Multifractal and joint multifractal analysis of water and soil losses from erosion plots: A case study under subtropical conditions in Santa Catarina highlands, Brazil Ildegardis Bertol a , Jefferson Schick b , Douglas H. Bandeira a,d , Jorge Paz-Ferreiro c , Eva Vidal Vázquez d, ⁎ a Soil Science Department CAV/UDESC, CEP 88520-00, Lages, SC, Brazil b Instituto Federal Catarinense, CEP 88965-000, Santa Rosa do Sul, SC, Brazil c School of Civil, Environmental and Chemical Engineering, RMIT University, GPOBox 2476, Melbourne, VIC, Australia d Centro de Investigaciones Científicas Avanzadas CICA, University of Corunna, 15071 Corunna, Spain abstract article info Article history: Received 28 January 2016 Received in revised form 11 August 2016 Accepted 12 August 2016 Available online xxxx Understanding and describing the temporal variability of soil surface runoff and the associated production of sed- iments are required for modeling soil erosion processes. We employed multifractal and joint multifractal tech- niques 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 (D q ) and singularity spectra [f(α)-α] functions were used to compare the scaling patterns of water and soil losses under the four stud- ied treatments. Temporal distributions of water losses showed a lower heterogeneity, were more evenly distrib- uted, and had a stronger persistence when compared with its soil losses counterparts. The scaling heterogeneity of water losses among treatments increased as: BT b CT b MT b NT, while that of soil losses ranked as: BT ≈ MT b CT ≈ NT. Conversely for water losses, evenness and persistence decreased as BT N CT ≈ MT N NT, while for soil losses ranked as: BT ≈ MT N 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 in- dices 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 vari- ability of soil and water losses and for appraising differences among treatments. © 2016 Elsevier B.V. All rights reserved. Keywords: Soil and water losses Temporal variability Tillage Multifractal analysis Joint multifractal analysis Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2. Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2.1. Experimental site location, climate and soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2.2. Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2.3. Data set studied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2.4. Multifractal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2.5. Joint multifractal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2.6. Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 3. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 3.1. Single scale analysis of water and soil losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 3.2. Singularity and generalized dimension spectra of water and soil losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 3.3. Multifractal parameters of water and soil losses under different tillage treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 3.4. Joint multifractal analysis of soil and water losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 Geoderma xxx (2016) xxx–xxx ⁎ Corresponding author. GEODER-12432; No of Pages 10 http://dx.doi.org/10.1016/j.geoderma.2016.08.008 0016-7061/© 2016 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Geoderma journal homepage: www.elsevier.com/locate/geoderma Please cite this article as: Bertol, I., et al., Multifractal and joint multifractal analysis of water and soil losses from erosion plots: A case study under subtropical condition..., Geoderma (2016), http://dx.doi.org/10.1016/j.geoderma.2016.08.008