Frequency Analysis

MetStat and our strategic partner, MGS Engineering Consultants, are uniquely qualified and experienced in computing extremely rare precipitation frequency estimates for use in hydrologic hazard studies, including Risk Informed Decision Making (RIDM) which is a method of dam safety evaluation that uses the likelihood of loading, dam fragility, and consequences of failure to estimate risk. We also specialize in Local Intense Precipitation (LIP) studies that provide 1-hour/1-square mile precipitation-frequency relationships for nuclear power plant sites.

L-moment regional frequency analysis methods, similar to those applied in NOAA Atlas 14, are used in producing site-specific and watershed PF estimates. In fact, several team members were key developers of NOAA Atlas 14. The unparalleled expertise and knowledge of MetStat serves our clients well by providing the insight into processes and procedures needed for probabilistic precipitation analyses.

Regional PF analyses which are intended for application for extreme precipitation events must be conducted with a very high level of attention to detail in all aspects of the analysis. The current state-of-practice in regional PF analysis uses methodologies originally developed by Hosking and Wallis as described in their classic text entitled “Regional Frequency Analysis, An Approach Based on L-Moments” (1997). These methodologies provide the foundation for regional analyses utilized in NOAA Atlas 14.  MetStat builds upon these accepted regional analysis methods along with the findings of existing PF studies. Recent advances in regional analysis methods and spatial mapping of precipitation are being used to improve the process and decrease uncertainty.

Our expertise provides rich data sets of precipitation frequency estimates, plus uncertainty bounds, for any watershed, storm type and duration out to 1 in 1,000,000 years for ensuring ultimate safe operation and design of high-impact infrastructure against the most extreme floods possible.

An example of a 3-day basin average precipitation, including the upper and lower confidence limits, frequency plot. Our robust statistical processes allow estimation of 1 in 1 million year events.

Isopluvial map of 24-hour precipitation with an average recurrence interval of 100 years in the state of Wyoming.

Regional Frequency Analysis Approach

We follow the following standard-of-practice approach to a regional frequency analysis:

  1. Assembly and quality-checking of annual maxima datasets, including delineating analyses for different storm types
  2. Analyses of the seasonality of storms for use in hydrologic modeling
  3. Delineation and verification of climatic regions that are homogeneous with respect to extreme precipitation
  4. Analysis of the spatial behavior of the station at-site means and regional L-moment ratios L-Cv and L-Skewness for use in spatial mapping of precipitation AEPs
  5. Identification of the regional probability distribution for computing precipitation AEPs
  6. Computation of Equivalent Independent Record Length (EIRL) for use in estimating the effective independent size of the regional dataset. This information is used in characterizing the uncertainty of L-moment ratios and distribution parameters and for computing uncertainty bounds for PF estimates
  7. Production of gridded datasets of precipitation for selected AEPs in the range from the median to 1E-9
  8. Conduct uncertainty analyses and develop templates for the mean frequency curve (best-estimate) and uncertainty bounds for representative locations. The uncertainty templates would be scalable/applicable to all locations in the study area
  9. Complete various precipitation-related gridded datasets and other deliverables, such as temporal distribution templates, needed to support products and applications needed by the client. This may include a graphical user interface for accessing the result.

Completed Project Profiles

All-Season 6- and 24-hour Precipitation in Texas - 2014-2015

MetStat produced gridded estimates for 2-year through 1,000-year recurrence intervals to support probable maximum precipitation estimation.  This included collecting and quality controlling precipitation annual maximum series for 6-hour and 24-hour data; creating statistically homogeneous regions across the state of Texas in climates ranging from arid inland to humid along the coast; and conducting precipitation frequency analyses using a regional L-moment approach.


The 100-year rainfall values for the 24-hour duration over Texas and adjacent regions.

Santa Clara, San Mateo, and Alameda County, CA Frequency Analysis - 2015-2016

MetStat built upon existing precipitation frequency studies and incorporated other local data and alternative approaches to provide all-season precipitation frequency estimates to the Counties for durations 15-minutes through 3-days and recurrence intervals of 1-year through 1,000-years with accompanying temporal distributions for durations 6-, 24- and 72-hours.  Stakeholders were actively engaged throughout regarding data quality and local climate concerns to provide the best possible results.  The approach and resulting precipitation frequency estimates and 90% confidence limits were compared with estimates previously published in other studies, such as NOAA Atlas 14.

