Evaluation of the extended applicability of a simulated hydrological Tank model at the Ca River Basin sub-catchments

Runoff is a combination of random spatially distributed processes that determine the structure, characteristics, and dynamics of riverine ecosystems (Zeiringer et al. 2018). The flows at any given point in a river are necessary data for forecasting floods, predicting sediment loads, evaluating the effects of climate change on water resources, assessing environmental quality, and managing water resources. However, the majority of the world's watersheds, flow reaches, and river systems are ungauged or poorly gauged (Sivapalan 2003; Young 2006). Estimating runoff in ungauged or poorly gauged watersheds is considered a particular challenge in many hydrological studies (Sivapalan 2003; He et al. 2011; Razavi & Coulibaly 2013). There are two general approaches used for predictions in ungauged basins: the first approach estimates model parameters based on selected optimal variables from calibrated model parameters (Wagener & Wheater 2006; Azmeri et al. 2012; Betterle et al. 2018; Yang et al. 2018; Arsenault et al. 2019), while the second approach is model-independent, utilizing streamflow signatures to establish constraints to define the physical and climatic features of watersheds (Wagener & Montanari 2011). The first approach allows applying model parameters using for areas that have similar hydrological regions. Hydrological similarity presupposes that watershed behavior maintains a certain level of organization and predictability, despite the complexity of basin responses caused by heterogeneity and variation in hydrological processes (Grimaldi et al. 2016). This concept enables the transfer of hydrological data from a reference basin to an ungauged basin (Betterle et al. 2018; Loritz et al. 2018).

The hydrological Tank model, which is designed and implemented by a Japanese scientist (Sugawara 1979), is a conceptual rainfall-runoff model that is widely applied for different purposes such as flood control (Chen et al. 2014), runoff prediction (Oeurng et al. 2011), water resource management (Wickramarachchi & Wijesekera 2022), estimation of external nutrient loading for a lake (Le Tien et al. 2020), and assessing historical runoff variation (Phuong et al. 2018). The hydrological Tank model can display flow distribution for each layer of the watershed area at a specific time (Arifjaya et al. 2011). Many studies have been published on the Tank model's ability to demonstrate the performance and accuracy of the hydrological processes of a variety of watersheds in Asian countries such as Japan (Basri et al. 1999), Malaysia (Kuok et al. 2010), Nepal (Pradhan 2001), Bangladesh (Mondal et al. 2009), Korea (Kang et al. 2013), Indonesia (Kadarisman 1993; Purwanto 1999; Azmeri & Herissandy 2012), Sri Lanka (Wickramarachchi & Wijesekera 2022), and Vietnam (Ngoc et al. 2011; Udo & Mano 2012). The advantages of Tank models include the representation of flow distributions over time for each layer of the watershed area, which is commonly used for long-term historical runoff estimation (Arifjaya et al. 2011). The model was also used to simulate hydrological processes in single-tank watersheds, and calibrated parameters could be transferred from gauged to ungauged sub-catchments, thus, providing a valid technique for runoff simulations of ungauged watersheds (Kang et al. 2013). Furthermore, the Tank model requires little data to simulate the hydrological process via tank cascade systems, which is widely applied in various regions from arid to humid areas and from tropical to snow-covered areas (Pradhan 2001). Based on the above review of the literature, it is clear that studies have used a rainfall-runoff model to estimate total long-term system inflows and to evaluate different potential future scenarios, particularly in areas with limited hydrological data availability. However, studies that simulate the parameters of the Tank model from small catchments to apply to larger catchments have not been fully documented. Therefore, the application of the Tank model needs to be performed with small- to large-scale sub-catchments in combination with simulation daily time steps in order to successfully identify parameters.

