The influence of topography on floods in southern Brazil

Kuchinski, Vinícius; Paiva, Rodrigo Cauduro Dias de

doi:10.1590/2318-0331.302520250009

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Scientific/Technical Article • RBRH 30 • 2025 • https://doi.org/10.1590/2318-0331.302520250009 linkcopy

The influence of topography on floods in southern Brazil

A influência da topografia nas inundações do extremo sul do Brasil

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Understanding the characteristics of watersheds is fundamental for hydrological studies. This study investigates the influence of topographic and hydrological features in watersheds located in the extreme south of Brazil about flood events, which are recurrent in the region. Watersheds were classified based on their exposure to flooding, and differences in their characteristics were analyzed and compared. The results indicate that greater watersheds, with larger area, perimeter, and drainage network, are more exposed to flooding. These watersheds exhibit a floodplain relief profile resembling a “U” shape and possess a larger floodable area, in contrast to less exposed watersheds, which display a “V”-shaped relief profile. Furthermore, the specific discharge values of the more exposed to flooding watersheds are lower than those of the less exposed watersheds, suggesting that the larger floodplain area may contribute to flood attenuation. These findings offer valuable insights for preliminary watershed management and flood risk assessment.

Keywords:
Flood susceptibility; Morphometric analysis; Floodplain; Watershed

Morphometric parameter	Formulae (unit)	Reference
Stream order ( $S_{u}$ )	Strahlers’ rank	Strahler (1952)
Total stream number ( $N_{u}$ )	$N_{u} = N_{1} + N_{2} + \dots + N_{n}$	Horton (1945)
Total stream length ( $L_{u}$ )	$L_{u} = L_{1} + L_{2} + \dots + L_{n}$ (km)	Horton (1945)
Mainstream length ( $L_{m s}$ )	Geoprocessing (km)	-
Stream length ratio ( $R_{l}$ )	$R_{l} = L_{u} / L_{u - 1}$	Horton (1945)
Mean stream length ( $L_{u m}$ )	$L_{u m} = L_{u} / N_{u}$ (km)	Horton (1945)
Bifurcation ratio ( $R_{b}$ )	$R_{b} = N_{u} / N_{u + 1}$	Horton (1945)
Stream length/Bifurcation ratio ( $ρ$ )	$ρ = R_{l} / R_{b}$	Horton (1945)

Morphometric parameter	Formulae (unit)	Reference
Basin area ( $A$ )	Geoprocessing (km²)	-
Basin perimeter ( $P$ )	Geoprocessing (km)	-
Drainage density ( $D_{d}$ )	$D_{d} = L_{u} / A$ (km/km²)	Horton (1945)
Stream frequency ( $F_{s}$ )	$F_{s} = N_{u} / A$ (Nu/km²)	Horton (1945)
Texture ratio ( $R_{t}$ )	$R_{t} = N_{u} / P$ (Nu/km)	Smith (1950)
Elongation ratio ( $R_{e}$ )	$R_{e} = (2 / L_{m s}) \times \sqrt{A / π}$	Schumm (1956)
Circularity ratio ( $R_{c}$ )	$R_{c} = 4 \times π \times A / P^{2}$	Schumm (1956)
Length of overland flow ( $l_{o})$	$l_{o} = D_{d} / 2$ (km²/km)	Horton (1945)
Compactness ratio ( $C_{c}$ )	$C_{c} = P / 2 \times \sqrt{π \times A}$	Horton (1932)

Morphometric parameter	Formulae (unit)	Reference
Basin relief ( $H$ )	$H = H_{m a x} - H_{m i n}$ (m)	Schumm (1956)
Relief ratio ( $R_{r}$ )	$R_{r} = H / L_{m s}$ (m/km)	Schumm (1956)
Slope ( $S$ )	Geoprocessing (rad)	-
Infiltration number ( $N_{i}$ )	$N_{i} = D_{d} \times F_{s}$	Alqahtani & Qaddah (2019)
Topographic wetness index ( $T W I$ )	$T W I = \ln (A / \tan (β))$	Beven & Kirkby (1979)
Relative topographic position ( $R T P$ )	$R T P = \{\begin{matrix} (Z_{0} - μ) / (μ - Z_{m i n}), if Z_{0} < μ \\ (Z_{0} - μ) / (Z_{m a x} - μ), if Z_{0} > μ \end{matrix}$	Newman et al. (2018)

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[1] where $L_{u - 1}$ is the total length of the order less than $L_{u}$ .