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Rainfall input requirements for hydrological calculations
Urban Water 3 (2001) 107±112
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Rainfall input requirements for hydrological calculations Guido Vaes *, Patrick Willems, Jean Berlamont Hydraulics Laboratory, University of Leuven, Kasteelpark Arenberg 40, B-3001 Heverlee, Belgium Received 8 May 2000; received in revised form 5 January 2001; accepted 30 March 2001
Abstract Rainfall is the most important input for many hydrological and hydraulic design calculations. Ideally, long historical rainfall series should be used and a statistical analysis should be performed on the hydraulic results afterwards. In combination with the detailed models that are commonly used nowadays, this leads to huge calculation times. This research was set up in order to verify which kind of simpli®cations can be made with respect to the rainfall input. One must ®nd an optimum between accuracy of the modelling results and calculation eort. This optimum can be dierent for dierent applications. The dierent types of rainfall simpli®cations which are considered here are composite design storms, short selected rainfall series and modi®ed single storm events. In many cases the optimum is more likely a simpli®ed model in combination with continuous long term simulations. Well-calibrated (physically based) simpli®ed models can reach almost the same accuracy as the corresponding detailed models within a fraction of the calculation time. Furthermore, these simpli®ed models are very useful in order to select or compose the proper rainfall input for detailed modelling. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Design storms; Hydrological models; Rainfall input; Short rainfall series; Simpli®ed models
1. Introduction For many design calculations, rainfall data is the most important input, e.g. for sewer system design, assessment of combined sewer over¯ows, ¯ood risk assessment, river discharges and river water quality. Long historical rainfall series should be used for such calculations, followed by a statistical analysis on the design parameters because of the high temporal variability. Ideally, spatially distributed rainfall should also be used. The proper consideration of rainfall variability in time and space is the main challenge in hydrological design calculations. Although it is obviously necessary to include these variations, this approach is often in con¯ict with economic reality. Often very detailed models are used, which require long calculation times. Performing long-term simulations with these models would lead to extremely time-consuming and practically unfeasible calculations. This problem is often solved by simpli®cation of the rainfall input into uniform rainfall and design storms, using only limited statistical information on the rainfall. The question can be raised whether this is the optimal simpli®cation. In the case of linear sys-
*
Corresponding author. Tel.: +32-1632-1658; fax: +32-1632-1989. E-mail address: [email protected] (G. Vaes).
tems, it can be assumed that the frequency of the simulated eect is equal to the frequency of the rainfall that causes this eect. An example is the design of combined sewer networks where relatively high return periods are used (e.g. 2 years). However, in many hydrological applications the system reacts in a non-linear way, for instance whenever the system contains several subsystems with dierent response times (e.g. Dahl, Harremoes, & Jacobsen, 1996), whenever the studied return periods decrease (e.g. frequent combined sewer over¯ows) or whenever the system contains large storage volumes controlled by non-linear components (e.g. pumps, nonlinear boundary conditions, etc.). Apart from this consideration, it is often unnecessary to use very detailed models. It is obvious that there must be an optimum between the degree of model detail and the degree of detail for the rainfall used. If models or rainfall data are simpli®ed, the accuracy of the design will decrease. It is important to simplify these in a way, which has a small in¯uence on the accuracy. One should aim to reach an optimal balance between model uncertainty and uncertainty of the input parameters and input data. This optimum is not ®xed, but depends on the application and on the availability and accuracy of the data. Choosing the proper rainfall input for each speci®c application has been studied extensively since decades (e.g. by Harremoes, Jensen, & Johansen, 1984), but modern
1462-0758/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 4 6 2 - 0 7 5 8 ( 0 1 ) 0 0 0 2 0 - 6
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G. Vaes et al. / Urban Water 3 (2001) 107±112
computer technology can give these methodologies a new dimension, which is shown, e.g., by Petrovic and Despotovic (1998). 2. Research set-up To address this problem research is carried out at the Hydraulics Laboratory of the University of Leuven in order to identify the rainfall input requirements and the optimal degree of model detail for dierent hydrological design applications, such as sewer system design, impact assessment of combined sewer over¯ows, ¯ood risk assessment for brooks and rivers, etc. In a ®rst stage most attention was paid to the temporal variability of the rainfall. The research on the spatial variability is more dicult, because of the limited availability of data. The primary applications addressed in this research were sewer system design and emissions of combined sewer over¯ows, because this was the initial goal for this research. However, the extension to other hydrologically driven systems was a logical consequence.
