# formula to convert precipitation in mm/h to runoff in m³/s

I have precipitation data in mm/h but to use them for my model I need them in m³/s. Is there a formula to convert them?

When we say there was 1 mm (or 0.001 m) of rain, it is assumed that it is on a 1 square meter area, so it is equivalent to a volume of water of 0.001 $$\small\mathsf{m^3}$$ (or one liter). So first you have to divide your data by 1000.

Then you have time, which is easy: there are 3600 seconds in one hour. So to convert L/h in m$$\small\mathsf{^3}$$/s, you have to divide your data by 3,600,000: 1 L/h = 2.7778 x 10$$\small\mathsf{^{-7}}$$ m$$\small\mathsf{^3}$$/s.

You can ask this sort of things in WolframAlpha; the trick here is to "convert" mm/h, assumed by the engine to be a speed, in L/h, the volume flow rate hidden by the mm/h unit.

There is no such simple relationship between rainfall and runoff (I wish there was!). How much of the rainfall ends up as runoff depends upon at least the following variables:

temperature, humidity, wind-run, hours per day of bright sunshine, latitude, altitude, type and density of vegetation cover, soil type, thickness and consistency, antecedent conditions, soil moisture content, land slope and orientation with respect to the sun, underlying geology (lithology, structure, connectivity with surface soils, degree of weathering), degree of urbanization, heat island effect, human intervention, seasonality.

That is why all catchment models used to estimate the overall rainfall-runoff have to be carefully calibrated using rainfall AND runoff time-series of data. You can't do it by remote sensing. For all the fancy gimmicks and new equipment there is no substitute for boots on the ground.

Golden Rule Nr 1: you can't manage what you don't understand

GRNr2: You can't understand it unless you measure it.

GRNr3: You can't measure it by sitting in an office.

You cannot make the conversion. mm/hr describes the amount of precipitation that falls over an area but is independent of the area over which the precipitation falls. Getting 1 mm/hour implies a light shower, whereas 20mm/hour a heavy rain. If you describe the precipitation as m3/s you don't really know the rate at which the precipitation is falling without also knowing the area over which it is measured. For example, if you have 1 m3/hr what does that really mean? it could mean a light dusting of snow if you are talking about 100 hectares of land, or a torrential downpour if your area was 10 meters squared of land. Typically m3/s is used to measure flow rates for a river, creek, or channel. You can use rate of precipitation mm/hr in conjunction with an area to determine the total volume of precipitation but overall the two rates are measuring somewhat different things.

Overall without an area you cannot convert mm/h to a volume uses in m3/s.