1 Introduction

Clayey terrains outcropping in many parts of Italy are frequently affected by accelerated erosion processes, producing landforms known as calanchi and biancane, generally considered as “badlands” (Fairbridge 1968). Calanchi badlands are composed of an extremely dissected, rapidly developing landscape, characterized by rill and gully landforms and a very dense dendritic drainage network (Alexander 1980). Biancane badlands appear as clay domes up to about 20 m high and dissected by rills (Torri et al. 1994; Torri and Bryan 1997; Calzolari and Ungaro 1998). The badlands formation and dynamics are mainly the result of the action of particularly aggressive climatic factors, such as the severe contrasts of the Mediterranean rainfall regime, on friable substrata consisting in clay, silt and sand of the Plio–Pleistocene marine cycles (Moretti and Rodolfi 2000). The morphogenetic activity is not only limited to channel erosion, but it is also due to piping and repeated superficial slides (Bryan and Yair 1982). Therefore, it should be better to consider the calanchi and biancane as the result of a “combined erosion” process (Zachar 1982). Also, areas where the natural equilibrium has been disrupted by inadequate land-use techniques can be transformed into badlands (Torri et al. 2000). The term of badlands currently refers to areas of unconsolidated sediment or poorly consolidated bedrock with little or no vegetation, which are useless for agriculture because of their intensely dissected landscape (Gallart et al. 2002).

Biancane generally develop on gentler slopes than calanchi and where lower values of amplitude of relief occur, due to the morphoevolutionary processes. Moreover, observations on present evolution biancane of Central Tuscany, Italy, confirm the leading role played by reticular systems of joints in dissection of the original, gently dipping surfaces (Colica and Guasparri 1990; Torri and Bryan 1997; Della Seta et al. 2009; Vergari et al. 2013a).

Calanchi badlands comprise very deep gullies and rills accompanied by mass movements, especially along the gully banks and gully heads. Calanchi are often initiated or reactivated by gully development, which may precede or follow some mass movements (Nogueras et al. 2000; Gallart et al. 2002).

The growing interest in studying badland dynamics reflects the need to increase knowledge of geomorphological processes and dynamics in badland areas (Nadal-Romero and Regüés 2010), particularly because of their importance in generating extreme water and sediment yields (Gallart et al. 2002; García-Ruíz and López-Bermudez 2009), loss and depletion of soil, landslides and, consequently, economic damages and hazardous conditions (Conoscenti et al. 2008a).

Thus, investigations aimed at monitoring and modelling gully erosion are needed as a basis for predicting the effects of environmental changes (climatic and land use) on gully erosion rates and determining the areas susceptible to gully formation, in order to properly design soil conservation plans and strategies (Gómez Gutiérrez et al. 2009a, b).

The prediction of the spatial distribution of gullies has been tackled by both assessing the topographic threshold required to be exceeded for the gully initiation (Montgomery and Dietrich 1992; Desmet et al. 1999; Kakembo et al. 2009; Nazari Samani et al. 2009; Svoray et al. 2012; Torri and Poesen 2014) and applying statistical methods to evaluate the relationships relating environmental controlling factors and the spatial distribution of gullies (Märker et al. 1999, 2011; Meyer and Martínez-Casasnovas 1999; Chaplot et al. 2005; Bou Kheir et al. 2007; Conoscenti et al. 2008a, 2013, 2014; Magliulo 2010, 2012; Akgün and Türk 2011; Conforti et al. 2011; Lucà et al. 2011). In these last investigations, the spatial probability has never been associated with the probability of a given erosion intensity to occur in the areas predicted as prone to gullying.

One method is proposed in this paper for water erosion hazard evaluation, which is based on integration and widening of the monitoring and estimation techniques applied in the key study area of Upper Orcia Valley, Southern Tuscany, as described in previous studies (Ciccacci et al. 2003, 2008, 2009; Del Monte 2003; Del Monte et al. 2002; Della Seta et al. 2005, 2007, 2009; Vergari et al. 2011, 2013a, b; Aucelli et al. 2014). A multivariate statistical approach has been applied to evaluate water erosion hazard within the Upper Orcia Valley, where the susceptibility evaluation method based on conditional analysis (Vergari et al. 2011) was combined with the Tu denudation index method, an erosion intensity estimation model. By using this approach, it was possible to assess the occurrence of water erosion hazard, in terms of both the spatial and temporal probability under a given intensity in calanchi badlands. Biancane landforms, widespread in the study area, were not considered for this analysis, as they have been more frequently reshaped, even erased, by farmers than calanchi on the less steep slopes. So that, their natural development is more easily and frequently limited by man activities and requires more complex investigations on their genesis and transformations (Torri et al. 2013).

An empirical statistical method, the Tu denudation index, was chosen for the erosion estimation model in order to maintain the simplicity of the proposed analysis, also associated with the susceptibility conditional analysis. Actually, the major limits of physically based models are the large data requirements, the limited knowledge of complex processes and interactions between these processes at catchment scale (de Vente et al. 2006). Thus, they are generally more suitable for small areas or for slope-specific studies. On the contrary, empirical models are primarily based on field observations and try to characterize response from these data. The computational and data requirements for such models are usually less if compared with other types and often capable of being supported by coarse measurements. Many empirical models are based on the analysis of catchment data using stochastic techniques. In this specific study, among the empirical models, Tu denudation index has been selected for its tested capability of identifying the very high soil losses typical to sub-catchments greatly affected by badlands developed on uplifted Plio–Pleistocene marine clays in Italy (e.g. Ciccacci et al. 1981; Della Seta et al. 2007, 2009).

