Introduction

In today’s world, more people are living in urban areas than in rural areas, with a global urban population growth that expects to reach 66% by 2015 (United Nations 2015). The metropolitan regions cause global environmental change (Grimmm et al. 2008, Flörke et al. 2018), expanding globally twice as faster as populations (Angel et al. 2011; Seto et al. 2011). Rapid urban growth coupled with poor planning leads to a modification of the hydrological system (e.g., Deng et al. 2015; Deng and Xu 2018; Shukla and Gedam 2019) and lead to accelerated erosion (e.g., Wang et al. 2018; Zolezzi et al. 2018; Jeong and Dorn 2019). The urbanization causes a significant increase in impervious surfaces such as paved roads, roofs, and parking lots, which reduce rainwater infiltration and increase the runoff (Gurnell et al. 2007; Taniguchi et al. 2018). Impervious surface changes the hydrologic system in different ways: (1) modify the drainage network; (2) decrease groundwater recharge; (3) decrease the lag interval between onset of precipitation and the higher runoff peaks; (4) increase the total volume of storm water runoff that in extreme cases could be significantly times greater than under natural conditions; and (5) decrease mean residence time of stream flow (Rose and Peters 2001; Burns et al. 2005). Therefore, runoff concentration from the impermeable areas is one of the main factors for the severe accelerated soil erosion and gully development in the urban landscape (e.g., Bouchnak et al. 2009; Adediji et al. 2011). Many urban gullies result from the following combination of elements: high-volume runoff on steep roads, unpaved drains, lack of engineering works, and the precarious state of drainage maintenance (Adedeji et al. 2013). Erosion processes decline with the consolidation of the urban landscape (Archibold et al. 2003). However, the peri-urban areas wherein many cities do not have adequate infrastructure are more susceptible to erosion and other environmental impacts (Meija and Moglen 2010; Costa et al. 2018; Pribadi et al. 2018). Moreover, the expansion often occurs in undervalued areas near the steep areas, coastal wetlands, and poorly drained floodplains (Gupta 2002).

Understanding and measuring patterns of accumulation, transport, and deposition of the Earth’s surface materials are primary factors to investigate, predict, and mitigate environmental and urban damage. An attractive approach for studying the spatial–temporal behavior of the surface processes is geomorphic change detection (James et al. 2012). The simplest method for geomorphic change detection is the difference between the successive Digital Elevation Model (DEM), which reveals spatial–temporal patterns of volumetric changes. This methodology estimates the rates of change and generates a spatial representation of the geomorphological dynamics. Potentially unstable areas consist of localities with morphological changes. DEM change detection include different geomorphological studies, such as tectonic (e.g., Oskin et al. 2012; Ren et al. 2014), slope processes and mass movement (e.g., Hsieh et al. 2016; Mora et al. 2018; Xiong et al. 2018; Peppa et al. 2019), fluvial (e.g., Grove et al. 2013; Norman et al. 2017; Carrivick and Smith 2019; Kasprak et al. 2019), coastal dunes (e.g., Walker et al. 2013; Duffy et al. 2018; Le Mauff et al. 2018; Guisado-Pintado et al. 2019), glacial (e.g., Nuth and Kääb 2011; Jones et al. 2013; Micheletti et al. 2017; Seier et al. 2017), and karst (e.g., Siart et al. 2009; Carvalho Junior et al. 2013; Kobal et al. 2015).

In this respect, many studies on the evolution of gully systems focus on comparisons of multi-date DEMs to monitor and calculate the volumetric changes (e.g., Cavalli et al. 2017; Balaguer‐Puig et al. 2017, 2018). In these studies, the development of DEMs used different techniques: aerial photographs (e.g., Martínez-Casasnovas 2009; Piccarreta et al. 2012; Aucelli et al. 2016), aerial photography from an unmanned aerial vehicle (e.g., Glendell et al. 2017; Pineux et al. 2017; Eltner et al. 2018), airborne and terrestrial laser scanning (e.g., DeLong et al. 2012; Goodwin et al. 2017; Taylor et al. 2018), and smartphone camera (Vinci et al. 2017). The multi-temporal analysis also allows an understanding of the effects of runoff terrain interaction. In search of an adequate indicator of the urban impacts on water flow and gullies, Junior et al. (2010) proposed an accumulated-flow differencing, enabling evaluate the drainage change and the appearance of gullies. The method evidences the runoff effects from urban morphological into a natural area, comparing pre- and post-urbanization scenarios.