The 100-year rainfall values at the 24-hour duration for the several counties in the Bay region of central California.

Duke Energy Local Intense Precipitation Analysis

Together with MGS Engineering Consultants, MetStat preformed a Local Intense Precipitation (LIP)  analyses for a Duke Energy-owned Nuclear Station.  According to the Nuclear Regulatory Commission (NRC), a LIP is a “hypothetical locally heavy rainfall event that is used to design flood protection features and/or procedures. LIP is typically assumed to be equivalent to the local probable maximum precipitation (PMP) derived from National Weather Service (NWS) Hydrometeorology Reports (HMRs), from a site-specific PMP study” or a precipitation frequency analysis.  In some locations of the U.S., rainfall in excess of 19 inches in 1-hour (over one square mile) are estimated from the HMRs. In our study, we leveraged storm analyses and results from nearby precipitation frequency studies to ascertain the annual exceedance probability of the LIP. We also provided temporal distributions (shown below) of extreme 1-hour events for hydrologic modeling of the cooling pond. This helped Duke Energy evaluate their flood impacts and risk on required structures, systems, and components (SSC’s).  In the end, our analysis helped eliminate an NRC-issued red violation based the Significance Determination Process (SDP).

Example high temporal resolution analysis of a local intense storm.

Friant Watershed Basin-Average Precipitation Frequency

A 72-hour basin-average precipitation-frequency relationship for the Friant watershed is needed for stochastic flood modeling of inflows to Friant Dam and dams operated by Southern California Edison in the Big Creek System of the Upper San Joaquin River basin. A regional precipitation-frequency analysis using L-moments was conducted for a study area consisting of the west face of the Sierra Mountains and adjacent lowland areas and for the east face of the Sierra Mountains extending from near Bakersfield, CA to near Mt. Shasta, CA.

Sixteen large storm events were identified in the historical record which produced noteworthy 72-hour precipitation totals over the Friant watershed. Isopercental analysis methods were used to develop the spatial distribution of 72-hour precipitation over the Friant watershed. Regression methods were used to establish a relationship between 72-hour point precipitation within the watershed and 72-hour 1,660-mi2 basin-average precipitation for the Friant watershed. Monte Carlo methods were used to develop the 72-hour basin-average precipitation-frequency relationship for the Friant watershed based on the findings of the regional precipitation-frequency analysis and the relationship between 72-hour point precipitation within the Friant watershed and 72-hour basin-average precipitation for the Friant watershed. Uncertainty analyses were conducted for the parameters used to derive the 72-hour basin-average precipitation-frequency analysis which allowed development of uncertainty bounds for the best-estimate 72-hour basin-average precipitation-frequency relationship for the Friant watershed.

The 72-hour basin-average value of Probable Maximum Precipitation (PMP) of 27.2-inches obtained from National Weather Service Hydrometeorological Report 59 for the Friant watershed is estimated to have an annual exceedance probability of 2 x10-5 based on the 72-hour basin-average precipitation-frequency relationship developed for the Friant watershed.

72-hour watershed-mean precipitation frequency curves for Friant Dam, CA.

Contributions to NOAA Atlas 14 Precipitation Frequency Estimates

For over a decade (1998-2013), Tye Parzybok and Debbie Martin of MetStat® played key roles in the development of NOAA Atlas 14, including the original design, development and maintenance of the Precipitation Frequency Data Server (PFDS).  We contributed to the completion of nine volumes of NOAA Atlas 14 for project areas covering a range of climates across the United States and affiliated territories: semiarid southwest U.S., Ohio River Basin and surrounding states, Puerto Rico and the U.S. Virgin Islands, Hawaii, selected Pacific Islands, California, Alaska, Midwestern U.S. and Southeastern U.S. The Atlas contains precipitation frequency estimates with 90% confidence intervals for durations 5-minutes through 60-days for average recurrence intervals of 1-year to 1,000-years along. Through the course of development, data from over 41,000 stations were collected and quality controlled from various sources. Precipitation data were regionalized using various climatological and geographical characteristics and also using a “region-of-influence” approach. L-moments were used to analyze annual maxima data and develop point precipitation-frequency estimates and IDF curves. Other statistical analyses were conducted including temporal distributions of heavy precipitation, trends in mean and variance of annual maximum series data and seasonality of heavy precipitation. Contributions to documentation included internal summaries of technical discussions, on-line Quarterly Progress Reports and final published documents for nine Volumes of NOAA Atlas 14.

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