Fig. 1. Variability over the years of the most extreme rainfall volumes for dierent aggregation levels (rainfall at Uccle, Belgium).
3. Temporal variation Rainfall has a large intrinsic temporal variability, certainly during thunderstorms. For sewer system design, the maximum time-step allowed for the rainfall data is 10 min in order to obtain an accurate calculation of the peak discharges in the upstream branches. For rivers, this time-step can be larger. As a rule, the timestep must be considerably smaller than the concentration time of the system (i.e. the time the rainfall needs to travel from the remotest place in the catchment to the point in the sewer system where the design calculation is made). Rainfall can vary largely from year to year. In Fig. 1 the variation over the years of the most extreme rainfall volumes in Flanders (100 most extreme peak over threshold values in 100 years) is shown for dierent aggregation levels (i.e. storm durations). Rainfall also varies from season to season. Short heavy thunderstorms often occur during summer, while in winter, rainfall intensities are lower and rainfall durations are larger. In Fig. 2 the variation of the extreme rainfall events over the dierent months of the year is shown for dierent storm durations. Which type of rainfall is critical depends on the system characteristics. Apparently, rainfall seems to vary quite a lot over the dierent years (Fig. 1). This annual variation mostly has a larger eect than the seasonal variation, because the seasonal distribution from year to year varies strongly. For that reason, it is necessary to use long historical rainfall data of at least several decades for hydrological design.
Fig. 2. Variation of the extreme rainfall volumes over the months of the year for dierent aggregation levels (rainfall at Uccle, Belgium, 1898±1997).
4. Design storms For sewer design, where the concentration times are small and runo mainly originates from impervious areas, it is acceptable to use single design storms for relatively high return periods. In Flanders, these design storms are based on intensity/duration/frequency-relationships (IDF-relationships) derived by POT extreme value statistics (Willems, 1998; Vaes, 1999). For one return period, all IDF-values up to a duration of 360 min are included in one composite storm, so that the IDF-relationships are ful®lled for each storm duration symmetrically around the centre of the design storm (Fig. 3). This corresponds with the well-known Chicago storms proposed by Keifer and Chu (1957). These composite design storms also include antecedent and posterior rainfall conditions for durations up to 120 min each, which are in good agreement with the mean antecedent and posterior rainfall within the original rainfall series. The dierence between antecedent and posterior rainfall is small and negligible as compared with the variability on the antecedent and
G. Vaes et al. / Urban Water 3 (2001) 107±112
Fig. 3. Flemish composite design storm for a return period of 2 years.
posteriori conditions as a function of the considered design rainfall. Therefore, a symmetric composite storms was found to be acceptable. The accuracy in predicting peak discharges and water levels with these composite storms has been checked by comparison to detailed hydrodynamic simulations with the original long-term rainfall series for a limited number of sewer systems. In Fig. 4, some of these results are shown, obtained from hydrodynamic simulations with Hydroworks (Wallingford Software, UK). For a sewer system with a linear behaviour (out¯ow varies linearly with the storage in the system) the results obtained with single storm simulations are much closer to those of the continuous long-term simulation as compared with the results of a sewer system with a non-linear behaviour (e.g. constant out¯ow, independently of the storage in the system). Analogously, composite storms with higher frequencies (up to 20 p.a.) were developed in order to assess the emissions at combined sewer over¯ows. However, for this application the non-linearity has an even larger in¯uence (Fig. 5). Therefore, these composite storms can only be used to obtain a rough estimate of the recurrence rate of combined sewer over¯ow emissions.
Fig. 4. Comparison of the simulation results in a downstream pipe for two sewer systems using continuous long-term simulations versus composite design storms.