2 Study area

The assessment of the water erosion hazard was applied in the Upper Orcia Valley, which is the easternmost portion of the Ombrone River basin (Fig. 1a). The area is located in the Tuscan Pre-Apennines, close to Siena, North of Radicofani, and it covers about 120 km2, with the altitude ranging between 350 and 1148 m a.s.l. (Cetona Mt.). The drainage pattern and catchment shape are structurally controlled by the regional morphostructure of the Radicofani graben (Baldi et al. 1994; Carmignani et al. 1994), whose major axis is NW–SE oriented.

The geological evolution of the study area is responsible for widespread outcrops of lithological units prone to denudation (Fig. 1a). These units are Plio–Pleistocene in age and infill the NW–SE-striking graben (Baldi et al. 1994; Carmignani et al. 1994). During Quaternary, the Plio–Pleistocene marine deposits were uplifted to several hundreds of metres above the present sea level (Liotta 1996). This severe uplifting was related to pluton emplacement and widespread volcanic activity along the Tyrrhenian side (Acocella and Rossetti 2002), underlined by the alignment of many volcanic complexes. Quaternary uplift has been particularly strong along the southern margin of the Radicofani Graben, where locally marine deposits outcrop at 900 m a.s.l., from the Amiata-Radicofani Mt. neck, on the western side, to Cetona Mt., on the eastern slope of the study area.

Fig. 1
figure 1

Location of the study area and geological sketch of the Tyrrhenian side of Central Italy (a) and biancane and calanchi badlands in the Upper Orcia Valley (b); (1) Quaternary volcanic rocks; (2) Quaternary undifferentiated continental deposits; (3) Plio–Pleistocene terrigenous marine deposits and Messinian evaporites; (4) sedimentary and metamorphic units of Ligurian and sub-Ligurian nappes (Trias to Lower Cretaceous); (5) sedimentary and metamorphic units of Tuscan nappe (Palaeozoic to Miocene); (6) normal fault; (7) overthrust and reverse fault; (8) undetermined fault; (9) watershed; (10) study area

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The climate is temperate warm, depicted by the typical Mediterranean variability. The average annual precipitation is about 700 mm, and the mean annual temperature is around 14 °C. Annual rainfall usually varies between 500 and 1100 mm, but precipitations are concentrated during autumn and winter months, with average peak of 93 mm in November. Conversely, the summer months are hot and dry, with average monthly minimum of 31 mm in July (Della Seta et al. 2009).

The present-day geomorphic processes in the Upper Orcia catchment are firstly controlled by water erosion and secondly by gravity (Della Seta et al. 2009). The badland landforms are characterized both by “calanchi” and by “biancane” (sensu Moretti and Rodolfi 2000) (Fig. 1b). The most evident and spectacular landforms are represented by calanchi, which are widespread on steeper slopes, and they are typically characterized by narrow to knife-edge ridges. Moreover, residuals of a typical rounded-edged badland landscape made of biancane withstand the agricultural levelling practices on some gently dipping slopes. Finally, in the badland areas, micro-piping and rilling processes extensively operate on slopes, whereas landforms similar to small pediments often develop at the foot slopes (Della Seta et al. 2007).

Calanchi are more frequent on very steep slopes, and their growth is supported by sandy, gravel, conglomeratic or volcanic caprocks at the summit. Piping is more widespread in biancane sites than in calanchi sites in the Upper Orcia valley. Ephemeral gullies develop also on cultivated or grazing land, where they represent an important sediment source.

Human activities have strongly contributed to the landscape evolution of this region through deforestation and reforestation, grazing and farming, especially cropland abandonment, etc. These land-use changes are the most important factor triggering accelerated water erosion, tillage erosion and gravitational movements on hillslopes (Calzolari et al. 1997; Torri et al. 2002; Vergari et al. 2013b). The reshaping of badlands slopes for agricultural purposes, often through heavy machinery reaching the head of calanchi areas, caused preferential deep infiltration tracks which favoured the development of landslides. The rapid destruction of their typical knife-edge ridge lines is resulting due to increased gravitational processes over time, and from here shifting the evolution of the calanchi badland morphology from type A to type B, as classified by Rodolfi and Frascati (1979). Ciccacci et al. (2008), using field monitoring and photogrammetric techniques in the study area, confirmed that over the past 50 years calanchi badlands have progressively changed from type A, with sharp edges and narrow and deep gullies, to type B (with trough-floored small valleys, separated by smaller convex ridges, affected by noticeable mass movements) and, finally, to type C, characterized by higher frequency of mass movements, which almost destroy the calanchi ridge and fill up the small valley bottoms.

The severe denudation processes that rapidly shaped the clayey slopes of the Crete Senesi area have been studied over several decades by implementing field monitoring techniques or by indirect estimations of suspended sediment yield from catchments (Ciccacci et al. 1986). Both the direct and indirect quantitative geomorphic investigations were widely applied in Central Italy (Alexander 1980; Busoni et al. 1995; Ciccacci et al. 2003; Del Monte 2003; Del Monte et al. 2002; Della Seta et al. 2007, 2009; Farabollini et al. 1992; Lupia Palmieri et al. 2001; Moretti and Rodolfi 2000; Vergari et al. 2011) and led to define the calanchi and biancane badlands as erosion “hot spots” (Della Seta et al. 2007, 2009).

