Average Recurrence Interval (ARI)

Since 2009, MetStat and Weather Decision Technologies (WDT) have teamed to produce average recurrence interval (ARI) maps/grids of near real-time precipitation and forecast precipitation to objectively convey rarity of storms. More often than not, extreme precipitation results in flooding; in fact, flooding is the most frequent severe weather threat, and is the costliest type of natural disaster facing the U.S. The general public as well as hydrologic engineers and emergency managers often have better sense of the consequences involved with a 100-year storm compared to an absolute amount of precipitation, therefore making the ARI a powerful way to convey the magnitude of occurring or forecasted precipitation events.

The ARI product is a color-shaded map of the average number of years between the recurrence of a similar precipitation event. This allows users to quickly ascertain areas with the most unusual precipitation and potential for flooding rather than using simple precipitation amounts, since what is deemed heavy rain in one part of the U.S. may be typical in another. ARI maps provide an objective, timely and accurate depiction of the magnitude and extent of high-impact precipitation and allow users to make appropriate decisions. The conversion of precipitation to a ARI removes the distraction of heavy, but not abnormal, precipitation thereby highlighting only the high-impact, most unusual precipitation.

Average recurrence interval maps are also packaged as the Extreme Precipitation Index (EPI) product, and are based on MetStormLive QPE and official precipitation frequency estimates published by the National Oceanic and Atmospheric Administration’s (NOAA) Hydrometeorological Design Studies Center.

Read our original article “Average Recurrence Interval of Extreme Rainfall in Real-time” at EarthZine.org.

Near Real-time Average Recurrence Interval

Using MetStormLive quantitative precipitation estimates (QPE), maps of average recurrence interval based on recent precipitation over the past 1-, 3-, 6-, and 24- hour periods are created. These maps are made available to clients through online interfaces making it easy for anyone to interpret the significance of recent or forecast precipitation events anywhere in the U.S., even without knowing anything about the precipitation climatology. This product proved to be popular with media outlets as a way of characterizing significant precipitation and potential flood events to the public, but it should be emphasized that the ARI product itself is not an indication of an equivalent flood occurrence or depth. In other words, a 100-year average recurrence interval for a given amount of precipitation may or may not result in a 100-year flood since an ARI does not account for runoff, drainage capacity, etc. However, the ARI product clearly shows when and where precipitation is or is forecast to significantly exceed climatological normals.

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RIGHT: An example of a forecast Average Recurrence Interval product for a 24-hour period. The colors indicate the ARI expected based upon a WRF precipitation forecast using WDT’s proprietary data assimilation techniques.

Forecast 24-hour ARI for the period ending 27 Aug 2017 at 7pm CDT (Hurricane Harvey).

Average Recurrence Interval Forecasts

Using WDT’s gridded national quantitative precipitation forecasts (QPF), ARI forecast maps are created for 6- and 24-hour time increments. WDT’s Weather Research and Forecasting model (WRF) features an objective analysis system with the WRF Four Dimensional Data Assimilation (FDDA) scheme. The objective analysis system employed is the Local Analysis and Prediction System (LAPS) analysis, developed and maintained by the Global Systems Division of the NOAA Earth Systems Research Laboratory. With LAPS, WDT is able to assimilate the IR, water vapor, and visible satellite image channels from geostationary satellites as well as WDT’s quality controlled three-dimensional radar mosaics. These two data sources, combined with traditional in situ observations, provide a more accurate initialization of the initial model moisture field through a three-dimensional cloud analysis. This technique has been shown to improve forecasts of precipitation and reduce model spin-up time.

24-hour QPE for Hurricane Irene
(ending Aug. 28, 2011)
24-hour Extreme Precipitation Index Forecast 24-hour Extreme Precipitation Index Observed

WDT is a private sector leader in the field of operational numerical weather prediction (NWP) and has been providing data services and decision tools based on locally run mesoscale NWP models since its foundation. A natural extension of its product suite is to apply the ARI technique to its automated quantitative precipitation forecasts (QPF) as a means to provide more useful guidance to decision makers. The forecast ARI product specifically uses WDT’s WRF domain. The ARI is updated four times per day (0300, 0900, 1500 and 2100 UTC) and provides a 5-day forecast.

Advances in the science of numerical weather prediction have significantly increased skill and resolution of QPF over the last decade. Mesoscale models such as WRF provide excellent forecast guidance, particularly for strongly forced events which can lead to widespread heavy precipitation and flooding.

Our ARI forecast products make it easy to identify areas for potential flood risk over the next five days.


Describing floods in terms of an average recurrence interval or “return period” (e.g. 100-year) has been used for decades to convey the rareness of flooding at stream gauges. However, describing the intensity of precipitation in a similar manner has not been done as routinely, but provides an equally objective perspective of extreme precipitation events. Official, gridded NOAA/NWS precipitation frequency estimates provide the statistical basis for translating observed or forecast precipitation into an equivalent ARI at any location in the U.S.

The average recurrence interval of precipitation does not necessarily equate to a flood of the same ARI. Floods can be caused by heavy rain, spring snowmelt, dam/levee failure and/or limited soil absorption. The degree of flooding from heavy precipitation depends on the precipitation intensity, storm duration, topography, antecedent soil conditions, ground cover, basin size and infrastructure design. Precipitation with ARIs as low as 1 to 5 years can cause significant urban flooding since most urban storm water systems are designed for 1 to 10 year ARI precipitation events, yet this may not equate to any flooding in well-drained rural areas. ARIs for the design of highway and other transportation infrastructure typically vary from 10 to 25 years. However, it is a near certainty that rainfall with ARIs greater than 100-year will cause major flooding, regardless of anything else. Dams and levees are generally designed for ARIs much larger than 500 years, but can be compromised during ARIs of 100-500+ year events.

The table below converts the different terminologies used to convey the rarity of precipitation and some potential consequences of each:

Categorical description of potential consequences from precipitation of the given rarityAverage Recurrence Interval (ARI)Approx. odds of occurring in a given yearProbability of occurring in any given year
Rivers at all-time peaks, potential small-mid sized dam and levee overtopping, catastrophic flooding likely1000 year1 in 10000.1%
Rivers at/near all-time peaks, potential small dam and levee overtopping, catastrophic flooding possible500 year1 in 5000.2%
Rivers near all-time peak flows, devastating flooding possible100 year1 in 1001%
Rivers above flood stage, major flooding possible50 year1 in 502%
Rivers at/near bankfull, low lying flooding25 year1 in 254%
Streams at bankfull, high river flows10 year1 in 1010%
Street flooding and small streams near bankfull5 year1 in 520%
Minor street flooding2 year1 in 250%
Little or no flooding1 year1 in 1Approaching 100%