Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Kim, Won

Lee, Chajoo

Lee, Heaeun

Yu, Minwook

English

Hydraulic Engineering Repository

Conference Paper, Published VersionLee, Chajoo; Yu, Minwook; Lee, Heaeun; Kim, WonA Method of Discharge Estimation Based on LateralVelocity Distribution Function Applied To UltrasonicVelocity Meter SystemZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/109820Vorgeschlagene Zitierweise/Suggested citation:Lee, Chajoo; Yu, Minwook; Lee, Heaeun; Kim, Won (2010): A Method of DischargeEstimation Based on Lateral Velocity Distribution Function Applied To Ultrasonic VelocityMeter System. In: Sundar, V.; Srinivasan, K.; Murali, K.; Sudheer, K.P. (Hg.): ICHE 2010.Proceedings of the 9th International Conference on Hydro-Science & Engineering, August2-5, 2010, Chennai, India. Chennai: Indian Institute of Technology Madras.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 A METHOD OF DISCHARGE ESTIMATION BASED ON LDM APPLIED TO UVM                         A METHOD OF DISCHARGE ESTIMATION BASED ON LATERAL VELOCITY DISTRIBUTION FUNCTION APPLIED TO ULTRASONIC VELOCITY METER SYSTEM  Chajoo Lee1, Minwook Yu2, Heaeun Lee2, Won Kim3                                              Abstract:  Lateral velocity distribution (LDM) based on the beta density function proposed by Seo and Baek (2004) is applied to compute discharge using the velocity data obtained from the ultrasonic velocity meter. Shape parameters α  and β  are estimated by using the 5 lateral velocity distribution datasets measured by an ADCP. Vertical velocity distribution is assumed to follow common one-sixth power law. Edge discharges are estimated by using the nearest velocities. Resultant discharge by LDM is roughly in accordance with the dam discharge. The method shows better accuracy for the high flow over 200m3/s with relative difference of 7.4% from the dam discharge. In a practical and economic view, LDM is considered as an accurate method to get discharge with a little effort.  Keywords: lateral velocity distribution; LDM; discharge; UVM;   INTRODUCTION Automatic and continuous measurement methods have been widely introduced to streamflow monitoring field in pla ce of traditional sta ge-discharge relationship. Among them, ultr asonic velocity meter (UVM) w hich as a one of the oldest methods, onl y gives information on line velocity has been still used due to its simplicity and robustness for natural condition. Discharge measurement by using the single path UVM generally needs relationship between line velocity which is directly measured by the UVM and mean velocity of the cross-section which is obtained b y making direct dischar ge measurements. Then conversion coefficient k  value is commonly used to represent the relationship. And cross-section area calculated from stage-area relationship is used to compute final discharge. For establishment of the relationship between the line and the mean velocities to derive the value k , generally at least a dozen direct discharge m easurements need t o be m ade for a ran ge of dischar ge as  wide as possible.  However, the work needs much time and manpower. So, there have been various effort to make this work efficient. In this study, we propose a new method to compute discharge based on a probabilistic density function to reproduce lateral velocity distribution. By using this method discharge in the whole                                                  1 Researcher, R iver, C oast an d Harbor  R esearch Divis ion, Korea In stitute o f C onstruction T echnology, 1190  Simindaero, Ilsanseo-Gu, Goyang-Si, Gyeonggi-Do, Republic of Korea, Email: c0gnitum@kict.re.kr 2 Former Researcher, River, Coast and Harbor Research Division, Korea Institute of Construction Technology, 1190 Simindaero, Ilsanseo-Gu, Goyang-Si, Gyeonggi-Do, Republic of Korea 3 Research Fellow, River, Coast and Harbor Research Division, Korea Institute of Construction Technology, 1190 Simindaero, Ilsanseo-Gu, Goyang-Si, Gyeonggi-Do, Republic of Korea, Email: wonkim@kict.re.kr  Proceedings of ninth International Conference on Hydro-Science and Engineering (ICHE 2010), IIT Madras, Chennai, India. 