Journal of Hydrology 319 (2006) 216–226 www.elsevier.com/locate/jhydrol

A run off-on-ponding method and models for the transient infiltration capability process of sloped soil surface under rainfall and erosion impacts Tingwu Leia,b,*, Yinghua Panc, Han Liua, Weihua Zhand, Jianping Yuand a

The Key Laboratory of Modern Precision Agriculture System Integration Research, College of Hydraulic and Civil Engineering, China Agricultural University, Beijing 100083, People’s Republic of China b State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Yangling, Shaanxi Province 712100, People’s Republic of China c Geographic and Resources Management College, Yantai Normal University, Shandong Province 264025, People’s Republic of China d Bureau of Comprehensive Development, Ministry of Water Resources, Beijing, 100053, People’s Republic of China Received 16 June 2004; revised 7 June 2005; accepted 28 June 2005

Abstract The transient infiltration capability process of sloped soil surface under rainfall, runoff, erosion impacts is of great significance in scientific researches such as hydrology, crop water use, irrigation system design and management as well as soil erosion, and etc. A new method, which involves rainwater run-off and run-on/ponding on hill slope, was advanced in this paper for the determination of the transient soil infiltrability under rainfall, runoff and erosion conditions. Mathematic models were derived to compute the transient infiltration rates with data from the advance process of runoff water on soil surface and depth of water ponded on the soil surface. Laboratory experiments of two cases under 30 mm/h rainfall intensity and 58 slope and 60 mm/h rainfall intensity and 208 slope were conducted to collect data for illustrating the experimental and computational procedures to determine the transient infiltrability curve under lower rainfall intensity with no water ponding and under higher rainfall intensity with water ponding. The rationale of the measurement and the related algorithm was validated with data from other sources. The measured infiltrability curves well explain the transient process of soil infiltration capability. The data also indicate that slope gradient, rainfall intensity and/or soil erosion have their influences on the infiltration capability of soil. Analysis was made to compute the relative error as caused by the error in measured run-on advance. In addition, the cumulative infiltrated water recovered from the infiltrability so determined was compared with the rainfall amount to estimate the overall accuracy of the method. The newly suggested method overcomes the shortcomings of the traditional rain simulator and double ring methods. This method has the capability of measuring the complete process of the transient soil infiltration capability under sloped surface as influenced by rainfall splash, runoff, and soil erosion. This method will supply the researchers in related fields a convenient yet useful tool. q 2005 Elsevier Ltd All rights reserved. Keywords: Infiltration capability; Transient process; Rainfall; Sloped surface; Measurement; Model; Error analysis

* Corresponding author. Address: China Agricultural University, Qinghua Donglu Road No. 17, Beijing 100083, People’s Republic of China. Fax: C86 10 6273 6367. E-mail address: [email protected] (T.W. Lei).

0022-1694/$ - see front matter q 2005 Elsevier Ltd All rights reserved. doi:10.1016/j.jhydrol.2005.06.029

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1. Introduction The infiltrability or infiltration capability of a soil is usually referred to as the infiltration flux of water at the soil surface, per unit area at a unit time, under unlimited water supply and standard atmospheric pressure (Brooks et al., 1997; Hillel, 1998). This parameter is determined by the soil properties and determines the amounts of water entering into the soil and running off of the hill slope. The infiltration capability is of importance in scientific researches in the fields such as hydrological processes, crop water availabilities, irrigation system design and scheduling as well as management, soil erosion and soil water and solute transport processes, etc (Brooks, 1997; Vijay, 1988). The infiltration capability of a soil determines the surface runoff, while runoff is closely related to the flood prediction, reservoir water resources estimation, irrigation water allocation, runoff induced pollutants transportation, etc. (Brooks, 1997). The soil infiltration capability also determines the amount of water getting into soil profile under a given rainfall condition. The infiltrated water is either recharged as the groundwater or transferred into soil water available to crops, which influences the irrigation scheduling. Runoff as influenced by infiltration process is the driving force responsible for soil erosion (Hillel, 1998; Jiang, 1997). The infiltration capability of soil is a function of soil texture, structure, soil profile moisture distribution (Hillel, 1998; Scott, 2000). It has a very high value at the initial when soil is dry, and decreases with time of the infiltration process and approaches a final constant, the steady infiltration rate. Only when the water supply to the soil surface reaches or exceeds the infiltration capability does the actual infiltration rate equal to the infiltration capability of the soil. This is the basis for measuring the infiltration capability of a soil. A commonly used method for infiltration rate measurement is rainfall simulator or sprinkler. Peterson and Bubenzer (1986); Ogden et al. (1997) reported the detailed procedures for measuring soil infiltration rate with sprinkle rainfall simulator. Yuan et al. (1999) developed a portable dripper rainfall simulator for field infiltration/runoff measurement. Many more or less similar work have been reported in the literatures. This kind of method has its

