A GIS-Enabled Kinematic Wave Approach for Calculating
the Transition between Sheet and Concentrated Flows
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).
Based on work by McCuen and Spiess (1995) showing the relationship between overland flow concentration and energy accumulation, an erosion potential
predictive tool was developed, nLS model. The nLS model was compared to previous erosion prediction tools (Meyer, A. and J.A. Martinez-Casasnovas,
1999; Prosser, I.P. and B. Abernethy, 1996; Tarboton, D.G., R.L. Bras, and I. Rodriguez-Iturbe, 1991) for determining ephemeral gully erosion points using a
data set from Cheney Reservoir watershed in south-central Kansas.
100%
87.1%
78.2%
80%
72.2%
66.5% 65.3%
66.5%
66.5%
60.0%
59.1%
60%
40%
20%
μ ± 1.0 σ
μ ± 0.5 σ
WTI
nLSCSS
nLS
WTI
nLSCSS
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.
nLS
0%
nLS
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.
Overall Accuracy in calibration
WTI
1Department
J.M. Shawn
2
Hutchinson ,
nLSCSS
Stacy L.
1
Hutchinson ,
μ ± 1.5 σ
Overall Accuracy in validation (nLS)
100%
92.4%
87.1% 87.3% 85.9%
88.9%
86.3%
78.2% 78.3% 76.4%
80%
81.7%
74.8%
72.2% 72.2%
74.8%
69.7%
60%
Shrubs – nutrient removal
40%
20%
Zone 3
Zone 2
Grass – control runoff, sediment
Zone 1
0%
Trees – bank stabilization
14
8
7
16 11 14
μ ± 0.5 σ
Uniform Sheet Flow
A=WxL
Concentrated Flow
A=WxLxβ
β = A – Ineffective Area
8
7
16 11 14
μ ± 1 .0 σ
8
7
16 11
μ ± 1 .5 σ
Figure 5. Overall accuracy (%) for the energy accumulation model (nLS), the
energy accumulation model including soil critical shear strength (nLSCSS), and
the wetness threshold index model (WTI) for the calibration watershed (top) and
the nLS model for the validation watersheds (bottom). Intervals of mean±
standard deviation (µ±σ) refer to the statistic for the gully point locations. The
total area considered in the model increases as σ increases.
L
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.
W
Figure 1. Schematic of “typical” vegetated buffer system with
diagram illustrating key differences between sheet and
concentrated flows.
watershed area total modeled identified gh true gh modeled
no of cell
no of cell
no of cell no of cell gh (%)
WTI
137,703
55,170
108
122 88.5%
nLSCSS
137,703
46,191
79
122 64.8%
nLS
137,703
30,040
65
122 53.3%
modeled
area(%)
40.1%
33.5%
21.8%
Table 1. Relationship between gully head location prediction and watershed
area required for the µ±1.0σ model run.
References
30m USGS
10 m
30 m
Figure 4. Energy accumulation grid for a subwatershed of Cheney Reservoir,
near Wichita, Kansas with actual ephemeral gully locations.
3m
Results
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.
Only the energy accumulation (nLS), the energy accumulation with soil shear strength (nLSCSS), and the wetness threshold index (WTI) models provided
reasonable gully head point predictions and were selected for further statistical analysis. The user accuracy (commission error), the area predicted to
contain a gully head location that does not contain a gully head, was very low for all models (<1%). While this result is disappointing, it is not surprising
based on the complexity of the erosion process and the difficulty in modeling this process with a simplified tool. The producer accuracy (omission error),
the number of gully head locations correctly predicted of the total number of gully heads in the watershed, was greatest for WTI (88%), followed by the
nLSCSS (53%), and then nLS (27-69% depending on statistical interval). However, because of the large area required to predict the gully head locations,
the total model accuracy was the lowest for WTI (figure 5). Using the statistical interval of µ±1.0σ the total area required by WTI was over 40% as
compared to the nLS model that required only 20% of the land area (table 1). Further work in being conducted to reduce the over prediction of gully head
locations, but the simplified nLS model reduces the amount of land area that needs to be searched for potential ephemeral gully heads by 80%.
McCuen, R.H. and J.M. Spiess. 1995. Assessment of kinematic wave time of concentration. Journal
of Hydrologic Engineering 121 (3):256-266.
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.