Tye W. Parzybok1, Beth Clarke2 and Douglas M. Hultstrand3
1METSTAT, Inc, 4764 Shavano Drive, Windsor, CO 80550; PH (970) 686-1253; email: firstname.lastname@example.org
2Weather Decision Technologies, Inc., 201 David L. Boren Blvd, Ste 270, Norman, OK 73072; PH (405) 579.7675; FAX (405) 579.7780; email: email@example.com
3METSTAT, Inc, 4764 Shavano Drive, Windsor, CO 80550; PH (970) 686-1253; email: firstname.lastname@example.org
As society and infrastructure become increasingly more vulnerable and impacted by extreme rainfall events, the requirement for timely, accurate and informative rainfall information is critical to protecting property, saving lives and efficiently managing water. Accurate rainfall data is becoming increasingly available, but translating it into meaningful information to support decisions is lacking. To make rainfall data more meaningful, an innovative technique for translating near real-time rainfall maps into “return period” maps has been created so users have an objective, timely, and accurate depiction of recent rainfall.
Knowing how much rainfall fell at a particular location during a certain amount of time is useful, but expressing the rarity of rainfall in terms of a “return period” provides an objective and useful perspective of the rainfall. Average recurrence interval (ARI) maps of rainfall provide information that is analogous to the 100-year flood, but for rainfall instead.
The use of the term “return period” has been criticized for leading to confusion in the minds of decision makers and the public. To clarify the meaning and to be consistent with NOAA’s National Weather Service Hydrometeorological Design Studies Center (HDSC), the term “average recurrence interval” (ARI) is used instead. For those who prefer a probability, an ARI can be easily converted into a probability. The ARI is the average number of years between exceedances of a given rainfall depth for a given duration at a specific point location.
Historically, calculating the ARI of a given rainfall event has been inefficient, because it is generalized for an area based on a single observation and/or lacking reliable underlying data. New methodologies address each of these issues. In a highly computational GIS environment, real-time ARIs are computed based on gauge-corrected radar-estimated rainfall maps/grids from the National Weather Service (NWS)> and Weather Decision Technologies, Inc. (WDT) together with official rainfall frequency grids/maps published by HDSC. Although the ARI of rainfall does not necessarily equate to a flood of the same ARI, the ARI of rainfall is an excellent indicator of flooding potential.
Describing floods in terms of a “return period” (e.g. 100-year) has been used for decades to convey the rareness of major flooding events. However, describing the intensity of heavy rainstorms in a similar manner has not been as routine but provides an equally good perspective of extreme rainfall events.
In order to compute the “return period” of a flood, pre-existing flood frequency statistics and a measure of the flood (i.e. peak discharge) need to be available at a specific location along a river or stream. Unlike flood frequency statistics, which are only available at gauged locations along rivers and streams, rainfall frequency statistics are available at any location in the United States.
The frequency and magnitude of rainfall is critically important to engineers, hydrologists and others involved in designing hydrologic structures, such as storm sewers, retention ponds, dams and levees.
To meet this need, NOAA’s National Weather Service Hydrometeorological Design Studies Center (HDSC) has been responsible for creating and publishing rainfall frequency atlases (e.g. 100-year 24-hour rainfall depth) for the United States since 1953. In 2003, the HDSC began updating the rainfall/precipitation frequency values for regions of the country as part of a series of atlases known as NOAA Atlas 14 (Bonnin, 2004). NOAA Atlas 14 not only provided updated information but also established clearer terminology.
The use of the term “return period” has been criticized for leading to confusion in the minds of decision makers and the public. “Return period” is sometimes misinterpreted as implying that the associated magnitude of a rain event is only exceeded at regular intervals. In other words, it is misunderstood that a 100-year event should only occur every 100 years.
Therefore to clarify the meaning, NOAA Atlas 14 uses the term “average recurrence interval” or ARI to describe frequency. The ARI, which is in units of years, is defined as the average, or expected, period of time between exceedances of a given rainfall amount over a given duration and location. For example, suppose five inches of rain in 24 hours at a particular location is equivalent to an ARI of 100 years. This means five inches of rain in 24 hours is expected to occur, on average, every 100 years at this location.
