Our objective was to evaluate the ability of different interpolation strategies to produce accurate representations of a known landscape under variable landscape heterogeneity, sampling regime, sample density, and spatial scale. Our simulations showed that, while there was limited influence of the interpolation method on sampling strategy (except in one case: random sampling for Universal Kriging), there was a consistent effect of increased sampling density on goodness-of-fit, as would be expected (Tsutsumi et al. 2007). However, the effect of sampling density was overshadowed by the effect of landscape heterogeneity, which increased accuracy considerably as the landscape became less heterogeneous. Trends in sampling density and heterogeneity indicate there are threshold levels of sampling given the heterogeneity encountered (Figure 3). Additionally, we found similar results for field estimates of NDVI, showing increased accuracy as sampling density was increased (Figure 4). When we manipulated heterogeneity in the NDVI layer by decreasing resolution, we found that decreased heterogeneity caused an increase in accuracy of all interpolation methods.
We demonstrated that there was limited influence of sampling strategy on accuracy estimates across sampling densities and heterogeneities in our simulations (Figure 3). This is surprising given it has been shown in other landscape simulations that random sampling is superior for estimating forage biomass on the landscape (Tsutsumi et al. 2007) and more accurately captures the necessary lag distance within a pine wood stands (Burrows et al. 2002). However, other authors used stratified random sampling which weights spatial sampling to areas of particular interest. Our results confirm the increased consistency and accuracy of gridded sampling when paired with Universal Kriging, which agrees with Burrows et al. (2002) and our simulation results suggest a systematic approach to landscape sampling better captures landscape structure than does a random sampling strategy.
In addition to the limited influence of sampling type on accuracy, we also showed consistent results across interpolation techniques in our simulations, except in the case of Universal Kriging under random sampling (Figure 3). This is again inconsistent with other studies; it has been shown that Inverse Distance Weighting and Universal Kriging can have a greater ability to capture landscape heterogeneity, particularly at lower sampling densities within more heterogenous landscapes, compared to other interpolation methods such as Nearest Neighbor (Coelho et al. 2008). Our use of random sampling with no prior attention given to matching sampling point distance to an expected variogram, inhibited Universal Kriging as we failed to capture the appropriate lag distance. Under these conditions, we would recommend a systematic sampling strategy using Universal Kriging if the sample point distance captured the appropriate lag as demonstrated by the variogram.
Our simulations show that, while there was a positive linear relationship between accuracy and sample density, this effect was relatively small compared to the increases in accuracy when landscape complexity diminished (Figure 3). While it is known that sampling density can increase accuracy (Jordan et al. 2003; Tsutsumi et al. 2000), this relationship is often described as asymptotic, which assumes that ever increasing numbers of samples will continue to push accuracy ever closer to 1:1 match at some diminishing rate. In our case, sampling never achieved an asymptote, which is most likely due to the low sampling densities explored within our simulations given the size of the simulated landscape. However, it is notable that even if our simulated data approached an asymptote, the increased level of accuracy (up to 20%) was inconsequential compared to the effect of landscape complexity (Figure 3). Indeed, a moderate sampling strategy is typically sufficient to accurately measure landscape mean and accuracy in creating interpolated maps of forage quality (Jordan et al. 2003), and simulation exercises within grasslands of varying levels of heterogeneity demonstrated a similar phenomenon (Tsutsumi et al. 2007). Like sample density, we observed a positive quadratic relationship between accuracy and landscape heterogeneity for most sampling strategies and interpolation methods. This is in line with our predictions, given that as the landscapes became more heterogenous, the distance over which self-similarity occurs increases; therefore, decreasing the total variability within the landscape while increasing the number of samples required to detect small or spatially isolated differences. These relationships were further emphasized when we applied the same techniques to real world data where we observed a decrease in the rate of return as heterogeneity diminished (Figure 4). While adequately measuring heterogeneity can be a complex endeavor in both cases, it is worthy of increased attention given its influence on accuracy.
We further demonstrated the relationship between data resolution and landscape heterogeneity. As the resolution decreased, the measured heterogeneity of the NDVI landscape also decreased, which indicates a loss of information (Supplementary Figure 1). Indeed, decreased resolution caused dominant values on the landscape to become more dominant with continued aggregation (Turneret al. 1989), effectively causing a reduction in the total observed plant productivity. This effect is driven by how dispersed the variation is across the landscape (Turner et al. 1989). Clearly, changing the resolution has dramatic impacts on the information available at that scale (Turner et al. 1989), and should be carefully considered with respect to meeting the needs and objectives of the analysis (Reynolds et al. 2016).
Our results indicate that it is critically important to carefully consider landscape heterogeneity and understand how heterogeneity is influenced by landscape-level processes in order to construct a useful sampling design. While we showed that capturing landscape-level heterogeneity can occur irrespective of most sampling regimes and interpolation methods, exploring how sampling density and heterogeneity perform under other sampling regimes may be useful. For example, cyclic sampling may provide yet another way to reduce sampling effort by applying prior knowledge of the landscape autocorrelation structure to the sampling design (Burrows et al., 2002; Turner and Gardner, 2015). Further, it is also expected that relationships between sampling density and heterogeneity may change with different metrics. This was demonstrated in the wide variation of samples required to predict within crop variation in nitrogen, phosphorous, potassium, and sulfur (Jordan et al. 2003). Thus, spatial sampling should be structured to capture the most heterogenous variable of interest to ensure adequate sampling of all variables given their heterogeneity within the landscape. Finally, while we look at the spatial relationships among sampling density, landscape heterogeneity, and accuracy, it is likely that these relationships also change temporally. Indeed, we examined these relationships at the height of the growing season, a time when factors affecting landscape heterogeneity, such as resource restriction and grazing pressure, are likely less influential (Cid and Brizuela 1998). We would expect sampling requirements to vary based on plant phenology and abiotic factors such as rainfall. For example, the sample number required to precisely measure silage production and plant nutrient values varies between cuttings over the summer and by metric of nutrient density (Jordan et al. 2003). As a result, more work on temporal changes in resource distribution is needed to accurately predict the level of heterogeneity to be expected within a given landscape; such an investigation is likely critical to target areas of rapid change.