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Gully erosion prediction across a large region: Murray-Darling Basin, Australia.


Gully erosion is a significant land degradation process and a source of increased sediment load to rivers (Wasson et al. 1998). Sand and fine gravel eroded from gullies can impact downstream ecosystems by creating sediment slugs that smother bed habitat and reduce the diversity of bedforms (Bartley and Rutherfurd 2005). Suspended sediments and attached nutrients eroded from gullies increase turbidity and nutrient loads of streams (Lemly 1982; Galloway et al. 1996). Erosion from stream and gully banks can generate up to 90% of the total sediment yield in Australian catchments (Olley et al. 1993; Prosser and Winchester 1996; Wallbrink et al. 1998; Wasson et al. 1998) and in parts of other continents (Simon 1989; Poesen et al. 1996).

Large regional catchments usually contain a diversity of environments that lead to strong spatial patterns in erosion processes. Some soil types, land uses, climates, and terrains are susceptible to gully erosion while others are not. Obtaining information on the extent and patterns of gully erosion can therefore allow us to assess its significance in the context of other erosion processes, and help to define catchment sediment budgets (e.g. NLWRA 2001; McKergow et al. 2005). An appreciation of the extent and location of gully erosion would assist national or regional planning to target erosion control and catchment restoration. Lu et al. (2004) demonstrated the significant cost savings that can be gained from effective targeting of erosion control. Indeed, one of the main reasons for undertaking the current study was to provide complete coverage of gully erosion across the Murray--Darling Basin as an input into spatial modelling of a catchment sediment budget (DeRose et al. 2004). The budgets aimed to identify the dominant sources of sediment and relate those to downstream sediment loads.

The length or density (length per unit area) of gullies is probably the most important single factor in assessing the significance of gullies as a sediment source. This is because, between landscapes, gully density varies more than other gully dimensions, and once gullies are established, sidewalls dominate head-cuts as sediment sources (Blong et al. 1982) so sediment yield should increase as the density of gullies increases. Gully length is also relatively easily measured by examination of remotely sensed data such as aerial photographs and satellite images (Bocco et al. 1990; Betts and DeRose 1999). At a regional or continental scale, such techniques alone are not practical because of the time taken to measure all gullies across such large areas, so an interpolation technique or spatial modelling needs to be considered. To determine the significance of gully erosion within the Murray Darling Basin, which has an area of >1 x [10.sup.6] [km.sup.2], the current study has predicted gully density via the generation of numeric rule-based statistical models using sample measurements of gully density and related environmental variables.

Much previous gully erosion research has focussed on the processes leading to their formation (Bocco 1991), rates of erosion (Vandekerckhove et al. 2001), or historical accounts of gully formation (Prosser and Winchester 1996; Wasson et al. 1998). There are also many examples in the literature where researchers have developed models of gully initiation and erosion processes (e.g. Sidorchuk 1999; Nachtergaele et al. 2001).

Several previous studies have used multivariate statistical techniques to model the spatial patterns of gullies, at relatively limited scales, in various part of the world. Meyer and Martinez-Casasnovas (1999) used statistical analysis to conclude that topographic factors (slope steepness and hillslope concavity) and land management factors were the main factors explaining the distribution of gullies in two ~25-[km.sup.2] catchments in north-east Spain. Kheir et al. (2007) used a regression-tree approach to predict gully location in a 675-[km.sup.2] area in Lebanon and found that slope and upslope contributing area were important predictors of gully distribution. One of the largest scale applications of gully spatial extent modelling was performed by Gutierrez et al. (2009), who used multivariate regression splines to determine that lithology and soil type best explained the location of gullies for a large area (>40 x [10.sup.3] [km.sup.2]) in south-west Spain. These previous spatial modelling studies, together with other gully erosion research (Table 1), provide us with information on what factors might be important when attempting to predict gully extent at a large scale.

The statistical relationships from these studies are applicable only to the range of the conditions considered, and new relationships need to be developed for different environments or scales of analysis. For example, at the regional or continental scale, climate and land use intensity are dominant factors, whereas at the local scale, factors such as soil type and land use practice are more important. When statistical knowledge of the patterns of erosion is obtained from an increasingly large number of situations, general patterns may emerge which will result in greater predictive ability for new situations. Eventually, these statistical relationships may be explained by physical reasoning provided by better understanding of gully erosion processes. This in turn will provide greater predictive ability and confidence that the statistical relationships are representing cause and effect. Conversely, the statistical relationships will give confidence that physical processes studied at small scales are indeed relevant for broader circumstances. At present though, we are still building our knowledge of the patterns of gully erosion. This paper, for example, is the first attempt to describe the patterns of gully erosion at the large scale in Australia, and to our knowledge predicts gully erosion across a more diverse range of environments than previous studies.

