Data Series 412

**U.S. GEOLOGICAL SURVEY
Data Series 412**

The methods used in this project consisted of the following steps:

- Development of 7
*Q*_{2}regression models, - Development of hydro-enforced DEMs,
- Computation of continuous parameter grids,
- Computation of continuous 7
*Q*_{2}estimates, and - Transfer of regression model results to NHD

Each step is described in detail in the following sections.

Regression models from Hortness (2006) were modified to enable extrapolation beyond the limits of available data from streamflow-gaging stations. The evaluation and comparisons of alternative regression models for 7*Q*_{2} is more completely described by Wood and others (2008). The final 7*Q*_{2} regression equations selected for modeling perennial streams in Idaho are shown in table 1. The regression regions are shown on figure 2. New regression models were selected for five of the eight regions; the original equations by Hortness (2006) were retained for regions 2, 4, and 6. These regression equations were applied to create continuous grids of 7*Q*_{2} estimates for the eight regression regions of Idaho. No equations are given for the undefined region in the Eastern Snake River Plain area, so no estimates of 7*Q*_{2} are possible, and no perennial streams are indicated in that area.

The datasets used in this project primarily were derived from the 10-m resolution DEMs produced by the USGS, and the 1:24,000-scale NHD Hi-Res. Previous experience with 30-m resolution DEM data processed with standard methods (see Elevation Derivatives for National Applications (EDNA) http://edna.usgs.gov) identified many shortcomings that we wished to avoid in the development of these datasets. Moore and others (2004) described a process used to produce a hydrologically conditioned DEM, referred to in this report as the “HydroDEM.” The HydroDEM process was further refined as part of this study, and subsequently was used to develop data for many USGS StreamStats web sites. The process also became the basis for the elevation-derived components of the NHDPlus. More information on the NHDPlus is available at http://www.horizon-systems.com/nhdplus/.

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 (known as IDTM83) for each 8-digit Hydrologic Unit Code (HUC), (also known as “Subbasin”) in Idaho. A buffer area 100-m wide was included around each 8-digit HUC area.

The NHD vector streams were integrated into the raster NED data, using a process often referred to as “stream burning” (Saunders, 2000). These modifications were needed because the drainage path defined by the NED surface often does not closely match the 1:24,000-scale NHD streams. The stream locations in the NHD, coming from the topographic maps, ultimately were derived from aerial photo interpretation and field verification. The drainage path derived from the NED surface, however, is sensitive to blockages at culverts and dams, and under sampling of tight channels in the rasterization process. In addition, in areas of low relief the NED surface often does not retain enough detail to represent stream channels accurately. Figure 3*A* illustrates a common example of the differences in the horizontal positions of NHD streams and NED-derived streams. Where this offset distance is greater than one grid-cell width, some cells may not be identified as being upslope from the NHD stream segment; therefore, cells would be erroneously excluded from watersheds or catchments (the area draining to a particular stream reach) delineated using these data (fig. 3*B*). For these reasons, the stream-burning process was used to give the NHD streams preference over the NED-derived streams. Figure 3*C* shows that the stream-burning process corrects for DEM flow path displacement errors.

The stream-burning process uses computer algorithms in an Arc Macro Language (AML) program called AGREE, developed by Hellweger and Maidment (1997). Figure 4 shows that AGREE “burns” a “canyon” into the NED-based DEM by subtracting a specified vertical distance from the elevation cells beneath the NHD vector streamlines. The vertical exaggeration of the canyon is controlled by specifying a “Sharp Drop Distance.” A negative “sharp” drop distance (-500 m) was used.

AGREE also “smooths” the elevation adjacent to NHD stream cell locations in the DEM within a buffer distance specified by the AGREE program user. Typically, the buffer distance used is related to a common horizontal displacement error between NHD and NED-derived streams; this distance is seldom exceeded. For this project, the buffer distance was set to 60 m on each side of the NHD flowline. The smoothing process changes the DEM grid-cell elevations within the buffer area to create a downward sloping gradient towards the canyon created beneath the NHD streams. The steepness of the slope within the buffer is controlled by the AGREE “Smooth Drop/Raise Distance” option. A smooth drop distance of -5 m was specified for this project. Figure 4 illustrates how AGREE changes the original DEM surface using all the specified parameters of AGREE.

The use of AGREE’s 60 m smooth drop buffer distance of the NHD streams potentially may cause problems at headwater flowlines that begin at or near drainage divides in the DEM. The 60 m buffer distance at these headwater streams may extend across the DEM drainage divides and into the adjacent basin area, thereby including areas outside the true catchment area. Input datasets were inspected to ensure this situation did not exist in relation to the 8-digit HUC boundaries, and if it did, the NHD streams were trimmed back from the divides.

