a conceptual model of sediment transport: application to the avon river basin in western australia

A conceptual model of sediment transport: applicationto the Avon River Basin in Western Australia

Neil R. Viney* and Murugesu SivapalanCentre for Water Research, Department of Environmental Engineering, University of Western Australia, Nedlands, WA 6907, Australia

Abstract:This paper deals with the coupling of a sediment modelling algorithm to an existing conceptual model of waterand salt ¯uxes (LASCAM). In the model, sediment generation is based on a modi®ed version of the universal

soil loss equation. The sediment transport processes of channel deposition and re-entrainment, and beddegradation are coupled with the existing stream-routing algorithm of LASCAM. The model is applied to theAvon River Basin, a large, dry catchment in Western Australia. The paper highlights some of the scienti®cissues involved in quantifying the sediment discharge processes in this catchment and presents validation results

comparing model predictions with observations of sediment transport at di�erent locations in the catchment.The results indicate that despite the strongly non-linear relationship between stream ¯ow and sediment load,both are predicted well by the model. The model also highlights that in the Avon River Basin, dispropor-

tionately more stream sediment is generated in the wheat belt region than in the lower catchment.Copyright # 1999 John Wiley & Sons, Ltd.

KEY WORDS catchment hydrology; conceptual modelling; sediment transport; erosion

INTRODUCTION

The estuary of the Swan River in Western Australia is shallow and poorly ¯ushed. These properties, coupledwith increasing nutrient transport to the estuary have led to increasingly severe algal blooms in recent years.The transport of nutrients from the catchment to the estuary is strongly linked to the transport of sediment,with a large percentage (especially phosphorus and organic nitrogen) being adsorbed to sediment particles(Donohue et al., 1994).

To investigate and propose solutions to these water quality problems the Western Australian governmenthas initiated a multidisciplinary research project to study the physical, chemical and biological structure ofthe estuary. Part of this response involves a hydrological modelling project to predict the e�ect of potentialland use remediation e�orts on the transport of water, salt, sediment and nutrients from the catchment of theAvon River, which contributes almost all the stream water to the Swan River estuary.

A large number of sediment models have been proposed in the literature, but the range of applicability ofeach is uncertain. Most have been developed to describe small-scale or event-based erosional processes(e.g. Knisel, 1980; Williams, 1980; Borah, 1989; Young et al., 1995). Models that are more widely applicablein space and time have been developed byWilliams et al. (1985) and Arnold et al. (1995), but are intended forungauged catchments (i.e. no calibration) and are therefore very data intensive. A conceptual modellingframework has been proposed recently by Jakeman et al. (1997) and is in many respects similar to the onepresented here. Their sediment model, however, has not yet been fully developed.

CCC 0885±6087/99/050727±17$17�50 Received 5 January 1998Copyright # 1999 John Wiley & Sons, Ltd. Revised 12 May 1998

Accepted 11 August 1998

HYDROLOGICAL PROCESSESHydrol. Process. 13, 727±743 (1999)

*Correspondence to: Dr N. R. Viney, Centre for Water Research, Department of Environmental Engineering, University of WesternAustralia, Nedlands, WA 6907, Australia.

None of the existing models have been developed to describe sediment processes in Western Australia.Indeed, there appears to have been very little work in Western Australia on even characterizing or measuringsediment yields in semi-arid catchments. This is despite there being considerable evidence that erosionalprocesses are important and have caused much stream channel damage and siltation in the Avon River.

In this paper, an existing water and salt balance model, LASCAM, has been adapted to include aconceptual sediment generation and transport algorithm. Predictions from the model are compared withobservations of sediment load at several locations in the Avon River catchment.

THE CATCHMENT

The Avon River basin occupies 119 000 km2 in south-western Australia (Figure 1) and is relatively ¯at anddry. Most of its annual average 400 mm of rainfall occurs during winter and exhibits a pronounced west±eastgradient (Figure 2). About 65% of the catchment has been cleared of its native dry sclerophyll woodlandvegetation; the alienated land being used for cereal production and sheep grazing (Figure 1). Much of thisland use change has involved broad-acre clearing since the 1950s, and has led to substantial increases in soilerosion.

