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Impact of rainfall data resolution in time and space on the urban flooding evaluation Vincenza Notaro, Chiara Maria Fontanazza, Gabriele Freni and Valeria Puleo
ABSTRACT Climate change and modification of the urban environment increase the frequency and the negative effects of flooding, increasing the interest of researchers and practitioners in this topic. Usually, flood frequency analysis in urban areas is indirectly carried out by adopting advanced hydraulic models to simulate long historical rainfall series or design storms. However, their results are affected by a level of uncertainty which has been extensively investigated in recent years. A major source of uncertainty inherent to hydraulic model results is linked to the imperfect knowledge of the rainfall input data
Vincenza Notaro (corresponding author) Chiara Maria Fontanazza Gabriele Freni University of Enna ‘Kore’, Italy E-mail: [email protected] Valeria Puleo University of Palermo, Italy
both in time and space. Several studies show that hydrological modelling in urban areas requires rainfall data with fine resolution in time and space. The present paper analyses the effect of rainfall knowledge on urban flood modelling results. A mathematical model of urban flooding propagation was applied to a real case study and the maximum efficiency conditions for the model and the uncertainty affecting the results were evaluated by means of generalised likelihood uncertainty estimation (GLUE) analysis. The added value provided by the adoption of finer temporal and spatial resolution of the rainfall was assessed. Key words
| rainfall resolution, rainfall-runoff transformation, urban drainage modeling
INTRODUCTION The surcharging of sanitary and stormwater drainage systems due solely to rainfall often causes local flooding in European cities where ageing of the infrastructure and growing urbanisation take place. In order to improve the proactive management of flooding, identification of the flood risk areas and development of strategies to reduce that risk are needed. To this end, a robust statistical frequency analysis of urban flooding could be a preliminary step. However, in most cases, historical series of flood data are often unavailable or too piecemeal for performing a statistical analysis of flooding events aimed at a reliable assessment of urban flood risk. Therefore, many standard approaches simulate long historical rainfall series or design storms by means of urban drainage mathematical models to indirectly estimate flood location, extension, frequency and volume/depth (Thorndahl & Willems ; Fontanazza et al. ). The application of advanced hydraulic models as diagnostic, design and decision-making support tools has become a standard practice in hydraulic research and doi: 10.2166/wst.2013.435
application. Although mathematical models have been significantly improved in recent years (Leandro et al. ), their results are affected by a high level of uncertainty due to input data errors, model structure and parameterization. The analysis and estimation of the uncertainty involved in urban drainage modelling have attracted considerable attention from researchers in recent years (Sen & Altunkaynak ; Willems ; Kleidorfer et al. ; Deletic et al. ; Fontanazza et al. ; Leandro et al. ). A major source of uncertainty inherent to model results is linked to imperfect knowledge of the rainfall input data both in time and space. Usually, rainfall is the driving phenomenon of runoff generation, particularly in urban areas where catchments are small and have a short concentration time producing runoff hydrographs sensitive to the temporal and spatial variation of rainfall. Several studies assess that the effects of storm spatial and temporal variability on runoff generation increase with decreasing catchment scale (Berne et al. ; Segond et al. ): an underestimation of the peak of the runoff hydrograph is systematically
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obtained when rainfall data with a low temporal resolution are used as input to the numerical simulations of urban drainage system behaviour (Aronica et al. ). Therefore, hydrological modelling in urban areas needs a fine resolution of rainfall data both in time and space: a resolution of 3–6 min in time and 2–4 km in space for urban catchments of 1–10 km2 should be enough, according to Berne et al. (). However, for practical applications, the available rainfall databases present temporal and spatial resolution that are often coarser than those required for a reliable rainfall–runoff simulation in urban areas, greatly compromising model accuracy. The present study aims to evaluate the impact of defective rainfall knowledge on urban flooding model outputs. The study analyses both the temporal and spatial resolution of rainfall data and compares the related uncertainty with the intrinsic model uncertainty that may be correlated to the model structure and to parameter estimation. The uncertainty affecting urban flooding modelling was evaluated by means of the generalised likelihood uncertainty estimation (GLUE) approach (Beven & Binley ) and the added value provided by the adoption of finer temporal and spatial resolutions of the rainfall was assessed. The GLUE approach was previously used for estimating
Figure 1
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The ‘Centro Storico’ catchment, with flooded areas.
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modelling uncertainty in urban drainage (Thorndahl et al. ). In the present application, the approach was used to estimate the uncertainty related to pluviometric input and to estimate the most reliable level of rainfall knowledge for a specific modelling aim. The analysis was carried out on single flooding locations (considering flooding depth uncertainty) and globally on the whole catchment (considering flooding damage). The use of different spatial aggregations of model response and different output objective functions showed the importance of selecting rainfall spatial and temporal resolution depending on the variable to be analysed. Analyses were carried out using the historical rainfall–flood data collected for a period of 5 years in the ‘Centro Storico’ catchment of Palermo (Italy) as a reference for rainfall events.
THE CASE STUDY The ‘Centro Storico’ catchment of Palermo (Italy) is the oldest part of the city, strongly urbanized (Figure 1). The analysed catchment is about 6.7 km2 with about 88% of impervious areas.
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The most common land use in the area is for residential dwellings. However, there are many monuments and other estates having a cultural or artistic significance (theatres, churches, monasteries etc.). The whole catchment is drained by a very old drainage system (about 118 years old), with a total length of about 56 km. It receives both storm and waste water, also from upstream less urbanized watersheds. Local surface flooding due to system insufficiency often occurs, even for high-frequency rainfall. During 1993– 2008, more than 40 flood events affected several areas of the watershed (Figure 1). An accurate database covering flooded areas, water depths and volumes, durations and damaged properties has been collected by querying fire brigades and insurance companies (Freni et al. ). Water depths are measured by means of local webcams (also used for activating emergency procedures in case of flooding) and graduated steel tapes (with resolution equal to 1 cm) fixed to building walls. The webcams are interrogated remotely every five minutes and the measure resolution is 5 cm. The maximum flooding depth is locally verified by fire brigades during field operations with centimetric accuracy (because steel tapes show signs of the maximum water depth). In the present paper, only maximum depth data were used because depthdamage curves are related to such variables. In the present study, rainfall data was recorded by a raingauge network made of eight raingauges located in the analysed catchment or with in a 1 km range. Analyses were carried out, adopting as reference rainfall 10 historical rainfall events recorded by the raingauge network between 1993 and 1997. During the 10 selected
Table 1
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events, all eight raingauges registered rainfall data and all 15 locations (Figure 1) were flooded. In this way, results from different events can be compared. The selected events represent extreme storms for the sewer system but they are not exceptional, having return periods of between 3 and 20 years. Table 1 shows the main characteristics of the selected rainfall events. Figure 2 shows the original historical hyetograph of 1st December 1995, recorded with a temporal resolution (Dt) of 1 min by all eight raingauges (RG).
