The ring infiltrometer described by Bouwer (1986) is the most commonly

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1 Published August 9, 06 Soil Physics & Hydrology Impact of Preferential and Lateral Flows of Water on Single-Ring Measured Infiltration Process and Its Analysis Jing Zhang College of Water Resources & Civil Engineering China Agricultural Univ. Beijing PR China Tingwu Lei* College of Water Resources & Civil Engineering China Agricultural Univ. Beijing PR China and State Key Lab. of Soil Erosion and Dryland Farming on the Loess Plateau Institute of Soil and Water Conservation CAS and MWR Yangling, Shaanxi 700 PR China Tianqin Chen College of Water Resources & Civil Engineering China Agricultural Univ. Beijing PR China Core Ideas A special device was developed to visually display the infiltration process. Impacts of preferential and lateral flow on infiltration rates were measured. Mathematical models were derived to correct the measured infiltration rates. The corrected infiltration processes agreed well with the D values. To improve the measurement accuracy of the soil infiltration rate, we studied the effects of preferential flow caused by the gap between the soil profile and the ring wall during its installation and lateral flow induced by the threedimensional impact of a single ring on the infiltration process. Laboratory experiments using silt loam taken from Beijing were conducted with a device designed to produce a soil profile that could visually display water movement during infiltration in the soil. Observations of the wetted soil profile inside and under the halved ring during the infiltration process were used to partition rates from the soil surface, preferential flow, and lateral movement of water. Mathematical models were derived to correct the measured infiltration rates affected by preferential and lateral flows during the initial and steady infiltration stages. Results indicated that in the initial infiltration stage (0 7 min), the preferential flow significantly increased the measured infiltration rates. Error caused by preferential flow ranged from 07 to %. In the following infiltration stage (7 0 min), the contribution of lateral flow ranged from to 77%. Steady infiltration rates estimated with the modified model were 7% higher than those of one-dimensional infiltration rates, and saturated hydraulic conductivities measured by single ring infiltrometer were 5% higher than rates estimated by the constant head method, which may have been caused by higher static water pressure inside the ring caused by preferential flow passage. This study offers a new analysis of ponded single-ring infiltrometer data. Abbreviations: D, one-dimensional. The ring infiltrometer described by Bouwer (986) is the most commonly used soil infiltration rate and soil saturated hydraulic conductivity measurement method (Angulo-Jaramillo et al., 000; Bouwer, 986; Jury and Horton, 004; Hills, 970; Prieksat et al., 99; Reynolds and Elrick, 990; Tricker, 978; Walsh and McDonnell, 0). In addition, the single-ring infiltrometer has been extensively applied as a basic infiltration measurement tool for studying storm runoff processes (Tilahun et al., 06), soil surface crusts (Ries and Hirt, 008), soil erosion (Francis, 986), the effects of cattle trampling on soil structural and hydrological properties (Mulholland and Fullen, 99; Pietola et al., 005), and the effect of the settlement of sediments on water infiltration (Lassabatere et al., 00). However, numerous reports indicated that the most reliable results measured by ring infiltrometer were remarkably distinct from that measured by rain simulator, which was more realistic and accurate (Cerdà, 997). Cerdà (996, 997) compared the infiltration rates measured by means of simulated rainfall and ring infiltrometer and reported that the infiltration rates measured by ring infiltrometer were 8 to 8.5 times greater than those obtained by rainfall simulator based on Soil Sci. Soc. Am. J. 80: doi:0.36/sssaj Received 7 Dec. 05. Accepted 5 June 06. *Corresponding author (leitingwu@cau.edu.cn). Soil Science Society of America, 5585 Guilford Rd., Madison WI 537 USA. All Rights reserved. Soil Science Society of America Journal

