Abstract

Key Words

Soil erosion, risk assessment, mining rehabilitation, SIBERIA.

Introduction

In the rehabilitation of ecosystems affected by large earth movements such as mining, the final result is primarily conditioned by topographic reconstruction (Toy and Hadley 1987). An understanding of the geomorphology of disturbed landscapes holds the key to successful rehabilitation as geomorphology influences soil and soil development down the slope (i.e. the soil catena), landscape hydrology, establishment and maintenance of vegetation as well as erosion. This requires that post-mining landscapes be designed using an understanding of geomorphic landscape processes together with best practice technology (Loch et al. 2000).

One method by which risk can be assessed is to quantify the error associated with model input parameters and include this error in the modelling process, either as a sensitivity study using the range of possible parameter values (Willgoose et al. 2003). In many cases the variability surrounding input parameter data may be unknown or difficult to quantify statistically, thus providing further uncertainty in the results. Also, in the case of soil erosion and landscape evolution modelling there is further uncertainty surrounding the initial conditions of the landscape being examined (Hancock 2003, Willgoose et al. 2003). In the case of landscape evolution models using digital elevation models as the catchment or hillslope input, questions remain as to the impact of errors in the digital elevation model on the landscape evolution model outputs such as soil erosion and catchment geomorphology.

The establishment of stable geometry for the final post-mining landform at the Energy Resources of Australia Ranger Mine (ERARM) in the Northern Territory, Australia requires accurate erosion prediction for up to 1000 years through modelling (Hancock et al. 2002). The SIBERIA landscape evolution model has been used as a tool for testing rehabilitation proposals for the ERARM after the completion of approximately 30 years of mining (Willgoose and Riley 1998). While SIBERIA is able to predict the development of landscapes, few field studies have been performed to prove that the landforms predicted by SIBERIA for the waste rock dump are correct. Validation of the ability of SIBERIA to predict over a range of time scales and landscapes required by ERARMs statutory obligation (i.e. up to 1000 years) is necessary.

This study examines the impact of digital elevation model error on soil loss of a well understood catchment in the Northern Territory, Australia. This catchment has uniform geology, soils, vegetation and, because of its small size, climate can be assumed to be uniform. The SIBERIA erosion and landscape evolution model is used to examine soil loss in the catchment and how this compares to independently determined erosion data.

The aims of this study are

1. Examine the impact of digital elevation model error on catchment soil erosion using the SIBERIA landscape evolution model to simulate catchment soil erosion.
2. Develop and test a probabilistic method for the evaluation of catchment erosion using an understanding of digital elevation model error.

Study site

Tin Camp Creek is a natural site undisturbed by Europeans in Arnhem Land, Northern Territory, Australia (Figure 1). This site is important as Tin Camp Creek is one of the few sites worldwide where the European management regime has not changed in recent history (the site has not been significantly impacted by European settlement), so the historical hydrology and erosion processes that shaped the landform can be reasonably assumed to be that of today, subject to the caveat of long-term climate fluctuations. There has been no intense grazing or other agricultural practices within the area as a result of European settlement. The catchment has a geology very similar to the Energy Resources Australia Ranger uranium mine (ERARM) and is thought to be an analogue for the long-term rehabilitated post-mining landscape and has therefore undergone extensive examination in recent years (Moliere et al. 2002; Hancock et al. 2002; Hancock 2003, 2004; Willgoose et al. 2003) (Figure 1).

Figure 1. Location of the Tin Camp Creek study site(left) and the Tin Camp Creek catchment (right).

