Environmental Modelling & Software 22 (2007) 406e413www.elsevier.com/locate/envsoft

Effect of data length on rainfallerunoff modelling

W.C. Boughton*

Griffith University, Brisbane, Australia

Received 7 September 2005; received in revised form 28 December 2005; accepted 10 January 2006

Available online 28 February 2006

Abstract

A 64-year data set of daily rainfall and runoff, and average monthly potential evapotranspiration (PET) was split into subsets of 2, 5, 10, 20and 30 years. Each subset was used to calibrate the AWBM daily rainfallerunoff model. Each subset calibration was then used to estimate runofffrom the 64 years of rainfall and PET data. The ratios of calculated to actual total runoff were used to determine the ranges of error from thedifferent lengths of data used for calibration. There was little difference in results from the 2- and 5-year subsets with 90% of estimates of longterm runoff in the range of �21% to þ31% of the recorded value. Overestimation of long term runoff reduced with length of calibration data of10 or more years; however, the chances of underestimating were only slightly reduced even with 30 years of calibration data. Some limitedrepetition of the calculations with the Curve Number rainfallerunoff model indicated that the error characteristics were inherent in the dataset and not an artifact of the model used. The ramifications for applications of rainfallerunoff modelling are briefly discussed.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Hydrologic modelling; Rainfallerunoff; Catchments; Watersheds

1. Introduction

Continuous simulation of the water balance of catchmentsis now a major tool for relating runoff to rainfall for wateryield studies (Boughton, 2005) and for loss estimation in floodstudies (Boughton and Droop, 2003). Computer simulationmodels are calibrated to a concurrent period of rainfall andrunoff data, and a longer period of rainfall data or a long pe-riod of stochastically generated rainfall data are used to esti-mate a longer period of runoff.

There is an implied assumption that the runoff processesrepresented by the model will be the same in the shorter andlonger periods, and the calibration based on the shorter periodwill be the same in the longer period. In practice, periods ofdata as short as 2 years are used to estimate long term runoff.This raises some doubt about the accuracy of the long termestimate, but there is little information available about suchaccuracy. There are some recommendations in the literaturefor split sampling, i.e. use half of the data for calibration

* 11 Preston Place, Brookfield, Qld., Australia. Tel.: þ61 7 3374 4785.

E-mail address: wboughto@bigpond.net.au

1364-8152/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.envsoft.2006.01.001

and the other half for testing the accuracy of estimation.This approach has little value when only very short periodsof data are available.

Australia is rich in mineral resources, but these are oftenlocated in sparsely populated regions where streamgaugingdata are unavailable. It is not unusual for a mining companyto establish a gauging station at a mining site when approvalfor the project is given, resulting in 1 or 2 years of data beingavailable when planning for essential water supplies must bemade for a project involving expenditure of some hundredsof millions of dollars.

The present study was designed to examine the errors fromcalibrating a daily rainfallerunoff model to short periods ofdata and then using a longer period of rainfall data to estimaterunoff in the longer period. A data set with 64 years of rainfalland runoff data was selected so that calibrations based on sub-periods of the data could be compared with the recorded 64years of runoff.

2. Data

The data used in this study are from the 407 km2 SnowyCreek catchment below Granite Flat, streamgauging station

407W.C. Boughton / Environmental Modelling & Software 22 (2007) 406e413

401210, a tributary of the Mitta Mitta River in the UpperMurray basin in north east Victoria. There were 64 years ofdata, 1933e1996, available for analysis. Average annual rain-fall, runoff and potential evapotranspiration (PET) were 1372,492 and 1022 mm, respectively. The ratio of runoff to rainfallis 0.36.

The data set was previously used in a project for the Na-tional Land and Water Resources Audit (Peel et al., 2001;Chiew et al., 2002) and in other studies by Boughton andChiew (2003, in press) and Boughton (in press). The sourceof the daily rainfall data is the Queensland Department of Nat-ural Resources & Mining 0.05 � � 0.05 � (about 5 km� 5 km)interpolated gridded rainfall data based on over 6000 rainfallstations in Australia (see www.dnr.qld.gov.au/silo). The inter-polation uses Ordinary Krigging of monthly rainfall data, anda variogram with zero nugget and a variable range. Themonthly rainfall for each 5 km� 5 km point is then disaggre-gated to daily rainfall using the daily rainfall distribution fromthe station closest to the point. The lumped catchment-averagedaily rainfall is estimated from the daily rainfall in5 km� 5 km points within the catchment.

