**6.1 R factor**

10 Soil Erosion Studies

Experimental semivariograms were determined until approximately 50% of the geometric camp, since after this value the semivariogram did not seem correct (Guerra, 1988), i.e., its accuracy was reduced due to a smaller number of possible pairs to calculate the semivariance at this distance. A geometric camp of 16 degrees (geographic coordinates) with partition groups (lags) of 1 degree was considered, as these lags are the estimators of the experimental semivariograms (Deutsch & Journel, 1998). Theoretical models considered, such as spherical, exponential, Gaussian and linear, were described by Guerra (1988) and

Only this theoretical semivariogram group was considered because it usually covers the general dispersion situation of soil science spatial events (Burrough & McDonnell, 1998; Soares, 2006). Correlation coefficient of selected models were obtained through Cross Validation routine of the geostatistical software GS+, version 9. The spatial dependence index (SDI) was used according to Zimback (2001), which measures a sample's structural variance effect on total variance (sill). SDI comprises the following interpretation break: weak SDI ≤ 25%, moderate SDI between 25% and 75% and strong SDI ≥ 75%. This index is a complement of the traditional method recommended by Cambardella et al. (1994) in which the nugget weight effect (randomness) on total variance is evaluated. Through structural parameters obtained from experimental semivariograms, maps of some properties were created using GIS ArcMap v.10 (ESRI, 2010). A punctual ordinary kriging estimator was

For LS layer (computed jointly), the Digital Elevation Model for Brazilian territory was obtained from SRTM project (Shuttle Radar Topography Mission) (Farr & Kobrik, 2000), that it is in the fourth version (Jarvis et al., 2008). The LS map was generated through the

Where λ = slope length (m); θ = slope gradient (%); and m = 0.5 if the percent of slope is 5 or more, 0.4 on slopes of 3.5 to 4.5 percent, 0.3 on slopes of 1 to 3 percent, and 0.2 on uniform

The values of λ and θ were derived from DEM (ESRI, 2010). For determination of λ value we

Where: Flow Accumulation is a grid theme of flow accumulation expressed as number of grid cells (readily derived from watershed delineation processing steps) and Cell Size is the length of a cell side (m). Flow Accumulation was derived from the DEM, after conducting

Using Equation 2 and approach shown at Figure 5, the NPE layer was created. The final map was reclassified into interpretative classes. We analyzed which feature(s) influence(s) more expressively the spatial variability of the values of NPE along the study area. Hence, we interpreted the map considering the possibilities of aggravation of erosive process by

Fill and Flow Direction processes in ArcGIS 10 (Theobald, 2007; ESRI, 2010).

LS = (λ/22.1)m \* (0.065 + 0.045 θ + 0.0065 θ2) (4)

λ = (Flow Accumulation \* Cell Size) (5)

Andriotti (2003).

used for geostatistic interpolation.

gradients of less than 1 percent.

**5.4 NPE map** 

algorithm available in Wischmeier and Smith (1978):

used the method proposed by Moore & Burch (1986).

present land use patterns which can be changed.

**5.3 Topographic factor** 

The annual rainfall erosivity ranges from 3,116 to 20,035 MJ mm ha-1 h-1 year-1 (Silva, 2004). The region with the lowest values is represented by the northeastern region and an occurrence in southeastern region. Highest values are found in the northern region, mostly in the Amazon region (Figure 6). Predominant class was "> 12,000 MJ mm ha-1 h-1 y-1" with 37.0% of occurrence (Table 2).

Spatial distribution of the rainfall amount and erosivity are irregular (Figures 4 and 6). In some regions the annual erosivity normally is incipient and others are extremely high (almost ten times more erosive than the areas with lowest erosivity). Maps elaborated by Rao et al. (1996) and showed in Figure 7 confirm this information. Such maps show that the trimester with major or minor contribution over seasonal distribution of amount of rain along Brazilian territory is also changeable.

Fig. 6. Annual erosivity map (MJ mm ha-1 h-1 y-1). Source: Silva (2004) – reclassified.


Table 2. Percentage of occurrence of each class of the R factor along Brazilian territory.

