# Morphometric delineation of administrative limits and classification of threatened categories of small basins in transboundary rivers

### Morphometric analysis

The Banki river basin (24° 23′ 6.42″ and 24° 10′ 17.71″ north latitude and 83° 23′ 9.55″ and 83° 43′ 19.96″ east longitude) is a integral component (518.35 km2) from the downstream Ganges river basin at a distance of ≈ 198.44 km to the southeast in the Garhwa district of Jharkhand, India. The 54.08 km long Banki River originates from the Sagma Hills (south-west) and the confluence with North Koel (north-east). Altitude ranged from 129 to 493 m above mean sea level in the basin (Supplementary Figure S1).

The five Survey of India (SOI) topographic sheets (63P/7, 63P/8, 63P/11, 63P/12 and 63P/15; Scale—1:50,000; 1977) were downloaded (https://onlinemaps.surveyofindia. gov.in/)sixteen and georeferenced based on the Universal Transverse Mercator (UTM) projection and the 1984 UTM Zone 44N datum of the World Geodetic System (WGS). All georectified survey sheets were mosaicked using Arc GIS 10.2 software. For the extraction of the drainage network, the mosaic topographic sheets were manually digitized using the Arc GIS 10.2 editing tool. Additionally, the digitized shape file was converted to a topology for error correction.17 and then filled in the attributes for each stream based on the Strahler method of stream ordering18. Unbranched streams were designated as first-order streams; two first-order currents joined to form second-order currents, the union of two second-order currents resulted in a third-order current, and so on. Delineation of the watershed and sub-watershed was carried out with the aid of the pour points on the Arc Hydro tools using ASTER (Advanced Spaceborne Thermal Emission and Reflection and Radiometer), a spatially resolved digital elevation dataset. 30 m (downloaded from https://search. earthdata.nasa.gov/search)19 and collated with the contours of the topographic sheet.

Drainage density, drainage source, drainage confluence, and drainage frequency maps were prepared with manual interpretation of the total stream length.18first-order total flows18total confluence flows and the total number of flowstwenty, respectively, on a 1 km × 1 km network grid and place them in the point shape file. Inverse Distance Weighting (IDW) interpolationtwenty-one it was used to create the final maps for the reference year (1977) in Arc GIS 10.2 software.

The field inventory updated current morphometric details using a global positioning system (GPS, Garmin eTrex 30 model) and drone survey (DJI AIR 2S) in November-December 2021. Qualitative and quantitative verifications involved the presence/absence of streams along with their Points of origin and confluence. Recorded field data was used to remove or retain streams in digitized shape files and to represent changes in the drainage network. Associated spatial data was generated by repeating the GIS processing exercises using Arc GIS 10.2 software.

Drainage data from the reference year (1977) and the current year (2021) were compared to illustrate changes in linear aspects (stream order, stream number, stream length, bifurcation relationship, and rho coefficient)18.20 and drainage texture parameters (drainage density, flow frequency, drainage texture, channel maintenance constant, and infiltration number).20,22,23 of the Banki basin and sub-basins. The ASTER DEM data was used in the calculation of elevation and perimeter22.

### GWPZ mapping

To understand the interactions between the river and the aquifer, the groundwater potential zone (GWPZ)24 was delineated where ten input variables were used under two LULC scenarios (1991 and 2021), two rainfall patterns (1961-1990 and 1991-2020), and two drainage densities (1977 and 2021): the slope was generated from ASTER DEM data (pixel size = 30 m resolution); The geomorphology, geology, lithology and lineament density shape files were taken from the Bhukosh portal (https://bhukosh.gsi.gov.in/Bhukosh/MapViewer.aspx)25; SOI topographic sheet drainage densitysixteen and field data; soil texture was obtained from the FAO soils portal (https://storage.googleapis.com/fao-maps-catalog-data/uuid/446ed430-8383-11db-b9b2-000d939bc5d8/resources/DSMW.zip)26; Mean annual precipitation maps (30 years: 1961–190 and 1991–2020) were prepared by collecting precipitation data (0.25° × 0.25° latitude-longitude resolution) from rainfall stations monitored by the India Meteorological Department (IMD).27. LULC maps were prepared by unsupervised classification28 of 7 bands from the Landsat 5 satellite data set (September 26, 1991)29 and 11 bands from the Landsat 8 satellite data set (October 14, 2021)30 using an iterative self-organizing data analysis technique (ISODATA) algorithm31 performed with 200 spectral classes, a convergence threshold of 0.950 and 10 iterations. The Euclidean distance in feature space assigned each pixel to a group through a few iterations, which introduces considerable subjectivity into the classification process.32. LULC classes include agriculture (lowland and upland crop fields with and without crops); barren (dry and bare with very few plants and no trees); urbanized (high, medium and low density settlements, scattered settlements, infrastructure such as schools, hospitals, industries, bridges and roads); vegetation (forest cover, trees outside forests, road planting, shrubs, and herbaceous layer); and water (wet and dry rivers, riverbanks, flooded areas, and small ponds).

