Performance evaluation of selected infiltration equations for irrigated (FADAMA) soils in Southern Kaduna Plain, Nigeria

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1 ISSN Vol. (4) pp. 01-xx January 014 Available online http// Copyright 01 Basi Researh Journal Full Length Researh Paper Performane evaluation of seleted infiltration equations for irrigated (FADAMA) soils in Southern Kaduna Plain, Nigeria A. I. Arab 1, O. J. Mudiare, M. A. Oyebode, and U. D. Idris 3 1 National Agriultural Extension and Researh Liaison Servies, Ahmadu Bello University, Zaria, Nigeria; Department of Agriultural Engineering, Ahmadu Bello University, Zaria, Nigeria. 3 Samaru College of Agriulture, Division of Agriultural Colleges, Ahmadu Bello University, Zaria, Nigeria. Correspondene: Adamu Ibrahim Arab, National Agriultural Extension and Researh Liaison Servies, Ahmadu Bello University, P.M.B. 1067, Zaria, Nigeria. *Corresponding author adamuarab@yahoo.o.uk OR adamuarab@gmail.om: Tel: Aepted 4 January 014 ABSTRACT The need for ontinuous and in-depth study on the appliability and auray of infiltration equations annot be exhausted sine equation parameters and performane vary for different soils. The study reported herein, has evaluated four infiltration equations (Kostiakov s; Philip s; Horton; Talsma and Parlange). The field water infiltration data used in these equations were based on double ring infiltrometer tests onduted for 4 hours at two fadama irrigation area (Kuda and Kukumdaji). Measurements were made at two sites in eah of the two Fadama irrigation area based on land management pratie (Cultivated/fallow) giving a total of four experimental sites. The results of the measured infiltration rates reveals that site (Kuda/fallow) gave the highest average final infiltration rate of 69mm/hr followed by site 1(Kuda/ultivated) of value 5mm/hr and then site 3(Kukumdaji/ultivated) of value 35mm/hr while site 4 (Kukumdaji/fallow) reorded the least of 18mm/hr. Results of the Comparism between measured and predited infiltration rates reveal that Kostiakov s and Philip s equation gives the best fit when ompared with the rest of the equations tested. Results from the study onlude that Kostiakov s and Philip s equation an be used to predit infiltration rates for the soil studied but that Kostiakov s equation approximated the measured infiltration rates with higher auray and best fit than did Philip s and Horton s equation. Talsma and Parlange s equation fail to approximate measured data partiularly in the early stage of measurement. Keywords: Performane, Evaluation, Infiltration, Equations, Irrigated, Fadama, Soils, Infiltrometer INTRODUCTION Infiltration is defined as the entry of water into the soil through its surfae (Mihael, 1978). It is a property of the soil and differs from deep perolation whih is the downward movement of soil water beyond the reah of plant roots. Infiltration rate is defined as the rate of water entry into the soil through its surfae (Yonts et al, 003). A falling drop of water may be interepted by vegetation or may fall diretly on to the ground. Water that reahes the ground may evaporate bak to the atmosphere; enter the soil (infiltrates) or runoff. Unlike runoff, whih starts only after surfae detention has been satisfied, infiltration starts as soon as the first drop of

2 Arab et al. 0 rainfall touhes the ground surfae and ontinues even after rainfall eases until all depressions on the land surfae are empty. Infiltration plays a vital role in the distribution of soil water, it determines the runoff and hene soil erosion and flood hazard (Babalola, 1986). In watershed modeling, a major hindrane to prediting surfae runoff is the unertainty in haraterizing soil infiltration. The diffiulty of prediting infiltration is mainly due to the variation of infiltration related soil physial properties from site to site in the field. Diret infiltration measurement is laborious, tiresome, time onsuming and ould be expensive partiularly where water is limiting. A method to predit infiltration is therefore desirable and is possible through some simple time dependent infiltration equations. In order to simplify infiltration preditions, researhers (Kostiakov, 193; Horton, 1940; Phillip, 1957; Talsma and Parlange, 197; Green and Ampt, 1911et) introdued a number of simple time dependent algebrai equations. However, these equations are not appliable in all onditions and therefore test on their appliability and auray are essential. Many researhers ontinue to develop several theoretial (physial) and empirial equations to predit either umulative infiltration or infiltration rate (Clemmens, 1983; Fok, 1986). The auray of infiltration rate predition with these equations depends to a large extent on the reliability and auray of the soil hydrauli properties. Clemmens (1983) reported that empirial equations predit field infiltration better than theoretial equations. In addition, he reommended use of the Kostiakov and modified Kostiakov equations for irrigation systems beause they desribe the infiltration proess reasonably well. Cherdhanpipat (1990) found after extensive field experiments that the infiltration data measured by the ylinder infiltrometer orrelated better with values predited by the Kostiakov, Modified Kostiakov and Philip equations. Although many researhes had been onduted in the appliability and auray of most of the equations but still the need for ontinuous and in-depth study of the appliability and auray of infiltration equations annot be exhausted sine equation parameters and performane vary for different soils. It is important therefore to test the appliability and auray of Kostiakov (193); Horton (1940); Phillip (1957); and Talsma and Parlange (197) equations in prediting soil infiltration for seleted inundated (fadama) irrigated soils in the southern Kaduna plain. LITERATURE REVIEW Infiltration theory Many approahes have been presented in an attempt to solve the problem of infiltration of water into a soil by many researhers. The Bukingham-Dary flux equation for a rigid, unsaturated porous medium ombines with the ontinuity equation to provide governing partial differential equations of various forms (Rihards, 1931). q = k h...1 dθ q =... dt Where: h = hydrauli potential (m) k = hydrauli ondutivity (m/se) q = flow rate (veloity vetor) (m 3 /se m) t = time (se) = gradient vetor or grad θ = volumetri moisture ontent (m 3 /m 3 ) Equations.1 and. are Dary s and ontinuity equation, respetively. The hydrauli potential, h is given as: h = ψ + Z...3 Where: ψ = apillary potential Z = gravitational potential From Eqs.1,. and.3, dθ = k + dt ( ψ Z )...4 For vertial flow, Eqs.4 beomes, dθ d d dk = k ( ψ )...5 dt dt + dz dz The variables k and ψ are funtions ofθ. That is, k = k (θ ); ψ = ψ (θ ) Due to hysteresis, some of these are not single-valued funtions. For simpliity, uniqueness of these relationships is assumed. Thus: d θ d ( ) d = k θ ( ψ ( θ )) d k ( θ ). dt dt + dz dz, ( ). d ψ but k θ ( θ ) = D ( θ ) dθ

