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Analysis of the effect of rainfall and streamflow data quality and catchment dynamics on streamflow prediction using the rainfall-runoff model IHACRES
Environmental Software, Vol. 11. Nos 1-3, pp. 193-202, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0266-9838/96/$15.00 + 0.130
P I I : S0266-9838(96)00048-2
ELSEVIER
Analysis of the effect of rainfall and streamflow data quality and catchment dynamics on streamflow prediction using the rainfall-runoff model IHACRES D. P. Hansen, a W. Ye," A. J. Jakeman, a R. Cooke, b P. S h a r m a b aCentre for Resource and Environmental Studies, The Australian National University, Canberra, ACT, Australia bDepartment of Land and Water Conservation, Parramatta, NSW, Australia
Abstract A lumped-parameter rainfall-runoff model, IHACRES, has been used to predict the long-term natural variability of runoff from approximately 100 years of daily rainfall and evaporation data for eight different catchments. The model efficiently encapsulates the response dynamics of a catchment and is a good predictor of stream discharge. It is well suited to illustrate the factors influencing the quality of stream discharge predictions, in terms of rainfall-runoff model fits to daily discharge in calibration and validation mode and to the flow duration curve. The predominant factors are rain gauge density, stream gauge rating quality, catchment response dynamics (especially slowflow/baseflow volume) and the sampling interval of rainfall discharge (always daily here). These factors manifest themselves to sufficiently different degrees in the range of catchments studied to reveal a useful appreciation of their individual and combined contributions to the quality of streamflow prediction. The predictive benefits of improvements in rain gauge coverage or in stream discharge rating are indicated. A large proportion of slowflow/baseflow in a catchment is a factor which can compensate for data quality problems. The analysis and findings in this paper can be used to improve rainfall-runoff model performance and the synthesis of long-term stream discharge records in a large number and variety of catchments. Copyright O 1996 Elsevier Science Ltd
Keywords: Surface hydrology; model error
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1. Introduction
To assess the natural variability o f runoff, l o n g - t e r m historical flow sequences are required. H o w e v e r , these records m a y not extend sufficiently into the past. One w a y to synthesise these historical records is to a p p l y r a i n f a l l - r u n o f f m o d e l l i n g , w h i c h uses precipitation records often e x t e n d i n g m u c h further into the past, to simulate the r u n o f f o v e r that period. Recently, the c o n c e p t u a l rainfall-runoff m o d e l k n o w n as I H A C R E S
R a i n f a l l - r u n o f f m o d e l s are being used i n c r e a s i n g l y to investigate the natural variability o f runoff. K n o w ledge o f the s u p p l y o f water for p l a n n i n g needs from agriculture to d o m e s t i c supply allocation underlies the reasons for e x a m i n i n g the a m o u n t o f r u n o f f under different conditions. 193
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D.P. Hansen et al./Ralnfall-runoff model IHACRES
(Jakeman and Hornberger, 1993; Jakeman et al., 1990) was used to extend the runoff records in this way for eight catchments in the Clarance Basin, Northern New South Wales, Australia (Fig. 1). The IHACRES model was chosen as it has been used to study a wide variety of catchments (Jakeman
and Hornberger, 1993; Ye et al., 1996) and has several advantages over other models. One of the main advantages over other models is the small number of parameters needed and its high predictive accuracy. The fact that these parameters can describe the essential dynamics of the hydrological response of a catchment
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D. P. Hansen et al./Rainfall-runoff model IHACRES (Jakeman and Hornberger, 1993) and have been shown to be related to physical catchment attributes (Post and Jakeman, 1995) is also an advantage. Such relationships improve our understanding of catchment behaviour and have the potential to be used to predict streamflow in ungauged catchments in the study region. The main purpose of this work, however, was to synthesise daily streamflow data for the catchments in the Clarence River Basin for the purpose of water supply evaluation. The success of the simulation of historical runoff was very much dependent on the spatial coverage of the historical rainfall data, the quality of the stream discharge rating and the underlying nature of each catchment's hydrological response. For example, with the eight catchments varying in size from 315 km 2 to 4550 km 2 and with some only having a single rainfall gauge, problems with the accuracy and spatial representativeness of the rainfall data certainly arise. In this paper we present a preliminary analysis and case study to highlight the issues and factors which affect the accuracy of the simulated streamflow records. Previous studies (Duncan et al., 1993; Fabry et al., 1994) have concentrated on the effect of rain gauge density and have come to the conclusion that "As with estimates of areal rainfall we find that gauge density has a very strong effect on the estimation accuracy of hydrograph parameters with the standard error generally falling off as a power law with increasing gauge density" (Duncan et al., 1993).
2. The IHACRES model The conceptual model used here, IHACRES (Jakeman et al., 1990; Jakeman and Hornberger, 1993), extends unit hydrograph theory by assuming a linear relationship not only between effective rainfall and quickflow, but between effective rainfall and other identifiable hydrograph response components. The model consists of a nonlinear rainfall loss module which converts observed rainfall, rk, at timestep k, into effective or excess rainfall, uk, and a linear module which converts the excess rainfall into observed streamflow, qk. Usually the two modules use, in total, seven or eight parameters, also called dynamic response characteristics (Jakeman and Hornberger, 1993), to describe the way in which observed rainfall becomes observed streamflow. The nonlinear rainfall loss module used here transforms the measured precipitation, r~, into effective rainfall, uk, using
u~ --
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st = r J c + [1 - 1/(Tw(tD)]sk_,
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(3)
where st is a catchment wetness index, a function of tk, the evaporation at time k, and three dynamic response characteristics - - zw, a time constant for the decline in the catchment wetness index, f, which regulates the degree of evaporation dependence of the loss time constant, and c, which is selected to conserve the mass-balance of the catchment. The exponential loss parameter p, and a nonzero threshold value for rain to give streamflow, l, may sometimes be required to account for extra loss of rainfall in the catchment (Ye et al., 1996). The linear module uses a transfer function to allow the effective rainfall to pass through any combination of stores, in parallel and series, to become streamflow. The most common configuration uses two stores in parallel, one attributed to quickflow, x~'1~, and one to slowflow, x~~,. These combine to yield the stream-
flow, '~k, Ok = xi q) + xi")
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The parameters can be rewritten to give an easier physical interpretation in terms of time constants, zq and z~., and relative volumetric throughputs, Vq and Vs. In this case the linear module has three dynamic response characteristics, "rq, r~ and Vq (v, = 1 - vq), making a total of seven or eight (if 1 is nonzero) parameters for the model. Various statistics of the modelled streamflow output are used to measure the performance of the model including the absolute deviation (A), the bias (B), the observed streamflow variance explained (R2), and an objective function, O: N
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Candidate models are typically chosen as those with superior values to the preferred statistics. To find or calibrate the appropriate values of the parameters for a particular data set, the parameter space of the parameters, ~'w, f, P and l, from the nonlinear module is sampled. The effective rainfall series is then calculated and a simple refined instrumental variable technique (SRIV) used to estimate the linear module parameters automatically (Jakeman et al., 1990). The preferred model here is tentatively the one which, for sample zw, f, p and l values, yields the best combination of low O, high R 2 and low A and B. Usually a subperiod of the entire data set is used to calibrate the model, and then those parameters can be used to simulate over other subperiods, with output statistics again being calculated.
