Streamflow information is of great significance for flood control, water resources utilization and management, ecological services, etc. Continuous streamflow prediction in ungauged basins remains a challenge, mainly due to data paucity and environmental changes. This study focuses on the modification of a nonlinear hydrological system approach known as the time variant gain model and the development of a regressive method based on the modified approach. This method directly correlates rainfall to runoff through physically based mathematical transformations without requiring additional information of evaporation or soil moisture. Also, it contains parsimonious parameters that can be derived from watershed properties. Both characteristics make this method suitable for practical uses in ungauged basins. The Huai River Basin of China was selected as the study area to test the regressive method. The results show that the proposed methodology provides an effective way to predict streamflow of ungauged basins with reasonable accuracy by incorporating regional watershed information (soil, land use, topography, etc.). This study provides a useful predictive tool for future water resources utilization and management for data-sparse areas or watersheds with environmental changes.
INTRODUCTION
Sustainable water resource management practices rely heavily on the accurate modeling of hydrological processes at watershed scales. In particular, numerical predictions of continuous streamflow is of paramount importance in a variety of fields, such as irrigation planning, flood control, engineering structure design, water resources utilization, and ecohydrological services (Parada & Liang 2010; Razavi & Coulibaly 2012; Cibin et al. 2014). In practical applications, however, we often need to deal with many ungauged or poorly gauged basins without adequate and accurate streamflow observations (Sivapalan et al. 2003). These data-sparse basins often exist in mountainous areas (Castellarin et al. 2007), unregulated regions (Stainton & Metcalfe 2007), and rural or remote areas (Makungo et al. 2010). Some gauged basins may also change to be ungauged when the previous streamflow information is no longer suitable to describe the hydrological responses to environmental changes, such as human-induced land use change. Furthermore, modified land surface processes in watersheds, e.g., heavily built terrains, will in turn influence the local hydroclimate via land–atmospheric interactions (Song & Wang 2015a, 2015b), thus resulting in higher uncertainty in predicting hydrological responses in the region.
In general, an effective hydrological prediction system consists of an appropriate model structure, a set of calibrated model parameters, and accurate model inputs. The hydrological system approach (Singh 1988) is found to be flexible as compared to other conceptual models in data-sparse areas under uncertainty perturbation and environmental change (Xia 1991; Xia et al. 2005). Xia (1991) developed a nonlinear hydrological system approach based on Volterra functional series, known as the time variant gain model (TVGM). The TVGM has been tested over ten different basins in China, Japan, the United States, and Australia (Xia et al. 1997), and found to be effective for daily and hourly streamflow forecasting under different climate conditions (semi-arid and humid) with parsimonious parameters. For better predictability, a modified TVGM with two runoff types is proposed here and selected as the hydrological modeling approach for ungauged catchments in this study.
Model parameters are often calibrated based on previous observation data, which are unavailable at ungauged or poorly gauged sites. The lack of model calibration and verification due to the paucity of measurement data therefore requires a different methodology for parameter estimation. Regionalization (Blöschl & Sivapalan 1995; Jin et al. 2009; Kizza et al. 2013) is a feasible way for predictions in ungauged basins by transferring hydrological information from gauged basins. There are three types of regionalization method: spatial proximity, physical similarity, and regression (Oudin et al. 2008). The spatial proximity method (Mosley 1981; Vandewiele & Elias 1995) focuses on the geographical similarity and employs the parameter values from the geographic neighbors without considering the heterogeneity of the catchments included. The physical similarity method (Reed 1999; Patil & Stieglitz 2012) is based on hydrological proximity, regardless of geographical location of the study area and the donor areas. The regression method (Abdulla & Lettenmaier 1997; Post & Jakeman 1999; Seibert 1999; Xu 1999, 2003; Li et al. 2010), in contrast, estimates the model parameters of ungauged catchments according to a posteriori relationships between catchment descriptors (both physical and climatic) and model parameter values calibrated at gauged sites. This approach is capable of incorporating more catchment information, but also exhibits more uncertainties in model parameter and catchment descriptor (Oudin et al. 2008).
