# Obtaining Streamflow Statistics for Ungaged Sites

A basin delineation is needed before flow estimates can be obtained for an ungaged site. Refer to the Version 3 User Instructions or the Beta Version 4 User Instructions to determine how to obtain a basin delineation and get estimates of flow statistics for an ungaged site. The Estimate Flows Using Regression Equations tool, which provided estimates in StreamStats version 2 by measuring needed basin characteristics and solving USGS-developed regression equations is under development in beta version 4. The Estimate Flows Based on Similar Streamgaging Stations tool estimated streamflow statistics by applying the flows per unit area for streamflow statistics at a nearby gaging station to the drainage area for the ungaged site.

The below instructions and description of the output for an ungaged site pertain to StreamStats version 3. Outputs for ungaged sites from beta version 4 appear differently than those in the captured screen images from version 3, but the content is mostly the same, with the exception that outputs from beta version 4 include boxes at the top in which users can type a title and a message about the output, and a map of the delineated basin is included.

## Estimate Flows Using Regression Equations Tool Output

When the *Estimate Flows Using Regression Equations* tool is used, StreamStats first measures whatever basin or climatic characteristics are used as explanatory variables in the regression equations that are available for the selected location. StreamStats then uses the National Streamflow Statistics (NSS) program to solve the equations. The NSS report by Ries (2006) provides a general description of the development and application of regression equations. The NSS Web site contains links to all reports that contain regression equations included in the software. The reports are also listed on the StreamStats introductory Web page for each State. These reports describe how the equations were developed and their limitations. Users should read and understand the limitations described in these reports before attempting to use the *Estimate Flows Using Regression Equations* tool to obtain flow estimates for ungaged sites.

The output from the *Estimate Flows Using Regression Equations* tool appears in a pop-up Web browser window. At the top is a banner identifying the output as a product of the USGS StreamStats program. The title, "StreamStats Ungaged Site Report" is below the banner. Following the title are several lines of text that give the processing date, the name of the state in which the ungaged site is located, the total drainage area, and the latitude and longitude for the site. Below this information is a series of two or more tables, described below.

Most states have been subdivided into hydrologic regions based on similarity of climate and physical characteristics, and regression equations have been developed separately for each region. The ungaged site reports list only the basin characteristics that are used in the regression equations for any hydrologic regions in which the site has drainage area.

The reports will always include at least one pair of tables; one for basin characteristics and one for streamflow statistics. One pair of tables will be provided for peak-flow statistics and the basin characteristics needed to solve the equations for peak-flow statistics. Another pair of tables will be provided for all other types of statistics and the basin characteristics needed to solve the equations for those statistics. Tables of basin characteristics are always presented before the tables of streamflow statistics.

## Basin Characteristics Tables:

- The top line in the table identifies the type of streamflow statistics for which the basin characteristics were measured.
- If the drainage basin for the ungaged site is within two or more regions, header lines appear above the basin characteristics listed for each region. This line contains the percentage of the basin area that is within the region, the name of the region and the drainage area, in square miles, in the region.
- The Parameter column gives short names for the basin characteristics, with units of measure shown in parentheses.
- The Value column contains the measured values of the basin characteristics. When a selected site has drainage area in multiple regions, the values shown are for the entire drainage area, not just the specific region.
- The Min and Max columns contain the minimum and maximum values of the basin characteristics that were measured for the streamgages that were used to develop the regression equations. Estimates of streamflow statistics for sites with basin characteristics that are not within the given minimum and maximum values have errors that are of unknown magnitude.
- In the example above, the mean basin elevation computed for the site is lower than the minimum value shown for region 2. Because of this, the message “below min value 2966.3” is shown along with the value in the Value column in the table. In addition, the message “Warning: some parameters are outside the suggested range. Estimates will be extrapolations with unknown errors” appears below the table.

## Streamflow Statistics Tables:

- The top line in the table identifies the hydrologic region for the selected site. If more than one type of statistic is available in the region, header lines are provided in the table for each statistic type, followed by lines for each statistic. If the drainage area for the site encompasses more than one hydrologic region, separate tables are presented for each region.
- The Statistic column provides the names of the statistics. Definitions for all basin characteristics and streamflow statistics also can be found on the Streamflow Statistics page. Names given in the output table correspond to the StatLabel field on the Streamflow Statistics page.
- The Flow field contains the estimated streamflow statistics. The values usually are in units of cubic feet per second.
- The third column will contain either the average standard errors of estimate, named Standard Error, or the average standard errors of prediction, named Prediction Error. Both errors are given in percent. Because percentage errors are not normally distributed, negative percentage errors tend to be smaller than positive percentage errors.
- The average standard error of estimate measures the average variation between the regression estimates and estimates derived from the station data for those stations used to develop the regression equations. About two-thirds of the regression estimates for the gaging stations used in the regression analyses have errors less than the average standard error of estimate. About one-third of the estimates have errors larger than the average standard error of estimate.
- The average standard error of prediction measures the average accuracy of the regression equations when predicting values for ungaged sites, which is the condition under which regression equations are most often applied for StreamStats. The average standard error of prediction is usually a few percent larger than the average standard error of estimate. About two-thirds of the regression estimates for ungaged sites will have errors less than the given average standard errors of prediction, and about one-third of estimates will have errors larger than the given standard errors of prediction.
- The equivalent years of record are shown in the fourth column, if available. These values indicate the length of time that a streamgaging station would need to be operated at the ungaged site to obtain an estimate of the streamflow statistic that is equal in accuracy to the estimate provided by the regression equation.
- The fifth and sixth columns contain the minimum and maximum values of the 90-percent prediction interval, if available. Ungaged sites with the same basin characteristics as the user-selected site will have actual flows that are within the given minimum and maximum values 90 percent of the time.
- Values in the fourth through sixth columns are not available for some equations in some regions. Indicators of errors will not be shown for estimates in a region when the values for any of the basin characteristics are outside of the Min and Max values shown in the Basin Characteristics tables.

