Journal of Geophysical Research: Earth Surface

Spatial uncertainty of 137Cs-derived net (1950s–1990) soil redistribution for Australia

Authors


Abstract

[1] The caesium-137 (137Cs) technique has been used successfully in many parts of the world to estimate net (ca. 30–50 years) soil redistribution by wind and water erosion and tillage activities. The point-based technique has hitherto been confined largely to individual fields and hillslopes, particularly in Australia. Its application here to the Australian continent (≈5 km grid) was achieved using geostatistics and nationally coordinated measurements (early 1990s) from ≈200 locations at the ≈1 km scale. A map of the 137Cs reference inventory for Australia has been previously established. Sequential indicator co-simulation of the 137Cs inventory and the Australian Soil Classification was used to estimate net (between mid-1950s and early 1990s) soil redistribution using the Australian Empirical Model. This geostatistical approach showed that nearly five times more soil was lost from cultivated land (−4.29 to +0.17 t ha−1 yr−1) than from uncultivated (−0.91 to +0.05 t ha−1 yr−1) land in Australia. This information on spatial uncertainty is essential for regional soil management to assess the risk to soil conservation. Soil erosion exceeding a tolerable threshold value (e.g., 0.5 t ha−1 yr−1) occurred over 16% of Australia, mainly in cultivated regions (median = −1.26 t ha−1 yr−1). Soil erosion estimates are neglected in carbon balances for greenhouse gas abatement and carbon accounting models. Reliable quantitative data on the recent extent and rates of soil erosion are needed to underpin the selection of effective soil conservation measures, to inform carbon balances and to understand regional soil function for sustainable agricultural systems.

 

1. Introduction

[2] There is an urgent need for quantitative data on the extent and rates of soil erosion worldwide to provide a comprehensive assessment of its magnitude, to underpin effective soil conservation [Zapata, 2003] and evaluate the implications for carbon sequestration [Quine and Van Oost, 2007; Van Oost et al., 2007]. The quantification of soil redistribution is complicated and often simplified to maps of the susceptibility to erosion (erodibility or erosivity). However, such risk maps have their own problems and may be misleading for policy or management because processes may not be adequately taken into account. Soil erosion is often insidious, requiring the removal of considerable quantities before loss is noticeable. Soil erosion measurement and monitoring approaches, particularly in semi-arid environments, require sufficiently long and expensive campaigns to provide representative and reliable estimates. Even then the extrapolation of results from often small experimental plots across large areas is notoriously unreliable. One of the main causes for this extrapolation problem is that estimates are always constrained by their spatial scale of measurement. The history of difficulties in measuring and monitoring soil erosion in space and time are likely responsible for its common neglect in carbon balances for greenhouse gas abatement and carbon storage and in understanding soil function across landscapes and agricultural systems.

[3] The caesium-137 (137Cs) technique for estimating soil redistribution overcomes some of these problems by providing retrospective information on medium-term (30–40 years) erosion/deposition rates without the need for long-term monitoring programs. It has been used successfully in many parts of the world to estimate net soil redistribution by the combined effect of wind, water and more recently by tillage erosion [Walling and Quine, 1993]. The use of the 137Cs technique is well established, although some limitations exist with dilution of unlabelled soil 137Cs, preferential removal of 137Cs-rich material by wind, the difficulty of establishing reference levels particularly in wind eroded environments [Chappell, 1999] and some uncertainties in cultivated situations [Bremer et al., 1995]. There are many examples of the application of the 137Cs technique to fields and small catchments in Australia [McCallan et al., 1980; Longmore et al., 1983; McFarlane et al., 1992; Loughran et al., 1989, 1990, 1993; Harper and Gilkes, 1994; Gillieson et al., 1996; Krause et al., 2003; Loughran and Balog, 2006; Hancock et al., 2008; Simms et al., 2008; Martinez et al., 2009]. The 137Cs technique is commonly based on establishing the local amount of 137Cs deposited with rainfall from atmospheric weapons testing, mainly during the 1960s [Ritchie and McHenry, 1990]. This local reference 137Cs inventory is often obtained from a site that has been undisturbed by erosion or deposition. Net soil redistribution is based on the relationship between the amount of 137Cs at the reference site and the amounts at selected sample locations. The 137Cs loss/gain, relative to the reference inventory, is used to establish a relationship with soil erosion/deposition, respectively. A range of calibration approaches may be used [Walling and Quine, 1990; Sutherland and de Jong, 1990; Walling and He, 2001; Walling et al., 2002]. In Australia empirical calibration relations between 137Cs loss/gain and soil erosion have been established from long-term experimental plots [Elliott et al., 1990].

[4] In 1990 a national reconnaissance survey of soil erosion in Australia was performed using the 137Cs technique. The survey was based on the 137Cs-slope model developed by Loughran and colleagues [e.g., Loughran et al., 1993] and the sampling was undertaken along single transects down complete slopes at paired sites in the same locality with typical land management practices within selected agricultural-economic regions. A similar approach to sampling 137Cs has been adopted elsewhere in the world and, when not taken over hillslopes, samples are confined often to single agricultural fields [cf. Walling and Quine, 1991; Sutherland and de Jong, 1990; Loughran et al., 1993]. These sampling approaches assume that many samples are required to represent adequately the highly variable patterns of soil redistribution by wind, water and tillage. Samples are usually taken from the nodes of a regular grid, because little is known about the spatial scale of variation in soil redistribution processes [Chappell et al., 2003]. Sampling grids are usually coarse, because the measurement of 137Cs is time-consuming, but if the grid spacing is too large, the samples may not represent the true variation, and could provide a biased estimate. Use of a fine grid, on the other hand, is prohibitively expensive and might create considerable redundancy [Chappell and Warren, 2003]. Consequently, the full potential for using point measurements of 137Cs to represent soil redistribution across scales of variation in the landscape has not been realized by most studies. It is worthwhile emphasizing that any outcome is always scale-dependent and the information content of soil redistribution maps is constrained by the sampling resolution.

[5] In recent years, several workers have recognized the difficulty in obtaining sufficient samples of 137Cs to represent the spatial variation in soil redistribution processes, particularly over areas larger than an individual field [de Roo, 1991; Chappell, 1998]. Maps of soil redistribution have been achieved using unbalanced sampling strategies [Webster and Oliver, 1990] such as stratified-nested-grid sampling designs in combination with geostatistics [Chappell et al., 1998]. These approaches differ from those traditional soil 137Cs studies, by sampling to develop a reliable description of the variability in soil 137Cs over space (variogram). That variogram is used to provide the weight of influence for surrounding values when making estimates at unsampled locations. Chappell et al. [1998] and Chappell [1999] have used this approach to show that the sampling design must represent the variability in the spatial scales of soil redistribution processes to provide an unbiased estimate of erosion and deposition. Chappell [1998] demonstrated how remote sensing data could be combined with 137Cs samples to improve the precision and accuracy of the estimates. Of particular interest to the current study, Chappell and Warren [2003] provided the largest map of 137Cs-derived net soil redistribution (approx. 20 km2) within and between fields, farms and across a region of eastern England using only 180 samples. Despite sufficient samples located to represent the variability in the property of interest, there remains uncertainty in the estimates made at unsampled locations. It is essential that the spatial uncertainty is reported to provide appropriate confidence in the map. Chappell and Agnew [2008] used geostatistics to estimate mean annual rainfall and its uncertainty at unsampled locations across the (1.5 million km2) West African Sahel with approximately 150 samples. Conventional estimates (inverse distance-squared interpolation) were shown to represent an extreme realization of the spatial uncertainty which was misleading for the temporal trend.