109
For the overland ¯ow to brooks and rivers, the same approach is tested. In this case, most of the runo originates from pervious areas. The initial soil moisture conditions, which are very important, vary strongly during the year. Therefore, the rainfall variation over the seasons was investigated (Willems, Vaes, & Berlamont, 1999; Willems, 2000a). This resulted in high peaked summer design storms and more ¯attened winter design storms with a total duration of 15 days (Vaes, 1999). In Fig. 6 the central part of these two storm types is shown for a return period of 5 years. When using these design storms, the initial conditions and runo model parameters must be chosen carefully. In addition, base¯ow (groundwater ¯ow) must be added to the overland ¯ow calculated with the design storms, because the response time for the base¯ow is often even longer than 15 days. This base¯ow is dierent for summer and winter events. Although this appears to be an acceptable design method for peak ¯ows and ¯ooding problems, it can only give a rough estimate of the return period of peak discharges and water levels, because the real
Fig. 5. Comparison of the simulation results for two combined sewer over¯ows using continuous long-term simulations versus composite design storms.
Fig. 6. Comparison of the central part (1 day) of the composite summer and winter storms for a return period of 5 years.
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G. Vaes et al. / Urban Water 3 (2001) 107±112
temporal rainfall variability is neglected using these single storms.
5. Simpli®ed models for long-term simulations Because of the importance of the rainfall variability, for many hydrological calculations long-term simulations are inevitable to reach a good probability estimation of the eects. Often, after appropriate calibration, simple physically based conceptual models give almost as good results as very detailed hydrodynamic calculations, e.g. the reservoir model Remuli developed at the University of Leuven (Fig. 7) (Vaes, 1999; Vaes & Berlamont, 1999; Vaes, Willems, & Berlamont, 1998). The use of simpli®ed models enormously reduces the calculation times (up to a factor 106 ), while leading to an optimum between model accuracy and uncertainty on the input data. This has been proved for emissions at combined sewer over¯ows (Vaes, 1999; Vaes & Berlamont, 1998a,b, 1999; Vaes et al., 1998). This approach has also been tested for runo to (and ¯ow in) brooks and rivers (Willems, 2000b). Both applications give remarkably good results. The major constraint for this approach on a large scale is the calibration of the simpli®ed models. The calibration requires good data and modelling experience. Fortunately, new techniques of data analysis and modern computer possibilities have made this calibration easier and more straightforward. This approach has the additional advantage that only the important parameters are included and modellers become more aware of how the system behaves.
Fig. 8. In¯uence of storage in rain water tanks on a design storm for a return period of 5 years (peak rainfall intensities for return periods of 1 and 2 years are given for comparison).
6. Modi®ed composite design storms The eect of source control on the design of sewer systems can in most cases only be correctly assessed using the full variability of the rainfall in time, because long antecedent periods can have an important in¯uence. This is, for example, the case for rain water tanks and in®ltration trenches. For rain water tanks the antecedent rainfall up to one month can have an eect. To incorporate the eect of rain water tanks on the sewer system design, a model was built to assess the eect of a such tank on the rainfall runo. For this, a simple reservoir model has been used with a constant out¯ow equal to the mean rain water use. After a continuous long-term simulation with this model, the ¯attening effect is incorporated into a modi®ed composite storm (Vaes, 1999; Vaes & Berlamont, 2000b). The out¯ow of the rain water tank model is converted to equivalent rainfall. An example of this ¯attening eect is shown in Fig. 8.
7. Selected short-time series
Fig. 7. Schematic representation of the reservoir modelling system Remuli (Vaes, 1999).