Natural Potential for Erosion for Brazilian Territory 13

Erodibility classes % null 6.0 weak 18.0 moderate 23.0 strong 20.0 very strong 33.0

The soil data were well fitted to an exponential theoretical model (Figure 9). They showed moderate SDI and the quality of cross-validation were considered normal for soil attributes

According to database provided by Cooper et al. (2005), Brazilian soils are predominantly loam. It seems that soils with higher erodibility are related with high sand percentage than low clay percentage. The soils with high percentages of clay are concentrated mainly in southeastern and southern Brazilian regions. The second biggest stain of clay soils occurs on "Brazilian highlands" (see Figure 10 – left). On the other hand, soils with high percentages of silt are concentrated mainly in northern Brazilian region. Sandy soils occur mainly on the

The estimated average values of erodibility of major groups of Brazilian soils are presented in Table 4. The Nitisols, Ferralsols and Histosols had the lowest average erodibility across their areas of occurrence, considered low erodibility. On the other hand, Regosols, Podzols,

Table 3. Percentage of occurrence of each class of the K factor.

central region (nor in the northern or the southern region).

Fig. 8. Soil erodibility classes.

(Vieira, 2000; Vieira et al., 2002).

Fig. 7. Percentage contribution of trimester to the annual rainfall amount (A – December, January, February) (B - March, April, May) (C – June, July, August) (D – September, October, November). Source: Rao et al. (1996). For more details, see Rao et al. (1996).

#### **6.2 K factor and semivariograms of soil texture**

Most of the Brazilian soils are highly erodibles, independently of climate and relief. This is supported by data of Figure 8 and Table 3. Classes with high erodibility (strong and very strong) occupy 53% of Brazilian territory. Soils classified as "very strong" occur mainly along northeastern and center-western Brazilian regions. For two states of the southern region (Paraná, Santa Catarina), the predominant occurrence is soils with low erodibility (green stain located in lower portion of the map).

Fig. 7. Percentage contribution of trimester to the annual rainfall amount (A – December, January, February) (B - March, April, May) (C – June, July, August) (D – September, October, November). Source: Rao et al. (1996). For more details, see Rao et al. (1996).

Most of the Brazilian soils are highly erodibles, independently of climate and relief. This is supported by data of Figure 8 and Table 3. Classes with high erodibility (strong and very strong) occupy 53% of Brazilian territory. Soils classified as "very strong" occur mainly along northeastern and center-western Brazilian regions. For two states of the southern region (Paraná, Santa Catarina), the predominant occurrence is soils with low erodibility

**6.2 K factor and semivariograms of soil texture** 

(green stain located in lower portion of the map).

Fig. 8. Soil erodibility classes.


Table 3. Percentage of occurrence of each class of the K factor.

The soil data were well fitted to an exponential theoretical model (Figure 9). They showed moderate SDI and the quality of cross-validation were considered normal for soil attributes (Vieira, 2000; Vieira et al., 2002).

According to database provided by Cooper et al. (2005), Brazilian soils are predominantly loam. It seems that soils with higher erodibility are related with high sand percentage than low clay percentage. The soils with high percentages of clay are concentrated mainly in southeastern and southern Brazilian regions. The second biggest stain of clay soils occurs on "Brazilian highlands" (see Figure 10 – left). On the other hand, soils with high percentages of silt are concentrated mainly in northern Brazilian region. Sandy soils occur mainly on the central region (nor in the northern or the southern region).

The estimated average values of erodibility of major groups of Brazilian soils are presented in Table 4. The Nitisols, Ferralsols and Histosols had the lowest average erodibility across their areas of occurrence, considered low erodibility. On the other hand, Regosols, Podzols,

Natural Potential for Erosion for Brazilian Territory 15

Fig. 9. Omnidirectional experimental semivariograms (sand, silt and clay) and maps of

amount of sand (b), silt (d) and clay (f).


Planosols, Arenosols, Luvisols, are the highest average soil erodibility. According to Table 1 they are interpreted as soils of high erodibility. These results are similar to those obtained by Silva & Alvares (2005), in State of Sao Paulo and Lino (2010), in State of Rio Grande do Sul.

