Modelling and testing spatially distributed sediment budgets to relate erosion processes to sediment yields

Environmental Modelling & Software 24 (2009) 489–501

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Environmental Modelling & Software journal homepage: www.elsevier.com/locate/envsoft

Modelling and testing spatially distributed sediment budgets to relate erosion processes to sediment yields Scott N. Wilkinson a, b, *, Ian P. Prosser c, Paul Rustomji d, Arthur M. Read d a

CSIRO Land and Water, Private Mail Bag, Aitkenvale, QLD 4814, Australia eWater Cooperative Research Centre, University of Canberra, ACT 2601, Australia c CSIRO Water for a Healthy Country Research Flagship, Black Mountain, ACT 2601, Australia d CSIRO Land and Water, GPO Box 1666, Black Mountain, ACT 2601, Australia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 August 2007 Received in revised form 12 September 2008 Accepted 16 September 2008 Available online 20 November 2008

Identifying the erosion processes contributing to increased basin fine sediment yield is important for reducing downstream impacts on aquatic ecosystems. However, erosion rates are spatially variable, and much eroded sediment is stored within river basins and not delivered downstream. A spatially distributed sediment budget model is described that assesses the primary sources (hillslope soil erosion, gully and riverbank erosion) and sinks (floodplain and reservoir deposition) of fine sediment for each link in a river network. The model performance is evaluated in a 17,000-km2 basin in south-east Australia using measured suspended sediment yields from eight catchments within the basin, each 100–700 km2 in area. Spatial variations within the basin in yield and area-specific yield were reliably predicted. Observed yields and area-specific yields varied by 17-fold and 15-fold respectively between the catchments, while predictions were generally within a factor of 2 of observations. Model efficiency at predicting variations in area-specific yield was good outside forested areas (0.58), and performance was weakly sensitive to parameter values. Yields from forested areas were under-predicted, and reducing the predicted influence of riparian vegetation on bank erosion improved model performance in those areas. The model provided more accurate and higher resolution predictions than catchment area interpolation of measured yields from neighbouring river basins. The model is suitable for guiding the targeting of remediation measures within river basins to reduce downstream sediment yields. Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved.

Keywords: Sediment budget Sediment yield Spatial modelling Erosion Planning Decision making

1. Introduction Erosion remediation programs to reduce yields of fine sediment are often managed at river basin scales (103–106 km2). This scale of approach is essential because upstream pollution sources can cause impacts hundreds of kilometres downstream (Shuyler et al., 1995). The limited funds typically available relative to the scale of the problems (White et al., 1999) mean that remediation must be effectively targeted (Bohn and Kershner, 2002). Such targeting requires river basin assessments of the spatial patterns of erosion and transport of fine sediment. Historically there has been a paucity of such assessments. Much of the fine sediment delivered to streams is deposited in riverbeds, on floodplains, and in reservoirs and so does not contribute to downstream reaches or to basin export (e.g., Dunne et al., 1998; Trimble and Crosson, 2000). Therefore, understanding the linkages between upstream sources

* Corresponding author. CSIRO Land and Water, Private Mail Bag, Aitkenvale, QLD 4814, Australia. Tel.: þ7 47538538; fax: þ7 47538600. E-mail address: [email protected] (S.N. Wilkinson).

and downstream impacts requires assessment of sediment storage as well as sources. Fine sediment is here defined as clay and silt material that moves predominantly in suspension; in contrast with coarser sand and gravel which predominantly moves close to the river bed and dominates bed material. The techniques employed for basin scale assessments of suspended sediment flux are between those for global and hillslope scale assessments. Global scale assessments of sediment delivery to oceans are used in the construction of global carbon budgets (e.g., Lal, 2003). Global approaches are generally empirical; basin area, total relief and lithology are typically the most important explanatory variables, and climatic (mean precipitation and temperature) and anthropogenic (deforestation and dams) variables are of somewhat lesser importance (Syvitski and Milliman, 2007). The focus of modelling at plot to hillslope scales is to simulate the erosion processes and controlling factors at fine spatial and temporal scales (e.g., Flanagan and Nearing, 1995). River basin assessments of erosion and sediment flux need to incorporate the primary controlling variables that control sediment transport over large areas. Measuring erosion and suspended sediment flux can be useful for identifying downstream trends in

1364-8152/$ – see front matter Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.envsoft.2008.09.006

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sediment yield (Singer and Dunne, 2001); but cost usually limits the spatial resolution and so measurements are generally insufficient for identifying source areas. Sediment tracer techniques can help to identify source areas and erosion processes (Walling et al., 2002), but are limited by the ability to define unique sediment ‘‘fingerprints’’ and by the cost of sample collection and analysis. In addition, short-term sediment sampling may not reflect long-term patterns of supply. Spatial modelling has potential for assessing patterns in sediment sources and yield at basin scale. Models can be based upon interpolation or synthesis of measurements, or upon physical reasoning of the environmental factors that control erosion and transport processes. Typically, a combination is used (De Roo, 1996), where process models provide spatial interpolation between measurement points and help to identify the upstream sources of sediment. Numerous spatial models of suspended sediment flux have been developed (Merritt et al., 2003; de Vente and Poesen, 2005). However, many are up-scaled physically based hillslope process models which simulate single events or have input data requirements that preclude their application to whole river basins or continents. Models which are more empirical usually have fewer parameters, but may require calibration to measured hillslope sediment yields; for example the WATEM/SEDEM model (Van Rompaey et al., 2001). In-depth treatment of surface erosion but exclusion of channel erosion and transport is common in catchment sediment models (de Vente and Poesen, 2005) despite channel erosion often being an important source of sediment at basin scale (e.g., Wallbrink et al., 1998; Walling, 2005). In many models runoff and sediment transport capacity play strong roles in the prediction of sediment yield, contrasting with indications from measured loads and concentrations that in the long-term yield is limited by sediment supply to river networks (Olive and Walker, 1982; Williams, 1989). A sediment budget is an appropriate framework for river basin assessments of sediment sources, transport and sinks. Lumped sediment budgets are widely used in geomorphology, but spatially distributed assessment is less common. A distributed sediment budget can be synthesised from field measurements such as geomorphic studies and recorded changes in human activity (e.g., Wasson et al., 1998; Curtis et al., 2005), but this approach is not predictive outside the areas studied. Spatially distributed sediment budgets have been used to investigate temporal changes in river channel stores of bed material in steep mountain catchments prone to landslides (Benda and Dunne, 1997). Prosser et al. (2001b) reviewed the basin scale understanding of sediment transport processes, and proposed a modelling framework to represent spatial variations in the variables controlling sediment generation and transport, that can be applied over large river basins. The framework was subsequently developed as the SedNet model (Sediment river Network model) (Prosser et al., 2001a; Wilkinson et al., 2004), which simulates the primary erosion and deposition processes and routes sediment through river networks using spatially distributed data on terrain, soils, runoff, vegetation cover, floodplains and impoundments. Sediment supply from hillslope, gully and riverbank erosion is included, and these are the important sources in rural Australian basins (Wallbrink et al., 1998; Prosser et al., 2001b), and elsewhere (Walling, 2005). This model has been applied in tropical (McKergow et al., 2005) and semi-arid temperate environments (DeRose et al., 2004; Lu et al., 2004). The bed material budget of SedNet is described and evaluated by Wilkinson et al. (2006a). Testing model performance against measurements is critical to evaluate model accuracy, and to challenge and improve the process representations. The SedNet model has been used for targeting management actions to reduce basin suspended sediment yield and for this application it is important to evaluate not only the predicted basin yield but also the spatial patterns of fine sediment generation

and deposition within the basin (Takken et al., 1999). Data on erosion and deposition rates across river basins are rarely available; hence the modelling imperative. However, suspended sediment yields that are independent of SedNet model algorithms can be estimated at multiple locations within a basin from routine water quality monitoring data. Such data can be used to estimate total model uncertainty arising from parameters, input data and model structure. Previous testing of SedNet against such yield estimates focussed on large catchments, and indicate that errors in predicted yield are higher for catchments smaller than 3000 km2 (DeRose et al., 2004; McKergow et al., 2005). Further evaluation of model yield predictions over smaller areas 100–1000 km2 is required to evaluate the predicted spatial variations at that scale. The only previous test of SedNet at the 100–1000 km2 scale is in a predominantly forested river basin (Rustomji et al., 2008). An alternative would be to use fallout radionuclides to estimate reservoir sedimentation rates and thus spatial variations in sediment yield (e.g., Wasson et al., 1987). Radionuclide sediment tracers can also be used to identify the contributions of surface and sub-surface sources to river sediment (e.g., Wallbrink et al., 1998). However, applying sediment tracing at multiple sites across large river basins is costly. This paper describes the algorithms and geomorphic basis of the suspended sediment budget of the SedNet model, including model developments since Prosser et al. (2001a). Model parameterisation is demonstrated in the 17,000 km2 Goulburn–Broken River basin in south-east Australia. The predicted spatial variations in suspended sediment sources and transport are evaluated using independent sediment yields estimated from water quality sampling for eight small catchments and one downstream station within the basin. Model performance is compared with catchment area interpolations of observed yields, and sensitivity to parameter values is assessed. 2. The Goulburn–Broken River basin The Goulburn–Broken River basin is in the south of the MurrayDarling basin and drains northwards to the Murray River (Fig. 1). The Goulburn and Broken Rivers drain separately to the Murray River but are interconnected by an anastomosing channel during large runoff events. Mean annual rainfall exceeds 1700 mm/year in the mountains in the south and decreases to 600 mm/year on the riverine plain to the north. The main land uses by area are national park and native forestry in the south (30% of area), dryland grazing in the middle of the basin (52%) and irrigated horticulture and dairy grazing in the north (9%). Following vegetation clearance in all but the steepest and highest-altitude areas by European settlers in 1850–1900, a phase of gully network extension and tributary incision occurred which is now stabilising in most areas (Erskine et al., 1993). The spatial and temporal heterogeneities of the hydrology and land use make the basin an ideal test of the capacity of the model to predict spatial patterns in sediment sources and yield. Current management activities are directed at improving water quality and riparian condition (GBCMA, 2004). 3. Model description 3.1. The river network A separate suspended sediment budget is constructed for each link in a river network. The river network is derived using GIS routines from a pit-free Digital Elevation Model (DEM). Each link extends between tributary junctions and has a sub-catchment that drains directly to it. The upstream extent of the river network begins at a specified threshold catchment area selected to limit the number of links modelled across large catchments. First-order links shorter than 1 km are pruned from the network, because the

