Journal of Hydrology (2006) 331, 242–256

ava i lab le at www.sc iencedi rec t . com

journal homepage: www.elsevier .com/ locate / jhydro l

Modelling monthly streamflows in twoAustralian dryland rivers: Matching modelcomplexity to spatial scale and data availability

William Young a,*, Kate Brandis b, Richard Kingsford b

a CSIRO Land and Water, Christian Laboratory, Clunies Ross Street, Black Mountain, P.O. Box 1666,Canberra, ACT 2601, Australiab School of Biological, Earth and Environmental Sciences, University of New South Wales, NSW 2052, Australia

Received 8 September 2004; received in revised form 12 May 2006; accepted 15 May 2006

Summary There is new pressure to develop some of Australia’s dryland river basins for irriga-tion as development on highly regulated rivers has halted with increasing ecological degrada-tion. Sparse populations, limited infrastructure, and minimal water resource development inAustralian dryland river basins mean streamflow records are few and typically short in duration.The Paroo and Warrego basins (74,003 and 62,908 km2, respectively; largely undeveloped) inthe northwest of the Murray-Darling Basin of Australia, each have four streamflow gauges withmore than 15 years of daily record, and four and eight years, respectively, of coincident record.These short records do not fully characterise the highly variable flow regimes. Improved char-acterisation of the flow regime and determination of the potential impacts of water resourcedevelopment can be based on streamflow simulation using climate data. Numerous floodplainlakes and wetlands are important ecological assets in these basins. For these environmentsimpacts will be a result of changes in the higher (above mean) flows, which can be reasonablyassessed by changes in monthly streamflows. However, high spatial and temporal variability ofrunoff generation, and the delicate hydrologic balance (runoff is a small fraction of rainfall) indryland regions means the relationship between rainfall and runoff is complex, and a daily timestep model was therefore required to adequately simulate monthly streamflow. It was neithernecessary, nor (because of limited data) possible to employ a complex spatially distributedmodel. Use of a highly parameterised, lumped-parameter conceptual model was also deemedunnecessarily complex, however, it was recognised that a simple black box model was unlikelyto be successful. As a compromise, we implemented a simple conceptualisation of the daily

KEYWORDSDryland rivers;Streamflow;Modelling;Water resourcedevelopment

0d

022-1694/$ - see front matter Crown Copyright �c 2006 Published by Elsevier B.V. All rights reserved.oi:10.1016/j.jhydrol.2006.05.014

* Corresponding author. Tel.: +46 8 166448; fax: +46 8 166405.E-mail address: bill.young@csiro.au (W. Young).

Modelling monthly streamflows in two Australian dryland rivers 243

water balance in PC spreadsheet software. The model was calibrated and validated usingmonthly streamflow volumes. The model accounts for 76–88% and 60–81% of the variance inmonthly streamflows in the Paroo (four stations) and Warrego (three stations) basins, respec-tively. We use the model to explore the relative importance of local and catchment rainfallin flood generation, and to predict the timing and magnitude of large floods in these basins overthe last 100 years.Crown Copyright �c 2006 Published by Elsevier B.V. All rights reserved.

Introduction

The pressure for water resource development in dryland re-gions in recent years has been high because of both the over-all scarcity of water and the insecurity of supply (Agnew andAnderson, 1992). However, lower levels of resource develop-ment in these regions often means there are few data avail-able for resource assessment and planning – including a lackof meteorological and hydrological information. In the dry-land regions of Australia streamflow gauges are sparse andtheir records typically short and often intermittent, owingto the costs and logistical difficulties inherent in maintaininggauge stations in remote locations with a harsh climate. Fur-thermore, the high flow variability in dryland regions meanslonger records are required to fully characterise flow re-gimes. To provide a more robust basis for water resourceplanning and environmental management than just observedstreamflow and climate, it is common to develop hydrologicmodels that relate streamflow to climate and thus allowextension of the streamflow time series.

Hydrologic modelling of dryland regions is however diffi-cult for several reasons other than the typically limited ex-tent and quality of data. The most important of thesedifficulties are summarised by Pilgram et al. (1998) and in-clude: (i) the high spatial and temporal variability of rain-fall, (ii) the delicate hydrological balance that meansstreamflows models are predicting a small residual in theoverall water balance, (iii) the sparse but variable plantcover dominated by species with widely differing waterretention adaptations, and (iv) the different mix of hydro-logical processes in dryland regions compared to humid re-gions. Furthermore, for ephemeral rivers the highproportion of zero flows means the information content ofeven a relatively long record can be small (Ye et al., 1997).

Hydrologic models that predict streamflow from rainfalland evapo-transpiration are commonly referred to as rain-fall-runoff models, and can be classified into process mod-els, conceptual models and ‘black box’ (or metric)models. Process models attempt to combine the suite ofphysically based equations that govern surface and sub-sur-face water flow, and are thus complex and have high datademands. Furthermore, they are based on equations thatdescribe small-scale spatially homogeneous processes thatdo necessarily apply well to large heterogeneous catch-ments. For all these reasons they are difficult to apply,and typically only provide improved predictions over sim-pler models in small data-rich catchments; they are mostuseful in studies of hydrologic processes.

Black box models include time series models and simplemathematical equations. When using a black box modelphysical meanings can only be attached to the input (rain-fall) and the output (runoff) time series – model parame-ters are merely fitted values that do not relate to realworld measurements of catchment characteristics. The costof the simplicity of these models is that the lack of anyphysical or even conceptual representation of the rainfall-runoff process limits their ability to capture the key charac-teristics of catchment response and thus allow predictionoutside the model calibration period.