3 03. Basi Res. J. Soil Environ. Si. Where, D therefore, ( θ ) = soil water diffusivity dθ d dθ d = D dt dz + dz dz if k is assumed ons tan t, i. e. ( θ ). k ( θ ) gravitational effets on k are negligible, dθ d dθ = D( ). dt dz θ dz for ons tan t average diffusivity, dθ d θ = D...6 dt dz Infiltration equation There are various infiltration equation proposed by many researhers. However, we shall onsider only four whih are: 1. Philip (1957) equation. Talsma and Parlange (197) equation. 4. Kostiakov (193) equation. 5. Horton (1940) equation. The first two equations above are physially based (i.e. derived from physial onsiderations), while the remaining two are empirial equations. 1. Philip equation Philip (1954, 1957) solved Eq. (.6) by a numerial proedure using the boundary onditions: θ = θ z f 0 t = 0 0 θ = θ z = 0 t f 0 1 Where: θ 0 = initial water ontent at t = 0 θ = water ontent at t > 0 1 z = depth of ponded water above the soil. The details of this proedure as given by Philip lead to the solution: 1 1 f = At + B + t Where: f = infiltration rate at time t. A, B and C are onstants For onveniene an approximation is ahieved by ignoring the third and higher terms. That is, 1 f = At + B...7 Equation (.7) is the Philip s equation for prediting infiltration rate. The drawbak of the equation is that it does not give aurate results for large values of time. The equation has been used for downward infiltration and upward apillary rise experiments for several soils and porous materials (Rawls et al, 1976; Ahmed, 198; Kouroush et al, 007; Igbadun and Idris, 007). Aurate preditions of soil-water movement have been attained whenever the soil did not shrink or swell upon wetting. The advantage of the equation is that it is simple and therefore, its use in applied hydrologi studies would seem desirable.. Talsma and Parlange equation Talsma and Parlange (197) developed an infiltration equation whih is similar to the Philip s (1957) two parameter equation. In dimensionless form, the equation is given as: τ = λ I + e λ...8 In whih, τ and λ are related to time t and umulative infiltration F by: Ks t τ =...9 S Ks F λ =...10 S Where: S = Sorptivity, and K s = Saturated hydrauli ondutivity Series expansion of Eq. (.8) and substitution of Eqs. (.9) and (.10) in the result gives, with rearrangement and trunation after t 3/ term, 3 s 1 K st K t F = St S...11 Equation (.11) is the Talsma and Parlange infiltration equation for alulating the umulative infiltration amount. Even though Eq. (.11) ontains three terms, it requires only two parameters whih haraterizes the soil, the sorptivity S and the saturated hydrauli ondutivity, K s. The advantage of this equation is that is simple and rapid, therefore many measurement an be made with limited fund and labour. Also, it was reported to be suitable for watershed infiltration haraterization and for light-textured soils (Chong and Green, 1979; Mudiare and Adewumi, 000). 3. Kostiakov equation Kostiakov (193) reported an empirial equation expressing infiltration rate f, as a power funtion of time, t. F = kt n...1

