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Published in Vadose Zone Journal 3:1017-1030 (2004)
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

ORIGINAL RESEARCH

Three-Dimensional Modeling of Hydrotropism Effects on Plant Root Architecture along a Hillslope

Daizo Tsutsumia,*, Ken'ichiro Kosugib and Takahisa Mizuyamab

a Div. of Fluvial and Marine Disaster, Disaster Prevention Research Institute, Kyoto Univ., Gokasyo, Uji, Kyoto 611-0011, Japan
b Div. of Forest Science, Graduate School of Agriculture, Kyoto Univ., Oiwakecyo, Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan
* Corresponding author (tsutsumi{at}sabom.dpri.kyoto-u.ac.jp)

Received 30 July 2003.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 MODEL DESCRIPTION
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
A three-dimensional model of root system development and soil water flow is described and applied to actual conditions along a hillslope. In the model, gravitropism, hydrotropism, and circumnutation were employed as the main factors controlling root elongation. Root systems of 2-yr-old pine trees (Pinus massoniana Lamb.) on natural slopes in southern China were excavated and examined, and their development was simulated through the use of continuously monitored temperature and rainfall data. In the simulated root systems, angles between first-order lateral root segments and the vertical direction on the upslope portion of a tree were larger than those on the downslope portion of the tree; hence, root systems exhibited asymmetric architectures. This asymmetry was more obvious for root systems developed on the downslope side of the hillslope. Because root systems simulated without the effect of hydrotropism did not develop asymmetric architectures, the direction of soil water flux and the effect of hydrotropism appear to be the main factors contributing to the observed architectural asymmetry, typical of root systems along hillslopes. Calculations with the proposed root system model were helpful in elucidating and understanding the predominant processes affecting root system development on hillslopes.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 MODEL DESCRIPTION
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
THE POTENTIAL CONTRIBUTION of plant root systems to slope stability is of interest in several areas of research, including erosion control and development of improved revegetation technology. Some studies suggest that plant root systems contribute to the stability of otherwise unstable hillslopes by increasing soil resistance against shear stress and decreasing the soil water content via transpiration (Greenway, 1987; Tsukamoto, 1987). These effects of root systems have been investigated extensively by considering root strength, growth, and rate of decay (Abe, 1996; Kato and Syuin, 2001; Sidle, 1991; Syuin, 1998; Syuin et al., 1998; Tsukamoto, 1987; Watson et al., 1999). As such modeling root system development and soil water flow on hillslopes may enhance our knowledge of the effects of root systems on slope stability, including the mechanisms of development, morphological architecture, and physiological functions of root systems. Numerous models have been developed that simulate root system development for various plant species and environmental conditions (Clausnitzer and Hopmans, 1994; Diggle, 1988; Doussan et al., 1998; Dunbabin et al., 2002a, 2002b; Jourdan and Rey, 1997; Lynch et al., 1997; Pages et al., 1989; Somma et al., 1998; Shibusawa, 1994). However, all of these models have been developed for planar surfaces; none are for hillslopes.

Several studies have shown that plants growing along slopes have asymmetric root systems (e.g., Scippa et al., 2001; Yamadera, 1990). To simulate root systems on slopes, it is necessary to understand the mechanisms of root growth as well as to consider the effects of slope on root growth. The influence of gravity on root elongation, or gravitropism (i.e., root elongation in the direction of gravity), has been studied extensively (e.g., Ishikawa et al., 1991; Kiss, 2000) and was used as a factor controlling root growth in all previous models (Fig. 1a) . The effect of soil mechanical resistance has also been incorporated in models (Clausnitzer and Hopmans, 1994; Diggle, 1988; Pages et al., 1989; Shibusawa, 1994), as has the influence of soil water and nutrient flow (Clausnitzer and Hopmans, 1994; Dunbabin et al., 2002a, 2002b; Somma et al., 1998). Among these factors, tropism induced by soil mechanical resistance (directional changes of roots that encounter compacted soil) is a possible cause of the asymmetric development of root systems in sloping soil profiles where soil density increases with depth (Fig. 1d). However, it is unlikely that roots can detect gradients of soil mechanical resistance at the root tip since differences in soil density may be too small. Therefore, although a root might alter its elongation rate according to changing soil mechanical resistance, the root doesn't necessarily change its growth direction toward lower soil mechanical resistance. However, when the mechanical resistance changes suddenly at a boundary, then it is plausible that a root will abruptly change its direction (thigmotropism, as shown schematically in Fig. 1c; Darwin, 1880).