Conceptual models are a compromise between processmodels and black box models in terms of complexity andphysical meaning. They typically conceptualise the catch-ment water balance using a series of interconnected sto-rages that do have a physical interpretation, but usuallyemploy empirically parameterised equations to describethe movement of water between storages. While some ofthe parameters in the equations in some conceptual modelsdo have a physical interpretation, they usually only repre-sent lumped, spatially averaged catchment characteristics,and so are not directly measurable (Ye et al., 1997). Cali-bration is therefore required against a reasonable periodof observed streamflow.

Finally, some models are best considered as hybrids be-tween black box and conceptual models. They combinethe use of relationships between observed rainfall andstreamflow (the black box approach) with a conceptualisa-tion of the catchment water balance. A well documentedexample of this type is the Identification of HydrographsAnd Components from Rainfall, Evaporation and Streamflowdata model (IHACRES) (Jakeman et al., 1990; Jakeman andHornberger, 1993).

The primary objective of this study was to use a hydro-logic model to extend monthly streamflows records forgauging stations in two large dryland floodplain rivers, theParoo and Warrego rivers. The modelling was intended to al-low prediction of the flows that lead to significant wetlandand floodplain inundation so as to allow investigation ofthe ecological impacts in floodplain environments of poten-tial water resource development. Such a priority has arisenmainly for two reasons. There is increasing understanding ofthe detrimental ecological effects of river regulation onfloodplain wetlands and rivers and their biota (Lemlyet al., 2000; Kingsford et al., 2004a) and a growing under-standing of the ecological importance of unregulated riversand their dependent wetlands (Kingsford et al., 1998; Shel-don et al., 2002). The Paroo and Warrego rivers supply

244 W. Young et al.

extensive floodplains and floodplain lakes (Kingsford et al.,2001), indicating the conservation importance of this areafor the entire state of New South Wales (Kingsford et al.,2004b). Once filled, the floodplain lakes remain inundatedfor many months until they eventually dry by evaporation(Kingsford et al., 2004a). This hydrologic regime drives theirecology which is characterised by ‘‘boom-bust cycles’’ –high production followed by high respiration and collapse(Kingsford et al., 1999) – which provides an important inter-mittent food supply for migratory waterbird populations(Kingsford et al., 1999, 2001, 2004a).

Hence, the model needed to capture the distribution ofthe larger (above average) monthly flows, and reasonablymatch the temporal sequence of flows to enable historicalmatching of wetland and floodplain inundation. Modellingof the low flow regime was less important in this study. Sec-ondary objectives were to use hydrologic model to (i) deter-mine the relative importance of local versus catchmentrainfall for floods, and (ii) estimate the timing and magni-tude of ungauged large floods during the past 100 years onthe Paroo and Warrego rivers.

In dryland regions the high spatial and temporal variabil-ity of runoff generation, and the delicate hydrologic bal-ance (runoff is a small fraction of rainfall) means therelationship between rainfall and runoff is complex and re-quires a characterisation at a fairly fine temporal scale.Modelling monthly streamflow on the basis of monthly rain-fall volumes is therefore seldom possible, and simple blackbox models are unlikely to be successful. Rather, modelsthat have some process or conceptual basis must be used,which use daily climate data to predict daily runoff and thenaggregate daily values to monthly totals. Complex process-based models were unnecessarily complex for the purposesof this study, and in any case their use was precluded bydata limitations. The best candidates were therefore con-ceptual or hybrid models.

Chiew et al. (1993) compared the performance of severalmodels (black box, conceptual and hybrid) including thestandard version of IHACRES on eight Australian catchments(3–700 km2), calibrated using two objective functions –one for high flows and one for low flows. In the most ephem-eral catchment they investigated all models performedpoorly at the daily and monthly time-scale. In a somewhatless ephemeral catchment only a complex conceptual modelgave adequate daily simulations; the black box modelsgenerally failed to even provide adequate monthly simula-tions – as did the standard IHACRES model. Ye et al.(1997) investigated the performance of three different con-ceptual and hybrid models in small (<1–500 km2) low-yield-ing ephemeral catchments. They concluded that to modelstreamflow in the catchments that they investigated itwas important to explicitly represent the non-linearity ofthe runoff generation process, and to explicitly representinteraction between deep groundwater and soil water. Boththese aspects were only included in the most complex of themodels (22 tunable parameters) they tested. However, theynoted that this second requirement could be relaxed for theprediction of monthly rather than daily streamflow volumes,for which purpose the hybrid model IHACRES performed rea-sonably well. Ye et al. (1997) modified the standard versionof IHACRES: two additional parameters were added to thenon-linear loss module to improve performance in ephem-

eral rivers, while one of the two stores in the linear modulethat converts effective rainfall to runoff was omitted (seealso Ye et al., 1998).

Reports of rainfall-runoff modelling in large drylandcatchments are rare, and IHACRES has not been applied insuch studies. For these cases application of any model isusually strongly constrained by a lack of calibration data,both in terms of the number of streamflow gauges availableand the length of record. Hence, in these cases algorithmi-cally simpler hybrid (partly conceptual and partly black box)models are more appropriate. In this study such a hybridmodel was developed and implemented in PC spreadsheetsoftware. We describe this model and report on its applica-tion to streamflow records from four gauge stations in theParoo Basin and three in the Warrego Basin. We use themodel to explore the relative importance of local andcatchment rainfall in flood generation, and to predict thetiming and magnitude of large floods in these basins overthe last 100 years.