Figure 1. Principal vegetation cover in the Avon catchment. Areas of native vegetation are white; areas of cleared land are shaded. Insetshows location of the Avon River Basin in Western Australia

Copyright # 1999 John Wiley & Sons, Ltd. HYDROLOGICAL PROCESSES, VOL. 13, 727±743 (1999)

728 N. R. VINEY AND M. SIVAPALAN

Drainage to the drier eastern and central parts of the catchment is primarily through a linked network ofephemeral playa lakes. Figure 3 shows the notional drainage network. Long-term stream ¯ow records areavailable for a number of gauging stations within the catchment, including four (Walyunga, DunbartonBridge, Northam and Broun's) on the main channel. These four have also been the sites of irregularsampling of sediment concentration which allows the construction of partially complete time-series of dailysediment loads.

THE WATER BALANCE MODEL

Basic features

LASCAM (Sivapalan et al., 1996a,b,c) was originally developed to predict the e�ects of land use andclimate change on the daily trends of water yield and quality in the forested water supply catchments of theDarling Ranges in south-west Western Australia. Its application to such catchments has been described byViney and Sivapalan (1994).

The model uses gridded topographic information to de®ne a stream network and to dissagregate thecatchment into a series of interconnected subcatchments of area 1±5 km2. The subcatchments are the basicbuilding blocks of the model. It is at the subcatchment scale that the hydrological processes are modelled,before being aggregated to yield the response of the entire catchment.

Figure 2. Isohyets of mean annual rainfall (mm) in the Avon catchment


7: SEDIMENT TRANSPORT 729

The hydrosalinity of each subcatchment is modelled in terms of three interconnected conceptual stores ofsoil water and salt (Figure 4) representing a perched near-stream aquifer (the A store), the permanentgroundwater (the B store) and an intermediate unsaturated store (the F store). For each subcatchment, a setof global constitutive relationships is used to direct water and salt transport between the stores and todistribute new rainfall either into the stores or directly into the stream. Any runo� generated by the

Figure 3. Coarse drainage network showing locations of the principal stream ¯ow gauges. The stream ¯ow gauges on the main channelare labelled: Walyunga (W), Dunbarton Bridge (D), Northam (N), Broun's (B) and Yenyenning Lakes (Y)

Figure 4. Schematic diagram of an idealized hillslope showing the three conceptual model stores and the principal modelled water¯uxes. Flux symbols are those used in Sivapalan et al. (1996a)



constitutive relationships is then routed (together with the salt it contains) along the stream network towardsthe catchment out¯ow.

The inputs to the model are daily rainfall (distributed), pan evaporation and land use information (e.g. leafarea index, which is allowed to vary with time), while topographic data are needed to de®ne the subcatch-ments and the stream network. For calibration purposes, measured stream ¯ow records are also required atone or more points in the catchment's stream network. The outputs from the model, for each subcatchmentand for the total catchment, are surface and subsurface runo�, actual evaporation, recharge to thepermanent groundwater table, base¯ow and measures of soil moisture.

Amendments for the Avon catchment

The Avon catchment includes several attributes and characteristics that are not present in any of thecatchments to which LASCAM has previously been applied. These present considerable challenges for waterbalance modelling and have led to the incorporation of several changes to the model described by Sivapalanet al. (1996a).

The most obvious di�erence is that the notional Avon basin (119 000 km2) is much larger than anycatchment modelled previously by LASCAM. It is nearly two orders of magnitude larger than the previouslargest Western Australian catchment (Collie, 2500 km2). Consequently, the `building block' subcatchmentson which the water balance modelling is based are considerably larger than those used previously. Theassumption of rainfall homogeneity over the subcatchment scale is therefore questionable. An analysis ofspatial scaling of rainfall across the Avon River catchment has demonstrated that subcatchments of the orderof 1600 km2 or less are adequate. This limit has been adopted for the wetter western half of the catchment. Asubcatchment disaggregation consisting of 134 subcatchments has been constructed. Subcatchments belowNortham have a mean area of 87 km2, those between Northam and Yenyenning Lakes have a mean area of560 km2, while the remainder have a mean area of 2300 km2. It was felt that since the easternmost sub-catchments contribute negligibly to basin stream ¯ow, there was little bene®t in their conforming to therainfall scaling limit.

