-
CAHMDA-DAFOH Joint Workshop, 8-12 Sep. 2014, Austin, Texas, USA
Session 7: Advancing Data Assimilation Science for Operational Hydrology (11 Sep. 2014)
Particle Filtering for Hydraulic Models: Probabilistic Urban Inundation Modeling and
Assimilation-based H-Q Relationships
Seong Jin Noh (PhD, KICT, Korea)
Yeonsu Kim (PhD, Chungnam University, Korea)
Seungsoo Lee (PhD, Kyoto University, Japan)
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2
Input &
parameter
ObservationModel
uncertainty
Model ensembles Data assimilation
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3
Integrated urban flood model (DPRI, Kyoto Univ.)
- 2-D inundation model on the ground surface
- 1-D network model of sewer pipes
- Combined by a sub-model to exchange storm water between
the ground surface and the sewerage system
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4
Governing equations
Ground surface
sewdraine qqry
N
x
M
t
h
3/4
222)()(
h
vuMgn
x
Hgh
y
vM
x
uM
t
M
3/4
222)()(
h
vuNgn
y
Hgh
y
vN
x
uN
t
N
h : water depth
H : water elevation
u : x-direction water velocity
v : y-direction water velocity
M : uh(x-direction flux)
N : vh(y-direction flux)
re : effective rainfall
qdrain : unit area drainage discharge between ground and drain box
qsew : unit area drainage discharge between ground and sewer pipe
g : acceleration of gravity
n : Manning’s roughness coefficient
drainqx
Q
t
A
drain box
A : box bottom area
Q : discharge
qdrain : unit area drainage discharge between ground and drain box
FDM & leap-frog methods are adopted
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5
drainsew qqx
Q
t
A
Governing equations (sewer pipe)
0
0
0
: )(
: )(
A Ab
AAD
A AAf
h
s
)21(cos2 1
d
h
2
sin
0
A
A
sin1
0
R
R
2
0
a
gABs
The a is decided as 5.0m/s in this study
Fig. Hydraulic characteristic curves of the circular sewer pipe
AR
QQgn
x
HgA
x
uQ
t
Q p3/4
2)(
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6
① Inlet
Cdo:orifice coefficient (0.57)Cdw :weir coefficient (0.48)Q:dischargehhd:piezometric head of drain channelhmd:piezometric head of sewer pipe A:area of bottom hole
)(2 hmhddo hhgACQ
2
3
)(23
2hmhddw hhgLCQ
,if
,if
5.0
o
mdhd
bhh
5.0
o
mdhd
bhh
② Overflow
hdh
mdh )(2 hdmddo hhgACQ
Interaction model (surface water - sewer pipe)
hdhhmh
,if5.0
o
hdmd
bhh
5.0
o
hdmd
bhh 2
3
)(23
2hdhmdw hhgLCQ
,if
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7
- Also known as sequential Monte Carlo (SMC)
- Applicable for non-linear, non-Gaussian state-space models (most of hydraulic and
hydrologic models)
- Point mass (“particle”) representations of probability densities with associated
weights
- Expensive computation but easy for parallelization
- Wide-spread applications including image processing, target tracking, and flood
forecasting
- Noh, S. J., Rakovec, O., Weerts, A. H., and Tachikawa, Y.: On noise specification in data assimilation schemes
for improved flood forecasting using distributed hydrological models. J. Hydrol. in press, 2014.
Particle filtering
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8
kk-1Time
Weight 1/n wk 1/n
Observation
Weighting Resampling
Prediction Analysis
Propagate state
SIR particle filter
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9
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10
Node : 60,411Mesh : 117,435Link : 177,843
Urban surface Sewer pipe network
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11
Deterministic modeling case
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12
• Water level and discharge at pumping station no. 3 were used as
synthetic observation
• Spatial distribution of rainfall was not considered
Synthetic observation
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13
Without particle filtering With particle filtering
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14
Inundation area - without particle filtering
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15
Inundation area - with particle filtering
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17
H-Q
relationship
Without
measuring Q
Uncertainties
Dynamic
characteristics
W.L
.
