A statistical method to calculate the radiance at the top of the atmosphere is described. This method solves the monochromatic radiative transfer equation at selected wavenumbers. A comparison with line-by-line calculations shows that the method is stable and converges to the line-by-line results with increasing number of selected points. The method has the advantage over other statistical methods that it is a strict monochromatic method, such that the exact information at the selected wavenumber is retained. This implies that overlapping absorption bands of different gases can be treated in a simple manner, which is exact at the selected wavenumbers. Since the method retains the correspondence of a monochromatic calculation to wavenumber, a folding of radiance simulations with the exact filter function of a satellite sensor is easily performed. The method is applied to simulate radiances of the future European geostationary meteorological satellites Meteosat Second Generation and to study the possibility of cross calibration of similar satellite sensors aboard different satellites.¿ 1997 American Geophysical Union