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  		Fig. 1. Schematic of possible environmental effects on root elongation: (a) tropism of gravity (gravitropism), (b) tropism of soil water (hydrotropism), (c) deflection by an obstacle (thigmotropism), and (d) tropism of soil mechanical resistance.

 
Moreover, a recent study indicated that the asymmetrical architecture of root systems on steep slopes increases the plant's stability by modifying the distribution of mechanical forces within the soil; considerable anatomical modifications in the shape and tissue organization of lateral roots on slopes support this hypothesis (Chiatante et al., 2002). However, the mechanism of asymmetric root elongation along a slope has not been adequately explained. Experimental studies (Takahashi, 1994; Takahashi and Scott, 1993; Takano et al., 1995) showed that root growth is influenced by hydrotropism (i.e., root elongation toward increasing water content), as shown schematically in Fig. 1b. Because soil water flows from upslope to downslope by gravity, root hydrotropism can be another factor that influences asymmetric root system development along hillslopes. The same question as encountered with mechanical resistance then arises. That is, can a root detect a soil water potential or water content gradient? The answer may again be no. However, for hydrotropism, roots may detect the direction of water flow, even if the root tip is a point, and change direction toward the wetter direction. An experimental study by Miyamoto et al. (2002) showed that when agar blocks with different water potentials were unilaterally applied directly to a root tip, the root showed differential growth bending toward the agar with the higher water potential. During the experiment, changes in the water potential of the agar blocks were measured. Results indicated that water flowed from the agar with the higher water potential to that with the lower water potential via the root tip. Although details of the mechanisms of a root detecting water flow through the root tip are not understood, directional changes of the root as a result of the root tip sensing water flow could be a possible mechanism of hydrotropism. Moreover, the experimental results of Miyamoto et al. (2002) implied that hydrotropism depends on water flux rate through the root tip. Clausnitzer and Hopmans (1994) implicitly considered the root's hydrotropic effect. Their study assumed that roots respond to a soil strength gradient as determined by soil moisture content changes. However, no model has been proposed that explicitly considers root hydrotropism.

In a previous study, Tsutsumi et al. (2003) proposed a two-dimensional model for root system development and water extraction that included gravitropism, and they incorporated hydrotropism using the differential growth method. Findings suggested that hydrotropism plays an important role in root system development, both on a plane and along a slope. In another study, Tsutsumi et al. (2002) modeled root hydrotropism in a two-dimensional root box experiment; results confirmed that root hydrotropism is a dominant factor in the establishment of soybean [Glycine max (L.) Merr.] root systems. However, a plant root system develops spatially in three dimensions. Therefore, to simulate the actual plant root system development on natural slopes, it is necessary to extend the model to three dimensions. In this study we propose a three-dimensional model of root system development and soil water flow that simulates plant root system development and soil water flow along a slope. In this model, gravitropism and hydrotropism together with circumnutation (i.e., the regular, helical growth of plant organs such as shoots, roots, and tendrils along a preferred growth direction, as investigated by Darwin (1880)) are employed as the main factors influencing root elongation rate and direction. Root circumnutation was demonstrated experimentally (Shimotashiro et al., 1998a, 1998b; Hirota, 2001) and is thought to be an important factor in determining root elongation direction as well as root tropisms (Inoue et al., 1993; Johnsson, 1997).

Before model simulations, actual plant root systems were excavated from natural hillslopes and examined for their architecture and morphology (i.e., elongation rate, maximum branching order, and branching intervals). The study was conducted in an experimental field in southern China where temperature and rainfall intensity have been monitored continuously. In addition to root system data, soil samples were taken to measure soil hydraulic properties, as used in the model simulation. The observed root systems were simulated and model results were compared with the observed root systems to examine model assumptions that root development is controlled mainly by gravitropism, hydrotropism, and circumnutation. The most important objective of this study is to clarify whether the effect of root hydrotropism can account for the asymmetric development of root systems on a slope.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
MODEL DESCRIPTION
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Root system observations and measurements were conducted in the Dahou experimental field located in JianXi Province, China (115° 28' E, 26° 30' N). The thin soils formed on weathered granite are heavily eroded. Vegetation is relatively poor (0.5 trees m–2; average tree height = 1.58 m), with pine as the dominant species in area close to the ridge. The mean annual precipitation from 1994 to 2000 was 1875 mm. The mean air temperature was 17.5°C, with the highest monthly mean temperature (27.8°C) in August and the lowest (5.9°C) in January. Altitude of the site ranges from 340 to 420 m, with slope gradients ranging from 15 to 40° (Kimoto et al., 2002). For such bare slope conditions, plant root systems play an important role in limiting erosion and landslides.

