The document discusses stochastic runoff forecasting and real-time control of urban drainage systems, emphasizing the importance of probabilistic forecasts for improved decision-making. It presents the advantages of greybox models for online applications, their ability to adapt to measurements, and their better prediction capabilities compared to deterministic models. The findings indicate that integrating probabilistic forecasts can significantly reduce overflow costs in real-time control scenarios.

1. 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)

2. 13/03/2013Stochastic runoff forecasting and RTC2 DTU Compute, Technical University of Denmark
Why do we need probabilistic forecasts? -
The way home
10min5min
20min

3. 13/03/2013Stochastic runoff forecasting and RTC3 DTU Compute, Technical University of Denmark
Why do we need probabilistic forecasts? -
The way home
20min5min
20min

4. 13/03/2013Stochastic runoff forecasting and RTC4 DTU Compute, Technical University of Denmark
Source: Vezzaro and Grum (2012)
Why do we need probabilistic forecasts? –
Stormwater Storage Basins

5. 13/03/2013Stochastic runoff forecasting and RTC5 DTU Compute, Technical University of Denmark
0100030005000
predictedrunoffvolume[m3]
12.08. 01:20 14.08. 00:00
0100030005000
predictedrunoffvolume[m3]
12.08. 01:20 14.08. 00:00
Generating probabilistic forecasts

6. 13/03/2013Stochastic runoff forecasting and RTC6 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

7. 13/03/2013Stochastic runoff forecasting and RTC7 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

8. 13/03/2013Stochastic runoff forecasting and RTC8 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
...

9. 13/03/2013Stochastic runoff forecasting and RTC9 DTU Compute, Technical University of Denmark
Generating probabilistic forecasts –
Runoff Forecasting Models
Graph from Breinholt et al.
(2011)
𝑑𝑆1 = 𝐴 ∙ 𝑃 + 𝑎0 −
1
𝑘
𝑆1 𝑑𝑡
𝑑𝑆2 =
1
𝑘
𝑆1 −
1
𝑘
𝑆2 𝑑𝑡
𝜎1 ∙ 𝑆1 𝑑𝜔1
𝜎2 ∙ 𝑆2 𝑑𝜔2
+
𝑄𝑡 =
1
𝑘
𝑆3 + 𝐷 + 𝜀𝑡
𝐴 – area parameter
k – time constant
𝑎0 – mean dry weather flow
𝑃 – rain input
𝑄𝑡 – observed flow
𝐷 – dry weather variation

10. 13/03/2013Stochastic runoff forecasting and RTC10 DTU Compute, Technical University of Denmark
Generating probabilistic forecasts –
Runoff Forecasting Models
Graph from Breinholt et al.
(2011)
𝑑𝑆1 = 𝐴 ∙ 𝑃 + 𝑎0 −
1
𝑘
𝑆1 𝑑𝑡
𝑑𝑆2 =
1
𝑘
𝑆1 −
1
𝑘
𝑆2 𝑑𝑡
𝜎1 ∙ 𝑆1 𝑑𝜔1
𝜎2 ∙ 𝑆2 𝑑𝜔2
+
0100030005000
predictedrunoffvolume[m3]
12.08. 01:20 13.08. 00:40 14.08. 00:00

11. 13/03/2013Stochastic runoff forecasting and RTC11 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

12. 13/03/2013Stochastic runoff forecasting and RTC12 DTU Compute, Technical University of Denmark
Generating probabilistic forecasts –
Runoff Forecasting Models - Updating
0100200300400500600
predictedrunoffvolume[m3]
11.08. 23:50 12.08. 23:10 13.08. 22:30

13. 13/03/2013Stochastic runoff forecasting and RTC13 DTU Compute, Technical University of Denmark
Generating probabilistic forecasts –
Runoff Forecasting Models - Adaptivity
rainintensity[mm/min]
600 800 1000 1200 1400
0.000.100.20
flow[m3/s]
600 800 1000 1200 1400
0.01.02.0
time steps [2min]
K
600 800 1000 1200 1400
040008000
𝑑𝑆1 = 𝐴 ∙ 𝑃 + 𝑎0 −
1
𝑘
𝑆1 𝑑𝑡 + 𝜎1 ∙ 𝑆1 𝑑𝜔1
𝑑𝑆2 =
1
𝑘
𝑆1 −
1
𝑘
𝑆2 𝑑𝑡 + 𝜎2 ∙ 𝑆2 𝑑𝜔2
𝒅𝒌 = 𝟎 𝒅𝒕 + 𝝈 𝟒 𝒅𝝎 𝟒
𝑄𝑡 =
1
𝑘
𝑆3 + 𝐷 + 𝜀𝑡

14. 13/03/2013Stochastic runoff forecasting and RTC14 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

15. 13/03/2013Stochastic runoff forecasting and RTC15 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)

16. 13/03/2013Stochastic runoff forecasting and RTC16 DTU Compute, Technical University of Denmark
Generating Probabilistic Forecasts –
What is a good forecast???
0100030005000
predictedrunoffvolume[m3]
12.08. 01:20 14.08. 00:00
0100030005000
predictedrunoffvolume[m3]
12.08. 01:20 14.08. 00:00
0100030005000
predictedrunoffvolume[m3]
12.08. 01:20 14.08. 00:00

17. 13/03/2013Stochastic runoff forecasting and RTC17 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 0100020003000400050006000
predictedrunoffvolume[m3]
12.08. 01:20 13.08. 00:40 14.08. 00:00

18. 13/03/2013Stochastic runoff forecasting and RTC18 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)

19. 13/03/2013Stochastic runoff forecasting and RTC19 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

20. 13/03/2013Stochastic runoff forecasting and RTC20 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

21. 13/03/2013Stochastic runoff forecasting and RTC21 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

22. 13/03/2013Stochastic runoff forecasting and RTC22 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

23. 13/03/2013Stochastic runoff forecasting and RTC23 DTU Compute, Technical University of Denmark
Case Study 2
Value of probabilistic runoff forecasts in real
time control
(in cooperation with Krüger AS)

24. 13/03/2013Stochastic runoff forecasting and RTC24 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

25. 13/03/2013Stochastic runoff forecasting and RTC25 DTU Compute, Technical University of Denmark
The Lynetten Catchment

26. 13/03/2013Stochastic runoff forecasting and RTC26 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

27. 13/03/2013Stochastic runoff forecasting and RTC27 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)

28. 13/03/2013Stochastic runoff forecasting and RTC28 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

29. 13/03/2013Stochastic runoff forecasting and RTC29 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

30. 13/03/2013Stochastic runoff forecasting and RTC30 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

31. 13/03/2013Stochastic runoff forecasting and RTC31 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

32. 13/03/2013Stochastic runoff forecasting and RTC32 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

33. 13/03/2013Stochastic runoff forecasting and RTC33 DTU Compute, Technical University of Denmark
Effect of Probabilistic Forecasts on Real
Time Control
0
100
200
300
400
500
600
700
800
1000m3
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)

34. 13/03/2013Stochastic runoff forecasting and RTC34 DTU Compute, Technical University of Denmark
Effect of Probabilistic Forecasts on Real
Time Control
0
2
4
6
8
10
12
14
16
18
Millions
Overflow Cost
deterministic forecast stochastic forecast
overflow cost in 7
sample events
reduced by -32%
(compared to
state-of-the-art)

35. 13/03/2013Stochastic runoff forecasting and RTC35 DTU Compute, Technical University of Denmark
Summary

36. 13/03/2013Stochastic runoff forecasting and RTC36 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)

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