The site is located in the seasonally wet/dry tropical environment of northern Australia, with an annual rainfall of 1389 mm, mostly falling in the wet season months from October to April. Short, high intensity storms are common, consequently fluvial erosion is the primary erosion process. The area is presently tectonically inactive (Needham 1988). Tin Camp Creek is part of the Ararat Land System (Story et al. 1976) and developed in the late Cainozoic by the retreat of the Arnhem Land escarpment, resulting in a landscape dissected by active gully erosion. In this study a smaller geologically uniform 50 hectare catchment was selected for study (Figure 1). This catchment is representative of many others in the area and is of sufficient size to be a useful study site. The catchment consists of closely dissected short, steep slopes 10-100m long and gradients generally between 15-50%. The soils are red loamy earths and shallow gravelly loams with some micaceous silty yellow earths and minor solodic soils on alluvial flats (Riley and Williams 1991). The native vegetation is open dry-sclerophyll forests and, although composed of a mixture of species, is dominated by Eucalyptus and Acacia species (Story et al. 1976). Melaleuca spp. and Pandanus spiralus are also found in the low-lying riparian areas with an understorey dominated by Heteropogon contortus and Sorghum sp. There is vigorous growth of annual grasses during the early stages of the wet season. These grasses often fall over during the wet season, providing a thick mulch which causes high reductions in erosion rates of bare soil.

The SIBERIA erosion model

SIBERIA is a physically based mathematical model that simulates the geomorphic evolution of landforms subjected to fluvial and diffusive erosion and mass transport processes. SIBERIA links widely accepted hydrology and erosion models under the action of runoff and erosion over long-time scales. SIBERIA is an important tool in the understanding of the interactions between geomorphology and erosion and hydrologic process because of its ability to explore the sensitivity of a system to changes in physical conditions, without many of the difficulties of identification and generalisation associated with the heterogeneity encountered in field studies. The sediment transport equation of SIBERIA is

qs = qsf + qsd

(1)

where q_s (m₃/s/m width) is the sediment transport rate per unit width, q_sf is the fluvial sediment transport term and q_sd is the diffusive transport term (both m₃/s/m width).

The fluvial sediment transport term (q_sf), based on the Einstein-Brown equation, models incision of the land surface and can be expressed as:

(2)

where q is the discharge per unit width (m₃/s/m width), S (metre/metre) the slope in the steepest downslope direction and β₁, m₁ and n₁ are calibrated parameters. The diffusive term, q_sd, is

qsd = DS

(3)

where D (m₃/s/m width) is diffusivity and S is slope. The diffusive term models smoothing of the land surface and combines the effects of creep, rainsplash and landsliding.

SIBERIA does not directly model runoff (Q, m₃ - for the area draining through a point) but uses a sub-grid effective parameterisation based on empirical observations and justified by theoretical analysis which conceptually relates discharge to area (A) draining through a point as

(4)

where β₃ is the runoff rate constant and m₃ is the non-dimensional exponent of area, both of which require calibration for the particular field site.

For long-term elevation changes it is convenient to model the average effect of the above processes with time. Accordingly, individual events are not normally modelled but rather the average effect of many aggregated events over time. Consequently, SIBERIA describes how the catchment is expected to look, on average, at any given time. The sophistication of SIBERIA lies in its use of digital terrain maps for the determination of drainage areas and geomorphology and also its ability to efficiently adjust the landform with time in response to the erosion that occurs on it. The SIBERIA erosion model has recently been tested and evaluated for erosion assessment of post-mining landforms (Evans and Willgoose 2000; Evans et al. 1999, 2000; Hancock and Willgoose 2004; Hancock et al. 2000, 2002; Willgoose and Riley 1998). A more detailed description of SIBERIA can be found in Willgoose et al. (1991).

Calibration of SIBERIA input parameters

Before SIBERIA can be used to simulate soil erosion and resultant landscape development, the sediment transport equation (Equation 1) and area-discharge relationship (Equation 4) require independent calibration.

The fluvial sediment transport equation (Equation 2) in SIBERIA is parameterised using input from field sediment transport and hydrology data. This parameterisation process is described in detail by Evans et al. (1998) and Hancock et al. (2000). For this study the SIBERIA model was calibrated from field data collected at Tin Camp Creek from a series of natural rainfall events. The calibration of SIBERIA for Tin Camp Creek is described in detail elsewhere (Moliere et al. 2002).

Two sub-catchments within the Tin Camp Creek catchment of size 2032m² and 2947m² with average slopes of 19% and 22% respectively were instrumented during the wet season of 1990. Both sites are incised and channelised and are representative of the overall 50ha catchment. The study sites were monitored during natural rainfall events from December to January 1992. At this time the catchments had a good covering of speargrass which quickly regenerates each wet season. To calibrate the erosion and hydrology models, complete data sets of sediment loss, rainfall and runoff for nine discrete rainfall events in both catchments were collected, allowing calibration for the two individual catchments.

