Galilean invariance of lattice Boltzmann models

It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this Letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments

How plot shape and spatial arrangement affect plant species richness counts: implications for sampling design and rarefaction analyses

Questions: How does the spatial configuration of sampling units influence recorded plant species richness values at small spatial scales? What are the consequences of these findings for sampling methodology and rarefaction analyses?. Location: Six semi-natural grasslands in Western Eurasia (France, Germany, Bulgaria, Hungary, Italy, Turkey). Methods: In each site we established six blocks of 40 cm × 280 cm, subdivided into 5 cm × 5 cm micro-quadrats, on which we recorded vascular plant species presence with the rooted (all sites) and shoot (four sites) presence method. Data of these micro-quadrats were then combined to achieve larger sampling units of 0.01, 0.04 and 0.16 m² grain size with six different spatial configurations (square, 4:1 rectangle, 16:1 rectangle, three variants of discontiguous randomly placed micro-quadrats). The effect of the spatial configurations on species richness was quantified as relative richness compared to the mean richness of the square of the same surface area. Results: Square sampling units had significantly lower species richness than other spatial configurations in all countries. For 4:1 and 16:1 rectangles, the increase of rooted richness was on average about 2% and 8%, respectively. In contrast, the average richness increase for discontiguous configurations was 7%, 17% and 40%. In general, increases were higher with shoot presence than with rooted presence. Overall, the patterns of richness increase were highly consistent across six countries, three grain sizes and two recording methods. Conclusions: Our findings suggest that the shape of sampling units has negligible effects on species richness values when the length–width ratio is up to 4:1, and the effects remain small even for more elongated contiguous configurations. In contrast, results from discontiguous sampling units are not directly comparable with those of contiguous sampling units, and are strongly confounded by spatial extent. This is particularly problematic for rarefaction studies where spatial extent is often not controlled for. We suggest that the concept of effective area is a useful tool to report effects of spatial configuration on richness values, and introduce species–extent relationships (SERs) to describe richness increases of different spatial configurations of sampling units. © 2016 International Association for Vegetation Scienc

Will interannual variability in sand grassland communities increase with climate change?

Decreasing diversity and plant cover, as well as increasing variability of these characteristics with increasing aridity are expected in grasslands due to climate change. These predictions were tested in perennial sand grasslands in Hungary. Two sites were chosen in different positions on an aridity gradient and two stands in each site were monitored for 9 years. Presence of plant species were recorded along 52 m long circular belt transects of 1040 units of 5 cm × 5 cm contiguous microquadrats. This sampling procedure — a version of line-intercept methods — enabled us to monitor diversity and total abundance in a sensitive, precise and non-destructive way. We found no trend but fluctuation in most community level attributes and in species composition. Contrary to fluctuations, between-site differences in diversity did not change and diversity remained lower in the more arid site during our 9-year-study. Compositional diversity performed better than species diversity because allowed us to detect vegetation changes that would have remained hidden if monitoring would be based only on the species richness. Comparing the magnitudes of fluctuations, five times higher relative interannual variability (CV%) was found for compositional diversity at the more arid site, while the relative temporal variability of total abundance and species richness did not show consistent patterns. We conclude that a 9 year-long study was too short to identify trends caused by the changing climate. However, the larger temporal variability of species combinations found in the more arid site suggests larger vulnerability and highlights the importance of non-linear dynamics during climate changes

High-Resolution transect sampling and multiple scale diversity analyses for evaluating grassland resilience to climatic extremes

Diversity responses to climatic factors in plant communities are well understood from experiments, but less known in natural conditions due to the rarity of appropriate long-term observational data. In this paper, we use long-term transect data sampled annually in three natural grasslands of different species pools, soils, landscape contexts and land use histories. Analyzing these specific belt transect data of contiguous small sampling units enabled us to explore scale dependence and spatial synchrony of diversity patterns within and among sites. The 14-year study period covered several droughts, including one extreme event between 2011 and 2012. We demonstrated that all natural grasslands responded to droughts by considerable fluctuations of diversity, but, overall, they remained stable. The plant functional group of annuals showed high resilience at all sites, while perennials were resistant to droughts. Our results were robust to changing spatial scales of observations, and we also demonstrated that within-site spatial synchrony could be used as a sensitive indicator of external climatic effects. We propose the broad application of high-resolution belt transects for powerful and adaptive vegetation monitoring in the future