Flood Depth Estimation in Agricultural Lands From L and C-Band Synthetic Aperture Radar Images and Digital Elevation Model

Flood depth is one of the important attributes in damage assessment especially in areas where agro-based activities takes place. Assessing impacted region turns out to be exceptionally difficult in the case of low-lying catchments with arable lands, which inundates due to extreme precipitation and flood modelling becomes impossible. Under these circumstances, SAR derived flood maps are valuable in removing different constraints related to flood modelling with high degree of profundity. Depth estimation from non-contact based methods requires, flood boundary as a primary input. However, detecting flood depth in emerging vegetation poses a complex challenge in terms of boundary estimation due to composite signatures that are manifested on SAR data. In this paper, a new approach is proposed to extract flood boundaries by fusing SAR data of two different frequencies, which are sensitive to water level changes. In the first step, wavelet fusion is applied to combine L- and C- band SAR data followed by Otsu’s segmentation method to extract varying levels of flood boundaries. In the second step, SRTM Digital Elevation Model (DEM) with 30m horizontal resolution is used on each boundary for statistical analysis based on which water surface levels are extracted. In the final step, depth levels are calculated from the water surface elevation and DEM. Floodwater Depth Estimation tool (FwDET) derived depth measurements are used to calibrate the statistical thresholds for derived flood depths. The study carried out on 2016 Assam flood event shows maximum flood depth of 1.56 meters in the selected study area and the results are verified with evidence-based ground truth collections which showed RMSE error of 0.25 meters from the measured values.


