Soil preferential flow in the dark coniferous forest of Gongga Mountain based on the kinetic wave model with dispersion wave (KDW preferential flow model)

ACTA ECOLOGICA SINICA Volume 27, Issue 9, September 2007 Online English edition of the Chinese language journal Cite this article as: Acta Ecologica Sinica, 2007, 27(9), 3541−3555.

RESEARCH PAPER

Soil preferential flow in the dark coniferous forest of Gongga Mountain based on the kinetic wave model with dispersion wave (KDW preferential flow model) Niu Jianzhi*, Yu Xinxiao, Zhang Zhiqiang Key Laboratory of Soil and Water Conservation & Desertification Combating, Ministry of Education, Beijing Forestry University, Beijing 100083, China

Abstract: Based on the law of soil water movement in unsaturated zones, the study discusses the effect of preferential flow on the movement of the researched soil through a soil column experiment using homemade experimental apparatus in four successive stages—young, middle-aged, mature and over-mature and combining dye-tracer analyses of the field process. The study proves that the preferential flow occurs in the area, and as indicated by the Reynolds numerical calculation of the preferential flow path in the 4 different successive stages, the preferential flow in the Gongga Mountain forest ecosystem is a transition flow between the laminar flow and the turbulent flow. By applying the kinetic wave model with dispersion wave (KDW preferential flow model) and comparing this model with the field experiment, the study finds that the preferential flow model has good practicability and high credibility. Verifying the KDW preferential flow model through statistic analysis indicates that the model can simulate the water movement in columns very well and the results are better in low rainfall than in high rainfall. Key Words: dark coniferous forest of Gongga Mountain; soil water movement; Reynolds; dye-tracer analyses of the field process; KDW preferential flow model

Preferential flow, a term brought forth only in recent years, refers to a common phenomenon of soil water movement. Considerable studies have shown that preferential flow occurs where water infiltrates through the permeable areas in the soil[1–3]. Preferential flow is vitally interrelated to people’s life, production and ecological security. The solutes it carries can cause the pollution in both surface water and ground water[4], and influence indirectly the process of runoff yield and concentration. The study on preferential flow symbolizes that the study on the mechanism of soil water movement has progressed from the homogeneous field to the heterogeneous field. Many experts have formed their own perception of preferential flow based on their research[5–8]. At present, the soil preferential flow is commonly defined as a term describing the uneven flow under various circumstances[9]. Preferential flow comes in various forms, such as macropore flow[10–13], bypass flow, pipe flow[14–18], finger flow[19–22], funnel flow[23,24], channel flow, short circuiting flow, partial displacement, subsur-

face storm flow, gravity-driven unstable flow[25–36], heterogeneity-driven flow[37,38], oscillatory flow, depression-focused recharge[39–43], etc. Its transport is normally characterized as by-pass[44,45] and imbalance[46,47]. Preferential flow is a rapid but uneven soil water movement[1], which leads to the unaccountability of the speed, time and distance of the transport calculated by the Darcy Law in the traditional way. The inaccuracy of the prediction made by the model was set up under the presumption of the homogeneity and inadequacy of the convection-dispersion model for solute transport in depicting the water movement in the field. All these points require that the preferential flow model be established. Currently, models established for the study of preferential flow mainly focus on the process of tracer transport, while taking into account the purpose of the study, the depth of the fundamental process, the sensitivity and accuracy of simulation and the variability in the circumstances, etc. The quantitative study on the model largely relies upon statistical

Received date: 2007-01-22; Accepted date: 2007-07-19 *Corresponding author. E-mail: [email protected] Copyright © 2007, Ecological Society of China. Published by Elsevier BV. All rights reserved.

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approach and phenomenological approach. The statistical approach is a type of simulation by using stochastic models based on the probability theory, without analyzing the kinetics of water and solutes. It does not produce precise prediction but a rough range. Bresler and Jury once set up their models by using this approach[48,49]. The phenomenological approach establishes a definite mathematic model and reaches a solution by either analysis or numerical calculation. In practice, it requires that relevant parameters and auxiliary approaches be chosen in accordance with the purpose of the study and the condition. The model for preferential flow should be based on both the statistical approach and the phenomenological approach, combined with a comprehensive consideration of the features of the model itself, the approach of the simulation and the choice of parameters. Generally, models for the study on preferential flow and preferential transport can be categorized into the mechanism model, random model, determinate model and transmission model[50]. Coats and Smith initiated the establishment of the preferential flow model and the analysis of its mechanism by conceiving the mobile-immobile model, which categorizes soil into mobile and immobile sections. The movement of water and solutes mainly takes place in the mobile water section. Mobile water section and immobile water section realize matter exchange through the difference in concentration and thus participate in the movement of mobile water section[51]. The mobile-immobile model was later applied by van Genuchten and his co-researchers to the study of solute transport in the soil column and subsequently to the study of preferential flow[52,53]. Skopp developed the two flow domain models, based on the mobile and immobile concept. It consists of the soil matrix area and the macropore area. Water and solutes not only transport at a much higher speed in the latter than in the former but also flow from the matrix area to the macropore area[47]. Based on the Newton Law, Germann and Beven developed the two flow domain models into a non-linear, single-value functional equation between flow capacity and water content in the mobile section of soils. It has been further integrated with the continuity equation to form the kinetic wave model, which describes the rules for water flow under gravity action in the macropore area. It deduces that water flow in the matrix area of soil micropore is affected by the matrix potential, which is in line with the Darcy Law[54]. Jarvis advanced in 1991 a double domain model which includes the expansion and contraction of clay[55,56]. Jürg proposed in 1993 a two phase model[57]. Also in 1993 Gerke and van Genuchten put forward a new numerical double-pore model[58]. In essence, the aforementioned models illustrating the mechanism of preferential flow all divide soil into two sections, according to the features of preferential flow and matrix flow. The Darcy Law deals with the micropore in the matrix area while researchers have adopted different approaches for

