Comparison of infiltration models in NIT Kurukshetra campus

Comparison of infiltration models in NIT Kurukshetra campus The aim of the present investigation is to evaluate the performance of infiltration models used to calculate the infiltration rate of the soils. Ten different locations were chosen to measure the infiltration rate in NIT Kurukshetra. The instrument used for the experimentation was double ring infiltrometer. Some of the popular infiltration models like Horton’s, Philip’s, Modified Philip’s and Green–Ampt were fitted with infiltration test data and performance of the models was determined using Nash– Sutcliffe efficiency (NSE), coefficient of correlation (C.C) and Root mean square error (RMSE) criteria. The result suggests that Modified Philip’s model is the most accurate model where values of C.C, NSE and RMSE vary from 0.9947–0.9999, 0.9877–0.9998 to 0.1402–0.6913 (mm/h), respectively. Thus, this model can be used to synthetically produce infiltration data in the absence of infiltration data under the same conditions. Keywords Infiltration rate · Double ring infiltrometer · Coefficient of correlation · Nash–Sutcliffe efficiency · Root mean square error Introduction Many infiltration models have been evolved to evalu - ate hydrologic process from about 1911 (Green and Ampt Infiltration of water through soils is a natural process. It is a 1911; Williams et al. 1998). These models were presented key component of the hydrological cycle. Infiltration is the and summarized systematically and extensively by Williams process of entering water through top surface of the soil. The et al. (1998). Several researchers were able to successfully actual amount of water percolating into the soil at any time compare and evaluate those available soil-infiltration mod - is known as the infiltration rate (Haghighi et al. 2010). Infil - els in different frameworks under field conditions (Mbagwu tration is related to groundwater recharge and surface runo ff 1995; Mishra and Singh 1999; Shukla et al. 2003; Chahinian (Uloma et al. 2014). It also helps in designing of irrigation, et al. 2005; Dashtaki et al. 2009). drainage and water supply systems, flood control measures, Mirzaee et al. (2013) thought about the capacity of eight landslides and many other natural and man-made processes diverse infiltration models (i.e. Green and Ampt, Philip, (Igbadun and Idris 2007). Various models (Philip’s, Kostia- Horton, Kostiakov, Modified Kostiakov, Swartzendruber, kov, US-Soil Conservation Service (SCS), Horton, Holton Revised Modified Kostiakov models and SCS (US-Soil Con - etc.) have been developed to evaluate the infiltration. servation Service)) which were assessed by least squares fitting to measured soil infiltration. Sihag et al. ( 2017a) have compared the various infiltration models (Kostiakov, SCS, Novel model and Modified Kostiakov) for the NIT Kuruk - * Balraj Singh shetra campus. Novel model was most suited as compared balrajzinder@gmail.com to others with field infiltration data. Parveen Sihag Sihag et al. (2017b, c) and Singh et al. (2017) utilized the parveen12sihag@gmail.com various soft computing techniques to predict the infiltration Karan Singh rate of the soil. The objective of the present investigation karans72@gmail.com is to determine the model parameters and find out the best suitable model for the soil of below mentioned study area. Civil Engineering Department, NIT Hamirpur, Hamirpur 177005, India Civil Engineering Department, NIT Kurukshetra, Thanesar 136119, India Vol.:(0123456789) 1 3 63 Page 2 of 8 Applied Water Science (2018) 8:63 Study area NIT Kurukshetra is one of the reputed institutes of India situated in Kurukshetra. Geographic coordinates of the insti- tute is 29.9655°N, 76.7106°E which comes under Upper - Ghaggar Basin. Generally, the major soil type in Kuruk- shetra is clayey loam and sandy loam. The details of the ten locations, which were selected to find out the infiltration rate, are described in Fig. 1. Methodology Fig. 2 Double ring Infiltrometer The instrument used for find out the infiltration rates was Double ring infiltrometer (ASTM 2009). As shown in Fig.  2, was filled at the same level of both rings. The profundity of the double ring infiltrometer has two parts: one was outer water in the