I. INTRODUCTION
According to Intergovernmental Panel on Climate Change [1], fifth assessment report AR5, an extreme event is defined as pattern of extreme weather persisting for some time in a season. Climate induced precipitation extending over longer periods catalyzes aforementioned events and eventually leads to flood. Development of inundation and depth maps during floods helps in formulation of depth-damage functions [2]. The implications of timely depth map preparation are of paramount concern to determine damage for economic The associate editor coordinating the review of this manuscript and approving it for publication was Gerardo Di Martino . estimation during floods [3], [4]. Most of the detailed inundation maps are produced with the help of hydraulic models. In the absence of high-resolution topographic data or information of stream and flood plain characteristics, it becomes challenging to develop hydraulic models [5]. In case of extreme precipitation events, large river basins with area extending over 400,000 Sq.km, presents complex flood configurations. Most of the low-lying areas accumulate rainwater after acute rainfall. With decreased holding capacity of soil, flooding occurs as result of overland flow. In this case, satellite derived methods provide acceptable alternative for getting depths not only in floodplains but also in areas distant from river. In agricultural areas, accurate depth information VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ is helpful for damage assessment. Assam is one of the states in India, which is a victim to regular extreme precipitation events resulting in flood. Moreover, 65.2% in rural Assam are agricultural households, which depends on agriculture as major source of income [5]. Numerous agencies rely upon satellite-based strategies for rapid monitoring. According to National Database for Emergency Management records, over 60% of the land in the state was under inundation by the end of monsoon month in year 2016. As many agencies depends on satellite based methods for rapid monitoring, increase in reliability of methods to extract extent and depth is necessary. For decades, Synthetic Aperture Radar (SAR) has been playing crucial role in flood detection and flood extent estimation. During monsoon, optical data fails to provide cloud free view of the earth, and SAR data in lower frequency bands provide information about the target regardless of the weather conditions [6]. The lower frequency bands has lesser attenuation rates compared to higher frequencies [7] also showed that, for rain rate of 150mm/hr the specific attenuation for L-Band and C-Band is <0.01 and 1.5dB/Km respectively which explains lesser tropospheric effects on L&C radar returns. Further advantage of the SAR, is its penetration capability, operation in multiple frequency bands and ability to provide information about the object in the form of returned scattering power and phase of the signal. Since last decade, several approaches have been proposed from for flood depth retrieval with the help of SAR data and DEM [5], [9], [10], [13], [15]. The key observations that affect the depth values extracted from SAR images are summarized at the end of (section A). The earliest study of the water level measurements from SAR data is proposed by [8] which has used Evidence Based Interpretation (EBIS) of ERS-1 Satellite images in combination with visually interpreted floods from aerial images to extract the flood boundary. The boundary is then plotted on foreland profiles. The water stage is extracted by superimposing foreland profile plot on maps (with 1:50,000 scales) and registering stages manually at each contour level. With this method, an error of 50cm to 2m in water level is reported. With the availability of DEMs, water stage retrieval from satellite data become more relevant [9] used high resolution LiDAR DEM to create water surface using two different approaches. First approach uses Triangulated Irregular Network (TIN) to create water surface elevation. Second is multiple regression approach that takes relation between water height and map coordinates along river reaches to estimate surface heights. ENVISAT ASAR images are used to derive water extents by applying active contour model in which water levels are calculated by above methods. Once water surface height is generated, they extracted depths by subtracting water surface elevation from high resolution LiDAR DEM. Hydraulic model simulation is carried out to compare the depth against simulated results as well as field measured watermarks. RMSE error of 68.0cm is reported against ground-based measurements by using TIN method and error of 13.0cm is reported against HEC-RAS derived measurements using multiple regression models. Later, [10] developed Regression and Elevation based Flood Information extraction (REFIX) model improving the method proposed by [8]. The model considers linear regression instead of multiple regression and takes slope and downstream distance as variables instead of map coordinates as proposed by [8]. The improved method showed an RMSE error below 20cm. This method also uses high resolution LiDAR DEM and thresholding method to extract water extents.
Evolution of new terrain models took place further from DEMs. Height Above Nearest Drainage (HAND) is a terrain model proposed by Nobre and Renne et.al. [11] which normalizes the topography according to local relative heights. The HAND model become a popular tool over the years for hydrologically relevant applications across different basins [12], [13], [14]. Reference [13] used HAND model to compute water depth across the flood plain. The study used hierarchical tiling approach on image to identify sub areas where probabilistic models are applied to separate open waters in flood plains. HAND model is used to obtain water surface heights and with the combination terrain information depths is extracted. For automation, [15] proposed a methodology that operates on the assumption that surface water level is constant in small areas. Accordingly, flood extent obtained from Landsat data is split into smaller subsets and LiDAR DEM is fitted into each subset to derive local water level on basis of kappa coefficient. Then interpolation methods are used to generate continuous water surface level. To obtain the stage information, water surface extent from above method is subtracted from DEM. Reference [15] proposed semi-automated methodology which used boundary derived from SAR data to estimate the flood surface elevation using TIN interpolation method by taking points around flooded area using LiDAR DEM acquired during flood. This study reported RMSE error of 15cm. In 2018, Cohen et.al developed Floodwater Estimation Tool (FwDET) which gives depth solely based on inundation extent and-DEM. The method uses automated floodwater depth estimation that is spatially continuous [15]. FwDET became a feasible solution in the later years for extracting depths with flood boundary and DEM as only inputs [15]. However, the values are experimental and it changes based on shape of the flood boundary.
From the evolution of methodologies it is observed that, all SAR based depth extraction methods are based on two key inputs, i) Extent of the flood boundary and ii) DEMs. The accuracy of the approaches depends on the vertical resolution of DEM and is significant for operational context [15]. However, global availability of high resolution LiDAR DEMs is highly challenging. Besides, most of the methods did not take into consideration, the underestimation and overestimation of flood boundary caused by double bounce returns from flooded vegetation. Approaches adopted in studies [5], [9], [10], [13], [15] provided information only in the flood plains and ignored places distant from the rivers. Cian et.al. [30] provided a semi-automatic methodology that is based on statistical analysis of the DEM to calculate water surface elevation and taken into consideration underestimation and over estimation errors in flood boundary. The study used Normalized Difference Flood index developed by [16] to detect flood boundaries.
Inspired by the statistical approach proposed by [15], in this study, development of a methodology is proposed that provides feasibility in extracting flood boundary in agricultural lands with high reliability in all places with limited data at hand. The novelty in the method lies in using two different frequencies of SAR data that are sensitive to water level changes and eliminate ambiguities caused by under estimation due to diminished penetration of higher frequency bands. The study is based on the following hypothesis. Penetration capacity of C-band is less than L-band and the backscatter from C-band is a result of top interactions with the objects on earth. Giving its penetration capacity, L-band SAR data is capable of capturing water under canopy. When same area sensed with two frequencies at same time, the backscatter from each frequency band differs. The central idea of the method is that each frequency band is sensitive to water levels which are manifested in the form of scattering returns on SAR data. On a SAR image, when the area shows double bounce on the C-band and specular reflectance on L-band, it has less depth compared to area that shows specular reflectance on both C and L bands. This study follows an assumption that water surface level is variable inside the flood boundary with an offset of few centimeters. Section III explains detailed methods with schematics for flood depth extraction followed by results and discussion, in section IV.

