Delineation of ﬂ ood-prone areas using modi ﬁ ed topographic index for a river basin

The modi ﬁ ed topographic index ( TI m ) based on digital elevation models (DEMs) was employed to delineate ﬂ ood-prone areas in Mahanadi basin, India. TI m and ﬂ ood inundation maps were compared to obtain the threshold ( t ) beyond which the area is assumed to be inundated by ﬂ ood and the exponent of the TI m . Scale dependence was also investigated to evaluate the sensitiveness of spatial resolution of the DEMs. DEMs of ﬁ ve resolutions, namely, ASTER global, SRTM, GMTED2010 (30 arc-seconds), GMTED 2010 (15 arc-seconds), and GMTED 2010 (7.5 arc-seconds) were used and ASTER global was preferred due to its low error compared to the remainder. Flood frequency analysis was conducted to obtain the relationship between ﬂ ood-prone areas and ﬂ ood magnitude. It was observed that (i) the exponent in the TI m showed little variation, (ii) t is reduced with reducing spatial resolution of the DEM, and (iii) error is also reduced as the DEMs ’ resolution is reduced.


INTRODUCTION
Flooding is the most frequent hazard worldwide and occurs due to continuous heavy rainfall and failure of hydraulic structures. The impact of floods has increased due to an increase in urbanization and climate change. With the increase in floods, it is important to have effective flood control mechanisms such as afforestation, reduction of deforestation, building flood warning systems. This alarming situation necessitates the creation of flood hazard maps. Clubb et al. (2017) opined that hydraulic/ flood modeling, even though expected to be informative and helpful, is computationally a burden to the modelers. This is mainly due to the enormous input data requirement, tedious calibration procedures of parameters, and lack of observed data in most of the situations, making the preparation and maintenance of precise flood mapping difficult and expensive. In addition, Sharma et al. (2018), as part of their studies on Northeast India, opined that reliance on satellite products is increasing due to insufficient hydrologic gauge stations. These restraints and opportunities suggest simple but effective digital elevation model (DEM)-based approaches that facilitate extraction of topographicbased indices to compute flood inundation area/mapping (Liu & Gupta 2007;Manfreda et al. 2008).
The easy availability of surface elevation data has increased the use of DEM-based hydrogeomorphic models. Consequently, more DEM-based methods for delineation of floodplains are used. Elevation of a region, surface slope of the area, distance from the stream, and drainage area are some of the parameters employed to predict the extent of flood inundation. Spatial distribution of the soil moisture and landscape processes can be described by the topographic index (TI). Manfreda et al. (2008) observed that a strong correlation exists between flood inundation areas and TI. Higher TI indicates the most susceptible flood-prone areas. Keeping this in mind, the spatial resolution of DEMs is found to be important in obtaining the TI (Mukherjee et al. 2013;Schumann & Andreadis 2016;Ettritch et al. 2018).
The present paper covers a literature review, a brief description of TI and modified topographic index (TI m ), study area, analysis of data and methodology, results and discussion, summary and conclusions. The proposed methodology is applied to the Mahanadi River basin, India.