Another possibility to reduce the calculation time is to select only the relevant rainfall data from the long time series. Historical rainfall series contain a lot of dry periods or periods with little rainfall which will never lead to an important eect. This selection approach has been used for the frequency estimation of emissions at combined sewer over¯ows and for the design of sewer systems. The rainfall selection tool is dierent for both cases, because it must take into account the system's behaviour. For the selection of short time series for emission calculations, a simple reservoir model is used (Vaes, 1999). In the ®rst stage, a global set of short time series
G. Vaes et al. / Urban Water 3 (2001) 107±112
is deduced for a wide range of possible sewer system parameters that can occur in Flanders. The main parameters are storage in the system, through¯ow capacity and concentration time. Because only the most important parameters are used in a simpli®ed model, some safety margins must be added while selecting the short time series. Each rainfall event that leads to an over¯ow event in one of the cases (dierent model parameters) is selected together with antecedent and posterior periods. With this approach, the historical rainfall series could be reduced by a factor of 3±5. However, this does not mean that the calculation time is also reduced by this factor, because the skipped periods with low rainfall usually run faster in a model than the selected periods with more severe rainfall. In a second stage, a further reduction is obtained by deducing more speci®c sets of short time series for a smaller range of sewer system parameters or even for one speci®c sewer system. In this way, the length of the rainfall time series for one speci®c sewer system can be reduced by a factor of 20±200. The disadvantage is that ®rst a simpli®ed model must be calibrated. For the selection of short time series for sewer design purposes, IDF-relations are used. For all storms with durations up to 720 min and a return period larger than or equal to 1 year, a reduction of the rainfall input can be obtained with a factor of 200 (Vaes, 1999; Vaes & Berlamont, 2000a). 8. Spatial rainfall variation The spatial variation of rainfall is a more recent ®eld of interest. This is mainly due to a lack of data and insucient research and simulation tools to handle this rainfall data. Nowadays, more dense networks of rain gauges are installed and also radar measurements become available. Including the spatial variability of the rainfall requires even more powerful calculation tools, so that model simpli®cations are consequently necessary. Rainfall can be very local. The mean diameter of a rain cell, as the smallest sub-element of a rain event, has been estimated as 15 km (Luyckx, Willems, & Berlamont, 1998). This makes it practically impossible to set up a global network of rain gauges to measure this spatial variability. Moreover, a point rainfall measurement will rarely register the maximum intensity of a storm. For that reason it is not acceptable to use simple areal reduction factors smaller than 1 as a function of the catchment size in combination with point rainfall measurements. Often uniform rainfall is used over a catchment, but the consideration of the movement of a rainstorm over a catchment can have a large in¯uence. For example, if the main ¯ow in a sewer system occurs in the same direction as the main moving direction of the rain storm, a cumulative eect occurs. This can lead
111
to an increasing risk of ¯ooding or to larger over¯ow emissions (Luyckx et al., 1998). Often, dierences in geography and land use can lead to a local microclimate, as around cities, hills and large rivers. Because of the high variability of the rainfall and the limited data availability, it is dicult to prove such eects and to assess the dierences. In addition, also the measuring equipment and environment are dierent and changing in time, so that measured dierences and changes do not necessarily correspond to climate differences and changes. 9. Conclusions The temporal variability of the rainfall is studied intensively around the world. As computers become continuously faster, more possibilities arise in order to take into account this temporal variability. Depending on the application and the system's behaviour it might be necessary to use other types of rainfall input as the standard design storms in order to obtain accurate simulation results. Dierent types of rainfall input are investigated and proposed as there are: selected short rainfall series for design and impact calculations and modi®ed single storm events for design calculations including upstream storage. In many cases the optimum between model and input uncertainty is leading towards simpli®ed models using continuous long-term simulations. This especially holds for capacitive systems, which behave non-linearly. In these cases physically based conceptual models can lead to very accurate simulation results. The spatial variability however is studied less intensively, mainly because of a lack of accurate data. Most rainfall data is obtained using point rainfall measurements. Further research is necessary to investigate the relationships between point rainfall data and spatial distributed rainfall for modelling purposes. There is a large need for methodologies to incorporate the spatial variability of the rainfall in the standard modelling practice. References Dahl, A., Harremoes, P., & Jacobsen, P. (1996). Joint probability of ¯ooding. In Seventh international conference on urban storm drainage, Hannover, Germany. Harremoes, P., Jensen, M., & Johansen, N. B. (1984). A staged approach to application of rainfall data to urban runo calculations. Water Science & Technology, 16(8/9). Keifer, C. J., & Chu, H. H. (1957). Synthetic storm patterns for drainage design. ASCE Journal of Hydraulic Engineering, 83(4). Luyckx, G., Willems, P., & Berlamont, J. (1998). In¯uence of the spatial variability of rainfall on sewer system design. Hydrology in a Changing Environment. In Proceedings of the British hydrological society international conference, Exeter, UK.
