n 11? de. l'te&ocâcutlon IrUe/inatlonale. dea Sciences Hydn.cslogiques Sympoi-ium de. Tokyo [Vécembie.!9?5)

Transcription

1 Publication n 11? de. l'te&ocâcutlon IrUe/inatlonale. dea Sciences Hydn.cslogiques Sympoi-ium de. Tokyo [Vécembie.!9?5) CHARACTERISTICS OF THE SHAPE OF THE RECESSION Taro EGAWA Chief,River Division, Chubu Regional Construction Bureau, Ministry of Construction, Nagoya City, Japan Toshio TAKENOUCHI Professor, The National Defense Academy of Japan, Yokohama City, Japan Synopsis This paper deals ith the estimation of volume of runoff from isolated and complex storms. The method is demonstrated by using the hydrological data obtained on the Kanna River Basin. In the case of runoff from isolated storms, the recession is considered to consist of to parts : (1) a hydrograph representing rapid change of flo and (2) that representing slo change of flo. The authors assume that the magnitude of peak flo, the variation in areal rainfall distribution over a basin, the total infiltration over a basin, etc., have effect on the shape of (1), hile the shape of (2) coincides ith a definite curve peculiar to a basin regardless of the factors above mentioned. Analysis is made on the determination of location of points here hydrograph (1) transfers to hydrograph (2). The results obtained for a runoff from isolated storms is applicable to a separation of runoff from complex storms. Resume Ce texte traite de l'estimation du volume du débit lors de tempêtes isolées et complexes. Pour faire la démonstration de cette méthode, on utilise les données hydrographiques obtanues au bassin de la rivière Kanna. Dans le cas de débits provoqués par des tempêtes isolées, on considère que l'invasion consiste en deux parties ; (1) une carte hydrographique qui montre le changement rapide du débit et une autre (2) montrant un changement lent dans le débit. Les auteurs estiment que l'importance du débit maximum, les variations dans la répartition des pluies en surface sur un bassin, le total des infiltrations dans un bassin, etc., influent sur la forme de (1), alors que la forme de (2) correspond à une courbe déterminée particulière à un bassin, sans rapport aucun avec les facteurs ci-dessus mentionnés. L'analyse est menée afin de déterminer la situation des points par lesquels la carte hydrographique (1) passe à la carte hydrographique (2). Les résultats obtenus pour un débit provoqué par une tempête isolée sont applicables à l'analyse du débit provoqué par des tempêtes complexes. 55

2 1 Data used for study The hydrological data used for this study ere obtained on the Kanna River Research Basin. The basin is located in the headaters of the Tone River hich drains the central part of Japan and flos into the Pacific Ocean. (Fig-1) The average annual precipitation over the basin is about 1,200 mm and the average annual runoff is about 800 mm. The area upstream from the gaging station is 374 km2 and the length of the main channel is 68 km. The shape of the basin is narro and long, and it ranges in elavation from sea level fro" 1,828 m to 100 m. The area is underlain by Paleozoic strata, and the depth of soil cover is not so thick, because the slope of mountainsides is very steep. The hole basin is forested moderately. Basides the gaging station on the basin outlet, another station is selected on one of tribuataries hich is located near the center of area of the basin. The drainage area upstream from the latter gaging station is 12.7 km. The number of rainfall stations over the basin is 31. The hourly records of rainfall and discharge at to stations are available from 1951 to The flood hydrographs used for this study are selected out of the above-mentioned records. Selected floods used at the gaging station on the basin outlet are not alays same as those used at the gaging station on the tributary. 2 Separation of hydrograph components Concerning a separation of hydrograph components after a flood peak for a runoff from isolated storms, a typical method is proposed.* This is only shon for a specific storm. The objective of this paper is to find a comon rule applicable to many floods. The authors demonstrate here empirically the factors hich have many extensive effects on the shape of rapidly changing hydrographs. Many examples hich satisfy the conditions that the floods are caused by isolated storms and that there are many no-rain days before and after isolated storms are selected out of the observed flood records. The selected flood hydrographs are arranged and given numbers according to the order of magnitude of discharge at the loest end of each flood. First, a comparison is made beteen to hydrographs hich have the samllest and second from smallest discharges at the loest end. These to hydrographs have usually common parts for a certain period, but separate from each other as the discharge of each hydrograph increases. Of the to hydrographs, the hydrograph hich comes undermeath is adopted for constructing a composite recession curve. The next step is to compare the flood hydrograph mentioned above and the flood hydrograph hich has the third from smallest discharge at the loest end. Selection and adoption are made beteen the to hydrographs as before. Continuing the procedures for all hydrographs, a composite recession curve can be co constructed by combining the segments obtained from each floods. Fig-2 shos the composite recession curve covering a ide variety of discharge. Flood hydrographs, hich sho rapid change of discharge after a flood peak for a certain period, finally follo the composite recession curve regardless of the magnitude of peak flo, the variation in areal rainfall distribution, etc. The problem is ho to decide the location of the transfer point on the composite recession curve. The characteristics of location of transfer points are analysed on the basis of observed data. * Lins ley and others : Applied Hydrology P