Previous studies have attempted to compare the three regionalization approaches, without reaching a clear consensus. This is mainly because these studies were based on a variety of catchment sets, climatic situations, donor catchment sets, catchment descriptors, and hydrological models, and comparisons were not made on the same ground (Oudin et al. 2008). It is found that the best choice of regionalization approach is site specific rather than universal. With an appropriate hydrological model, regression approach works best in most warm temperate regions (Razavi & Coulibaly 2012). While our study area of the Huai River Basin, China is located in a warm temperate region, the choice of regression approach is appropriate.
Our objective in this study is to predict 3-hourly streamflow for ungauged catchments by regression approach based on the modified TVGM. The structure of this paper is arranged as follows. First, the study area and data collection are introduced. In the next section, the modified TVGM is described followed by its validated. Based on the modified TVGM, a parametric regression approach is established and applied for streamflow predictions. Then, results of the regression approach and discussions on its underlying physics are presented. Lastly, findings and implications of this article are presented.
STUDY AREA AND AVAILABLE DATA
Study area
Available data
Catchment . | A (km2) . | Np . | α . | top (m) . | P (mm) . | Mean rainfall centroid . | ||
---|---|---|---|---|---|---|---|---|
LON . | LAT . | d (km) . | ||||||
Huangchuan | 2,050 | 6 | 0.0045 | 19.02 | 931.61 | 115.05 | 32.13 | 45.68 |
Jiangjiaji | 5,930 | 12 | 0.0052 | 20.42 | 803.94 | 115.73 | 32.3 | 56.39 |
Xixian | 10,190 | 24 | 0.0029 | 22.2 | 848.28 | 114.73 | 32.33 | 72.21 |
Bantai | 11,280 | 26 | 0.001 | 18.18 | 744.92 | 115.07 | 32.72 | 109.16 |
Luohe | 12,150 | 12 | 0.0051 | 20.21 | 702.22 | 114.03 | 33.58 | 83.92 |
Mengcheng | 15,475 | 13 | 0.0002 | 20.54 | 633.67 | 116.55 | 33.28 | 145.74 |
Huaibin | 16,005 | 34 | 0.0022 | 22.67 | 798.58 | 115.42 | 32.43 | 111.5 |
Zhoukou | 25,800 | 42 | 0.0031 | 21.31 | 453.79 | 114.65 | 33.63 | 151.11 |
Jieshou | 29,290 | 45 | 0.0024 | 21.47 | 630.16 | 115.35 | 33.27 | 207.76 |
Wangjiaba | 30,630 | 61 | 0.002 | 22.67 | 651.28 | 115.6 | 32.43 | 131.12 |
Runheji | 40,360 | 68 | 0.0029 | 22.67 | 704.41 | 116.1 | 32.52 | 164.77 |
Lutaizi | 88,630 | 91 | 0.0027 | 22.67 | 695.39 | 116.63 | 32.57 | 178.38 |
Bengbu | 121,330 | 158 | 0.0018 | 23.18 | 720.05 | 117.38 | 32.93 | 272.93 |
Catchment . | A (km2) . | Np . | α . | top (m) . | P (mm) . | Mean rainfall centroid . | ||
---|---|---|---|---|---|---|---|---|
LON . | LAT . | d (km) . | ||||||
Huangchuan | 2,050 | 6 | 0.0045 | 19.02 | 931.61 | 115.05 | 32.13 | 45.68 |
Jiangjiaji | 5,930 | 12 | 0.0052 | 20.42 | 803.94 | 115.73 | 32.3 | 56.39 |
Xixian | 10,190 | 24 | 0.0029 | 22.2 | 848.28 | 114.73 | 32.33 | 72.21 |
Bantai | 11,280 | 26 | 0.001 | 18.18 | 744.92 | 115.07 | 32.72 | 109.16 |
Luohe | 12,150 | 12 | 0.0051 | 20.21 | 702.22 | 114.03 | 33.58 | 83.92 |
Mengcheng | 15,475 | 13 | 0.0002 | 20.54 | 633.67 | 116.55 | 33.28 | 145.74 |
Huaibin | 16,005 | 34 | 0.0022 | 22.67 | 798.58 | 115.42 | 32.43 | 111.5 |
Zhoukou | 25,800 | 42 | 0.0031 | 21.31 | 453.79 | 114.65 | 33.63 | 151.11 |
Jieshou | 29,290 | 45 | 0.0024 | 21.47 | 630.16 | 115.35 | 33.27 | 207.76 |
Wangjiaba | 30,630 | 61 | 0.002 | 22.67 | 651.28 | 115.6 | 32.43 | 131.12 |
Runheji | 40,360 | 68 | 0.0029 | 22.67 | 704.41 | 116.1 | 32.52 | 164.77 |
Lutaizi | 88,630 | 91 | 0.0027 | 22.67 | 695.39 | 116.63 | 32.57 | 178.38 |
Bengbu | 121,330 | 158 | 0.0018 | 23.18 | 720.05 | 117.38 | 32.93 | 272.93 |
A is the catchment area; Np is the number of dominant rainfall stations; α is the mainstream slope; top is the topographical wetness index related to soil state; P is the long-term average precipitation; LON and LAT refer to the longitude and latitude of mean rainfall centroid respectively; d is the distance between the mean rainfall centroid and the corresponding hydrological station.