2 40 groups of field measurements. Wu et al. (003) reported that steady infiltration rates estimated by the cylinder method were.8 to 3.0 times and. to 3. times greater than those obtained by rainfall simulator for gully region of the Loess Plateau and hilly area of the Loess Plateau, respectively, based on 48 groups of field experiments. Verbist et al. (03) compared methods to determine hydraulic conductivities on stony soils and found that the single-ring infiltrometer gave considerably higher field saturated hydraulic conductivity (K fs ) values than the constant head well infiltrometer, the inverse auger hole method, the tension infiltrometer, and a rainfall simulator and had higher measurement variability. Torfs (008) evaluated field methods to determine hydraulic properties of stony soils in arid zones of Chile and also found that single infiltrometer produced higher K fs values than the other methods, including the inverse auger hole method, the constant head well infiltrometer, the rainfall simulator, and the tension infiltrometer. The single-ring infiltrometer also had significantly higher variation. Gómez et al. (00) reported that the saturated hydraulic conductivity (K s ) measured by a singlering infiltrometer was.93 and.4 times greater than values obtained using simulated rainfall for the inter-row among trees and below the canopy, respectively. Several possible reasons for the higher results of infiltration rate can be identified. First, cracks caused by vibration during installation are formed between the sidewall and soil inside the ring, which produce a passage for preferential flow to cause a much higher initial infiltration rate (Lei et al., 03) and higher K s (Verbist et al., 03). However, the effect of preferential flow on the infiltration rate is uncertain, and no detailed study has reported the ring infiltrometer s overestimation of the infiltration rate as caused by the preferential flow, despite the fact that soil compaction and shattering phenomena can occur in the initial wetting process (Fattah and Upadhyaya, 996; Hills, 970; Orradottir et al., 008; Reynolds, 008; Verbist et al., 03) and can affect the soil infiltration process (Cerdà, 997). The effect of soil disturbance during the installation procedure of the ring infiltrometer on the measured infiltration rate has not been quantitatively studied (Bagarello and Sgroi, 004). Another possible factor affecting the measured infiltration rate is the lateral flow of infiltrated water (driven by soil capillarity). This feature causes higher infiltration rates measured by a ring infiltrometer. Tricker (978) argued that the total infiltration capacity of a single-ring infiltrometer was a three-dimensional problem involving vertical and lateral flows (Cerdà, 997; Jačka et al., 04; Reynolds and Elrick, 990). Wu et al. (997) reported that soil infiltration rate was different from that obtained by a single-ring infiltrometer, which needed to be corrected by a factor depending on soil hydraulic properties, initial and boundary conditions, and ring geometry. For instance, Marshall and Stirk (950) reported that the effects of lateral water movement on infiltration rate measurement decreased as the ring diameter increased. Chowdary et al. (006) showed that the lateral flow component accounted for 43.7 to 67.9% of cumulative infiltration measured using a single-ring infiltrometer. Therefore, buffer rings have been recommended and widely used to reduce the effects of lateral water movement on measured infiltration rate. Lai et al. (00) reported that a buffer ring with a diameter greater than 80 cm was recommended to obtain reliable in situ measurement of soil K fs. In a study by Ahuja et al. (976), the lateral flow was practically eliminated when a buffer ring of 0.9 m diameter was used for an inner ring of 0.3 m diameter. Wu et al. (997) reported that when the buffer ring s diameter was increased to 0 cm with the inner-ring diameter kept at 0 cm, the infiltration rates measured by the double-ring method were 0 to 33% of the one-dimensional (D) infiltration rates for three test soil samples. However, using a very large buffer and inner rings with a small diameter may not be effective in obtaining correct D infiltration rates (Wu et al., 997). To address the abovementioned research gaps, the current study aims to (i) suggest and describe the experimental procedures of a device for visualizing the infiltration process under ring infiltrometer, (ii) derive the algorithm and mathematic models for correcting infiltration process affected by preferential flow and lateral flow, and (iii) compare the modified results with D infiltration rates measured by simulated infiltration ring. materials and methods Disassembled and See-Through Soil Container for Observing the Infiltration Process A see-through soil container was designed for observing the infiltration process after the disassembled ring infiltrometer was hammered into the soil body. The