Using orthogonal functions, a harmonic analysis of sky radiance is developed, and energy transfer functions are defined to predict the contribution of each harmonic towards the irradiance within a greenhouse. Using Fourier series for azimuth, and odd power Legendre functions, P1P3, P5… for elevation, outside irradiance is shown to depend only on the zero order Fourier (azimuthally symmetric) and first order Legendre function (P1), but internal greenhouse irradiance depends on all the harmonics because of perturbations introduced by the transparent surfaces. However, contributions towards average irradiance from above the third harmonic in elevation are shown to be small, and correlations are developed between greenhouse transmissivity and the ratio of the second to first Legendre amplitudes in the sky radiance. Symmetric and asymmetric multispan houses are shown to have similar transfer functions under azimuthally symmetric radiance, markedly different to those for single spans. The asymmetric roofed multispan is also shown to produce non-zero transfer functions arising from the first azimuthal radiance harmonics, which are of the same order as those arising from the zero order (symmetric) Fourier harmonic The energy transfer functions arc themselves analysed by straightforward Fourier analysis in terms of greenhouse north roof angle of elevation, to provide a matrix representation of energy transfer, depending only on roof symmetry and number of spans. These matrices may be used in more general greenhouse optimization programs.