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Impact of time displaced precipitation estimates for online updated models
- 1. Impact of time displaced precipitation estimates for online updated models Uncertainty and adaptive estimation in storm- and wastewater system modelling Morten Borup DTU Environment & Krüger A/S, Veolia VWS Denmark Morten Grum Krüger A/S, Veolia VWS Denmark Peter Steen Mikkelsen DTU Environment
- 2. Rain detection for runoff modelling Gauges: No Movement, no spatial distribution. Accurate. Radar: Movement, Spatial distribution. Inaccurate. Rain detection method affect nature of model errors GAUGES: Time displacements RADAR: Scaling RUNOFF
- 3. Rain detection for runoff modelling Gauges: No Movement, no spatial distribution. Accurate. Radar: Movement, Spatial distribution. Inaccurate. RUNOFF Updated online models Can not distinguish time shifts from magnitude errors. Updating: Synchronization issues. Objective: Compare impact of time displaced rain data with that of scaled rain data for online updated models.
- 4. Simplification/assumptions Gauges: No Movement, no spatial distribution. Accurate. Radar: Movement, Spatial distribution. Inaccurate. RUNOFF 1d setup Movement = time displacement
- 5. Online storm water model Model Measured Modelled vs. Measured
- 6. Online storm water model Model With Updating Analysis Forecast error
- 7. Online storm water model Model With Updating (rain gauge)
- 8. Online storm water model Model With Updating (RADAR)
- 9. Size of displacements Average rain cell velocity in northern Europe 10 m/s 5 m/s not unusual 0 2 4 6 8 10 0 1 2 3 Time[min] Distance [km] Travel time 5 m/s 10 m/s
- 10. Methodology 011001 010011 011100 11 True rain 011001 010011 011100 11 Time displaced rain data 011001 010011 011100 11 Biased rain data Model True model states Updated Model Updated Model 011001 010011 011100 11 Displaced Forecast 011001 010011 011100 11 Biased Forecast Comparisons
- 11. Precipitation truth Displaced rain data(rain gauge) Biased rain Rain data 2005)(199528184SvkPtrue −= )()( atPtP truedisp −= 100 1),()( bias truebias ctPctP ±=⋅=
- 12. Time Area model Observation (true runoff) Updated forecast model (x min. forecast) Model ∑−= = t Tcti iP Tc A tQ )()( ∑−= = t Tcti trueobs iP Tc A tQ )()( TcxforiPiP Tc A tQ t xti f xt Tcti truex < += ∑∑ −= −− −= ,)()()( 1 Time Area 100% Tc
- 13. Error quantification Forecast error SSerr ( ) TcxforiPiP Tc A iPiPiP Tc A tQtQte t xti ftrue t xti f xt Tcti true t Tcti truexobs <−= −−=−= ∑ ∑∑∑ −= −= −− −=−= )()( )()()()()()( 1 ( )∑ ∑∑ = −== − = n j t xti ftrue n i iPiP Tc A ie 1 2 2 1 2 ))()(()( Catchment specific Rain estimation error
- 14. SSerr(disp)/SSerr(bias) independent of catchment: Direction of time displacement without importance: No importance if bias is negative or positive: Convenient properties ∑∑ ∞ + ∞ − −=− n cnn n cnn aaaa ∑∑ ∞∞ −=− nn PPPP 10.1*90.0* ( ) ( )∑ ∑ ∑ ∑ = −= = −= ⋅− −− = n j t xti ftrue n j t xti truetrue err err iPciP Tc A aiPiP Tc A biasSS dispSS 1 22 1 22 )()( )()( )( )(
- 15. Results Tc = 40 minutes
- 16. Results SSerr(disp.)= SSerr(bias) Any TcTc = 40 minutes
- 17. Conclusion Rain data requirements are different for updated models. Independent of Tc: Frequent updating/short term forecasts: Correct timing essential -> (1) Radar better than gauges. (2) Many bad gauges better than few good gauges. Infrequent updating/long forecasts: Accuracy the more important.
- 18. Questions?