Abstract
The objective of this study is to investigate spatial structures of error in the assessment of continuous raster data. The use of conventional diagnostics of error often overlooks the possible spatial variation in error because such diagnostics report only average error or deviation between predicted and reference values. In this respect, this work uses a moving window (kernel) approach to generate geographically weighted (GW) versions of the mean signed deviation, the mean absolute error and the root mean squared error and to quantify their spatial variations. Such approach computes local error diagnostics from data weighted by its distance to the centre of a moving kernel and allows to map spatial surfaces of each type of error. In addition, a GW correlation analysis between predicted and reference values provides an alternative view of local error. These diagnostics are applied to two earth observation case studies. The results reveal important spatial structures of error and unusual clusters of error can be identified through Monte Carlo permutation tests. The first case study demonstrates the use of GW diagnostics to fractional impervious surface area datasets generated by four different models for the Jakarta metropolitan area, Indonesia. The GW diagnostics reveal where the models perform differently and similarly, and found areas of under-prediction in the urban core, with larger errors in peri-urban areas. The second case study uses the GW diagnostics to four remotely sensed aboveground biomass datasets for the Yucatan Peninsula, Mexico. The mapping of GW diagnostics provides a means to compare the accuracy of these four continuous raster datasets locally. The discussion considers the relative nature of diagnostics of error, determining moving window size and issues around the interpretation of different error diagnostic measures. Investigating spatial structures of error hidden in conventional diagnostics of error provides informative descriptions of error in continuous raster data.
Highlights
All spatial data are subject to error
The negative msd values indicate that all four models under-predict, where Random Forest (RF) regression provides the closest msd to zero (−2.95) and less errors than the other three models, with the smallest mae (15.51) and rmse (21.34) and the largest r (0.73)
RF probability is the poorest predictor of %ISA as it shows the largest mae and rmse together with the smallest r, of all four models
Summary
All spatial data are subject to error. Sensed (RS) imagery routinely contains sensor-related errors, atmospheric effects, and geometric errors. Environmental datasets that describe landscape features and properties from RS products (e.g. forest aboveground biomass, species distribution, and climate change scenarios) inherently contain prediction errors. Errors can manifest themselves as systematic deviations and/or noise which require careful assessment in order to avoid mis-interpretations of the data, to support reliable conclusions and to make informed decisions (Daly, 2006; Foody, 2002). Error assessments provide a guide to data quality and reliability (Foody, 2002) and can provide earth observation (EO) scientists with an understanding of the sources of error both in RS imagery and products (Liu et al, 2007; Stehman and Czaplewski, 1998).
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