device consisted of a disassembled soil container, a halved infiltration ring, and a see-through container surface made of Plexiglas. The soil container consisted of two halved containers (30 cm by 50 cm by 75 cm). A piece of Plexiglas plate was fixed at the lower half of the container on the outside of one halved soil container. The other halved soil container of the same size was fixed to form a complete disassembled soil container (Fig. a). With this container, the dynamic movement process in the soil profile of the infiltrated water could be monitored on a real-time basis through the Plexiglas plate. This can be achieved after disassembling the soil container and removing the halved ring outside the glass. Disassembled Ring Infiltrometer The specially constructed ring can be disassembled into two halves to prepare a see-through surface; this way, we can observe the movement of infiltrated water into the soil body. The disassembled ring was made of a steel sheet (.5 mm thickness, 35 cm diameter, 0 cm height) (Fig. b). Soil The experimental soil was silt loam, which consisted of 5.0% clay, 50.% silt, and 34.8% sand particles. Soil samples were collected from the top layer of cultivated land at the Fangshan District, Beijing. The soil was air-dried (.5% volumetric soil moisture content), and visible organic residues were removed. Soil materials were gently crushed by hand and allowed to pass 860 Soil Science Society of America Journal

3 Fig.. The experimental device for (a) the soil container, (b) the disassembled ring infiltrometer, (c) the finished see-through soil section after ring installation in the see-through container, and (d) the ideal infiltration ring used for measuring D soil infiltrability, showing the half soil container () connecting plate (), bolts fixing Plexiglas plate and soil container (3), Plexiglas plate (4), bolts fixing the two half containers (5), the half ring (6), connecting plate (7), and bolts (8). through a 4-mm mesh before use. Soil materials were mixed with sprayed water to obtain a volumetric soil moisture content of about 0%, which was about 40% of the field capacity of the soil. Weighted soil materials were packed uniformly into the soil container and compacted to 5-cm thickness by rakes. The packed soil surface of each layer was scrubbed roughly before the next layer was added to prevent discontinuity between the soil layers. The total depth of the soil packed into the container was 70 cm. The silt loam was packed to a soil bulk density of.4 g cm 3. Once the soil was packed into the assembled soil container, the separation surface of the halved rings was placed in alignment with the divided plate of the soil container and hammered into the soil to a depth of 5 cm. The top soil layer (5 cm thickness) outside the halved ring to be removed was cut and removed in alignment with the divided line between the two halved rings. The bolts on the single ring were unscrewed, and the top soil layer (5-cm depth) inside the ring was cut in alignment with the halved line before the outside-halved ring was removed and the Plexiglas plate was screw-fixed onto the other halved ring. Two silica strips were glued between the connecting plates of the halved ring and the Plexiglas plate to prevent water leakage. The halved soil container outside the lower Plexiglas plate and the soil in it were removed. The soil profiles at the top and the lower part of the container were contained in the see-through Plexiglas plate. The possible gap between the two Plexiglas plates was filled with sealant to prevent water leakage. Figure c shows the finished experimental container. The experiment was replicated twice. A halved infiltration ring made of a Plexiglas tube with a diameter of 35 cm and height of 65 cm was used to record the ideal D infiltration process with refilled soil of the same density (Fig. d). The water supply capacity of the Marriotte bottle was limited by the flow capability of the outlet and could not supply sufficient water flow to meet the requirement of the initial soil infiltration. To overcome this problem, the initial infiltration rate was measured using the falling head method. When the ring was filled with water equivalent to a 3-cm depth, a stopwatch was started as quickly as possible to record the time during which the water level dropped 0.5 cm. When the depth of the water level in the ring lowered to cm, water was added to 3 cm depth. The procedure was repeated three times. Thereafter, the Marriotte bottle was used to supply water in the ring. The time durations of 0.5 cm water infiltration were recorded with a stopwatch until the infiltration time did not change for three consecutive mea86