[6] The aim here is to combine geostatistics with approximately 200 samples of 137Cs and its reference inventory from the national reconnaissance survey of Australia to provide a preliminary baseline map across Australia (≈7.6 million km2) of net (1950s–1990) soil redistribution and its uncertainty. The baseline map contains information at the regional (e.g., >1 km) scale and consequently should benefit regional soil management and soil conservation decision-making. Multiple realizations or equally likely maps will form the baseline and identify areas across Australia that underwent net soil loss and gain. Furthermore, net soil redistribution across Australia will be classified according to land use for a preliminary assessment of land management. The assessment of spatial uncertainty will also identify those areas in Australia where additional 137Cs samples would make the greatest difference to the reliability of the outcomes. To place these estimates in to context a comparison is made between the 137Cs-derived net soil redistribution map and other national assessments of wind and water erosion.

[7] To achieve this aim the baseline 137Cs reference inventory is required and was recently completed [Chappell et al., 2011]. The objectives to achieve the aim are to: (1) compute multiple realizations of the 137Cs inventory associated with soil redistribution; (2) calculate the 137Cs loss or gain and the combined uncertainty, relative to the 137Cs reference inventory by sampling, without replacement, the realizations; (3) estimate the soil redistribution rates using the regression models between 137Cs and soil redistribution and its uncertainty by performing a bootstrap (re-sampling with replacement) of the regression models; (4) calculate soil redistribution for Australia as a whole and separated between land-use patterns in 1992/93; (5) compare the national 137Cs-derived soil redistribution rates with (a) the national assessment of soil erosion [National Land and Water Resources Audit, 2002] based on the predictions of mean annual (gross) sheetwash or hillslope and rill erosion [Lu et al., 2001, 2003] and (b) the current national monitoring method for wind erosion based on the Dust Storm Index (DSI) [McTainsh et al., 2001].

2. Data

2.1. National Reconnaissance Survey of Fallout and Soil 137Cs

[8] In 1990 a national reconnaissance survey of soil erosion in Australia was performed using the 137Cs technique. Details of that survey can be found in the State and Territory reports, summarized by Chappell et al. [2011] and described by Loughran et al. [2004]. The sites used in the national survey represent an irregular spacing, which has the potential to represent soil redistribution across multiple scales of variation [Chappell et al., 2011, Figure 2]. The large scale is considered using the variability across the continent and the medium spatial scale is represented using proximity of samples within and between states. The smallest scale of variability was not included in this study because the individual samples along transects did not have geographical coordinates nor did they have any ancillary information with which to estimate their approximate location. Consequently, for each of the reconnaissance survey geographical locations we required a single 137Cs inventory value, which ‘represented’ the samples from transects. This was possible by assuming that the hillslope provided the net exchange of soil between sampled geomorphic units. In other words, the net result of soil redistribution at the hillslope scale (e.g., 1 km) using sampled transects across Australia is used to estimate soil redistribution. Although wind has the potential to redistribute soil beyond the hillslope scale, we assumed that it was accounted for in existing samples. We determined the minimum and maximum 137Cs inventory values from each set of samples and calculated the mean. This is the same method used to represent temperature data elsewhere. An area-weighted approach would have been preferable but contributing area (upslope length) was not available. To ensure that this treatment of the distribution of 137Cs transect samples was reasonable and appropriate we conducted a sensitivity analysis on the calculation of the variogram of the selection of values for each geographical location (see Results section).

2.2. Land-Use Data

[9] The Bureau of Rural Sciences provides a series of land use maps of Australia. We used here data from 1992/93 which are closest in time to the national 137Cs reconnaissance survey. These land use data include non-agricultural uses based on existing digital maps covering four themes: protected areas, topographic features, tenure and forest. The agricultural land uses are based on the Australian Bureau of Statistics' agricultural censuses and surveys for the years mapped. The spatial distribution of agricultural land uses was determined using Advanced Very High Resolution Radiometer (AVHRR) satellite imagery with ground control data [Knapp et al., 2006]. The data were supplied at a 0.01° grid size with geographical coordinates (GDA94). The summary map (Figure 1a) provides an integer grid with a value attribute table with attributes defining the agricultural commodity group, irrigation status and land use according to the Australian Land Use and Management Classification (ALUMC), Version 5 (Table 1). The data were re-sampled to a 0.05° degree grid for compatibility with the sequential indicator simulation estimates and attribute values were associated with every grid point (Figure 1a). For use with the 137Cs-derived net soil redistribution models (section 3.1), the classification was aggregated to land which had never been cultivated (classes <=220) and that which had been used for cultivation (>220 classes) (Figure 1b). Intensive land uses (classes >530) and Water (classes >600) were excluded from the analysis. Figure 1b shows the map used to determine which model was used in the later 137Cs conversion to soil redistribution.

Figure 1.

(a) Land-use for Australia from the Bureau of Rural Sciences likelihood maps. The first 13 classes shown are used in subsequent analyses and represent the main attributes of the Australian Land use and Management Classification version 5 (see Table 1). (b) Re-classified Australian land use (1992/93) used to determine which model to use in the 137Cs calibration to soil redistribution (1 = never cultivated; 2 = cultivated).

Table 1. Values and Meaning of the Australian Land Use and Management Classification (ALUMC), Version 5
ValuesAttributeMeaning
110–1171Nature conservation
120–1252Other protected areas including indigenous uses
130–1343Minimal use
200, 210–2104Grazing natural vegetation
220–2225Production Forestry
310–314, 410–4146Plantation Forestry
300, 320–3257Grazing modified pastures
330–3388Dryland cropping
340–3549Dryland horticulture
400, 420–43810Irrigated pastures and cropping
440–45411Irrigated horticulture
500, 510–52612Intensive animal and plant production
54213Rural residential
530–541, 550–57514Urban intensive uses
580–59515Mining and Waste
600, 610–66316Water

2.3. Australian Soil Classification

[10] Much of Australia is formed from old, deeply weathered soils. These old surfaces are being dissected and new soils have developed in the weathered material and on unweathered parent rocks exposed by erosion [Isbell et al., 1997]. Past and present climates have interacted with the soil to produce environments in which the modern soil pattern has developed [Beckmann, 1983]. This rejuvenation of Australian landscapes in terms of soil development makes for a complex genetic history. The Australian Soil Classification is an attempt to encapsulate that history using a hierarchical, multicategorical general purpose scheme with classes defined on the basis of diagnostic horizons or materials and their arrangement in vertical sequence as seen in exposed profiles [Isbell, 1996].

