## Tuesday, July 22, 2014

### Precipitation Percentiles

A few weeks ago Rick started a discussion (via e-mail) regarding precipitation percentiles. Since temperatures are pretty normally distributed, the terms 'above normal' and 'below normal' are universal when the time scale is a single day. However, precipitation is an entirely different matter. If a station receives precipitation on 20% of days throughout the year, then 80% of days will experience below normal precipitation. From a statistical perspective this is counter intuitive. Using a probabilistic measure provides a meaningful baseline from which to compare a single day's precipitation to determine whether or not it is a high or low probability event.

Figure 1 shows the daily precipitation values for the 75th, 80th, 85th, 90th, 95th, and 99th percentiles for Fairbanks between 1915 and 2013. Measurable precipitation values for 2014 are overlaid as blue diamonds. The daily values were interpolated from a spline of monthly values. Importantly, all values were included when developing the percentile lines – including days with no precipitation.

For example, on March 1st, the 99th precipitation percentile is 0.25". In other words, there is a 1% chance of observing a precipitation value greater than 0.25" on March 1st. Since there are 365 days in a year, we expect to exceed the 99th percentile 3.65 times annually. Figure 2 shows the number of exceedences of the 99th percentile for every year since 1915. So far in 2014 the 99th percentile has been exceeded 6 times. In fact, those 6 exceedences occurred in a span of 20 days. The only time that occurred in a shorter time period was back in March of 1918 when 6 exceedences occurred in a span of 11 days.

Figure 1. Precipitation percentiles for Fairbanks (1915-2013) with 2014 precipitation shown as diamonds.

Figure 2. Number of days that the 99th percentile was exceeded for Fairbanks (1915-2014). 2014 data is through July 20th.

#### 1 comment:

1. Nice work, Brian! This is a great way to visualize how anomalous daily precipitation events are. I suppose the percentile lines could also be labeled in terms of recurrence interval, e.g. 100 days for the 99th percentile? Although I suspect the larger events are not statistically random but are clustered together in time more than would be expected from random chance.