infiltrometer was recorded at regular interims ring whose diameter was 450 mm, and second was inner until the steady infiltration rate was achieved. The soil ring whose diameter is 300 mm. The rings of infiltrometer sample (about 100–150 g) for calculating moisture content were driven 100 mm depth into the soil. The hammer should was collected from a site nearest to the location chosen for strike uniformly on steel plate which is placed on the top of experimentation. the ring without disturbing the top soil surface. The water Fig. 1 Location map of study area 1 3 Applied Water Science (2018) 8:63 Page 3 of 8 63 Fig. 3 Comparison of the field infiltration rate with various models estimated infiltration rate for the study area (site no. 1–10) 1 3 63 Page 4 of 8 Applied Water Science (2018) 8:63 Fig. 3 (continued) 1 3 Applied Water Science (2018) 8:63 Page 5 of 8 63 Table 1 Detail of initial, final Test no. 1 2 3 4 5 6 7 8 9 10 infiltration rates and moisture contents of ten locations Initial infiltration rate (mm/h) 48 60 48 96 84 48 60 60 48 48 Final infiltration rate (mm/h) 15 15 10 5 4 9 8 8 11 11 Moisture content (%) 3.44 2.65 1.93 7.98 7.65 3.51 3.40 4.20 5.27 3.83 Infiltration models and parameters −kt m = m − m e + m , (3) 0 c c −1 where m is the steady infiltration rate (LT ); m is the ini- In this study, four popular infiltration models were selected c 0 −1 tial infiltration rate (LT ), and t is time (T). k is the infiltra- and model parameters are driven by using the data obtained tion decay factor. from field measurement. Green–Ampt’s model Philip’s model There are many equations derived from applying Darcy’s Philip’s (1957) model expressed as follows: law to the wetted zone in the soil, using the fact that a dis- −0.5 tinct wetting front exists. Green and Ampt (1911) were the m = St + A, (1) first with this approach, and their equation is in the form of −1 −0.5 where m is the infiltration rate (LT ); S is the (LT ); A m = K +(K ⋅ (⋅s)∕M, (4) s s is the soil parameter related to the transmission of water where s is the capillary suction at the wetting front; K is −1 s through the soil or gravity force (LT ), and t is time (T). saturated hydraulic conductivity, and M is the cumulative infiltration (L). The equation may be written as follows: Modified Philip’s model m = b + c∕M, (5) The modified model of Philip (Su 2010) is defined as where b = K and c = K ·(·s). s s m = St + A, (2) Estimation and inter‑comparison of models where β is an empirical constant. parameters Horton’s model Comparison of difference between the predicted infiltration rate values and measured values was done to evaluate the The Horton’s infiltration model (Horton 1941) is expressed infiltration rate. Those model performances are addressed as follows: below: Table 2 Parameters of the Test no. Equation parameters selected infiltration model Philip’s model Hortron’s model Green–Ampt Modified Philip’s model Model S A k b c S β A 1 176.96 8.08 0.048 13.20 138.75 2.547 − 1.452 0.046 2 357.91 2.62 0.027 19.15 233.98 7.186 − 1.178 − 5.063 3 167.85 4.21 0.038 8.47 174.92 3.830 − 1.229 − 0.449 4 42.91 3.35 0.078 0.34 410.75 6.027 − 0.833 3.805 5 85.83 0.70 0.052 1.62 483.61 230.227 − 0.106 − 117.905 6 79.31 6.20 0.060 2.73 164.51 2.297 − 1.329 1.030 7 96.05 5.06 0.060 3.082 243.88 2.945 − 1.235 2.113 8 196.89 0.11 0.052 0.22 289.88 8.256 − 0.910 − 4.103 9 180.66 4.12 0.042 9.08 162.12 4.110 − 1.221 − 1.564 10 180.66 4.12 0.042 9.08 162.12 4.110 − 1.221 − 1.564 −0.5 −1 S sorptivity (mm min ), A transmissivity (mm min ), b and c equation parameters, k infiltration decay factor 1 3 63 Page 6 of 8 Applied Water Science (2018) 8:63 Table 3 Performance evaluation Sr. no. Test no. Philip’s model Horton’s model Green–Ampt Modified parameters of infiltration model Philip’s model models (i) Coefficient of correlation (C.C)  1 1 0.975 0.967 0.931 0.9997  2 2 0.978 0.969 0.952 0.9997  3 3 0.936 0.942 0.942 0.9997  4 4 0.983 0.974 0.941 0.9947  5 5 0.964 0.938 0.948 0.9995  6 6 0.971 0.953 0.983 0.9996  7 7 0.984 0.947 0.967 0.9994  8 8 0.985 0.952 0.993 0.9997  9 9 0.985 0.952 0.980 0.9999  10 10 0.985 0.952 0.980 0.9999 Average 0.975 0.955 0.964 0.9992 (ii) Nash–Sutcliffe efficiency (NSE)  11 1 0.924 0.842 0.947 0.9995  12 2 0.621 0.933 0.866 0.9994  13 3 0.887 0.931 0.782 