Because the DEM and derived gridded datasets are large, the data were divided into tiles based on the 8-digit Hydrologic Units, also known as “Subbasins,” of the National Watershed Boundary Dataset (WBD). A dataset of Subbasin boundaries was developed and digitized for this project. These boundaries became the first draft (June 2005) of the WBD Subbasin boundaries for Idaho. Further refinements to these boundaries have been made, but these refinements were not reflected in the datasets used for this project. Current status and updated draft WBD datasets for Idaho are available at http://www.idwr.idaho.gov/watersheds/default.htm (Idaho Department of Water Resources, 2008).

The Subbasin boundaries were used to generate simulated “walls” around each Subbasin, by raising the elevation of grid cells by 1,000 m in a 50-m buffer around each Subbasin. The NHD hydrography was edited to ensure it crossed this “wall” only at the designated outlet of the Subbasin. The grid was then processed so that the NHD cut a narrow slot through the “wall” at the outlet. This procedure ensured that no grid cell within the Subbasin would receive a flow direction that crossed the Subbasin boundary anywhere except at the outlet. In this manner, the NED DEM and derived datasets could be processed independently for each Subbasin.

The process was further refined by imposing a “bathymetric gradient” within wide rivers and lakes or ponds. The bathymetric gradient ensured that the surface sloped toward the artificial-path flowlines of the NHD, which generally follow the centerlines of these NHD water-body features. The gradient was applied prior to running AGREE. The bathymetric gradient process applied algorithms similar to those used in AGREE, to create a gently sloping gradient from water-body shorelines toward the artificial path flow lines. The result of this process was flow routed across these areas, which were perfectly flat in the original DEM, closely matched the pattern of the artificial-path flowlines. The resulting synthetic drainage pattern matched the NHD drainage network much more closely than the parallel synthetic drainage lines that often are produced from standard DEMs. This greatly improves the usability of the surface for watershed and catchment delineations. Figures 5*A* and 5*B* show the improvement resulting from the bathymetric gradient process.

The last step in the process creates a “filled” DEM surface grid with the ARC/INFO GRID command “FILL,” which removes depressions. This step ensured all elevation cells in the basin had a defined drainage direction. A flow direction grid then was produced from the filled DEM surface. This flow-direction grid was the foundation for developing a flow-accumulation grid and other hydrologic derivatives, using the techniques described by Jenson and Domingue (1988).

Figures 5 through 7 illustrate some of the improvements made in the DEM hydrologic derivatives as a result of this project. Figure 5 shows the area around the outlet of Arrowrock Reservoir. Figure 5*A* shows the shaded relief and synthetic drainage network (dark blue pixels) derived from 30-m NED DEMs, using the standard processes described by Jenson and Domingue (1988). Known as EDNA, these data have been the basis for the Idaho StreamStats web application since its development. Figure 5*B* shows the shaded relief and improved synthetic drainage network derived from the 10-m HydroDEM specially processed for this project. Figures 6*A* and 6*B* show similar images for an area in which the surface has been modified by placer mining.

Figures 7*A* and 7*B* show similar images for a relatively flat, valley location. Similar improvements are available in the datasets statewide.

Verdin and Worstell (2008) describe a method using a weighted flow accumulation function to compute continuous parameter grids. In this discussion, a grid where each cell contains the value of some parameter, measured for the entire drainage area upstream of that cell is referred to as a continuous parameter grid. 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.

The ARC/INFO GRID flow accumulation function (Environmental Systems Research Institute, Inc., 1999) allows the use of an optional “weight” grid. When using a weight grid, the flow accumulation function sums values from the weight grid for each cell as it accumulates values downstream. Using a precipitation grid for a weight grid, for example, the weighted flow accumulation function sums the precipitation depths from all upstream cells, producing a grid that represents—after appropriate unit conversions—the total volume of precipitation in the watershed upstream of each cell. In contrast, if no weight grid is given, the flow accumulation function simply totals the *number* of upstream cells, a process called “unweighted flow accumulation” in this report. The weighted flow accumulation value, divided by the unweighted flow accumulation value, gives the average of the weight grid upstream of any grid cell. Adjusting to include the cell of interest, the formula given in equation 1 may be used to compute the mean value of a weight grid for the watershed above and including the cell.

* P*_{i}* = ( facWp*_{i}* + p*_{i}* ) / ( fac*_{i}* + *1* ) * (1)

where

* P*_{i} is the average value of parameter *P* in the watershed of cell *i*.

* facWp*_{i} is the weighted flow accumulation at cell *i*,

* p*_{i} is the value of the parameter grid *P* at cell *i*, and

* fac*_{i} is the value of the unweighted flow accumulation at cell *i.*

Equation 1 may be used with continuous-value parameters, such as elevation or precipitation, which may be expressed as a grid of real values. Equation 1 also may be used with single-value categorical grids. For example, using a grid containing 1 for every cell categorized as forested in a land-cover dataset, and 0 for every other cell, equation 1 may be used to compute the fraction of the watershed area for grid cell *i* that is forested.

The basic assumption of equation 1 is that the quantity of interest may be determined by an area-weighted average of the upstream cell values in the weight grid. Therefore, equation 1 may not be used with maximum, minimum, or range type parameters, or parameters that depend on the geometric shape of the entire watershed or stream channel.

