Fractal Description of the Spatial and Temporal Variability of Soil Water Content Across an Agricultural Field
Bibliographic record
Abstract
There is an increasing interest in quantifying the space-time variation of soil properties. This issue offers a unique set of problems that have been addressed using various methods. Here, the spatial and temporal scaling behavior of topsoil water content at the field scale was explored using the fractal approach. Results from fractal analysis were compared with those from other methods describing either spatial variability or temporal trends and stability of soil moisture. Time domain reflectometry probes were installed at the 0- to 20-cm depth in a clay loam soil under natural pasture in Ottawa, Ontario, Canada. Soil water content was measured 34 times at 164 points on a square grid with 10-m spacing. Mean soil water content and coefficients of variation showed significant negative linear relationship for both sampling dates (r2 = 0.783) and sampling points (r2 = 0.804). Both spatial and temporal data sets were characterized by a self-affine fractal Brownian motion model that requires two parameters, fractal dimension, D, and crossover length, l. For spatially sampled data sets at different times, D ranged from 2.589 to 2.910 and l ranged from 0.95 to 6.97 m. For temporal data sets measured on 10-m grid nodes, D was between 1.145 and 1.919 and l was from 0.069 to 9.40 days. Fractal analysis added information on the scale dependence of spatially and temporally sampled data sets, which is not taken into account by classical statistics. Also, interpretation of fractal parameters provided further insight when contrasted with temporal stability analysis. Fractal dimension and crossover length of temporal series showed spatial dependence, and ordinary kriging was used to map these two fractal parameters.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".