3.3 Regional patterns in spatial variation of FDCs
The estimation parameter α and β of FDCs at 224 hydrological stations were fitted and calculated in the middle and lower reaches of the Yangtze River Basin,then α and β of PDC of these stations in corresponding watersheds were calculated too using the Tyson polygon method. As depicted in Figure 5 , α andβ of different flow duration curves present different regional distribution patterns.
According to gamma distribution estimation parameters, in stochastic process, shape parameter α represents the number of events, while the scale parameter β indicates the occurrence rate of the event, i.e β =,For a fixed time rate, if we expect more time to occur, i.e the larger the α , the longer the waiting time T will be; For a fixed number of events , when the event rate is high, it means that the smaller β , the shorter the waiting time T will be.
From Figure 5 , it can be seen that the value α of FFDCs is basically smaller than that of other duration curves. Among the four duration curves, the value α of SFDC is relatively larger, due to the shorter duration time of fast flow and longer duration time of slow flow. The steeper the slope of the area, the shorter the diffusion time of the duration curve, that is the smaller the value α will be. In contrast, the spatial distribution of the values α of PDCs and FFDCs and those of TFDCs and SFDCs have a similar regional pattern. However, the value α of PDCs is generally greater than FFDCs, and the value α of SFDCs is generally greater than TFDCs. What’s more, the range of value α of PDC and FFDCs is much narrower than that of TFDCs and SFDCs, which is consistent with Cheng’s research. Similarly, among the four duration curves, the value β of FFDCs is relatively smaller, due to the higher occurrence rate of fast flow, considering the shorter duration of fast flow and the longer duration of slow flow.
Overall, the regional patterns of α and β in 224 hydrological stations in the Figure 5 indicate that they are influenced by climate differences, but their differences within the same spatial patterns related to climate zones are also significant. This may indicate that other secondary climate and physiological characteristics may also be the reasons for the differences in FDC shape. Possible factors could include climate seasonality, groundwater contribution, vegetation, slope, and watershed shape. The following analysis aims to determine which of these controls may dominate.