Equation 1 gives us the ability to compute most, though not necessarily all, basin characteristics on a continuous basis, for every grid cell. 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. In this manner, equations described by Wood and others (2008) may be used to compute estimates of the 7*Q*_{2} for every 10 by 10 m grid cell in Idaho. By comparing these estimates to the criterion of 0.1 ft^{3}/s to determine perennial flows, a map of perennial streams may be developed.

The 7*Q*_{2} low-flow values were calculated for each grid cell of the eight regions using the corresponding regression equation listed in table 1. Vector stream lines then were created from the 7*Q*_{2} grids using cells with a 7*Q*_{2} value of 0.1 ft^{3}/s or greater to represent perennial streams. Because these representations of perennial streams are derived from the gridded elevation model, they are referred to in this report as “synthetic streams.” Because no equations are given for the undefined region in the Eastern Snake River Plain area, no estimates of 7*Q*_{2} are possible, and no perennial streams are modeled in that area.

The continuous parameter grid computations use the flow accumulation locally within each HUC. For HUC’s downstream of other HUC’s, the parameter estimates and, therefore, the flow estimates, for main-stem streams do not take into account the flows entering from upstream HUC’s. For this project, the assumption was made that any streams downstream of one or more entire 8-digit HUCs are perennial; these stream segments were given PerCode attribute values of 3.

To provide an approximation of the level of uncertainty of the regression equations, synthetic stream lines were created from the 7*Q*_{2} grids using the 0.1 ft^{3}/s criterion plus and minus the standard error of prediction range. This range of 7*Q*_{2} values provides a spatial context to the level of uncertainty in the regression equations and may approximate the transitional reach in which a stream transitions from intermittent to perennial. The transitional reach represents the part of the stream that, given annual climate fluctuations and inherent statistical uncertainty, is assumed to contain the point where a stream changes from perennial to intermittent. In other words, flow in reaches upstream of the top of the transitional reach is considered intermittent, and flow in reaches downstream of the bottom of the transitional reach is considered perennial. Within the transition zone, flow could be perennial or intermittent. However, few data points are available to verify the regression models in this low-flow regime, and extrapolation of the regression models was necessary. More data are needed in the low-flow regime to verify the statistical confidence of these estimates. The synthetic stream line dataset contains lines coded in the PerCode attribute field, with value “1” for the error range less than 0.1 ft^{3}/s, “2” for the error range greater than 0.1 ft^{3}/s (these two error ranges together represent the transitional reach), and “3” for 7*Q*_{2} values greater than the error ranges. Additional statistical analysis of the perennial streams model is available in Wood and others (2008).

Figure 8 shows the synthetic stream line dataset for lines having 7*Q*_{2} values greater than 0.1 ft^{3}/s for the area shown in figure 1. The model has corrected many of the most obvious drainage-density problems in the NHD version; however, in some areas the model appears to overestimate perennial streams.

Although the synthetic streams derived from the regression models provide a consistent, connected representation of the stream network, many users need the results referenced to the NHD, the commonly recognized hydrography framework. An initial attempt to reference the synthetic streams linearly to the NHD by matching synthetic streams to NHD flowlines resulted in a large number of errors. These errors mostly were due to minor deviations between the synthetic streams and the NHD flowlines, and caused numerous breaks in the connectivity of the resulting network. To provide a better matchup, an alternative procedure was used to snap transition points to the NHD network, and then to trace downstream of these points, selecting all the downstream NHD flowline features. A detailed description of the following general procedure is available in the metadata for the “ds412_PerennialStreamsEvents” dataset.

Points were generated on the synthetic streams wherever the flow category changed (for example, from PerCode 1 to 2 or 3). In effect, this identified all stream segments with estimated 7*Q*_{2} flows of 0.1 ft^{3}/s or greater. These points were snapped to the nearest 1:100,000-scale NHDPlus flowlines, using a snapping tolerance of 100 m. Points were not snapped if they were farther than 100 m from any NHDPlus flowline. This resulted in some segments of synthetic streams modeled as perennial not being transferred onto the NHD. The snapped points were inserted as junctions into a geometric network, splitting the flowline features. The ArcMap geometric network “Trace Downstream” task in ArcMap 9.2 (Environmental Systems Research Institute, Inc., 2006) was used to trace downstream of 53,219 points, and to select the traced flowline features. These selected features then were converted to a “linear event table” (ds412_PerennialStreamsEvents.dbf).

Extensive checking or editing of the resulting dataset was beyond the scope of this project. Features estimated to be perennial streams in the synthetic streams dataset may have no corresponding feature in the 1:100,000-scale NHDPlus flowline feature class, often, due to scale generalization in the NHD. No attempt was made to address these discrepancies. The synthetic streams dataset (ds412_SyntheticPerennialStreams.shp) represents a more complete representation of the model simulation results; however, it does not provide any direct linkage to the NHD.