1【Memoirs of Construction Engineering Research Institute Vol.64(papers)Nov.2022】

APPLICATION OF A PARTICLE METHOD TO SIMULATION OF RUNOFF FROMSHORT BUT INTENSE RAINFALL AND STREET FLOODING IN A SMALL
CATCHMENT
Sin Ying Tan Akihiko Nakayama Xin Yan Lye

ＡＢＳＴＲＡＣＴThe runoff from a short-duration rainfall has been simulated using a three-dimensional Smoothed Particle
Hydrodynamics (SPH) method developed for simulation of overland flow on natural and urban terrain. The
method is based on the three-dimensional weakly-compressible SPH applied to sparsely distributed surface
flow due to rainfalls in a small urban catchment at a foot of mountainous terrain. The rainwater is lumped into
discrete particles and their infiltration into the ground, the motion of the excess flow and its accumulation are
simulated for a real small catchment in Malaysia. The simulation results are compared with the observation of
flash flooding of streets. The results for an assumed rainfall are found to show details of surface water
movement in agreement with the observation. It can further be refined to simulate overland flow patterns inmore general situations.

１． ＩＮＴＲＯＤＵＣＴＩＯＮ
As the global climate is changing the heavy rainfalls and the resulting water hazards are not diminishing. Accurate
forecasting of rainfalls, the runoff and possible flooding areas remain as important as ever. The methods and models of
rainfall and runoff analyses that have been used are reviewd in various literature (e.g. Sitterson, et al.1), Gayathri, et.al.2)).
Many of them are data-driven models that use statistical correlations between input rainfall and the runoff occurences ofthe past events (Kokkonen, et al.3)). The process of predicting runoffs from rainfall is being improved by making use ofrecent approach based on machine learning artificial inteligence and deep neural networks but the direct physical processes
are not used. It is difficult to predict local phenomena specific to local areas of concern (Beven4)). The methods based on
physical processes such as the conventional curve number method developed by United States Department of Agriculture
Natural Resources Conservation Service (USDA NRCS)5) treat the runoffs as lump sums in a cathment or sub catchments
and again the detailed local phenomenon is not addressed. The surface flow and inundation simulation based on physicalprocesses can treat individual surface flow but they are two-dimensional (2-d) analyses of Shallow-Water Equations(SWE)6,7,8) with simplified hydrostatic approach. Rainfall-runoff-inundation (RRI) model makes use of 2-d diffusive wave
equations with infiltration. These models are based on Eulerian fixed grids that cover the area to be simulated and thecomputation is carried out over the whole area. Recent localized intense rainfalls (e.g. Jamaludin et al.9)) that are causing
flash floods in short time at specific locations are difficult to be predicted by either of the data-driven method or lumped
model analysis.
In recent years, in contrast to the fixed grid methods, meshless methods that treat the motion of indivisual portion ofwater has been applied to various free surface flow motion. Smoothed Particle Hydrodynamics method, in particular has
successfully been applied to various free surface flows10,11,12). These meshless particle interpolation methods have great

2potential in representing the rainfall itself and the subsequent motion on and in the ground. The 2-dimensional version has
been extensively developed and used in overland flow analysis10,11,12). However they are still limited to the surface flow
only and the flows in channels where the shallow surface need to be analyzed separately by 1-d channel flow analysis12).
The 3-d SPH method13,14) on the other hand has been shown to represent the motion of sparsely distributed surface flows
as well as ponded patches of water and the channel flows at the same time. The present authors15,16) have proposed suchmethod and indicated that it can be applied to simulation of the rainfall, runoff, the overland flow, infiltration and thechannel flows including stagnant bodies of water. The present work is to apply this method in the simulation of runoff
from a rainfall in a real catchment. The observation of a typical rainfall-runoff events has also been made to assess theeffectiveness of this new method.

