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Logistics Regression

A Logistic Regression Equation for Estimating the Probability of a Stream Flowing Perennially in Massachusetts

Water-Resources Investigations Report 02-4043
By Gardner C. Bent and Stacey A. Archfield

ABSTRACT

A logistic regression equation was developed for estimating the probability of a stream flowing perennially at a specific site in Massachusetts. The equation provides city and town conservation commissions and the Massachusetts Department of Environmental Protection with an additional method for assessing whether streams are perennial or intermittent at a specific site in Massachusetts. This information is needed to assist these environmental agencies, who administer the Commonwealth of Massachusetts Rivers Protection Act of 1996, which establishes a 200-foot-wide protected riverfront area extending along the length of each side of the stream from the mean annual high-water line along each side of perennial streams, with exceptions in some urban areas. The equation was developed by relating the verified perennial or intermittent status of a stream site to selected basin characteristics of naturally flowing streams (no regulation by dams, surface-water withdrawals, ground-water withdrawals, diversion, waste-water discharge, and so forth) in Massachusetts. Stream sites used in the analysis were identified as perennial or intermittent on the basis of review of measured streamflow at sites throughout Massachusetts and on visual observation at sites in the South Coastal Basin, southeastern Massachusetts. Measured or observed zero flow(s) during months of extended drought as defined by the 310 Code of Massachusetts Regulations (CMR) 10.58(2)(a) were not considered when designating the perennial or intermittent status of a stream site. The database used to develop the equation included a total of 305 stream sites (84 intermittent- and 89 perennial-stream sites in the State, and 50 intermittent- and 82 perennial-stream sites in the South Coastal Basin). Stream sites included in the database had drainage areas that ranged from 0.14 to 8.94 square miles in the State and from 0.02 to 7.00 square miles in the South Coastal Basin.
Results of the logistic regression analysis indicate that the probability of a stream flowing perennially at a specific site in Massachusetts can be estimated as a function of (1) drainage area (cube root), (2) drainage density, (3) areal percentage of stratified-drift deposits (square root), (4) mean basin slope, and (5) location in the South Coastal Basin or the remainder of the State. Although the equation developed provides an objective means for estimating the probability of a stream flowing perennially at a specific site, the reliability of the equation is constrained by the data used to develop the equation. The equation may not be reliable for (1) drainage areas less than 0.14 square mile in the State or less than 0.02 square mile in the South Coastal Basin, (2) streams with losing reaches, or (3) streams draining the southern part of the South Coastal Basin and the eastern part of the Buzzards Bay Basin and the entire area of Cape Cod and the Islands Basins.

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