the macropore water flow in the preferential area and therefore formed various simulations. The kinetic wave model is the most commonly used in the analysis of preferential flow[59,60]. However, through practice, people have discovered that the kinetic wave exclusively depicts a process of convection, regardless of other factors. Preferential flow, on the other hand, is a reflection of an uneven, unstable phenomenon taking place in an instantaneous fluid region. As fraction and gravity can not achieve a balance in a short time[61], it is possible that an unneglectable lag force of inertia time is needed to maintain the overall balance. In the meantime, capillary pressure and inertial force as well as resistance produced along the complicated path through the pores may occur, all of which can lead to the dispersion of flow in the drainage pore, if they achieve the climax effect in a large-scale process[62,63]. Consequently, the exclusive use of the kinetic wave model in the analysis of preferential flow can result in an overestimation of the preferential flow[64]. With time going by, considerable experiments and simulations have revealed that the inclusion of the dispersion factor in the kinetic wave model can effectively reduce the factor of kinetic wave and show the preferential flow better[63,65,66]. The analysis can be regarded as a revision of the pure convection kinetic wave model by the introduction of the dispersion factor. This paper aims at analyzing the preferential flow of the dark coniferous forest ecosystem in the upper area of Yangtze River, based on the kinetic wave model with dispersion wave (KDW preferential flow model) set up by Dr. Di Pietro[63] , while accommodating the characteristics of the studied area.

1

Study area

The study site is a primitive forest of Abies fabric with an elevation of 3000 m, situated in Hailuo Ravine, the eastern slope of Gongga Mountain, Sichuan Province, the upper area of Yangtze River, at 29°20′–30°20′ north latitude and 101°30′ –102°15′ east longitude. In terms of the geomorphologic location, it stands on the accumulated glacial lateral moraines formed on the left bank of the glacial valley and the eastern edges of the alluvial fan of glacier debris flow. Inside the area, with the influence of temperate valley glaciers and debris flow, there are two different soil types, namely, moraine soil pushed by glaciers and the soil of slope deposit lashed by debris flow. The research area mainly consists of Abies fabric and Populus purdomii. Generally, according to the succession process of Abies fabric, the research area can be divided into the young, mid-aged, mature and over-mature forest areas. The mature forest grew in the soil of slope deposit while the young, midaged and over-mature forests grew in moraine soil. Since it is easier to get a sample in the soil of slope deposit in the mature forest where zones of litters and moss are thicker, researchers conducted most of sampling analyses in the soil of slope deposit in the mature forest.

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The zones of soils at the study site are thin, containing a lot of pebbles, and moisture permeates quickly. There is virtually no surface runoff and soil erosions belong mainly to gravity erosion. The study site has a dry season (from Nov. to Apr.) and a rain season (from May to Oct.). Rainfall during the rain reason accounts for about 80% of the annual rainfall, most of which has a low intensity but lasts for a long time. 33.33% of field rainfall has an intensity of 1.0–1.5 mm/h, and only 24.24% of the field rainfall has an intensity of 1.5 mm/h. Rainfall with a low intensity will not cause any splashing effect on the soil, but will be beneficial for the creation of preferential flow along small openings in the soil or holes in plant roots. In the meantime, as long-lasting rainfalls continue, moisture and solutes it carries continue to move downwards along this path, paving the way for the phenomenon of the preferential flow to come into being.

2

Methods

2.1 Soil column experiment 2.1.1 Experiment devices Although very common, preferential flow is still hard to occur under general situation. The experiment device used in the paper was combined with the water supply device, artificial rain device, soil column device and catchment device. The water supply device consisted of an organic glass barrel with three holes and an ordinary plastic barrel. The organic glass barrel was placed above the rainfall generator with its lower hole for outflow of water, which led to the rainfall generator, its middle hole for inflow of water, provided by a water pump which worked continuously down to up, and its upper hole for overflow of water. In this way, a stable water surface was formed with a stable water head. Along with the control of a water gate, rainfall of certain stable amount could be obtained. The artificial rain device consisted of a rainfall generator and a flowmeter. The basic material of the rainfall generator was organic glass. Two concentric boards of different radiuses nipped a revolving cylinder up and down to create a hollow but closed environment. A small piece of board was placed on the revolving cylinder to distribute the flow, to reduce the impact of flowing water with a certain speed on the central hole on the lower board and to make the raindrop evenly distributed. There were several small holes distributed evenly on the lower board that were connected to the hard pipes with small diameter of aperture mounted with medical pinhead, which was useful for controlling the water head and making the rainfall produced by the rainfall generator evenly distributed and the diameter of artificial raindrops similar to that of natural raindrops. There was also a big central hole on the upper board with one pipe inserted to receive the external solution. The soil column device was made up of a stainless steel