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D.P. Hansen et al./Rainfall-runoff model IHACRES
2.1. Calibration procedure Since we are examining the factors which most affect the output from a rainfall-runoff model, an attempt is made to find the best possible calibration of the model for each individual catchment. Hence, the best sections of the streamflow and rainfall data are chosen for the calibration procedure for each catchment. This means that some catchments have longer calibration periods than others and that usually the calibration periods encompass different time frames (in this case the length of the calibration and validation periods were between 5 and 10 years). Selecting the best section of the data involves checking the reliability and quality of the available rainfall and streamflow data. This consists of checking • • • • •
for missing data that the data are consistent for years which are drier consistency of rainfall-runoff ratios for irregularities in the data.
Double mass plots and flow duration curves can be used to check the reliability and consistency of the data in many ways. They can show the degree of nonlinearity in the rainfall-runoff relationship or error in the data, for example, when there is no flow but there is rainfall and vice versa. They can also give an indication of dry and wet periods, and of the varying proportion of flow to rain. The quality of the calibration and validation was finally judged by both visual and statistical comparison between simulated and observed flows. These judgements were based on: • time series plots • flow duration curves • various statistics, as described above. Based on the above assessment, the model is calibrated and then validated for each catchment. The model can then be run, given the rainfall since 1899, to simulate the daily streamflow record for the years 1899 - present. 2.2. Initial conditions The IHACRES model needs few preset initial conditions. However, there are some variables which may be used. One model variable which is sometimes used is a pure, integer time delay variable. If, after checking of the data, peak streamflow response generally occurs sometime after the rain, then the effective rain can be moved forward in time. In some of the catchments in the Clarence Basin, the timing of streamflow peaks, when checked against rainfall peaks, was noticed to be a day or two after the rainfall and the time delay was dependent on the size of the effective rain. Smaller
rainfall took some days to first appear in the streamflow record, while larger peaks may appear almost immediately. While this was a general rule, there were certainly exceptions, which can possibly be ascribed to the size of the catchment and the position and spacing of rain gauges. To deal with this general problem, a variable time delay was introduced. The time delays for different effective rainfall class sizes were plotted, and values selected for time delays of streamflow response. These delays improve the timing problems. However, it should be noted that a much better relationship could be found if rainfall--discharge data at a finer time scale were examined, and if the spatial density of the rain gauge recording network was higher.
3. Data 3.1. The Clarence Basin The catchments studied are in the Clarence Basin in northern New South Wales, Australia and are shown in Fig. 1. All catchments are relatively large, with the areas of the eight catchments being between 315 km z and 4550 km 2. The Clarence Basin for the most part traverses undulating or hilly country, but also contains some high peaks in the central and southern portions. It is bounded in the west by the Great Dividing Range, in the south by an eastward spur of the same range, in the east by the hilly to steep ranges from Coffs Harbour to Woodenborg and in the north by the McPherson Range. Within these boundaries a variety of landforms exists. The northern tributaries of the upper Clarence flow southwards and have generally widened their valleys in the soft, sedimentary rocks, resulting in the development of considerable areas of good, arable land, Some of these streams have formed alluvial flood plains. Between the valleys are steep, basalt capped ridges supporting dense vegetative cover. The streams flowing east from the New England Tablelands enter some very rugged country after they leave the plateau margin. On the descent to the lowlands they have become entrenched in deep valleys and gorges and the surrounding country is deeply dissected by their tributaries. Much of this broken country is suitable only for low-density grazing. Land slopes over the Clarence Valley are classified proportionately as follows: one-sixth of the valley has a generally flat surface; one-sixth is undulating to hilly; one-third is hilly to steep; one-third is rugged or mountainous terrain. Thus, rugged and steep slopes are predominant in the Clarence River Valley. The original land cover of the valley has been little disturbed over much of the central, rugged area, but medium or heavy cleating has taken place in other sections. Rainforests are found on the coastal plateau
D. P. Hansen et al./Rainfall-runoff model IHACRES and range tops which are of the subtropical jungle type. Arable land is limited, being confined by virtue of topography to about one-third of the catchment.
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Table 2 lists the availability of data, including the number of rainfall gauges in each catchment and the percentage of missing data.
3.2. Climate data for catchments
4. Factors affecting model performance Table 1 lists the eight catchments used in this study along with their area, mean annual rainfall, mean annual runoff and average percent runoff. For the eight catchments being modelled, rainfall stations, with data from 1899 to 1994, in or near the catchment were selected to determine the representative catchment rainfalls for use in the IHACRES models. Missing daily data or periods not covered in the major station record were infilled from other stations. Calculation of average daily rainfall for the catchments were based on the use of Thiessen polygons, with individual weights assigned to each of the rainfall records of the stations selected. Each catchment was analysed separately so that the representative rainfalls for each catchment would be independent. A daily time series of evaporation was synthesised for the period between 1899 and 1994 for evaporation stations at Coffs Harbour (059040) and Glen Innes (056013). The extended data were determined using the mean monthly pan evaporation data for the stations and a corresponding rainfall recording station for the period 1899-1994. The methodology for synthesising daily time series evaporation data is discussed in the IQQM Reference Manual (Department of Land and Water Conservation, 1995). Coifs Harbour evaporation data were applied to the catchments of the Orara River and Nymboida River, while Glen Innes evaporation was applied to the remainder of the catchments. Areas of influence were derived using an average annual evaporation map for NSW (Water Conservation and Irrigation Commission, 1971). Eight stream gauging stations have been used for calibration and validation of the IHACRES model. The reliability of recorded streamflow at these gauging stations is dependent on the accuracy of the measurement of stream (stage) heights and the rating curves which are used to derive streamflows.
When modelling flows in a natural system, such as discharge response in a catchment, there are several factors which will have an effect on the quality of the information extracted by a model. Some of the factors which constrain the quality of the results in this case, and which will be considered below, are: • • • • •
rain gauge coverage and reliability stream gauge quality catchment dynamics sampling interval of rainfall-discharge ratio of runoff to rainfall
The importance of rain gauge coverage, or more basically the representation of areal rainfall, and stream gauge rating is obvious - - good-quality data are needed for the inputs and outputs of a system to calibrate model parameters. The role of underlying catchment dynamics and the sampling interval for the rainfalldischarge time series requires some elaboration. With the IHACRES model, the dynamic response is characterised in terms of the following: a conceptual catchment store of maximum volume c; a loss for evapotranspiration from that store with a time constant ~w at 20 °C; modulation of the loss by a factor f per unit change of temperature; a quickflow recession time constant ~-q; a slowflow recession time constant %; and a volumetric proportion of quickflow (Vq) to total flow (Vq + v,). Our ability to identify these dynamics and the associated parameter values may affect the predictive accuracy of our model. Principally, it is difficult to estimate Vq or v~ accurately when either is less than about 10%. It is more difficult to estimate ~-q accurately if the sampling interval A (daily here) is not substantially more frequent than the value of ~-q - - while A < rq/4 is preferred, lower frequencies can be tolerated. Suffice it to say that A >> rq makes identification
Table 1 Eight catchments analysed: size and average annual rainfall and discharge Catchment name
Catchment area (km 2)
Mean Ann. rainfall (mm)
Mean Ann. discharge (ML)
Average % runoff (run/rain)
Nymboida River at Nymboida Orara River at Glenreagh Boyd River at Broadmeadows Mann River at Mitchell Henry River at Newton Boyd Clarence River at Tabulam Timbarra River at Drake Gordon Brook at Fine Flower
1660 446 2670 881 389 4550 1720 315
1547 1649 912 903 943
96,614 32,025 52,252 16,993 6479 124,643 59,400 105,066
23 33 14 12 10 17 22 31
1146 1006 1200
D. P. Hansen et al./Rainfall-runoff model IHACRES
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Table 2 Data availability for the eight catchments Catchment
Nymboida River Orara River Boyd River Mann River Henry River Clarence River Timbarra River Gordon Brook
Rainfall data
Streamflow data
No. of stations
Length of data
Length of data
Stream gauge % missing
3 2 4 4 2 5 3 *
1887-1994 1899-1994 1885-1994 1881-1994 1890-1994 1870-1994 1870-1994 *
5/5/56-31/5/93 6/11/72-30/4/93 6/5/70-30/4/93 10/5/72-30/4/93 7/8/71-30/4/93 1/1/70--4/8/93 7/7/69-30/4/93 15/6/69-31/5/93
16.9 2.2 2.6 1.2 1.2 5.4 1.6 16.9
*Gordon Brook catchment has no long-term rainfall stations within the catchment. Representative catchment rainfall was determined using the rainfall records from a nearby station.
