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)

2

Input &

parameter

ObservationModel

uncertainty

Model ensembles Data assimilation

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

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

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)(

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

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

8

kk-1Time

Weight 1/n wk 1/n

Observation

Weighting Resampling

Prediction Analysis

Propagate state

SIR particle filter

9

10

Node : 60,411Mesh : 117,435Link : 177,843

Urban surface Sewer pipe network

11

Deterministic modeling case

12

• Water level and discharge at pumping station no. 3 were used as

synthetic observation

• Spatial distribution of rainfall was not considered

Synthetic observation

13

Without particle filtering With particle filtering

14

Inundation area - without particle filtering

15

Inundation area - with particle filtering

17

H-Q

relationship

Without

measuring Q

Uncertainties

Dynamic

characteristics

W.L

.

Q

W.L

.

QImages from www.hsc.re.kr

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

19

Likelihood

Resampling

uptQ

downth

: Updated Obs. W.L.

up

tQlateral

tQ: Upstream Q

: Lateral Qdown

th : Downstream W.L. : Noise

Upstream

Downstream

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

21

• 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

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

23

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

24

• 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

25

• 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

Thank you for your attention!seongjin.noh@gmail.com

27

• 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

28

파티클 필터 적용 시

Real-time monitoring system of sewer water level in Seoul, Korea

29

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

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

31

- 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.