The soil-type dataset was obtained from the United Nations Food and Agriculture Organization (FAO) and the soil types were defined by global soil classification of FAO and UNESCO. Soil properties and soil water characteristics of different catchments are derived as presented in Tables 2 and 3, respectively. The land use type data with a scale of 1:1,000,000 were obtained from the Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences. The land use types in the study area can be divided into the following six types: forest (FRST), range of grassland and meadow (RNGE), water area (WATER), urban areas with high density (URHD), rice paddy (RICE), and agricultural dry land (AGRR). The ratios of different land use types in each catchment are presented in Table 4.
Catchment . | Soil layer depth (mm) . | Sand (%) . | Silt (%) . | Clay (%) . |
---|---|---|---|---|
Huangchuan | 1,117.94 | 46.68 | 23.22 | 28.55 |
Jiangjiaji | 766.05 | 46.83 | 26.03 | 21.36 |
Xixian | 1,015.23 | 39.88 | 30.26 | 21.74 |
Bantai | 1,162.59 | 38.08 | 33.69 | 22.97 |
Luohe | 913.82 | 37.7 | 30.87 | 25.43 |
Mengcheng | 968.36 | 44.42 | 26.44 | 22.68 |
Huaibin | 1,027.46 | 37.59 | 30.97 | 24.15 |
Zhoukou | 917.38 | 38.54 | 31.3 | 18.47 |
Jieshou | 904.42 | 35.21 | 30.63 | 21.42 |
Wangjiaba | 1,046.85 | 36.03 | 31.42 | 23.96 |
Runheji | 964.23 | 35.38 | 29.63 | 23.19 |
Lutaizi | 923.86 | 34.01 | 28.77 | 22.6 |
Bengbu | 800.22 | 28.45 | 25.27 | 19.79 |
Catchment . | Soil layer depth (mm) . | Sand (%) . | Silt (%) . | Clay (%) . |
---|---|---|---|---|
Huangchuan | 1,117.94 | 46.68 | 23.22 | 28.55 |
Jiangjiaji | 766.05 | 46.83 | 26.03 | 21.36 |
Xixian | 1,015.23 | 39.88 | 30.26 | 21.74 |
Bantai | 1,162.59 | 38.08 | 33.69 | 22.97 |
Luohe | 913.82 | 37.7 | 30.87 | 25.43 |
Mengcheng | 968.36 | 44.42 | 26.44 | 22.68 |
Huaibin | 1,027.46 | 37.59 | 30.97 | 24.15 |
Zhoukou | 917.38 | 38.54 | 31.3 | 18.47 |
Jieshou | 904.42 | 35.21 | 30.63 | 21.42 |
Wangjiaba | 1,046.85 | 36.03 | 31.42 | 23.96 |
Runheji | 964.23 | 35.38 | 29.63 | 23.19 |
Lutaizi | 923.86 | 34.01 | 28.77 | 22.6 |
Bengbu | 800.22 | 28.45 | 25.27 | 19.79 |
Catchment . | Wilting point (% Vol.) . | Field capacity (% Vol.) . | Saturation (% Vol.) . | Available water (mm/m) . |
---|---|---|---|---|
Huangchuan | 15.01 | 25.62 | 45.79 | 106.67 |
Jiangjiaji | 13.26 | 23.82 | 44.08 | 105.83 |
Xixian | 13.81 | 25.16 | 43.46 | 111.67 |
Bantai | 15.15 | 28.18 | 44.03 | 130.00 |
Luohe | 16.37 | 28.49 | 44.40 | 120.83 |
Mengcheng | 14.04 | 23.75 | 45.25 | 96.67 |
Huaibin | 14.83 | 26.59 | 43.86 | 116.67 |
Zhoukou | 12.46 | 24.04 | 40.99 | 115.83 |
Jieshou | 14.00 | 25.54 | 40.87 | 115.00 |
Wangjiaba | 14.91 | 26.92 | 43.00 | 119.17 |
Runheji | 14.43 | 25.86 | 41.54 | 114.17 |