0.9993  14 4 -0.096 0.853 0.548 0.9876  15 5 -0.044 0.924 0.771 0.9989  16 6 0.464 0.872 0.942 0.9992  17 7 0.406 0.893 0.917 0.9978  18 8 0.872 0.892 0.981 0.9994  19 9 0.961 0.902 0.959 0.9998  20 10 0.961 0.902 0.959 0.9998  Average 0.596 0.895 0.867 0.9981 (iii) Root mean square error (RMSE) (mm/h)  21 1 2.609 3.767 2.166 0.3217  22 2 3.989 3.119 3.600 0.4496  23 3 27.084 9.897 8.703 0.3151  24 4 25.427 6.855 17.38 0.6913  25 5 7.941 3.870 11.89 0.2450  26 6 11.418 4.846 2.692 0.2583  27 7 5.188 4.763 4.254 0.3671  28 8 2.104 3.331 0.315 0.2537  29 9 2.104 3.331 2.139 0.1402  30 10 2.104 3.331 2.139 0.1402  Average 8.997 4.711 5.528 0.3182 Coefficient of correlation Nash–Sutcliffe efficiency Coefficient of correlation is a measure of the linear regres- The Nash–Sutcliffe efficiency (NSE) (Nash and Sutcliffe sion between the predicted values and the targets of models. 1970) has value between − ∞ and 1. Its value is defined by The coefficient of correlation (C.C) is computed as (a − b ) i i i=1 ∑ ∑ ∑ NSE = 1 − . ∑ (7) z ab−( a)( b) z (a − a ̄) C.C = . i=1 √ √ (6) ∑ ∑ ∑ ∑ 2 2 2 2 z( a )−( a) z( b )−( b) 1 3 Applied Water Science (2018) 8:63 Page 7 of 8 63 Infiltration models were evaluated using C.C, NSE and RMSE methods. The most suitable model was selected on the basis of maximum values of C.C and NSE and RMSE criteria. Findings are summarized in Table 3. The computed average values of C.C values were 0.975 0.955, 0.964 and 0.9992, NSE were 0.596, 0.895, 0.868 and 0.998, and those RMSE values were 8.997, 4.711, 5.528, and 0.3182 mm/h for Philip’s, Horton’s, Green–Ampt and Modified Philip’s model, respectively. Figure 4 provides the information about observed infil- tration rate and predicted values of infiltration rate of the above-mentioned models and suggests that all the values Fig. 4 Observed infiltration rate and predicted infiltration rate of vari- of Modified Philip’s model are lying inside the ± 10% error ous models band from the line of perfect agreement than the other infil- tration models (Horton’s model, Green–Ampt model and Root mean square error (RMSE) Philip’s model). Similarly, comparison of the C.C, NSE, RMSE suggests a better performance by Modified Philip’s This method exaggerates the prediction error—the differ - model in comparison to Philip’s, Horton’s and Green–Ampt model. Thus, Modified Philip’s model performs best amid ence between prediction value and actual value. The root mean squared error (RMSE) is evaluated by all models mentioned above for the study area, and hence, this model was used to assess the infiltration rate of this study area. RMSE = (a − b ) , (8) i i i=1 Conclusion where a is the calculated and b is observed values of infiltra- tion rate and z is the number of observations. Infiltration is an important parameter in the hydrological cycle and one of the thrust areas in hydrology. Infiltration rate data for different soils are essential for understanding Result and discussion of the rainfall-runoff process and for planning and design of water resource systems. While comparing infiltration mod- Infiltration  tests  were carried  out within the  field  in els with field data, it is observed that infiltration rate versus order  to  deal with  the  spatial  variability of infiltration time plots for field data and modelled data do not accurately rate. Based on the field tests at 10 different locations in NIT match; but the Modified Philip’s model is much closer to Kurukshetra area, results were analysed and individual infil- observed field data having C.C, NSE and RMSE values tration curves have been developed in Fig. 3. Table 1 shows of 0.9992, 0.9981 and 0.3182 (mm/h), respectively. It can the values of initial infiltration rate, final infiltration rate thus be used to synthetically generate infiltration data in the and moisture content of soil sample of various locations. absence of observed infiltration data for NIT Kurukshetra, The initial infiltration rate, final infiltration rate and mois- Haryana (India). ture contents fluctuate from 96–48 mm/h, 15–11 mm/h to 7.98–1.93%, respectively, for the study area. Open Access This article is distributed under the terms of the Crea- A number  of  infiltration  models  are  projected  to find tive Commons Attribution 4.0 International License (http://creat iveco mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- out field infiltration rates. The projected models Philip’s, tion, and reproduction in any medium, provided you give appropriate Horton’s, Green–Ampt and Modified Philip’s were chosen credit to the original author(s) and the source, provide a link to the for evaluation in the study. To study these models, actual Creative Commons license, and indicate if changes were made. field infiltration data have been used. Attempt was made to evaluate these infiltration equations on the basis of experi- mental  data  of the study  area  and  to obtain  numerical References values for the parameters of the models (Table  2). For the analysis of infiltration  data  and  find out  the param- ASTM (2009) Standard test method for infiltration rate of soils in field using double-ring infiltrometer. D3385-09, West Conshohocken, eters of the  above  model  using  least  square  techniques, PA XLSTAT software has been used. 1 3 63 Page 8 of 8 Applied Water Science (2018) 8:63 Chahinian N, Moussa R, Andrieux P, Voltz M (2005) Comparison of Sihag P, Tiwari NK, Ranjan S (2017a) Estimation and inter-comparison infiltration models to simulate flood events at the field scale. J of infiltration models. Water Sci 31(1):34–43 Hydrol 306(1):191–214 Sihag P, Tiwari NK, Ranjan S (2017b) Modelling of infiltration of Dashtaki SG, Homaee M, Mahdian MH, Kouchakzadeh M (2009) Site- sandy soil using gaussian process regression. Model Earth Syst dependence performance of infiltration models. Water Resour Environ 3(3):1091–1100 Manag 23(13):2777–2790 Sihag P, Tiwari NK, Ranjan S (2017c) Prediction of unsaturated Green WH, Ampt GA (1911) Studies in soil physics. J Agric Sci 4:1–24 hydraulic conductivity using adaptive neuro-fuzzy inference sys- Haghighi F, Gorji M, Shorafa M, Sarmadian F, Mohammadi MH tem (ANFIS). ISH J Hydraul Eng. https ://doi.org/10.1080/09715 (2010) Evaluation of some infiltration models and hydraulic 010.2017.13818 61 parameters. Span J Agric Res 8(1):210–217 Singh B, Sihag P, Singh K (2017) Modelling of impact of water qual- Horton RE (1941) An approach toward a physical interpretation of ity on infiltration rate of soil by random forest regression. Model infiltration-capacity. Soil Sci Soc Am J 5(C):399–417 Earth Syst Environ 3(3):999–1004 Igbadun HE, Idris UD (2007) Performance evaluation of infiltra- Su N (2010) Theory of infiltration: infiltration into swelling soils in a tion models in a hydromorphic soil. Niger J Soil Environ Res material coordinate. J Hydrol 395(1):103–108 7(1):53–59 Uloma AR, Samuel AC, Kingsley IK (2014) Estimation of Kostia- Mbagwu JSC (1995) Testing the goodness of fit of infiltration models kov’s infiltration model parameters of some sandy loam soils of for highly permeable soils under different tropical soil manage- Ikwuano-Umuahia, Nigeria. Open Trans Geosci 1(1):34–38 ment systems. Soil Tillage Res 34(3):199–205 Williams JR, Ying O, Chen JS, Ravi V (1998) Estimation of infiltration Mirzaee S, Zolfaghari AA, Gorji M, Dyck M, Ghorbani Dashtaki S rate in the vadose zone: application of selected mathematical mod- (2013) Evaluation of infiltration models with different numbers els, vol 2 (No. PB–98-147317/XAB). ManTech Environmental of fitting in different soil texture classes. Arch Agron Soil Sci Technology, Inc., Research Triangle Park, NC (United States); 2013:1–13 Dynamac Corp., Ada, OK (United States); National Risk Manage- Mishra SK, Singh VP (1999) Another look at SCS-CN method. J ment Research Lab., Subsurface Protection and Remediation Div., Hydrol Eng 4(3):257–264 Ada, OK (United States) Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10(3):282–290 Publisher’s Note Springer Nature remains neutral with regard to Philip JR (1957) The theory of infiltration: 1. The infiltration equation jurisdictional claims in published maps and institutional affiliations. and its solution. Soil Sci 83(5):345–358 Shukla MK, Lal R, Unkefer P (2003) Experimental evaluation of infil- tration models for different land use and soil management systems. Soil Sci 168(3):178–191 1 3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Water Science Springer Journals

Comparison of infiltration models in NIT Kurukshetra campus

Free
8 pages

Loading next page...
