HYDROLOGICAL PROCESSES, VOL. 10, 81-88 (1996)

SIGNIFICANCE OF STEMFLOW IN GROUNDWATER RECHARGE. 2: A CYLINDRICAL INFILTRATION MODEL FOR EVALUATING

THE STEMFLOW CONTRIBUTION TO GROUNDWATER RECHARGE

TADASHI TANAKA Institute of Geoscience, University of Tsukuba, Ibaraki 305, Japan

MAKOTO TANIGUCHI Department of Earth Sciences, Nara University of Education, Nara 630, Japan

AND MAKI TSUJIMURA

Institute of Geoscience, University of Tsukuba, Ibaraki 305, Japan

ABSTRACT A primary model for evaluating the effect of stemflow on groundwater recharge has been developed. The model, a cylindrical infiltration model (CI model), is based on the infiltration area of stemflow-induced water instead of canopy projected area for determining the stemflow inputs to the soil surface. The estimated ratio of recharge rate by stemflow to the total recharge rate determined with this model agrees closely with values obtained from the mass balance of chloride in subsurface waters. This primary model is considered to be useful for estimating the effect of stemflow on groundwater recharge.

KEY WORDS: stemflow; spatial variability; infiltration area; forest environment; cylindrical infiltration model

INTRODUCTION

The contribution of stemflow per unit of canopy projected area to the water balance of forest catchments is just a few per cent of the net precipitation. However, the effect of stemflow on the groundwater recharge is relatively large (Taniguchi et al., 1995). This means that the process of recharge by stemflow, as a point source input, should be evaluated in a different manner from simple water balance considerations.

In the context of the ecological importance of stemflow and soil moisture patterning, Pressland (1976) observed infiltration phenomena of stemflow during rainfall events of various sizes and intensities. His observations indicated that all stemflow infiltrates into the soil within the area of 50 cm around large trees with circumferences larger than 40 cm and within the area of 30 cm around the smaller trees with circum- ferences less than 20 cm. He also indicated the potential increases in soil water content due to stemflow by comparing the stemflow calculated on a tree canopy area basis with the values calculated on the basis of the area of infiltration.

Tanaka et al. (1991) also observed the areal extent of stemflow-induced infiltration water and found that stemflow inputs are concentrated over more localized circular areas at the tree base. These phenomena indicate that the stemflow infiltrates into a certain area as point source inputs in the recharge process.

On the other hand, preferential flows in the vadose zone have been a subject of great interest to sub- surface hydrologists, because the rapid arrival of water and contaminants in the deeper zone cannot be

CCC 0885-6087/96/01008 1-08 0 1996 by John Wiley & Sons, Ltd.

Received 28 February 1994 Accepted 26 August 1994

82 T. TANAKA ET A L .

predicted by traditional analysis. Nevertheless, water and solute transport in the vadose zone is very important in determining both groundwater recharge and contaminant loading. Many proposed explanations for preferential flow have arisen. One of these explanations is macropore flow (German, 1988; German et al., 1986) and another is unstable flow (Hillel, 1987; Glass et af . , 1989; 1991). The former preferential flow is essentially a point source input in the recharge process.

In an ecologically oriented study, Rampazzo and Blum (1992) have observed chemical and mineralogical changes in forest soils due to acid atmospheric deposition and found that the soils were modified by acid rain in the infiltration zone of stemflow. Therefore, it is important to evaluate the infiltration process of stemflow for not only water quantity, but also for water quality in forest environments.

The objectives of this paper are to develop a primary model to explain the effect of stemflow on ground- water recharge and to apply the model to the results described by Taniguchi et al. (1995).

