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Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 48 B, 2005

3D Simulation of Overland Flow

Dayong SHEN, Kaoru TAKARA and Yasuto TACHIKAWASynopsis
In this research, overland flow is simulated based on GIS Flow Element (FE), which isrepresented by a fine cylinder. The height of the cylinder is in direct proportion to thevelocity of overland flow; the inclination of the cylinder represents the direction of themovement; the diameter of the cylinder is in direct proportion to the depth of overland flow;
and the depth of cylinder color is related to sediment concentration. The deeper the cylindercolor is, the greater sediment concentration it represents. Via collecting data from awatershed in China Loess Plateau region and selecting geoscientific models, we simulate
the dynamic change of velocity and direction of overland flow in each pixel.
Keywords: overland flow, GIS Flow Element, velocity, direction, geoscientific models, pixel

1.

Introduction

Overland flow, which is formed by rainfall andforced by gravity, is flowing water along hillslopes. It
will be generated when precipitation excesses theamount of soil infiltration and depression storage.
Usually, overland flow is 3D non-uniform, unsteadyand progressive. However, to solve practicalproblems, related research mainly supposes that theflow is 1D steady, non-uniform and progressive tosimplify the computation (Yao, 1993). Since 1920’s,
many researchers have applied theoretical methods orpartially theoretical and partially empirical methods
to solve the velocity of overland flow. Some are easy
to combine with GIS e.g. the methods proposed byJiang and Song (1988), Lu (1991) and Yao (1993).
Algorithms for tracing the direction of overland flow
mainly include 8-neighourhood method (O’Callaghanand Mark, 1984), multiple nearest neighbor nodes
method (Freeman, 1991), random-eight nodeapproach (Fairfield and Leymarie, 1991), 360
directions of flow with the vector-grid algorithm(Mitasova and Hofierka, 1993, Mitasova et al., 1995)
and others. Among them, 8-neighourhood method is
accepted as a standard algorithm (Mitasova et al.,1996), which assigns the direction of flow same to thedirection of steepest downward slope and has been
widely used in hydrology for flow direction mapping
and to evaluate hydrological attributes (Shrestha et al.,2005). Approaches for the visualization of overland
flow mainly include texture mapping (Ziegler et al.,2001), choroplethic mapping (Taddei et al., 2000;
Miller et al., 2002; Soulis et al., 2005), arrowhead
method (Wu et al., 1999; Endreny and Wood, 2003)
and path sampling (Mitas and Mitasova, 1998) andothers. Texture mapping can make a realistic scenario,
but it can hardly represent dynamic effects;
choroplethic mapping and arrowhead method canmake a scenario, which concisely reflects
geoscientific principles but lacks the stereoscopic
effect. Path sampling is a true 3D method, which canrepresent dynamic effects but cannot intuitively
represent velocity difference. This paper aims at 3D
simulation of overland flow based on GIS FE, andutilizes data from a rainfall event in a watershed in
China Loess Plateau region to simulate overland flow
and shows the information of related parameters pixelby pixel during that event.
2.

Overland Flow Simulation based on GIS FEs

2.1 GIS FE
Built based on a pixel from remotely sensed
imagery and controlled by geoscientific models, aGIS FE is used for simulating parameters such as
velocity and direction of the transport of dynamic soft
geoobjects and taken as a basic simulation unit. AGIS FE has position, velocity and direction, butneglects volume. The appearance of a GIS FE can berendered as an arbitrary point, line segment, face orvolume. But considering that it is built based on apixel, the perpendicular projection of a GIS FE in thepixel plane should be completely within the pixel. Via
adding color or changing shape, a GIS FE will havemore geoscientific attributes.

Fig. 1 Schematic map of GIS FEs
ZR3YX

7VFig. 2 Geometric structure of a GIS FE
2.2 Simulation of overland flow
Suppose that pixel a is current research objective,b , c , d ,e , f , g , h ,i are its 8 neighbourhoods (asshown in Figs. 1, 3 and 4). To describe conveniently,
an arrow with direction is used to represent thesampled overland flow. Meanwhile, to enhancecomputation efficiency, 8 directions are used torepresent the transport direction of overland flow.
Arrows from pixel a to one of its neighbourhoods
represent overland flow output of current pixel while
arrows from neighbourhoods of a to a represent
overland flow input current pixel. Transport route is
located in the line segment, which connects the center
point of current pixel and the center point of one
neighbourhood of a . In this study, overland flow isrepresented by a streamline structured GIS FE, a finecylinder (as shown in Fig. 2). The height of thecylinder is in direct proportion to the velocity ofoverland flow; the inclination of the cylinder
represents the direction of the movement; thediameter of the cylinder is in direct proportion to thedepth of overland flow; and the depth of cylindercolor is related to sediment concentration. The deeper
the cylinder color is, the greater sedimentconcentration it represents. When overland flow runs
into river channel, it will not be rendered any more.

