Recipes for spatial statistics with global datasets: A martian case study

The Mars Odyssey Gamma Ray Spectrometer has yielded planetary data of global extent. Such remote-sensing missions usually assign the value of a continuous-valued geospatial attribute to a uniform latitude-longitude grid of bins. Typical attributes include elemental-mass fraction, areal fraction of a mineral type, areal fraction of rocks, thermal inertia, etc. The fineness of the grid is chosen according to the spatial resolution of the orbiter and concomitant data processing. We describe methods to maximize the information extracted from both bin and regional data. Rigorous use of statistical parameters and related methods for inter- and intra- regional comparisons are also discussed. While we discuss results from the Mars Odyssey mission, the techniques we describe are applicable whenever continuous-valued attributes of a planet's surface are characterized with bins and regions. Our goal is to distill the simplest statistical methods for regional comparisons that would be intuitively accessible to planetary scientists.