The rainfall-runoff monitoring data were used to parameterise the DISTFW (Field and Williams, 1983) rainfall-runoff model. The parameterised model was used to derive long-term average parameters for SIBERIA. The parameters of SIBERIA represent temporal average properties of the runoff and erosion processes occurring on the landscapes (Table 1) (Moliere et al. 2002).

Table 1. Input parameters for SIBERIA.

	Catchment 1	Catchment 2
m1	1.70	1.69
n1	0.69	0.69
β3	0.000186	0.000144
m3	0.79	0.83
β1	1067	384

Methods

A digital elevation model for Tin Camp Creek was created from digital photogrammetry of the area. Further digital elevation models of the catchment were created by incorporating error into each coordinate. This process is discussed below.

Tin Camp Creek digital elevation model

A high quality digital elevation model of the area exists and has been used extensively in past studies (Hancock et al. 2002; Hancock 2003, 2004; Willgoose et al. 2003). The digital elevation model was created using digital photogrammetry by AIRESEARCH Pty Ltd, Darwin, and was supplied as 240 000 irregularly spaced data points within an irregularly shaped boundary. To place this data onto a regular grid, Delaunay triangulation (Sloan 1987) was used to interpolate the landscape elevation data on to a 10 m by 10 m grid, producing a data set of approximately 82 000 points. This spacing was equivalent to the average spacing of the original AIRESEARCH data over the study catchment. All pits were removed from the digital elevation model using the Tarboton et al. (1989) method.

Creation of multiple digital elevation models

As with all coordinate systems there is an error associated with coordinate component. In this case the error associated with each point is uniformly distributed with a maximum value of ±0.5m in the x and y and ±0.5m in elevation (personal communication, AIRESEARCH Pty Ltd). Using this information a random number generator (Vetterling et al. 1985) was used to create random numbers matching that of the error in the digital elevation model (±0.5m) and was then added to each x, y and z component of the digital elevation model. As done for the original digital elevation model, the data was gridded by Delaunay triangulation on to a 10 m by 10 m grid and all pits removed from the digital elevation model using the Tarboton et al. (1989) method. As the study catchment (Figure 1) was located well within the boundaries of the digital elevation model data this allowed the catchment boundaries to be defined according to the digital elevation model data. Using this process ten individual digital elevation models or catchment realisations were created in this way, each representing a valid realisation of the catchment. This provides eleven individual digital elevation models including the original data.

Results

The catchment realisations of Tin Camp Creek were examined for their geomorphological properties. The digital elevation models were then input into SIBERIA and catchment geomorphology together with soil erosion examined after a simulation period of 1000 years.

Initial catchment realisations

An examination of catchment area shows that there is some small difference between the catchment realisations with catchment area ranging from 5057 to 5115 pixels. Comparison of the area-slope relationship (Flint 1974), cumulative area distribution (Perera and Willgoose 1998) and hypsometric curve (Strahler 1964) also demonstrate that there is little difference between different catchment realisations. There is some subtle difference in Strahler networking statistics (Strahler 1964) and also the width function (Naden 1992). This is likely to be the result of differences in flow paths from the different surface roughness of each realization and the difference in catchment size and shape. Nevertheless, network convergence (which is the average number of channels draining to a point) is nearly identical for all realizations, indicating little difference in the networking properties of the catchments. The stability of the hypsometric integral (and area-slope data) demonstrates that the area-elevation properties of the catchments are very similar. This data suggests that the eleven catchment realizations have strong geomorphological and hydrological similarity yet have subtly different networking properties as a result of the small differences in catchment size and shape together with different surface roughness.

SIBERIA simulations

The SIBERIA erosion model was run using the calibrated erosion parameters for the catchment (Table 1). The model was run for 1000 simulation years as this is the expected minimum design life of the rehabilitated ERARM. Graphical comparison of the area-slope relationship, hypsometric curve and cumulative area distribution after 1000 years of erosion using the eleven different catchment realisations demonstrates little geomorphological differences.