4 Arab et al. 04 ( ) ( ) Where : F = ummulative inf iltration mm hr t = time hr k and n are empirial ons tan t Equation.1 does provide an infinite initial infiltration rate, but asserts infiltration rate to approah zero as t inreases, rather than a onstant non-zero final infiltration rate. This ould have relevane for homogenous soils and purely horizontal water absorption. Obviously if an impermeable horizon underlies a more permeable superfiial horizon, n may fall well below the limit of ½. In general, however, the Kostiakov equation is very seriously weakened by the absene of a onstant infiltration term. Despite these diffiulties, the equation has advantage of simpliity and does desribe infiltration at the lower end of the time sale quite well (Swartzendruber and Huberty, 1958; Ahmed, 198). 4. Horton equation Horton (1933, 1939) devoted a great deal of attention to the investigation of infiltration and developed an equation using the exhaustion proess approah. He stated that; df = k ( f f )...13 dt ( ) W here : t = tim e sin e inf iltration started hr k = proprtionality ons tan t After rearranging and integrating Eq. (.13), one obtains, kt f = f = ( f0 f ) e ( ) i ( ) ( ) ( ) Where : f = inf iltration rate at time t mm hr f = inf iltration rate as t mm hr f = inf iltration rate at t = 0 mm hr k = extintion oeffiient t = time hr Horton (1940) felt that the redution in infiltration rate with time after the initiation of infiltration was largely ontrolled by fators operating at the soil surfae. They inluded swelling of soil olloids and the losing of small raks whih progressively sealed the soil surfae. Compation of the soil surfae by raindrop ation was also onsidered important where it was not mitigated by rop over. Horton s field data, similar to those of many workers, indiated a dereasing infiltration rate for or 3 hours after the initiation of storm. The infiltration rate eventually approahed a onstant value whih was often somewhat smaller than the saturated hydrauli ondutivity of the soil. Air entrapment and inomplete saturation of the soil were assumed to be responsible for this latter finding. Methods of measuring infiltration Several methods for measuring infiltration have been developed from the time Horton (1933) explained its signifiane in the hydrologi yle. Some of the methods widely used inlude: 1. Rainfall simulators. Runoff plots 3. Basin method 4. Furrow method 5. Cylinder infiltrometers 1. Rainfall Simulators Method Presently this is one of the most popular methods of measuring infiltration rates of soils (Evans et al, 1997). The method involves simulation of rainfall over a given plot from some overhead nozzles. The plots are equipped with outlet through whih is olleted. The nozzles spray upwards or downwards depending upon the design and the intensity of appliation is ontrolled by the number of nozzles or the nozzles pressure. In some ases drip towers or ontainers with perforated bottom are used. Many of the sprinkling devies were essentially developed for erosion studies. However, in most ases, the differene between water applied and the amount of runoff olleted is assumed to be the infiltration. The desription and onstrution of various rainfall simulators an be found elsewhere (Constanz and Murphy, 1987; Franes et al, 00). A omprehensive literature review on rainfall simulators is given by Muthler and Hermsmeier (1965) and USDA-SEA (1979).. Runoff Plots Method This method is essentially similar to the rainfall simulator exept that the runoff plots tehnique use natural rainfall. This has the advantage of giving the infiltration rate under natural rainfall onditions. However, this has the disadvantage of less ontrol beause it is pratially impossible to have natural storms with the same harateristis repeated at different times and loation. This makes it diffiult to ompare infiltration rates for different soils. 3. Basin Method This method employs some plots as large as 0.1hatare, with a border arrangement so that water an be applied to the basin, providing impounded ondition. A given amount of water is applied to the basin and rate of infiltration is reorded. This method has been used by others (Pillsbury, 1947; Parr and Bertrand, 1960). 4. Furrow Method This was developed essentially for furrow irrigation. It onsists of three adjaent furrows into whih water is applied. Infiltration measurements are arried out from the entre furrow by means of small flow measuring

5 05. Basi Res. J. Soil Environ. Si. Table 1. List of seleted fadama irrigation areas. s/no Loation LGA Size (ha) 1 Kuda Kahia 19 Kukumdaji Kaura 13 devies, suh as, weirs and flumes. The two outer furrows at as buffer area. The design of a furrow infiltrometer was reported by Bondurant (1957). 5. Cylinder Infiltrometers Various types of ylinder infiltrometers have been used in the study of infiltration rates and hydrauli ondutivity of soils. Usually these metal rings or ompartments are driven into the ground to some depth so as to prevent any blow out effets around the bottom of the ylinders. Water is ponded in the ylinder to some depth at subsequent times thereafter; water is added to the ylinders. The methods of adding water to these ylinders inlude suh priniples as onstant heads or falling heads. The infiltration rate is measured by noting the amount of water added or by the drop in head in the ompartment in a given time. In some ases, mostly earlier studies, only single rings were employed (Evans, 1950). This had no ontrol on lateral movement of water from the ring. In most studies, however, double-ring (Bedwany and Shumaher, 1976; Keith, 007) infiltrometers were used so that divergent flow ould be minimized by means of a buffer area surrounding the entral ompartment. The method of plaement of the ring devie in the soil auses serious limitations to ylinder infiltrometers. In driving the rings into the soil, a ertain degree of disturbane of natural strutural onditions is aused, and the resulting disturbane manifested as shattering or ompation may ause a large variation in infiltration rates between repliated runs. Also, the soil metal interfae may ause unnatural seepage planes whih results in abnormally high infiltration rates. A further limitation to the use of rings infiltrometer is the problem of entrapped air in the soil olumn, aused when a onstant head of water is applied upon the surfae. Under onditions of saturated flow, the entrapped air is unable to esape from the soil. This results in reation of internal air ushions whih eventually impedes downward flow movement. Choie of infiltration measurement method All the methods disussed above are developed for different purposes and eah method serves its purpose. In spite of some marginal differenes, all these methods have a plae in the evaluation of the fators that affet infiltration and also in the evaluation of different parts of a watershed. The hoie of any method depends on the purpose of study, operation osts and the availability of the equipment. The rainfall simulation method gives results loser to those under natural rainfall onditions. However, the onstrution osts and time for rainfall simulators when ompare to the ylinder infiltrometers limit it use. Cylinder infiltrometers are heap to onstrut, easy to operate, transport and do not need any site preparations as does the rainfall simulator. As a result, ylinder infiltrometer was used for this study. MATRIALS AND METHOD Desription of Experimental Area The experiments were arried out at two () Fadama irrigated areas in southern Kaduna plain. The first area is loated in a village alled Kuda in Kahia Loal Government area of Kaduna State; the seond area is loated in a village alled Kukumdaji in Kaura Loal Government area of Kaduna State. Southern Kaduna plain is an area bounded by longitudes to E and latitudes to N and lies mainly within Kaduna State with smaller areas in Niger State, Plateau State and the Federal Capital Territory. The altitude ranges between 500 to 1000m above sea level (Enarta, 007). The plain omprises of undulating to gently undulating topography with hills sattered throughout the area rising to about 50-00m above the surrounding land. The area falls within Southern Guinea Savannah Eologial Zone. The mean annual rainfall ranges from 1300mm to 1700mm as one move southward and the length of the rainy period ranges between days starting from April to Otober (Kowal and Knabe, 197). Site seletion A total of two () fadama irrigation areas were seleted for the experiment. Table 1 above shows the list of seleted areas. In eah of the seleted areas, two () sites were seleted based on the land management pratie (that is, ultivated/fallow). Therefore a total of four (4) experimental sites were seleted (that is, two sites on eah fadama irrigation area). Table below shows the list of seleted experimental sites and the orresponding soil series.