The model root simulation was conducted with two necessary limitations. First, root decay was not considered. Second, tree age was restricted to 2 yr or less, since the simulation of older tree root systems drastically increased computation time. Because of these limitations, two 2-yr-old pine trees located close to the ridge of two slopes (Slopes 1 and 2) were selected for observation. The geographical characteristics of the slopes are given in Table 1. The root systems were excavated and soil around the root systems carefully removed so as not to disturb the root system architecture. Photos of the bare root systems were taken. Characteristics of the root architecture (i.e., branching intervals, root lengths by root branching order, and maximum branching order) were measured. Characteristics of the root architecture and plants are listed in Table 2. Undisturbed soils were sampled at the surface (0.0–5.0 cm depth for both hillslopes) and bottom (12.0–17.0 cm depth for Slope 1, and 40.0–45.0 cm depth for Slope 2) of the soil profile to obtain soil hydrological characteristics. The corresponding fitted soil water retention curves are shown in Fig. 2 , whereas the soil unsaturated hydraulic conductivity function was defined using the lognormal model proposed by Kosugi (1996).


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  		Table 1. Characteristics of Slopes 1 and 2.

 

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  		Table 2. Root system and plant characteristics.

 


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  		Fig. 2. Soil hydraulic properties for the soils of Slopes 1 and 2. The equations in the figures represent the lognormal model, where the function Q represents the complementary cumulative distribution function.

 

   MODEL DESCRIPTION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 MODEL DESCRIPTION
RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Root Elongation (Differential Growth Method)
As in the two-dimensional root elongation model of Tsutsumi et al. (2003), three-dimensional root tropism is simulated by using differences in the maximum and minimum elongation rates, ERmax and ERmin (cm s–1), at elongation points P1 and P2, located on opposite sides of the root (Fig. 3) . The three-dimensional root elongation model differs from its two-dimensional equivalent in that it is necessary to determine the maximum and minimum (ERmax, ERmin) of the elongation rate ER around an individual root cross-section. Once the elongation rates ERmax and ERmin are determined, the behavior of root tropism can be obtained in the same way as in the two-dimensional model. Here, the radius r (cm) and the angle {alpha} (rad) for time period {Delta}t (s) were obtained using

[1]

[2]
where d (cm) is the diameter of the root at the elongation point. The elongation rate at the center of the root, ERc, was obtained from

[3]



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  		Fig. 3. Schematic showing the differential growth of three-dimensional root elongation of a root segment. The root elongation rate has a minimum (ERmin) and maximum (ERmax) at points P1 and P2, respectively.

 
From Fig. 3 and Eq. [1], [2], and [3], tropism can be represented by the elongation rates ER at each of the elongation points. To determine root elongation, it is necessary to describe the elongation rate as a function of all tropism factors. Because gravitropism, hydrotropism, and circumnutation are considered, the elongation rate functions of gravitropism, hydrotropism, and circumnutation are written as ERg, ERh, and ERn, respectively, and the composite elongation rate for the root cross-section ER is written as

[4]

To extend the model into three-dimensional form, ER was expressed as

[5]
where ß (rad) is the angle around the root cross-sectional circle from the top point of the circle. When ß = ßs, ER has a maximum value of ERmax (Fig. 3). Therefore, when ß = ßs + {pi}, ER has a minimum value of ERmin. The elongation rate of each tropism factor around the root cross-section ERi (i = g, h, n) is expressed by an equation similar to Eq. [5];

[6]

When ß = ßi and ßi + {pi}, ERi has a maximum value of ERi,max and a minimum value of ERi,min. In Eq. [4] through [6], ßs, ERmax, and ERmin were obtained as follows:

[7]

[8]

[9a]

[9b]
where

[10]

[11]

[12]

From these values of ßs, ERmax, and ERmin, the three-dimensional trajectory of the root tip can be obtained in a similar fashion as in the two-dimensional model (Tsutsumi et al., 2003). The next step is to define the elongation rate function of each factor ERi (i.e., gravitropism, hydrotropism, and circumnutation).

The maximum and minimum elongation rate functions of gravitropism are defined as follows:

[13a]

[13b]

[14a]

[14b]

[15]
where {gamma} (rad) is the angle between the direction of gravity and the root's orientation, ERg,0 presents the value of the gravitropic elongation rate when the root is directed toward gravity ({gamma} = 0), and {Delta}ERg is the coefficient that determines the intensity of gravitropism.

