1. INTRODUCTION
Flow duration curves (FDC) is a statistical expression of the flow
changes observed during the period of record (long-term flow duration
curves or annual flow duration curves) based on the daily runoff series,
which explains the relationship between the flow size and the
probability of occurrence (Ghotbi et al., 2020; Leong and Yokoo, 2021).
The probability value of a specified flow equal to or exceeding a
certain flow size can be read from FDC, so it is essentially the
cumulative distribution function of daily flow (Yokoo and Sivapalan,
2011). There are two options about the data recording time of FDC: the
total duration method (Cheng et al., 2012) and the multi-year average
method (Cheng et al., 2012; Karst et al., 2019; Liang, 2019). Cheng et
al. used the three-parameter mixed gamma distribution to characterize
the shape of the normalized FDC using the total data record, and
observed the change of FDC year by year in eight representative
catchments. The total duration method more closely represents the
rainfall and runoff of a specific basin, while the fitting curve
calculated by the multi-year average method can fully capture the
changes of FDC between years (Cheng et al., 2012; Costa and Fernandes,
2021; Liang, 2019). FDC can be used to diagnose the rainfall-runoff
response of a watershed to help develop or validate rainfall-runoff
models through the transition from precipitation change to runoff (Wang
et al., 2023). It can be also used to analyze the similarity and
difference between watersheds, establish a model using precipitation and
watershed characteristics as input, and predict the hydrological
elements of ungauged sub-watersheds from a limited number of stations
observed in the past (Burgan and Aksoy, 2022a; Wolff and Duarte, 2021).
In the past, the physical control of FDC involved graphics
(non-parametric method), statistics (parametric method) and
process-based methods (Ghotbi et al., 2020; Ghotbi et al., 2020; Karst
et al., 2019; Müller and Thompson, 2016). The graphic method is based on
exploring the relationship between the shape characteristics of FDC and
the climate and geomorphologic characteristics of the catchment, such as
the steepness or quantile of the curve, to estimate the shape of the FDC
which represents the flow condition of unmeasured catchments (MOHAMOUD,
2008). The statistical method aims to fit the empirical FDC through
appropriate distribution functions (such as gamma distribution,
lognormal distribution, generalized Pareto distribution, kappa
distribution, etc.) (Almeida et al., 2021; Burgan and Aksoy, 2022b;
Cheng et al., 2012; Ghotbi et al., 2020; Yire Shin, 2022), and then find
the quantitative and qualitative relationship between the estimated
parameters of the fitting function and the characteristics of the local
climate and geographical environment of the measured catchment.
Villalobos and Neelin explained why the gamma distribution can well fit
the daily precipitation distribution. The control of climate and
watershed geographical environment characteristics on FDC always tends
to be empirical (Ridolfi et al., 2020). Based on these empirical
properties and the diversity of climate and geographical impact factors
in different watersheds, the main hydrological processes are not
explicitly included. The main hydrological processes are complex and
specific in different watersheds and climatic regions, so the follow-up
research is mostly the process-based method. The essence of the
process-based method is to combine graphic with statistical methods,
take into account the dominant process of time flow change, take
rainfall series as random input, take seasonal and other meteorological
factors as random influence, establish a deterministic model of runoff
involving precipitation, and derive the explicit statistical
distribution form of FDC (Chouaib et al., 2018; Leong and Yokoo, 2021).
Among these three methods, the parametric method shows that the
geographical characteristics of the catchment will affect the shape of
FDC. For example, topographic features, including the area, average
elevation and gradient of the catchment area (Luan et al., 2021; Yang et
al., 2023), have a great impact on the shape of FDC. Stephen Oppong
Kwakye and András confirmed the control effect of rainfall events and
dry conditions on the FDC of most rivers in West Africa (Kwakye and
Bárdossy, 2022). Cheng et al. found that in the control of 197
watersheds in the United States, daily precipitation, probability of
non-rainy days and Aridity index (AI ) has a great impact on the
parameter α estimated by gamma distribution. Although there may
be significant differences in the key control factors of FDCs at
different geographical locations and times, the shape of FDCs represents
the comprehensive impact of rainfall, topography, soil, geology and
other climatic and geomorphologic characteristics.
The main problem of the three methods is that the process of
precipitation input and runoff generation involves different time scales
(Huang et al., 2020). For example, the runoff generation process usually
includes fast land flow and groundwater flow. The fast flow is the
hydrological response to the change of precipitation and the result of
land flow generated by the mechanism of excess infiltration, which is
related to many factors such as rainfall intensity, soil infiltration
capacity and early soil moisture content, etc. While the slow flow is
related to climate seasonality and is controlled by soil permeability
and terrain slope. Therefore, when establishing hydrological models and
performing numerical simulation, the total flow was always divided into
two parts: fast flow and slow flow, so as to have a deeper understanding
of the shape characteristics and process control of FDC. Based on the
work of Yokoo and Sivapalan (2011) and Cheng et al. Ghotbi et al. (2020)
proposed a new stochastic framework to construct total flow, involving
three parts of partition (total, fast and slow flow), fitted their
distributions and then combined them together as an FDC model of total
flow. In this way, the FDC is usually divided into total flow duration
curve (TFDC), fast flow duration curve (FFDC) and slow flow duration
curve (SFDC). However, the fast flow is usually highly intermittent,
while the slow flow is usually more continuous, which poses a challenge
to explain the statistical dependence between slow flow and fast flow.
In addition, in previous work, Ghotbi et al. (2020) did not further
implement it to explore the climate and landscape controls of FDC. At
present, most research about FDC is distributed in many countries such
as the United States, Africa and Italy (Chouaib et al., 2019; Cislaghi
et al., 2020; Kwakye and Bárdossy, 2022; Over T M, 2018; SMAKHTIN et
al., 1997; Ye et al., 2012). Due to China’s vast area, complex terrain,
and many unmeasured catchment areas, it is very meaningful to study the
FDC of unmeasured catchments across China, and provide a good
theoretical and practical basis for its research.
In this paper, based on the continuous daily precipitation data (56yr)
of 698 weather stations in China and streamflow data (30yr) of 244
gauging stations in watersheds in the middle and lower Yangtze River
basin, we carried out the gamma distribution fitting and parameter
estimation of PDC and FDCs, and explored the internal and external
interfering factors of each fitting parameter. Firstly, data sources
were described for the analyses and a brief overview of methodology
adopted were gave. Secondly, the fitting images of PDC and FDCs were
shown and the values of R2 and Nse were
calculated to evaluate the fitting effect. Then the spatial distribution
pattern of fitting parameters which controls the shape of PDC and FDCs
were presented. Finally we analyzed the estimated parameters with their
correlation with regional meteorological physical characteristics, took
the middle and lower Yangtze River basin as an example with base flow
segmentation, and studied the relationship, similarity, regional
patterns and response mechanism of parameters between PDC and FDCs.