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

491

A USTRALIA

405204

Broke

n

r ve Ri

Goulburn-Broken River basin 404207

River Network Gauge stations

Goulburn Weir

404206 Reservoirs Forest

Eildon Reservoir GoulburnRiv

405214

er

405231

405209

405219

405205 405264 0

15

30

60 km

Fig. 1. The Goulburn–Broken River basin showing shaded elevation, the modelled river network, reservoirs and numbered river gauging stations. Inset shows the basin location.

associated small sub-catchments can produce noisy results due to input data resolution. In the Goulburn–Broken River basin a 20 m resolution DEM was used, generated by the ANUDEM routine (Hutchinson, 1989) from 10 m air-photo-derived contour lines. A river network threshold area of 20 km2 was applied. The modelled river network has a total length of 4768 km, divided into 826 links of length 1–12 km and sub-catchment areas of 1–100 km2.

3.2. The river link sediment budget The sediment sources to each link are sheet-wash and rill erosion on sub-catchment hillslopes Hx, gully erosion in the subcatchment Gx, riverbank erosion along the link Bx and yield from upstream tributaries Tx. The sinks are deposition on floodplains Fx, and in reservoir impoundments Rx (Fig. 2) (Prosser et al., 2001a). The processes of land-sliding, debris flow, and hillslope soil creep (e.g., Benda and Dunne, 1997) are typically not significant sediment sources in Australia, although they could be added for model application elsewhere. The yield at the downstream end of the link Yx, is the sum of local and tributary supply less deposition along the link (Equation (1)):

suspended sediment within the river network is neglected because the net change in river network stores over decades will be small relative to total yield. The residence time of suspended sediment within river basins ranges from months up to 5–20 years (Wallbrink et al., 2002; Matisoff et al., 2005) and typically all suspended sediment supplied to the river network is either exported or deposited on floodplains or in reservoirs within this time. The upper threshold particle size used to define suspended sediment may vary between applications, and a threshold of 63 mm was applied in the Goulburn–Broken River basin. Model parameterisation in the Goulburn–Broken River basin is described at the end of each section below. 3.3. Hillslope erosion and delivery The SedNet model predicts soil erosion on hillslopes using the Revised Universal Soil Loss Equation (RUSLE) (Renard et al., 1997), given by: Hillslope erosion (t/y)

Gully erosion (t/y)

Riverbank erosion (t/y)

HSDR

Yx ¼ Hx þ Gx þ Bx þ Tx  Fx  Rx

(1)

Each budget term is predicted for each link using parsimonious algorithms that represent the process and empirical knowledge of the primary environmental controls, including land management practices. The link budgets represent mean annual behaviour (tonnes per year) by integrating the effects of hydrological variability on each source and sink over several decades, so that the effects of historical, current or future land management scenarios can be compared. Transient storage and re-entrainment of

Tributary supply (t/y) Downstream yield (t/y) Floodplain deposition (t/y)

Reservoir deposition (t/y)

Fig. 2. Sources and sinks represented in the river link suspended sediment budget. HSDR is Hillslope Sediment Delivery Ratio. Units are tonnes per year.

492

E ¼ R:K:L:S:C:P

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

(2)

Where E is erosion in tonnes per hectare per year, and the right hand side are empirical factors representing rainfall erosivity (R), soil erodability (K), slope length and gradient (L.S), vegetation cover (C) and management practices (P) such as tillage practises. GIS modelling is used to predict continuous surfaces of each factor in the equation. The RUSLE distils soil erosion into a set of measurable primary environmental controls that can be estimated over river basins. Physics-based soil erosion models are more complex; however, their data requirements commonly exceed data availability over river basins, particularly for the long periods of interest for planning. Also, the process understanding encapsulated by physics-based models has not generally been demonstrated to match measurements across large landscapes (e.g., Renschler and Harbor, 2002). However, the empiricism of the RUSLE limits its extrapolation into land uses not included in the measured sites. The proportion of hillslope sediment delivered to the river network is represented through a hillslope sediment delivery ratio (HSDR). Observed sediment yields from small catchments are often about an order of magnitude lower than erosion rates on hillslope plots (Edwards, 1993; Wasson, 1994; Slattery et al., 2002), implying that most sediment travels only a short distance on hillslopes (Parsons and Stromberg, 1998) and is deposited before leaving the hillslope. The HSDR is arguably the least well constrained parameter the in application of the RUSLE to each sub-catchment’s sediment budget. Hillslope deposition varies with terrain, soil permeability and vegetation cover (Bonell and Williams, 1987; Prosser and Williams, 1998; Croke et al., 1999). Farm dams, contour banks and other farming practices can also trap sediment. The local influences on deposition make it difficult to predict spatial variations in HSDR across river basins. Empirical models of HSDR are generally based on data of only local extent (Khanbilvardi and Rogowski, 1984). A large-scale assessment of the HSDR in Australia examined the influence of runoff travel times on deposition (Lu et al., 2003a, 2005); however, better representation of soil permeability is required before routine application. The SEDEM/ WATEM model predicts the spatial variation in HSDR by calibrating a sediment transport capacity parameter to measured hillslope sediment yields (Verstraeten et al., 2007). However such data were not available for the Goulburn–Broken River basin. In the Goulburn–Broken River basin the RUSLE formulations for vegetation cover and soil erodability were modified to suit Australian conditions (Lu et al., 2003b). The interaction of seasonal variations in rainfall erosivity and vegetation cover was represented by calculating mean-monthly cover factors using a timeseries of satellite imagery (Lu et al., 2003c) and incorporating the mean-monthly distribution of rainfall erosivity (Lu and Yu, 2002; Lu et al., 2003b). The support practice factor was omitted due to lack of data. The HSDR was set at 0.1 to match measurements of hillslope yields derived from farm dam deposits (Prosser et al., 2001a). This value also results in hillslope erosion being predicted as a minor source relative to gully and riverbank erosion, which agrees with the results of radionuclide tracer studies of river sediment in south-east Australia (e.g., Wallbrink et al., 1998). 3.4. Gully erosion Gully erosion represents incision and extension of drainage lines upstream of the modelled river network defined using the area threshold mentioned above. Following European settlement the extent of gully erosion in parts of south-east Australia greatly expanded (Wasson et al., 1998; Rutherfurd, 2000; Olley and Wasson, 2003). The long-term average sediment yield from gullies is the volume of gully erosion in each sub-catchment divided by the

length of time over which they have developed. The contemporary mean annual sediment supply from gully erosion within each subcatchment Gx in tonnes per year is:

Gx ¼

rs aps f T

lx

(3)

where lx is the length of gully in the sub-catchment; rs is the dry bulk density of sediment; a is the mean cross-sectional area of a gully; ps is the proportion of gully material that contributes to suspended sediment and T is the age of the gullies. f is a factor that is used to account for temporal variations in gully suspended sediment yield relative to the average since gullying commenced. In south-east Australia the main phase of gully extension is largely complete (Wasson et al., 1998; Zierholz et al., 2001; Olley and Wasson, 2003; Rustomji and Pietsch, 2007); and so contemporary gully suspended sediment yields are represented by f < 1. In the Goulburn–Broken River basin lx was calculated from gully mapping conducted in the 1960s (Ford et al., 1993). Available soil texture data suggest a relatively even contribution to suspended and bed material sediment from gully and bank erosion (e.g., Dietrich and Dunne, 1978; Rustomji, 2006), so ps is set to 0.5 for both sources. Studies of gully morphology indicated uniform values a ¼ 10 m2, rs ¼ 1:5 tonnes=m3 , and T ¼ 100 years, on the basis that spatial variation in these parameters is second order in comparison to spatial variation in gully density (Prosser et al., 2001a). The contemporary-yield factor f was set at 0.25 based on a study showing that total catchment sediment yield from a gullied catchment in south-east Australia has approximately halved in recent decades (Olley and Wasson, 2003); suggesting a 75% decline in gully erosion, with hillslope and bank erosion continuing at similar rates.