The minimum and maximum elongation rates of hydrotropism for the wet end and dry end of the root were defined as Wet end:

[16]

Dry end:

[17]

[18]
where |q'| (cm s–1) is the magnitude of the component of water flux q (cm s–1), perpendicular to the root at the root tip, and ERh,0 denotes the value of the hydrotropic elongation rate when |q'| = 0, ßh(q') is the angle between the direction of gravity and the flux q' in the root cross-sectional circle. The coefficient kh determines the intensity of hydrotropism and is assumed to increase with decreasing soil water potential {psi} (cm) at the root tip as

[19]
where ah (>0) and bh (>0) (cm–1) are constants.

There are two main types of models describing plant circumnutation: (i) an "internal oscillator model" in which gravity does not influence the generation of circumnutations and (ii) a "gravitropic overshoot model" in which the gravitropic reactions strongly affect circumnutation (Johnsson, 1997; Lubkin, 1994). Because gravity effects are already included as a separate tropism, the internal oscillator model was employed in our study to describe the pattern of a ring structure within a transverse section of the circumnutating plant as a rotating wave pattern:

[20a]

[20b]

[21]
where ERn,0 is the elongation rate of circumnutation when the intensity of circumnutation is zero, {Delta}ERn is the intensity of circumnutation, and {omega}n (rad s–1) is the angular velocity of circumnutation. Because ERn is a function of time only, the circumnutation movement is independent of the surrounding environment, even though gravitropism and hydrotropism depend on gravity and soil water flow, respectively.

From the definitions of root elongation rate using Eq. [13] to [21], the elongation rate at the center of the root (Eq. [3]), is redefined as

[22]

According to Eq. [22], the elongation rate at the center of the root does not vary with values of {Delta}ERg, kh, and {Delta}ERn. Therefore, the value of ERc is evaluated and used in the model simulations, instead of using independent values for ERg,0, ERh,0, and ERn,0.

In addition to the differential growth of roots by the various tropisms, the elongation behavior of roots is influenced by obstacles (e.g., Fig. 1c). If the calculated coordinate of the center of a root tip reaches an impermeable boundary, the root tip is redirected to a point that is d/2 away from the boundary (Fig. 4) , with root growth over {Delta}t equal to that of the unimpeded case (i.e., l2 = l1).



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  		Fig. 4. Elongation behavior of a root that is forced to change its direction because of an obstacle.

 
Root Branching
Root branching is as important as root elongation in root system development. According to root classification systems (e.g., Hackett and Rose, 1972), 2-yr-old pine trees have a main root system with only second-order lateral roots. For simplicity we assumed a constant branching interval. Therefore, the combination of this constant branching interval and the elongation rate controls the emergence of lateral roots. We also assumed that the branching direction is not affected by the surrounding environment (i.e., the lateral roots branch in all directions uniformly). Details of the branching parameters are according to Pages et al. (1989). Figure 5a shows the assumed behavior of root branching; I (cm) in this figure is the branching interval, Lb (cm) the basal nonbranched zone, La (cm) the apical nonbranching zone, and {phi}i the angle between a parent root and lateral roots. The direction and order of lateral root branching around a parent root are shown in Fig. 5b, where N is the branching order number. When N becomes more than 7, the branching directions slip 30° from those of N = 1 to 6.



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  		Fig. 5. Branching model showing (a) the branching interval and angle and (b) branching direction and order around a parent root (N is the branching order number).

 
Soil Water Flow
To combine root system development with root soil water extraction and soil water flow (Eq. [16] and [17]) in the hillslope, variably saturated flow was numerically simulated according to the three-dimensional Richards' equation:

[23]
where z (cm) is the vertical coordinate (positive upwards), t (s) is time, Cp({psi}) (cm–1) is the soil water capacity, and K({psi}) (cm s–1) is the hydraulic conductivity. To represent Cp({psi}) and K({psi}), the lognormal model proposed by Kosugi (1996) was employed. S (s–1) in Eq. [23] denotes the water extraction intensity by the root system. Equation [23] was solved numerically by the finite element method (Zienkiewicz, 1971; Istoke, 1989).

Boundary and Initial Conditions
The potential evapotranspiration rate Et (cm d–1) was estimated by means of an empirical method proposed by Thornthwaite (1948), using measured temperatures. Et was divided into potential evaporation Ep (cm d–1) and potential transpiration Tp (cm d–1) using the ratio RE (Ep/Et; RE = 0.75 in the simulation, assuming a 0.3-m2 area for each 2-yr-old plant). Because the potential transpiration rate changes with plant growth, Tp was multiplied by a linearly increasing function of time rT(t):

[24]
where tmax (s) is the maximum calculation time that corresponds to the plant growth period. Values for Ep and Tp were modified into daily changing values of potential evaporation E'p (cm s–1) and transpiration T'p (cm s–1) according to sine curves, in a method similar to that proposed by Tsutsumi et al. (2003).