The main objective of this study is to evaluate the spatial patterns of geomorphic change caused by urbanization and its effects on gullies in the city of Jacareí. In this context, the research has two secondary objectives: (1) elaboration of the pre- and post-urbanization scenarios from a DEM derived from aerial photographs and digital processing techniques; and (2) change detection analysis considering topographic attributes. In the prediction of the spatial pattern of gullies, we compare the contributing area (A) and three topographic indices: (1) Topographic Humidity Index (W); (2) Flow Power Index (P); and (3) Composite Topographic Index (CTI), also known as Thorne Index. The present research evaluates the difference of terrain attributes in surface runoff and drainage channels, not evaluating the behavior in large rivers that suffer severe anthropogenic changes with constant riverbank movement (Dewan et al 2017; Güneralp and Rhoads 2009).

Study area

The Jacareí municipality is in the eastern part of the São Paulo State, a region known as the Valley of the River Paraiba do Sul (VRPS). The study area has a size of 3.9 km2, with an average altitude of 580 m between the Mantiqueira and Mar mountain ranges (Fig. 1). The city of Jacarei originated from a small settlement in 1652, changed to condition village in 1653, and became a city only on April 3, 1849. Historically, the urbanization process in the VRPS occurred with railway and highways (Presidente Dutra, Ayrton Senna, Dom Pedro I, and Carvalho Pinto). Jacarei City developed along the Dutra highway, the main road connecting the two largest Brazilian cities (Rio de Janeiro and São Paulo). Jacareí City showed a marked increase in population growth during the period 1940–2010 (IPEADATA 2014), located in a region with sizeable urban conurbation. However, urban growth also occurs in inappropriate areas for urbanization, such as slopes and floodplains.

Fig. 1
figure 1

Study area location

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The VRPS region has a warm subtropical climate with Cwa Köppen classification, containing hot summers, milder winters, and an average annual temperature of 21 ºC. The VRPS region has an average annual rainfall between 1200 and 1300 mm lower than the extended system of mountain ranges: Mantiqueira (1300–2000 mm) and the Serra do Mar (1300–2800 mm) (São Paulo 2006). The highest rainfall regime occurs from December to January with average accumulated rainfall between 200 and 250 mm/month, while the driest period is from May to August with lower rainfall 50 mm/month (Marengo and Alves 2005). Climate dynamic of VRPS do not suffer significant variations due to the presence of mass Tropical Atlantic in most of the year (Conti 1975).

The Taubaté Basin is part of the Continental Rift of Southeastern Brazil, comprising Tertiary sedimentary basins distributed over a prolonged depression with around 250 km and NE-trending, almost parallel to the coastline (Riccomini 1989; Riccomini et al. 2004). The Taubaté Basin is the largest of the Tertiary basins having about 170 km long, 20 km wide, and 800–850 m sedimentary thickness according to seismic profiles and gravimetric data (Fernandes and Chang 2002; Mendonça Filho et al. 2010; Carvalho et al. 2011). The Taubaté Basin is a pull-apart basin formed during the Palaeogene due to left-lateral transtension with the NE-SW trend, which reactivated during the Neogene (after quiescence period from Oligocene to Early Miocene) under right-lateral transpression with E-W trend (Cogné et al. 2013). Continental sediments fill the Tabaté Basin, where coarse granulometric sedimentary deposits are at the basin fault edges, and sandy and clay deposits, associated with fluvial-lacustrine environments, occur in the central portion (Riccomini 1989). The Precambrian crystalline basement consists of the banded gneisses and migmatites, which establish the Ribeira Fold Belt, a complex orogenic belt formed during the Pan-African assembly of the Gondwana Supercontinent (Valeriano et al. 2011). Geomorphological features of the Middle VRPS correspond to geological units formed by hills (crystalline basement) and river valley (continental sediments from the Taubaté Basin) (Ross and Moroz 1997). The relief varies from flat to gently rolling hills, with altitudes between 400 and 500 m.

