Rainfall–runoff modelling approach for ungauged catchments: A case study of Nzhelele River sub-quaternary catchment

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Abstract

This paper presents a rainfall–runoff (RR) modelling method aimed at generating natural streamflow from the modified nearest neighbour regionalization approach applied to two ungauged sub-quaternary catchments (SQCs) nested within an ungauged quaternary catchment. It differs from the commonly used nearest neighbour regionalization approach involving a gauged quaternary catchment and an ungauged quaternary catchment. This approach ensures improvement in homogeneity of the estimated hydrological parameters. Lack of gauged streamflows hampers water resources planning and management, and water resources systems operation including allocations for environmental flows. The method has been applied in the Tshiluvhadi and the Nzhelele Rivers SQCs in quaternary catchment A80A of the Nzhelele River Catchment in the Limpopo River Basin. The modelling approach involved computing inflow hydrograph from a water balance model for Mutshedzi Dam. The hydrograph was then used in the calibration and verification of the RR model for the Tshiluvhadi River SQC using the Mike 11 NAM and Australian Water Balance Model (AWBM) in order to determine the model with better performance. The performance of each of the two models assessed by using the Root Mean Square Error, Nash Sutcliffe coefficient of efficiency, the correlation coefficient, % Bias and the overall water balance error was good and comparable. The two models, however, tended to underestimate the high flows. The models were used to simulate runoff hydrographs for the ungauged Nzhelele River SQC using model parameters obtained from the Tshiluvhadi SQC RR modelling. The streamflow hydrographs for the Nzhelele River SQC simulated from both the models are comparable and show behaviour similar to that reported in earlier studies. They also correlate well with the areal rainfall for the Nzhelele River SQC. The modelling results show that the approach is reasonably good and therefore can be used in predicting runoff in ungauged catchments. The simulated runoff hydrographs can be used in water resources planning and management, and water resources systems operation.

Introduction

Streamflow is one of the most important hydrological variables required for water resources planning and management, and water resources systems operation including allocations for environmental flows. However, many river catchments are ungauged for streamflow data. According to Sivapalan et al. (2003), “an ungauged catchment is one with inadequate records (in terms of both data quantity and quality) of hydrological observations to enable computation of hydrological variables of interest (both water quantity and/or quality) at the appropriate spatial and temporal scales, and to the accuracy acceptable for practical applications. For example, if the variable of interest has not been measured at the required resolution or for the length of period required for predictions or for model calibration, the catchment would be classified as ungauged with respect to this variable.” Ungauged catchments are common in rural and remote areas, for example Nzhelele River Catchment in the Limpopo Province of South Africa (SA) which is the study area of this research.

Rainfall–runoff models have been used to predict streamflow in ungauged catchments in many studies. Typically, rainfall–runoff modelling requires streamflow data for calibration and verification. Since such data is not available in ungauged catchments, other approaches may need to be resorted to in order to obtain representative streamflows.

De Hamer et al., 2007, Liebe et al., 2008 have used water balance from a reservoir to generate streamflow. De Hamer et al. (2007) used the water balance of a reservoir for calibrating a rainfall–runoff model for two small ungauged catchments in Zimbabwe. The inflow was estimated by relating the increase in water level after a rain event and the dimensions of the reservoirs. Liebe et al. (2008) related a remotely sensed time series of reservoir surface areas with the known relationship between reservoir volume and surface area to obtain changes in reservoir storage. These were used to calibrate and verify flows from a water balance model in the Upper East Region of Ghana. The limitations of this approach are data requirements, especially the repeated coverage with satellite images, can be challenging and expensive if these data cannot be obtained through a cost-free arrangement. The application of the method requires trained personnel who are familiar with remote sensing, GIS, and hydrology. The accuracy of storage volume estimates determined with remote sensing is higher, where reservoirs have gentle side slopes, but may be less accurate, where topography is steep.

The current study differs from that of Liebe et al. (2008) because it uses the observed data sets including dam water levels (used to compute the dam storage), rainfall, evaporation, uncontrolled spills and abstractions in the water balance model to estimate the inflow hydrograph into the reservoir. The computation of the inflows with daily data for a relatively longer period (5 years) is likely to produce an inflow time series which is more natural, realistic and representative. To the knowledge of the authors, this type of study has not been done previously in the study area.