Methods

The study area

The Paroo andWarrego basins are large, dryland basins in thefar northwest margin of the Murray–Darling Basin, Australia(Fig. 1 and Table 1). The upper catchment of the Paroo Riverincludes the Warrego, Willies and Walters ranges (Kingsfordet al., 1994). In the mid-basin the river fills the large LakeNumalla, and during particularly high flows may also flowinto Lake Wyara (Timms, 1999). Further south, the riverforms a complex system of distributary channels before ter-minating in a series of large freshwater lakes (Kingsfordet al., 2001); during flood the river inundates extensivefloodplains (Kingsford et al., 2001). The upper catchmentof the Warrego River includes the Warrego and Chestertonranges. In the mid-basin the large distributary CuttaburraCreek takes flows to Yantabulla Swamp, and thence intothe Cuttaburra Channels and Kulkyne Creek which eventuallyjoin the Paroo River (Fig. 1). Further south, a series of dis-tributary creeks (including the Irara, Kerribree and Greencreeks) leave the Warrego River. These creeks inundatefloodplains and fill lakes while the main channel of the Warr-ego eventually reaches the Darling River.

Model definition

The input daily rainfall (RF) time series for the model is aproportional mix (k1) of catchment daily rainfall (CR) and lo-cal daily rainfall (LR) (1). In this study CR was the un-weighted mean of one to three daily rainfall records forcatchment rainfall stations and LR was the daily rainfall re-cord for the rainfall station closest to the streamflow gaug-ing station. RF thus generally captured some of the spatialvariation in contributing rainfall.

RF ¼ k1LRþ ð1� k1Þ � CR where 0 6 k1 6 1 ð1Þ

The daily rainfall excess (RX) time series is non-linearly (k3)dependent on RF and linearly dependent on catchmentvalues of daily pan evaporation (CE) (2). RX may be positiveor negative. In this study CE was either a single daily

Figure 1 Location of Paroo andWarrego catchments indicating major stream network, major riverine lakes and floodplain wetlandsand the location of streamflow gauging stations: 1 = Augathella, 2 = Charleville, 3 = Wyandra, 4 = Cunnamulla Weir, 5 = Barringun,6 = Fords Bridge, 7 = Yarronvale, 8 = Caiwarro, 9 = Willara Crossing, 10 = Wanaaring. The river network was derived from a June 1990flood image from the Landsat Multi-spectral Scanner (MSS) satellite.

Modelling monthly streamflows in two Australian dryland rivers 245

evaporation record or an unweighted mean of two dailyevaporation records for catchment climate stations.

RXt ¼ k2 � ðRFk3t � CEtÞ where 0 6 k2 6 1 ð2Þ

The rainfall excess is scaled (k2) to ensure equivalence ofthe volumes of rainfall excess and the total generated (re-corded) streamflow during the modelling period.

The rainfall excess is then passed through a single linearstore (of capacity STC) to evaluate the volume in store (ST)

(3). ST can be considered to lump interception storage, sur-face depression storage and soil moisture storage.

STt ¼ STt�1 þ RXt ð3Þ

Storage-excess runoff (Q) occurs when ST > STC (4).

Qt ¼ STt � STC ð4Þ

As a simple means of modelling hydrograph recession afterstorage-excess runoff ceases, a linear hydrograph recession

Table 1 Basin areas, mean annual rainfall, number ofstreamflow gauges, and number and density of climatestations in the Paroo and Warrego basins

Basin Paroo Warrego

Area (km2) 73,650 69,290Mean annual rainfall (mm) 300a 363b

Streamflow stations 4 6Climate stationsc 69 (67) 66 (64)Density of climate stations(No. per 10,000 km2)

9.4 9.5

a Cunnamulla Post Office 1879–1997.b Hungerford Post Office 1884–1997.c Number of stations that record rainfall only in parentheses.

246 W. Young et al.

parameter is used, such that if STt = STC and Qt�1 > k4 then(5):

Qt ¼ k5 � Qt�1 where 0 < k5 < 1 ð5Þ

and if Qt�1 6 k4 then Qt = 0. Here, k4 is an arbitrary lowerlimit at which the proportional flow recession of (5) isdeemed to be equivalent to no-flow. The inclusion ofparameter k4 does not affect the model performance as as-sessed in this study (see below), and so was not a parameterrequiring calibration. The hydrograph recession parameter(k5) is a constrained proportioning factor.

The model therefore has three input daily time series(CR, LR, and CE) and six parameters (k1–k5 and STC). Fiveof these parameters require calibration – all except k4.

In this study, the model as defined above was applieddirectly at the most upstream gauge station record in eachbasin. For successive downstream gauging stations, therunoff generated between gauges (QIC) was simulated usingthe model as defined above, and added to a proportion ofthe modelled streamflow at the proximate upstream gauge(QUC) to estimate runoff at the downstream gauge (QDS)(6). Because runoff depths not volumes are modelled,the addition of streamflow depths was proportionedaccording to the areas of the upstream catchment (AUC)

Table 2 Streamflow gauges in the Paroo and Warrego basins and

Basin Streamflow station Longitude Latitud

Paroo Yarronvalea 145:20:20 �26:47Caiwarro 144:47:14 �28:41Willara Crossing 144:27:30 �29:14Wanaaringa 144:09:10 �29:42

Warrego Augathella 146:34:59 �25:47Charlevillea 146:14:02 �26:24Wyandra 145:58:00 �27:14Cunnamulla Weir 145:41:12 �28:07Barringuna 145:46:25 �29:05Barringun No. 2 145:26:25 �29:05Fords Bridge (main channel) 145:25:35 �29:45Fords Bridge (bywash) 145:26:25 �29:45

a Station closed.

and incremental (between gauge) catchment (AIC), relativeto the total catchment area (AT) to ensure conservation offlow volumes (6).

