Evaluation of probabilistic flow predictions in sewer systems using grey box models and a skill score criterion

Stochastic Environmental Research and Risk Assessment

Volumn 26, Issue 8, 2012, Pages 1151-1162

  Thordarson, Fannar Örn ^a   Breinholt, Anders ^a   Møller, Jan Kloppenborg ^a   Mikkelsen, Peter Steen ^a   Grum, Morten ^b   Madsen, Henrik ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b Veolia Water Solutions & Technologies   (Denmark)

Author keywords

Grey box modelling; Interval prediction; Reliability; Sharpness; Skill score; Urban drainage

Indexed keywords

FORECASTING; RELIABILITY; SEWERS; STOCHASTIC SYSTEMS; UNCERTAINTY ANALYSIS;

GREY-BOX MODELLING; INTERVAL PREDICTION; SHARPNESS; SKILL SCORE; URBAN DRAINAGE;

STOCHASTIC MODELS;

FLOW MEASUREMENT; MODELING; PREDICTION; PROBABILITY; SEWER NETWORK; UNCERTAINTY ANALYSIS; URBAN DRAINAGE;

EID: 84871475633     PISSN: 14363240     EISSN: 14363259     Source Type: Journal    
DOI: 10.1007/s00477-012-0563-3     Document Type: Article

References (34)

1. Baadsgaard M, Nielsen JN, Spliid H, Madsen H, Preisel M (1997) Estimation in stochastic differential equations with a state dependent diffusion term. SYSID'97-11th IFAC symposium of system identification, IFAC.
2. Barbera PL, Lanza LG, Stagi L (2002) Tipping bucket mechanical errors and their influence on rainfall statistics and extremes. Water Sci Technol 45(2): 1-9.
3. Bertrand-Krajewski JL, Bardin JP, Mourad M, Béranger Y (2003) Accounting for sensor calibration, data validation, measurement and sampling uncertainties in monitoring urban drainage systems. Water Sci Technol 47(2): 95-102.
4. Breinholt A, Thordarson FÖ, Møller JK, Mikkelsen PS, Grum M, Madsen H (2011) Grey box modelling of flow in sewer systems with state dependent diffusion. Environmetrics 22(8): 946-961.
5. Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction and estimation. J Am Stat Assoc 102(477): 359-378.
6. Gneiting T, Balabdaoui F, Raftery AE (2007) Probabilistic forecasts, calibration and sharpness. J R Stat Soc B 69(2): 243-268.
7. Giraldo JM, Leirens S, Díaz-Grenados MA, Rodríguez JP (2010) Nonlinear optimization for improving the operation of sewer systems: the Bogotá Case Study. International Environmental Modelling and Software Society (iEMSs). 2010 International Congress on Environmental Modelling and Software Modelling for Environments Sake, Fifth Biennial Meeting, Ottawa, Canada.
8. Iacus SM (2008) Simulation and Inference for stochastic differential equations-with R examples. Springer series of Statistics.
9. Jacobsen JL, Madsen H, Harremoës P (1997) A stochastic model for two-station hydraulics exhibiting transient impact. Water Sci Technol 36(5): 19-26.
10. Jazwinski AH (2007) Stochastic processes and filtering theory. Dover Publications, Mineola, NY.
11. Jonsdottir H, Jacobsen, JL, Madsen H (2001) A grey-box model describing the hydraulics in a creek. Environmetrics 12: 347-356.
12. Jonsdottir H, Madsen H, Palsson OP (2006) Parameter estimation in stochastic rainfall-runoff models. J Hydrol 326(1-4): 379-393.
13. Kloeden P, Platen E (1999) Numerical solutions of stochastic differential equations. Springer.
14. Kristensen NR, Madsen H (2003) Continuous time stochastic modeling-CTSM 2. 3-mathematics guide. Technical Unversity of Denmark.
15. Kristensen NR, Madsen H, Jørgensen SB (2004a) Parameter estimation in stochastic grey-box models. Automatica 40: 225-237.
16. Kristensen NR, Madsen H, Jørgensen SB (2004b) A method for systematic improvement of stochastic grey-box models. Comput Chem Eng 28(8): 1431-1449.
17. Limpert E, Stahel WA, Abbt M (2001) Log-normal distributions across the sciences: keys and clues. BioScience 51(5): 341-352.
18. Madsen H (2008) Time series analysis. Chapman & Hall/CRC.
19. Mannina G, Freni G, Viviani G, Saegrov S, Hafskjold L (2006) Integrated urban water modelling with uncertainty analysis. Water Sci Technol-WST 54(6-7): 379-386.
20. Møller JK, Nielsen HA, Madsen H (2008) Time-adaptive quantile regression. Comput Stat Data Anal 52: 1292-1303.
21. Møller JK, Madsen H, Carstensen J (2011) Parameter estimation in a simple stochastic differential equation for phytoplankton modelling. Ecol Model 222: 1793-1799.
22. Molini A, Lanza LG, Barbera Pl (2005) The impact of tipping-bucket raingauge measurement errors on design rainfall for urban-scale applications. Hydrol Process 19: 1073-1088.
23. Nielsen HA, Madsen H (2006) Modelling the heat consumption in district heating systems using a grey-box approach. Energy Build 38(1): 63-71.
24. Ocampo-Martinez C, Puig V (2010) Piece-wise linear functions-based model predictive control of large-scale sewage systems. IET Control Theory Appl 4(9): 1581-1593.
25. Øksendal B (2003) Stochastic differential equations-an introduction with applications, 6th edn. Springer.
26. Pedersen L, Jensen NE, Christensen LE, Nielsen HA, Madsen H (2010) Quantification of the spatial variability of rainfall based on a dense network of rain gauges. Atmospheric Res 95(4): 441-454.
27. Pinson P, Nielsen HA, Møller JK, Madsen H (2007) Non-parametric probabilistic forecasts of wind power: required properties and evaluation. Wind Energy 10(6): 497-516.
28. Puig V, Cembrano G, Romera J, Quevedo J, Aznar B, Ramoń G, Cabot J (2009) Predictive optimal control of sewer networks using CORAL tool: application to Riera Blanca catchment in Barcelona. Water Sci Technol 60(4): 869-878.
29. Shedekar VS, King KW, Brown LC, Fausey NR, Heckel M, Harmel DR (2009) Measurement errors in tipping bucket rain gauges under different rainfall Intensities and their implication to hydrologic models. Conf. paper, ASABE Annual International Meeting, June 21-24, pp 1-9.
30. Tornøe CW, Jacobsen J, Pedersen O, Hansen T, Madsen H (2006) Grey-box Modelling of pharmacokinetic/pharmacodynamic systems. J Pharmacokinet Pharmacodyn 31(5): 401-417.
31. Vaes G, Willems P, Berlamont J (2005) Areal rainfall correction coefficients for small urban catchments. Atmospheric Res 77(1-4): 48-59.
32. Vestergaard M (1998) Nonlinear filtering in stochastic volatility models. Master's thesis, Technical University of Denmark. Department of Mathematical Modelling, Lyngby, Denmark.
33. Willems P (2001) Stochastic description of the rainfall input errors in lumped hydrological models. Stoch Environ Res Risk Assess 15: 132-152.
34. Willems P (2010) Parsimonious model for combined sewer overflow pollution. J Environ Eng 136(3): 316-325.