From a scientific point of view, it is unquestioned that numerical models for technical systems need to be calibrated. However, in sufficiently calibrated models are still used in engineering practice. Case studies in the scientific literature that deal with urban water management are mostly large cities, while little attention is paid to the differing boundary conditions of smaller municipalities. Consequently, the aim of this paper is to discuss the calibration of a hydrodynamic model of a small municipality (15,000 inhabitants). To represent the spatial distribution of precipitation, three distributed rain gauges were used for model calibration. To show the uncertainties imminent to the calibration process, 17 scenarios, differing in assumptions for calibration, were distinguished. To compare the impact of the different calibration scenarios on actual design values, design rainfall events were applied. The comparison of the model results using the different typical design storm events from all the surrounding data points showed substantial differences for the assessment of the sewers regarding urban flooding, emphasizing the necessity of uncertainty analysis for hydrodynamic models. Furthermore, model calibration is of the utmost importance, because uncalibrated models tend to overestimate flooding volume and therefore result in larger diameters and retention volumes.
The necessity of calibration of numerical models for technical systems is unquestioned from a scientific point of view. However, in engineering practice, often uncalibrated or not sufficiently calibrated models are used. This might result in under- or overestimation of design values and, consequently, in a waste of resources. In this paper, we discuss aspects of calibration of a hydrodynamic urban drainage model from a practical point of view. We show the impact on model results when input or calibration data are not available in the required quality and we give guidance as to how small and medium sized operators with limited financial and human resources can calibrate their urban drainage models.
In the literature, model calibration is often discussed as a question of finding the perfect calibration algorithm (Rauch & Harremoës 1999; Di Pierro et al. 2005), the best objective function choice (Hauduc et al. 2011) or in context of accuracy, the accuracy of input and output data (Bertrand-Krajewski et al. 2003; Korving & Clemens 2005; Kleidorfer et al. 2009a; Dotto et al. 2014; Notaro et al. 2015). Modern approaches of calibration try to incorporate different sources of uncertainty to identify model parameters in a way that uncertainty bands of model predictions can be evaluated (Deletic et al. 2009; Freni et al. 2009b; Lindblom et al. 2011; Dotto et al. 2012). However, in practical engineering applications, model calibration is still highly influenced by questions of data availability (Freni et al. 2009a; Kleidorfer et al. 2009b) or data quality, despite several efforts to improve this situation for input (Einfalt et al. 2004) or calibration data (Gamerith et al. 2008; Dotto et al. 2011). For example, the Austrian guideline (ÖWAV-Regelblatt 19 2007), which describes how to predict combined sewer overflow (CSO) volumes and defines the standards for CSO emissions in Austria (Kleidorfer & Rauch 2011), requires the calibration of a conceptual model based on just three rainfall events. Often, these very low requirements are still seen as a barrier. Hence, for a small municipality, the guideline leaves a loophole and allows model use without calibration.
Case studies in the scientific literature that deal with urban water management are mostly large, prestigious cities which have the financial and human resources to participate in research projects. They are selected because they have data over many years and/or the required infrastructure for further data collection and management. Owing to this, there is the risk that research outcomes are biased towards the large municipalities. Such case studies are not always representative for the actual situation of the living environment in a country. The difference is not only the present or absent data but also the system layout and the catchment land use. The network length per capita in smaller municipalities is longer, as the distances between houses are higher and the population density is lower. The imperviousness of the drained area is lower, pipe diameters are smaller and the diurnal pattern of wastewater generation is more pronounced. Also, pollutant characteristics in surface runoff are expected to be different due to a different land use and reduced traffic compared to large cities (Brombach et al. 2005).
Consequently, the aim of this paper is to discuss calibration of a hydrodynamic model for the representative example of a small Austrian municipality (15,000 inhabitants). We investigate different calibration scenarios (number of events, data uncertainties) and the impact of the spatial resolution of catchment information on the predictive performance of the model (expressed as Nash–Sutcliffe efficiency (NSE) of measured and predicted water levels). Finally, we compare these calibration results with another important source of uncertainty, the uncertainty in the design rainfall.
