Physics and Chemistry of the Earth 35 (2010) 596–607
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Rainfall–runoff modelling approach for ungauged catchments: A case study of Nzhelele River sub-quaternary catchment R. Makungo a,⇑, J.O. Odiyo a, J.G. Ndiritu b, B. Mwaka c a
University of Venda, Department of Hydrology and Water Resources, P/Bag X5050, Thohoyandou 0950, South Africa University of the Witwatersrand, School of Civil and Environmental Engineering, P/Bag X3, Wits 2050, South Africa c Department of Water Affairs and Forestry, Water Resource Planning Systems Directorate, P/Bag X313, Pretoria 0001, South Africa b
a r t i c l e
i n f o
Article history: Received 1 February 2010 Received in revised form 12 July 2010 Accepted 7 August 2010 Available online 12 August 2010 Keywords: Rainfall–runoff modelling Ungauged catchment Water balance Regionalization
a b s t r a c t 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. Ó 2010 Elsevier Ltd. All rights reserved.
1. 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 pre⇑ Corresponding author. Tel.: +27 15 962 8568; fax: +27 15 962 8597. E-mail address:
[email protected] (R. Makungo). 1474-7065/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2010.08.001
dictions 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) and 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
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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) and 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
597
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), and 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
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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.
This inflow time series was used to calibrate the Mike 11 NAM and AWBM rainfall–runoff models for the ungauged Tshiluvhadi SQC to determine the model parameters. The AWBM was used for comparing the simulated runoff results with those obtained from Mike 11 NAM. The derived model parameters were then transferred for use in simulating the streamflow hydrograph for the ungauged Nzhelele River SQC which is the SQC of interest. This approach differs from the commonly used nearest neighbour regionalization approach involving a gauged quaternary catchment and an ungauged quaternary catchment. The proposed modified nearest neighbour regionalization approach in this study is therefore a slight modification of the nearest neighbour regionalization approach.
2. The study area
The required data sets include rainfall, evaporation, uncontrolled spills, downstream flow releases, dam water levels, storage-area relationship for Mutshedzi Dam, domestic abstractions, area under irrigation, crop factors, types of crops grown and the irrigation schedule. Evaporation, uncontrolled spills, downstream flow releases, dam water levels and storage-area relationships for Mutshedzi Dam were obtained from the Department of Water Affairs (DWA) while rainfall data was obtained from the South African Weather Services (SAWS). Irrigation data and the crop factors were obtained from the farmers and Allen et al. (1998) respectively. The domestic abstractions were obtained from the Mutshedzi Water Treatment Plant. The station numbers for the rainfall, evaporation, downstream flow releases and uncontrolled spills are 0766327, A8E004, A8H011, and A8R004 respectively. These data sets were used in the computation of the inflows into the Mutshedzi Dam. The locations of rainfall, evaporation and streamflow stations are shown in Fig. 2. The crop factors, the area under irrigation, crops grown, irrigation schedule and the evaporation data from station number A8E004 were used to compute the irrigation water demand. This was done to determine the highest amount of water required for irrigation, and was also useful in establishing the significance of irrigation water use and its influence on the computed inflows to justify the exclusion of daily irrigation time series demand from the water balance. This was necessary because it was not possible to obtain the daily irrigation time series data. Rainfall data for station numbers 0766327, 0766324, 0766269, and 0766563 and evaporation data for station number A8E004 were used as inputs into the Mike 11 NAM rainfall–runoff model. The evaporation data from A8E004 station together with the weighted areal rainfall computed in Mike 11 NAM rainfall–runoff model were also used for rainfall–runoff modelling using the AWBM.
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°530 15.800 S and 22°540 500 S latitudes and 30°110 10.200 E and 30°110 23.500 E longitudes (Fig. 2). 3. 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, with respect to natural streamflow data required for model calibration and validation, the A80A quaternary catchment is ungauged. It was therefore necessary to obtain a time series of natural inflows into the Mutshedzi Dam using the reservoir water balance.
3.1. Data requirements and sources
3.2. Data analysis methods 3.2.1. Determining inflow time series into Mutshedzi Dam The inflow into the dam has been computed using the water balance equation below
Idam ¼ Q d þ Q irr þ Q s þ E Ds R þ Q r
Fig. 1. Location of quaternary catchment A80A.
ð1Þ
where, Idam is the inflow into the dam, Qd are the domestic abstractions, Qirr are the irrigation abstractions, Qs are the uncontrolled spills, E are the evaporation, R is the rainfall, Qr are the downstream flow releases, and Ds is the change in storage. All the above parameters are in m3/day. Eq. (1) was used to compute the inflow into the dam taking into account the estimated irrigation water demand. To compute the inflow into the dam excluding the estimated irrigation water demand, the following equation was used:
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Fig. 2. Locations of rainfall, evaporation and streamflow.
