Where

• Q º daily, weekly or monthly discharge

• A º contributing area upstream

• CN º average curve number of the contributing area

• M º mean annual precipitation over the contributing area

The proportional method assumes that the gaged and ungaged locations are close enough on the stream network that the incremental change in their discharge with respect to the change in their hydrologic parameters can be approximated with a linear relationship.   

The second method listed above, the modified NRCS method, involves solving for precipitation at the gaged location knowing the discharge and upstream curve number.  Then the precipitation at the gaged location is multiplied by the ratio of mean annual precipitation at the ungaged to gaged location.  The adjusted precipitation and curve number for the ungaged location is then used to compute ungaged discharge.  A description of the NRCS curve number equation can be found here. 

WRAP has options for using the first 3 methods listed above for distributing flow from gaged to ungaged locations.  The user must supply the hydrologic parameters or regression coefficients.  To facilitate building datasets of the hydrologic parameters for control points used in WRAP, Brad Hudgens developed a GIS method for computing the parameters.  Mr. Hudgens research can be found in the CRWR online report 99-4.  Also, his ArcView 3.x script, wrap1117.apr, for computing the parameters is available free of charge.  This project makes use of ArcView 3.2 and Mr. Hudgens script. 

As part of the Water Availability Modeling (WAM) requirements established by the 1997 Texas Senate Bill 1, the Brazos River has been modeled using WRAP to asses the current state of water availability in the basin.  In the report submitted to the TNRCC in December 2001, the consulting firm in charge of the WRAP modeling, HDR Engineering, Inc., compared the USGS contributing area versus the CRWR contributing area at locations of USGS stream gages in the Brazos.  HDR Engineering, Inc. used the latter set of contributing area values in their WRAP simulations.  Though there were thousands of control points located in the Brazos River for the WRAP simulation, only the values for contributing area at the USGS stream gages were compared.  This project will attempt to re-create the contributing area shown in the report as well as compute average curve number and annual precipitation at these 67 control points.   

The Brazos River Basin is about 46,000 square miles of total drainage area.  However, only about 36,000 square miles contributes to stream flow.  The non-contributing area is located in the northern headwaters of the basin.  Only the contributing areas and the respective value of curve number and mean annual precipitation are needed for distributing discharge from gaged to ungaged locations.   During the GIS stream delineation in this project, the entire Brazos River Basin is assumed to contribute flow.  The contributing area initially computed will be equal to the total drainage area.  Likewise, the curve number and mean annual precipitation will correspond to values computed over the entire basin.  To correct this error, the contributing area, curve number and annual precipitation values will be adjusted in Excel using data reported for contributing area by the USGS.  An alternative method not taken in this project is to specify non-contributing area prior to computing the parameters.  However, exact spatial location of the non-contributing area was not part of the author’s available data at the time of this project.

METHODOLOGY

A complete detail of the use of the tools and buttons on Mr. Hudgens ArcView script can be viewed in the CRWR online report 99-4.  While this project did utilize the ArcView script, the purpose of this project is not to instruct the reader on the use of the script.  Rather, the following is a general outline of the steps required for the GIS stream network delineation and hydrologic parameter computation. 

Required datasets:

1. DEM (raster)
2. Stream lines (vector: lines)
3. Control point locations (vector: points)
4. Curve number and mean annual precipitation (raster)

The stream lines must first be checked and edited for features that will cause errors in the development of the stream network.  These features include: braided streams, broken streams, open waterbody boundaries and dangling nodes.  An example of the first three features mentioned is presented below.  Dangling nodes occur when stream lines have a slight mismatch in their nodes and a broken channel is formed.   Visually the lines appear to connect, but in actuality their nodes must be snapped.

Braided and broken lines must be deleted or redrawn by the user in order to avoid misregistration of the stream location on the DEM.  Open waterbody boundaries must be removed and replaced with a single connecting centerline in order to avoid loops in the stream network, which would cause problems for determining contributing area and network connectivity. 

