Hydrological Sciences- Jour-nal-des Sciences Hydrologiques. 47( 1 ) February 2002

Calibrating a rainfall-runoff model for a catchment with limited data

J. WILK Department of Water and Environmental Studies, Linkoping University, S-5HI H3 Linkôping, Sweden iulwi@tema.liu.se

D. A. HUGHES Institute for Water Research, Rhodes University, PO Box 94, Grahamstmrn, 6140 South Africa

Abstract A rainfall-runoff model has been established to simulate streamflow in a regulated catchment in southern India, where data were limited in relation to the basin's complexity. Within the basin is a network of hydropower reservoirs and tunnels that complicate the relationships between observed and natural flows. The basin is affected by two monsoons that dominate in different areas and can only be quantified through a relatively sparse raingauge network. These characteristics combine to make it difficult to satisfactorily define the spatial distribution of rainfall inputs to the basin. After critically assessing the data that were found to be inconsistent and unrepresentative, various assumptions about the operation of the system were tested. Despite incomplete streamflow data and the complex hydropower system, the limiting factor affecting successful simulations of streamflow at the basin outlet was the uncertain representativeness of the calculated areal rainfall. The final outcome is a model, which despite shortcomings, is considered to be a useful water resources management tool that provides a sound basis for further studies. Key words rainfall-runoff modelling; Pitman model; limited data; land-use change; India

Calibrer un modèle pluie-débit pour un bassin versant avec des données limitées Résumé Un modèle pluie-débit a été établi pour simuler le débit dans un bassin versant régulé dans le sud de l'Inde, où les données sont limitées par rapport à la complexité du bassin. Il existe au sein du bassin un réseau de réservoirs hydro­électriques et de tunnels qui complique les relations entre les débits observés et naturels. Le bassin est affecté par deux moussons qui dominent dans des régions différentes et qui peuvent être quantifiées uniquement grâce à un réseau de pluviomètres relativement clairsemé. La combinaison de ces caractéristiques rend l'observation de la distribution spatiale des apports pluviométriques difficile. Après avoir évalué les données et montré qu'elles sont incohérentes et non représentatives, nous avons testé plusieurs hypothèses sur le fonctionnement du système. Malgré des données de débit incomplètes et la complexité du réseau hydro-électrique, le facteur le plus limitant dans les simulations de débit a été la mauvaise représentativité des calculs de pluie moyenne. Le résultat final est un modèle qui, malgré ses défauts, est vu comme un outil utile de gestion des ressources en eau, qui fournit une base solide pour des études supplémentaires. Mots clefs modélisation pluie-débit; modèle de Pitman; manque de données; changement d'occupation du sol; bilan de barrage; Inde

INTRODUCTION

In the application of rainfall-runoff models, some of the greatest uncertainties arise from inaccuracies in, or uncertainties about, the input data. While it is a reality that many catchments are not represented by sufficient data of good quality, there is a need

Open for discussion until I August 2002

4 J. Wilk & D. A. Hughes

to understand the water balance of a catchment as a basis for making sound water resource management decisions. This paper describes an attempt to establish a rainfall-runoff model and simulate runoff time series for a catchment in India for the eventual purpose of assessing the impact of land-use change on the streamflow regime. Although the catchment has a number of rainfall and streamflow recording stations, the accuracy as well as representativeness of the hydrometeorological records is questionable. Besides the existence of complex rainfall patterns caused by the occurrence of two monsoons, the catchment contains a network of reservoirs and transfer tunnels for hydropower purposes, which make understanding the system especially challenging. It is necessary to disaggregate the artificial and natural flow regime influences before modelling the hydrological response of the system.

The original intention of the study was to establish a rainfall-runoff model through calibration against observed flow data for a relatively short period when the land use was more or less static and then to assess the model results for longer periods over which known land-use changes had occurred. Without complete information on the historical variation of artificial transfers, it became apparent that disaggregating land-use effects from other influences on the streamflow regime would have been extremely difficult. The objective was therefore modified to one of establishing a suitable model to represent rainfall-runoff response characteristics under fixed land-use conditions so that sensi­tivity tests of the effects of different land-use scenarios could be carried out (Wilk & Hughes, 2002). To this end, the pre-modelling component of the study involved four main steps: - Obtain a better understanding of the spatial and temporal characteristics of rainfall

over the region and determine the procedures necessary to compile time series of rainfall input to the model for sub-catchments within the total basin area.