of the quickflow component highly uncertain. On the other hand, some dynamics aid the identification. A larger value of vs produces a less noisy streamflow time series, and a larger ~s (and ~-q) produces a more slowly varying series. These dynamics, but especially a larger v~, allow streamflow to be fitted with a lower variance, which is a common desirable outcome of many predictive exercises. Of course, the proficiency of the model construction exercise itself can also affect model performance. It is assumed here that we have an appropriately structured model and a sensible calibration procedure. Support for this can be obtained by reference to the numerous successful applications of IHACRES over a wide range of hydroclimatologies and catchment sizes (e.g. (Jakeman and Hornberger, 1993; Schreider et al., 1996; Post and Jakeman, 1995; Jakeman et al., 1993). Another possible factor is the yield or volume of runoff to rainfall. Yields are not extremely low in the eight catchments and comment on the importance of this factor is given later in the paper. Now we examine the role of the different factors affecting the performance of the model in order to ascertain how future improvements in model prediction can be obtained.
5. Results Table 3 provides the model parameters obtained from calibration of the model on each catchment, which were then used to validate the model and perform the long-term simulation. Table 4 shows for each catchment the area per rain gauge, the (monitoring agency) rating for stream gauge quality (poor, average or good), a daily model performance rating (poor, average, good or very good, based on the R 2 for calibration and validation) and our rating for quality of model fit to the flow duration curve. Figure 2 shows the observed
Table 3 Essential IHACRES model parameters for the eight catchments Catchment name ~'w f
c
lnp l
%
%
v,
Nymboida River Orara River Boyd River Mann River Henry River Clarence River Timbarra River Gordon Brook
666 250 278 232 333 312 333 476
0.0 0.8 0.0 1.2 1.1 1.0 0.9 1.8
1.57 1.12 2.08 1.02 1.88 1.81 1.57 1.29
78 65 54 69 115 125 141 *
0.44 0.25 0.71 0.62 0.27 0.75 0.29 *
25 21 43 52 43 10 36 92
22 16 21 24 34 36 31 3
0.00 0.13 0.00 0.00 0.10 0.00 0.08 0.00
*Gordon Brook has no identifiable slowflow component. and modelled flow duration curves for each catchment from which the authors determined the latter rating as poor, fair or good. The following discussion for each catchment considers the performance ratings given in the two righthand columns in Table 4 and seeks to explain model performance, using the factors listed in the previous section.
5.1. Nymboida River at Nymboida The Nymbodia River catchment provided quite good results, with the R 2 for the validation period actually higher than for the calibration period, and the model fit to the flow duration curve in Fig. 2 rated (by the authors) qualitatively as good. The stream gauge rating is good, although the average area per rain gauge was quite large. The underlying dynamics of the catchment make for relatively easy identification of model parameters: the percentage runoff, at 23%, is modest but not low, so that the catchment passes a reasonable amount of information; and the IHACRES model parameters indicate a not very nonlinear response (In(p) = 0), roughly equivalent amounts of quickflow and slow-
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D. P. Hansen et a/./Rainfall-runoff model IHACRES Table 4 Model performance results, ratings and recommendations for the eight catchments Catchment
Area/ gauge (kin 2)
Stream gauge Slowflow Calibration rating volume R2
Validation Daily model R2 performance rating
Flow duration performance rating
Recommendation to improve performance*
Nymboida River Orara River Boyd River Mann River Henry River Clarence River Timbarra River Gordon Brook
553 223 667 220 195 910 573 315
good average poor averge poor average average poor
0.82 0.80 0.80 0.97 0.55 0.62 0.77 0.80
good good fair fair-good fair-good poor fair-good poor
1 3(2) 12 3(2) 2 1(2) 1(2) 12
0.44 0.25 0.71 0.62 0.27 0.75 0.29
0.75 0.91 0.85 0.99 0.72 0.75 0.58 0.85
good good good very good poor poor-fair poor-fair good
*Recommendation in parentheses could be followed if first recommendationdoes not yield performance enhancement. 1 = Improve accuracy of spatial representation of rainfall. 2 = Improve stream gauge rating. 3 = Estimate model parameters on a subdaily time step. flow (Vq =0.44, v~ = 0.56) with quite different time constants (1.6 versus 78.2). Small amounts of a flow component, either quickflow or slowflow, (e.g. <10%) make identification of that component difficult. With the dynamics of the Nymboida catchment well identified and the stream gauge rating good, one would expect model performance to be most improved for this catchment by an increase in the accuracy of the spatial representation of rainfall. 5.2. Orara River at Glenreagh The Orara River catchment is smaller than the Nymboida River catchment and has over twice the rain gauge density. This is revealed by the better calibration R 2. However, the lower stream gauge rating reflects itself in the lower validation R 2. The high calibration R 2 is also a reflection of the high percentage runoff, and easily identifiable catchment response dynamics, except for the quickflow time constant. With rq = 1.11 days, the sampling interval of rainfall--discharge could be shortened to less than a day to estimate the quickflow dynamics with more certainty. Improvement of the stream gauge rating would also be helpful to improve model predictions for this catchment.
density and/or stream discharge rating could easily push the model performance rating for this catchment much higher. 5.4. Mann River at Mitchell Although the Mann River catchment has only an average stream gauge rating, it has one of the best rain gauge coverages. The model does a very good job of modelling the daily streamflow and its fit to the flow duration curve is fair to good. In a similar way to the Boyd River catchment, a likely reason for these positive results lies in the catchment dynamics. With a slowflow volume ratio of 0.62, most of the flow is due to slowflow and most models, including IHACRES, find this slowflow much easier to fit. The Mann River results are, however, much better than the Boyd River, which is probably due to the much better rain gauge coverage and an average (versus poor) stream gauge rating. Since rq---1.02 days, representing the lowest value in all catchments, improvement in the identification, and possibly the prediction of quickflow, could be obtained by estimating model parameters using a subdaily time step. 5.5. Henry River at Newton Boyd
5.3. Boyd River at Broadmeadows Although the Boyd River catchment has low rain gauge density and a poor stream gauge rating, the model does a good job of modelling the streamflow. The major reason for this good rating lies in the catchment dynamics. With a slowflow volume ratio of vs = 0.71, most of the stream discharge is due to slowflow, which contributes, along with the longest quickflow time constant of the eight catchments (% = 2.08), to a smooth, more slowly changing, discharge curve that is easy to fit. These factors also permit a fair fit to the flow duration curve. Improvements in rain gauge
The Henry River catchment has a very similar rain gauge coverage to the Mann River. However, the stream gauge quality is poor, and a low percentage of flow comes through in the form of slowflow (v, = 0.27). While the calibration R 2 is quite good, probably a reflection of choosing a good period on which to calibrate, and the rain gauge coverage good, the validation R 2 is quite poor, reflecting the inferior quality of the discharge data. The average fit between the observed and modelled flow duration curve also reflects the quality of the model fit. Improvement to the stream gauge rating seems necessary for this catchment.