２． WEAKLY COMPRESSIBLE SMOOTHED PARTICLE METHOD APPLIED TO RAINFALL AND
DIRECT RUNOFF
2.1 Basic equations of 3d-SPH method
In 3-d SPH methods, the motion of the fluid is represented by the motion of particles that represent the position, the velocity,
the pressure of continuous fluid body at discrete points. By giving the volume and the mass of each particle the particle
can also be interpreted to represent a lump of fluid. The forms of the equations are the same as those described in
Nakayama et al.15). The forces acting on these particles are the gravitational force, the pressure force and the viscous forcesfrom surrounding particles and the normal and tangential resistance forces from the solid boundary. Therefore, theequation of particle a moving with velocity va at time t is
𝑑𝑑𝑑𝑑�
𝑻𝑻�
= � + � 𝑷𝑷�� + � 𝚷𝚷�� +
𝑑𝑑𝑑𝑑
𝜌𝜌�
�

�

(1)

where the summation is taken over the neighboring particles b that are within the influence distance h of 2.3 times the sizeof the particle, Pab is the pressure force due to particle b, ab is the viscous force due to particle b and Tw is the force dueto the solid boundary. The forms of Pab and ab are derived from the spatial interpolation of continuous flow and𝑷𝑷�� = �𝚷𝚷�� =

𝑝𝑝� 𝑝𝑝� 𝑚𝑚�+ �∇ 𝑊𝑊𝜌𝜌� 𝜌𝜌� 𝜌𝜌� � ��𝑚𝑚� (𝜇𝜇� + 𝜇𝜇 �� ) + (𝜇𝜇� + 𝜇𝜇 �� )(𝒓𝒓� − 𝒓𝒓� )�� (𝑑𝑑� − 𝒗𝒗� )∙ ∇ 𝑊𝑊|𝒓𝒓� − 𝒓𝒓� |� � ��𝜌𝜌� 𝜌𝜌�
𝜌𝜌�

(2)
(3)

where pa and pb are the pressure, a and b are the density, a and b are the molecular viscosity, Ta and Tb are theturbulent viscosity, ra and rb are the positions of particles a and b, respectively, mb is the mass of particle b and ∇� 𝑊𝑊��is the weight of the forces depended on the distance and the direction of the separation between particles a and b given by𝒓𝒓� − 𝒓𝒓�1
, 0 ≤ 𝑞𝑞 𝑞𝑞⎧− �(2 − 𝑞𝑞𝑞� − 4(1 − 𝑞𝑞𝑞� �|𝒓𝒓
2ℎ⎪� − 𝒓𝒓� |𝒓𝒓� − 𝒓𝒓�1
∇� 𝑊𝑊�� =, 1 ≤ 𝑞𝑞 𝑞𝑞− (2 − 𝑞𝑞𝑞�⎨|𝒓𝒓� − 𝒓𝒓� |2ℎ⎪0, 2 < 𝑞𝑞⎩(4)where 𝑞𝑞 𝑞 |𝒓𝒓� − 𝒓𝒓� |/ℎ.
The resistance force Tw from the nearby solid surface is the tangential force in the direction opposite of the particle velocity.
If t is the unit vector in the local flow direction, it is expressed as

3𝑻𝑻� = −𝐶𝐶�𝜏𝜏�𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕ℎ�(5)

where CT (=1.0) is an empirical constant hw is the thickness of the wall layer (taken as 2h) next to the solid boundary andw is the wall shear stress determined by the wall law

𝑛𝑛𝑛𝑛�
𝑛𝑛𝑛𝑛�
⎧ A ln � 𝜈𝜈 � + 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝐵 𝐵 𝜈𝜈 ,
𝑛𝑛𝑛𝑛�
𝑛𝑛𝑛𝑛�
𝑣𝑣� ⎪
<30,
= C ln �
� + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
𝜈𝜈
𝜈𝜈
𝑢𝑢� ⎨
𝑛𝑛𝑛𝑛�
𝑛𝑛𝑛𝑛�
⎪
,
<5
⎩
𝜈𝜈
𝜈𝜈

(6)

where vt is the tangential velocity of particle a, n is the normal distance from particle a to the boundary, 𝑢𝑢� = �𝜏𝜏� /𝜌𝜌� ,A(=2.5),B(=5.5),C(=5.0) and D(=3.05) are constants and =a /a, for hydraulically smooth surface with the roughness

Reynolds number Rk= ku/ where k is the roughness height. For hydraulically rough surface with Rk>100, the wall
law for fully rough surface𝑛𝑛𝑣𝑣�
= A ln � � + 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸
𝑢𝑢�
𝑘𝑘

(7)

𝑑𝑑𝑑𝑑�
= � �� �(𝒗𝒗� − 𝒗𝒗� )�∇� 𝑊𝑊�� + � �� �(𝑹𝑹� /𝜌𝜌� − 𝑹𝑹� /𝜌𝜌� )�∇� 𝑊𝑊��
𝑑𝑑𝑑𝑑

(8)

with E=8.5 is used. The density is calculated from the discretized form of the continuity equation with a density diffusionthat comes from the turbulent random motion��where Ra and Rb are the density diffusion of particle a and b. The density is assumed to determine the pressure via a state
equation𝜌𝜌� �(9)𝑝𝑝� = 𝐵𝐵 �� � − 1�𝜌𝜌�with the value of B is chosen so that the speed of sound is 10 times the maximum expected flow velocity at the reference

density 0 at the atmospheric pressure and =7.

