Urban Hydrology is a scientific and technical discipline devoted to the study of relationships between urbanization and the natural water cycle. It leads:
- to scientific studies related to the effects of urbanization on weather and storms, on atmospheric exchanges, on environmetal and sanitary impacts, etc…
- to technical studies in order to control urban runoff drainage, flooding risk, impacts on receiving waters bodies, etc…
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))
Two main questions when applying the rational formula:
- how can t c be estimated?
- what is i m ?
For t c : in anglosaxon countries: formulae based on flow velocity in sewers; in France: formulae based on sewers structure analysis (Caquot, 1941; Desbordes, 1974, 1984)
For i m : very few raingauge networks. General formula:
i m = α i max with α = A - ε and i max the maximum rainfall over A. Later ε = f(t c , T) with T return period of the design storm.
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)
Dynamic sampling of rain fields, rainfall intensities estimates through calibrations using rain gauges networks. Aims in Urban Hydology:
- testing of distributed rainfall-runoff models performances, of non linearity of these models, of the adequacy of design linear models (such as linear
« reservoir » model (Desbordes, 1974))
- looking for real time control of sewerage systems (Frerot, 1987) in order to prevent environmental impacts or local floodings (CSO, runoff storage, etc…)
- 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.
- a 10 to 20 % uncertainty on radar measurement implies a 25 to 50 % uncertainty on flow estimates (Bristol University, SHE/MIKE 11 model, fully « physically » based and distributed)
- lowering the spatial resolution from 5 to 1 km introduces a stroboscopic effect under strong winds
Research needs for Urban Hydrology (according to Inter Agency Committee on Hydrological Uses of Weather Radar, UK, 2010; more than 600 referenced publications covering the past 30 years)
http://www.iac.rl.ac.uk/
- is a 5’ resolution time sufficient or should it be lowered to 2,5’ for urban hydrology?
- should the spatial resolution be lowered from 1 km to 500 m?
- can historical heavy rainfall data given by radars be used to study the behaviour of storm drainage systems of major cities?
- can radar data related to extreme rainfall events, which have lead to severe damages in areas with very few or no rain gauges, be used for post crisis analysis or evidence of damages origin?
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