A new metric for evaluating the correspondence of spatial patterns in vegetation models

Aim  To present a new metric, the 'opposite and identity' (OI) index, for evaluating the correspondence between two sets of simulated time-series dynamics of an ecological variable.
Innovation  The OI index is introduced and its mathematical expression is defined using vectors to denote simulated variations of an ecological variable on the basis of the vector addition rule. The value of the OI index varies from 0 to 1 with a value 0 (or 1) indicating that compared simulations are opposite (or identical). An OI index with a value near 0.5 suggests that the difference in the amplitudes of variations between compared simulations is large. The OI index can be calculated in a grid cell, for a given biome and for time-series simulations. The OI indices calculated in each grid cell can be used to map the spatial agreement between compared simulations, allowing researchers to pinpoint the extent of agreement or disagreement between two simulations. The OI indices calculated for time-series simulations allow researchers to identify the time at which one simulation differs from another. A case study demonstrates the application and reliability of the OI index for comparing two simulated time-series dynamics of terrestrial net primary productivity in Asia from 1982 to 2000. In the case study, the OI index performs better than the correlation coefficient at accurately quantifying the agreement between two simulated time-series dynamics of terrestrial net primary productivity in Asia.
Main conclusions  The OI index provides researchers with a useful tool and multiple flexible ways to compare two simulation results or to evaluate simulation results against observed spatiotemporal data. The OI index can, in some cases, quantify the agreement between compared spatiotemporal data more accurately than the correlation coefficient because of its insensitivity to influential data and outliers and the autocorrelation of simulated spatiotemporal data.