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Petrovic, J., & Despotovic, J. (1998). Historical rainfall for urban storm drainage design. Water Science & Technology, 37(11). Vaes, G. (1999). The in¯uence of rainfall and model simpli®cation on combined sewer system design. Ph.D. Thesis, University of Leuven, Belgium. Vaes, G., & Berlamont, J. (1998a). Conceptual modelling of over¯ow emissions. In IAWQ 19th biennial international conference on water quality, Vancouver, Canada. Vaes, G., & Berlamont, J. (1998b). Modelling of over¯ow emissions in Flanders. Water Science & Technology, 38(10). Vaes, G., & Berlamont, J. (1999). Emission predictions with a multilinear reservoir model. Water Science & Technology, 39(2). Vaes, G., & Berlamont, J. (2000a). Selection of appropriate short rainfall series for design of combined sewer systems. In 1st International conference on urban drainage on internet, Hydroinform, Czech Republic. Vaes, G., & Berlamont, J. (2000b). The eect of rain water storage tanks on design storms. In 1st international conference on urban drainage on internet, Hydroinform, Czech Republic.
Vaes, G., Willems, P., & Berlamont, J. (1998). Assessment of combined sewer over¯ow emissions. In UDM`98, 4th international conference on developments in urban drainage modelling, London, UK. Willems, P. (1998). Hydrological applications of extreme value analysis, Hydrology in a Changing Environment. In Proceedings of the British hydrological society international conference, Exeter, UK. Willems, P. (2000a). Compound intensity/duration/frequency-relationships of extreme precipitation for two seasons and two storm types. Journal of Hydrology, 233. Willems, P. (2000b). Probabilistic immission modelling of receiving surface waters. Ph.D. Thesis, University of Leuven, Belgium. Willems, P., Vaes, G., & Berlamont, J. (1999). Compound IDFrelationships and design storms for two seasons and storm types. In 8th international conference on urban storm drainage, Sydney, Australia.
www.elsevier.com/locate/urbwat
Rainfall input requirements for hydrological calculations Guido Vaes *, Patrick Willems, Jean Berlamont Hydraulics Laboratory, University of Leuven, Kasteelpark Arenberg 40, B-3001 Heverlee, Belgium Received 8 May 2000; received in revised form 5 January 2001; accepted 30 March 2001
Abstract Rainfall is the most important input for many hydrological and hydraulic design calculations. Ideally, long historical rainfall series should be used and a statistical analysis should be performed on the hydraulic results afterwards. In combination with the detailed models that are commonly used nowadays, this leads to huge calculation times. This research was set up in order to verify which kind of simpli®cations can be made with respect to the rainfall input. One must ®nd an optimum between accuracy of the modelling results and calculation eort. This optimum can be dierent for dierent applications. The dierent types of rainfall simpli®cations which are considered here are composite design storms, short selected rainfall series and modi®ed single storm events. In many cases the optimum is more likely a simpli®ed model in combination with continuous long term simulations. Well-calibrated (physically based) simpli®ed models can reach almost the same accuracy as the corresponding detailed models within a fraction of the calculation time. Furthermore, these simpli®ed models are very useful in order to select or compose the proper rainfall input for detailed modelling. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Design storms; Hydrological models; Rainfall input; Short rainfall series; Simpli®ed models
1. Introduction For many design calculations, rainfall data is the most important input, e.g. for sewer system design, assessment of combined sewer over¯ows, ¯ood risk assessment, river discharges and river water quality. Long historical rainfall series should be used for such calculations, followed by a statistical analysis on the design parameters because of the high temporal variability. Ideally, spatially distributed rainfall should also be used. The proper consideration of rainfall variability in time and space is the main challenge in hydrological design calculations. Although it is obviously necessary to include these variations, this approach is often in con¯ict with economic reality. Often very detailed models are used, which require long calculation times. Performing long-term simulations with these models would lead to extremely time-consuming and practically unfeasible calculations. This problem is often solved by simpli®cation of the rainfall input into uniform rainfall and design storms, using only limited statistical information on the rainfall. The question can be raised whether this is the optimal simpli®cation. In the case of linear sys-
*
Corresponding author. Tel.: +32-1632-1658; fax: +32-1632-1989. E-mail address: [email protected] (G. Vaes).