Idam ¼ Q d þ Q s þ E Ds R þ Q r
ð2Þ
This was done to establish the significance of irrigation water use on the computed inflows and to justify the exclusion of daily irrigation time series demand from the water balance. Initial checking of all the data sets and minimum patching of evaporation data series using arithmetic mean were done. Minimum patching of daily domestic abstractions was also done using the arithmetic mean method, where possible (i.e. in cases, where there were missing data for a long period of time, e.g. 1 year, patching was not done and that period was therefore not included in the analysis). The irrigation water demands for the two irrigation schemes (Cordon and Phadzima) located upstream of Mutshedzi Dam were computed using:
Q irr ¼ ET o A
ð3Þ 3
where Qirr is the daily irrigation demand in m /day, A is the area irrigated daily in m2/day and ETo is the reference crop evapotranspiration in m/day. Further details on computation of ETo are found in Makungo (2009). The dam downstream flow releases were only available for the period 1991/02/13–2000/02/15 while the domestic abstractions were available from 1994/04/22 to 2007/10/31 with some years having completely no data. This has limited the computation of the water balance to the period 1994/04/22–1999/03/06. Though the computation would have been expected to continue up to 2000/02/15, this was not possible because there were no domestic abstractions data between this date and 1999/03/06. It is important to note that the computed inflow into the dam includes the inflows from both the Tshiluvhadi and Phangani Rivers. Phangani River is an intermittent ungauged stream that only flows during periods of high rainfall. It thus only contributes flows into the Mutshedzi Dam during high flow periods. 3.2.2. Rainfall–runoff modelling for Tshiluvhadi and Nzhelele River sub-quaternary catchments 3.2.2.1. Delineation of the sub-quaternary catchments. The sub-quaternary catchments drained by the upper part of Nzhelele and Tshiluvhadi Rivers in quaternary catchment A80A were delineated
from the 1:50000 topographical map and a topographical map obtained from the GRDM software (Dennis and Wentzel, 2006) and their respective areas determined. Since the purpose of the water balance was to obtain natural flows upstream of the dam, the sub-quaternary catchment had to be delineated in such a way that its outlet is at the inlet of Tshiluvhadi River into the dam. This is because both Tshiluvhadi and Phangani Rivers that contribute inflows into the dam are in different sub-quaternary catchments and it was not possible to establish one inflow outlet into the dam for both and could thus only be treated separately. A combined inlet would also have been impacted by the dam making it difficult to generate natural inflows. 3.2.2.2. Mike 11 NAM and AWBM models structure, setup, calibration, and verification. The Mike 11 NAM model structure (Fig. 3) is an imitation of the land phase of the hydrological cycle (DHI, 2004). The model simulates the rainfall–runoff process by continuously accounting for the water content in four different and mutually interrelated storages that represent different physical elements of the catchment, which are snow storage, surface storage, lower or root zone storage and groundwater storage (Madsen et al., 2002). The main inputs of the model are evaporation and rainfall data. Table 1 provides the description of the Mike 11 NAM model parameters. The AWBM is a conceptual model developed from the concept of saturation overland flow generation of runoff (Wheater et al., 1993). At each time step, rainfall is added to each of the surface stores and evapotranspiration is subtracted (Boughton, 2004). If there is any excess from any store, it becomes runoff and is divided between surface runoff and baseflow (Boughton, 2004). The structure of the AWBM is shown in Fig. 4 while the description of the model parameters is given in Table 2. The sub-quaternary catchment area, weighted areal rainfall, evaporation and streamflow data were required for the models set up for the Tshiluvhadi sub-quaternary catchment. These data were input into the models and were used in the calibration and verification. The weighted areal rainfall was automatically computed by
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Fig. 3. Mike 11 NAM model structure (DHI, 2004).
