Streams are classified into perennial, intermittent, and ephemeral streams based on flow durations. Perennial stream is the basic network, while intermittent or ephemeral stream is the expanded network. Connection between perennial stream and base flow at the mean annual scale exists since one of the hydrologic functions of perennial stream is to deliver runoff even in low flow seasons. The partitioning of precipitation into runoff and evaporation at the mean annual scale, on the first order, is captured by the ratio of potential evaporation to precipitation (Ep/P called climate aridity index) based on the Budyko hypothesis. The primary focus of this thesis is the relationship between base flow and perennial stream density (Dp) in the Budyko framework. In this thesis, perennial stream density is quantified from the high resolution National Hydrography Dataset for 185 watersheds; the climate control (represented by the climate aridity index) on perennial stream density and on base flow is quantified; and the correlation between base flow and perennial stream density is analyzed. Perennial stream density declines monotonically with the climate aridity index, and an inversely proportional function is proposed to model the relationship between Dp and Ep/P. This monotonic trend of perennial stream density reconciles with the Abrahams curve, and the perennial stream density is only a small portion of the total drainage density. The dependences of base flow ratio (Qb/P) and the normalized perennial stream density on the climate aridity index follow a similar complementary Budyko-type curve. The correlation coefficient between iv the ratio of base flow to precipitation and perennial stream density is found to be 0.74. The similarity between the base flow and perennial stream density reveals the co-evolution between water balance and perennial stream network.