The natural vegetation of Jacareí municipality restricts to Atlantic Forest fragments in the mountainous areas separated by vast pastures. The grazing areas extend along the valley between the Coast Range and the lowlands of Mantiqueira.

Materials and methods

Digital photographs and orthophotos

We used digital photographs and orthophotos from the Aerophotogrammetric Survey of the São Paulo State, developed by the “Empresa Paulista de Planejamento Metropolitano” (EMPLASA) in the years 2010/2011 (available through the license agreement number 024/15). In the study area, the acquisition date of the aerophotographs was November 7, 2011. The aerophotogrammetric survey used Ultracam cameras (X and XP models) (Scholz and Gruber 2009), which generated digital color aerial images (RGB composition) with 0.45 m resolution. The photo survey considered 60% forward overlap and 30% lateral overlap. Each photo had a corresponding metadata file containing aerotriangulation information. The EMPLASA generated digital orthophotos with 1 m resolution.

Pre- and post-urbanization digital model

The reconstruction of the pre-erosion surface using interpolation techniques for the removal of gully features in DEMs is a technique widely used to quantify the volume of eroded material (Bergonse and Reis 2015; Buccolini et al. 2012; Evans and Lindsay 2010; Perroy et al. 2010). In this research, the reconstruction of the past environment is without the presence of erosions and urban structures, being different from the investigation done in natural and rural settings.

The elaboration of the Digital Surface Model (DSM) used the MATCH-T DSM module of the Trimble INPHO commercial software based on an automatic and sequential multi-image matching method in several scales, combining feature-based and least-squares matching (Lemaire 2008). This software has been widely used by the scientific community (Gülch 2009; Höhle 2009; Costantino and Angelini 2011). However, the DSM contains natural vegetation and built features on the Earth’s surface. The preparation of the pre- and post-urbanization DEMs used the techniques of filtering and extracting objects from the DSM, which are available in DTMaster software (Heuchel et al. 2011). The DTMaster tolls enable three-dimensional visualization of the point clouds and their changes while continuing to edit (Fig. 2). In the post-urbanization model, the correction of the drainage network, lake, and street errors in the DSM utilized the interpolation of digitized lines at ground level. The topological revision of the vectors eliminated errors in lines, points, and polygons such as overlap, the absence of connectivity, intersection, among others. The post-urbanization model maintained the constructions (houses, buildings, streets, among others) and eliminated the woody vegetation. Other studies to obtain the Digital Terrain Models (DTM) in forest areas and to estimate canopy height used DTMaster software (e.g., Granholm et al. 2017; Piermattei et al. 2018). Differently, the pre-urbanization model removed non-ground objects, reaching the bare ground. In this case, the interpolation considered the digitized lines parallel to the streets at ground level, eliminating the urban elements by the altimetry of the roads (Fig. 2b). Smoothing the ravines prevented the influence of urban features in the pre-urbanization flow model.

Fig. 2
figure 2

Block diagram containing the cloud of elevation points from stereophotogrammetric methods, evidencing the filtering process with the elimination of artifacts above the surface

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Pre- and post-urbanization differencing using contributing area and topographic indices

In the gully analysis, we used the following terrain attributes: A; W; P; and CTI. The elaboration of the A attribute used the D-infinity method (Tarboton 1997). The application of the logarithmic function (base 10) in this attribute facilitated the surface flow visualization. Many surveys for the prediction and localization of gullies used the relationship between slope (S) and A (Desmet et al. 1999; Moore et al. 1988), considering a division or multiplication operation. The W index (Beven and Kirkby 1979; O’Loughlin 1986), widely applied to soil saturation, performs a division operation expressed by:

$$W\, = \,{\ln}\left( {A/\tan S} \right).$$
(1)

In contrast, the P indicates the erosive power (flow intensity) or the incise capacity of the runoff (Moore et al. 1988), which establishes a multiplicative relationship defined as:

$$P\, = \,A\;{\tan}\left( S \right).$$
(2)

