Ferdowsi University of MashhadWater and Soil2008-475734120200320Evaluation Different Methods of Scaling the Philip EquationEvaluation Different Methods of Scaling the Philip Equation27423878310.22067/jsw.v34i1.82567FAM.T. PozanZabol0000-0001-9517-3569M.M. ChariZabolP. AfrasiabZabolJournal Article20190821Introduction: Infiltration is found to be the most important process that influences uniformity and efficiency of surface irrigation. Prediction of infiltration rate is a prerequisite for estimating the amount of water entering into the soil and its distribution. Since the infiltration properties are a function of time and space, a relatively large number of field measurements is needed to represent an average of farm conditions (Bautista and Wallender, 1985). In recent years, researchers have proposed methods to reduce the requirement of the regional and field data in order to describe water dynamic in the soil. One of these methods is scaling which at the first was presented by Miller and Miller (1956) and developed on the similar media theory in the soil and water sciences (Miller and Miller, 1956; Sadeghi et al., 2016). According to similar media theory, soils can be similar, provided that different soils can be placed on a reference curve with ratios of a physical characteristic length, called "scaling factor". The objective of the present study was scaling the Philip infiltration equation and analyzing the spatial variability of infiltration characteristics by using minimum field measurements. In this research, a new method was presented for scaling infiltration equation and compared with previous methods scaling including: based on sorptivity (), transmissivity (), the optimum scaling factors () arithmetic, geometric and harmonic.
Materials and Methods: The basic assumption of scaling through this method was “the shape of the infiltration characteristics curve is almost constant despite the variations in the rate and depth of infiltration”. The data required for infiltration scaling were a reference infiltration curve (whose parameters are known) and the depth of water infiltrated within a specified time period in other infiltration curves. In this method, first, equation infiltration parameters are specified for one infiltration curve, called the reference infiltration curve (). If, for other infiltration equations, the depth of water infiltrated is obtained after the specified time(ts) (for example, depth of infiltration water after 4 hours), the scale factor (Fs, dimensionless) is equal to the depth of water infiltrated after ts in the reference infiltration equation to depth of infiltrated water after ts even infiltration equation is as follows:
(1)
where Ii (i=1,2, …,n) is depth of infiltrated water after a given time (ts) for each infiltration families and is depth of infiltrated water after a given time in reference, and and are parameters of reference curve.In order to assess the proposed scaling method, root mean square error (RMSE), mean bias error (MBE) and coefficient of determination (R2) were used for a totally 24 infiltration tests.
Results and Discussion: The parameters of this model (i.e. sorptivity S and transmissivity factor A) showed a wide variation among the study sites. The variation of these parameters showed no significant difference between sorptivity and transmissivity factors. In addition, Talsama et al. (1969) illustrated that there is a weak relationship between sorptivity and saturated hydraulic conductivity. Results showed that scaling achieved using αA was better than that obtained using αS. Mean curve was chosen as reference curve and scale curve was obtained by different methods. The results of statistical analysis showed that the proposed method had the best performance (RMSE=0.006, MBE=0.0019 and R2=0.9996). In order to evaluate the effect of the reference curve selection on the results, the scaled cumulative infiltration curve based on different reference curves (different infiltration equation) was evaluated. The results showed that the selection of the reference infiltration curve is optional and each cumulative infiltration families can be selected as the reference curve. For defining the relationship between and , , αS، αA ، ، ، data, a statistical analysis was performed. According to our results, had the highest correlation with .
Conclusion: In this study, a new method for penetration scaling was presented. In this method, the infiltration curve can be obtained using the minimum information including a reference curve and the depth of infiltrated water after a given time. The selection of the reference infiltration curve is optional and each cumulative infiltration equation can be selected as the reference curve. In the light of the results of this research, it can be concluded that the proposed method in this study is promising to be used for surface irrigation management.Introduction: Infiltration is found to be the most important process that influences uniformity and efficiency of surface irrigation. Prediction of infiltration rate is a prerequisite for estimating the amount of water entering into the soil and its distribution. Since the infiltration properties are a function of time and space, a relatively large number of field measurements is needed to represent an average of farm conditions (Bautista and Wallender, 1985). In recent years, researchers have proposed methods to reduce the requirement of the regional and field data in order to describe water dynamic in the soil. One of these methods is scaling which at the first was presented by Miller and Miller (1956) and developed on the similar media theory in the soil and water sciences (Miller and Miller, 1956; Sadeghi et al., 2016). According to similar media theory, soils can be similar, provided that different soils can be placed on a reference curve with ratios of a physical characteristic length, called "scaling factor". The objective of the present study was scaling the Philip infiltration equation and analyzing the spatial variability of infiltration characteristics by using minimum field measurements. In this research, a new method was presented for scaling infiltration equation and compared with previous methods scaling including: based on sorptivity (), transmissivity (), the optimum scaling factors () arithmetic, geometric and harmonic.
Materials and Methods: The basic assumption of scaling through this method was “the shape of the infiltration characteristics curve is almost constant despite the variations in the rate and depth of infiltration”. The data required for infiltration scaling were a reference infiltration curve (whose parameters are known) and the depth of water infiltrated within a specified time period in other infiltration curves. In this method, first, equation infiltration parameters are specified for one infiltration curve, called the reference infiltration curve (). If, for other infiltration equations, the depth of water infiltrated is obtained after the specified time(ts) (for example, depth of infiltration water after 4 hours), the scale factor (Fs, dimensionless) is equal to the depth of water infiltrated after ts in the reference infiltration equation to depth of infiltrated water after ts even infiltration equation is as follows:
(1)
where Ii (i=1,2, …,n) is depth of infiltrated water after a given time (ts) for each infiltration families and is depth of infiltrated water after a given time in reference, and and are parameters of reference curve.In order to assess the proposed scaling method, root mean square error (RMSE), mean bias error (MBE) and coefficient of determination (R2) were used for a totally 24 infiltration tests.
Results and Discussion: The parameters of this model (i.e. sorptivity S and transmissivity factor A) showed a wide variation among the study sites. The variation of these parameters showed no significant difference between sorptivity and transmissivity factors. In addition, Talsama et al. (1969) illustrated that there is a weak relationship between sorptivity and saturated hydraulic conductivity. Results showed that scaling achieved using αA was better than that obtained using αS. Mean curve was chosen as reference curve and scale curve was obtained by different methods. The results of statistical analysis showed that the proposed method had the best performance (RMSE=0.006, MBE=0.0019 and R2=0.9996). In order to evaluate the effect of the reference curve selection on the results, the scaled cumulative infiltration curve based on different reference curves (different infiltration equation) was evaluated. The results showed that the selection of the reference infiltration curve is optional and each cumulative infiltration families can be selected as the reference curve. For defining the relationship between and , , αS، αA ، ، ، data, a statistical analysis was performed. According to our results, had the highest correlation with .
Conclusion: In this study, a new method for penetration scaling was presented. In this method, the infiltration curve can be obtained using the minimum information including a reference curve and the depth of infiltrated water after a given time. The selection of the reference infiltration curve is optional and each cumulative infiltration equation can be selected as the reference curve. In the light of the results of this research, it can be concluded that the proposed method in this study is promising to be used for surface irrigation management.https://jsw.um.ac.ir/article_38783_2fa75c78ab01464257ae788179952a30.pdf