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limitation: the very high infiltration capability of the soil cannot be determine due to the limitation of water supply. Many reported the double ring infiltrometer, such as Bouwer (1986). The double ring method uses a Mariotte bottle for its water supply. The infiltrated amount of water is automatically replaced, so that the complete transient process of infiltration capability can be determined. The double ring method requires the soil surface be more or less flattened and leveled. It is not applicable to (steeply) sloped soil surface. To level a sloped surface to suit the double ring application would inevitably disturb the structure of the surface soil and the continuity of the slope. Furthermore, the double ring method cannot take into account the impacts of rain drop splashes and the soil erosion on infiltration capability. Numerous studies (Helalia et al., 1988; Morin and Van Winkel, 1996; Levy et al., 1994) showed that both raindrop splash and soil erosion cause crusting or sealing at soil surface through soil pores filled with washed in particles and/or deposition of eroded materials, which inevitably results in significant reduction in soil infiltration capability and induces higher runoff rate. Yuan et al. (1999) reported that double ring infiltrometer, as compared with sprinkler method, overestimated the steady infiltration rate of a loess soil by 1.43–1.78 times. No data is yet available as how much higher the double overestimates the transient rate at initial state of infiltration, since there is no sound method with which the early soil infiltration capability can be determined. Therefore, the research on the transient process of infiltration capability on sloped soil surface as influenced by raindrop splash, runoff, and soil erosion is of great importance to many related researches and applications. The objectives of this study were: (1) to suggest a rational method to measure the complete transient process of infiltration capability of (sloped) soil surface under raindrop splash, runoff and erosion; (2) to derive the related algorithm and models for the determination of soil infiltration capability under such conditions; (3) to obtain necessary data from laboratory experiments; and (4) to illustrate and/or validate the method and the procedures for the application of the method.

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2. The methodology and the algorithm models As mentioned above, soil infiltration capability is the actual infiltration rate under unlimited water supply at soil surface. The very high infiltration capability at very beginning of the infiltration process requires very high rate of water supply. As the process proceeds, soil infiltration capability decreases. To fulfill these requirements fully, the measurement system is given in Fig. 1. In Fig. 1, P is the constant precipitation intensity from a sprinkler or drippers. The section AB up the slope with a length of x1 is covered with impermeable materials such as plastic or metal sheet with infiltration rate equal to 0 and is used for runoff surface which is used for supplemental water supply added upon the constant precipitation. The section BC with a length x2 is for the run-on and infiltrating surface. At this section, the soil infiltrates not only the direct rainfall but also the water runoff from the upslope section AB. Under a given precipitation intensity, the dynamic infiltration process and its interaction with soil infiltration capability, rainfall and run-on water are as the following. Initially, the soil has very high infiltration capability. The infiltrating section does not only infiltrate the direct rainfall but also infiltrate the runon water. With the very high infiltration capability, the run-on water advances a very short distance (denoted as x in Fig. 1) from the origin of axis X. With the rainfall-infiltration process goes on, the soil infiltration capability decreases gradually (and rapidly). In addition to infiltrate the direct rainfall, the infiltrating surface has lowered capability to infiltrate the run-on

Fig. 1. The schematic illustration for the measurement of infiltration capability.

