Geostatistical characterization of local accuracies in remotely sensed land cover change categorization with complexly configured reference samples

Abstract Accuracy is an integral component in consumption of land cover and change information. Accuracy characterization in change categorization is more complicated than that in single-date classifications, especially when pursued at a local or per-pixel basis. In this paper, reference sample data consisting of reference class labels at sample locations are referred to as (model) training and validation sample data, respectively, when they are used for building and testing predictive models of local accuracy. They are preferably collocated to verify land cover and change types at the same locations across multiple single-date classifications. With collocated training data, methods devised for local accuracy mapping were usually implemented as direct extensions to those designed for accuracy predictions in single-date land cover maps, given that both response and explanatory variables are defined properly based on change maps. However, alternative methods are required when collocated training sample data are unavailable or sparse but non-collocated data collected at sample units not aligned across time exist or can be made available more conveniently and flexibly. This is typically the case for change-classification accuracy analyses, whereby prior sampling design and sample data may not remain informative in time but can be made adaptive by restructuring and augmentation to better represent strata of transitions as well as persistence. Such adaptability leads to great cost-saving in sampling than undertaking collocated sampling anew each time performing or revising accuracy mapping for a specific change analysis over a particular period. With a coherent review of related research, this paper proposes a geostatistical method for predictive mapping of local accuracies in any land-cover change maps created properly through adaptive use of complexly configured training sample data. This method works on a functional relation between accuracies in change-categorization and single-date classifications whereby temporal correlation (cross-correlation) between bi-temporal classification correctness is accommodated. In this cross-correlation-adjusted product method (named PXCOV), quantification of single-date classification accuracies is based on logistic regression. Cross-correlation is estimated via cross-validation cokriging through exploiting a useful relation between traditional and pseudo cross-variograms in the absence of collocated sample data or calculated more easily on the basis of collocated sample data if available. Studies were undertaken to test this method and compare it with direct logistic-regression-kriging (named LogRK direct), its simpler version, direct logistic regression without kriging (named LogR direct), and the baseline product method (named Product, being a simpler option of PXCOV without accounting for cross-correlation), using GlobeLand30 2000 and 2010 land cover at five sites in China. For each site, eleven training samples of equal sizes but differing configurations and one independent validation sample were collected. Logistic regression was performed on map class occurrence pattern indices quantified in size-optimized moving windows for mapping local accuracies in single-date classifications (as necessary intermediate steps in Product and PXCOV) and bi-temporal change-categorization (LogR direct and LogRK direct). In LogRK direct, geostatistical modeling and kriging were based on standardized residuals after logistic regression (based on change maps directly). In PXCOV, cross-correlation between single-date classification correctness was estimated and accounted for properly, with their non-stationarity in change vs. no-change strata of sample pixels accommodated, after estimating aforementioned single-date local accuracies. Statistical testing of relative performances of alternative methods was undertaken based on validation samples for individual study sites. It was confirmed that the proposed method PXCOV is more accurate than LogR direct and LogRK direct when there are relatively few collocated sample pixels (i.e., the typical scenarios justifying use of PXCOV). PXCOV is generally more accurate than Product and should be pursued when enough collocated data are available for estimating cross-correlation, although Product is sometimes adequate for practical purposes. LogR direct is recommended over LogRK direct because collocated sample data are often sparse due to low sampling intensities as in large-area applications. Therefore, as a method complementing LogR direct and similar methods, PXCOV facilitates adaptive use of training sample data of complex configurations for increased accuracy and efficiency in predictive mapping of local change-categorization accuracies.