 
/lp/springer_journal/comparison-of-infiltration-models-in-nit-kurukshetra-campus-k0injX7NOg
Publisher
Springer Journals
Copyright
Copyright © 2018 by The Author(s)
Subject
Earth Sciences; Hydrogeology; Water Industry/Water Technologies; Industrial and Production Engineering; Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution; Nanotechnology; Private International Law, International & Foreign Law, Comparative Law
ISSN
2190-5487
eISSN
2190-5495
D.O.I.
10.1007/s13201-018-0708-8
Publisher site
See Article on Publisher Site

Abstract

The aim of the present investigation is to evaluate the performance of infiltration models used to calculate the infiltration rate of the soils. Ten different locations were chosen to measure the infiltration rate in NIT Kurukshetra. The instrument used for the experimentation was double ring infiltrometer. Some of the popular infiltration models like Horton’s, Philip’s, Modified Philip’s and Green–Ampt were fitted with infiltration test data and performance of the models was determined using Nash– Sutcliffe efficiency (NSE), coefficient of correlation (C.C) and Root mean square error (RMSE) criteria. The result suggests that Modified Philip’s model is the most accurate model where values of C.C, NSE and RMSE vary from 0.9947–0.9999, 0.9877–0.9998 to 0.1402–0.6913 (mm/h), respectively. Thus, this model can be used to synthetically produce infiltration data in the absence of infiltration data under the same conditions. Keywords Infiltration rate · Double ring infiltrometer · Coefficient of correlation · Nash–Sutcliffe efficiency · Root mean square error Introduction Many infiltration models have been evolved to evalu - ate hydrologic process from about 1911 (Green and Ampt Infiltration of water through soils is a natural process. It is a 1911; Williams et al. 1998). These models were presented key component of the hydrological cycle. Infiltration is the and summarized systematically and extensively by Williams process of entering water through top surface of the soil. The et al. (1998). Several researchers were able to successfully actual amount of water percolating into the soil at any time compare and evaluate those available soil-infiltration mod - is known as the infiltration rate (Haghighi et al. 2010). Infil - els in different frameworks under field conditions (Mbagwu tration is related to groundwater recharge and surface runo ff 1995; Mishra and Singh 1999; Shukla et al. 2003; Chahinian (Uloma et al. 2014). It also helps in designing of irrigation, et al. 2005; Dashtaki et al. 2009). drainage and water supply systems, flood control measures, Mirzaee et al. (2013) thought about the capacity of eight landslides and many other natural and man-made processes diverse infiltration models (i.e. Green and Ampt, Philip, (Igbadun and Idris 2007). Various models (Philip’s, Kostia- Horton, Kostiakov, Modified Kostiakov, Swartzendruber, kov, US-Soil Conservation Service (SCS), Horton, Holton Revised Modified Kostiakov models and SCS (US-Soil Con - etc.) have been developed to evaluate the infiltration. servation Service)) which were assessed by least squares fitting to measured soil infiltration. Sihag et al. ( 2017a) have compared the various infiltration models (Kostiakov, SCS, Novel model and Modified Kostiakov) for the NIT Kuruk - * Balraj Singh shetra campus. Novel model was most suited as compared balrajzinder@gmail.com to others with field infiltration data. Parveen Sihag Sihag et al. (2017b, c) and Singh et al. (2017) utilized the parveen12sihag@gmail.com various soft computing techniques to predict the infiltration Karan Singh rate of the soil. The objective of the present investigation karans72@gmail.com is to determine the model parameters and find out the best suitable model for the soil of below mentioned study area. Civil Engineering Department, NIT Hamirpur, Hamirpur 177005, India Civil Engineering Department, NIT Kurukshetra, Thanesar 136119, India Vol.:(0123456789) 1 3 63 Page 2 of 8 Applied Water Science (2018) 8:63 Study area NIT Kurukshetra is one of the reputed institutes of India situated in Kurukshetra. Geographic coordinates of the insti- tute is 29.9655°N, 76.7106°E which comes under Upper - Ghaggar Basin. Generally, the major soil type in Kuruk- shetra is clayey loam and sandy loam. The details of the ten locations, which were selected to find out the infiltration