Table 1 Description of the Mike 11 NAM model parameters (source: DHI, 2004). Parameter
Description
Parameter
Description
QOF QIF OF IF CK1 CK2 Sy Lmax G CKBF BF L hwp hFC TG TOF
The part of PN that contributes to overland flow Interflow contribution Overland flow Interflow Inflow hydrograph Outflow hydrograph Specific yield Upper limit of the amount of water in root zone storage. Groundwater recharge Time constant for routing baseflow Baseflow Depth of the lower zone storage Wilting point Field capacity Threshold value for recharge Threshold value for overland flow
hSAT Umax P Ep PN PS Ea DL CAFLUX GWL GWLBF0 GWPUMP CQOF CKIF CK1,2 TIF
Saturation zone Upper limit of the amount of water in the surface storage Precipitation Potential evapotranspiration Excess water that gives rise to overland flow Excess melt water contribution Actual evapotranspiration Portion of the water available for infiltration Capillary flux Groundwater table below the ground surface The maximum groundwater table depth Net groundwater abstraction Overland flow runoff coefficient Time constant for interflow from the surface storage Time constant for overland flow and interflow routing Threshold value for interflow
the Mike 11 NAM rainfall–runoff model from point rainfall from station numbers 0766269 and 0766327 using Thiessen polygon method. The Shuffled Complex Evolution optimizer in-built within Mike 11 was used in auto calibration using the root mean square error (RMSE) as an objective function. Rosenbrock single start optimization technique (Rosenbrock, 1960) was selected for the most efficient AWBM model calibration also using RMSE as an objective
function. The daily data sets for a period of 3 years (1994/04/22– 1997/04/22) and a period of 2 years (1997/04/23–1999/03/06) were used for model calibration and verification respectively. Three years is the minimum calibration period recommended by DHI (2004). The Nash Sutcliffe coefficient of efficiency (E) (Nash and Sutcliffe, 1970), correlation coefficient (R) (van Liew et al., 2007; Moriasi
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4. Results and discussion 4.1. Computed inflow into Mutshedzi Dam
Fig. 4. Structure of the AWBM model (Source: Boughton, 2006).
Table 2 Description of the AWBM model parameters (Boughton, 2006). Parameter
Description
P E A1 A2 A3 BFI C1 C2 C3 KBase KSurf
Precipitation Evaporation Partial area of smallest store Partial area of middle store Partial area of largest store Baseflow index Surface storage capacity of smallest store Surface storage capacity of middle store Surface storage capacity of largest store Baseflow recession constant Surface runoff recession constant
et al., 2007), RMSE, the overall water balance error (OWBE) and % Bias (PBIAS) (Yapo et al., 1996; Gupta et al., 1999) were used to assess the calibration and verification performances of the models. Verification was performed to assess whether the calibrated parameter values could be used to successfully estimate streamflow for an independent test period that was not used to calibrate the model. Weighted areal rainfall computed from observed point daily rainfall for station numbers 0766327, 0766324, and 0766563; observed daily evaporation and model parameters obtained from Tshiluvhadi sub-quaternary catchment calibration were used for Mike 11 NAM and AWBM rainfall–runoff modelling for the Nzhelele River sub-quaternary catchment. The data for the period 1991/07/01–2000/07/31 was used in the latter simulations. The transfer of model parameters was done on the basis of similar physical and hydrological characteristics (Table 3).
Table 3 Comparison of hydrologic conditions in Tshiluvhadi and Nzhelele SQCs. Hydrologic condition
Tshiluvhadi SQC
Nzhelele SQC
Soil type
Medium sandy clay loam to sandy clay loam Basalt and sandstone of the Soutpansberg Group with diabase dykes intrusions Settlement and subsistence farming 350–400
Medium sandy clay loam to sandy clay loam Basalt and sandstone of the Soutpansberg Group with diabase dykes intrusions Settlement and subsistence farming 350–400
1300–1400
1300–1400
800–1280
800–1280
Geology
Land use Mean annual rainfall (mm) Mean annual evaporation (mm) Topography (m)
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 therefore not possible to compute inflow time series using water balance equation during that period. The inflows into the dam computed above from the water balance equation in which the irrigation water demand was excluded was compared with the inflows into the dam computed with the irrigation water demand included (Fig. 6). The results show that incorporating the irrigation water demand in the computation has negligible effect compared to the scenario that excludes the irrigation water demand in its computation. Its exclusion increases the inflows by a maximum of 0.004 m3/day in some of the days. This shows that the actual irrigation water demand has negligible effects on the inflows into the dam and justifies the exclusion of this component in the computation of the inflow time series for Mutshedzi Dam from the water balance equation. This was necessitated by lack of daily time series of irrigation water demand.
