important for runoff predictions. Rainfall spatially heterogeneity has been caused to create a spatial heterogeneity of sediment. Therefore, all the essential variables that indicate sediment dynamics are to be taken into consideration, especially sediment concentrations, sediment yield and transportability of soil particles (Defersha, and Melesse, 2012).1.2.3. Topography and sediment spatial heterogeneityTopography is one of the main factors controlling sediment transport at the catchment scale through spatial patterns of upslope contributing area and local slope. The microtopography can be divided to three types of terrains: plane, slope, and uneven terrain (Zhang et al. 2011). The microto¬pography in tilled loess slopes generated by human management is not only the direct result of slope erosion but also the principal factor leading to the further development of slope erosion. Based on Kirkby (2001) microtopography can be examined to be a lively place which can reflect various elements of slope erosion kinetics as well as their interaction. Furthermore, the microtopography affects the amount of surface depression storage, which is the part of the soil surface cov¬ered by water. Topography influence not only surface hydrological and hydraulic characteristics (Yang and Chu, 2013; Peñuela et al., 2015), but also many abiotic processes and biotic interactions(Burke et al., 1999; Frouz and Kindlmann, 2001) surface depression storage (Planchon and Darboux, 2002), infiltration rate (Morbidelli et al., 2015), surface runoff (Rai et al., 2010; Vermang et al., 2015) and transition and deposition of soil particles during water erosion process (Shi et al., 2012; Wang et al., 2014) and relationship between microtopology and soil erosion, hydrological processes on sloped surfaces (Abell et al. 2008; Yvonne et al. 2008; Zhao et al. 2010) .It is necessary to study the spatial heterogeneity in linking microtopography and soil erosion, hydrological processes on sloped surfaces.The evolution of spatial heterogeneity variability in the soil erosion process on a microtopography scale, has drastically hindered our under¬standing of the role that microtopography plays in the soil erosion process (Huang et al. 1992, 2001, 2003).Since slope and length of slope are the main factor in topography. Hence, it is important that these factors were studied in soil erosion and sediment process. Several studies presented that soil loss increased with increasing slope gradient (e.g. Kinnell, 2000; Assouline and Ben-Hur, 2006; Berger et al., 2010), while some studies determined that there is no correlations between soil loss and slope gradient (Chaplot and Le Bissonnais, 2003). As steep land eroded sediments reach the stream network, river capacity reduces, and flood risk increases (Morgan, 2005). Sedimentation also can reduce the capacity of reservoirs, decreasing water storage and shortening the lifespan of hydroelectric power plants (Verstraeten et al., 2003). Hence, most of soil properties display remarkable spatial variations in erosion and sediment dynamics, which may lead to spatial heterogeneity of soil detachment processes. Spatial heterogeneity stem from long-term temporal–spatial interaction between basic ecological processes and physical processes (Li and Wu, 1992). Soil properties (physical, chemical, and biological) differ in space; this difference is termed spatial heterogeneity of soil. It means that spatial pattern of slopes in different environment produce different sediment spatial heterogeneity. 1.2.4. Soil moisture and sediment spatial heterogeneitySoil resources are spatially heterogeneous at various scales (Kelly and Canham 1992; Jackson and Caldwell 1993; Maestre and Cortina 2002). Among soil resources properties, antecedent soil moisture is one of the most important soil properties which affects on soil erosion because it affects the structure and hydraulic response of the soil (Cresswell et al. 1992; Luk, 1985).As an important research subject in hydrological research, pedology and environmental studies (Lin et al., 2006), soil moisture is influenced by many environmental factors, such as rainfall, topography (Qiu et al., 2001; Kim, 2012), solar radiation (Lu et al., 2002; Western and Blöschl, 1999), soil texture (Baroni et al., 2013; Jawson and Niemann, 2007) and land use (Fu et al., 2003; Venkatesh et al, 2011). The spatial distribution of soil moisture is complex, and the factors controlling the pattern’s formation are disputable, due to the scale dependence of the spatial variability of soil moisture and the increase in soil moisture heterogeneity as scale expansion (Mark et al., 2007; Famiglietti et al., 2008). Therefore, the strong spatial heterogeneity of soil moisture is controlled by many environmental factors, including topography and land use. Further, the spatial patterns and soil hydrological processes belong to the scale of the site being investigated, which engenders a challenge for soil moisture spatially heterogeneity.Based on factors affecting on spatial heterogeneity on soil erosion and sediment, it is