Variations in Spectral Slope in Lake Taihu,a Large Subtropical Shallow Lake in China

Spectral slope (S), describing the exponential decrease of the absorption spectrum over a given wavelength range, is an important parameter in the study of of chromophoric dissolved organic matter (CDOM) dynamics, and also an essential input parameter in remote sensing models. Furthermore, S is often used as a proxy for CDOM composition, including the ratio of fulvic to humic acids and molecular weight. The relative broad range in S values reported in the literature can be explained by the different spectral ranges and fitting methods used. A single exponential model is used to fit the S values for 17 investigations involving 458 samples in Lake Taihu from January to October in 2004. The average S value was 15.18 ± 1.39 μm⁻¹ for the range of 280–500 nm, which fell within the range reported in the literature. The frequency distribution of S value basically obeyed a normal distribution. Significant differences in S values between summer and other seasons showed that phytoplankton degradation was one of the important sources of CDOM in summer, whereas CDOM mainly came from the river input in other seasons. Furthermore, the estimated S value decreased with increasing wavelength range used in regression. The maximum and minimum values derived from the regression were 17.89 ± 1.25 μm⁻¹ and 13.62 ± 2.11 μm⁻¹ for the wavelength ranges of 280–380 nm and 400–500 nm, respectively, a decrease of 23.9%. S values significantly decreased with the increase of CDOM absorption coefficients. CDOM absorption coefficients could be more appropriately estimated from exponential model introducing the variation of S with absorption coefficients, making them useful for a remote sensing bio-optical model of Lake Taihu. DOC-specific absorption coefficient a*(λ) and the parameter M describing molecular size of the humic molecules could also be used as a proxy for the sources and types of CDOM. A general relationship was found between S and a*(λ), and M values. S increased with the decrease of DOC-specific absorption coefficient and the increase of M corresponding to the decrease of molecular weight.     

Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity

This article proposes an approach for investigating the exponential stability of a nonlinear interval dynamical system with the nonlinearity of a quadratic type on the basis of the Lyapunov’s direct method. It also constructs an inner estimate of the attraction domain to the origin for the system under consideration.     

Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies.