Bias of area counted from sub-pixel map: Origin and correction

With the increasingly widespread use of sub-pixel mapping techniques in land cover/use mapping, more accurate area information is often required for a specific land cover type in a particular study region. However, the bias of area counted from sub-pixel maps (called area bias below), and the inadequate understanding of the area bias's origin and influential factors pose a challenge to using this information accurately. Traditional model-assisted estimators combining the map and the reference sample showed unreliable performances in the case of small sample sizes collected in target regions. This work presented a theoretical analysis of the origin of area bias. It then proposed a novel bias-adjusted estimator which can effectively deal with the small sample sizes. The theoretical analysis illustrated that area bias mainly originates from two terms, i.e., the abundance-dependent error and the probability distribution of abundances. We next developed a stratified bias-adjusted area estimator named the two-term method (TTM) by incorporating the sub-pixel map and a reference sample obtained from both target and external regions. We validated the effects of different sub-pixel mapping methods, different spatial resolutions, the varying spatial structures of statistical units on area bias, and the performance of TTM in correcting the biased areas in multiple cases. The results showed that area bias varied from zero to approximately 20% with the variation of three influential factors. TTM effectively corrected the biased area values to nearly the true values, showing approximate equivalence with the traditional stratified regression estimator (STRE) when adequate reference samples are collected sorely inside target regions. However, in cases of small samples from target regions, TTM showed significant superiority over STRE in reducing the variance and MSE due to the incorporation of external reference samples. We conclude that the theoretical analysis resulted in a better understanding of area bias counted from sub-pixel maps and an improved area estimator for dealing with the cases of small sample sizes inside target regions.