This study uses a multivariate statistical model to predict the density of erosional gullies across the Murray--Darling Basin in south-eastern Australia. The principle aims of this paper are to (i) assess the significance of gully erosion as a sediment source in the Murray Darling Basin; and (ii) identify the Factors that contribute to gully erosion in the Murray Darling Basin.

Study area

The Murray--Darling Basin, at ~1 x [10.sup.6] [km.sup.2], makes up 14% of the area of Australia (Fig. 1). It includes small alpine plateaus and the steep to moderate relief of the Great Dividing Range. The Basin is, however, dominated by the lowland relief of the Murray--Murrumbidgee Riverine plain, the Darling floodplain, and alluvial floodplains of other tributaries (Fig. 2a). There is a broad transition of decreasing relief from the ranges to the plains. The climatic conditions vary from the subtropics of south Queensland to the more temperate and Mediterranean climates of Victoria and South Australia. Much of the western Basin is either semi-arid or arid. Mean annual rainfall varies from <200mm in the western plains to >2400mm in the Australian Alps (Fig. 2b). Rainfall and runoff are highly variable at both the inter-annual and inter-decadal scales. The inter-annual variability of runoff in the basin is almost twice that of comparable catchments in other parts of the world (Potter et al. 2008).

Land use in the Basin is diverse, with primary production activities such as cattle and sheep grazing, horticulture, forestry, grain crops, and vineyards dominating. The Murray--Darling Basin generates ~39% of the Australian national income derived from agriculture and grazing (MDBC 2011). Consequently, it is an economically important area and degradation of land resources has the potential to affect not only the ecological health of the Basin but also the health of the regional economy.


The multivariate statistical modelling of gully density was based upon aerial photograph mapping of gullies over two parts of the Basin. First, 227 x [10.sup.3] [km.sup.2] of the New South Wales (NSW) part of the Basin was mapped in 1998 by the then NSW Department of Land and Water Conservation (DLWC, now known as the NSW Office of Environment and Heritage). All visible gullies were mapped within the area, using stereo interpretation of aerial photographs that were typically of 1:40 000 scale. Second, a gully map of 34 x [10.sup.3] [km.sup.2] of Victoria was produced by L.E. Milton and others in the 1970s and 1980s, also by stereo interpretation of a complete coverage of aerial photographs (Ford et al. 1993). Both datasets were in vector format with gullies represented by single lines. Figure 3a shows the areas covered by these two data sources within the Murray--Darling Basin.

A third source of gully erosion mapping was available for the whole of NSW, from the 1988 New South Wales Land Degradation Survey (Graham 1989). This survey measured gully length from aerial photographs in a 1-[km.sup.2] sample circle on a regular grid of 10-km spacing in western NSW and 5-km spacing in eastern NSW. Coverage across the whole of NSW gave the advantage of including the semi-arid, western parts of the Basin that are not included in the other two datasets. We found that it was not possible to construct accurate statistical models of gully density from these data, because of the very small sample window. Even in heavily gullied areas, many of the samples recorded no erosion simply because they happened to fall between gullies in ridge and spur localities. This created a lot of noise in the data and meant that coherent patterns of gully density only emerged at a very coarse resolution of 40 km when many of the data points were combined. What this dataset did show, however, was that there were very few gullies in the western part of the Basin; therefore, the lack of mapping there was not of consequence. This was, in fact, why the government agencies did not extend their surveys into those areas.

Although the datasets used are several decades old, the data are still of value as the expansion of the gully network into previously unchannelled parts of the landscape occurred rapidly after the initial land disturbance and had largely stabilised by around the mid-20th Century (Eyles 1977; Prosser and Winchester 1996). Despite the gully network being largely complete, these gullies continue to contribute fine sediment and degrade water quality, mainly through sidewall erosion.

From the two sets of mapping, gully density sample sets were generated by averaging the measured gully data over a grid. For each individual grid cell, the entire length of gullies was measured (in km) and then divided by the total area (in [km.sup.2]) of the grid cell. This gave a gully density measured as length of gully per unit area (km [km.sup.-2]). This averaging procedure was performed at grid cell resolutions of 5 km (Fig. 3b) and 10 km (Fig. 3c), equivalent to 25 [km.sup.2] and 100 [km.sup.2].