Erosion in the catchment was assessed from the eleven digital elevation models after 1000 years of erosion using SIBERIA (Tables 2 and 3). After 1000 years mean maximum depth of erosion in the catchment is 3.74m (range of 3.184 to 4.53 for mean ± two standard deviations) and 3.01m (range of 2.24m to 3.65m for mean ± two standard deviations) for the two different erosion parameter data sets. In both cases erosion was concentrated in the major drainage lines. Average soil loss over the entire catchment was 3.57 t/ha/yr (range of 3.54 t/ha/yr to 3.87 t/ha/yr for mean ± two standard deviations) and 1.65 t/ha/yr (range of 1.47 t/ha/yr to 1.83 t/ha/yr for mean ± two standard deviations) for the two different erosion parameter data sets. The results demonstrate that Catchment 1 erosion parameters produce a higher rate of erosion and sediment transport than Catchment 2 parameters.

Table 2. Statistics for maximum depth (metres) of erosion for the SIBERIA simulations

	10 years	100 years	1000 years
	SIBERIA parameter set 1
Mean	0.846	1.55	3.74
Standard deviation	0.132	0.31	0.398
Range	0.38-0.846	0.90-1.94	2.64-4.02
	SIBERIA parameter set 2
Mean	0.473	1.29	3.01
Standard deviation	0.13	0.27	0.322
Range	0.23-0.738	0.905-1.67	2.16-3.25

Table 3. Average erosion statistics (t/ha/yr) for the SIBERIA simulations.

	10 years	100 years	1000 years
	SIBERIA parameter set 1
Mean	9.50	5.52	3.57
Standard deviation	0.94	0.38	0.15
Range	7.47-10.86	4.61-6.03	3.48-3.72
	SIBERIA parameter set 2
Mean	5.45	2.87	1.65
Standard deviation	0.74	0.22	0.17
Range	3.51-6.36	2.39-3.21	1.41-1.76

Discussion

The community interest in soil erosion depends largely on the extent to which soil erosion and its impacts are evident over short and long time scales. Therefore it is extremely important that improved methods for environmental risk assessment be developed and evaluated (Evans 2000). Computer models and data input into models provide one method for assessment of this risk. In the past numerical modelling has been performed with little assessment of model input variability. This study provides a method for undertaking a risk-based approach to soil erosion using easily quantifiable error as a model input and the probabilistic assessment of erosion in a catchment (Hancock 2004).

Given the importance of the impact of erosion model parameter variability on model output, little work has been done to understand and utilise this information for environmental assessment. The incorporation of error into the digital elevation model provides a method for construction of multiple catchment realisations, each of which is unique but an equally valid representation of the catchment (Hancock 2003; Willgoose et al. 2003). This provides an effective and statistically valid method of providing an assessment of the variability of geomorphic outcomes in catchments. This data can then be used as input into models that utilize landscape information providing considerably more output data than a single model run. The method provides a more rational basis for environmental decision making.

Catchment soil erosion and geomorphology

Results from SIBERIA provide an erosion risk assessment over the catchment at two different spatial scales. The results are presented as both spatially averaged data over the catchment and also as point based values of maximum depth of incision. Average erosion in the catchment ranges from 1.47 to 1.83 t/ha/yr and 3.24 to 3.87 t/ha/yr (for mean ±two standard deviations) and maximum depth of erosion ranges from 2.24 to 3.65m and 3.18 to 4.53m (for mean ±two standard deviations) for simulations using the two erosion parameter data sets. Both data sets are statistically significantly different from each other for the 1000 year simulation. As both data sets have been determined for subcatchments within the overall catchment, both are equally likely parameter data sets to be relied upon to provide a range of expected erosion values.

Despite an average maximum and mean erosion depth in the catchment of 4.02m and 3.74m respectively, there is little change in geomorphological descriptors such as the hypsometric curve, cumulative area distribution and area-slope relationship, indicating that the catchment has not had any major change in area-elevation properties over the 1000 year modelling period. This suggests that any significant geomorphological change occurs at time periods greater than 1000 years, given that the future climate is similar in the future to that from which the model was calibrated. An increase or decrease in rainfall amount and or intensity will change the erosion process and rate of erosion. This is an area where future climate modelling can be coupled to this probabilistic approach to further assess environmental risk.