tems, it can be assumed that the frequency of the simulated eect is equal to the frequency of the rainfall that causes this eect. An example is the design of combined sewer networks where relatively high return periods are used (e.g. 2 years). However, in many hydrological applications the system reacts in a non-linear way, for instance whenever the system contains several subsystems with dierent response times (e.g. Dahl, Harremoes, & Jacobsen, 1996), whenever the studied return periods decrease (e.g. frequent combined sewer over¯ows) or whenever the system contains large storage volumes controlled by non-linear components (e.g. pumps, nonlinear boundary conditions, etc.). Apart from this consideration, it is often unnecessary to use very detailed models. It is obvious that there must be an optimum between the degree of model detail and the degree of detail for the rainfall used. If models or rainfall data are simpli®ed, the accuracy of the design will decrease. It is important to simplify these in a way, which has a small in¯uence on the accuracy. One should aim to reach an optimal balance between model uncertainty and uncertainty of the input parameters and input data. This optimum is not ®xed, but depends on the application and on the availability and accuracy of the data. Choosing the proper rainfall input for each speci®c application has been studied extensively since decades (e.g. by Harremoes, Jensen, & Johansen, 1984), but modern
1462-0758/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 4 6 2 - 0 7 5 8 ( 0 1 ) 0 0 0 2 0 - 6
108
G. Vaes et al. / Urban Water 3 (2001) 107±112
computer technology can give these methodologies a new dimension, which is shown, e.g., by Petrovic and Despotovic (1998). 2. Research set-up To address this problem research is carried out at the Hydraulics Laboratory of the University of Leuven in order to identify the rainfall input requirements and the optimal degree of model detail for dierent hydrological design applications, such as sewer system design, impact assessment of combined sewer over¯ows, ¯ood risk assessment for brooks and rivers, etc. In a ®rst stage most attention was paid to the temporal variability of the rainfall. The research on the spatial variability is more dicult, because of the limited availability of data. The primary applications addressed in this research were sewer system design and emissions of combined sewer over¯ows, because this was the initial goal for this research. However, the extension to other hydrologically driven systems was a logical consequence.
Fig. 1. Variability over the years of the most extreme rainfall volumes for dierent aggregation levels (rainfall at Uccle, Belgium).
3. Temporal variation Rainfall has a large intrinsic temporal variability, certainly during thunderstorms. For sewer system design, the maximum time-step allowed for the rainfall data is 10 min in order to obtain an accurate calculation of the peak discharges in the upstream branches. For rivers, this time-step can be larger. As a rule, the timestep must be considerably smaller than the concentration time of the system (i.e. the time the rainfall needs to travel from the remotest place in the catchment to the point in the sewer system where the design calculation is made). Rainfall can vary largely from year to year. In Fig. 1 the variation over the years of the most extreme rainfall volumes in Flanders (100 most extreme peak over threshold values in 100 years) is shown for dierent aggregation levels (i.e. storm durations). Rainfall also varies from season to season. Short heavy thunderstorms often occur during summer, while in winter, rainfall intensities are lower and rainfall durations are larger. In Fig. 2 the variation of the extreme rainfall events over the dierent months of the year is shown for dierent storm durations. Which type of rainfall is critical depends on the system characteristics. Apparently, rainfall seems to vary quite a lot over the dierent years (Fig. 1). This annual variation mostly has a larger eect than the seasonal variation, because the seasonal distribution from year to year varies strongly. For that reason, it is necessary to use long historical rainfall data of at least several decades for hydrological design.
Fig. 2. Variation of the extreme rainfall volumes over the months of the year for dierent aggregation levels (rainfall at Uccle, Belgium, 1898±1997).