To estimate gully density for the rest of the Murray--Darling Basin and to examine how well the mapped data could be modelled by environmental factors, statistical models were constructed using the data mining software package Cubist (RuleQuest Research Pty Ltd, Sydney; We used Cubist because of its ability to rapidly process large datasets with many contributing variables. It has been successfully applied in several studies of similar scale and complexity (Gallant 2001; Lu et al. 2003b; Henderson et al. 2005). Simple linear regression is unlikely to be successful for such an application due to the complex nature and number of variables used in this study. Cubist's ability to process both continuous and categorical datasets was also an important factor in the selection of this software package.

Cubist constructs models that are expressed as a series of rules where each rule has an associated multivariate linear model. When a situation satisfies a rule's conditions, the associated model is used to predict a value; hence, Cubist models are similar to piecewise linear regression models except overlap of the rules is permitted (RuleQuest Research Pty Ltd, Sydney;; hence, a Cubist model is similar to a piecewise linear regression model except the rules are able to overlap. The performance of Cubist models is determined by assessing the summary statistics generated by each model run. The summary statistics include correlation coefficient and the relative error. The correlation coefficient is a measure of the agreement between the actual values of the target attribute and those values predicted by the model. The relative error is the ratio of the average error magnitude to the error magnitude that would result from predicting the mean. If there is limited improvement on the mean, the variables used have little predictive ability and the relative error will be near one. A perfectly predicting model will have a relative error of zero. Model performance was determined by subtracting the relative error from the correlation coefficient, with higher differences indicating better performing models. For a more detailed description of the statistical background to the Cubist software see Henderson et al. (2005).

Models generated using Cubist estimated gully density for the Murray--Darling Basin in terms of known gully densities (from measured data) and environmental attributes available for the whole of the Murray--Darling Basin. Cubist is also able to use an independent set of samples to test model accuracy, and report both summary statistics and the predictions for each validation point. In constructing gully density models, 70% of the measured gully data were randomly selected and were used for model building (training data), while the remaining 30% were used for model validation (test data). However, to maximise the use of a limited dataset, when the strongest model was identified it was refitted using all the data with the same model options.

The resulting sample set was made up of 12 428 data points for the 5-km resolution data and 3395 data points for the 10-km resolution data. Each point had a measured gully density value and a corresponding averaged value for each predictive environmental variable at that location. Fourteen environmental variables that were available for the entire basin were tested to construct the gully density models (Table 2). In order to construct simple, robust models, the categorical data were aggregated into fewer classes; the geology data was aggregated to eight classes based on lithology and age, while land use was aggregated into four classes: forest, grazing, cropping, and other land uses.

For categorical variables, a 'grid cell majority' technique was employed to determine the dominant class for each known gully density grid cell. For example, in the case of land use, the averaged gully density grid was overlayed upon the land-use grid and the dominant land-use class that was represented within each individual cell was selected as the land-use class to represent the entire cell. For continuous value variables, such as mean annual precipitation, the arithmetic mean was calculated for each grid cell.

To determine which of the above variables were important for the prediction of gully density, combinations of variables were tested. Examining all combinations of variables was prohibitively time-consuming, so a stepwise approach was used. For the first step, each variable was used independently and the best variable identified using statistical diagnostics from Cubist outputs (correlation and relative error). This one variable was then used with each other variable, and the best second variable identified. This process was repeated until all variables were included. Final selection of the model was based on statistical diagnostics and visual comparisons of predicted and measured gully density maps.

Results and discussion

Decision-tree modelling of gully density

The best models in terms of summary statistics for the 5-km and 10-km resolution model runs are shown in Table 3. The training and test data statistical diagnostics indicate that reasonable models were constructed for both for the 5-km and 10-km data. The 10-km resolution data, however, consistently produced the best results in terms of coherent spatial patterns, and this resolution was used to construct the final gully density model. Figure 4 shows the plot of observed v. predicted gully densities for the 10-km resolution model. The model showed some tendency to over-predict at lower densities and underpredict at higher densities. Approximately 65% of the predictions for data <0.2 km [km.sup.-2] were over-predicted, while >60% of the predictions for data >0.2 km [km.sup.-2] were underpredicted. However, the model performs reasonably well, with a correlation coefficient of 0.78 ([R.sup.2] = 61) and a relative error of 0.53. Indeed, our results compare favourably with the only other study known to have made predictions of erosion processes over an equally large and diverse area (see Lu et al. 2003b). In their prediction of surface-wash erosion across the entire Australian continent, Lu et al. (2003b) obtained an [R.sup.2] of 0.64 in a regression between modelled soil erosion rates and 83 measurements from Australian soil erosion studies.