MODEL DESCRIPTION

Pressland (1976) observed infiltration areas of stemflow inputs during rainfall events and found that all stemflow infiltrates into the soil surface within the areal radius of 50cm around the tree base. Rutter (1963) showed that stemflow increases linearly with the increasing square of stem diameter. Tanaka et ul. (1991) also found that the infiltration area of stemflow increases with increasing diameter of the tree base with a maximum limitation. Considering these data for stemflow input during the infiltration process, it is reasonable to assume that the relationship between the radius of infiltration area of stemflow inputs and the diameter of the tree base is as follows

Y = a l n X - b (1)

where X is the diameter of the tree base and Y the radius of infiltration area of stemflow inputs from the centre of the trunk; a and b are constants. Equation (1) indicates that no stemflow input occurs at a small tree diameters and the infiltration area of stemflow inputs does not expand linearly with increasing diameter of the tree base.

Assuming that the infiltration area is a ring, the area of stemflow inputs can be calculated as

A , = 7r[Y2 - ( X / 2 ) * ]

where A , is an infiltration area of stemflow input. Using a similar approach, the canopy projected area is also assumed to be described by

A , = c lnX - d (3) where A, is the canopy projected area, X is the diameter of a tree, and c and d are positive constants.

To simplify the relationship between stemflow inputs and groundwater recharge processes, it is assumed that: (a) the stemflow infiltrates into an area which is described as in Equation (2); and (b) the ratio of recharge rate by stemflow to the total recharge rate is the same as the ratio of stemflow per infiltration area to the net precipitation. Therefore, the relationship between stemflow per infiltration area and recharge rate by stemflow is described as

S ’ / ( S ’ + T ) = R , / R (4)

S‘ = SA, /A, ( 5 )

where

where S and T are the stemflow per canopy projected area (A , ) and the throughfall, respectively. A , is the infiltration area of stemflow and R , and R are the groundwater recharge rate by stemflow and the total recharge rate, respectively. A schematic diagram of a cylindrical infiltration model is shown in Figure 1.

SIGNIFICANCE OF STEMFLOW IN GROUNDWATER RECHARGE 2 83

Figure 1. Schematic diagram of a cylindrical infiltration model for stemflow inputs into the forest soil

MODEL VALIDATION

To validate the cylindrical infiltration model (CI model) for use in explaining the effect of stemflow on groundwater recharge, evaluations of the model and some error estimations were performed.

Equation (1) indicates that no stemflow input occurs at small tree diameters and the infiltration area of stemflow inputs gradually approaches a finite value with increasing diameter of the tree base. Therefore, the infiltration area of stemflow inputs changes within a certain range. As mentioned previously, Pressland (1976) found that all stemflow infiltrates into the soil within 50cm radius from the tree. Voigt (1960) also found that the infiltration area for the stemflow has a radius of less than about 30cm. These results support the assumption that the present cylindrical infiltration model has a critical area for stemflow inputs.

Equation (5) means that the stemflow input to the groundwater recharge in the CI model decreases with increasing A,. As the infiltration area of stemflow has a critical value for the maximum, the rate of stemflow input does not approach zero. On the other hand, for a small diameter of tree base, no stemflow occurs (Tanaka et al., 1991). The value of A , has the minimum limitation, therefore that the rate of stemflow inputs does not approach infinity. Under these limitations, the effect of stemflow on groundwater recharge is large with large values of A , / A , and small with small values of A J A , because the throughfall is usually larger than S’.

In general, the infiltration area of stemflow ( A , ) increases with increasing canopy projected area ( A , ) and decreases with decreasing values of A,. Therefore, the ratio & / A , does not approach zero or infinity under natural conditions. This means that the ratio of R, to R, i.e. the effect of stemflow on groundwater recharge, also varies within a certain range.

An error in the estimation of the diameter of infiltration area of stemflow inputs can be evaluated by using Equation (1). For example, an overestimation in the diameter of the tree base by 5% would result

84 T. TANAKA ET AL.

in an excessive radius of infiltration area by 0.0487a, whereas underestimation of the diameter of the tree base by 5% would result in too small a radius of infiltration area by 0.0513a. Similar consideration for an error in estimation of the effect of stemflow on the groundwater recharge can also be evaluated by using Equations (4) and (5). If the model overestimates the infiltration area of stemflow (A , ) by 5%, it would result in a decrease in R , / R of 44%, whereas an underestimate of A , by 5% would result in an increase in R,IR of 5.3%.