[11] The 13 Soil Orders (excluding Anthroposols) are used here to provide data which relate to contemporary medium-term soil erosion and deposition across the continent (Figure 2). The rationale for its use here is that it provides information on the relative erodibility of the soils. The categorical nature of these data makes that relationship more complicated to establish than with continuous rainfall data used to improve the estimation of the 137Cs reference inventory across Australia [Chappell et al., 2011]. However, the reduction of the data to indicators and the Bayesian approach ensures that different types of data may be combined to improve the estimation procedure (see section 3.2). In this analysis Soil Orders were obtained from the Atlas of Australian Soils, where the dominant soil type for each mapping unit had been interpreted from soil-landscape descriptions and Northcote Principal Profile Forms [Isbell et al., 1997]. This data set was converted to a 0.05° degree grid with an origin that aligned with other data sets in this study. The conversion process selected the mapping unit that fell in the center point of the pixel, although a majority filter may have provided a more appropriate point value.

Figure 2.

Distribution of the orders of the Australian Soil Classification.

2.4. Data Sets From Other National Assessments of Soil Redistribution

[12] A comparison is made between the 137Cs-derived net soil redistribution and the only other two national assessments of soil redistribution. In 2001 the National Land and Water Resources Audit (NLWRA) commissioned an assessment of sheetwash and rill erosion (hillslope erosion). In 2006 a trial was commissioned by the NLWRA to monitor wind erosion at the national scale using the Dust Storm Index (DSI).

[13] Hillslope erosion was estimated using the Revised Universal Soil Loss Equation (RUSLE) [Lu et al., 2001, 2003]. This model estimated the average annual soil loss (t ha−1 yr−1) by sheetwash and rill erosion at the hillslope scale (∼1 km) using data sources with sample supports which ranged from 8 km remote sensing data to point digital elevation data. It is noteworthy for the subsequent comparison with the 137Cs technique that the RUSLE model is a gross estimate, does not account for deposition and aeolian and tillage processes. Nevertheless, Lu et al. [2001] compared their model estimates with, among other data, many point estimates of 137Cs-derived net soil redistribution. Since the current study provides many more estimates of 137Cs-derived net soil redistribution it was reasonable to revisit this comparison with the RUSLE data. The RUSLE estimates were made using 0.01° spacing of grid nodes (approx. 1 km) but the work presented here made estimates using 0.05° spacing of grid nodes (approx. 5 km). To enable the comparison between the approaches the former data were transformed to GDA94 and then resampled and aligned using a cubic convolution algorithm. Comparing the absolute difference across Australia makes a direct comparison, while a relative comparison is made using a quantile-quantile plot (qq-plot) of the sample quantiles from each of the model data distributions.

[14] The current national monitoring method for wind erosion is based on the Dust Storm Index (DSI) [McTainsh et al., 2001]. The DSI uses data from the Australia Dust Event Database which contains quality controlled records for those times when the Bureau of Meteorology records contain a ‘phenomena’ dust code and Dustwatch observational data are available. The DSI is a non-dimensional index rather than a direct measure of dust concentration or soil loss. McTainsh and Tews [2008] provide a full description of the DSI. The map of average annual DSI between 1960 and 1990 (approx. 5 km grid) were compared qualitatively with the map of 137Cs-derived net (1950s–1990) soil erosion rate and also quantitatively using the same qq-plot approach introduced above. The DSI was not calculated to coincide exactly with the time period of the 137Cs technique because too few reliable data were available between 1950 and 1960 (G. McTainsh, personal communication, 2010).

3. Methods

3.1. 137Cs-Derived Estimates of Soil Redistribution

[15] The 137Cs technique assumes that once the 137Cs fallout reached the soil surface it was fixed rapidly and firmly to soils and can therefore be used as a tracer of post-1950s soil redistribution by wind and water erosion and tillage practices [Ritchie and McHenry, 1975, 1990]. The technique is an important erosion assessment tool in Australia because of the difficulty, particularly in semi-arid environments, of capturing the magnitude and frequency of soil redistribution episodes using traditional measurements. The technique has the considerable benefit of requiring only one site visit to retrieve a soil sample to provide an estimate.

[16] At locations in the landscape where there is little or no soil erosion or deposition (undisturbed) the amount of 137Cs in the soil is reduced only by radioactive decay (137Cs half-life 30.2 years). At other locations the amount of soil 137Cs is a function of the intensity and duration of erosion and/or deposition. The soil sample is measured for background levels of the artificial radionuclide 137Cs using gamma-ray spectroscopy. The amount of 137Cs is compared to a reference value obtained from a stable site unaffected by soil erosion and deposition. The result is expressed as a percentage 137Cs loss or gain. A calibration relationship is required to convert the percentage of 137Cs lost or gained (X) relative to the 137Cs inventory at the undisturbed reference location. Several reviews of the available calibration relationships are available [Walling and Quine, 1990; Walling and He, 2001; Walling et al., 2002]. Recent applications of the Australian Empirical Model (AEM) to hillslopes in the Northern Territory [Hancock et al., 2008] and in southeastern Australia [Martinez et al., 2009] compared well with published regional rates derived using rainfall-runoff plots and sediment yields. This study follows that of Loughran et al. [2004] and uses the Australian Empirical Models (AEMs); one for calculating net soil loss (Y; kg ha−1 yr−1) for sites which had never been cultivated (N = 31; equation (1)) and the other for sites which had been used for cultivation (N = 61; equation (2)):

equation image
equation image

Net soil accumulation was calculated using these equations in reverse mode for sites, which had gained 137Cs. In this case, Y is net soil gain and X is the percentage 137Cs gain relative to the reference value. Both relations were derived from long-term soil-loss measurements using runoff-erosion plots, or similar experiments in New South Wales, Queensland and Western Australia [Loughran and Elliott, 1996]. Equations (1) and (2) are revisions of the original equations presented by Elliott et al. [1990], following correction of the measured sediment yields from plots of the Soil Conservation Service of New South Wales [Lang, 1992; Loughran and Elliott, 1996].

[17] In common with Loughran et al. [2004] and regardless of whether land was cultivated continuously or in rotation, the Australian Empirical Model (AEM) for cultivated land was applied. This is expected to over-estimate the net soil redistribution at locations cultivated in rotation. However, information necessary to resolve this issue was not available for the modeling conducted here. A similar issue relates to the use of these models to account for wind erosion when the calibration has been primarily based on runoff-erosion plots. In the absence of more appropriate 137Cs-wind erosion models, use of the AEM here is based on the implicit assumption that the amount of 137Cs removed by wind is the same as that removed by water. An anonymous reviewer of an early version of this manuscript suggested that the use of the AEM constructed using experiments from the past may be limited in its application to subsequent soil erosion. These issues surrounding the nature of the models may introduce additional sources of uncertainty. We consider these in the discussion below. They are unfortunately beyond the scope of this paper, but are ripe for investigation.