tube with an exterior diameter of 159 mm, an interior diameter of 149 mm and a height of 650 mm. It looked like a big cutting ring, opening at two ends. It was blunt at one end altogether with a square-shaped board with a hole whose interior diameter was the same as the interior diameter of the cylinder and whose exterior diameter was wide enough with 4 holes at 4 angles for fixing wholly; it was sharp at the other end for getting undisturbed soil column. When establishing undisturbed soil column in the soil of slope deposit in the mature forest, the first step was to remove litters and moss from the upper soil layer. Then the next steps were to make the soil column vertical to the sampling place with the sharp end downside downwards, to hit the stainless steel tube into the soil with a depth of about 60 cm and then to take the soil column wholly out of the soil with sponges plugged into both ends for not dropping any soil out. After packed up with plastic adhesive tapes, it was taken back to the lab. In the lab, a filter layer was made in a way of cutting down a soil cylinder of 5 cm thickness at the bottom of the stainless steel tube. Then to place three kinds of sand-gravel with diameters of 5– 10 mm, 2–5 mm and under 2 mm, respectively, was placed at the bottom of the steel tube in sequence. A filter layer was constructed by using big-size gravel of 2 cm thick, medium-size gravel of 2 cm thick and small- size gravel of 1 cm thick. Finally, the filter layer was placed at the bottom of the steel tube upside down by using a stainless steel plate with 4 holes at 4 angles welded with an open thin pipe at the center; meanwhile, the quadrate board, stainless steel plate and cylinder were fixed firmly with 4 steel sticks and 8 screws. The 6 holes with a diameter of 25 mm opened on the steel tube wall of the undisturbed soil column were for installing tensiometers to measure and analyze the water changes in soil columns of different heights during the process of leaching. The distance between these six holes was 5.5 cm, and the distance between the lowest hole and the lower opening of the stainless steel tube was 7 cm. For the moraine soil in the young, mid-aged and over-mature forests, it was hard to collect undisturbed soil columns because of the thin soil layer and numerous gravels and stones. As a result, it was advisable to collect soil in different layers according to the laws of soil growth. After taken back to the lab, the soil was dried with sunshine and put into the stainless steel tube again with the large root system being wiped out. The concrete approaches were in the same way as getting the undisturbed soil column of slope deposit and then repacking soil column for simulating the moraine soil. The catchment device was one using several cone bottles with a volume of 200 ml to get water and to satisfy liquid needs for leaching and analysis. And it was also necessary to replace the cone bottles at given time internals. 2.1.2 Experiment materials The experiment materials were obtained from the soil of slope deposit in the mature forest of Abies fabric to make the

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

undisturbed column containing litters and moss, the undisturbed column containing no litters and moss and the undisturbed column made up of litters and moss as well as the repacked sieved soil column used for comparison analysis (each soil column must be obtained three times for repeated tests). 2.1.3 Experiment process The artificial rainfall densities were 0.22 mm/min, 0.5 mm/min and 1 mm/min, respectively, in the experiment simulating the natural preferential flow movement. With the above 3 rainfall densities, the clear water flowed stably and evenly from the soil surface into the soil column. The time of first flowing and the amount of outflow in a certain time period were needed to record strictly; the effect of litters and moss on the soil preferential flow in the research area were needed to study by recording the amount of outflow through the bottom of the soil column and the changes in the tensiometer during the experiment. The changes of matric potential in the soil column can be judged by using the tensiometer in the undisturbed soil column experiment and the repacked soil column experiment. The equation of soil water retention curve S = 10.07θ v−0.74 [67] can be used to calculate the changes in soil moisture during the whole process. 2.2 Field tracer experiment Flow paths and transport processes in soils can be further characterized by using different dye tracers. The soil in the Gongga Mountain area is yellow and a bit of red. According to the characteristics of the soil, the black Chinese ink was used as the tracer for reflecting the movement path of the tracer in the field. The soil sections were dug in 4 different places and the procedures were as follows: 1. First of all, the initial water content was measured on the testing day with TRIME (a portable time domain reflectometry) for estimating water quantities. 2. One tracer section of 1 m×1 m was dug out in 4 sampling places surrounded with galvanized iron sheet of 1 m×1 m and 30 cm in height to avoid side permeating. The black Chinese ink was sprayed evenly on the surface of the tracer section according to the estimated quantities. 3. The research area belonged to a moist climate, especially during the experiment period of May and June, and there was rainfall every night; therefore, the soil section was analyzed in the second day after the rainfall by opening the galvanized iron sheet and digging out the section layer by layer to observe the tracer route of the black Chinese ink. 2.3 Average diameter of the soil particles Sample soils from 8 survey plots in 4 survey patches of young, middle-aged, mature and over-mature forest were treated. The average diameter of the soil particles was calculated after drying and sifting[68].