THE URBAN DRAINAGE MODEL The methodology proposed in the present study required the application of a mathematical model to simulate the runoff formation and flooding propagation phenomena in the analysed urban watersheds. An urban drainage model based on the storm water management model (SWMM) application (Huber & Dickinson ) was adopted to simulate urban drainage-system behaviour. That model can be used to examine a wider range of problems, from frequent and limited local flooding to a global system surcharge with high discharges and water levels on streets. A distributed ‘non-linear reservoir’ model was used to simulate surface runoff, which takes into account both surface storage and infiltration (Rossman ). A dual drainage approach was employed to simulate surface flood propagation (Leandro et al. ) where underground and surface drainage systems (streets, sidewalks, etc.) are schematised in a unique network made by
Historical rainfall events
Flooding event Parameter
Unit 1
Data event
2
3
4
5
6
7
8
9
10
d/m/y
25/10/93 08/01/95 01/12/95 18/09/96 26/09/96 05/10/96 12/08/97 22/08/97 25/09/97 07/12/97
Duration
hms
14.05.03
19.05.02
13.17.03
15.01.00
6.19.01
10.55.01
12.18.20
15.33.30
10.34.02
16.29.50
Mean rainfall intensity
mm h1 7.27
8.67
6.79
20.20
24.39
9.02
19.45
38.70
3.47
9.53
Median rainfall intensity
mm h1 5.66
8.21
5.20
12.34
13.77
7.74
14.55
18.88
3.32
7.83
Min. non-null mm h1 2.11 rainfall intensity
1.23
3.77
1.83
1.22
1.65
2.66
1.10
0.81
1.87
144.89
172.08
125.54
212.73
111.03
115.02
271.42
135.64
100.66
Max. rainfall intensity
mm h1 144.9
Rain volume
mm
Rain return period years
60.51
33.55
49.77
16.38
19.91
44.85
47.36
47.50
20.34
39.59
8
3
4
3
3
4
10
20
2
3
1987
Figure 2
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Event of 1st December 1995 – real hyetographs recorded by the all raingauges located in the ‘Centro Storico’ catchment or in 1 km range.
two sets of channels that are dynamically interconnected by sewer manholes. The flow into the underground pipes and surface channels was simulated by solving the complete one-dimensional de Saint Venant equations with a time step of 1 s. The model is made of more than 500 pipes and more than 700 surface channel connections. Pipe cross-sections are circular, egg-shaped and rectangular while all streets were simulated as rectangular channels. All pipes are made of concrete and their age ranges between 20 and more than 100 years. Details about the adopted model can be found in Freni et al. (). The model allows for the taking account of rainfall variability in space, by linking different rainfall input data for the same simulation to the various sub-catchments identified in the whole analysed watershed. Namely, the analysed watershed was divided into more than 300 sub-catchments and a specific rainfall time series was assigned to each of these, according to the following described procedure. Finally, the model runs under the hypothesis that each sub-catchment is connected to a single inlet manhole.
METHODOLOGY The proposed procedure aims to assess the effect of the temporal and spatial resolution of rainfall input data on urban
flooding evaluation, when an urban drainage mathematical model is adopted to simulate the runoff formation and flood propagation phenomena in an urban watershed. As the first step of the methodology, a temporal resampling procedure (Aronica et al. ) was applied to a set of 10 historical rainfall time series with high temporal resolution (1–3 min) recorded by the raingauge network in the analysed area (Figure 1). The temporal resampling procedure was based on a fixed window average by means of the following steps: 1. The duration of each historical rainfall event was divided into a number n of equal time intervals ranging from 5 to 15 min with step of 1 min. 2. For each of these temporal windows the average intensity was evaluated. According to the mass balance principle, for each time step, the real event and the resampled one are characterised by the same rainfall volume. As a result of applying the above temporal resampling procedure, 11 hyetographs with a coarser temporal resolution were obtained by each of the 10 historical rainfall time series analysed. Figure 3 shows, in terms of rainfall intensity, the real event of 1st December 1995 recorded with a time resolution (Dt) of 1 min by the raingauges RG3 (13 200 54,62″ E, 38 60 20.27″ N) and three resampled hyetographs with a coarser temporal resolution (Dt) equal to
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pffiffiffiffiffi2 Pn qffiffiffiffiffiffi PEi Pi i¼1 GORE ¼ 1 Pn pffiffiffiffiffi pffiffiffiffiffi2 Pi Pi i¼1
Figure 3
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Event of 1st December 1995 – real and resampled hyetographs recorded by the raingauge RG3.
5, 10 and 15 min, respectively, obtained by applying the temporal resampled procedure to the real event. To analyse the influence of the spatial rainfall aggregation on the efficiency of rainfall-runoff model predictions, a spatial resampling procedure was carried out by neglecting data from some of the eight raingauges present inside or near to the analysed watershed. The spatial resampling procedure was carried out according to the following steps: 1. The number of sampled raingauges was selected between one and eight and all possible combinations of raingauges were evaluated. 2. For each combination, each urban sub-catchment was linked to the closer raingauge according to the minimum Euclidean distance criterion. No geo-statistical averaging approach was used because it would require the implementation of spatial and temporal re-sampling on each sub-catchment, making the analysis too time consuming. The total number of raingauge combinations was 255 and, considering that the analysis was carried out for each considered rainfall temporal resolution (11), the total number of analysed spatial and temporal resolution scenarios was 2805. In order to quantify the goodness of rainfall estimates with respect to the reference rainfall that is devised from the whole raingauge network, and to evaluate the dependencies between model performance and accuracy in the description of a rainfall event in time and space, two indices or rainfall performance indicators, BALANCE and goodness of rainfall estimation (GORE) (Andreassian et al. ), were computed as follows: Pn PEi BALANCE ¼ Pi¼1 n i¼1 Pi
(1)
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(2)
where n is the number of time steps of the study period; Pi is the reference precipitation input to the watershed on the i-th time step, computed as the mean amount of precipitation recorded at the same time i by the whole raingauge network with the highest available temporal resolution; PEi is at time i-th the estimate of precipitation input computed with a subset of the raingauge network, obtained as the mean of the precipitations recorded at the same time; pffiffiffiffiffi Pi is the mean of the reference precipitation over the study period. The two indices can describe both the goodness in the estimation of total rainfall volume and the rainfall spatial and temporal distribution. Namely, the BALANCE index quantifies the overestimation (when it is greater than 1) or underestimation (when it is smaller than 1) of the rainfall volume in each analysed scenario. The GORE index compares the sum of squared errors in the rainfall estimate in each scenario to the temporal variance of the reference precipitation (obtained with the maximum temporal resolution and the maximum number of available raingauges). The index can assume values ranging between ∞ and 1. The maximum value equal to 1 is obtained when the estimated rainfall PEi equals the reference rainfall Pi. At the event scale, the two indices are computed for each raingauge and then the average values are used as indicators of the overall performance for each rainfall event. Finally, modelling results obtained with historical rainfall events were compared with those obtained by adopting coarser estimate rainfall data and the relative impact on the uncertainty inherent in urban flood modelling results was assessed in terms of the Nash-Sutcliffe (N-S) criterion adopted as likelihood measure within the GLUE framework. The GLUE procedure is a statistical method for quantifying the uncertainty of model predictions. It is based on the concept that whatever the model, it permits only a conceptualized representation of the physical processes occurring in nature. Therefore, there will always be several different models that mimic equally well an observed natural process. According to this equifinality concept, for a given model structure no single parameter set represents the observed catchment responses, but a number of parameter combinations may represent the observed catchment behaviour equally well. Parameters values are sampled in a user-defined range (usually
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obtained by prior knowledge or by expert judgement of the modeller, as in the present case), adopting a user-defined prior distribution (uniform, in the present case, because no prior knowledge is available). The parameter variation range is presented in Table 2. This approach requires a large number of Monte Carlo simulations where the random sampling of individual parameters from probability distributions is used to determine a set of parameter values. The performance of an individual parameter set is characterised by a likelihood weight, computed by comparing predicted to observed model outputs using a likelihood measure.