4 surements and steady-state infiltration was assumed. The steadystate infiltration rate was calculated based on the last three infiltration rates. Before the experiment, a tape measure was placed inside the water supply cylinder of the Marriotte bottle to indicate the changing water level, and the height of the air inlet of the Marriotte bottle was adjusted to supply the water flow into the ring so as to maintain a water depth of 3 cm at the soil surface. The soil infiltration curve was computed from the change in water level. A video camera was used to record water movement in the soil profile. Advanced horizontal/lateral width and vertical depth were measured from the recorded photographs using AutoCAD software. Infiltration and modification algorithm models Movement Process of Infiltrating Water into the Soil Profile The gaps between the ring wall and soil were filled with water in the early stage of the experiment, causing horizontal infiltration (Fig. a). During the early infiltration stage, water movement in the soil was mainly controlled by soil capillarity. Therefore, the horizontal infiltration width and the vertical infiltration depth were approximately equal, with a proportional coefficient of 0.95 (Fig. 3). Owing to the effect of horizontal infiltration, wetted soil volume inside the ring consisted of horizontal and vertical wetted volumes. Horizontal wetted soil volume caused by preferential flow between the ring wall and the soil body significantly increased infiltrating water. This increase caused the measured infiltration rates to be higher than that of Fig.. Wetted area inside and beneath the infiltration ring at (a) the initial infiltration stage and (b) the steady infiltration stage. 86 Fig. 3. Comparison of vertical and horizontal infiltration depths. D infiltration during the initial infiltration stage (the period before the soil materials inside the ring were all wetted). For example, the initial infiltration rate at min was 683 mm h measured by the single-ring infiltrometer; this value was.7 times the D infiltration rate (40 mm h at min). As for the initial infiltration rate at 0 min, the value measured by the single-ring infiltrometer (54 mm h ) was. times the D infiltration rate (7.5 mm h ). When all soil materials in the ring were wetted, the lateral flow driven by soil capillarity beneath the ring became a main factor that affected the accuracy of infiltration rate measurement. After water infiltrated to the soil body beneath the ring, the depth of the wetting front in the middle of the ring increased faster than that in the outside soil because of the side effect of lateral flow. The shape of the wetting front gradually formed a semi-elliptic curve (Angulo-Jaramillo et al., 000; Chowdary et al., 006) (Fig. b). The continuous process of wetted soil volume as a function of time is shown in Fig. 4. As compared with D vertical infiltration (no sidewall preferential flow), soil materials in the ring became saturated at a faster pace because of the influence of preferential flow, thus producing hydraulic pressure at the lower part of the ring. This hydraulic pressure could cause infiltration rates to become high- Fig. 4. The wetted area in the soil profile. Soil Science Society of America Journal

5 er than D vertical infiltration rates during the steady period of infiltration. Based on water mass balance, the infiltration rate measured with ring method was estimated from DQ i= 600 Dt A [] where i is the infiltration rate (mm h ), DQ is the amount of water supplied by the Marriotte bottle in Dt time period (ml), A is the infiltration area (cm ), Dt is the period of infiltration time (min), and 600 is the conversion coefficient. Figures 5a and 5b show the infiltration processes of the initial 30-min period and the subsequent 30-min period, respectively. The differences during these two periods were obvious. The estimated infiltration processes were capable of presenting a very high initial infiltration rate during the 0- to 30-min period and relatively low infiltration rates during the 30- to 0-min period for Replicates and, respectively (Fig. 5). Preferential flow might have caused too much horizontal infiltration, which caused the initial infiltration rate to reach as high as 947 mm h. After some time, the infiltration curves decreased slowly to a lower and relatively steady infiltration rate, which was affected by lateral flow and hydraulic pressure. This result indicated that infiltration rate, which was affected by