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Fig. 2. Clarence Basin catchments: observed and modelled flow discharge over the calibration and validation periods with author's rating in brackets.
D. P. Hansen et al./Rainfall-runoff model IHACRES 5.6. Clarence River at Tabulam
The Clarence River catchment is the largest of the catchments and with only five rain gauges within its boundaries has quite a poor rain gauge coverage. Even though the stream gauge rating is average, the results, especially for the validation period, reflect the poor rain gauge coverage. Even a very large slowflow component cannot compensate for the poor-quality rain data. The flow duration curve and rating show that for small to medium flows the fit is poor, again reflecting the poor rain data. It would seem that the rain gauge density should at least be doubled to improve model performance most easily. 5.7. Timbarra River at Drake
The Timbarra River catchment has average rain gauge density and stream gauge quality. It also has only 29% of slowflow as runoff. This results in a poor calibration R2, and a fair to good flow duration curve fit. 5.8. Gordon Brook at Fine Flower
Of all the catchments, the Gordon Brook catchment was felt to possess the worst streamflow records. The rainfall data comes from one rain gauge, outside the boundaries of the catchment. Careful selection of calibration and validation periods was required, which allowed good daily performance to be obtained. However, only the high flow end of the flow duration curve could be fitted well.
6. Conclusions Factors influencing the quality of stream discharge predictions, in terms of rainfall-runoff model fits to daily discharge in calibration and validation mode and to the flow duration curve, have been considered in an empirical fashion for eight catchments in the Clarence Basin of New South Wales, Australia. The predominant factors are rain gauge density (195-910km2/gauge), stream gauge rating quality (poor, average or good), catchment response dynamics (especially slowflow/baseflow volume), and sampling interval of rainfall-discharge (always daily here). An average (and good) stream gauge rating is capable of producing top performance, provided the rain gauge density is adequate. The performance in two of the catchments (Orara and Mann) with average stream gauge rating was as good overall as performance in the Nymbodia catchment where the stream gauge rating is good but the rain gauge density is less than half (553 kmZ/gauge versus 223 and 220). On the other hand, the other two catchments (Clarence and Timbarra) with average stream gauge rating but lower
201
densities of rain gauge coverage (910 and 573 km2/gauge) produce only fair performance overall. A poor stream gauge rating can to some extent be circumvented by judicious selection of calibration and validation periods but never allows good performance overall. Fortuitous catchment dynamics can enhance the model performance. Of most significance is the slowflow/baseflow value ratio (Vs) to total flow. The larger this volume (and secondarily the larger its time constant), the easier it is for a model to fit the medium and high flows of such a slowly evolving, smooth discharge curve. Mann catchment, like Orara, has an average stream gauge rating and low density of rain gauging (220 km2/gauge), but its daily fit to discharge in calibration and validation mode is very impressive with R2=0.99 and 0.97, respectively, because of its high proportion of slowflow (62% versus 27% for Orara). Similarly, the performance for Boyd (v,=0.71) is good for daily fitting, despite the poor stream gauge rating and a fairly low rain gauge density. As expected, it does not fit the lower (and medium) part of the flow duration curve well at all. However, for the Clarence, a high vs (0.75) and an average stream gauge rating does not mitigate the effect of a very low rain gauge density. Typically, a high vs does not help fit the lower portion of the flow duration curve, but it does help produce an almost fair daily fitting performance. In general, the rain gauge density does not impact upon the upper portion of the flow duration curve fit. High flow probabilities are explained well. This is probably due to the synoptic, spatially uniform nature of the rainfall associated with high flows. The rainfall losses in these catchments vary between 67 and 90%. The highest losses do not seem large enough to make prediction difficult in this region unless rain gauge coverage is poor (e.g. Clarence and Gordon Brook), or the stream gauge rating is poor and the slowflow volume ratio is small (Henry, vs = 0.27). This is consistent with Ye et al. (1996) who obtain good performance using IHACRES on low-yielding catchments (losses of 85-99%) with good-quality records. The nonlinearity of response in these catchments, as indicated by the p-value, covers a wide range but is not particularly high. Much larger p-values are usually accompanied by an absence of slowflow/baseflow, as is the case for the Gordon catchment. It would seem from our experience (e.g. Ye et al., 1996) that high nonlinearity does not make the prediction more difficult than in catchments with modest slowflow, the nonlinearity being compensated for by removal of the need to model baseflow. Higher slowflow catchments do not show this nonlinearity very strongly. The analysis and findings here obviously can be used to improve rainfall-runoff model performance and the synthesis of long-term stream discharge records in the Clarence Basin catchments. It is expected, however,
202
D . P . Hansen et al./Rainfall-runoff model IHACRES
that the methodology and the conclusions will be of benefit for similar modelling and synthesis in other regions of the world and in climates ranging from semi-arid, through temperate to tropical.
References Department of Land and Water Conservation (1995) Integrated Quality-Quantity Model, IQQM, Reference Manual. Technical report, Parramatta, New South Wales. Duncan, M. R., Austin, B., Fabry, F. and Austin, G. L. (1993) The effect of gauge sampling density on the accuracy of streamflow prediction for rural catchments. J. Hydrol. 142, 445-476. Fabry, F., Bellon, A., Duncan, M. R. and Austin, G. L. (1994) High resolution rainfall measurements by radar for very small basins: the sampling problem reexamined. J. Hydrol. 161, 415-428. Jakeman, A. J., Chen, T. H., Post, D. A., Homberger, G. M., Littlewood, I. G. and Whitehead, P. G. (1993) Assessing uncertainties in hydrological response to climate at large scale. In Macroscale Modelling of the Hydrosphere, ed. W. B. Wilkinson, pp. 37-47.
IAHS Publication No. 214, IAHS Press, Wallingford, UK. Jakeman, A. J. and Hornberger, G. M. (1993) How much complexity is warranted in a rainfall-runoff model. Water Res. Res 29(8), 2637-2649. Jakeman, A. J., Littlewood, I. G. and Whitehead, P. G. (1990) Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments. ]. Hydrol. 117, 275-300. Post, D. A. and Jakeman, A. J. (1995) Relationships between catchment attributes and hydrologic response characteristics in small Australian Mountain Ash catchments. Hydro. Proc. 10(6), 877-892. Schreider, S. Y., Jakeman, A. J. and Pittock, A. B. (1996) Modelling rainfall-runoff from large catchment to basin scale: the Goulburn Valley, Victoria. Hydro. Proc. 10(6), 863-876. Water Conservation and Irrigation Commission (1971) Water Resources of NSW. Technical report, Parramatta, New South Wales. Ye, W., Bates, B. C., Viney, N. R., Sivapalan, M. and Jakeman, A. J. (1996). Performance of conceptual rainfall-runoff models in low yeilding catchments. Water Resources Research (in press).