- Critically assess the available observed streamflow and water transfer data. - Obtain a reasonable understanding of the physical characteristics of the catch­

ments, such as soil and vegetation, to assist in the calibration of the model and the realistic quantification of model parameters.

- Select a rainfall-runoff model that has been demonstrated to have parameters that can reflect the effects of different land uses. The Pitman monthly time-step model (Pitman, 1973) was considered appropriate

as it does not have very stringent data requirements, has been applied to a wide range of catchment types and climate zones in southern Africa and has been demonstrated to be sensitive to land-use changes (Hughes, 1997). In a study involving catchments in Zimbabwe and South Africa, the model was used to investigate land-use impacts related to afforestation with pines and eucalypts or clear felling (ibid). Annual rainfall in these catchments was generally around 1000 mm, but reached as high as 2200 mm in mountain areas. Most of the land-use change impacts could be simulated using model parameter values that "made sense" in terms of the conceptual basis of the model and the expected impact of the land-use change on hydrological processes.

THE UPPER BHAVANI RIVER BASIN

The study area consists of the Upper Bhavani drainage basin lying upstream of the Bhavanisagar Reservoir; the two main rivers being the Bhavani and Moyar (Fig. 1).

Calibrating a rainfall runoff model for a catchment with limited data

30 Km ;

Fig. 1 The Upper Bhavani river basin showing the major river system and topography (m a.m.s.l.) at 200-m intervals.

The basin has a total area of 4100 knr and is a high altitude area at the confluence of the Eastern and Western Ghats with topography that is undulating in the lower plateau and uplands and rugged in the western parts. The elevation ranges from 300 m a.m.s.l. on the plains to 2600 m a.m.s.l. on the Nilgris Plateau, while mean annual precipitation varies from 700 mm on the lowlands to over 3000 mm in the hills (Fig. 1). The vegeta­tion cover is a mosaic of grassland, deciduous and coniferous mountain forests, planta­tion and agricultural crops. The soils in the basin are very deep and well drained, and only in the southeastern parts are there areas where more shallow soils exist with poorer drainage (based on soil map information from the Indian Department of Agriculture).

The main part of the basin experiences a humid equatorial climate, although the lowland plains are sub-humid. The dry season is from January to May, while heavy rains are common during the southwest (SW) monsoon (June-September), and the northeast (NE) monsoon (October-December). The SW-monsoon dominates in the western part of the river basin while the NE-monsoon prevails in the eastern region, due to the hills acting as a barrier to both monsoons. Both the western and eastern areas can therefore be regarded as rain shadow areas during one of the monsoon periods. Satisfactory calcula­tions of areal precipitation, based on regression equations, were found only after a division of the basin into areas dominated by one of the monsoons (Wilk & Andersson, 2000). It was demonstrated that distance to the southwestern border was the main factor influencing rainfall at stations dominated by the SW-monsoon, while for stations experiencing most of their rainfall during the NE-monsoon, altitude and slope were the most important factors. The basin has been divided into regions with characteristics that are typical of either the NE- or SW-monsoons which can be used to determine spatial rainfall variations that are expected to be more representative than methods based simply on distance between gauges.

M a.m.s.l.

200-399 400 - 599 600-799 800-999 1000-1199 1 200 - 1399 1400-1599 1600-1799 1800-1999 2000-2199 2200-2399 2400-2600

6 J. Wilk & D. A. Hughes

Fig. 2 The Upper Bhavani river basin showing major reservoirs, powerhouses, streamflow gauging stations (GS) and tunnels.

Apart from the Bhavanisagar Reservoir, which has a capacity of 986 Mm', there are 11 large reservoirs in the catchment, which provide an additional 481 Mm ' storage for hydropower generation (Fig. 2). There is a complex tunnel system between the reservoirs (Fig. 2), with water from Porthimund, Sandynallah and Parsons Valley reservoirs being transferred to Mukurthy and Pykara. Thereafter water flows into the smaller reservoirs (Glenmorgan and Moyar) before entering the Moyar River. Tunnels connect Porthimund and Parsons Valley to Avalanche Reservoir, which is in the Bhavani catchment and water is also transferred to Avalanche from the Upper Bhavani Reservoir. From Avalanche, water passes through three powerhouses and the Kundah Reservoir before reaching Pillur, the last reservoir in the hydropower system. From there it flows to the Bhavanisagar Reservoir at the basin outlet.

