Statistical Summaries of Streamflow in Montana and Adjacent Areas, Water Years 1900 through 2002 By Peter M. McCarthy Abstract economical design of highway bridges, culverts, dams, levees, and other structures on or near streams. The U.S. Geological Survey (USGS) has previously pub- In response to the need to have more current information lished reports that describe and document streamflow character- about streamflow characteristics in Montana, the U.S. Geologi- istics at streamflow-gaging stations in Montana (Shields and cal Survey, in cooperation with the Montana Department of White, 1981; Waltemeyer and Shields, 1982; and Omang, Environmental Quality, Confederated Salish and Kootenai 1984). Two of these reports were based on data through 1979, Tribes, and Bureau of Land Management, conducted a study to and one used data through 1982. Since the completion of these analyze streamflow data. Updated statistical summaries of reports, nearly 20 years of additional data have become avail- streamflow characteristics are presented for 286 streamflow- able, and many new gages have been installed which now have gaging sites in Montana and adjacent areas having 10 or more 10 or more years of streamflow records. In response to the need years of record for water years 1900 through 2002. Data to have more current information about streamflow characteris- include the magnitude and probability of annual low and high tics in Montana, the USGS, in cooperation with the Montana flow, the magnitude and probability of low flow for three sea - Department of Environmental Quality, Confederated Salish and sons (March-June, July-October, and November-February), Kootenai Tribes, and Bureau of Land Management, conducted flow duration of the daily mean discharge, and the monthly and a study to analyze streamflow data from 286 sites having at least annual mean discharges. For streamflow-gaging stations where 10 years of streamflow record. 20 percent or more of the contributing drainage basin is affected by dams or other large-scale human modification, streamflow is considered regulated. Separate streamflow characteristics are Purpose and Scope presented for the unregulated and regulated periods of record for sites with sufficient data. The purpose of this report is to provide statistical summa- ries of streamflow characteristics at selected sites in Montana and adjacent areas for water years 1900 through 2002. Data Introduction include the magnitude and probability of annual low and high flow, the magnitude and probability of low flow for three sea- sons (March-June, July-October, and November-February), Information about streamflow characteristics is essential flow duration of the daily mean discharge, and the monthly and for development and management of surface-water resources. annual mean discharges. For streamflow-gaging stations where Water and land-use managers, planners, administrators, 20 percent or more of the contributing drainage basin is affected builders, engineers, recreationists, and the general public use by dams or other large-scale human modification, streamflow is information on all aspects of streamflow to evaluate various considered regulated. Separate streamflow-characteristics data water conditions and land-use alternatives. are presented for the unregulated and regulated periods of Annual low-flow and seasonal streamflow characteristics record for sites with sufficient data. and annual high-flow streamflow characteristics are particu- larly important for characterizing streamflow variability. Low- flow frequency data for annual and seasonal periods indicate Site Selection how frequently small values of discharge might occur and are used for assessing the capability of streams to receive and The sites selected for analysis are shown in figure 1 and assimilate treated wastewater, developing wastewater permits, described in table 1. A total of 286 streamflow-gaging stations determining total maximum daily loads of streams, and assess- were selected—269 of these stations are in Montana, 3 are at or ing aquatic habitat. Annual high-flow frequency data, in con- near the international boundary between the United States and junction with flood-frequency data (Parrett and Johnson, 2004), Canada, 2 are in Alberta, 2 are in British Columbia, 1 is in indicate how frequently large values of discharge might occur Idaho, and 9 are in Yellowstone National Park, Wyoming. Of and are useful for effective flood planning and for safe and the 286 sites, data for 224 stations were analyzed for periods of 2 Statistical Summaries of Streamflow in Montana and Adjacent Areas, Water Years 1900 through 2002 unregulated flow only, data for 47 stations were analyzed for are developed from annual series of the lowest mean discharges periods of regulated flow only, and data for 15 stations were for each of the spring (March through June), summer (July analyzed for separate periods of unregulated and regulated flow through September), and winter (October through February) (fig. 1). For clarity in table 1 and figure 1, stations were seasons for specified consecutive