Geomorphological field monitoring on badlands carried out over the last 20 years showed that mean annual values of denudation rates range between 1 and 2.5 cm year−1 (Del Monte 2003; Della Seta et al. 2007, 2009). Nonetheless, considerable space variability of ground-level changes was observed along hillslope (Fig. 2): between −1 and −8 cm year−1 at different positions on biancane slopes, between +11 (net accumulation) and −5 cm year−1 at different positions on calanchi slopes (Aucelli et al. 2014). The dominant role of different processes involved in shaping these different badlands types causes differences of in-site erosion/accumulation budget. As to the off-site effects, the estimated values of mean annual suspended sediment load for the major catchments increase exponentially with the ratio of badlands area to the whole catchments (Della Seta et al. 2009). Instant suspended load measurements at the outlet of some major catchments have testified for the pulsating connectivity of the small badlands catchment to the major streams. In particular, few extreme denudation events can deliver enough sediment in the major streams to reach the overall estimated mean annual suspended sediment load (Della Seta et al. 2007, 2009).

Fig. 2
figure 2

Summary of the mean erosion rates recorded at calanchi and biancane badlands sites during long-lasting geomorphological studies in Tyrrhenian side of Central Italy (updated from Della Seta et al. 2009). Both vertical (Δy) and horizontal (Δx) variations of ground level were recorded at different sites and positions on slopes

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3 Materials and methods

The statistical susceptibility evaluation method, described by Vergari et al. (2011) for the landslide susceptibility assessment, has been applied to the denudation landforms due to run-off, calanchi badland areas, in order to evaluate the water erosion spatial proneness of the study area. The relation between the calanchi badland areas and the distribution of the values of some potential quantitative environmental parameters was explored to achieve this goal. As illustrated in Fig. 3, the water erosion hazard assessment was obtained by combining the evaluated spatial prediction with the estimation of the water erosion rates of the unstable landforms, performed by using the “Tu denudation index” (Ciccacci et al. 1981, 1986; Della Seta et al. 2009; Vergari et al. 2014). Vector data sets in GIS environment were used to obtain vector susceptibility outputs, which are expected to be less fragmented than the raster ones and, consequently, easier to be interpreted by users. For temporal uniformity, all the input data (Digital Elevation Model, drainage network and calanchi inventory map) were derived from the topographic maps at scale 1:10,000 (1994 Regional Topographic maps) or other contemporaneous data.

Fig. 3
figure 3

Conceptual frame of the proposed method for water erosion hazard evaluation

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3.1 Input data thematic maps

Aerial photograph interpretation and field survey have allowed the assessment of the spatial distribution of water erosion processes, resulting in an inventory map of calanchi badland landforms (Fig. 4). The mapped calanchi badland area consists of slope units widely affected by gully erosion, which represent micro-basins.

Fig. 4
figure 4

Distribution of calanchi badlands areas overlaid to the drainage network map of Upper Orcia Valley

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Calanchi landforms are the most evident and spectacular ones related to gully erosion in the study area, almost exclusively developed into clayey layers, with a channel network mainly by dendritic pattern. The calanchi are often characterized by landslide escarpments at their headwater, which promote concentration of surface running water (Morgan 2005; Conforti et al. 2011). The geomorphological survey inside the badland areas from the Upper Orcia valley shows that small mass movements generate smoothed ridges within the main gullies. Moreover, along badland slopes micro-piping and rilling processes operate, whereas mud flow cones are often accumulated at the mouth of various order drainage channels.

Figure 5 shows that eight parameters have been considered to quantify the potential erosion causal factors, namely altitude (Al), amplitude of relief (AR), slope curvature (C), aspect (A), drainage density (D), lithology (L), slope gradient (S) and stream power index (SPI). A DEM with 25-m resolution was used to derive the topographic factors. The output raster layers were then aggregated in 50-m cell-sized grids to avoid the excessive fragmentation of map units and to reconstruct the average slope conditions, as the terrain conditions preceding the instability events should be considered for a well-structured susceptibility analysis.

Fig. 5
figure 5

Potential causal factors considered in the water erosion hazard evaluation in the Upper Orcia Valley: a altimetry, b amplitude of relief, c slope curvature, d aspect, e drainage density, f lithology, g slope, h stream power index

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Altimetry was taken into account to investigate the possible concentration of badland areas in particular elevation intervals (Fig. 5a). The highest altitude values are concentrated along the south-eastern divide corresponding to the horst bordering the Radicofani graben, to the east and to the strongest Quaternary uplift of the Plio–Pleistocene marine deposits, to the South.

The amplitude of relief map illustrates the maximum difference in height per unit area (1 km2) and was derived by raster calculations from the DEM in ArcGIS environment (Fig. 5b). The results are visualized using contour lines and deriving from them a polygonal vector data set, which was classified by using the natural breaks method. This parameter provides a measure of fluvial erosive action. Other conditions being equal, it was verified that the spatial distribution of this parameter can provide information about vertical displacements such as local fault activity or regional uplift (Della Seta et al. 2004). In addition, the highest AR values are clustered along the basin’s eastern divide, where the western flank of the Castelluccio–Cetona Mt. horst is bounded by fault scarps.

Slope curvature was investigated with respect to its effect on badland triggering and development (Fig. 5c). The term curvature is theoretically defined as the rate of change of slope gradient or aspect, usually in a particular direction (Wilson and Gallant 2000). The curvature of the surface is computed on a cell-by-cell basis, as fitted through that cell and its eight surrounding neighbours. Curvature is the second derivative of the surface or the slope of the slope. Positive values of curvatures define convexity, and the negative values of curvatures characterize concavity of slope curvature. Values of curvatures around zero indicate flat surfaces.

The aspect map was derived using the terrain analysis tool in GIS environment (Fig. 5d). The 50-m cell-size raster output was classified into five groups of A (flat, N, S, E, W). The horizontal areas do not have significant extent, while the other classes are all well distributed in the study area.