Actual evaporation Ea was calculated from

[25]
where Ea({theta}) is an evaporation reduction factor as a function of water content {theta} (cm3 cm–3) near the soil surface, defined as follows:

[26a]

[26b]

[26c]
where {theta}1 and {theta}2 are the threshold values of the soil water content. In our study {theta}1 was assumed equal to 0.20 and {theta}2 was set equal to the residual soil water content {theta}r. Potential transpiration T'p (cm s–1) was partitioned between finite elements, with the potential water extraction intensity Sp (s–1) for each finite element, Sp,n (s–1) proportional to the root length density L (cm cm–3) or

[27]
where Cs (cm2 s–1) is a coefficient, and L was calculated as the root length within the element divided by the volume of the element. Because soil water is more actively extracted by younger than by older roots (Varney and Canny, 1993), root lengths of the main and first-order lateral roots older than 90 d were assumed to not absorb water and were excluded from L. Using the observed average elongation rate (0.055 cm d–1), the length of the apical portion of first-order lateral roots that absorb water was estimated to be 4.95 cm, which was approximately equal to the observed apical nonbranching zone (4.52 cm in Slope 1, 6.38 cm in Slope 2, Table 2). The time-dependent potential transpiration T'p was related to Sp,n by

[28]
where Vn (cm3) is the volume of finite element n, and A (cm2) is the total surface area of the considered soil domain. Substitution of Eq. [27] into Eq. [28] gives the value for Cs:

[29]

Therefore, the potential water extraction intensity for each element Sp,n is given by

[30]

To estimate the actual water extraction intensity Sa (s–1), the model of Feddes et al. (1978) was adopted:

[31]
where {psi} is the soil water potential at the root surface as obtained by averaging the {psi} values at the four nodes of each element, and {alpha}T({psi}) is the reduction factor for root water extraction, represented as

[32a]

[32b]

[32c]

[32d]

For the model simulations, values of {psi}1 = –30, {psi}2 = –500, {psi}3 = –20000 cm were assumed, according to Feddes et al. (1978).

Daily measured rainfall intensity data were used. During rainfall, evaporation and transpiration were assumed to be zero. Figure 6 shows changes in the temperature, the estimated potential evaporation Ep, the potential transpiration Tp, and the rainfall rates during the total simulation period (April 2000–March 2002). No-flux boundary conditions for the bottom, upslope end, and side boundaries of the sloping soil domain were imposed. The water potential values of nodes at the downstream end boundary were assumed to be equal to their corresponding values at the adjacent upper nodes, thus assuming that the soil water potential distributes parallel to the slope if the slope is long compared with the soil depth.



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  		Fig. 6. Weather conditions used for the simulation: (a) monthly mean temperature, (b) evapotranspiration, and (c) rainfall intensity.

 
As the initial condition, the soil water potential was assumed to distribute parallel to the slope ({psi} = –40 cm at the bottom of the soil domain). However, this condition has little effect on soil water flow and root system development since soil water distribution and soil water flow become identical once rainfall is applied to the soil surface.

Geometry
The soil domain was divided into grids for our finite element calculations, with values of Lx, Ly, and Lz (length of the soil domain in x, y, and z directions) of 700, 50, and 25 cm, respectively, for Slope 1, and 700, 50, and 53 cm, respectively, for Slope 2 (Fig. 7) . Each parallelepiped domain was divided into six tetrahedral finite elements. Root system development in the upslope (Root System a), midslope (Root System b), and downslope (Root System c) position of the same hillslope were simulated to examine differences due to slope position. The soil domain around the root systems was divided into small grids in the x direction to facilitate detailed simulations of soil water flow around the root systems (Fig. 7).



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  		Fig. 7. Soil domain and selected finite element grid.

 
Simulation Parameters
Root development parameters are listed in Table 3. Based on observations and measurements of the root systems (Table 2), the root elongation rates ERc of the first- and second-order lateral roots were obtained by dividing the average root length of each order by the average root age (assumed 365 d). As defined previously (Tsutsumi et al., 2003), the elongation rate ERc of the main root was assumed to change during the growth period. Parameters that define these changes (d, {Delta}ERg, ah, bh, {Delta}ERn, and {omega}n in Table 3) were determined by trial and error, so that the model emulated natural root systems (especially asymmetric architecture). Branching parameters, such as the apical nonbranching zone La, the basal nonbranched zone Lb, and the branching interval I (Fig. 5a), were determined from actual root measurements on Slope 1 (Table 2) and subsequently used in the simulations of both Slopes 1 and 2.