P I I : S0266-9838(96)00048-2
ELSEVIER
Analysis of the effect of rainfall and streamflow data quality and catchment dynamics on streamflow prediction using the rainfall-runoff model IHACRES D. P. Hansen, a W. Ye," A. J. Jakeman, a R. Cooke, b P. S h a r m a b aCentre for Resource and Environmental Studies, The Australian National University, Canberra, ACT, Australia bDepartment of Land and Water Conservation, Parramatta, NSW, Australia
Abstract A lumped-parameter rainfall-runoff model, IHACRES, has been used to predict the long-term natural variability of runoff from approximately 100 years of daily rainfall and evaporation data for eight different catchments. The model efficiently encapsulates the response dynamics of a catchment and is a good predictor of stream discharge. It is well suited to illustrate the factors influencing the quality of stream discharge predictions, in terms of rainfall-runoff model fits to daily discharge in calibration and validation mode and to the flow duration curve. The predominant factors are rain gauge density, stream gauge rating quality, catchment response dynamics (especially slowflow/baseflow volume) and the sampling interval of rainfall discharge (always daily here). These factors manifest themselves to sufficiently different degrees in the range of catchments studied to reveal a useful appreciation of their individual and combined contributions to the quality of streamflow prediction. The predictive benefits of improvements in rain gauge coverage or in stream discharge rating are indicated. A large proportion of slowflow/baseflow in a catchment is a factor which can compensate for data quality problems. The analysis and findings in this paper can be used to improve rainfall-runoff model performance and the synthesis of long-term stream discharge records in a large number and variety of catchments. Copyright O 1996 Elsevier Science Ltd
Keywords: Surface hydrology; model error
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1. Introduction
To assess the natural variability o f runoff, l o n g - t e r m historical flow sequences are required. H o w e v e r , these records m a y not extend sufficiently into the past. One w a y to synthesise these historical records is to a p p l y r a i n f a l l - r u n o f f m o d e l l i n g , w h i c h uses precipitation records often e x t e n d i n g m u c h further into the past, to simulate the r u n o f f o v e r that period. Recently, the c o n c e p t u a l rainfall-runoff m o d e l k n o w n as I H A C R E S
R a i n f a l l - r u n o f f m o d e l s are being used i n c r e a s i n g l y to investigate the natural variability o f runoff. K n o w ledge o f the s u p p l y o f water for p l a n n i n g needs from agriculture to d o m e s t i c supply allocation underlies the reasons for e x a m i n i n g the a m o u n t o f r u n o f f under different conditions. 193
194
D.P. Hansen et al./Ralnfall-runoff model IHACRES
(Jakeman and Hornberger, 1993; Jakeman et al., 1990) was used to extend the runoff records in this way for eight catchments in the Clarance Basin, Northern New South Wales, Australia (Fig. 1). The IHACRES model was chosen as it has been used to study a wide variety of catchments (Jakeman
and Hornberger, 1993; Ye et al., 1996) and has several advantages over other models. One of the main advantages over other models is the small number of parameters needed and its high predictive accuracy. The fact that these parameters can describe the essential dynamics of the hydrological response of a catchment
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D. P. Hansen et al./Rainfall-runoff model IHACRES (Jakeman and Hornberger, 1993) and have been shown to be related to physical catchment attributes (Post and Jakeman, 1995) is also an advantage. Such relationships improve our understanding of catchment behaviour and have the potential to be used to predict streamflow in ungauged catchments in the study region. The main purpose of this work, however, was to synthesise daily streamflow data for the catchments in the Clarence River Basin for the purpose of water supply evaluation. The success of the simulation of historical runoff was very much dependent on the spatial coverage of the historical rainfall data, the quality of the stream discharge rating and the underlying nature of each catchment's hydrological response. For example, with the eight catchments varying in size from 315 km 2 to 4550 km 2 and with some only having a single rainfall gauge, problems with the accuracy and spatial representativeness of the rainfall data certainly arise. In this paper we present a preliminary analysis and case study to highlight the issues and factors which affect the accuracy of the simulated streamflow records. Previous studies (Duncan et al., 1993; Fabry et al., 1994) have concentrated on the effect of rain gauge density and have come to the conclusion that "As with estimates of areal rainfall we find that gauge density has a very strong effect on the estimation accuracy of hydrograph parameters with the standard error generally falling off as a power law with increasing gauge density" (Duncan et al., 1993).
2. The IHACRES model The conceptual model used here, IHACRES (Jakeman et al., 1990; Jakeman and Hornberger, 1993), extends unit hydrograph theory by assuming a linear relationship not only between effective rainfall and quickflow, but between effective rainfall and other identifiable hydrograph response components. The model consists of a nonlinear rainfall loss module which converts observed rainfall, rk, at timestep k, into effective or excess rainfall, uk, and a linear module which converts the excess rainfall into observed streamflow, qk. Usually the two modules use, in total, seven or eight parameters, also called dynamic response characteristics (Jakeman and Hornberger, 1993), to describe the way in which observed rainfall becomes observed streamflow. The nonlinear rainfall loss module used here transforms the measured precipitation, r~, into effective rainfall, uk, using
u~ --
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st = r J c + [1 - 1/(Tw(tD)]sk_,
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195
(3)
where st is a catchment wetness index, a function of tk, the evaporation at time k, and three dynamic response characteristics - - zw, a time constant for the decline in the catchment wetness index, f, which regulates the degree of evaporation dependence of the loss time constant, and c, which is selected to conserve the mass-balance of the catchment. The exponential loss parameter p, and a nonzero threshold value for rain to give streamflow, l, may sometimes be required to account for extra loss of rainfall in the catchment (Ye et al., 1996). The linear module uses a transfer function to allow the effective rainfall to pass through any combination of stores, in parallel and series, to become streamflow. The most common configuration uses two stores in parallel, one attributed to quickflow, x~'1~, and one to slowflow, x~~,. These combine to yield the stream-
flow, '~k, Ok = xi q) + xi")
(4)
The parameters can be rewritten to give an easier physical interpretation in terms of time constants, zq and z~., and relative volumetric throughputs, Vq and Vs. In this case the linear module has three dynamic response characteristics, "rq, r~ and Vq (v, = 1 - vq), making a total of seven or eight (if 1 is nonzero) parameters for the model. Various statistics of the modelled streamflow output are used to measure the performance of the model including the absolute deviation (A), the bias (B), the observed streamflow variance explained (R2), and an objective function, O: N
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Candidate models are typically chosen as those with superior values to the preferred statistics. To find or calibrate the appropriate values of the parameters for a particular data set, the parameter space of the parameters, ~'w, f, P and l, from the nonlinear module is sampled. The effective rainfall series is then calculated and a simple refined instrumental variable technique (SRIV) used to estimate the linear module parameters automatically (Jakeman et al., 1990). The preferred model here is tentatively the one which, for sample zw, f, p and l values, yields the best combination of low O, high R 2 and low A and B. Usually a subperiod of the entire data set is used to calibrate the model, and then those parameters can be used to simulate over other subperiods, with output statistics again being calculated.