Since the ARI is an average, a similar or even larger, rainfall amount could occur again this year, next year or any other year. The ARI can be also be approximated as a probability or percent chance of occurring in any given year. For example, a 100-year ARI could also be expressed as having a 1 in 100 chance or a 1 percent chance of occurring in any given year. Table 1 converts the different terminologies.
Although rainfall frequency estimates have been available since the 1950s, they have been largely overlooked as a means of translating actual rainfall observations into an ARI and instead used primarily for the design of infrastructure.
This translation has been hampered by the generalized, hard-copy maps of rainfall frequency estimates buried in government documents. Before an ARI can be computed for a given rainfall depth and duration, a tedious interpolation of known rainfall frequency estimates needs to be drawn from the rainfall frequency maps. This is changing since rainfall frequency estimates from NOAA Atlas 14 are available online and as Geographic Information System (GIS) compatible files (Parzybok and Yekta, 2003). Access to reliable rainfall measurements at locations of interest is perhaps another reason that has hampered more frequent calculations of ARIs associated with rainfall amounts.
However, given today’s radar-adjusted rainfall products and the plethora of rain gauge observations/networks, observed rainfall amounts are no longer lacking in most parts of the United States. Real-time rainfall maps and observations are available from a number of on-line sources, including CoCoRaHS, Meteorological Assimilation Data Ingest System (MADIS), and the NWS (to name a few).
Given the government-issued rainfall frequency atlases and observed rainfall, climatologists and hydrometeorologists have computed the ARI of major rainstorms for purposes of insurance claims, media requests and post-storm reports. For example, according to a study conducted by the Peachtree, GA NWS Forecast office, the rainfall across portions of northern Georgia during the period September 20-21, 2009 was in excess of a 10,000-year rainfall event (Belanger, 2010). The heavy rainfall resulted in epic flooding, which according to the United States Geological Survey (USGS) was a 500-year flood in parts of Cobb and Douglas counties (Shepherd, et. al. 2010). The ARI of rainfall does not necessarily equate to a flood of the same ARI. The degree of flooding from heavy rainfall depends on the rainfall intensity, duration, topography, soil conditions, ground cover, basin size and infrastructure design.
Floods can be caused by heavy rain, spring snowmelt, dam/levee failure and/or limited soil absorption. Rain associated with a 1 to 5 year ARI can cause significant urban flooding since most urban storm water systems are designed for 1-10 year ARI rainfall events. ARIs for highway and other transportation infrastructure typically vary from 10 to 25. However, it is a near certainty that rainfall associated with ARIs greater than 100-year will cause major flooding, regardless of anything else. Dams and levees are generally designed for rainfall ARIs much larger than 500 years, but can be compromised during ARIs of 100-500+ year events.
There have been countless other cases where point rainfall values have been translated into an ARI, but computing the ARI for a number of points across an affected area for the same storm provides a unique sense of both the magnitude and spatial extent of the storm. Until recently, maps of this nature were not created due to the extensive calculations necessary.
To our knowledge, the spatial depiction of rainfall in terms of an ARI is something first done by Goodridge et al. in the Historic Rainstorms in California document, published in August 1997 by the California Department of Water Resources (Goodridge, 1997). The Historic Rainstorms document contains a comprehensive storm catalog. Each storm is documented by a brief discussion, observed rainfall amounts and a map of rainfall amounts coupled with contours of ARI (Figure 1). The ARI contours have the unique capability to clearly and objectively convey the severity of rainfall, even to those not familiar with rainfall in California.
A web search turned up one international instance of extreme rainfall depicted as a map of ARI in New Zealand. The High Intensity Rainfall Design System (HIRS), developed by New Zealand’s National Institute of Water and Atmospheric Research, was used to develop an ARI map of rainfall associated with an extraordinary rainstorm on February 14-17, 2004 (National Institute of Water and Atmospheric Research, 2010). The storm produced widespread flooding and extensive infrastructure damage in the lower North Island (Figure 2.) Although the storm event lasted four days, the ARI map depicts the ARI of the maximum 24-hour rainfall during the 4-day storm period. The map shows large areas where rainfall exceeded ARIs of 150 years.
More recently, maps of the ARI of rainfall have been created to convey the rareness of two major rainfall events in the United States. The ARI maps were created by the National Oceanic and Atmospheric Administration (NOAA) National Weather Service for the May 1-2, 2010 epic flood event across western and middle Tennessee. The map of the 48-hour rainfall average recurrence intervals (Figure 3) indicated a large area of 1000+ ARIs.