The drainage density map was derived by calculating the cumulative length of stream segments of the drainage network digitized from 1:10,000 topographic maps (CTR of Tuscany Region) falling within unit areas of 1 km2 (Fig. 5e). As for the amplitude of relief map, contour lines were derived and a polygonal vector data set was classified into equal intervals of D (2.5 km km−2). D is a parameter that indirectly accounts for the erodibility and permeability of outcropping rocks, the degree of tectonization, the vegetation cover, the slope gradient, and the mean annual rainfall in the drainage basin. Due to the widespread outcrop of clays amounting 73 % of the total area, more than half of the study area is characterized by high or very high D values, between 5 and 12.5 km km−2. Moreover, the heads of several catchments are affected by badlands, where run-off is absolutely dominant with respect to infiltration.

The lithological map was drawn by grouping the outcropping rocks according to their response to denudation processes (Fig. 5f). The geological setting of the area is well known, and the rock units reported in the existing geological map have been grouped into eight lithological units.

The slope map was derived from the 25-m cell-sized DTM by using the analysis tools in ArcGIS 3D Analyst (Fig. 5g). S values were grouped into six classes using the Jenks’ natural breaks method (Jenks 1967), and the raster data set was converted to a vector format. The first four classes are widespread within the study area (16–26 %), whereas classes 5 and 6 comprise mainly the most coherent lithologies crop.

The stream power index (SPI), as shown in Fig. 5h, is a measure of the erosive power of streamflow based on the assumption that discharge is proportional to the specific catchment area (As) (Moore et al. 1991). The map was carried out by applying the following formula to each cell, using Raster Calculator in ArcGIS:

$${\text{SPI}} = \ln [{\text{As}} \times \tan (S)]$$

where As is the specific catchment area in square metres and S is the slope gradient in radians. When S was >30 %, tan(S) was substituted by sin(S), as suggested by Torri and Poesen (2014). Stream power index can be used to describe the potential run-off erosion at a given point of the topographic surface. That means as the catchment area and slope gradient increase the amount of water delivered by upslope areas and the velocity of run-off increase, hence stream power index and erosion risk are higher. Thus, the SPI is one of the main factors controlling slope erosion processes, since erosive power of overland flow directly influences slope undermining and river incision by streamflow. It is also indicative of the potential energy available to entrain sediment, and therefore, the areas with high stream power indices have great potential for erosion (Bagnold 1966; Yang and Stall 1974; Moore et al. 1991; Nefeslioglu et al. 2008; Kakembo et al. 2009; Florinsky 2012).

3.2 Water erosion susceptibility assessment method

The susceptibility evaluation method, proposed by Vergari et al. (2011) for landslide susceptibility assessment, was here applied to quantify the probability of the study area to host water erosion landforms. This procedure is based on the statistical conditional analysis (Bonham-Carter et al. 1989; Carrara et al. 1995), used to quantify the multivariate relationships between environmental attributes (or instability causal factors) and past and present instability landforms occurrence. The analysis is preceded by an unbiased bivariate statistical procedure for selecting the most influential causal factors (Vergari et al. 2011).

In particular, the factor selection (Fig. 6) consists of measures of inequality distributions (Gini 1914) and computation of Lorenz curves (Lorenz 1905). The Lorenz curves are constructed after the intersection of each causal factor map with each instability landform map, in this case the calanchi landforms. Gini’s index of inequality and Lorenz curves is applied to understand the distribution of occurred hazardous events within the different classes of influencing factors: each point on the Lorenz curve represents the cumulative area affected by a given hazardous event type versus the cumulative portion of the study area characterized by a certain class of a given potential causal factor. The line of perfect inequality (dotted line in Fig. 6a) represents the situation in which all the landforms are clustered in a single factor class, whereas their homogeneous distribution in all the factor classes is represented by the line of perfect equality (the 1:1 solid line in Fig. 6a).

Fig. 6
figure 6

Factor selection procedure (modified after Vergari et al. 2011)

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The Gini coefficient (G) is graphically represented by the area between the line of perfect equality and the computed Lorenz curve, and it is expressed as the portion of the area between the line of perfect equality and the line of perfect inequality (Gini 1914). This area can be approximated with trapezoids and can be calculated using the following formula:

$$G = 1 - \sum\limits_{n = 1}^{N} {(X_{n} - X_{n - 1} )(Y_{n} + Y_{n - 1} )}$$
(1)

where n = factor class, N = total number of factor classes, X n  = cumulative portion of the study area characterized by the factor class k, with X 0 = 0, X N  = 1, Y n  = cumulative portion of instability landform area falling in the factor class k, with Y 0 = 0, Y N  = 1.

For each instability landform type analysis, a factor is selected if the corresponding G value is higher than the average of the coefficient values of all of the considered factors (Fig. 6b). In this way, independently of the absolute G values, factors with G higher than the mean value will be more discriminant than the others for the same instability process type occurrence in the study area.

The susceptibility evaluation for each instability landform type has to be preceded by a careful evaluation of the best factor classification method.

Once the causal factors are finally selected for each instability type, the conditional analysis allows obtaining a number of vUCUs map units (vector Unique Condition Units) from all of the possible selected factor combinations in the study area. Conceptually, these map units correspond to the Unique Condition Units (UCUs) proposed by Carrara et al. (1995). The susceptibility index for each vUCU, used to draw up the susceptibility map, is successively calculated using the Bayesian interpretation of probability. The importance of applying conditional probability models has been strongly emphasized in the Earth Sciences literature, especially for predicting hazardous events or mapping mineral potential (Bonham-Carter et al. 1989). Afterwards, these models have been applied by several authors for landslide susceptibility evaluation (Chung and Fabbri 1999; Irigaray Fernàndez et al. 1999; Clerici et al. 2006, 2010; Zêzere et al. 2004; Conoscenti et al. 2008b) and gully erosion susceptibility (Conoscenti et al. 2008a; Conforti et al. 2011). The Bayes rule allows the probability of future hazardous events to be predicted once the area of each vUCU affected by past events is known. The Bayes rule specifies a prior probability, which is then updated in the light of new relevant data (called “likelihood” in Bayesian theory). In the study case, this means that the simple attribution of an a priori determined probability has to be updated considering information on past events. Thus, the susceptibility index corresponds to the conditional or posterior probability P(f|vUCU), which is the probability of the occurrence of a hazardous event type, given a certain combination of selected causal factors (vUCU).

