Hilbert curves isometrically filling a spherical shell, and their application to the estimation of spatial data density
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Hilbert curves isometrically filling a spherical shell, and their application to the estimation of spatial data density

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    We review ways of constucting space-filling Hilbert curves that isometrically occupy rectangular or spherical regions in either two or three dimensions, together with a proposal for using the projection and sorting of observational data locations on such curves to facilitate the rough but efficient estimation of the spatial density of these data. For data whose spatial distributions tend to exhibit sporadic clumping, these density estimates can be used to trigger the progressive down-weighting within the assimilation of those data whose perceived density has exceeded a threshold related to the effective resolution of the assimilation. In this way, we are able to partially and approximately account for some of the effects that strongly correlated representativeness errors in the data at short distances should have on the proper assignment of measurement weights where the data are excessively crowded, as occurs, for example, in aircraft reports near busy terminal hubs. The advantage of using space-filling curves, as opposed to direct spatial estimation of data density on a regular fine grid, is that we can avoid the wasted computations that the latter method would entail in large expanses of the domain where the data are too sparse to be of concern. Since our proposed method is, in effect, essentially a stochastic one, a superior estimate of the density, with improved isotropy of the implied spatial averaging of neighboring data, can be obtained by averages of repeated trials in which the particular orientations of the frameworks used to construct the space-filling curves are randomized. Strategies for systematic randomization are suggested
  • Content Notes:
    R. James Purser

    "May 11, 2018."

    "This is an unreviewed manuscript, primarily intended for informal exchange of information among the NCEP staff members."

    Includes bibliographical references (page 23)

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