MODEL APPLICATION

To apply the CI model to the field data, Akamatsu stands, Japanese red pine (Pinus densflora Sieb. et Zucc.) in Tsukuba, Japan was selected as the study area. The physical conditions of the study area have been described in detail by Taniguchi et al. (1995).

Tanaka et al. (1991) reported the relationship between the infiltration area of stemflow inputs and the diameter of tree base for the Keyaki stand, Japanese zelkova (Zelkova serrata Maki.) based on the data obtained in Tsukuba, Japan. In this study, the values of a and b in Equation ( 1 ) were estimated to be 25.07 and 34.92, respectively. These values were used in this paper to apply the model to the Akamatsu stand. Figure 2 shows the relationship between the diameter of the tree base and calculated value of A, by Equations (1) and (2) with values of a = 25.07 and b = 34.92.

The relationship between the canopy projected area and the diameter of the trees in the study area is shown in Figure 3. According to the regression analysis, the values of c and d in Equation (3) were estimated to be 108 394 and 221 980, respectively.

To determine the relationship between bulk precipitation and stemflow per actual infiltration area, which is determined using Equation (1) with a = 25.07 and b = 34.92, regression analysis was performed for the subject stands in two sites, B and D, in the forest. Figures 4a and 4b provide the relationships between stemflow and bulk precipitation (Pb) in sites B and D, respectively. Regression lines for the relationships

- 0 Observed value

Diameter of the tree (cm)

Figure 2. Relationship between infiltration area of stemflow ( A , ) and the diameter of the tree

SIGNIFICANCE OF STEMFLOW IN GROUNDWATER RECHARGE 2

- 15- N s - 0 0 0 -

K

4

- 0 10- 4

m 0) $4 m a 0) w

85

0 This study 0 Majima KI Tase (1982)

0

O O 0

0

o o

50 - E E

4 m m a w - o m

L i m 0, a e 0

4 m W L I E w 0 ) r l

- 40- a

E 30-

8 : 20-

q 10- '4

Figure 3. Relationship between the canopy projected area (A,) and the diameter of the tree

-

in both sites are reported as

S,' = 0.095Pb - 1.202

SD' = 0.23OPb - 1.841

( r 2 = 0.732)

( r 2 = 0.785)

- P~=0.095Pb-1.202 r7=0.732

r l m m a a u .

Bulk precipitation, Pb (m)

(b)

P~=0.230Pb-1.841 r2=0. 785

0 0

/ i O a 80 I 120 I 160 ' 200 Bulk precipitation, Pb (mm)

Figure 4. Relationship between stemflow and bulk precipitation at (a) site B and (b) site D

86

20

Ac/As

10-

T. TANAKA ET A L .

-

-

*This study oMajima & Tase (1982)

Table I. Calculated stemflow per canopy projected area (case A) and that per in- filtration area (case B)

Site B Site D

Bulk precipitation (Pb, mm) Throughfall ( T , mm) Case A

Stemflow (S, mm) Net precipitation (P, = T + S, mm) Interception loss (Ei, mm)

Stemflow (S’, mm) Net precipitation (P”’ = T + S’, mm) Interception loss (Ei’, mm)

Case B

1290.5 (100.0%) 1290.5 (lOO~O?’O) 1007’8 (78.1%) 889.6 (68.9%)

6.6 (0.5%) 15.7 (1.2%) 1014.4 (78.6%) 905.3 (70.2%) 276.1 (21.4%) 385.2 (29.8%)

100’6 (7.8%) 264.1 (20.5%) 1108.4 (85.9%) 1153.7 (89.4%) 182.1 (14.1%) 136.8 (10.6%)

where

S D ’ = S,A,/A,

Table I gives the results of calculated stemflow, net precipitation and interception loss in two cases at sites B and D. In case A, the stemflow is calculated per canopy projected area and in case B per infiltration area. In the CI model (case B), stemflow is estimated to be 100.6mm at site B and 264.1 mm at site D. As the net precipitation ( S ’ + T ) at sites B and D is 1108.4 and 1153.7mm/year, respectively (Table I), the ratio of recharge rate by stemflow to the total recharge rate at sites B and D is estimated to be 0.091 and 0.229, respectively, from Equations (4) and (5). On the other hand, the estimated values of RsB and R,D, which were obtained by Taniguchi er al. (1995)

based on the mass balance method of chloride, were 62.0mm at site B and 139.4mm at site D. The ratios of recharge rate by stemflow to total recharge rate were 0.109 and 0.191 at sites B and D, respectively. There- fore, the estimated ratio of recharge rate by stemflow to the total recharge rate using the CI model agrees