3.5. Riverbank erosion Spatial variation in the rate of riverbank erosion is predicted using three primary controls. Firstly, stream power is used as a hydraulic predictor of channel widening or meandering, and is calculated for each link as rgQbf Sx where r is the density of water, g is acceleration due to gravity, Qbf is bankfull discharge (ML/d) and Sx is the river bed slope. Secondly, the presence of intact riparian vegetation reduces bank erosion in undisturbed areas such as national parks. Thirdly, bank erosion rates in bedrock areas, without soil adjacent to the channel, are negligible in old Australian landscapes, although this may not be the case in younger mountainous landscapes (e.g., Finlayson and Montgomery, 2003). The process understanding and data regarding spatial variations in bank erosion are more limited than for other sediment sources and so the predictions are less well constrained. However, the three primary controls provide a better prediction than assuming that bank erosion is spatially uniform (Wilkinson et al., 2006a). Relating bank erosion rates to stream power is supported by comparison against measured rates (Rutherfurd, 2000), and stream power predicts more realistic spatial patterns across river basins than does bankfull discharge alone (DeRose et al., 2005). Following degradation or removal of riparian vegetation and drainage works, valleyfloor streams in south-east Australia have widened extensively (Rutherfurd, 2000). Erosion rates in vegetated reaches have been measured at 17% of those in reaches where riparian vegetation had been damaged by livestock (Micheli and Kirchner, 2002). Here we assume riparian vegetation reduces bank erosion rates to 10% of what would occur without vegetation, because riparian vegetation can be expected to have a greater effect on bank stability in small streams that make up the majority of the river network. Other processes such as clear-water scour downstream of dams and wave erosion may be important elsewhere (Rutherfurd, 2000) but are not

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

represented. Variations in bank soil erosion resistance within nonbedrock areas may also occur but are difficult to parameterise given the poor accuracy of available spatial predictions of subsoil texture (Rustomji, 2006). The average bank erosion rate for each link (m/year) is predicted by multiplying stream power by an erodability factor ðEi Þ, which represents the combined effects of riparian vegetation and bank erodability, and by a coefficient which is adjusted so that the predicted bank erosion rates agree with available estimates. The sediment supply from bank erosion Bx (tonnes/year) is then the product of bank erosion rate, link length (Lx), bank height (h), sediment bulk density ðrs Þ and the proportion of fine sediment (ps) in bank material (Equation 4):

Bx ¼ 0:00004rgQbf Sx Ei ðLx hrs ps Þ

(4)

where 0.00004 is the coefficient applied to give bank erosion predictions in line with observations in the Goulburn–Broken River basin (see Sediment budget results) and stream power is as given above. Ei is the mean erodability of the i pixels in the riparian area, where Ei ¼ 1 for pixels with soil and degraded riparian vegetation, Ei ¼ 0.1 for pixels with soil and intact riparian vegetation, and Ei ¼ 0 for pixels with bedrock rather than soil. rs and ps are as defined for gully erosion. Equation 4 updates the previous SedNet bank erosion model (Wilkinson et al., 2006a), by accounting for spatial correlation along the riparian zone between riparian vegetation and erodable soil. In the Goulburn–Broken River basin Sx was estimated from the DEM stream node elevations. The riparian zone was defined using GIS routines as 40 m buffer strips either side of the channel margins; the channel margins being defined by a channel width regionalisation against upstream catchment area. Riparian vegetation extent was represented by the Tree Density 1:25,000 data set derived from SPOT Panchromatic satellite imagery (Department of Sustainability and Environment, 2006a). The extent of erodable soil was defined using the Multi-resolution Valley Bottom Flatness (MrVBF) terrain index which identifies flatter, low-lying areas of the landscape associated with depositional soil (Gallant and Dowling, 2003); a threshold index of 1.5 was used to separate soil (>1.5) from bedrock. 3.6. Floodplain deposition Comparisons of catchment erosion rates with river sediment loads show that in large catchments a substantial proportion of the transported sediment load is deposited on floodplains (Walling and Webb, 1983; Dunne et al., 1998). The amount of sediment deposited on a floodplain is represented in SedNet as a function of three controls (Prosser et al., 2001b); the amount of sediment supplied to a river link, the proportion of the sediment load delivered overbank to the floodplain and the proportion of the overbank sediment that settles on the floodplain. The proportion of sediment that settles on the floodplain increases exponentially with residence time, assuming that no re-entrainment of sediment occurs (Dabney et al., 1995; Prosser et al., 2001b). The proportion of sediment delivered to the floodplain is assumed to be equal to the proportion of discharge delivered to the floodplain, Qf/Q where floodplain discharge Qf is the amount by which total discharge Q exceeds bankfull discharge Qbf. Floodplain deposition Dx (tonnes per event) is thus given by Equation 5:

Qf  Dx ¼ ðIx Þ 1  e Q

 ! nAf Qf

(5)

where Ix is total suspended sediment supply to the link, Af is floodplain area and n is the particle settling velocity.

493

Mean annual deposition is determined by integrating Equation 5 over the discharge record. Considering event magnitude and frequency, sediment concentration and the exponential effect of settling time, the median value of daily overbank discharges is used to represent mean annual deposition. Thus, Qf/Q is replaced with Qmo/ (Qmo þ Qbf), where Qmo is the median overbank discharge (ML/d). The floodplain model predicts total deposition on the floodplain of each river link; the location of deposition will often be biased towards channel levees or meander point bars within the floodplain. In the Goulburn–Broken River basin, floodplain extent was defined using MrVBF > 1.5 as for bank erosion. The settling velocity (106 m/s) was based on Stokes Law, which translates to a particle diameter of 1–4 mm; this is at the lower end of expected suspended sediment particle sizes, and so all larger particles can be expected to settle within this floodplain residence time. 3.7. Reservoir deposition Large reservoirs are very effective sediment stores. The proportion of supplied sediment load that is trapped by a reservoir is calculated by an update (Heinemann, 1981) of the empirical Brune rule (Brune, 1953) which uses a residence time approach to express sediment trap efficiency as a function of the storage volume of the reservoir and the mean annual input discharge. The trap efficiency is applied to the total (suspended plus bed material) load to determine the proportion of suspended sediment trapped, assuming that all bed material is trapped. The capacities and predicted trap efficiencies of reservoirs in the Goulburn–Broken River basin are listed in Table 1. 3.8. Hydrological regionalisation The erosion and deposition algorithms require estimates of several river discharge statistics for each river link. The reservoirtrapping rule requires mean annual discharge (Qma); the bank erosion algorithm requires bankfull discharge (Qbf) and floodplain deposition requires median overbank discharge (Qmo). Each of these statistics represents the integrated effects of discharge variability on the process, as an alternative to running the sediment model at daily time-steps (Prosser et al., 2001b; Wilkinson et al., 2006a). To calculate each statistic for every river link, they are first calculated at river gauging stations within the basin that have longterm records of daily discharge. The discharge statistics are then extrapolated or ‘‘regionalised’’ to un-gauged river links using regression models based on catchment area, rainfall and potential evapotranspiration. Mean annual discharge is predicted using a physically based regionalisation of mean annual runoff coefficient, which is based on potential evaporation and rainfall as described in Wilkinson et al. (2006b). Compared with total runoff, the physical basis for regionalising the flood peaks Qbf and Qmo is weaker and some variation in approach between river basins may be justified; here they are regionalised as ratios by dividing by mean daily discharge (Qmd; ML/d). The Qbf/Qmd and Qmo/Qmd ratios Table 1 Reservoirs in the Goulburn–Broken River basin, and predicted suspended sediment trap efficiencies. Reservoir

Capacity (GL)

Catchment area (km2)

Trap efficiency (%)

Lake Eildon Waranga Basin Lake Mokoan Lake Nillahcootie Lake Cooper, Green Lake & Horse Shoe Lake Goulburn Weir and Lake Nagambie

3390 411 365 40 33 25

3900 130 300 410 430 10,500

95 95 95 92 94 29

494

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

are measures of flow variability. They are regionalised against upstream catchment area (A; km2) and upstream mean annual precipitation (P; mm/year) using multiple linear regressions of the following form:

log



Qbf Qmd



¼ k þ m logðAÞ þ n logðPÞ

(6)

  0 Qbf 0 Qma 365:25 Qmd

4.2. Evaluation metrics A discrepancy ratio dr is defined to evaluate predicted suspended sediment yield at each gauge; equivalent to the maximum ratio of o/p or p/o where o and p are the observed and predicted yields, and given by: dr ¼ 10jlogðpÞlogðoÞj

Then Qbf for each link is calculated as: 0 Qbf ¼

Goulburn–Broken River basin, and to a regression to observed yields from southeast Australian uplands, compiled by Wasson (1994).