The susceptibility index (S index) for each ith vUCU can be computed more easily because it corresponds to the ratio of the instability landform area affecting vUCU i (\(Af_{{{\text{vUCU}}_{i} }}\)) to the area of vUCU i (\(A_{{{\text{vUCU}}_{i} }}\)):

$$S_{\text{index}} = \frac{{Af_{{{\text{vUCU}}_{i} }} }}{{A_{{{\text{vUCU}}_{i} }} }}$$
(2)

The S index values for each vUCU indicate the probability of the instability process type occurrence conditioned by the concomitant presence of the selected causal factor categories. S index of a vUCU may be expressed by a percentage and thus theoretically ranges between 0 and 100 %, where 100 % is the maximum probability of a hazardous event, given by the complete coverage of the vUCU by hazardous events.

3.3 Water erosion intensity estimation

In order to estimate the erosion intensity at the scale of slopes where badlands develop, an adjustment of a methodology implemented to predict catchment scale erosion rates is here proposed. Ciccacci et al. (1981, 1986) obtained empirical equations for the “Tu denudation index” by statistically correlating the values of measured suspended sediment yield at the outlets of several Italian catchments to some geomorphic and climatic parameters, such as drainage density, pluviometric regime indices, mean annual discharge and other parameters expressing the hierarchical structure of the drainage network (Fig. 7). The suspended sediment yield (Tu, t km−2year−1) seems to be the most suitable expression of erosion rate, because it is easily measured and represents approximately 50 % under arid and semi-arid climates to 90 % under humid climates of total sediment yield by rivers (Cooke and Doornkamp 1974; Lupia Palmieri 1983). The “denudation index” (Tu) showed noticeable spatial variability of estimated denudation, with the highest Tu values indicating erosion “hot spots”, represented by small sub-catchments affected by badlands developed on uplifted Plio–Pleistocene marine clays in Italy (Della Seta et al. 2009).

Fig. 7
figure 7

Italian sampled drainage basins used to carry out the “Tu denudation index” (a) and the empirical equation proposed by Ciccacci et al. (1981) (b)

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Given these encouraging results, during the last years some attempts have been made to perform more detailed zonations of the predicted denudation rates, called “Tu grid analysis” (Aucelli et al. 2010; Maerker et al. 2012; Vergari et al. 2014), in order to better zoning the negative ground-level changes on badland sites within the catchment area (cm year−1). To this end, Eqs. (3) and (4) derived by Ciccacci et al. (1981) were used, where only the density (D) of 14 Italian sampled drainage basins has been considered as the independent variable:

$$\log Tu = 0.35312D + 1.43225\quad R^{2} = 0.962\quad ({\text{with}}\;D < 6\,{\text{km km}}^{ - 2} )$$
(3)
$$\log Tu = 2.93936\log D + 1.13430\quad R^{2} = 0.950\quad ({\text{with}}\;D > 6\,{\text{km km}}^{ - 2} )$$
(4)

D parameter synthetically expresses many of the factors controlling erosion entity, namely (a) it is strongly depending on climatic conditions and terrain topography; (b) it is tied to the type and density of vegetation cover; (c) it can be partially modified in response to human activity; (d) it is a function of rock permeability and fracturing degree, synthesizing the erodibility level of the sedimentary substratum outcropping in the studied areas.

Ciccacci et al. (1981, 1986) showed how these equations succeeded in estimating the suspended sediment yield of Upper Orcia Valley measured at the Monte Amiata Hydrological Station with a 6 % error.

The Upper Orcia catchment was divided into a grid of 1 km2 cells to evaluate the Tu index for unit areas. Then, the grid was spatially shifted diagonally by √2 km to double the number of cells for Tu computation and thus the analytical detail, one value for each unit area of 0.25 km2. The D value for each cell was calculated from drainage network digitized from topographic maps at scale 1:10,000. The Tu index value (t km−2 year−1) was estimated for each cell, corresponding to the estimated sediment output from the same cell. The Tu value was then converted into the average negative ground-level change of the cell (cm year−1), assuming a mean bulk density of outcropping clays equal to 1.6 t m−3. This average value was chosen, considering that bulk density in arable land from the study area is about 1.4 t m−3 (De Alba et al. 2006), while in regolith crust of the badland areas it has been quantified at 1.8 t m−3 (Torri and Bryan 1997). The so-estimated erosion rates were assigned to the cells’ centroids to get a point cloud to be used for geostatistical interpolations, thus obtaining the estimated erosion rate map of the Upper Orcia catchment. The spline interpolation method was applied, since the interpolated surface can exceed the known value range, but must pass through all of the sample points. The smoothing effect of the interpolator was in this case applied, since the input data do not represent point values measured in the field but values over unit areas.

