Development of Regression Equations for the Estimation of the Magnitude and Frequency of Floods at Rural, Unregulated Gaged and Ungaged Streams in Puerto Rico Through Water Year 2017

Scientific Investigations Report 2021-5062
By: , and 



The methods of computation and estimates of the magnitude of flood flows were updated for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent chance exceedance levels for 91 streamgages on the main island of Puerto Rico by using annual peak-flow data through 2017. Since the previous flood frequency study in 1994, the U.S. Geological Survey has collected additional peak flows at additional streamgages, and Puerto Rico has experienced numerous flood events. This updated study was performed using longer annual peak-flow datasets from more stations to provide more representative equations to predict flood flows. Screening criteria for these streamgages included 10 or more years of annual peak-flow data, unregulated flow, and less than 10 percent impervious drainage area.

The magnitude and frequency of floods at selected streamgages in Puerto Rico were estimated using updated methods outlined in Bulletin 17C. The new procedures include a regional skew analysis that incorporates Bayesian regression techniques, the Expected Moments Algorithm to better represent missing record and estimate parameters of the log-Pearson Type III distribution, and the Multiple Grubbs-Beck test for low outlier detection.

Regional regression equations were developed to estimate peak-flow statistics at ungaged locations by using selected basin and climatic characteristics as explanatory variables. These variables were determined from digital spatial datasets and geographic information systems by using the most recent data available. Ordinary least-squares regression techniques were used to filter the basin characteristics and determine two separate regions, region 1 (west) and region 2 (east), based on residuals. A generalized least-squares procedure was used to account for cross-correlation of sites and develop the final set of equations that have drainage area as the only explanatory variable. The average standard errors of prediction ranged from 18.7 to 46.7 percent in region 1 and 33.4 to 57.6 percent in region 2 for all annual exceedance probabilities (AEPs) examined. The updated statistics showed a greater accuracy of prediction when compared to those from the previous study using drainage area as the only explanatory variable for all AEPs examined in region 1 and the 0.01 and 0.002 AEP flows for region 2. When compared to equations developed in the previous study that have drainage area, mean annual rainfall, and (or) depth-to-rock as explanatory variables, the updated statistics show a greater accuracy of prediction in region 1 at AEP flows of 0.02 and lower (that is, higher flows). Those developed for region 2 do not show a greater accuracy of prediction for any AEP flows when compared to the equations having multiple explanatory variables in the previous study.

The calculated regression equations, basin characteristics, and at-site statistics will be incorporated into the U.S. Geological Survey web application, StreamStats ( This application allows users to select a location on a stream, whether gaged or ungaged, to obtain estimates of basin characteristics and flow statistics.

Suggested Citation

Ryan, P.J., Gotvald, A.J., Hazelbaker, C.L., Veilleux, A.G., and Wagner, D.M., 2021, Development of regression equations for the estimation of the magnitude and frequency of floods at rural, unregulated gaged and ungaged streams in Puerto Rico through water year 2017: U.S. Geological Survey Scientific Investigations Report 2021–5062, 37 p.,

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Abstract
  • Introduction
  • Purpose and Scope
  • Data Compilation
  • Analysis of Flow at Gaged Locations
  • Estimating Flood Frequency Statistics at Ungaged Locations
  • General Guidelines for the Estimation of Magnitude and Frequency of Peak Flows
  • Summary
  • Acknowledgments
  • References Cited
  • Appendix 1. Streamgages Considered for Development of Regional Regression Equations in Puerto Rico and Details of At-Site Statistic Inputs
  • Appendix 2. Regional Skew Regression Analysis for Puerto Rico
  • Appendix 3. At-Site, Regression Equation, and Weighted Magnitude, Variance, and Prediction Intervals of Annual Exceedance Probability Floods for Select Unregulated Streamgages in Puerto Rico
Publication type Report
Publication Subtype USGS Numbered Series
Title Development of regression equations for the estimation of the magnitude and frequency of floods at rural, unregulated gaged and ungaged streams in Puerto Rico through water year 2017
Series title Scientific Investigations Report
Series number 2021-5062
DOI 10.3133/sir20215062
Year Published 2021
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) South Atlantic Water Science Center, Caribbean-Florida Water Science Center
Description Report: v, 37 p.; Appendix Tables: 3; Data Release
Country United States
Other Geospatial Puerto Rico
Online Only (Y/N) Y
Additional Online Files (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details