Using Two Parallel Linear Reservoirs to Express Multiple Relations of Power-Law Recession Curves

Nonlinear and linear reservoirs are popularly used in simulation and characteristic analysis of streamflow recessions after various rainfall events. In this study, the power-law function $-(dQ/dt)=a{Q}^b$ for streamflow ($Q$) recessions over time ($t$) was mathematically expressed by using a two parallel linear reservoirs model as an approximation of fast and slow base flows in the subsurface layers. The two parallel linear reservoirs model displays multiple curves of $-(dQ/dt)=a{Q}^b$ in which the recession slope $b$ and intercept $a$ depend not only on catchment features, e.g., recession timescale parameters of fast and slow base flows, but also on time-varying flow composition and initial streamflow. The two parallel linear reservoirs model is applied in the Lantang Watershed of Southeast China where the subsurface flows come from the soil and underlying weathered bedrock with distinctly different hydraulic characteristics. The model replicates well the individual recessions and the multiple curves of $-(dQ/dt)=a{Q}^b$ in the log-log space. The results indicate that the single-valued relations of $-(dQ/dt)=a{Q}^b$ and storage-discharge with constant values of $a$ and $b$ are a specified approximation of the multiple curves of $-(dQ/dt)=a{Q}^b$ with variables $a$ and $b$, and the two parallel linear reservoir model is flexible to capture the complex recession characteristics in the heterogeneous watershed.