Similarity of climate control on base flow and perennial stream density in the Budyko framework

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 (<i>E</i>_P/<i>P</i> called climate aridity index) based on Budyko hypothesis. Perennial stream density (<i>D</i>_P), which is obtained from the high resolution National Hydrography Dataset, for 185 watersheds declines monotonically with climate aridity index, and an inversely proportional function is proposed to model the relationship between <i>D</i>_P and <i>E</i>_P/<i>P</i>. The monotonic trend of perennial stream density reconciles with the Abrahams curve since perennial stream density is only a small portion of the total drainage density. The correlation coefficient between the ratio of base flow to precipitation (<i>Q</i>_b/<i>P</i>), which follows a complementary Budyko type curve and perennial stream density is found to be 0.74. The similarity between <i>Q</i>_b/<i>P</i> and <i>D</i>_P reveals the co-evolution between water balance and perennial stream network.