In this research, we applied the Napierian logarithmic function for the P index to decrease the data variations, highlighting runoff features. The CTI adds the planform curvature (PC) in the multiplicative expression from the following equation (Thorne et al. 1986; Zevenbergen and Thorne 1987):

$${\text{CTI}}\, = \,A \times S \times {\text{PC}}{.}$$
(3)

The planform curvature is the terrain curvature perpendicular to the highest change in the slope gradient (Zevenbergen and Thorne 1987). In the bibliography, other names are suggested for the planform curvature, such as the term tangential curvature (Mitasova and Hofierka 1993; Schmidt et al. 2003) and plan curvature used in Arc/Info for the Zevenbergen and Thorne’s equations (Rana 2006). The planform curvature represents the degree of convergence (concave) or divergence (convex) of the terrain, where the converging profile concentrates and accelerates the flow (Moore and Burch, 1986; Mitasova et al., 1996). According to Momm et al. (2013), a normalization of CTI values is to disregard the negative planform curvature (ridges) and apply a logarithmic function only to the pixels containing positive CTI values that are possible locations for gully initiation. Similarly, we proposed a normalized CTI (CTIn) by the formulation:

$${\text{CTI}}_{n} \, = \,{\ln}\left( {{\text{abs}}\left( {{\text{CTI}}} \right)} \right)\; \times \;b,$$
(4)

where

$$b\, = \,{\text{CTI}}/{\text{abs}}\left( {{\text{CTI}}} \right).$$
(5)

The “b” term establishes different signals for the concave (+ 1) and convex (− 1) areas. Finally, the application of the difference (post-urbanization minus pre-urbanization) sought to emphasize the changes of the topographic indices and their implications in triggering the erosions.

Results and discussion

Pre- and post-urbanization models

Stereophotogrammetric analysis of the DEM datasets in the DTMaster software package allowed us to reconstruct the elevation of the ground surface from the DSM. Figure 3a, b demonstrates the DSM with the elimination of above-surface features from human-made objects and forest vegetation, generating a topography that shows the natural drainage without anthropic interference. Complementarily, the visualization of three-dimensional models of contour lines (Fig. 3c, d) and surfaces (Fig. 3e, f) illustrated the result of the filtering process. The reconstructed three-dimensional model obtained continuous level contours consistent with the watershed configuration (Fig. 3d and f).

Fig. 3
figure 3

Shaded relief of the digital surface model (DSM) from stereoscopic aerial photographs (a); digital terrain model (DTM) with a separation of above-surface features (b); block diagram with the DSM contour line (c); and block diagram of the DTM contour line (d)

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Comparison between the pre- and post-urbanization DEMs revealed a significant change in the elevation data (Fig. 4a, b). Pre-urbanization topography resulted in a smoothed DEM, removing urban and vegetation features. Meanwhile, post-urbanization topography also eliminated forest features but preserved and corrected urban elements with caution in restoring roads, which became runoff routes. Therefore, urban environments were particularly vulnerable to elevation change because of the interaction of streets, houses, buildings, and other urban features on landscape configuration. The maximum altitude in the pre-urban model was of 664 m, while in the post-urban model was of 671 m due to the values with the elevations of urban elements such as buildings. The topographic profiles became more apparent the differences between the models, with the urban model emphasized the differences among building areas and street level (Figs. 4c, d).

Fig. 4
figure 4

a Pre-urbanization DEM; b post-urbanization DEM; c topographic profile from pre-urbanization DEM; and d topographic profile from post-urbanization

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Geomorphic attributes

Figure 5 shows the results of the contributing area attribute and topographic indices from the pre- and post-urbanization models. In the pre-urbanization contributing area map, the runoff had a diffuse behavior with flow concentration only in the main drainages (Fig. 5a). In contrast, the post-urbanization contributing area map showed a higher flow concentration in the streets (Fig. 5b). The built-up areas inside the blocks acted as drainage dividers directing the flow to the streets, which function as channels that concentrated the surface water flow. In this context, the corrections of the surface flow routing on the natural (drainage network) and urban (highways, roads, and streets) environments were essentials in the elaborations of the DEMs, directly influencing the terrain attributes and indices. The urban surface model was challenging because of the topographically complex environment, being possible on the same street to change the flow direction. Thus, the comparison of the contributing area maps highlighted the profound changes caused by urbanization in the surface flow dynamics.