30c 0

0 0

0 - 0 //

Diameter of the tree (cm)

Figure 5. Relationship between A,/A, and the diameter of the tree

SIGNIFICANCE OF STEMFLOW IN GROUNDWATER RECHARGE 2 87

closely with the value obtained from the mass balance method of chloride. Thus the CI model developed in this study can well describe the effect of stemflow on the groundwater recharge.

Voigt (1960) observed that stemflow does not distribute over the entire canopy projected area, but is limited to a restricted area closely adjoining the stem of trees. He also found that this absorption area for stemflow has a radius of less than 1 ft (about 30.5 cm). The stemflow calculated on the basis of absorp- tion area was larger by 7.4 times for beech, 12.0 times for red pine and 15.9 times for hemlock than those calculated on the basis of the canopy projected area. Pressland (1976) has also noted that the stemflow calculated on the basis of infiltration area was 10.0 to 18.1 larger, with mean of 12.7, for mulga (Acacia aneura F. Muell) than those calculated on the basis of canopy projected area. In the present CI model for red pines, the stemflow evaluated on the basis of infiltration area in two sites ranges from 15.2 to 16.8 times those calculated on the basis of canopy projected area.

Figure 5 shows the relationship between the diameter of the tree and the ratio of canopy projected area (A, ) to the infiltration area of stemflow (As) . Data obtained in this study and that of Majima and Tase (1982) are shown in this figure. The curve in Figure 5 was derived using Equations (l), (2) and (3) with values of a = 25.07, b = 34.92, c = 108 394 and d = 221 980. As can be seen from Figure 5, the observed and calculated values of ASIA, range from almost 15 to 25 for trees of diameter 10-30cm. This may be a character of red pines.

Majima and Tase (1982) also discussed the effect of infiltration area of stemflow inputs on the infiltration processes. They calculated the ratio of stemflow to bulk precipitation using ideal data with a fixed value of 50 cm for the radius of the infiltration area of stemflow. The estimated values of the ratio were 0.15 and 0.27 when the collected volume of stemflow was 1 and 101, respectively. In the case of the present CI model, the ratio is calculated to be 0.078 and 0.205 at sites B and D, respectively (Table I, case B). These values agree well with the values obtained by Majima and Tase (1982) and we can generalize the effect of stemflow on recharge process by using the CI model.

As Tanaka et al. (1991) noted, stemflow has a unique form of water input to the ground surface and cannot be evaluated by only the water balance consideration of forest environments. In the primary CI model, the effect of stemflow on the groundwater recharge can be evaluated by treating stemflow as a point source input within a certain area.

CONCLUSIONS

A cylindrical infiltration model (CI model) for stemflow enables us to evaluate the effect of stemflow on groundwater recharge. The concept of the primary CI model is based on the evaluation of stemflow in terms of the infiltration area of stemflow-induced water instead of canopy projected area. The model explains why the effect of stemflow on groundwater recharge is relatively large although the ratio of stem- flow to net precipitation is small in the forest water balance. The estimated ratio of recharge rate by stemflow to the total recharge rate by using CI model agrees well with values obtained from the mass balance method of environmental chloride in subsurface waters. The CI model may be useful for evaluating the effect of stemflow on the groundwater recharge problem.

ACKNOWLEDGEMENTS

The authors thank the staff of the Environmental Research Center, University of Tsukuba. Japan for useful discussions and field assistance. This study was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan, Nos. 01916005 and 03680209 and by a University of Tsukuba Project Research in 1991.

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