A GIS-Enabled Kinematic Wave Approach for Calculating
the Transition between Sheet and Concentrated Flows
Stacy L.
1
Hutchinson ,
1Department
J.M. Shawn
2
Hutchinson ,
of Biological and Agricultural Engineering and
and Ik-Jae
2Department
1
Kim
of Geography, Kansas State University, Manhattan, Kansas 66506
Introduction
Data and Methods
Non-point source (NPS) pollution has been called the nation’s largest water quality
problem, and its reduction is a major challenge facing our society today. As of 1998
over 290,000 miles of river, almost 7,900,000 acres of lake and 12,500 square miles of
estuaries failed to meet water quality standards. Military training maneuvers have the
potential to significantly alter land surfaces in a manner that promotes NPS pollution,
resulting in the inability of military installations to meet water quality standards and the
decline of training lands.
USGS National Elevation Dataset (NED) 30m digital elevation model (DEM) data was
used to develop three raster data layers using ESRI’s ArcGIS 9.1 software: Slope,
flow direction, and flow accumulation. Slope (S) was calculated using the
deterministic eight direction method (D8) in 3 by 3 cells. Unlike the normal procedure
for delineating stream networks, flow direction was determined without “filling”
because characteristics of land curvature affect the transition from sheet flow to
concentrated flow and the potential for gully erosion. A flow accumulation grid, which
connects the direction of flow from cell to cell and determines the number of cells
accumulating within a downslope flowpath, was estimated using standard ArcGIS flow
direction tools. The flow accumulation values (no. of cells) was converted into a slope
length grid by multiple number of cells by 30, then by 3.208 to determine the upslope
slope length for each cell (L). Kansas GAP landcover data for the installation were
used to create a grid dataset for Manning’s coefficient (n) data layers. From this
information, a continuous “energy accumulation” grid calculated as the product of
three separate data layers representing Manning’s coefficient (n), slope length (L), and
the square root of slope (S-0.5).
Currently, most efforts to reduce NPS pollution focus on the use of watershed water
quality models. Identification of overland flow networks is a vital preprocessing step
for these NPS models. Flow networks are used to determine transport routes for
pollution and optimal placement of best management practices. One practice that is
widely adopted for reducing NPS pollution is the vegetated buffer system (VBS). The
primary hydrologic consideration for VBS design and function is uniform sheet flow.
With time, however, overland flow concentrates and channelizes, reducing contact
time with vegetation and NPS pollution reduction efficiency.
The kinematic wave approximation is a useful technique for calculating overland flow
time of concentration within a drainage area. Digital elevation models (DEMs) are
widely used for determining various landscape variables, as well as for delineating
overland flowpath networks and drainage area boundaries. Using topographic
variables estimated from DEMs and applying the kinematic wave theory in a GIS
environment, it is possible to estimate the length and travel time of overland flow
providing an improved understanding of VBS placement for maximum water quality
benefit, as well as a reduction in gully erosion caused by concentrated flow.
tov= [0.93(nL)0.6] / [i0.4(S0.5)0.6]
Figure 3. The Fort Riley
installation with grid surfaces
representing (from bottom to top):
Manning’s coefficient, flow length,
slope, and nLS-0.5 energy
accumulation.
Figure 4. Tables showing reported efficiencies of vegetated buffer
systems and McCuen and Spiess’ (1995) Tov calculation with
evaluation criteria.
Shrubs – nutrient removal
Zone 3
Zone 2
Grass – control runoff, sediment
Uniform Sheet Flow
A=WxL
Zone 1
Trees – bank stabilization
Concentrated Flow
A=WxLxβ
β = A – Ineffective Area
L
W
Figure 1. Schematic of “typical” vegetated buffer system with
diagram illustrating key differences between sheet and
concentrated flows.
Figure 5. Energy accumulation grid for a subwatershed of Cheney
Reservoir, near Wichita, Kansas with actual ephemeral gully
locations.
References
McCuen, R.H. and J.M. Spiess. 1995. Assessment of kinematic wave time of
concentration. Journal of Hydrologic Engineering 121 (3):256-266.
Preliminary Results
30m USGS
10 m
30 m
3m
Figure 2. Digital elevation models of varying spatial resolutions
with resulting flow networks superimposed upon a false color
composite aerial photograph of the Fort Riley study site.
The location of ephemeral gullies were recorded, as part of a separate project, within a
subwatershed of Cheney Reservoir in south-central Kansas. Gully point locations
were overlayed on top of a continuous “energy accumulation” grid calculated as the
product of three separate data layers representing Manning’s coefficient (n), slope
length (L), and the square root of slope (S-0.5). Energy accumulation values for each
gully point were extracted, as were the values for 500 additional points located
randomly within the subwatershed. The mean values for these two datasets were
then compared using a one-tailed two sample for means z-test in order to determine
whether they were significantly different. The alternate hypothesis is that nLS-0.05
energy values at the gully locations would be greater than those for the randomlyplaced points.
Initial data analysis indicates that the mean energy accumulation values for the gully
and random point datasets are significantly different at p = 0.21. Mean (standard
deviation) nLS-0.05 values for the gully and random points were 32,532.5 (66,334.9)
and 26,989.6 (123,110.7), respectively. Though the p-value is not in the preferred
range of 0.01-0.05, this is an encouraging result given that very coarse resolution
DEMs, and no soil characteristics, were used in this study.
Meyer, A. and J.A. Martinez-Casasnovas. 1999. Prediction of existing gully erosion in
vineyard parcels of the NE Spain: a logistic modeling approach. Soil & Tillage
Research 50: 319-331.
Prosser, I.P. and B. Abernethy. 1996. Predicting the topographic limits to a gully
network using a digital terrain model and process thresholds. Water Resources
Research 32(7): 2289-2298.
Tarboton, D.G., R.L. Bras, and I. Rodriguez-Iturbe. 1991. On the extraction of channel
networks from digital elevation model. Hydrological Processes 5:81-100.
Acknowledgements
This work is funded through CPSON-03-02 (Characterizing and Monitoring Non-Point
Source Runoff from Military Ranges and Identifying their Impacts to Receiving Water
Bodies) and the Kansas Agricultural Experiment Station. Special thanks to Mr. Phil
Woodford and the Fort Riley Integrated Training Area Management (ITAM) for
assistance with field site development and data collection.