Peak Flow Regression Equations for Small Drainage Basins in Central and Eastern Montana

Accurate peak-flow rates are needed by the Montana Department of Transportation (MDT) to properly size culverts and bridges on highway stream crossings. For stream crossings with drainage areas less than one square mile, one of the current methods available for estimating peak-flow rates is the set of Nallick peak-flow regression equations in the MDT hydraulics manual (MDT, 2022). The Nallick regression equations as presented in MDT (2022) use drainage area, average annual precipitation, and 25-year 1-hour rainfall intensity to estimate peak streamflow for 2, 5, 10, 25, 50, and 100-year return intervals and are applicable to small drainage basins (less than 1 square mile) in the plains east of the Continental Divide. The equations were developed using data collected through 1988. Since 1988, more advanced methodologies have emerged for determining the three explanatory variables (drainage area, average annual precipitation, and 25-year 1-hour rainfall intensity) used in the equations. Furthermore, additional peak-flow data collected on small drainage basins and improved methods of peak-flow frequency analysis offer opportunities to improve the streamgage peak-flow frequency estimates used to develop the regression equations. Generalized least-squares (GLS) analysis and machine learning methods offer further potential to improve the mathematical development of the equations. Records in the Transportation Research Board (TRB) database have emphasized the need for accurate peak-flow information to use in hydrologic modeling and infrastructure design. MDT and the U.S. Geological Survey (USGS) have been addressing this deficiency in peak-flow information by maintaining a crest-stage gage (CSG) network in Montana that has been collecting peak-flow data since 1955 (Sando, 2021). CSGs are simple streamgages that only record the peak stage between visits to the gage. This CSG system is especially important for collecting data in small drainage basins that are often overlooked by continuous streamflow gages. Part of the goal of the CSG network is to collect data for developing peak-flow regression equations at ungaged sites. Peak-flow variability in Montana generally increases as drainage area decreases (Sando, 2021). This variability emphasizes the need for updated regression equations that can effectively predict peak-flow rates in smaller drainage basins. The work proposed in this project will produce updated regression equations to replace the Nallick peak-flow equations. Project tasks include camera monitoring on small streamgages, Lidar-derived basin delineations, calculation of basin characteristics, and peak-flow frequency analysis to supply the inputs needed for updated regression equations. The updated equations will be derived using generalized or weighted least squares methods and informed by exploratory machine learning analysis. By integrating advanced methods for estimating the explanatory variables and utilizing the extensive peak-flow data collected through the CSG network, this project has the potential to enhance the accuracy and reliability of peak-flow predictions for small drainage basins. Ultimately, this project aims to provide MDT with improved tools for infrastructure design, ensuring that stream crossings are appropriately sized to accommodate the peak-flows occurring in small drainage basins.

Language

• English

Project

• Status: Active
• Funding: $475,000.00
• Contract Numbers:

  25RSJFA046

• Sponsor Organizations:

  Montana Department of Transportation

  2701 Prospect Avenue
  P.O. Box 201001
  Helena, MT  United States  59620-1001
• Managing Organizations:

  Montana Department of Transportation

  2701 Prospect Avenue
  P.O. Box 201001
  Helena, MT  United States  59620-1001
• Project Managers:

  Nelson, Alexandra

• Performing Organizations:

  U.S. Geological Survey

  6480 Doubletree Ave.
  Columbus, OH  United States  43229-1111
• Start Date: 20251101
• Expected Completion Date: 20281231
• Actual Completion Date: 0

Subject/Index Terms

• TRT Terms: Bridges; Culverts; Measuring instruments; Regression analysis; Streamflow
• Geographic Terms: Montana
• Subject Areas: Highways; Hydraulics and Hydrology; Maintenance and Preservation;

Filing Info

• Accession Number: 01970348
• Record Type: Research project
• Source Agency: Montana Department of Transportation
• Contract Numbers: 25RSJFA046
• Files: RIP, STATEDOT
• Created Date: Nov 3 2025 11:55AM