Fig. 5
figure 5

Maps of topographic attributes: a logarithm of the contributing area (ln (A)) in the pre-urbanization scenario; b ln (A) in the post-urbanization scenario; c topographic wetness index (W) in the pre-urbanization scenario; d W in the post-urbanization scenario; e logarithm of the stream power (ln (P)) in the pre-urbanization scenario; f ln (P) in the post-urbanization scenario; g normalized compound topographic index (CTIn) in the pre-urbanization scenario; and h CTIn in the post-urbanization scenario

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In the study area, only the drainage channels or streets concentrated significant W, ln (P), and CTIn values due to the high contributing area values (Fig. 5). Outside the drainage channels, the W index highlighted a general pattern with lower values in the plateau edges and higher values in the flat areas such as the plateau and valley bottom (Fig. 5c, d). In these localities, the P index showed an inverse behavior with higher values in the plateau edges and lower values in the flat areas (Fig. 5e, f). These variations were more visible in the pre-urbanization model, because of the lack of striking urban features that imposed the flow along the streets (Fig. 5c and e). This spatial configuration of the W index, with higher values in the watershed dividers on the flat plateaus, diverged from the contributing area attribute and the other index. Unlike, the W index evidenced zones of saturation, which could be source areas for runoff generation. In this perspective, the W index did not improve the gully detection at the plateau edges but complemented the analysis by indicating nearby saturated zones with the potential to trigger a runoff. Moreover, debris deposition zones from gullies in a diffuse downslope streaking acquired higher W values.

The CTIn evidenced topographic convergence into hollows, fragments of hillslopes with contours concave-out from the ridge (Hack and Goodlett 1960). Shapes concave in plan control the concentrated water flow route, increasing erosion, and solifluction. Therefore, the hollows evidenced the most prone areas to erosion. The convergent relief features in the CTIn map acquired proportionally higher values than the P index (Fig. 5g, h). In the urban area, the presence of the houses and constructions generated an artificial curvature that delineates the streets.

Geomorphic changes

A comparison of geomorphic changes is not a purely competitive but complementary approach since it represents different aspects of the terrain analysis. The topographic index profiles of a gully considered the pre- and post-urbanization period and the relief position proposed by Ruhe (1975): summit, shoulder, backslope, footslope, and toeslope for each topographic attribute (Fig. 6). The contributing area showed for both models increasing values from summit to footslope and decreasing in toeslope. However, the contributing area differencing (post- urbanization minus pre-urbanization) denoted a profile with reduced values between summit and footslope due to the presence in the upslope convexity of diffuse flow in the pre-urbanization model and of concentrated flow coming from the city in the post-urbanization model, which makes the difference at summit greater than at footslope (Fig. 6).

Fig. 6
figure 6

Profiles of topographic indices along four gullies, considering the logarithm of the contributing area (ln (A)); topographic wetness index (W); logarithm of the stream power index (ln (P)); and normalized compound topographic index (CTIn). The slope profile comprises the following landform positions: summit (SU); shoulder (SH); backslope (BS); footslope (FS), and toeslope (TS)

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In both models, the W index showed higher values in the relief positions with a low slope (summit, footslope, and toeslope), decreasing in the backslope. In contrast, the ln (P) index showed an inverse behavior with a higher value in the backslope position. The W and ln (P) differences (dW and dP) also showed an opposite response, where the dW values increased from the summit to the toeslope, while dP values decreased.

The CTIn presented a behavior like the ln (P) in both scenarios, containing the highest values in the backslope due to the higher slope and concavity. The erosion process along the slope profile tended to intensify the drainage concavity, mainly in the backslope and footslope position due to the drain deepening. The difference values of CTIn and ln (P) presented similarity, decreasing from the summit to the toeslope. The highest value at the summit was due to post-urbanization flow concentration. The CTIn points of the gullies and non-gullies showed the largest distance between the indices.