(7)

where apostrophes denote regionalised quantities. This somewhat indirect approach to regionalising Qbf and Qmo reduces the degree of extrapolation required to first-order and downstream links, which are often poorly represented by river gauging stations. Also, the approach is better in hydrologically diverse basins than regionalising against Qma alone (e.g., Surian and Andrews, 1999) because floods comprise a smaller proportion of total runoff in wet catchments; i.e., for a given Qma, links draining wetter areas will have smaller Qbf/Qmd than do links that drain larger but drier catchments. Thirdly, the effect of flow regulation and diversion can be accounted 0 to match the locally observed discharge. for by adjusting Qma Fourthly, the effect of different regulation patterns could be examined by modifying the ratios in regulated reaches if required. Topographic metrics such as mean elevation, catchment relief and channel slope were not necessary for the relatively small recurrence interval floods used to represent Qbf (Surian and Andrews, 1999). In the Goulburn–Broken River basin, 27 river gauging stations with daily records of median length 24 years and ending in the year 2000 were used to fit the regionalisations. A further 12 gauging 0 to account for diversions from the stations were used to adjust Qma reservoirs listed in Table 1. Bankfull discharge was represented by the 2.5-year recurrence interval discharge on the annual maximum series, which is appropriate for rivers in south-east Australia (Stewardson et al., 2005). The regionalisations can be applied to discharge data in any consistent units, although the bank erosion coefficient quoted for the Goulburn–Broken River basin assumes that bankfull discharge is in ML/d. 4. Evaluation methods 4.1. Sediment yield estimation In the Goulburn–Broken River basin, the predicted spatial variation in suspended sediment yield (t/year) was evaluated using suspended sediment yields independently estimated from water quality monitoring data (‘‘observed yields’’) for eight small catchments 100–700 km2 in drainage area and one downstream station (16,000 km2). The predicted variation in area-specific yield (t/km2/year) between the catchments was also evaluated. Total suspended solids (TSS) concentrations have been monitored at river gauging stations in the Goulburn–Broken River basin at fortnightly intervals since 1990 (Department of Sustainability and Environment, 2006b). At nine stations which had sufficient event data, concentrations from 1990 to 2006 were modelled using a modified rating curve technique (Rustomji and Wilkinson, 2008). The method used the ‘re-sampling of residuals’ bootstrap method (Davison and Hinkley, 1997) to fit multiple rating curves, each of which were combined with instantaneous discharge records to calculate annual suspended sediment yields. The distribution of the annual yields represented the uncertainties in the rating curve shape and the residual scatter in measured concentrations. Monte Carlo re-sampling techniques were then applied to the distribution of annual yields to estimate a representative mean annual yield and a 95% bootstrap percentile confidence interval. The lengths of the discharge records were 30–48 years, which are sufficient to represent the variability of hydrologic conditions in recent decades. The sensitivity of model performance to parameter values was evaluated by running the model with selected parameters varied by 30%, one at a time. For each erosion process, one parameter was selected to which the erosion prediction was directly proportional. Two additional parameter variations were trialled to investigate model performance issues (see Section 7). The model performance was also compared to a catchment area regression to the estimated yields in the

(8)

A ratio of 1 indicates perfect agreement and dr is always greater than or equal to 1. dr ¼ 1.2 means that the prediction is within approximately 20% of the observation and dr ¼ 2 means that the prediction is within a factor of 2 of the observation (either higher or lower). The ratio scales over-predictions and under-predictions evenly; making it more meaningful than relative error, which becomes biased when the error magnitudes are large relative to the observations. A standard error ratio sr is defined, which describes the mean square error across the set of nine river stations as: sr ¼ 10

ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 1 n

i¼1

½logðpi Þlogðoi Þ

(9)

where oi and pi represent observed and predicted yields for the ith river station and n is the number of stations. This measure is a ratio, interpreted in the same way as dr. Expressing the residuals in log units provides equal weighting of the residuals between small magnitude observations, and large magnitude observations that can be expected to have larger magnitude residuals. While sr is an overall measure of model error it does not relate that error to the amount of variation between the observations. The efficiency at predicting the variation between the observations is evaluated using a coefficient of model efficiency (E*) defined by Nash and Sutcliffe (1970). As for sr, the residuals are expressed in log units: Pn ½logðpi Þ  logðoi Þ2 E* ¼ 1  Pin¼ 1 2 i ¼ 1 ½logðoi Þ  logðoÞ

(10)

where oi, pi and n are as defined previously. E* ¼ 1 represents perfect prediction and E* ¼ zero means that the model performance is equivalent to predicting the mean observation everywhere.

5. Sediment budget results The predicted suspended sediment budget aggregated over the Goulburn–Broken River basin is given in Table 2. Riverbank erosion is predicted to be the largest suspended sediment source, with hillslope erosion and gully erosion predicted to be smaller sources. Only 27% of the total suspended sediment supplied to the river network is predicted to be exported from the basin outlet. Floodplain deposition within the river basin is predicted to be concentrated along the trunks of the Goulburn and Broken Rivers and it accounts for 49% of total suspended sediment supply. The median predicted floodplain deposition rate was 5 mm per 100 years. Reservoir deposition is predicted to trap 24% of the total sediment supply, mainly in the Eildon Reservoir and Goulburn Weir. The small export relative to net erosion is typical of Australian river basins, with their relatively low slopes and abundant opportunity for storage (Olive and Rieger, 1986). Each sediment source has a different spatial pattern because of the different environmental controls represented. Hillslope erosion (Fig. 3a) is predicted to be highest across the middle and east of the basin, covering foothill areas where slopes are moderate, but excluding the steep forest areas south-east of Lake Eildon (terrain Table 2 Suspended sediment sources and losses in the SedNet budget, totalled across the Goulburn–Broken River basin. Sediment inputs

kt/year

Sediment outputs

kt/year

Suspended sediment from hillslopes Suspended sediment from gullies Suspended sediment from riverbanks

110

Floodplain suspended deposition

160

75

Reservoir suspended deposition

78

143

Export suspended sediment

90

328

Total outputs

Total inputs

328

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

495

Fig. 3. Model predictions in the Goulburn–Broken River basin for (a) Specific suspended sediment supply from hillslope erosion to the river network (t/km2/year), (b) specific suspended sediment supply from gully erosion (t/km2/year), (c) riverbank erosion rate (cm/year), (d) link specific suspended sediment yield over the upstream catchment (t/km2/year). Reservoirs are shown in blue. The river gauging stations used in model evaluation are black points.

and forest extent shown in Fig. 1). Gully erosion (Fig. 3b) is highest in the eastern and western extremities, moderate across the middle foothills and zero in southern forest areas. Bank erosion (Fig. 3c) is predicted to be highest along the Goulburn and upper Broken Rivers, and steeper, wetter tributary streams outside forest areas. The sediment load at each river gauging station is predicted to be dominated by different sources (Table 3); hillslope erosion dominates at stations 404,207 and 405,205, and bank erosion dominates

for the five stations numbered 405,209 and above. Gully erosion is predicted to be a relatively minor contributor of suspended sediment to all stations. The applied bank erosion coefficient appears reasonable given the available data. Contemporary bank erosion rates along the Goulburn River are estimated to be generally 5–7 cm/year, up to 50 cm/year on a few active bends (Erskine et al., 1993). This compares well with the mean predicted bank erosion rate along the

Table 3 Observed suspended sediment yields estimated using the method of (Rustomji and Wilkinson, 2008) compared with the predicted suspended sediment yield and discrepancy ratio, and the predicted proportions of suspended sediment yield from each sediment source at each river station. Station

Location

Area (km2)

404,206

Broken River at Moorngag

497

404,207

Holland Ck at Kelfeera

451

405,204

Goulburn River at Shepparton

405,205

Murrindindi River above Colwells

16,125 108

405,209

Acheron River at Taggerty

619

405,214

Delatite River at Tonga Bridge

368

405,219

Goulburn River at Doherty’s

694

405,231

King Parrot Ck at Flowerdale

181

405,264

Big River D/S of Frenchman Ck Jn.

333

Observed yield with 95% confidence bounds (t/year)

(t/km2/year)

893þ62 57 4660þ936 452 66; 490þ2296 2592 557þ15 15 3863þ107 117 9459þ10;230 2902 3908þ510 367 603þ192 66 1604þ67 77

1:80þ0:13 0:11 10:3þ2:1 1:0 4:12þ0:14 0:16 5:15þ0:14 0:14 6:24þ0:17 0:19 25:7þ27:8 7:9 5:63þ0:73 0:53 3:33þ1:06 0:37 4:82þ0:20 0:23

Predicted yield (t/year)

Discrepancy ratio

Prop. Hill.