QDS ¼ k6 �AUC

ATQUC þ

AIC

ATQ IC where 0 < k6 < 1 ð6Þ

In (6) k6 is a constrained proportioning parameter that rep-resents the downstream losses in streamflow that are oftensignificant in dryland regions. These losses are usually dom-inated by evapo-transpiration, from both channel and flood-plain flows, but also include losses to groundwater from thechannel and floodplain. The loss parameter (k6) was only ap-plied to QUC in (6) as equivalence between rainfall excessand generated streamflow for the incremental catchment(QIC) was separately enforced by k2. The separate applica-tion of k6 to the upstream flows allows k2 values to be com-pared between models implementations. This proportionalrepresentation of losses did not of course handle thresholdloss processes. Losses of this type – for example high flowdistributary channels – are known to occur in these catch-ments, but without reliable data to indicate the importantthresholds, a more realistically parameterised modellingof losses was not possible.

The described model produced a time series of daily flowvolumes which were then aggregated to give monthly flowvolumes. The monthly flow volumes were used as the basisfor model calibration (see Section ‘Model calibration,cross-validation and performance’).

Streamflow records

Observations are available from a total of four and six con-tinuous stage height recording locations in the Paroo andWarrego basins, respectively, for which there are reason-ably reliable ratings to convert stage height to flow (Fig. 1and Table 2). Barringun No. 2 is a relocation of the earlierBarringun gauge and hence is considered to be the samelocation. The two Fords Bridge stations gauge flows in twoseparate channels (as the river is bifurcated here), but areconsidered as the same location. There are additional floodwarning stations not considered here. Observations are no

the period and length of record available for this study

e Upstreamarea (km2)

Available periodof record

Available lengthof record (yrs)

:28 1890 1967–1988 19.6:09 23,570 1967–2001 34.2:13 31,000 1976–2000 24.1:30 34,000 1968–1989 15.9

:43 8070 1967–2000 29.7:12 16,590 1926–1974 46.3:52 42,865 1967–2001 34.9:05 48,690 1992–2002 10.6:45 56,200 1968–1981 12.9:45 56,200 1993–1999 5.7:15 60,600 1972–1997 23.6:30 60,600 1922–2000 77.7

Modelling monthly streamflows in two Australian dryland rivers 247

longer being made at Yarronvale, Wanaaring and Charleville(Table 2). Because of the high flow variability in these rivers15 years of contiguous record was set as a minimum require-ment for modelling. This restricted the number of stationsavailable for modelling to four in each of the Paroo (Yarron-vale, Caiwarro, Willara Crossing and Wanaaring) and Warr-ego (Augathella, Charleville, Wyandra and Fords Bridge)basins. However, for Fords Bridge, the complexity of thedistributary channel system and large flow losses meant areliable model of streamflow could not be developed. Theflow data for Barringun and Fords Bridge are only used in thisstudy in comparative descriptions of the flow regime at dif-ferent locations. The data for Cunnamulla Weir are notused.

Model input data

The density of rain gauges and climate stations in thesecatchments is low (Table 1) (cf. 322.6 per 10,000 km2 inthe Hawkesbury Basin in the greater Sydney region) and re-cords often short and/or intermittent. Substantial exten-sions of streamflow records were therefore not possible

Table 3 Locations and names of climate stations used for develo

Streamflow Model Station name Longitude

Yarronvale Yarronvale 145.35Cheepie – Gumbardo 144.87Cheepie – Pingine 145.00Charleville Aero 146.26Thargomindah 143.82

Caiwarro Caiwarro 144.78Eulo Post Office 145.05Spring Creek 145.38Beirbank 145.07Thargomindah 143.82

Willara Hungerford Post Office 144.41Crossing Boorara 144.38

Currawinya 144.48Thargomindah 143.82

Wanaaring Wanaaring 144.39Thargomindah 143.82

Augathella Augathella Post Office 146.58Rolleston 148.63KillarneyBabbiloora Station 147.13

Charleville Charleville Aero 146.26Yandarloo 146.50Tambo 146.26Nive Downs 146.54

Wyandra Wyandra Railway Station 145.98Mount Morris 145.57Narada Downs 146.10Perola Park 146.30Charleville Aero 146.26

X’s indicate the data used for modelling.

using only historic rainfall and evaporation as model inputdata. Two datasets were available to overcome the limita-tions of historic observations: firstly ‘‘point-patched data-sets’’ (PPD) and secondly ‘‘spatially-patched datasets’’(SPD) (or grided surfaces). The PPDs are semi-synthetic re-cords that retain the historical measurements collected bythe Australian Bureau of Meteorology and use interpolationalgorithms to complete the time series. The SPDs are 0.05�(about 5 km) grids of synthetic data generated for Australiausing point rainfall data collected by the Australian Bureauof Meteorology (Jeffery et al., 2001). The SPDs are typicallyused in continental-scale modelling (e.g. Carter et al.,2000; NLWRA, 2001) and PPDs used in local or catchment-scale modelling.

Daily SPD rainfall and evaporation for the Paroo andWarrego basins are, respectively, in the lower half and themiddle of the reliability ranges for Australia (Jefferyet al., 2001) because of the high spatial variability of rain-fall and the low density of rain gauges and climate stations.The average coefficients of determination for the daily rain-fall and daily evaporation SPDs in the main runoff-generat-ing parts of the Paroo and Warrego catchments (0.2–0.4)

pment of streamflow models in the Paroo and Warrego rivers

Latitude Localrainfall

Catchmentrainfall

Catchmentevaporation

�26.80 X�26.11 X�26.42 X�26.41 X�28.00 X

�28.70 X�28.16 X�27.27 X�26.78 X�28.00 X

�29.00 X�28.66 X X�28.83 X�28.00 X�29.44 X X�28.00 X

�25.80 X�24.45 X X

X X�25.19 X

�26.41 X X�25.17 X�24.88 X�25.50 X

�27.25 X�25.81 X�24.98 X�25.71 X�26.41 X

248 W. Young et al.

are lower than most values for runoff-generating areas inthe Murray-Darling Basin (0.4–0.5) (Jeffery et al., 2001).For these reasons, the PPDs (1 January 1889 to 30 December2001) for selected climate stations were used in themodelling.

