Magnitude and frequency of floods on Kauaʻi, Oʻahu, Molokaʻi, Maui, and Hawaiʻi, State of Hawaiʻi, based on data through water year 2020

Accurate estimates of flood magnitude and frequency are needed to (1) optimize the design and location of infrastructure, including dams, culverts, bridges, industrial buildings, and highways, and (2) inform flood-zoning and flood-insurance studies. The U.S. Geological Survey (USGS), in cooperation with the State of Hawaiʻi Department of Transportation, estimated flood magnitudes for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (AEP) for unregulated streamgages in Kauaʻi, Oʻahu, Molokaʻi, Maui, and Hawaiʻi, State of Hawaiʻi, using data through water year 2020. Regression equations were developed to estimate flood magnitude and associated frequency at ungaged streams. This study improves upon a previous USGS flood-frequency report (Oki and others, 2010) by including more peak-flow data, implementing new statistical methods in flood-frequency analysis, and using updated techniques to estimate the regional-skewness coefficient (regional skew).

Flood magnitude and frequency at 238 streamgages were estimated—following national guidelines established in Bulletin 17C (England and others, 2019)—by fitting annual peak-flow data to the Log-Pearson Type III distribution using the expected moments algorithm and the PeakFQ flood-frequency software. Potentially influential low outliers in the data were identified and removed using the Multiple Grubbs-Beck Test. An updated regional skew for Hawaiʻi was estimated using the Bayesian weighted least squares/Bayesian generalized least squares method. The updated regional skew employs a constant model for the five islands in the study area and has a value of −0.157 (mean square error of 0.212).

Multiple linear regression techniques were used to develop regression equations that relate basin and climatic characteristics to peak flows at streamgages. The regression equations can be applied to estimate flood magnitude and frequency at ungaged sites. The study area was split into 10 regions—2 regions per island, generally following a leeward/windward division—containing from 9 to 49 streamgages each. The final regression equations for each region were determined with generalized least-squares analysis using the USGS weighted-multiple-linear regression (WREG) program. The standard error of prediction at the 1-percent AEP for the regression equations ranged from 18 to 164 percent; the pseudo coefficient of determination (pseudo-R2) at the 1-percent AEP ranged from 46 to 100 percent. The regression equations performed well for all regions except leeward Molokaʻi and southern Island of Hawaiʻi; for all other regions, the pseudo-R2 values ranged from about 75 to 100 percent. Compared to the regression equations developed by Oki and others (2010), the regression equations in this study generally showed modest improvements, although the magnitude of differences varied for each region.

Peak-flow estimates at the 238 streamgages included in this study are improved by weighting the at-site statistics computed with PeakFQ and the predicted flows based on the regression equations. Results of this study—including the final peak-flow estimates at streamgages and the regional regression equations—are implemented in the USGS StreamStats web application (U.S. Geological Survey, 2023, StreamStats: https://streamstats.usgs.gov/ss/). StreamStats provides a consistent approach for obtaining peak-flow estimates at streamgages and for applying the regional regression equations for estimating peak flows at ungaged locations.