Figure 1. Examples of broken and braided stream lines

Figure 2. Example of open waterbody boundary and the corresponding centerline

Once a cleaned set of stream lines are developed, they are used to alter the elevation value of corresponding grid cells on the DEM in a process commonly called “burning”.   Burning a DEM will result in all grid cells that fall on a stream line to have an artificially lower elevation that the surrounding grid cells.  This conditions to the DEM to force the location of the rasterized streams to match the original vector stream lines.   

After burning, the DEM is processed to remove depressions that cause non-contributing area to be formed in the basin.  The DEM is now called a filled DEM.  These non-contributing areas are called sinks.  It is assumed that these sinks are artifacts of DEM construction and do not represent actual non-contributing areas.  However, as will be shown later in this project, non-contributing areas do exist and ignoring their presence can significantly inflate the contributing area that is reported in the output. 

Next, a grid representing flow direction is produced from the filled DEM.  The values of grid cells in the flow direction grid represent a code for defining one of eight possible directions for water to move out of that cell.  The directions of this grid define a unique path from each cell to the DEM outlet.  From the flow direction grid, the flow accumulation grid is formed.  By tracing the unique downstream path of each cell, the total number of upstream cells draining through each cell is calculated.  The flow accumulation defines the contributing area flowing into each cell. 

Figure 3. Example of a portion of the flow accumulation grid for the Brazos

Once the flow accumulation grid is formed, the stream grid is usually defined as the grid cells where the flow accumulation grid exceeds a certain threshold of contributing area.  However, in this project, the stream grid is defined as the downstream path on the flow direction grid from each headwater node of the original vector stream line dataset. These raster streams are then vectorized to form a set of stream lines.   One line is formed for each unique downstream path from the headwater nodes.  Thus, many overlapping stream lines are formed.  ArcInfo is used to erase overlapping lines.  The difference between this set of stream lines and the original set is that the computed stream lines intersect the grid cell centers of the DEM and DEM derived grids.  Finally, the computed stream lines are assigned a unique segment identification number and the identification number of the segment into which it flows.   The stream lines now form a true dendritic network. 

Figure 4. Example of the difference between the original (vector) stream line dataset and the delineated stream network dataset after it's raster-to-vector conversion

Figure 5. A closer view of the stream network

The curve number and mean annual precipitation grids are each transformed into average accumulation grids.  These average accumulation grids are much like the flow accumulation grid except that the area weighted average of the upstream parameter value is reported and not the cumulative value.  Conceptually, the area average at each grid cell is computed as:

       Equation 2

where `P º area weighted average parameter value

            P_i º parameter value of an grid cell upstream of the location of `P

            A_i º contributing area corresponding to  P_i's grid cell

            A_T º summation of A_i’s 

Next, the control points are snapped to the nearest vertex on the stream network.  Aligning the control points to the stream network ensures that each control point lies directly on the grid cells defining the stream network and also allows downstream control point to be identified on the stream network.  With the control points snapped to the stream network, the corresponding value of the flow accumulation, average curve number and annual precipitation grids are read and assigned to the control point. 

This concludes the steps needed to assemble hydrologic parameters at the control points.   Additionally, subwatershed boundaries can be defined using the control points as subwatershed outlets and tracing the flow paths radiating upstream from the control points.

DATA AND STUDY AREA

This project involves the entire Brazos River Basin.  The Brazos covers 25 hydrologic unit codes (HUC’s) from the Gulf of Mexico to the Llano Estacado.  The basin encompasses about 16% of the surface area of Texas. 