Prop. Gully

Prop. Bank

(t/km2/year)

1957

3.97

2.19

0.44

0.16

0.40

5059

11.03

1.09

0.55

0.05

0.41

102,900

6.44

1.55

0.35

0.20

0.45

188

1.75

2.96

0.68

0.00

0.32

6650

10.69

1.72

0.33

0.00

0.66

3650

10.51

2.59

0.30

0.19

0.51

2440

3.49

1.60

0.47

0.00

0.53

549

3.01

1.10

0.31

0.12

0.57

437

1.31

3.67

0.46

0.00

0.54

496

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

middle Goulburn River between Eildon Reservoir and Goulburn Weir of 7.4 cm/year, and along the lower Goulburn River of 6.2 cm/ year. A separate bank erosion estimate made by digitally comparing 1935 and 1985 channel surveys indicates a higher bank erosion rate of 19  16 cm/year (DeRose et al., 2005). However, digital registration of the survey data caused the large uncertainty and also biased this method towards over-estimation. The predicted specific sediment yield (SSY; t/km2/y) of each link indicates the net effect of upstream supply and deposition. SSY is variable between river links, but is generally highest for links across the middle of the basin where all three erosion rates are high (Fig. 3d). Plotting the predicted SSY against catchment area also indicates the detailed spatial variation (Fig. 4). Below 1000 km2, the high variability in predicted SSY can be attributed to variability in predicted erosion rates in first-order sub-catchments. The decline in maximum SSY up to 3000 km2 can be attributed largely to averaging of sediment supply between river links as catchment area increases. The drop in SSY at 4000 km2 is associated with sediment deposition in Lake Eildon. Links with catchment areas 4000–10,000 km2 are along the Goulburn River downstream of Lake Eildon. The downstream increase in SSY predicted in this reach is a consequence of high erosion rates in local sub-catchments (Fig. 3), which outweigh local losses to floodplain deposition. This foothills area has non-forest land uses (mainly grazing) and moderate slopes (Fig. 1). Above 10,000 km2, the decline in SSY indicates that predicted sediment supply along the Lower Goulburn River is smaller than predicted losses to floodplain deposition. 6. Model evaluation results The yields predicted by the model and estimated using the rating curve method are listed in Table 3. The discrepancy ratios dr at each station range between 1.09 and 3.67. The standard error ratio for predicted suspended sediment yields sr is 2.13 for both total and specific yield, meaning that predicted yields are on average within a factor of approximately 2 of the observed yields. The predicted suspended sediment yields are plotted against the observed yields in Fig. 5(a) and specific yields in Fig. 5(b). Model yield predictions are not significantly biased, with mean error being 0.1  0.1 log units. Fig. 5(c) suggests that the maximum discrepancy ratio may be smaller for larger catchment areas. There is no apparent trend in the discrepancy ratio with specific sediment yield

(Fig. 5d), indicating that low erosion rate predictions are not less certain than high erosion rate predictions. The model efficiency E* for total yield is 0.84, which indicates good performance at predicting spatial variation. Model efficiency for specific yield is 0.04, which is poor; caused by under-prediction of sediment yield from forest areas. For the three stations that have catchments more than 90% forested (405,205, 405,219 and 405,264), the predicted yields are a factor of 1.6–3.6 below the observed yields (Table 3). Over the 6 non-forested catchments having predominantly grazing land use, model performance is better with sr ¼ 1.79, and E* is 0.94 for total yield and 0.58 for specific yield. The hydrologic regionalisations can be excluded as sources of systematic error in predicted sediment yield. Student t-tests indicate that there is 70–90% chance that the slope of regressions between the residuals in yield and in each regionalisation statistic are random rather than significant. The observed and predicted suspended sediment yields show a similar increase with catchment area (Fig. 6a). The gradient of the increase represents the balance between upstream sediment supply and deposition. A linear regression between the predicted yields and catchment area (for links of area above 100 km2) has a gradient of 1.04. A linear regression to the observed yields shows a slightly more gradual increase with catchment area (gradient of 0.94), but the difference in gradients is far from significant at p ¼ 0.05. The intersection of the observed and predicted regression lines reflects the negligible model bias. The regressions between the observed and predicted yields from the Goulburn–Broken River basin are compared with a spatially broader data set of sediment yields collated by Wasson (1994) for the south-east uplands of Australia, of which the Goulburn–Broken River basin is a part (Fig. 6b). A linear regression fitted to the Wasson (1994) data set (again for catchments larger than 100 km2) sits higher than the regressions to the Goulburn–Broken River basin observed and predicted yields for the entire range of catchment areas by at least 0.4 log units or a factor of 2.5, and the difference is significant at p ¼ 0.05. While the gradient (1.12) is higher than either the observed or predicted gradients for the Goulburn–Broken River basin, the differences in gradient are again insignificant. The model performance at predicting total yield is weakly sensitive to variations in individual erosion predictions; with E* changing by 0.03 or less for 30% changes in hillslope and bank erosion, and remaining unchanged for 30% changes in gully erosion

Specific Suspended Sediment Yield t / km2 / y

35

30

25

20

15

10

5

0 0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

Upstream Catchment Area km2 Fig. 4. Predicted specific sediment yield (SSY) plotted against upstream catchment area.

18,000

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

106

102

a

Predicted yield (t/y)

Predicted specific yield (t/ km2/ yr)

b

105

405204

104 405209 404207 405214 405219 404206

103 405231 405264

101

405209

405214

404206 405219 405231

405205 405264

102

100 102

103

104

105

106

100

101

102

Observed specific yield (t/km2/yr)

Observed yield (t/y) 6

6

c

d 5

Discrepancy ratio

5

Discrepancy ratio

404207

405204

405205

4 405264

3

497

405205 405214 404206

2

4 405264

3

405205 405214 404206

2

405209 405219 405231

405209 405219 405204

405204

405231

404207

1

404207

1 102

103

104

105

Catchment Area (km2)

100

101

102

Observed specific yield (t/km2/y)

Fig. 5. (a) Observed versus predicted mean annual suspended sediment yields; (b) Observed versus predicted mean annual specific yields; (c) Discrepancy ratios between observed and predicted yield plotted against upstream catchment area, and also as a boxplot; (d) Discrepancy ratios between observed and predicted yield plotted against observed specific sediment yield, and also as a boxplot. The bars through the points show the 95% confidence interval on the observed yields.

(Table 4). Model errors sr changed by 7% or less from the baseline run. Specific yield predictions are sensitive to parameter values, with E* changing by up to 0.19 for 30% changes in hillslope and bank erosion. Increases in erosion generally improved performance. An area regression to the Goulburn–Broken observed yields provided slightly better performance than the baseline SedNet run over the catchments used to develop the regression, but performed poorly over non-forest catchments only (Table 4); indicating weak predictive capacity once the set of yields was changed from that used to fit the regression. The area regression to the data of Wasson (1994) provided considerably poorer performance. 7. Discussion Three aspects of the study are discussed; the estimates of model performance and model uncertainty are compared with previous tests of SedNet and other models; the effectiveness of the test method is compared with other methods; and model limitations and areas for improvement are explored. The results demonstrate that spatially distributed suspended sediment budget modelling is capable of predicting spatial

variations in sediment yield and area-specific yield between catchments of several-hundred km2 in area, and so it can be used for prioritising remediation measures at that scale, especially in non-forest areas. The uncertainty in predicted sediment yield and area-specific yield for the evaluation catchments (median area ¼ 450 km2) was approximately 2-fold (sr ¼ 2.13 overall, and sr ¼ 1.79 outside forest areas), which is a small fraction of the 17fold and 15-fold variations in observed yield and specific yield, respectively, between the evaluation catchments. Predicted total yield was weakly sensitive to parameter values. For a given set of inputs, model uncertainty is smaller over larger catchment areas. The range in environmental gradients tends to be larger over larger catchments and the predicted spatial patterns are most robust when environmental gradients are large relative to the uncertainties in data inputs and process representations. A previous comparison between SedNet and independent yield estimates (DeRose et al., 2004) obtained sr ¼ 1.91 with yield estimates from catchments of median area ¼ 9000 km2. The present study achieved similar performance over much smaller catchment areas by using higher resolution DEM, land use and riparian vegetation data (25 m versus 250 m), and more stream flow records.

498

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

Log(Suspended Sediment Yield t/y)

7

a

6 y=1.04x + 0.63 5 y=0.94x + 0.91 4

3

2 Goulburn−Broken observed yields and linear model Goulburn−Broken predicted link yields and linear model

1

0 1

2

3

4

5

Log(Catchment Area km2) 7

Log(Suspended Sediment Yield t/y)

b 6 y=1.12x + 0.94 5

4

3 Goulburn−Broken observed yields linear model Goulburn−Broken predicted link yields linear model Wasson (1994) observed yields, and linear model with 95% conf. bounds

2

1

0 1

2

3

Log(Catchment Area

4

5

km2)

Fig. 6. (a) Suspended sediment yields in the Goulburn–Broken River basin observed at gauging stations (solid circles, solid line, lower equation), and predicted by the SedNet model (open triangles, dashed line, upper equation). (b) Linear regressions to the observed and predicted suspended sediment yields from the Goulburn–Broken River basin, compared with the observed yields from catchments across the southern uplands of Australia (Wasson, 1994); only those above 100 km2 in area are shown. The linear regression to the Wasson (1994) data is shown by the long dashed line with dotted 95% confidence bounds.

Table 4 Sensitivity of model performance to parameter values; NF indicates performance for the non-forest gauges and spec. indicates performance for specific suspended sediment yield. Model run

HSDR

Gully fact. f

Bank coefficient

b

E*

E* NF

E* spec.