4.2. Rainfall–runoff modelling for Tshiluvhadi and Nzhelele subquaternary catchments The delineated sub-quaternary catchments of the Nzhelele and Tshiluvhadi Rivers whose areas have been used in rainfall–runoff modelling are represented by A and B, respectively (Fig. 7). Their estimated areas are 98.25 and 85 km2 respectively. Since it was not possible to separate the inflow into Mutshedzi Dam into two separate components for Phangani and Tshiluvhadi sub-quaternary catchments, the Phangani sub-quaternary catchment has not been included in the rainfall–runoff modelling and therefore it was not necessary to delineate the SQC. This was based on the fact that Phangani River is intermittent and its smaller area (7 km2) which is only 8% of the total inflow area of Tshiluvhadi and Phangani sub-quaternary catchments (92 km2), does not contribute significant flows compared to the bulk of the inflow area. Several trials during the calibration of Mike 11 NAM for Tshiluvhadi SQC revealed that the most sensitive parameters provided in Table 1 are Lmax, Umax, CQOF, and CKIF. These findings are similar to those in Keskin et al. (2007). The parameters Lmax, Umax, CQOF, and CKIF define the base flow in the basin (Keskin et al., 2007). It was also found that the parameters TOF and TIF (Table 1) do not have much influence on the total runoff volume. This finding was also confirmed by Keskin et al. (2007) while calibrating a rainfall–runoff model for Yuvacik Dam Basin in Turkey. All the parameters obtained from the Mike 11 NAM calibration for Tshiluvhadi SQC are given in Table 4. Similarly, the parameters obtained from the AWBM model calibration for Tshiluvhadi SQC are given in Table 5. The parameters from both the models fall within the acceptable lower and upper limits of the individual model parameters. The Mike 11 NAM and AWBM rainfall–runoff simulated and observed results have been presented in Figs. 8 and 9, and compared using the measures of performance in Table 6. All the results have been presented only for part of the calibration and verification periods to avoid overcrowding. The E value for the calibration run is slightly lower than for the verification run for both models.
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Computed Inflow (x106 m3/day)
3 2.5 2 1.5 1 0.5
1994/04/22 1994/06/22 1994/08/22 1994/10/22 1994/12/22 1995/02/22 1995/04/22 1995/06/22 1995/08/22 1995/10/22 1995/12/22 1996/02/22 1996/04/22 1996/06/22 1996/08/22 1996/10/22 1996/12/22 1997/02/22 1997/04/22 1997/06/22 1997/08/22 1997/10/22 1997/12/22 1998/02/22 1998/04/22 1998/06/22 1998/08/22 1998/10/22 1998/12/22 1999/02/22
0
Date (yyyy/mm/dd) Fig. 5. Computed inflow into the Mutshedzi Dam.
InflowWithNoIrr InflowWithIrr
2.50 2.00
6
3
Inflow (x 10 m /day)
3.00
1.50 1.00 0.50
1999/02/25
1999/02/05
1999/01/16
1998/12/07
1998/12/27
1998/11/17
1998/10/28
1998/10/08
1998/09/18
1998/08/29
1998/08/09
1998/07/20
1998/06/30
1998/06/10
1998/05/21
1998/04/11
1998/05/01
1998/03/22
1998/03/02
1998/02/10
1998/01/21
1998/01/01
0.00
Time (yyyy/mm/dd) Fig. 6. Comparison of inflows into Mutshedzi Dam with and without irrigation water supply.
The improvement of the satisfactory E values during verification indicates that reasonably good model parameters were obtained during the calibration. Shamsudin and Hashim (2002) indicated that missing data, on site data acquisition and the nature of rainfall pattern affected calibration of the Mike 11 NAM rainfall–runoff modelling for the Layang River, resulting in an E value of 0.75. The study area is characterized by uneven rainfall distribution and missing data that could have affected the E value. The E values obtained in the current study fall within the range 0.66–0.82 obtained by Vai niene˙ (2005) during the calibration of the Mike 11 NAM tieku rainfall–runoff model for 66 catchments in the Lithuanian River Basin. In the latter study, the lower E values were due to inadequately distributed precipitation data and errors in the observed discharge. Xu and Argent (2005) used the Rosenbrock Single Start optimization method while calibrating AWBM model for 37 catchments in the Port Phillip Bay Catchment, Australia. The E values varying from 0.16 to 0.85, with a median across 37 gauged catchments of 0.60 were obtained in the latter study. Thus, E values obtained in this study are acceptable as they are within the ranges obtained in other studies and fall within the reasonable and good modelling range described by Chiew and McMahon (1993). The E values for the calibration and verification runs for both the models are >0.6
and they suggest a reasonable modelling of runoff according to Chiew and McMahon (1993). The E values for the AWBM rainfall–runoff model are comparable though slightly higher than those of MIKE 11 NAM rainfall–runoff model (Table 6). The computed R values for both the calibration and verification runs with both models (Table 6) are acceptable according to Van Liew et al. (2007). Since the R values are all >0.8 and are approaching 1, the relationship between the simulated and measured values tends towards a perfect positive linear relationship according to Moriasi et al. (2007). The computed RMSE for both the calibration and the verification runs for both models (Table 6) are reasonable as they fall within the ranges obtained in other studies. RMSE values in the ranges 0.067–0.92 and 0.05–1.03 have been obtained in studies by Madsen et al. (2002) and Madsen (2003) respectively. The RMSE values obtained from both the calibration and verification of the Mike 11 NAM rainfall–runoff model are lower than those obtained from the AWBM rainfall–runoff model. Thus Mike 11 NAM model did slightly better than AWBM with regard to RMSE since a perfect value according to Shamsudin and Hashim (2002) is zero. The OWBE for both the models (Table 6) fall within the acceptable ranges of ±5–10% (Madsen et al., 2002). The OWBE obtained from the AWBM and Mike 11 NAM rainfall–runoff models suggest
R. Makungo et al. / Physics and Chemistry of the Earth 35 (2010) 596–607
603
Fig. 7. Delineated sub-quaternary catchments for the Nzhelele and Mutshedzi Rivers.
