Apparent breakdown of reciprocity in reflected solar radiances

Observations of reflected solar radiation measurements from natural surfaces (e.g., clouds and forested biomes) are often noted as disobeying the principle of reciprocity. In these contexts the application of reciprocity has been in its directional form. We note that the general principle of reciprocity also encompasses spatial attributes and reduces to a directional form only when the areas of illumination and measurement are the same. In either form a proper reciprocal set of reflected solar radiation measurements can never be obtained due to our inability to control the area illuminated by the Sun. This may appear as a breakdown in the directional reciprocity of the observations, which has serious implications for remote sensing. Using Monte Carlo radiative transfer simulations, we demonstrate that the magnitude of the apparent reciprocity breakdown depends on three factors: (1) measurement resolution, with larger deviations occurring for higher resolutions; (2) Sun-view geometry, with larger deviations occurring for larger Sun/view zenith angles and differences between Sun and view angles; and (3) the distribution of scatterers within and surrounding the measurement area, making the deviations depend on scene type.