2 - 5  August 2010 910Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 A METHOD OF DISCHARGE ESTIMATION BASED ON LDM APPLIED TO UVM                     cross-section can be computed. It only needs several direct lateral velocity measurements for parameter estimation. The procedures of and the results by this new method are described and presented in the following paragraphs.   SITE In this study we use a UVM installed at the midstream of the Dalcheon River which is located near the cente r of the South Korea. It is a c obble-bed river which is stable even durin g high flow. Its flow is regulated by the upstream dam for hydroelectric power generation and flood control. Dam releases discharges ranging from 6 to over 1,000m3/s. Its discharge is to be used as a reference value to measured discharge by the UVM. In the study site, a doubl e layer UVM is installe d across the river. But only a lower sensor is used f or this stud y. It i s insta lled a t the  lowe r part in the  me asurement c ross-section f or unceasing monitoring throughout a year. Figure 1 shows cross-section and plan view of the  installation site.   Figure 1. Cross-section and plan view of the UVM installed site   LATERAL VELOCITY DISTIRIBUTION The UVM onl y gives t he l ine vel ocity across the ri ver for di scharge m easurement. It i s regarded as integration of lateral velocity distribution along in the narrow water layer through which acoustic beam penetrates. To obtain cross-sectional velocity distribution for discharge, there should be two elements: la teral and vertical. F or the late ral velocity distribution, beta density function (BDF ) is used for this  stud y. In this s tudy, w e call this method as lateral  distribution method ( LDM). Paramet ers in th e BDF a re estimated b y u sing the  measur ed velocity distribution acq uired w ith an A DCP f or the  acoustic b eam la yer. F or the ver tical velocity distribution, simple power law is adopted.  Beta Density Function BDF for the lateral velocity distribution is previously used by Seo and Baek (2004). It is known that the BDF well reproduce the lateral velocity distribution pattern in the natural channels. The BDF is established b y combination of g amma probability density function. It can r eproduce both symmetric and asymmetric distribution. General equation for the BDF is just as Eq. (1).  911Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 A METHOD OF DISCHARGE ESTIMATION BASED ON LDM APPLIED TO UVM                     11 )1()()()()( −− −Γ+Γ+Γ= βαβαβαxxxf, 10 << x                                                          (1)  where, α  and β  are pa rameters whic h de termine the sha pe of  the  distr ibution. )(αΓ  and )(βΓ are defined by Eq. (2) and Eq. (3).  dxexx x−∞ −∫=Γ 01),( αα, 0>α                                                                                (2) dxexx x−∞ −∫=Γ 01),( ββ, 0>β                                                                                (3)  Dimensionless Lateral Velocity Distribution Dimensionless lateral velocity distribution along in the acoustic beam layer can be expressed in the form of the BDF like Eq. (4).  11 )'1()'()()()( −− −Γ+Γ+Γ= βαβαβαyyUu, 1'0 << y                                                       (4)  in which u  is a point velocity at the UVM height, whose position is 'y  in the lateral direction, U  is laterally integrated velocity and 'y  is dimensionless lateral distance from the left end.  Parameter Estimation Parameters α  and β  may be de termined b y two ways. F irst, if  the re is la terally m easured velocity dataset at the UVM height, they can be estimated by least square method. But there no velocity distribution data, they may be estimated from only two figures: maximum velocity and its horiz ontal posit ion along  the width. In this  study, ADC P t ransect d ata we re used t o determine the parameters. Cell velocity data at the UVM height are extracted considering depth and cell size of the ADCP data. Figure 2 shows lateral velocities for the 5 cases measured by ADCP in the cross-section. Used ADCP datas et and best fitted values for the p arameters α  and β  are shown in Table 1.    Figure 2  Measured lateral velocity distribution by the ADCP  912Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 A METHOD OF DISCHARGE ESTIMATION BASED ON LDM APPLIED TO UVM                      Table 1  Parameter estimation for the measured dataset Data set Discharge (m3/s) Width Water level (m) Best fitted Mean value applied Differenceα  β  RMSE α  β  RMSE #1 46.2  117.5 108.38 1.58 1.16 0.788 1.52 1.15 0.795 0.007#2 257.2  128 109.16 1.47 1.17 0.564 1.52 1.15 0.6 0.036#3 58.9  119 108.44 1.47 1.11 0.752 1.52 1.15 0.768 0.016#4 97.7  124 108.61 1.48 1.14 0.776 1.52 1.15 0.777 0.001#5 43 118 108.44 1.6 1.17 0.753 1.52 1.15 0.768 0.015Average 1.52 1.15 0.727 0.741 0.015 After judgment from the fitted parameters shown in Table 1, which have only slight difference from each other, the parameters α  and β  are assumed to be approximately the same for whole discharge range. Thus, mean values of 1.52 and 1.15 for the parameters α  and β , respectively are used to compute the lateral velocity distribution in the acoustic beam layer.    Figure 3  The BDF fitted to measured lateral velocity distribution (case #2)    VERTICAL VELOCITY DISTRIBUTION To g et d epth-averaged v elocities for all the di scretized lateral positions , it is necessar y to establish ve rtical ve locity distribution f or the m. In this stud y, simple  po wer la w in which one-sixth e xponent is adopted is assumed. According to Chen (1991) and Simpson and  Oltmann (1990) power law equivalent of Manning’s formulae for open channels is expressed as Eq. (5). From the computed lateral velocity for a single position in the acoustic beam layer, depth-averaged velocity for it can be expressed as Eq. (5).  6/10* )/(5.9/ zzvv = ,                                                                                           (5)  0.0 0.5 1.0 1.5 2.0 2.5 ‐0.4  ‐0.2  0.0  0.2  0.4  0.6  0.8  1.0  1.2 u/Uy'/WObserved velocityBeta density functionTop widthWater surface width at sensor depthSensor width913Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 A METHOD OF DISCHARGE ESTIMATION BASED ON LDM APPLIED TO UVM                     here, z  is distance to the channel bed, 0z  is bottom roughness height, v  is velocity at distance z  from the bed, *v  is shear velocity. For a condition in which there are known velocities in the vertical, Eq. (5) can be rewritten as Eq. (6).  6/1azv = ,                                                                                                            (6)  in whic h a can be  de termined f rom a t le ast one  velocity va lue in the  ve rtical. F rom the computed la teral ve locity f or a sing le discr etized position in the a coustic be am lay er, depth-averaged velocity for it can be expressed as Eq. (7).  6/176⎟⎟⎠⎞⎜⎜⎝⎛=iiiihduV,                                                                                                 (7)  where iV  is depth-averaged velocity for the la terally discretized vertical, iu  is the calculated velocity by Eq. (4) for the laterally discretized real coordinate (distance) from the left sensor, id  and ih are depth and the height of the acoustic beam layer in the vertical.   DISCHARGE COMPUTATION The lateral velocity distribution can only be calculated for the width between the two acoustic transducers. For this width, discharge is calculated by multiplying the depth-averaged velocity by sub-areas defined by the product of the discretized width and depth. Finally, remaining area of the both sides beyond the sensor position should be estimated. For these areas, traditional triangular computation method expressed by Eq. (8) is used.  RLnRL AVQ ,,1, 707.0= ,                                                                                           (8)  In which, RLQ ,  is edge discharge near the le ft or  the r ight bank,  nV ,1  is the  f irst or  the  last velocity near the sensor, and RLA ,  is edge area.   