water and longer slope length is needed to infiltrate the same flow rate of run-on water. That means that with the proceeding of the rainfall-infiltration with increasingly lowered soil infiltration capability, the run-on water advances down the slope. The runoff water on one hand supplies the supplemental water to meet the requirement of very high rate of infiltration capability at the early stage of infiltration. On the other hand, the advances of the runoff water with time at the soil surface indicate quantitatively the reduction with time in the soil infiltration capability. The process continues until the infiltration rate reaches its steady value. The lowered infiltration capability could cause water runoff of the section BC when the direct rainfall and the runon water is higher than the infiltration capability of the section BC. Water runs off the section BC or ponded if stored and infiltration process under ponding condition starts at the bottom. When time goes on, the ponded water level rises at the bottom as the infiltration capability decreases further. The rising rate of the ponded water level is also an indicator, which can be used to estimate the continuous reduction in infiltration capability. To quantify the soil infiltration capability with the idea stated above, the following assumptions were made: (1) Since the rainfall lasts for a limited period of time and the humidity at the soil surface is very high during the rainfall period, the evaporation from the soil surface is neglected. (2) A very thin layer of topsoil is saturated in a very short period of time during the rainfall and the infiltration capability is a function of time only and is not influenced by cumulated infiltration. The infiltration capability along the infiltrating slope section BC is quantified with an identical infiltration curve. (3) Under ponding condition, the very small difference in infiltration rates between the ponding slope and no-ponding section is ignored since the ponding depth is very small. In addition, the whole slope length is under the same infiltration rate as no ponding infiltration process. The basic principle for the determination of the soil infiltration rate is water/mass balance.

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2.1. Algorithm model for infiltration rate at the run-on advance stage

Therefore, the infiltration rate during the run-on advance stage is given as:

The run-on advance stage is defined as the period of time when the run-on water moves from xZ0 to x2. The following variables are defined for the computational model of infiltration rate during this stage.

i Z P CP

W P x1 x2 x

t I i(t) t0

the width of the soil body (m) the precipitation intensity (mm/h) the length of run-off section (m) the length of run-on and infiltrating section (m) the coordinative value of run-on water advances upon the run-on section with origin at the transitional point between the run-off surface and run-on section (m) time (h) accumulative infiltration (mm or m3/m2) infiltration rate (mm/h) the transitional time at which run-on water starts ponding at the soil surface (h)

During a given time period from t to tCDt when t%t0, the run-off water advances on the run-on surface from x to xCDx, and the cumulative infiltration during this period is DI. Water balance during this time period requires that the cumulative infiltration in the slope length of xCDx is the sum of direct rainfall plus the amount of run-on water at the same section and the same time period with 8 cumulative infiltration Z DIðx C Dx=2Þcos a W > < direct rainfall Z Pðx C Dx=2Þcos a WDt > : run-on water Z Px1 cos a WDt (1) where a is the slope gradient in degrees. Using Eq. (1), the water balance is presented as: DI x cos a Z Pðx1 C xÞcos a Dt

(2)

Then the infiltration rate, as the derivative of cumulative infiltration is given as:    dI DI x  i Z Z lim ZP 1C 1 Dt/0 Dt dt x

(3)

x1 x

(4)

Eq. (4) indicates, during the period when the runon water advances on the infiltrating section, the soil infiltration rate is the sum of direction rainfall intensity and the infiltration of run-on water. Eq. (4) also indicates that at the initial stage of rainfall, run-on water advances a very short distance upon the slope, and x is infinitely small. The second term on the right hand side of Eq. (4) approaches infinity. This models the actual transient infiltration process, including the very high infiltration rate at the initial stage of infiltration.

2.2. Algorithm model for infiltration rate at the ponding stage During this stage, not all the run-off water and rainfall can be infiltrated into the soil in the infiltrating section. Water starts to run-off of the infiltrating section, and ponding at the bottom of the section with a border installed. The ponding depth increases with time if the infiltration rate continuously decreases with time. During the time period from t to tCDt, the water balance requires that the total rainfall to be either infiltrated into soil or running off of the slope, while: ( cumulative infiltration Z DI x2 cos a W (5) cumulative rainfall Z Pðx1 C x2 Þcos a WDt The volume of ponding water, as a function with time is given as 1 V Z h hctg a W 2

(6)

where h, a function of time, is the depth of the ponding water, m. The increment in volume of ponding water upon the slope is given from Eq. (6) as: DV Z

dV dh Dt Z hctg a W Dt dt dt

(7)

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From Eqs. (5) and (7), the water balance gives the following:

3.2. The experimental arrangements

DI x2 cos a W

Two cases were arranged in this experimental study, to illustrate, to demonstrate the experimental procedures, and to validate the computational models and the procedures discussed above. The two cases are specified as the following.