Compared to rainfall, evapotranspiration has little influenceon the water balance at a daily time scale. The inter-annualvariability of PET is also relatively small (typically less than0.05). For these reasons, the mean monthly areal PET isused. The 12 mean monthly areal PET values are obtainedfrom the evapotranspiration maps produced jointly by the Co-operative Research Centre for Catchment Hydrology and theAustralian Bureau of Meteorology (Australian Bureau of Me-teorology, 2001; and www.bom.gov.au/climate/averages). Theareal PET values are derived using Morton’s complementaryrelationship model (Morton, 1983; Chiew and McMahon,1991).

The data from the Snowy Creek catchment are of goodquality. A preliminary calibration of the AWBM to the entire64 years gave a coefficient of efficiency of 0.871 from a com-parison of actual and modeled monthly runoff, and 0.796 froma comparison of yearly totals. The data were checked for anyinconsistencies between rainfall and runoff, but no major er-rors were found. For sake of brevity, the average annual runoffbased on the 64 years of record is used as ‘‘the long termrunoff’’.

3. AWBM model

3.1. Structure

The AWBM catchment water balance model (Boughton,2004) is used to estimate daily, monthly and annual runofffrom a daily rainfall record and PET estimates. The model cal-culates surface runoff and baseflow components of streamflowat daily time steps. The AWBM generates runoff by saturationexcess from three surface stores that allow for partial arearunoff. The surface storage parameters are the three capacitiesand their partial areas. There are two baseflow parameters, thebaseflow index (BFI) that determines how much of the runoffis baseflow, and the baseflow recession constant (Kb) that

determines how fast the water is discharged from the baseflowstore. A surface recession constant (Ks) determines the dis-charge from the surface runoff store. Discharge from the sur-face runoff store¼ (1.0� Ks) times the amount of water in thesurface runoff store. Discharge from the baseflow store¼(1.0�Kb) times the amount of water in the baseflow store.The structure of the model is shown in Fig. 1.

The amount of runoff is determined wholly by the threesurface stores and their partial areas. The other parameters af-fect only the temporal pattern of runoff. By selecting a numberof high quality data sets, i.e. with very high correlation be-tween calculated and actual monthly values of runoff, it wasfound that the average value of surface storage capacity(Ave¼ C1A1þ C2A2þ C3A3) was far more important for cal-ibration than the individual set of capacities and partial areas.An average pattern was found that could be used to disaggre-gate an average capacity (Ave) into three capacities and threepartial areas, as follows:

Partial area of smallest store A1¼ 0.134;Partial area of middle store A2¼ 0.433;Partial area of largest store A3¼ 0.433;Capacity of smallest store C1¼ 0.075�Ave;Capacity of middle store C2¼ 0.762�Ave;Capacity of largest store C3¼ 1.524�Ave;

Fig. 2 shows the average pattern based on an average ca-pacity of 100 arbitrary units.

3.2. Automatic calibration

The AWBM2002 version of the model self-calibrates toa data set of daily rainfall, daily runoff and monthly (or aver-age monthly) PET, and this version was used for all calibra-tions. The model starts by assuming default values of thebaseflow parameters, BFI and Kb, and the surface runoff reces-sion constant Ks to make a preliminary calibration of the sur-face stores. This preliminary calibration makes total calculated

Surface Runoff

Baseflow

A1

A2

A3

C1

C2

C3Baseflow RechargeBFI * Excess

(1.0 - BFI) * ExcessExcess

P E

Fig. 1. Structure of the AWBM model.

408 W.C. Boughton / Environmental Modelling & Software 22 (2007) 406e413

runoff equal to the total recorded runoff. After this preliminarycalibration, the BFI, Kb and Ks are calibrated in that order andthen again in the same order, using a measure of differencesbetween calculated and recorded daily flow hydrographs.The square root of the absolute differences between dailyflows is summed over the period of calibration data with trialand error adjustment of the parameters to minimize the errorfunction. In this way, the runoff generating parameters arecalibrated against the amount of runoff and the parametersthat affect the temporal pattern of runoff are calibrated againstthat pattern.

Fig. 3 shows how average annual runoff on the SnowyCreek catchment varies with change in average surface storagecapacity, using the 64 years of available data. The automaticcalibration matches calculated and recorded runoff to within0.1 mm/year. The recorded average annual runoff of492 mm/year in the 64 years of data is estimated by an averagesurface storage capacity of 223 mm.

After all parameter values have been determined by the au-tomatic calibration procedure, starting values in the surface

7.5

76

152

0.1340.433 0.433

Ave100

Fig. 2. Average pattern of surface storage based on 100 units of storage.