understand that every watershed is unique and the way every watershed has evolved in response to unique climatic and geological features and the history and initial conditions is different. And so the exact pattern and process that outcome will be different, even under similar conditions. However, the more we understand the general, the more we accept and understand the anomaly or the outlier from the mainstream (Bloschl, 2006).It can be stated that watersheds/sub watersheds affect each together under similar conditions. Therefore, understanding the effects of spatial heterogeneity on subclass watersheds is necessity to quantify interactions among factors of affecting on spatial heterogeneity on soil erosion and sediment. The key objectives of this review is to provide concepts of spatial heterogeneity, major issues facing spatial heterogeneity of soil erosion and sediment, understanding the natural complexity and its quantification.2. Methods for quantification of heterogeneityDutilleul and Legendre’s (1993) discussion of the definition and quantification of spatial heterogeneity is timely. Recently, heterogeneity has become a buzz word in the ecological studies. It is a result of a broad recognition by the ecological community that heterogeneity is a main characteristic of ecological systems and affects a wide range of theoretical and practical issues (Kolasa and Rollo 1991, Dutilleuland Legendre, 1993). The quantification of the heterogeneity is necessary to add value for better understanding of heterogeneity. Otherwise, quantification of heterogeneity without a clear notion is a danger (Li and Reynolds 1994; O’Neill, 1979). Given the many characteristics of heterogeneity that has been identified (Kolasa and Rollo 1991, Dutilleuland Legendre 1993). To overcome these serious issues, it is require that investigated the quantification of heterogeneity. However, relatively scarce attemots have been made to quantify the spatial heterogeneity of soil erosion and sediment. Thereby, (Loehle, 1988, Palmer and White, 1994) bring out operational definition of heterogeneity. The operational definition developed with other researchers (Dutilleul and Legendre (1993) and Kolasa and Rollo (1991).The operational definition described based on two components that includes system property and complexity. A system property can be anything that is of ecological interest, e.g., plant biomass, soil nutrients, temperature, rainfall and so on. Complexity alludes to qualitative or categorical descriptors of this property, while variability alludes to quantitative or numerical descriptors of the property. Fig1. A landscape example of quantification of spatial heterogeneity (Li and Reynolds, 2013)One of the operational definitions is structural heterogeneity, that is, the complexity or variability of a system property measured without reference to any functional effects (e.g., Kolasa and Rollo 1991). Therefore, functional heterogeneity is the complexity or variability of a system property that can be display to affect ecological and environmental processes, e.g., population density, discharge behavior, nesting or foraging behavior, growth rate, etc. Another one the operational definitions related to heterogeneity in function of scale. (e.g. Kolasa and Rollo, 1991, Allen and Hoekstra1992, Dutilleul and Legendre, 1993). It is including grain and extent that are the primary scaling factors that affect complexity or variability and heterogeneity. Grain is the finest resolution of data (e.g., pixel size for lattice data, minimum time step for time series data) (Turner et al. 1989; Wiens, 1989), and extent is the area or duration enclosed by a study. The desired scale (grain and extent) is dependent on the nature of the phenomenon (Kotliar and Wiens, 1990) and research objectives. According to data analysis, resealing of data, including data transformations, data reduction, data aggregation, and resampling (e.g., Allen and Hoekstra, 1992) is secondary scaling factor. Rescaling may modify grain or extent or both and, hence, plays a role in quantification of heterogeneity. Fig2.Components of scale based on grain and extent (Wiens, 1989).Quantitative heterogeneity perhaps viewed as a continuum of variability and complexity- from low to high with homogeneity being the low end (i.e. the minimum)(Wu, 2004). Thus, two basic strategies can be used to quantify heterogeneity :(1) directly, by measuring complexity and variability and (2) indirectly, by measuring departure from homogeneity. For example, heterogeneity in categorical maps can be described as complexity in number of patch types, proportion, patch shape, and contrast between neighboring patches, and different methods can be used to quantify these aspects of heterogeneity. Furthermore, heterogeneity in numerical maps can be measured as degree of departure from randomness when homogeneity is defined as the randomness of the distribution of a system property. Allen and Hoekstra (1992) and Dutilleul and Legendre (1993) imply- that quantification of spatial heterogeneity should be based upon data types. Spatial