The aim of this study is to establish a monthly model for the entire Upper Bhavani basin, which has been divided into four linked modelling "projects". These projects were further divided into a total of 15 sub-catchments (Fig. 3) based on the hydrological layout of the catchment, with consideration given to establishing sub-areas where the climatic characteristics are reasonably homogeneous. Sub-catchment 2.1 thus refers to project 2, area 1.

HYDROMETEOROLOGICAL DATA

Precipitation

Data were available for 29 raingauges in or near the catchment, 16 with daily data and the remainder with monthly totals. A previous study (Wilk & Andersson, 2000)

Calibrating a rainfall-runoff model for a catchment with limited data 7

\J^A)3-W« >Curion V -•^y f { "^ \/ ( m Nh-monsoon group

1.1>-v (£^ V. \ 4 1 f • SW-monsoon group

< _ /~ 2.6 /

Fig. 3 The Upper Bhavani river basin showing numbered sub-catchments (the first digit refers to the project (PR) and the second to the sub-catchment) and locations of precipitation stations.

utilized all of the available stations to establish a gridded representation of mean rainfall for the main seasons (dry, NE-monsoon, SW-monsoon). The results were used to quantify the first component of the point-to-area weighting procedure, which generates representative rainfalls over the defined sub-catchments and accounts for the spatial variations that occur as a consequence of the two monsoons dominating different parts of the catchment. The second component of the point-to-area rainfall generation procedure uses an inverse distance (between sub-catchment centres and each raingauge) squared weighting technique. In summary, the point-to-area rainfall generation procedure is made up of two components: - a distance weight which determines the proportion of rainfall at a gauge to include

in the areal estimate; and - an additional weight that scales the gauge contribution by the ratio of the mean

value of the monthly or seasonal grid values in the sub-catchment to the grid value at the gauge. Only the 16 daily raingauges were used to generate the model input time series for

two reasons. The first was that any anomalous monthly rainfalls could be examined in more detail and the second was that consistent inputs could be generated for this monthly modelling study and a parallel study that used a daily rainfall-runoff model.

A critical issue that emerged was the combination of strongly systematic seasonal variations in monthly rainfall distribution and the frequency of missing values at key gauges. Missing values at gauges are replaced by the nearest station where data is available. However, when calculating areal rainfalls, it is important to use raingauges that belong to the monsoon group that best represents the rainfall over the sub-catchment. For example, even if three raingauges are close to the sub-catchment and in the same monsoon group as that which best represents the area, gaps in the observations can force the model to look further afield to raingauges which are in a different monsoon group. For each sub-catchment, the maximum number of raingauges to use and the maximum search distance were set, so that all gauges were in the same group with respect to the dominant monsoon. However, some gauges have experienced anomalously high or low values that may be due to one of the monsoons occasionally experiencing an extended area of influence. For example (cf. Fig. 3),

8 J. Will & D. A. Hughes

Curzon has 1053 mm in November 1979 compared to 762 mm at Corsely, its closest neighbour. The Curzon gauge was identified as a critical station for determining rainfall input to several sub-catchments and three extremely anomalous months were identified and adjusted to be closer to the rainfall at neighbouring stations.

Evapotranspiration data

A series of average potential évapotranspiration (PET) data for the entire basin were created by averaging Thornthwaite calculations at three stations. One was located on the lower plains just outside the catchment and the other two on the high plateau.

Observed flow data

Daily inflow (I) and outflow (O) data for Mukurthy (I), Porthimund (I&O), Parsons Valley (I&O), Upper Bhavani (I), Pillur (I) and Sandynallah (O) were obtained from the Tamil Nadu Electricity Board (TNEB) while daily streamflow data for the Moyar (GS3) and Bhavani rivers (GS2) were obtained from the Central Water Commission. Monthly inflow data to the Bhavanisagar Reservoir were made available from the Public Works Department.

The available flow records were provided without explanations about the measuring and data-processing techniques used and the individuals responsible were often difficult to contact, such that uncertainties in the data were difficult to resolve. It was therefore necessary to make assumptions about some of the data, based on a hydrological scheme that made most sense, using the records that were deemed most reliable.