3

Results and analysis

3.1 Proposal of the preferential flow problem After an overnight rainfall with a low intensity but long time, the obvious trace paths in the soil section from top to bottom is shown in Figs. 1, 2, 3 and 4. Though these image charts above do not quantitatively reflect the features of the process of soil moisture movement,

Fig. 1 Image chart of the tracer movement in the young forest

Fig. 2 Image chart of the tracer movement in the mid-aged forest

Fig. 3 Image chart of the tracer movement in the mature forest

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

Because of the unevenness of soil particles and soil pores on micro levels, solutes, while moving, usually enter into pore channels after being fractionized. These pore channels are different in size and shape, and are connected with each other. Suppose that these pore channels are pipe-like. Then the movement of water flow accords with the Poiseuille Law. The expression of Poiseuille Law is shown in Equ. (2): π r 4 ⎛ dp ⎞ π r 4 Δp Q = uπ r 2 = (2) ⎜− ⎟ = 8η ⎝ dz ⎠ 8η l

Fig. 4 Image chart of the tracer movement in the over-mature forest

they clearly show the path of soil moisture movement after the rainfall with a comparatively high dissolving power. The color of the path is obviously darker than that of other parts of the soil and the soil moisture moves downwards basically along one or several independent paths. Tracer moves downwards along this path, but by-passes other parts of the soil. The appearance of this sort of evident paths is one reflection of the phenomenon on the paths of the preferential flow of the tracer, and therefor shows the occurrences of the preferential flow in the 4 different succession forests in the Gongga Mountain. The tracer moves down along these several specified paths, indicating that the downward gravity action is the main force in the tracer movement. 3.2 Determining the occurrence of the preferential flow Normally, the Darcy Law is used in calculating the movement of soil moisture when Re is below 10. The appearance of the preferential flow leads to the inaccuracy of the speed, time and distance of the movement calculated by the Darcy Law in the traditional way. The range of Re in line with the preferential flow should exceed that in line with the Darcy Law. In the present paper, therefore, researchers take into a comprehensive account the limit of the application of the Darcy Law and the realities such as the large amount of pebbles in the study area. When the preferential flow was determined by using Re, Re > 10 was used as the research basis of the preferential flow because Re > 10 can not be used to calculate the soil moisture movement according to the Darcy Law. The equation to calculate Re is; Du Re = (1) v where u stands for the average current velocity (cm/s), D stands for the feature length (cm), and ν stands for the coefficient of kinetic viscosity (cm2/s). The calculation of Re in Equ. (1) mainly depends on the selection of the feature length. In this paper, feature length is represented with the average diameter of soil particles.

where Q stands for the volume of outflow per unit area in unit time (cm3/s); r stands for the radius of the soil pore tube (cm) (this paper uses half of the average diameter of soil particles to represent r; Δp stands for the difference of water potential; η is the coefficient of dynamic viscosity (g·cm/s); l stands, in this experiment, for the height of column (cm). We thereby get the average speed of the movement: r 2 Δp u= (3) 8η l The relationship between the coefficient of dynamic viscosity (η) and the coefficient of kinetic viscosity (ν) is as follows:

v=

η ρ

(4)

The coefficient of kinetic viscosity (ν) is related to the temperature, and can be calculated with the empirical Equ. (5); η 0.01775 v= = (5) ρ 1 + 0.0337t + 0.00022lt 2 where ρ stands for the density of water, and t stands for the temperature of the moisture in the soil. Researchers then take soil samples from different zones of soil at 8 different sites from young, mid-age, mature and over-mature forests, dry and sieve them, calculate the average diameter of the soil particles, and finally use Equs. (2) and (3) to calculate the average speed of the flow to get the result of Re (see Table 1). In 1981, Luxmoore pointed out his classification system of soil pores that were normally classified into 3 classes, namely, small, mid-sized and big. The corresponding ranges of pore diameters were <10 μm, 10–1000 μm, >1000 μm, respectively, and the latter two both referred to draining pores. This paper uses the diameter of soil particles to reflect the size of soil pores, from which we know that the soil pores in the 4 succession forests in the study area are all draining pores. Therefore, we can see from the classification of pores that the soil in the study area meets the requirements for soil pores to have the preferential flow. Re’s of the soil in different succession forests calculated by using Equ. (1) are all above 10. We thereby know that the phenomena of the preferential flow occur in the different succession forests. When calculating Re by using the average diameter of the soil particles to represent the feature length, we find that when

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

Table 1 Table of estimations and analyses of Re in the different succession forests in the study area Succession forest Young Mature Mid-age Over-mature

Soil type Moraine Slope Deposit Moraine Moraine

Number of sample sites

Average diameter of soil particles (mm)

Radius of pore tubes (mm)

Coefficient of kinetic viscosity (cm2/s)