The catchment size, together with its relative aridity, ensures that transmission losses are much greaterthan in catchments in the Darling Ranges for which LASCAM was originally developed. A rein®ltrationalgorithm and a more comprehensive stream evaporation algorithm have been incorporated into LASCAMto account for transmission losses. Rein®ltration is assumed to occur when a subcatchment whose soil storesare too dry to generate base¯ow receives in¯ows from subcatchments further upstream. The rein®ltratingwater is added to the near-stream perched aquifer of the receiving subcatchment and continues until theaquifer reaches its base¯ow threshold or until the in¯ow is fully depleted. The stream evaporation algorithminvolves the introduction of a new rate parameter, O, describing the proportion of the stream ¯ow that isevaporated in one day per unit of potential evaporation. Then the daily stream evaporation (ML) is

es � 0�001 Oepl�q=v�1=2 �1�

where ep is potential daily evaporation (mm), l is the length of the stream link (km), q is the daily stream ¯owvolume (ML) and v is the stream velocity (km dÿ1). Equation (1) is based on the assumption that streamwidth is proportional to (q/v)1/2, so the parameter, O, is a channel shape parameter.

A further modelling problem arose during calibration of the water balance component. It was found thatthe model overestimated stream ¯ow generation in the wheat belt region. It is thought that this over-prediction stems from the relative ¯atness of the terrain, which contrasts with the well-de®ned V-shapedvalley and hillslope topography of the Darling Ranges. In the wheat belt, where stream density is muchsmaller, a signi®cant proportion of rainfall is likely to be diverted away from the main stream channels by thelocal topography. Consequently, an upslope perching factor depending on mean annual rainfall (since



regional geomorphology is largely dependent on rainfall climate) has been incorporated into the model. Theupslope perching factor is

m � 1 ÿM1�1 ÿ R=M2�M3

where R is mean annual rainfall (mm) and M1 , M2 and M3 are calibration parameters. Parameter M2

represents the threshold mean annual rainfall below which m takes a value less than one. For subcatchmentswith R4M2 , m is set to one. The factor m now represents the proportion of the subcatchment hillslope that isavailable for surface and subsurface runo� processes; any rain falling on the proportion 1 ÿ m of thesubcatchment is assumed to percolate entirely to the F store. Consequently, the expressions for surface andsubsurface runo� in Sivapalan et al. (1996a) are adjusted accordingly. The region of upslope perching isshown schematically in Figure 4.

Rainfall inputs were generated from observed daily rainfall observations at more than 500 gaugesthroughout the catchment. For each subcatchment, only the two nearest operational rain gauges in eachquadrant about the subcatchment centroid were considered. The subcatchment daily rainfall input was thencalculated as the inverse distance-weighted average of these eight gauges.

THE SEDIMENT MODEL

The aim of this work is to construct a sediment generation and transport model that is sensitive to the majorlumped processes and controls (e.g. hillslope erosion, stream power, etc.) with not unreasonable require-ments for model input data and measured sediment concentration data.

One of the main requirements of a new LASCAM sediment model is that it should be compatible with theexisting water transport model. In particular, it must be capable of operating on a daily time-step andpreferably should not utilize any water pathway or store that is not already explicitly modelled by LASCAM.Given our incomplete understanding of sediment processes at the catchment scale and the overwhelmingnumber of unresolvable factors involved, the sediment model should remain as conceptually simple aspossible, while retaining the capacity to model the e�ects of land use changes.

Sediment modelling is a much more di�cult task than salt balance modelling, since the latter is a con-servative tracer whose observed concentration in a particular reach seldom varies by as much as an order ofmagnitude. In contrast, the rates of sediment mobilization and transport are strongly a�ected by stream ¯owvolume, and, in consequence, so is sediment concentration. Furthermore, there does not appear to be anysimple rating curve solution to the modelling of sediment concentration in the Avon River.