After the velocity va is solved the position ra is determined bywhich complete the basic equations.

𝑑𝑑𝑑𝑑�
= 𝒗𝒗�
𝑑𝑑𝑑𝑑

(10)

The boundary conditions are the zero normal velocity on solid surface except for infiltration. Rather than introducing
artificial repulsive force, the normal velocity component is set to zero when the particle comes within the distance hw fromthe boundary. The distance to the boundary is obtained by searching for the closest boundary particle which has theinformation of position and the normal direction as well as the roughness eight and the infiltration capacity. The enforced
normal velocity in the wall layer goes in the continuity equation (8) and to automatically increase the density and hence
the pressure.

３． SIMULATION AREA AND ITS RUNOFF CHARACTERISTICS
The present rainfall-runoff simulation is applied to a small catchment in a town in Malaysia. It is located in a subcatchment of a tributary of Perak River in Peninsular Malaysia in Kinta district of Perak State as shown in the red coloredarea of Fig.1. The focus is on a part of the catchment in a small town of Kampar centered at coordinates 4°19’12”N,
101°8’54”E shown in pink shaded area in Fig.2. It is located at the foot of Gunung Bujung Melaka of the highest elevationof 1234m and is irrigated by Keranji River (Sungai Keranji, Fig.2) and Kampar River (Sungai Kampar, Fig. 2) consisting4

Fig.1 location of simulation area in Kinta district in Peninsula Malaysia.

Fig.2 location of Kampar (Kampung Masjid) in Kinta District.

of alluvial soil enriched in tin minerals (Majlis Daerah Kampar17)). After the decline of the tin mining activities in 1980’s,
this area is left with tailing ponds that were formed by the ore digging at the low catchment area of Sungai Keranji. The
urbanized areas with paved streets nowadays, however, are subjected to frequent flash floodings in rainy seasons. Typicalrainfalls that cause street flooding are intense but of relatively short duration of less than one hour. The direct runoff fromthe mountain side rushes in certain areas called the flood hotspots resulting in more than a foot of water in half an hour.
The map in Fig.3 shows some details of the areas of frequent street flooding. Majlis Daerah Kampar17) started recording
the flood prone areas within the Kampar River catchment since 1999. The first area is in front of Maybank Kampar (Fig.3)
on the main street of Jalan Ipoh Kampar (the center of the map) where the traffic is affected by the street flooding 1 to 2
times every year. The second area is New Wah Loong which is the residential area located at the southwest part of themap. The flood in New Wah Loong is mainly due to the capacity of the bed of Sungai Keranji not deep enough to drain

5

Fig.3 Observation of Kampar Flash Flood Event on 8 March 2022.

the water coming from the mountains down steep slopes near Hospital Kampar (center of the map in Fig.3). This causes
the overflowed river flooding into the outlet drain on Jalan 4 and into the low-lying area of New Wah Long. According to
the villagers, the river water level will rise nearly 1m in less than 30 minutes and recedes after 2 hours.
Flood events were observed by the present authors in March 2022 and photos around the first hotspot near Maybank
Kampar and those near New Wah Long were taken and shown in Fig.3. The rainfall started at about 4:10pm. The sequenceof photos show how the runoff and flooding took place in about 20 minutes after the rain started. The rainfall intensity is
estimated to be about 50mm/h at the first 20minutes and reduced gradually and stopped by 4:30pm. The location involvedin the flash flood is mainly along Jalan Ampang, Jalan Masjid, Jalan Persekutuan Ipoh Kampar, 36 Food Court, Jalan 3
and Jalan 5 of New Wah Loong. Jalan Ampang, Jalan Masjid and Federal Road Ipoh Kampar also were all seriously
flooded. The drains at the small village located at the eastern end of Jalan Ampang was almost full of runoff although it is
wide and deep. Stormwater was collected from this village and Taman Golden Dragan and sent westward to naturalretention pond through the major drains along Jalan Ampang, Jalan Masjid and Jalan Persekutuan Ipoh Kampar. 10minafter the start of the rainfall, the overflow in front of Maybank Kampar, Jalan Ampang and Jalan Masjid started to occur
including the back lane. The drain is filled with the brown water with sediments transported from the hill. From theobservation, the final discharge outlets of the drainage system into the retention pond were not submerged and just the
inlet and upstream are flooded. It shows that the existing drain capacity is not sufficient to convey the peak runoff flowfrom the hill during high intensity storm. Some parts of Jalan Ipoh Kampar were also hit by heavy rain causing the traffic
jam in front of Maybank Kampar. The present runoff simulation is targeted to reproduce some of these flash flood events.

