1 / 19

Bayesian model averaging approach for urban drainage water quality modelling

Bayesian model averaging approach for urban drainage water quality modelling. Gabriele Freni gabriele.freni@unikore.it. Università degli Studi di Enna “ Kore ”. Introduction. The model approach has to be chosen in order to obtain a compromise between. Complexity. Accuracy.

abbott
Download Presentation

Bayesian model averaging approach for urban drainage water quality modelling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Bayesian model averagingapproach for urban drainage water qualitymodelling Gabriele Freni gabriele.freni@unikore.it Università degli Studi di Enna “Kore”

  2. Introduction The model approach has to be chosen in order to obtain a compromise between Complexity Accuracy • Lack in knowledge sewer quality processes • Low level of over-parameterization as well as low degree of auto-correlation and possible compensation effects among the parameters • Common available field data: TSS, BOD, COD, NH4

  3. State of the art in Uncertainty Analysis • Uncertainty analysis can provide useful hints for evaluating model reliability in dependence with data availability • getting knowledge on thesources of errorsin the modelling process todefinepriorities for model improvement (Willems, 2005) • for assessing riskswhen model results are used on the basis of decisions • quantitative uncertainty analysis can provide an illuminating role to helptarget data gatheringefforts (Frey, 1992). • The evaluation of parameter uncertainties is necessary to estimate theimpact of these onmodel performance(Beck, 1987). • BUT…. • Sometimes the modeller ends up with more questions than at the beginning

  4. Few possible model alternatives 8 modelling approaches have been analysed considering the combination of 4build-up models and 2 wash-off models:

  5. Few possible structural alternatives Parameters variation range:

  6. Fossolo (near Bologna - Italy) The experimental catchment: Fossolo Catchment Bologna (IT) • 12 recorded eventsfrom 22/4/94 to 21/8/97 • Drained area 40,71 ha, with an impervious percentage of 75% • The drainage network ends in a polycentric section pipe 144 cm high and 180 cm wide  200 m N

  7. Fossolo (near Bologna) Event 21st August 1997 • ADWP = 3 [d] • Imax = 56 [mm/h] • Iaver = 16 [mm/h] • Qmax = 1 [m3/s] • Ttot = 100 [min]

  8. Final Bayesian update (with all the ev.) SIM_01 SIM_02 SIM_03 SIM_04 SIM_05 SIM_06 SIM_07 SIM_08 (using all the database)

  9. Which model to choose? NO Maybe Maybenot NO NO YES Maybe Maybenot

  10. Which model to choose? • Best efficiency is not informative: several modelling structure have similar efficiencies (model structure equifinality)

  11. Model Averaging techniques (MA) Y Y Y Y Y Y Model 4 Average Model 1 Model 3 Model 2 Model 5 t t t t t t w3 w1 w2 w5 w4

  12. The Bayesian Model Average (BMA) Posterior probability is obtained as conditional sum of the posterior probabilities provided by each possible model: Each model is treated by Bayesian uncertainty analysis: Weights are computed by Bayesian uncertainty analysis

  13. BMA application to Fossolo -83.4% -14.1% -38.3% with respect to the average uncertainty band

  14. Conclusions • Model structure is responsible for a relevant part of the uncertainty • …. And more significantly, it is responsible of unhandled uncertainties because, usually, model selection is done before the uncertainty analysis • Model selection may depend on too many case-specific variables • BMA can help to run models safely and reduce the overall uncertainty • Computational cost is a limitation (we have to run a Bayesian analysis on each possible model)

  15. Bayesian model averagingapproach for urban drainage water qualitymodelling Gabriele Freni gabriele.freni@unikore.it Università degli Studi di Enna “Kore”

  16. BMA application to Fossolo

  17. Net rainfall (S, f) Rainfall - runoff processes Inlet sewer hydrograph Sewer propagation outlet sewer hydrograph The mathematical model Rainfall Quantity module The choice of the cascade of two linear reservoirs in series and a linear channel allows to split the hydraulic phenomena in the catchment from those in the sewer system.

  18. The mathematical model Qualitymodule

  19. Bayesian update (after using 6 ev.) SIM_01 SIM_02 SIM_03 SIM_04 SIM_05 SIM_06 SIM_07 SIM_08

More Related