4.1 Mechanism of flood wave affecting HE
The dynamic process of q , between the stream and aquifer, was not only affected by variation of the stream water level, but also by the rate of variation. This was due to the fact that groundwater moves rather slowly compared to open water flow. When the stream water level rose or fell to a certain height with different rates, the response time left for groundwater would be different and the corresponding groundwater level at such moment would never be the same, resulting in variations of the surface water-groundwater hydraulic gradient and consequently the q values. Hence, we concluded that q was proportional to the polynomial of water level and its change rate:q \(\ \mathrm{\propto}\mathrm{\ }\)(ω \(\bullet\)h +v ), where ω is the angular frequency of the flood wave. The rate of water level change was less influential on q than that of the water level itself due to the influence weight of water level (ω= 2pi/T) was generally greater than 1. This was also why many studies (e.g. Chen & Chen, 2003; Gu et al., 2012; Shuai et al., 2017) have concluded that q is positively correlated with the water level as a whole.
Typical flood wave parameters (A , T , r ,t p) characterized the height, width, roundness and skewness of a wave, respectively. Essentially, an increase inA signifies an increase in water level and its change rate at any time; an increase in T mainly reduces the overall change rate of the water level; an increase in r leads to an increase of change rate near the wave peak and a decrease of change rate near the initial value of the wave; increasing t p has the opposite effect to increasing r . In summary, different parameters reflected the water level and its rate of change with different regularities throughout the duration of the flood wave, thus leading to the very different influences on q . Similarly, under CUFV condition the increase in T /A is equivalent to the simultaneous increase in T and decrease in A . Therefore, the influence mechanism of T /A on q was similar to that of T , but its influence was greater. The effect on qof increasing N was equivalent to shortening the duration of each pulse and increasing the overall change rate of water level accordingly.
The Q max induced by a flood wave was mainly controlled by the wave duration and the average water level height, showing positive correlations with both (e.g. Liu et al., 2018). When the flood wave duration was constant, the higher (A ↗), rounder (r ↘) and less skewed (t p↗) the flood wave,the larger the integral of the flood wave over time, resulting in a larger Q max. RT was generally positively correlated with Q max (e.g. Siergieiev et al., 2015), but this relationship was not valid for the flood wave under CUFV condition. Fig. 7 showed that the change trends of RT andQ max were completely different under CUFV condition. The main reason was that T and A were related variables under CUFV condition. An increase in T would inevitably lead to a decrease in A , and A was dominant toQ max.