Q
W.L
.
QImages from www.hsc.re.kr
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18
W.L
.Q
W.L
.Q
Assimilation-based H-Q
W.L.
W.L. and Q
Setup of 2-D dynamic wave model (observed data and Aerial photo)
Noise specification(inflow and roughness)
+Particle filtering
using observed H
Updating ensembles using observed W.L.
Likelihood
Particle filters
Updated W.L.
Flood routing using a hydraulic model
Upstream Q Lateral Q Downstream W.L.
Noise
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Likelihood
Resampling
uptQ
downth
: Updated Obs. W.L.
up
tQlateral
tQ: Upstream Q
: Lateral Qdown
th : Downstream W.L. : Noise
Upstream
Downstream
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20
– The Katsura river located in Kyoto, Japan
– Tenryuji station ~ Hazukshi station
– (total length: about 12.8km)
天竜寺
羽束師
桂
Tenryuji
Katsura
Hazukashi
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• Classification of Manning’s n
Flood plain
Main channel
Vegetated area
Flood plain(0.03~0.07)
Main channel(0.02~0.04)
Vegetated area(0.03~0.07)
Initial range of n for simulation
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22
• Estimated and observed H at Tenryuji station
• Estimated and observed Q at Tenryuji station
2004 2011 2013
2004 2011 2013
http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4
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34
35
36
37
38
0 1000 2000 3000 4000
Wate
r le
vel
(m)
Discharge(m3/s)
Particle
2004_OBS
2013_OBS
EST_H-Q
±AVG_Error
±MAX_Error
26.5%
Tenryuji
21
22
23
24
25
0 1000 2000 3000 4000
Wate
r le
vel
(m)
Discharge(m3/s)
Particle
2004_OBS
2013_OBS
EST_H-Q
±AVG_Error
±MAX_Error
Katsura
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• Applicability of particle filtering for twohydraulic models were evaluated.
• PF is sound when momentum equilibriumis important in the prediction models
• Assimilation-based estimation using 2-Dmodel and PF could provide reliable H-Qrelationships for poorly-gauged orungauged basins
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• PF and dimensionality• Different ensembles are required for
estimation of states and parameters• Hybrid DA to reduce dimensionality
• PF-MLEF, PF-EnKF, …
• Real-time applications• Parallel computing for ensembles• Parallel computing within a ensemble
• More attention is needed to improve DAto consider both covariance and dynamicsof the system
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Thank you for your [email protected]
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• Estimated Manning’s n at main channel
• Estimated lateral inflow from Tenryuji to Katsura station
2004 2011 2013
2004 2011 2013
http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4http://www.sameshow.com/powerpoint-to-flash.php?sid=4
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파티클 필터 적용 시
Real-time monitoring system of sewer water level in Seoul, Korea
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0
500
1,000
1,500
2,000
2,500
3,000
3,500
10 12 14 16 18 20
Dis
cha
rge(
m3/s
)
Water level(m)
2004
2011
2013
0.020
0.022
0.024
0.026
0.028
0.030
0.032
0 500 1000 1500 2000 2500 3000
Ma
nn
ing
n a
t m
ain
ch
an
nel
Upstream discharge(m3/s)
2004
2011
2013Q & n at the main channel
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30
AmAm
pp ghAQ 235.0
)(291.0 mpm hhgAQ
• In the case of (hp >= hm)
If, (hm / hp > 2/3)
If, (hm / hp = hp)
If, (hp / hm > 2/3)
If , (hp / hm
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- Urban inundation due to heavy rainfall and climate change is an inevitable
problem for many cities around the world and constitutes a severe threat
to residential life, property and infrastructure(Mark et al., 2004)
- Therefore, it is important to accurately simulate urban hydrological
processes and efficiently predict the potential risks of urban floods (Lee et
al., 2009)
- However, it is insufficient to obtain accurate predictions due to various
uncertainties coming from input forcing data, model parameters, and
observations.