3.2. Sequential Indicator Co-Simulations of 137Cs and Soil Class Data

[18] The methodology for establishing the uncertainty of the maps using stochastic conditional co-simulation is the same as that used by Chappell et al. [2011] to establish the 137Cs reference inventory for Australia. In addition to the 137Cs (primary) data only a single ancillary variable can be used to improve the estimates of the indicator co-simulation. In the situation where the explanation of spatial variation requires multiple variables a principal component may be used. We used the Markov-Bayes approach to establish the local prior probabilities of the 137Cs inventory (primary data) and the Australian Soil Classification (secondary data). Sequential indicator co-simulation was used here to generate 100 realizations separately of the 137Cs inventory data using the Australian Soil Classification data. The Australian continent was discretized into a grid with 572721 nodes (841 × 681) using a square grid-spacing of approximately 5 km which was 0.05° in latitude and longitude. The estimates were made to coincide with the nodes used by Chappell et al. [2011] to establish the 137Cs reference inventory. The 100 realizations were post-processed by calculating the per-point median and interquartile range (75th-25th percentile) to summarize the uncertainty.

3.3. Modeling the Spatial Variation of Soil 137Cs

[19] We explored the possibility of mapping using the estimates of (weighted) net soil redistribution provided from each transect of the national reconnaissance survey. Unfortunately, the variogram of those data contained no spatial structure (not shown). This means that there is no evidence of spatial variation in the data and it would not be useful to make estimates at unsampled locations. This finding is consistent with the lead author's unpublished research on wind erosion in Eastern England using the 137Cs technique [Chappell and Warren, 2003]. Consequently, we adopted a similar technique to that earlier study and modeled the 137Cs inventory.

[20] We also considered the impact of selecting the mean of the distribution of 137Cs inventory values available from each transect of the national reconnaissance survey. The results of repeatedly sampling those distributions and calculating the variogram showed little difference in the fitted model and the nugget variance (not shown). Some variation was noted in the sill variance. On the whole these results were consistent with our expectations. Despite variation about those mean values there was very little difference in the amount of information available at the smallest lag separation distances and the broad scale spatial structure remained approximately constant. This was deemed sufficient to justify our selection of the mean value of the distribution to represent the range of values obtained along transects.

[21] There is a basis for the 137Cs distribution to be anisotropic, particularly over large regions and in directions of preferential soil movement (e.g., prevailing wind direction). However, there were insufficient data to model reliably the anisotropic spatial variation [Webster and Oliver, 1992]. Furthermore, it could be argued that the spatial variation in 137Cs is closely related to some systematic change across the continent. There was no evidence for this type of underlying trend in the variograms and so it was assumed not to exist. Consequently, omni-directional sample indicator variograms represented the average variation in all directions and were calculated for the 137Cs inventory data. The median indicator variogram of 137Cs inventory data was calculated and the mosaic model [Journel, 1984] was used to infer the variogram at percentile thresholds other than the median. The median approximation also reduced the two major causes of order relations problems [Deutsch and Journel, 1998]. The 137Cs inventory cumulative distribution function was calculated for all locations. The K = 7 quantiles (0.05, 0.1, 0.25, 0.5, 0.75, 0.9 and 0.95) were established and also used in the simulations. These percentiles were used to transform the 137Cs values into indicator variables. The median indicator omni-directional variogram of 137Cs inventory was computed to under half (2500 km) the maximum separation distance between soil 137Cs sample locations. These variograms were fitted, using weighted least squares, with several models authorized for kriging. The models that fitted best, in the least squares sense, were selected using the square root of the mean squared difference between the model and the observations (RMSE) and the Akaike Information Criterion (AIC) [Akaike, 1973] was used to judge the level of complexity in the nesting of models. The model judged to fit the sample variograms best, in the least squares sense, was a single spherical model and it is described below in its isotropic form where the lag h becomes the scalar h = ∣h∣ [Webster and Oliver, 1990]. The quantity c is the sill variance and a is the range of the bounded models:

equation image

The parameters of these models describe the structure of spatial variation [Chappell and Oliver, 1997] and were used in the co-simulations.

3.4. Compounding Uncertainty Between 137Cs Maps and the Soil Redistribution Calibration Model

[22] The realizations of the 137Cs reference inventory and 137Cs inventory each provide an assessment of uncertainty in the estimates over space (spatial uncertainty). The realizations are equally likely and consequently each of these sources of spatial uncertainty was combined when forming the percentage 137Cs difference relative to the reference inventory. This process was performed by random selection of a realization without replacement. Spatial uncertainty needed to be considered when using the calibration models that relate percentage 137Cs difference (X) to soil redistribution (Y) in equations (1) and (2). A bootstrap procedure [Efron and Tibshirani, 1986] was selected to provide the uncertainty in the calibration model due to variation in the underlying data [Elliott et al., 1990]. To undertake the bootstrap procedure the original soil erosion and 137Cs measurements of the calibration plots were required. Unfortunately, these data could not be obtained and instead were digitized from Elliott et al. [1990, Figures 1 and 2]. The digitized data were corrected following Lang [1992] and treated as original data for the purposes of the bootstrap procedure here. With replacement, 100 samples of the data were selected randomly and a log linear regression equation was calculated. Each bootstrap outcome produced values for each of two regression parameters. In this procedure a particular datum from the original set could appear multiple times in a given bootstrap sample. This means that more or less of the original data are used and therefore different configurations of the data (in property space) were included in the regression analysis. The bootstrap was performed in the following steps.

[23] (1) The calibration data set ZN was randomly sampled with replacement so that ZN = (z1, z2, … zn) where zn = (xn, yn) and the data set is denoted by N.

[24] (2) This was done b times, b = 1, 2, …, B, producing B bootstrap data sets, where each of these bootstrap samples (or realizations of the original population), ZNb, is the same size as the original. In this case N = 100 and B = 30.

4. Results

4.1. Stochastic Modeling of the Spatial Variation of Soil 137Cs

[25] The omni-directional experimental variograms of the 137Cs inventory data are shown in Figure 3 (top). The median indicator variograms of the same data are shown in Figure 3 (bottom). The models that fitted the variograms best in a least squares sense are described in Table 2. Spherical models fitted the variograms of the original data values and of the data transformed to the median indicator.

Figure 3.

Omni-directional variograms of the (top) 137Cs inventory and (bottom) median indicator.

Table 2. Statistics of the Variogram Models Fitted to the 137Cs Reference Inventory and 137Cs Inventory Data and Their Respective Median Indicator Data
 Model TypeNugget (c0)Spatial Correlation (c1)c0/(c0 + c1)* 100 (%)Range (km)RMSE
137Cs inventorySpherical428.05267.4262384.6201.21
Median indicatorSpherical0.170.10632155.10.010

[26] The variograms of the median indicator were expected to provide the most reliable measures of the spatial variation. The model identified a range of spatial dependence of around 2155 km (Table 2). A large proportion (>60%) of the total variance was nugget. This finding suggests that a considerable amount of variation in these properties has not been captured by the mean values of the reconnaissance survey samples. The values of the optimized model parameters were used in the median approximation sequential indicator co-simulations.

4.2. Sequential Indicator (Median Approximation) Co-Simulation of 137Cs Inventory

[27] The simulations of 137Cs inventory were performed using the Australia Soil Classification. The per-point median of the realizations (Figure 4a) shows large values of 137Cs inventory along the southeastern and southwestern coastal regions and those large values extend inland in southeastern Australia. There is an overall approximate correspondence between the per-point median and interquartile range (Figure 4b) of the realizations. The latter map is speckled indicating small scale variability, due to the large nugget variance in the 137Cs inventory variogram.

