Multifractal and joint multifractal analysis of water and soil losses from erosion plots: A case study under subtropical conditions in Santa Catarina highlands, Brazil

- Water and soil losses were monitored for 20 years under different tillage systems.
- Time series of water and soil losses were multifractally distributed.
- Water losses showed a weaker heterogeneity and a stronger evenness than soil losses.
- Multifractal parameters detected effects of tillage system on water and soil losses.
- Joint multifractal analysis confirmed scale dependency between water and soil losses.

Understanding and describing the temporal variability of soil surface runoff and the associated production of sediments are required for modeling soil erosion processes. We employed multifractal and joint multifractal techniques to quantify the temporal scaling relationships of water and soil losses measured in standard erosion plots across a period of about 20 years. The time series studied consisted of 795 erosive events, monitored in Lages, SC, Brazil. Water and soil losses were recorded in bare soil (BS) and under crops in rotation, managed by three different soil tillage systems, namely conventional tillage (CT), minimum tillage (MT) and no tillage (NT). All the treatments were replicated twice. Both water and soil losses were multifractally distributed over the study period. Several parameters and indices extracted from the generalized dimension (Dq) and singularity spectra [f(α)-α] functions were used to compare the scaling patterns of water and soil losses under the four studied treatments. Temporal distributions of water losses showed a lower heterogeneity, were more evenly distributed, and had a stronger persistence when compared with its soil losses counterparts. The scaling heterogeneity of water losses among treatments increased as: BT < CT < MT < NT, while that of soil losses ranked as: BT ≈ MT < CT ≈ NT. Conversely for water losses, evenness and persistence decreased as BT > CT ≈ MT > NT, while for soil losses ranked as: BT ≈ MT > CT ≈ NT. Joint multifractal analysis showed that the relationships between soil and water losses were scale dependent across the temporal domain studied, and that their respective scaling indices had various degrees of association under different tillage treatments. Therefore, multifractal and joint multifractal techniques have been demonstrated to be useful for assessing multiscale patterns of temporal variability of soil and water losses and for appraising differences among treatments.