preferential and lateral flows, followed the same trend of the general soil infiltration (Wu et al., 009; Zhang et al., 04). When the infiltration rate was slow, such as during the subsequent 30-min period shown in Fig. 5b, infiltration occurred slowly. Under a similar circumstance, reading the scale of the Marriotte bottle after short time intervals could have caused high relative errors. This step could have cause the infiltration rate to fluctuate. Thus, increasing the time interval between readings can reduce the fluctuation to produce smoother infiltration curve (Fig. 5b). Correction of the Measured Infiltration Rate The horizontal and lateral wetted volumes generated more infiltrated water, resulting in the infiltration rate measured by the ring infiltrometer being higher than the D infiltration rate. The modified algorithm was used to eliminate the effect of horizontal/lateral wetted volume, based on the Green Ampt model. Under the Green Ampt piston assumption of water distribution in the soil profile, a sharp wetting front separates the soil profile into saturated and unsaturated zones at the initial soil water content. The water infiltrated in the wetted volume was calculated by ( q q ) Q= - V [] s v where Q is the infiltrated water volume [L 3 ], q s is the saturated volumetric water content (%), q i is the initial volumetric water content (%), and V is the wetted soil volume [L 3 ]. The total infiltrated water is computed by Q = Q + Q [3] l v where Q l is horizontal or lateral infiltrated water volume [L 3 ], and Q v is the vertical infiltrated water volume [L 3 ]. The measurement error caused by lateral infiltration is calculated as l = Vv ( q -q ) ( q -q ) Q V d= = Q V 00% l s i l 00% 00% v s i Vv [4] where d is the measurement error (%), V l is horizontal or lateral wetted soil volume [L 3 ], and V v is vertical wetted soil volume [L 3 ]. The corrected infiltration rate is calculated by ic = i [5] + d where i is the infiltration rate calculated by Eq. [] [L T ], and i c is the corrected infiltration rate [L T ]. Fig. 5. Soil infiltrability as estimated with variable water level method in (a) the 0- to 30-min infiltration process and (b) the 30- to 0-min infiltration process. Initial Infiltration Stage Figure 6 shows the wetted soil volume during the initial infiltration stage. Vertical wetted volume (V ) was an inverted truncated cone of h in height, and D and D w are two diameters at the top and the bottom, respectively. The value for V is calculated as 863

6 Fig. 6. Schematic diagram of the wetted soil volume in the initial infiltration stage: vertical wetted volume(v ), horizontal wetted volume (V ), and lateral wetted volume under the cut edge of the ring (V 3 ). p ( ) ( ) 4 3 V = D + D D- w + D- w h [6] where V is wetted volume of the inverted truncated cone [L 3 ], D is the diameter of the infiltration ring [L], w is the horizontal infiltration width [L], and h is the vertical infiltration depth [L]. Horizontal wetted volume (V ) is calculated by V= pdh- V+ pd ( d-h) 4 4 [7] - p( D-w) ( d-h) 4 where V is the horizontal wetted volume inside the ring [L 3 ]; D, h, and w are as defined in Eq. [6]; and d is the depth of cylinder insertion into the soil profile [L]. Finally, V 3 is calculated as 0 V3 = d S y -r 0 = - = p Rr 4pR r y dy ( R r) [8] -r Fig. 7. Advancing process of wetted area in the soil profile. x a ( z-d) + = [9] c where x and z are the lateral and vertical advance distances of the wetting front [L], respectively; d is as defined in in Eq. [7] [L]; and a and c are long and short semi-axis of the elliptical [L], respectively. Figure 7 shows the fitting results. The wetted soil profile was close to the semielliptical given coefficients of determination that were >0.95 (R = 0.98, 0.997, 0.995, 0.987, 0.996, and at 30, 40, 50, 60, 85, and 00 min, respectively). The gaps between the ring wall and the soil produced a passage for preferential flow, which caused the soil materials in the ring being to be saturated in a short time. Therefore, after the soil in the ring is wetted, the soil in the ring can be replaced with the same height of water. The lateral wetted volume was the wetted volume outside the ring (Fig. 8). The boundary in the vertical profile was still defined by Eq. [9]. In the lateral direction, infiltration into the soil was mainly controlled by soil capillarity. Therefore, the lateral wetting front was equal to the downward wetting front, and the wetted area became a circle on the horizontal plane. The ellipsoidal equation is where V 3 is the lateral wetted volume under the cut edge of the ring [L 3 ], r is the radius of the wetted circle under the cut edge of ring [L], and R is the radius of the ring infiltrometer [L]. Steady Infiltration Stage During this stage, the wetting front was approximately close to a semielliptical shape (Angulo-Jaramillo et al., 000; Chowdary et al., 006). In the study by Chowdary et al. (006), the elliptical equation fitted well with wetting zone with coefficients of determination from 0.93 to Therefore, the lateral and vertical distances of the wetting front at different moments were fit by Fig. 8. Schematic diagram of wetted soil volume in the steady infiltration stage. 864 Soil Science Society of America Journal