Rainfall interpolations in the historic time series usemonthly data within a 75 km radius of the target station,with interpolated monthly values partitioned to daily val-ues, according to the computed daily distribution of rain-fall. Evaporation interpolations are based on data fromclass A pans that measure potential evaporation but arenot interpolated before 1970 because of inconsistentand unreliable data. Before 1970, recorded daily averagevalues are used. Rainfall and climate stations were se-lected for the modelling on the basis of the proportionof observations in the PPD and their location in thecatchment.

For each streamflow model, input data were taken fromup to three well separated stations in the contributingcatchment with rainfall PPDs, the station closest to thestreamflow gauge with a rainfall PPD, and one or two ofthe nearest stations with evaporation PPDs (Table 3).Evaporation records are very few and only four PPDs wereavailable in the region, with one being from Thargomindah –located to the west of the Paroo in the Bulloo Basin. Rain-fall PPDs from 23 different stations within the Paroo andWarrego basins were used (Table 3). The distributions ofdaily rainfall for the PPD records for the seven stationsused for local rainfall in the modelling are shown as excee-dence curves in Fig. 2; these show that rainfall occurs onbetween about 9% (Wanaaring) and 19% (Charleville Aero)of the days. For these records the mean daily rainfallranges from 0.75 mm (Wanaaring) to 1.47 mm (AugathellaPost Office).

Figure 2 Exceedence frequency curves for point-patched daily rato the modelling.

Model calibration, cross-validation andperformance

Models were calibrated by trial and error adjustments of themodel parameters to minimise an objective function OBJ(7), while keeping the total estimated streamflow within5% of the total recorded streamflow.

OBJ ¼Xn

i¼1ðESTi � RECiÞ2 ð7Þ

where EST and REC are the estimated and recorded monthlystreamflows and n is the number of months in the record.

OBJ is the commonly used sum of squares of the differ-ences and biases the calibration towards fitting high flowsbetter than low flows. This objective function is thus appro-priate both for models intended for total streamflow (oryield) prediction and for predicting wetland and floodplaininundation.

The small number of model parameters (and fewer freeparameters) meant that, with sensibly selected initial val-ues, the chance of obtaining a local optimum set of param-eters with trial and error adjustment of model parameterswas low, and hence automated optimisation routines wereunnecessary. Model performance was assessed using thecoefficient of efficiency E, which expresses the proportionof the variance of the recorded flows that can be accountedfor by the model (Nash and Sutcliffe, 1970) (8).

E ¼

Pn

i¼1ðRECi � RECÞ2 �

Pn

i¼1ðESTi � RECiÞ2

Pn

i¼1ðRECi � RECÞ2

ð8Þ

where REC is the mean monthly recorded streamflow.

infall records for the seven stations used as local rainfall inputs

Table 4 Parameters from the calibrated models

k1 k2 k3 k5 k6 STC

Yarronvale 0.32 0.03600 1.540 0.00 – 6.10Caiwarro 0.25 0.01450 1.709 0.21 1.00 2.74WillaraCrossing

0.30 0.02000 1.640 0.00 0.51 18.30

Wanaaring 0.00 0.01110 1.200 0.90 0.85 0.00Augathella 0.44 0.01235 1.387 0.78 – 5.23Charleville 0.64 0.01880 1.428 0.62 0.00 5.05Wyandra 0.81 0.05110 1.410 0.00 0.00 16.00

Modelling monthly streamflows in two Australian dryland rivers 249

The K-fold cross-validation method of Efron and Tibsh-irani (1993) was used to cross-validate the calibrated mod-el. The recorded streamflow was divided into threeapproximately equal parts, and the model calibratedagainst two parts of the recorded streamflow. The cali-brated parameters were then used to estimate the stream-flow of the remaining part. This process was repeated threetimes, so that all parts were estimated once. The quality ofthe calibration was then shown by a comparison of the cal-ibration E value with the cross-validation E value.

In addition to the coefficient of efficiency, visual inspec-tion of the time series plots of recorded and modelledmonthly streamflows flows and the residuals (recordedminus modelled) and the flow duration curves of recordedand modelled monthly streamflows were used to assessmodel performance.

Analysis of modelled monthly streamflow timesseries

To analyse the flow regimes of the Paroo and Warrego rivers100-year point-patched daily times series were calculatedusing the calibrated models and the point-patched climateinput data series. The point-patched flow series includedall recorded flows, with the remainder of the time seriesgenerated using the model and the climate time series.The daily point-patched time series were then aggregatedto monthly time series for analysis.

To assess the relative importance of local versus catch-ment rainfall in flood generation for the Paroo and WarregoBasins, the monthly flow ranks for the 100-year point-patched times series between upstream and downstreamgauge stations were determined. For each basin, those flowvalues ranked within the hundred highest flows at everygauge station in the basin were selected and Pearson corre-lation coefficients calculated. Pearson correlation coeffi-cients of the flow ranks are equivalent to the Spearmanrank correlation coefficients of flow values. This analysisdetermines whether ranked floods at one gauge are alsoranked floods at other gauges in the basin. Where largefloods occur at one station but not at upstream or down-stream stations, it is inferred that the flood is largely dueto local rather than catchment rainfall. The full datasetsof ranks of adjacent stations were also compared on x–y

Table 5 Average monthly flows and model calibration and valida

Model Average monthly flow (mm) Average m

Yarronvale 2.367 4474Caiwarro 1.554 36,628WillaraCrossing

0.764 23,684

Wanaaring 0.849 28,866Augathella 0.441 3559Charleville 0.901 14,948Wyandra 0.993 42,565Barringun 0.133 7475Fords Bridge 0.190 11,514a The efficiency values for Willara Crossing ignore one month, for whi

plots. To estimate the timing and magnitude of ungaugedlarge floods during the past 100 years, the 10 highestmonthly flows in each patched monthly time series weredetermined.