LITERATURE REVIEW
In recent times, many researchers have studied flood modeling, flood simulation, flood management, and flood damage evaluations. With climate change and the increasing impact of floods in urban areas, it becomes important to assess the risk due to natural hazards for planning mitigation measures and management. Hence, the delineation of areas prone to flood inundation is essential. A brief literature review follows.
Flood-prone areas using topographic index Manfreda et al. (2008) evaluated the flood exposure by using morphological indices, namely, local slope, drainage area, curvature, and TI for the Arno River basin, Italy. It was observed that the TI and local slope show maximum dependency on the flood inundation exposure. TI m was proposed and used for flood-prone area delineation by identifying the areas which exceeded a given threshold t. They suggested higher resolution DEMs. Manfreda et al. (2011) tested the sensitiveness to DEM spatial resolution by using DEMs of different spatial resolutions for the Arno River basin. It was found that 100 m cell size yielded good performance. Mukherjee et al. (2013) carried out TI studies on four small watersheds, positioned over the Himalayan terrain. They also explained in detail the computational procedure of specific catchment area, slope, and TI. They found that DEM grid spacing significantly affected mean TI. Cooper (2014) examined two approaches for Chao Phraya River basin and Bangkok Metropolitan region, Thailand. The first approach handled an up-to-date composite flood hazard map whereas the second explored TI m for delineating flood-prone areas. He concluded that TI m is promising. Manfreda et al. (2014) employed linear binary classifier, TI m , and hydrogeomorphic methods to ascertain the potentiality of geomorphic algorithms for preliminary flood hazard graduation and hydraulic risk mapping for two sub-catchments of the Tiber River, central Italy. Simulated flood areas were compared with standard flood maps and it was concluded that the hydrogeomorphic method is effective for ungauged basins. Di  emphasized the role of GRASS and QGIS add-ons including r. hazard flood, that uses a TI m for the flooding delineation.
De Risi et al. (2014) studied DEM as well as a probabilistic framework for Ouagadougou, Burkina Faso, Africa for the year 2009. They concluded that the Bayesian updating procedure was useful for computing the topographic wetness index (TWI) threshold. Aksoy et al. (2016) assessed flood-prone areas in a Turkish watershed and explored the topographical and automated geoscientific analyses wetness indices. Mattivi et al. (2019) compared different open source GIS software for computation of TWI for a case study of the Rio Sinigo basin, in northern Italy. Similar studies are reported by Kazakis et al. (2015) for Rhodope-Evros region, Greece and two specific sites, Cottonwood Lake Study area and Nelson Eddy in Prairie Pothole region, USA. Marthews et al. (2015) expands upon the importance, necessity, and advantages of TI and the limitations. Schumann & Andreadis (2016) discussed the associated economic impacts/benefits achieved in flood prediction in detail and its relevance to society.
Flood-prone areas using other related approaches Cook & Merwade (2009) evaluated maps from LiDAR data with those obtained by using different geometry, topography, and modeling aspects for Strouds Creek, North Carolina and the Brazos River in Texas. The inundation area was found to be reduced with vertical accuracy in the topographic data and improved with horizontal resolution. Kourgialas & Karatzas (2011)  In line with the introduction and literature review, the following objectives were formulated: • efficacy of TI m for delineating flood-prone areas; • evaluate the sensitiveness of the resolution of the DEM data; • establish relationship between the flood inundated area and the magnitude of the flood.

MODIFIED TOPOGRAPHIC INDEX AND FLOOD-PRONE AREAS' DELINEATION
The topographic index is: where a d and tan b are, respectively, drained area/unit contour length and local slope (Kirkby 1975). Manfreda et al. (2011) modified the TI as: where n is an exponent with value 1. 7. TI m allows delineation of the flood-prone area considering that it is the area characterized by the TI m exceeding a chosen threshold t. The TI m map was compared with a flood inundation map for flood-prone areas' delineation by identifying the areas which had the value of TI m . t. To estimate t and the value of n, two error functions are defined (Manfreda et al. 2008: where S sim and S TI are sets of territory predicted as flooded and by TI. NS sim and NS TI are non-flooded regions predicted by hydraulic model and TI. ER1 is related to precise identification of flood areas whereas ER2 is related to error occurring due to overestimation. The objective function is minimization of (ER1 þ ER2) which can be solved iteratively for estimation of τ and n .

STUDY AREA
The area of interest considered for the present work is the Mahanadi basin ( Figure 1). The study area lies between longitude 80°30 0 and 86°50 0 E and latitude 19°15 0 and 23°35 0 N. The length of the river and the catchment area are 900 km and 141,600 km 2 , respectively. Mahanadi flows through Jharkhand, Orissa, Maharashtra, and Chhattisgarh states in an easterly direction. It originates at a place located 6 km from Pharsiya village, Chhattisgarh. The monsoon season starts during the first week of June and continues until October and contributes 90% of the total annual rainfall. Average rainfall is 1,438.1 mm. The climate is sub-tropical. The mean summer and winter temperatures are around 29°C and 21°C. More details about Mahanadi River Basin are available in Baliarsingh (2000) and Apoorva (2013).