3.4 Validation procedure

While field erosion monitoring data collected in some of the badlands were used to validate the estimation of the erosion rates, a validation procedure based on a spatial random partition strategy was applied to test the effectiveness of the susceptibility predictive model. The method proposed by Chung and Fabbri (2003) for landslide susceptibility model validation was applied, aimed at constructing both the prediction-rate and the success-rate curves. This method requires partition of the instability landform database into a training subset and a test subset, considering the second one as the unknown future target pattern of instability events and, thus, pretending that the instability events of the test subset have not yet developed. When possible, a temporal partition of the landforms is recommended by using the air photograph mosaic of a specific year within the inventory time span. When not possible, an alternative is the one here adopted that is based on random spatial partition of the instability landforms. Once the partition of the landforms affected by water erosion is carried out, the susceptibility analysis already applied to the whole landform inventory can be shifted to the only training subset, thus obtaining the training susceptibility map. Finally, the distribution of the test subset landforms is compared with the training susceptibility map in order to construct the prediction-rate curve. Success-rate and prediction-rate curves plot the percentage of the study area in each susceptibility class against the percentage of instability landform area in the same class. While the success-rate curve is constructed considering the same inventory used to construct the susceptibility model and hence represents a measure of model fit, the prediction-rate curve is built considering independent instability landform information (i.e. by intersecting the training susceptibility map and the instability landforms of the test subset) and measures the prediction skill of the classification.

Since this study used vector layers, the curves were constructed by plotting the cumulative area of vUCUs, ordered by decreasing S index values (x-axis) and versus the cumulative area affected by instability processes within each vUCU (y-axis).

Ideally, the tangent of a prediction-rate curve should be monotonically decreasing to indicate that the most hazardous classes predict most of the “future” events, and the trend regularly decreases with the gradual reduction of the susceptibility value. However, as described by Chung and Fabbri (2003), empirical prediction-rate curves usually do not satisfy this condition. A 1:1 trend of the prediction-rate curve indicates that the prediction map is randomly generated. Thus, the further the prediction-rate curve is far from a straight line, the more the susceptibility estimation is significant. Moreover, the steeper the curve is in its first part, the greater the predictive power of the prediction map (Remondo et al. 2003).

4 Results

4.1 Erosion rates estimation in the calanchi badlands

Starting from the drainage network of the Upper Orcia Valley, digitized from 1:10,000 topographic maps (CTR, Tuscany Region), the erosion rates map was carried out through the Tu grid analysis and using Eqs. 3 and 4 (Fig. 8). The map shows that the highest erosion rates correspond to the biancane and calanchi badlands or to some areas where badlands have been remodelled for agricultural purposes.

Fig. 8
figure 8

Estimated erosion rate map of Upper Orcia Valley, performed by applying the Tu grid analysis

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The map was then validated by comparing the estimated erosion rates with those measured during the last 20 years. The graph from Fig. 2 summarizes the average ground-level changes measured in the last two decades using erosion pins and photogrammetric analysis located in different erosion landforms. The average measured erosion rate, only due to run-off, in badlands areas was 1.5–2.5 cm year−1 that corresponds to the range 240–400 t ha−1 year−1, values comparable to the estimated ones.

Taking into account the only drainage network of the areas affected by calanchi badlands, whose mean density value is 16.62 km km−2, a zonal statistics analysis allowed to calculate an average erosion rate exceeding 2 cm year−1 (320 t ha−1 year−1) in these areas. This value agrees with the magnitude order of erosion rates measured at calanchi badlands sites of Central Italy (Della Seta et al. 2009; Vergari et al. 2013a, b; Aucelli et al. 2014).

4.2 Factor selection

The most influential causal factors in determining water erosion effects have been selected by applying the factor selection procedure described in Sect. 3.2. Figure 9a shows the Lorenz curves for the considered eight potential causal factors, computed after the intersection of the badland inventory map with each of the factor maps.

Fig. 9
figure 9

Lorenz curves for the considered potential causal factors with the Gini coefficient values for each factor (a) and histogram showing the Gini coefficient values and the selected causal factors (b)

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Altimetry, drainage density, amplitude of relief and slope are the selected factors (Fig. 9b).

Drainage density is the most important causal factor in discriminating areas affected by badland erosion, as high D values identify areas where overland flow is favoured and run-off increases. Altimetry is the second most important factor, since most of calanchi areas are stretching up to 700 m a.s.l., which is the maximum elevation of clayey outcrops in the study area. At higher altitudes, other more resistant layers outcrop. This means that even if lithology was discarded, the information provided by the lithology map is still beheld in the model. As for slope and amplitude of relief, calanchi badlands are concentrated in medium slope gradient values (15–40 %) and in 100–200 m km−2 amplitude of relief interval. Higher amplitude of relief values characterizes the eastern part of the study area, where calcareous outcrops prevail.

4.3 Water erosion hazard assessment

By intersecting the selected causal factors, the water erosion hazard map was carried out (Fig. 10). The hazard values represent the conditional probability of the occurrence of calanchi badland erosion with a soil erosion rate higher than 2 cm year−1 (320 t ha−1 year−1). Hazard values were classified into nine classes of increasing hazard level. The highest hazard values are located in the western sector of the study area, where clayey outcrops are characterized by very high slope gradient. At present, most of that area is totally affected by badlands and, therefore, included in the very high hazard class. However, in this sector a wider land is very prone to water erosion, and the development of badlands is frequently restrained by the agricultural land remodelling practices.

Fig. 10
figure 10

Water erosion hazard map of Upper Orcia Valley. The probability of the study area of being affected by erosion rates higher than 2 cm year−1 (320 t ha year−1) is zoned

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4.4 Validation results

In order to validate the susceptibility map by drawing the prediction-rate and the success-rate curves, the gully areas data set has been split into two subsets using a random partition (Chung and Fabbri 2003). One subset (training set, 70 % of all water erosion landforms) has been used to obtain the training susceptibility map, and the second subset (test subset with the remaining 30 %) has been used to validate the susceptibility map. The selected environmental factors used to obtain the training susceptibility map were altimetry, drainage density, lithology and slope.