6 Arab et al. 06 Table. List of seleted experimental sites. Sites Soil Series* Loation Management pratie 1 48 Kuda Cultivated 48 Kuda Fallow 3 30 Kukumdaji Cultivated 4 30 Kukumdaji Fallow *See appendix A for soil series desription as provided by LRD (1977) Infiltration measurement Infiltration measurements were made by ponding water in a double ring infiltrometer. The inner ylinder had a diameter of 300mm while the outer ylinder was 400mm in diameter. Both infiltrometers were driven 100mm into the soil by hammering on a wooden bar plaed diametrially on top of the rings. The soil surfae was proteted from diret impat of water by a layer of dry grass. Water from a buket was poured into the infiltrometer ompartments simultaneously as quikly as possible to an approximate depth of 100mm. Three pairs of infiltrometers were used at one per set and two set were done per site in a day, giving six repliates per site in a day. Water level readings were taken in the inner ring with the aid of a plasti rule attahed to a float at 3-minute intervals for the first 15minutes, 5-minute intervals for the next 15minutes, 10-minute intervals for the next 30minutes, 15-minute intervals for the next 45minutes, 30-minute intervals for the next 90minutes and finally 15- minute intervals for the last 45minutes. Water was added to both ompartments to ensure approximately the same levels throughout the period of measurement. Eah repliate was allowed time duration of 40minutes (4hours). A total of twenty four (4) infiltration measurements were made in all the four (4) experimental sites giving six (6) repliates on eah site. The infiltration measurement points were seleted randomly by eye inspetion and arefully so as not to plae the infiltrometers on visible ant and rabs holes. The infiltrometers were spaed at least 10m from eah other. Soil sampling Soil samples were taken from eah site for determining the following:- 1. Initial moisture ontent. Bulk density 3. Soil texture 4. Hydrauli ondutivity. Infiltration estimation Seletion of infiltration equations was neessarily somewhat arbitrary due to their great numbers; however, those that are believed to be widely used were inluded. Infiltration equations tested are Kostiakov, Phillips, Horton, Talsma and Parlange. The oeffiients involved in the equations were determined as follows: 1. Kostiakov s equation (193) F = kt n. Kostiakov s equation was linearized by taking logarithms of both sides. The umulative infiltration was plotted versus time on a logarithm graph sheet and the best-fit line was obtained by least-square urve fitting tehnique. The slope and interept of the best-fit line gives the values of n and k respetively.. Philip s (1957) Equation. 1 f = At + B Thus, there is a linear relationship between the average infiltration rate f and t -1/ and if these are plotted on a linear graph paper, then A and B are the slope and interept of the best-fit line respetively. A least square regression an also be used to obtain the values of A and B. 3. Horton s (1940) Equation. ( ) f = f = f f e 0 Here we had a slightly different problem than the other two equations in that Horton s equation requires at least one predetermined parameter, f. However the value of f obtained in the field experiment is to be used, that is, the last infiltration rate for eah run and ( f 0 f ) was assumed onstant, A. Thus it implies that; f f = Ae Taking logarithms of both sides, kt ln ( f f ) = ln A k ln t Whih is a linear equation and a graph of ln ( f f ) versus t will give a straight line with ln A as interept and kt