E* spec. NF

sr

sr NF

Baseline run Hillslope þ30% Hillslope 30% Gully þ30% Gully 30% Bank þ30% Bank 30% a Steep Hillslope þ100% b Veg Bank þ100% c Goulburn regression d SE Uplands regression

0.1 0.13 0.07 0.1 0.1 0.1 0.1 0.2 0.1 – –

0.25 0.25 0.25 0.325 0.175 0.25 0.25 0.25 0.25 – –

0.00004 0.00004 0.00004 0.00004 0.00004 0.000052 0.000028 0.00004 0.00004 – –

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 – –

0.84 0.86 0.81 0.84 0.84 0.85 0.81 0.83 0.88 0.86 0.44

0.94 0.93 0.94 0.94 0.93 0.93 0.94 0.95 0.93 0.86 0.58

0.04 0.14 0.15 0.04 0.03 0.10 0.12 0.03 0.31 0.16 2.32

0.58 0.53 0.61 0.59 0.57 0.52 0.60 0.64 0.57 0.09 1.73

2.13 2.04 2.28 2.12 2.13 2.07 2.26 2.18 1.89 2.03 4.06

1.79 1.86 1.75 1.78 1.80 1.87 1.77 1.71 1.80 2.36 4.43

a b c d

Veg. Bank Ei

HSDR was increased to 0.2 where hillslope gradient was steeper than 20 . The rate of bank erosion on vegetated banks compared with non-vegetated banks Ei. Regression to the observed yields in the Goulburn–Broken River catchment (Fig. 6a). Regression to yields across the south-east Uplands of Australia, compiled by Wasson (1994) (Fig. 6b).

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501

For three reasons, spatial modelling is a more appropriate method to assess spatial variations in sediment yield within river basins than generic rules based on catchment area (e.g., Lawler, 1992). Firstly, the dominance of different erosion processes causes different downstream variations in sediment yield (Birkinshaw and Bathurst, 2006), and the present study demonstrates that spatial variations in floodplain and reservoir deposition are also important controls on sediment yield. Secondly, spatial variations within each sediment source cause considerable variation in specific suspended sediment yield across river basins, and such variations are specific to each river basin (e.g., Fig. 3). Thirdly, spatial models can predict differences in sediment yield between river basins caused by different environmental or land management factors, which relationships with catchment area cannot. Consequently, the sediment budget model provided significantly better yield predictions in the Goulburn–Broken River basin than a catchment area-based regression to yield observations across the south-east Australian uplands (Fig. 6b; Table 4). Predicting yields in the Goulburn–Broken River basin as high as that regression would require unrealistic parameterisation of SedNet (e.g., bank and gully erosion rates, and HSDR double those observed). The poorer performance of the catchment area regression can be partly attributed to some of the Wasson (1994) yields including bed material; and the inclusion of longer-duration sediment yield proxies such as reservoir sedimentation, which covered wetter periods and a large forest fire in 1939. Although the model evaluation used sediment yield data, it also indicates that the spatial variations of each sediment source are reasonably predicted, which is important for prioritising and simulating land management changes. There are limited opportunities for floodplain deposition in the small evaluation catchments, and so the observed yields are representative of total sediment supply and erosion intensity. Further, individual evaluation catchments were dominated by different sediment sources. Between the catchments, there was a 9-fold variation in specific supply from hillslope and bank erosion (product of the predicted specific yield by the proportion of sediment supply from each source; Table 3), which is several times larger than the factor of 2 uncertainty in specific sediment yield and so these variations are reasonably predicted. The predicted spatial patterns of gully erosion are constrained by the mapped gully extent (Ford et al., 1993). Also, the basin-wide dominance of subsoil erosion from gullies and riverbanks (Table 2) is consistent with sediment tracer and geomorphic studies in other gullied river basins in south-east Australia (Wallbrink et al., 1998; Wasson et al., 1998). As for any model, the major limitations are the process understanding and data availability. The results indicate that the model under-predicts sediment yield in steep forest areas, and a similar result was obtained in the Sydney catchment (Rustomji et al., 2008). Two hypotheses are proposed to explain this error; (a) HSDR may be greater than 0.1 on steep slopes, which are much more prevalent in forested areas, and (b) the effectiveness of riparian vegetation at reducing bank erosion rates may be over-predicted. These hypotheses were investigated by running the model (a) with HSDR ¼ 0.2 for the 23% of the basin with slopes steeper than 20 (0.1 elsewhere), and (b) with Ei ¼ 0.2 (vegetated bank erodability; increased from 0.1). The effect of (a) was to improve performance slightly in non-forest areas, but not overall. For (b), performance did not improve outside forest areas but improved considerably overall, with E* for specific suspended sediment yield being 0.31 overall (Table 4). Potential explanations for riparian vegetation being less effective than expected at reducing bank erosion in forested areas of the Goulburn–Broken River basin are (i) propagation of river bed incision from non-vegetated areas downstream (Rutherfurd, 2000); (ii) channel depth exceeding the rooting depth of riparian vegetation, and (iii) historical alluvial gold mining (Erskine et al., 1993). Further research is required on the spatial variations in bank erosion and the effect of riparian

499

vegetation. Sediment tracers that can ‘‘fingerprint’’ erosion processes (e.g., Wallbrink et al., 1998; Walling et al., 2002; Douglas et al., 2003) are likely to be useful in helping to improve local process understanding. For application elsewhere, the model also requires some knowledge of the decadal-scale history of gully enlargement and stabilisation to set the contemporary suspended sediment yield parameter in the gully erosion model. Testing against independent sediment yield data has advantages over statistical methods to estimate model uncertainty such as Monte Carlo simulation or sensitivity analysis. Using independent yield data assesses total model uncertainty from all sources, including model structure, input data sets and model parameters, while Monte Carlo simulation cannot generally assess uncertainty from model structure. Also, the accuracy of Monte Carlo uncertainty estimates depends on the ability to define parameter distributions and parameter interactions. Model sensitivity analysis can identify important data sets, but does not assess the uncertainty in those data sets. While SedNet is sensitive to hydrological regionalisation parameters (Newham et al., 2003; Fentie et al., 2005); those parameters have relatively low uncertainty when they are fitted to a comprehensive stream flow data set (Wilkinson et al., 2006b), and can be expected to make small contributions to model uncertainty at the scale of the present model evaluation. Model predictions are also sensitive to some erosion and deposition parameters (Newham et al., 2003; Fentie et al., 2005); and some such parameters have larger uncertainty; such as the hillslope sediment delivery ratio, the gully contemporary-yield parameter, the bank erosion coefficient, and the effect of riparian vegetation on bank erosion. The lumping of sediment budgets over sub-catchments in SedNet reduces the sensitivity to input data resolution, however model uncertainty is still affected by the accuracy and resolution of input data. For example, the vertical accuracy of the DEM affects slope and bank erosion estimates for individual links, particularly in lowgradient reaches. Predicted bank erosion rates were therefore compared with average measured rates over river distances long enough to have several times the elevation change of the 10 m contours from which the DEM was generated. The bank erosion coefficient corrects for any systematic bias in slope prediction (see e.g., Finlayson and Montgomery, 2003). Provided care is taken in model parameterisation as described in the Model Description, the test results can be regarded as applicable to other river basins in south-east Australia, at least. Several other SedNet studies using input data sets of comparable resolution reported similar levels of uncertainty in predicted yields (Wilkinson, 2008). The predictive capacity of the model is assisted by each parameter having a physical interpretation, and the estimated uncertainty in predicted yields is only weakly sensitive to parameter values. Also, parameter uncertainty affects the predicted relative spatial variations to a lesser degree than absolute sediment yields, and it is the relative spatial patterns which are of interest for targeting erosion control measures within river basins. The approach of spatially distributed sediment budgets is also applicable to other environments, provided that sufficient process understanding and data are available. Different process representations would be required in snow-covered, terraced or landslip-prone mountain environments, or in arid zones. The effect of severe forest fire was also not represented in the Goulburn–Broken River basin; since no such event occurred during the modelling period. More complex water quality models may be calibrated to provide smaller errors in predicted yields (e.g., Lumb et al., 1994), but in the absence of well-tested more sophisticated approaches, pragmatic models of erosion and sediment yield are useful. Increasing model complexity only improves model predictions if the input data provides more information than noise. The ‘‘flip-side’’ can be reduced confidence in parameter values, and in the predictive capacity of the model to identify spatial patterns in sources (e.g., Grayson et al., 1992).