Hydrodynamic model and calibration approach
For the assessment of the scenarios, the EPA Storm Water Management Model (SWMM) was used. It is a well-known dynamic rainfall–runoff model used for single event or long-term simulation of runoff quantity and quality from primarily urban areas (Gironás et al. 2010). It is widely used for analysis, design and planning related to stormwater runoff, combined and sanitary sewers, and other drainage systems (Granata et al. 2016). Its numerous capabilities make it suitable for application to many hydrologic urban watersheds for a single event or continuous events. SWMM consists of several different blocks (subroutines) that can be simulated separately (Wang & Altunkaynak 2012). Infiltration is modelled for this paper using Horton's equation.
One challenge in developing an SWMM model for a large watershed is defining representative precipitation data. Rainfall data drive the model and produce runoff, which means that an accurate estimation of rainfall data determine the success of the modelling effort (Barco et al. 2008). Some parameters that characterize the hydrological behaviour of the watershed are difficult to evaluate reliably. Therefore, a calibration stage to estimate an optimal set of these parameters is essential (Granata et al. 2016). This calibration was carried through using the automated PC-SWMM calibration tool (James et al. 2002, 2010; James 2005). It is a genetic algorithm-based software tool for calibration of the SWMM modules (James et al. 2002).
The analysed case study in this paper is a small municipality with 15,000 inhabitants in Tyrol, Austria. It is characterized by alpine climatic conditions, implying cold winters and heavy convective precipitation during the summer period (Kleidorfer et al. 2014). In Austria, 68% of the population lives in such small municipalities with less than 50,000 inhabitants (Statistik Austria 2015), and the vast majority of water utilities in the world serve populations of less than 100,000 inhabitants (Alegre & Coelho 2012).
The network data were available in a geographic pipe information system including diameters and slopes, which could be easily and automatically included into the hydrodynamic model. However, the detailed information about special structures had to be taken from analogue or digital blueprints and implemented manually into the model. The characteristics of the subcatchments were taken from available maps (e.g. land register) and typical imperviousness values for the uncalibrated model were chosen depending on the land use (e.g. streets with 0.95, residential areas with 0.5 (Butler & Davies 2011)). The slopes (ranging from 0 up to 30%) of the subcatchments were determined from a digital elevation map.
For model calibration and validation, precipitation was measured over the period of 1 year (2014). The abbreviations for the measurement sites (GWT and WW, as shown in Figure 1) derive from geographical names. To represent the areal distribution of precipitation, three rain gauges (one totalizer – GWT and two tipping bucket rain gauges – WWTP and WW) were used, fulfilling the specifications of Quirmbach & Schultz (2002) of one site per 16 km² and a maximal distance to the catchment of 4 km. The temporal resolution of the totalizer is 1 min, while the tipping bucket rain gauge records each tip. The water level and the flow were measured in the main collector at a position which allowed an integrated view of the entire catchment area. The installed flow meter was a combination of two sensors. At the bottom of the sewer a flow velocity sensor (flow velocity measurement using ultrasonic cross correlation, transit time and pressure for level measurement) was installed. At the top of the sewer, some distance upstream of the flow sensor an ultrasonic sensor for water level measurement was installed. The results of the flow measurement were repeatedly checked for their plausibility, determining snapshots of the flow velocity. The measurement of the flow velocity (and in consequence the flow volume) was hampered by a clogging of the sensor mounted at the pipe floor. As a result, only the water level was used for calibration (James et al. 2002, 2010; James 2005).
Catchment fragmentation analysis
The medium resolution model is tailored to the inlet points of the sewer network and represents the configuration used for the calibration. It separates parcels and streets. The detailed model is based on an orthophoto and discretizes green space, paved area and rooftops. The imperviousness of the land use types is adjusted to the orthophoto and harmonized with the overall imperviousness of the medium model. As a reference model, the whole area is represented as one subcatchment and consists of the merged subcatchments of the medium model. The entire rain series, measured at the site GWT, was used for the simulations.