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D.P. Hansen et al./Rainfall-runoff model IHACRES
2.1. Calibration procedure Since we are examining the factors which most affect the output from a rainfall-runoff model, an attempt is made to find the best possible calibration of the model for each individual catchment. Hence, the best sections of the streamflow and rainfall data are chosen for the calibration procedure for each catchment. This means that some catchments have longer calibration periods than others and that usually the calibration periods encompass different time frames (in this case the length of the calibration and validation periods were between 5 and 10 years). Selecting the best section of the data involves checking the reliability and quality of the available rainfall and streamflow data. This consists of checking • • • • •
for missing data that the data are consistent for years which are drier consistency of rainfall-runoff ratios for irregularities in the data.
Double mass plots and flow duration curves can be used to check the reliability and consistency of the data in many ways. They can show the degree of nonlinearity in the rainfall-runoff relationship or error in the data, for example, when there is no flow but there is rainfall and vice versa. They can also give an indication of dry and wet periods, and of the varying proportion of flow to rain. The quality of the calibration and validation was finally judged by both visual and statistical comparison between simulated and observed flows. These judgements were based on: • time series plots • flow duration curves • various statistics, as described above. Based on the above assessment, the model is calibrated and then validated for each catchment. The model can then be run, given the rainfall since 1899, to simulate the daily streamflow record for the years 1899 - present. 2.2. Initial conditions The IHACRES model needs few preset initial conditions. However, there are some variables which may be used. One model variable which is sometimes used is a pure, integer time delay variable. If, after checking of the data, peak streamflow response generally occurs sometime after the rain, then the effective rain can be moved forward in time. In some of the catchments in the Clarence Basin, the timing of streamflow peaks, when checked against rainfall peaks, was noticed to be a day or two after the rainfall and the time delay was dependent on the size of the effective rain. Smaller
rainfall took some days to first appear in the streamflow record, while larger peaks may appear almost immediately. While this was a general rule, there were certainly exceptions, which can possibly be ascribed to the size of the catchment and the position and spacing of rain gauges. To deal with this general problem, a variable time delay was introduced. The time delays for different effective rainfall class sizes were plotted, and values selected for time delays of streamflow response. These delays improve the timing problems. However, it should be noted that a much better relationship could be found if rainfall--discharge data at a finer time scale were examined, and if the spatial density of the rain gauge recording network was higher.
3. Data 3.1. The Clarence Basin The catchments studied are in the Clarence Basin in northern New South Wales, Australia and are shown in Fig. 1. All catchments are relatively large, with the areas of the eight catchments being between 315 km z and 4550 km 2. The Clarence Basin for the most part traverses undulating or hilly country, but also contains some high peaks in the central and southern portions. It is bounded in the west by the Great Dividing Range, in the south by an eastward spur of the same range, in the east by the hilly to steep ranges from Coffs Harbour to Woodenborg and in the north by the McPherson Range. Within these boundaries a variety of landforms exists. The northern tributaries of the upper Clarence flow southwards and have generally widened their valleys in the soft, sedimentary rocks, resulting in the development of considerable areas of good, arable land, Some of these streams have formed alluvial flood plains. Between the valleys are steep, basalt capped ridges supporting dense vegetative cover. The streams flowing east from the New England Tablelands enter some very rugged country after they leave the plateau margin. On the descent to the lowlands they have become entrenched in deep valleys and gorges and the surrounding country is deeply dissected by their tributaries. Much of this broken country is suitable only for low-density grazing. Land slopes over the Clarence Valley are classified proportionately as follows: one-sixth of the valley has a generally flat surface; one-sixth is undulating to hilly; one-third is hilly to steep; one-third is rugged or mountainous terrain. Thus, rugged and steep slopes are predominant in the Clarence River Valley. The original land cover of the valley has been little disturbed over much of the central, rugged area, but medium or heavy cleating has taken place in other sections. Rainforests are found on the coastal plateau
D. P. Hansen et al./Rainfall-runoff model IHACRES and range tops which are of the subtropical jungle type. Arable land is limited, being confined by virtue of topography to about one-third of the catchment.
197
Table 2 lists the availability of data, including the number of rainfall gauges in each catchment and the percentage of missing data.
3.2. Climate data for catchments
4. Factors affecting model performance Table 1 lists the eight catchments used in this study along with their area, mean annual rainfall, mean annual runoff and average percent runoff. For the eight catchments being modelled, rainfall stations, with data from 1899 to 1994, in or near the catchment were selected to determine the representative catchment rainfalls for use in the IHACRES models. Missing daily data or periods not covered in the major station record were infilled from other stations. Calculation of average daily rainfall for the catchments were based on the use of Thiessen polygons, with individual weights assigned to each of the rainfall records of the stations selected. Each catchment was analysed separately so that the representative rainfalls for each catchment would be independent. A daily time series of evaporation was synthesised for the period between 1899 and 1994 for evaporation stations at Coffs Harbour (059040) and Glen Innes (056013). The extended data were determined using the mean monthly pan evaporation data for the stations and a corresponding rainfall recording station for the period 1899-1994. The methodology for synthesising daily time series evaporation data is discussed in the IQQM Reference Manual (Department of Land and Water Conservation, 1995). Coifs Harbour evaporation data were applied to the catchments of the Orara River and Nymboida River, while Glen Innes evaporation was applied to the remainder of the catchments. Areas of influence were derived using an average annual evaporation map for NSW (Water Conservation and Irrigation Commission, 1971). Eight stream gauging stations have been used for calibration and validation of the IHACRES model. The reliability of recorded streamflow at these gauging stations is dependent on the accuracy of the measurement of stream (stage) heights and the rating curves which are used to derive streamflows.
When modelling flows in a natural system, such as discharge response in a catchment, there are several factors which will have an effect on the quality of the information extracted by a model. Some of the factors which constrain the quality of the results in this case, and which will be considered below, are: • • • • •
rain gauge coverage and reliability stream gauge quality catchment dynamics sampling interval of rainfall-discharge ratio of runoff to rainfall
The importance of rain gauge coverage, or more basically the representation of areal rainfall, and stream gauge rating is obvious - - good-quality data are needed for the inputs and outputs of a system to calibrate model parameters. The role of underlying catchment dynamics and the sampling interval for the rainfalldischarge time series requires some elaboration. With the IHACRES model, the dynamic response is characterised in terms of the following: a conceptual catchment store of maximum volume c; a loss for evapotranspiration from that store with a time constant ~w at 20 °C; modulation of the loss by a factor f per unit change of temperature; a quickflow recession time constant ~-q; a slowflow recession time constant %; and a volumetric proportion of quickflow (Vq) to total flow (Vq + v,). Our ability to identify these dynamics and the associated parameter values may affect the predictive accuracy of our model. Principally, it is difficult to estimate Vq or v~ accurately when either is less than about 10%. It is more difficult to estimate ~-q accurately if the sampling interval A (daily here) is not substantially more frequent than the value of ~-q - - while A < rq/4 is preferred, lower frequencies can be tolerated. Suffice it to say that A >> rq makes identification
Table 1 Eight catchments analysed: size and average annual rainfall and discharge Catchment name
Catchment area (km 2)
Mean Ann. rainfall (mm)
Mean Ann. discharge (ML)
Average % runoff (run/rain)
Nymboida River at Nymboida Orara River at Glenreagh Boyd River at Broadmeadows Mann River at Mitchell Henry River at Newton Boyd Clarence River at Tabulam Timbarra River at Drake Gordon Brook at Fine Flower
1660 446 2670 881 389 4550 1720 315
1547 1649 912 903 943
96,614 32,025 52,252 16,993 6479 124,643 59,400 105,066
23 33 14 12 10 17 22 31
1146 1006 1200
D. P. Hansen et al./Rainfall-runoff model IHACRES
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Table 2 Data availability for the eight catchments Catchment
Nymboida River Orara River Boyd River Mann River Henry River Clarence River Timbarra River Gordon Brook
Rainfall data
Streamflow data
No. of stations
Length of data
Length of data
Stream gauge % missing
3 2 4 4 2 5 3 *
1887-1994 1899-1994 1885-1994 1881-1994 1890-1994 1870-1994 1870-1994 *
5/5/56-31/5/93 6/11/72-30/4/93 6/5/70-30/4/93 10/5/72-30/4/93 7/8/71-30/4/93 1/1/70--4/8/93 7/7/69-30/4/93 15/6/69-31/5/93
16.9 2.2 2.6 1.2 1.2 5.4 1.6 16.9
*Gordon Brook catchment has no long-term rainfall stations within the catchment. Representative catchment rainfall was determined using the rainfall records from a nearby station.
