### Seaman, RS (2002)

#### The relevance of Benford's Law to background field errors in data assimilation

Australian Meteorological Magazine 51(1), 25-33.

**ISSN/ISBN:** 0004-9743
**DOI:** Not available at this time.

**Abstract:** Benford's Law is a logarithmic distribution of first significant digits that is well satisfied by many naturally occurring datasets. This particular distribution of first significant digits can be considered as the asymptotic result of combining random samples from many different distributions. The goodness of fit to Benford's Law may therefore provide some indication of the degree of mixing in a dataset.
Current objective analysis and data assimilation systems usually assume that background ('first guess') field errors are normally distributed. A quasi-inverse relation between goodness of fit to Benford's Law, and goodness of fit to a Gaussian distribution, is illustrated using ensembles of background field error obtained in several different ways. The ensembles utilise mainly 1000 hPa geopotential analysis and forecast data from an operational global data assimilation system, together with SYNOP observations, over Australia. Statistical simulations are consistent with the results from real data. Overall, the results are consitent with the suggestion, by others, that background field errors typically may be considered as arising from a mixture of Gaussian error distributions, rather than from a single Gaussian distribution.
Other detailed findings, are (a) other things being equal, observations minus 6 h forecasts are closer to Gaussian than are 48 h minus 24 h forecasts, (b) background field errors represented by 48 h minus 24 h forecasts over smaller spatial domains, and (c) the effects in (a) and (b) may be reduced but not removed by normalisation with respect to latitude-varying standard deviations.

**Bibtex:**

```
@article{
TITLE = {The relevance of Benford’s Law to background field errors in data assimilation},
AUTHOR ={Seaman, R.S.},
JOURNAL = {Australian Meteorological Magazine},
VOLUME = {51},
PAGES = {25--33},
YEAR = {2002},
ISSN = {0004-9743},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Environmental Sciences, Statistics