rate, are described in Fig. 1. Methodology Fig. 2 Double ring Infiltrometer The instrument used for find out the infiltration rates was Double ring infiltrometer (ASTM 2009). As shown in Fig.  2, was filled at the same level of both rings. The profundity of the double ring infiltrometer has two parts: one was outer water in the infiltrometer was recorded at regular interims ring whose diameter was 450 mm, and second was inner until the steady infiltration rate was achieved. The soil ring whose diameter is 300 mm. The rings of infiltrometer sample (about 100–150 g) for calculating moisture content were driven 100 mm depth into the soil. The hammer should was collected from a site nearest to the location chosen for strike uniformly on steel plate which is placed on the top of experimentation. the ring without disturbing the top soil surface. The water Fig. 1 Location map of study area 1 3 Applied Water Science (2018) 8:63 Page 3 of 8 63 Fig. 3 Comparison of the field infiltration rate with various models estimated infiltration rate for the study area (site no. 1–10) 1 3 63 Page 4 of 8 Applied Water Science (2018) 8:63 Fig. 3 (continued) 1 3 Applied Water Science (2018) 8:63 Page 5 of 8 63 Table 1 Detail of initial, final Test no. 1 2 3 4 5 6 7 8 9 10 infiltration rates and moisture contents of ten locations Initial infiltration rate (mm/h) 48 60 48 96 84 48 60 60 48 48 Final infiltration rate (mm/h) 15 15 10 5 4 9 8 8 11 11 Moisture content (%) 3.44 2.65 1.93 7.98 7.65 3.51 3.40 4.20 5.27 3.83 Infiltration models and parameters −kt m = m − m e + m , (3) 0 c c −1 where m is the steady infiltration rate (LT ); m is the ini- In this study, four popular infiltration models were selected c 0 −1 tial infiltration rate (LT ), and t is time (T). k is the infiltra- and model parameters are driven by using the data obtained tion decay factor. from field measurement. Green–Ampt’s model Philip’s model There are many equations derived from applying Darcy’s Philip’s (1957) model expressed as follows: law to the wetted zone in the soil, using the fact that a dis- −0.5 tinct wetting front exists. Green and Ampt (1911) were the m = St + A, (1) first with this approach, and their equation is in the form of −1 −0.5 where m is the infiltration rate (LT ); S is the (LT ); A m = K +(K ⋅ (⋅s)∕M, (4) s s is the soil parameter related to the transmission of water where s is the capillary suction at the wetting front; K is −1 s through the soil or gravity force (LT ), and t is time (T). saturated hydraulic conductivity, and M is the cumulative infiltration (L). The equation may be written as follows: Modified Philip’s model m = b + c∕M, (5) The modified model of Philip (Su 2010) is defined as where b = K and c = K ·(·s). s s m = St + A, (2) Estimation and inter‑comparison of models where β is an empirical constant. parameters Horton’s model Comparison of difference between the predicted infiltration rate values and measured values was done to evaluate the The Horton’s infiltration model (Horton 1941) is expressed infiltration rate. Those model performances are addressed as follows: below: Table 2 Parameters of the Test no. Equation parameters selected infiltration model Philip’s model Hortron’s model Green–Ampt Modified Philip’s model Model S A k b c S β A 1 176.96 8.08 0.048 13.20 138.75 2.547 − 1.452 0.046 2 357.91 2.62 0.027 19.15 233.98 7.186 − 1.178 − 5.063 3 167.85 4.21 0.038 8.47 174.92 3.830 − 1.229 − 0.449 4 42.91 3.35 0.078 0.34 410.75 6.027 − 0.833 3.805 5 85.83 0.70 0.052 1.62 483.61 230.227 − 0.106 − 117.905 6 79.31 6.20 0.060 2.73 164.51 2.297 − 1.329 1.030 7 96.05 5.06 0.060 3.082 243.88 2.945 − 1.235 2.113 8 196.89 0.11 0.052 0.22 289.88 8.256 − 0.910 − 4.103 9 180.66 4.12 0.042 9.08 162.12 4.110 − 1.221 − 1.564 10 180.66 4.12 0.042 9.08 162.12 4.110 − 1.221 − 1.564 −0.5 −1 S sorptivity (mm min ), A transmissivity (mm min ), b and c equation parameters, k infiltration decay factor 1 3 63 Page 6 of 8 Applied Water Science (2018) 8:63 Table 3 Performance evaluation Sr. no. Test no. Philip’s model Horton’s model Green–Ampt Modified parameters of infiltration model Philip’s model models (i) Coefficient of correlation (C.C)  1 1 0.975 0.967 0.931 0.9997  2 2 0.978 0.969 0.952 0.9997  3 3 0.936 0.942 0.942 0.9997  4 4 0.983 0.974 0.941 0.9947  5 5 0.964 0.938 0.948 0.9995  6 6 0.971 0.953 0.983 0.9996  7 7 0.984 0.947 0.967 0.9994  8 8 