Figure 4.

(a) Per-point median (mBq cm−2) and (b) interquartile range (mBq cm−2) for the 137Cs inventory realizations of sequential indicator (median approximation) co-simulations using the Australian Soil Classification as a secondary variable. The dots in the second panel represent the location of the 137Cs inventory measurements.

[28] Areas of large per-point variability are generally associated with the large 137Cs values (Figure 5). Uncertainty in the cumulative distribution function (cdf; Figure 5a) and the qq-plot (Figure 5b) increases with 137Cs values which are greater than approximately 75 mBq cm−2. The cdf shows that 70–80% of the values are below 50 mBq cm−2. The performance of the simulations using the soil classification is shown in the qq-plot (Figure 5b). There is good correspondence between the simulations and the 1:1 line which indicates that there is little bias in the estimates. This indicates that the simulations have faithfully reproduced the characteristics of the 137Cs inventory sample distribution.

Figure 5.

(a) Cumulative distribution function of the 137Cs inventory realizations and (b) a qq-plot showing their relationship with the sample values.

4.3. Difference Between 137Cs Reference Inventory and 137Cs Inventory Values

[29] The percentage loss or gain of 137Cs includes the uncertainty in the 137Cs reference inventory and 137Cs inventory realizations. The cumulative distribution function of the difference values is shown in Figure 6. These results show that between 60% and 80% of Australia has lost 137Cs, between 20% and 40% of Australia has gained 137Cs and that around 20% of Australia has neither lost nor gained 137Cs. The uncertainty in these estimates is derived from the differences in the 137Cs reference inventory realizations and how they have been combined randomly with the 137Cs inventory realizations.

Figure 6.

Cumulative distribution function of the percentage difference between 137Cs inventory and 137Cs reference inventory values relative to the latter.

[30] The map of per-point median difference (%) shows the areas across Australia which have lost and gained 137Cs, relative to the reference inventory (Figure 7a). The main areas to have lost 137Cs are concentrated in southeastern Australia, the coastal region of Western Australia and part of the Northern Territory and Queensland. Most 137Cs has been gained in South Australia and western New South Wales. The uncertainty appears greatest in areas where the percentage 137Cs difference is positive (Figure 7b).

Figure 7.

(a) Per-point median and (b) interquartile range of the difference (%) between 137Cs reference inventory and 137Cs inventory realizations of sequential indicator (median approximation) co-simulations.

4.4. Calibration of 137Cs Difference to Soil Redistribution

[31] The calibration of percentage 137Cs difference to net soil redistribution (t ha−1 yr−1) makes use of the Australian Empirical Models (AEMs) described above. These models also contribute a source of uncertainty. To examine the impact of this model uncertainty combined with that of the spatial uncertainty, the AEMs were used initially without uncertainty (results not shown) and then the AEMs were applied after the bootstrap procedure to introduce uncertainty. In each case the models were applied to erosion on uncultivated and cultivated situations and used in reverse mode for depositional locations (Figure 8). There is much less variation in the cultivated model gradient coefficients than in those of the uncultivated model. This variation is due largely to the former model being better constrained by twice the number of data than in the latter model.

Figure 8.

Histograms showing the distribution of the Australian Empirical Model equation coefficients for the (a and c) cutoff and (b and d) gradient coefficients for the uncultivated (Figures 8a and 8b) and cultivated (Figures 8c and 8d) situations.

[32] The results of combining the spatial uncertainty and model uncertainty are shown in Figure 9a. The map of net soil redistribution (Figure 9a) displays a pattern which is similar to that of the percentage 137Cs difference map (Figure 7a). It is also very similar to the map of net soil redistribution without model uncertainty (not shown). Evidently, the inclusion of calibration model uncertainty has made only subtle differences to the map of net soil redistribution. The map of net soil redistribution interquartile range with model uncertainty (Figure 9b) has a similar pattern to the map without model uncertainty (not shown) but the magnitude of the interquartile range has changed in some places.

Figure 9.

(a) The 137Cs-derived net (1950s–1990) soil redistribution rate (t ha−1 yr−1) of Australia and (b) its interquartile range (t ha−1 yr−1) with bootstrap uncertainty.

[33] The map (Figure 9) shows areas that are stable, depositional or have very small erosion rates in southeastern Australia, and the northern parts of Australia. The remainder of Australia is eroding. Areas that have large erosion rates include the main cultivated areas along the coastal regions of Western Australia, South Australia, Victoria, New South Wales and Queensland. The most eroded area is in the western most region of Western Australia (Gascoyne/Pilbara region) which has average erosion rates of more than 6 t ha−1 yr−1. The median rate should be considered with its spatial uncertainty which is represented by the interquartile ranges of between 4 and 8 t ha−1 yr−1. Assuming a symmetrical distribution this would be equivalent to an erosion rate with uncertainty of >6 ± 3 t ha−1 yr−1. The areas of greatest uncertainty include mid South Australia, mid New South Wales and southwest Queensland (Figure 9b) and coincide with the stable or net depositional areas (Figure 9a). The main cultivation regions (1992/93) of Australia have a similar uncertainty of ±3 t ha−1 yr−1. This means that we can be reasonably certain that these areas are net eroding while other areas have less certainty. This issue of the uncertainty is explored in further detail in the Discussion.

[34] The cumulative distribution function of net soil redistribution with model uncertainty is shown in Figure 10a. These results show that around 20% of Australia was net stable or lost very small amounts of soil. Approximately 25% of Australia gained soil and consequently around 55% of Australia lost substantial amounts of soil. The performance of the estimates (with model uncertainty) is shown in the qq-plot (Figure 10b) of the soil erosion realizations compared with the estimates made at the sample locations. Overall there is good correspondence between the simulations and the soil redistribution rate based on the samples alone. There is a modest bias in the realizations relative to the sample estimates since the former fall above the 1:1 line. This indicates that between 0.1 and 5 t ha−1 yr−1 the realizations have under-estimated net soil redistribution by about 1 t ha−1 yr−1.

Figure 10.

(a) Cumulative distribution function of 137Cs-derived net soil redistribution (with bootstrap uncertainty) realizations and (b) a qq-plot showing their relationship with the sample estimates.

[35] The statistics of net soil redistribution with model uncertainty are shown in Table 3. For Australia as a whole soil erosion ranged between −1.02 t ha−1 yr−1 to +0.04 t ha−1 yr−1 with a median of −0.19 t ha−1 yr−1 (Table 3). More than five times (at the 25th percentile) more soil was lost from cultivated land (−4.11 to +0.34 t ha−1 yr−1) than from uncultivated (−0.80 to +0.04 t ha−1 yr−1) land in Australia. However, at the median level the soil loss from cultivated land was nearly eight times larger than that from uncultivated land. The land-use classification of Australia provided a breakdown of these losses (Table 3). The first four classes (Nature conservation, Other protected areas, Minimal use and Grazing natural vegetation) had smaller amounts of soil erosion than the other land-use classes including Grazing modified pastures and Dryland cropping.