7 x y z + + = [0] x t x t z t ( ) ( ) ( ) m m m where x m (t) is the maximum of x at moment t [L], and z m (t) is the maximum of z at moment t [L]. The lateral wetted volume is given by l m ( ) V= f x, yz, dxdydz Ω ( ) ( ) m ( t) ( t) -R = x t z t d q RdR dz z = p ( ) - 3 x 0 Ra / 0 m xm t R m p 3/ [] where V l is the lateral wetted volume [L 3 ], x m (t) and z m (t) are as defined in Eq. [0], and R is the radius of the ring [L]. The vertical wetted volume is calculated by 4p Vv= xm( t) zm( t) 4 3 p z - ( ) - 3 x ( t) ( t) m xm t R m 3/ [] where V v is the vertical wetted volume [L 3 ], and x m (t), z m (t), and R are as defined in Eq. [0] and []. Results and discussion Wetted Volume The wetted volume as a function of time for the two replicates is shown in Fig. 9. In the first 5 min, the average increasing rate of wetted volume was cm 3 min (increasing from 38 cm 3 at min to 677 cm 3 at 5 min). The rapid increase could be attributed to the horizontal infiltrated water caused by preferential flow. Given that the wetted volume was limited by the total wetted volume of the ring in the following infiltration stage (5 7 min), wetted volume increased at a slower rate of 0. cm 3 min (increasing from 677 cm 3 at 5 min to 7930 cm 3 at 7 min). After the soil materials inside the ring were wetted (about 7 min), the increasing rate gradually became less. The process of wetted volume could be proportional to that of cumulative infiltration. Thus, the changing processes of wetted volume over time were fitted with the modified Kostiakov infiltration model. Fitting results (Fig. 9) indicated that cumulative infiltration influenced by preferential and lateral flows could be well fitted by the classic infiltration model with R greater than This result indicated that cumulative infiltration affected by preferential and lateral flows followed the same trends as those shown by D vertical cumulative infiltration. Error due to Preferential Flow at the Initial Stage The error caused by preferential flow included horizontal infiltrating water and water contained in the gaps between the ring walls and the soil. The latter (about 3 ml) was less than 5% of the volume of water infiltrated into the soil (about Fig. 9. The wetted volume as a function of time in (a) Replicate and (b) Replicate. 973 ml), which was negligible in comparison to the volume of water infiltrated into the soil. Therefore, the error discussed here refers to the horizontal infiltrated water caused by preferential flow. During this infiltration stage, the error decreased over time (from 07 to %) (Fig. 0) because the vertical wetting depth in the middle of the ring became larger than the horizontal wetting width owing to the effects of gravity potential on infiltration rates gradually reaching a relatively significant level. At the beginning of infiltration (0 3 min), infiltrating water movement was mainly controlled by soil capillarity. The increasing rate in horizontal wetting width was identical to that of vertical wetting depth. Therefore, the measurement error caused by horizontal infiltration at the beginning stage decreased slowly with time. Contribution of Lateral Flow during the Steady Infiltration Stage After water infiltrated the horizon beneath the single cylinder, the lateral flow occurred outside the ring as driven by the capillarity of the unsaturated soil to cause an overestimated infiltration rate as compared with the D infiltration. The error caused by lateral flow (capillarity-driven flow) increased with the lateral wetting width advancing over time. As the effects of soil s capillarity on infiltration process gradually weakened over time, the advancement in the lateral wetting front gradually decreased

