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Open AccessArticle

Entropy Parameter M in Modeling a Flow Duration Curve

1
Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX 77840, USA
2
Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843-2117, USA
3
Hydrologic Systems Branch, Coastal and Hydraulics Laboratory, Engineer Research Development Center, U.S. Army Corps of Engineers, Vicksburg, MS 39181, USA
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(12), 654; https://doi.org/10.3390/e19120654
Received: 20 September 2017 / Revised: 28 November 2017 / Accepted: 30 November 2017 / Published: 1 December 2017
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
A flow duration curve (FDC) is widely used for predicting water supply, hydropower, environmental flow, sediment load, and pollutant load. Among different methods of constructing an FDC, the entropy-based method, developed recently, is appealing because of its several desirable characteristics, such as simplicity, flexibility, and statistical basis. This method contains a parameter, called entropy parameter M, which constitutes the basis for constructing the FDC. Since M is related to the ratio of the average streamflow to the maximum streamflow which, in turn, is related to the drainage area, it may be possible to determine M a priori and construct an FDC for ungauged basins. This paper, therefore, analyzed the characteristics of M in both space and time using streamflow data from 73 gauging stations in the Brazos River basin, Texas, USA. Results showed that the M values were impacted by reservoir operation and possibly climate change. The values were fluctuating, but relatively stable, after the operation of the reservoirs. Parameter M was found to change inversely with the ratio of average streamflow to the maximum streamflow. When there was an extreme event, there occurred a jump in the M value. Further, spatially, M had a larger value if the drainage area was small. View Full-Text
Keywords: flow duration curve; Shannon entropy; entropy parameter; modeling; spatial and dynamics characteristic flow duration curve; Shannon entropy; entropy parameter; modeling; spatial and dynamics characteristic
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MDPI and ACS Style

Zhang, Y.; Singh, V.P.; Byrd, A.R. Entropy Parameter M in Modeling a Flow Duration Curve. Entropy 2017, 19, 654. https://doi.org/10.3390/e19120654

AMA Style

Zhang Y, Singh VP, Byrd AR. Entropy Parameter M in Modeling a Flow Duration Curve. Entropy. 2017; 19(12):654. https://doi.org/10.3390/e19120654

Chicago/Turabian Style

Zhang, Yu; Singh, Vijay P.; Byrd, Aaron R. 2017. "Entropy Parameter M in Modeling a Flow Duration Curve" Entropy 19, no. 12: 654. https://doi.org/10.3390/e19120654

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