4. Design storms For sewer design, where the concentration times are small and runo mainly originates from impervious areas, it is acceptable to use single design storms for relatively high return periods. In Flanders, these design storms are based on intensity/duration/frequency-relationships (IDF-relationships) derived by POT extreme value statistics (Willems, 1998; Vaes, 1999). For one return period, all IDF-values up to a duration of 360 min are included in one composite storm, so that the IDF-relationships are ful®lled for each storm duration symmetrically around the centre of the design storm (Fig. 3). This corresponds with the well-known Chicago storms proposed by Keifer and Chu (1957). These composite design storms also include antecedent and posterior rainfall conditions for durations up to 120 min each, which are in good agreement with the mean antecedent and posterior rainfall within the original rainfall series. The dierence between antecedent and posterior rainfall is small and negligible as compared with the variability on the antecedent and
G. Vaes et al. / Urban Water 3 (2001) 107±112
Fig. 3. Flemish composite design storm for a return period of 2 years.
posteriori conditions as a function of the considered design rainfall. Therefore, a symmetric composite storms was found to be acceptable. The accuracy in predicting peak discharges and water levels with these composite storms has been checked by comparison to detailed hydrodynamic simulations with the original long-term rainfall series for a limited number of sewer systems. In Fig. 4, some of these results are shown, obtained from hydrodynamic simulations with Hydroworks (Wallingford Software, UK). For a sewer system with a linear behaviour (out¯ow varies linearly with the storage in the system) the results obtained with single storm simulations are much closer to those of the continuous long-term simulation as compared with the results of a sewer system with a non-linear behaviour (e.g. constant out¯ow, independently of the storage in the system). Analogously, composite storms with higher frequencies (up to 20 p.a.) were developed in order to assess the emissions at combined sewer over¯ows. However, for this application the non-linearity has an even larger in¯uence (Fig. 5). Therefore, these composite storms can only be used to obtain a rough estimate of the recurrence rate of combined sewer over¯ow emissions.
Fig. 4. Comparison of the simulation results in a downstream pipe for two sewer systems using continuous long-term simulations versus composite design storms.
109
For the overland ¯ow to brooks and rivers, the same approach is tested. In this case, most of the runo originates from pervious areas. The initial soil moisture conditions, which are very important, vary strongly during the year. Therefore, the rainfall variation over the seasons was investigated (Willems, Vaes, & Berlamont, 1999; Willems, 2000a). This resulted in high peaked summer design storms and more ¯attened winter design storms with a total duration of 15 days (Vaes, 1999). In Fig. 6 the central part of these two storm types is shown for a return period of 5 years. When using these design storms, the initial conditions and runo model parameters must be chosen carefully. In addition, base¯ow (groundwater ¯ow) must be added to the overland ¯ow calculated with the design storms, because the response time for the base¯ow is often even longer than 15 days. This base¯ow is dierent for summer and winter events. Although this appears to be an acceptable design method for peak ¯ows and ¯ooding problems, it can only give a rough estimate of the return period of peak discharges and water levels, because the real
Fig. 5. Comparison of the simulation results for two combined sewer over¯ows using continuous long-term simulations versus composite design storms.
Fig. 6. Comparison of the central part (1 day) of the composite summer and winter storms for a return period of 5 years.
110
G. Vaes et al. / Urban Water 3 (2001) 107±112
temporal rainfall variability is neglected using these single storms.
5. Simpli®ed models for long-term simulations Because of the importance of the rainfall variability, for many hydrological calculations long-term simulations are inevitable to reach a good probability estimation of the eects. Often, after appropriate calibration, simple physically based conceptual models give almost as good results as very detailed hydrodynamic calculations, e.g. the reservoir model Remuli developed at the University of Leuven (Fig. 7) (Vaes, 1999; Vaes & Berlamont, 1999; Vaes, Willems, & Berlamont, 1998). The use of simpli®ed models enormously reduces the calculation times (up to a factor 106 ), while leading to an optimum between model accuracy and uncertainty on the input data. This has been proved for emissions at combined sewer over¯ows (Vaes, 1999; Vaes & Berlamont, 1998a,b, 1999; Vaes et al., 1998). This approach has also been tested for runo to (and ¯ow in) brooks and rivers (Willems, 2000b). Both applications give remarkably good results. The major constraint for this approach on a large scale is the calibration of the simpli®ed models. The calibration requires good data and modelling experience. Fortunately, new techniques of data analysis and modern computer possibilities have made this calibration easier and more straightforward. This approach has the additional advantage that only the important parameters are included and modellers become more aware of how the system behaves.