1 Brazilian System of Soil Classification (EMBRAPA, 2006); 2 World reference base for soil resources (FAO, 1998); 3 Soil taxonomy (Soil Survey Staff, 1999).

Table 4. Computed K values for Brazilian soils in different classifications systems

## **6.3 DEM and topographic factor**

More than a half of Brazilian territory presented LS factor values lower than 1 (Table 5). Class "< 1", that occurs in 53.6% (Figure 10), was especially separated because locals presenting LS < 1 mathematically represent diminution of the rates of soil loss and a possible opportunity for sediment deposition. For cells with LS values = 1 there is no influence of the topography over soil loss, at least mathematically. For locals where the LS > 1 topography accelerates the erosion process.

Planosols, Arenosols, Luvisols, are the highest average soil erodibility. According to Table 1 they are interpreted as soils of high erodibility. These results are similar to those obtained by Silva & Alvares (2005), in State of Sao Paulo and Lino (2010), in State of Rio Grande do Sul.

Embrapa1 FAO2 Soil Survey Staff3 K (t h MJ-1 mm-1)

Argissolos Acrisols Ultisols 0.0374

Cambissolos Cambisols Inceptisols 0.0353

Chernossolos Chernozems Molisols 0.0287

Espodossolos Podzols Spodosols 0.0736

Gleissolos Gleysols Entisols 0.0344

Latossolos Ferrasols Oxisols 0.0246

Luvissolos Luvisols Aridisols 0.0478

Neossolos Flúvicos Fluvisols Fluvents 0.0450

Neossolos Litólicos Leptosols Lithic 0.0351

Neossolos Quartzarênicos Arenosols Quartzipsamments 0.0534

Neossolos Regolítcos Regosols Psamments 0.0791

Nitossolos Nitisols Oxisols Kandic 0.0132

Organossolos Histosols Histosols 0.0197

Planossolos Planosols Alfisols 0.0650

Plintossolos Plinthosols Plintic 0.0429

Vertissolos Vertisols Vertisols 0.0374 1 Brazilian System of Soil Classification (EMBRAPA, 2006); 2 World reference base for soil resources

More than a half of Brazilian territory presented LS factor values lower than 1 (Table 5). Class "< 1", that occurs in 53.6% (Figure 10), was especially separated because locals presenting LS < 1 mathematically represent diminution of the rates of soil loss and a possible opportunity for sediment deposition. For cells with LS values = 1 there is no influence of the topography over soil loss, at least mathematically. For locals where the LS >

Table 4. Computed K values for Brazilian soils in different classifications systems

(FAO, 1998); 3 Soil taxonomy (Soil Survey Staff, 1999).

1 topography accelerates the erosion process.

**6.3 DEM and topographic factor** 

Fig. 9. Omnidirectional experimental semivariograms (sand, silt and clay) and maps of amount of sand (b), silt (d) and clay (f).

urban.

where the land use is more intensive.

Fig. 11. NPE map for Brazilian territory.

Natural Potential for Erosion for Brazilian Territory 17

influence of relief (LS factors) in eastern portion. This information takes an important role on the establishment of land use politics in order to promote a sustainable land use, as rural or

The pressure of population, among other factors, is leading to increased cultivation of tropical steeplands, generally defined as land with slope exceeding 20% (Presbitero et al., 2005). Brazil is a typical case of this problem, especially for southeastern Brazilian region,

In rural context, many crops have been cultivated in hilly areas and favoring the erosion process. Coffee, orchards (orange) and sugar-cane sometimes cultivated in steep lands in São Paulo State are examples. On the other hand, areas currently used for grain production, especially soy—located in western region of the *gaucho* countryside, Mato Grosso do Sul and Mato Grosso, and the Central Plateau from Goias to Tocantins, generally correspond to those areas with a high potential for sediment production (Castro & Queiroz Neto, 2010). However, Brazil has adopted over the last two decades the use no-tillage in agriculture, mainly soybeans and corn (Lino, 2010). In forestry, the sector employs mainly the technique of "minimum cultivation", which provides the least impact on soil (Gonçalves et al., 2000). In urban context, in metropolitan regions like São Paulo, Rio de Janeiro, Belo Horizonte and Recife, there are a significant number of people living in sloped areas, characterizing risk areas. Catastrophic mass movements recorded in Brazil are concentrated in the southeastern (São Paulo, Rio de Janeiro, Minas Gerais, and Espirito Santo states) and southern (Rio Grande do Sul, Santa Catarina, and Paraná states) regions of the country. They are predominantly related to the occurrence of rainfall, that is of great intensity and short duration, and sometimes

happen after rainy periods of long duration (Coelho-Netto et al., 2010).