Lutaizi | 14.13 | 25.09 | 40.51 | 109.17 |
Bengbu | 12.55 | 21.94 | 35.07 | 93.33 |
Catchment . | Wilting point (% Vol.) . | Field capacity (% Vol.) . | Saturation (% Vol.) . | Available water (mm/m) . |
---|---|---|---|---|
Huangchuan | 15.01 | 25.62 | 45.79 | 106.67 |
Jiangjiaji | 13.26 | 23.82 | 44.08 | 105.83 |
Xixian | 13.81 | 25.16 | 43.46 | 111.67 |
Bantai | 15.15 | 28.18 | 44.03 | 130.00 |
Luohe | 16.37 | 28.49 | 44.40 | 120.83 |
Mengcheng | 14.04 | 23.75 | 45.25 | 96.67 |
Huaibin | 14.83 | 26.59 | 43.86 | 116.67 |
Zhoukou | 12.46 | 24.04 | 40.99 | 115.83 |
Jieshou | 14.00 | 25.54 | 40.87 | 115.00 |
Wangjiaba | 14.91 | 26.92 | 43.00 | 119.17 |
Runheji | 14.43 | 25.86 | 41.54 | 114.17 |
Lutaizi | 14.13 | 25.09 | 40.51 | 109.17 |
Bengbu | 12.55 | 21.94 | 35.07 | 93.33 |
Catchment . | FRST (%) . | RNGE (%) . | WATER (%) . | URHD (%) . | RICE (%) . | AGRR (%) . |
---|---|---|---|---|---|---|
Huangchuan | 19 | 1 | 2 | 1 | 32 | 44 |
Jiangjiaji | 32 | 12 | 3 | 1 | 35 | 18 |
Xixian | 36 | 0 | 3 | 1 | 20 | 40 |
Bantai | 9 | 2 | 3 | 1 | 1 | 84 |
Luohe | 21 | 5 | 5 | 1 | 0 | 68 |
Mengcheng | 1 | 1 | 3 | 0 | 1 | 95 |
Huaibin | 26 | 0 | 3 | 1 | 24 | 46 |
Zhoukou | 9 | 4 | 2 | 3 | 1 | 81 |
Jieshou | 10 | 3 | 2 | 3 | 1 | 81 |
Wangjiaba | 23 | 1 | 3 | 1 | 28 | 45 |
Runheji | 19 | 3 | 3 | 1 | 20 | 54 |
Lutaizi | 21 | 4 | 3 | 1 | 26 | 45 |
Bengbu | 12 | 3 | 2 | 2 | 16 | 65 |
Catchment . | FRST (%) . | RNGE (%) . | WATER (%) . | URHD (%) . | RICE (%) . | AGRR (%) . |
---|---|---|---|---|---|---|
Huangchuan | 19 | 1 | 2 | 1 | 32 | 44 |
Jiangjiaji | 32 | 12 | 3 | 1 | 35 | 18 |
Xixian | 36 | 0 | 3 | 1 | 20 | 40 |
Bantai | 9 | 2 | 3 | 1 | 1 | 84 |
Luohe | 21 | 5 | 5 | 1 | 0 | 68 |
Mengcheng | 1 | 1 | 3 | 0 | 1 | 95 |
Huaibin | 26 | 0 | 3 | 1 | 24 | 46 |
Zhoukou | 9 | 4 | 2 | 3 | 1 | 81 |
Jieshou | 10 | 3 | 2 | 3 | 1 | 81 |
Wangjiaba | 23 | 1 | 3 | 1 | 28 | 45 |
Runheji | 19 | 3 | 3 | 1 | 20 | 54 |
Lutaizi | 21 | 4 | 3 | 1 | 26 | 45 |
Bengbu | 12 | 3 | 2 | 2 | 16 | 65 |
METHODOLOGY
TVGM
Modified TVGM
Derivation of model parameters
RESULTS AND DISCUSSION
Model calibration and verification
In this section, the modified TVGM is applied to 13 catchments in Huai River Basin. Due to limited data availability, lengths of data records for different catchments are different. For each catchment, about two-thirds of the collected rainfall–runoff data were used for model calibration while the remaining third was used for model verification. The available data in calibration and verification periods for different catchments are summarized in Table 5. As introduced previously, the parameters of the modified TVGM were calibrated via the Householder least square method and genetic algorithm, as presented in Table 6.