II. STUDY AREA AND DATA USED
According to Assam State Disaster Management Authority reports, and local media reports the first wave of the flood started on 17 th July 2016 as the rivers cross the danger levels at various stations resulted from high intensity rainfall. The waters started receding from 28 th July to 1 st August and the minor second wave started from 3 rd August as a result of onset of rainfall [17], [18], [19]. Both C-band and L-band used in the study are acquired during peak flood time on 29.07.2016 and 31.07.2016 respectively. The study area chosen for implementation of the algorithm is situated in Nagaon district of Assam state, in India. The study site falls under moderate to high-risk area according to National Remote Sensing Centre flood hazard report and other studies [20]. The area is distributed with farmlands and surrounded by highlands in the east. The maximum elevation observed in the area is 257.3 meters in highland areas and the minimum elevation is 8.95m in farmlands. According to Indian Meteorological Department (IMD) reports, the district of Nagaon received maximum rainfall of 754.3-mm during monsoon season in the year 2016 [21]. Geographical location of the study area where SAR scenes were acquired is shown in Figure.1. Two different SAR sensors captured the study area VOLUME 11, 2023

FIGURE 2.
Step wise workflow for extraction of flood depth from SAR data.
in different frequency bands with a time lag of 54:34:21 hrs during flood. ALOS-2/PALSAR-2 data with swath width of 70km and pixel spacing of 6.25m operating at a frequency of 1.2Gz is used in the study along with Sentinel -1A C-band SAR sensor at operational frequency 5.405Gz with 10m pixel spacing.. Along with two SAR scenes, DEM is taken which is an important input in the study. ESA's Sentinel Application Platform (SNAP) is used to generate digital elevation raster. SRTM 1arc SEC HGT product for test site is generated and exported for the study.

A. FIELD INFORMATION
Complementary data used in this study includes measured height values from road level and past knowledge of flood collected from local administrative authorities during field visit in Nagaon. This information has been used in the absence of data during synchronous pass of the satellite during flood. Combined with the information from local authorities and SAR images, it has been observed that the inundation used to be below the road level. Three points are taken in each following village/location in the study area viz., Mahamrityunjay, Halowagaon, Niz Chalchali, Auniati jalah and Kaziranga and measurements are taken along the sides of roadways sampled with in 40m range. Results and discussion section has the details of the field information.

