Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory

The one-dimensional (1D) power law velocity distribution, commonly used for computing velocities in open channel flow, has been derived empirically. However, a multitude of problems, such as scour around bridge piers, cutoffs and diversions, pollutant dispersion, and so on, require the velocity distribution in two dimensions. This paper employs the Shannon entropy theory for deriving the power law velocity distribution in two-dimensions (2D). The development encompasses the rectangular domain, but can be extended to any arbitrary domain, including a trapezoidal domain. The derived methodology requires only a few parameters and the good agreement is confirmed by comparing the velocity values calculated using the proposed methodology with values derived from both the 1D power law model and a logarithmic velocity distribution available in the literature

Variability and Trends in Streamflow in Northeast United States

Abstract There is general consensus that climate is undergoing change but whether climate change is occurring or not is still being debated in certain scientific, political, and religious quarters. Hydrologic variability influences the design of civil works and assessment of long-term climate change would help improve design criteria. To this end, long-term variability of streamflow was estimated using Shannon entropy. Three statistical tests were applied to determine trends in annual and seasonal daily streamflow with 5% two-sided confidence limit. Daily streamflow data spanning 70 years (from 1943 to 2012) from 669 stream gauge stations located in 23 states in the northeastern part of United States of America, covering six different water regions were employed. The time variability of annual and seasonal daily streamflow was assessed using the Mean Decadal Apportionment Disorder Index ( MDADI ). Analysis showed that in all cases minimum and maximum streamflows had higher variability than average and median streamflows. A significant number of stations exhibited trends. Considering annual minimum, average and median daily streamflows, approximately 50% of the stations followed trends and for almost all these stations trends were increasing. Only for annual maximum daily streamflow, 15% of the stations showed increasing trend and 10% decreasing trend. In terms of geographical distribution, the stations with increasing trend were essentially located along the Atlantic coast and near Great Lakes and in the Upper Mississippi Water Region. Similar considerations apply for seasonal time series as well

Three Methods for Estimating the Entropy Parameter M Based on a Decreasing Number of Velocity Measurements in a River Cross-Section

The theoretical development and practical application of three new methods for estimating the entropy parameter M used within the framework of the entropy method proposed by Chiu in the 1980s as a valid alternative to the velocity-area method for measuring the discharge in a river is here illustrated. The first method is based on reproducing the cumulative velocity distribution function associated with a flood event and requires measurements regarding the entire cross-section, whereas, in the second and third method, the estimate of M is based on reproducing the cross-sectional mean velocity by following two different procedures. Both of them rely on the entropy parameter M alone and look for that value of M that brings two different estimates of , obtained by using two different M-dependent-approaches, as close as possible. From an operational viewpoint, the acquisition of velocity data becomes increasingly simplified going from the first to the third approach, which uses only one surface velocity measurement. The procedures proposed are applied in a case study based on the Ponte Nuovo hydrometric station on the Tiber River in central Italy

Hot Spots and Persistence of Nitrate in Aquifers Across Scales

Nitrate-N (NO3 -- N) is one of the most pervasive contaminants in groundwater. Nitrate in groundwater exhibits long-term behavior due to complex interactions at multiple scales among various geophysical factors, such as sources of nitrate-N, characteristics of the vadose zone and aquifer attributes. To minimize contamination of nitrate-N in groundwater, it is important to estimate hot spots (>10 mg/L of NO3 -- N), trends and persistence of nitrate-N in groundwater. To analyze the trends and persistence of nitrate-N in groundwater at multiple spatio-temporal scales, we developed and used an entropy-based method along with the Hurst exponent in two different hydrogeologic settings: the Trinity and Ogallala Aquifers in Texas at fine (2 km × 2 km), intermediate (10 km × 10 km) and coarse (100 km × 100 km) scales. Results show that nitrate-N exhibits long-term persistence at the intermediate and coarse scales. In the Trinity Aquifer, overall mean nitrate-N has declined with a slight increase in normalized marginal entropy (NME) over each decade from 1940 to 2008; however, the number of hot spots has increased over time. In the Ogallala Aquifer, overall mean nitrate-N has increased with slight moderation in NME since 1940; however, the number of hot spots has significantly decreased for the same period at all scales

Derivation of 2D Power-Law Velocity Distribution Using Entropy Theory

The one-dimensional (1D) power law velocity distribution, commonly used for computing velocities in open channel flow, has been derived empirically. However, a multitude of problems, such as scour around bridge piers, cutoffs and diversions, pollutant dispersion, and so on, require the velocity distribution in two dimensions. This paper employs the Shannon entropy theory for deriving the power law velocity distribution in two-dimensions (2D). The development encompasses the rectangular domain, but can be extended to any arbitrary domain, including a trapezoidal domain. The derived methodology requires only a few parameters and the good agreement is confirmed by comparing the velocity values calculated using the proposed methodology with values derived from both the 1D power law model and a logarithmic velocity distribution available in the literature