EGU23-6835, updated on 25 Feb 2023
EGU General Assembly 2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

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

Ernesto Sanz1,2, Andrés Almeida-Ñauñay1,2, Carlos G. Díaz-Ambrona1,3, Antonio Saa-Requejo1,4, Margarita Ruíz-Ramos1,3, Alfredo Rodriguez1,5, and Ana M. Tarquis1,2
Ernesto Sanz et al.
  • 1Universidad Politécnica de Madrid, CEIGRAM, Madrid, Spain (
  • 2Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, 28040 Madrid, Spain (
  • 3AgSystems, ETSI Agronómica, Alimentaria y Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain (
  • 4Evaluación de Recursos Naturales, ETSI Agronómica, Alimentaria y Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain (
  • 5Departamento de Análisis Económico y Finanzas, Universidad de Castilla-La Mancha, 45071 Toledo, Spain (

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).


Baranowski, Piotr, et al. "Multifractal analysis of meteorological time series to assess climate impacts." Climate Research 65 (2015): 39-52.

Sanz, Ernesto, et al. "Generalized structure functions and multifractal detrended fluctuation analysis applied to vegetation index time series: An arid rangeland study." Entropy 23.5 (2021): 576.

Sanz, Ernesto, et al. "Clustering Arid Rangelands Based on NDVI Annual Patterns and Their Persistence." Remote Sensing 14.19 (2022): 4949.


How to cite: Sanz, E., Almeida-Ñauñay, A., Díaz-Ambrona, C. G., Saa-Requejo, A., Ruíz-Ramos, M., Rodriguez, A., and Tarquis, A. M.: Multiscaling behavior of vegetation, precipitation and aridity time series in semiarid grasslands. Persistence and multifractal sources., EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-6835,, 2023.