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  		Table 3. Simulation parameters.

 

   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 MODEL DESCRIPTION
 RESULTS AND DISCUSSION
CONCLUSIONS
 APPENDIX
 REFERENCES
 
Observed Plant Root Systems
Photographs of the root system architecture were transformed into binary images using image-analysis software (Scion Image, Scion Co., Frederick, MD, USA). The images showed the architecture of root systems projected on the x–z plane (Fig. 8a, 8b) . The roots of Slope 1 were distributed within a thin soil layer, and the main root elongation was constrained. The main root of Slope 2 grew longer because of a deeper soil, although the overall root system was shallow. For both slopes, the angles between lateral roots and the vertical direction upslope were larger than for those in the downslope side of the hill. Root systems of both slopes exhibited asymmetric root architectures.



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  		Fig. 8. Observed architecture of actual root systems of 2-yr-old pine trees: (a) Slope 1 (slope angle = 31°, soil layer thickness = 25 cm), and (b) Slope 2 (slope angle = 37°, soil layer thickness = 53 cm). Dashed lines indicate the soil surface.

 
Simulated Soil Water Flow along the Hillslope
To realistically model plant root growth, simulations of root system development and soil water flow were conducted for a 2-yr period (April 2000–March 2002). Calculated cumulative values of potential and actual transpiration and evaporation rates are shown in Fig. 9 . The actual evaporation rate from Slope 1 was smaller than that from Slope 2 because of the thinner soil. Actual transpiration was also smaller than its potential rate. The actual transpiration values from Slopes 1 and 2 were very similar, possibly due to the low transpiration rate at the early stage of plant growth.



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  		Fig. 9. Calculated cumulative values of the potential and actual (a) evaporation and (b) transpiration rates.

 
On the basis of these simulations, the following hydrological characteristics of the slopes were obtained:
  1. For Slope 1, water output from the downslope end of the soil domain responded abruptly to rainfall and decreased rapidly after rainfall stopped.
  2. For Slope 2, water output from the downslope end of soil domain responded gradually to rainfall and continued for more than 2 wk after a storm, with fluctuating values due to its control by evapotranspiration.
  3. For Slope 2, peak values of the water output from the downslope end of the soil domain were much smaller than those for Slope 1.
  4. The effect of transpiration on soil water distribution was more evident for Slope 1 than Slope 2.
  5. Total water potential contour lines indicate that soil water continuously flowed downslope.

The different hydraulic responses of the slopes are mainly due to differences in soil depths. The simulations suggest that the fifth result above may be an important factor affecting root system development, contributing significantly to the effect of hydrotropism.

Simulated Plant Root Systems
Three simulated root systems for the upslope (Root System a), midslope (Root System b), and downslope (Root System c) are shown as projections on the x–y and x–z planes (Fig. 10 and 11) . The dotted lines in the x–z plane indicate the boundaries at the bottom and surface of the soil. On both slopes, the main root of all root systems elongated mostly vertically downwards due to the high elongation rate and the effect of gravitropism (Table 3), while also exhibiting a slightly tortuous pattern as a result of circumnutation. After reaching the bottom of the soil layer, the main roots were deflected by mechanical resistance of the bedrock, thus changing their direction downslope. Effects of hydrotropism on the elongation of some first-order lateral roots are apparent. To compare first-order lateral roots along the upslope portion of the tree and those on the downslope portion, two sets of first-order lateral roots were approximated by straight lines between the root base and the root tip, with angles of {phi}u (°) between the line segment on the upslope portion of the tree and the vertical and {phi}d (°) on downslope portion of the tree (Fig. 10a, 10c). For Root System c (Fig. 10c), the angle {phi}u was obviously larger than {phi}d. The effect of hydrotropism and infiltrated rainwater moving downslope forced root elongations toward the upslope direction. As a result of hydrotropism and root deflection, angles between the lateral roots and the vertical along the upslope portion of the tree tended to be larger than those along the downslope portion. Comparing Root Systems a, b, and c, the effects of hydrotropism and the resulting asymmetric architectures are more obvious for Root Systems b and c than for Root System a for both slopes. Because the same parameters of hydrotropism were used for all root systems, differences among Root Systems a, b, and c were due to spatial differences in hydrological behavior in the soil domain. In general, as subsurface water flows downslope, the water flux increases in the downslope direction, thereby accentuating the effect of water flow and hydrotropism on Root Systems b and c, as compared with Root System a.