of the quickflow component highly uncertain. On the other hand, some dynamics aid the identification. A larger value of vs produces a less noisy streamflow time series, and a larger ~s (and ~-q) produces a more slowly varying series. These dynamics, but especially a larger v~, allow streamflow to be fitted with a lower variance, which is a common desirable outcome of many predictive exercises. Of course, the proficiency of the model construction exercise itself can also affect model performance. It is assumed here that we have an appropriately structured model and a sensible calibration procedure. Support for this can be obtained by reference to the numerous successful applications of IHACRES over a wide range of hydroclimatologies and catchment sizes (e.g. (Jakeman and Hornberger, 1993; Schreider et al., 1996; Post and Jakeman, 1995; Jakeman et al., 1993). Another possible factor is the yield or volume of runoff to rainfall. Yields are not extremely low in the eight catchments and comment on the importance of this factor is given later in the paper. Now we examine the role of the different factors affecting the performance of the model in order to ascertain how future improvements in model prediction can be obtained.
5. Results Table 3 provides the model parameters obtained from calibration of the model on each catchment, which were then used to validate the model and perform the long-term simulation. Table 4 shows for each catchment the area per rain gauge, the (monitoring agency) rating for stream gauge quality (poor, average or good), a daily model performance rating (poor, average, good or very good, based on the R 2 for calibration and validation) and our rating for quality of model fit to the flow duration curve. Figure 2 shows the observed
Table 3 Essential IHACRES model parameters for the eight catchments Catchment name ~'w f
c
lnp l
%
%
v,
Nymboida River Orara River Boyd River Mann River Henry River Clarence River Timbarra River Gordon Brook
666 250 278 232 333 312 333 476
0.0 0.8 0.0 1.2 1.1 1.0 0.9 1.8
1.57 1.12 2.08 1.02 1.88 1.81 1.57 1.29
78 65 54 69 115 125 141 *
0.44 0.25 0.71 0.62 0.27 0.75 0.29 *
25 21 43 52 43 10 36 92
22 16 21 24 34 36 31 3
0.00 0.13 0.00 0.00 0.10 0.00 0.08 0.00
*Gordon Brook has no identifiable slowflow component. and modelled flow duration curves for each catchment from which the authors determined the latter rating as poor, fair or good. The following discussion for each catchment considers the performance ratings given in the two righthand columns in Table 4 and seeks to explain model performance, using the factors listed in the previous section.
5.1. Nymboida River at Nymboida The Nymbodia River catchment provided quite good results, with the R 2 for the validation period actually higher than for the calibration period, and the model fit to the flow duration curve in Fig. 2 rated (by the authors) qualitatively as good. The stream gauge rating is good, although the average area per rain gauge was quite large. The underlying dynamics of the catchment make for relatively easy identification of model parameters: the percentage runoff, at 23%, is modest but not low, so that the catchment passes a reasonable amount of information; and the IHACRES model parameters indicate a not very nonlinear response (In(p) = 0), roughly equivalent amounts of quickflow and slow-
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D. P. Hansen et a/./Rainfall-runoff model IHACRES Table 4 Model performance results, ratings and recommendations for the eight catchments Catchment
Area/ gauge (kin 2)
Stream gauge Slowflow Calibration rating volume R2
Validation Daily model R2 performance rating
Flow duration performance rating
Recommendation to improve performance*
Nymboida River Orara River Boyd River Mann River Henry River Clarence River Timbarra River Gordon Brook
553 223 667 220 195 910 573 315
good average poor averge poor average average poor
0.82 0.80 0.80 0.97 0.55 0.62 0.77 0.80
good good fair fair-good fair-good poor fair-good poor
1 3(2) 12 3(2) 2 1(2) 1(2) 12
0.44 0.25 0.71 0.62 0.27 0.75 0.29
0.75 0.91 0.85 0.99 0.72 0.75 0.58 0.85
good good good very good poor poor-fair poor-fair good
*Recommendation in parentheses could be followed if first recommendationdoes not yield performance enhancement. 1 = Improve accuracy of spatial representation of rainfall. 2 = Improve stream gauge rating. 3 = Estimate model parameters on a subdaily time step. flow (Vq =0.44, v~ = 0.56) with quite different time constants (1.6 versus 78.2). Small amounts of a flow component, either quickflow or slowflow, (e.g. <10%) make identification of that component difficult. With the dynamics of the Nymboida catchment well identified and the stream gauge rating good, one would expect model performance to be most improved for this catchment by an increase in the accuracy of the spatial representation of rainfall. 5.2. Orara River at Glenreagh The Orara River catchment is smaller than the Nymboida River catchment and has over twice the rain gauge density. This is revealed by the better calibration R 2. However, the lower stream gauge rating reflects itself in the lower validation R 2. The high calibration R 2 is also a reflection of the high percentage runoff, and easily identifiable catchment response dynamics, except for the quickflow time constant. With rq = 1.11 days, the sampling interval of rainfall--discharge could be shortened to less than a day to estimate the quickflow dynamics with more certainty. Improvement of the stream gauge rating would also be helpful to improve model predictions for this catchment.
density and/or stream discharge rating could easily push the model performance rating for this catchment much higher. 5.4. Mann River at Mitchell Although the Mann River catchment has only an average stream gauge rating, it has one of the best rain gauge coverages. The model does a very good job of modelling the daily streamflow and its fit to the flow duration curve is fair to good. In a similar way to the Boyd River catchment, a likely reason for these positive results lies in the catchment dynamics. With a slowflow volume ratio of 0.62, most of the flow is due to slowflow and most models, including IHACRES, find this slowflow much easier to fit. The Mann River results are, however, much better than the Boyd River, which is probably due to the much better rain gauge coverage and an average (versus poor) stream gauge rating. Since rq---1.02 days, representing the lowest value in all catchments, improvement in the identification, and possibly the prediction of quickflow, could be obtained by estimating model parameters using a subdaily time step. 5.5. Henry River at Newton Boyd
5.3. Boyd River at Broadmeadows Although the Boyd River catchment has low rain gauge density and a poor stream gauge rating, the model does a good job of modelling the streamflow. The major reason for this good rating lies in the catchment dynamics. With a slowflow volume ratio of vs = 0.71, most of the stream discharge is due to slowflow, which contributes, along with the longest quickflow time constant of the eight catchments (% = 2.08), to a smooth, more slowly changing, discharge curve that is easy to fit. These factors also permit a fair fit to the flow duration curve. Improvements in rain gauge
The Henry River catchment has a very similar rain gauge coverage to the Mann River. However, the stream gauge quality is poor, and a low percentage of flow comes through in the form of slowflow (v, = 0.27). While the calibration R 2 is quite good, probably a reflection of choosing a good period on which to calibrate, and the rain gauge coverage good, the validation R 2 is quite poor, reflecting the inferior quality of the discharge data. The average fit between the observed and modelled flow duration curve also reflects the quality of the model fit. Improvement to the stream gauge rating seems necessary for this catchment.
