Water Resources of the United States

The following documentation was taken from:

U.S. Geological Survey Water-Resources Investigations Report 94-4002:*
Nationwide summary of U.S. Geological Survey regional regression equations for
estimating magnitude and frequency of floods for ungaged sites, 1993*

## STATEWIDE RURAL

### Summary

Montana is divided into eight hydrologic regions (fig. 1). The
regression equations developed for these regions are for
estimating peak discharges (QT) having recurrence intervals T
that range from 2 to 500 years. The explanatory basin variables
used in the equations are drainage area (A), in square miles;
mean annual precipitation (P), in inches; basin high elevation
index (HE+10), which is the percentage of the total basin area
above 6,000 feet, plus 10; and mean basin elevation (E), in feet,
divided by 1000 (E/1000). The constant 10 is added to HE and E is
divided by 1000 in the computer application of the regression
equation. The user should enter the actual values of HE and E.
The variable P is taken from a map developed by the U.S. Soil
Conservation Service (1980). The other variables can be measured
from topographic maps. The regression equations were developed
from peak-discharge records available as of 1988 for 476 stations
in Montana and 46 stations in adjacent states and Canada. The
regression equations apply to unregulated streams having a
drainage area ranging from 0.04 to 2,554 square miles, but are
not valid where unique topographic or geologic features affect
floods. The standard errors of prediction of the equations range
from 22 to 128 percent. The report by Omang (1992) includes
graphs of flood characteristics along seven major streams, and a
table showing basin and flood characteristics and maximum floods
of record at gaging stations.

### Procedure

Topographic maps, the hydrologic regions map (fig. 1), the
mean annual precipitation map in U.S. Soil Conservation Service
(1980), and the following equations are used to estimate the
needed peak discharges QT, in cubic feet per second, having
selected recurrence intervals T.

### Northwest-Foothills Region

### Northeast Plains Region

### East-Central Plains Region

### Southeast Plains Region

### West Region

### Northwest Region

### Southwest Region

### Upper Yellowstone-Central Mountain Region

### Reference

Omang, R.J., 1992, Analysis of the
magnitude and frequency of floods and the peak-flow gaging
network in Montana: U.S. Geological Survey Water-Resources
Investigations Report 92-4048, 70 p.

Figure 1. Flood-frequency region map for Montana. (PostScript file of Figure 1.)