Table 3. Selected Percentiles of Net (1950s–1990) Soil Redistribution Realizations for Several Classifications of Locations Across Australiaa
Land-Use ClassSpatial Uncertainty With Calibration Model Uncertainty (t ha−1 yr−1)
25th50th75th
  • a

    Negative values indicate erosion and positive values indicate deposition. Bold font is used to discriminate between cultivated and uncultivated land uses.

Australia−1.02−0.190.04
    
Uncultivated−0.80−0.160.04
Cultivated−4.11−1.260.34
    
Nature conservation−0.76−0.150.03
Other protected areas including indigenous uses−0.71−0.170.03
Minimal use−1.05−0.24−0.01
Grazing natural vegetation−0.76−0.140.05
Production Forestry−3.79−1.130.42
Plantation Forestry−4.45−1.350.25
Grazing modified pastures−4.25−1.350.30
Dryland cropping−4.24−1.310.33
Dryland horticulture−3.21−0.930.54
Irrigated pastures and cropping−4.12−1.46−0.32
Irrigated horticulture−3.62−1.260.30
Intensive animal and plant production−3.30−1.16−0.28
Rural residential−3.55−1.070.41

4.5. Comparison of 137Cs-Derived Net Soil Redistribution With Other National Assessments

[36] The map of Australian hillslope and sheetwash erosion produced by Lu et al. [2001, 2003] using the Revised Universal Soil Loss Equation is shown in Figure 11. Small erosion rates are evident across the agricultural areas in Western Australia, South Australia, Victoria and parts of New South Wales. Larger erosion rates are evident along the agricultural coastal strip from the southern part of New South Wales, into Queensland and western Queensland. By far the largest erosion rates occur in the northern part of Australia in the Pilbara of Western Australia and the Northern Territory and northern and western Queensland.

Figure 11.

(a) Predicted [Lu et al., 2001] mean annual sheetwash and rill erosion (t ha−1 yr−1) and (b) the difference (t ha−1 yr−1) between it and the realizations median 137Cs-derived net (1950s–1990) soil redistribution.

[37] It is noteworthy for the subsequent comparison with the 137Cs technique that the RUSLE model is a gross estimate, does not account for deposition and aeolian and tillage processes. Despite the estimates being made at a grid resolution of 0.01° across Australia, it is not clear at what spatial scale the RUSLE estimates are made because the input data sources range in sample supports from 8 km remote sensing data to point digital elevation data. These aspects of the RUSLE estimates suggest substantially different information content than that of 137Cs-derived net soil redistribution. Nevertheless, Lu et al. [2001] validated their RUSLE estimates with, among other data, many of the point estimates of 137Cs-derived net soil redistribution used in this study. Since the current study estimates 137Cs-derived net soil redistribution across Australia it appears reasonable to revisit this comparison with the RUSLE estimates.

[38] The absolute difference between this map of hillslope erosion (Figure 11a) and the 137Cs-derived net soil redistribution map (Figure 9a) is shown in Figure 11b. The greatest differences between the maps occur generally in the areas of northern Australia and the Pilbara region of Western Australia. Intermediate differences between the maps occur in the major cultivated areas throughout Australia because hillslope erosion rates are predicted to be much larger than those of the 137Cs technique.

[39] Evidently, Lu et al. [2003] predicted a large proportion of Australia to have small erosion rates and many of those areas coincide with small estimates of 137Cs-derived net soil erosion. Lu et al. [2003] describe the average erosion rate for the continent as 4.1 t ha−1 yr−1. This rate is more than 20 times larger than the median erosion rate using the 137Cs technique (0.19 t ha−1 yr−1). A qq-plot of the 137Cs-derived soil erosion data against the hillslope and rill erosion data (Figure 12) shows only good correspondence between the approaches for values between 1 and 20 t ha−1 yr−1. Between this range of erosion rates there is considerable uncertainty in the 137Cs-derived soil erosion rates which do not fall around the 1:1 line and which suggest that the RUSLE hillslope erosion rates are much larger than those of the 137Cs technique. Perhaps more significantly, the 137Cs-derived soil erosion rates between 20 and 100 t ha−1 yr−1 have a corresponding range in RUSLE hillslope erosion rates between 20 and 700 t ha−1 yr−1. The RUSLE hillslope erosion rates between 0.011 and 1 t ha−1 yr−1 are over-estimated relative to the 137Cs-derived soil erosion rates. The tails of the RUSLE hillslope erosion rate distribution are extreme relative to those of the 137Cs-derived soil erosion rates. This is also indicated by the red dashed lines which represent the quantiles of a standard Normal distribution. It is likely that the national average hillslope erosion rate of Lu et al. [2003] is influenced by the extreme rates predicted by their model.

Figure 12.

Quantiles of the 137Cs-derived net (1950s–1990) soil erosion rate (t ha−1 yr−1) and the mean annual sheetwash and rill erosion (t ha−1 yr−1) for Australia.

[40] The dust storm index (DSI) is the only national assessment of wind erosion that accounts for variation over time (Figure 13). The map was produced for events between 1960 and 1990 to match approximately the time period of the analysis here using the same standard approach as that used in previous Australian State of the Environment reports. There is some broad agreement between the index and some areas where 137Cs-derived net soil erosion is large. Large erosion rates are approximately associated with the DSI data which indicate a large number of dust events and similarly small erosion rates coincide with DSI data which indicate few dust events. For example, the DSI is large in the Pilbara region, in western Queensland and the southern part of the Northern Territory and a central part of the Northern Territory. There are other similarities between the maps but the strongly concentric patterns of the DSI are an artifact of the interpolation procedure and make it difficult to be confident about the comparison.

Figure 13.

Dust storm index (DSI) of 1960–1990 for Australia at 0.05 using Nearest Neighbor interpolation (see data section 2.4 for details).

5. Discussion

5.1. Performance of the Stochastic (Conditional) Simulation of 137Cs-Derived Net Soil Redistribution

[41] Multiple realizations of the soil 137Cs inventory values benefited from the use of the soil classification information as a secondary data source. The rationale for the incorporation of the Australian Soil Classification was that it provided information on the relative erodibility of the soils. Despite these two data types being different from each other they were integrated using the Markov-Bayes algorithm [Deutsch and Journel, 1998]. In the 137Cs inventory there was good correspondence between the simulations and the 1:1 line which indicates that there was little bias in the estimates (Figure 5b). Consequently, the simulations were deemed to have faithfully reproduced the characteristics of the respective 137Cs inventory sample distributions.