RESULTS AND DISCUSSION The analysis was carried out in two phases: (i) the rainfall performance indicators were compared with model efficiency in the estimation of flood depths; and (ii) the model uncertainty was correlated to the availability of rainfall data, considering the impact of different possible combinations of a fixed number of raingauges. The first analysis was carried out by calibrating the adopted urban drainage model for all 2805 considered scenarios. The calibrated parameters were the rainfall – runoff parameters and drainage system roughness (both considering underground pipes and surface channels). Table 2 reports the variation ranges adopted in the calibration procedure. The model calibration was done by defining 500 random Monte Carlo sets of parameters and then selecting the one providing the highest N-S criterion computed on flooding depths. Namely, the model parameters were globally attributed to all sub-catchments. The number of simulations was selected in order to avoid bias in the uncertainty analysis
Table 2
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and 500 simulations proved to be sufficient, considering that the model is identified by nine parameters globally assigned to the whole catchment. Details on the adopted method are described in Freni & Mannina (). Figure 4 shows the comparison of the indicators BALANCE and GORE and the N-S criterion computed on the flooding depths obtained in each of the 15 flooding locations of the analysed urban area by the simulations carried out for each considered scenario. The results are shown for one event (1st December 1995) but similar results were obtained for the other rainfall events. The figure shows the importance of both indicators with a higher sensitivity of BALANCE indicator (Figure 4(a)). This can be easily explained by the fact that BALANCE provides the deviation of the considered rainfall with respect to the reference rainfall; rainfall depth has a major impact on flooding and the graphs confirm that its wrong estimation can impact negatively on model performance. By definition, the GORE parameter is the transposition of the N-S criterion in the rainfall estimation (considering the rainfall obtained from the highest number of raingauges as the reference rainfall). Figure 4(b) shows that the ratio between the two parameters
Variation ranges and measuring units of the calibrated model parameters
Parameters
Unit
Min
Max
Impervious area surface storage
mm
0.5
2.0
Pervious area surface storage
mm
3.5
8.5
Impervious area Manning’s roughness
–
0.020
0.033
Pervious area Manning’s roughness
–
0.025
0.050
Maximum filtration rate (Horton)
mm/h
62.0
117.2
Saturated soil infiltration rate (Horton)
mm/h
12.2
22.7
Underground drainage system Manning’s roughness
–
0.014
0.025
Surface channels Manning’s roughness
–
0.021
0.034
Figure 4
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Comparison of indices and flood depth N-S criterion for the event of 1st December 1995.
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is nearly linear, implying that the model, during the calibration phase, is able to slightly compensate for the wrong estimation of rainfall input and to obtain a reliable estimation of the flooding depth. As demonstrated in the literature (Kavetski et al. ), when the adopted input is not reliable, the model is still able to provide a reliable estimation of the outputs and the parameters partially compensate the insufficient input data quality during the calibration process. A further analysis was carried out, separating the upstream flooding locations (1, 2, 3, 4, 8 and 9 in Figure 1) and the downstream ones (5, 6, 7, 10, 11, 12, 13, 14 and 15 in Figure 1). Figure 5 shows the comparison between indices and N-S criterion for the upstream flooding locations and Figure 6 shows the same data for the downstream locations only. Comparing the two figures, some interesting considerations can be expressed:
•
The flooding estimation criterion is more influenced by BALANCE when considering the downstream locations, whereas the influence is lower in the upstream ones, which is indicated by the higher scatter in the points
Figure 6
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Comparison of indices and flood depth N-S criterion for the event of 1st December 1995 and for the downstream flood locations.
• •
Figure 5
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Comparison of indices and flood depth N-S criterion for the event of 1st December 1995 and for the upstream flood locations.
distribution; this means that the downstream flooding locations are more influenced by rainfall volume and an inaccurate appraisal of such a variable is rapidly reflected in flooding estimations. Conversely, downstream flooding is less influenced by GORE, confirming that the model calibration partially compensates for defective rainfall knowledge. Better rainfall knowledge generally means a better estimation of flood depths but the uncertainty related to rainfall knowledge is still high considering, for example, that GORE values equal to 0.8 can produce N-S flooding estimation criterion ranging from 0.5 to 0.75.
In order to evaluate the uncertainty affecting urban flooding modelling results and flood damage estimates, in particular, a GLUE analysis was carried out for each of the 2805 considered scenarios by running 500 Monte Carlo simulations related to 500 different model parameter sets. Table 2 presents model parameters and the ranges in which the prior uniform distribution was applied. The ranges were fixed on the basis of experience, considering the calibration values obtained by the same model in flood
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analysis applications in the same area. The details of the method can be found in Freni & Mannina (). In Figure 7 the obtained uncertainty bands for maximum flooding depths in four locations (Area 2 in the upper part of the system; Area 5 in the lower part near the sea; Areas 6 and 15 in the central part of the system) for another rainfall event (26th September 1996) are presented. The figure shows the maximum efficiency simulation compared with measured flooding depths and the 5th and 95th percentiles of the Monte Carlo simulations. Maximum efficiency increases with the increment of the number of available raingauges. After five raingauges are available, the added value of increasing their number is limited, with the exclusion of flooded Area 5, being in the downstream part of the system. The width of the uncertainty band has a minimum that is not associated with the maximum number of raingauges used, showing that the addition of new data may not necessarily produce an increase in model reliability. From this point of view, the four flooded locations in Figure 7 reveal different behaviours: the flooded Area 2 (the most upstream) shows that a smaller uncertainty band is given by the use of five raingauges probably because several raingauges (from four to eight) measure rainfall that are not directly influencing the analysed flooding; the flooded locations 6 and 15 (in the middle part of the
Figure 7
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system) show the smallest width of the uncertainty band with the use of six raingauges because, in this case, the number of raingauges having a direct impact on flooding is higher; finally, flooding location 5 shows the smallest width of the uncertainty band with the maximum number of available raingauges. Similar results were obtained for the other events even if the position of uncertainty minima moves depending on the analysed event. For all the analysed events, only flooding location 5 shows minimum uncertainty bands for the maximum number of available raingauges, demonstrating that additional data may cause deterioration in model response if the data are not really representing the physical processes producing the flooding. In addition to flooding depth uncertainty, a specific analysis was carried out on total catchment damage. The analysis of flooding damage is useful because the catchment averaging process that is carried out, considering the overall flooding damage, reduces uncertainty and increases maximum efficiency, confirming that the model is able to slightly compensate for input data uncertainty if average responses are needed. Moreover, damage uncertainty band width dependency on the number of adopted raingauges follows the most relevant flooding locations (namely the upstream ones) and this is another example of the importance of rainfall input data selection depending on the
Uncertainty bands of the flood depth in 4 flooding locations for the event of 26th September 1996.
