Select the correct water balance identity that defines total runoff from a basin in terms of its component contributions.

Introduction / Context:
Total streamflow at a catchment outlet comprises quick components and delayed components. Correctly expressing this identity helps in hydrograph separation and modeling.

Given Data / Assumptions:

• Surface runoff (direct runoff) and groundwater flow (baseflow) are additive components of streamflow.
• Units are consistent so volumetric or rate addition is meaningful.

Concept / Approach:
At any instant or over an event period, total runoff equals the sum of direct runoff and baseflow. Additional minor components like interflow are often grouped with one of these terms depending on the method.

Step-by-Step Solution:
Define total runoff Q_total.Let Q_surface denote the overland and quick channel contributions.Let Q_base denote delayed contributions from groundwater discharge.Identity: Q_total = Q_surface + Q_base.

Verification / Alternative check:
Hydrograph separation techniques decompose observed discharge into baseflow and direct runoff, whose sum reconstructs the measured hydrograph.

Why Other Options Are Wrong:

• Subtraction, division, or multiplication do not represent mass-conserving combination of independent flow contributions.

Common Pitfalls:

• Double counting interflow or misclassifying contributions; ensure consistent component definitions.

Final Answer:
Runoff = Surface runoff + Groundwater flow