![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-5-320.jpg)
![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-10-320.jpg)
![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-12-320.jpg)
![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-13-320.jpg)
![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-16-320.jpg)
![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-17-320.jpg)
![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-20-320.jpg)
![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](https://image.slidesharecdn.com/stochasticrunoffforecastingandrealtimecontrolofurbandrainagesystems-170507210533/85/Stochastic-runoff-forecasting-and-real-time-control-of-urban-drainage-systems-22-320.jpg)
Stochastic runoff forecasting and real time control of urban drainage systems
- 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 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! !. !. !. !. !. !. !. !. !. !. !. !. !. !. !. !. !. 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 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! !. !. !. !. !. !. !. !. !. !. !. !. !. !. !. !. !. 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