As expected, the reference model with one catchment shows a much slower reaction for occurring rainfall events. Short peaks are cut off up to 45% (first peak) with decreasing effect the longer the rain event takes (11% at the last peak in Figure 3) and drainage lasts longer. This results from the initial abstraction resulting in a lack of highly paved areas and therefore a higher retention capacity. The shape of the curve differs considerably from the other two models; however, the overall runoff volume is only 2.5% less compared to the medium and 0.9% compared to the detailed model.
Considering the results of this examination, a medium resolution model was chosen which represents a good approximation of the investigation area. The runoff calculation does not benefit from the detailed model whereas the low resolution causes large deviations in the shape of the hydrograph.
To exemplify the uncertainties imminent to the calibration process, 17 scenarios – differing in assumptions for calibration – were used. The first scenario was the base scenario without calibration (UK_00). Then, a calibration for each rainfall event took place individually (KR_01 to KR_10 – compare with Figure 4). Then the model was calibrated using the entire rain series (KG_11). This rain series consists of the 10 rainfall events and artificially made intermediate dry weather periods which should ensure that the events do not interact in terms of remaining water in the network. According to DWA-A 118 (2006), a dry weather period of 4 h was chosen, considering that the maximum flow time is smaller. By including these 4 h intervals, the overall length of the rain series summed to 158 h. For these calibrations, the data from all three rain measurements were used by assigning the data from the closest rain gauge to each catchment. For the next scenarios, the rain series was used for calibration with only one rain gauge – GWT (KE_12), WWTP (KE_13) and WW (KE_14) – respectively. Furthermore, the model was calibrated twice under the assumptions of a systematic 30% error of the depth monitoring data (KF_15 for +30% and KF_16 for −30%) to show the influence of measured calibration data uncertainties (Deletic et al. 2012).
One model parameter that was adapted during calibration was the flow time on the surface of each subcatchment. In SWMM, this is related to the rectangular shape of the catchment and is expressed by the parameter ‘width’. This parameter influences the shape of the hydrograph on each subcatchment. Another important parameter is the fraction of imperviousness in a subcatchment, which is directly related to the amount of stormwater runoff that is generated from rainfall. The pipe roughness (the third parameter used) in the sewer pipes influences the flow velocity in the pipes and, consequently, the shape of the hydrograph and the water depth in the pipes. Other model parameters (losses, surface roughness, etc.) were not changed as a sensitivity analysis showed a negligible impact on model results. Using parameters influencing different qualities of the hydrograph puts forward the possibility that an excellent match in peak value and timing could be compromised by pure volume match. To minimize this risk, an analysis of the general hydraulic behaviour over the entire measurement campaign (2014) has been made. We compared the manholes that suffered overflows during this period as well as the inflow at the WWTP using the available measurement there (daily inflow) with our model results.
The following ranges of physically reasonable boundaries of model parameters, which have to be considered during calibration, were assumed to be:
minimum width of 1 m for the subcatchments;
fraction imperviousness between 0 and 100%;
pipe roughness – Manning's n between 0.01 and 0.02.
The NSE was chosen as the objective function for model calibration (Nash & Sutcliffe 1970). NSE is a measure to compare time series. It ranges from −∞ to 1 (perfect match). The calibration caused notable deviations from the uncalibrated model. For example, for KG_11, the imperviousness decreased by 31%, the conduit roughness by 7% and the width by 67%.
RESULTS AND DISCUSSION
To compare the scenarios, the absolute distance of the NSE of every model (UK_00, KG_11 and KR_01 to KR_10) for every rainfall event compared to the individually best NSE for each rainfall event (which is always the scenario calibrated on that rainfall event) was calculated and summed to get a total distance. This verifies that scenario KG_11 (calibration on all 10 events) shows the best overall performance with a distance of 1.9 in comparison to the next best scenario, KR_09 with 2.2, followed by KR_06 (2.4) and KR_05 (2.5), while the uncalibrated model UK_00 sums to a value of 3.34.