In the model that has been developed, sediment generation in the subcatchments is assumed to occur byerosion processes associated with surface runo�. The model that has been adopted is a conceptualization ofthe universal soil loss equation (USLE) (Wischmeier and Smith, 1978), giving daily hillslope sedimentgeneration, E (tonnes), as

E � gCqds �2�

where qs is the daily surface runo� (ML) and C is the USLE crop factor, and is assumed to be linearly relatedto leaf area index. The variables g and d are optimizable parameters. Equation (2) assumes that peakinstantaneous runo� is proportional to the daily total, qs . The remaining USLE variables are incorporatedinto the parameter g and, as a consequence, are uniform across the catchment. While this assumption ispossibly reasonable for the soil factor, it will not necessarily be true for the slope length or erosion mitigationfactors that are commonly employed in the modi®ed USLE (Williams and Berndt, 1977). These factors,however, depend on variables that are di�cult to prescribe for a large subcatchment. For instance, it isdi�cult to specify a slope length and steepness factor for a large subcatchment with perhaps hundreds of



hillslopes. The model assumes that hillslope sediment generation is not limited by raindrop detachmentprocesses.

Sediment transport involves the processes of channel deposition and re-entrainment, and bed degradation(Figure 5). The model assumes that these processes are governed by a stream sediment capacity that is afunction of stream power. The stream sediment capacity, Z (tonnes), is adapted from the SPNM model(Williams, 1980) and is given by

Z � av3=2�q=v�b=A1=2 �3�

where q is the daily stream ¯ow volume (ML), v is the stream velocity (km dÿ1),A is the catchment area (km2)and a and b are optimizable parameters. In Equation (3), it is assumed that the term q/v approximates thestream cross-sectional area and that stream depth is proportional to (q/v)1/2. Stream ¯ow of a given volume isable to carry a mass Z of sediment in suspension, provided su�cient material is available either from thehillslope, from upstream or from previously deposited channel sediment.

In such a case, sediment re-entrainment, R (tonnes), is thus given by

R � minfZ ÿ Yi ÿ E;Sg �4�

where Yi is the sediment ¯ow (t) from upstream subcatchments and S is the amount of loose sediment (t) onthe channel ¯oor available for re-entrainment. The ®rst argument in Equation (4) represents the stream'ssediment demand, while the second term represents the available sediment supply. Obviously if R is negative,part of the in¯owing sediment is deposited into S. On the other hand, if re-entrainment fully depletes thesupply, S, without satisfying the demand, Z ÿ Yi ÿ E, then the stream seeks to partially ful®l demand bybed and bank degradation. This degradation (t), which is assumed to occur at a rate governed by streampower and the USLE crop factor (Williams, 1980), is given by

B � minfeClZ;Z ÿ Yi ÿ E ÿ Rg �5�

Figure 5. Structure of the sediment transport algorithm



and is zero otherwise. In Equation (5), l is the length of the stream link (km) and e is an optimizableparameter.

Sediment in suspension within a subcatchment is subject to a delivery ratio that describes the settling ratefor sediment particles. The sediment delivery ratio c is conceptualized from Arnold et al. (1995) and is givenby

c � 1 ÿ 12X; if X 5 1

1=�2X�; if X 5 1

�where

X � zl=�qv�1=2

The delivery ratio is the proportion of suspended sediment that leaves the subcatchment within the currentday's stream ¯ow. The remainder is assumed to settle to the channel bottom where it is available for ready re-entrainment on subsequent days.

The sediment yield Y0 (tonnes) from a subcatchment is then given by

Y0 � c�Yi � E � R � B�The change in channel sediment store (t) is therefore

DS � �1 ÿ c��Yi � E � R � B� ÿ R

The LASCAM sediment model thus requires optimization of six new parameters (a, b, g, d, e and z) and alsorequires the maintenance of a channel sediment store for each subcatchment. The sediment model para-meters, like those for the water balance, apply globally. That is, the same parameter value is used in eachsubcatchment; there is no recalibration for di�erent subcatchments.

APPLICATION TO THE SWAN/AVON BASIN

For application of the LASCAM water and sediment balance models, the Avon River catchment wasdisaggregated into a network of 134 subcatchments. Long-term observations of stream ¯ow and sedimentyield were available at the catchment outlet (the Walyunga gauging station, 616011; area 119 000 km2) and atthe outlets of several internal subcatchments. Model calibration was achieved in two stages. First, the waterbalance parameters were optimized using an algorithm based on the shu�ed complex evolution approach(Duan et al., 1993) subject to an objective function that represented a weighted least-squares minimization ofstream ¯ows at several gauging stations. Secondly, the calibrated water balance model was used to optimizethe six sediment parameters against the observed sediment load record for Walyunga only. Su�cient spin-uptime was allowed for the channel sediment stores to reach equilibrium values prior to the calibration periodin order to avoid the need to specify initial storage values.