Both the success-rate and the prediction-rate curves for the Upper Orcia Valley show a high gradient in the first part and smoothly decrease monotonically (Fig. 11). The prediction curve shows that 70 % of the total badland area of the test subset falls within 30 % of the areas predicted as the most prone to badland development. This result confirms both the validity of the susceptibility method and the high spatial correlation between controlling factors used for the analysis and the instability landform distribution. Furthermore, the validation procedure results show that the predictive power of the model is generally satisfactory. Therefore, about 85 % of the instability landform area of the training subset is correctly classified falling in high and very high susceptibility classes.

Fig. 11
figure 11

Validation curves

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The estimated erosion rates, already compared with those measured during field monitoring with pins over the last 20 years in the badland areas, were further validated through their comparison with the volumetric estimation of material removed by denudation processes, carried out in a small sub-catchment of the study area in a previous study (Aucelli et al. 2014). The Landola sub-catchment, widely affected by water erosion landforms, corresponds to the area between the Radicofani and Contignano towns, where the highest susceptibility index values have been predicted. During the Landola investigations, multitemporal photogrammetric analysis was performed in order to evaluate the time and space evolution of erosion processes mainly triggered by surface run-off and landslides for about the last 60 years. The analysis allowed to calculate an average erosion rate of 1.2 cm year−1 (about 200 t ha−1 year−1) in the whole sub-catchment, but higher average values were obtained when considering only the areas affected by badlands (up to 6 cm year−1). Centimetric erosion rates were also observed by De Alba et al. (2006) on croplands, where tillage erosion is caused by uphill and downhill farming, especially mouldboard ploughing.

5 Discussion

The most important innovative aspect of this investigation refers to the proposal of the integration of soil erosion susceptibility analysis with water erosion rate estimation method. Thus, the water erosion hazard assessment is obtained that can predict the probability of the area to develop water erosion landforms characterized by a given erosion rate. The choice of the Upper Orcia Valley as test area was driven by the wide availability of multitemporal morphodynamics studies and erosion monitoring data covering decadal periods. This allowed validating estimates of the denudation intensity and, given the encouraging results, to propose the methodology for similar Mediterranean badlands where long monitoring series are not available.

It has to be underlined that the proposed estimation of erosion rates has been validated for water erosion contribution to soil losses, monitored by means of erosion pins in the studied badland areas (Ciccacci et al. 2003, 2008; Della Seta et al. 2007, 2009; Vergari et al. 2013a). Even so, higher denudation in the calanchi sites can be locally due to considerable removal of material caused by mass movements, as resulted after multitemporal digital photogrammetric analysis (Aucelli et al. 2012, 2014). Moreover, further investigations could extend the applicability of the erosion rate estimation model to other land uses than bare soils under badlands (e.g. cropland).

The obtained erosion rates confirm how these Mediterranean badlands can be considered “erosion hot spots”, as they were defined by Della Seta et al. (2007, 2009). If compared to the soil erosion rates estimated at European and Mediterranean scales by using different techniques (Grimm et al. 2003; Cerdan et al. 2010; Maetens et al. 2012), the entire study area shows considerable higher values, resulting from the very high dispersivity of the clays (Vergari et al. 2013a). In particular, for the whole Italian territory, Cerdan et al. (2010) estimate a mean erosion rate of 2.3 t ha−1 year−1, contributing to the 12.5 % of the total European erosion, even if when considering the different land-use categories bare land clearly shows the highest values of 15 t ha−1 year−1 on average. These authors underline that the Italian Apennine slopes show the highest estimated erosion rates exceeding 20 t ha−1 year−1 in the Mediterranean zone, a trend confirmed by Van Rompaey et al. (2005). Considering the study area, it is included in the European and Italian zones with the highest potential soil erosion risk identified by Grimm et al. (2003), showing an annual approximate soil losses exceeding 20–40 t ha−1 year−1. All these studies were carried out at very different spatial scales from that of this study, as they investigate very large areas and at very low spatial resolution. Moreover, their environmental contexts are very wide, as Europe and the Mediterranean include a great variability of climates, land uses, topography, outcropping lithologies and soils.

As recently underlined by García-Ruíz et al. (2015), there is a negative relationship between the erosion rate and the size of the study area involved. Thus, the results of this study can be more properly compared to areas with similar environmental conditions, such as the Mediterranean badlands. Taking into account these particular landscapes, the high denudation intensity measured and estimated in Upper Orcia Valley is not so surprising. In fact, a review of monitoring investigations, performed in different Mediterranean badland sites (France, Spain, Southern Italy) and with different techniques (erosion pins, profile metres, sediment traps, volumetric analyses, instrumented catchments), shows erosion rates ranging between 100 and 600 t ha−1 year−1, depending on the site altitude and average annual precipitation amount and seasonality, and reaching more than 1000 t ha−1 year−1 when very small badlands areas are considered (Bufalo and Nahon 1992; Brochot 1993; Martínez-Casasnovas and Poch 1998; Regüés et al. 2000a; Gallart et al. 2002; Martínez-Carreras et al. 2007; Sirvent et al. 1997; Nadal-Romero et al. 2008; Nadal-Romero and Regüés 2010; Piccarreta et al. 2012). In Mediterranean badland areas, Nadal-Romero et al. (2011, 2014) noticed that for less than 10 ha areas erosion rates are very high because of the absence of sediment storage in badlands. Instead, in the catchment larger than 10 ha the erosion rate decreases nonlinearly as the area increases because sediment is trapped in the valley bottoms and in the footslopes.