The calibration of the scenarios KE_12 to KE_14 (consideration of all rainfall events but only one rain gauge) behaved differently. The calibration for the rainfall measurement at the site GWT was successful (NSE = 0.776), but for the other two sites only an NSE of 0.444 (WWTP) and 0.238 (WW) could be reached using the entire rain series for calibration omitting the artificial dry weather periods. In this case, the GWT site seemed to represent the actual rainfall the best of the three sites. This could be caused either by the usage of a totalizer instead of tipping bucket rain gauges or the more central location of the site in comparison to the other two. This shows the importance of a careful selection of the position for the rainfall measurement. The spatial precipitation distribution, especially in alpine regions, is heavily dependent on the topography (Mikovits et al. 2015a). The simple spatial interpolation of rainfall measurements (as shown here or using Voronoi-polygons (Muthusamy et al. 2015)) delivers different results than, for example, the usage of radar data (Einfalt et al. 2004; Fencl et al. 2013).
The scenarios KF_15 (NSE = 0.717) and KF_16 (NSE = 0.346) were calibrated using the three parameters mentioned before, showing that a systematic error can be balanced by calibration. They could be calibrated to a higher NSE (i.e. systematic errors could be compensated by adaption of model parameters), but the parameters would have to be chosen beyond plausibility limits.
Figure 7(b) shows the four model scenarios which showed the best overall performance regarding the absolute distance to the optimal NSE. The range of the different rain data is shown as the background filling, while for highlighting the difference between the calibration scenarios, the design rainfall of data point 4626 is used (solid line). While data point 4627 is nearer to the WWTP the main part of the subcatchments is nearer to point 4626. It can be seen that with a return period of 2 years, flooding already occurs in the models KR_05 and KR_06, while KG_11 and KR_09 start flooding at a return period of 3 years.
Differences between the calibrated (KG_11) and the uncalibrated model (UK_00) can be in the same magnitude as differences between different return periods. This can be observed in Figure 7(c). It shows that for a return period of 2 years flooding already occurs in UK_00 whereas none of the rainfall events causes flooding in KG_11. What can also be seen in Figure 7(c) are the effects of measurement errors (scenarios KF_15 and KF_16) on the flooding values and, consequently, on required pipe diameters, retention volume and required construction costs. The influences of the different rain measurements (see Figure 7(d)) are smaller in comparison but are still recognizable.
The comparison of the three different levels of detail in the representation of the subcatchments shows that they cause little effect on total runoff volume but substantial differences in the shape of the hydrograph. This is due to the similar overall imperviousness in the models. The runoff calculation does not benefit from the detailed model and therefore does not justify the extra work for the model preparation. Since the rough model, besides the runoff rate deviations, provides less scope for calibration, the medium resolution model was used for the investigation.
Furthermore, the investigations show that model calibration is of utmost importance. It was demonstrated that the uncalibrated model tended to overestimate flooding volume, thus resulting in larger diameter pipes and retention volumes. Although a conservative model could make sense in terms of safety and resilience, it should be a conscious choice of the modeller (e.g. by adding safety factors to pipe sizing and retention volume estimation) and not driven by calibration uncertainties. By calibration of the model parameters, only one type of uncertainty can be concretized while there is still substantial uncertainty in the measurement data. The necessity of calibration speaks of the importance of measurement data being available in sufficient quantity and quality. It can be seen that spatial distributed rainfall measurement is advisable to minimize the uncertainties stemming from differences in rain intensities and distribution occurring in relatively small catchments, especially in mountainous regions. Additionally, the usage of a rain series is advantageous in comparison to the usage of single rainfall events, because it accurately represents antecedent moisture conditions.
The comparison of the model results using the different typical design storm events from all the surrounding data points (Austrian rainfall database for design storm events) showed substantial differences for the assessment of the sewers regarding urban flooding. The selection of the data point for the design storm event can have enormous consequences for the design of the network and, consequently, for the construction costs. This could be counteracted by either the usage of several data points in the planning process or the strict allocation of the nearest data points to the individual subcatchments. This emphasizes also the need of uncertainty analysis for hydrodynamic models in urban water management.
This work is part of the project ‘DatMod – An efficient way from data to model’ funded by the Austrian Federal Ministry of Agriculture, Forestry, Environment and Water Management. We would like to acknowledge the input and good cooperation with the operating company Gemeindewerke Telfs.