Fig. 10. Left: Digital elevation map for Brazilian territory (m). Right: map of LS factor values (dimensionless).


Table 5. Percentage of occurrence of each class of the LS factor.

DEM presented in Figure 10 suggests that higher LS values are associated with high altimetric values. Such high LS values are more concentrated along mountainous regions (see Figure 3 – relief). Along Brazilian territory occur predominantly regions with low altimetry, due: (a) antique lithology, (b) no occurrence of modern geological folding, and (c) due to be situated in the core area of a tectonic plate called South America Plate (IBGE, n.d.). Some of hilly or scarped regions are located near the shoreline and in regions with high population concentration, as cities of Santos and Rio de Janeiro. The three classes that represent most severe topographic condition occur in 9.3%.

## **6.4 NPE map**

The integration of the three factors early described (R, K and LS) outcomes the NPE map, shown in Figure 11. Possibly due to relief influences, the predominant class was "< 200 t.ha-1.y-1", with 61%. Surprisingly, the second major class was "> 1600 t.ha-1.y-1", with 14% (Table 6). Besides of the occurrence of soils highly erodibles along Brazilian territory, the geographical distribution of high values of NPE has two notable distinct influences. The first one is an evident influence of very high erosivity values (R factor). The second one is major

Fig. 10. Left: Digital elevation map for Brazilian territory (m). Right: map of LS factor values

LS intervals % < 1 53.6 1 13.5 1-10 23.6 10-50 7.8 50-100 1.1 > 100 0.4

DEM presented in Figure 10 suggests that higher LS values are associated with high altimetric values. Such high LS values are more concentrated along mountainous regions (see Figure 3 – relief). Along Brazilian territory occur predominantly regions with low altimetry, due: (a) antique lithology, (b) no occurrence of modern geological folding, and (c) due to be situated in the core area of a tectonic plate called South America Plate (IBGE, n.d.). Some of hilly or scarped regions are located near the shoreline and in regions with high population concentration, as cities of Santos and Rio de Janeiro. The three classes that

The integration of the three factors early described (R, K and LS) outcomes the NPE map, shown in Figure 11. Possibly due to relief influences, the predominant class was "< 200 t.ha-1.y-1", with 61%. Surprisingly, the second major class was "> 1600 t.ha-1.y-1", with 14% (Table 6). Besides of the occurrence of soils highly erodibles along Brazilian territory, the geographical distribution of high values of NPE has two notable distinct influences. The first one is an evident influence of very high erosivity values (R factor). The second one is major

Table 5. Percentage of occurrence of each class of the LS factor.

represent most severe topographic condition occur in 9.3%.

(dimensionless).

**6.4 NPE map** 

influence of relief (LS factors) in eastern portion. This information takes an important role on the establishment of land use politics in order to promote a sustainable land use, as rural or urban.

The pressure of population, among other factors, is leading to increased cultivation of tropical steeplands, generally defined as land with slope exceeding 20% (Presbitero et al., 2005). Brazil is a typical case of this problem, especially for southeastern Brazilian region, where the land use is more intensive.

In rural context, many crops have been cultivated in hilly areas and favoring the erosion process. Coffee, orchards (orange) and sugar-cane sometimes cultivated in steep lands in São Paulo State are examples. On the other hand, areas currently used for grain production, especially soy—located in western region of the *gaucho* countryside, Mato Grosso do Sul and Mato Grosso, and the Central Plateau from Goias to Tocantins, generally correspond to those areas with a high potential for sediment production (Castro & Queiroz Neto, 2010). However, Brazil has adopted over the last two decades the use no-tillage in agriculture, mainly soybeans and corn (Lino, 2010). In forestry, the sector employs mainly the technique of "minimum cultivation", which provides the least impact on soil (Gonçalves et al., 2000).