III. METHODOLOGY
A three-stage methodology for extraction of flood depth from SAR images is presented in Figure. 2. Stages include (i) data preparation and pre-processing (ii) flood boundary extraction and (iii) flood depth calculation. Radar backscatter from the flooded areas varies as a function of flood depth at given transmitted frequency. As the frequency varies the interactions of the radar pulses with water levels also varies. The methodology explains the technique of extracting flood boundaries with each boundary corresponding to a depth level. It is achieved by combining data from two different frequency bands, which are sensitive to water level changes. In each step, the result obtained is given as input to the next step. The interactions of L-band and C-band radar under flooded vegetation conditions at different depth levels is shown in Figure. 3. When the water level crosses a defined threshold say, the height of the vegetation, no significant power will be recorded because of specular reflectance irrespective of transmitted frequency. In case of partially submerged areas, L-band is able to penetrate through vegetation whereas C-band shows random scattering. Thus, the same area when observed on L band & C band, the specular reflected areas seen on C-band can be said to have higher depth level from the ground compared to L-band. In this paper, wavelet based fusion is used to combine two SAR images of different frequencies to identify and extract varying levels of flood boundaries. The paper is organised as follows. Each step in the methodology is explained starting with data preparation from section A

A. DATA PREPARATION
All the datasets used in this study have different resolution and dimensions. C-band SAR scene is taken as reference raster to bring all other rasters to same resolution and dimensions. The first step in data preparation stage is to resample the L-band SAR data to match with the resolution of the C-band SAR. Similarly, SRTM DEM with 30m horizontal resolution is interpolated using Inverse Distance Weighting method to generate pixels at equal space to match with dimensions of the other two rasters. The height values from SRTM DEM are calibrated with the field measured values from GPS device for the portion of study area. The two SAR scenes are calibrated and speckle removed with Lee-Sigma filter of window size 5 × 5 to preserve sensitive details at the edges or high frequency components of an image. Geographical subset is applied on all three rasters to match the spatial extent and maintain equal raster width and height. Co-polarized channel VV of Sentinel-1A data and HH in ALOS-2 data are used in this study.

B. FLOOD BOUNDARY EXTRACTION BY WAVELET IMAGE FUSION
Given two images, image fusion produces a single image of greater quality containing the best aspects coming from both the images [22]. Fusion applied on two different band SAR images brings out the distinctive characteristics that are unique to each frequency band such as details logged from penetration of radar pulses at each frequency. In SAR based flood mapping, the water height information intrinsically expressed through radar backscatter is sensitive to sensor frequency. The methodology followed here is built on the hypothesis that when two images from different frequency bands acquires flood scene of an area with no or less temporal resolution, the radar backscatter conforming to water bodies manifested from low penetration radar wavelengths has more depth compared to water bodies visibly shown in higher wavelengths. The fused image contains components of high frequencies such as flood boundaries from both images as well as low frequency image components that represents topography. For the convenience of the readers, to not to be confused with the sensor frequency, we mention frequencies in wavelet theory as image frequencies. Wavelet image fusion is based on multiresolution decomposition. Multi Resolution Analysis (MRA) generates approximation coefficients corresponding to low image frequencies and detail coefficients corresponding the high image frequencies. The approximation coefficients are recursively passed through low and high band filters at each level to produce coefficients at lower resolutions. Fusion results depends on number of decomposition levels [23]. and fusion method that inadvertently affects spatial quality and structural similarity. With the experimental analysis carried out, the images taken in this research are decomposed at four levels with first level preserving the boundaries to final level preserving vertical structures in both images. The theory behind the method used for fusing two SAR image is described below in three steps.
Step1. Discrete Wavelet Transform (DWT) is computed for each of the two source images at each frequency band (C&L) and coefficients of wavelet transform are calculated at each scale as explained in [24] The Discrete Wavelet Transform (DWT) of a given image I (X , Y ) is obtained from the scaling function φ(X , Y ) and wavelet function. The wavelet basis used here is Haar wavelet shown on equation (1), which belongs to family of orthogonal wavelets.
The scaling equation φ(X ) in 1D multi resolution theory is given as shown in equation (2).
where, l(k) are low frequency or approximation coefficients. The wavelet function ϕ(X ) that computes high frequency or detail coefficients h(k) is shown in equation (3).
Let, I c (X , Y ) and I L (X , Y ) are two images taken in frequency bands C and L respectively, then the decomposition of each image I (X , Y ) taken at scale j is given by equation (4) I where, C(j, k), D(j, k) are scaling and wavelet coefficients at scale j computed by equation (5) C(j, k) = k l(k − 2m)C(j + 1, k) where l(k) and h(k) are low frequency, high frequency image components respectively as represented in scaling and VOLUME 11, 2023 wavelet equations (2) and (3). 'm represents the shifting factor. In image, the 2D scaling and wavelet functions φ j,k (x, y), ϕ j,k (x, y) are given by Step 2. The corresponding detail and approximation coefficients for both images are combined at each level according to weighted average method.
The DWT with N decomposition levels will have 3N + 1 image frequency bands. All the low frequency image bands and high frequency image bands at every level after decomposition are combined by the fusion rule shown in the equation (6) where, D F represents fused image, D C/L LL represents low frequency coefficients and D C/L HH represents high frequency components at C&L bands. α, β are weights.
where, D C/L LL (p) is the multiresolution decomposition representation of coefficient P at index (x, y), at level j and frequency band l.
Step 3. Inverse Discrete Wavelet Transform (IDWT) is applied to obtain the fused image.
In the final step inverse DWT is applied to obtain the fused image from the newly combined coefficients. The backscatter values of the water bodies in the final image shows diverse values than the traditional SAR water backscatter. The obtained image is embodiment of water boundaries with different depth levels.