Table 4 Parameter values resulting from auto calibration of MIKE 11 NAM and default values. Parameter
Lower limit
Upper limit
Modelled value
Umax (mm) Lmax (mm) CQOF (–) CKIF (h) CK 1,2 (h) TG CKBF (h) TOF TIF
5 50 0 500 3 0 50 0 0
35 350 1 1000 72 1 5000 1 1
10.5 267 0.82 856.3 29.1 0.129 3066 0.478 0.569
Table 5 Parameter values resulting from the calibration of AWBM rainfall–runoff model and default values. Parameter
Lower limit
Upper limit
Modelled value
A1 A2 BFI C1 C2 C3 KBase KSurf
0 0 0 0 0 0 0 0
1 1 1 50 200 500 1 1
0.74 0.26 0.67 0.00 126.92 119.10 0.96 0.84
that the models underestimated the simulated runoff since the results indicate that the observed flows are greater than the simulated flows. However, the OWBE obtained from the AWBM are lower than those obtained from Mike 11 NAM due to the fact that AWBM overestimated some of the peak flows while Mike 11 NAM underestimated some of the peak flows. Madsen et al. (2002) indicated that the inherent uncertainties in measuring the catchment average rainfall and the corresponding runoff make it difficult to obtain perfect water balance. The computed PBIAS for the Mike 11 NAM were 10.45% and 10.09% respectively while PBIAS for AWBM calibration and verification runs were 3.94% and 5.36% respectively (Table 6). The PBIAS values obtained in the calibration and verification of Mike 11 NAM and AWBM are acceptable and indicate underestimation of simulated runoff according to Yapo et al. (1996).
The Mike 11 NAM model calibration and verification runs underestimated most of the peak flows (Figs. 8 and 9). The peak flow which occurred on 1998/10/18 was well predicted though it was of relatively small magnitude (Fig. 9). Most of the low flows for the calibration run were well predicted (Fig. 8). The estimation of the low flows on verification run approached the observed values if not slightly underestimated them. The model underestimated most of the peak flows for the calibration run (Fig. 8). The AWBM overestimated most of the small to medium peak flows and underestimated the major peak flows in both calibration and verification runs (Figs. 8 and 9). For example, the peak flows which occurred on 1995/03/28, 1995/08/12, 1997/09/15, 1997/12/09, 1998/10/20, 1998/11/10, etc. were overestimated while the peak flows which occurred on 1995/02/20, 1995/04/29, 1998/01/30, and 1998/12/15 were underestimated. Both models were able to estimate the low flow events correctly for both the calibration and the verification runs, except in a few cases, where they underestimated the low flows (Figs. 8 and 9). The inclusion of the contribution from Phangani River in the inflow from the water balance equation can partly explain the underestimation of the peak flows by the models. This therefore is an area that requires improvement. However, the Mike 11 NAM has generally been known to underestimate peak flows as observed in the results of studies such as Madsen et al. (2002), Madsen (2003), and Cra˘ciun (2003). The latter study noted that the hydrological phenomena during high flow periods are too complex for rainfall–runoff models to predict accurately. Good and reasonable objective measures (i.e. RMSE, E, R, PBIAS, and OWBE) were obtained during calibration and verification of both the Mike 11 NAM and AWBM rainfall–runoff models (Table 6). This indicates that reasonably good model parameters were obtained during model calibration. Thus, the parameter sets obtained in calibration can be transferred to another sub-quaternary catchment with similar hydrological conditions (see Table 3) for use in rainfall–runoff modelling. The results in Table 6 and Figs. 8 and 9 show that the AWBM and Mike 11 NAM rainfall–runoff models have generally comparable performance in the Tshiluvhadi SQC though the AWBM performed relatively better than the Mike 11 NAM. It was therefore decided to simulate the runoff hydrograph for the ungauged Nzhelele River SQC, which is within the same quaternary catchment, using both models. The results were then compared.