[42] The Australian Empirical Models (AEMs) were used to convert the 137Cs residuals to estimates of soil erosion and deposition. The AEMs rely on runoff erosion plot measurements from only part of the continent and may not be entirely appropriate for all other points in Australia [Loughran et al., 2004]. The AEMs also do not account for deposition but in the absence of any other information they were used in reverse mode to estimate rates of deposition. Loughran et al. [2004] and other recent studies [Hancock et al., 2008; Martinez et al., 2009] used this approach. Martinez et al. [2009] justified their use of the AEMs with their finding that the theoretical 137Cs conversion model over-estimated soil redistribution rates on uncultivated hillslopes in southeastern Australia. The realizations showed systematic correspondence with the estimated rates from the samples alone and plotted approximately along the 1:1 line which indicates that there was only a modest bias. The bias indicates that between 0.1 and 5 t ha−1 y−1 the realizations have under-estimated net soil redistribution by about 1 t ha−1 yr−1. Generally, the simulations performed well by reproducing approximately the characteristics of the sampled estimates of soil erosion. Since the qq-plot of the 137Cs residuals showed little bias (Figure 5b) the bias in the qq-plot of net soil redistribution (Figure 10b) is most likely due to the aggregation of the net soil redistribution estimates from the samples alone. Remember that individual samples were not geo-referenced along each hillslope transect and the reported net soil redistribution was area-weighted [Loughran et al., 2004]. Evidently that area-weighting has systematically increased the estimate of net soil redistribution.

5.2. Implications for National, Hillslope Scale Soil Conservation and Remediation

[43] The map of net soil redistribution showed areas that were stable, depositional or have very small erosion rates in southeastern Australia, and the northern parts of Australia (Figure 9a). The remainder of Australia was eroding. Areas that had large erosion rates include the main cultivated areas along the coastal regions of Western Australia, South Australia, Victoria, New South Wales and Queensland. The most eroded area was in the western-most region of Western Australia (Pilbara region) which had average erosion rates of more than 6 t ha−1 yr−1. The areas of greatest uncertainty include the Pilbara region and the cultivated coastal region in Western Australia and parts of South Australia and New South Wales (Figure 9b) associated with net deposition.

[44] The realizations provided a range of net soil redistribution which showed that the soil redistribution rate for Australia was between −1.02 t ha−1 y−1 and +0.04 t ha−1 y−1 and that the median erosion rate was −0.19 t ha−1 y−1. Using the median values of the results approximately 4.7 × 105 t y−1 was eroded, 1.9 × 105 t y−1 was deposited and hence the net flux was −2.8 × 105 t y−1 of soil. The erosion occurred over >94% of Australia leaving only 6% of the land surface associated with deposition. Compared with a global soil erosion estimate (75 × 109 t y−1 [Pimentel et al., 1995]) these results suggest that Australia contributes <1% of global soil erosion from about 5% of the world land area. Nearly 5 times (25th percentile) more soil was lost from cultivated land (−4.29 to +0.17 t ha−1 yr−1) than from uncultivated (−0.91 to +0.05 t ha−1 yr−1) land in Australia.

[45] Analysis of the national 137Cs reconnaissance samples [Loughran et al., 2004] found that time-averaged soil losses (1950s to 1990s) for Australia were significantly greater under intensive agriculture and on rangelands (≈5.5 t ha−1 yr−1) compared with sites on uncultivated pastures and forest (≈1 t ha−1 yr−1). A comparison was made between the results presented here and those of comparable land classifications (Table 3). Our results showed that intensive agriculture was estimated to be (1.4 t ha−1 yr−1) four times smaller than that from the 137Cs samples alone. Rangelands had net soil redistribution of 0.3 t ha−1 yr−1 which was 18 times smaller than the estimate from the 137Cs samples alone. Uncultivated pastures and forest (0.2 t ha−1 yr−1) were approximately five times smaller than the estimate from the 137Cs samples alone. When aggregating across sites Loughran et al. [2004] found that 60% of sites had net soil losses greater than 1 t ha−1 yr−1 and that 74% of sites had losses of more than 0.5 t ha−1 yr−1. Our results show that approximately 7% of Australia had soil losses of more than 1 t ha−1 yr−1 and that 16% of Australia had soil losses of more than 0.5 t ha−1 yr−1. These differences between the median of the realizations and the samples are likely caused by the samples not representing the population of each soil redistribution class. The estimation on a regular grid ensures that these aggregated statistics are representative of the land use class or population. Considering only the best local estimates and hence a single realization or map such as provided by kriging does not provide a comprehensive understanding of the uncertainty which is available here using stochastic (conditional) simulation.

[46] Loughran et al. [2004] suggested that the value of 0.5 t ha−1 yr−1 could be considered as a threshold for tolerable soil loss. Using that threshold, the results presented here show that 55% of Australia was relatively net stable. The realizations provide the opportunity to calculate the probability of exceeding that threshold (Figure 14). On this basis, the areas that were (up to the early 1990s) in urgent need of remediation were those identified with a large probability and include the Pilbara, some of the agricultural regions of southwestern Western Australia, a small portion of South Australia, the majority of Victoria and the cultivated areas (in 1992/93) of New South Wales and Queensland. Additional areas that might have been considered for treatment or soil conservation were those identified with a probability >0.5 and include the majority of Western Australia and the cultivated areas (in 1992/93) of New South Wales and Queensland. The map provides a useful tool for assisting with decision-making and the allocation of resources to tackle soil erosion in Australia.

Figure 14.

Probability of exceeding the threshold of −0.5 t ha−1 yr−1 based on per-point realizations across Australia.

5.3. Comparison Between the 137Cs Technique and Other National Assessments in Australia

[47] Many studies have compared the 137Cs-derived estimates of net soil redistribution to other soil erosion models [Soileau et al., 1990; Busacca et al., 1993; Sidorchuk and Golosov, 1996; Gillieson et al., 1996; Bajracharya et al., 1998]. In Australia Loughran et al. [2004] found good agreement between results from the AEMs and SOILOSS [Rosewell, 1993; Loughran et al., 2004]. Hancock et al. [2008] found that the range of results from the AEMs were similar to those of the Revised Universal Soil Loss Equation (RUSLE) [Renard et al., 1991] and the SIBERIA model [Willgoose, 1994]. Martinez et al. [2009] found that the results of the SIBERIA model were similar to those of the 137Cs method but that the RUSLE over-estimated soil erosion rates.

[48] Lu et al. [2001, 2003] validated their RUSLE model of sheetwash and rill erosion for continental Australia with published soil erosion rates including 137Cs-derived net soil redistribution of the national reconnaissance survey at 83 locations (the same data used in this study). They reported a statistically significant linear correlation (R2 = 0.64) with a root mean squared error of 3.84 t ha−1 yr−1. These statistics were used as evidence for adequate performance of their model. However, there are a number of issues with that comparison. First, the comparison involved an estimate at 0.01° (≈1 km) using an average of modeled data from within a circle of 0.05° (≈5 km). The measured data were expressed with an error but that did not include error of the measurement nor of the model. Second and perhaps more fundamentally, the validation data included 137Cs-derived estimates of net soil redistribution which represent erosion and deposition by wind, water and tillage processes. These validation data are a considerably different measure to that of gross sheetwash and rill erosion.