In urban context, in metropolitan regions like São Paulo, Rio de Janeiro, Belo Horizonte and Recife, there are a significant number of people living in sloped areas, characterizing risk areas. Catastrophic mass movements recorded in Brazil are concentrated in the southeastern (São Paulo, Rio de Janeiro, Minas Gerais, and Espirito Santo states) and southern (Rio Grande do Sul, Santa Catarina, and Paraná states) regions of the country. They are predominantly related to the occurrence of rainfall, that is of great intensity and short duration, and sometimes happen after rainy periods of long duration (Coelho-Netto et al., 2010).

Fig. 11. NPE map for Brazilian territory.

Natural Potential for Erosion for Brazilian Territory 19

Decline of biodiversity

ation

ification

Morphometric changes

Channel changes

Channel density changes

changes Morphometric

*rphology Water Vegetation* 

Morphometric changes

Channel

Channel density changes

changes

changes Infestation

Decline of biodiversity

> Biomass changes

Forest fragmentation

*Human interference Natural process* 

*Agriculture Urban Mining Industrial Soil / Rock Geomo-*

Air, soil and water pollution

Erosion rate Acid rain Cement-

changes Deforestation Desert-

load Flooding

Air, soil and water pollution

changes Deforestation Runoff

Channel density changes

Geomorphologic changes

Mass movement

> Relief changes

├──────── Climatic change ───────┤

Table 7. Main types of land degradation found in Brazil.

Air, water and soil pollution

Soil compactation

Water balance

Decrease in biomass, carbon and biodiversity

> Desertification

> > Silting

Deforestation

Air, soil and water pollution

> Soil compactation

Erosion rate Erosion rate Runoff

Salinization Flooding Sediment

Deforestation

load

Channel density changes

Morphometric changes

├───Land cover change ───┤

Source: Zuquette et al. (2004) - modified.

Crusting Runoff

Leaching Sediment


Table 6. Percentage of occurrence of each class of the NPE.

Table 7 shows a summary of the main types of land degradation found in Brazil (Zuquete et al., 2004). Many of them are strictly related to erosion process, alter the hydrologic balance, and present some (hydro)geomorphologic consequences according to kind of human interference. Associating the human interferences (consequences according to activity), the NPE map, and the population density map (Figure 12), it is possible perceive that the zone of 300 km from shoreline to west is probably the most "problematic" region of Brazilian territory, because there is high concentration with high NPE values and simultaneously high population density, with many kinds of interferences.

Today, more than 20% of the total dissolved and suspended mass delivered to the oceans comes from the Himalaya and the Andes, carried by three rivers: the Brahmaputra, Ganges and Amazon (Goddéris, 2010). As early informed, some areas surrounding the Amazon basin has high potential for sediment production (Castro & Queiroz Neto, 2010), as well as the hilly areas located on southeastern Brazilian region (Figure 13).

Fig. 12. Cartogram of Brazilian population density. Source: IBGE (n.d.).

NPE % < 200 61.0 200-400 8.0 400-800 9.0 800-1600 8.0 > 1600 14.0

Table 7 shows a summary of the main types of land degradation found in Brazil (Zuquete et al., 2004). Many of them are strictly related to erosion process, alter the hydrologic balance, and present some (hydro)geomorphologic consequences according to kind of human interference. Associating the human interferences (consequences according to activity), the NPE map, and the population density map (Figure 12), it is possible perceive that the zone of 300 km from shoreline to west is probably the most "problematic" region of Brazilian territory, because there is high concentration with high NPE values and simultaneously high

Today, more than 20% of the total dissolved and suspended mass delivered to the oceans comes from the Himalaya and the Andes, carried by three rivers: the Brahmaputra, Ganges and Amazon (Goddéris, 2010). As early informed, some areas surrounding the Amazon basin has high potential for sediment production (Castro & Queiroz Neto, 2010), as well as

Table 6. Percentage of occurrence of each class of the NPE.

population density, with many kinds of interferences.

the hilly areas located on southeastern Brazilian region (Figure 13).

Fig. 12. Cartogram of Brazilian population density. Source: IBGE (n.d.).