604
R. Makungo et al. / Physics and Chemistry of the Earth 35 (2010) 596–607
8
AWBM
7
Mike 11 NAM
6
Observed
3
Runoff (m /s)
9
5 4 3 2 1 1994/12/22 1995/01/01 1995/01/11 1995/01/21 1995/01/31 1995/02/10 1995/02/20 1995/03/02 1995/03/12 1995/03/22 1995/04/01 1995/04/11 1995/04/21 1995/05/01 1995/05/11 1995/05/21 1995/05/31 1995/06/10 1995/06/20 1995/06/30 1995/07/10 1995/07/20 1995/07/30 1995/08/09 1995/08/19 1995/08/29 1995/09/08 1995/09/18 1995/09/28 1995/10/08 1995/10/18 1995/10/28 1995/11/07 1995/11/17 1995/11/27 1995/12/07 1995/12/17
0
Date (yyyy/mm/dd) Fig. 8. Comparisons of the Mike 11 NAM, AWBM and observed runoff hydrographs for the calibration run of Mutshedzi SQC.
AWBM
14
Mike 11 NAM Observed
10
3
Discharge (m /s)
12
8 6 4 2
1997/08/23 1997/09/02 1997/09/12 1997/09/22 1997/10/02 1997/10/12 1997/10/22 1997/11/01 1997/11/11 1997/11/21 1997/12/01 1997/12/11 1997/12/21 1997/12/31 1998/01/10 1998/01/20 1998/01/30 1998/02/09 1998/02/19 1998/03/01 1998/03/11 1998/03/21 1998/03/31 1998/04/10 1998/04/20 1998/04/30 1998/05/10 1998/05/20 1998/05/30 1998/06/09 1998/06/19 1998/06/29 1998/07/09 1998/07/19 1998/07/29 1998/08/08 1998/08/18 1998/08/28 1998/09/07 1998/09/17 1998/09/27 1998/10/07 1998/10/17 1998/10/27 1998/11/06 1998/11/16 1998/11/26 1998/12/06 1998/12/16 1998/12/26
0
Date (yyyy/mm/dd) Fig. 9. Comparisons of the Mike 11 NAM, AWBM and observed runoff hydrographs for the verification run of Mutshedzi SQC.
Table 6 Summary of Mike 11 NAM and AWBM models performance for Tshiluvhadi SQC. Performance measure
Nash Sutcliffe coefficient of efficiency RMSE Overall water balance error (%) Correlation coefficient PBIAS (%) a b c d e
Mike 11 NAM
AWBM
Acceptable ranges
Calibration
Verification
Calibration
Verification
0.67 0.96 9.89 0.82 10.45
0.74 0.92 9.13 0.86 10.09
0.72 1.01 3.34 0.85 3.94
0.77 1.14 4.37 0.88 5.36
P0.6- Satisfactorya P 0.8- Gooda 0 = Perfectb ±5–10%- Acceptablec >0.5- Acceptabled ±25%- Acceptablee
Chiew and McMahon (1993). Shamsudin and Hashim (2002). Madsen et al. (2002). Van Liew et al. (2007). Yapo et al. (1996).
The simulated runoff for Nzhelele River has been obtained using the model parameters in Tables 4 and 5 which were adopted based on the modified nearest neighbour regionalization technique. The simulated flows are comparable though the AWBM simulated flows are generally higher than the Mike 11 NAM simulated flows (Fig. 10).
Figs. 11 and 12 show the correlation of the simulated runoff and the areal rainfall hydrographs for the Nzhelele River SQC. The graphs show that the major peak rainfall events are well correlated with the major peak runoff events. This shows that the runoffs simulated by the AWBM and Mike 11 NAM models for Nzhelele River at Siloam Village are reasonable.
1991/07/01 1991/08/20 1991/10/09 1991/11/28 1992/01/17 1992/03/07 1992/04/26 1992/06/15 1992/08/04 1992/09/23 1992/11/12 1993/01/01 1993/02/20 1993/04/11 1993/05/31 1993/07/20 1993/09/08 1993/10/28 1993/12/17 1994/02/05 1994/03/27 1994/05/16 1994/07/05 1994/08/24 1994/10/13 1994/12/02 1995/01/21 1995/03/12 1995/05/01 1995/06/20 1995/08/09 1995/09/28 1995/11/17 1996/01/06 1996/02/25 1996/04/15 1996/06/04 1996/07/24 1996/09/12
Rainfall (mm) 120
150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0
40 AWBM
35 30 Mike 11 NAM
160
140
100 20
80 15
60 10
20
0
Rainfall
Mike 11 NAM simulated runoff
20
15
10
5
0
Date (yyyy/mm/dd)
Fig. 12. Correlation of the simulated runoff (Mike 11 NAM) and the areal rainfall for the Nzhelele River SQC.