3 3 Composite recession curve The reason hy such a complicated procedure is necessary for constructing a composite recession curve is that no-rain days usually do not last long in this country except in inter. But the range of observed iischarge is small in inter. Supposing that no-rain days continue for more than 50 days after an isolated storm ith uniform rainfall distribution in rainy season, a recession curve obtained from this storm ould represent a ide range of composite recession curve. Actually it is almost impossible to get such a curve as an observed value and the complicated procedure mentioned in 2 should be adopted. Areal rainfall distribution differs much especially on the long basin. Besides the variation in areal rainfall distribution, the magnitude of peak flo, the total infiltration over a basin, etc., have much effect on the shape of the hydrograph after a flood peak. After a long elapse of time, the effect decreases to zero hen the hydrograph transfers to a composite recession curve Characteristics of flood hydrograph from a flood peak to a transfer point Analysis is made on the shape of flood hydrographs ranging from a flood peak to a transfer point on a composite recession curve. Here, the authors are not interested in detail analysis of the shape of flood hydrographs, but in a rough estimation method of location of transfer point on a composite recession curve. Absissa and ordinate of a transfer point are selected in the folloing ay. The time difference beteen a flood peak and a transfer point is considered to be a function of a peak flo for each flood. Fig-3 shos the relation beteen the time difference t and the peak flo Q.. A parameter hich represents the variation in areal rainfall distribution is introduced to explain the scattering points. The pattern of rainfall distribution is classified in three categories: the uniform distribution, the concentration in the headaters and the concentration in the vicinity of the outflo. The scattered points belong to one of three categories. The same procedure is folloed as to the hydrological data obtained on the tributary basin. The plotted points shon on Fig-4 mostly belong to one of three categories, though the boundaries of each category on the tributary basin are not so clear as before. The next procedure aims at obtaining the ordinate of a transfer point. Fig-5 shos a flood hydrograph from an isolated storm. A initial flo Qj> on a composite recession curve increases to a transfer flo Q 0 on another composite recession curve by an isolated storm. It represents that an increase in a groundater potential is related to Q 0-Qb. The amount related to QQ-QJ, is assumed to be effected primarily by the total infiltration amount and secondarily by the ater amount hich reaches the groundater aquifer. The total infiltration P2 is hypothetically calculated by summing hourly rainfall less than 2 mm/hr during an isolated storm. Out of the total infiltration, some is reserved as soil moisture during percolation. This amount P0.5 is hypothetically calculated by summing hourly rainfall less than 0.5 mm/hr during an isolated storm. The amount P2~- E> 0.5 is considered to be the amount hich increases the groundater potential after reaching the groundater aquifer. Fig-6 shos the relatife^een Q The 0 o-0b and the total infiltration 2 scattered points on the figure ai^t^ ell explained by introducing the parameter P2~ p 0.5- ' 57

4 7.4 A similar relation is also demonstrated on Fig-7 by using the data obtained on the tributary. In this case the to factors have nearly a straight-line relation, because the data are so selected that the areal rainfall distribution is almost uniform. 5 Calculation of total runoff For an isolated storm, calculation of total runoff can be made by the folloing procedure. In this case it is necessary that there are many no-rain days bebore the isolated storm and that a point of rise for the isolated storm lies on the composite recession curve for the previous storm. The total volume of runoff from an isolated storm is expressed by the figure EAPCF. (Fig-8) It is not easy to calculate the area of this figure directly, because the recession curve continues indefinitely. Then, a transformation of this figure is made for the convenience of calculation. A recession curve CF is parallel to a recession curve AF. The area of the figure EACF equals that of rectangular BACD. Accordingly, the area of figure EAPCF equals that of figure BAPCD. The total runoff from an isolated storm can be calculated by summing the discharge of the hydrograph from point B to point D. For a complex storm, the hydrograph for the first storm should be separated from that for the second one. At the beginning, it is necessary to estimate the location of the transfer point on a composite recession curve for the first storm. The horizontal and vertical distance of the transfer point can be obtained by using the results shon on Fig-3 and Fig-6. The horizontal distance beteen a flo peak and a transfer point is expressed as a function of the magnitude of peak flo and the rainfall pattern over a basin. The magnitude of flo at a transfer point Qj, can be claculated from Cj,-0[, hich is derived from the total infiltration P2 and the ater amount reaching the groundater aquifer P2~P().5- Finally, an arbitrary curve can be dran beteen the end of crest seqment A on the Fig-9 and a transfer point B. From the latter point a composite recession curve starts. TRIBUTARY KAMA RIVER ^ O JMW (km)" 135 E PACIFIC OCEAN Fig. 1. Location of the Kanna research basin 58

5 Fig. 2, Composite recession curve -100 o z È 50 Q W ^aée """" RAINFALL DISTRIBUTION UNIFORM -CONCENTRATION IN HEADWATERS Q CONCENTRATION IN VICINITY OF THE OUTLET PEAK FLOW Q P (m 3 /s) Fig. 3. Relation beteen the time difference t and the peak flo Qp (Main basin) 150 T loo o z OS Pu 3 50 RAIN FALL DISTRIBUTION UNIFORM * CONCENTRATION IN- / HEADWATERS /, a CONCENTRATION / INVJCpNITY /* OFJHE / OUTLET// / / / l.7A9 l>0 10 PEAK FLOW Q p (m 3 /s) Fig. 4. Relation beteen the time difference t and the peak flo Qp (Tributary basin) 59

6 HOURLY RAINFALL 2mni/hr 0.5mm/hr= Qb Fig. 5. Relation beteen the discharge Qb at an initial point and the discharge Qo at a transfer point Qo 15 PARAMETER P2 Po.5(mm! TOTAL INFILTRATION P2 (mm) Fig. 6. Relation beteen the discharge difference Q 0 Qb and the total infiltration?2 (Main basin)

7 7.7 J3 at I at J^-^ -^T 6.8 PARAMETER P*- 10 l0.3 -"" '5.8, Po.5 (mm) ^^- " ^^--^16.8 ^ ^ 1..!. i TOTAL INFILTRATION P 2 (mm) I Fig. 7. Relation beteen the discharge difference Q 0-Qb and the total infiltration P2 (Tributary basin) Fig. 8. Total runoff from an isolated storm COMPOSITE RECESSION CURVE Qo Fig. 9. Total runoff from a complex storm 61

8