Assessing the Susceptibility of Sensors to Local Property Variability.

We consider the general problem of spatial averaging by sensors. Specifically, we consider the dependence of an instrument response on the local calibration relationship, the spatially variable sensitivity of the instrument, and the spatially heterogeneous distribution of the property of interest. Our objective is to show that the effects of each of these relationships can be calculated for simple checkerboard patterns. Further, that the response of an instrument to more complex spatial distributions can be understood by combining the responses to multiple checkerboards through the use of two-dimensional Fourier transforms. This will allow for quantification of the sensitivity of sensors to sub-sample-volume variability, which can be used to predict the uncertainty of indirect measurements as a function of the spatial scale of variability of the property of interest. We show this for several instruments with differing spatial sensitivity distributions with simple but realistic Fourier transforms.