6

４． SIMULATION AND RESULTS
4.1 Simulation conditions
The view of the simulation area looking east (which is different from the map of Fig.2) is shown in the satellite image of
Fig.4(a). The corresponding numerical model of the terrain represented by the boundary particles spaced at 2m interval(the total of 0.75 million particles) that include the roads and the buildings is shown in Fig.4(b) with color indicating theelevation. The rectangular coordinates are set so that x direction is from east to west, y vertically upward and z from south
to north. The surface runoff from the mountain slopes flows mainly through the urban area and into a retention pond (bluearea near bottom center of Fig.4(b)). The simulation is mainly the overland flow in the area 1.5km east to west by 2.0km
north to south. The rain is simulated by lumps of water of volume 1m3 each and placed at intervals of 80m near the groundelevation as shown in black dots in Fig.4(b). 475 rain particles are introduced at one time. The positions of introducing
the rain particles are varied in time and the volume of the rain particles and the frequency of introducing rain particles areadjusted so that they correspond to the rainfall intensity of 80mm/h. The rainfall intensity is assumed constant through thesimulation period and is a little more intense than that observed in March 2022. The simulation calculation is run on aworkstation consisting of Intel 3.8GHz Xeon Gold 5222. The simulation computation for 30 minute rainfall runoff took
about 2 weeks of computation time.
The main objective in the present simulation is to find if the characteristics of the runoff and urban flash floods like thatobserved in March 2022 can be reproduced. Therefore, the runoff simulation was conducted for rainfall of 80mm/h for
30 minutes. The surface roughness height k is set to 1m in mountain areas with trees, while those for the natural groundwithout trees, paved surfaces and building surfaces are set as 0.5m, 0.1m and 0, respectively. Although the present modelallows initial abstraction and the infiltration depending on the ground conditions, the infiltration and the subsurface flow
are neglected. The ground infiltration delays the overland flow but the runoff due to sudden tropical rain storm takes placesuddenly and the effects of the slow infiltration and the subsurface flow are expected to be small.
The two areas where street inundation occurs frequently are indicated by circles in Fig. 4(a).

(a) Google satellite image of the simulation area(b) Numerical representation of the simulation area

Fig.4 Simulation area and the numerical model.

7

4.2 Simulation results
Fig. 5 shows the distribution and movement of the surface water represented by rain particles on the ground, at 6 minutes(Fig.5(a)) and at 25 minutes (Fig.5(b)) after the start of rainfall. The black dots indicate the rain particles. Each dot
corresponds to a lump of water with the volume corresponding to 1m3. In practice this volume is spread flat on the groundinitially but as the volume of water gets collected, they interact each other forming large body of water. It is seen that due
to the sudden rain of strong intensity, the overland flow pattern develops very quickly. This is the feature of the runoff inthis region with tropical rainstorms. The flow paths are seen to depend strongly on the topographical characteristics andtend to follow small valleys. The surface flow then appears to collect to certain locations at the foot of the mountain slopesthat correspond closely to the frequently flooded hot spots.
The runoff is accelerating as it travels down the steep hill slope to the lower elevation area. Until it reaches the town area,
the runoff from the hill is slowed down by the residential houses situated at the foot of the hill. The flow direction andvelocity of the runoff from the hill are determine by the topological feature of the terrain including the friction. Much of
the rainwater in the simulation area drains into the small lake located at the lower center. The lake works as a retention
pond, and it flows out to the small river (Keranji River) flowing near the west (lower) border of the simulated region.
Few minutes after the start of the rain, three major waterways are formed as a results of water flow from the hill. The
constructed new residential houses on Taman Golden Dragon (near the top of the map in Fig. 3 and indicated by TGD in
Fig. 5) have redirected the runoff towards the village located at the east end of Jalan Ampang as shown in Fig. 5. Due tothe rising elevation of Kampar Hospital (center of the map in Fig. 3, and indicated by KH in Fig.5), the runoff from thehill is divided into the villages located at both north and south parts of Kampar Hospital. This results in a total of two
water paths from Taman Golden Dragon and Kampar Hospital is flow towards the village located at the end of Jalan
Ampang eventually accumulating in this small valley. This village has a lower elevation compared to the surrounding
terrain, so it forms a bowl geometry and collecting runoff directly from the steep mountain. As seen in Fig.5(b), anotherwater paths toward the south of Kampar Hospital creates another patch of water.
In order to examine the water movement and accumulation in detail, three subareas Area A, Area B and Area C shown in(a) 6 minutes after start of rain(b) 25 minutes after start of rain