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Henry River (fair-good)
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Gordon Brook (poor)
Fig. 2. Clarence Basin catchments: observed and modelled flow discharge over the calibration and validation periods with author's rating in brackets.
D. P. Hansen et al./Rainfall-runoff model IHACRES 5.6. Clarence River at Tabulam
The Clarence River catchment is the largest of the catchments and with only five rain gauges within its boundaries has quite a poor rain gauge coverage. Even though the stream gauge rating is average, the results, especially for the validation period, reflect the poor rain gauge coverage. Even a very large slowflow component cannot compensate for the poor-quality rain data. The flow duration curve and rating show that for small to medium flows the fit is poor, again reflecting the poor rain data. It would seem that the rain gauge density should at least be doubled to improve model performance most easily. 5.7. Timbarra River at Drake
The Timbarra River catchment has average rain gauge density and stream gauge quality. It also has only 29% of slowflow as runoff. This results in a poor calibration R2, and a fair to good flow duration curve fit. 5.8. Gordon Brook at Fine Flower
Of all the catchments, the Gordon Brook catchment was felt to possess the worst streamflow records. The rainfall data comes from one rain gauge, outside the boundaries of the catchment. Careful selection of calibration and validation periods was required, which allowed good daily performance to be obtained. However, only the high flow end of the flow duration curve could be fitted well.
6. Conclusions Factors influencing the quality of stream discharge predictions, in terms of rainfall-runoff model fits to daily discharge in calibration and validation mode and to the flow duration curve, have been considered in an empirical fashion for eight catchments in the Clarence Basin of New South Wales, Australia. The predominant factors are rain gauge density (195-910km2/gauge), stream gauge rating quality (poor, average or good), catchment response dynamics (especially slowflow/baseflow volume), and sampling interval of rainfall-discharge (always daily here). An average (and good) stream gauge rating is capable of producing top performance, provided the rain gauge density is adequate. The performance in two of the catchments (Orara and Mann) with average stream gauge rating was as good overall as performance in the Nymbodia catchment where the stream gauge rating is good but the rain gauge density is less than half (553 kmZ/gauge versus 223 and 220). On the other hand, the other two catchments (Clarence and Timbarra) with average stream gauge rating but lower
201
densities of rain gauge coverage (910 and 573 km2/gauge) produce only fair performance overall. A poor stream gauge rating can to some extent be circumvented by judicious selection of calibration and validation periods but never allows good performance overall. Fortuitous catchment dynamics can enhance the model performance. Of most significance is the slowflow/baseflow value ratio (Vs) to total flow. The larger this volume (and secondarily the larger its time constant), the easier it is for a model to fit the medium and high flows of such a slowly evolving, smooth discharge curve. Mann catchment, like Orara, has an average stream gauge rating and low density of rain gauging (220 km2/gauge), but its daily fit to discharge in calibration and validation mode is very impressive with R2=0.99 and 0.97, respectively, because of its high proportion of slowflow (62% versus 27% for Orara). Similarly, the performance for Boyd (v,=0.71) is good for daily fitting, despite the poor stream gauge rating and a fairly low rain gauge density. As expected, it does not fit the lower (and medium) part of the flow duration curve well at all. However, for the Clarence, a high vs (0.75) and an average stream gauge rating does not mitigate the effect of a very low rain gauge density. Typically, a high vs does not help fit the lower portion of the flow duration curve, but it does help produce an almost fair daily fitting performance. In general, the rain gauge density does not impact upon the upper portion of the flow duration curve fit. High flow probabilities are explained well. This is probably due to the synoptic, spatially uniform nature of the rainfall associated with high flows. The rainfall losses in these catchments vary between 67 and 90%. The highest losses do not seem large enough to make prediction difficult in this region unless rain gauge coverage is poor (e.g. Clarence and Gordon Brook), or the stream gauge rating is poor and the slowflow volume ratio is small (Henry, vs = 0.27). This is consistent with Ye et al. (1996) who obtain good performance using IHACRES on low-yielding catchments (losses of 85-99%) with good-quality records. The nonlinearity of response in these catchments, as indicated by the p-value, covers a wide range but is not particularly high. Much larger p-values are usually accompanied by an absence of slowflow/baseflow, as is the case for the Gordon catchment. It would seem from our experience (e.g. Ye et al., 1996) that high nonlinearity does not make the prediction more difficult than in catchments with modest slowflow, the nonlinearity being compensated for by removal of the need to model baseflow. Higher slowflow catchments do not show this nonlinearity very strongly. The analysis and findings here obviously can be used to improve rainfall-runoff model performance and the synthesis of long-term stream discharge records in the Clarence Basin catchments. It is expected, however,
202
D . P . Hansen et al./Rainfall-runoff model IHACRES
that the methodology and the conclusions will be of benefit for similar modelling and synthesis in other regions of the world and in climates ranging from semi-arid, through temperate to tropical.
References Department of Land and Water Conservation (1995) Integrated Quality-Quantity Model, IQQM, Reference Manual. Technical report, Parramatta, New South Wales. Duncan, M. R., Austin, B., Fabry, F. and Austin, G. L. (1993) The effect of gauge sampling density on the accuracy of streamflow prediction for rural catchments. J. Hydrol. 142, 445-476. Fabry, F., Bellon, A., Duncan, M. R. and Austin, G. L. (1994) High resolution rainfall measurements by radar for very small basins: the sampling problem reexamined. J. Hydrol. 161, 415-428. Jakeman, A. J., Chen, T. H., Post, D. A., Homberger, G. M., Littlewood, I. G. and Whitehead, P. G. (1993) Assessing uncertainties in hydrological response to climate at large scale. In Macroscale Modelling of the Hydrosphere, ed. W. B. Wilkinson, pp. 37-47.
IAHS Publication No. 214, IAHS Press, Wallingford, UK. Jakeman, A. J. and Hornberger, G. M. (1993) How much complexity is warranted in a rainfall-runoff model. Water Res. Res 29(8), 2637-2649. Jakeman, A. J., Littlewood, I. G. and Whitehead, P. G. (1990) Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments. ]. Hydrol. 117, 275-300. Post, D. A. and Jakeman, A. J. (1995) Relationships between catchment attributes and hydrologic response characteristics in small Australian Mountain Ash catchments. Hydro. Proc. 10(6), 877-892. Schreider, S. Y., Jakeman, A. J. and Pittock, A. B. (1996) Modelling rainfall-runoff from large catchment to basin scale: the Goulburn Valley, Victoria. Hydro. Proc. 10(6), 863-876. Water Conservation and Irrigation Commission (1971) Water Resources of NSW. Technical report, Parramatta, New South Wales. Ye, W., Bates, B. C., Viney, N. R., Sivapalan, M. and Jakeman, A. J. (1996). Performance of conceptual rainfall-runoff models in low yeilding catchments. Water Resources Research (in press).