Snowy Creek

0

100

200

300

400

500

600

700

800

900

0 200 400 600 800

Average Surface Storage Capacity mm

Calcu

late

d A

verag

e A

nn

ual R

un

off

mm

Fig. 3. Variation of calculated runoff with average capacity on Snowy Creek.

stores are optimised by trial and error to provide a best matchof calculated and recorded runoff in the first three months ofdata. Starting values rarely have any significant effect afterthis period. In the rare cases where the effect on later monthsis of significance, other versions of the AWBM can be used formanual calibration of the starting values. This was not neces-sary with the Snowy Creek data.

4. Method of analysis

The method used in the study is illustrated by use of the 10-year subsets of data. Every possible 10-year sub-period withinthe 64 years of data was tested. Starting with years 1 to 10,then 2 to 11, and finally 55 to 64, there were 55 sub-periodseach 10 years in length. The AWBM was calibrated to eachsub-period in turn. Each of these calibrations was then usedwith the 64 years of rainfall and PET data to estimate runofffor the data period. Each estimate of average annual runoffwas then divided by the actual average from the 64 years ofrunoff to give a ratio of modeled runoff to actual runoff. Forexample, the calibration based on the sub-period years 1 to10 estimated an average annual runoff of 540 mm/year fromthe 64 years of rainfall and PET data, compared with the re-corded average of 492 mm/year, i.e. a ratio of 1.097.

Fig. 4 shows the ratio of 1.097 as the first of the 55 esti-mates that are summarized in the figure. The ratios variedfrom the lowest of 0.771 in the period starting in year 23 tothe maximum of 1.241 in the very last sub-period.

The 55 estimates of long term runoff were ranked in orderof magnitude from the smallest of 380 mm/year to the largestof 610 mm/year. Fig. 5 shows the ranked set of estimates toillustration the range of variation. Twenty-five percent of thevalues are less than 405 mm/year (the 25-percentile) and25% were larger than 532 mm/year (the 75-percentile); i.e.50% of the values were within the range of 405 to 532 mm/year (�18% to þ8% of the recorded value) and 50% were out-side of this range. Similarly, the 5-percentile and 95-percentilevalues of 386 and 565 mm/year (�22% and þ15% of the re-corded value) mark the limits that contain 90% of the valueswith 10% outside the limits.

The method outlined above with 10-year sub-periods wasthen repeated with four other sub-periods to determine howthe ranges of estimates vary if different lengths of data areavailable for the initial calibration e see next section.

5. Results

5.1. Errors in estimates of long term runoff

The calculations demonstrated with 10-year sub-periods inthe previous section were repeated with data periods of 2, 5,20 and 30 years, and the ranges of estimates were determined.There were 63 subsets of 2 years duration, 60 of 5 years, 45 of20 years and 35 of 30 years. The results are summarized inTable 1. For example, if 2 years of data are available forcalibration and the calibration is used with the 64 years ofrainfall and PET data, then 90% of the estimates of average

409W.C. Boughton / Environmental Modelling & Software 22 (2007) 406e413

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55Start Year Number

Ratio

to

L

on

g T

erm

R

un

off

Fig. 4. Ratios of modeled to actual average annual runoff from 55 10-year sub-periods.

annual runoff were within the range �21% to þ30%, and 10%were outside of this range.

The error ranges are very similar for 2 and 5 years of cal-ibration data for each of the percentiles in Table 1, which iscontrary to expectation. The overestimation of long term run-off (‘‘þ’’ error range) reduces significantly when 10 or moreyears of calibration data are available, but the underestimation(‘‘�’’ error range) remains high even when 20 years of calibra-tion data are available.

5.2. Baseflow parameters

In the automatic self-calibration version of the AWBM, theamount of runoff is determined by a single parameter, the av-erage surface storage capacity. The two baseflow parameters,BFI and Kb, affect the temporal pattern of the runoff but do

10-year Samples

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60Sequence number of ranked samples

Calcu

lated

A

verag

e A

nn

ual R

un

off

mm

/yr

Fig. 5. Ranked estimates of average annual runoff based on 10-year sub-

periods.

not affect the amount. In addition, the baseflow parameters af-fect the distribution of daily flows but have only a small effecton monthly totals of runoff.

The results shown in Section 5.1 deal with the amount ofrunoff in terms of average annual runoff. In order to examinethe effect of short periods of data on baseflow parameters, theparameter values were collated for all 2-year and 5-yearsubsets.