The Ca River Basin is an international river and one of the main river systems of Vietnam. It is located at 18°15′00″N to 20°10′30″N and 103°45′20″E to 105°15′20″E and occupies an area of 27,200 km², of which 17,730 km² in Vietnam and 9,470 km² in Laos. The basin is located in a tropical climate with two distinct seasons: a dry season from November to April and a rainy season from May to October. The Ca River Basin is the largest system in the central northern region of Vietnam. However, the number of gauging stations is limited with only seven managed hydrological gauging stations along the Ca River. This leads to a challenge in flow estimation in ungauged sub-catchments. Therefore, this study primarily focuses on a hydrological Tank model for streamflow estimation in gauged catchments in order to extend the investigation to a continuous large catchment that lacks data.

The Hieu River Basin is the largest tributary on the left bank of the Ca River. There are two hydrological stations located in this basin: Quy Chau (105°08′20″N, 19°23′30″E) and Nghia Khanh (105°20′00″N, 19°26′00″E) stations. Hydro-meteorological monitoring daily data are available at Quy Chau station, including rainfall, evaporation, and discharge data since 1961. In this study, the hydro-meteorological daily data during the periods from 2011 to 2020 at the Quy Chau station were collected for simulating the Tank model (Table 2). The collected data revealed that average annual rainfall and discharge at Quy Chau were 1,717 mm/year and 2,377 million m³/year, respectively.

The Trai River Basin is a tributary on the right bank of the Ca River, and the Hoa Quan hydrological station (105°15′43″N, 18°46′45″E) has been located on this tributary from 1976 to 1985. Therefore, hydrological daily data are available for this period, which were collected for the model simulation (Table 2). The average annual discharge at Hoa Quan was 197 million m³/year. The meteorological data at the Do Luong station (105°17′60″N, 18°53′60″E) were used as input to simulate the Tank model for the Hoa Quan sub-catchment. The annual rainfall at the Do Luong station was 2,226 mm/year.

The runoff from side outlets of a storage tank is proportional to the water head over the outlet of tanks and defined as the surface runoff (q₁₁), sub-surface runoff (q₁₁), intermediate runoff (q₂), sub-base runoff (q₃), and base runoff (q₄). The discharge at the bottom hole of each tank is considered the infiltration (p₁), percolation (p₂), and deep percolation (p₃) flows into lower soil layers, which is proportional to the water depth.

The Tank model is calibrated to determine 16 parameter values (α₁₁, α_12,α₂, α₃, α₄, β₁, β₂, β₃, z₁₁, z₁₂, z₂, z₃, h₁, h₂, h_3, and h₄). These parameters vary from one basin to another due to different characteristic properties such as climatic conditions, land use, soil type, watershed geomorphology, and hydrograph response (Arifjaya et al. 2011). Thus, in order to calibrate the Tank model, it is important to determine the initial parameters representing the physical natural component processes of the target basin. Parameter ranges are generally roughly estimated due to the lack of knowledge concerning the physical settings of a local catchment (Wu et al. 2017). Table 3 shows the range and initial values of parameters suggested by Sugawara (1995), which were used in the calibration trials in this study. The initial values of the storage parameters in the top tank, second tank, third tank, and fourth tank are 0, 0, 10–100, and 100–1,000 mm, respectively (Suryoputro et al. 2017). Parameters of the Tank model are optimized by manual trial and error. The optimal parameter set is ascertained by comparing the fitness of simulated data with observed hydrograph data. However, the optimal processes of the Tank model need to follow certain principles. Specifically, the sum of the runoff and infiltration coefficients of each tank must be less than or equal to one (e.g. α₁₁ + α₁₂ + β₁ ≤ 1; α₂ + β₂ ≤ 1) (Sugawara 1979; Basri et al. 1999). The height of the top side outlet must be bigger than the height of the lower side outlet in the first tank (z₁₁ < z₁₂) (Chen et al. 2014).

In order to calibrate the Tank model, several well-known quantitative criteria were used in this study for evaluating model performance. The four criteria include R², NSE, PBIAS, and RSR as recommended by Krause et al. (2005) and Moriasi et al. (2007).