Figure 6. The Brazos River Basin

The data used in the above methodology described include:

1. USGS 1-degree DEM
2. National Hydrography Dataset (NHD) drainage features
3. 67 USGS stream gage locations as a longitude/latitude event theme in ArcView
4. Curve number and mean annual precipitation grids developed for the HUMUS project 

Figure 7.  The DEM for the Brazos River Basin

The USGS 1-degree DEM has a resolution of about 92 m for the latitudes of the Brazos River Basin.  The grid was resampled to 90 m.  The NHD drainage features were selected because they were digitized from USGS 1:100,000 digital line graphs (DLG) and unlike the RF3 stream lines, the NHD drainage features have open waterbody boundaries replaced with centerlines.  Thus, some stream editing tasks were avoided.  The curve number and mean annual precipitation grids have a cell size of 250 m.  The 67 USGS stream gages serve as the control points in this project and are listed below.

USGS Gage ID, Description 08079550     Buffalo Springs Lk nr Lubbock, TX 08079600     DMF Brazos Rv at Justiceburg, TX 08080500     DMF Brazos Rv nr Aspermont, TX 08080700     Running Water Draw at Plainview, TX 08080910     White Rv Res nr Spur, TX 08080950     Duck Ck nr Girard, TX 08081000     Salt Fk Brazos Rv nr Peacock, TX 08081200     Croton Ck nr Jayton, TX 08082000     Salt Fk Brazos Rv nr Aspermont, TX 08082180     N Croton Ck nr Knox City, TX 08082500     Brazos Rv at Seymour, TX 08082700     Millers Ck nr Munday, TX 08083100     Clear Fk Brazos Rv nr Roby, TX 08083240     Clear Fk Brazos Rv at Hawley, TX 08083245     Mulberry Ck nr Hawley, TX 08084000     Clear Fk Brazos Rv at Nugent, TX 08084800     California Ck nr Stamford, TX 08085500     Clear Fk Brazos Rv at Ft Griffin, TX 08086212     Hubbard Ck bl Albany, TX 08086500     Hubbard Ck nr Breckenridge, TX 08087300     Clear Fk Brazos Rv at Eliasville, TX 08088000     Brazos Rv nr South Bend, TX 08088400     Lk Graham nr Graham, TX 08088450     Big Cedar Ck nr Ivan, TX 08089000     Brazos Rv nr Palo Pinto, TX 08090800     Brazos Rv nr Dennis, TX 08091500     Paluxy Rv at Glen Rose, TX 08092000     Nolan Rv at Blum, TX 08093100     Brazos Rv nr Aquilla, TX 08093500     Aquilla Ck nr Aquilla, TX 08094800     N Bosque Rv at Hico, TX 08095000     N Bosque Rv nr Clifton, TX 08095200     N Bosque Rv at Valley Mills, TX 08095300     Middle Bosque Rv nr McGregor, TX 08095400     Hog Ck nr Crawford, TX 08095600     Bosque Rv nr Waco, TX 08096500     Brazos Rv at Waco, TX 08098290     Brazos Rv nr Highbank, TX 08099100     Leon Rv nr De Leon, TX 08099300     Sabana Rv nr De Leon, TX 08099500     Leon Rv nr Hasse, TX 08100000     Leon Rv nr Hamilton, TX 08100500     Leon Rv at Gatesville, TX 08101000     Cowhouse Ck at Pidcoke, TX 08102500     Leon Rv nr Belton, TX 08103800     Lampasas Rv nr Kempner, TX 08104000     Lampasas Rv at Youngsport, TX 08104100     Lampasas Rv nr Belton, TX 08104500     Little Rv nr Little Rv, TX 08104700     N Fk San Gabriel Rv nr Georgetown, TX 08104900     S Fk San Gabriel Rv at Georgetown, TX 08105000     San Gabriel Rv at Georgetown, TX 08105700     San Gabriel Rv at Laneport, TX 08106500     Little Rv at Cameron, TX 08109000     Brazos Rv nr Bryan, TX 08109700     Middle Yegua Ck nr Dime Box, TX 08109800     E Yegua Ck nr Dime Box, TX 08110000     Yegua Ck nr Somerville, TX 08110100     Davidson Ck nr Lyons, TX 08110325     Navasota Rv abv Groesbeck, TX 08110430     Big Ck nr Freestone, TX 08110500     Navasota Rv nr Easterly, TX 08111000     Navasota Rv nr Bryan, TX 08111500     Brazos Rv nr Hempstead, TX 08111700     Mill Ck nr Bellville, TX 08115000     Big Ck nr Needville, TX 08116650     Brazos Rv nr Rosharon, TX

RESULTS AND DISCUSSION

Figure 8.  The 67 control points used in this project which correspond to USGS stream gaging stations.