Source: Zuquette et al. (2004) - modified.

Table 7. Main types of land degradation found in Brazil.

NPE.

The NPE is a tool that helps achieving this aim.

Leopoldo, RS, Brazil.

*Catena*, Vol.79, pp. 49–59.

pp. 1501-1511.

Vol.21, pp. 419 – 426.

York: Oxford University Press, 333 p.

Processes. Elsevier, Vol 13, 510 pages.

Earth Surface Processes. Elsevier, vol 13, 510 pages.

**8. Acknowledgments** 

**9. References** 

Natural Potential for Erosion for Brazilian Territory 21

However, the study in such broad scale here presented permitted we found the major influences over the NPE values according to region of the Brazilian territory. Also, comparing the NPE map with population density, with specific sediment yield and with complementary bibliographic data, we identified major socio-environmental risk areas of

The great challenge is establish regional and local land use politics conformable with the average rate of soil formation. There are hundreds of cultivars that can be cultivated along the Brazilian territory according to local edaphoclimatic conditions. But they should be managed (both the cultivar and the soil) in order to reduce the soil loss to acceptable rates.

Andriotti, J. L. S. (2003). *Fundamentos de Estatística e Geoestatística*. Editora UNISINOS, São

Bai, Z. G.; Dent, D. L.; Olsonn, M. E. (2008). Proxy global assessment of land degradation.

Beskow, S.; Mello, C. R.; Norton, L. D.; Curi, N.; Viola, M. R.; Avanzi, J. C. (2009). Soil

Boardman, J.; Shepheard, .M. L.; Walter, E.; Foster, I. D. L. (2009). Soil erosion and risk-

Burrough, P. A.; Mcdonnell, R. A. (1998). *Principles of Geographical Information Systems.* New

Cambardella, C. A.; Moorman, T. B.; Parkin, T. B.; Karlen, D. L. (1994). Field-scale variability

Castro, A. G.; Valério Filho, M. (1997). Simulação da expectativa de perdas de solo em

Castro, S. S.; Queiroz Neto, J. P. (2010). Soil Erosion in Brazil from Coffee to the Present-day

Coelho-Netto, A. L.; Avelar, A. S.; Lacerda, W. A. (2010). Landslides and Disasters in

Sussex, UK. *Journal of Environmental Management*, Vol.90, pp. 2578-2588. Bouyoucos, G. J. (1935). The clay ratio as a criterion of susceptibility of soils to erosion.

*Journal of the American Society of Agronomy,* Vol.27, pp. 738-741.

erosion prediction in the Grande River Basin, Brazil using distributed modeling.

assessment for on- and off-farm impacts: A test case using the Midhurst area, West

of soil properties in central Iowa soils. *Soil Science Society of America Journal,* Vol.58,

microbacia sob diferentes manejos florestais. *Revista Brasileira de Ciência do Solo*,

Soy Bean Production, Pages 195 – 221. *In*: Latrubesse, E. M. *Natural Hazards and Human-Exacerbated Disasters in Latin America*. Developments in Earth Surface

Southeastern and Southern Brazil. Chapter 12, pages 223 – 243. *In*: Latrubesse, E. M. *Natural Hazards and Human-Exacerbated Disasters in Latin America*. Developments in

To Fapesp and Pró-reitoria de Pós-Graduação - Unesp, for financial support.

*Soil Use and Management*, Vol.24, pp. 223 – 234.

Fig. 13. Map of sediment yield in Brazil. Source: Castro & Queiroz Neto (2010). Legend modified from t.km-2.y-1 to t.ha-1.y-1.

If we adopt the soil density value 1,200 kg m-3. and average rate of soil formation -0.0002 m y-1 (Sparovek & Schnug, 2001), we infer the maximum tolerable soil loss is 2.4 t.ha-1.y-1. Using equation 6 (Valerio Filho, 1994) it is possible estimating the recommended CP value(s) that is in accordance with sustainable principles of soil conservation, i.e., the annual soil loss rate is smaller or equivalent to average rate of soil formation.

$$\text{Tolerable CP} = \text{tolerance soil loss} \;/\text{NPE value} \tag{6}$$