Average speed of movement (cm/s)

B

0.6653

0.33265

0.0130601

10.37922

C

0.7021

0.35108

0.0134347

11.23878

D

0.6129

0.30647

0.012879

8.933436

53 59 43

E

0.5989

0.2994

0.0130601

G

0.7098

0.3549

0.0132453

H

0.7236

0.3618

0.0134347

11.93728

64

I

0.7257

0.3628

0.0134347

12.00434

65

J

0.7346

0.3673

0.0136285

12.12532

66

Re is below 10, the movement of soil moisture is laminar flow, and the Darcy Law is applicable at this time. Yet as Re increases, the effect of inertia increases as well, which results in a gradual appearance of turbulence. When Re is above 150– 300, the movement of soil moisture is mainly turbulent. Re’s in Table 1 are almost below 150, and we therefore come to the conclusion that the preferential flow in the coniferous forest of the upper reach area of Yangtze River is a transitional type between laminar flow and turbulence. 3.3 Soil water flow At the beginning of the soil column experiment, comparatively high rainfall intensity was produced to make the soil column saturated. It was observed that there was an immediate flow from the outlet with a time discrepancy between the inflow and the outflow that is almost undetectable. This swift outflow was a result of the preferential flow, which kept the soil column unsaturated. The soil particles in the researched area had a comparatively large diameter, which indicated large pores in the soil or large space between these pores. Shortly after the outflow occurred, the concentration in the outflow increased and approximated to that of the inflow. Therefore, there was a period when the concentration of the outflow undergone a great change, which was also a sign of the preferential flow. To give a focused analysis on the characteristics of preferential flow in the researched soil, a function between the accumulative outflow in the undisturbed soil column collected in the mature forest and the time was used to study water flow in the researched area (see Figs. 5 and 6). From Fig. 5, it is observed that with a rainfall intensity of 0.22 mm/min, there is an accumulative inflow of 3426.06 ml and an outflow of 3301 ml during the experiment. The inflow is almost the same as the outflow. With a rainfall intensity of 0.5 mm/min, there is an accumulative inflow of 7699.5 ml and an outflow of 4825 ml, and the latter accounts for 63% of the former. With a rainfall intensity of 1 mm/min, there is an accumulative inflow of 12963 ml and an outflow of 5319 ml, and the latter accounts for 41% of the former. From Fig. 6, it is observed that with a rainfall intensity of 0.22 mm/min, there is an accumulative inflow of 3426.06 ml and an outflow of 3253.5 ml, and the latter accounts for 95%

8.410818

Re

11.64894

39 62

of the former; the inflow is almost the same as the outflow. With a rainfall intensity of 0.5 mm/min, there is an accumulative inflow of 7699.5 ml and an outflow of 4704 ml, and the latter accounts for 61.1% of the former. With a rainfall intensity of 1 mm/min, there is an accumulative inflow of 12963 ml and an outflow of 5000 ml, and the latter accounts for 39% of the former. It can be told from Figs. 5 and 6 that with the increase in the rainfall intensity, the accumulative outflow in the undisturbed soil column collected form the mature forest increases correspondingly. The accumulative outflow in the undisturbed soil column is directly proportional to the rainfall intensity. More-

Fig. 5 Relative schematic graph of accumulative outflow and time in plot D of mature forests with different rainfall intensities

Fig. 6 Relative schematic graph of accumulative outflow and time in plot E of mature forests with different rainfall intensities

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

over, there is approximately a linear relation between the accumulative outflow and the time. As a result, during the outflow, the soil flow in the mature forest is influenced by either the matrix flow or the preferential flow. It has been analyzed through the Reynolds numerical calculation and field tracer experiment that preferential flow occurs throughout the experiment in the researched area. Thus, the interflow in the 4 successive phases in the researched area mainly takes in the form of preferential flow. Additionally, there are generally two types of pore structure in the soil, namely, connected and unconnected. There are also two types of soil section, namely, mobile and immobile. Mobile water section includes the matrix flow, which flows at a uniform speed, and the preferential flow which flows at a comparatively faster speed. It is the preferential flow that causes considerable difference in the flow speed at different survey spots where the water content is high. Preferential flow also leaves some water in the unconnected pores, isolating it from the convective transport of the solutes[69] . Under a rainfall intensity of 0.22 mm/min, the outflow almost equates with the inflow, which demonstrates that once the rainfall enters into the soil column, it directly flows out without being absorbed and leaves the soil column in an unsaturated state. This state results from the large pores in the soil. Under a rainfall intensity of 0.5 mm/min and 1 mm/min, respectively, there is fewer outflow than inflow, which indicates that a little water is retained in the soil column, enabling the soil to contain certain amount of water content. In this case, water is retained in the immobile area with unconnected pores. It is shown that preferential flow is the main path of soil water movement in the soil of slope deposit in the mature forest, while immobile area in the soil matrix reduces the effective exchange of flow area. 3.4 KDW preferential flow model 3.4.1 Introduction to the KDW preferential flow model The fundamental requirements for the model are listed as follows: 1. The micropores in the researched soil belong to the immobile water section and do not take part in the flow exchanges. The model is established mainly in the mobile water section; 2. The flow capacity is a function exclusively of the water content in the mobile area; 3. As mesopores also play a major role in the process, the term ‘draining porosity’ is used throughout the process, referring to those which have the potential to contribute to the preferential flow; 4. Gravitational force outplays the capillary force as the dominant force. It can be refurbished instantaneously by the fraction produced by the viscous effects; 5. The increase and decrease of any other forces are not to be considered in the system; 6. The water movement is a vertically downward process.

