The aim of this paper is to assess the extent to which the Sad-Kalan watershed in Iran participates in floods and rank the Sad-Kalan sub-watersheds in terms of flooding potential by utilizing multi-criteria decision-making approaches. We employed the entropy of a drainage network, stream power index (SPI), slope, topographic control index (TCI), and compactness coefficient (Cc) in this investigation. After forming a decision matrix with 25 possibilities (sub-watersheds) and 5 evaluation indices, we used four MCDM approaches, including the analytic hierarchy process (AHP), best–worst method (BWM), interval rough numbers AHP (IRNAHP), picture fuzzy with AHP (PF-AHP), and picture fuzzy with linear assignment model (PF-LAM, hereafter PICALAM) algorithms, to rank the sub-watersheds. The study results demonstrated that PICALAM exhibited superior performance compared to the other methods due to its consideration of both local and global weights for each criterion. Additionally, among the methods used (AHP, BWM, and IRNAHP) that showed similar performances in ranking the sub-watersheds, the BWM method proved to be more time-efficient in the ranking process.

The hydrous bed of the rivers covered with coarse alluvial materials is a goodresource along with other resources to provide the needs of the water. Therefore,studying and investigating the flow behavior around wells excavated in these bedsand determining their discharge capacity is very important. Since the flow to thewells is radial and previous research on coarse, porous media, there has beenmainly for parallel flows, and yet any equation replacing the Laplace relationship incoarse, porous media, is not provided for non-Darcy radial flows with a free surface,Therefore, the extraction of the differential equation ruling on these types of flowsin the cylindrical coordinates and a method for numerical solution of them in thisresearch has been followed. Based on the research carried out in this research, thepower (exponential) equation as the most suitable basic relation for the analysis ofradial flows was determined and used. Also, in order to solve the governingequations a numerical model was developed using finite volume method. Thedeveloped numerical model act well for the analysis of radial flows in the coarsealluvial beds. The results of the implementation of the numerical model indicate thatthe pressure distribution can be considered hydrostatic.

The outflow depth from the radial porous media (inflow to the well) is very useful as the downstream boundary condition and the starting point for water surface profile calculations. Based on the studies, unlike the Stephenson's hypothesis (the outflow depth is equal to the critical depth), the outflow depth from the rockfill media is a coefficient (Γ) of the critical depth. In the present study, using several (large scale and almost real) experimental data in the radial non-Darcy flow condition, dimensional analysis and the PSO algorithm, an equation was presented to calculate the mentioned coefficient based on upstream water depth (h) and distance between the well center and the upstream (R). Then, using the calculated outflow depth and the 1D flow analysis equations, the water surface profile in the radial non-Darcy condition was calculated for the first time. The results showed that considering an outflow depth equal to the critical depth and using the proposed solution in the present study, the Mean Relative Error (MRE) values of 83.43% and 3.53% were obtained, respectively. In addition, using the proposed solution for different experimental conditions, an average MRE of 2.58% was calculated for the water surface profile.