Stochastic Models for Remote Sensing Coverage Analysis Limited by Geophysical Conditions

Earth Science Decadal Survey (2018) directives call for spaceborne remote sensing architectures capable of collecting measurements on targeted observables for multiple science objectives, either by traditionally monolithic design, or by a distributed spacecraft missions (DSM). Beyond trades in instrument modality, launch availability, and orbital element selection, simulated spatial and temporal coverage of Earth's surface is a first-step to quantify figures-of-merit (FOMs) to determine mission architecture effectiveness. Typically, FOMs are limited to coverage geometry. However, geophysical conditions, such as cloud cover, can partially obscure observations, creating a probability for successful measurement collection at a given geographical location on Earth. In this study, we apply frequentist probability models assuming independent and uniformly distributed observations per geographical grid cell (GC), to quantify the stochastic number of observations <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex>, percent coverage <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P$</tex>, and revisit interval statistics <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R$</tex> (minimum, maximum, and mean), for both wide- and small-swath sensor coverage simulation. We leverage the same probabilistic framework to estimate small swath coverage (SSC, < 10 km swath), such as lidar or highresolution stereophotogrammetry. The coverage statistics for these technologies cannot be otherwise quantified in a grid-point (GP) based framework due to quadratic runtime complexity in GP sampling, required to sufficiently quantify the swath signal. In SSC, we estimate the area of the GC covered by the swath for every overpass, and couple the area with geophysical quality, producing a probabilistic spatial coverage per GC. The assumptions are that the swath is ~ 20x smaller than the GC size, and the swath and ground track motion are constant per GC access period. We show through rigorous monte-carlo (MC) validation that the proposed models match the limiting estimates of MC. SSC is shown to be accurate to <10% relative error in estimating N and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P$</tex>, despite linear runtime complexity. We present examples of the methods applied to the spatial coverage of the Landsat-8 sun-synchronous orbit, with a 185 km and 1 km swath, propagated over 16 days during the summer solstice of 2019, given both solar illumination and cloud cover observability constraints. The examples demonstrate that stochastic models for FOMs and SSC are a promising research focus, to both reduce the spatial dimensionality of the coverage problem, and to rigorously quantify probabilistic measurement capability for remote sensing mission design.