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8. Conclusions This paper has demonstrated the SedNet river network model of suspended sediment sources and deposition processes, which uses readily available spatial data to predict spatial patterns in suspended sediment sources and transport. It is concluded that the model can correctly predict spatial variations in suspended sediment yield across river basins, with a spatial resolution of 100– 1000 km2. The uncertainty in predicted suspended sediment yield is a factor of 2 at that scale, decreasing over larger areas, but variations in yield were 17-fold across the river basin; several times larger than model uncertainty. Model yield predictions were more accurate and with a finer spatial resolution than catchment area interpolations of sediment yield from other river basins. The model identifies the dominant sources, and enables simulation of management scenarios. The model can thus be used for targeting field investigation and rehabilitation activities to where they will be most effective in reducing basin suspended sediment yield. Model performance was poorer in forest areas. Improved understanding of spatial controls on erosion would improve accuracy; particularly hillslope sediment delivery, and the effect of riparian vegetation on bank erosion. Acknowledgements This study was supported by Land & Water Australia and eWater CRC. Paul Rustomji’s contribution was supported by the Water for a Healthy Country Research Flagship. Yun Chen (CSIRO) assisted with model setup. Peter Hairsine, Tim Ellis and David McJannet (CSIRO), and two anonymous reviewers, provided constructive comments on the manuscript. References Benda, L., Dunne, T., 1997. Stochastic forcing of sediment routing and storage in channel networks. Water Resources Research 33 (12), 2865–2880. Birkinshaw, S.J., Bathurst, J.C., 2006. Model study of the relationship between sediment yield and river basin area. Earth Surface Processes and Landforms 31 (6), 750–761, doi:10.1002/esp.1291. Bohn, B.A., Kershner, J.L., 2002. Establishing aquatic restoration priorities using a watershed approach. Journal of Environmental Management 64, 355–363, doi:10.1006/jema.2001.0496. Bonell, M., Williams, J., 1987. Infiltration and redistribution of overland flow and sediment on a low relief landscape of semi-arid, tropical Queensland. In: Swanson, R.H., Bernier, P.Y., Woodard, P.D. (Eds.), Forest Hydrology and Watershed Management. IAHS Publication, 167. IAHS Press, pp. 199–211. Brune, G.M., 1953. Trap efficiency of reservoirs. Transactions. American Geophysical Union 34, 407–418. Croke, J., Hairsine, P., Fogarty, P., 1999. Sediment transport, redistribution and storage on logged forest hillslopes in south-eastern Australia. Hydrological Processes 13, 2705–2720. Curtis, J.A., Flint, L.E., Alpers, C.N., Yarnell, S.M., 2005. Conceptual model of sediment processes in the upper Yuba River watershed, Sierra Nevada, CA. Geomorphology 68 (3–4), 149–166, doi:10.1016/j.geomorph.2004.11.019. Dabney, S.M., Meyer, L.D., Harmon, W.C., Alonso, C.V., Foster, G.R., 1995. Depositional patterns of sediment trapped by grass hedges. Transactions A.S.A.E. 38, 1719– 1729. Davison, A.C., Hinkley, D.V., 1997. Bootstrap Methods and their Application. Cambridge University Press. De Roo, A.P.J., 1996. Soil erosion assessment using G.I.S. In: Singh, V.P., Fiorentino, M. (Eds.), Geographical Information Systems in Hydrology. Kluwer Academic Publishers, Dordrecht/Boston/London. Department of Sustainability and Environment, 2006a. Tree Density 1:25,000– Vicmap Vegetation dataset. Victorian Spatial Data Directory Available from: www.land.vic.gov.au/vsdd. Department of Sustainability and Environment, 2006b. Victorian Water Resources Data Warehouse Available from: www.dse.vic.gov.au/waterdata/ (accessed October 2006). DeRose, R., Prosser, I.P., Weisse, M., 2004. Patterns of erosion and sediment transport in the Murray-Darling Basin. In: Sediment Transfer through the Fluvial System. IAHS Publ., vol. 288. IAHS Press, pp. 245–252. DeRose, R.C., Wilson, D.J., Bartley, R., Wilkinson, S.N., 2005. Riverbank erosion and its importance to uncertainties in large scale sediment budgets. In: Walling, D.E., Horowitz, J.A. (Eds.), Proceedings of the International Symposium on Sediment Budgets (S1) Held During the Seventh Scientific Assembly of the

IAHS at Foz do Iguacu, Brazil, 3–9 April 2005. Sediment Budgets 1, IAHS Publ., vol. 291. IAHS Press, pp. 85–92. Dietrich, W.E., Dunne, T., 1978. Sediment budget for a small catchment in mountainous terrain. Zeitschrift fur Geomorphologie 29, 191–206. Douglas, G., Palmer, M., Caitcheon, G., 2003. The provenance of sediments in Moreton Bay, Australia: a synthesis of major, trace element and Sr–Nd–Pb isotopic geochemistry, modelling and landscape analysis. Hydrobiologia 494 (1/ 3), 145–152. Dunne, T., Mertes, L.A.K., Meade, R.H., Richey, J.E., Forsberg, B.R., 1998. Exchanges of sediment between the flood plain and channel of the Amazon River in Brazil. Geological Society of America Bulletin 110, 450–466. Edwards, K., 1993. Soil erosion and conservation in Australia. In: Pimental, D. (Ed.), World Soil Erosion and Conservation. Cambridge University Press, Cambridge, pp. 147–169. Erskine, W.D., Rutherfurd, I.D., Ladson, A.R., Tilleard, J.W., 1993. Fluvial Geomorphology of the Goulburn River Basin. Report for the Mid-Goulburn Catchment Co-ordinating Group Inc. Ian Drummond and Associates. Fentie, B., March, N., Steven, A., 2005. Sensitivity analysis of a catchment scale sediment generation and transport model. In: MODSIM 2005, International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand, pp. 1140–1146. Finlayson, D.P., Montgomery, D.R., 2003. Modeling large-scale fluvial erosion in geographic information systems. Geomorphology 53 (1–2), 147–164, doi:10.1016/S0169-555X(02)00351-3. Flanagan, D.C., Nearing, M.A., 1995. USDA Water Erosion Prediction Project: Hillslope Profile and Watershed Model Documentation, NSERL Report #10. Ford, G.W., Martin, J.J., Rengasamy, P., Boucher, S.C., Ellington, A., 1993. Soil sodicity in Victoria. Australian Geographer 13, 377–387. Gallant, J.C., Dowling, T.I., 2003. A multiresolution index of valley bottom flatness for mapping depositional areas. Water Resources Research 39 (12), 1347, doi:10.1029/2002WR001426. GBCMA, 2004. Regional River Health Strategy 2004. Goulburn Broken Catchment Management Authority, Shepparton. Grayson, R.B., Moore, I.D., McMahon, T.A., 1992. Physically based hydrologic modeling 1. A terrain-based model for investigative purposes. Water Resources Research 28 (10), 2639–2658. Heinemann, H.G., 1981. A new sediment trap efficiency curve for small reservoirs. Water Resources Bulletin 17, 825–830. Hutchinson, M.F., 1989. A new procedure for gridding elevation and stream line data with automatic removal of spurious pits. Journal of Hydrology 106, 211–232. Khanbilvardi, R.M., Rogowski, A.S., 1984. Quantitative evaluation of sediment delivery ratios. Water Resources Bulletin 20, 865–874. Lal, R., 2003. Soil erosion and the global carbon budget. Environment International 29 (4), 437–450, doi:10.1016/S0160-4120(02)00192-7. Lawler, D.M., 1992. Process dominance in bank erosion systems. In: Carling, P.A., Petts, G.E. (Eds.), Lowland Floodplain Rivers. Wiley, Chichester, New York, pp. 117–143. Lu, H., Yu, B., 2002. Spatial and seasonal distribution of rainfall erosivity in Australia. Australian Journal of Soil Research 40, 877–901, doi:10.1071/SR01117. Lu, H., Moran, C.J., Prosser, I.P., Raupach, M.R., Olley, J., Petheram, C., 2003a. Sheet and rill erosion and sediment delivery to streams: a basin wide estimation at hillslope to medium catchment scale. CSIRO Land and Water, Canberra, Technical Report 15/0355 pp. Lu, H., Prosser, I.P., Moran, C.J., Gallant, J., Priestley, G., Stevenson, J., 2003b. Predicting sheetwash and rill erosion over the Australian continent. Australian Journal of Soil Research 41, 1037–1062, doi:10.1071/SR02157. Lu, H., Raupach, M.R., McVicar, T.R., Barrett, D.J., 2003c. Decomposition of vegetation cover into woody and herbaceous components using AVHRR NDVI time series. Remote Sensing of Environment 86 (1), 1–18, doi:10.1016/S0034-4257(03)00054-3. Lu, H., Moran, C.J., Prosser, I.P., DeRose, R., 2004. Investment prioritization based on broadscale spatial budgeting to meet downstream targets for suspended sediment loads. Water Resources Research 40, doi:10.1029/2003WR002966 W09501. Lu, H., Moran, C.J., Sivapalan, M., 2005. A theoretical exploration of catchment-scale sediment delivery. Water Resources Research 41, doi:10.1029/2005WR004018 W09415. Lumb, A.M., McCammon, R.B., Kittle, J.L., Jr., 1994. Users manual for an expert system (HSPEXP) for calibration of the hydrological simulation program; Fortran. Water-Resources Investigations Report 94–4168, 102 pp. Matisoff, G., Wilson, C.G., Whiting, P.J., 2005. The 7Be/210Pbxs ratio as an indicator of suspended sediment age or fraction new sediment in suspension. Earth Surface Processes and Landforms 30 (9), 1191–1201, doi:10.1002/esp.1270. McKergow, L., Prosser, I., Hughes, A., Brodie, J., 2005. Sources of sediment to the Great Barrier Reef world heritage area. Marine Pollution Bulletin 51, 200–211, doi:10.1016/j.marpolbul.2004.11.029. Merritt, W.S., Letcher, R.A., Jakeman, A.J., 2003. A review of erosion and sediment transport models. Environmental modelling and software 18, 761–799, doi:10.1016/S1364-8152(03)00078-1. Micheli, E.R., Kirchner, J.W., 2002. Effects of wet meadow riparian vegetation on streambank erosion. 1. Remote sensing measurements of streambank migration and erodibility. Earth Surface Processes and Landforms 27 (6), 627–639, doi:10.1002/esp.338. Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I – a discussion of principles. Journal of Hydrology 10 (3), 282. Newham, L.T.H., Norton, J.P., Prosser, I.P., Croke, B.F.W., Jakeman, A.J., 2003. Sensitivity analysis for assessing the behaviour of a landscape based sediment source and transport model. Environmental modelling and software 18, 741–751.

