Evaluating the performance of the flexible discriminant analysis model in predicting the flooding potential of the Zarrineh-Rood Watershed

Introduction
Floods cause financial losses and countless lives in the world every year. Identifying flood-prone areas is one of the basic steps in flood management. In the past, careful observation and note-taking of the mechanism of occurrence and the natural course of the cause and effect of the effective factors that led to the final occurrence of the phenomenon in a chain manner helped to understand the pattern and process of the occurrence to some extent. Because the processes of creating floods are numerous and affected by various factors and the flood phenomenon is multidimensional and dynamic, all-natural, human, and organizational-management factors affect the occurrence, intensity, extent, and continuity of floods. So far, many efforts have been made to use data-mining models and artificial intelligence in the spatial prediction of floods. The models try to better and more accurately estimate the distribution of the flood phenomenon by examining the relationships between each flood event (dependent factor) and the set of underlying and stimulating factors (independent factors) and fitting them to educational evidence. Since the applicability of the flexible discriminant analysis model has not been fully investigated in the field of flood susceptibility prediction, this research quantitatively evaluated its performance using real-world flood data.
 
Materials and Methods
Based on the availability of periodic history of flood events, the Zarrineh-Rood Watershed of Kurdistan Province, Iran, was chosen as the study area. It was tried to select the factors based on different criteria such as familiarity with the process of flood inundation, ease of data preparation, having the most spatial variability at the regional level (not uniform), and containing the most information for the model should be selected to separate areas with different levels of flood susceptibility. Thirteen diverse geo-environmental factors including elevation, aspect, slope percent, land use, drainage density, lithology, plan curvature, profile curvature, mean annual precipitation, soil texture, stream power index, distance from the stream, and topographic wetness index were used as independent variables. The maps of elevation, aspect, slope percent, plan and profile curvatures, stream power index, and topographic wetness index were produced using a digital elevation model. Hydrological layers including distance from the stream and drainage density were produced using the stream network layer. The location of the flooding events was also collected as the dependent variable. The spatial data of flooding were randomly divided into two groups of training and validation with a ratio of 70:30. After running the model (i.e., Flexible Discriminant Analysis) based on the training group, the flood susceptibility map was produced. The validation of the model results was conducted using the area under the receiver operating characteristic curve (AUROC) and the true skill statistic (TSS) metrics.
 
Results and Discussion
The results indicated that the FDA model with the value of AUROC= 0.96 and TSS= 0.86 efficiently and accurately produced the flood susceptibility map. The flexible nature of the model in the selection of regression equations, as well as the possibility of weighting, and determining the priority of the evidence of presence over the evidence of absence, are among the special capabilities of the FDA model, which many machine learning models lack. Using probability distribution estimation algorithms in the model is very important and can not only extract the hidden spatial pattern of occurrence from a set of data but also help to predict flood-prone areas in data-scarce Watersheds. Based on the results, about 14% (62 thousand ha) of the study area was categorized in the high and very high flood susceptibility zones, which include the northern, northwestern, and southeastern areas. Spatial analysis of the flood susceptibility map showed that in total 25897 ha (18.12%) of agricultural lands, 343 ha (50.91%) of garden lands, and 2126 ha (39.93%) of residential areas located in high and very high susceptible zones. Considering the successfulness of the FDA model in goodness-of-fit and validation phases, the flood susceptibility map can be used as a basis for planning flood control and management measures.
 
Conclusion
The findings of this study proved that the flexible discriminant analysis model provides the possibility of processing diverse and big geo-environmental data to predict the flood susceptibility of Watersheds and it had a high efficiency in this context. There is a lot of spatial correspondence between the vegetation status map and the flood susceptibility map; in such a way that the places that had a high flood susceptibility degree, their upstream areas were generally destroyed in terms of vegetation. The results of this research showed that a significant area of the Zarineh-Rood Watershed had a high and very high flood potential, which was characterized by the interaction of low slope and flat areas, formations and soils with low penetration and dense drainage network, and more importantly, flood-prone areas located in the northern, northwestern and southeastern parts of the Watershed. The situation of the flood probability of the Zarineh-Rood Watershed has been determined and managers and decision-makers must put the critical areas in the priority of flood management programs. More flood-driver factors are suggested to be used as predictor variables in flood susceptibility modeling in future studies. On the other hand, it is very important to determine the role of predictor variables in the flood susceptibility degree at the Watershed scale, which can be investigated in future research.