[49] We compared at the nodes of a 5 km grid across Australia the RUSLE estimates [Lu et al., 2001, 2003] and the realizations of the 137Cs-derived net soil erosion (Figure 11). The 137Cs-derived soil erosion rates ranged between 20 and 60 t ha−1 yr−1 and those of the RUSLE hillslope erosion rates ranged between 20 and 700 t ha−1 yr−1 (Figure 11). The RUSLE hillslope erosion rates between 0.01 and 1 t ha−1 yr−1 are over-estimated relative to the 137Cs-derived soil erosion rates. The tails of the RUSLE hillslope erosion rate distribution are extreme relative to those of the 137Cs-derived soil erosion rates (Figure 11). This over-estimation is largely accepted for catchments across northern Australia (S. Wilkinson, personal communication, 2010). Our comparison between the 137Cs-derived net soil erosion rates and the RUSLE estimates of Lu et al. [2001, 2003] show considerable differences which were not evident in the validation of the RUSLE model against 137Cs-derived estimates. These differences are caused by the fundamental difference in the information content of the two approaches and the implicit assumption of Lu et al. [2001, 2003] that the 137Cs-derived net soil redistribution samples represent the variability in soil redistribution of Australia. The RUSLE estimates are arguably a measure of potential soil mobilization at the field or paddock scale. The 137Cs-derived estimates provide a robust measure of net soil redistribution appropriate for regional soil management. These results cast doubt on the validity of any temporal extrapolation and in particular the ratio of pre-European to current hillslope erosion rates [Lu et al., 2003].

[50] One of the limitations of the RUSLE model within the context of commenting on soil erosion by all processes is the inability to account for wind erosion and deposition. This is important because the wind preferentially, and often insidiously, removes fine nutrient-rich material which changes the fertility and water-holding capacity of the soil and ultimately degrades it. One of the main reasons for the neglect of wind erosion is the long history of work on water erosion [Livingstone and Warren, 1996] and the perceived difficulty of tackling wind erosion. Despite the development of models to estimate the quantity of soil eroded by wind [e.g., Shao et al., 2007] the only national perspective currently available for multiple years uses a surrogate measure. The Dust Storm Index uses observations of visibility as a surrogate measure of the location and relative intensity of wind erosion. There appears to be some agreement between the index and areas where 137Cs-derived net soil erosion is large (Figure 13). For example, the DSI is large in the Pilbarra region, in western Queensland and the southern part of the Northern Territory and a central part of the Northern Territory. The strongly concentric patterns of the DSI are an artifact of the arbitrary mathematical interpolation procedure and make it difficult to be confident about the comparison. However, there is a positive relationship between 137Cs-derived erosion rate and the DSI suggesting a linear relationship between erosion rates and the DSI data (Figure 13).

6. Conclusion

[51] Soil erosion estimates from direct measurement and monitoring approaches are confounded, particularly in semi-arid environments, by the highly variable nature of the processes in space and time. These difficulties are likely responsible for their common neglect in carbon balances for greenhouse gas abatement and carbon storage and in studies of soil function. The 137Cs technique overcomes many of these problems by providing retrospective information on medium-term (30–40 years) erosion/deposition rates. It has been used successfully in many parts of the world to estimate net soil redistribution by the combined effect of wind, water and more recently by tillage erosion. However, most studies that use the 137Cs technique commonly limit their sampling to the hillslope or field scale perhaps because of the misconception that many samples are required everywhere to make estimates. The national reconnaissance survey of soil erosion in Australia in 1990 was also conducted over hillslopes. The results were examined to consider the effect of land-use and environmental controlling factors [Loughran et al., 2004]. However, those findings only represent the variability in the interaction between soil type, land–use and erosion if the samples represent the variability in these factors across the scales of variation (e.g., hillslope, catchment, region etc.). It is difficult to assess the extent to which such a national survey represents the variability in these factors across these scales. Our geostatistical analysis made estimates of 137Cs-derived net soil redistribution and its uncertainty on a regular grid across the continent using the samples and related ancillary soil class data. Between the mid-1950s to early 1990s the median of the net soil redistribution realizations for the Australian continent was −0.19 t ha−1 yr−1. Soil erosion exceeding 0.5 t ha−1 yr−1 occurred over 16% of Australia, mainly in the cultivated regions where the median of the net soil redistribution realizations was −1.26 t ha−1 yr−1, more than eight times larger than the sampled rate on uncultivated land (−0.16 t ha−1 yr−1). The net total of soil redistributed in Australia was −2.8 × 105 t y−1 which is <1% of global soil erosion from approximately 5% of the world land area. A previous [Lu et al., 2001, 2003] Revised Universal Soil Loss Equation (RUSLE) national assessment of mean annual gross sheetwash and rill erosion (4.1 t ha−1 yr−1) is an order of magnitude larger than the median for the continent and its range of estimates (0–700 t ha−1 yr−1) is an order of magnitude larger than that of the realizations. Based on the results presented here and their comparison with other national estimates it appears that RUSLE-based models are unreliable estimators of soil erosion in Australia, particularly as they do not produce expressions of uncertainty.

[52] The study by Van Oost et al. [2007] raised the stakes of soil erosion studies from soil conservation to carbon sequestration by considering its impact on global carbon accounting. With the soil erosion data presented here and a map of the spatial distribution of carbon it is feasible to improve the precision and accuracy of carbon cycling in Australia which will likely have implications for carbon accounting in Australia and perhaps offer a methodology suitable for global application. These soil erosion estimates are approximately 20 years old and soil conservation and management practices are likely to have changed over this period. There is an urgent need to repeat the analysis presented here. The map of the probability of exceeding (more than) the threshold of −0.5 t ha−1 yr−1 shows that the main cultivated areas of Australia in 1992/93 were the main areas in need of soil conservation and perhaps even, in some area, remediation. It is worth emphasizing that these estimates do not contain information about variability in soil redistribution at e.g., <1 km within hillslopes or paddocks (fields), but provide a valuable regional perspective. The opportunity exists within current programs to investigate the effectiveness of previous policy and conservation approaches and to establish the relationship between soil erosion and carbon sequestration. For example, 137Cs could be measured on samples currently being gathered as part of other national programs (e.g., national carbon program funded by national agencies). Although the sample locations of the previous national reconnaissance survey were sub-optimal for mapping the continent they provided essential information about the 137Cs inventory that could not otherwise be obtained. Similarly, the use of other national campaigns, which may not have been designed for this purpose, combined with the measurement of 137Cs could enable a rapid initiation of a new reconnaissance survey program of 137Cs-derived soil redistribution. A future study of this type may provide net (since 1950s) soil redistribution and a comparison against the results presented here will provide a rate for the last ca. 20 years. The use of recently gathered samples will also ensure that 137Cs measurements are made before the detection limit is reached and the 137Cs technique can no longer be used.

Acknowledgments

[53] We gratefully acknowledge the data of the national reconnaissance survey and the Dust Storm Index data supplied by Grant McTainsh and Kenn Tews and the support with data manipulation provided by Linda Gregory. Some critical comments on a larger report of this work provided by Gary Hancock and Elisabeth Bui are also appreciated. The comments provided by two anonymous reviewers as part of the internal CSIRO review of the manuscript and by anonymous external reviewers are gratefully acknowledged. We also appreciate the support during the reviewing process provided by the journal's managing editor Mike Church. Any errors or omissions in the manuscript remain the sole responsibility of the authors.

Ancillary