1) IMAGE SEGMENTATION
The second step towards flood boundary extraction is the segmentation of the fused image. Otsu's algorithm is used to generate five threshold points which gives six segmented regions. It is assumed that water level information is contained up to four segmented regions (Level-2 to Level-5) after fusion, based on the distribution of elevation values registered with the fused image. The algorithm partitions the image using thresholds generated based on maximum interclass variance between the classes [25]. Each region after the segmentation is exported as a separate raster layer. The illustration of water manifestations on SAR data with its elevation counterpart and schematic segmented layers is shown in Figure 4.
Let us assume the fused image holds the backscatter values in the range (−a, b). To segment the image, we divide the total range of values into five classes in the ranges say (−a 0 , .. − a k ), (−a k+1 , .. − a k+n ), (−a k+n , ..b 0 ), (b 0 , ..b k ), (b k+1 , ..b k+n ). If p c i is probability of occurrence of backscatter value in each class c and w c is the probability of each class and u c indicates the class mean, the variance of each class are given in equations (10) The total mean µ T of the image is given by To find the best threshold value that separate each class, Otsu's algorithm defines three discriminant parameters λ, k, η called measures of class separability. The value that maximizes one of the three measures is chosen as the threshold that best separates each class from another. Three measures of separability are defined based on σ 2 σ 2 W , σ 2 B , σ 2 T are with-in class variance, between class variance and total class variance shown in the following three equations (13), (14) and (15).
As the value η depends on both first order and second order statistics, η is used to evaluate the threshold. The optimal threshold at level a k that maximizes η in turn maximizes σ 2 B and is given in the expression (16).
The optimal threshold a k is Five such thresholds (17) that maximize the interclass variance produce six raster layers out of which four are picked 3246 VOLUME 11, 2023 as flood boundaries. The boundary corresponding to the first threshold −a k contains more depth than the second raster layer and so on.