Hydrological station . | Calibration period . | Verification period . |
---|---|---|
Huangchuan | 2007 2008 | 2005 |
Jiangjiaji | 2002 2003 2004 2005 | 2007 |
Xixian | 2002 2004 2005 | 2007 2008 |
Bantai | 2004 2005 2006 | 2007 2008 |
Luohe | 2004 2007 | 2001 |
Mengcheng | 2008 | 2007 |
Huaibin | 2005 2006 2007 | 2008 |
Zhoukou | 2004 2005 | 2000 |
Jieshou | 2004 2007 | 2006 2008 |
Wangjiaba | 2000 2002 2004 2006 | 2007 2008 |
Runheji | 2000 2002 2004 2006 | 2007 2008 |
Lutaizi | 2002 2004 2006 2008 | 2000 2008 |
Bengbu | 2000 2002 2004 2005 | 2007 2008 |
Hydrological station . | Calibration period . | Verification period . |
---|---|---|
Huangchuan | 2007 2008 | 2005 |
Jiangjiaji | 2002 2003 2004 2005 | 2007 |
Xixian | 2002 2004 2005 | 2007 2008 |
Bantai | 2004 2005 2006 | 2007 2008 |
Luohe | 2004 2007 | 2001 |
Mengcheng | 2008 | 2007 |
Huaibin | 2005 2006 2007 | 2008 |
Zhoukou | 2004 2005 | 2000 |
Jieshou | 2004 2007 | 2006 2008 |
Wangjiaba | 2000 2002 2004 2006 | 2007 2008 |
Runheji | 2000 2002 2004 2006 | 2007 2008 |
Lutaizi | 2002 2004 2006 2008 | 2000 2008 |
Bengbu | 2000 2002 2004 2005 | 2007 2008 |
Notes: Different hydrological stations have different lengths of available data. The time period of each year was from April 1, 8:00 to September 30, 8:00 with a time step of 3 hours.
Catchment . | g1 . | g2 . | g3 . | g4 . | n . | K . | KKG . |
---|---|---|---|---|---|---|---|
Huangchuan | −0.07 | 0.34 | 0.05 | 0.21 | 3.23 | 1.83 | 0.92 |
Jiangjiaji | 0.02 | 0.22 | 0.00 | 0.28 | 8.17 | 1.12 | 0.91 |
Xixian | 0.00 | 0.26 | −0.01 | 0.28 | 4.27 | 2.42 | 0.91 |
Bantai | −0.13 | 0.38 | −0.09 | 0.38 | 4.25 | 4.21 | 0.91 |
Luohe | −0.06 | 0.21 | −0.06 | 0.21 | 2.67 | 4.06 | 0.91 |
Mengcheng | 0.02 | 0.14 | 0.07 | 0.06 | 7.05 | 2.08 | 0.91 |
Huaibin | −0.02 | 0.36 | −0.07 | 0.44 | 7.05 | 3.02 | 0.91 |
Zhoukou | −0.05 | 0.22 | −0.08 | 0.31 | 4.59 | 3.89 | 0.90 |
Jieshou | −0.04 | 0.19 | −0.02 | 0.17 | 7.94 | 2.79 | 0.91 |
Wangjiaba | 0.01 | 0.21 | 0.08 | 0.19 | 5.90 | 3.80 | 0.91 |
Runheji | −0.03 | 0.27 | −0.01 | 0.30 | 8.56 | 4.21 | 0.91 |
Lutaizi | −0.03 | 0.30 | −0.02 | 0.36 | 7.34 | 5.77 | 0.90 |
Bengbu | 0.03 | 0.24 | 0.19 | 0.03 | 7.94 | 6.51 | 0.91 |
Catchment . | g1 . | g2 . | g3 . | g4 . | n . | K . | KKG . |
---|---|---|---|---|---|---|---|
Huangchuan | −0.07 | 0.34 | 0.05 | 0.21 | 3.23 | 1.83 | 0.92 |
Jiangjiaji | 0.02 | 0.22 | 0.00 | 0.28 | 8.17 | 1.12 | 0.91 |
Xixian | 0.00 | 0.26 | −0.01 | 0.28 | 4.27 | 2.42 | 0.91 |
Bantai | −0.13 | 0.38 | −0.09 | 0.38 | 4.25 | 4.21 | 0.91 |
Luohe | −0.06 | 0.21 | −0.06 | 0.21 | 2.67 | 4.06 | 0.91 |
Mengcheng | 0.02 | 0.14 | 0.07 | 0.06 | 7.05 | 2.08 | 0.91 |
Huaibin | −0.02 | 0.36 | −0.07 | 0.44 | 7.05 | 3.02 | 0.91 |
Zhoukou | −0.05 | 0.22 | −0.08 | 0.31 | 4.59 | 3.89 | 0.90 |
Jieshou | −0.04 | 0.19 | −0.02 | 0.17 | 7.94 | 2.79 | 0.91 |
Wangjiaba | 0.01 | 0.21 | 0.08 | 0.19 | 5.90 | 3.80 | 0.91 |
Runheji | −0.03 | 0.27 | −0.01 | 0.30 | 8.56 | 4.21 | 0.91 |
Lutaizi | −0.03 | 0.30 | −0.02 | 0.36 | 7.34 | 5.77 | 0.90 |
Bengbu | 0.03 | 0.24 | 0.19 | 0.03 | 7.94 | 6.51 | 0.91 |
From Table 6, it is clear that the coefficients g2 and g4 are always positive, while g1 and g3 take values around 0 (either positive or negative). This can be physically explained based on the runoff generation mechanisms described in Equations (9)–(12). If the time variant gain coefficient of quick flow, i.e., Gs obtained from Equation (10) is positive, the generation of quick flow Rs begins according to Equation (9). If g2 = 0, Gs becomes a constant factor, (i.e., Gs = g1) rather than a time variant factor. If g2 < 0, Gs becomes a time-decreasing factor, which is not reasonable since the quick flow amount increases with API or soil moisture. Therefore, g2 must be positive. On the other hand, g1 does not have the positive constraint. If g1 ≤ 0, quick flow begins to generate when the initial API is large enough, leading to Gs > 0, which is physically reasonable in arid areas. If g1 > 0, quick flow starts instantaneously with precipitation, which is possible for humid areas. Based on a similar argument, it is straightforward to show that g4 is always positive, while g3 is negative or positive in arid or humid areas, respectively. Additionally, all flow routing parameters (i.e., N, K, and KKG) are positive and KKG is found to be site-insensitive.