7 07. Basi Res. J. Soil Environ. Si. k as the slope. The method of least square regression analysis an also be used to obtain the value of k. 4. Talsma and Parlange (197) equation. 3 s 1 Kst K t F = St S Talsma (1969) and Dunin (1970) found that for the very early portion of infiltration, the seond term of the right hand side of the Phillip s two parameter equation an be negleted. Thus, if one plots the early portion of the experimental umulative infiltration versus square roots of the elapsed time on a linear graph paper, the sorptivity S for the existing anteedent soil onditions is obtained from the slope of the linear portion of the urve. The saturated hydrauli ondutivity, K s, of the soil was determined in the laboratory using onstant head permeameter. Infiltration equation performane evaluation The evaluation of the performane of infiltration equations was arried out in three steps. The first evaluation of equation performane was to use test statistis to ompare measured data against predited results (mean, standard deviation, oeffiient of determination R, mean differene MD, and standard error differene SED). For perfet equation performane, the mean differene (MD), standard error differene (SED), and oeffiient of determination (R ) should be zero, zero and one respetively. The seond was to use statistial paired-sample t-test to see whether the differene between measured and predited results is signifiant or not signifiant using the following equations. X 1 X t n1 + n = S p + n1 n W h e r e : S X p = ( 1) + ( 1) n S n S 1 1 n + n 1 m ea n o f m ea su red va lu es X = m ea n o f p red ited va lu es S S = var ia n e o f p red ited va lu es n = = var ia n e o f m ea su red va lu es = n u m b er o f m ea su red o b serva tio n s n = n u m b er o f p red ited o b serva tio n s The third was to verify the infiltration equations performane by omparing the slope and interept of the measured and predited using the hypothesis b - β = 0 for slope, whih will only happen when measured values (f m ) is equal to predited values (f p ). b β tb = S yx x Where : S yx =...17 y. x ( xy) ( n ). x...18 For the interept, the hypothesis that a = α0 was tested using: a α 0 b = X Syx + t Where : n x x = X X and y = Y Y Y = measured inf iltration rates X = Pr edited inf iltration rates RESULT AND DISCUSSION Measured infiltration rates...19 The measured infiltration rates data is given in table 3, 4, 5 and 6 for site 1,, 3 and 4 respetively while the infiltration urves from measured data are shown in figure 1,, 3 and 4 for site 1,, 3 and 4 respetively. The infiltration urves have a general shape, starting from very high values, reduing sharply to almost half the initial values within the first 0 minutes, ontinued to derease gradually until a onstant value is reahed. Most of the runs attained this onstant value within the first 4 hours and quite a number of them as early as.5 to 3 hours after starting. It has been observed that not all the runs redue steadily. In other words, sometimes a run was reduing

8 Arab et al. 08 Table 3. The measured infiltration rates data for site 1 SITE NUMBER 1 SOIL SERIES 48 CULTIVATED INITIAL SOIL MOISTURE CONTENT = 18% BY WEIGHT REPLICATE 1 REPLICATE REPLICATE 3 REPLICATE 4 REPLICATE 5 REPLICATE 6 AVERAGE CUM. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. TIME. INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE

9 09. Basi Res. J. Soil Environ. Si. Table 4. The measured infiltration rates data for site SITE NUMBER SOIL SERIES 48 FALLOW INITIAL MOISTURE CONTENT = 9% BY WEIGHT REPLICATE 1 REPLICATE REPLICAT 3 REPLICATE 4 REPLICATE 5 REPLICATE 6 AVERAGE CUM. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. TIME. INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE

10 Arab et al. 10 Table 5. The measured infiltration rates data for site 3 SITE NUMBER 3 SOIL SERIES 30 CULTIVATED INITIAL MOISTURE CONTENT = 9% BY WEIGHT REPLICATE 1 REPLICATE REPLICATE 3 REPLICATE 4 REPLICATE 5 REPLICATE 6 AVERAGE CUM. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. TIME. INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE

11 11. Basi Res. J. Soil Environ. Si. Table 6. The measured infiltration rates data for site 4 SITE NUMBER 4 SOIL SERIES 30 FALLOW INITIAL MOISTURE CONTENT = 9% BY WEIGHT REPLICATE 1 REPLICATE REPLICATE 3 REPLICATE 4 REPLICATE 5 REPLICATE 6 AVERAGE CUM. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. CUM. INF. TIME. INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE INF. RATE Figure 1. Measured infiltration urves for site 1 Figure. Measured infiltration urves for site

12 Arab et al. 1 Figure 3. Measured infiltration urves for site 3 Figure 4. Measured infiltration urves for site 4 then it rose again. This ould be understood learly by looking at the data in table 3 (site 1) repliate 3 and 5, and table 4 (site ) repliate 1, 3 and 4. This was not expeted but ould perhaps be explained by the heterogeneity of the soil. Another possible reason might be due to entrapped air as reported and explained by many researhers (Christiansen, 1944; and Ahmed, 198). Water may ompress the air below the advaning moisture front and gravitational movement eased. The front ontinues to rise until finally, there was suffiient pressure to ause an upward release of air through the pore holding apillary water. One this happened, gravitational movement ontinues again resulting in a subsequent inrease in infiltration rate. Another possibility is the presene of animal burrows, rabs holes or raks within the soil. In some ases, refilling the infiltrometer ause an inrease in water head whih eventually result in a slight inrease in the rate of infiltration. The effet of head, though slight, ertainly ontributed to this rise and fall in infiltration rates. Errors in reading and timing may have a signifiant ontribution. During the experiments, water level readings were taken to the nearest millimeter and it is therefore possible to trunate some readings and exaggerate others due to parallax. With the above explanations, one would say that water level in the infiltrometer, entrapped air, and errors in reading and timing affeted the auray of a ylinder infiltrometer. Predited infiltration rate Curve fitting was arried out as explained in setion 3.5 and Table 7 gives the average values of the parameters in the four equations (over four repliations) for eah site. One partiular thing observed onerns the onstant, B, in Philip s equation (Eq..7). In site 4 negative values were obtained as opposed to positive values of B. The soil in site 4 is a Fadama soil haraterized by a heavy textured soil (lay) whih was dry and raked at the time measurement took plae and beause it is left fallowed for quite some time, hard apping had started to develop in many plaes within the site. The rates started from very high values (for all the