The daily inflow records were assumed to be derived from calculated water balances of the reservoirs, but contain gaps that are unlikely to represent zero-flow periods. In order to generate a relatively complete monthly time series, it has been necessary to interpolate to fill in the gaps, a process that will be prone to error. However, most of the gaps are of short duration (less than 3 days) and expected to have a relatively minor impact on the monthly time series. A comparison of the inflow and outflow values for Parsons Valley and Porthimund showed that the outflow values were often higher than inflows. Given that the tunnel transfers are from these two reservoirs to Avalanche, the outflows would be expected to be less than the inflows. Unfortunately, there are no outflow data for either Upper Bhavani or Pillur, which are the most important reservoirs from a model calibration point of view. The records suggest that the inflow data are more accurate since they are recorded as daily volumetric values while the outflows are recorded as instantaneous spot measurements, which may fluctuate during the day.

The daily flow data from GS2 are derived from water level readings related to a rating curve. These showed large fluctuations (Fig. 4), possibly due to the influence of releases from Pillur. Recorded discharge values at GS3 also fluctuated to a greater extent than might be expected in a natural flow regime and suggest much lower runoff from the upstream catchment compared to GS2. Over the period 1980-1990 (for which the flow data were available), a mean annual precipitation (MAP) of 1130 mm over the catchment upstream of GS2 resulted in 460 mm of runoff measured at GS2. The catchment upstream of GS3 experienced an estimated MAP of 1400 mm, but a mean

Calibrating a rainfall-runoff model for a catchment with limited data 9

_ 250

?5 200

October 1983 November 1983

Fig. 4 Daily flow data at streamflow gauging station 2 (GS2) for October-November 1983.

annual runoff (MAR) of only 195 mm was recorded. These relative differences in rainfall-runoff response are difficult to account for, given the similarity in physical characteristics of the soils and topography of the two areas, even when allowing for the known transfers. The very high fluctuations in the daily data over short time intervals suggest that these gauging records are based on discrete flow observations, rather than continuous recording. Given the influence of fluctuating releases from the reservoirs upstream of these two sites, it is unlikely that these records can be used to compile accurate representations of monthly flow volumes.

Transfer flow data

There is a dense network of tunnels in the area, the five major ones being shown in Fig. 2. The tunnels have uncontrolled inlets (M. Bosc, Superintending Engineer, TNEB Kundah, personal communication, 1999) and the transfer volumes are estimated from the powerhouse (PH) discharges, obtained from the TNEB and assumed to be reasonably reliable. The powerhouse data represent the only source of information with which to quantify the difference between historical reservoir inflows or river discharges (at GS2 and GS3) and those flows that would be expected naturally.

Water is transferred from Upper Bhavani Reservoir to Avalanche via PH5. Mean monthly transfers vary between 5 and 12 MmJ with an overall mean annual value of 92 Mm1. Water is transferred from Porthimund and Parsons Valley (in Project 3— PR3) to Avalanche (in PR2), but there are no powerhouses located on these tunnels and direct measurements of transfer volumes are not available. The total mean annual inflow for Porthimund and Parsons Valley reservoirs (part of PR3) amounts to approximately 110 Mm', which represents the maximum possible transfer.

Transfers from Avalanche pass through Kundah via PHI and then to Pillur via PH2 and PH3. The mean annual flow through PH3 appears to be some 340 Mm', with a very even monthly distribution. An approximate water balance for Avalanche Reservoir can be summarized as follows:

Inflows (422 Mm3): 110 Mm3 from Porthimund and Parsons Valley (PR3) 92 Mm'1 from Upper Bhavani (PR1)

220 Mm'1 from the upstream catchment Outflows (422 Mm3): 340 Mm3 to PH3

82 Mm'1 in evaporation or as reservoir outflow

10 J. Wilk & D. A. Hughes

The estimate of 220 Mm from the upstream catchment has been based on scaling the inflows to Porthimund, Parsons Valley and Upper Bhavani by relative catchment sizes and is therefore very approximate.

