Unsaturated Solute Transport in a Semiarid Catchment - Nonlinear Analyses and Modelling

Pernilla Öhrström

Research output: ThesisDoctoral Thesis (compilation)


Unsaturated solute transport is highly variable and therefore difficult to predict. In semi-arid areas, where water resources are limited, the presence of macropores is of great importance for crop production. The bromide ion (Br-) and dye tracers are useful for studies of water movement. One approach to describe the heterogeneous solute transport is to apply the concept of fractals to a dataset. Preferential paths stained with dye often exhibit geometries reminiscent of fractals allowing fractal analyses and modeling. This thesis concentrates on the case of semiarid clay soils in Tunisia. The objectives of this study were: (1) to test whether dye tracing experiments using Vitasyn Blau AE 85 can be employed to visualize solute transport in the unsaturated zone, (2) to characterize the spatial variability of solute transport at the catchment and plot scales in the semi-arid soils, (3) to determine whether solute transport patterns displays scaling behavior, and (4) to apply fractal models to simulate the heterogeneity of solute transport.

To test whether tracing can indeed be used to detect the wetting front, a field experiment was conducted in Sweden with simultaneous application of bromide and the dye Vitasyn-Blau AE 85 to a single plot. To investigate spatial variability of a semi-arid soil with preferential pathways, three sites in the catchment M?Richet el Anze, Tunisia, were selected. On each site, two framed plots were established and irrigated with water mixed with the dye tracer Vitasyn-Blau AE 85. The plots were excavated and the dye patterns were photographed. For the semiarid soils, dye penetration data was stored as both 1D series with a resolution of 0.14cm/pixel, and as 2D fields, with a resolution of 2.5 cm/pixel.

The results from the pilot study in Sweden showed that the two tracers are transported in soils in a similar way and are therefore comparable. The dye as compared to bromide was retarded with a factor of 1.5, which is within the range of previous published results for sandy soils. For the semiarid soils, it was found that the spatial variability of the dye patterns increased with scale. The soils from the different physiographic areas (nose, slope, and hollow) of the catchment displayed significantly different responses to the infiltrating dye. Nose and hollow areas exhibited larger susceptibility to preferential flow while the slope soils had less deep cracks and fissures. At the plot-scale, cross-correlations and power spectrum analyses indicated that the preferential pathways were randomly distributed. The power-law behavior of the dye patterns spectral density suggested scale invariance and self-similarity. For probability density functions (pdf) of the 2D fields, plots P1 (hollow) and P3 (slope) displayed clear hyperbolic behavior. The pdfs of the breakdown coefficients (bdcs) for the first three scales (0.14 to 0.56 cm) for P1 and P3 were well related to each other, indicating scale-invariance. For the 2D analysis, raw statistical moments and K(q) functions showed that the fields were multiscaling. For the 1D field with higher resolutions, a scale break was indicated in the moment functions for all plots except P4 at a flow path width of 4.4 cm. The K(q)-functions were linear for P3, P4 and P5 and for low scales (<4.4 cm) at P1, indicating monoscaling behavior. For the high scales (>4.4cm) at P1, the functions were non-linear, implying multifractal behavior. The Diffusion Limited Aggregation (DLA) model was tested on the 1D data fields. The model was calibrated against one plot (P3) and was able to accurately simulate both the depth distribution of dye coverage and its variability for a second plot (P4). The Universal Multifractal (UM) random cascade model was tested on the 2D data fields to model preferential flow. There was good agreement between observations and simulations which implies that the model is able to describe the data.

The results collected within the appended papers indicate scaling behavior of dye stained solute pathways in unsaturated semiarid clay soils. The high resolution and quality of the datasets used in this work should be emphasized. Such data are important because they can be used to test new models and theoretical approaches. It would be interesting to investigate large-scale variability (m-km) and small-scale (cm-mm) variability. Moreover, the connection between fractal analyses of flow patterns, soil structure and physical processes, such as dispersion should be further examined.
Original languageEnglish
Awarding Institution
  • Division of Water Resources Engineering
  • Berndtsson, Ronny, Supervisor
Award date2005 Oct 28
Print ISBNs91-628-6635-4
Publication statusPublished - 2005

Bibliographical note

Defence details

Date: 2005-10-28
Time: 10:15
Place: IDEON, Beta, Enok Thulinsalen, Scheelevägen 17, Lund

External reviewer(s)

Name: Jarvis, Nicholas
Title: Professor
Affiliation: Department of Soil Sciences, SLU, Sweden


Subject classification (UKÄ)

  • Water Engineering


  • teknisk geografi
  • Hydrogeologi
  • teknisk geologi
  • unsaturated zone
  • Hydrogeology
  • geographical and geological engineering
  • solute transport
  • scaling
  • soils
  • semiarid regions
  • heterogeneity
  • preferential flow
  • fractals


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