and non-spatial data types example of methods that can be used in quantifying heterogeneity (Turner et al. 1991). Each data type has its specific characteristic variability and complexity. For point pattern data (Chou, 1997), spatial heterogeneity can be measured by its variability in density and nearest neighbor distance (Cressie, 1993). For categorical maps, spatial heterogeneity can be measured by its complexity in composition and configuration of patches (Fig. 1). Composition includes the number and proportions of patch types, while configuration includes spatial arrangement of patches, patch shape, contrast between neighboring patches, connectivity among patches of the same type, and anisotropy (i.e., variation indifferent directions).For numerical maps, spatial heterogeneity can be measured by its variability in trend (the magnitude of the mean or variance and the deterministic changes of the mean in space), autocorrelation (the degree of autocorrelation, the intensity of autocorrelation, and the range of autocorrelation), and anisotropy (variation of trend and autocorrelation in different direction)(Fig. 1). Geostatistical data is a major branch of statistical analysis related to the spatial relationships among data situated in two- or three-dimensional coordinate space (Krige, 1951). It includes variogram, Correlogram, Fractal dimension, distribution and partial least squares regression (PLS regression) (Table 1). PLS regression is a statistical method that investigate a linear regression model by projecting the predicted variables and the observable variables to a new space. It is a new technique that incorporates features of principal component analysis and multiple linear regressions and generalizes these two analytical approaches (Wold et al., 2001; Abdi, 2010). The PLSR can apply highly correlated noise-corrupted data sets by explicitly assuming dependency among the variables and estimating the underlying structures, which are essentially linear combinations of the original variables (Carrascal et al., 2009). Another outstanding feature of PLSR is that it is particularly suitable for multivariate problems when the number of observations is less than the number of possible predictors (Onderka et al., 2012; Shi et al., 2013).Table1. Quantifying the spatial heterogeneity of soil erosion and sediment based on data typesData type Description Method ReferencesNon-spatial No reference to sampling Variance Gergel S. E (2005) Interquartile range (IQR) Gries T.H(2007) Spatial Directly or indirectly referenced to a surface earth location … … Point pattern The occurrence of points in a particular space Cluster Gabson, 1992; Phillips, 2007; Okweye et al., 2016 Random (Pickup and Chewings,1986; Kashyap,1981; Kashyap and Chellappa, 1983) Geostatical Regular and irregular sample variables in space Variogram (Nielsennand Wendroth,2003;Bivand et al., 2008; Pyrcz and Deutsch, 2003) Correlogram (Almeida and Journel 1994; Journel,1999; Gangyan et al,2002) Fractal dimension (Eltz and Norton, 1997; Burrough, 1983; Jiang et al., 2012; Moreno et al., 2008) Distribution (An et al., 2012; Zhao et al., 2011) Partial least squares regression(PLS) (Umetrics, 2012;Shi et al., 2014)Quantitative lattice Numerical maps Autocorrelation (Sudheer et al. 2002; Salas et al. 1980;Kumar et al. 2012) Anisotropy (Angulo-Mart´?nez et al.,2009;Zhang et al.,2014)Qualitative lattice Categorical maps Diversity indices (Casermeiro et al., 2004; Tanser and Palmer (1999); Ballayan, 2000) Patchiness index (Ziegler et al. 2007; Micheli and Peterson, 1999) Contagion index (Xiao and Ji, 2007; Lee et al., 2009)3. Recent literature review related to spatial heterogeneity erosion and sedimentSpatial heterogeneity now has a wide range of descriptions, quantitative definitions and metrics in which it is seen as part of the set of variables that describe and control ecological processes and patterns (Turner and Chapin, 2004). However, as knowledge has progressed and new methods developed, it has become manifest that heterogeneity is a multidimensional problem and that it is often more efficient to partition it into several components. Recent reviews can assistant to major advances in understanding the broader problems. This part of paper point out the recently researches about spatial heterogeneity of soil erosion and sediment dynamic.Due to factors affecting on heterogeneity in a basin system, hydrological and geomorphological processes utilizing at different scale levels are related and linked to induce the development of soil erosion across scales (Belnap et al. 2005; Boix-Fayos et al. 2006; Cammeraat 2002), although significantly varied scale dependency of controlling processes of sediment movement in the downstream direction (De Vente and Poesen 2005; Osterkamp and Toy 1997; Puigdef Bregas 2005). This result emphasized on the systematic functions of scale interactions and feedback relationships between predominating processes in spatial heterogeneity development and basin system evolution, within and across different scale levels (Boix-Fayos et al. 