MODELLING APPROACH

The Pitman model

The Pitman model is a semi-distributed water resource model designed to simulate river flows from monthly meteorological data (Fig. 5). The version used in this study is slightly modified from the original and these changes are referred to in Hughes (1995). The inputs to the model are monthly precipitation and mean monthly potential évapo­transpiration. The interception function is controlled by interception parameters (PIV and PIF) for open and afforested conditions (Table 1). There are two main functions that generate runoff. The first is a non-symmetrical triangular distribution that allows for heterogeneous spatial infiltration, defined by minimum, mean and maximum infiltration parameters, ZMIN, ZAVE and ZMAX. The greater the difference between ZMIN and ZMAX, the lower the runoff for any rainfall greater than ZMIN. The second function is controlled by a maximum moisture storage parameter (ST). Runoff occurs if a minimum storage value (SL) is exceeded and the runoff at ST is equal to FT. At moisture storages between SL and ST runoff is generated as a nonlinear function (defined by a power parameter, POW) of storage. Runoff from moisture storage can also be divided into two components that are routed separately to distinguish between slowly responding groundwater and more rapidly responding soil water. Once runoff is generated, it will reach the catchment outlet if there are no artificial abstractions. Actual évapotranspiration is determined by parameter R and monthly potential évapo­transpiration as a function of the moisture storage level. The parameter FF allows for an adjustment of the input potential évapotranspiration for two different land uses, i.e. forest and open land.

The Pitman model is appropriate for simulating the effect of land-use changes because it has parameters that control interception (PT), infiltration (AI, ZMIN, ZA VE and ZMAX) and actual évapotranspiration (R and FF). These parameters can be altered

Table 1 Definition of main Pitman model parameters.

Parameter Units Description

PIV, PIF

AI Z:

ZMIN ZAVE ZMAX ST FT FF R POW

%

mm month' mm month mm month" mm mm month"

Interception storage parameters for natural grassland and for forest cover Impervious part of the sub-catchment Three parameters defining the asymmetric triangular frequency distribution of catchment absorption rates: Minimum Average Maximum Maximum moisture storage capacity Runoff from moisture storage at full capacity (ST) Ratio of forest/grassland potential évapotranspiration Evaporation-moisture storage relationship parameter Power of the (runoff-soil moisture) curve

Calibrating a rainfall-runoff model for a catchment with limited data 11

Actual Evapotranspiration

Potential Evapotranspiration

Precipitation & Distribution

R and FF Interception (PIV/PIF)

Vegetation Growth Function

 < ^ 4

Impervious Area (AI)

Catchment Absorption

ZMIN ZMAX 1 1 Surface

Runoff

Soil Moisture & Groundwater Store

Runoff from Lower Zone

Runoff from Upper Zone

Small Dam Function

Lag and Attenuation

Lag and Attenuation

Upstream Inflow Irrigation Abstractions

and Return Flow

I Downstream Outflow

Fig. 5 Flow diagram representation of the Pitman model. The boxes with bold outline indicate changes from the original version.

to represent conditions under various vegetation covers, given their known effects on different hydrological processes based on previous scientific studies.

Occurrence of trends in the flow data

Annual, wet season (June-December) and dry season (January-May) flow volumes and QIP ratios were tested, where Q is the recorded discharge and P the estimated areal precipitation. All tests were performed on the data available during the period 1954-1994, as well as for 1970-1990, the period used for Pitman model calibration. The analysis program calculates the Seasonal Mann-Kendall test for trend according to

12 J. Wilk & D. A. Hughes

Hirsch et al. (1982) and Hirsch & Slack (1984) and the size of the trend using the Seasonal Kendall slope estimator (Hirsch et al., 1982). Trends were considered significant when the probability level of the results obtained by chance was less than 0.05.

Significant decreasing trends were found for annual and wet season inflow to Bhavanisagar for the period 1954-1994 and for annual and wet season QIP for the same time period, but no trends were detected for the modelling period 1970-1990. The latter period was therefore considered to be stationary and suitable for model calibration. Because of the lack of identifiable trends, the land-use related parameters were quantified on the basis of average land-use conditions over the simulation period and no attempt was made to account for temporal variation.

Calibration procedures

Reconstruction of the natural flow regime of the Upper Bhavani and Moyar catchments involved an exploratory modelling approach where various assumptions about the observed data were considered and tested. Those which gave the most sensible overall answers for all projects were accepted as being the most likely. The reservoir operations and transfers were not incorporated into the model because the data were not complete enough for time series variations to be defined.

The observed data used for calibration and the main assumptions (hypotheses) about how those data differ from natural are explained below for each project.

Project 1 The inflow data for the Upper Bhavani Reservoir are adequately representative of natural runoff in this catchment and can be used for model calibration purposes. The gaps in the data that are not clearly identified as missing by TNEB, are also assumed to represent missing data (rather than zero inflows) and have been filled using a simple linear interpolation procedure.