Runoff (m3/s)
1995/10/01 1995/12/01 1996/02/01 1996/04/01 1996/06/01 1996/08/01 1996/10/01 1996/12/01 1997/02/01 1997/04/01 1997/06/01 1997/08/01 1997/10/01 1997/12/01 1998/02/01 1998/04/01 1998/06/01 1998/08/01 1998/10/01 1998/12/01 1999/02/01 1999/04/01 1999/06/01 1999/08/01 1999/10/01 1999/12/01 2000/02/01 2000/04/01 2000/06/01
3
Simulated runoff (m /s)
Nethengwe (2007) and Odiyo et al. (2007) have indicated that the Nzhelele River Catchment is dominated by dry rainfall years
Runoff (m3 /s)
1991/07/01 1991/08/20 1991/10/09 1991/11/28 1992/01/17 1992/03/07 1992/04/26 1992/06/15 1992/08/04 1992/09/23 1992/11/12 1993/01/01 1993/02/20 1993/04/11 1993/05/31 1993/07/20 1993/09/08 1993/10/28 1993/12/17 1994/02/05 1994/03/27 1994/05/16 1994/07/05 1994/08/24 1994/10/13 1994/12/02 1995/01/21 1995/03/12 1995/05/01 1995/06/20 1995/08/09 1995/09/28 1995/11/17 1996/01/06 1996/02/25 1996/04/15 1996/06/04 1996/07/24 1996/09/12
Rainfall (mm)
R. Makungo et al. / Physics and Chemistry of the Earth 35 (2010) 596–607 605
(drought) which result in low flows. This is because Nzhelele River is located on the leeward side of the Soutpansberg Mountains and
25
20 15
10 5
0
Date (yyyy/mm/dd)
Fig. 10. Simulated runoff for the Nzhelele SQC using Mike 11 NAM and AWBM models.
Rainfall 30
AWBM simulated runoff 25
40
5
0
Date (yyyy/mm/dd)
Fig. 11. Correlation of the simulated runoff (AWBM) and the areal rainfall for the Nzhelele River SQC.
30
25
606
R. Makungo et al. / Physics and Chemistry of the Earth 35 (2010) 596–607
receives low rainfall resulting in low runoff. However, there are sporadic flood events with return periods >1:15 years which occur in the Nzhelele River (Nethengwe, 2007). These contribute to the occasional flood peaks. These confirm the dominance of low flows and occasionals sporadic floods. The 1995/96 hydrological year flood event predicted in this study (Fig. 10) was also predicted by Nethengwe (2007) on performing flood analysis for the Nzhelele River downstream of the Nzhelele Dam, though of different magnitude. Nethengwe (2007) could not perform the flood analysis for the hydrological year 1999/2000 because of lack of streamflow data for that year. However, a number of studies such as Smithers et al. (2001) and Odiyo and Maluleke (2005) have indicated that a major flood event occurred in February 2000 in the Limpopo Province and the north eastern parts of SA. The coincidence of the major flood peaks with those obtained in other studies shows that the AWBM and Mike 11 NAM models were able to simulate the runoff hydrograph for Nzhelele River at Siloam Village well.
