Specific Runoff (Flow per Unit of Catchment Area)

Specific runoff is a definition, not a fitted relation: the flow $Q$ at a gauge divided by the area $A$ of the catchment above it. Dividing by area makes rivers of different sizes comparable, which the raw flow cannot do, because a big river always carries more than a small one. Karlsen and colleagues (2016) define specific discharge as runoff per unit catchment area, and their paper questions the assumption that neighbouring catchments shed the same amount.

The units deserve a moment. A flow per area is a volume per time per area, so $q$ is a depth per time: metres of water per second in SI. For a river it is usually quoted in millimetres per day, which means multiplying by 86 400 seconds in a day and by 1000 millimetres in a metre. Another way to say the same thing is litres per second per square kilometre, where 1 L/s/km² is 0.001 m³/s from 1 km², or 0.0864 mm per day.

Take 10 m³/s from a catchment of 100 km². That is $10 / (1\times10^{8}\ \text{m}^2) = 1\times10^{-7}$ m/s, and $1\times10^{-7} \times 86\,400 \times 1000 = 8.64$ mm/day. The formula runs the other ways too. A catchment of 174.2 km² shedding 5 mm/day carries 10.081 m³/s, and 2.5 m³/s at 12 mm/day drains 18 km².

The area is the drainage area to the gauge, the land that drains past it. The result is an average over that whole area, so it says how much water the catchment sheds but nothing about where in it the water came from. Take care when comparing catchments: it is often assumed that neighbouring catchments with similar land cover shed the same, but measurements show that the difference between them can be a third or more on a given day. The rational method and SCS curve number pages work with the storm side of the same quantities.