13 13. Basi Res. J. Soil Environ. Si. Table 7. Average values of soil parameters for infiltration equation from urve fittings Kostiakov Philip Horton Talsma & Parlange Site K n A B A k S Initial MC MC = Moisture ontent (%) Figure 5. Measured Vs Predited Infiltration rates urves for site 1 Figure 6. Measured Vs Predited Infiltration rates urves for site repliates exept repliate 4) of about 60 to 140mm/hr and redued rapidly to about 1 to 40mm/hr within the first three hours (Table 6). The initial low rate obtained for repliate 4 was attributable to hard apping beause the test for this repliate was onduted on the area within the site where hard apping had fully developed. The rapid derease of the infiltration rate ould be explained by the nature of lay upon wetting. Initially, the soil was raked and dry and water intake was high to fill those raks, as infiltration ontinued, the lay swelled at the expense of the pores thereby ausing a rapid derease in infiltration rate. This rapid derease resulted in steep slope of the regression line (f versus t -1/ ) to the extent that its extension ut the f-axis below f = 0 giving a negative interept, B. this implies that Philip s equation must have restrition on swelling soils sine for longer time periods when the first term is insignifiant, the equation will give a negative infiltration rate. However, in spite of this negative onstant, the R square values of all the repliates in site 4 ranges from to This definitely indiates that the auray in prediting infiltration rate using Philip s equation is possible within a limited time range for swelling soils, a point made by many researhers: (Taylor, 197; Skaggs, 1969; Ahmed, 198). Ahmed (198) suggested that this time range be three hours. The author suggests that this time range be extended to 3.5 hours for lay-loam to lay soil beause all the repliates in site 4 reahed their final value within this time range. Figures 5, 6, 7 and 8 shows the urves from the

14 Arab et al. 14 Figure 7. Measured Vs Predited Infiltration rates urves for site 3 Figure 8. Measured Vs Predited Infiltration rates urves for site 4 Table 8. Summary of regression oeffiient and standard error differene R SED Philip equation Horton equation Kostiakov equation Talsma & Parlange equation 0.99 to to to to to to to to R = Regression oeffiient, SED = Standard error differene predited equation together with average urves from field measured data. The average measured urves were obtained by averaging the infiltration rates of the repliates 5 and 6 for eah time interval and the predited urves from the values given in Table 7. The method used to fit Horton s equation (Eq..15) as explained in setion 3.5 did not approximate field measured data when the value of A (interept) obtained from urve fitting was used rather it gives nearly onstant values throughout the time intervals. Another method was used whih is similar to the former exept that both values of f 0 and f measured from the field were used instead of A to predit the infiltration rate. The result was found to be more aurate than the approximate field measured data. As a result, the latter method was aepted and used throughout to obtain the predited infiltration rates from Horton s equation. Comparison between measured and predited infiltration rates Table 8 gives the summary of regression oeffiient and standard error differene for eah infiltration equation and Table 9 and 10 shows the average measured and predited infiltration rates for Kuda (sites 1 and ) and Kukumdaji (sites 3 and 4) Fadama irrigation areas respetively. The Kostiakov s equation with R value ranging from 0.93 to and the orresponding standard error differene ranging from 1.57 to 7.65 and Philip s equation

15 15. Basi Res. J. Soil Environ. Si. Table 9. Average Measured (over repliates 5 and 6) and Average Predited Infiltration Rates (over repliates 1 to 4) for Sites 1 and SITE NUMBER 1 SITE NUMBER Predited Predited T (Min) M P H K T &P M P H K T &P R SED Note: P = Philip; H = Horton; K = Kostiakov; M = Measured; T & P = Talsma & Parlange; R =Regression Coeffiient; SED=Standard error differene Table 10. Average Measured (over repliates 5 and 6) and Average Predited Infiltration Rates (over repliates 1 to 4) for Sites 3 and 4 SITE NUMBER 3 SITE NUMBER 4 Predited Predited T(Min) M P H K T &P M P H K T &P R SED Note: P = Philip; H = Horton; K = Kostiakov; M = Measured; T & P = Talsma & Parlange; R =Regression Coeffiient; SED=Standard error differene

