Multiscaling behavior of vegetation, precipitation and aridity time series in semiarid grasslands. Persistence and multifractal sources.

Grazing is an important ecosystem process affecting more than a third of the global land surface. However, it is challenging to predict responses of rangelands to changing grazing regimes due to complex interactions between grazers, vegetation and climate. Understanding the multiscaling behavior of vegetation and climate time series can be key to improving grazing and vegetation management in semiarid areas where climate change is heavily affecting vegetation-climate complex systems. 

A grassland plot in central Spain (Madrid) was selected to study this system. This plot was selected based on proximity to a meteorological station and maximum surface covered by grasses. For this plot, reflectance data were collected from MODIS (MOD09A1.006) to study the Normalized Difference Vegetation Index (NDVI). These series, from 2002 to 2020, have a 250 m spatial resolution and 8-days temporal resolution. Daily meteorological precipitation and evapotranspiration were obtained from the closest station from AEMET (Spanish Meteorological Agency). Precipitation was accumulated over 8-days and the aridity index was calculated (accumulated precipitation over accumulated potential evapotranspiration) for every 8-days to match the temporal resolution of NDVI. With these three series (NDVI, precipitation and aridity), multifractal detrended fluctuation analysis was performed, to calculate the persistence (H2) and multifractality. Furthermore, this was also done to these series after shuffling and surrogating them. 

The aridity index showed a high persistent character, while precipitation had a light persistence and NDVI showed no persistence or antipersistence, instead, it had a random character. The aridity index and NDVI displayed a decrease in H2, progressively, when surrogate and shuffle series were used. On the other hand, precipitation showed a higher H2 when the surrogate series was used compared to the original series. The shuffle precipitation series had a lesser value of H2 than the original and surrogate precipitation series. The increase in persistence on the precipitation surrogate series, have been reported in other precipitation series and it may indicate that the year that cause a decrease in persistence in the original series are separated along the original series. 

The most multifractal series was found to be NDVI followed by aridity index and finally precipitation. The multifractality always declined when the surrogate series was used in all series. Moreover, when shuffle series were used multifractality was almost eliminated in NDVI shuffle series, but some was retained for precipitation and aridity index, showing a larger source of multifractality due to the probability density function in these two series, mixing with a long-range correlation source of multifractality (mostly dominant for NDVI). 

Acknowledgements: The authors acknowledge the support of Clasificación de Pastizales Mediante Métodos Supervisados - SANTO, from Universidad Politécnica de Madrid (project number: RP220220C024).

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