Agreement measures for continuous, ratio-scale data: cJaccard, cPrecision, cRecall and cF-score

Continuous, spatially explicit estimates of environmental attributes are increasingly provided as gridded data. The accuracy of gridded data, including classifications derived from remotely-sensed data, is typically evaluated using measures based on confusion matrices with site-specific class allocations; however, these measures are defined for categorical variables and are therefore not applicable to ratio-scale attribute estimates representing quantities, such as canopy height or population abundance.

We present an approach that extends commonly used agreement measures, i.e. the Jaccard index, Precision, Recall, and F-score, to non-negative, continuous ratio-scale attributes. The extended measures (cJaccard, cPrecision, cRecall, and cF-score) are viable equivalents to their binary counterparts, invariant to data imbalance and suitable for evaluating the agreement of various types of data representing ratio-scale attribute estimates. The cJaccard measure has proven useful for a range of applications in the geospatial domain, illustrating the broader potential of these measures for evaluating large-scale environmental gridded data products and beyond.

The aim of this contribution is to showcase and discuss the practical application of these continuous agreement measures to real-world gridded datasets representing spatial-environmental variables. Through applied examples, we demonstrate how cPrecision and cRecall enable a directional interpretation of disagreement, disentangling commission and omission errors in the total proportion of misallocated magnitudes. We further illustrate how cJaccard provides a bounded, scale-independent measure of agreement that complements typically used error-based measures (such as Mean Absolute Error or Root Mean Square Error) in the data comparison process.