*3.1. Monthly Data*

The fitting interpolation distribution maps for July 2008 and May 2013 are shown in Figures 4 and 5, respectively.

**Figure 4.** The fitting interpolation distribution map for geographically weighted regression (GWR), GTWR(M), GTWR(D), GTWR(E), and GTWR(C) corresponding to July 2008.

**Figure 5.** The interpolation distribution maps for GWR, GTWR(M), GTWR(D), GTWR(E), and GTWR(C) corresponding to May 2013.

The average error maps of MAE, MRE, and RMSE for monthly scale data are shown in Figure 6.

**Figure 6.** *Cont.*

(**c**) RMSE distribution chart of monthly scale data

**Figure 6.** The average error maps for monthly scale data from 2006 through 2014. (**a**–**c**) represent the average distribution chart of mean average error (MAE), mean root error (MRE), and root mean square error (RMSE), respectively.

It can be seen in Figure 6 and Table 2 that the optimal timescale of the GTWR model is daily for the monthly scale data. The MAE, MRE, and RMSE decrease by 36%, 56%, and 35%, respectively, when choosing GTWR(D) instead of GTWR(M). The GTWR(E) improves the accuracy of the results compared to GTWR(D), by reducing the MAE, MRE, and RMSE by 0.7%, 1.1%, and 0.6%, respectively. The fitting accuracy of GTWR(E) and GWR are similar, with a difference of about 3% for the monthly scale data results shown in Table 2. The GTWR(C) has a lower accuracy compared with GWR, and increased MAE, MRE, and RMSE by 25%, 45%, and 24%. The GTWRK has the highest accuracy compared with GWR, and decreased MAE, MRE, and RMSE by 3%, 10%, and 1%, respectively.

Figure 7 shows the MAE, MRE, and RMSE of monthly GWR and GTWRK models in different seasons. According to the character, the fitting accuracy of the GTWRK model is higher than that of the GWR model as a whole, especially in spring, autumn, and winter.


**Table 2.** The average MAE, MRE, and RMSE for the monthly scale data.

(**d**) Comparison of evaluation indicators of GWR and GTWRK models in winter

**Figure 7.** Applicability of GWR and GTWRK models in different seasons. (**a**–**d**) represent the distribution chart of MAE (Units: mm), MRE, and RMSE (Units: mm) in the four seasons, respectively.

#### *3.2. Annual Data*

The interpolation distribution maps corresponding to 2010 and 2012 are shown in Figures 8 and 9, respectively.

**Figure 8.** The interpolation distribution maps for GWR, GTWR(Y), GTWR(M), GTWR(D), and GTWR(E) corresponding to 2010.

**Figure 9.** The interpolation distribution maps for GWR, GTWR(Y), GTWR(M), GTWR(D), and GTWR(E) corresponding to 2012.

It is seen in Figure 10 and Table 3 that the optimal timescale of the GTWR model is daily for the annual scale data. The MAE, MRE, RMSE decrease by 13%, 15%, and 14%, respectively, when choosing the GTWR(Y) over the GTWR(D). In the results, the accuracy error of GTWR(E) can be reduced by about 0.2%, compared to GTWR(D). When the GTWRK is compared to the GWR model, MAE, MRE, and RMSE decrease by 3%, 10%, and 5%, respectively.

**Figure 10.** The average error for annual data.


