Thorndahl S.,University of Aalborg |
Poulsen T.S.,Kruger |
Bovith T.,Danish Meteorological Institute |
Borup M.,Technical University of Denmark |
And 6 more authors.
Water Science and Technology | Year: 2013
Forecast-based flow prediction in drainage systems can be used to implement real-time control of drainage systems. This study compares two different types of rainfall forecast - a radar rainfall extrapolation-based nowcast model and a numerical weather prediction model. The models are applied as input to an urban runoff model predicting the inlet flow to a waste water treatment plant. The modelled flows are auto-calibrated against real-time flow observations in order to certify the best possible forecast. Results show that it is possible to forecast flows with a lead time of 24 h. The best performance of the system is found using the radar nowcast for the short lead times and the weather model for larger lead times.
Breinholt A.,Bldg. |
Thordarson F.O.,Bldg. |
Moller J.K.,Bldg. |
Grum M.,Kruger |
And 2 more authors.
Environmetrics | Year: 2011
Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both forecasting and control purposes. The grey-box model is based on stochastic differential equations and a key feature is the separation of the total noise into process and measurement noise. The grey-box approach is properly introduced and hypothesis regarding the noise terms are formulated. Three different hypotheses for the diffusion term are investigated and compared: one that assumes additive diffusion; one that assumes state proportional diffusion; and one that assumes state exponentiated diffusion. To implement the state dependent diffusion terms Itô's formula and the Lamperti transform are applied. It is shown that an additive diffusion noise term description leads to a violation of the physical constraints of the system, whereas a state dependent diffusion noise avoids this problem and should be favoured. It is also shown that a logarithmic transformation of the flow measurements secures positive lower flow prediction limits, because the observation noise is proportionally scaled with the modelled output. Finally it is concluded that a state proportional diffusion term best and adequately describes the one-step flow prediction uncertainty, and a proper description of the system noise is important for ascertaining the physical parameters in question. © 2011 John Wiley & Sons, Ltd.
Thordarson F.O.,Technical University of Denmark |
Breinholt A.,Technical University of Denmark |
Moller J.K.,Technical University of Denmark |
Mikkelsen P.S.,Technical University of Denmark |
And 2 more authors.
Stochastic Environmental Research and Risk Assessment | Year: 2012
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. © 2012 Springer-Verlag.
Lopato L.,Technical University of Denmark |
Galaj Z.,Kruger |
Delpont S.,BeCitizen |
Binning P.J.,Technical University of Denmark |
Arvin E.,Technical University of Denmark
Journal of Environmental Engineering | Year: 2011
Laboratory and full-scale experiments were conducted to investigate the development and effect of heterogeneity caused by filter media nonuniformity, biofilm, particles, precipitates, and gas bubbles in rapid sand filters used for drinking-water treatment. Salt tracer experiments were conducted in laboratory columns and in a waterworks, where a new tracer method for rapid sand filters was developed. Pore-water velocities and dispersivities were estimated by fitting an analytical solution to the measured breakthrough curves. Results of the column experiments showed an increase in average longitudinal dispersivity of more than 33% in the 116h after the start of filtration with a constant pore-water velocity and a zero-order nitrification rate of 9 mg N/L/h. The full-scale experiments showed that the rapid sand filter was heterogeneous with pore-water velocities ranging from 2.2 to 3.3 m/h for the same inlet flow. A first-order nitrification reaction with spatially variable pore-water velocity could be interpreted as a zero-order reaction with a constant pore-water velocity. A model demonstrated that filter heterogeneity could result in higher filter outlet ammonium concentrations. © 2011 American Society of Civil Engineers.
Lee C.,Technical University of Denmark |
Albrechtsen H.-J.,Technical University of Denmark |
Smets B.F.,Technical University of Denmark |
Boe-Hansen R.,Kruger |
And 2 more authors.
2013 Water Quality Technology Conference and Exposition, WQTC 2013 | Year: 2013
Removing ammonium from drinking water is important for maintaining biological stability in distribution systems. This is especially important in regions that do not use disinfectants in the treatment process or keep a disinfectant residual in the distribution system. Problems with nitrification can occur with increased ammonium loads caused by seasonal or operational changes and can lead to extensive periods of elevated ammonium and nitrite concentrations in the effluent. One possible cause of nitrification problems in these filters maybe due to phosphate limitation. This was investigated using a pilot scale sand column which initial analysis confirmed performed similarly to the full scale filters. Long term increased ammonium loads were applied to the pilot filter both with and without phosphate addition. Phosphate was added at a concentration of 0.5 mg PO4-P/L to ensure that it was not the limiting substrate. Preliminary results showed an increased nitrification capacity both with and without phosphate addition although the addition of phosphate doubled the ammonium and nitrite removal capacity of the filter compared to non-phosphate dosing conditions. Phosphate addition also increased the total number of ammonium oxidizing bacteria in the column. © 2013 American Water Works Association AWWA WQTC Conference Proceedings All Rights Reserved.
Breinholt A.,Technical University of Denmark |
Grum M.,Kruger |
Madsen H.,Technical University of Denmark |
Orn Thordarson F.,Technical University of Denmark |
Mikkelsen P.S.,Technical University of Denmark
Hydrology and Earth System Sciences | Year: 2013
Monitoring of flows in sewer systems is increasingly applied to calibrate urban drainage models used for long-term simulation. However, most often models are calibrated without considering the uncertainties. The generalized likelihood uncertainty estimation (GLUE) methodology is here applied to assess parameter and flow simulation uncertainty using a simplified lumped sewer model that accounts for three separate flow contributions: wastewater, fast runoff from paved areas, and slow infiltrating water from permeable areas. Recently GLUE methodology has been critisised for generating prediction limits without statistical coherence and consistency and for the subjectivity in the choice of a threshold value to distinguish "behavioural" from "non-behavioural" parameter sets. In this paper we examine how well the GLUE methodology performs when the behavioural parameter sets deduced from a calibration period are applied to generate prediction bounds in validation periods. By retaining an increasing number of parameter sets we aim at obtaining consistency between the GLUE generated 90% prediction limits and the actual containment ratio (CR) in calibration. Due to the large uncertainties related to spatiooral rain variability during heavy convective rain events, flow measurement errors, possible model deficiencies as well as epistemic uncertainties, it was not possible to obtain an overall CR of more than 80%. However, the GLUE generated prediction limits still proved rather consistent, since the overall CRs obtained in calibration corresponded well with the overall CRs obtained in validation periods for all proportions of retained parameter sets evaluated. When focusing on wet and dry weather periods separately, some inconsistencies were however found between calibration and validation and we address here some of the reasons why we should not expect the coverage of the prediction limits to be identical in calibration and validation periods in real-world applications. The large uncertainties result in wide posterior parameter limits, that cannot be used for interpretation of, for example, the relative size of paved area vs. the size of infiltrating area. We should therefore try to learn from the significant discrepancies between model and observations from this study, possibly by using some form of non-stationary error correction procedure, but it seems crucial to obtain more representative rain inputs and more accurate flow observations to reduce parameter and model simulation uncertainty. © Author(s) 2013.