0.985 0.952 0.993 0.9997  9 9 0.985 0.952 0.980 0.9999  10 10 0.985 0.952 0.980 0.9999 Average 0.975 0.955 0.964 0.9992 (ii) Nash–Sutcliffe efficiency (NSE)  11 1 0.924 0.842 0.947 0.9995  12 2 0.621 0.933 0.866 0.9994  13 3 0.887 0.931 0.782 0.9993  14 4 -0.096 0.853 0.548 0.9876  15 5 -0.044 0.924 0.771 0.9989  16 6 0.464 0.872 0.942 0.9992  17 7 0.406 0.893 0.917 0.9978  18 8 0.872 0.892 0.981 0.9994  19 9 0.961 0.902 0.959 0.9998  20 10 0.961 0.902 0.959 0.9998  Average 0.596 0.895 0.867 0.9981 (iii) Root mean square error (RMSE) (mm/h)  21 1 2.609 3.767 2.166 0.3217  22 2 3.989 3.119 3.600 0.4496  23 3 27.084 9.897 8.703 0.3151  24 4 25.427 6.855 17.38 0.6913  25 5 7.941 3.870 11.89 0.2450  26 6 11.418 4.846 2.692 0.2583  27 7 5.188 4.763 4.254 0.3671  28 8 2.104 3.331 0.315 0.2537  29 9 2.104 3.331 2.139 0.1402  30 10 2.104 3.331 2.139 0.1402  Average 8.997 4.711 5.528 0.3182 Coefficient of correlation Nash–Sutcliffe efficiency Coefficient of correlation is a measure of the linear regres- The Nash–Sutcliffe efficiency (NSE) (Nash and Sutcliffe sion between the predicted values and the targets of models. 1970) has value between − ∞ and 1. Its value is defined by The coefficient of correlation (C.C) is computed as (a − b ) i i i=1 ∑ ∑ ∑ NSE = 1 − . ∑ (7) z ab−( a)( b) z (a − a ̄) C.C = . i=1 √ √ (6) ∑ ∑ ∑ ∑ 2 2 2 2 z( a )−( a) z( b )−( b) 1 3 Applied Water Science (2018) 8:63 Page 7 of 8 63 Infiltration models were evaluated using C.C, NSE and RMSE methods. The most suitable model was selected on the basis of maximum values of C.C and NSE and RMSE criteria. Findings are summarized in Table 3. The computed average values of C.C values were 0.975 0.955, 0.964 and 0.9992, NSE were 0.596, 0.895, 0.868 and 0.998, and those RMSE values were 8.997, 4.711, 5.528, and 0.3182 mm/h for Philip’s, Horton’s, Green–Ampt and Modified Philip’s model, respectively. Figure 4 provides the information about observed infil- tration rate and predicted values of infiltration rate of the above-mentioned models and suggests that all the values Fig. 4 Observed infiltration rate and predicted infiltration rate of vari- of Modified Philip’s model are lying inside the ± 10% error ous models band from the line of perfect agreement than the other infil- tration models (Horton’s model, Green–Ampt model and Root mean square error (RMSE) Philip’s model). Similarly, comparison of the C.C, NSE, RMSE suggests a better performance by Modified Philip’s This method exaggerates the prediction error—the differ - model in comparison to Philip’s, Horton’s and Green–Ampt model. Thus, Modified Philip’s model performs best amid ence between prediction value and actual value. The root mean squared error (RMSE) is evaluated by all models mentioned above for the study area, and hence, this model was used to assess the infiltration rate of this study area. RMSE = (a − b ) , (8) i i i=1 Conclusion where a is the calculated and b is observed values of infiltra- tion rate and z is the number of observations. Infiltration is an important parameter in the hydrological cycle and one of the thrust areas in hydrology. Infiltration rate data for different soils are essential for understanding Result and discussion of the rainfall-runoff process and for planning and design of water resource systems. While comparing infiltration mod- Infiltration  tests  were carried  out within the  field  in els with field data, it is observed that infiltration rate versus order  to  deal with  the  spatial  variability of infiltration time plots for field data and modelled data do not accurately rate. Based on the field tests at 10 different locations in NIT match; but the Modified Philip’s model is much closer to Kurukshetra area, results were analysed and individual infil- observed field data having C.C, NSE and RMSE values tration curves have been developed in Fig. 3. Table 1 shows of 0.9992, 0.9981 and 0.3182 (mm/h), respectively. It can the values of initial infiltration rate, final infiltration rate thus be used to synthetically generate infiltration data in the and moisture content of soil sample of various locations. absence of observed infiltration data for NIT Kurukshetra, The initial infiltration rate, final infiltration rate and mois- Haryana (India). ture contents fluctuate from 96–48 mm/h, 15–11 mm/h to 7.98–1.93%, respectively, for the study area. Open Access This article is