Last article I described the methods of calculating climate normals, not much mentioning their interpretation and uses. These issues can become quite involved - much more so than a rather short article as this can thoroughly disucss. Thus I mention a few of the more relevant ideas and show a few specific examples.

One of Chuck Doswell's many fine essays deals with the issue of the notion of "normal" weather, with a rather practical though perhaps unconventional perspective. Though certainly aware of the definitions involved, he argues that the only thing truly normal about weather is its variability, and any discussion of "normal" weather must consider this. This (of course) refers to the common rather than statistical connotation of the word normal, the latter of which perhaps causes great confusion.

On the other proverbial hand, some people think the definition of normal is fine, but they should perhaps be calculated differently. Cathy Smith (maintainer of a fine Boulder, CO weather & climate site) mentioned to me a Journal of Climate article (reference and abstract) regarding a study of climate normals for which predictive skill of the normals was considered. This showed that climate normals for that (predictive) purpose were best if fewer (than 30) years were used and if they were recalculated annually. This makes sense considering that the 930 monthly values I previously mentioned are much more than statistically significant. Using climate normals for predicitve purposes differs from the notion of a climate normal being the average weather for a very large or infinite number of years, the latter of which is perhaps absurd considering how changes of the solar system may make the weather we currently experience much different from the average for all years of Earth's existence and that a location as we consider it would not even exist that long. Enough of things about which I am no expert.

I now discuss something I am a @ least a little of an expert about - the climate the Detroit-Ann Arbor, MI region, for which I showed a couple diagrams last article. I say that because I am a meteorologist who lived there most of my life, with an interest regarding weather. Seeing climate statistics is one thing, but also experiencing the weather provides a better understanding of what is causing those statistics. Below are monthly climate normals and interpolation curves for DTW (Detroit Metro Airport) in Romulus, MI for temperature :

A series of smooth periodic functions, Fourier series should interpolate yearly climate and much other periodic weather data well (beginning and ending of year are same). Fourier series interpolation has the advantage of being a global interpolation (one function for the entire interval) rather than a local interpolation as the cubic splines are (combinations of cubic polynomials at portions of the interval). Thus, it may portray seasonal variability better. This is not evident on the temperature plot (for which interpolations are almost identical); but on the precipitation plot, the cubic spline rides the proverbial roller coaster from one point to the next, whereas the Fourier series more so interpolates all points. A very relevant question is why should the monthly averages even be interpolated ? As illustrated in Doswell's essay, the normals can quite significantly change from one decade to the next. Quite possibly, July precipitation at DTW is really more than that during August, when the jet stream is typically well north of there. I suppose a good answer would be that if you want climate averages for reference purposes, anything which does not interpolate the monthly averages should darn closely do so, lest they greatly differ from them the opposite way they should !

I chose 36 rather than 30 years because the data set extends from 1959-1996, and I wanted the largest number of years divisble with 4 (thus no February 29 bias). Considering some of the above, perhaps much fewer than 30 years should be used (though if you want unbiased normals, the number should be divisible with 4). Another consideration is natural cyclical processes which may affect climate. Among these are the sunspot cycle and ENSO. The sunspot cycle is approximately 11 years (regarding numbers of them), and ENSO cycles are generally thought to be 3-7 years ? ENSO events which clearly affect worldwide climate are seemingly rare, but the quasi-periodic changes of solar flux associated with sunspots (even if only a few tenths of a %) should be climatologically significant. Unfortunately, the least common multiple of 4 & 11 is 44

Following my mapping procedure previously explained, I then calculated daily normals for temperature :

Staring at the daily normal plots, you likely notice some differences among averages and normals which are probably real and would be evident if an infinite number of years with the same climate characteristics of the period could be used.

Text and embedded images are copyright of Joseph Bartlo, though may be used with proper crediting.