Mike 11 NAM (DHI, 2004) and AWBM (Boughton, 2004) daily models were used for RR modelling for ungauged sub-quaternary catchments in the study in preference to the more complex south African daily models (e.g. ACRU (Schulze, 1995) and VTI (Hughes and Sami, 1994) that require lots of data, experience, time and effort. In particular, the study presents the first application of the daily AWBM for RR modelling in SA.

Regionalization techniques are used to transfer model parameters from catchments with known parameters to ungauged catchments of similar hydrological characteristics. Regionalization techniques that are commonly used include the model averaging framework (McIntyre et al., 2005, Reichl et al., 2006); the use of parameter sets from the closest upstream and downstream catchments; the parameter regression approach (Hughes, 1989, Servat and Dezetter, 1993, Seibert, 1999, Peel et al., 2000, Merz and Bloschl, 2004, Vogel, 2005), the use of parameter values from the nearest gauged catchment (nearest neighbour approach) (Merz and Bloschl, 2004, Chiew and Siriwardena, 2005, He and Bárdossy, 2007) and parameter regionalization (Kapangaziwiri and Hughes, 2008). Zhang and Chiew (2009) described three regionalization methods that have been widely used to choose the donor gauged catchment whose optimized parameter values are used to model runoff for the target ungauged catchment. These are regression, spatial proximity (nearest neighbour approach), and physical similarity methods. Parajka et al. (2005) gives a review of the applications of these regionalization methods in a number of studies including their successes and failures.

The nearest neighbour approach has been found to produce the best results as compared to most of the above methods in studies such as Merz and Bloschl, 2004, Chiew and Siriwardena, 2005. Zhang and Chiew (2009) noted that recent studies suggest that regression method performs worse than the spatial proximity and physical similarity methods (Bardossy, 2007, McIntyre et al., 2005, Oudin et al., 2008, Parajka et al., 2007), though there is an unresolved debate on whether spatial/geographical proximity necessarily implies homogeneous hydrological response in some areas (for example see Vandewiele and Elias, 1995, Shu and Burn, 2003, Parajka et al., 2005).

Regionalization techniques have been applied for the purposes of deriving flow duration curves for generation of synthetic time series of daily discharges, regional flood estimation and rainfall–runoff modelling in ungaguged catchments in SA. Smakhtin et al. (1997) developed a regionalization method that allows derivation of 1-day annual and seasonal flow duration curves using regional observed streamflow data and used the curves to generate a complete synthetic time series of daily discharges in ungauged locations. The method is applicable in any drainage regions of SA. The initial tests of the proposed technique gave satisfactory daily flow simulations at an ungauged site (Smakhtin et al., 1997).

van Bladeren, 1993, Mkhandi and Kachroo, 1997, Meigh et al., 1997 developed regression models for regional flood estimation and flood frequency analysis in SA. The aim of developing regional flood estimation methods was to produce practical solutions which provide flood estimation tools at ungauged sites. The results of the studies indicated that a grouping of catchments based on geographical location rather than catchment area is preferable (Kjeldsen et al., 2001). The latter study attempted to relate the mean annual flood (MAF) to site characteristics of ungauged catchments in KwaZulu-Natal, SA. This was done to aid in the estimation of the MAF using the index-flood method at ungauged sites that lack the index-flood parameter. The study revealed problems with the estimation of the mean annual flood in the coastal areas of the study region (Kjeldsen et al., 2001).

The parameterization of the quaternary catchments in SA (Midgley et al., 1994) in the WR90 study which was upgraded to WR2005, as reported in Kapangaziwiri and Hughes (2008) were both achieved by mapping parameters from gauged to ungauged basins on the basis of similar basin physical properties and hydrological response. These data are only available as monthly flow time series on quaternary catchment scale and cannot be readily used for daily water resource assessments particularly at a scale smaller than the quaternary scale. Though, simple linear scaling function is available to downscale the monthly flow time series to a sub-quaternary scale, Hughes (2004) explained that it is not adequate since the relationship between flow volumes from a sub-catchment and the total flow volume for the whole catchment depends upon a wide range of factors. Such factors include rainfall, evaporation, soil, geology and land cover characteristics and the way in which they influence runoff generation processes.

