Accounting for missing data in monthly temperature series: Testing rule‐of‐thumb omission of months with missing values
Bibliographic record
Abstract
The “3/5 rule” is a commonly used rule‐of‐thumb for dealing with missing data when calculating monthly climate normals. The rule states that any month that is missing more than three consecutive daily values, or more than five daily values in total, should not be included in calculated monthly climate normals. We quantify the impact of missing data in a given year–month for between 1 and 25 missing values. As such, we describe the error the “3/5 rule” (and a related rule that we have dubbed the “4/10 rule”) permits. We tested the statistical robustness of these rules using observed temperature data from a temperate station and a tropical station. We show that, for observed data, the “3/5 rule” permits an average of between 0.06 and 0.07 standard deviations of error in the calculated monthly mean ( ɛ ) when three consecutive or five random values are missing. For its part, the “4/10 rule” permits a maximum ɛ of between 0.07 and 0.09 when four consecutive values are missing, or up to 0.10 when 10 random values are missing. The proportional impact of missing values was similar across variables. We performed a correlation analysis and show that each additional missing value from a year–month of data increases ɛ by between 0.008 and 0.018 for up to 19 missing values. There is a significant relationship between the lag‐1 autocorrelation of a year–month, and ɛ. ɛ can be reduced by simple linear interpolation when values are missing at random and the year–month exhibits lag‐1 autocorrelation. Overall, we find that the application of any “rule‐of‐thumb” should be based on the particular characteristics of the source data and the goals of the research project.
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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 | 0.144 | 0.388 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.005 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".