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  		Fig. 10. Simulated root architectures: (a) upslope, (b) midslope, and (c) downslope for Slope 1.

 


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  		Fig. 11. Simulated root architectures: (a) upslope, (b) midslope, and (c) downslope for Slope 2.

 
To more clearly elucidate the effect of hydrotropism on root system architecture, we also simulated root system development without hydrotropism (ah = 0.0); results are shown in Fig. 12 . Because slope position does not affect root system development when hydrotropism is absent, only the downslope position (Root System c) was considered (Fig. 12). For both slopes, the oldest first-order lateral roots on the downslope side of the main root were deflected by the soil surface near the main root base. These deflections made the root systems asymmetric, especially for Slope 2, since the steeper slope (37°) deflected the root more strongly. However, except for such deflected first-order lateral roots, no first-order lateral roots grew upward along the upslope portion of the tree ({phi}u < 90°; whereas upward growing roots, {phi}u > 90°, are seen in Fig. 10 and 11), and no particular tendency of asymmetric root development was apparent on either slope.



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  		Fig. 12. Simulated root architectures for Slopes 1 and 2 with no hydrotropism, downslope only.

 
To quantitatively compare the asymmetric architecture of simulated and observed root systems, we again approximated the first-order lateral roots by straight lines from the root base and to the root tip (examples are shown in Fig. 10a and 10c). Angles between these line segments and the vertical direction for both the upslope and downslope portions of the tree, {phi}u and {phi}d, were calculated for all first-order lateral roots. The average angles ({phi}u,av and {phi}d,av) for the upslope and the downslope were computed by weighting with their respective length, ls (cm):

[33]

For Slope 1, differences between the average angles of the upslope and downslope portions of the tree for simulated Root System a were small (Fig. 13) . Differences were greater for Root Systems b and c and were similar to those of the observed root system. For Slope 2, the simulated differences of average angles between the upslope and downslope portions of the tree were larger than for Slope 1, since the steeper slope deflected more roots downslope and forced roots to direct upwards due to hydrotropism effects. For both hillslopes, the simulated average angles of the upslope and downslope portions of the tree did not agree with the respective values of observed root systems. However, when comparing simulated root system angles with those without hydrotropism, it was clear that differences in lateral root angles were caused by the combined effects of soil water flow and hydrotropism.



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  		Fig. 13. Averaged angle, {phi}av of the simulated and observed root systems for (a) Slope 1 and (b) Slope 2.

 
Simulated root systems (Fig. 10 and 11) appear to overestimate actual root lengths (Fig. 8a, 8b). The observed and simulated root lengths were 303 and 605 cm for Slope 1 and 333 and 706 cm for Slope 2, respectively. Such differences may be attributed to overestimation of the elongation rates (Table 3). However, the overall morphologies of the root systems simulated by the model closely represented the asymmetric architecture observed in the field. Although certain developmental aspects were not considered, such as the effects of mechanical impedance or nutrient distribution, the proposed three-dimensional root system model successfully predicted asymmetric root system development along a hillslope by considering only the combined effect of hydrotropism and soil water flow, without considering soil mechanical resistance.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 MODEL DESCRIPTION
 RESULTS AND DISCUSSION
 CONCLUSIONS
APPENDIX
 REFERENCES
 
In this study we proposed a three-dimensional model that combines root system development and soil water flow. The model is based on the two-dimensional root system development model proposed by Tsutsumi et al. (2003). Root hydrotropism was considered as a dominant factor in root elongation, as well as gravitropism. In addition to these tropisms, circumnutation was introduced into the model. The simulated root systems differed in several aspects from the observed root systems, specifically root length and average angle between first-order lateral roots and the vertical direction. However, the asymmetric architecture of the simulated root systems agreed well with those observed here, as well as with those reported in previous studies (Scippa et al., 2001; Yamadera, 1990). The asymmetric development of the root system was due to the combined effects of root hydrotropism and water flow within an inclined soil layer, and also due to deflection at the soil surface.

