NON-CONTACT DISCHARGE ESTIMATION USING ENTROPY THEORY

Abstract

Among various discharge estimation methods employed in hydrometric practices, the velocity-area method is traditionally used by river engineers and hydrologists of many countries. The WMO also has recommended the application of the same for river discharge estimation. Though the velocity-area method is more popular in many countries, its use involves tedious procedures requiring measurement of pointvelocities at many pre-specified flow verticals across the flow section, and at many points along each of these verticals using the current meter in order to estimate the mean velocity of flow passing the section. Fortunately, the developments in technology over the last few decades have enabled the introduction of advanced river flow velocity measurement instruments, some being water contact based, such as the Acoustic Doppler Current Profiler (ADCP) and, some other being non-contact-based instruments, such as the Surface Velocity Radar (SVR), the Large-Scale Particle Image Velocimetry (LSPIV), and the Space-Time Image Velocimetry (STIV). The use of these instruments have improved the accuracy of mean flow velocity estimation, besides enabling quick and easy velocity measurement and, hence, improving the accuracy of discharge passing a river section in comparison with the traditionally employed tedious, time consuming and operator safety concerned current meter velocity measurement. It is pertinent to understand that the basis behind the use of these improved instruments is to estimate the mean velocity of flow passing a river section easily and accurately, besides ensuring safety of the operator. Having estimated the mean flow velocity of each of the verticals of flow section of a flow event using the specified measurements of flow characteristics of the flow event, the mean flow velocity of flow section is computed in the same way as adopted in the velocity-area method. An ingenious way of estimating the mean flow velocity across a desired flow section can be achieved, if attention is paid to the systematic point-velocity variation realized across the flow section, and extracting the information behind the velocity distribution pattern that prevails therein using the entropy principle. A step in this direction is to study the vertical point- velocity distribution across the flow section using Prantl-Von Karmarn logarithmic law, and the power-law which are the traditional velocity distribution laws described in many open channel hydraulics text books. But these distribution laws can describe only the one-dimensional flow which prevails in wide-width channels and rivers, and for which the maximum point-velocity occurs at the water surface of central section of river. But for narrow width channels and rivers, the flow may be characterized by two-dimensional point-velocity field and the maximum point-velocity, generally, occurs below the water surface. Therefore, considering the limitations of the traditional vertical point-velocity distribution laws, Chiu (1988) advocated the use of entropy concept to estimate the cross-sectional mean velocity, and he established a relationship between the cross-sectional mean flow velocity and the maximum pointvelocity of the flow event. It is a quick as well as a reliable approach of estimating the cross-sectional mean flow velocity. The study presented herein is undertaken with the following objectives: 1 Establishment of a relationship between the maximum point-velocity of flow field across the section of a river for a flow event with the corresponding event’s mean flow velocity using the Tsallis entropy theory, and performing the comparative evaluation of the Tsallis entropy theory based estimated discharges with the corresponding discharges estimated by the Shannon entropy theory, 2 Replacing the tedious computational procedure involved in the traditional velocityarea method in arriving at the mean flow velocity at a flow section using the measured maximum 0.6D point-velocity information across different verticals of the section of a flow event using the entropy theory and, 3 The development of a non-contact discharge estimation technique at an ungauged river section using the entropy theory. Taking up the first objective, the study establishes the Tsallis entropy-based relationship between the surface flow velocity and maximum flow velocity, and presents the details of the comparative study of the Tsallis entropy theory with the Shannon entropy theory at different river sites of the Italian rivers. It is inferred from the study that the efficiency of the Tsallis entropy concept based estimated discharge is similar as that of the Shannon entropy conceptbased discharge as revealed by high metrics of NSE and R2, and very low percentage of error as evaluated using the data of Italian river gauging stations. Taking up the second objective, the study establishes a relationship between the maximum of the point-velocity measured at 0.6D depths, as used in the well-known velocity-area method for mean flow velocity estimation, with that of the maximum point-velocity of the flow field as used in the entropy theory-based method. In this study the state equilibrium constant or the entropic constant was computed using the historical records of the velocity-area method for the Indian Rivers. This concept was first verified for the flow measurements of Italian River gauging stations, where the maximum flow velocity and the velocity at 0.6D depths are measured across different vertical of the flow section of a flow event. The NSE values of the discharges estimated using this proposed method in reproducing the estimated discharges using the velocity-area method at various gauging stations of the Indian rivers are found to be more than 0.99 and the percentage of error is well within the acceptable limits. Therefore, by measuring only the maximum 0.6D point-velocity of the flow section of a flow event, one can estimate the mean flow velocity of any flow event. This approach reduces the effort and time spent for 0.6D depth velocity measurements at different verticals of the flow section of a flow event as carried out in the velocity-area method of the current hydrometric practices. With regard to the last objective, the study presents the development of an entropy theory-based approach for non-contact discharge estimation at ungauged river sites, where any form of a priory velocity measurements are not available. For this purpose, the study utilized the gauged Italian river sites data treating them as ungauged river sites. The estimated discharges using the proposed method in reproducing the benchmark discharges estimated at these stations are found to be characterized by high NSE values, and the range of percentage of error of the estimated discharges in comparison with the benchmark discharges is well within the acceptable limit.