Stochastic runoff forecasting and real time control of urban drainage systems

Ude af øje, ude af sind, ude af kontrol, 13/03/2013

Roland Löwe (DTU Compute) rolo@imm.dtu.dk

Luca Vezzaro (DTU Environment / Krüger A/S)

Morten Grum (Krüger A/S)

Peter Steen Mikkelsen (DTU Environment)

Henrik Madsen (DTU Compute)

13/03/2013 Stochastic runoff forecasting and RTC 2 DTU Compute, Technical University of Denmark

Why do we need probabilistic forecasts? - The way home

10min 5min

20min

13/03/2013 Stochastic runoff forecasting and RTC 3 DTU Compute, Technical University of Denmark

Why do we need probabilistic forecasts? - The way home

20min 5min

20min

13/03/2013 Stochastic runoff forecasting and RTC 4 DTU Compute, Technical University of Denmark

Source: Vezzaro and Grum (2012)

Why do we need probabilistic forecasts? – Stormwater Storage Basins

13/03/2013 Stochastic runoff forecasting and RTC 5 DTU Compute, Technical University of Denmark

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Generating probabilistic forecasts

13/03/2013 Stochastic runoff forecasting and RTC 6 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts

Output Y Model f(X) Stochastic term σ(X) = +

e.g. flow e.g. reservoir cascade,

simple clarifier model

describes error in model description

13/03/2013 Stochastic runoff forecasting and RTC 7 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts – The Greybox Modeling Approach

• combines prior physical knowledge with data

• the system is not completely described by physical equations, but equations and parameters are physically interpretable

13/03/2013 Stochastic runoff forecasting and RTC 8 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts – Why Greybox Models

vs. white box models

• online applications – need simple, fast models for real time operation

• greybox models can be tuned for forecasting

• white box models typically do not account for uncertainty

vs. black box models

• include physical knowledge about the system in the model

• model nonlinear relationships which is not possible e.g. in ARX, ARMAX ...

13/03/2013 Stochastic runoff forecasting and RTC 9 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts – Runoff Forecasting Models

Graph from Breinholt et al. (2011)

𝑑𝑆1 = 𝐴 ∙ 𝑃 + 𝑎0 −1

𝑘𝑆1 𝑑𝑡

𝑑𝑆2 =1

𝑘𝑆1 −

1

𝑘𝑆2 𝑑𝑡

𝜎1 ∙ 𝑆1 𝑑𝜔1

𝜎2 ∙ 𝑆2 𝑑𝜔2

+

𝑄𝑡 =1

𝑘𝑆3 + 𝐷 + 𝜀𝑡

𝐴 – area parameter

k – time constant

𝑎0 – mean dry weather flow

𝑃 – rain input

𝑄𝑡 – observed flow

𝐷 – dry weather variation

13/03/2013 Stochastic runoff forecasting and RTC 10 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts – Runoff Forecasting Models

Graph from Breinholt et al. (2011)

𝑑𝑆1 = 𝐴 ∙ 𝑃 + 𝑎0 −1

𝑘𝑆1 𝑑𝑡

𝑑𝑆2 =1

𝑘𝑆1 −

1

𝑘𝑆2 𝑑𝑡

𝜎1 ∙ 𝑆1 𝑑𝜔1

𝜎2 ∙ 𝑆2 𝑑𝜔2

+

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13/03/2013 Stochastic runoff forecasting and RTC 11 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts – Runoff Forecasting Models - Updating

Predicted states (Basin storage)

Graph from Breinholt et al. (2011)

Input

predict

Flow

predict

Difference predicted -measured flow

Reconstructed states

update weighting by state and observation uncertainty

13/03/2013 Stochastic runoff forecasting and RTC 12 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts – Runoff Forecasting Models - Updating

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13/03/2013 Stochastic runoff forecasting and RTC 13 DTU Compute, Technical University of Denmark

Generating probabilistic forecasts – Runoff Forecasting Models - Adaptivity

rain

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time steps [2min]

