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Equations using basin characteristics were developed for estimating mean annual runoff at ungaged streams in central and eastern Montana. The study area was divided into three regions and separate multiple-regression equations were developed for each region. Drainage area was determined to be the most significant basin characteristic in all three regions. The standard error of estimate was 31 percent in Region 1 based on data from 17 stations. The standard error of estimate ranged from 64 to 51 percent in Region 2 based on 27 stations and ranged from 103 to 37 percent in Region 3 based on 29 stations; the standard error decreased as more independent variables were added to the estimating equation. Data from stations with less than 10 years of record were extended based on correlation with stations having long-term record. Coefficients of determination (R^) and equivalent years of record were determined and used as a basis for adjusting the record. INTRODUCTION The purpose of this report is to describe a method for estimating mean annual runoff of ungaged streams in central and eastern Montana. The estimating equations were developed by relating physiographic and climatic characteristics of the drainage basin to mean annual runoff. The estimating relations of this report are based on a current (1982) data base and are considered to be more reliable than a previous report by Boner and Buswell (1970) because of more extensive streamflow-gaging records and improved analytical procedures. The report is based on basin characteristics and data for 73 streamflow-gaging stations on unregulated streams having at least 5 years of streamflow record. Some streamflow-gaging sites having record in excess of 5 years were excluded from the analysis because the data were considered to be unreliable or unrepresentative of the region owing to stock dams, surface geology, or bad record. Recent reports by Parrett and others (1983) and Omang and others (1983) provide methods for estimating mean annual runoff based on channel-geometry measurements. The report by Boner and Buswell is the only previous report that provides estimating equations for mean annual runoff based on basin characteristics. A report by Ferreira (1981) includes a mean annual runoff map for selected drainage basins in the coal area of southeastern Montana. The estimating equations presented herein will be useful to land-use managers, water-rights administrators, designers, and others who need to estimate streamflow on an annual basis. This report was prepared in cooperation with the U.S. Bureau of Land Management. GENERAL DESCRIPTION OF THE AREA Montana is an area of 147,100 square miles having widely varying geographic and climatic conditions. East of the Rocky Mountains, in a broad belt extending generally north-south through the central part of the State, plains are interrupted by isolated mountain ranges. East of the isolated mountains the land is generally flat or rolling prairie with deeply incised larger streams. The location of the area studied is shown in figure 1. The climate of central and eastern Montana is affected significantly by the topography. Annual precipitation in the mountainous areas ranges from 20 to 40 inches and much of this occurs as snow. Most of the yearly runoff from the mountainous areas results from snowmelt. In the eastern plains, precipitation ranges from 12 to 16 inches and is more variable, more intense, and generally less, on an annual basis, than in the mountains. Runoff generally results from snowmelt during the spring, thunderstorms during the summer, and occasionally a combination of late snowmelt and rain. Because of the diverse topography and climate, the area was divided into three regions for the mean annual runoff analysis. These regions are illustrated in figure 1. Region 1 is predominantly flat plains north of the Missouri River. Runoff is variable, with most smaller streams being ephemeral or intermittent. Runoff is produced by snowmelt and rainfall. Region 2 is also mostly flat plains, but runoff tends to be more variable than in Region 1. The area north of the Yellowstone River is the area most affected by intense summer thunderstorms. The area south of the Yellowstone River has intense thunderstorms, but they generally are not as prevalent as in the area north of the Yellowstone River. Region 3 contains mountainous areas and is generally forested. Annual precipitation results in accumulated snowpack, and runoff occurs primarily as a result of snowmelt. DATA USED Streamflow data Streamflow data from 73 streamflow-gaging stations with 5 or more years of continuous record were used in this study. Data from stations with less than 10 years of record were then extended based on correlation with stations having long-term record. Each correlation of short-term versus long-term records was examined closely to make sure that spurious correlation did not exist. These stations then were used to develop the final regression equations. Data through the 1982 water year were used in the analysis. Gaging stations where the flows are substantially affected by regulation or diversion were generally not used in the analysis. The location and station number of all gaging stations from which data were used are shown in figure 1. The mean annual runoff for each gaging station is listed in table 4 (at back of report). The mean annual runoff is the average daily discharge, in cubic feet per second, for the period of record. Basin-characteristics data Basin characteristics tested for inclusion as independent variables in the development of estimating equations for mean annual runoff included: A drainage area, in square miles; p mean annual precipitation, in inches; F+10 forest cover index, in percent; B/1000 mean basin elevation index, in feet above sea level; #£+10 basin high-elevation index, in percent; JarH-10 mean January minimum temperature index, in degrees Fahrenheit; L main channel length, in miles; S main channel slope, in feet per mile; J24 precipitation intensity index for a storm of 24 hours duration having an exceedance probability of 50 percent, in inches per hour; and 5_£ soil-infiltration index in inches. Basin characteristics found to be important in the various estimating equations were drainage area, mean annual precipitation, forest cover index, and main channel slope. Drainage area is expressed in square miles and is determined for ungaged sites by planimetering the outline of the drainage basin on the best scale topographic map available. Mean annual precipitation is the basin average, in inches, determined from the maps contained in the report of the U.S. Soil Conservation Service (1977). The forest cover index is the percentage of the drainage basin covered by forest (F) plus 10; it is determined by planimetering the forest (green) areas shown on the best scale U.S. Geological Survey topographic maps, multiplying by 100, dividing the result by the total basin drainage area, and adding a value of 10. The value 10 is added to the percentage to ensure that values close to zero do not occur. Main channel slope, in feet per mile, is determined from the main channel elevations determined at points 10 and 85 percent of the main channel length. The difference in elevation at the two points is divided by 75 percent of the main channel length to obtain main channel slope. The values for each gaging station used in the analysis are listed in table 4 (at back of report). METHOD OF ANALYSIS Extension of streamflow records The mean annual runoff record for gaging stations with less than 10 years of record was extended based on correlation between the record at the site of interest and the record at a nearby hydrologically similar long-term gaging station. The extension was done using simple linear regression (Riggs, 1968). Correlation coefficients (r) were computed for each set of stations that were correlated. If the coefficient of determination (R.2) was greater than 0.60, the station was considered to be a potential correlating station. These stations then were used to develop the final regression equations.

A method for estimating mean annual runoff of ungaged streams based on basin characteristics in central and eastern Montana