Similarly, NOAA created a 4-day ARI map of the rainfall (and melted snow) associated with the record-breaking rain and snow (generally above 5,000 feet elevation) event across Arizona during the period January 19-23, 2010. The map was published as part of a Local Service Assessment by the Weather Forecast Offices in Arizona, Las Vegas, NV and the Colorado Basin River Forecast Center in Salt Lake City, UT (NOAA, 2010).
Rainfall Frequency Estimates
Before the ARI of a specific rainfall event can be ascertained, ARIs must first be computed using historical rainfall data collected by long-term climatological weather stations. It is generally understood that one can estimate reliable ARIs twice that of the length of the rainfall record. For example, the analysis of 50 years of historical rainfall data can confidently result in ARIs up to 100 years. In order to estimate rainfall frequency estimates for rarer ARIs, a regional frequency analysis approach is used, which leverages historical rainfall data from a cluster of stations to confidently extend the ARIs well beyond the period of record of any given station (Hosking and Wallis, 1997). The approach “trades space for time” and has been widely used in recent rainfall frequency atlases, including NOAA Atlas 14.
In 2003, HDSC began updating the old, out-dated rainfall frequency atlases published in the 1950s, 1960s and 1970s as different volumes of NOAA Atlas 14 (Bonnin, 2004). NOAA Atlas 14 is based on a much larger and longer sample of observed rainfall data than was available for previous atlases, therefore reducing the uncertainty of the rainfall frequency values (Bonnin, et al., 2003). Eventually, NOAA Atlas 14 will cover the entire United States, but currently the Southwest, Ohio River Basin and Surrounding States, California, Hawaii, Pacific Islands, Puerto Rico and the U.S Virgin Islands have updated precipitation frequency estimates as volumes 1, 2, 3, 4 and 5 respectively. Figure 5 shows a map of current NOAA Atlas 14 projects and areas included in future volumes of NOAA Atlas 14.
Some states and local governments have funded development of their own state, city or regional rainfall frequency analyses, but NOAA publishes the nation’s de-facto standard rainfall frequency values for the United States (Bonnin, et al., 2003).
NOAA Atlas 14 is a web-based document and all of its associated gridded data are available through the Precipitation Frequency Data Server. (Parzybok and Yekta, 2003). Those areas not already updated by NOAA Atlas 14 are covered by older precipitation frequency documents, such as Technical Paper 40 (eastern U.S.) and NOAA Atlas 2 (western U.S.) for durations less than 24-hours and Technical Paper 49 (entire U.S.) for longer (up to 10-days) durations.
(U.S. Weather Bureau 1964; Hershfield, 1961; Miller et. al., 1973). NOAA Atlas 14 contains rainfall frequency estimates for durations as short as 5-minutes to as long a 60-days, and ARIs from 1-year to 1000-year.
In order to create seamless ARI maps of the continental U.S., the precipitation frequency estimate maps from the older atlases were digitized and converted into a format, resolution and projection consistent with those from NOAA Atlas 14. In a GIS, grids of rainfall frequency estimates were merged into seamless rainfall frequency grids for 24- and 6-hour durations and ARIs from 1-year to 1000-year, thus providing the basis for translating rainfall into an equivalent ARI for anywhere in the country.
To attain the unique perspective of ARIs across the U.S., one must also acquire rainfall values for all locations in the Continental United States (CONUS). There are a growing number of on-line sources of rainfall maps/grids, including the National Weather
Service and Weather Decision Technologies, Inc. (WDT). Gridded NWS rainfall data can be accessed from http://water.weather.gov/precip/ as shown in Figure 6. Meanwhile, Figure 7 is a CONUS map of precipitation from WDT. The NWS gauge-adjusted radar-estimated precipitation data is available at a spatial resolution of 4 km x 4km, while from WDT it is available at 1 km x 1 km. Both are available every one hour.
