In this paper, the well-established multi-layer model originally devised by Waggoner and Reifsnyder (1968) is used. This steady-state model based on an electrical analogue simulates the energy exchange between the vegetation and the atmosphere. A purely mathematical development of the basic equations of this model yields explicit expressions of the total fluxes of sensible and latent heat at the top of the canopy as a function of the net radiation absorbed in each layer, the soil heat flux, the water vapour pressure deficit at a reference height and the whole set of elementary conductances (stomatal, boundarylayer and aerodynamic). These new equations can be considered as a generalization of the familiar Penman's formulae to a multi-layer model. C 5 D, 4 e, e,(T) ga gb 8s ge, ge, Jo K LA1 Rn S j-0 TL 1; 6Zi 6LAI; 6C; 62E, bRn, rZE P List of Symbols Sensible heat flux density in vertical direction (W m -a); specific heat of air at constant pressure (J kg-i K-i); saturation deficit of air (Pa); defined by Equation (19) (s m-'); air water vapour pressure (Pa); saturated vapour pressure at temperature T (Pa); aerodynamic conductance in vertical direction (m s -'); boundary-layer conductance of leaves (m s -'); stomata1 conductance (m s-'); equivalent conductance for horizontal heat transfer (m s ') equivalent conductance for horizontal vapour transfer (m s-') defined by Equation (35) (W m-'); eddy diffusivity for heat and vapour (mZ s -'); leaf area index (m* m -2); net radiation flux density (W mm'); soil heat flux density (W mm*); air temperature (' C); leaf temperature ("C); psychrometric constant (66 Pa K-'); slope of the saturated vapour pressure curve (Pa K-'); thickness of layer i (m); leaf area index of layer i (m' m -*); sensible heat Rux density emanating from layer i (W m -*); latent heat flux density emanating from layer i (W me2); net radiation flux density absorbed in layer i (W m -*); latent heat flux density in vertical direction (W m-'); air density (kg m-3);