Project 2 The inflow data for Pillur Reservoir represents all the natural runoff from the upstream catchment, less that which is transferred through PH3. From the approximate water balance figures given above for Avalanche Reservoir, 312 MmJ

(92 + 220) represents the average annual inflow from within the Pillur catchment and less than 82 MmJ is assumed to flow through the catchment rather than to PH3. The balance of 230 MmJ should therefore represent the natural runoff above Pillur that is diverted to PH3 and not included in historical inflow measurements. Consequently a simulation of natural conditions should over-simulate the historical Pillur inflow data by approximately 230 Mm'. There is very little seasonal fluctuation in PH3 flows and it is assumed that the biggest impact would be in the dry season when natural inflows to Avalanche are lowest.

Project 3 The assumptions made for Project 2 are partly based on the approximate water balance of Avalanche Reservoir, which includes a maximum component of 110 Mnr' transferred from PR3. It must therefore be assumed that GS3 under-represents the natural runoff in PR3 by the same amount. However, the problems with the flow data at GS3 have already been noted.

Calibrating a rainfall-runoff model for a catchment with limited data 13

Project 4 The inflow represents runoff from the upstream catchment less evaporation losses from the reservoirs that are assumed to be 27 MmJ year"1 (based on regional evaporation data and reservoir surface areas). The seasonal distribution is expected to be flattened because of water stored during the wet season that is released through the powerhouses during the dry season.

RESULTS AND DISCUSSION

The simulations for all projects were carried out for the period January 1970-December 1990, although calibration data for PR1 were limited to the first 11 years. The main model parameters established for the different projects and their sub-areas are listed in Table 2. The results in terms of observed and simulated MAR, as well as coefficient of determination (R") and coefficient of efficiency (CE), are given in Table 3. The two coefficients are calculated as follows:

CE = 1 - ^(obsj - simj)lYX°bs, - obsM)

R~ = (L(obsj - obsM)(sim, - simM)ln-obsS-simS)~

Table 2 Range of the main Pitman model parameters for the calibrated projects.

AI POW ST FT ZMIN ZMAX R

PR1

0.10 2.0 350 80 500 600 1.0

PR2

0 2.0-2.5 500-900 30-70 500-800 700-1000 0.6-0.8

PR3

0-0.12 2.0-2.5 350-1200 30-80 500-1000 600-1200 0.7-0.9

PR4

0 2.5 1200 30 1000 1200 0.6-0.8

Table 3 Results of the model runs for each of the sub-catchments. The numbered sub-catchments are shown in Fig. 3. Observed MAR is shown only for the sub-catchments at the outlets of each project.

Project Sub-catchment

Total area (km2)

Mean annual precipitation MAP (mm)

Observed MAR (Mm3)

Simulated MAR (Mm3)

CE

1 2

3

4

1.1 2.1 2.2 2.3 2.4 2.5 2.6 3.1 3.2 3.3 3.4 3.5 3.6 4.1 4.2

37 367 122 264 258 117 353 531 120 100 206 215 183 664 522

3311 1638 1248 1252 2342 2100 1462 1429 1811 2514 1621 1252 1508 1135 1467

106

761

299

1699

101.8 881.8 929.4 979.5 405.1 115.6 122.0 622.4 311.7 185.4 126.3 51.3

737.9 1207 2060.3

0.79

0.70

0.44

0.75

0.78

0.61

-4.09

0.37

14 1 Wilk & D. A. Hughes

where obs, and sim, are the monthly observed and simulated flows, obsM and simM are the mean monthly flows, obsS and simS are the monthly standard deviations and n the number of months. R~ is always greater than CE and the difference between them represents the degree of systematic error in the simulation.

Project 1 area lies at an elevation of over 2000 m a.m.s.l. and experiences an annual rainfall in excess of 3000 mm. Table 3 indicates that the MAR has been simulated to within 5% of the observed data and there is very little systematic error. Fig. 6(a) illustrates that the biggest problem is under-simulation of the wet season peaks, which is possibly related to underestimation of wet season rainfall but cannot be confirmed. The parameter values used (Table 2) are reasonably consistent with values established for high rainfall, steep topography and well vegetated catchments in southern Africa (Hughes, 1997).