Calibration predictions for the water balance component of LASCAM are shown in Figures 6a and 11a.Clearly, the model is predicting stream ¯ow well for such a dry, ephemeral catchment. In particular, it copeswell with the atypical summer storm of early 1990. Figure 11a also indicates that recession rates are wellrepresented, but there is a tendency to underpredict the peak ¯ows.

This calibration also produced excellent agreement between predictions and observations on many of theinternal gauged subcatchments (Figures 6±9). Relative prediction quality tends to decrease as one moveseastwards across the catchment, but the easternmost gauges measure very little stream ¯ow, so the absoluteerrors (and their consequent e�ect on downstream gauges) are small. Of particular note is the observationthat LASCAM is able to predict well the substantial spatial heterogeneity of stream ¯ows, with peak monthlydischarges ranging from less than 1 mm to 75 mm.



Thus, we have considerable con®dence that the model is providing good predictions of stream ¯ow acrossmost of the catchment, and presumably (since the parameters are global) across the ungauged, as well as thegauged, subcatchments. Given this con®dence, we can now proceed with calibration of the sediment model.

Predictions of sediment yield at Walyunga are shown in Figures 10±11. Comparison of the monthly waterand sediment yields (Figure 10) indicates clearly the importance of extreme events in dominating sedimentyield. Sediment concentrations are comparably much greater in the large stream ¯ow years of 1978, 1981 and1983 than in small stream ¯ow years. Also evident in Figures 10 and 11 is a seasonal bias in sedimenttransport, whereby a greater mass of sediment is transported by a given stream ¯ow early in the winter thanby a stream ¯ow of similar magnitude later in the winter. Two possible reasons may be advanced to explainthis seasonal bias. One is that wheat cropping across much of the catchment leads to strong seasonality in

Figure 6. Monthly stream ¯ow observations and predictions at three locations on the Avon River: (a) Walyunga, (b) Northam and (c)Broun's, 1973±1994



leaf area index, with peak values occurring in spring following a build-up of biomass during winter.Consequently, one might expect greater erosion during the more sparsely vegetated autumn and early winterperiods. Secondly, it is possible that more loose sediment is available for re-entrainment by early-seasonstream ¯ows after having been deposited by receding ¯ows at the end of the previous winter. Whatever thereason, the modelled sediment yields clearly re¯ect this seasonal bias remarkably well.

Sediment yield observations are also available for a few locations within the catchment. One is theDunbarton Bridge gauging station (station 615021) on the Avon River, about 65 km upstream of Walyunga.Whilst the Dunbarton Bridge gauge has a notional catchment area of more than 115 000 km2, or about 97%of the Walyunga catchment area, it records less than 50% of the ¯ow volume. Once again, the sedimentmodel provides good calibration ®ts of the load at this location (Figures 12 and 13).

Figure 7. Monthly stream ¯ow observations and predictions for three tributaries of the Avon River: (a) Wooroloo Brook, (b) EllenBrook and (c) Brockman River, 1976±1994



Figure 14 shows the sediment load responses for two signi®cant erosive events at three locations along themain channel of the Avon River. There is evidence of overprediction of sediment load at Walyunga in 1978and underprediction at Dunbarton Bridge and Northam in 1981. However, the sediment transport eventsdepicted in Figure 14 appear to be quite dissimilar. In 1978, most of the sediment appears to have originatedupstream of Northam. In contrast, most of the sediment load in the June 1981 peak ¯ow is sourceddownstream of Dunbarton Bridge, with a relatively small contribution from Northam. The August 1981peak, on the other hand, originates mainly from the region between Dunbarton Bridge and Northam, withlittle contribution upstream of Northam or downstream of Dunbarton Bridge. Encouragingly, and not-withstanding the overprediction and underpredictions, the model is at least qualitatively re¯ecting thesedi�erent sediment load regimes.