Analysis of data and methodology
Data used for the present study are as follows: Geographical information system (GIS) operations were carried out on the DEMs to obtain all relevant information required for flood inundation maps. Figure 1 was used to obtain the outline of the Mahanadi basin. The map was georeferenced with the help of Georeferencing toolbar in ArcMap. The latitudes and longitudes on the map were used as the reference for georeferencing.
Once the map was georegistered, a shape-file of the catchment area was created with the help of the georeferenced map by using Editor toolbar in ArcMap. The shapefile is of polygon type.
The flood inundation maps for three flood events of 2006, 2008, and 2011, were georeferenced using the Georeferencing toolbar in ArcMap. The latitudes and longitudes on the map were used as the reference for carrying out the georegistration. The georegistered maps were classified into two classes, i.e., of flooded areas and non-flooded areas. After classification, the areas corresponding to the catchment area present on the maps were selected by superimposing the flood inundation maps over the shape file. The selected area was extracted by using the spatial analyst tool. Once classified maps were obtained, each of these maps was resampled such that the output cell sizes were equal to those of all the DEMs considered in the study, i.e., each of the maps was resampled to have cell sizes 911.19 m, 455.59 m, 227.80 m, 92.28 m, and 30.35 m. Nearest neighbor algorithm was used for resampling such that the flood inundation and TI m maps would be of the same size for comparison.
The DEMs were processed using ArcMap and MapWindow GIS. To cover the entire Mahanadi basin, a number of DEM tiles of SRTM and ASTER global had to be joined. This was done in ArcMap and processing was done to all the DEMs, i.e., GMTED2010, SRTM, and ASTER global. First, the area corresponding to the flood inundation maps in the Mahanadi basin was extracted using the Arc Toolbox. The extracted flood inundation maps were used to mask and obtain the new image. The DEMs were filled and the filled DEMs were then used to calculate the flow directions. This process takes one input raster, i.e., the filled DEM and produces two output rasters, i.e., Dinf Flow Direction Grid and the Dinf Slope Grid. Specific catchment area is also calculated. The contribution at each grid cell is taken as the grid cell length. This process takes one input raster, the Dinf Flow Direction Raster and produces the specific catchment area raster as the output. The specific catchment area raster and slope raster are used to calculate the TI m . Iterations are continued  Uncorrected Proof for each value of the exponent to obtain the TI m . The calculated TI m is compared to the flood inundation map to calculate ER1 and ER2. The exponent and the threshold which gives the minimum of the sum of errors ER1 and ER2 are recorded. Figure 2 presents the procedure involved in arriving at the minimum error, its corresponding exponent and the threshold.
The specific catchment area map, slope map, and the flood inundation map are studied, and from the flooded area map, the count of the number of pixels of flooded area and non-flooded area are calculated. Varying the exponent from 0.01 to 1, TI m is calculated. Each case of the TI m is compared with the flood inundation map to obtain a threshold, such that minimum error is obtained while classifying the TI m map into flooded and non-flooded areas. This is performed by taking a value of TI m , and classifying all values greater than or equal to it, and if the corresponding pixel in the flood inundation map is flooded area, as correctly identified flooded area, and if the corresponding pixel in flood inundation  Uncorrected Proof map is non-flooded area, as wrongly identified non-flooded area. The wrongly identified flooded and non-flooded area values are used to calculate the error. This procedure is repeated for each value of the TI m (with an interval of 0.01). The exponent and threshold which produce the minimum error are obtained. They are used to obtain the flood inundation map using ArcMap. While obtaining the flood inundation maps, it is assumed that the entire basin has similar characteristics to that of the test area used in each case of the flood events. The process used to obtain the TI m map is as follows. The specific catchment area map is first raised to the power of the exponent obtained. Then this image is divided by the slope. The threshold value obtained is used to classify the map into flooded and non-flooded regions. From the created inundation maps, the number of pixels having flooded and non-flooded areas are obtained. Accordingly, the area under flood inundation is calculated and tabulated for all three flood events.

RESULTS AND DISCUSSION
Delineation of flood-prone areas Table 1 shows the values of n, τ and the corresponding error (ER1 þ ER2) for the three flood events for all the DEMs.
• It can be seen from Table 1 that the value of n is very low (ranging from 0.01 to 0.04), indicating that the error is minimum when the upslope catchment area has less weightage compared to the downslope. n value of 0.01 is observed for 2011 and 2008 floods for all resolutions.
• The threshold value t shows a reasonably good trend. These vary from 6.24 to 3.22, 5.49 to 3.22, and 5.27 to 2.87 for 2006, 2011, and 2008 flood events, respectively. The threshold reduced with the reduction in the spatial resolution of the DEM. It can also be seen that as the flood magnitude increased, the threshold has reduced, indicating that a larger area will be under inundation.
• Table 1 also shows the total error. The error also shows a good trend and reduces as spatial resolution of the DEM reduces. It is in agreement with the results that the ideal scale for TI in the case of application in hydrological applications is 10-25 m (Zhang & Montgomery 1994). However, it does not match with the findings of Manfreda et al. (2011), where it was found that this method did not provide much improvement with error when the resolution was reduced below 100 m. It was also noted that ER1 (the overestimation) was significantly larger than ER2 in all the cases and as the DEM resolution is reduced to 30 m, the error reduces drastically.
• Table 1 presents the extent of area inundated by flood in the catchment obtained with the present method for all the five DEMs used. It is observed that ASTER global DEM (30 m) shows a high  Table 1 and the magnitude of these values are 34,803.11 km 2 , 27,126.18 km 2 , and 21,036.98 km 2 , respectively, which clearly indicates that spatial resolution plays a major role.
The relationships established between discharge (Q in m 3 /s) and inundation area (A in km 2 ) for GMTED 2010 (900), GMTED 2010 (450), GMTED 2010 (225), SRTM, and ASTER, respectively, are A ¼ À265.94 þ 1.234 Q, A ¼ 551.29 þ 1.013 Q, A ¼ 38,337.13 þ 0.371 Q, A ¼ À3,239.45 þ 1.87 Q, and A ¼ 69,494.74 À 0.116 Q with corresponding R 2 values 0.1834, 0.1533, 0.006173, 0.5153, and 0.05942. We observed that R 2 value is low for the three inundation maps considered. However, we wish to bring attention to the fact that on a relative scale, SRTM performed much better compared to all other DEM sources. Note that only three flood inundation maps are used for establishing relationship for demonstration. We believe that R 2 value will improve if a greater number of flood events are considered in order to develop a robust and sustainable relationship, and this is targeted for further studies.

