Scientific Investigations Report 2009–5015

**U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2009–5015**

The USGS has developed a GIS-based map of the locations of streams in Idaho with perennial flow based on generalized least-squares (GLS) regression models of 7*Q*_{2} flows and continuous parameter estimation of 7*Q*_{2} at ungaged locations. A transition zone of plus or minus 1 standard error was modeled around the 7*Q*_{2} cutpoint of 0.1 ft^{3}/s to account for statistical, climatic, and hydrologic variability. Flow downstream of the transition zone is considered perennial, and flow upstream of the transition zone is considered intermittent.

The USGS operates a network of streamflow-gaging stations in Idaho that provides data for various purposes, and low-flow statistics can be calculated from the streamflow data collected at these locations. Because streamflow-gaging stations cannot be located at all sites where streamflow information is needed, other methods are used to estimate streamflow statistics for these ungaged sites. One of the most common methods is to develop regression equations that relate streamflow statistics to selected basin characteristics. With certain limitations, this allows for the estimation of streamflow statistics at ungaged stream locations throughout the State.

During the equation development process, the study area was divided into eight separate geographic regions of similar characteristics. Data from a total of 234 streamflow-gaging stations were included in the analysis. This included all streamflow-gaging stations in Idaho and those in adjacent States within an approximate 80-mi buffer surrounding Idaho with 10 or more years of record through water year 2003, which exhibited little or no sign of trends, and were unaffected by regulations, diversions, or both. More than 50 basin characteristics were obtained for each of the 234 streamflow-gaging stations included in the study. The basin characteristics were obtained using GIS techniques from digital datasets such as DEMs, precipitation grids, and land-use grids. Several basin characteristics were removed from consideration after a review of the correlation plots of the data. Generally, if two basin characteristics correlated well with each other, the characteristic least difficult to obtain was kept and the other was removed. Other characteristics were removed because of missing data or difficulty in obtaining the data.

Relevant low-flow frequency statistics (including 7*Q*_{2}) were computed for the 234 streamflow-gaging stations. Low-flow frequency statistics are determined using the annual minimum mean flows for any given number of days (N-day low flows) during an annual period. The mean flow for each N-day period throughout the annual period is computed, and the minimum value is selected. The series of annual minimum N-day values are then fit to a log-Pearson Type III distribution to determine the recurrence intervals. The annual period referred to as a climatic year (April 1 through March 31) is often used in low-flow analyses because the annual low-flow period in most parts of the country occurs during the late summer and autumn months. Use of the climatic year allows for inclusion of the entire low-flow period in the same year, whereas use of the traditional water year (October 1 through September 30) may artificially separate the low-flow period into two years.

Multiple linear regression techniques then were used to develop equations for each region that related each low-flow frequency statistic to one or more basin characteristics. A GLS technique that weights the station data to compensate for spatial correlation and differences in record length was used to obtain the equations. The analyses resulted in the development of equations to estimate low-flow frequency statistics for unregulated streams in each of the eight regions in the State. These equations are published and described in more detail in Hortness (2006).

The datasets used in this project primarily are derived from the 10-m resolution DEMs produced by the USGS and the 1:24,000-scale NHD. The source DEM was obtained from the 1/3-arc-second resolution National Elevation Dataset (NED) and was projected into the Idaho Transverse Mercator projection based on the North American Datum of 1983 for each 8-digit HUC in Idaho. The NHD vector streams were integrated into the raster NED data, using a process often referred to as stream burning (Saunders, 2000). This process uses the AGREE computer program developed by Hellweger and Maidment (1998). The AGREE program corrects for DEM flow path displacement errors when delineating catchments. The AGREE process and additional manipulation of NED DEM and NHD datasets are presented in more detail in Rea and Skinner (2009).

A continuous parameter grid of 10 by 10 m cells was established for the perennial streams map. In a continuous parameter grid, each cell contains the value of some parameter measured for the entire drainage area upstream of that cell. The flow-accumulation grid described by Jenson and Domingue (1988) is the most basic continuous parameter grid. Each cell in a flow-accumulation grid contains the number of cells upstream of that cell. The upstream drainage area may be determined by multiplying the number of cells by the area of a cell. This area should be adjusted by adding the area of the cell of interest because the flow accumulation grid does not include this cell.

Values of most basin characteristics, such as mean elevation, were assigned to every cell to create a “weight” grid. A flow accumulation function in ARC/INFO (Environmental Systems Research Institute, 1999) sums values from the weight grid for each cell and accumulates cell values as it moves downgradient. In contrast, if no weight grid is assigned, the flow accumulation function simply totals the number of upstream cells, a process called “unweighted flow accumulation.” The weighted flow accumulation value, divided by the unweighted flow accumulation value, gives the mean value of the basin characteristic in the weight grid upstream of any grid cell.

This concept may be used with continuous-value parameters, such as elevation or precipitation, and with categorical-value parameters. For example, using a grid containing 1 for every cell categorized as forested in a land-cover dataset, and 0 for every other cell, the fraction of the watershed area draining to a particular forested grid cell can be computed. The development of the continuous parameter grid is described in more detail in Rea and Skinner (2009).

Most basin characteristics can be calculated on a continuous basis for every grid cell using the method described in the previous section and in Rea and Skinner (2009). If all parameters of a regression equation can be computed in this manner, then the result of the regression equation also may be computed continuously for every grid cell; therefore, the equations developed by Hortness (2006) were used to compute preliminary estimates of the 7*Q*_{2} statistic for every grid cell in the study area. A map of streams with perennial flow then was developed by comparing these estimates to the state standard of intermittent flow as less than 0.1 ft^{3}/s. A transition zone also was modeled corresponding to flow estimates of 0.1 ft^{3}/s plus and minus one standard error. It should be noted that although standard error is valid only for the range of predictor variables, it was used to model the transition zone in the range of extrapolation because no other statistical measure was available. The transition zone represents the part of the stream that, given annual climate and hydrologic fluctuations as well as inherent statistical uncertainty, is assumed to contain the point at which a stream changes from perennial to intermittent. In other words, flow in reaches upstream of the top of the transition zone is considered intermittent, and flow in reaches downstream of the bottom of the transition zone is considered perennial. Within the transition zone, flow could be perennial or intermittent. The preliminary map generated some anomalous stream patterns that necessitated some revisions to the 7*Q*_{2} equations developed by Hortness (2006).