The R² value (Equation (14)) describes the degree of co-linearity between simulated and observed data. R² ranges between 0 and 1 and values greater than 0.5 are considered acceptable (Golmohammadi et al. 2014). As the model conformity improves, R² approaches unity.

Meanwhile, the NSE (Equation (15)) is a normalized statistic that determines the relative magnitude of the residual variance (‘noise’) compared to the measured data variance (‘information’) (Nash & Sutcliffe 1970). The NSE ranges from −∞ to 1, with the NSE by one being the optimal value. Values less than 0 occur (−∞ < NSE < 0) when the mean value of the observed data is a better predictor than the model, which indicates unacceptable performance (Krause et al. 2005).

The PBIAS (Equation (16)) measures the average tendency of the simulated data to be larger or smaller than their observed ones. The optimal value of PBIAS is 0, with low-magnitude values indicating accurate model simulation. A positive value indicates a tendency to underestimate and a negative value indicates a tendency to overestimate.

The river discharge prediction can be evaluated as ‘Satisfactory’, ‘Good’, ‘Very good’, and ‘Unsatisfactory’ for a daily time step according to the obtained model evaluation values (Table 4) (Moriasi et al. 2007).

The calibration period was 5 years from 2011 to 2015, and the validation period was 5 years from 2016 to 2020 at the Quy Chau sub-catchment. The same parameters were simulated at the Quy Chau sub-catchment, with an area of just 2,084 km², and were verified for use at the larger catchment area, Nghia Khanh, which has an area of 4,084 km² (Figure 1). The runoff data at Nghia Khanh cover the period from 2011 to 2015.

Similarly, the calibration period was 5 years from 1976 to 1980, and the validation period was 5 years from 1981 to 1985, at the Hoa Quan sub-catchment. The same parameters calibrated at the Hoa Quan sub-catchment with an area of 119 km² were verified for use at the catchment between Dua (105°02′20″N, 18°59′20″E) and Yen Thuong (105°23′00″N, 18°41′10″E) stations, which have an area of 2,000 km² (Figure 1). The runoff data at Dua and Yen Thuong stations for the period of 1976–1985 were collected corresponding to the simulated period.

In order to verify the Tank model for the catchment between Dua and Yen Thuong and the catchment at the Nghia Khanh station, meteorological data were used at the Do Luong station and the Quy Chau station, respectively. All necessary hydro-meteorological data were provided by the North Central Hydro-meteorological Centre, Vietnam.

A Tank model was set up to evaluate the long-term daily inflow discharge (1976–1985). The calibration period was from 1976 to 1981, and the validation period was from 1982 to 1985 (Figure 5). Statistical analysis revealed that the performance of the Tank model was acceptable during the calibration period at the Hoa Quan station (NSE = 0.78, RSR = 0.05, PBIAS = 4.8%, R² = 0.78). The NSE, RSR, PBIAS, and R² values during the validation period were 0.52, 0.01, 1.3%, and 0.4, respectively (Table 6). The NSE value in the validation period (0.52) was lower than that for the calibration period (0.78) as all of the statistics computed for this period were more deficient than those computed for the calibration period, but the value was acceptable. A bias of 4.8% was found for the calibration period, whereas the validation period had a bias of 1.3%. This indicates that there was an overestimation bias for the calibration period and the validation period. The calculated discharge at the Hoa Quan station differs from the observed peak discharge measured from 1978 to 1979. This could be due to the representativeness of the meteorological station, given that the measuring station is located downstream, while there is abnormal rainfall in upstream areas, which could not be fully recorded and tracked. In a nutshell, the hydrological Tank model at the Hoa Quan station was performed with acceptable computed data as compared to the observation data. The calibrated parameters at the Hoa Quan sub-catchments are shown in Figure 6(b).