Fig.5 Distribution of surface water represented by particles after rainfall. The color scale
representing the elevation is the same as in Fig.4 and the black dots indicate rain particles. Taman Golden
Dragon is indicated by TGD and Kampar Hospital is indicated by KH.

8

Fig.6 are chosen. The close-up view of the surface water between Taman Golden Dragon and Hospital Kampar are shownin Fig.7. The color of water particles indicates the pressure. 10KPa corresponds to hydrostatic pressure of about 1m deep
water. The stream of surface water is seen to come down from the mountain and gathers at the foot of the slope. This isa few blocks east of the Hotspot A on Jalan Ipoh Kamar. At t=6 min small patch of water is seen there and at t=20min, thepressure is about 8kPa and the depth of water is reaching 1m. The patches of water collected along some buildings after
t=10 min. seem to correspond to street flooding seen in the photos Fig.3 (d) and (e) taken at 4:12.
Fig.8 shows similar accumulation of water in Area B south of Kampar Hospital. The water depth there is seen to increase
more than 0.5m and over some area. This water does flow into Keranji River but the water seems to stagnate and inundate
the area in short time. In the observation shown in Fig.3, no photos were taken in the area between Kampar Hospital and
Keranji River but this area has been known to be flooded frequently.
The overland flow in the urban area depends not only on the ground topography but on the layout of blocks and buildings.
Fig.9 shows the water particles in Area C in New Wah Loong. Though the depth indicated by the pressure is small, there
are areas with quite large patches of collected water. Some rainwater falling on the sloping rooftop drains directly to theground and to the lower elevation region. Some makes their way into the natural retention pond and Sungai Keranji but
some gets gathered in the low-lying areas, particularly Jalan 2 and 3 in New Wah Loong. This corresponds to photos (h),(i) and (j) in Fig.3 which show inundation of the streets by the buildings.

Fig.6 Locations of areas for detailed examination.

9(a) t=6 min.

(b) t=10min.

(c) t=20 min,Fig.7 Surface flow and inundation in Area A between Taman Golden Dragon and Hospital Kampar, the gray scale
indicates pressure in KPa(a) t=6 min.

(b) t=10min.

(c) t=20 min,.
Fig.8 Surface flow and inundation in Area B south of Kampar Hospital, the gray scale indicates pressure
in KPa.
(a) t=6 min.

(b) t=10min.

(c) t=20 min,Fig.9 Surface water in Area C in New Wah Loong area, the gray scale indicates pressure in KPa.

５． CONCLUSION
The three-dimensional weakly compressible smoothed particle hydrodynamics (WCSPH) has been applied to the10simulation of the direct runoff and the overland flow due to rainfall. It is applied to a small catchment area of 1.5km x
2km near a mountain in the town of Kampar, Perak, Malaysia. The targeted rainfall and flood events that were observedin March 2022 were simulated. The pattern of the surface water distribution in a complex real mountainous topography
appears to match the observation at the simulated site. The simulation result represents important features of the observed
flood events. The results do have limitation that the smallest volume of water is 1m3, but the resolution can be improved
if a computer with larger power is used. Although the present method has not been evaluated and directly compared withthe existing inundation prediction methods, it can be a new method that directly simulates the overland flow and inundation
due to rainfall in mountainous and urban terrains including structures. The subsurface water has totally been ignored but
the model allows the effects of the subsurface flow to be included for longer duration events.

ACKNOWLEDGEMENT
The present work was partly supported by Universiti Tunku Abdul Rahman Research Fund UTARRF/2022-C1/A03 and Malaysian
Ministry of Higher Education Fundamental Research Grant System FRGS/1/2019/TK01/UTAR/01/1.

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AUTHORSTan Sin Ying

Undergraduate student

Akihiko Nakayama Ph D. Fluid Mechanics, Hydraulics
Lye Xin Yan

Graduate student B.S.