Z Pðx1 C x2 Þcos a WDtKhctg a W

dh Dt dt

Then the infiltration rate is determined as:     DI x1 h 1 dh i1 Z lim C1 K ZP Dt/0 Dt x2 sin a dt x2

(8)

Case I. The rainfall intensity was 60 mm/h, slope at 58, and the ratio of the run-off length to the run-on section CZ1:2. Case II. The rainfall intensity was 30 mm/h, slope at 208, and CZ1.5:1.5.

(9)

The computational model for infiltration rate during the ponding stage is given as:   x h 1 dh i1 Z P 1 C 1 K (10) x2 sin a dt x2

And two replicates were adopted for each of the two cases. 3.3. The experimental method and the observations

3. Experimental methodology and materials To verify the method, laboratory rainfall simulation experiments were made in the State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, China. 3.1. Experimental materials The experimental soil was a sandy silt loess from the top layer of cultivated land on Loess Plateau of China. The particle size distribution is listed in Table 1. The experiments were conducted with laboratory flume of 6!1!0.6 m with movable rain simulator of dripper type, which gives more precise and uniform rainfall intensity than a sprinkler rainfall simulator system. The 1 m wide flume was divided into two equal parts of 0.5 m wide each in its width direction to represent two replicates for each experimental run. The rainfall simulator has a dimension of 3!2 m with raindrop sized between 1 and 3 mm and rainfall intensity of 12–150 mm/h.

When packing the soil materials into the flume, a sand layer of 2 to 4 mm was laid at the bottom of the flume to form an air leaking and water drainage boundary passage. The air-dried soil materials were passed through a sieve of 4 mm before use. Soil was weighted before packed into the flume at 5 cm thick layer each time, at dry bulk density of 1.3 g/cm3, equivalent to that of a consolidated loess soil. Each layer of soil was compacted to the given density and the next was filled upon top of the previous layer crashed to a rough surface for better contact and conductivity of water between the two layers of soil. The overall depth of packed soil was 50 cm. Then the flume was setup at the desired slope gradient. A metal sheet was placed at lowered end of the slope during the packing, at a reverse slope so that when the flume was setup at the desired slope, the metal sheet was at the upright/vertical position. This sheet and the flume boundaries form a space to hold the water running off the slope. From the discussions above, the advances of runon water at soil surface and the change in the depth of

Table 1 The particle size distribution Size (mm)

1–0.25

0.25–0.05

0.05–0.01

0.01–0.005

0.005–0.001

!0.001

!0.01

%

1.11

31.70

41.57

5.43

4.47

15.72

25.62

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ponding water are the basic data for computing the infiltration rate. Therefore, the following observations were made in the experiments. (1) The distance of run-on advance on the surface was recorded as a function of time. This was done visually, with the scales marked on each side of the flume walls, each for one of the two replicates. During the rainfall period, the distance of advancing water and the corresponding time were recorded. The run-on normally did not advance exactly uniformly or evenly on the soil surface. A ruler was used to visually average the advancing front of the run on water. The averaged advance distances were then measured by the scales setup along the outsides of the flume, with a resolution of 1 cm. These measured distances from the 2 replicates were averaged again. (2) The depth of ponded water. The ponding water depth was recorded from the scale (with accuracy of 1 mm) marked on the vertical board installed at the bottom of the flume, from where water ponding starts. With rainfall proceeding, excessive run-on water advances and reaches the bottom of the flume. Water ponding starts. With the further decrease in infiltration capability of the soil, the ponding water depth increases with time. The depth of ponded water as a function of time was recorded.