The rainfall-to-ARI conversion is especially sensitive to erroneous rainfall data, so it is of critical importance to have good-quality rainfall data. Erroneously high rainfall data will be amplified in the ARI product and result in ARI values that are spatially inconsistent and hence cause a “bulls eye” on the ARI map. It has only been within the past decade that gauge-adjusted radar-estimated rainfall has become reliable enough to support computations like ARI. For areas of complex terrain, particularly in the western United States, radar-based rainfall estimation still suffers from radar beam blockages, but new technologies like the Storm Precipitation Analysis System (SPAS) offers new ways to blend radar and climatologically-based rainfall estimation to produce seamless rainfall grids across any terrain (Parzybok, 2010). Figure 8 depicts a rainfall event as modeled by SPAS across the rugged terrain of the Pacific Northwest that produced ARIs in excess of 80 years in parts of the northern Cascades of Washington.
Rainfall to ARI Conversion
ARI grids/maps are created by translating each grid cell of rainfall across the CONUS into an ARI given the ARI statistics at each grid cell. The rainfall to ARI conversion uses proprietary software but begins with summing up rainfall for a desired duration (e.g. 24-hours). Given an observed rainfall amount, duration and location (e.g. 2.00 inches in 24 hours at a grid cell near Phoenix, Arizona), the corresponding ARI is computed by determining bounding ARIs of the observed rainfall amount. For instance,
according to NOAA Atlas 14 Volume 1, the 24-hour rainfall for a 5-year ARI at Phoenix is 1.81 inches, while the 10-year ARI is 2.14 inches. Using the bounding ARIs (5 and 10 years) and rainfall frequency estimates (1.81 and 2.14), the ARI of the observed rainfall amount is interpolated. In this example, a 24-hour 2.00 inch rainfall value at Phoenix is equivalent to an ARI of 7.9 years.
The rainfall-to-ARI process is highly computational given the millions of grid cells that comprise the CONUS domain, but software has been optimized in to operate in a highly reliable, fast and redundant data center. Depending on the extent of rainfall across the country, a CONUS ARI grid/map, based on gauge-adjusted radar estimated rainfall, is processed in 4-8 minutes on a multiple-processor Linux computer. The ARI map is available within 25 minutes of its valid time. In other words, a CONUS ARI map for 24-hours ending at 1200 UTC would be available by about 1225 UTC. As shown in Figure 9, a free 24-hour CONUS ARI map, based on gridded NWS precipitation data, is available daily from METSTAT.com.
Once ARI maps for discrete periods are created (e.g. January 8, 2011 1100 UTC through January 2, 2011 1200 UTC), grids/maps of the maximum ARI over a given period of time (e.g. 72-hours) can easily be created. These so-called maximum ARI maps have the unique ability of indicating the maximum ARI, regardless of when it exactly occurred for a storm event. Maximum ARI maps better depict the ARI history of a “storm” than an instantaneous ARI map since the maximum ARI occurs at different times and places as the storm passes through a region. Figure 10 shows the maximum 6-hour ARI for the U.S. based on high-resolution gauge-adjusted radar rainfall from WDT during the period September 30, 2010 through October 1, 2010, a period of particularly wet weather across the northeastern United States.
Willapa Hills, December 2007
Two powerful storms brought extremely heavy rain and high winds to the Pacific Northwest during early December 2007. The intense low pressure areas fed an “atmospheric river” of very moist tropical air into the region. Orographic lifting caused copious amounts of rain to fall across western Oregon and Washington. Several rivers in northwestern Oregon and western Washington surpassed major flood stages. Rainfall intensities at 12- and 24-hours were particularly intense. Figure 11 shows the maximum 24-hour rainfall amounts during a five day period. Twenty-four hour rain values approached twenty inches in the Willapa Hills region, which equated to an ARI of 500+ years.
Tropical Storm Hermine
Tropical storm Hermine moved ashore just south of Brownsville, Texas on September 6, 2010. Although the storm packed a light punch when it moved ashore, its moist, tropical air mass unleashed heavy rainfall across Texas. The storm and its moist air mass slowly moved over San Antonio and into central Texas late on September 7th, then into Oklahoma on the 8th and 9th. The storm’s flooding caused eight deaths and nearly two million dollars in damage. Figure 12 shows a 24-hour snapshot of rainfall and the associated ARI. Rainfall across central Texas reached 13 inches, which equated to an ARI of about 300 years.