Project 2 area varies in altitude from 400 m a.m.s.l. to the 2000-m plateau. Soils are shallower on the lower elevations. A MAR of 1600 mm is experienced during the modelling period (1970-1990). Sub-area 2 of PR2 represents the outflow of Pillur Reservoir and Table 3 indicates that the MAR has been over-simulated by 169 Mm3, compared to the 230 Mm" which was expected given the assumptions outlined in the previous section. The natural MAR is assumed to be 991 MmJ (761 + 230), which means that the simulated MAR is 6% lower. The differences between the observed and simulated monthly distributions are as expected in that the dry season flows are over-simulated and the wet season peaks are reasonably well simulated in most years (Fig. 6(b)). The parameter values are consistent with PR1 given that the majority of PR2 has less steep topography and deeper soils (Table 2).

Project 3 extends from the high plateau to lower elevations of 800 m a.m.s.l. in the northern areas. Soils are very deep and annual average rainfall is 1690 mm. Table 3 indicates that there is little correspondence between the simulated and observed runoff patterns, which was anticipated given the assumed lack of representativeness of the flow data at GS3. The parameter values for PR3 have been established on a similar basis as for PR1 and PR2. Despite not being able to adequately assess the simulation for PR3, it was noted that for at least two years the peak wet season flows appeared to be anomalously high, which is thought to be a result of the rainfall weighting procedure. The rainfall is highly uncertain because of lack of precipitation gauges in the northern section.

The northern region of Project 4 lies at high altitude while the southern part is at 400 m a.m.s.l. Soils are shallower and annual average rainfall is the lowest in the basin at 1300 mm. The results for PR4 are illustrated in Fig. 6(c) and Table 3. Given the assumption that the observed MAR is expected to be less than the natural MAR by 27 Mm" (the estimated losses from the upstream reservoirs, which are not included in the model simulations), the results represent a 19% over-simulation. This appears to be mostly due to excessive peak flows in the wet seasons. The relatively high values for parameters ST and ZMIN for the majority of Projects 2, 3 and 4 (Table 2) suggest that further calibration will not have a great deal of impact on these peak flows. It is therefore suggested that the major cause of over-simulation for PR4 is related to a lack of representativeness of the input rainfall data for PR3. The spatial weighting procedure used to scale gauged rainfall to generate sub-catchment rainfall inputs relies upon a reasonably consistent relationship between observed rainfall at a gauge and expected rainfall over a sub-area. If a single gauge experiences an abnormally high

Calibrating a rainfall-runoff model for a catchment with limited data 15

(a) Project 1

(b)

60000

50000

40000

30000

20000

10000

0

500000

400000

300000

I 200000

100000

-Simulated

Observed

co r-U)

m r--O)

Project 2

Simulated

CO CO

(c) Project <

1400000

1200000

1000000

800000

600000

400000

200000

0 A/VW

Simulated

Observed

r -i h-c :>

CN r-o>

r̂ i~-Ol

CD t~-CD

00

|-~ o>

o 00 o>

CM 00 O)

• *

CO o>

CD CO O)

CO CO a>

o o> en

Fig. 6 Calibration curves for (a) Project 1, 1970-1980; (b) Project 2, 1970-1990; and (c) Project 4, 1970-1990.

monthly rainfall, this may result in an overexaggerated sub-area rainfall, if the sub-area/gauge weighting factor for that particular month is high. This effect is more likely

16 1 Wilk & D. A. Hughes

to occur with sparse networks where sub-area rainfall input relies upon gauges that are distant from the sub-area and where there is quite high spatial variation in monthly rainfall patterns. Both of these conditions apply in this study and especially in the northern area, which is part of PR3.

It should be noted that the results presented in this paper represent model cali­brations and no validation has been carried out at this stage of the study. Any valida­tion exercise would have been inconclusive given the uncertainties in the artificial transfer data that are currently available and can only be carried out when these uncertainties are clarified. While parameter interactions are known to occur within the Pitman model (as in any model of this type), the calibrated parameter set provides a unique result, within the range of values for the parameters that are realistic. The relative success of the simulations for PR1 and PR2 coupled with the assumption that the rainfall inputs for these projects are more reliable, suggests that the model parameters can be considered satisfactory to generate natural flow time series. The problem of over-simulation in PR4 is believed to be caused mainly by the poor results for PR3, since the over-simulated peaks in PR4 are also seen in PR3. The absorption and storage parameters used for PR3 are already higher than for PR2, despite the broad similarity in their soils and topography. It would therefore be difficult to justify changes to the parameter values that would result in a sufficient reduction in simulated runoff. Because this was judged to result from the poor model representation of rainfall for PR3, no further calibration was attempted, especially as it was deemed that this would not remedy the situation. Further evidence for the suspected errors in the catchment rainfall inputs to PR3 is provided by a comparison of the coefficients of variation (CV) for monthly runoff with those for monthly rainfall. The peak wet season month for the NE-monsoon dominated areas is November and the gauged rainfall data indicate a CV of between 0.6 and 0.7. For the SW-monsoon dominated areas, the peak rainfall month is July and the equivalent CV range is 0.5-0.9. However, the November simulated flow data (the peak flow month for PR3 and PR4) have CV values of 0.98-1.1, while the July simulated flow data (the peak flow month for PR2) have CV values between 0.5 and 0.6. The November flow CV values appear to be inconsistent with those of the gauged rainfall, which could be caused by the sub-area rainfall weighting procedure, as suggested previously.