## Area-Averaged Streamflow Statistics Tables:

StreamStats provides area-averaged estimates of streamflow statistics when the drainage basin for an ungaged site is in more than one region. The area-averaged estimates will appear below the basin characteristics tables and above the tables of estimates for individual regions.

- The information shown in the area-averaged table is very similar to a normal streamflow statistics table.
- The estimates are obtained by multiplying the estimated flow for each region by the drainage area for each region, summing these values, and then dividing by the total drainage area. Prediction errors and equivalent years of record are computed by the same weighting method.
- Prediction errors and equivalent years of record will be provided for area-averaged estimates only if all regions have this information available.

## Obtaining Estimates for User-Selected Sites With Drainage Area in More Than One State

Flow estimates obtained from regression equations for watersheds that span state boundaries may give different results depending on which state’s equations are used. Each state’s regression equations typically are applicable only within the state for which the equations were developed. Ries (2006, p. 8) indicates that in cases where a delineated watershed has area in multiple states, flow estimates should be determined using the regression equations for each state, and then final estimates should be determined by weighting the separate sets of flow estimates according to the proportion of the drainage area that is in each state. However, because of programing and data limitations, StreamStats typically will only provide estimates using the regression equations for the state in which the selected site is located. In cases where StreamStats is available for each state, it may be possible to determine weighted estimates by use of the following process:

- Determine the state in which the site of interest is located, and using that state’s application, (a) select the site of interest, (b) delineate the drainage basin using the Watershed Delineation from a Point tool, (c) obtain flow estimates using the Estimate Flows Using Regression Equations tool, and (d) then save the output.
- Open the application for the upstream state, and then follow the same process as in step 1, except select the point for delineation just upstream from where the stream of interest crosses the state border.
- It will be necessary to adjust the estimates that were determined using the upstream state’s application to represent the full drainage area at the initial point of interest. Such adjustments may be possible by one of the following approaches:
- If the output from the downstream state’s application has provided all of the basin characteristics needed to solve the upstream state’s regression equations, then use the Edit Parameters and Recompute Flow tool for the upstream state’s application, changing the computed basin characteristics to be those from the output for the downstream state.
- If the output from the downstream state’s application has not provided all of the basin characteristics needed to solve the upstream state’s regression equations, then determine if the downstream state’s Basin Characteristics tool will provide the additional basin characteristics needed to solve the upstream states’ equations. If so, compute the additional basin characteristics using the downstream state’s application, and then use the Edit Parameters and Recompute Flow tool for the upstream state’s application, as described above.
- If not all of the basin characteristics needed to solve the regression equations for the upstream state are available from the downstream state’s application, and if the proportion of the drainage area that is in the downstream state is small, then it may be reasonable to use the values of some basin characteristics that were obtained from the upstream state’s application to determine the final weighted estimates. For example, if the upstream state’s application requires the percent forest, but the downstream state’s application does not provide it, then if the area in the downstream state is small and the percent forest within the downstream state appears similar to that for the upstream state, then when using the Edit Parameters and Recompute Flow tool for the upstream state, edit the drainage area to be that from the output for downstream state, but do not edit the percent forest before recomputing the flow estimates.
- If none of the above three conditions exists, then it will not be possible to weight the flow estimates from the two state applications.
- If it was possible to adjust the estimates that were determined using the upstream state’s application to represent the full drainage area at the initial point of interest, then manually weight the adjusted flow estimate from the upstream state’s application with those from the downstream state’s application according to the proportion of the total drainage area that is in each state. An example manual computation is provided by Ries (2006, p. 8).

**NOTICE:** Reports with regression equations for some states recommend the use of different weighting methods than those that are used in StreamStats, although the results usually are very similar. StreamStats users should refer to the individual reports to determine if different weighting methods should be used. In some cases, report authors have provided spreadsheets or programs in which the basin characteristics from StreamStats can be inserted and estimates can be obtained according to the methods that are described in those reports. Links to the applicable reports are provided on the StreamStats introductory page for each individual state.