distributed under the terms of the Crea- A number  of  infiltration  models  are  projected  to find tive Commons Attribution 4.0 International License (http://creat iveco mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- out field infiltration rates. The projected models Philip’s, tion, and reproduction in any medium, provided you give appropriate Horton’s, Green–Ampt and Modified Philip’s were chosen credit to the original author(s) and the source, provide a link to the for evaluation in the study. To study these models, actual Creative Commons license, and indicate if changes were made. field infiltration data have been used. Attempt was made to evaluate these infiltration equations on the basis of experi- mental  data  of the study  area  and  to obtain  numerical References values for the parameters of the models (Table  2). For the analysis of infiltration  data  and  find out  the param- ASTM (2009) Standard test method for infiltration rate of soils in field using double-ring infiltrometer. D3385-09, West Conshohocken, eters of the  above  model  using  least  square  techniques, PA XLSTAT software has been used. 1 3 63 Page 8 of 8 Applied Water Science (2018) 8:63 Chahinian N, Moussa R, Andrieux P, Voltz M (2005) Comparison of Sihag P, Tiwari NK, Ranjan S (2017a) Estimation and inter-comparison infiltration models to simulate flood events at the field scale. J of infiltration models. Water Sci 31(1):34–43 Hydrol 306(1):191–214 Sihag P, Tiwari NK, Ranjan S (2017b) Modelling of infiltration of Dashtaki SG, Homaee M, Mahdian MH, Kouchakzadeh M (2009) Site- sandy soil using gaussian process regression. Model Earth Syst dependence performance of infiltration models. Water Resour Environ 3(3):1091–1100 Manag 23(13):2777–2790 Sihag P, Tiwari NK, Ranjan S (2017c) Prediction of unsaturated Green WH, Ampt GA (1911) Studies in soil physics. J Agric Sci 4:1–24 hydraulic conductivity using adaptive neuro-fuzzy inference sys- Haghighi F, Gorji M, Shorafa M, Sarmadian F, Mohammadi MH tem (ANFIS). ISH J Hydraul Eng. https ://doi.org/10.1080/09715 (2010) Evaluation of some infiltration models and hydraulic 010.2017.13818 61 parameters. Span J Agric Res 8(1):210–217 Singh B, Sihag P, Singh K (2017) Modelling of impact of water qual- Horton RE (1941) An approach toward a physical interpretation of ity on infiltration rate of soil by random forest regression. Model infiltration-capacity. Soil Sci Soc Am J 5(C):399–417 Earth Syst Environ 3(3):999–1004 Igbadun HE, Idris UD (2007) Performance evaluation of infiltra- Su N (2010) Theory of infiltration: infiltration into swelling soils in a tion models in a hydromorphic soil. Niger J Soil Environ Res material coordinate. J Hydrol 395(1):103–108 7(1):53–59 Uloma AR, Samuel AC, Kingsley IK (2014) Estimation of Kostia- Mbagwu JSC (1995) Testing the goodness of fit of infiltration models kov’s infiltration model parameters of some sandy loam soils of for highly permeable soils under different tropical soil manage- Ikwuano-Umuahia, Nigeria. Open Trans Geosci 1(1):34–38 ment systems. Soil Tillage Res 34(3):199–205 Williams JR, Ying O, Chen JS, Ravi V (1998) Estimation of infiltration Mirzaee S, Zolfaghari AA, Gorji M, Dyck M, Ghorbani Dashtaki S rate in the vadose zone: application of selected mathematical mod- (2013) Evaluation of infiltration models with different numbers els, vol 2 (No. PB–98-147317/XAB). ManTech Environmental of fitting in different soil texture classes. Arch Agron Soil Sci Technology, Inc., Research Triangle Park, NC (United States); 2013:1–13 Dynamac Corp., Ada, OK (United States); National Risk Manage- Mishra SK, Singh VP (1999) Another look at SCS-CN method. J ment Research Lab., Subsurface Protection and Remediation Div., Hydrol Eng 4(3):257–264 Ada, OK (United States) Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10(3):282–290 Publisher’s Note Springer Nature remains neutral with regard to Philip JR (1957) The theory of infiltration: 1. The infiltration equation jurisdictional claims in published maps and institutional affiliations. and its solution. Soil Sci 83(5):345–358 Shukla MK, Lal R, Unkefer P (2003) Experimental evaluation of infil- tration models for different land use and soil management systems. Soil Sci 168(3):178–191 1 3

Journal

Applied Water ScienceSpringer Journals

Published: Apr 20, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off