The following table is a sample of the uncorrected values obtained for all 67 control points.  The 20 control points in Table 1 are affected by the non-contributing area of the northern control points in the Brazos for this project.  The red highlighted control points have, according to the USGS data presented, non-contributing area in their incremental subwatershed.  The gray highlighted control points are downstream of the control points with non-contributing area.  Gage 08082500, located at Seymour, is the outlet of all of the control points with non-contributing area.  A complete table of the uncorrected values for all 67 control points can be found here.

Table 1.  Uncorrected contributing area, curve number and precipitation for selected control points

Figure 9. Total drainage upstream of each control point prior to corrections for non-contributing area.   Note, the control points are shown as the subwatershed outlets (red points) and the lines connecting control points illustrate network connectivity only.

Figure 10. Average upstream curve number value at each control point prior to correcting for non-contributing area

Figure 11. Average upstream annual precipitation value at each control point prior to correcting for non-contributing area

The hydrologic parameters listed in Table 1 consider all portions of the Brazos River Basin draining into the stream network.  According to the USGS data, there is 9,566 square miles of non-contributing area located in the northern headwaters of the Brazos River.  This non-contributing area is located above gages 08080500 and 08081000, which includes 7 subwatersheds in this project.  There area 13 subwatershed located downstream of these subwatersheds with non-contributing area.  These 20 control points will require their contributing area, curve number and mean precipitation values be adjusted to account for the loss of drainage area.  

Figure 12. The 7 red colored control points have non-contributing drainage area within their subwatershed according to USGS data.

To adjust the contributing area of the 7 control points with non-contributing area, the percentage of decrease in USGS incremental drainage area is calculated in Table 2.   This percentage is used as a correction factor to reduce the incremental drainage area calculated in this project for the 7 affected subwatersheds.  The incremental drainage area of the remaining 13 control points downstream is reduced by the total amount of drainage area lost as calculated at 08082500.  Using the correction factors, this project predicts 9,218 square miles of non-contributing area.  The comparison between this project's corrected drainage area and the USGS and CRWR data is shown in Table 3.

Table 2. USGS data quantifying non-contributing area amounts

Table 3. Comparison between this project's corrected contributing area and the USGS and CRWR.  A complete listing of all control point comparisons can be found here.

Figure 13. Reduction in drainage area per control point after non-contributing area was removed

Figure 14. Change in upstream curve number per control point after removing non-contributing area. 

Note, in Figure 14 control points with non-contributing area that are at the headwaters of the network do not show a change in curve number.  This is a result of the assumption that the original incremental parameter values would be preserved in all subwatersheds but their weighting downstream would be reduced due to a reduction in their contributing area.   The incremental parameter values can not be adjusted without the explicit spatial location of the non-contributing area.    The incremental parameter values are used to re-calculate the average upstream parameter using Equation 2. 

Figure 15.   Change in upstream average annual precipitation per control point after removing non-contributing area

In Table 3, it is clear there are some disagreements with this contributing areas computed in this project and those reported by the USGS and CRWR.  Possible reasons include loss of terrain features using a 1-degree DEM, estimating the percentage of non-contributing area rather than explicitly defining it on the DEM and also using a set of stream lines that don’t identify very small creeks and ditches that might appear on USGS quarter quadrangles with a scale 1:24,000.   The contributing area in this project generally has less disagreement with the CRWR reported values which is probably due to the use of GIS to determine both sets of values whereas the USGS contributing area values were likely manually delineated from contour maps.