Results

Model development and performance

Streamflow models were developed, calibrated and vali-dated for the four gauge stations in the Paroo Basin, andthe three most upstream gauge stations in the Warrego Ba-sin. For all models k4 was set arbitrarily at 0.0001 mm.Other parameters from the calibrated models (Table 4) con-firm the non-linear relationship between rainfall and runoff(k3), and reflect the substantial losses in streamflow in thelower portion of the Paroo Basin (k6). Model optimisationbalances the effect of one parameter against the effect ofothers, that is, changing one parameter to improve E oftenrequires changing another parameter (to a less realistic va-lue) to meet the constraint placed on total streamflow er-ror. Hence, no physical significance is attached to theremaining model parameter values.

The Paroo Basin models and the upper and lower gaugestation models in the Warrego all show good calibrations(E > 75%) and validations (>70%), while the Charleville modelcalibration is only passable and the validation poor (Table5). The poorer model for the Charleville gauge station didnot prevent development of a robust model for the Wyandragauge station.

tion coefficients of efficiency

onthly flow (ML) Calibration E Validation E

0.84 0.720.80 0.780.88a 0.71a

0.76 0.740.81 0.760.60 0.370.77 0.72Not modelledNot modelled

ch there was an obvious and large error in the recorded flow value.

250 W. Young et al.

The flow duration curves for recorded and modelledmonthly flows indicate that in all cases – includingCharleville – the models meet the study objective ofadequately representing the distribution of flows abovethe mean flow (Fig. 3). Flows below the mean aregenerally poorly modelled (with the exception of WillaraCrossing) – a result expected from the calibration method

Yarronvale

Flow

()

mm

0.01

0.1

1

10

100

1000

Caiwarro

lFow

m()

m

0.01

0.1

1

10

100

1000

Willara Crossing

lFow

m()

m

0.01

0.1

1

10

100

Perce

0 10 20

Flow

()

mm

0.01

0.1

1

10

100

Percent Exceeded

0 10 20 30 40 50

Figure 3 Flow duration curves for the seven modelled streamflowmonthly streamflow distributions. The dashed lines indicate the me

adopted. The time series and residual plots show agenerally good matching of the flow sequences (Fig. 4),and a good matching of the timing and magnitude of floodpeaks. In spite of the long record at Charleville, theresidual plot confirms that the Charleville model wasthe least efficient. A disproportionately large residual isseen in the Willara Crossing record in April 1990. This

Wanaaring

nt Exceeded

30 40 50

Augathella

0.01

0.1

1

10

100

Charleville

0.01

0.1

1

10

100

Wyandra

Percent Exceeded

0 10 20 30 40 500.01

0.1

1

10

100

records showing observed (thin line) and modelled (heavy line)an monthly flows.

Modelling monthly streamflows in two Australian dryland rivers 251

residual was ignored in the model fitting and determina-tion of the efficiency value (Table 5) as it is obviouslydue to an error in the gauged value for this historicallywell-known flood that is clearly evident in the upstreamgauge record.

Yarronvale

0

50

100

150

200

1965 1970 1975

Year

Caiwarro

0

20

40

60

80

100

1965 1970 1975 1980 1985

Year

Willara Crossing

0

20

40

60

80

1975 1980 1985Year

Wanaaring

0

10

20

30

40

50

60

1965 1970 1975

Year

Run

off

(mm

)R

unof

f (m

m)

Run

off

(mm

)R

unof

f (m

m)

Figure 4 Observed (heavy black line), modelled (heavy grey line)scales) for the seven modelled streamflow records.

Analysis of modelled monthly streamflow timeseries

In this analysis floods are assessed in terms of total monthlyflow volumes; it is total flood volume that is important when

1980 1985 1990-150

-100

-50

0

50

Res

idua

l (m

m)

Res

idua

l (m

m)

Res

idua

l (m

m)

Res

idua

l (m

m)

1990 1995 2000 2005-75

-65

-55

-45

-35

-25

-15

-5

5

15

25

1990 1995 2000-60

-50

-40

-30

-20

-10

0

10

20

1980 1985-40

-30

-20

-10

0

10

20

and residual (line black line) monthly flows (mm, on equivalent

Augathella

0

10

20

30

40

1965 1970 1975 1980 1985 1990 1995 2000

Year

-30

-20

-10

0

10

Charleville

0

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50

1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975Year

-30

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-10

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Wyandra

0

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60

80

100

1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

Run

off

(mm

)R

unof

f (m

m)

Run

off

(mm

)

-70

-60

-50

-40

-30

-20

-10

0

10

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30

Res

idua

l (m

m)

Res

idua

l (m

m)

Res

idua

l (m

m)

Figure 4 (continued)

252 W. Young et al.

considering the inundation of laterally or terminally remotefloodplain lakes and wetlands. The correlation coefficientsfor the filtered time series of flow ranks within each basinindicate the co-occurrence of floods at different gauge sta-tions and thus suggest the relative importance of local rain-

Table 6 Significant (P = 0.05) correlation coefficients of filtered

Yarronvale Caiwarro Willara W

Yarronvale 1.00 0.44Caiwarro 1.00 0.73 0Willara 1.00 0Wanaaring 1AugathellaCharlevilleWyandra

fall versus catchment rainfall in flood generation (Table 6).The correlation coefficients indicate that the largest floodsin the lower sections of these basins are not coincident withlargest floods higher in the basin. Close inspection of thedata (see below) confirm that this is not simply an affect

monthly flow ranks for flood flows in each basin

anaaring Augathella Charleville Wyandra

.59

.85

.001.00 0.44

1.001.00

Figure 5 Scatter plots of high flow ranks between adjacent gauge stations in the Paroo and Warrego basins.

