HYDROLOGICAL PROCESSES Hydrol. Process. 18, 1671–1684 (2004) Published online 8 March 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.1476 A fast method of flood discharge estimation Yen-Chang Chen1* and Chao-Lin Chiu2 1 Department of Civil Engineering, National Taipei University of Technology, Taipei, Taiwan 2 Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA Abstract: Discharge, especially during flood periods, is among the most important information necessary for flood control, water resources planning and management. Owing to the high flood velocities, flood discharge usually cannot be measured efficiently by conventional methods, which explains why records of flood discharge are scarce or do not exist for the watersheds in Taiwan. A fast method of flood discharge estimation is presented. The greatest advantage of the proposed method is its application to estimate flood discharge that cannot be measured by conventional methods. It has as its basis the regularity of open-channel flows, i.e. that nature maintains a constant ratio of mean to maximum velocities at a given channel section by adjusting the velocity distribution and the channel geometry. The maximum velocity at a given section can be determined easily over a single vertical profile, which tends to remain invariant with time and discharge, and can be converted to the mean velocity of the entire cross-section by multying by the constant ratio. Therefore the mean velocity is a common multiple of maximum velocity and the mean/maximum velocity ratio. The channel cross-sectional area can be determined from the gauge height, the water depth at the y-axis or the product of the channel width multiplied by the water depth at the y-axis. Then the most commonly used method, i.e. the velocity–area method, which determines discharge as the product of the cross-sectional area multiplied by mean velocity, is applied to estimate the flood discharge. Only a few velocity measurements on the y-axis are necessary to estimate flood discharge. Moreover the location of the y-axis will not vary with time and water stage. Once the relationship of mean and maximum velocities is established, the flood estimation can be determined efficiently. This method avoids exposure to hazardous environments and sharply reduces the measurement time and cost. The method can be applied in both high and low flows in rivers. Available laboratory flume and stream-flow data are used to illustrate accuracy and reliability, and results show that this method can quickly and accurately estimate flood discharges. Copyright 2004 John Wiley & Sons, Ltd. KEY WORDS discharge; entropy; flood estimation; mean/maximum velocity ratio; probability INTRODUCTION Discharge, the volume of water flowing through a cross-section of a stream in a given amount of time provides useful information for understanding hydrological processes. These data are very useful for water resources planning, design of hydraulic structures, flood control and decision making. A continuous record of discharge and stage can be used to construct a stage–discharge rating curve that is the most commonly used method to estimate discharge. A stage–discharge rating curve commonly obeys the equation of the form (Rantz, 1982b) Q D pG eN 1 where Q is the discharge that is usually made by current meter, p and N are constants, G is the stage and e is the water stage of zero flow. Under uniform flow conditions, discharge is then obtained by the measured stage and stage–discharge rating curve. However, a large portion of the annual transportation of water and sediment occurs during floods. It is particularly important to make discharge measurements when stream * Correspondence to: Yen-Chang Chen, Department of Civil Engineering, National Taipei University of Technology, Taipei, Taiwan. E-mail: [email protected] Copyright 2004 John Wiley & Sons, Ltd. 1672 Y.-C. CHEN AND C.-L. CHIU stages are high. Such measurements form the basis for flood warning, flood forecasting, reservoir operation and estimates of annual flow volumes. The stage–discharge relationship is subject to shifts as a result of flood wave during high water. Owing to the energy slope varying with time, the stage–discharge rating curve cannot be used to estimate discharge when backwater or highly unsteady flow exits. During a flood period, which is invariably unsteady, the stage–discharge relation is a loop as described in Figure 1, which shows that at a given water level the stage–discharge relationship obtained during steady flow periods tends to underestimate the discharge when the flow is rising, and overestimate it when the flow is subsiding. The individual conditions of an unsteady flow have individual energy slopes. Each individual flood should have an individual loop. Each loop therefore can only display only an individual flood. Consequently, it would be difficult to estimate flood discharge accurately by using a stage–discharge rating curve. Many indirect methods (Rantz, 1982b; Bureau of Reclamation, 1997) are