Although the importance of hydrotropism was suggested in previous studies (Clausnitzer and Hopmans, 1994; Dunbabin et al., 2002a, 2002b; Tsutsumi et al., 2003), the hypothesis that root hydrotropism is an important factor influencing the asymmetric architecture of root systems in hillslopes was not confirmed earlier. In this study, the assumption that root hydrotropism is one of the more important factors controlling the asymmetric architecture of root systems is supported by model simulations based on observed root systems and environmental conditions. Although many other complex environmental effects were not included in our model, the simulation results strongly suggest that root hydrotropism is an important process. Modification of the model to include other factors such as soil mechanical impedance and nutrient uptake for longer-term growth of plant root systems would make the model a very useful tool for studying hillslope stability problems.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 MODEL DESCRIPTION
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
REFERENCES
 
List of Variables
Atotal surface area of considered soil domain (cm2)ahparameter of kh (-)bhparameter of kh (cm–1)Cp({psi})soil water capacity (cm–1)Cscoefficient for Sp (cm2 s–1)droot diameter at elongation point (cm)Eaactual evaporation (cm s–1)Etpotential rate of evapotranspiration (cm d–1)Eppotential evaporation (cm d–1)Ep'daily change of Ep (cm s–1)ERroot elongation rate around the cross-sectional circle (cm s–1)ERcelongation rate at root center (cm s–1)ERhelongation rate functions of hydrotropism (cm s–1)ERh,0standard elongation rate of the hydrotropism (cm s–1)ERgelongation rate functions of gravitropism (cm s–1)ERg,0standard elongation rate of gravitropism (cm s–1)ERmaxmaximum value of ER (cm s–1)ERminminimum value of ER (cm s–1)ERnelongation rate functions of circumnutation (cm s–1)ERn,0standard elongation rate of circumnutation (cm s–1){Delta}ERncoefficient determining intensity of circum- nutation (cm s–1){Delta}ERgcoefficient determining intensity of gravi- tropism (cm s–1)Ibranching interval (cm)K({psi})soil hydraulic conductivity (cm s–1)khcoefficient determining intensity of hydro- tropism (-)Lroot length density (cm cm–3)Laapical nonbranching zone (cm)Lbbasal nonbranched zone (cm)Lx, Ly, Lzlength of considered soil domain in x, y, z directions (cm)lslength of the root segment (cm)Nbranching order number of first-order lateral root (-)nnumber of finite element (-)qwater flux (cm s–1)|q'|magnitude of the component of water flux q (cm s–1)REdividing ratio of evapotranspiration (-)rradius of curvature of root elongation (cm)rT(t)coefficient of transpiration intensity (-)Swater extraction intensity (s–1)S1, 2, 3functions for determination of ERmax, ERmin, and ß (cm s–1)Saactual water extraction intensity (s–1)Sppotential water extraction intensity from each finite element (s–1)Tppotential transpiration (cm d–1)Tp'daily change of Tp (cm s–1){Delta}tcalculation time (s)tmaxmaximum calculation time (s){Delta}tcalculation time step (s)Vnvolume of the element n (cm3)x, y, zthree-dimensional coordinate (cm){alpha}angle of curvature of root elongation (rad){alpha}T({psi})reduction factor of soil water extraction (-){alpha}E({theta})reduction factor of evaporation (-)ßangle around root cross-sectional circle from top point of the circle (rad)ßsß that indicates the point where ER has the maximum value ERmax (rad)ßh(q')angle between direction of gravity and flux q' in the root cross-sectional circle (°){phi}dangle between root segment and vertical di- rection on downslope portion of a tree (°){phi}d,avaverage angle between segments and vertical direction on downslope portion of a tree (°){phi}iangle between a parent root and lateral roots (°){phi}uangle between root segment and vertical direction on upslope portion of a tree (°){phi}u,avaverage angle between segments and vertical direction on upslope portion of a tree (°){gamma}angle between the direction of gravity and root orientation (rad){theta}soil water content (cm3 cm–3){theta}1, {theta}2threshold values of soil water content in {alpha}E({theta}) (cm3 cm–3){theta}rresidual soil water content (cm3 cm–3){omega}nangular velocity of circumnutation (rad s–1){psi}soil water potential (cm){psi}1, 2, 3threshold values of soil water potential in {alpha}T({psi}) (cm)


   ACKNOWLEDGMENTS
 
We thank Dr. Kimoto, Mr. Miyata and Ms. Yamagishi of Kyoto University for their helpful support in the field research, Dr. Sidle of Kyoto University for his valuable suggestions and vigorous help in preparing the manuscript, Dr. Tani and Dr. Takeda of Kyoto University and Dr. Dunbabin of University of Tasmania for their valuable comments and suggestions, and the anonymous reviewers for their constructive comments and suggestions.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 MODEL DESCRIPTION
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES