The main idea of a parametric approach is to represent FDCs with analytical relationships. Thus, the procedure evolves to obtain the parameters of these analytical relations. The parameters are usually related to the physical, hydrological, and/or meteorological characteristics of the relevant stream basin. Parametric approaches have widely been used in various forms (simple linear regression, multi linear regression, exponential regression, and logarithmic regression) for basins in various parts of the world, and scientists have dealt with the problem of estimating FDCs at ungauged or partially gauged basins using regression methods for a long time (e.g., Quimpo et al. 1983; Mimikou and Kaemaki 1985; Fennessey and Vogel 1990; Franchini and Suppo 1996; Singh et al. 2001; Yu et al. 2002; Castellarin et al. 2004; Mohamoud 2008; Viola et al 2011; Müller et al. 2014; Pugliese et al. 2016; Ridolfi et al. 2018).
Quimpo et al. (1983) conducted a regionalization study to estimate water availability at small hydroelectric plants in the Philippines. They first parameterized the flow–duration characteristics and mapped the geographical variation of one of the parameters to cover the entire archipelago. They then defined another parameter related to the basin area.
Mimikou and Kaemaki (1985) parameterized the monthly flow–duration characteristics of flow measurement stations in the western and northwestern regions of Greece. Then, using multiple regression methods, they obtained the parameters of the flow–duration model depending on characteristics such as geographical variability, average annual precipitation, and basin drainage area.
Fenensey and Vogel (1990) stated that the aim is to develop regression models that relate the parameters of the daily FDC at a site to basin characteristics. To obtain such regression models, they aimed to define the FDC with as few parameters as possible. They argued that a complex trade-off between the number of parameters needed to define FDCs and the ability to develop regional regression models that uses parameters related to the basin characteristics exists. Fennessey and Vogel modeled the lower portion of the FDC (only the portion of the probability of exceedance within P = 0.50–0.99 range) in their study.
Franchini and Suppo (1996) proposed a methodology that addresses the regional analysis of the lower part of the FDC that refers to low flows. This methodology requires deriving an equation characterized by a set of parameters that define the lower part of the FDC and defining the statistical model that allows the parameters of the chosen equation to be estimated correctly. Unlike other parametric approaches, Franchini and Suppo regionalized streamflow quantiles (Q30, Q70, Q90, and Q95) instead of parameters. They considered Molise Region (Italy) in applying the methodology to a real-world case.
Singh et al. (2001) developed models for the 1,200 unmeasured basins of the Lower Himalayan region of India. The formulation of the models is based on empirical regional relationship and data transfer between measured basins of the same region. They used a simple power relationship for the average flow estimation.
Yu et al. (2002) applied the parametric method (polynomial) and the area-index method to produce FDCs, and estimate their uncertainties at ungauged sites for the upper reaches of the Cho-Shuei Stream in Taiwan. They used annual precipitation, altitude, and drainage area in the parametric method to explain regional variation.
Castellarin et al. (2004) conducted a regionalization study based on statistical, parametric, and graphical approaches for a large region of East Central Italy to regionalize the lower portion of FDCs (the region of FDC for probability of exceedance P = 0.3–0.99). They showed that all three approaches were equally successful.
Mohamoud (2008) presented a method for estimating FDCs for ungauged basins in the Mid-Atlantic Region, USA. Using a stepwise multiple regression analysis, they identified important geographic and meteorological characteristics in constructing the flow–duration relationship.
Viola et al. (2011) developed a regional model to predict FDCs in ungauged basins in Sicily, Italy. They analyzed a large flow dataset and derived the parameters of FDCs for nearly 50 basins. They developed regional regression equations to construct FDCs.
Müller et al. (2014) derived a process-based analytical expression for FDCs in seasonally dry climates. They applied their FDC model to 38 basins of Nepal, California coast of USA, and Western Australia, and showed that FDCs were successfully demonstrated using five significant parameters.
Pugliese et al. (2016) compared two methods, one based on geostatistics and the other based on regional multiple linear regression, to estimate FDC in ungauged basins. They compared these two methods in 182 unregulated basins in Southeastern USA. Their findings revealed that the geostatistical and linear regression models performed similarly.
Ridolfi et al. (2018) proposed a new methodology for estimating FDCs and applied this methodology to sub-basins located in two different basins from different parts of the world. Ten basins are situated in the upper Neckar River basin of Germany, whereas 10 are located in Eastern USA. They indicated that FDC is characterized by the basin and the weather.
In the study of Castellarin et al. (2004), one of the most comprehensive of the studies summarized above, three different parametric approaches were applied (Quimpo et al. 1993; Mimikou and Kaemaki 1985; Franchini and Suppo 1996). They noted that all analytical expressions with two or more parameters successfully reproduced FDCs. By contrast, the validation stage showed controversial results. Especially in analytical expressions where the physical meaning of the parameters is uncertain, not all parameters could be defined through multiple regression analyses. However, Franchini and Suppo’s (1996) parametric approach, unlike other parametric approaches, regionalizes flow quantiles (Q30, Q70, Q90, and Q95) instead of parameters, and probably because of this feature, it outperformed all other parametric approaches in the validation phase. Considering this, our paper intends to establish a relationship between the streamflow quantiles (Q30, Q40, ...,Q99) and the hydrological, geographical, and meteorological characteristics of the basins.