There are several criteria for building up networks from time series related to different points in geographical space. The most used criterion is the Global-Threshold (GT). Using a weather radar dataset, this paper shows that the Backbone (BB) - a local-threshold criterion - generates networks whose geographical configuration is complementary to the GT networks. We compare the results for two well-known similarities measures: the Pearson Correlation (PC) coefficient and the Mutual Information (MI). The extracted backbone network (miBB), whose number of links is the same as the global MI (miGT), has the lowest average shortest path and presents a small-world effect. Regarding the global PC (pcGT) and its corresponding BB network (pcBB), there is a significant linear relationship: $R2=0.77$ with a slope of $1.15$ (p-value $<E-7$) for the pcGT network, and $R2=0.68$ with a slope of $0.76$ (p-value $<E-7$) for the pcBB network. In relation to the MI ones, only the miGT present a high $R2$ ($0.79$, with slope = $1.95$), whereas the miBB has an $R2$ of only $0.20$ ($\text{slope} =0.24$). On the one hand, the GT networks present a sizeable connected component in the central area, close to the main rivers. On the other hand, the BB networks present a few meaningful connected components surrounding the watershed and dominating cells close to the outlet, with significant statistical differences in the altimetry distribution.