The combination of low-level moist flow from the Atlantic Ocean and moist southwest flow above that from the Gulf of Mexico, coupled with terrain enhancement, caused slow moving thunderstorms to occur over northern Georgia for several days (NOAA, 2009). The extreme rainfall caused catastrophic flooding across northern Georgia on September 18-23, 2009. The most intense rain occurred during a 24-hour period from September 20-21 when 10 to 20 inches of rain fell. The flooding claimed eleven lives and caused over $250 million in property damage (NOAA, 2009). Figure 13 shows the distribution and magnitude of rainfall and the corresponding ARI for the 24-hour period ending at 1200 UTC on September 21, 2009. Technical Paper 40 on provides ARI up to 100 –years, but we extrapolated ARIs to 500 years for purposes of gauging the severity of the rainfall. As noted earlier, Belanger (2011) calculated 24-hour rainfall associated with this storm exceeded the 10,000-year ARI in places.
Descriptions of floods in terms of “return periods” have been used for decades to convey the rareness of major flooding events. While similar descriptions of heavy rainstorms have not been as common, they provide an equally useful perspective on extreme rainfall events. Hampered by lack of known ARIs, rain gauge data and computational computing power, ARIs of specific events have not been routinely computed. Given the recent availability of real-time rainfall data and pre-existing rainfall frequency statistics, however, the natural evolution has been to create maps depicting the ARI of rainfall in real-time. Use of official rainfall frequency atlases in conjunction with observed rainfall grids/maps provides an objective and powerful means of conveying the rareness (or commonness) of rainfall, even to those not familiar with the rainfall of the area. Maximum ARI maps for a defined duration depict the ARI of a “storm” since the maximum ARI occurs at different times and places as the storm pass through a region.
The information conveyed via an ARI map has been illustrated in post-storm studies, but real-time ARI maps of rainfall provide a new and powerful tool that benefits a number of disciplines. Having the capability of seeing ARIs of rainfall in near real-time is an important part of determining how to respond, and puts the rainfall into a perspective (ARI, probability or percent chance) that is understood by most people. Real-time ARI maps can help city and flood control district planners and engineers determine the intensity of downpours with which storm water drainage systems and other structures are designed to cope. In addition, real-time ARI maps could provide forecasters with a critical alternative to stream gauge discharge frequency estimated during extreme events. This is especially significant because flooding can often wipe out or cause stream gauges to malfunction. In fact, the flooding in Georgia during September 2009 was so severe that 20 percent of the stream gauges failed (NOAA 2009). Although the ARI of rainfall does not necessarily equate to the same ARI of flooding, if the ARI of rainfall (based on radar-estimated and/or gauge precipitation) were available, it would have provided a critical alternative for inferring the situation as the flooding unfolded.
A near real-time 24-hour ARI map for the continental United States is available at http://www.metstat.com. The ARI map, which is based on 24-hour NWS gauge-adjusted radar rainfall data, is routinely updated three times per day, at approximately 11am (16Z), 2pm (19Z) and 6pm (23Z) Eastern Standard Time which coincides with the updates of the observed precipitation available at http://water.weather.gov/precip/. A portion of an extensive ARI map/grid archive, dating back to 1999, is available online.
Efforts are underway to expand ARI mapping to Puerto Rico and Hawaii, but the immediate focus is on providing additional durations and various area sizes. The ARI maps discussed thus far represent point rainfall values and do not reflect the ARI of differing area sizes. Hydrologists, in particular, would find the ARI of a real rainfall to be more useful than point rainfall ARIs. However, in order to ascertain the ARI of areal rainfall amounts, it is necessary to know the actual areal rainfall depth and frequencies.
The areal rainfall depth can be easily computed, but areal rainfall frequencies are more difficult to come by. Existing point rainfall frequency estimates from NOAA can be converted into areal estimates via an Areal Reduction Factor (ARF), however reliable ARFs for all areas of the United States are not available. NOAA is in the process of updating the ARFs for the United States, but the project results are not scheduled to be available until 2012 (Hydrometeorological Design Studies Center, 2011). Until then, ARFs published in the existing precipitation frequency documents (NOAA Atlas 2 and Technical Paper 40) may be used to produce ARFs of rainfall for common area sizes (e.g. 10, 20, 50,100, 200, 500 square-miles).