Fig. 2. Run-on water advance for Case I (rainfall intensity: 60 mm/h, slope: 58, and run-off/on ratio: 1:2).

depth and those directly computed from the experimental data (referred to as Experiment) were presented. Figs. 4 and 6 indicated that the computed infiltration rate as a function of time conceptually very well presents the infiltration capacity of a soil. The general trends of the infiltration rates well demonstrate the process of soil infiltration capability. Figs. 4 and 6 also indicated that the infiltration curves computed directly from the experimental data and those calculated with the regressed run-on advance model and the water ponding depth model are about

4. Results and discussions Figs. 2 and 5 showed the water advances at soil surface for Case I and Case II, respectively. The water advance is either linearly correlated to time with the determination coefficient of 0.98 (Case I) or regressed with time with some other functions, such as logarithm function as in Case II. The water ponding process for Case I, as shown in Fig. 3, was regressed with a natural logarithm function, with the determination coefficient of nearly 1. The infiltration rate during the water advance stage was computed with Eq. (4) and that during water ponding stage was calculated with Eq. (10). The computed infiltration curves for Cases I and II were shown in Figs. 4 and 6, respectively. In Figs. 4 and 6, both the infiltration curves as computed with regressed functions (referred to as Model) of run-on advance and water ponding

Fig. 3. Water ponding for Case I (rainfall intensity: 60 mm/h, slope: 58, and run-off/on ratio: 1:2).

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Fig. 4. Computed infiltration capability for Case I (rainfall intensity: 60 mm/h, slope: 58, and run-off/on ratio: 1:2).

Fig. 6. Computed infiltration capability for Case II(rainfall intensity: 30 mm/h, slope: 208, and run-off/on ratio: 1.5:1.5).

the same. These indicated that the water advance and ponding models have little influences on the computed infiltration rate, as long as the models well correlate the run-on advances and/or ponding water depth with time. Furthermore, Figs. 4 and 6 or 7 give a complete process of soil infiltration capability, which has not been possible with the traditional sprinkler (rain simulation) method. The early and very high infiltration rate of a soil cannot be measured with the conventional sprinkler methods. Fig. 5 indicated that under Case II, with a rainfall intensity of 30 mm/h, water advances on the soil

surface reached only about 70 cm and tended to stop there. This indicated that the steady infiltration rate of the soil is capable of infiltrating the direct rainfall and the run-on water in this section of the slope. Run-on water will not further advance significantly with time. Figs. 4 and 6 indicated that the types of functions used for describing the water advance on the soil surface are not very important as long as they can well describe the correlation between the water advance and time. Linear, log and direct experimental data can all be used for good computational results of infiltration rates. They also demonstrated that the models given as Eqs. (4) and (10) well shape the dynamic process of soil infiltration capability. Fig. 7 compared the infiltration processes of the two studied cases. The infiltration capability curve for Case I was well lower than that for Case II. The most possible reasons could at least be the following two. First, the rainfall intensity of Case I was higher than that of Case II. Raindrop splashes under Case I have much high impacts on soil surface, in terms of both compaction of surface soil and splash erosion, than those under Case II. Higher rainfall gives higher flowing rate of water running off the covered surface, which causes higher soil (sheet) erosion. Both splash and sheet flow erosions cause soil surface sealing or crusting. Seal and/or crust formation are highly responsible for the lowered infiltration rate (Helalia et al., 1988; Morin and Van Winkel, 1996).

Fig. 5. Run-on water advance for Case II (rainfall intensity: 30 mm/h, slope: 208, and run-off/on ratio: 1.5:1.5).

T.W. Lei et al. / Journal of Hydrology 319 (2006) 216–226

Fig. 7. Infiltration capability comparison for Case I and II (rainfall intensity: 30 mm/h, slope: 208, and run-off/on ratio: 1.5:1.5).

These kind influences of soil erosion on infiltration reduction cannot be taken into account with double ring method. Another possible reason is the higher wetting rate caused by higher rainfall intensity and higher run-on flow rate. Faster wetting rate causes air to be entrapped in the soil aggregates. The ‘explosive’ actions of the air bubbles entrapped in soil aggregates may cause severe breaking down of soil aggregates or structures, which blocks the pores at soil surface to cause reduction in infiltration rate, increment in runoff and erosion (Mamedov et al., 2001; Levy et al., 1997). This indicates that the method suggested in this paper can be used for studies on infiltration capabilities of soils under influences of raindrop splashes, sheet flow erosion and surface sealing/crusting. For Case I, the steady infiltration rates were reached after water ponding started. Therefore the steady infiltration rate in this Case should be lower than 90 mm/h, (60 mm/h!(1C2) m)/2 mZ 90 mm/h, where (1C2) m was the slope length intercepting rainfall and 2 m is the slope length infiltrating water. Water ponding indicated that not all rainfall water was infiltrated. The actually computed steady infiltration rate was 58 mm/h, as shown in Fig. 4 or Fig. 7. Case II indicated that when the infiltration rate approached to the steady value (run-on water stopped advance on soil surface), all direct rainfall and the run-on water was infiltrated in this section of the slope, at a length about 70 cm, Fig. 5.

