Real time modeling of water infrastructure using hydraulic models and data assimilation

Smart Sustainable Cities seminar

DTU Lyngby

6th of February 2017

By

Asst. Prof.

Morten Borup

DTU Environment

20 October 2016

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Contents

• Detailed urban hydrological models (HIFI models)

– Why online HIFI models

• The Ensemble Kalman Filter (EnKF)

• Surrogates of HIFI models

Detailed urban hydrological models (HIFI models)

Mike Urban (DHI) model of Avedøre

WWTP catchment

1707 sub-catchments

6601 Manholes

7749 Pipe & channel sections

40 Pumps

40 Basins

Etc.

5 km

Can potentially be all-knowing: Water levels, volumes, flows, concentrations - everywhere

Outlet

The models can be made automatically - If the asset data base is well maintained! Can adapt to system

changes (as opposed to data driven models)

Full 1D St. Venant equations

Conservation of mass:

Conservation of momentum:

Hydraulic computations

Potential of online HIFI model • Warning system

• Real time control

• Online supervision of gauges

• Error detection

Not used because:

• Computational cost

• Very uncertain rain input

• Lack of update algorithm’s

Main model input:

Rain data

Water consumption (waste water production)

5 km 5

Outlet

Detailed urban hydrological models (HIFI models)

Input data uncertain: All input data uncertain – Data assimilation is needed

......

.....

Measured rain

Perturbated

rain

MIKE URBAN

MIKE URBAN

MIKE URBAN

......

.....

Observation

EnKF

Ensemble based updating

Ensemble Kalman Filter

q Value

Xi,3 Xi,2 Xi,1

X1

Ensemble Kalman Filter

q Value

Ensemble of models used to represent state uncertainty (model error)

Estimate of the error covariance can be calculated directly from ensemble:

Xi,3 Xi,2 Xi,1

X4

X5

X1 X2

X3

σ1,3 = 1

𝑁 − 1 (𝑋𝑖,1 − 𝑋,1)(𝑋𝑖,3 − 𝑋,3)

𝑁

𝑖

𝜎𝑧2 z

𝑋1,3= 𝑋1,3 + 𝜎𝑋1,3,𝑞

𝜎𝑞2+𝜎𝑧

2 (𝑧 − 𝑞)

Ensemble Kalman Filter

z

Value Xi,1 Xi,2 Xi,3 q

𝜎𝑧2

Ensemble of models used to represent state uncertainty (model error)

Estimate of the error covariance can be calculated directly from ensemble:

σ1,3 =

1

𝑁 − 1 (𝑋𝑖,1 − 𝑋,1)(𝑋𝑖,3 − 𝑋,3)

𝑁

𝑖

𝑋1,3= 𝑋1,3 + 𝜎𝑋1,3,𝑞

𝜎𝑞2+𝜎𝑧

2 (𝑧 − 𝑞)

X4

X5

X1 X2

X3

Model setup: Link and weir

A =57 ha Tc = 60 min

Weir

Point at Link 7

Situation without update

20:00 22:00 00:00 02:00 04:00 06:00

12.4

12.6

12.8

13

13.2

13.4

13.6

time

Wate

r Level [m

]

Water level at link 7

Truth

Base

Ensemble of 20 – No update

Weir Link 7

When updating using EnKF

3:00 4:00 5:0012

12.2

12.4

12.6

12.8

13

13.2

13.4

13.6

time

Wate

r Level [m

]

WL at Link7 chainage 935 - 5/11 2010

Base

Truth

Updated

Weir Link 7

It works

Synthetic test on distributed system

• Updating using upstream wl gauge

• Downstream flow validation

Two rainfall observation scenarios: Scenario 1: Known rainfall error statistics Scenario 2: Rain observations 2.5 or 0 um/s

Two wl gauge scenarios: No bias: White noise on observation Bias: + Coloured noise (+5 cm)

R2

Downstream flow validation

Poor rain data + poor observations

=> good model

Benefits in using EnKF for HIFI models

• Robust • Flexible • Good uncertainty estimates • Can utilize ensemble input • Can utilize most kinds of observations Drawbacks: - computational cost

04/10/2016 Surrogate modelling of inundation 16 DTU Environment, Technical University of Denmark

Making Surrogates of HIFI models

• Division of system into compartments:

• Model volume of water with mass balance:

MU SM

Slides by Cecilie Thrysøe

04/10/2016 Surrogate modelling of inundation 17 DTU Environment, Technical University of Denmark

Training data for SM

• Vol-Q relationships are extracted from steady state values

Rain input Original model output Training data

• Drainage system results

04/10/2016 Surrogate modelling of inundation 19 DTU Environment, Technical University of Denmark

Preliminary results

• Elster Creek catchment, Melbourne, Australia

04/10/2016 Surrogate modelling of inundation 20 DTU Environment, Technical University of Denmark

Preliminary results

• Elster Creek catchment, Melbourne, Australia

04/10/2016 Surrogate modelling of inundation 21 DTU Environment, Technical University of Denmark

Preliminary results

• Elster Creek catchment, Melbourne, Australia

• Steady state training data

• SM output

04/10/2016 Surrogate modelling of inundation 22 DTU Environment, Technical University of Denmark

Preliminary results

• Elster Creek catchment, Melbourne, Australia

• Steady state training data

04/10/2016 Surrogate modelling of inundation 23 DTU Environment, Technical University of Denmark

Preliminary results

• Elster Creek catchment, Melbourne, Australia

• Steady state training data

• Splitting compartment

• Splitting compartment gives the best results!

04/10/2016 Surrogate modelling of inundation 24 DTU Environment, Technical University of Denmark

Conclusions

• EnKF can be used to make online models with HIFI models

• Surrogate models can be made for HIFI models to achieve large reduction in computational costs.

20 October 2016

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25

Questions?