used to estimate flood discharge. The slope–area method, which makes use of empirical equations along with the energy slope, is the most commonly used technique to make determinations of peak discharge. The channel-geometry method, which relies on discharge and channel dimensions, is used to estimate mean annual flood (Wharton and Tomlinson, 1999). However, it is difficult to measure real-time flood discharge accurately. The indirect methods cannot be of sufficient accuracy even when the flood discharge is estimated by floats (Chow, 1964). Floats are used under conditions for which no conventional method is available. Moreover flood discharge estimated by indirect methods is unreliable (Quick, 1991) and usually cannot be verified. The current-meter method is the most popular, convenient and widely used direct method of discharge measurement. The concept of the current-meter method is to divide the cross-section of an open channel into several elemental strips, and measure the velocities and depths by current meter and cable at the centre of each strip. The discharge of the stream cross-section is computed by using the mid-section or mean-section methods. The disadvantages of the current-meter method are that they are costly, labour intensive and tedious. Thus flood discharge measurement is difficult using the current-meter method. The moving-boat method is usually used to measure discharge rapidly on large steams and estuaries. However, it is frequently impractical and dangerous to use the moving-boat method during floods. Accurate 30 Unsteady flow in flume with unvegetated flood plain (Tu et al. 1995) Observed data (5) 25 Variation with time (4) t(s) (3) (1) 99 (2) (2) 100 (1) 20 (3) 105 (4) 120 (5) 150 Steady (6) (6) 200 (7) 220 15 (8) 250 (7) Q (l/s) (9) 254 (8) 10 (9) 5 0 45678910 D (cm) Figure 1. Stage–discharge loop during a flood simulated in the laboratory. Reproduced from Chiu and Chen, 2003 Copyright 2004 John Wiley & Sons, Ltd. Hydrol. Process. 18, 1671–1684 (2004) FLOOD DISCHARGE ESTIMATION 1673 estimation of flood discharge requires velocity sampling and measurement of water depths across the channel. Measuring flood discharge during highly unsteady flow has to be completed as rapidly as possible, owing to the fact that flow conditions change rapidly. Flood discharge measurement can be hazardous to personnel and instruments. In order to avoid exposure to the hazardous environment too long, some non-contact methods (Spicer et al., 1997; Herschy, 1999; Costa et al., 2000) that do not involve immersing equipment in the stream have been developed to measure flood discharge. They measure only water surface velocities. A surface-velocity coefficient of 0Ð85 or 0Ð86 is preferred to convert water surface velocity to mean velocity when a surface-velocity method is used (Rantz, 1982a). However, the maximum velocity usually occurs beneath the water surface during flood periods. The higher the water stage is, the deeper the location of maximum velocity. It is, thus, easy to underestimate flood discharges by using non-contact methods. Figure 2 shows the velocity distribution of unsteady flow. The mean velocity is 54Ð1 cm/s, and the maximum velocity occurs beneath the water surface at around 0Ð6 depth. If the mean velocity is estimated by non-contact methods, and the surface-velocity coefficient 0Ð85 is used, it will be underestimated and be only 41Ð1 cm/s. Consequently, flood discharge cannot be determined easily and accurately using conventional methods, particularly in wide open-channels. Until recently, a key limitation to understanding flood flow has been the difficulty and expense associated with using conventional methods. Owing to rapid change of flow conditions allowing very little time for measurements, new techniques have been applied to measure velocity quickly (Klein et al., 1993; Schultz, 1996; Callede et al., 2000; Sulzer et al., 2002). However, a new method to determine flood discharge efficiently is still required. A fast method of flood discharge measurement that is efficient and requires only a small number of velocity samples is preferred. (Chen and Chiu, 2002) have successfully used an efficient method to estimate discharge in tidal streams with the strong effects of turbulent flow. The concept of the method presented in this study is to attain efficiency of discharge measurements by observing and understanding the physical process of flood flow and by taking advantage of regularities recognizable in the flow. Discharge through a cross-section in a natural channel is estimated from the mean velocity in the section and the cross- sectional area. The method proposed is based on the constant ratio of mean to maximum velocities (Chiu and 8 Flume Data (Tu et al., 1995) Water in unvegetated flood plain Surface velocity = 48.4 cm/s 7 Unsteady flow, t=120 s Φ=0.78 umax=59.1 cm/s 6 D=8.4 cm h=5.4 cm h/D=0.645 5 Mean velocity = 54.1 cm/s Mean velocity by surface-velocity method = 41.1 cm/s 4 y (cm) 3 2 1 0 0 10203040506070 u (cm/s) Figure 2.