Catchment . | Calibration period . | Verification period . | ||
---|---|---|---|---|
NSE . | CWB . | NSE . | CWB . | |
Huangchuan | 0.95 | 0.82 | 0.92 | 0.83 |
Jiangjiaji | 0.92 | 0.83 | 0.98 | 1.40 |
Xixian | 0.94 | 0.88 | 0.96 | 0.92 |
Bantai | 0.91 | 0.86 | 0.89 | 0.86 |
Luohe | 0.91 | 0.83 | 0.99 | 1.28 |
Mengcheng | 0.89 | 0.83 | 0.96 | 0.91 |
Huaibin | 0.93 | 0.83 | 0.84 | 0.83 |
Zhoukou | 0.94 | 0.76 | 0.96 | 1.24 |
Jieshou | 0.90 | 0.87 | 0.87 | 0.79 |
Wangjiaba | 0.89 | 0.86 | 0.88 | 0.88 |
Runheji | 0.91 | 0.85 | 0.91 | 0.74 |
Lutaizi | 0.89 | 0.83 | 0.84 | 0.76 |
Bengbu | 0.82 | 0.74 | 0.88 | 0.84 |
Catchment . | Calibration period . | Verification period . | ||
---|---|---|---|---|
NSE . | CWB . | NSE . | CWB . | |
Huangchuan | 0.95 | 0.82 | 0.92 | 0.83 |
Jiangjiaji | 0.92 | 0.83 | 0.98 | 1.40 |
Xixian | 0.94 | 0.88 | 0.96 | 0.92 |
Bantai | 0.91 | 0.86 | 0.89 | 0.86 |
Luohe | 0.91 | 0.83 | 0.99 | 1.28 |
Mengcheng | 0.89 | 0.83 | 0.96 | 0.91 |
Huaibin | 0.93 | 0.83 | 0.84 | 0.83 |
Zhoukou | 0.94 | 0.76 | 0.96 | 1.24 |
Jieshou | 0.90 | 0.87 | 0.87 | 0.79 |
Wangjiaba | 0.89 | 0.86 | 0.88 | 0.88 |
Runheji | 0.91 | 0.85 | 0.91 | 0.74 |
Lutaizi | 0.89 | 0.83 | 0.84 | 0.76 |
Bengbu | 0.82 | 0.74 | 0.88 | 0.84 |
Regressive regionalization analysis
After testing the modified TVGM in gauged basins, we then conduct a regionalization process to predict hydrological processes of ungauged basins. As introduced in Razavi & Coulibaly (2012), regression is more efficient than other regionalization approaches for warm temperate regions, and is adopted in this study. To verify the applicability of regionalization, we apply the model, using parameters derived from regressive analysis rather than by calibration against actual measurements, to reproduce the previous streamflow. The general criterion for catchment selection follows that both catchments for equation derivation and verification should cover a variety of catchment size (i.e., small, medium, and large) for better representativeness and applicability of the derived equations. Specifically, in this study, eight catchments with a range of area from 5,930 to 88,630 km2, including Jiangjiaji, Xixian, Bantai, Huaibin, Zhoukou, Jieshou, Runheji, and Lutaizi were selected for derivation of regression equations, while the remaining five catchments with a range of area from 2,050 to 121,330 km2, including Huangchuan, Luohe, Mengcheng, Wangjiaba, and Bengbu were used for verification of derived regression equations (check Table 1 for more catchment area information). Due to data availability and limitation in quality, we excluded some catchments while deriving regression equations such as Mengcheng (highly impacted by human activities) and Bengbu (with very large area and strong heterogeneous land surface conditions). The regression approach can be repeated with different combinations of catchments for calibration and validation. Under different combination cases, the empirical coefficients of the proposed model, being site-specific, will change correspondingly whereas the impact on the overall model predictability is insignificant.
Catchment . | Regionalized model parameters . | Model evaluation . | ||||||
---|---|---|---|---|---|---|---|---|
g1 . | g2 . | g3 . | g4 . | n . | K . | Mean NSE . | Mean CWB . | |
Huangchuan | 0.02 | 0.22 | 0.10 | 0.11 | 14.75 | 0.80 | 0.70 | 0.79 |
Luohe | −0.04 | 0.21 | 0 | 0.13 | 7.69 | 2.06 | 0.83 | 0.93 |
Mengcheng | 0.01 | 0.04 | 0.02 | 0.1 | 3.69 | 4.65 | 0.58 | 0.45 |
Wangjiaba | −0.03 | 0.35 | 0.01 | 0.3 | 5.97 | 3.89 | 0.89 | 0.92 |
Bengbu | −0.03 | 0.29 | −0.14 | 0.68 | 13.81 | 4.31 | 0.76 | 0.69 |
Catchment . | Regionalized model parameters . | Model evaluation . | ||||||
---|---|---|---|---|---|---|---|---|
g1 . | g2 . | g3 . | g4 . | n . | K . | Mean NSE . | Mean CWB . | |
Huangchuan | 0.02 | 0.22 | 0.10 | 0.11 | 14.75 | 0.80 | 0.70 | 0.79 |
Luohe | −0.04 | 0.21 | 0 | 0.13 | 7.69 | 2.06 | 0.83 | 0.93 |
Mengcheng | 0.01 | 0.04 | 0.02 | 0.1 | 3.69 | 4.65 | 0.58 | 0.45 |
Wangjiaba | −0.03 | 0.35 | 0.01 | 0.3 | 5.97 | 3.89 | 0.89 | 0.92 |
Bengbu | −0.03 | 0.29 | −0.14 | 0.68 | 13.81 | 4.31 | 0.76 | 0.69 |