C. FLOOD DEPTH CALCULATION 1) EXTRACTION OF SURFACE WATER LEVELS
The final stage in the framework of calculating the flood depth requires extraction of surface water levels within the flood boundaries. Then flood depth is calculated by subtracting the water surface elevation from corresponding elevation in DEM. Extreme precipitation in low-lying areas leads to decreased soil infiltration with accumulation of water in the pits of low elevation gradually filling up the land around it. DEM provides information of earth's surface as raster grid. As the runoff increases, the number of cells filling the elevation raster increases. The statistical methodology proposed by Cian et.al. [30] is used to get surface water elevation. With the availability of number of inundated cells from SAR data, extraction of water level in detected polygon is made possible. The water surface elevation in the flooded polygon is extracted by analysing the DEM elevation inside VOLUME 11, 2023 the boundaries. However, the number of elevation points falls in each inundated cell in the SAR data depends on the horizontal resolution of DEM. In the case of SRTM DEM, the number of points for each cell varies from minimum of one to maximum of three. To reduce this uncertainty, the DEM is interpolated using Inverse Distance Weightage using nearest neighbour searching method to ensure each cell gets one corresponding elevation point. For densely vegetated areas and highly mountainous regions the artefacts in the DEM need to be corrected. Following methods proposed by [26], [27], and [28] can be used to remove the artefacts before proceeding to next step. Afterwards the elevation points that falls under each flood boundary is extracted and corresponding percentiles are computed. Starting from n=95, the difference between the elevation values corresponding to n th and (n-5) th percentiles are computed. However, the accuracy of the information depends on vertical resolution of the DEM [26]. The methodology explained by [27] uses LiDAR DEM with a vertical resolution of 2m and LiDAR DTM of 1m resolution. Above methodology uses the percentile difference greater than 10cm to continue the algorithm to iterate. However, in the following study it is observed that according to resolution of the DEM the difference between the percentiles should be less than the DEM resolution which is 30m. The water surface elevation is then calculated as the mean between the five percentile interval if the condition satisfies. The condition is that the difference between nth and (n-5)th less than 30 meters then water level is calculated as mean of five percentile interval at that iteration. As final step, we calculate the flood depth by subtracting the water level values derived from above methodology, from corresponding elevation values. This method gives linearly produced depth values. To get accurate depth values, for each elevation sample (elevation values inside flood boundary), a new surface distribution is created that synonymously follows the elevation distribution. We assume all the samples follow Gaussian distribution. Although it is not ideal, the assumption is made after observing majority of samples. Starting from 0 to the highest value in the depth result of each sample a new column of values is created. Each sample is fitted with normal distribution. The parameters taken by fitting the column of depth values (original) is used to make new distribution. New flood depth values are then calculated by taking inverse of distribution. The same procedure is repeated for each level in flood boundary layer. The entire procedure is carried out in Matlab version 2020a.

2) CALIBRATION WITH FWDET TOOL AND MEASUREMENTS
To select optimal threshold check, for depth values they are calibrated against the depth levels derived from Floodwater Depth Estimation tool. Python script for FwDET is downloaded for QGIS and flood depths are calculated using fusion derived flood boundaries and SRTM DEM as input. The maximum value obtained from FwDET derived depths is taken as mean percentile threshold and the values with twice the mean on both sides of threshold are taken as upper and lower percentile threshold bounds. The depths corresponding to these ranges are derived. A new percentile vector is created between lower and upper bounds to the length of the elevation vector (with in flood boundary) and depth values are linearly interpolated in this range. The depth levels created in this process explained in the previous section are taken to produce depth map in raster format. By comparing the values derived from FwDET tool, a threshold limit between 50 th and 54 th percentiles is chosen as optimal values for depths. The newly created depth vector is converted to raster for visualization. This methodology provides two major advantages -Flood boundaries derived from the fusion reduce the uncertainty of underestimation in flood boundary.
-Flexibility in multilevel thresholding allows us to choose multiple threshold values to produce more than one flood boundary layer.
For the validation of algorithm, we used evidence-based approach as the event is past event. Five points are observed and marked on SAR data to measure depth below the roadway. The outcomes from the algorithm are approved with field-estimated levels. As the roadway shows the high backscatter value, it is assumed that the inundation is below the road level. The area of agriculture fields stretches constantly across few square kilometres below the road level and so the depth level is assumed to spread within range of few meters less or more from the value. This could be confirmed with near constant elevation values from DEM. Depth of the fields from the road level are measured at these points.
The Root Mean Square Error (RMSE) in equation 18 is used to measure the error for algorithm derived depth values against the field measured values.The RMSE obtained from the proposed method is compared with the RMSE of depth values obtained using the flood boundary derived from Normalized Difference Flood Index (NDFI) method.
where,ŷ i = Field measured depth, y i = Algorithm derived depth N = Total number of observed points