K

600 800 1000 1200 1400

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𝑑𝑆1 = 𝐴 ∙ 𝑃 + 𝑎0 −1

𝑘𝑆1 𝑑𝑡 + 𝜎1 ∙ 𝑆1 𝑑𝜔1

𝑑𝑆2 =1

𝑘𝑆1 −

1

𝑘𝑆2 𝑑𝑡 + 𝜎2 ∙ 𝑆2 𝑑𝜔2

𝒅𝒌 = 𝟎 𝒅𝒕 + 𝝈𝟒 𝒅𝝎𝟒

𝑄𝑡 =1

𝑘𝑆3 + 𝐷 + 𝜀𝑡

13/03/2013 Stochastic runoff forecasting and RTC 14 DTU Compute, Technical University of Denmark

Stochastic Greybox Models – Pros and Cons

application range for greybox models

• online applications and forecasting

• quantifying simulation / forecast uncertainty

advantages

• simple, fast models

• state updating – models adapt to observations

• flexible framework for modeling forecast uncertainty

• typically better predictions than deterministic model

• adaptivity can be implemented

limitation

• complex, physical models cannot be handled in the current framework

13/03/2013 Stochastic runoff forecasting and RTC 15 DTU Compute, Technical University of Denmark

Stochastic Greybox Models –Software CTSM

CTSM = Continuous Time Stochastic Modeling

• model development, parameter estimation, simulation and forecasting

• developed at DTU Compute

• implement as a package in R (‘open source MATLAB’)

• download from www.ctsm.info (and www.r-project.org + www.rstudio.com)

13/03/2013 Stochastic runoff forecasting and RTC 16 DTU Compute, Technical University of Denmark

Generating Probabilistic Forecasts – What is a good forecast???

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13/03/2013 Stochastic runoff forecasting and RTC 17 DTU Compute, Technical University of Denmark

Generating Probabilistic Forecasts – What is a good forecast???

reliability

% of observations not included in a ‘x %’ prediction interval

Requirement

sharpness

width of a ‘x %’ prediction interval

Minimize

skillscores

(e.g. CRPS – continuous ranked probability score)

Minimize 0

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13/03/2013 Stochastic runoff forecasting and RTC 18 DTU Compute, Technical University of Denmark

Case Study 1

Value of radar rainfall observations and forecasts for online runoff forecasting

(thank you to Aalborg University and DMI for providing radar data)

13/03/2013 Stochastic runoff forecasting and RTC 19 DTU Compute, Technical University of Denmark

Radar rainfall and online runoff forecasting !

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0 1.500 3.000 Meters

• Ballerup and Damhusåen catchments

• 5min rain gauge observations

• 10min C-band radar data from Stevns (DMI / AAU)

• Period 25/06-06/09/2010

13/03/2013 Stochastic runoff forecasting and RTC 20 DTU Compute, Technical University of Denmark

Radar rainfall and online runoff forecasting – comparing radar and rain gauge input

• use mean area rainfall

• 100min runoff forecasts with different rainfall inputs

• using radar rainfall measurements and forecasts reduces error of probabilistic runoff forecasts (compared to input from rain gauges)

Ballerup Damhusåen

RMSE Raingauge

276.8 3464.1

RMSE Radar

260.3 2624.7

CRPS Raingauge

152.3 1463.3

CRPS Radar

144.9 1399.1

RMSE (root mean square error) – average error of 100min point forecast [m3]

CRPS (continuous ranked probability score) – average error of probabilistic forecast

13/03/2013 Stochastic runoff forecasting and RTC 21 DTU Compute, Technical University of Denmark

Radar rainfall and online runoff forecasting – comparing model complexity

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0 1.500 3.000 Meters

13/03/2013 Stochastic runoff forecasting and RTC 22 DTU Compute, Technical University of Denmark

Radar rainfall and online runoff forecasting – comparing model complexity

• use rain gauge input

• model 1 – mean area rainfall

• model 2 – subcatchment model

• 100min runoff forecasts with different model structures

• accounting for spatial distribution of rainfall in the model improves forecasts

Ballerup Damhusåen

RMSE model 1

276.8 3464.1

RMSE model 2

262.4 2631.3

CRPS model 1

152.3 1463.3

CRPS model 2

146.0 1352.2

RMSE (root mean square error) – average error of 100min point forecast [m3]

CRPS (continuous ranked probability score) – average error of probabilistic forecast

13/03/2013 Stochastic runoff forecasting and RTC 23 DTU Compute, Technical University of Denmark

Case Study 2

Value of probabilistic runoff forecasts in real time control

(in cooperation with Krüger AS)

13/03/2013 Stochastic runoff forecasting and RTC 24 DTU Compute, Technical University of Denmark

Real Time Control of Stormwater Flows

• dynamic operation of drainage system

• objectives:

– reduction of combined sewer overflows

– avoiding flooding

– ...