In order to meet the aforementioned basic requirements for the establishment of the model, it is supposed that w stands for water content in the mobile part of the soil profile volume V (where the draining pore flows through) and u stands for the volumetric flux of mobile water in volume V. wt = ∂w / ∂t is the first partial derivative of w with respect to time. Therefore, the continuity law for the flow of w may be expressed as Equ. (6), ∂w + ∇ ⋅u = 0 (6) ∂t Suppose that the volumetric water flux u is in a nonlinear functional relation with w and wt, which can be shown as: (7) u = u ( w, wt ) The equation for the spatial gradient of the flow capacity is: ∇ ⋅ u = c∇w + vw∇wt (8) where c =

∂u ∂u and vw = ∂w wt = constant ∂wt

w =constant

As the entire flow is a vertically downward movement, Equs. (6) and (7) can be written into Equs. (9) and (10), ∂w ∂u (9) + =0 ∂t ∂z ∂w ∂2w ∂u (10) =c + vw ∂z ∂z ∂z∂t Equs. (9) and (10) can be synthesized into Equ. (11), ∂w ∂2w ∂u (11) +c = −v w ∂t ∂z ∂z∂t If both sides of Equ. (11) are multiplied by ∂u ∂w , then according to ∂ 2 w ∂z∂t = − ∂ 2 u ∂z 2 , Equ. (11) can be represented by Equ. (12),

∂u ∂u ∂ 2u +c = vu 2 ∂t ∂z ∂z where vu = cv w .

(12)

Equs. (11) and (12) are nonlinear convection-dispersion equations for water content in the mobile area (w) and flow capacity, respectively. Thus, we know that the function between flow capacity and water content in the mobile area affects the hydrodynamic coefficient c, vu and vw. However, it does not change the composition of the entire differential equation. The two terms on the left of Equ. (12) stand for the whole time derivative of the flow capacity u(z,t) along plane (z,t) and the curve formed by slope c. These curves are called the feature lines of different equations. Because c=dz/dt, The two terms on the left of Equ. (12) can be replaced by Equ. (13). du ∂u dz ∂u = + (13) dt ∂t dt ∂z When v=0, Equ. (12) can be put as: du ∂u ∂u = + c ( w) = 0 (14) dt ∂t ∂z

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

It can be seen from Equ. (14) that flow capacity u(z,t) is a constant and remains invariant along the feature curve. It is the kinetic wave model, which has been widely applied to the establishment of the water resource models. The initial value of u(z,t) can be written as follows: u = f ( z) , t=0, −∞ < z < ∞ (15) When solving Equ. (14), Germann put forward the following relevant initial and boundary conditions: u ( z, t ) = u in (t ) , z = 0 , t > 0

(16) z > 0, t = 0 u (z, t ) = u 0 , In Equ. (16), uin(t) represents the inflow volume within a free boundary (z=0), and a continuous time period ts with a volume flow density us . Germann put the basic relationship between the flow capacity and the kinetic wave of water content in the mobile area into the equation u=bwa in which a and b are both positive coefficients. Equ. (14) describes the process in which the path of non-dispersion transport wave moves forward with velocity c(w) along the feature curve. If f(z) is a descending power function of z, the phenomenon can occur that the fast wave keeps advancing and overwhelms the slow wave, propelling the wave of oscillation forward. However, through considerable practical studies it has been discovered that the feature curve is a line related to two waves of oscillation, which move forward but do not spread. One of the two is the wetting front when t=0, with the surface applied flow capacity us. The other is the draining front at t=ts when the inflow stops and the surface inflow is dwindled to 0. Moreover, when the draining front transports at a faster speed than the wetting front does, the former disturbs the latter. Flow capacity u(z,t) becomes the mono-peak function of time. Water content at the peak begins to decrease, which indicates that the hysteretic phenomenon appears, and heralds that at depth z=L, both the wetting and draining fronts will occur. The time at which it reaches the wetting front and the draining front, respectively, can be represented as ∇t1 = L / cw and ∇t2 = L / cd , in which velocity cw and cd stand for the signal speed related to us and u=0, respectively. In the area of (z,t), the effect of the signal speed is continuously expanded, which shows that it is inaccurate to use the approximate value of the kinetic wave. When vu≠0, the second-order function on the right of Equ. (12) illustrates the dispersion phenomenon. If Equ. (13) is introduced to Equ. (12), flow capacity u is no longer a constant on each of the feature curve. Its changing rate is shown as in Equ. (17), indicating that u is relevant to vu and the spatial variation of the gradient of the flux. du ∂ 2u = vu 2 (17) dt ∂z It is known through a large number of experiments and analyses that the free boundary (front or interface) for the nonlinear convection-dispersion equation is equivalent to that

