Scaling categorical spatial data for earth systems models

Abstract

Efforts to deduce the appropriate scales of ecosystem functions and how patterns change with scale have a long history in ecology and landscape ecology (Levin, 1992; O'Neill et al., 1996). Ecosystem function models are critical to predicting ecosystem responses to global change, but are limited by the technical challenges of model–data synthesis. Accurately relating phenomena across multiple scales is an important challenge in ecological modeling, as information is lost when converting between scales of analysis. Researchers must determine how much information is necessary to preserve the landscape signature of the ecological processes under study. Zhao & Liu (2014) sought to determine the appropriate spatial resolution for categorical land cover data to use in regional-scale models of carbon dynamics, and compared the use of two common categorical data resampling methods: majority (MR) and nearest neighbor (NNR). Their analysis of the NNR method showed a power-law relationship between study extent and grain, but results from MR method showed a different relationship, suggesting that the resampling method drove the results. Zhao & Liu (2014) concluded the NNR method to be superior and reported the MR approach produced ‘devastatingly deficient’ results. We discuss the lack of robustness of their power-law relationship by analyzing the configuration and composition of simulated landscapes subjected to different resampling methods. The authors stated that NNR is clearly preferential to the MR method because NNR preserves uncommon land cover types. They support their use of NNR by mis-citing Cain et al. (1997). Zhao & Liu (2014) state that the critical spatial resolution in scaling exercises follows a power-law function of the study region extent. We argue that the pattern of the landscape process to be modeled determines the results of the resampling method. We illustrate, using a simple simulated landscape, how the effect of resampling algorithm is related to the proportion of landscape within each land cover class and the spatial configuration (clumpiness) of the class. If land covers are spatially random, the NNR resampling preserves the proportions of the original landscape while MR significantly increases the dominant class (Fig. 1a). However, when land covers are spatially aggregated, as occurs in real landscapes, this dominance effect of MR is muted significantly (Fig. 1b). As the factor of aggregation increases, the effects of MR will be the dominance of one class (Fig. 2). Zhao & Liu (2014) found that error increases at grain sizes over 2 km. This result is not related to the extent, as the authors conclude, but to the operational scale (proportions and clumpiness) of the important phenomenon (forest harvests in the Southeast) that influence their carbon dynamics model (Schmit et al., 2006). Zhao & Liu (2014) provided a review of ecosystems, yet they omit classic works from landscape ecology (e.g. Levin, 1992; O'Neill et al., 1996) and carbon cycling (Harmon, 2001). For example, Levin (1992) contends that we should understand the loss of information between scales to preserve key ecological processes. Subpixel heterogeneity of land covers increases with grain size, thus other model parameters, such as LAI and ET, should be adjusted accordingly, which was not discussed in Zhao & Liu (2014). Researchers using scaled categorical data in ecological models should explicitly state how they resample other model parameters related to the scaled dataset. Zhao & Liu (2014) do not discuss the largely unstable and extreme effect of NNR spatial aggregation on their underlying carbon dynamics model outputs (Zhao & Liu, 2014; fig. 5a and c). Ignoring potential limitations in the contextualization of scaling for the modeling of ecosystem dynamics can undermine the accurate and objective interpretation of research findings. We recommend that caution be used when applying Zhao and Liu's power-law relationship. The choice of scaling method should depend upon each specific research question, as well as the spatial configuration and composition of the landscape. If preserving the relative proportions of rare land covers is the only important aspect for ecosystem model inputs, then NNR may be an appropriate approach (He et al., 2002). Researchers should first identify the configuration of the dominant and rare landscape attributes that are important to the process under study. One might also consider other methods for scaling biophysical data, for example, concurrent spatial-temporal scaling, which links landscape heterogeneity to ecosystem process (Southworth et al., 2006), and hierarchical, multiscale variance analysis (Wu et al., 2000). A number of researchers have also recognized the superiority of proportional datasets over categorical data to describe land cover at broader scales (e.g. Bouzidi et al., 2000).