n-day periods within a cli- assigned site numbers 1 through 286. The period of record by matic year. The periods selected for spring, summer, and winter type of streamflow condition is listed in table 1. Of the 224 sites were based on consultations with the Montana Department of where data were analyzed for periods of unregulated flow only, Environmental Quality (Tom Reid, Montana Department of 8 stations were analyzed for periods before regulation only, and Environmental Quality, oral commun., 2002) and reflect typical the remaining 216 stations were analyzed for the entire period runoff and irrigation patterns in Montana. of record for unregulated flows. The Pearson Type III probability distribution was used to The statistical summaries provided for periods of unregu- estimate annual and seasonal low-flow frequency data (U.S. lated flow might differ from summaries provided for periods of Geological Survey, 2002b). The Pearson Type III distribution regulated flow. Typically these differences are the result of is a three-parameter distribution, commonly applied to the base changes in regulation. However, differences in statistical sum- 10 logarithms of streamflow data, that requires estimates of the maries also might be the result of different climatic conditions logarithms of the population mean, the standard deviation, and rather than difference in regulation. the skew coefficient to determine streamflow magnitude for various non-exceedance or exceedance probabilities. For low- flow frequency, the population values are assumed to be equal to the values computed from the station record, and streamflow Methods of Creating the Statistical magnitudes are determined for non-exceedance probabilities. Summaries The annual low-flow frequency data indicate the lowest mean discharges for consecutive periods of 1, 3, 7, 14, 30, 60, 90, 120, and 183 days and for non-exceedance probabilities of The tables of statistical summaries of streamflow are pre- 50, 20, 10, 5, 2, and 1 percent. The non-exceedance probability ceded by a station description which typically includes station (in decimal form before conversion to percent) associated with location, drainage area, period of record (by water years or by a low flow is the reciprocal of the recurrence interval, in years. month and year), revised records, gage information, and The seasonal low-flow frequency data indicate lowest mean remarks. The period of record included in the station descrip- discharges for consecutive periods of 1, 3, 7, 14, and 30 days for tions might not include all years in which data were recorded at non-exceedance probabilities of 50, 20, 10, 5, 2, and 1 percent. the station, and thus, might not coincide with the period of Each value of discharge in the annual and seasonal low- record used for analysis (table 1). Information about the num- flow tables is a mean low flow within the year or season for a ber of years, seasons, or months used for analysis are included consecutive n-day period that can be expected to be lower, on in the table headings. Remarks include information on the his- average, once in any specified recurrence interval (every y tory of regulating structures, if any, and comments on the other years). Similarly, each value of discharge in the low-flow factors that may affect flow. Remarks are based on information tables has a specified (x-percent) non-exceedance probability available at the time the stations were in operation, and thus, that, in any given year, a smaller value n-day mean low-flow might not represent streamflow conditions in 2002. However, value will occur. For example, the low-flow value for a consec- the latitude and longitude for stations that were discontinued utive 7-day period and the 2-year recurrence interval can be before about 1960 have been updated (2004). expected to be lower, on average, once every 2 years. Similarly, Daily mean streamflow values for each station were a low flow for a consecutive 7-day period and 50-percent non- retrieved using the computer program Automated Data Process- exceedance probability has a 50-percent chance of being lower ing System (ADAPS) (U. S. Geological Survey, 2003) and pro- in any given year. cessed using the computer program Input and Output for Water- For any n-day period, discharges decrease with increasing shed Data Management (IOWDM) (U.S. Geological Survey, recurrence interval and decreasing non-exceedance probability. 2002a). High- and low-flow frequency data, monthly and Conversely, for any given recurrence interval or non-exceed- annual-flow characteristics, and flow-duration data were then ance probability, discharge increases with increasing n-day computed using the computer program Surface-Water Statistics periods. Seasonal and annual low-flow frequency data are only (SWSTAT) (U.S. Geological Survey, 2000b). reported in the tables for recurrence intervals of twice the period of record or less (Parrett, 1997). For example, if the period of Annual and Seasonal Low-Flow Frequencies record is 10 years, only low-flow data for recurrence intervals of 20 years or less were presented.