Modelling monthly streamflows in two Australian dryland rivers 253

254 W. Young et al.

of a time lag of flood progression through the basin. Rather,the larger floods in the lower basin are at least partially gen-erated by rainfall in the middle and lower basin. This con-clusion is supported by the relatively low but significantcorrelations between the most upstream gauge station andthe mid-basin in each case (Table 6). The extremely highflow losses down these rivers (apparent in Fig. 4), and thesometimes localised extent of storms make this lack of floodconcordance between stations unsurprising. The scatterplots of the higher flow ranks between adjacent stationsillustrate the good correlation of flood flow ranks betweenWillara Crossing and Wanaaring, and the generally poorercorrelations between other adjacent stations (Fig. 5).

It was recognised of course that some of the lack of con-cordance of floods is attributable to the errors in therespective models. In particular, the correlation betweenfloods (monthly volumes) at Charleville and Wyandra is only

Table 7 Month and year of the largest 10 monthly flows in for e

Rank Yarronvale Cariwarro Willara

Crossing Wana

1 Jan, 1974 Apr, 1990 Feb, 1976 Feb

2 Jan, 1954 Jan, 1974 Jan, 1891 Jan

3 Jan, 1891 Mar, 1956 Jan, 1974 Jan

4 Apr, 1990 Jan, 1964 Mar, 1949 Mar

5 Feb, 1896 Jan, 1891 Mar, 1956 Mar

6 Mar, 1950 Mar, 1950 Jan, 1964 May

7 Jul, 1920 Feb, 1976 May, 1989 Jun

8 Feb, 1955 Jan, 1941 Jan, 1941 Jan

9 Feb, 1997 Jan, 1995 Mar, 1950 Mar

10 Feb, 1976 Mar, 1949 Mar, 1967 Jan

Shading indicates the number of contiguous stations within one basin astation, ( ) two stations, ( ) three stations, ( ) for four stations.

Table 8 Magnitude of the largest 10 monthly flows for each gaexpressed as a ratio of the mean monthly flow

Rank Yarronvale Caiwarro Willara Crossing

1 52.8 34.7 68.72 33.5 33.5 37.03 30.4 29.7 30.34 27.4 27.8 29.35 27.1 26.8 27.16 24.3 22.7 24.87 22.3 21.1 19.88 21.0 20.6 18.09 18.9 19.7 17.910 18.1 17.8 17.5

just above the P = 0.05 threshold for significance, and theCharleville model has the lowest coefficient of efficiencyvalues for both calibration and validation (Table 5). Further-more, errors in the observed records will affect these re-sults, the most obvious being the erroneously low gaugedvalue for the April 1990 flood at Willara Crossing as notedabove.

The timing of the 10 largest floods in each of the 100-year monthly time series (Table 7) further illustrate the de-gree of flood concordance between stations. In the ParooBasin three of the largest floods (January 1891, January1974, and February 1976) ranked in the top 10 floods at allfour stations, five other floods ranked in the top 10 at threecontiguous stations, one flood ranked in the top 10 at twocontiguous stations, and the remaining floods (a total of11 different floods) ranked in the top 10 at a single station(Table 7). In the Warrego Basin only the March 1910 flood

ach gauge station based on point-patched flow time series

aring Augathella Charleville Wyandra

, 1976 Feb 1997 Jan, 1974 Mar, 1990

, 1974 Mar 1910 Apr, 1990 Jan, 1997

, 1891 Apr 1955 Feb, 1954 Mar, 1956

, 1949 Mar 1890 Feb, 1956 Jan, 1941

, 1956 Apr 1894 Feb, 1890 Jan, 1973

, 1968 Feb 1906 Feb, 1997 Mar, 1910

, 1983 Feb 1917 Apr, 1956 Feb, 1956

, 1941 Apr 1990 Mar, 1910 Feb, 1906

, 1936 May 1983 Jun, 1894 Mar, 1890

, 1964 Jul, 1921 Mar, 1924 Mar, 1963

t which a given flood (month) ranked in the top 10 floods: ( ) one

uge station based on the point-patched flow time series, and

Wanaaring Augathella Charleville Wyandra

35.6 60.0 39.3 56.725.1 51.8 36.0 52.323.5 45.5 25.8 32.617.8 31.0 25.6 32.116.8 30.4 24.8 28.516.5 28.5 24.3 27.616.0 27.6 23.7 27.515.3 27.6 21.2 27.214.7 26.6 21.1 26.213.8 26.2 20.7 24.7

Modelling monthly streamflows in two Australian dryland rivers 255

ranked in the top 10 floods at all three stations, six otherfloods ranked in the top 10 at two contiguous stations,and remaining floods (a total of 15 different floods) rankedin the top 10 at a single station (Table 7). In this assessmentfloods occurring in consecutive months at adjacent stationswere assumed to be the same event, because of slow floodprogression down these low gradient (slope around0.5 · 10�3) channels.

The magnitude of the largest floods (monthly flow vol-umes) range from 13.8 times the mean up to as high as68.7 times the mean (Table 8). The skew in the flood distri-bution appears to be strongest at the mid-basin stations(Willara Crossing and Wyandra), and weakest in the lowerParoo basin (Wanaaring).

