Huijuan Cui

On the Cumulative Distribution Function for Entropy-Based Hydrologic Modeling

In spatial or temporal physically based entropy-based modeling in hydrology and water resources, the cumulative distribution function (CDF) of a design variable (e.g., flux, say discharge) is hypothesized in terms of concentration (e.g., stage of flow). Thus far, a linear hypothesis has been employed when applying entropy to derive relationships for design variables, but without empirical evidence or physical justification. Examples of such relationships include velocity distribution as a function of flow depth, wind velocity as a function of height, sediment concentration profile along the flow depth, rating curve, infiltration capacity rate as a function of time, soil moisture profile along the depth below the soil surface, runoff as a function of rainfall amount, unit hydrograph, and groundwater discharge along the horizontal direction of flow. This study proposes a general nonlinear form of the CDF that specializes into commonly used linear forms. The general form is tested using empirical data on velocity, sediment concentration, soil moisture, and stage-discharge and compared with those reported in the literature. It is found that a simpler form of the general nonlinear hypothesis seems satisfactory for the data tested, and it is quite likely that this simple form will suffice for other data as well. The linear hypothesis does not seem to hold for the data employed in the study.

Entropy Theory for Streamflow Forecasting

Streamflow forecasting is used in river training and management, river restoration, reservoir operation, power generation, irrigation, and navigation. In hydrology, streamflow forecasting is often done using time series analysis. Although monthly streamflow time series are stochastic, they exhibit seasonal and periodic patterns. Therefore, streamflow forecasting entails modeling two main aspects: seasonality and correlation structure. Spectral analysis can be employed to characterize patterns of streamflow variation and identify the periodicity of streamflow. That is, it permits to extract significant information for understanding the streamflow process and prediction thereof. For forecasting streamflow, spectral analysis has, however, not yet been widely applied. Streamflow spectra can be determined using entropy theory. There are three ways to employ entropy theory: (1) Burg entropy, (2) configurational entropy, and (3) relative entropy. In either way, the methodology involves determination of spectral density, determination of parameters, and extension of autocorrelation function. This paper reviews the methods of spectral analysis using the entropy theory and tests them using streamflow data.

Suspended Sediment Concentration in Open Channels Using Tsallis Entropy

AbstractConcentration of suspended sediment is of fundamental importance in environmental management, assessment of best management practices, water quality evaluation, reservoir ecosystem integrity, and fluvial hydraulics. Assuming time-averaged sediment concentration along a vertical as a random variable, a probability distribution of suspended sediment concentration is derived by maximizing the Tsallis entropy subject to the constraint given by the mean concentration and under the assumption that the sediment concentration is zero at the water surface. For deriving the sediment concentration profile along the vertical, a nonlinear cumulative distribution function is hypothesized and verified with observed data. The derived sediment concentration profile is tested using experimental and field data; however, the clear water surface assumption does not seem to be valid for field data. The Tsallis entropy-based concentration profile method is compared with three sediment concentration profile methods. Comp...

Computation of Suspended Sediment Discharge in Open Channels by Combining Tsallis Entropy–Based Methods and Empirical Formulas

AbstractSediment discharge is computed by using different combinations of entropy-based and empirical methods of channel cross-section velocity and suspended sediment concentration distribution, and the results of these different methods are compared. The comparison shows that the entropy-based methods are more accurate than the empirical method and that the Tsallis entropy–based method is more accurate than the one based on Shannon entropy. The accuracy of the computation for all methods can generally be improved by introducing a correction factor; however, the fully entropy-based methods still remain the most accurate.

Tsallis Entropy Theory for Modeling in Water Engineering: A Review

Water engineering is an amalgam of engineering (e.g., hydraulics, hydrology, irrigation, ecosystems, environment, water resources) and non-engineering (e.g., social, economic, political) aspects that are needed for planning, designing and managing water systems. These aspects and the associated issues have been dealt with in the literature using different techniques that are based on different concepts and assumptions. A fundamental question that still remains is: Can we develop a unifying theory for addressing these? The second law of thermodynamics permits us to develop a theory that helps address these in a unified manner. This theory can be referred to as the entropy theory. The thermodynamic entropy theory is analogous to the Shannon entropy or the information theory. Perhaps, the most popular generalization of the Shannon entropy is the Tsallis entropy. The Tsallis entropy has been applied to a wide spectrum of problems in water engineering. This paper provides an overview of Tsallis entropy theory in water engineering. After some basic description of entropy and Tsallis entropy, a review of its applications in water engineering is presented, based on three types of problems: (1) problems requiring entropy maximization; (2) problems requiring coupling Tsallis entropy theory with another theory; and (3) problems involving physical relations.

Sediment Graphs Based on Entropy Theory

AbstractUsing the entropy theory, this paper derives an instantaneous unit sediment graph (IUSG or USG) to determine sediment discharge and the relation between sediment yield and runoff volume. The derivation of IUSG requires an expression of the effective sediment erosion intensity whose relation with rainfall is revisited. The entropy theory provides an efficient way to estimate the parameters involved in the derivations. Sediment discharge is also computed using the instantaneous unit hydrograph (IUH), which can also be derived using the entropy theory. This method works as well as the IUSG method, especially when the peak sediment discharge and peak runoff occur at the same time. The entropy theory yields the probability distribution of sediment yield and of sediment discharge, which can then be used to estimate uncertainty in sediment yield prediction.

Entropy Applications in Environmental and Water Engineering

Huijuan Cui 1,* ID , Bellie Sivakumar 2,3,4 ID and Vijay P. Singh 5 1 Key Laboratory of Land Surface Pattern and Simulation, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China 2 UNSW Water Research Centre, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia; s.bellie@unsw.edu.au 3 Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India 4 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China 5 Department of Biological and Agricultural Engineering & Zachry Department of Civil Engineering, Texas A and M University, College Station, TX 77843-2117, USA; vsiingh@tamu.edu * Correspondence: cuihj@igsnrr.ac.cn