Atmospheric Correction Bias in Multispectral Aerial Sensing of Smallholder Soil Variability: A Geographically Weighted Regression Assessment of Carbon-Stock Estimation Error for Precision Agriculture Planning

Low-altitude multispectral surveys promise field-level soil information for Nigerian smallholdings, yet variable haze, dust and viewing geometry leave spatially structured atmospheric correction bias in surface reflectance that propagates into soil organic carbon calculations and distorts precision agriculture plans. This methodological article develops a bias-aware framework that couples radiative-transfer reasoning with geographically weighted regression and a geographic information systems derived composite spatial index built from Slope, Drainage density, Rainfall intensity, Land cover, Soil permeability, Elevation and Distance to channels. Figure 1 delineates the administrative units that bound the spatial domain, Figure 2 characterises settlement network connectivity that conditions field fragmentation, and Figure 3 organises the criterion weights that govern the composite spatial index. The framework proposes formal conditions under which local correction bias induces nonstationary carbon-stock distortion, derives bandwidth-dependent error bounds, and specifies a reproducible workflow for mapping where correction uncertainty most threatens agronomic decisions. The contribution is a transferable specification for diagnosing and containing correction-induced distortion before carbon maps inform input allocation, conservation targeting and credit baselines.