Quantitative fun

Sailors (including windsurfers and kiters) sometimes wonder when the windiest time of day is. Or how the wind varies from month to month, or where the prevailing wind blows from.

On Lake Mendota in Wisconsin, a buoy in the middle of the lake collects wind (and lots of other) data throughout the ice-off season, from April through November. Data go back to 2006, and although there are gaps when the buoy goes offline because of electronic outages or vandalism, you can download enough data to get some idea of wind patterns. (You'll want to look for and excise bad data though. There are nearly 1.5 million observations but hundreds of thousands of them are suspicious, including isolated near hurricane force wind speeds or tens of thousands of contiguous zeros, evidently captured when the instruments are down or recording faulty values.)

The first view shows the distribution of wind speed data from July 2006 to August 2012, excluding anomalous observations.

Sailors know that winds tend to follow a diurnal pattern. For example, overnight winds tend to be lower because the sun isn't around to produce thermal effects. Here are the hour to hour speeds on Lake Mendota. (The median is the speed at which half the observations are higher and half are lower.) Note that if you're seeking stronger wind, your best bet is to be on the water from 3:00 PM to 4:00 PM.

Next, here's the overall distribution of wind speeds and directions. We immediately see that the prevailing wind over Lake Mendota is westerly. You can also (very) roughly see that the wind exceeds 15 mph about 15% of the time. (Just add up the dark red percentages below. With a little more effort you can also eyeball this percentage from the yellow distribution chart above.) Windsurfers pay attention to the 15 mph threshold because that is about the speed at which they are able to get up and planing, skimming atop the waves as it were.

The distributions vary from month to month. For example these plots uphold the conventional local wisdom that August is an impoverished month for wind while October is strong. And one seldom experiences strong easterlies, except sometimes early in springtime.

Since you know from the hourly plot above that the wind is generally strongest from 1-4 PM you will want to know whether we can detect this intensification in these distributional plots. Indeed the following plot shows markedly heftier winds than the one above. For one, just compare the relative lengths of the dark red ends of the paddles.

The buoy that is the source of all these remarkable data is maintained through the heroic efforts of Luke Winslow of the Center for Limnology at the University of Wisconsin, Madison.