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Figure 8
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Uncertainty bands of the flood damage in ‘Centro Storico’ watershed for the event of 1st December 1995.
required analysis. Depth-damage curves for buildings (Equation (3)) and vehicles (Equation (4)) were obtained from available data in the area (Freni et al. ): D ¼ 867:85 h0:8409
(3)
D ¼ 1035:70 h0:5110
(4)
where D is the flood damage in Euros and h is the flood depth over the street level in cm. Figure 8 shows the uncertainty bands (5th and 95th percentiles) around the measured and calibrated flood damage in the entire catchment during the event on 1st December 1995. The figure shows that the model is generally able to provide a good estimate of the measured damage. The total monetary damage estimate is in the range of ± 10% around the measured value. The calibration efficiency is progressively better if more rainfall data are available but the added value of the single raingauge after the fourth is not relevant. In the scenario with one available raingauge, the uncertainty bands are twice as wide as in the case with five available raingauges. This shows that the availability of more data ensures the setup of a more robust model. Uncertainty bands enlarge slightly if more raingauges are available after the fifth, showing that the use of the maximum number of raingauges can introduce more uncertainty in the model than expected, providing no advantage in terms of model robustness.
CONCLUSIONS The present paper describes the impact of rainfall imperfect knowledge on urban flood modelling. The study was carried
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out by means of a network consisting of eight raingauges with 1–3 min temporal resolution data. Spatial and temporal rainfall resolution was degraded using different combinations of raingauges (neglecting up to seven time series) and rescaling rainfall data with a temporal resolution ranging between 5 and 15 min. The analysis shows that rainfall information has a higher impact on the upstream flooding area and the mathematical model has the ability of partially compensating for imperfect rainfall knowledge. Rainfall introduces uncertainty in the model; however, a higher level of knowledge does not necessarily produce lower uncertainty in modelling results; conversely, the use of more raingauges may result in higher uncertainty in the model response. For all of the analysed events, uncertainty is strongly reduced when at least four raingauges are used but the minimum uncertainty configuration depends on the event and the location of the analysed flooding. The obtained results suggest a minimum spatial resolution of one raingauge for each 1.7 km2, being slightly higher than the values proposed by Berne et al. (). The study instead confirmed that temporal resolution should be the lowest possible and not higher than 5–6 min as with the study proposed by Berne et al. (). The use of different spatial aggregations of model response (single flooding locations or the whole catchment) and different output objective functions (flooding depth and total flooding damage) show the importance of selecting rainfall spatial and temporal resolution depending on the variable to be analysed. The results cannot be rigorously generalised to any similar catchment but the analysis results demonstrate that the number of raingauges producing the smaller uncertainty bands depends on the analysed location (single flooding or group of nearby flooded areas) and variable (flooding depth or flooding damage). In the end, this result should suggest that modellers evaluate the reliability of available data by means of uncertainty analysis and eventually use only a sub-set of available data.
REFERENCES Andreassian, V., Perrin, C., Michel, C., Usart-Sanchez, I. & Lavabre, J. Impact of imperfect rainfall knowledge on the efficiency and the parameters of watershed models. Journal of Hydrology 250, 206–223. Aronica, G. T., Freni, G. & Oliveri, E. Uncertainty analysis of the influence of rainfall time resolution in the modelling of urban drainage systems. Hydrological Processes 19, 1055–1071.
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Berne, A., Delrieu, G., Creutin, J. D. & Obled, C. Temporal and spatial resolution of rainfall measurements required for urban hydrology. Journal of Hydrology 299, 166–179. Beven, K. J. & Binley, A. M. The future of distributed models— model calibration and uncertainty prediction. Hydrological Processes 6 (3), 279–298. Deletic, A., Dotto, C. B. S., McCarthy, D. T., Kleidorfer, M., Freni, G., Mannina, G., Henrichs, M., Fletcher, D., Rauch, W., Bertrand-Krajewski, J. L. & Tait, S. Assessing uncertainties in urban drainage models. Physics and Chemistry of the Earth 42–44, 3–10. Fontanazza, C. M., Freni, G., La Loggia, G. & Notaro, V. Uncertainty evaluation of design rainfall for urban flood risk analysis. Water Science and Technology 63 (11), 2641–2650. Fontanazza, C. M., Freni, G. & Notaro, V. Bayesian inference analysis of the uncertainty linked to the evaluation of potential flood damage in urban areas. Water Science and Technology 66 (8), 1669–1677. Freni, G., La Loggia, G. & Notaro, V. Uncertainty in urban flood damage assessment due to urban drainage modelling and depth–damage curve estimation. Water Science and Technology 61 (12), 2979–2993. Freni, G. & Mannina, G. Bayesian approach for uncertainty quantification in water quality modeling: the influence of prior distribution. Journal of Hydrology 392, 31–39. Huber, W. C. & Dickinson, R. E. Storm Water Management Model-SWMM, Version 4 User’s Manual. US Environmental Protection Agency, Athens Georgia, USA. Kavetski, M., Kuczera, G. & Franks, S. W. Calibration of conceptual hydrological models revisited: 2. Improving optimisation and analysis. Journal of Hydrology 320 (1–2), 187–201.
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Kleidorfer, M., Deletic, A., Fletcher, T. D. & Rauch, W. Impact of input data uncertainties on urban stormwater model parameters. Water Science and Technology 60 (6), 1545–1554. Leandro, J., Chen, A. S., Djordjevic´, S. & Savic´, D. A. A comparison of 1D/1D and 1D/2D coupled (sewer/surface) hydraulic models for urban flood simulation. Journal of Hydraulic Engineering 135 (6), 495–504. Leandro, J., Leitão, J. P. & de Lima, J. L. M. P. Quantifying the uncertainty in the Soil Conservation Service flood hydrographs: a case study in the Azores Islands. Journal of Flood Risk Management. Article first published online: 27 Nov 2012. Rossman, L. A. Storm Water Management Model, User’s Manual. US Environmental Protection Agency, Cincinnati, Ohio. Segond, M. L., Wheater, H. S. & Onof, C. The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation based on the Lee catchment, UK. Journal of Hydrology 347, 116–131. Sen, Z. & Altunkaynak, A. A comparative fuzzy logic approach to runoff coefficient and runoff estimation. Hydrological Processes 20 (9), 1993–2009. Thorndahl, S. & Willems, P. Probabilistic modelling of overflow, surcharge and flooding in urban drainage using the first-order reliability method and parameterization of local rain series. Water Research 42 (1–2), 455–466. Thorndahl, S., Beven, K. J., Jensen, J. B. & Schaarup-Jensen, K. Event based uncertainty assessment in urban drainage modelling, applying the GLUE methodology. Journal of Hydrology 357 (3–4), 421–437. Willems, P. Quantification and relative comparison of different types of uncertainties in sewer water quality modeling. Water Research 42 (13), 3539–3551.