Fig. 3 Schematic map of the transport route for GIS
FEs

Fig. 4 Schematic map of moving water flow
simulation based on GIS FEs

2.3 Geoscientific models(1) Flow velocity computation (as seen in Eq. 1)
aV a q / h a1 S 20(1)Eq. (1) was built using the method of dimensional
analysis and mathematical statistics (Shen et al., 2003),
where V is velocity of overland flow (m s-1); q isdischarge per unit width (m-3m-1s-1); h is depth ofpractical (as seen in Eq. 2):

overland flow (m); S is slope angle (º); a 0 isR

geoscientific coefficient and a1 , a 2 are geoscientificindices.
(2) Flow direction tracing
In this study, we simulate overland flow based on
pixels from remote imagery. The size for one pixel is5m‫ڜ‬5m. DEM of the research area is not complicated.
Moreover, we smooth the DEM prior to analysis toreduce the size and number of sinks. Therefore, we use
8-neighbourhood tracing algorithm, which is fasterthan other flow direction tracing algorithms andsuitable for real time rendering of 3D scenarios formed
with huge data.
(3) Flow depth computation
Wang et al. (1992) proposed a forecast model ofoverland flow in hilly and gully regions on China
Loess Plateau. Via experiments, the model is proved[( P  Z )  FLu T ] Pt C(2)where R is depth of overland flow (mm), P is total
precipitation (mm), Z is vegetation interception (mm),F is mean infiltration rate (mm/min), Lu is land use
factor, T is rainfall duration (min), Pt is farming
measure factor, and C is soil crust factor. Vegetationinterception is computed by Hartley method as seen inEq. 3:
ZZ max C v(3)where Zmax is maximum interception (mm), Cv isvegetation coverage (%). When S. asperum was used
to do experiments, Z max =9.5mm (Wang et al., 1992).
Considering that the leaf surface of S. asperum bears
burs, which has high water-holding capacity, the value
is possibly a little large when it is applied to othervegetations. Additionally, the influence of wind andleaf area index (LAI) has not been contained.
Table 1 shows the value of parameters in Eq. (2).

Table 1 Some Factors in the Overland flow Model (Wang et al., 1992)
ParameterFcZ max
LuPtCValue

Sample data

Standard Variation

Notes

0.30

Unit: mm/min

9.50

Unit: mm0.2050

0.12

Surface soil compaction

0.23

130.16Shrub and uncultivated slope

0.33

40.14

Forest land

0.75

200.21

Contour farming

1.25

21.00

Farming up and down slope

1.00
1.50

Without crust
60.23(4) Calculation of discharge per unit width (as seenin Eq. 4)
Suppose that water flow denudes and transports
surface sediment on hillslope layer by layer, andWith crust

rainfall intensity and infiltration rate are stable during
Ǎt, we will get (Lu, 1991):
qx I  f cos S

(4)
3-1-1

where q is discharge per unit width (mm mm s ), x

is the averaged slope length from slope top (mm), S is
the averaged slope angle (rad), I is intensity of rainfall(mm min-1), and f is infiltration rate (mm min-1).
(5) Computation of sediment concentration (as seenin Eq. 5)
In China Loess Plateau region, a combination ofsmall mean depth of overland flow with big soil loss
(sum of bed load and suspended load) was commonly
observed in the field data. This necessitatesconsideration of the total volume being occupied by
the soil sediments, which is normally assumed to makea negligible contribution to the total volume of thewater-soil sediment mixture. Then the definition for
sediment concentration was derived as follows(Presbitero, 2003):

cMSV S  VW

Table 2 Water flow simulation based on GIS FEs
Parameters

Representation

shapefine cylinder

colourlight yellow

transparency

semi-transparent

initial position

center point of a pixel

velocity

computed by geoscientific model

direction

8-neighborhoods
tracing algorithm

lifetime

Its lifetime will be ended when it
moves out of control boundaries.

read DEM data(5)where c is sediment concentration; M S is total mass of

trace flow direction

dry soil sediment, which is computed by erosion

compute slope lengthmodel; V S is total volume occupied by the soil
compute unit discharge
sediment; and VW is total volume occupied by water.
compute the depth of overland flow
2.4 Overland flow renderingcompute the velocity of flow

(1) Representation and geometry
define the structure of a GIS FE

Table 2 shows 7 parameters of overland flow, which
can be well represented by a GIS FE.

preset the route of overland flow(2) Technical routerender DEM

As shown in Fig. 5, there are mainly 10 steps for
simulation of overland flow. We do it based on theplatforms of Visual C++ and OpenGL.

render dynamic overland flow

(3) Computer rendering
When basic rendering method is applied, we draw
each GIS FE as a linear light source with constantcolor, no luminance or hue difference and no obstacles.
Then we accumulate the contribution from each GISFE, save it into frame buffer and integrate it withnormal rendering scenarios as shown in Fig. 6. Whileadvanced rendering method is used, we add light andshadow effect, and delete all GIS FEs in hidden
surfaces as shown in Fig. 7.

Fig. 5 Flow chart of rendering overland flow
3.

Case Study

The experiment plot is Wufendigou small watershed,which is located in Zhunger Qi, Inner Mongolia ofChina. Main data sources: 1:10,000 color infraredaerial photograph, 1:5,000 relief map and measured
precipitation. Based on remotely sensed and measured
data, we simulate the dynamic change of velocity anddirection of overland flow in each pixel as shown inFigs. 6-7.

Fig. 6 Grids and GIS FE based overland flow simulation

Fig. 7 Overland flow simulation with light and shadow effect4.

Conclusion and Prospects

We apply the approach of GIS FE to represent
velocity, direction, depth, transparency and othercharacteristics of overland flow. Collecting data from
China Loess Plateau region, we successfully use
computer-rendering skills to generate 3D scenarios,

which can show dynamic overland flow realistically.
Acknowledgment
This research currently is supported by JSPS (JapanSociety for the Promotion of Science) Fellowship andthe Grant-in-Aid for Scientific Research (No.:16004360). We are grateful to Takahiro Sayama, Ainai
Ma, Hui Lin, Zhengping Jin, Hujun Bao and Shanjun
Mao for their help and advice.
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