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Therefore, the steady infiltration rate for this Case should not be smaller than 94 mm/h, (1.5C0.7) m ! 30 mm/h/0.7 mZ94 mm/h. The actually computed value of the steady infiltration rate was 113 mm/h. The steady infiltration rate for Case II was about twice as higher as that for Case I. This quantitatively indicated that rainfall intensity or sprinkler intensity has significant influence on infiltration rate. If one uses very high sprinkler intensity to try to get as much high early soil infiltration rate as possible, he would have to use much higher sprinkling intensity which produce much lowered steady infiltration rate if the sprinkler intensity is maintained. This suggested another advantage of the newly developed method. And the presented data also indicated the measured data is reasonable from the reasoning above. It is wealth to note that the method, though the demonstration experiments were made in laboratory, is not difficult to be applied to field conditions. For field applications, portability of the device should not be an important issue. Good quality of water for rainfall simulation is required. In addition, the soil surface should be clear off obstacles such as residues for easy visual tracking of the advance front of the flowing water. This method could also be used to investigate the infiltrability of a soil under the impacts of high splash erosion if a pressurized rain simulation system is used to supply equivalent kinetic energy of raindrops.

5. Error analysis 5.1. Error in infiltration rate (IR) caused by the error in measured advance distance The error in estimated IR as caused by the error in the measured distance of water advance on soil surface is given as the following. From Eq. (4), the differential change (di) in IR as caused by that in measured distance (error) (dx) is given as: di ZKP

x1 dx x2

(11)

Then the relative error (z) in IR caused by the same differential change in the measured distance is given

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Fig. 8. Relative error in estimated IR as caused by the error in measured distance.

as, from Eqs. (4) and (11):



di

x z Z



!100% Z 2 1 !100% dx i x C xx1

(12)

Eq. (12) indicates that the relative error in IR is a function of the distance of the advancing front of running-on water, x. With a resolution of the measuring scale being 1 cm, theoretically the estimated error (dx) in distance is 0.5 cm. With the two Cases presented above, x1 is 100 (Case I) or 150 cm (Case II). With these known data, the relative estimation error in IR caused by the error in distance measurement is given in Fig. 8. Fig. 8 indicates that the maximum error could be as higher as some 50% for both Cases. But the error decrease rapidly as the advance distance increases. Quantitatively, when the measured distance reaches 5 cm, the relative errors in the estimated IR decrease to less than 10%. This is equivalently at a time period of less than 0.5 and 2 min after the rainfall start for Cases I and II, respectively, and the IR was still very high.

the measured results with those from double ring and sprinkler methods could not be done directly. Instead, Pan (2004) analyzed the measurement accuracy of the newly suggested method. The procedures are as the following. The infiltration rates, as a function of time at different locations upon the slope were estimated, with the models advanced in this study. These infiltration rates were used to calculate the cumulative infiltration along the slope by integrating the infiltration rate over time. Then the integration over the slope was made to estimate the total infiltrated amount, as the computed (recovered) infiltrated amount Q (m3, or l). This Q value needs to be readjusted when there is water ponding, by adding the ponded water into the recovered water. The actual precipitation over the slope and in the infiltration period was known, Q0 (m3, or l). Then the relative error between the actual precipitation amount and that of infiltrated water is given as the following:



Q0 KQ



!100% (13) d Z

Q0

where, d is the relative error, %; Q0 is the cumulated rainfall amount over the slope, m3; and Q is the recovered infiltrated water with the infiltration rate estimated, m3. The computation procedures for Q are as the following: ðL ðT QZ

iðt; xÞdt dx 0 0

where i(t,x) is the infiltration rate, a function of time t and distance x, mm/s/m2; L is the slope length, m; and T is the time period of rainfall, s or h. Numerically, Eq. (14) is given as the following Eq. (15): ! X X X Q zW iðtj ; xk ÞDtj Dxk Z W Iðxk ÞDxk j

k

k

(15)