16 Arab et al. 16 with R value and standard error differene ranging from 0.99 to and 1.36 to 6.55 respetively gives the best fit when ompared with the rest of the equations tested. The differenes between measured and predited infiltration rates by Kostiakov s and Philip s equation were found not to be statistially signifiant at 5% signifiane level for all the four sites exept site where predited infiltration rates by Philip s equation were found to be signifiant. Furthermore, the regression oeffiient for Kostiakov s and Philip s equation ranges from 0.93 to and 0.99 to respetively (lose to unity) whih established the fat that the predited infiltration rates were reasonably more loser to the measured than the other rates predited by the rest of the equation tested. The differene between measured and predited infiltration rates by Horton s equation was found to be statistially signifiant at 5% signifiant level for sites, 3 and 4 while that of site 1 is not signifiant. The Talsma and Parlange equation fails to approximate measured data till after about 30 to 40 minutes after the ommenement of measurements (see Table 9 and 10). The differene between measured and predited values was highest at the first 3-minutes for the whole four sites studied. This implies that Talsma and Parlange equation is sensitive to instability in the set-up at the initial stage of the measurement and that the equation is not suitable for heavy-textured soils. Similar observation was made by Mudiare and Adewumi (000). Verifiation of infiltration equations performane was done as desribed in setion 3.6. The result of the hypothesis test for both the slope and interept indiates that Kostiakov s and Philip s equation performed better than Horton s and Talsma & Parlange s equation. The result further reveals that there is no signifiant differene at 5% and 1% level of signifiane with (n -) = 18 degrees of freedom between the measured and predited slope by Kostiakov s and Philip s equation in site 3 and 4 while the differene is highly signifiant in site 1 and. For interept test, the result reveals that there is no signifiant differene at 5% and 1% level of signifiane with (n ) = 18 between the measured and predited by Kostiakov s and Philip s equation in site 1, and 4 while the differene is highly signifiant in site 3 for both Kostiakov s and Philip s equation. The Talsma and Parlange s equation performed very poor beause the result of the hypothesis test indiates that the differene between measured and predited slope and interept at 5% and 1% level of signifiane with (n ) = 18 is highly signifiant for all the four sites exept site 4 in whih the differene between predited and measured interept was not signifiant. CONCLUSION AND RECOMMENDATION Conlusion The need for ontinuous and in-depth study on the appliability and auray of infiltration equations annot be exhausted sine equation parameters and performane vary for different soils. The study reported herein, has evaluated four infiltration equations (Kostiakov s; Philip s; Horton; Talsma and Parlange) for fadama soils in Southern Kaduna plain. Results from the study reveals that Kostiakov s and Philip s equation an be used to predit infiltration rates for the soil studied but that Kostiakov s equation approximated the measured infiltration rates with higher auray and best fit than did Philip s and Horton s equation. Talsma and Parlange s equation fail to approximate measured data partiularly in the early stage of measurement. Finally, this study is therefore a ontribution towards the adaptation and utilizations of Kostiakov s equation in Southern Kaduna Plain Fadama soils, it is hoped that in due ourse other infiltration equations will be evaluated for irrigated Fadama soils. Reommendation Based on the result of the study, the following reommendations were made:- 1. Kostiakov s equation showed greater auray in estimating field infiltration rates than did Philip s; Horton s; Talsma and Parlange s equation. In view of this, Kostiakov s equation is reommended for the soils tested and other similar soils.. Finally, it is reommended that similar researhes and data doumentation on infiltration rates should be arried out anywhere in the ountry until the data is suffiient for omplete watershed modeling and hydrologi lassifiation of Nigerian soils. This is possible through effetive oordination among researhers and between researhers and water resoures authorities in the ountry. ACKNOWLEGEMENT My profound gratitude goes to Professor O. J. Mudiare for his ontinued support, enouragement, onstrutive ritiism, orretions and suggestions throughout the