Although there was very little statistical difference between the 5-km and 10-km resolution model, the 10-km data consistently produced more spatially coherent models than the 5-km resolution data. We attribute this to the additional spatial complexity of the 5-km data and the resulting failure of Cubist to resolve this complexity given the relatively coarse-scale predictive data used. Furthermore, there is an apparent arbitrariness to gully erosion at the fine scale. Depending upon local conditions and the precise timing of land-use change and intense storms (Prosser and Soufi 1998), some valleys may erode while others may not in an otherwise apparently uniform landscape. Therefore, while the 10-km resolution data are of coarser spatial resolution, the benefits of a more robust predictive model are considered to outweigh the limitations of the larger grid size.

Significance of predictive variables

The Cubist model used to construct the final gully density map used 12 predictive variables and contained 16 rules. Slope was the strongest predictive variable (r = 0.43), followed by mean annual rainfall (r=0.36). The order in which variables were selected in the decision tree model was: slope, annual temperature range, moisture index seasonality, mean annual ground cover, temperature seasonality, lowest period moisture index, solum thickness, hillslope length, mean annual rainfall, B-horizon soil texture, coldest period minimum temperature, geology.

The correlation coefficient did not improve much after the addition of ~10 predictive variables. However, when compared with the original gully mapping, the spatial pattern produced by using 12 variables was superior to that of the models using fewer variables.

Producing a model using 12 predictive variables and 16 different rules presents problems in terms of interpreting the significance of the predictive variables. Cubist has several functions that control the number of rules that are generated and therefore it enables simpler models to be constructed; however, these are at the cost of model accuracy. The first function specifies the minimum proportion of the training cases that must be covered by a rule, while the second caps the number of rules generated. These functions were tested and it was determined that the best balance between model accuracy and model complexity was achieved by setting a 3% minimum of training cases for rule generation and no limit on the number of rules.

In general, the results are indicative of the difficulty in modelling a natural process with high short-range variability. The statistical diagnostics generated by the Cubist model indicate that, while the distribution of gullies can be explained to a certain degree, there is still a considerable amount of error in the predicted models. Table 4 shows five of the 16 rules used to generate the gully density model. These rules, which accounted for 74% of the training data used to construct the final model, illustrate the significance of slope in particular as a predictor of gully density. Various climatic variables, including mean annual rainfall, temperature seasonality, and mean annual temperature range also appear to be important factors. Temperature seasonality and mean annual temperature range are closely correlated ([r.sup.2] = 0.89), with the higher values of each being generally associated with the inland semi-arid to arid areas while the lower values occur along the eastern and southern basin boundary. Given that there is likely to be some correlation with mean annual rainfall, it is difficult to determine the importance of these factors. However, it appears that these variables may be acting as surrogates of historical variations in groundcover, because as temperature seasonality and mean annual temperature range values increase, the probability of highly temporally variable groundcover increases.

The significance of slope and mean annual rainfall is clear when the model training data are examined. Figure 5 presents plots of the 10 x 10 km averaged gully density measurements v. slope and mean annual rainfall. Figure 5a shows that gully densities increase from around 0[degrees] slope to a peak of highest density at ~1.5-2.0[degrees] slope, with densities tapering away as slope increases. These are average slopes over the sample cell, not the slope of locations in which gullies have formed. Very flat areas generally have insufficient flow energy for a gully to form, and observations within the Basin suggest that very steep areas do not have gullies because they retain the natural vegetation cover or contain insufficient colluvial material for a gully to form. Areas of intermediate slope store considerable amounts of colluvium, which are prone to erosion when the vegetation cover is disturbed (Prosser and Abernethy 1996). This interpretation of the training data is supported by the rules in Table 4; the lower gully densities are predicted by the rules (rules 1 and 2) that encompass the lower slopes (<0.49[degrees]), while the higher gully densities are predicted by the rules (rules 7 and 15) that include hillslope gradients >0.49[degrees]. This result compares favourably with the study of Meyer and Martinez-Casasnovas (1999), which found using multivariate analytical statistics, that slope was the most significant factor in predicting erosion. Garg and Harrison (1992) and Radoane et al. (1995) also identified slope as an important controlling factor on the distribution of gullies.