5. 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 Nzhelele sub-quaternary catchment with Mike 11 NAM and AWBM. Due to lack of irrigation abstractions data, analysis was carried out to establish the significance of irrigation water use on the computed inflows. The inflow time series computed for the Mutshedzi Dam with and without irrigation water demand were compared. This was necessary to justify the exclusion of daily irrigation water demand time series from the water balance. Despite applying a method that overestimated the irrigation water demand, the inclusion of the computed irrigation water demand in the water balance equation was found to have negligible effects on the computed inflows. The inflow time series computed without the irrigation water demand was therefore adopted for the calibration and verification of the rainfall–runoff models for Tshiluvhadi River SQC using the Mike 11 NAM and AWBM. Satisfactory calibration and verification was achieved with both the models. The performance of Mike 11 NAM and the AWBM rainfall–runoff models were assessed using measures of goodness of fit between the simulated and observed runoff including RMSE, E, R, OWBE and PBIAS. The Mike 11 NAM and AWBM rainfall–runoff models performances were good and comparable though the AWBM performance was relatively better than that of the Mike 11 NAM. This therefore justified the use of both models in the simulation of the streamflow hydrograph for Nzhelele River SQC. The satisfactory performance and ease of application of AWBM will encourage its use in daily catchment RR modelling in ungauged catchments in South Africa. The streamflow hydrograph for the Nzhelele River SQC simulated from both the models is comparable and show behaviour similar to that reported in earlier studies. It also correlates well with the areal rainfall for the Nzhelele River SQC from upstream to Siloam Village. The simulated streamflow has been extended and used in the derivation of a generic operating strategy for run-of-river abstractions in a study by Makungo (2009). The modified nearest neighbour regionalization approach developed in this study has been shown to produce reasonably good results at daily and sub-quaternary catchment scales, which
is of better resolution than the other methods such as Kapangaziwiri and Hughes (2008), the WR90 (Midgley et al., 1994) and its update WR2005 that have been used in SA at monthly and quaternary catchment scales. Thus, the approach has the potential to be used for daily water resources assessments at sub-quaternary catchment scale and hence can be applied in near-real time modelling. Data on irrigation abstractions is the main limitation of the developed approach in South Africa since there is lack of monitoring in most parts of the country. The approach is applicable with ease in rural areas, where there is minimal irrigation water use that can be quantified accurately. Errors in estimating the irrigation abstractions and errors in measurement of the hydrological variables in the water balance may result in inaccurate estimations of the inflows. 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. References Allen, R.G., Pereira, L.S., Rae, D., Smith, M., 1998. Crop Evapotranspiration (Guidelines for Computing Crop Water Requirements). FAO Irrigation and Drainage Paper No. 56. Bardossy, A., 2007. Calibration of hydrological model parameters for ungauged catchments. Hydrology and Earth System Sciences 11, 703–710. Boughton, W.C., 2004. The Australian water balance model. Environmental Modelling and Software Journal 19, 943–956. Boughton, W.C., 2006. Calibrations of a daily rainfall–runoff model with poor quality data. Environmental Modelling and Software Journal 21, 1114–1128. Chiew, F.H.S., McMahon, T.A., 1993. Assessing the adequacy of catchment streamflow yield estimates. Australian Journal of Soil Research 31, 665–680. Chiew, F.H.S. and Siriwardena, L., 2005. Estimation of SimHyd parameter values for application in ungauged catchments. In: Zerger, A., Argent, R.M. (Eds.), ModSim 2005, International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand, pp. 2883–2889. Cra˘ciun, I., 2003. The validation of the Mike 11-N.A.M. hydrological model on the hydrographic basin Bahluetß. Ovidius University Annals Series: Civil Engineering 1 (50), 109–112. Danish Hydraulic Institute (DHI), 2004. Mike 11: a modelling system for rivers and channels, Reference manual, Denmark. De Hamer, W., Love, D., Owen, R.J.S., Booij, M.J., Hoekstra, A., 2007. A simple rainfall– runoff model for an ungauged catchment using the water balance of a reservoir for calibration. In: 8th WaterNet/WARFSA/GWP-SA Symposium, Livingstone, Zambia. Dennis, I., Wentzel, J., 2006. Groundwater resource-directed measures software. Water SA 33 (1), 79–86. Gupta, H.V., Sorooshian, S., Yapo, P.O., 1999. Status of automatic calibration for hydrologic models: comparison with multilevel expert calibration. Journal of Hydrologic Engineering 4 (2), 135–143. He, Y., Bárdossy, A., 2007. Application of a non-parametric regionalization technique to a rainfall runoff model. Geophysical Research Abstracts 9. Hughes, D.A., 1989. Estimation of the parameters of an isolated event conceptual model from physical catchment characteristics. Hydrological Sciences Journal 34 (5), 539–557. Hughes, D.A., 2004. Problems of estimating hydrological characteristics for small catchments based on information from the South African national surface water resource database. Water SA 30 (3), 1–6. Hughes, D.A., Sami, K., 1994. A semi-distributed variable time interval model of catchment hydrology-structure and parameter estimation procedures. Journal of Hydrology 155, 265–291. Kapangaziwiri, E., Hughes, D.A., 2008. Towards revised physically based parameter estimation methods for the Pitman monthly rainfall–runoff model. Water SA 34 (2), 183–192. Keskin, F., S ß ensoy, A., Sßorman, A.U., 2007. Application of Mike 11 model for the simulation of snowmelt runoff in Yuvacik Dam basin, Turkey. In: International Congress on River Basin Management, Antalya–Turkey, pp. 472–484. Kjeldsen, T.R., Smithers, J.C., Schulze, R.E., 2001. Flood frequency analysis at ungauged sites in the KwaZulu-Natal Province, South Africa. Water SA 27 (3), 315–324. Liebe, J., van de Giesen, N., Andah, W., Andreini, M., Walter, T., Steenhuis, T., 2008. Calibrating runoff models in ungauged basins using small reservoirs as satellite
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