RESULTS AND DISCUSSION Figure 4 shows time-series discharge data of the two during the flood season of July 2009. The one is dam released discharge which serves as reference and the other is computed discharge by LDM in this stud y. LDM disc harge is in a  good agre ement with dam discharge, but ove r approximately 450m3/s it shows no data because acoustic signals could not detected over this discharge. Figure 5 shows one to one comparison between the dam and LDM discharges for various flow condition which maintain relatively constant dam release. It can be easily noted that the LDM gives slightly larger discharge than the dam does, especially for the low flow. Due to this, RMS error for the low flow comes to about 20%. However, for discharge larger than 100m3/s, RMS error decreases to 11.7% and for  over 200m3/s, it diminishes to only 7.4%. Judging from this 914Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 A METHOD OF DISCHARGE ESTIMATION BASED ON LDM APPLIED TO UVM                     result, it is  infe rred tha t the  LDM mode l unde r the  condition mentioned above g ives more accurate discharge for the relatively high flow.  Figure 4  Time-series discharge comparison Figure 5  Comparison of the LDM discharge with the dam discharge  Under the consideration that the LDM in this stu dy has two fixed assumptions on the  lateral and vertical velocity distribution and only 5 times of direct measurements are used to estimate the param eters, this resu lt is very good. Conv ersely sp eaking, its assump tions are rou ghly suitable f or the  r eal c ondition. E specially, la teral ve locity distr ibution pa ttern se ems to be  relatively consistent for the entire discharge range. Nevertheless, the LDM are not so accurate for the low flow. There should be a detailed analysis. Though not tested, effect of parameter estimation based on the fewer cases of data on accuracy of computed discharge is necessary to be evaluated. In this study, we used 5 data for parameter fitting. Resultant α  and β  values for the 5 cases are nearly the same. So, with a fewer direct measurement, largely the same result is  expected to be obtained. I n this point, this  method is economic and applicable for discharge computation.   SUMMARY AND CONCLUSIONS  In this study, lateral velocity distribution (LDM) based on the beta density function proposed by Seo and Baek (2004) is applied to compute discharge with the ultrasonic velocity meter data. Shape parameters α  and β  are estimated by using the 5 la teral velocity distribution datasets measured b y ADCP. Vert ical vel ocity di stribution is a ssumed to  f ollow power la w w ith a  common one-sixth exponent. Edge discharges are estimated by using the nearest velocities.  Discharge computed b y using  the LDM are ro ughly in ac cordance wit h the dam released discharge. The method shows large errors for the low flow, while it shows better accuracy over 200m3/s by showing 7.4% of relative difference from the dam discharge. Under the condition that the  LDM h as som e r ather fixed a ssumption conc erning late ral and vertical  velocit y distribution together with relatively few direct measurements, it is considered as a practical and economic wa y to get a ccurate disc harge, especially for th e hi gh flow using  the ultrasonic  velocity meter.   915Proceedings of ICHE2010, IIT Madras, Aug 2-5,2010 A METHOD OF DISCHARGE ESTIMATION BASED ON LDM APPLIED TO UVM                   ACKNOWLEDGEMENTS This research was suppo rted by a grant from Sustainable Water Resour ces Research Cent er (2-1-3) of 21st Century Frontier Research Program of Republic of Korea.   REFERENCES  Chen, C- L. 1991. Unifi ed theor y on po wer la ws for flow resistan ce. Journal of Hydraulic Engineering, ASCE, 117 (3), 371-389. Seo, I. W. and Back, K. O. 2004. Estimation of the Longitudinal Dispersion Coefficient Using the Velocity Profile in Natural Streams. Journal of Hydraulic Engineering, ASCE, 130 (3), 227-236. Simpson, M. R. and Olt mann, R. N. 1990. An Acoustic Doppler Dis charge Me asurement System. Proceedings of the 1990 National Conference on Hydraulic Engineering, 2,  903-908 916

A Method of Discharge Estimation Based on Lateral Velocity Distribution Function Applied To Ultrasonic Velocity Meter System

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A Method of Discharge Estimation Based on Lateral Velocity Distribution Function Applied To Ultrasonic Velocity Meter System

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