Discussion

For most of the gauge stations in the Paroo and Warrego ba-sins the 100-year point-patched time series was used as abasis for describing and contrasting at least the higher flowsin the flow regimes of these two basins. For the lower Warr-ego however, the absence of a calibrated model meantdescriptions for Barringun are based on the 19-year gaugerecord, and descriptions for Fords Bridge are based on a78-year composite record using both the Main Channel andthe Bywash gauge data (Table 5). Gauge station averagesshow that the upper Paroo Basin generates nearly threetimes the runoff depth of the upper Warrego Basin, and thatboth the average flow volume and average runoff depth re-duce with distance downstream in both basins, but mark-edly so in the Warrego (Table 5 and Fig. 4). In the Paroo,much of the mid-basin flow loss is to lakes such as Numallaand Wyara, while in the Warrego flow loss is largely to dis-tributary channels such as the Cuttaburra Channel that car-ries flow to Yantabulla Swamp and Cuttaburra Creek.

While it is not unusual for large, low-gradient dryland riv-ers to be in flood under clear skies because of the slow tra-vel times for floods generated in the upper-basin, theanalyses of the modelled monthly flow series reveal thatin Paroo and Warrego basins local rainfall is often an impor-tant contributor to flood magnitude. Across the four mod-elled stations in the Paroo the top 10 ranking floods(monthly flow volumes) represent 20 different flood events,and across the three modelled stations in the Warrego thetop 10 ranking floods represent 22 different flood events.The majority of these floods were only top-ranking floodsat a single station.

The monthly flow duration curves (Fig. 3) show that evenat the monthly scale flow is ephemeral. The simple modelused in this study does not reproduce the distribution oflow flows; to achieve this would require a calibration thatwas not biased towards higher flows. Options for such cali-brations are described by Croke et al. (2005). While thereis usually little baseflow in these rivers, inclusion in themodel of an explicit representation of the interactions be-tween soil water and deeper groundwater might also im-prove the modelling of low flows; the deeper groundwaterstore often acts as a ‘‘flywheel’’ on the dynamics of runoffgeneration (Ye et al., 1997).

In spite of the poor matching of low daily flows, themodel generally performed well for the purpose for whichit was developed – the simulation of high monthly flows.

The model conceptualisation captures key components ofthe water balance including a non-linear loss to transformrainfall to effective rainfall, and a linear soil water storeof limited capacity to transform effective rainfall intostreamflow. The non-linear loss is based on a simple powerfunction, with rainfall excess a function of rainfall andevapo-transpiration in the same time step. This contrastswith the algorithmically more complex IHACRES model thatpredicts rainfall excess using weightings of the rainfalltime series with weights decaying exponentially backwardsin time. While the single store used here in the lineartransformation of effective rainfall into runoff is simplerthan the standard two-store (quick-flow and slow-flow)implementation of IHACRES, it is similar to the versionmodified for use in low-yielding ephemeral catchments(Ye et al., 1997). The use of a single store is reasonablein catchments without regular base flow. Hence, whilethe model used herein is similar to the modified versionof IHACRES, the model formulation is simpler, facilitatingquick implementation in widely available PC spreadsheetsoftware. Calibration is likely to be simpler with one fewertunable parameters than for the modified IHACRES. As suchthe model may be an attractive option for those with littlemodelling expertise wishing to model streamflow in situa-tions where pure black box models are unlikely to berobust.

These models provide opportunities to test relation-ships between river flows and floodplain inundation pat-terns by examining satellite imagery during high floodperiods. Simple scenarios of potential water diversion atdifferent locations and in different temporal patternscould then be used to simulate the likely impact of waterresource development on floodplain inundation and wet-land filling. Relationships between wetland inundation ex-tent and frequency and waterbird populations establishedfrom environmental monitoring (Kingsford et al., 2004a)have been used to translate these inundation predictionsinto ecological currency (Kingsford et al., 2004a). Rela-tionships between flow, flood extent and duration needto then be developed with key ecological processes suchas floodplain use, breeding and recruitment of drylandfloodplains by biota (Boulton et al., 2005; Brock et al.,2005; Bunn et al., 2005; Kingsford et al., 2005).

Conclusions

Water resource planning and environmental managementin dryland regions is often hampered by a lack of resourcedata including hydrologic data. With pressure on water re-sources in dryland rivers, scrutiny on water resources thataffect ecosystems is high. Hydrologic modelling to extendobserved streamflow records is therefore valuable, butnonetheless difficult because of the complexities and highspatial and temporal variability of streamflow generationin these regions. Finding the best modelling approach isa compromise between model complexity and datarequirements, within the context of the particular model-ling purpose and available expertise and resources for aninvestigation. For modelling large dryland basins data lim-itations typically preclude the use of complex models,while the simplest models are unable to adequately mimiccatchment response. In this paper we showed that a model

256 W. Young et al.

of intermediate complexity – part conceptual and partstrictly empirical – is able to adequately capture the mag-nitude and sequencing of above average streamflows at amonthly timescale in the dendritic drainage sections ofthe large dryland Paroo and Warrego basins. The modelis sufficiently simple that spreadsheet implementation withtrial and error calibration is possible. The model has appli-cation in investigations of the impacts on floodplain andterminal wetland environments of potential water resourcedevelopment.

Acknowledgements

The authors thank the Queensland Department of NaturalResources and Mines for access to observed hydrologic data-sets and modelled meteorological datasets, and the NewSouth Wales Department of Land and Water Conservationfor access to observed hydrologic datasets. The construc-tive comments of Barry Croke, Tony Jakeman and one anon-ymous reviewer are also gratefully acknowledged. Fundingwas provided by the Australian Natural Heritage Trust.

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