*3.4. Cross Wavelet Spectral Analysis*

Cross wavelet spectra are given in Figure 7. The averaged phase angles are 2.40 rad, 0.40 rad, 2.50 rad, and 1.02 rad for W1, W2, W3, and W4, respectively. That is, the groundwater lags behind precipitation by 139.14 days at W1, 23.27 days at W2, 145.01 days at W3, and 59.22 days at W4, respectively (Table 4).

**Figure 7.** Cross wavelet spectra (left) with global wavelet spectra (right) between rainfall and GWLs at (**a**) W1, (**b**) W2, (**c**) W3, and (**d**) W4. Zones surrounded by black lines have significant wavelet power at the 95% confidence level. White lines denote the cone of influence. The phase angles are indicated by the black arrows.


**Table 4.** Time lags from the cross wavelet spectra between rainfall and GWLs (period of 365 days band).

The temporal lags for the wet years are also calculated. The time lags for the wet years at W1, W3, and W4 have been shortened by 12 days, 13 days, and 10 days, respectively. This further strengthens the conclusion that high rainfall shortens aquifer response time [2,3]. However, the time lags for wet years at W2 have been prolonged by 16 days. This is mainly caused by human pumping activities, which will be further discussed in Section 4.2.

Compared to the results of other studies shown in Table 5, the response times of W1 and W3 are comparable to those of most wells located in the Yellow River Basin [6,23,40,41]. The response time of W2 is close to the minimum value observed in the Yellow River Delta [23]. The response time of W4 is close to the shortest lags of Jinan Baiquan Spring Watershed and the largest ones of Pingtung Plain. There are many factors that can affect the groundwater response time. Here, we only considered the effects of rainfall intensity, pumping activities, and humidity index in the next section.

**Table 5.** Time lags of groundwater to rainfall at different study areas.


#### **4. Discussion**

#### *4.1. Rainfall Intensity*

The time series of response times obtained from the sliding-window cross-correlation method is shown in Figure 7. It can be seen that the fluctuation of groundwater at W2 is almost consistent with that of precipitation: when the rainfall intensity becomes smaller, the GWLs become lower, and vice versa. The fast response leads to a short response time, which is within one month through the year. The same is true for W4 under wet and normal conditions, during which the response time is no more than 1.7 months. However, under dry conditions such as the year of 2014, the response time becomes larger, reaching up to 3 months. Generally speaking, aquifers at W2 and W4 react quickly to local rainfall. In contrast, wells one and three respond slowly to the rainfall with visible time lags as shown in Figure 7a,c. The variation range of the response time is 0~3.7 months for W1 and 0~3.5 months for W3. These values further verified the time lags as shown in Table 4.

#### *4.2. Pumping*

As we have mentioned above, agricultural development in this area relies heavily on groundwater. To ensure the winter wheat production, groundwater has to be extracted from March to June if there is not sufficient rainwater. For W2, we can see a significant decline in the water level from 2008 to 2009 despite the wet year, during which the maximum time lag could reach 45 days. This phenomenon is also observed at W4: the maximum response time over the drought period of 2014–2015 was prolonged to 113 days, which was very close to the response time obtained from the sliding-window cross-correlation method as shown in Figure 8.

**Figure 8.** Time series of rainfall intensity, response time, and 6-month moving average of GWLs at (**a**) W1, (**b**) W2, (**c**) W3, and (**d**) W4. The blue and orange bands indicate the wet and dry years, respectively.

To further explore the effect of pumping on the time lags, we counted the lags in the years of pumping and those in the years of no or little pumping for each well (Table 4). The results show that the temporal lags for the pumping years are 1.3~2.0 times those

during the years without pumping. Pumping can lead to a dropdown of the GWLs, with an increasing unsaturated zone thickness, and thus a longer time is needed for the aquifer to receive the infiltrated rainfall signal. Therefore, the time lags between groundwater and precipitation will be enlarged by groundwater pumping activities.