A similar pattern is apparent with mean annual rainfall (Fig. 5b), with the higher gully densities being concentrated between 400 and 800 mm [year.sup.-1]. Again, this pattern is supported by the rules in Table 4 which show that gully densities generally decrease at >~850 mm [year.sup.-1] (rule 3) while the higher gully densities are explained in part by mean annual rainfall <~830 mm [year.sup.-1] (rule 15). Mean annual rainfall appears to be an important factor; however, due to correlation with slope ([r.sup.2] = 0.56), determining whether mean annual rainfall is actually more or less significant than slope is not possible with the methods used in this study. It is likely that both factors contribute to varying degrees depending on the location in the Basin. For example, due to the variable groundcover and hence increased susceptibility to disturbance, semi-arid (400-800 mm [year.sup.-1]), low to moderately sloping areas are likely to have higher gully densities. However, the arid areas within the Basin, which also are potentially susceptible to erosion due to low groundcover, are less like to experience gully erosion due to the dominance of very flat terrain in these areas.

The predictive variables also have limitations inasmuch as the data are either derived from coarse-scale sources or are themselves the result of previous interpolations. For example, the hillslope length variable was derived from a Cubist-based interpolation study of the relationship in terrain properties between the coarse-resolution 9s (~250m) digital elevation model (DEM) that covered the whole study area, and 25 m resolution data that covered some of the area (Gallant 2001). Furthermore, categorical variables such as land use and geology did not rank highly, which may also indicate some problem in the way categorical data are treated during the data preparation phase, either through the majority rule used to produce a single value, or through combining of different classes to a smaller number of classes where it was hoped that like were combined with like.

The spatial pattern of gully erosion across the Murray-Darling Basin

The predicted gully density for the entire Murray--Darling Basin is shown in Fig. 3d. Our model predicts gully densities of 0-1.2 km [km.sup.-2], with 22% of the Basin having a density >0.1 km [km.sup.-2] and 3% of the Basin a density >0.5 km [km.sup.-2]. Comparing the predicted gully density with the observed data in Fig. 3c indicates the same general pattern of gully density over the area of observed data. Although the model is able to reproduce a similar pattern to the measured data, it is apparent that the predicted gully density map is more generalised than the observed data in Fig. 3c, with the measured densities showing some degree of variability from one cell to the next. This smoothing is a result of the relatively simple rules that went into constructing the model. While the rules are able to reproduce the general pattern, they cannot resolve the complexity displayed in the measured data that may be due to specific local conditions.

The highest gully densities in the Basin occur on the eastern rim amid the moderately sloping, western slopes of the Great Dividing Range. Much of this area was subject to European settlement and land-use change in the late 19th Century that triggered extensive gully development (Eyles 1977; Prosser and Winchester 1996). These gullies continue to contribute fine sediment and degrade water quality, although gully expansion is largely complete (Eyles 1977). Furthermore, sediment that has been eroded from gullies since European settlement is still present in many rivers and continues to impact upon fiver ecosystems (Bartley and Rutherfurd 2005). This area also consists of large areas of erodible soils on sloping land in a climate that leads to periods of low ground cover.

Another area of moderate to high gully density is in the southern part of the Basin. This area was also subjected to early European settlement and intensive land uses, particularly gold mining in the 1850s. This human impact, in conjunction with physiographic factors such as slope and climate, produced a zone of particularly high gully density.

The other area of moderate to high gully density is in the south-west of the Basin around the Mount Lofty Ranges, South Australia. This area is similar in terrain, land use, and climate to the areas of high gully erosion density in the south-eastern parts of the Basin. This area of moderate to high gully density was predicted in the absence of any gully measurements from this region. This prediction is consistent with what is known about gully extent in this region (Wilkinson et al. 2005; Forward 2007).

There is little gully erosion predicted over the central and north-western parts of the Basin. Much of this region is far from areas of measured gully erosion, but we have confidence in the predictions because they compare favourably with the 1988 reconnaissance-scale survey of land degradation in New South Wales (Graham 1989), which showed very little gully erosion where rainfall and slope were both low. There is no gully erosion mapping for the northern part of the basin within the state of Queensland but much of that region has similar environmental conditions to northern and western New South Wales. It is therefore considered that the modelling is not being used to make long extrapolations, giving some confidence in the results.

