TY - JOUR
T1 - Evaluation of probabilistic flow predictions in sewer systems using grey box models and a skill score criterion
AU - Thordarson, Fannar Ørn
AU - Breinholt, Anders
AU - Møller, Jan Kloppenborg
AU - Mikkelsen, Peter Steen
AU - Grum, M.
AU - Madsen, Henrik
PY - 2012
Y1 - 2012
N2 - In this paper we show how the grey box methodology can be applied to find models that can describe the flow prediction uncertainty in a sewer system where rain data are used as input, and flow measurements are used for calibration and updating model states. Grey box models are composed of a drift term and a diffusion term, respectively accounting for the deterministic and stochastic part of the models. Furthermore, a distinction is made between the process noise and the observation noise. We compare five different model candidates’ predictive performances that solely differ with respect to the diffusion term description up to a 4 h prediction horizon by adopting the prediction performance measures; reliability, sharpness and skill score to pinpoint the preferred model. The prediction performance of a model is reliable if the observed coverage of the prediction intervals corresponds to the nominal coverage of the prediction intervals, i.e. the bias between these coverages should ideally be zero. The sharpness is a measure of the distance between the lower and upper prediction limits, and skill score criterion makes it possible to pinpoint the preferred model by taking into account both reliability and sharpness. In this paper, we illustrate the power of the introduced grey box methodology and the probabilistic performance measures in an urban drainage context.
AB - In this paper we show how the grey box methodology can be applied to find models that can describe the flow prediction uncertainty in a sewer system where rain data are used as input, and flow measurements are used for calibration and updating model states. Grey box models are composed of a drift term and a diffusion term, respectively accounting for the deterministic and stochastic part of the models. Furthermore, a distinction is made between the process noise and the observation noise. We compare five different model candidates’ predictive performances that solely differ with respect to the diffusion term description up to a 4 h prediction horizon by adopting the prediction performance measures; reliability, sharpness and skill score to pinpoint the preferred model. The prediction performance of a model is reliable if the observed coverage of the prediction intervals corresponds to the nominal coverage of the prediction intervals, i.e. the bias between these coverages should ideally be zero. The sharpness is a measure of the distance between the lower and upper prediction limits, and skill score criterion makes it possible to pinpoint the preferred model by taking into account both reliability and sharpness. In this paper, we illustrate the power of the introduced grey box methodology and the probabilistic performance measures in an urban drainage context.
KW - Grey box modelling
KW - Interval prediction
KW - Reliability
KW - Sharpness
KW - Skill score
KW - Urban drainage
U2 - 10.1007/s00477-012-0563-3
DO - 10.1007/s00477-012-0563-3
M3 - Journal article
VL - 26
SP - 1151
EP - 1162
JO - Stochastic Environmental Research and Risk Assessment
JF - Stochastic Environmental Research and Risk Assessment
SN - 1436-3240
IS - 8
ER -