The streamflows of Luohe and Wangjiaba were best simulated among the five catchments with mean NSE of 0.83 and 0.89, respectively, and mean CWB of 0.93 and 0.92, respectively. The two catchments are medium size catchments with an area of 12,150 km2 and 30,630 km2, covering about 10% and 40% of the total study area, respectively. Thus the catchment characteristics are similar to average characteristics of the study area and can be captured by the above derived regression equations with reasonable accuracy. In contrast, two extreme examples, including Huangchuan catchment, i.e., the smallest sub-catchment with an area of only 2,050 km2 and Bengbu catchment, i.e., the largest sub-catchment with an area of 121,330 km2 are analyzed (see Figures 1 and 2). The streamflows of Huangchuan and Bengbu are predicted with mean NSE of 0.70 and 0.76, respectively, and mean CWB of 0.79 and 0.69, respectively. Compared with Luohe and Wangjiaba catchments, the streamflow of Huangchuan catchment is predicted with reduced accuracy since it is practically difficult to represent the land surface characteristics at the upstream area of such a small catchment by average regionalization equations. As for Bengbu, given that it has the largest drainage area with various underlying surfaces and numerous sluice gates and dams, the modeling of hydrological balance in the regionalized sense is computationally challenging. Lastly, the prediction of streamflows of Mengcheng catchment is of least accuracy with mean NSE of 0.58 and mean CWB of 0.45. The primary reason may be that Mengcheng is located at the boundary of the study area (see Figures 1 and 2) so that the average regionalization equations are less representative, especially for the land surface characteristics across the watershed boundaries. Also, observed flows are severely influenced by sluice gates and dams. From Figure 7(d), the hydrographs at Mengcheng hydrological station are often attenuated as a straight line parallel to time axis, which implies that the outflow of Mengcheng is manipulated by human control to maintain a constant discharge value.
In addition, the equifinality phenomenon (Beven & Freer 2001; Todini 2007; Zhang et al. 2012; Hailegeorgis & Alfredsen 2015), i.e., same model performances with different model parameters, inevitably affects the results of parameter calibration. By analyzing the model parameters, we determine the ranges of calibrated parameters with the most probable values being site-specific so that the uncertainty resulting from equifinality can be reduced. Overall, regression is an effective regionalization approach for predictions of streamflow and other hydrological responses in ungauged regions by transferring the relationships between model parameters and catchment characteristics that are established in gauged basins. Due to limited data availability, the land use and cover change of this study area were not considered in this article, but will be pursued in a future study.
CONCLUSION
This paper presents a regressive model incorporating regionalized watershed information for streamflow predictions in ungauged basins based on a hydrological system approach (i.e., the modified TVGM). This approach converts rainfall to streamflow through physically based mathematical transformations without information of evaporation or soil moisture. Also, the model has parsimonious physical parameters that can be derived from watershed descriptors (such as the underlying surface properties and precipitation characteristics) according to derived regressive equations. The regressive model was applied to predict the streamflow of five ungauged catchments in Huai River Basin with reasonable accuracy, demonstrating its effectiveness for hydrological prediction and water resources management in data-sparse areas.
In a future study, we will incorporate more watershed descriptors such as climatic factors while establishing regressive equations, and test the regressive model robustness in more watersheds with different characteristics. In addition, physical mechanisms should be carefully investigated not only during the selection of correlative factors but also during the determination of linear or nonlinear regression relations. The model can be further improved with more available measurement datasets as well as regional geographic information. In the context of rapid urbanization within major watersheds in China, future model development using regression analysis by incorporation of, for example, anthropogenic factors will be critical in understanding the evolution of catchments' hydrological responses to potential landscape modification scenarios. The numerical predictions of the improved regionalization model will also shed new light onto the modified physics of hydrological cycle under emergent climatic patterns, and provide useful guidelines for sustainable landscape planning in a developing China.
ACKNOWLEDGEMENTS
This study was supported by the National Natural Science Foundation of China (No. 41571028 and No. 51279139). The authors J. Song and Z. H. Wang are also supported by the US National Science Foundation under grant number CBET-1435881.