• actuators: pumps, valves

• operational examples: Québec, Paris, Dresden

Source: Stadtentwässerung Dresden

13/03/2013 Stochastic runoff forecasting and RTC 25 DTU Compute, Technical University of Denmark

The Lynetten Catchment

13/03/2013 Stochastic runoff forecasting and RTC 26 DTU Compute, Technical University of Denmark

Real Time Control Lynetten Catchment (METSAM project)

Source: Krüger A/S

Sewer Network Control

(DORA)

Current state Desired State

13/03/2013 Stochastic runoff forecasting and RTC 27 DTU Compute, Technical University of Denmark

Integrated control strategy (Dynamic Overflow Risk Analysis – DORA)

• runoff forecasts are uncertain

• uncertainty varies

– between wet and dry weather

– in the course of events

– from event to event

• proper decision making requires dynamic quantification of forecast uncertainty Source: Vezzaro and Grum (2012)

13/03/2013 Stochastic runoff forecasting and RTC 28 DTU Compute, Technical University of Denmark

Real Time Control Lynetten Catchment (METSAM project)

Control Strategy (DORA)

Model

now future

Fixed uncertainty

distribution

Measurements (flows & volumes)

rain

flow future

Current state Future evolution

13/03/2013 Stochastic runoff forecasting and RTC 29 DTU Compute, Technical University of Denmark

Stochastic runoff models

Control Strategy (DORA)

Model

now future

Fixed uncertainty

distribution

Measurements (flows & volumes)

rain

flow future

Current state Future evolution

13/03/2013 Stochastic runoff forecasting and RTC 30 DTU Compute, Technical University of Denmark

Stochastic runoff models

Control Strategy (DORA)

Model

now future

Measurements (flows & volumes)

rain

Current state Future evolution

Greybox model

13/03/2013 Stochastic runoff forecasting and RTC 31 DTU Compute, Technical University of Denmark

Probabilistic Runoff Forecasting – Example

Forecast horizon 4 min Forecast horizon 120 min

black – observation, green – state of the art deterministic forecast, red / blue – probabilistic forecast with 95% confidence bounds

13/03/2013 Stochastic runoff forecasting and RTC 32 DTU Compute, Technical University of Denmark

Experimental design

Stochastic Greybox Model

(CTSM)

Control Algorithm

(DORA)

Simplified Catchment

Model

(Water Aspects)

simulated basin overflow resulting

from control decisions

generates probabilistic

forecasts

evaluates risk of overflow and sends

control decision

13/03/2013 Stochastic runoff forecasting and RTC 33 DTU Compute, Technical University of Denmark

Effect of Probabilistic Forecasts on Real Time Control

0

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Overflow Volume

deterministic forecast stochastic forecast

overflow volume in 7 sample events increased by +3%

(compared to state-of-the-art)

control objective is not overflow volume but overflow cost

(overflow volume weighted by location where it occurs)

13/03/2013 Stochastic runoff forecasting and RTC 34 DTU Compute, Technical University of Denmark

Effect of Probabilistic Forecasts on Real Time Control

0

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Overflow Cost

deterministic forecast stochastic forecast

overflow cost in 7 sample events reduced by -32%

(compared to state-of-the-art)

13/03/2013 Stochastic runoff forecasting and RTC 35 DTU Compute, Technical University of Denmark

Summary

13/03/2013 Stochastic runoff forecasting and RTC 36 DTU Compute, Technical University of Denmark

Summary and Outlook

Use greybox models for

• online applications –simple, fast models for real time operation that adapt to online measurements

• quantifying predictive uncertainties

Applications

• runoff forecasting – simulation studies indicate improved decisions in real time control

• other applications where forecasts and quantification of uncertainties are required (predicting capacity of secondary clarifiers, predicting TSS)

Future work

• study effect of probabilistic forecasts on real time control in more detail

• model runoff forecast uncertainties depending on rainfall input (rainfall patterns, weather model data)

Thank you! For further info: rolo@dtu.dk