5.2. Error in infiltrated water With the problems mentioned above concerning the traditional sprinkler and the double ring method for measuring soil infiltrabilities under rainfall/runoff influences at a slope surface, the comparisons of

(14)

Iðxk Þ Z

X

iðtj ; xk ÞDtj

(15a)

j

where Dt(dt) is the length of time step, s; and Dx(dx) is the length of slope distance, m.

T.W. Lei et al. / Journal of Hydrology 319 (2006) 216–226 Table 2 Measurement accuracy analysis Case

P (l)

Infiltrated (l)

Error (%)

I II

134.49 89.73

125.46 85.70

6.71 4.49

The cumulated rainfall over the same period of time (T) and the same slope length and the run-off water (Q0) is given as: Q0 Z PWðx1 C X0 ÞT cos a;

16

where X0 is the slope length at which run-on water stops, or X0Zx2 when there is water ponding (m). The errors so estimated for the two cases were listed in Table 2. Table 2 indicates that the overall measurement accuracy of the method advanced here. These data further demonstrate the feasibilities of the method.

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method, including the experimental method and the derived computational models can overcome the problems of the conventional sprinkler method for infiltration capability, such as incapability of neither getting the very high initial infiltration rate, or/and lowered infiltration capability obtained when using very high rainfall intensity. And also, the problems associated with the double ring method, such as unsuitable to sloped soil surface and reduced infiltration rate caused by surface sealing due to raindrop splash and sheet flow erosions. Therefore, this method supplies a useful tool to the related researches, such as hydrology, soil erosion, water resources, irrigation system design and management, and agronomy, to measure the soil infiltration capability under the impacts of raindrop splash and runoff on sloped hill slopes. With this method, variations in soil infiltration capabilities as influenced by slope, rainfall intensities and surface sealing caused by erosion can be investigated.

6. Conclusions Acknowledgements A method was advanced to measure the soil infiltration capability of sloped soil surface under rainfall situation with rain-off and run-on of rainwater. Computational models were formulated based on water balance to compute the soil infiltration capability from run-on water advance and rainwater ponding depth under the assumption that the soil infiltration capability of a soil follows a unique curve. Laboratory rain simulation experiments were arranged to demonstrate the whole procedure and to verify the feasibility and the models with the measured data. Two experimental Cases were arranged. One was a low rainfall intensity with no water ponding at the lower end of the flume. The other Case was for a higher rainfall intensity with both runon water advance and water ponding processes. The measured/computed infiltration capabilities indicated that the models well represent the transient processes of soil Infiltration capabilities. Analysis indicates that the error in estimated IR caused by the error in the measurement of advance distance is high at the beginning of run-on process and rapidly reduces to a very lower level. The overall accuracy as estimated by comparing the recovered infiltrated water and the precipitation was about 5%. The newly suggested

This paper is based on the work supported by the Major State Basic Research Development Projects of China (2002CB111502), Chinese Academy of Sciences (KZCX3-SW), and by Natural Sciences Foundation of Chins (50179035). Thanks to Mr B.J. Wang and Ms Y.C. Yuan from China Agricultural University Library for their services of the literature search.

References Bouwer, H., 1986. Intake rate: cylinder infiltrometer. In: Klute, A. (Ed.), Methods of Soil Analysis. Am. Soc. Agron, Madison, WI. [Monograph No. 9]. Brooks, K.N., Ffolliott, P.F., Gregersen, H.M., DeBano, L.F, 1997. Hydrology and the Management of Watersheds. Iowa State University Press, Ames. Helalia, A.M., Letey, J., Graham, R.C., 1988. Crust formation and clay migration effects on infiltration rate. Soil Sci. Soc. Am. J. 52, 251–255. Hillel, D., 1998. Environmental Soil Physics. Academic Press, New York. Jiang, D.S., 1997. Soil erosion and Control Models in the Loess Plateau. China Water Power Press, Beijing.

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