Flood frequency analysis
All extreme value distribution functions are considered. Among them Gumbel is found to fit well (Odry & Arnaud 2017;Onen & Bagatur 2017;Kobierska et al. 2018). Accordingly, Gumbel method is used for the comparison of flood magnitude and area under flood inundation. It is noted that irrespective of the flood, sufficient and effective infrastructures are required for handling the recurring floods of this magnitude in the catchment. Infrastructure initiatives such as stabilization of slopes, channel regulation, and protection of riverbank and non-structural initiatives such as catchment land management, awareness about insurance facilities, preparedness of emergency management and evacuation, and public education are required and should be implemented in a sustainable manner. Figure 3 presents the flood inundation map for the year 2011 obtained by incorporating the exponent n and τ with reference to ASTER global for representative purposes. The parameters were computed using a part of the catchment area, and it was assumed that the entire catchment area is similar in behavior. This was performed because the flood inundation map was available only for certain parts of the catchment area. Dark and light shading represent non-flooded area and flooded area, respectively. Figures related to the other four DEMs are not presented here due to the limitation of space. It is a very common phenomenon to study flood magnitude of different recurrence intervals. The flooded area and the non-flooded area on the flood maps provide insight to the officials responsible for flood plain management for remedial/mitigation measures.

SUMMARY AND CONCLUSIONS
In this study, DEMs are used to calculate the TI m on the basis of which the flood-prone areas are delineated. It was observed that (i) the exponent in the TI m showed little variation, (ii) τ reduced with reducing spatial resolution of the DEM, and (iii) error also reduced as the DEMs' resolution was reduced. The ASTER provided the best results, and the error is considerably reduced from SRTM to ASTER. This is in agreement with the available literature which has found that 10-25 m scale is the best scale for hydraulic applications using the topographic index (Quinn et al. 1995).
The present study has a number of similarities and dissimilarities as compared to Manfreda et al. (2011). They preferred SRTM for 11 sub-basins of the Arno River basin with 12 cell sizes whereas the authors of this study suggested ASTER for the Mahanadi River basin in India with five cell sizes by considering three flood events. The highest and lowest values of n, t, and ER1 þ ER2 obtained, respectively, are 0.48 and 0.02 (range 0.46), 7.9 and 2.3 (range 5.6), 53.6 and 7.5 (range 46.1) whereas these values obtained by the authors are 0.04 and 0.01 (range 0.03), 6.24 and 2.87 (range 3.37), 43.97 and 17.4 (range 26.57). Compared to the findings of the authors, the ranges obtained by Manfreda et al. (2011) are wider, which may be due to the large number of sub-basins and more cell sizes.
To prove the philosophy and to confirm the potentiality of our work, we are using the gauged Mahanadi basin. We want to develop a suitable exponent as a function of basin area and flood magnitude. By analyzing a large number of river basins with the number of flood inundation maps with satisfactory relationship, such a developed relation can be extended to any ungauged basins seamlessly with more confidence.
However, this is an approximate method and cannot be considered as an alternative to detailed hydrologic and hydraulic studies. In our opinion, this is the first case study where potentiality of the methodology suggested by Manfreda and his team is explored for similar Indian conditions.

ACKNOWLEDGEMENTS
This work is supported by Council of Scientific and Industrial Research, New Delhi, through project no. 22(0782)/19/EMR-II dated 24.7.19. The authors are grateful to NRSC, Hyderabad, India for providing flood inundation maps and greatly benefited from Prof. Manfreda and his team's research papers.