Flood hazard and the unfavorable effects of floods combine to create flood risk. There are three steps in the process used to evaluate flood risk. Flood hazard rating, Flood susceptibility (using Fuzzy AHP) and AUC curve to validate.
To understand the probable risk zone of flood hazard, Flood Hazard Rating map has been prepared based on the following formula-
Primary data has been collected from field to execute the analysis.
Flood Susceptibility Mapping:
After analysis of previous literatures and field investigation, certain parameters have been chosen to prepare the flood susceptibility mapping [Table 1]. The parameters have been computed on ArcGIS 10.4.1 platform and then have been classified into five classes. Weightage to the parameters have been assigned using FUZZY-AHP method which is described below-
The fuzzy AHP approach might be viewed as a developed explanatory tactic from the conventional AHP. Researchers that have utilized fuzzy AHP, including Chang 1996, Van Laarhoven and Pedrycz1983, and Boender et al. 1989, have demonstrated that fuzzy AHP typically delivers a more accurate picture of fundamental leadership. There are several ways to decide the weights in the fuzzy AHP technique. Using TFNs, the degree approach first proposed by Chang (1992) is used to determine fuzzy weights for selecting criteria (Chang 1996). Chang's fuzzy AHP degree analysis method has been explained by (Boutkhoum et al. 2015)
Assuming Y and A are the objects, the goal sets for Y and A are Y= {y1, y2, y3….,yn}and A= {a1, a2, a3……., am) respectively (Chang 1992, 1996). For each item that may be obtained, the extent analysis estimates for m are (Meshram2019):
$${{M}^{1}}_{ai, }{{M}^{2}}_{ai,}{{M}^{3}}_{ai, } i=\text{1,2},3,\dots ..,n$$
$$Where, {M}_{ai}^{m}\left(j=\text{1,2},2,\dots ..m\right)are TFNs$$
According to the ithobject, the estimation of fuzzy synthetic extent is described as:
$${F}_{i}=\sum _{j=1}^{m}{M}_{ai}^{j}*{\left[\sum _{j=1}^{n}\sum _{j=1}^{m}{M}_{ai}^{j}\right]}^{-1}$$
$$\sum _{j=1}^{m}{M}_{ai}^{j}=\left(\sum _{j=1}^{m}{\alpha }_{j}{\beta }_{j}{\gamma }_{j}\right)$$
$$\sum _{j=1}^{n}\sum _{j=1}^{m}{M}_{ai}^{j}=\left(\sum _{j=1}^{n}{\alpha }_{j}{\beta }_{j}{\gamma }_{j}\right)$$
$$\text{T}\text{h}\text{e} \text{d}\text{e}\text{g}\text{r}\text{e}\text{e} \text{o}\text{f} \text{l}\text{i}\text{k}\text{e}\text{l}\text{i}\text{h}\text{o}\text{o}\text{d} \text{o}\text{f}{M}_{2}=\left({\alpha }_{2}{\beta }_{2}{\gamma }_{2}\right)\ge {M}_{1}=\left({\alpha }_{1}{\beta }_{1}{\gamma }_{1}\right) is defined as:$$
$$V\left({M}_{2}\ge {M}_{1}\right)=\text{sup}\left[\text{min}\left(\mu {M}_{1}\left(y\right),\mu {M}_{2}\left(y\right)\right)\right]$$
It can also be stated as:
$$V\left({M}_{2}\ge {M}_{1}\right)=tgh\left({M}_{1}\cap {M}_{2}\right)$$
$$=\left\{\begin{array}{c}1, if {\beta }_{2}>{\beta }_{1}\\ 0,if {\alpha }_{1}\ge {\gamma }_{2}\\ \frac{\left({\alpha }_{1}-{\gamma }_{2}\right)}{\left({\beta }_{2}-{\gamma }_{2}\right)-\left({\beta }_{1}-{\gamma }_{1}\right)}, ifotherwise\end{array}\right.$$
$${M}_{i}\left(i=\text{1,2},2,\dots ,k\right)can be categorized as:$$
$$V\left(M>{M}_{1},{M}_{2,}\dots ,{M}_{k}\right)=V\left(M\ge {M}_{1}\right) and \left(M\ge {M}_{2}\right) and\dots \left(M\ge {M}_{k}\right)$$
$$V\left(M>{M}_{1},{M}_{2,}\dots ,{M}_{k}\right)=minV\left(M\ge {M}_{1}\right), if m\left({P}_{i}\right)=minV\left({S}_{i}\ge {S}_{k}\right)for k=\text{1,2},\dots ,n;k\ne i$$
The weight vector can be specified as:
$${W}_{p}=({m\left({P}_{1}\right),m\left({P}_{2}\right),\dots ,m\left({P}_{n}\right))}^{T} where, {P}_{i}\left(i=\text{1,2},\dots n\right)are n elements.$$
Phase 4 Normalizing weight vector:
$$W={\left(W\left({P}_{1}\right), W\left({P}_{2}\right), \dots ,W\left({P}_{n}\right)\right)}^{T} where W is a non-fuzzy number$$
Land use land cover map:
To understand the effects of flood hazards on different land use, LULC map has been prepared from secondary source (Karra, Kontgis, et al. “Global land use/land cover with Sentinel-2 and deep learning.” IGARSS 2021–2021 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2021).