First received 11 December 2012; accepted in revised form 18 June 2013. Available online 19 October 2013
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Impact of rainfall data resolution in time and space on the urban flooding evaluation Vincenza Notaro, Chiara Maria Fontanazza, Gabriele Freni and Valeria Puleo
ABSTRACT Climate change and modification of the urban environment increase the frequency and the negative effects of flooding, increasing the interest of researchers and practitioners in this topic. Usually, flood frequency analysis in urban areas is indirectly carried out by adopting advanced hydraulic models to simulate long historical rainfall series or design storms. However, their results are affected by a level of uncertainty which has been extensively investigated in recent years. A major source of uncertainty inherent to hydraulic model results is linked to the imperfect knowledge of the rainfall input data
Vincenza Notaro (corresponding author) Chiara Maria Fontanazza Gabriele Freni University of Enna ‘Kore’, Italy E-mail: [email protected] Valeria Puleo University of Palermo, Italy
both in time and space. Several studies show that hydrological modelling in urban areas requires rainfall data with fine resolution in time and space. The present paper analyses the effect of rainfall knowledge on urban flood modelling results. A mathematical model of urban flooding propagation was applied to a real case study and the maximum efficiency conditions for the model and the uncertainty affecting the results were evaluated by means of generalised likelihood uncertainty estimation (GLUE) analysis. The added value provided by the adoption of finer temporal and spatial resolution of the rainfall was assessed. Key words
| rainfall resolution, rainfall-runoff transformation, urban drainage modeling
INTRODUCTION The surcharging of sanitary and stormwater drainage systems due solely to rainfall often causes local flooding in European cities where ageing of the infrastructure and growing urbanisation take place. In order to improve the proactive management of flooding, identification of the flood risk areas and development of strategies to reduce that risk are needed. To this end, a robust statistical frequency analysis of urban flooding could be a preliminary step. However, in most cases, historical series of flood data are often unavailable or too piecemeal for performing a statistical analysis of flooding events aimed at a reliable assessment of urban flood risk. Therefore, many standard approaches simulate long historical rainfall series or design storms by means of urban drainage mathematical models to indirectly estimate flood location, extension, frequency and volume/depth (Thorndahl & Willems ; Fontanazza et al. ). The application of advanced hydraulic models as diagnostic, design and decision-making support tools has become a standard practice in hydraulic research and doi: 10.2166/wst.2013.435
application. Although mathematical models have been significantly improved in recent years (Leandro et al. ), their results are affected by a high level of uncertainty due to input data errors, model structure and parameterization. The analysis and estimation of the uncertainty involved in urban drainage modelling have attracted considerable attention from researchers in recent years (Sen & Altunkaynak ; Willems ; Kleidorfer et al. ; Deletic et al. ; Fontanazza et al. ; Leandro et al. ). A major source of uncertainty inherent to model results is linked to imperfect knowledge of the rainfall input data both in time and space. Usually, rainfall is the driving phenomenon of runoff generation, particularly in urban areas where catchments are small and have a short concentration time producing runoff hydrographs sensitive to the temporal and spatial variation of rainfall. Several studies assess that the effects of storm spatial and temporal variability on runoff generation increase with decreasing catchment scale (Berne et al. ; Segond et al. ): an underestimation of the peak of the runoff hydrograph is systematically
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obtained when rainfall data with a low temporal resolution are used as input to the numerical simulations of urban drainage system behaviour (Aronica et al. ). Therefore, hydrological modelling in urban areas needs a fine resolution of rainfall data both in time and space: a resolution of 3–6 min in time and 2–4 km in space for urban catchments of 1–10 km2 should be enough, according to Berne et al. (). However, for practical applications, the available rainfall databases present temporal and spatial resolution that are often coarser than those required for a reliable rainfall–runoff simulation in urban areas, greatly compromising model accuracy. The present study aims to evaluate the impact of defective rainfall knowledge on urban flooding model outputs. The study analyses both the temporal and spatial resolution of rainfall data and compares the related uncertainty with the intrinsic model uncertainty that may be correlated to the model structure and to parameter estimation. The uncertainty affecting urban flooding modelling was evaluated by means of the generalised likelihood uncertainty estimation (GLUE) approach (Beven & Binley ) and the added value provided by the adoption of finer temporal and spatial resolutions of the rainfall was assessed. The GLUE approach was previously used for estimating
Figure 1
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The ‘Centro Storico’ catchment, with flooded areas.
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modelling uncertainty in urban drainage (Thorndahl et al. ). In the present application, the approach was used to estimate the uncertainty related to pluviometric input and to estimate the most reliable level of rainfall knowledge for a specific modelling aim. The analysis was carried out on single flooding locations (considering flooding depth uncertainty) and globally on the whole catchment (considering flooding damage). The use of different spatial aggregations of model response and different output objective functions showed the importance of selecting rainfall spatial and temporal resolution depending on the variable to be analysed. Analyses were carried out using the historical rainfall–flood data collected for a period of 5 years in the ‘Centro Storico’ catchment of Palermo (Italy) as a reference for rainfall events.
THE CASE STUDY The ‘Centro Storico’ catchment of Palermo (Italy) is the oldest part of the city, strongly urbanized (Figure 1). The analysed catchment is about 6.7 km2 with about 88% of impervious areas.
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The most common land use in the area is for residential dwellings. However, there are many monuments and other estates having a cultural or artistic significance (theatres, churches, monasteries etc.). The whole catchment is drained by a very old drainage system (about 118 years old), with a total length of about 56 km. It receives both storm and waste water, also from upstream less urbanized watersheds. Local surface flooding due to system insufficiency often occurs, even for high-frequency rainfall. During 1993– 2008, more than 40 flood events affected several areas of the watershed (Figure 1). An accurate database covering flooded areas, water depths and volumes, durations and damaged properties has been collected by querying fire brigades and insurance companies (Freni et al. ). Water depths are measured by means of local webcams (also used for activating emergency procedures in case of flooding) and graduated steel tapes (with resolution equal to 1 cm) fixed to building walls. The webcams are interrogated remotely every five minutes and the measure resolution is 5 cm. The maximum flooding depth is locally verified by fire brigades during field operations with centimetric accuracy (because steel tapes show signs of the maximum water depth). In the present paper, only maximum depth data were used because depthdamage curves are related to such variables. In the present study, rainfall data was recorded by a raingauge network made of eight raingauges located in the analysed catchment or with in a 1 km range. Analyses were carried out, adopting as reference rainfall 10 historical rainfall events recorded by the raingauge network between 1993 and 1997. During the 10 selected
Table 1
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events, all eight raingauges registered rainfall data and all 15 locations (Figure 1) were flooded. In this way, results from different events can be compared. The selected events represent extreme storms for the sewer system but they are not exceptional, having return periods of between 3 and 20 years. Table 1 shows the main characteristics of the selected rainfall events. Figure 2 shows the original historical hyetograph of 1st December 1995, recorded with a temporal resolution (Dt) of 1 min by all eight raingauges (RG).