Previous studies on the Tank model used historical hydro-meteorological data in the basin with the aim of finding a representative set of parameters for that river basin. Several authors simulated the Tank model for basin areas with a range from 1 to 100 km², which include the Ciriung watershed with an area of 1.2 km² in Indonesia, the Terauchi watershed with an area of 50.55 km² in Japan (Setiawan et al. 2003), the Bedup watershed with an area of 47.5 km² in Malaysia (Kuok et al. 2010), and the Cisadane Upper Catchment with an area of 18 km² in Indonesia (Arifjaya et al. 2011). The others developed the Tank model for the basin with an area less than 1,000 km² including the Namatala River Catchment (155 km²) in Eastern Uganda (Okiria et al. 2020) and the Nilwala River at Pitabeddara (291.4 km²) in Sri Lanka (Wickramarachchi & Wijesekera 2022). There are also few authors who investigated the Tank model for a large basin with up to thousands of square kilometers, such as the Upper Dau Tieng River Basin in Vietnam with 2,700 km² (Ngoc et al. 2011). In fact, it will not be easy to determine representative parameters of large river basins or basins lacking hydro-meteorological data. Applying calibrated parameters from a gauged watershed to similar watersheds can be a solution to calculate discharges for watersheds lacking data. Pradhan's study is one of the few studies focusing on the applicability of the same set of model parameters to sub-basins (Pradhan 2001). Pradhan simulated the Tank model for the Jhikhu River watershed, a small-scale watershed (111.41 km²), and the Sun Kosi River watershed (4,882 km²), a larger watershed. The study indicated that in the case of small watersheds, parameters estimated for one sub-catchment did not match the next sub-catchment response. However, in the case of larger catchments, the estimated parameters for one large-scale sub-catchment give an accurate response for the next large-scale sub-catchment. Pradhan concluded that if the basin was large, the effects of random hydrological phenomena would cancel each other out and the change would be minimal. However, in a small basin, these effects of random hydrological and geomorphological phenomena may cause instability in predictions. Their study, on the other hand, developed a model to estimate the neighborhood catchment, whereas our study uses a calibrated model for small catchments and then extends that to larger areas of similar hydrological conditions. The simulated parameters could be applied to calculate discharge at ungauged locations within the study area. However, this study has some limitations related to hydrological data in the Hoa Quan sub-catchment, where the hydrological station has been inactive since 1986. In addition, the measured meteorological data are quite sparse, which are the causes of the model-reduced effectiveness.

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  This study assessed the applicability of a Tank model to simulate the river discharge of two poor gauged sub-catchments in the Ca River Basin.

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  The model was first simulated by fitting observed and simulated daily runoff data for the Quy Chau and Hoa Quan sub-catchments, then the obtained model parameters were used for verifying the daily flow of Nghia Khanh and Dua–Yen Thuong sub-catchments, respectively.

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  The model evaluation criteria at Quy Chau performed ‘good’ to ‘very good’ for the calibrated period of 2011–2015 and ‘very good’ for the validated period of 2016–2020.

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  The model evaluation criteria at Hoa Quan performed ‘very good’ for the calibrated period of 1976–1981 and ‘satisfactory’ to ‘very good’ for the validated period of 1982–1985, except for the R² index. The effectiveness of the model in the Hoa Quan sub-catchment is limited by the lack of meteorological and hydrological data.

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  The simulated daily time step Tank model parameter sets were applied to larger sub-catchments. The model performance indicators indicated ‘satisfactory’ to ‘very good’ for the Nghia Khanh sub-catchment and ‘very good’ for the Dua–Yen Thuong sub-catchment.

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  The results of this study indicated the potential for using parameters identified in a local basin to calculate the flow process in similar, larger locations in the Ca River Basin sub-catchments. As such, the model can be used to simulate runoff from watersheds, and the simulated inflow data have the potential to benefit watershed management.

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  Further studies could include simulations for large sub-catchments and an effectiveness assessment for small sub-catchments.

The authors are grateful for financial support provided by the Science and Technology Project of the Ministry of Education and Training of Vietnam (B2021-TDV-09)

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.