Gross erosion from the site, under the prevailing vegetation conditions of the time, were taken as being representative of the vegetated site which had not been burnt when parameter values were collected. How sediment output changes as vegetation continues to grow through the wet season has not been quantified but it is very likely that sediment output would be reduced. Consequently, sediment loss is likely to be considerable higher if there is a complete absence of vegetation. Fire generally removes all understorey vegetation (Evans et al. 1999) and results in an exposed surface, vulnerable to the highly erosive rains of the North Australian wet season. Gross erosion under non-vegetated conditions has been shown to be approximately 70 percent greater than under vegetated conditions at Nabarlek, a site close to Tin Camp Creek (Hancock et al. 2004). Also Evans et al. (1999) has found sediment loss increased by 50 percent once a site at ERA Ranger mine was burnt.

Under natural conditions following a fire, understorey vegetation increases with most species providing some protection from erosion by the end of the wet season. This increase in the protection afforded by vegetation growth is an extremely complex system due to the varying growth rates of a diversity of plant species and natural variations in climate. Modelling this situation is beyond the scope of this study. Nevertheless, it is very likely that erosion rates predicted by SIBERIA in this study are less than the long-term average.

Rates of erosion predicted by SIBERIA in this study have been validated by use of the caesium-137 method for soil erosion assessment (Hancock et al. 2004). Caesium provides an integrative measure of erosion and deposition in a catchment that has occurred of an approximately fifty year period. This study showed that soil loss in the catchment ranged from 2.9 to 14.1 t/ha/yr. Consequently, the soil erosion values obtained for the SIBERIA simulations compare very favourably to this independently determined soil loss data.

Application to landscape rehabilitation

While it is extremely unlikely that the study catchment will ever be disturbed by mining activities its geological similarity to the ERARM makes it a useful study catchment to examine long-term geomorphic properties of the rehabilitated mine. Results demonstrate that if a catchment such as this was reconstructed post-mining to represent the original landscape then it could be expected that the landscape could be incised within the range of 2.16m to 4.02m (Table 2). Consequently, if radioactive tailings or potentially acid forming materials were located at depths less than 4.02m then there is a chance that this material may be exposed. Therefore, if this was a rehabilitation design, a management strategy could be configured to manage this risk.

In this catchment only error that accompanies the derivation of the digital elevation model is incorporated but in the assessment of reconstructed landscapes such as those in post-mining landscapes other error, such as that expected from the vertical settling of fresh material and construction error (i.e. the inability of a dozer driver to construct a landscape to a pre-defined level or design contours), can also be incorporated.

This probabilistic approach provides a methodology for the design of landscapes, especially where buried materials may pose a threat if exposed. An approach such as this can be used to evaluate tailings dams, waste rock dumps and other at-risk landscapes and provides a framework for investigating soil erosion and methods for assessing control techniques (Loch et al. 2000; Hancock and Willgoose 2004; Hancock 2004). The probabilistic assessment approach can be taken one step further in that a Monte Carlo approach can be applied using the known variability in the SIBERIA model parameters. This requires that parameters are randomly selected within their feasible range to simulate a landform history. Another set of random parameters and inputs are selected and another landform history simulated. Each landform history is a realisation of the random inputs and each landform realisation varies randomly because of the such inputs. In this study two available data sets have been used and provide a sensitivity study of maximum and minimum likely outcomes as there is insufficient data to reliably determine probability field for the SIBERIA erosion parameter data.

Conclusion

There is a need for a methodology to probabilistically assess risk both in the undisturbed environment and also in catchments heavily disturbed by humans. Methods are needed that can provide robust results using available and reliable model input data. Computer models and data input into models provide one method for assessment of this risk. The incorporation of error into the digital elevation model provides a method for construction of multiple catchment realisations, each of which is unique but an equivalent of all others. This provides an effective and statistically valid method of providing an error assessment of the variability of geomorphic outcomes in catchments. This data can then be reliably used as input into models that utilize landscape information providing considerably more data than a single model run.

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