IV. RESULTS AND DISCUSSIONS
Two SAR scenes (C band &L-band) of the study area acquired with time difference of 54:34 hours during flood 3248 VOLUME 11, 2023 The hourly rainfall trend on each day is derived using HEM data product. The data trends from INSAT 3D with corresponding SAR acquisition time for entire state is shown in Figure.6. From readings observed in study region, the increased flood extent shown on L-band SAR data is result of the penetration. Maps of six-hour cumulative rainfall in the state of Assam and in study area are shown in Figure.7. It is observed that the state received a cumulative maximum rainfall of 167mm/hr on 29 th July 2016 between 06:30hrs and 12:30hrs when the scheduled satellite data is acquired. The study area received little or no rainfall of 0.749mm on 30 th July 2016 in the later hours, which continued with total accumulated precipitation of 217 mm by the time of second acquisition. This justifies the increased extent as penetration of L-band radar. After data acquisitions, a series of data preprocessing steps are carried out on input images to prepare the data for algorithm implementation. Two scenes are subsetted to maintain equal spatial extents. Both scenes are calibrated, speckle removed and orthorectified. Different speckle filters are applied on dataset, out of which Lee-sigma filter showed better performance in preserving high frequency components of image, which corresponds to flood boundaries.

A. FLOOD BOUNDARY EXTRACTION
Fusion result from l-and c-band images after applying second stage of methodology (refer section III) is shown in   Table 1. Fusion results depends on the number of decomposition levels [23] which explains that fewer levels gives poor spatial quality and too many levels reduce structural similarity. It is observed here that fusion carried out at four levels preserved all the important details. The result of the segmented image is shown in Figure.9. The threshold ranges generated using the Otsu's algorithm for segmentation is tabulated in Table-1. In Figure.9 each segmented portion is assigned a level starting from 1. For boundary extraction, it is assumed that two hypothesis holds true. a) The surface water level in level-1 is less that the water level in level-2 and so on up to level-5. b) The depth is not constant in a given level but highest level holds the maximum flood depth value in entire image. Therefore, fifth boundary holds maximum flood depth. (Refer Figure. Staring from 95 th percentile value the difference of five percentile intervals are calculated and when the difference is less than 30m, the mean value of the difference is taken as water surface elevation. The same procedure is repeated on   elevation vectors from each boundary. The values greater than 54 th percentile are removed as outliers as mentioned in the methodology after calibration from FwDET tool. For example, the maximum elevation of the study area is 257.3 meters and the corresponding water surface elevation shown to be 157m. The depth calculated from the difference is 100m which falls into 93 rd percentile is considered as outlier and removed. The high elevation points cannot store water as it drains to lower elevation points or pits. The schematic illustration of water levels raise up in each level as the elevation changes is shown in Figure 12. Water Surface Levels (WSL) of boundary 1 is used for representation in schematic of the Figure 12. The final depth map produced is shown in Figure.13. Figure 11a shows the surface distribution of elevation for the entire study area. The surface distribution of elevation for small sample S1 in study area is shown in Figure 11b. The QQ plot of sample S1 of elevation taken from level-5 flood boundary (refer Figure 9) is shown in Figure 10. The length of sample S1 shown here is of length 50 × 1. From the Figure 10, it can be observed that the elevation closely follows normal distribution for the chosen sample S1, above 10 meters. These values which highly deviate from the sample are considered as outliers. Outliers in any sample inside the flood boundaries which show deviation from normal elevation values are considered as outliers and corresponding flood depths produced from these values are removed. A new depth distribution is created as explained in methodology for each sample of elevation that fall inside flood boundary of every level. Figure 11c shows the initial flood depth results for sample S1 without calibration. Figure 11d shows the simulated flood depth result. It can be observed that the depth values inversely follow surface elevation. Total of 884 samples in level-1 boundary, 1027 samples in level-2, 1037 samples in level-3,4,5 are used to create depth values as mentioned in part-C of VOLUME 11, 2023 FIGURE 11. a) Surface distribution of elevation shown for entire study area with S1 showing sampled area that fall under the flood boundary b) Surface distribution of elevation values for sampled area S1 c) Flood depth values calculated from statistical method d) Newly created flood depth values that synonymously follows the elevation distribution. section III. The parameters for the distribution fitted for each sample are calculated using maximum likelihood estimation method. Each boundary/level contains depth values for every pixel varying from minimum to maximum. Figure 14 shows increase in depth from minimum values of 0.0011m in level-1 to 0.016m in level-5. The maximum depth in level-5 is 1.56m. The depth map with five levels with each level corresponding to values from one boundary can be seen in Figure 14. The elevation values that falls into each segmented boundary layer of the fused image show gradual increase in value and therefore gradual decrease is observed in terms of depth. The negative values produced in the calculation are result of under estimation of the flood boundary and are removed. Although the resolution of the DEM plays major role in accuracy of depth [29], [30] this can be compensated improving the accuracy in flood boundary and method of creating the water elevation plane [30]. We carry out the validation of algorithm obtained results by comparing the height values from field measurements. From the SAR data, it is observed that the inundation take shape below the road level. Roads in the study area are showing high scattering during floods, which indicates that the inundation is below the road level. Since the event is past in time, obtaining the field depth values for the study is unfeasible. Therefore, the depths of the fields from the road level are taken as benchmark for flood depth measurements. Five such points scattered across the entire study area are shown in Figure.14. The locations of the points and depth measurements from field as well as the algorithm are tabulated in Table 2.