CONCLUSIONS

There are many inconsistencies and potential inaccuracies in the available flow and transfer data that were evident at the beginning of the study, but have been emphasized through the modelling exercise. It is unfortunate that a lack of ready access to the data collecting agencies and possibly inappropriate flow observation methods, makes it almost impossible to resolve these problems at this stage. The situation is further exacerbated by the sparseness of the available rainfall data relative to the complex spatial variations that exist in this region. To improve the areal rainfall inputs to the model, it could be of benefit to modify the rainfall weighting procedure in the Pitman model so that it more fully utilizes the results from the areal rainfall study of Wilk & Andersson (2000). It would also be of interest to add the monthly raingauge series, which were not utilized in this study, to see if the calibrations can be improved. However, these stations are mainly located in the central region and would not help in

Calibrating a rainfall-runoff model for a catchment with limited data 17

the problematic northern region. To improve areal rainfall totals in this region, it would be necessary to find rainfall data of acceptable quality, if not in the northern area, then as close as possible to the watershed boundary.

When inconsistencies and gaps are apparent in input data, the data should be critically assessed and based on their reliability, assumptions made that provide for these inaccuracies and allow a reasonable conceptualization of the system to be developed. Through cross-checking, some of these assumptions can be discarded, while others, which may not be totally confirmed, can be retained to fill in gaps to create a quantitative working model of the hydrological regime. Despite shortcomings, the calibrated model is considered a useful tool for a land-use scenario study. The greatest errors are believed to be due to the complex rainfall regime in relation to scarce data availability. The model forms a basis for further studies in the basin, highlighting where additional data need to be collected, or assumptions confirmed, so that a more refined model can be established.

Acknowledgements The authors would like to thank the Tamil Nadu Electricity Board, the Central Water Commission and the Public Works Department of Tamil Nadu for providing data for this study. Special thanks go to K. Palanisamy and R. Sivanappan for all help with the adventure of data collection, M. Bosc for patience during various visits to the TNEB office in Kundah and Ramaraj for entering the original records into a computer database. Financing for the project was generously provided by SAREC (Swedish Agency for Research Co-operation with developing countries). The Swedish Institute also provided funding to facilitate research co­operation between Linkôping and Rhodes Universities.

REFERENCES

Hughes, D. A. (1995) Monthly rainfall-runoff models applied to arid and semiarid catchment for water resource estimation purposes. Hydro!. Sci. J. 40(6). 751-769.

Hughes, D. A. (1997) Southern Africa "FRIEND" -The Application of Rainfall-Runoff Models in the SADC Region. Report to the Water Research Commission bv the Institute for Water Research, Rhodes University. WRC Report no. 235/1.

Hirseh, R. M. & Slack, J. R. ( 1984) A nonparamelric trend test for seasonal data with serial dependence. Wat. Resour. Res. 20, 727-732.

Hirseh, R. M., Slack, J. R. & Smith, R. A. (1982) Techniques of trend analysis for monthly water quality data. Wat. Resour. Res. 18, 107-121.

Pitman, W. V. (1973) A mathematical model for generating monthly river flows from meteorological data in South Africa. Report no. 2, Hydrological Research Unit, Univ. of the Witwatersrand, South Africa.

Wilk, .1. & Andersson, L. (2000) GIS-supported modelling of areal rainfall in a mountainous river basin with monsoon climate in southern India. Hydro! Sci. J. 45(2), 185-202.

Wilk, J. & Hughes, D. A. (2002) Simulating the impacts of land-use and climate change on water resources availability in a large southern Indian catchment. Hydro! Sci. J. 47( 1 ), 19-30.

Received 6 March 2000; accepted 4 April 2001