Kapangaziwiri and Hughes (2008) presented the development of an alternative parameter regionalization approach based on the physical attributes of a basin. The study investigated a total of 71 basins from Southern Africa on physically based parameters which were compared against those of the current regionalized parameters for the same inputs, most of which were taken from Midgley et al. (1994). Of the 30 SA basins investigated only two failed to produce results that were as good as the current regionalized parameter sets or better (Kapangaziwiri and Hughes, 2008). The approach demonstrated the potential of using measurable physical basin attributes to directly quantify the soil moisture accounting, runoff, recharge and infiltration parameters of the Pitman model (Kapangaziwiri and Hughes, 2008).

Wolf et al. (2009) presented Hydrological Response Units regionalization method that is dependent on the differentiation of landscape classes to allow transfer of model parameters to catchments with comparable relief characteristics. Comparative modelling was done to determine model parameter selections that are especially significant and sensitive with regard to different landscape classes and relief characteristics in German test sites (Wolf et al., 2009). The approach yielded reliable results in the German test sites. In the next step of this research the acquired and post-calibrated ‘Predictions in Ungauged Basins (PUB) model parameter selections’ from the three German test sites were to be transferred to catchments in SA with corresponding landscape characteristics (Wolf et al., 2009).

The above literature review shows that a number of regionalization methods have been applied in SA and elsewhere with varied results/successes. The review further shows that the nearest neighbour regionalization approach mostly produce better results than other methods, though its limitations in some areas have been recognized.

The modified nearest neighbour regionalization approach in which a reservoir water balance is used to generate natural inflow time series for calibration and verification of RR models for an ungauged SQC to allow the transfer of RR modelling parameters from a SQC ungauged for natural streamflows to model flows in a neighbouring ungauged SQC has been proposed in this study. The time (day) and spatial (sub-quaternary catchment) scales at which the current approach is proposed to work is of better resolution than the other methods that have been used in SA at monthly and quaternary catchment or catchment scales. Thus, the data generated from this approach can be readily used for daily water resources assessments at a sub-quaternary catchment scale and hence can easily be used for near-real time modelling.

Section snippets

The study area

The study area falls under quaternary catchment A80A of the Nzhelele River Catchment (Fig. 1) which is located in the northern region of the Limpopo Province of SA. It is on the leeward side of the Soutpansberg Mountains with an average rainfall of 350–400 mm/annum. The rainfall is seasonal and occurs during summer months from October–March. The location of the study area is between 22°53′15.8″ S and 22°54′5″ S latitudes and 30°11′10.2″ E and 30°11′23.5″ E longitudes (Fig. 2).

Proposed regionalization approach

The proposed modified nearest neighbour regionalization approach has been necessitated by lack of natural streamflow data in the study area. The only stream gauging station (A8H011) in the A80A quaternary catchment, which was in operation from 1991 to 2000, is located immediately after the Mutshedzi Dam for the purpose of monitoring the downstream flow releases from the dam on the Mutshedzi River. The streamflow data from this gauging station have been impacted on by the Mutshedzi Dam. Thus,

Computed inflow into Mutshedzi Dam

The inflow into Mutshedzi Dam computed from the water balance Eq. (2) using the downstream flow releases, domestic water abstractions, rainfall, evaporation, uncontrolled spills and dam water storage has been presented in Fig. 5. The computed inflow time series was considered reasonable. The discontinuity observed in the inflow time series between 1996/02/01 and 1996/03/31 was because the domestic abstractions data for Mutshedzi Water Treatment Plant were not available for that period. It was

Conclusions

Rainfall–runoff modelling approach has been developed to generate natural streamflow for ungauged Nzhelele sub-quaternary catchment. This involved computing inflow hydrograph from a water balance model for Mutshedzi Dam which was then used in the calibration and verification of the RR model for the Tshiluvhadi River SQC using the Mike 11 NAM and AWBM. The model parameters were then transferred using the nearest neighbour regionalization technique and used for RR modelling of the ungauged

Acknowledgements

The authors wish to acknowledge the Department of Water Affairs, particularly Mrs. Celiwe Ntuli, for supporting this study in order to promote capacity building. Mr. Jason Hallowes from Danish Hydraulic Institute South Africa is also highly acknowledged for providing the educational training version of Mike 11 modelling package.

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