S.N. Wilkinson et al. / Environmental Modelling & Software 24 (2009) 489–501 Olive, L.J., Rieger, W.A., 1986. Low Australian sediment yields – a question of inefficient sediment delivery. In: Drainage Basin Sediment Delivery, Proceedings of a Symposium Held During the Second Scientific Assembly of IAHS at Albuquerque. IAHS Publ., vol. 159. IAHS Press, pp. 355–364. Olive, L.J., Walker, P.H., 1982. Processes in overland flow – erosion and production of suspended material. In: O’Loughlin, E.M., Cullen, P. (Eds.), Prediction in Water Quality. Australian Academy of Science, Canberra, pp. 87–119. Olley, J.M., Wasson, R.J., 2003. Changes in the flux of sediment in the upper Murrumbidgee catchment, south eastern Australia, since European settlement. Hydrological Processes 17, 3307–3320, doi:10.1002/hyp.1388. Parsons, A.J., Stromberg, G.L.,1998. Experimental analysis of size and distance of travel of unconstrained particles in interill flow. Water Resources Research 34, 2377–2381. Prosser, I.P., Williams, L., 1998. The effect of wildfire on runoff and erosion in native Eucalyptus forest. Hydrological Processes 12 (2), 251–265. Prosser, I.P., Rustomji, P., Young, B., Moran, C., Hughes, A., 2001a. Constructing river basin sediment budgets for the National Land and Water Resources Audit. CSIRO Land and Water Technical Report 15/01, 34 pp. Prosser, I.P., Rutherfurd, I.D., Olley, J.M., Young, W.J., Wallbrink, P.J., Moran, C.J., 2001b. Large-scale patterns of erosion and sediment transport in river networks, with examples from Australia. Marine and Freshwater Research 52 (1), 81–99, doi:10.1071/MF00033. Renard, K.G., Foster, G.A., Weesies, D.K., McCool, D.K., Yoder, D.C., 1997. Predicting Soil Erosion by Water: a Guide to Conservation Planning with the Revised Universal Soil Loss Equation. In: Agriculture Handbook, vol. 703. United States Department of Agriculture, Washington, DC. Renschler, C.S., Harbor, J., 2002. Soil erosion assessment tools from point to regional scales – the role of geomorphologists in land management research and implementation. Geomorphology 47, 189–209. Rustomji, P., 2006. Analysis of gully dimensions and sediment texture from southeast Australia for catchment sediment budgeting. Catena 67 (2), 119–127, doi:10.1016/j.catena.2006.03.004. Rustomji, P., Pietsch, T., 2007. Alluvial sedimentation rates from south eastern Australia indicate post-European settlement landscape recovery. Geomorphology 90, 73–90, doi:10.1016/j.geomorph.2007.01.009. Rustomji, P., Caitcheon, G., Hairsine, P., 2008. Combining a spatial model with geochemical tracers and river station data to construct a catchment sediment budget. Water Resources Research 44 W01422 doi:10.1029/2007WR006112. Rustomji, P., Wilkinson, S.N., 2008. Applying bootstrap resampling to quantify uncertainty in fluvial suspended sediment loads estimated using rating curves. Water Resources Research, 44, W09434, doi: 10.1029/2007WR006088. Rutherfurd, I.D., 2000. Some human impacts on Australian stream channel morphology. In: Brizga, S., Finlayson, B. (Eds.), River Management: the Australasian Experience. John Wiley and Sons, England, pp. 11–49. Shuyler, L.R., Linker, L.C., Walters, C.P., 1995. The Chesapeake Bay story: the science behind the program. Water Science and Technology 31 (8), 133–139. Singer, M.B., Dunne, T., 2001. Identifying eroding and depositional reaches of valley by analysis of suspended sediment transport in the Sacramento River, California. Water Resources Research 37 (12), 3371–3381, doi:10.1029/2001WR000457. Slattery, M.C., Gares, P.A., Phillips, J.D., 2002. Slope-channel linkage and sediment delivery on North Carolina coastal plain cropland. Earth Surface Processes and Landforms 27, 1377–1387, doi:10.1002/esp.436. Stewardson, M., DeRose, R., Harman, C., 2005. Regional models of stream channel metrics. Technical Report 05/16, Cooperative Research Centre for Catchment Hydrology, Melbourne. Surian, N., Andrews, E.D., 1999. Estimation of geomorphically significant flows in alpine streams of the Rocky Mountains, Colorado (USA). Regulated Rivers: Research & Management 15 (4), 273–288. Syvitski, J.P.M., Milliman, J.D., 2007. Geology, geography, and humans battle for dominance over the delivery of fluvial sediment to the coastal ocean. Journal of Geology 115, 1–19. Takken, I., Beuselinck, L., Nachtergaele, J., Govers, G., Poesen, J., Degraer, G., 1999. Spatial evaluation of a physically based distributed erosion model (LISEM). Catena 37 (3–4), 431–447.

501

Trimble, S.W., Crosson, P., 2000. U.S. soil erosion rates – myth and reality. Science 289, 248–250. de Vente, J., Poesen, J., 2005. Predicting soil erosion and sediment yield at the basin scale: scale issues and semi-quantitative models. Earth Science Reviews 71 (1–2), 95–125, doi:10.1016/j.earscirev.2005.02.002. Van Rompaey, A.J.J., Verstraeten, G., Van Oost, K., Govers, G., Poesen, J., 2001. Modelling mean annual sediment yield using a distributed approach. Earth Surface Processes and Landforms 26, 1221–1236, doi:10.1002/esp.275. Verstraeten, G., Prosser, I.P., Fogarty, P., 2007. Predicting the spatial patterns of hillslope sediment delivery to river channels in the Murrumbidgee catchment, Australia. Journal of Hydrology 334 (3–4), 440–454, doi:10.1016/ j.jhydrol.2006.10.025. Wallbrink, P., Olley, J., Hancock, G., 2002. Estimating residence times of fine sediment in river channels using fallout 210Pb. In: The Structure, Function and Management Implications of Fluvial Sedimentary Systems, Proceedings of an International Symposium Held at Alice Springs, Australia, September 2002. IAHS Publ., vol. 276. IAHS Press, pp. 425–432. Wallbrink, P.J., Murray, A.S., Olley, J.M., Olive, L.J., 1998. Determining the sources and transit times of suspended sediment in the Murrumbidgee River, New South Wales, Australia, using fallout 137C and 210Pb. Water Resources Research 34 (4), 879–887. Walling, D.E., Webb, B.W., 1983. Patterns of sediment yield. In: Gregory, K.J. (Ed.), Background to Palaeohydrology. Wiley, pp. 69–100. Walling, D.E., Russell, M.A., Hodgkinson, R.A., Zhang, Y., 2002. Establishing sediment budgets for two small lowland agricultural catchments in the UK. Catena 47 (4), 323–353. Walling, D.E., 2005. Tracing suspended sediment sources in catchments and river systems. Science of the Total Environment 344 (1–3), 159–184, doi:10.1016/ j.scitotenv.2005.02.011. Wasson, R.J., Clark, R.L., Nanninga, P.M., 1987. 210Pb as a chronometer and tracer, Burrinjuck Reservoir, Australia. Earth Surface Processes and Landforms 12, 399– 414, doi:10.1002/esp.3290120406. Wasson, R.J., 1994. Annual and decadal variation of sediment yield in Australia, and some global comparisons. In: Variability in Stream Erosion and Sediment Transport, Proceedings of a Symposium in Canberra, December 1994. IAHS Publ., vol. 224. IAHS Press, pp. 269–279. Wasson, R.J., Mazari, R.K., Starr, B., Clifton, G., 1998. The recent history of erosion and sedimentation on the Southern Tablelands of southeastern Australia: sediment flux dominated by channel incision. Geomorphology 24, 291–308. White, L.J., Rutherfurd, I.D., Hardie, R.E., 1999. On the cost of stream management and rehabilitation in Australia. In: Second Australian Stream Management Conference, Melbourne, Cooperative Research Centre for Catchment Hydrology, Melbourne, pp. 697–704 Wilkinson, S., Henderson, A., Chen, Y., Sherman, B., 2004. SedNet User Guide, Version 2. Client Report, CSIRO Land and Water, Canberra. Available from: www.toolkit.net.au/sednet. Wilkinson, S.N., Prosser, I.P., Hughes, A.O., 2006a. Predicting the distribution of bed material accumulation using river network sediment budgets. Water Resources Research 42, doi:10.1029/2006WR004958 W10419. Wilkinson, S.N., Young, W.J., DeRose, R.C., 2006b. Regionalising mean annual flow and daily flow variability for sediment transport modelling. Hydrological Processes 20 (13), 2769–2786, doi:10.1002/hyp.6070. Wilkinson, S.N., 2008. Testing the capability of a sediment budget model to target remediation measures to reduce suspended-sediment yield. In: Sediment Dynamics in Changing Environments, Proceedings of a Symposium Held in Christchurch, New Zealand, December 2008. IAHS Publ., vol. 325. IAHS Press. Williams, G.P., 1989. Sediment concentration versus water discharge during single hydrologic events. Journal of Hydrology 111, 89–106. Zierholz, C., Prosser, I.P., Fogarty, P.J., Rustomji, P., 2001. Instream wetlands and their significance for channel filling and the catchment sediment budget, Jugiong Ck, New South Wales. Geomorphology 38, 221–235.