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.