At the end of 19 th century, in major european and american cities, engineers have tried to estimate the runoff carried to sewer systems. A model has been widely chosen: the « rational formula »:
Q = k . i m (t c ) . C. A
Q being the peak runoff created by an upstream area A, with a « concentration time » t c and a runoff coefficient C, i m being the mean rainfall over A and during t c (Kuilching, Chicago, 1889; Llyod-Davies, London 1906; in France Belgrand for Paris gave 40 l/(s.ha))
Now, considering i m means that the rainfall-runoff relationship is linear . So appears the so called generalized rational formula or « isochrone curves » method which is a linear distributed model (Larrieu, 1954):
Research at the end of the 60’ s has shown that the rational formula was related to the kinematic wave hydrodynamic model (Eagleson, MIT, 1969) which means that the rational formula is not linear and that the spatial distribution of rainfall must be known when applying the formula.
1970: Developement of raingauge networks in urban areas. METROMEX (Métropolitan Meteorological Experiment): 225 rain gauges over Saint-Louis (USA) with Radar measurements in 1980 (Braham, 1981). In France Seine-Saint-Denis Department at the beginning of the 70’s, then Bordeaux, Lyon, Nancy, Marseille, etc…(Blanchet, 1993)
- predict urban runoff flooding risk, improve flooding crisis management, and post crisis analysis (ESPADA concept in Nîmes, Marseille, etc…)
Theoretically the radar reflectivity Z is related to rainfall R by: Z = a R b with a ≈ 200 and b ≈ 1,6.
But, under intense rainfall, attenuation can reach up to 90% so that rainfall intensity estimate is less than 50% that measured by gauges. This implies the radar calibration with another measure of rainfall intensity.
An approach to correct for such an attenuation has been first proposed in 2001 by F. Fabry (McGill univ., Canada): rainfall drops of heavy storms under radar signal must, in turn, emit radiation at same frequency. These microwaves emissions look like an increase in measured « noise » at far range, i.e. behind the storm. As noise levels seem to be relatively stable at each radar site during dry weather, one can think that it may be possible to estimate noise changes during heavy storms and to relate them to attenuation in order to correct the radar data in term of rainfall intensity.