When the AWBM was calibrated to the total 64 years of re-cord, the values of the baseflow parameters were BFI¼ 0.63(determined to the nearest 0.01) and Kb¼ 0.990 (determinedto the nearest 0.001). In the 63 subsets of 2-year periods, 57calibrated the BFI to 0.63 and only 6 to another value. Theother values were one each of 0.62, 0.61, 0.60 0.57, 0.56and 0.55. For the baseflow recession constant, Kb, 62 of the63 values were within 0.004 of the long term value of 0.990,and one value was 0.983. The biggest errors of BFI¼ 0.55and Kb¼ 0.983 have such a small effect on the monthly totalsof runoff that it would be difficult to express the difference inany meaningful way.

In the 60 subsets of 5-year periods, 57 values of the BFIwere the same as the full calibration (0.63). The other threevalues were 0.62, 0.60 and 0.59. All values of the baseflow

Table 1

Percentiles of estimates of long term runoff using 10-year samples for

calibration

Sample

length

years

No of

samples

Percentiles of estimates of long term runoff (mm/year)

5% 25% 75% 95%

2 63 388 (�21%) 413 (�16%) 533 (þ8%) 640 (þ30%)

5 60 385 (�22%) 409 (�17%) 532 (þ8%) 640 (þ30%)

10 55 386 (�22%) 405 (�18%) 532 (þ8%) 565 (þ15%)

20 45 389 (�21%) 421 (�16%) 505 (þ3%) 540 (þ10%)

30 35 414 (�16%) 433 (�12%) 478 (�3%) 499 (þ1%)

410 W.C. Boughton / Environmental Modelling & Software 22 (2007) 406e413

recession constant Kb were within 0.004 of the full calibrationvalue of 0.990.

There was little purpose in extending the study to the longersubsets. It is clear that short periods of data are much better inestimating the long term values of the baseflow parametersthan in estimating the average surface storage capacity that de-termines the amount of runoff.

5.3. Surface runoff recession constant

The surface runoff recession constant Ks is the least sensi-tive parameter in the AWBM. It has no effect at all on theamount of calculated runoff, and it has much smaller effecton the temporal pattern of runoff than either of the baseflowparameters. There was very little variation in Ks among allof the calibrations with values clustered about 0.65.

5.4. Repeat results with a different model

The amount of modelling work in the study is too dauntingfor much repetition with different models; however, it waspossible to repeat enough with a different rainfallerunoffmodel to demonstrate that the results are inherent in the dataand are not a feature of the model.

Fortuitously, a computer program for calibration of theUSDA SCS Curve Number model (USDA Soil ConservationService, 1985), using the same format of input data as theAWBM, was available. To examine the difference betweenthe two models, the Curve Number model was calibrated toeach of the 55 10-year sub-periods in the same manner asthe AWBM in Section 4.

To obtain sufficient accuracy for the purpose, it was neces-sary to calibrate the Curve Numbers to the nearest 0.1. In thenormal manner, calibration was made of the Curve Number formiddle antecedent moisture (CN2) and the CN1 and CN3

determined from the published relationships with CN2 (Ponceand Hawkins, 1996). Calibration was made to match the totalcalculated runoff with total actual runoff in each 10-year pe-riod. Each calibration from a 10-year period was then usedwith the 64 years of rainfall data to estimate 64 years of runoff.This was divided by the actual runoff to give a ratio of calcu-lated to actual runoff. Fig. 6 shows the ratios from the 55 sub-sets of data using the Curve Number model.

Fig. 6 based on the Curve Number is very similar to Fig. 4that shows the same results from the AWBM. The two tempo-ral patterns of change in the ratio from start to finish of thedata set are very similar. The regions of ratios> 1.0 and ra-tios< 1.0 occur in similar areas of the two graphs.

The calibration of CN2 for the entire 64 years of data was95.5, which is higher than the range of CN2 in published rec-ommendations. Calibrations of CN2 in the individual 10-yearsub-periods ranged from 94.0 to 96.7. When used with the 64years of data, these gave estimates of long term runoff of394 mm/year and 599 mm/year, equal to �20% and þ22%.This range of error is very similar to that produced by theAWBM (�22% to þ15%). The very high Curve Numbersare probably due to the large percentage of rainfall (36%)that becomes runoff. The study catchment is very differentfrom the small and usually drier agricultural scale catchmentson which the Curve Number is usually used.