8 Fig. 0. Error caused by preferential flow in (a) Replicate and (b) Replicate. In turn, this phenomenon caused the increasing rate of error to reduce with time. The error was fitted well by the exponential function, which could express the characteristics of error-changing process, with very high R values (R = and 0.99, respectively) (Fig. ). Corrected Infiltration Rates The corrected infiltration curves were compared with those measured with the ideal D infiltration. These data sets of the replicates were almost identical to those measured by the ideal infiltration ring, both at the initial and steady infiltration stages (Fig. ). Taking Replicate as an example, the infiltration rates were and 03 mm h at 5 min for the corrected and the ideal D infiltration, respectively. At 55 min, infiltration rates decreased to 38 and 34 mm h for the corrected and the ideal D infiltration, respectively. Infiltration rates were very high at the initial stage, after which they decreased quickly. After some time, infiltration rate decreased slowly to steady infiltration rate values of 4.9 and 3.3 mm h for the corrected and ideal D infiltration rates, respectively. The corrected infiltration rate was a little higher (7%) than the ideal D infiltration rates. The corrected infiltration rates at different moments were compared with the D rates (Fig. ). Visual observation of Fig. suggests that the corrected infiltration rates agreed well with D ones, with the proportional coefficients very close to (0.983 and 0.996) and R > 0.9. Fig.. Contribution of the lateral flow in (a) Replicate and (b) Replicate. The rising importance of soil infiltration has led to the development of infiltration models to represent soil infiltration time function. The equations proposed by Kostiakov (93) and Horton (94) are the most commonly used empirical models derived from a large number of field and laboratory experiments. The Kostiakov equation is given by ( 0 ) -b i = at < b < [3] where i is infiltration rate [L T ], a and b are fitted parameters that determine or are determined by the shape features of the infiltration curves (dimensionless), respectively, and t is infiltrating time [T]. The Kostiakov model is popular because of its simplicity and ability to fit well to a wide variety of soils (Mishra et al., 003). The Horton infiltration model is given by ( ) ( ) i= i0 -i exp - bt + i [4] where i is the infiltration rate [L T ], i 0 is the infiltration rate at time t = 0 [L T ], i is the steady infiltration rate [L T ], and b is a constant to represent the speed showing infiltration reduction with time [T ]. The Philip infiltration model (Philip, 957) is a well-known representative physical infiltration model. This model is derived from an analytical approximation by using the first two terms of 866 Soil Science Society of America Journal

9 Fig.. The comparisons of the corrected soil infiltrability as a function of time with the one-dimensional infiltration soil infiltrability in (a,b) Replicate and (c,d) Replicate. the power series as the solution to the Richard s partial differential equation: -0.5 i 0.5t i = + [5] where i is the infiltration rate [L T ], S is the soil sorptivity [L T / ], and i is the steady infiltration rate [L T ]. In the current study, the most commonly used empirical and physical infiltration models were selected to represent quantitatively the infiltration process. Table presents the regressed results of the corrected and ideal D infiltration data by three commonly used infiltration models. Table suggests that all the models represented the measured data very well, with all R values above 0.9. Although the Philip model produced high R values, the negative values of the constants, which were conceptually supposed to represent the steady infiltration rates, indicated poor performances of predicting steady infiltration rates and procedures. These results were consistent with those of Liu et al. (0), Mao et al. (0), and Mishra et al. (003). The constant values in Horton model were well approximated to the steady infiltration rate. Table indicates that the constant infiltration values of Replicates and were slightly higher than those obtained by the ideal D method. The most likely reason for this phenomenon could be that the preferential flow caused higher water pressure, inducing an infiltration rate higher than that of ideal D. This result indicated that higher water pressure in the traditional ring infiltrometer might cause the measured infiltration rate to become higher than D soil infiltration. Estimation of Soil Saturated Hydraulic Conductivity Saturated hydraulic conductivity was calculated from data obtained with a single ring infiltrometer at steady state based on the widely applied method of Reynolds and Elrick (990). The Table. Model representations of infiltrability, as expressed by the infiltration rate (i, mm h ) and time (t, min), for Replicates and and an ideal one-dimensional (D) case. Kostiakov Horton Philip Replicate Model R Model R Model R Replicate i = 3.47t i = exp( 0.5t) 0.96 i = t Replicate i = 57.5t i = exp( 0.3t) 0.97 i = t Ideal D case i = 8.7t i = exp( 0.t) 0.95 i = t

