Evaluation Different Methods of Scaling the Philip Equation

Document Type : Research Article

Authors

• M.T. Pozan
• M.M. Chari
• P. Afrasiab

Zabol

https://doi.org/10.22067/jsw.v34i1.82567

Abstract

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.

Keywords

• Infiltration
• Scaling
• transmissivity
• Sorptivity

References

1- Babaei F., Zolfaghari A.S., Yazdani M.R., and Sadeghipour A. 2018. Spatial analysis of infiltration in agricultural lands in arid areas of Iran. Catena 170: 25–35.

2- Bautista E., and Wallender W.W. 1985. Spatial variability of infiltration in furrows. Transactions of the ASAE 28: 1846–1851.

3- Childs J., Wallender W.W., and Hopmans J.W. 1993. Spatial and seasonal variation of furrow infiltration. Irrigation and Drainage Engineering 119(1): 74-90.

4- Duan R., Fedler C.B., and Borrelli J. 2011. Field evaluation of infiltration models in lawn soils. Irrigtion Science 29: 379–389.

5- Green W.H., and Ampt G.A. 1911. Studies on soil physics, 1.The flow of air and water through soils. Agriculture Science 4(1): 1-24.

6- Guzman-Rojo D.P., Bautista E., Gonzalez-Trinidad J.G., and Bronson K.F. 2019.Variability of furrow infiltration and estimated infiltration parameters in a macroporous Soil. Irrigation and Drainage Engineering 145(2): 04018041.

7- Haise H.R., Donnan W.W., Phelan J.T., Lawhon L.F., and Shockley D.G. 1956. The use of ring infiltrometers to determine the infiltration characteristics of irrigated soils. Publ ARS41 USDA. Agricultueral Resarch Service and Soil conservation Service 26(6): 451-463.

8- Holtan H.N. 1961. Concept for infiltration estimates in watershed engineering. USDA-ARS Bull. 41–51.

9- Horton R.E. 1941. An approach toward a physical interpretation of infiltration-capacity. Soil Science Society of America 5(C): 399-417.

10- Khatri K.L., and Smith R.J. 2006. Real-time prediction of soil infiltration characteristics for the management of furrow irrigation. Irrigation Science 25(1): 33-43.

11- Koech RK., Smith R.J., and Gillies M.H. 2014 . A real-time optimisation system for automation of furrow irrigation. Irrigation Science 32(4): 319-327.

12- Kostiakov A.N. 1932. On the dynamics of the coefficient of water percolation in soils and the necessity of studying it from the dynamic point of view for the purposes of amelioration. Trans. Sixth Comm. International. Soil Science Society 7-21.

13- Kutilek M., and Nielsen D.R. 1994. Soil hydrology: texbook for students of soil science, agriculture, forestry, geoecology, hydrology, geomorphology and other related disciplines. Catena Verlag 370 pp.

14- Kutilek M., Zayani K., Haverkamp R., Parlange J.Y., and Vachaud G. 1991. Scaling of Richards’ equation under invariant flux boundary conditions. Water Resource Research 27: 2181–2185.

15- Machiwal D., Jha M.K., and Mal B.C. 2006. Modelling infiltration and quantifying spatial soil variability in a wasteland of Kharagpur, India. Biosystems Engineering 95(4): 569-582.

16- Mehrabi F., and Sepaskhah A.R. 2013. Spatial Variability of Infiltration Characteristics at Watershed Scale: acase study of Bajgah plain. Journal of Agricultural Engineering Research 14 (1): 13-32. (In Persian with English abstract)

17- Miller E.E., and Miller R.D. 1956. Physical theory for capillary flow phenomena. Journal of Applied Physics 27(4): 324-332.

18- Nie W.B., Li Y.B., Zhang F., Dong S.X., Wang H., and Ma XY. 2018. A Method for Determining the Discharge of Closed-End Furrow Irrigation Based on the Representative Value of Manning’s Roughness and Field Mean Infiltration Parameters Estimated Using the PTF at Regional Scale. Water 10, 1825; doi:10.3390/w10121825.

19- Nielsen D.R., Biggar J.W., and Erh K.T. 1973. Spatial variability of field-measured soil-water properties. Hilgardia 42: 215–259.

20- Oyonarte N.A., Mateos L., and Palomo M.J. 2002. Infiltration variability in furrow irrigation. Irrigation and Drainage Engineering 128(1): 26-33.

21- Philip J.R. 1969. Theory of Infiltration. Academic Press, New York Vol. 9, pp 215–295

22- Philip J.R. 1957. The theory of infiltration: 3. Moisture profiles and relation to experiment. Soil Science 84(2): 163-178.

23- Rasoulzadeh A., and Sepaskhah A.R. 2003. Scaled infiltration equations for furrow irrigation. Biosystems Engineering 86(3): 375-383.

24- Sadeghi M., Ghahraman B., Davary K., Hasheminia S.M., and Reichardt K. 2011. Scaling to generalize a single solution of Richards’ equation for soil water redistribution. Science Agriculture 68: 582–591.

25- Sadeghi M., Ghahraman B., Warrick A.W., Tuller M., and Jones S.B. 2016. A critical evalution of Miller and Miller similar media theory for application to natural soils. Water Resources Research 52(4): 1-18

26- Sadeghi M., Ghahraman B., Ziaei A.N., Davary K., and Reichardt K. 2012. Additional scaled solutions to Richards’ equation for infiltration and drainage. Soil and Tillage Research 119: 60-69.

27- Schwankl L.J., Raghuwanshi N.S., and Wallender W.W. 2000. Furrow irrigation performance under spatially varying conditions. Irrigation and drainage engineering 126: 355–361.

28- Sharma M L., Gander G.A., Hunt C.G. 1980. Spatial variability of infiltration in a watershed. Journal of Hydrology 45: 122-101.

29- Shahriari M., Delbari, M., Afrasiab P., Pahlavan-Rad M.R. 2019. Predicting regional spatial distribution of soil texture in floodplains using remote sensing data: A case of southeastern Iran. Catena 182: 1-12.

30- Talsma T. 1969. In situ measurement of sorptivity. Soil Research 7(3): 269-276.

31- .Tsegaye T., and Hill R. L. 1998. Intensive tillage effects on spatial variability of soil physical properties. Soil Science 16(2): 143-154.

32- US Department of Agriculture, Natural Resources and Conservation Service. 1974. National Engineering Handbook. Section 15. Border Irrigation. National Technical Information Service, Washington, DC, Chapter 4.

33- Van Beek E., Bozorgy B., Vekerdy Z., and Meijer K. 2008. Limits to agricultural growth in the Sistan Closed Inland Delta, Iran. Irrigation Drainage System 22:131–143.

34- Warrick A.W. 1998. Spatial variability. In: Environmental Soil Physics (Hillel D, ed), pp 655–676. Academic Press, San Diego, CA.

35- Warrick A.W., and Nielsen D.R. 1980. Spatial variability of soil physical properties in the field. In: Applications of Soil Physics (Hillel D, ed), pp 319–344. Academic Press, New York.

36- Warrick A.W., Mullen G.J., and Nielsen D.R. 1977. Scaling field‐measured soil hydraulic properties using a similar media concept. Water Resources Research 13(2): 355-362.

37- Warrick A.W., and Hussen A.A. 1993. Scaling of Richards’ equation for infiltration and drainage. Soil Science Society of America 57: 15-18.

38- Zapata, N., and Playan E. 2000. Elevation and infiltration in a level basin. I. Characterizing variability. Irrigation Science 19(4): 155-164.