What is the water balance equation for a drainage basin?

• A. P = ET + Q + ΔS
• B. ET = P + Q + ΔS
• C. Q = P + ET + ΔS
• D. ΔS = P + ET + Q

Answer: (D)

In a drainage basin, water balance ties together what comes in, what leaves, and what storage changes over a period. The precipitation that falls into the basin is the input, while evapotranspiration and discharge (streamflow leaving the basin) are the outputs. Any net change in stored water inside the basin is the storage term, ΔS. The usual mass-balance form is P = ET + Q + ΔS, showing that inputs equal the sum of outputs and any change in storage. If you solve for storage change, you get ΔS = P − ET − Q, which is positive when precipitation exceeds the combined losses to ET and discharge, and negative when it does not. The expression ΔS = P + ET + Q would require a nonstandard sign convention for ΔS and isn’t the typical way we represent basin water balance.