Thank you to Geoff Bonnin, Chief Hydrologic Science and Modeling Branch at National Weather Service, for the decade of inspiring and rewarding work at the Hydrometeorological Design Center where I gained my unique wealth of rainfall frequency knowledge. The real-time ARI capability could not have evolved as it has without the confidence and support of Weather Decision Technologies, Inc. Thank you to Michael Eilts of WDT for the years of trust, collaborative support and gauge-adjusted radar-estimated precipitation data for testing, development and now an operational product.
Belanger, Laura Griffith (2011). “Extreme rainfall frequency in the Atlanta metropolitan area: An analysis of September 2009.” 25th Conference on Hydrology, Impact of Weather and Climate Extremes on Hydrologic Processes, Responses and Hazards I, January 24, 2011, Seattle, WA.
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Parzybok, T.W., Hultstrand, D.M., B. Clarke, W.D. Kappel and E.M. Tomlinson (2010). “The Use of Gauge Data, Radar Reflectivity and the Storm Precipitation Analysis System for Deriving Accurate Precipitation in Complex Terrain.” In Proc. of the ALERT Users Group 23rd Flood Warning Systems Training Conference and Exposition, Palm Springs, CA, May 4-7, 2010.
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Mr. Parzybok is President and Chief Meteorologist of METSTAT, Inc in Windsor, Colorado. He has 20 years of GIS and meteorological/climatological experience and is a Certified GIS Professional (GISP). Author of “Weather Extremes of the West” as well as numerous other technical articles, Mr. Parzybok is an established professional meteorologist. His expertise in spatial interpolation, GIS, meteorology/climatology and quality control have played key roles in several major projects for the National Center for Atmospheric Research (NCAR), National Climatic Data Center (NCDC) , USDA Natural Resources Conservation Service (NRCS), National Forest Service and NOAA’s National Weather Service (NOAA/NWS). He is the lead programmer/developer of the Storm Precipitation Analysis System and SPAS in Real-Time; furthermore he manages several real-time weather applications, including one that translates rainfall into its equivalent Average Recurrence Interval. Mr. Parzybok has a long history of supplying the necessary meteorological information to improve hydrologic modeling, optimize hydrologic design, facilitate water management and monitor rainfall, and is uniquely qualified in providing the necessary components of probable maximum precipitation (PMP) studies. Given Mr. Parzybok’s comprehensive precipitation expertise, he is on the WMO extreme precipitation evaluation committee for assessing the potentially new world record rainfall intensities.
Mr. Hultstrand is a Senior Hydrometeorologist of Metstat Inc. in Portland, OR. He has over ten years of meteorologic/hydrologic experience. Mr. Hultstrand is currently finishing a Doctor of Philosophy degree in Earth Science from Colorado State University. His research will quantity the local to regional impacts of snowpack sublimation on a seasonal water balance, the importance of spatial rainfall data to stream runoff modeling, and assess the accuracy of snow sampling design methods for mountain catchments. He earned a Master of Science degree in Watershed Science from Colorado State University, and a Bachelor of Arts degree in Physical Geography and a Hydrology Certificate from the University of Colorado. Mr. Hultstrand has gained his expertise through work experience with the U.S. Geological Survey (USGS) Alpine Hydrology Research Group (AHRG), the Institute of Arctic and Alpine Research (INSTAAR), the U.S. Forest Service Rocky Mountain Research Station (RMRS), and Metstat, Inc. At these positions, he has managed and applied the scientific method in order to design, collect, test, analyze, document, and present scientific results. Mr. Hultstrand has a passion for scale and spatial variability in precipitation processes related to hydrology and hydrometeorology. His research and expertise are in modeling the spatial variability in snowpack processes and rainfall as function of terrain parameters and atmospheric energy to better understand and model hydrologic regimes.
Beth Clarke is a Hydro-Meteorologist and Product Manager at Weather Decision Technologies Inc (WDT). She received her B.S. in Meteorology with Honors from the University of Reading , England and a Masters degree in Professional Meteorology from the University of Oklahoma, USA. Beth’s expertise is in high quality precipitation estimation via the integration of multiple radar data with rain gauges and other meteorological sources for the purpose of water resource management and flood control. Prior to joining WDT in 2005, Beth worked for 4 years as a Research Assistant/Associate at the National Severe Storms Laboratory (NSSL) for the Hydro-Meteorological research team on the development of Quantitative Precipitation Estimation techniques using multiple sensors.