2006; Cammeraat 2004; Cammeraat 2002; Peters and Havstad 2006).Very little was found in the literature on the question of spatial heterogeneity of soil erosion and sediment. A number of studies have been reported about this topic follow as: Zhang et al (2015) studied on the spatial heterogeneity of surface roughness during different erosive stages of tilled loess slopes under a rainfall intensity of 1.5 mm min-1. They presented that understanding the spatial heterogeneity of surface roughness (SR) will assistant to the understanding of the developmental process of slope erosion and manifest the coupled relationship between SR and slope erosion in this area. The results showed that multifractal analysis revealed the spatial heterogeneity of SR at diverse scales or at different erosion processes better than a single fractal dimension. Other researchers has been took similar results from spatial heterogeneity of surface roughness (Kirkby, 2010; Yvonne et al., 2008; Ollesch et al., 2005).Shi et al. (2013) studied on partial least-squares regression for linking land-cover patterns to soil erosion and sediment yield in watersheds. The results about the soil erosion and sediment yield within the watershed showed that diversity indices are often correlated with the contagion indices. The diversity and contagion indices exhibit different aspects of the heterogeneity of the landscape in the study area.In other researches, Mills and Bathurst (2015) investigated the scatter plot of specific suspended sediment yield and catchment area for sub catchments within the Eden catchment, with error bars. They suggested that variability in yield between sub catchments is greater for smaller catchment areas, while, as catchment area increases, between-catchment variability is reduced. This may relate to the greater heterogeneity in rates of sediment supply and transfer found in larger catchments, which results in an ‘averaging’ effect on sediment yields. However, the apparent lack of relationship between specific suspended sediment yield and catchment area indicates that the variables that influence rates of suspended sediment input in the Eden catchment are not related to spatial scale.Zhang et al. (2016) investigated on spatial scale effect on sediment dynamics in basin-wide floods within a typical agro-watershed in the hilly loess region of the Chinese Loess Plateau. They found that the event-based suspended sediment concentration, as well as the intra- and inter-scale flow–sediment relationships remained spatially constant.Liu et al. (2014; 2015) demonstrated that ridge tillage may even speed up soil erosion because variations in field slope and microtopographic relief can produce useless erosion control. And some researches stated that ridge tillage can reduce soil and water loss (Zhang et al., 2014) .Such differences may be owing to spatial heterogeneity of microtopography in the process of water erosion. As well as, Luo et al. (2017) noted that the lower spatial heterogeneity of microtopography was not contributed to runoff collection, and runoff were scattered along the slope, which could lead to higher spatial heterogeneity of drainage networks. Unlikely, a higher spatial heterogeneity of microtopography could result in lower spatial heterogeneity of drainage networks on sloping farmland.4. ConclusionWatershed area is intrinsically heterogeneous. To develop an ecological understanding of watershed systems is vital to quantify spatial heterogeneity of the sediment dynamic. This study set out to determine general concept and quantifying of spatial heterogeneity in watershed system. The results of this review show that the study and quantifying of conceptual frameworks of spatial heterogeneity and addressing these complicated problems are indispensable. Taken together, these results suggest that additive quantifying and classification of spatial heterogeneity contribute to facilitate understanding of nature complexities. Therefore, the study has gone some way towards enhancing our understanding of spatial heterogeneity of soil erosion and sediment. Finally, a number of important limitations need to be considered. First, spatial data tend to be remarkably more heterogeneous when the size of data becomes large. Second, it is require to extending information to quantify spatial heterogeneity in soil erosion and sediment topic. Third, little review has been done related to spatial heterogeneity and it available complexity. Further investigations are needed to provide techniques, and technologies to advance our understanding the relationships between spatial heterogeneity and soil erosion and sediment. One example is modeling approaches based on factors of affection on spatial heterogeneity that have been measured and quantified the soil erosion and sediment issues. Another example is new and relevant technologies with prominent potential such as LIDAR, a remote sensing technology using laser radar with high resolution spectrophotometry that can be applied, among other things, to assess the three-dimensional structure of soil erosion and sediment.