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Evaluation of Drainage-Area Ratio Method Used to Estimate Streamflow for the Red River of the North Basin, North Dakota and Minnesota

Scientific Investigations Report 2005-5017—ONLINE ONLY


By Douglas G. Emerson, Aldo V. Vecchia, and Ann L. Dahl


In cooperation with the Bureau of Reclamation


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The drainage-area ratio method commonly is used to estimate streamflow for sites where no streamflow data were collected. To evaluate the validity of the drainage-area ratio method and to determine if an improved method could be developed to estimate streamflow, a multiple-regression technique was used to determine if drainage area, main channel slope, and precipitation were significant variables for estimating streamflow in the Red River of the North Basin. A separate regression analysis was performed for streamflow for each of three seasons-- winter, spring, and summer. Drainage area and summer precipitation were the most significant variables. However, the regression equations generally overestimated streamflows for North Dakota stations and underestimated streamflows for Minnesota stations. To correct the bias in the residuals for the two groups of stations, indicator variables were included to allow both the intercept and the coefficient for the logarithm of drainage area to depend on the group. Drainage area was the only significant variable in the revised regression equations. The exponents for the drainage-area ratio were 0.85 for the winter season, 0.91 for the spring season, and 1.02 for the summer season.


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Table of Contents



Description of the Red River of the North Basin

Drainage-basin characteristics

Evaluation of drainage-area ratio method





  1. Map showing locations of streamflow-gaging stations used in study

  2. Isohyetal map of mean annual winter/spring (January, February, March, April, May, November, and December) precipitation for 1971 through 2000

  3. Isohyetal map of mean annual summer (June, July, August, September, and October) precipitation for 1971 through 2000

  4. Graph showing recorded spring streamflow and fitted spring streamflow computed from the regression model with the logarithm of drainage area and the logarithm of winter/spring precipitation as explanatory variables

  5. Graphs showing regression lines for winter, spring, and summer streamflows computed from the revised regression model with drainage area as the explanatory variable


  1. Basin characteristics for 27 streamflow-gaging stations in the Red River of the North Basin, North Dakota and Minnesota

  2. Regression equations used to estimate log-transformed seasonal streamflow for the Red River of the North Basin, North Dakota and Minnesota


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