Evaluation of the regression equations of seepage losses in the earthen canals

Lack of water resources is one of the important issues in the world. seepage losses from the canals are the most important part of losses during agricultural water conveyance. Considering the share of agriculture in the consumption of water resources, the estimation of water losses from the body of earthen canals is one of the major issues in the design and management of irrigation and drainage networks. According to the researches, unlined canals lose 50% of their transfer water through leakage. In addition to water losses due to seepage, one of the main reasons for the importance of checking the amount of leakage is the reduction of the quality of the land and soil around the water conveyance and distribution canals and the threat to the environment of the region. Average losses of water from irrigation canals in Iran, are on around 60%. The methods of estimating seepage losses from the earthen canals include the field method, empirical relationships, and theoretical methods. There are many empirical relationships in this field, but experience has shown that the coefficients of these relationships are different according to the conditions of each region and should be calibrated for local conditions (Rostamian and Abedi Kopaee, 2014). Mutema and Dhavu, (2021) stated that the characteristics of the canal such as wetted perimeter and wetted area, have a significant effect on water losses. The purpose of this research is to investigate the regression relationship between the leakage flow from earthen canals with hydraulic characteristics and flow.

In this study, using the information of the study conducted in the east of the Zayandeh Rood basin, the non-linear regression relationship between the seepage (s) and the inflow rate (Q), wetted perimeter, hydraulic radius (R), and hydraulic depth (D) was investigated. In order to derive regression relationships, 70% of the data related to two series of measurements in 9 canals were used. Validation of regression relationships was done using 30% of the data, which is related to the measurement in the third time and related to the same canals. The data were obtained from the direct measurement of the inlet and outlet flow rates and the geometric and hydraulic characteristics of the earthen canals, such as the shape and dimensions of the canal section and the water depth. In this research, the relative value of root means square error, RRMSE, mean absolute error, MAE, and mean error, MBE, were used to evaluate the accuracy of the relations extracted from the indices. The difference between the value calculated in the validation step obtained with each of the regression relations, with the measured values, is shown using RRMSE and MAE statistical indices. The smaller the values of these two statistics are, the more accurate the regression relationship will be in estimating the seepage from the canals under study. Also, the MBE index will be a positive or negative value, which will be an indicator of underestimation or overestimation of seepage losses, respectively.

The results showed that all three regression relationships the seepage (s) and the inflow rate (Q), wetted perimeter, hydraulic radius (R), had better accuracy than the best empirical relationship used in the study area (the Ingham equation). It should be noted that the above relations are probably valid for the flow ranges between 30 and 390 liters per second (values measured in the research of Salemi and Sepaskhah (2015) and in using these relations in this area for flow rates outside of this range, should be cautious. The values of the mentioned indices, RRMSE, MAE and MBE, related to the regression relationship between the amount of seepage and the inflow rate, were 0.1954, 0.0082, and 0.0058, respectively and in the regression relationship between the amount of seepage and the wetted perimeter, respectively, it is equal to 0.2113. 0.0091, 0.0058 were obtained. Also, according to the positive values of the MBE, it can be concluded that in all the extracted relationships, the average of the estimated data showed a lower estimate than the observed values. Comparing the results of this research with Heidarizadeh and Salemi's (2013) shows that except for the regression relation related to hydraulic depth regression relations have better accuracy than the best experimental equations that studied by them, that is, the Ingham relation. Also, compared to Vedernikov's theoretical method, the accuracy of the estimation of the mentioned regression relationships is lower, but the difference in the statistical indicators is not significant. Therefore, according to the previous studies and comparing it with the regression relationships obtained in this research, it is recommended that in the case of using empirical relationships to estimate the amount of leakage losses from earthen canals in this region, these relationships should be used instead of the empirical relationships. In this regard, Salmasi and Abraham (2020) in a research also dealt with the prediction of leakage from earthen canals using the finite element method as well as multivariable nonlinear regression, and their results also showed the high accuracy of the resulting regression relationships. Water crisis and its management and planning require detailed design of all components of water distribution and consumption systems. Assessing and quantifying leakage loss from irrigation canals is high important for the protection and management of water resources, and specifying the intensity of leakage loss, and for the evaluation of the potential benefits of leakage reduction techniques and technologies. In this research, the non-linear regression relationship between the seepage and some hydraulic characteristics of flow in irrigation canals, by using the information obtained from the studies of the seepage losses of earthen canals in the eastern region of Zayandeh Rood basin, were extracted to estimate these losses. The results of this research have shown the appropriate accuracy of regression relationships compared to other experimental equations used in the study area. Therefore, it is recommended to use the obtained regression relationships to estimate the loss of water leakage in this area. Of course, in using these relationships, it is better to control the inflow rate range and then use these relationships. In addition, in order to complete the studies, it is recommended to carry out similar studies on the channels of this region with a larger inflow rate.