The significance of gully erosion as a sediment source in the Murray--Darling Basin

Gully density in itself provides an indication of how severe the gully erosion is at a particular location; however, it does not provide any quantitative information on the amount of sediment produced by a gully and therefore the potential impact on downstream waterways. To make some assessment of the amount and rate of sediment produced by a gully, we require information on its dimensions and age. The measured gully data used in this study do not include any reliable data on the depth and width of the gullies within the Basin. To obtain an estimate of the amount of sediment produced by gullies within the Murray--Darling Basin, we can assign average dimensions to the gullies. Previous limited research suggests that the average cross-sectional area of gullies in south-eastern Australia is 10-23 [m.sup.2] (Prosser and Winchester 1996; Rustomji 2006). Given these dimensions, and assuming a soil bulk density of 1.5 kg [m.sup.-3], a 1-[km.sup.2] area with a gully density of 1 km [km.sup.-2] would produce between 15 x [10.sup.3] and 35 x [10.sup.3] t of sediment. If that material was eroded over an average gully age of 100 years (the approximate number of years since land cleating in many parts of the Basin), the mean annual rate of erosion would be 1.5-3.5 t [ha.sup.-1] [year.sup.1].

Overall, the average predicted gully density for the Murray Darling Basin is 0.08 km [km.sup.-2]. From this density, we calculate that there are ~85 x [10.sup.3] km of gullies in the Basin, which on average have generated in the order of 13-27 x [10.sup.6] t of sediment per year over the last 100 years. This approximation assumes that the time-averaged sediment yield from gullies is a reasonable approximation of the current sediment yield. Several studies (Eyles 1977; Prosser and Winchester 1996; Wasson et al. 1998) in the upper Murrumbidgee River catchment (near Canberra) have found that the gullies there were formed between 1850 and 1900, soon after settlement of the region, following clearing of forests and degradation of valley-floor vegetation. Subsoil sediment, presumably from gully and riverbank erosion, is the dominant type of sediment carried by the Murrumbidgee River (Wallbrink et al. 1998). The gullies have expanded little since the 1940s, suggesting that sediment yield might be declining. However, it should also be noted that the vast bulk of sediment yielded from gullies is derived from the sidewalls rather than the gully head (Blong et al. 1982; Radoane et al. 1995), so that stability of gully extent since the 1940s does not necessarily imply a reduction in sediment yield. Thus, a steady-state prediction of erosion is reasonable in the absence of detailed knowledge of erosion history.

The significance of gully erosion in fiver sediment budgets is apparent when gully sediment yield is compared with similar Murray--Darling Basin-wide assessments of the yields from riverbank and sheetwash and rill erosion. Sheetwash and rill erosion contributes an estimated 14 x [10.sup.6] t [year.sup.-1] (Lu et al. 2003a) and fiver bank erosion is estimated to yield 8.6 x [10.sup.6] t [year.sup.-1] (Hughes and Prosser 2003). Therefore, gullies may contribute more than these two other sources combined. Gullies are, in many cases, connected directly to streams and rivers, so most of eroded sediment will be delivered directly to the river network. Furthermore, gullies supply a large amount of the coarse sediment that is transported by rivers. In rivers where the sediment transport capacity is limited, this accelerated delivery of sand- and gravel-sized sediment has smothered fiver habitats (Prosser et al. 2001; Bartley and Rutherfurd 2005). Indeed in extreme cases, such as parts of the southern Murray--Darling Basin, river beds can become flat sheets of dry sand during low flow conditions that can persist for decades (Bartley and Rutherfurd 2005).

It is important to note that gully erosion, like other forms of erosion, is a natural process, but before European settlement gullies formed for only 100 years or so every few thousand years, and only in a few valleys at any time (Prosser and Winchester 1996). The current extent of erosion along valleys is also considerably longer than occurred before European settlement. The current extensive and relatively synchronous erosion of many valleys represents the effects of increased runoff and disturbance of valley floors and is unprecedented over at least the last 15 000 years.

We believe that we have made good use of the available data in assessing the pattern of gully erosion and sediment yield across the Murray Darling Basin, but improvements could be made in future. Smaller scale process studies on the limits of gully erosion have shown value from comparing the erosive power of concentrated runoff with the resistance to erosion provided by soil and vegetation cover (Montgomery and Dietrich 1988; Prosser and Abernethy 1996). High resolution DEMs, soil property mapping, runoff predictions, and remote sensing of vegetation cover could be used to explore statistical models that have a closer physical interpretation. This will only be possible where higher quality input data are available. Gully sediment yield prediction could be improved by developing empirical relationships that can be used to better predict or map patterns in gully erosion. These could focus on predicting gully dimensions, the connection of gullies to streams, their age, and the characteristics of the material in the gully walls that influence their form and the type of sediment yielded.


