Spatial and Temporal Network Sampling Effects on the Correlation and Variance Structures of Rain Observations

Network observations are affected by the length of the temporal interval over which measurements are combined as well as by the size of the network. When the observation interval is small, only network size matters. Networks then act as high-pass filters that distort both the spatial correlation function ρr and, consequently, the variance spectrum. For an exponentially decreasing ρr, a method is presented for returning the observed spatial correlation to its original, intrinsic value. This can be accomplished for other forms of ρr. When the observation interval becomes large, however, advection enhances the contributions from longer wavelengths, leading to a distortion of ρr and the associated variance spectrum. However, there is no known way to correct for this effect, which means that the observation interval should be kept as small as possible in order to measure the spatial correlation correctly. Finally, it is shown that, in contrast to network measurements, remote sensing instruments act as low-pass filters, thus complicating comparisons between the two sets of observations. It is shown that when the network-observed spatial correlation function can be corrected to become a good estimate of the intrinsic spatial correlation function, the Fourier transform of this function (variance spectrum) can then be spatially low-pass filtered in a manner appropriate for the remote sensor. If desired, this filtered field can then be Fourier transformed to yield the spatial correlation function relevant to the remote sensor. The network and simulations of the remote sensor observations can then be compared to better understand the physics of differences between the two set of observations.