As for the erosion susceptibility analysis, the validation confirmed the efficiency of the factor selection procedure, which allowed using few causal factors without losing information on the indirect influence of the discarded ones. For example, the lithology factor was discarded, but its information is still indirectly provided by the selected causal factors, which are spatially correlated with it. Actually, clayey outcropping deposits, being barely permeable, are characterized by high values of drainage density and are concentrated in the altimetry classes up to 700 m a.s.l. More resistant layers outcropping at higher altitude favour low drainage density, high amplitude of relief and steeper slopes. Thus, the use of the lithology factor in the analysis would have resulted in the inclusion of redundant information about the badland distribution. At the same time, the aspect factor that might be used by an expert operator for its well-known influence on badland distribution was not selected. Slope aspect clearly plays a relevant role in controlling regolith moisture and its influence on weathering and erosion processes (Yair and Lavee 1985) with a greater strength from arid to semi-arid badlands, as sunny aspects show poor or null vegetation cover causing badlands typical asymmetry (Kirkby et al. 1990; Solé et al. 1997; Cantón 1999). As the annual precipitation increases, exceeding 700 mm in humid Mediterranean badlands, there is enough water to allow development of vegetation cover, which limits high erosion rates more than dryness linked to aspect (Richard and Mathys 1999; Regüés et al. 2000b; Gallart et al. 2002; Nadal-Romero et al. 2014). The factor selection procedure used in this study revealed that, differently from other badland areas, badlands are not so much concentrated on south-facing slopes. The geomorphological survey in the area showed that hillslope aspect is much more important in determining the different denudation processes acting at badland sites, resulting in the two types of calanchi morphology described by Rodolfi and Frascati (1979) and Moretti and Rodolfi (2000), namely the south-facing calanchi are more affected by rill and gully erosion, producing the type A morphology (with steep, deeply incised, sharp knife-edged ridges, and a very dense drainage pattern), while in the north-facing calanchi frequent shallow landslides coexist with water erosion, resulting in the type B morphology, characterized by gentler slopes and smooth divides with a less dense drainage system.

The obtained results confirm that the unbiased selection of controlling factors is a crucial phase for geomorphological susceptibility evaluations (Vergari et al. 2011). However, both the heuristic and the statistical choice of causal factors require previous knowledge of the main causes of geomorphological instability. That means the potential factors must be not only spatially correlated with the distribution of the target landforms but also in cause/effect relations with them. This can sometimes lead to the exclusion of variables spatially well correlated with hazardous events distribution but representing an instability process effect more than its cause. This was the reason for which the land-use map was not included in the list of the potential causal factor in this study. Farming in the Upper Orcia Valley represents the most common anthropic activity, but its distribution is strongly driven by the extension of soil erosion processes. A lot of cropland is subjected to soil erosion or results from the levelling of badland areas, and it is often limited by the most steep calanchi sites, where terrain reshaping was not possible. By considering the Corine Land Cover classification (EEA 2007), almost all the calanchi badland areas would coincide to shrubby vegetation or bare areas. Therefore, in this case this land-use class represents a water erosion effect and not a cause. As already underlined by Vergari et al. (2011), the factors that may vary in response to environmental changes or economical needs, such as land cover, should be used only if significant changes have not been observed during the time interval considered for the instability landform inventory.

The important anthropic changes that affected the Upper Orcia Valley, aimed at land reclamation, resulted in many badland areas levelling, but they were erased before 1994, the age of the input data. However, these areas maintain some of the environmental factor characteristics that favour intense water erosion processes, as they have been predicted as areas with high and very high water erosion hazard. As a matter of fact, the field survey showed that high erosion rates still persist due to gully and shallow landslide development on cropland. Thus, the performed hazard analysis outlines that badlands could rapidly develop together with their associated very high soil erosion rates, particularly when cropland is abandoned.

This is in accordance with previous studies which confirmed that cropland abandonment in this area, if not followed by efficient land management strategies, can lead to land degradation and soil loss due to a rapid enhancement of piping, gullying and shallow landslide development, up to the return to the initial badland conditions (De Alba et al. 2006; Vergari et al. 2013a, b).

6 Conclusion

The water erosion hazard assessment in the Upper Orcia Valley was carried out by combining the badland susceptibility analysis to the water erosion rate estimation, performed by means of an empirical statistical method (Tu grid analysis) aimed at the evaluation of erosion intensity. The Tu grid analysis allowed obtaining the erosion rate estimation map from which the average water erosion rate for calanchi areas was deduced. This value was integrated in the spatial prediction of the possible distribution of areas prone to calanchi badland development, performed by applying a susceptibility assessment method based on conditional statistical analysis, with the final aim of assessing the water erosion hazard. The analysis showed that more than 30 % of the study area is prone to very severe denudation processes, being included in the high and very high hazard classes, even if recently development of badlands has frequently been restrained by the agricultural practices. This result outlines how important is the application of appropriate management practices because, when cropland is turned into abandoned, the badlands could rapidly develop.

The susceptibility evaluation was preceded by a bivariate and simple to apply selection of the most important factors controlling the intensity of water erosion processes. A validation procedure was finally applied, in which a random subdivision of calanchi badlands was performed. The results confirmed the efficiency of the factor selection procedure, which allowed using few causal factors in the susceptibility analysis without losing information on the indirect influence of the discarded ones.

Moreover, the comparison of the estimated erosion rates with the results of decadal investigations on denudation processes from the study area, deployed by different monitoring methods, confirmed the validity of the proposed erosion hazard assessment method. It represents a useful tool to be applied for soil protection strategy planning in land management, even when direct erosion rate measures are not available.