Figure 7Cross-correlation of parameters p0 and αof the mixed gamma distribution between PDC and FFDC ((a) and (c)), and between TFDC and SFDC ((b) and (d)).
The values of parametersα p and α of PDC and FFDC have similar spatial patterns, and those of TFDC and SFDC also exhibit similar spatial patterns (Figure 5 and Figure 6 ). As shown inFigure 7 , compared with TFDC and SFDC, the parameterα p of PDC and FFDC is correlated, but the deviation is much greater. The proportion of zero flow days (α p) of FFDCs can be converted from the proportion of PDC on the daily time scale, but it may be a non-linear relationship (Yokoo and Sivapalan, 2011). The parameterα p of FFDC is related to the total days of non-precipitation, that is, the p0 parameter of PDC. However, fast flow only occurs when precipitation meets the initial loss, field capacity of soil, and/or exceeds the infiltration capacity of the surface soil layer. In addition, after fast flow is generated., watershed characteristics such as slope, shape, and water system will have additional effects. Therefore, there is a correlation between PDC and FFDCs’ parameters, but there also exist a certain degree of dispersion, which is a challenge for us to infer the parameters of FFDC based on existing precipitation data. The spatial distribution of the value α of PDC and FFDC and that of TFDC and SFDC have a similar regional pattern (Figure 5 ). It can also be seen fromFigure 7 that there is a strong correlation between PDCs and FFDCs, as well as between TFDC and SFDC. However, the similarity in shape between TFDC and SFDC is more related than that between PDC and FFDC, with the former having the Spearman’s rank correlation coefficient of 0.9351 while the latter having the correlation coefficient of 0.5455. The discrete relationship of parameters α between PDC and FFDC indicates that other factors may also have an impact on the correlation between PDC and FFDC, including terrain effects. The response of fast flow to precipitation is influenced by the terrain characteristics of the watershed, including vegetation coverage, gradient, and soil characteristics. Because little rain will not generate fast flow, the similarity between PDC and FFDCs’ lower tail is weak,FFDC is steeper, and the value α of FFDC is generally lower than that of PDC.
For the similarity between TFDC and SFDC, the parameter α of SFDC is generally greater than that of TFDC, because higher flow is separated and the duration of the slow flow is longer. Therefore, the SFDC is flatter and its α is larger. The shape difference between TFDC and SFDC also appears at the bottom of the duration curves. It can be discovered from Figure 7 (c) and (d) that the linear relationship is good distributed within smaller values, reflecting both similarities decrease as αincrease. The conclusions of spatial pattern research on four duration curves’ parameters may not be directly applied to practical life, but it is conducive to more future work about processes based on physical influencing factors.