10 value of K s can be obtained as (Reynolds, 008; Reynolds and Elrick, 990): K i * = s s H ( Cd + Ca ) + a ( Cd + Ca ) + [6] where i s is the quasi-steady infiltration rate out of the cylinder [L T ], a is the inside radius of the cylinder [L], H is the steady depth of ponded water in the cylinder [L], d is the depth of cylinder insertion into the porous medium [L], a* is sorptive number of the porous medium [L ] (a value of 0.0 cm in the experiment was estimated based on the textural classes by HYDRUS- D [Šimůnek et al., 005]), and C = 0.36p and C = 0.84p are shape parameters. A laboratory measurement was conducted to determine K s with the most classic and commonly applied method (CH method) based on the direct application of the Darcy equation to a saturated soil column of uniform cross-sectional area (Klute and Dirksen, 986): VL = [7] K s AtDH where V [L 3 ] is the volume of water that flows through the sample of cross-sectional area A [L ] during time interval t [T], and DH [L] is the hydraulic head difference imposed across the sample of length L [L]. Before measurement, soil samples with bulk density of.4 g cm 3 were saturated for 48 h. Discharge water volume V [L 3 ] was measured at 0-min intervals by an electronic balance with 0.0-g accuracy. Each experiment lasted for 5 h, and two replicates were adopted. The measured K s of the experimental soil was.0 mm h, which was a little higher (5%) than the values measured by constant head method at 0.40 mm h (0.9 mm h ). The singlering infiltrometer gave higher K s estimates, consistent with the results reported by Torfs (008) and Verbist et al. (03). Higher values could be explained by the influence of additional hydraulic water pressure caused by preferential flow inside the ring. The soil depth saturated by preferential flow tended to increase the hydrostatic pressure, which consequently increased the measured i s in Eq. [7]. If the ponded depth H = 3 cm was replaced by H = 8 cm (5 cm represented the depth of the ring inserted into the soil) in Eq. [7], the computed K s estimated by Eq. [7] was 0.07 mm h, which was basically identical to the one measured by the constant head method. The preferential flow caused overestimation of the measured infiltration rates by increasing the horizontal infiltrated water and hydraulic pressure head. Conclusions A disassembled soil container and ring infiltrometer were proposed to display water movement process in the soil profile during infiltration. Mathematical models were formulated based on the Green Ampt model to correct soil infiltration capability from calculating vertical and horizontal/lateral wetted soil volume. Experiments were conducted in the laboratory to demonstrate the procedure and to verify the models with measured data. The dynamic process of wetted area in the soil profile inside the ring indicated that the preferential flow increased the initial infiltration rate. Lateral infiltrated water affected the accuracy of the infiltration rate measured after the soil in the ring was fully wetted. Furthermore, the modified infiltration rates indicated that the modified model eliminated the effect of preferential and lateral flows driven by soil capillarity on measured infiltration rate. The K s estimated by ring infiltrometer was a little higher (5%) than that measured by constant head method. This study provides a new device to display the water movement inside ring and formulates mathematical models to eliminate the effect of the preferential and lateral flows on infiltration rate measurement. Acknowledgments This research was supported by the National Natural Science Foundation of China under Project no and no We thank the associate editor and the three reviewers for their valuable comments. References Ahuja, L.R., S.A. El-Swaify, and A. Rahman Measuring hydrologic properties of soil with a double-ring infiltrometer and multipledepth tensiometers. Soil Sci. Soc. Am. J. 40: doi:0.36/ sssaj x Angulo-Jaramillo, R., J. Vandervaere, S. Roulier, J. Thony, J. Gaudet, and M. Vauclin Field measurement of soil surface hydraulic properties by disc and ring infiltrometers: A review and recent developments. Soil Tillage Res. 55: 9. doi:0.06/s (00) Bagarello, V., and A. 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