Figure 8. Monthly stream ¯ow observations and predictions for three tributaries of the Avon River: (a) Dale River, (b) Mortlock RiverNorth Branch and (c) Mortlock River East Branch, 1975±1994



Finally, Figure 15 shows 25-year means of predicted stream ¯ows and sediment loads as proportions of thecatchment yield for a transect along the main channel between the catchment outlet and the Yenyenninggauge. The catchment's water yield can be seen to be sourced throughout the transect with signi®cantcontributions from Ellen and Wooroloo Brooks and Brockman, Mortlock and Dale Rivers. With theexception of the Mortlock River, all these tributaries supply far in excess of the catchment average stream¯ow. The catchment's sediment yield, however, originates mostly in the region between 45 and 100 kmupstream, a region that corresponds with the westernmost extent of the agricultural area (Figure 1). Rela-tively little sediment is sourced in the forested, high rainfall, high stream ¯ow areas further downstream, or inthe more arid, but still agricultural, regions further upstream.

Figure 9. Monthly stream ¯ow observations and predictions for three tributaries of the Avon River: (a) Yenyenning Lakes, (b)Southeast Lakes and (c) Northeast Lakes, 1975±1994



Figure 10. Monthly observations and predictions of (a) stream ¯ow and (b) sediment yield for the Avon River at Walyunga, 1976±1992

Figure 11. Daily observations and predictions of (a) stream ¯ow and (b) sediment yield for the Avon River at Walyunga, 1981



Figure 12. Monthly observations and predictions of (a) stream ¯ow and (b) sediment yield for the Avon River at Dunbarton Bridge,1978±1981

Figure 13. Daily observations and predictions of (a) stream ¯ow and (b) sediment yield for the Avon River at Dunbarton Bridge, 1978



CONCLUSIONS

Srinivasan and Engel (1994) observed that the utility of many of the common physically-based erosion andsediment transport models is limited by the need for large data and input parameter requirements, forparameters that are di�cult to estimate or obtain and by uncertainty in inputs. These problems inevitablycompromise the predictions of even the most rigorously constructed physical models. Similar concerns havebeen raised over the utility of physically based hydrological models (Beven, 1989; Grayson et al., 1992),which must inevitably be the basis of any physically based water quality model. Furthermore, the accuracy ofobservations of sediment data are often questionable. For example, the sediment concentrations used in thisstudy were derived from laboratory analysis of grab samples taken once per day (at irregular times) and

Figure 14. Monthly sediment yield observations and predictions for three locations on the Avon River: (a) Walyunga, (b) DunbartonBridge and (c) Northam, 1977±1981



converted to a daily sediment load by weighting with the daily stream ¯ow. Given the large intradayvariability of stream heights in the Avon River, the uncertainty of stage heights at the time of sampling andthe strong dependence of sediment concentration on stream ¯ow, there is clearly considerable scope for errorin estimating the daily sediment loadings.

In the light of these data and parameter uncertainties, there seems little advantage in applying a physicallybased sediment model; a simpler conceptual approach is likely to prove adequate. Such an approach hasbeen adopted in this paper and the results of this application to the Avon River show that it has considerablepotential.

Considerable improvement in the de®nition of the sediment model parameters could be obtained with theavailability of suspended sediment concentration data in other subcatchments, particularly those on themajor tributaries. This would further assist interpretation of the spatial and landscape controls on sedimentproduction. Furthermore, the temporal extent of the observed sediment concentration data is limited anddoes not, for example, include the extreme stream ¯ow year of 1974 (Figure 6). Therefore, given the non-linearity of the relationship between sediment yield and stream ¯ow, some caution must be exercised inapplying the model to extreme events.

At present, the model does not discriminate between di�erent sediment size classes, largely because theobservational data is not available to support its calibration. However, the future coupling of a nutrienttransport model is likely to require sediment size class discrimination, since there is observational evidencethat some nutrient species attach preferentially to sediment particles of particular size.

Finally, the e�ects, if any, of the prominent network of playa lakes in the dry, eastern part of thecatchment have not been adequately addressed. While the lakes contribute very little stream ¯ow to the AvonRiver, their rates of sediment export are poorly quanti®ed and are not well understood. Consequently, nospecial e�ort has been taken to amend the sediment model in those subcatchments.

Figure 15. Transect along the main stream channel showing relative discharges for water and sediment (long-term means)



ACKNOWLEDGEMENTS

The stream ¯ow and sediment load observations used in this study were made available by the Water andRivers Commission of Western Australia. Centre for Water Research reference ED 1351 NV.

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a conceptual model of sediment transport: application to the avon river basin in western australia

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