B. FLOOD DEPTH ESTIMATION
To validate the algorithm, RMSE is computed from equation 18 which represents average error in flood depth values in comparison with field measured values. The statistical methodology explained in Section III, Part -C is applied on flood boundary derived from NDFI method and the RMSE is calculated for the same. Two L-Band SAR images in HH polarization one during pre-monsoon i.e., on 28 th Feb 2016 and other during flood on 31 st July 2016 are used to produce flood boundary from NDFI as explained in [16]. It is observed an average of 0.209 meters difference in the VOLUME 11, 2023  depth values produced from our boundary extraction method and NDFI method. The graph in Figure 12a represents the depth values at field points for both the methods. Figure 12b shows the simulated depth values for a sample containing 70 points from both the methods and the difference in level at each point. RMSE of 0.259meters is observed for the proposed method whereas RMSE of RMSE of 0.35 meters is observed for NDFI method. As the study is carried out in flat agricultural lands, the elevation varies around few centimetres to meters and using DEMs of high vertical resolution will bring out capability of the proposed method.

V. CONCLUSION
In this paper, a technique primarily based on L -and C-Band SAR data fusion to decipher flood boundary and a statistical method that generates water depth that closely follows surface undulations in agricultural lands is presented. Two major remarks are made in this study. In satellite derived depth methods the results varies depending on the area engaged by the flood boundaries, and flood boundary from SAR data depends on interactions of electromagnetic waves with water. The idea behind this work is to improve the detection of flood boundary in vegetated areas with the help of higher frequency bands when coarse resolution DEMs are available. A methodology for selection of boundaries in arable lands is provided using dual frequency SAR data. The depth values from the algorithm are compared with evidence based field measurements and other flood boundary extraction method like NDFI. An RMSE of 0.259 meters is reported on 30m resolution DEM using the current method. It showed improved performance in comparison with methodology that derives the boundary using NDFI. With upcoming missions like NISAR with dual frequency SAR in L and S band, the hypothesis can be experimented more efficiently. It also showed that depths could vary up to few centimetres to meters inside a flood boundary based on pits and elevations that shapes the land. This method proved reliable flood depths over larger spatial extents with basic data in places where hydrological modelling cannot be applied.