This paper has illustrated that multivariate modelling can be successfully used to predict gully density at the regional or subcontinental scale. Our results indicate that there are several factors that contribute to the spatial extent of gully erosion, although hillslope gradient and mean annual rainfall appear to be the most important. The resultant model indicates that the density of gullies is highest on the eastern tim of the Basin in the moderately sloping area immediately west of the Great Dividing Range. Other areas of high gully density include northern Victoria and the Mount Lofty Ranges of South Australia. The lowest gully densities are found in the western plains area of the Basin, where densities are either zero or close to zero. The mean gully density across the Basin is 0.08 km [km.sup.-2], and depending on what is used as a representative cross-sectional area, gullies contribute up to 27 x [10.sup.6] t of sediment per year. This is more than the amount that has been estimated from the combined contribution of hillslope and riverbank erosion by other studies within the Basin.

Complex natural processes, such as gully erosion, exhibit a large degree of variability in their spatial and temporal extent. As a result, producing accurate modelling results can be difficult to achieve. Limitations in the source data used in this study also need to be considered when assessing the results. Despite these limitations, the resultant gully density map illustrates the broad spatial patterns of gully erosion and demonstrates that gullies are a significant source of sediment within the Murray--Darling Basin. The results are of use in regional planning for erosion control and fiver restoration and in assessment of the extent of catchment degradation. In areas of specific interest to catchment managers, more intensive mapping of gully extent and evaluation of current sediment yields and impacts is warranted. 10.1071/SR12025


This research was carried out as part of the Murray--Darling Basin Commission Project D10012. The New South Wales gully density data were supplied by the former New South Wales Department of Infrastructure, Planning and Natural Resources. Thanks to Hua Lu and John Gallant for assistance on the efficient application of the Cubist decision tree software and Paul Rustomji, Scott Wilkinson, Lucy McKergow, and two anonymous reviewers for comments that improved the manuscript.

Received 10 February 2012, accepted 7 May 2012, published online 3 July 2012


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Andrew O. Hughes (A,B,C) and Ian P. Prosser A

(A) CSIRO Land and Water, GPO Box 1666, Canberra, ACT 2601, Australia.

(B) Current address: National Institute of Water and Atmospheric Research, PO Box 11115, Hamilton, New Zealand.

(C) Corresponding author. Email:

Table 1. Factors that have been identified by previous
studies as significant in the formation of gullies
gdf, Gully development factors; gha, gully-head advancement

Reference                      Location      Scale
                                                     Slope    Basin
de AP Bacellar et al. (2005)   Brazil        gdf       x
Bocco et al. (1990)            Mexico        gdf
Kheir et al. (2007)            Lebanon       gdf       x        x
De Oliveira (1990)             Brazil        gdf       x
Facial et al. (1999)           Sudan         gdf
Gutierrez et al. (2009)        Spain         gdf
Meyer and Martinez-            Spain         gdf       x
Casasnovas (1999)
Oostwoud Wijdenes              Kenya         gha                x
and Bryan (2001)
Parkner et al. (2006)          New Zealand   gdf                x
Prosser and Soufi (1998)       Australia     gdf
Samani et al. (2010)           Iran          gha                x
Seginer (1966)                 Israel        gha                x
Thompson (1964)                U.S.A.        gha       x        x
Vandekerckhove et              Spain         gha       x        x
al. (2001)
Vazquez-Selem and              Mexico        gdf       x
Zinek (1994)

Reference                              Significant factors
                               Land    Lithology    Soil   Hillslope
                                use                          shape
de AP Bacellar et al. (2005)     x     x
Bocco et al. (1990)              x     x
Kheir et al. (2007)
De Oliveira (1990)                     x                       x
Facial et al. (1999)             x
Gutierrez et al. (2009)                x             x
Meyer and Martinez-              x                   x         x
Casasnovas (1999)
Oostwoud Wijdenes
and Bryan (2001)
Parkner et al. (2006)            x
Prosser and Soufi (1998)         x
Samani et al. (2010)
Seginer (1966)                                       x
Thompson (1964)                                      x
Vandekerckhove et
al. (2001)
Vazquez-Selem and                x     x             x         x
Zinek (1994)


de AP Bacellar et al. (2005)
Bocco et al. (1990)
Kheir et al. (2007)
De Oliveira (1990)
Facial et al. (1999)
Gutierrez et al. (2009)
Meyer and Martinez-
Casasnovas (1999)
Oostwoud Wijdenes
and Bryan (2001)
Parkner et al. (2006)             x
Prosser and Soufi (1998)
Samani et al. (2010)              x
Seginer (1966)
Thompson (1964)                   x
Vandekerckhove et
al. (2001)
Vazquez-Selem and
Zinek (1994)