for the kinetic-dispersion equation. Therefore, the functional relation represented in Equ. (7) can be put into Equ. (18), (18) u = f (w) + g (wt ) In the equation, f ( w) = bwa , g ( wt ) = −vw (∂w / ∂t ) , a, b and vw are all positive, and are usually constant. Equ. (18) is often used to simulate and analyze infiltration-drainage experiment on the soil column. The u(w) curve attained has a hysteresis effect. As for a given value of w, a value of u can be calculated, which is usually much smaller in the infiltration area than in the drainage area. For the sake of analysis, it is usually hypothesized that in the transient period of infiltration and drainage, there is an internal force which maintains the overall balance of the rise and fall of the linear factors. This internal force is directly proportional to the increase or decrease of the water content. Moreover, it is zero during the stable stage. Correction term g(wt) is proportional to the first temporal derivative of the water content. The term g(wt) has a negative value during the infiltration period (when the value of w increases), has a value of zero during the stable stage (when w is a constant), and has a positive value during the drainage period (when the value of w decreases). Lighthill and Whitman proposed that the area between the ascending curve and the descending curve could be used to correct dispersion by estimation when a flux density relation like u(w) showed hysteresis[74]. In Equ. (18), the value of signal speed c can be decided by: ∂u c( w) = wt = cte = nwn (19) ∂w where n=a–1, m=ab. Therefore, the equation for vu is as follows: vu = cvw = mwnvw (20) Under this hypothesized condition, without taking g(wt) into consideration, c is similar to the approximation value of the first-order kinetic approximation as Germann has depicted[59,75]. Introducing w=(u/b)1/a into Equs. (12), (18) and (19) leads to: ∂u ∂u ∂ 2u (21) + pu q = v w pu q 2 ∂t ∂z ∂z where (22) p = ab1 a , q = a − 1 . a

The numerical solution for Equ. (21) that meets the initial and boundary conditions given by Equ. (16) can be obtained by means of explicit finite difference schemes. The time derivative can be estimated by the forward difference during the jth time period, while the spatial derivative by the central difference during the same time period. Therefore, Equ. (21) can be restated as: τv τ u ij +1 = u ij + 2w c(u ) u ij+1 − 2u ij + u ij−1 − c(u ) u ij+1 − u ij−1 2h h (23)

(

)

(

)

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

where the subscript i represents the space discretization and the superscript j represents the time discretization; h stands for the space interval; τ stands for the time step; c(u) stands for the faster speed during convection, and is in functional relation with u; the relation between h and τ has to meet the stability requirement in Equ. (24). The stability condition is to facilitate equation u=uS. 2

⎛⎛τ ⎞ ⎞ τ vw ⎜ ⎜ ⎟ c ( u ) ⎟ ≤ 2 2 c (u ) ≤1 h ⎝⎝ h ⎠ ⎠

(24)

According to Equ. (19), the relation between c and u can be written as: ab (25) c = (a −1) a u ( a −1) a b As u is closely related to time and space, the transport process studied in this paper should be considered in the scope of each time step and space interval. When the input signal is intermittent or when u=0, the speedy disappearance, and the time step and space interval needed for the calculation of c are all imperative. It can achieve better transmission of signal input through space. Generally, better result can be achieved at

u ij−+00.5.5 . The equation for the calculation of c is: c=

ab ⎛ u ij + u ij−+11 ⎞ ⎜ ⎟⎟ 2 b (a −1) a ⎜⎝ ⎠

( a −1) a

(26)

See Fig. 7 for the frame of the preferential flow model. 3.4.2 Parameters in the KDW preferential flow model It is known from Equ. (21) that the model is mainly represented by 3 parameters, namely, p, q and v(w), which are obtainable through the experiment of u(w) relation. The values of p and q are related to the marking speed of first-order kinetics, and can be calculated indirectly from the values of a and b in Equ. (18). In the equation of u(w), the value of u can be obtained by the outflow capacity from the soil column, while the value of w can be decided by putting the reading of tensiometer into S = 10.07θ v−0.74 , the equation of soil water retention curve. Throughout the infiltration-drainage soil

column experiment, u is in some functional relation to w. u(w), the approximate value of u for the first-order kinetics, is a single-valued function of w, u(w) = f(w) = bwa. In the undisturbed soil column experiment in the mature forest, there is only minor change on the tensiometer after the outflow occurs, which results from the minor change in the water content of the soil column. Under the rainfall intensities of 0.22 mm/min, 0.5 mm/min and 1 mm/min, the function between the change of flux in the soil column and that in the water content can be delineated by setting the ratio of the outflow and inflow capacities in the soil of slope deposit in the mature forest as the ordinate, and the soil moisture as the abscissa (see Fig. 8). The value of parameters a, b and v(w) can be determined by Fig. 8 and Equ. (18). The values of parameters p and q can be calculated through Equ. (22). Parameters for the model can be seen from Table 2. 3.4.3 Evaluation and analysis of the KDW preferential flow model The parameters for the model come from the calculation of plot D in the soil of slope deposit in the mature forest, which are tested and evaluated by plot E. This method is called alternative simulation. The establishment of the model concerns the relation between water flux and time as well as between water flux and displacement. In the soil column experiment, the distance of water flow transport in the soil column is a constant. Therefore a functional graph can be built up between water flux and transport time. The results of the experiment and simulation are compared and analyzed to test the applicability of the model. It can be observed from Fig. 9 that the KDW preferential flow model is capable of simulating measured data in the field

