On the use of remotely sensed data to estimate spatially averaged geophysical variables

This paper examines certain errors that arise when estimating spatially averaged geophysical parameter fields from some satellite and other earth observation measurement systems. Of particular concern is the error that is caused by nonuniform sampling of radiance within the field of view. This effect causes a proportion of the amplitude of surface fluctuations in the parameter to be inherited as uncertainty by the estimated area average. This proportion is small if the correlation length for variations of the surface parameter is either much larger, or much smaller, than the size of the instrument´s resolution element (suitably defined). It may be significant when the two length scales are similar. For Gaussian spatial sampling functions, it is shown that the error is minimized if the area over which the simple average is required is about one and a half to two times the square of the projected full width at half maximum of the Gaussian. The results are used to study the problem of estimating surface fractional cover from linear mixture models, where it is confirmed that significant errors can be encountered if the estimated fractions are carelessly assigned to areas defined by the sampling interval of an imaging system.