Abstract-We present here the analytical solution of a one-dimensional dam-break problem over inclined planes. This solution is used to test a numerical model developed for debris avalanches. We consider a dam with infinite length in one direction where material is released from rest at the initial instant. We solve analytically and numerically the depth-averaged long-wave equations derived in a topography-linked coordinate system. The numerical and analytical solutions provide for a Coulombtype friction law at the base of the flow. The analytical solution is obtained by using the method of characteristics and describes the flow over a constant slope, provided that the angle is higher than the friction angle. The numerical model utilizes a finite-difference method based on a Godunov-type scheme.Comparison between analytical and numerical results illustrates the remarkable stability and precision of the numerical method as well as its ability to deal with strong discontinuities.

[1] The experiment LSO (Lightning and Sprite Observations) is dedicated to the optical study, from the International Space Station, of sprites occurring in the upper atmosphere above thunderstorms. The objectives were to study these phenomena and to validate a new measurement concept for future measurements of sprites from space at the nadir. The first measurements were performed in the frame of the flight of the French Astronaut Claudie Haigneré (mission Andromède) in October 2001. Observations were performed by two microcameras, one in the visible and near-infrared and the other equipped with a moderately wide band filter at 761 nm. This filter includes the most intense N 2 1P emission of the sprites and partly the oxygen absorption A band of the atmosphere. The light emissions from sprites occurring in the middle and upper atmosphere are then differentiated from the emissions from lightning, occurring more deeply in the atmosphere and then more absorbed. This paper presents the first observations of sprites from space at the nadir and statistics about the respective intensities of lightning and sprites emissions as observed with this experiment.

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