Field-scale N fertilizer recommendations: The spatial covariance problem
Bibliographic record
Abstract
Theory is needed to estimate field-scale crop response and calibration relationships (soil test versus recommended fertilize r rate) from local scale measurements, in fields with spatially variable soil properties. The objective of this study is to present a theoretical stochastic framework for examining the influence of the spatial variability of soil properties, and covariance between soil properties, on field-scale crop response to fertilizer. An analytical solution of the general stochastic scaling equation is given for the specific case of wheat grain yield response to applied N fertilizer with variable soil-N test and available water in Saskatchewan, Canada. The analytical solution indicates spatial variance of soil properties within fields influences field average yield response to applied fertilizer. The field-scale maximum economic rate of fertilizer N (MERN), depends not only on the average soil properties, but also on (1) the amount of variability of soil properties in the field, and (2) the correlation between the spatial patterns of soil properties (e.g., soil test and available water). For the specific soil examined, positive spatial correlation between soil-N test and available water significantly increases MERN, for the same average soil test and available water. Negative correlation decreases MERN. Key Words: Fertilizer recommendation, soil test, spatial variability, crop response, soil water
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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 teacher head, 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".