Predicting surf zone injuries along the Delaware coast using a Bayesian network

  • Matthew B. DoelpEmail author
  • Jack A. Puleo
  • Nathaniel G. Plant
Original Paper


More than 2000 surf zone injury (SZI) events, including 196 spinal injuries and 6 fatalities, were recorded at the five most populated beaches along the 25 miles of Atlantic-fronting Delaware coast from 2010 through 2017. The episodic nature of SZI indicates the importance of linking the environmental conditions and human behavior in the surf zone to predict days with high injury rates. Higher order statistics are necessary to effectively consider all associated factors related to SZI. Two unique Bayesian networks were constructed to model SZI and predict changes in injury rate (proportion of injuries to bathers) and injury likelihood (probability of at least one injury occurrence) on an hourly basis. The models incorporate environmental data collected by weather stations, wave gauges, and researcher personnel on the beach as prior (e.g., historic) information to infer relationships between provided parameters. Sensitivity analysis determined the most influential parameters related to injury rates were significant wave height, foreshore slope, and water temperature. Log-likelihood ratio scores indicate the network predicts SZI likelihood during any specified hour with more skill than prior predictions with the best performing model improving prediction 69.1% of the time (log-likelihood ratio = 69.1%). Issues persist with predicting SZI that have a log-likelihood ratio ≪ − 1 (< 5% of 2017 injuries) and occur in conditions different than when most other SZI occur. Better understanding of SZI will improve awareness techniques to educate beachgoers and assist beach patrol decision making during high-risk conditions.


Surf zone injuries Hazard Delaware Beach Bayesian network 



This research was supported by National Sea Grant College Program of the US Department of Commerce’s National Oceanic and Atmospheric Administration (Delaware Sea Grant; Grant No. NA14OAR4170087) and the University of Delaware. The authors would like to acknowledge local town managers, Delaware Beach Patrols, and those individuals that assisted with counting beach populations. The authors also express their gratitude to the two anonymous reviewers and Dr. Sara Ziegler for improving the clarity of this manuscript.

Data availability

Data are available upon request from the authors at


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Center for Applied Coastal ResearchUniversity of DelawareNewarkUSA
  2. 2.U.S. Geological SurveySt. PetersburgUSA

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