THE URBAN DRAINAGE MODEL The methodology proposed in the present study required the application of a mathematical model to simulate the runoff formation and flooding propagation phenomena in the analysed urban watersheds. An urban drainage model based on the storm water management model (SWMM) application (Huber & Dickinson ) was adopted to simulate urban drainage-system behaviour. That model can be used to examine a wider range of problems, from frequent and limited local flooding to a global system surcharge with high discharges and water levels on streets. A distributed ‘non-linear reservoir’ model was used to simulate surface runoff, which takes into account both surface storage and infiltration (Rossman ). A dual drainage approach was employed to simulate surface flood propagation (Leandro et al. ) where underground and surface drainage systems (streets, sidewalks, etc.) are schematised in a unique network made by
Historical rainfall events
Flooding event Parameter
Unit 1
Data event
2
3
4
5
6
7
8
9
10
d/m/y
25/10/93 08/01/95 01/12/95 18/09/96 26/09/96 05/10/96 12/08/97 22/08/97 25/09/97 07/12/97
Duration
hms
14.05.03
19.05.02
13.17.03
15.01.00
6.19.01
10.55.01
12.18.20
15.33.30
10.34.02
16.29.50
Mean rainfall intensity
mm h1 7.27
8.67
6.79
20.20
24.39
9.02
19.45
38.70
3.47
9.53
Median rainfall intensity
mm h1 5.66
8.21
5.20
12.34
13.77
7.74
14.55
18.88
3.32
7.83
Min. non-null mm h1 2.11 rainfall intensity
1.23
3.77
1.83
1.22
1.65
2.66
1.10
0.81
1.87
144.89
172.08
125.54
212.73
111.03
115.02
271.42
135.64
100.66
Max. rainfall intensity
mm h1 144.9
Rain volume
mm
Rain return period years
60.51
33.55
49.77
16.38
19.91
44.85
47.36
47.50
20.34
39.59
8
3
4
3
3
4
10
20
2
3
1987
Figure 2
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Event of 1st December 1995 – real hyetographs recorded by the all raingauges located in the ‘Centro Storico’ catchment or in 1 km range.
two sets of channels that are dynamically interconnected by sewer manholes. The flow into the underground pipes and surface channels was simulated by solving the complete one-dimensional de Saint Venant equations with a time step of 1 s. The model is made of more than 500 pipes and more than 700 surface channel connections. Pipe cross-sections are circular, egg-shaped and rectangular while all streets were simulated as rectangular channels. All pipes are made of concrete and their age ranges between 20 and more than 100 years. Details about the adopted model can be found in Freni et al. (). The model allows for the taking account of rainfall variability in space, by linking different rainfall input data for the same simulation to the various sub-catchments identified in the whole analysed watershed. Namely, the analysed watershed was divided into more than 300 sub-catchments and a specific rainfall time series was assigned to each of these, according to the following described procedure. Finally, the model runs under the hypothesis that each sub-catchment is connected to a single inlet manhole.
METHODOLOGY The proposed procedure aims to assess the effect of the temporal and spatial resolution of rainfall input data on urban
flooding evaluation, when an urban drainage mathematical model is adopted to simulate the runoff formation and flood propagation phenomena in an urban watershed. As the first step of the methodology, a temporal resampling procedure (Aronica et al. ) was applied to a set of 10 historical rainfall time series with high temporal resolution (1–3 min) recorded by the raingauge network in the analysed area (Figure 1). The temporal resampling procedure was based on a fixed window average by means of the following steps: 1. The duration of each historical rainfall event was divided into a number n of equal time intervals ranging from 5 to 15 min with step of 1 min. 2. For each of these temporal windows the average intensity was evaluated. According to the mass balance principle, for each time step, the real event and the resampled one are characterised by the same rainfall volume. As a result of applying the above temporal resampling procedure, 11 hyetographs with a coarser temporal resolution were obtained by each of the 10 historical rainfall time series analysed. Figure 3 shows, in terms of rainfall intensity, the real event of 1st December 1995 recorded with a time resolution (Dt) of 1 min by the raingauges RG3 (13 200 54,62″ E, 38 60 20.27″ N) and three resampled hyetographs with a coarser temporal resolution (Dt) equal to
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pffiffiffiffiffi2 Pn qffiffiffiffiffiffi PEi Pi i¼1 GORE ¼ 1 Pn pffiffiffiffiffi pffiffiffiffiffi2 Pi Pi i¼1
Figure 3
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Event of 1st December 1995 – real and resampled hyetographs recorded by the raingauge RG3.
5, 10 and 15 min, respectively, obtained by applying the temporal resampled procedure to the real event. To analyse the influence of the spatial rainfall aggregation on the efficiency of rainfall-runoff model predictions, a spatial resampling procedure was carried out by neglecting data from some of the eight raingauges present inside or near to the analysed watershed. The spatial resampling procedure was carried out according to the following steps: 1. The number of sampled raingauges was selected between one and eight and all possible combinations of raingauges were evaluated. 2. For each combination, each urban sub-catchment was linked to the closer raingauge according to the minimum Euclidean distance criterion. No geo-statistical averaging approach was used because it would require the implementation of spatial and temporal re-sampling on each sub-catchment, making the analysis too time consuming. The total number of raingauge combinations was 255 and, considering that the analysis was carried out for each considered rainfall temporal resolution (11), the total number of analysed spatial and temporal resolution scenarios was 2805. In order to quantify the goodness of rainfall estimates with respect to the reference rainfall that is devised from the whole raingauge network, and to evaluate the dependencies between model performance and accuracy in the description of a rainfall event in time and space, two indices or rainfall performance indicators, BALANCE and goodness of rainfall estimation (GORE) (Andreassian et al. ), were computed as follows: Pn PEi BALANCE ¼ Pi¼1 n i¼1 Pi
(1)
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(2)
where n is the number of time steps of the study period; Pi is the reference precipitation input to the watershed on the i-th time step, computed as the mean amount of precipitation recorded at the same time i by the whole raingauge network with the highest available temporal resolution; PEi is at time i-th the estimate of precipitation input computed with a subset of the raingauge network, obtained as the mean of the precipitations recorded at the same time; pffiffiffiffiffi Pi is the mean of the reference precipitation over the study period. The two indices can describe both the goodness in the estimation of total rainfall volume and the rainfall spatial and temporal distribution. Namely, the BALANCE index quantifies the overestimation (when it is greater than 1) or underestimation (when it is smaller than 1) of the rainfall volume in each analysed scenario. The GORE index compares the sum of squared errors in the rainfall estimate in each scenario to the temporal variance of the reference precipitation (obtained with the maximum temporal resolution and the maximum number of available raingauges). The index can assume values ranging between ∞ and 1. The maximum value equal to 1 is obtained when the estimated rainfall PEi equals the reference rainfall Pi. At the event scale, the two indices are computed for each raingauge and then the average values are used as indicators of the overall performance for each rainfall event. Finally, modelling results obtained with historical rainfall events were compared with those obtained by adopting coarser estimate rainfall data and the relative impact on the uncertainty inherent in urban flood modelling results was assessed in terms of the Nash-Sutcliffe (N-S) criterion adopted as likelihood measure within the GLUE framework. The GLUE procedure is a statistical method for quantifying the uncertainty of model predictions. It is based on the concept that whatever the model, it permits only a conceptualized representation of the physical processes occurring in nature. Therefore, there will always be several different models that mimic equally well an observed natural process. According to this equifinality concept, for a given model structure no single parameter set represents the observed catchment responses, but a number of parameter combinations may represent the observed catchment behaviour equally well. Parameters values are sampled in a user-defined range (usually
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obtained by prior knowledge or by expert judgement of the modeller, as in the present case), adopting a user-defined prior distribution (uniform, in the present case, because no prior knowledge is available). The parameter variation range is presented in Table 2. This approach requires a large number of Monte Carlo simulations where the random sampling of individual parameters from probability distributions is used to determine a set of parameter values. The performance of an individual parameter set is characterised by a likelihood weight, computed by comparing predicted to observed model outputs using a likelihood measure.
RESULTS AND DISCUSSION The analysis was carried out in two phases: (i) the rainfall performance indicators were compared with model efficiency in the estimation of flood depths; and (ii) the model uncertainty was correlated to the availability of rainfall data, considering the impact of different possible combinations of a fixed number of raingauges. The first analysis was carried out by calibrating the adopted urban drainage model for all 2805 considered scenarios. The calibrated parameters were the rainfall – runoff parameters and drainage system roughness (both considering underground pipes and surface channels). Table 2 reports the variation ranges adopted in the calibration procedure. The model calibration was done by defining 500 random Monte Carlo sets of parameters and then selecting the one providing the highest N-S criterion computed on flooding depths. Namely, the model parameters were globally attributed to all sub-catchments. The number of simulations was selected in order to avoid bias in the uncertainty analysis
Table 2
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and 500 simulations proved to be sufficient, considering that the model is identified by nine parameters globally assigned to the whole catchment. Details on the adopted method are described in Freni & Mannina (). Figure 4 shows the comparison of the indicators BALANCE and GORE and the N-S criterion computed on the flooding depths obtained in each of the 15 flooding locations of the analysed urban area by the simulations carried out for each considered scenario. The results are shown for one event (1st December 1995) but similar results were obtained for the other rainfall events. The figure shows the importance of both indicators with a higher sensitivity of BALANCE indicator (Figure 4(a)). This can be easily explained by the fact that BALANCE provides the deviation of the considered rainfall with respect to the reference rainfall; rainfall depth has a major impact on flooding and the graphs confirm that its wrong estimation can impact negatively on model performance. By definition, the GORE parameter is the transposition of the N-S criterion in the rainfall estimation (considering the rainfall obtained from the highest number of raingauges as the reference rainfall). Figure 4(b) shows that the ratio between the two parameters
Variation ranges and measuring units of the calibrated model parameters
Parameters
Unit
Min
Max
Impervious area surface storage
mm
0.5
2.0
Pervious area surface storage
mm
3.5
8.5
Impervious area Manning’s roughness
–
0.020
0.033
Pervious area Manning’s roughness
–
0.025
0.050
Maximum filtration rate (Horton)
mm/h
62.0
117.2
Saturated soil infiltration rate (Horton)
mm/h
12.2
22.7
Underground drainage system Manning’s roughness
–
0.014
0.025
Surface channels Manning’s roughness
–
0.021
0.034
Figure 4
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Comparison of indices and flood depth N-S criterion for the event of 1st December 1995.
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is nearly linear, implying that the model, during the calibration phase, is able to slightly compensate for the wrong estimation of rainfall input and to obtain a reliable estimation of the flooding depth. As demonstrated in the literature (Kavetski et al. ), when the adopted input is not reliable, the model is still able to provide a reliable estimation of the outputs and the parameters partially compensate the insufficient input data quality during the calibration process. A further analysis was carried out, separating the upstream flooding locations (1, 2, 3, 4, 8 and 9 in Figure 1) and the downstream ones (5, 6, 7, 10, 11, 12, 13, 14 and 15 in Figure 1). Figure 5 shows the comparison between indices and N-S criterion for the upstream flooding locations and Figure 6 shows the same data for the downstream locations only. Comparing the two figures, some interesting considerations can be expressed:
•
The flooding estimation criterion is more influenced by BALANCE when considering the downstream locations, whereas the influence is lower in the upstream ones, which is indicated by the higher scatter in the points
Figure 6
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Comparison of indices and flood depth N-S criterion for the event of 1st December 1995 and for the downstream flood locations.
• •
Figure 5
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Comparison of indices and flood depth N-S criterion for the event of 1st December 1995 and for the upstream flood locations.
distribution; this means that the downstream flooding locations are more influenced by rainfall volume and an inaccurate appraisal of such a variable is rapidly reflected in flooding estimations. Conversely, downstream flooding is less influenced by GORE, confirming that the model calibration partially compensates for defective rainfall knowledge. Better rainfall knowledge generally means a better estimation of flood depths but the uncertainty related to rainfall knowledge is still high considering, for example, that GORE values equal to 0.8 can produce N-S flooding estimation criterion ranging from 0.5 to 0.75.
In order to evaluate the uncertainty affecting urban flooding modelling results and flood damage estimates, in particular, a GLUE analysis was carried out for each of the 2805 considered scenarios by running 500 Monte Carlo simulations related to 500 different model parameter sets. Table 2 presents model parameters and the ranges in which the prior uniform distribution was applied. The ranges were fixed on the basis of experience, considering the calibration values obtained by the same model in flood
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analysis applications in the same area. The details of the method can be found in Freni & Mannina (). In Figure 7 the obtained uncertainty bands for maximum flooding depths in four locations (Area 2 in the upper part of the system; Area 5 in the lower part near the sea; Areas 6 and 15 in the central part of the system) for another rainfall event (26th September 1996) are presented. The figure shows the maximum efficiency simulation compared with measured flooding depths and the 5th and 95th percentiles of the Monte Carlo simulations. Maximum efficiency increases with the increment of the number of available raingauges. After five raingauges are available, the added value of increasing their number is limited, with the exclusion of flooded Area 5, being in the downstream part of the system. The width of the uncertainty band has a minimum that is not associated with the maximum number of raingauges used, showing that the addition of new data may not necessarily produce an increase in model reliability. From this point of view, the four flooded locations in Figure 7 reveal different behaviours: the flooded Area 2 (the most upstream) shows that a smaller uncertainty band is given by the use of five raingauges probably because several raingauges (from four to eight) measure rainfall that are not directly influencing the analysed flooding; the flooded locations 6 and 15 (in the middle part of the
Figure 7
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system) show the smallest width of the uncertainty band with the use of six raingauges because, in this case, the number of raingauges having a direct impact on flooding is higher; finally, flooding location 5 shows the smallest width of the uncertainty band with the maximum number of available raingauges. Similar results were obtained for the other events even if the position of uncertainty minima moves depending on the analysed event. For all the analysed events, only flooding location 5 shows minimum uncertainty bands for the maximum number of available raingauges, demonstrating that additional data may cause deterioration in model response if the data are not really representing the physical processes producing the flooding. In addition to flooding depth uncertainty, a specific analysis was carried out on total catchment damage. The analysis of flooding damage is useful because the catchment averaging process that is carried out, considering the overall flooding damage, reduces uncertainty and increases maximum efficiency, confirming that the model is able to slightly compensate for input data uncertainty if average responses are needed. Moreover, damage uncertainty band width dependency on the number of adopted raingauges follows the most relevant flooding locations (namely the upstream ones) and this is another example of the importance of rainfall input data selection depending on the
Uncertainty bands of the flood depth in 4 flooding locations for the event of 26th September 1996.