17 17. Basi Res. J. Soil Environ. Si. ondut of this researh. My sinere appreiation also goes to Dr. M. A. Oyebode for his in-depth vetting, ritial omments and advie whih greatly ontributed to the suessful ompletion of this researh. I thank the Head of Department, Prof. V. I. O. Ndirka and Dr H.E. Igbadun and Prof. S. Z. Abubakar for their keen interest in my work. Thanks also to Dr U.S. Mohammed, Prof. Abdullahi Okene, Prof. D. D. Yusuf, Dr. B. Baba-shani and other staff of the department of Agriultural Engineering for their onern throughout the period of this work. My speial appreiation goes to Dr. Malgwi of soil survey unit, Institute of Agriultural Researh. My thanks are also due to the Divisional Irrigation Engineer (KADP) Mr. Peter Aluwong and the entire staff of Irrigation department of Kaduna State Agriultural Development Projet (KADP) for their assistane during the ondut of the experiment. REFERENCES Ahmed A (198). Infiltration rates and related soil parameter for some seleted Samaru soils, M.S. Thesis, Agri. Eng. Dept., ABU, Zaria. Babalola O (1986). Soil Properties affeting infiltration and erodibility. A paper presented at the National workshop on Erosion held in Federal University of Tehnology, Owerri, 8 th -1 th September, Bedwany AL, Shumaher AE (1979). A omprehensive study of two methods of infiltration rate measurements on some soils in Lesotho. Montreal Engineering Company Limited, Calgary, Alberta. 11pp. Chong SK, Green RE (1979). Appliation of field measured sorptivity for simplified infiltration predition. Pro. Hydroxyl. Transport Modeling symp. ASAE. Publ. 4-80: Christiansen JE (1944). Effet of entrapped air upon the permeability of soils. Soil. Si. 58; Clemmens AJ (1983). Infiltration equation for border irrigation equations. In: Advanes in infiltration. ASAE Publiation 11: Constanz J, Murphy F (1987). An automated tehnique for flow measurement from Marriotte reservoirs. Soil Si. So. Am. J. 51, Enarta (007). Mirosoft student with Enarta Premium 007 DVD, World Atlas. Evans DD (1950). Infiltration and permeability in soil over-laying an impermeable layer. Soil Si. So. Amer. Pro. 15; Evans KG, Loh RJ, Aspinall TO, Bell LC (1997). Laboratory rainfall simulator studies of seleted open-ut oal mine over burden spoils from entral Queensland. Aust. J. of Soil Res. 35 (1) Fok YS (1986). Derivation of Lewis-Kostiakov intake equation. J. Irrigation and Drainage Engineering, ASCE 1 (): Franes XM, Cassey, Nathan ED (00). Improved design for an automated tension infiltrometer. Soil Si. So. Am. J. 66: Green WH, Ampt GA (1911): Studies on soil physis 1. The flow of air and water through soils. J. Agr. Si. 4: 1 4. Horton RE (1933). The role of infiltration in the hydrologi yle. Trans. 14 th annual meeting of Am. Geophys. Union, pp Horton RE (1939). Analysis of plot experiments with varying infiltration apaity. Trans. Am. Geophys. Union, part iv, pp Horton RE (1940). An approah toward a physial interpretation of infiltration apaity. Soil Si. So. Amer. Pro. 5; Igbadun HE, Idris UD (007). Performane evaluation of infiltration equations in a hydromorphi soil. Nig. J. Soil and Env. Res. Vol.7: 007, Keith, L. (007). Simple design for simultaneous steady-state infiltration experiments with double ring infiltrometers. Journ. of the Am. Wat. Resour. Asso. Vol.6 (6): pp Kostiakov AN (193). On the dynamis of the oeffiients of water perolation in soils and the neessity for studying it from a dynami point of view for purposes of amelioration. Trans. 6 th omm. Inter. Soil Si. So. Russia, part A Kouroush SZ, Adel S, Hurbert JM, Garry F (007). Evaluation of infiltration equations in ontaminated landsape. Environ. Si., and Health, part A, vol. 4, issue 7 th June, 007, pp Retrieved Otober 9, 007 from: =all~jumptype=rss. Kowal JK., Knabe DT (197). An Agro-limatologial Atlas of the Northern States of Nigeria. Mihael AM (1978.Irrigation theory and pratie. 1 st ed., Vikas publ. House DVT, Delhi. Mudiare OJ, Adewumi JK (000). Estimation of infiltration from Field measure sorptivity values. Nig. J. Soil. Res. Vol. 1: 13. Muthler CK, Hermsmeier LF (1965). A review of rainfall simulators. Amer. So. Agri. Eng. Trans. 8(1); Parr JF, Bertrand AR (1960). Water infiltration into soils. Adv. Agron. 1: Philip JR (1954). An infiltration equation with physial signifiane. Soil Si. 77; Philip JR (1957). The theory of infiltration: 4 sorptivity and algebrai infiltration equations. Soil Si 84; Pillsbury AF (1947). Fators influening infiltration rates into Yolo loam. Soil Si. 64; Rawls W, Yates P, Asmussen L (1976). Calibration of seleted infiltration equations for Georgia Coastal Plain soils. Report ARS-S- 113 July Retrieved on February, 007 from: =ENV&reid= &q=infiltrati... Rihards A (1931). Capillary ondition of liquids through porous. Physis, 1, Yonts CD, Eisenhauer DE, Varner D (003). Managing Furrow Irrigation Systems. Published by Cooperative Extension, Institute of Agriulture and Natural Resoure, University of Nebraska Linoln.

18 Arab et al. 18 APPENDIX A: SOIL SERIES DESCRIPTION SERIES 48 Series parameter: Deep, poorly drained ground water gley, fine textured, weak and moderate strutures on basalt, laking suffiient oarse material for a designated oarse material layer. Typial Profile Desription HORIZON DEPTH PREDOMINANT COLOUR TEXTURE STRUCTURE CONSISTENCE/MOISTURE (CM) YR 4/3 brown - dark brown Sandy-loam w. m. sab* Hard/dry YR 5/4 yellowish brown Sandy-lay loam w. m. sab* Very hard/dry YR 5/4 yellowish brown Sandy-lay md. m. sab* Very hard/dry YR 5/ greyish brown Sandy-lay md. m. sab* Very hard/dry YR 6/1 light grey/grey Clay w. m. sab* Very hard/dry *w weak; m Medium size; md Moderate; sab sub-angular bloky SERIES 30 Series parameter: Deep, poorly drained, fine textured, ground water gley, having dominantly strong prismati struture in the B horizon, developed on basement omplex and laking suffiient oarse material for a designated oarse material horizon. Typial Profile Desription HORIZON DEPTH (CM) PREDOMINANT COLOUR TEXTURE STRUCTURE CONSISTENCE/MOISTURE YR 4/3 brown - dark brown Loam s. /m. pr/sab* Soft/dry YR 4/ dark greyish brown Clay loam s. m/f. pr/sab* Hard/dry YR 4/ dark greyish brown Clay s. /m. pr* Extremely hard/dry YR 5/1 grey Gravelly lay s. v. pr Moist m - medium; s strong; oarse; f fine; v very oarse; pr prismati; sab sub-angular bloky