Artificial Neural Network (ANN) processing was implemented using the Neural Network ToolBox for MATLAB33. The structure of the Feedforward neural network3. 4 selected in this study consists of an input layer (ten input variables described above), a hidden layer (hidden neurons) and an output layer (well water level) for the delimitation of potential groundwater zones. Input and target data were entered into MATLAB R2020b software, and all factors related to groundwater in raster format and well water levels were converted to ASCII format files in GIS.35. Before running the ANN model, we selected training, test, and validation data corresponding to 70%, 15%, and 15% of the total study area (575,944 pixels). Six numeric matrices were generated using specific scripts: the X-train-input, Y-train-target, X-test-input, Y-test-target, X-validation-input and Y-validation-target matrices36.

The input data matrices were normalized to train the neural network. Initial weights were randomly selected, followed by the Levenberg-Marquardt backpropagation algorithm.37.38 to minimize errors between the predicted (target) and calculated output values. The number of epochs was set at 1000 and the mean square error (MSE) of 0.001 was used as the stopping criterion.39. After multiple tests, the network was optimized to have ten nodes in the input layer, three hundred twenty-five nodes in the hidden layer, and one node in the output layer structure (10 × 325 × 1) in 587 epochs (1991). and 302 epochs (2021). The results showed MSE and correlation (R) 0.005 and 0.73, respectively, for 1991 and 0.006 and 0.71, respectively, for the year 2021. The ten thematic maps were integrated with the weighted overlay analysis method in the GIS platform using the equation . (one)40.41 to generate the GWPZ:

$${\text{GWPZ }} = \, \sum ({\text{Wi}} \times {\text{Xi}}),$$

(one)

where Wi represents the weight of the thematic layers and Xi represents the rank of the subclass of the thematic map.

### Delineation of AB and derivation of RRLCC

Administrative boundaries are highly relevant from an implementation standpoint, as they capture the hierarchy implicit in authority structures that shape multilevel governance of environmental resources.10,12,13,42. In this reference, we develop an empirical method to delineate the BA along the left and right banks of streams, regardless of their order, number, length, and width. After performing all the permutations and combinations, we found that Dd emerged as the most suitable morphometric parameter for the derivation of AB because Dd is the only parameter that mainly represents one dimension (Lu) and two dimensions (area, A) of the basin. . The DdR (proportion of Dd1977 in the reference year to Dd2021 in the current year) was calculated to incorporate the unitless “watershed factor” and overcome biases in the BA estimate (equation 2).

$${\text{Drainage}}\,{\text{density}}\,{\text{proportion}}\left( {{\text{DoR}}} \right) \, = {\text{ Dd }}_{{{1977}}} /{\text{ Dd}}_{{{2}0{21}}}$$

(2)

The width of the administrative boundary (WAB) was the product of DdR and the mean width of the stream (MSOUTHWEST) (Eq. 3). ThemSOUTHWEST it was determined taking into account the width of each stream in order 1, 2 and 3 in three locations (point of origin, midstream and before the point of confluence). ThemSOUTHWEST of the fourth-order main stem (Banki River) was determined by measuring the width at nine locations considering spatial variation in LULC, geomorphology, geology, and soil types in the 1 km × 1 km gridded basin. Finally, the WRAB (width of the administrative boundary on the right bank) and WLABORATORY (width of the administrative boundary on the left bank) were calculated as half of the WAB (Eq. 4).

$${\text{W}}_{{{\text{AB}}}} = {\text{ M}}_{{{\text{SW}}}} \times {\text{ DoR,} }$$

(3)

$${\text{W}}_{{{\text{RAB}}}} \,{\text{o}}\,{\text{W}}_{{{\text{LAB}}} } = {\text{ W}}_{{{\text{AB}}}} /{ 2}{\text{.}}$$

(4)

The essential information to develop the RRLCC, we rigorously review the evolution of the IUCN Red List, where qualitative and quantitative data on the population and habitat of flora and fauna are taken into consideration to define threatened categories and criteria.43. We also review the six IUCN protected area management categoriesfifteen determine and incorporate the RRLCC into this framework. The proposed concept of the RRLCC addresses the percentage change in Nu, Lu and Dd in basins and sub-basins and strongly advocates for the protection and conservation of abiotic components such as rivers along with flora and fauna within and outside protected areas.