The results are enough to suggest that the variations in cal-ibration from short periods of data are a feature of the data andnot of the model. The similarities between Figs. 4 and 6 areheartening; however, there are so many different rainfallerunoff models now available that it is impossible to suggestthat the results are typical of all models. For the present pur-pose, the results are sufficient to avoid concerns that theyare attributable to the use of a particular model. There areother versions of the Curve Number available (e.g. Youngand Carleton, in press) but the version used is sufficiently

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55Start Year Number

Ratio

calcu

lated

/A

ctu

al

Fig. 6. Ratios of calculated to actual runoff from calibrations of the Curve Number model to 10-year samples of data.

411W.C. Boughton / Environmental Modelling & Software 22 (2007) 406e413

different from the AWBM that the results cannot be attributedto a particular model.

5.5. Sample versus model estimates of long term runoff

The study provided an opportunity to compare the results ofrainfallerunoff modelling for estimating long term averageannual runoff against the estimates from the data samples.For example, there were 63 data samples each of 2 years du-ration within the 64 years of record. The average annual runoffin each of the 2-year periods was taken as a ‘‘sample esti-mate’’ of the long term runoff, and compared with the ‘‘mod-elling estimate’’ obtained by calibrating the AWBM model tothe available data and then using 64 years of rainfall andevapotranspiration data to estimate runoff. Each estimatewas expressed as an absolute error from the recorded averagerunoff of 492 mm/year.

Fig. 7 compares the 63 pairs of sample and modelling esti-mates from the 2-year data samples. As expected, the esti-mates from the short samples have a great deal of variabilityand the modelling estimates have much smaller errors of esti-mate. The average error from the modelling was only 13.8%whereas the average error from the data samples was 24.7%.Of more significance, the maximum error from the sampleswas 121.5% compared with 41.5% from the modelling.

As the length of the data sample increases, errors decreasein both sample and model estimates. Table 2 summarizes theresults from each of the 2, 5, 10, 20 and 30 years length ofdata sample.

The modelling estimates are better than the sample esti-mates for 2, 5 and 10 years length of data sample. Unexpect-edly, the data samples provided the better estimates of longterm runoff with 20 and 30 years of available data. Modellinginvolves establishing a relationship between runoff and catch-ment rainfall, and the errors involved in estimating catchmentareal rainfall appear to limit the accuracy of long term runoffestimation even when a lengthy data sample is available forcalibration.

It seems that a length of data of about 15 years is whena change occurs. If less than 15 years of runoff data are avail-able, then using a rainfallerunoff model to extend the recordwill improve the estimate of long term runoff. If more than

15 years are available, then rainfallerunoff modelling is lesslikely to improve the estimate of long term runoff. At present,it is not certain if these results apply to other data sets andother rainfallerunoff models.

Long term average annual runoff is a very simple measureof the results of rainfallerunoff modelling. The main benefitobtained from calibrating a model and extending the runoff re-cord with longer records or stochastically generated rainfalldata is the longer temporal pattern of wet and dry spells, par-ticularly the latter, that determine the availability of water forany of the many different uses of streamflow. The simple mea-sure of average long term runoff has been used in this study togive a preliminary indication of the order of magnitude of er-ror in rainfallerunoff modelling as a guide to where futurestudies can be directed. Other studies are already being di-rected towards uncertainty in peak flows (Uhlenbrook andSieber, 2005) and to change in land use (Koivusalo et al., inpress).

6. Discussion

The calibration of the two baseflow parameters on all 2-year and 5-year subsets of data showed that BFI and Kb canbe estimated much better than the surface storage parametersfrom short periods of data. The baseflow parameters dependonly on the daily streamflow data and are not affected byany errors in estimation of areal rainfall. Techniques for sepa-ration of baseflow and surface runoff have been establishedand well tested for many years (Boughton, 1988; Chapman,1999). The results from the present study show that the base-flow characteristics are relatively constant from year to year inthe daily runoff record, and that the automatic calibration pro-cedure in the AWBM does not introduce spurious variation.The main problem is the variation in the runoff generationparameters.

The similarity of results from two different rainfallerunoffmodels, AWBM and the Curve Number, is evidence that thevariations in estimates of long term runoff from short periodsof record are inherent in the data, and are not an artifact ofmodelling. The version of the Curve Number used was theoriginal event-based method that is significantly different tothe continuous simulation of the AWBM. Although the

Sample v. Model Estimates of Long Term Runoff - 2

Year Samples

0.05.0

10.015.020.025.030.035.040.045.0

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0Absolute Error of Sample Estimate - Percent

Ab

so

lu

te E

rro

r o

f

Mo

del E

stim

ate - P

ercen

t

Fig. 7. Comparison of sample and model estimates of long term runoff using 2-year samples.