Fig. 8 Schematic graph of the function of flux and soil moisture in plot D of the mature forest Table 2 Estimated parameters for KDW Rainfall intensity (mm/min)

Fig. 7 Frame of KDW preferential flow model

a

b (mm/min)

v(w) (mm)

p

q

0.22

2.09

0.78

83

1.176067

0.521531

0.5

2.17

1.89

82

0.501823

0.539171

1

2.92

4.78

75

0.017412

0.657534

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

process. It usually requires the statistical fitting equation to test the applicability of the model. See Equ. (27) for the statistical method.

∑ (P − Q ) ∑ (Q − Q ) N

EF = 1 −

i =1 N

i =1

i

2

(27)

i

2

i

where Pi stands for the predicted value for the flow capacity, Qi stands for the measured flow capacity, and Q is the average of the measured flow capacity. The statistics theory holds that when the value of EF is 1, the ideal value is achieved. The closer the EF value is to 1, the more ideal the result is. Table 3 is about the statistical value of water flux at

Fig. 9 Schematic graph of stimulation analyses in measured and predicted value for the 3 rainfall intensities of (1) 0.22 mm/min; (2) 0.5 mm/min,(3) 1 mm/min Table 3 Simulation analyses of water flux at plot E of the mature forest Plot E of the mature forest

EF

0.22 m/min

0.5 m/min

1 mm/min

0.921

0.896

0.834

0.95

0.887

0.845

0.943

0.904

0.856

plot E in the soil of slope deposit in the mature forest. As indicated by Table 3, under the 3 rainfall intensities, an alternative simulation has proven that the KDW preferential flow model has successfully fulfilled the simulation. Meanwhile, it is discovered that results are better in low rainfall than in high rainfall.

4

Conclusions and suggestions

This study conducts indoor soil column experiment by using homemade experimental apparatus, and combines with dye-tracer analyses of the field process. The study applies the kinetic wave model with dispersion wave (KDW preferential flow model) to the analysis of preferential flow in the ecosystem of the dark coniferous forest in Gongga Mountain in the upper area of Yangtze River. The conclusions and suggestions are summarized as follows: As judged by the dye-tracer experiment of the field process and indicated by the Reynolds numerical calculation, preferential flow occurs in the 4 different successive stages in the ecosystem of the dark coniferous forest in Gongga Mountain in the upper area of Yangtze River. With the increase in the intensity of rainfall and the advancement of time, the accumulative outflow in the undisturbed soil column in the mature forest increases gradually. The accumulative outflow in the undisturbed soil column varies directly with the rainfall intensity and the transport time, which indicates that the preferential flow is the dominant representation of the soil moisture movement in the 4 successive stages of the researched area. However, in the matrix area of soils, the preferential flow is represented as the immobile area. As preferential flow is the main path of soil moisture transport in the studied area, the commonly used kinetic wave model can not adequately exhibit the case. It is necessary that relevant factors such as dispersion are introduced. Therefore, this paper adopts a kinetic wave model with dispersion wave (KDW preferential flow model) and applies it to the soil column experiment in the soil of slope deposit in the mature forest. The simulation suggests that the KDW preferential flow model can effectively simulate the water movement in the soil column. The parameters of the model are calculated by an alternative simulation. The alternative test has proven the high practicability and credibility of the preferential flow model. Meanwhile, this study has corroborated by statistical means that the statistical data obtained contribute to the practicability of the preferential flow model. Moreover, results are better in low rainfall than in high rainfall. The KDW preferential flow model characterizes preferential flow as the result of the two waves of oscillation: the dispersion wave and the kinetic wave, among which the latter plays a dominant role. Preferential flow is the rapid but uneven movement produced by the traction of the two waves, combined with the hysteretic phenomenon.

NIU Jianzhi et al. / Acta Ecologica Sinica, 2007, 27(9): 3541–3555

In the study, we have observed from the mapping of the field tracer experiment that soil moisture moves downwards along one or a few apparently preferential pipe-like paths. It has thus been suggested that the preferential flow in the studied area is an uneven, pipe-like flow. In future studies, it is recommended that preferential flow in the forest ecosystem of Gongga Mountain should be examined through the pipe hydraulic equation and whether it is featured pipe-like should also be decided.

Acknowledgements The project was financially supported by National Natural Science Foundation of China(No. 30471379), The Research Fund for the Doctoral Program of Higher Education (No. 20060022002 ) and the State Key Project of Fundamental Research (973) (No. 2002CB111502).

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