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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
in
ten
sity [
mm
/min
]
600 800 1000 1200 1400
0.0
00
.10
0.2
0
flo
w [m
3/s
]
600 800 1000 1200 1400
0.0
1.0
2.0
time steps [2min]
K
600 800 1000 1200 1400
04
00
08
00
0
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
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800
10
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m3
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
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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
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