412 W.C. Boughton / Environmental Modelling & Software 22 (2007) 406e413

replication of calculations was limited, the results were suffi-cient to point the source of variation to the data and not tothe model. It is hoped that the study will be repeated withother models such as IHACRES (Croke et al., 2006) thathave already been tested under a wide range of conditions.

Table 1 shows that 90% of the estimates of long term runoffwere within the range of �21% to þ30% when there is only 2years of data to calibrate the rainfallerunoff model. The erroris very similar even when 5 years of data are available. Thereare several aspects of the results in Table 1 that are specific tothe Snowy Creek data, as follows:

� Fig. 4 shows an extended period in the data, starting inyear 17 and extending to year 49, when calibrations basedon a subset will underestimate the long term runoff. Theperiods when subsets of data will overestimate the longterm runoff are split between the start and end of thedata set. The consequence is that the probability of under-estimation of long term runoff is high even when subsetsof 20 and 30 years are available for calibration, whereasthe probability of overestimation decreases as the lengthof data for calibration increases.� Because of the separation of the periods producing under

and overestimation of long term runoff, there is very littledifference in error when either 2 years of data or 5 yearsof data are available for calibration. The overestimationsin the 75-percentile and 95-percentile values begin to de-crease when 10 or more years of data are available, butthe error of underestimation persists to the 20-year subsetsof data. It is highly likely that this lack of sensitivity to thelength of data available for calibration is inherent in theSnowy Creek data but might not be so with other data sets.

Evaporation has much less spatial and temporal variabilitythan rainfall; hence the output from rainfallerunoff models isless sensitive to change or errors in evaporation than in rain-fall. Chapman (2003) showed that average monthly evapora-tion can be used as a surrogate for daily evaporation withoutany significant loss of accuracy in the modelling of runoff.However, the sparse network of point measurements of panevaporation and the need to extrapolate to large catchmentarea provides some uncertainty.

The most probable reason for variations in the calibrationof the AWBM is the inevitable errors in estimating areal rain-fall over a 407 km2 catchment from point measurements ina few rain gauges. Over a period of 64 years, the operating

Table 2

Comparison of sample and modelling estimates of long term runoff

Sample

length

years

No of

samples

Absolute error (%)

Average Maximum

Sample Model Sample Model

2 63 24.7 13.8 121.5 41.5

5 60 20.3 13.7 62.5 37.8

10 55 14.2 11.9 33.6 24.0

20 45 4.3 9.8 9.2 21.5

30 35 4.1 8.6 10.6 16.3

rainfall stations change such that there are different point mea-surements available in different periods of the record. Hall andBarclay (1975) reported that ‘‘Areal rainfall estimates basedon point measurements should only be regarded as an indexof the true mean rainfall over a catchment and errors between10 and 20% can be regarded as normal. Where strong wind ef-fects or mountainous catchments are being experienced, errorsup to 60% can be experienced’’. These ranges of errors in rain-fall estimation can easily account for the variations in calibra-tion of the rainfallerunoff models found in this study.

The percent errors in estimates of long term runoff do nottranslate directly to errors in the safe yield of reservoirs orin probability of failure of a water supply system. The signif-icance of the errors will depend wholly on the purpose andspecific application of the modelling. The worst result fromuse of a short period of data is overestimation of the longterm runoff. While there was a bias towards underestimationof long term runoff in the data set used in the study, it is likelythat other data sets will produce the opposite bias. The SnowyCreek data were of good quality and there was no evidence tosuggest that it was abnormal or unusual in any way.

7. Conclusions

There are two significant results from the study of how cal-ibration of a rainfallerunoff model with a short period of dataaffects the estimate of long term runoff:

� The potential errors from use of short periods of data aresignificant, in the order of 20e30% when 2 to 5 years ofdata were available for calibration;� Results seem to be dependent most on the specific data set

but not much on the rainfallerunoff model used.

A significant result is that baseflow parameters can be cali-brated with little error from short periods of data. The problemcan be focused on the runoff generating parameters.

Because the characteristics of the data have a big influenceon the results, there is an obvious need for repetition of thestudy with other data sets. There is no shortage of other datasets with at least the 64 years of data used in the present study;however, the method is laborious and it would be optimistic toexpect a rush of other studies to extend the results. The mainhope is that the calculations can be automated to reduce thelabor content and allow a group of data sets to be studied.

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