Table 2. Environmental variables tested in the construction of the
gully density model

Environmental variable             Source

Geology                            Australian National Resources
Solum thickness                    Data Library (
Median soil texture (13-horizon)   au/anrdl/php/anrdlSearch. htm1)
Median soil texture (A-horizon)
Temperature seasonality
Minimum temperature
(coldest period)
Mean annual temperature range
Mean annual precipitation
Lowest period moisture index
Moisture index seasonality
Land use
Hillslope gradient

Hillslope length                   Derived from scaling rules of
                                   finer scale topography applied
                                   to a 9" DEM (Gallant 2001)
Groundcover                        Derived from advanced very
                                   high resolution radiometer
                                   (AVHRR) remote sensing
                                   (Lu et al. 2003c).

Table 3. Training and test data summary statistics for the two tested
gully density model resolutions

Prediction                   Training data
             No. of          Correlation       Relative
             sample points   coefficient (r)   error

5 km         8700            0.73              0.55
10 km        2377            0.81              0.50

Prediction                   Test data
             No. of          Correlation       Relative
             sample points   coefficient (r)   error

5 km         3728            0.71              0.59
10 km        1018            0.78              0.53

Table 4. The five most inclusive rules (accounting for 2515 of the
3395 training cases) used to generate the gully density model GD,
gully density (km [km.sup.-2]); slope, Hillslope gradient (degrees);
clim4, temperature seasonality (coefficient of variation); climb,
minimum temperature (coldest period) ([degrees]C); clim7, mean annual
temperature range ([degrees]C); clim12, mean annual precipitation (mm
[year.sup.-1]); clim30, lowest period moisture index; clim31, moisture
index seasonality; btext50, median b-horizon soil texture; solumthick,
solum thickness (m); annualgc, annual ground cover (%)

Rule number and statistics            Rule

Rule l. 816 cases, mean GD 0.038,     If slope [less than or equal to]
  GD range 0-0.67, est. error 0.038   0.4909 and clim4 >1.8282 then

Rule 2. 648 cases, mean GD 0.047,     If slope >0.1900 and slope [less
  GD range 0-0.67, est. error 0.052   than or equal to] 0.4909 and
                                      clim4 >1.8282 then GD=
                                      1.754+0.634 * slope * -0.00043
                                      clim7 -5.9e-005 * clim31 -
                                      0.00051 * climb -0.0056 * clim30
                                      + 0.0032 * annualgc -0.0003 *

Rule 3. 291 cases, mean GD 0.058,     If clim12 >848.54 then GD=0.038
  GD range 0-0.78, est. error 0.065   + 0.00015 * climb

Rule 7. 481 cases, mean GD 0.152,     If slope >0.4909 and slope [less
  GD range 0 0.21, est. error 0.119   than or equal to] 1.017 and
                                      clim7 >27.923 then GD = 1.839
                                      0.0086 * clim4 -3.9e-006 *
                                      clim12 -0.00047 * climb + 0.0044
                                      * annualgc -2.5e-005 * clim31 +
                                      0.0001 * clim7

Rule 15. 279 cases, mean GD 0.471,    If slope >0.4909 and clim7
  GD range 0-1.54, est. error 0.225   >27.798 and clim12 [less than or
                                      equal to] 833.33 and btext50 =
                                      (sands) or (clay loams) or
                                      (clay) and geology = (Mesozoic
                                      felsic volcanics) or (Mesozoic
                                      felsic to mafic volcanics) then
                                      GD = 2.36 -0.00168 * clim6 +
                                      0.00085 * clim7 + 0.00069 *
                                      solumthick -0.0007 * clim4 + 5e-
                                      007 * clim12 -0.0009 * clim30 +
                                      0.0005 * annualgc
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Author:Hughes, Andrew O.; Prosser, Ian P.
Publication:Soil Research
Article Type:Report
Geographic Code:8AUST
Date:Jul 1, 2012
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