Application of Integrated Shannon’s Entropy and VIKOR Techniques in Prioritization of Flood Risk in the Shemshak Watershed, Iran

Abstract

Watersheds are known as the most significant unit of flood management. Prior to the implementation of structural and/or non-structural flood mitigation measures, it is vital to prioritize the hydrological units based upon their potential for flooding. Yet, watershed prioritization is generally faced with such major methodological challenges as existence of multiple conflicting criteria, and difficulty of providing a balance between subjective and objective judgments. To overcome this issue, an integrated multiple criteria analysis (MCA) context, constituting Shannon’s Entropy and VIKOR, was creatively applied to prioritize Shemshak’s hydrological units located in Iran, according to their flooding potentials. Throughout the present study, Shannon’s Entropy technique was applied to select the evaluation criteria by consideration of subjective and objective weights of the criteria. Meanwhile, VIKOR determined the compromise solution from a set of alternatives based on the particular measure of closeness to the ideal solution. The proposed methodology included two different sorts of sensitivity analysis for investigating the impacts of criteria weights’ modifications on the final ranking. The proposed integrated MCA procedure made a valid contribution to the problem. With the aid of Shannon’s Entropy, the feature selection was done based on the experts’ view-points and intrinsic significance of the factors, simultaneously. VIKOR ranked the alternatives based on the maximum group utility of the majority and the minimum of the individual regret of the opponent. Furthermore, performing sensitivity analysis of the criteria weights illustrated the robustness of the decision making process. Overall, the highest priority of flood potential belonged to Sh2, the largest hydrological unit of Shemshak. Due to appropriate performance of proposed integrated MCA procedure, it could potentially be employed in different fields associated to the watershed management.

Appendix

1.1 Gravelious Compactness Coefficient

$$ Cc=0.282\frac{P}{\sqrt{A}} $$

(a)

where P is the perimeter of the watershed and A is its area.

1.2 Hydrologic form Coefficient

$$ H.F=\frac{A}{P} $$

(b)

where P is the perimeter of the watershed and A is its area.

1.3 Length (La) and Width (Wa) of Equivalent Rectangular

$$ \left\{\begin{array}{l}La=\frac{Cc\times \sqrt{A}}{1.12}\times {\left[1+\left(1-{\left(\frac{1.12}{Cc}\right)}^2\right.\right]}^{0.5}\\ {}Wa=\frac{Cc\times \sqrt{A}}{1.12}\times {\left[1-{\left(1-\left(\frac{1.12}{Cc}\right)\right.}^2\right]}^{0.5}\end{array}\right. $$

(c)

where P is the perimeter of the watershed, A is its area, and Cc the Gravelious compactness coefficient.

1.4 Drainage Density

$$ Dd={\displaystyle \sum \frac{Li}{A}} $$

(d)

where Li is the length of each stream in the watershed, and A is its area.

1.5 Potential Flood Coefficient

$$ {K}_T=10\times \left(1-\frac{Log\left({Q}_T\right)-6}{Log(A)-8}\right) $$

(e)

where Q _T is the discharge for a return period, and A is its area.