Analysis of stormflow and its source area expansion through a simple kinematic wave equation

Transcription

1 Forest Hydrology and Watershed Management - Hydrologie Forestiere et Amenagement des Bassins Hydrologiques (Proceedings of the Vancouver Symposium, August 1987; Actes du Co1loque de Vancouver, Aout 1987):IAHS-AISH Pub1.no.167,1987. Analysis of stormflow and its source area expansion through a simple kinematic wave equation MAKOTO TANI & TOSHIO ABE Kansai Branch, Forestry & Forest Products Research Institute, Momoyama, Fushimi, Kyoto, 612, Japan ABSTRACT Characteristics of stormflow and its source area expansion in a mountainous basin were considered by analyzing responses of stormflow to rainfall. A simple kinematic wave equation was used for the analysis. Hydrographs for various storms observed in an experimental basin (17.3 ha) were well simulated through the analysis. It was found that the stormflow had more intense nonlinearity than that derived from the Manning formula, and that the source of the stormflow originated from the channel area and expanded upslope as rainfall increased. Analyse du debit de crue et de I 'expansion de l'aire contributrice par une simple equation cinematique RESUME La relation cruejprecipitation sur un bassin de montagne de 17.3 ha a ete analysee en tenant compte des caracteristiques des debits de crue et de l'expansion de l'aire contributrice au moyen d'une equation cinematique. L'equation a bien reproduit l'hydrogramme de crues observees sur Ie bassin. L'analyse a demontre que la crue exhibait une non-linearite plus forte que celie prevue par l'equation de Manning, et que l'aire contributrice comprennait, a partir de la zone riparienne, de plus en plus de la pente a mesure que la quantite de pluie augmentait. INTRODUCTION In humid, well vegetated regions, the usual range of rainfall intensity is smaller than that of the saturated conductivity of the forest floor, and all rain falling onto unsaturated areas must enter the soil. Conventional thinking holds that the water in the soil moves too slowly to contribute to stormflow, and that overland flow generated by rain, on the saturated area, should dominate storm runoff (Dunne, 1978). However, Yasuhara (1984) has demonstrated that subsurface flow was one of the dominant components of storm runoff in a small forested basin in Japan. For Maimai 8, a similar basin in New Zealand, Mosley (1979) reported that overland flow was not observed except in limited areas along stream channels, even 69

2 61 Makoto Tani & Toshio Abe though quick flow as a proportion of net rainfall reached 99% during some large storms with wet antecedent conditions. In Maimai 8, contributions of old water stored in soil were dominant even in rapid responses of runoff to storm rainfall (Pearce et al., 1986). Stormflow passes through complicated pathways which consist of the ground surface, the soil matrix, macropores within the soil, and so forth. Tracing the flow through such mixed pathways is difficult, but analyzing the responses of storm runoff to rainfall may show the characteristics of the complex flow. Downslope flow has been expressed by kinematic wave equations to approximate not only overland and saturated subsurface flow (Ishihara & Takasao, 1963), but also saturated and unsaturated flow (Suzuki, 1984; Hurley & Pantelis, 1985). In this paper, we assume that the complex flow can be described by a single kinematic wave equation. Using this equation, we aim to assess the characteristics of the flow and to follow the expansion of its source area. GOVERNING EQUATIONS Consider a thin soil layer overlaying impermeable bed rock on a hillslope. Flow through this soil layer can be described by equation (1). S = k QP (1) where Sand Q are the total water content and the downslope flow, of a normal profile of the layer, and p and k are parameters. If Darcy's law for saturated soil or the Manning formula is applicable, p is 1. or.6, respectively. The continuity equation can be written as: as at +ao ax = r cos e (2) where r is the rainfall intensity, and e is the slope angle. Equations (1) and (2) form a kinematic wave equation. STUDY AREA Stormflow responses were monitored at Kitatani basin (17.3 ha) in the Tatsunokuchi-yama Experimental Forest near Okayama, Japan (Fig.l). Effects of forest changes on streamflow have been studied there since 1937 (Abe & Tani, 1985; Tani & Abe, 1986). The average slope length and gradient are 123 m and The basin is underlain by Palaeozoic formations (65% of the area) and quartz-porphyry (35%). Most of the soils are thick (>1 m) stony clay loam with a thin (5-1 cm) A horizon. The hydraulic conductivity values of the A horizon and the clay loam ranged from 1 to 2xlO-3cm s-l and from.1 to 6xIO-3cm S-l, respectively. The vegetative cover is a natural forest of hardwoods. The average values of annual precipitation and annual mean temperature are mm and 14.3 C, respectively. Although there is

3 Kinematic wave analysis of stormflow 611 much rain in early summer and early autumn, fine days usually occur during midsummer. Snow is rare. 1 ~ 1 I 2 I 3m f FIG.l Map of Kitatani basin in the Tatsunokuchi-yama Experimental Forest. RESULTS Rainfall runoff relations Relations of storm period rainfall to storm runoff in Kitatani are shown in Fig.2. They depend strongly on the antecedent wetness, as indicated by the initial runoff rate, Qi. Storm runoff is less than 1% of rainfall if the antecedent condition is dry and the rainfall is not over 1 mm. When the cumulated rainfall is greater than 1 mm, runoff is almost equal to rainfall. In the wettest condition, almost all rain contributes to storm runoff. According to the authors' observation, during heavy storms, seepage from the soil matrix and flow from natural pipes were generated on exposed vertical soil faces but overland flow was not found except on beaten paths. Runoff response in the wettest duration A storm between 8 and 14, September 1976, with a dry antecedent condition, is used as an example here. The volumes of rainfall,

4 612 Makoto Tani & Toshio Abe runoff,and storm runoffwere 372.2,281.4,and 27.4 mm, respectively. Fig.3 shows the hydrographs observed and simulated with equations (1) and (2). In these simulations, the slope length and gradient were their average values at Kitatani, effects of channel storage were neglected, and 1 minute values of rainfall and runoff were used. 3 QT mm 2. Qi~.3mm hour-i A.3<Qi~.6 'V.6 <Qi~.1 Q;>.1 1 'V'V 'V ~A A p 4 mm FIG.2 runoff Relations of storm period rainfall (P) to storm (QT). The dashed line in Fig.3 indicates a hydrograph calculated on the assumption that all rainfall in the basin contributed to runoff throughout the storm event. In the early stage, the simulated runoff is much larger than observed. In the latter stages of the storm the volumes of the observed ahd simulated hydrographs are essentially the same. Parameters, p and k, were easily optimised during wettest soil conditions, between 14 hours on September 11 and 23 hours on September 12. The objective function E used for the optimization is given by: E = - E n 1 n IQb - Qsl Qb (3) where Qb and Qs are the observed and simulated runoff rates, and n is the length of the time series. A minimum value for E (7%) was attained when p =.3 and k=.6 mo.4s.3 and the simulated hydro-

5 Kinematic wave analysis of stormflow 613 graph agreed with that observed. This value for p results in an equation for the stormflow that is more non linear than that derived from the Manning formula with p of ~,-, :J,." I-'.c 1 I \."' ~ I, ", I EE, -"J V ( -.1.1', 2' e'3 ;;t_. 4::J -c (1) :: September FIG.3 Observed and simulated hydrographs between 8 and 14, September Observed Simulated with source area variation Simulated without source area variation Two simulated hydrographs converged with each other in the latter stage. Source area expansion Assume that stormflow is not generated until cumulative rainfall reaches an initial threshold soil water deficit which increases upslope with distance from the channel. All rain falling onto the source area where cumulative rainfall has exceeded the threshold, is assumed to contribute to stormflow. The source area expands from the channel area toward the hilltop as rainfall amount or duration. The spatial distribution of the threshold soil water deficit adjusted to obtain reasonable agreement between the observed and simulated hydrographs. The distribution estimated is shown in Fig.4. The initial deficit at the hilltop is more than 1 mm, although there is no deficit in the channel area. The hydrograph including various peaks and a long recession limb was satisfactorily simulated (Fig.3) with the objective function value of 13%. Application to other storms Runoff was simulated for several other storms using the p and k parameters derived above. The spatial distribution of the threshold soil water deficit were derived with equation (4):

6 614 Makoto Tani & Toshio Abe I = 1 + Id but I > (4) where I is the threshold soil water deficit at any position of the slope for a given storm event, 1 is that for the September 1976 storm, and Id is the difference between them. 1 I mm 5O~' Top lei j '...June ',1969 " x/l Channel FIG.4 Distribution of threshold soil water deficit (I) versus dimensionless distance (x/l) from the hilltop. The result of simulation for a storm between 29 June and 3 July 1969 is shown in Fig.5, for example. The antecedent condition was much wetter than the 1976 storm, considering that the respective initial runoff rates were.23 and.47 mm h-l. The best value of Id was estimated to be -53 mm, as shown in Fig.4. The source area, in which 1=, was found to be much greater for this storm than the September 1976 storm. The difference between the observed and simulated hydrographs (E=2%) in Fig.5 are satisfactory except on the rising limb of the second peak. Possible shrinkage of the source area was not considered here. CONCLUSIONS We have obtained the equation of motion for stormflow with p of.3, which has intense nonlin~arity. This result is believed to be reliable, because p was estimated by the simulation without any separation process of rainfall excess. This equation of motion may be applicable to a complex rather than a single flow system. Further tests are needed. We have ascertained that its source area expands upslope from the channel area toward the hilltop as rainfall increases. The expansion is generated by the distribution of threshold soil water deficit, and it should also be reduced by the soil water movement after rainfall ceases. The shrinkage process of the source area after a storm need further study.

7 Kinematic wave analysis of stormflow ::J..c E E C ~.1.., <5 ' 2 _.3 ::J-. """::J 4 ~ -II) June FIG.5 Observed and 29 and July 3, Observed Simulated 2 July 1969 simulated hydrographs between June 3 REFERENCES Abe, T. & Tani, M. (1985) Streamflow changes after killing of pine trees by the pine-wood nematode. J. Japanese For. Soc. 67(7), Dunne, T. (1978) Field studies of hillslope flow processes. In: Hillslope Hydrology (ed. by M.J.Kirkby), Wiley-Interscience, Chichester. Hurley, D.G. & Pantelis,G. (1985)Unsaturatedand saturatedflow through a thin porous layer on a hillslope. Wat. Resour. Res. 21(6), Ishihara, T. & Takasao, T. (1963) A study on runoff pattern and its characteristics. Bull. Disaster Prevention Research Institute, Kyoto Univ. 65, Mosley, M.P. (1979) Streamflow generation in a forested watershed, New Zealand. Wat. Resour. Res. 15(4), Pearce, A.J., Stewart, M.K. & Sklash, M.G. (1986) Storm runoff generation in humid headwater catchments, 1. Where does the water come from? Wat. Resour. Res. 22(8), Suzuki, M. (1984) The properties of a base-flow recession on small mountainous watersheds (1) Numerical analysis using the saturated-unsaturated flow model. J. Japanese For. Soc. 66(5), Tani, M. & Abe, T. (1986) An evaluation of the effects of forest change on streamflow using a runoff model. Bull. Forestry and Forest Products Research Inst. 342, Yasuhara, M. (1984) Watershed response to a storm rainfall. Science Reports Inst. Geoscience, Univ. Tsukuba, Section A 5, 1-27.

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