evaluated empirical formulas can be sorted from the better validated to the worse validated as Ingham, Molesworth-Yennidumia, Davis-Wilson, Moritz, Affengendon, Garg, Egyptian Irrigation Department, Misra and Indian Punjab. The χ2 values of the evaluated empirical formulas were 0.077 for Ingham formula to 0.757 for Misra formula. It can be concluded from this research that the uncalibrated empirical seepage formulas had significant difference to the inflow-outflow direct method. However, all of the calibrated formulas had a mean relative error less than 20 percent comparing to inflow-outflow method. Ingham formula was the best formula due to less calibration error. Moritz and Misra formulas had the best and worst validation condition in the study, respectively.