In the study area, the presence of urban structures significantly modified the landscape and triggered the appearance of five gullies (Fig. 7). These urban gullies were likely a result of a combination of factors related to both natural and anthropogenic processes, which interact to increase the concentration of surface water flow and its erosive effect. The development of gullies occurs in areas adjacent to urban settlements when the rainwater concentration increases in the built area due to the lack or insufficiency of the rainwater sewage system and reaches peri-urban areas. During heavy tropical rainfall, storm sewer systems may not capture all the runoff, causing ravines in the natural drainage channels connected to the discharge of water from urban surfaces. Figure 7 shows a scatterplot comparing the behavior of topographic indices between pre- versus post-urbanization for gullied and ungullied sites. In the gully site, there is a significant increase of contributing area and topographic indices from the pre-urbanization condition to the post-urbanization, evidencing the runoff-concentration effect from the city’s streets to drainages on the outskirts of the built-up areas. On the other hand, ungullied sites showed lower topographic indices with the urbanization.

Fig. 7
figure 7

Pre- and post-urbanization difference maps and their respective scatter plots in gullied (circles) and ungullied (squares) locations, considering the following attributes: a logarithm of the contributing area, b topographic wetness index; c logarithm of the stream power index; and d normalized compound topographic index

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Comparison of results with other researches

Diverse researches show the soil erosion is a major environmental problem in the rapid urban expansion (Lu et al. 2015; Wang et al. 2018). Changes in water flux either because of human activities (such as urbanization) or natural (climate change driven extreme flood events) are mainly driving erosion risk. In Brazil, the two factors are combined, having a tropical climate that favors the presence of heavy rains in the summer season and many cities with a disorderly urban expansion (Zuquette et al. 2004; Xavier et al. 2019).

The urbanization process replaces natural areas with impermeable surfaces that reduce the amount of groundwater recharge and increase the runoff. The results of this research are consistent with other studies that observed the intensification of erosion instability from the concentrated runoff at the road surface, establishing threshold values for the contributing area and slope (Montgomery 1994; Imwangana et al. 2014). The backslope for being in steep areas presented an intense erosive action, containing the highest values of P and CTIn. According to (Conforti et al. 2011), the susceptibility to gully erosion is strong control by the P factor. Kakembo et al. (2009) demonstrated the predisposition of abandoned lands to gully erosion using the P index.

Most studies of geomorphic changes in the gully system occurred in natural or rural settings (Aucelli et al. 2016, Betts et al. 2003), with few studies in urban environments. The results obtained by Junior (2010), restricted to the change detection of contributing areas, were compatible with those found in this study. The spatial analysis of the gullies in the study area showed that the road network was a conditioning factor for the concentration of water and erosion development. Therefore, the methods evaluated provide the spatial pattern of surface water flux change and its associated erosive processes, but these methods have limitations for accurate quantification requiring more effective field methods.

Conclusions

The results of this investigation demonstrate a strong relationship between urbanization and erosion processes. The urban morphology causes changes in the flow and volume of water that accentuate the erosive process around the built urban areas. In the evaluation of urban outflow from the digital elevation model, streets and their flow directions should be detailed, not requiring the definition of discrete and geometrically accurate objects such as walls and roofs of buildings. The geomorphological and hydrological change detections from the pre- and post-urbanization measures provide a description of the rerouting and an order of magnitude of the water volume changes, identifying the locations with the potential for accelerated erosion. In the study area, the urban intervention led to a concentration of flow along the slopes that causes instability in the landscape and accelerated erosion. The topographic indices have a complementarity, where ln (P) and CTIn highlights the backslope, ln (A) evidences the footslope, and W the footslope and toeslope. Understanding the geomorphic changes by urbanization is essential for the automated identification of gully initiation points in the peri-urban areas, allowing the establishment of strategies for the improvement of urban drainage and watershed conservation. Despite their significant potential in urban erosion studies, few types of research use the geomorphic changes for urban environments and should be further explored.