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Figure 8
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Uncertainty bands of the flood damage in ‘Centro Storico’ watershed for the event of 1st December 1995.
required analysis. Depth-damage curves for buildings (Equation (3)) and vehicles (Equation (4)) were obtained from available data in the area (Freni et al. ): D ¼ 867:85 h0:8409
(3)
D ¼ 1035:70 h0:5110
(4)
where D is the flood damage in Euros and h is the flood depth over the street level in cm. Figure 8 shows the uncertainty bands (5th and 95th percentiles) around the measured and calibrated flood damage in the entire catchment during the event on 1st December 1995. The figure shows that the model is generally able to provide a good estimate of the measured damage. The total monetary damage estimate is in the range of ± 10% around the measured value. The calibration efficiency is progressively better if more rainfall data are available but the added value of the single raingauge after the fourth is not relevant. In the scenario with one available raingauge, the uncertainty bands are twice as wide as in the case with five available raingauges. This shows that the availability of more data ensures the setup of a more robust model. Uncertainty bands enlarge slightly if more raingauges are available after the fifth, showing that the use of the maximum number of raingauges can introduce more uncertainty in the model than expected, providing no advantage in terms of model robustness.
CONCLUSIONS The present paper describes the impact of rainfall imperfect knowledge on urban flood modelling. The study was carried
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out by means of a network consisting of eight raingauges with 1–3 min temporal resolution data. Spatial and temporal rainfall resolution was degraded using different combinations of raingauges (neglecting up to seven time series) and rescaling rainfall data with a temporal resolution ranging between 5 and 15 min. The analysis shows that rainfall information has a higher impact on the upstream flooding area and the mathematical model has the ability of partially compensating for imperfect rainfall knowledge. Rainfall introduces uncertainty in the model; however, a higher level of knowledge does not necessarily produce lower uncertainty in modelling results; conversely, the use of more raingauges may result in higher uncertainty in the model response. For all of the analysed events, uncertainty is strongly reduced when at least four raingauges are used but the minimum uncertainty configuration depends on the event and the location of the analysed flooding. The obtained results suggest a minimum spatial resolution of one raingauge for each 1.7 km2, being slightly higher than the values proposed by Berne et al. (). The study instead confirmed that temporal resolution should be the lowest possible and not higher than 5–6 min as with the study proposed by Berne et al. (). The use of different spatial aggregations of model response (single flooding locations or the whole catchment) and different output objective functions (flooding depth and total flooding damage) show the importance of selecting rainfall spatial and temporal resolution depending on the variable to be analysed. The results cannot be rigorously generalised to any similar catchment but the analysis results demonstrate that the number of raingauges producing the smaller uncertainty bands depends on the analysed location (single flooding or group of nearby flooded areas) and variable (flooding depth or flooding damage). In the end, this result should suggest that modellers evaluate the reliability of available data by means of uncertainty analysis and eventually use only a sub-set of available data.
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Berne, A., Delrieu, G., Creutin, J. D. & Obled, C. Temporal and spatial resolution of rainfall measurements required for urban hydrology. Journal of Hydrology 299, 166–179. Beven, K. J. & Binley, A. M. The future of distributed models— model calibration and uncertainty prediction. Hydrological Processes 6 (3), 279–298. Deletic, A., Dotto, C. B. S., McCarthy, D. T., Kleidorfer, M., Freni, G., Mannina, G., Henrichs, M., Fletcher, D., Rauch, W., Bertrand-Krajewski, J. L. & Tait, S. Assessing uncertainties in urban drainage models. Physics and Chemistry of the Earth 42–44, 3–10. Fontanazza, C. M., Freni, G., La Loggia, G. & Notaro, V. Uncertainty evaluation of design rainfall for urban flood risk analysis. Water Science and Technology 63 (11), 2641–2650. Fontanazza, C. M., Freni, G. & Notaro, V. Bayesian inference analysis of the uncertainty linked to the evaluation of potential flood damage in urban areas. Water Science and Technology 66 (8), 1669–1677. Freni, G., La Loggia, G. & Notaro, V. Uncertainty in urban flood damage assessment due to urban drainage modelling and depth–damage curve estimation. Water Science and Technology 61 (12), 2979–2993. Freni, G. & Mannina, G. Bayesian approach for uncertainty quantification in water quality modeling: the influence of prior distribution. Journal of Hydrology 392, 31–39. Huber, W. C. & Dickinson, R. E. Storm Water Management Model-SWMM, Version 4 User’s Manual. US Environmental Protection Agency, Athens Georgia, USA. Kavetski, M., Kuczera, G. & Franks, S. W. Calibration of conceptual hydrological models revisited: 2. Improving optimisation and analysis. Journal of Hydrology 320 (1–2), 187–201.
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Kleidorfer, M., Deletic, A., Fletcher, T. D. & Rauch, W. Impact of input data uncertainties on urban stormwater model parameters. Water Science and Technology 60 (6), 1545–1554. Leandro, J., Chen, A. S., Djordjevic´, S. & Savic´, D. A. A comparison of 1D/1D and 1D/2D coupled (sewer/surface) hydraulic models for urban flood simulation. Journal of Hydraulic Engineering 135 (6), 495–504. Leandro, J., Leitão, J. P. & de Lima, J. L. M. P. Quantifying the uncertainty in the Soil Conservation Service flood hydrographs: a case study in the Azores Islands. Journal of Flood Risk Management. Article first published online: 27 Nov 2012. Rossman, L. A. Storm Water Management Model, User’s Manual. US Environmental Protection Agency, Cincinnati, Ohio. Segond, M. L., Wheater, H. S. & Onof, C. The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation based on the Lee catchment, UK. Journal of Hydrology 347, 116–131. Sen, Z. & Altunkaynak, A. A comparative fuzzy logic approach to runoff coefficient and runoff estimation. Hydrological Processes 20 (9), 1993–2009. Thorndahl, S. & Willems, P. Probabilistic modelling of overflow, surcharge and flooding in urban drainage using the first-order reliability method and parameterization of local rain series. Water Research 42 (1–2), 455–466. Thorndahl, S., Beven, K. J., Jensen, J. B. & Schaarup-Jensen, K. Event based uncertainty assessment in urban drainage modelling, applying the GLUE methodology. Journal of Hydrology 357 (3–4), 421–437. Willems, P. Quantification and relative comparison of different types of uncertainties in sewer water quality modeling. Water Research 42 (13), 3539–3551.
First received 11 December 2012; accepted in revised form 18 June 2013. Available online 19 October 2013
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