Fig. 8. In¯uence of storage in rain water tanks on a design storm for a return period of 5 years (peak rainfall intensities for return periods of 1 and 2 years are given for comparison).
6. Modi®ed composite design storms The eect of source control on the design of sewer systems can in most cases only be correctly assessed using the full variability of the rainfall in time, because long antecedent periods can have an important in¯uence. This is, for example, the case for rain water tanks and in®ltration trenches. For rain water tanks the antecedent rainfall up to one month can have an eect. To incorporate the eect of rain water tanks on the sewer system design, a model was built to assess the eect of a such tank on the rainfall runo. For this, a simple reservoir model has been used with a constant out¯ow equal to the mean rain water use. After a continuous long-term simulation with this model, the ¯attening effect is incorporated into a modi®ed composite storm (Vaes, 1999; Vaes & Berlamont, 2000b). The out¯ow of the rain water tank model is converted to equivalent rainfall. An example of this ¯attening eect is shown in Fig. 8.
7. Selected short-time series
Fig. 7. Schematic representation of the reservoir modelling system Remuli (Vaes, 1999).
Another possibility to reduce the calculation time is to select only the relevant rainfall data from the long time series. Historical rainfall series contain a lot of dry periods or periods with little rainfall which will never lead to an important eect. This selection approach has been used for the frequency estimation of emissions at combined sewer over¯ows and for the design of sewer systems. The rainfall selection tool is dierent for both cases, because it must take into account the system's behaviour. For the selection of short time series for emission calculations, a simple reservoir model is used (Vaes, 1999). In the ®rst stage, a global set of short time series
G. Vaes et al. / Urban Water 3 (2001) 107±112
is deduced for a wide range of possible sewer system parameters that can occur in Flanders. The main parameters are storage in the system, through¯ow capacity and concentration time. Because only the most important parameters are used in a simpli®ed model, some safety margins must be added while selecting the short time series. Each rainfall event that leads to an over¯ow event in one of the cases (dierent model parameters) is selected together with antecedent and posterior periods. With this approach, the historical rainfall series could be reduced by a factor of 3±5. However, this does not mean that the calculation time is also reduced by this factor, because the skipped periods with low rainfall usually run faster in a model than the selected periods with more severe rainfall. In a second stage, a further reduction is obtained by deducing more speci®c sets of short time series for a smaller range of sewer system parameters or even for one speci®c sewer system. In this way, the length of the rainfall time series for one speci®c sewer system can be reduced by a factor of 20±200. The disadvantage is that ®rst a simpli®ed model must be calibrated. For the selection of short time series for sewer design purposes, IDF-relations are used. For all storms with durations up to 720 min and a return period larger than or equal to 1 year, a reduction of the rainfall input can be obtained with a factor of 200 (Vaes, 1999; Vaes & Berlamont, 2000a). 8. Spatial rainfall variation The spatial variation of rainfall is a more recent ®eld of interest. This is mainly due to a lack of data and insucient research and simulation tools to handle this rainfall data. Nowadays, more dense networks of rain gauges are installed and also radar measurements become available. Including the spatial variability of the rainfall requires even more powerful calculation tools, so that model simpli®cations are consequently necessary. Rainfall can be very local. The mean diameter of a rain cell, as the smallest sub-element of a rain event, has been estimated as 15 km (Luyckx, Willems, & Berlamont, 1998). This makes it practically impossible to set up a global network of rain gauges to measure this spatial variability. Moreover, a point rainfall measurement will rarely register the maximum intensity of a storm. For that reason it is not acceptable to use simple areal reduction factors smaller than 1 as a function of the catchment size in combination with point rainfall measurements. Often uniform rainfall is used over a catchment, but the consideration of the movement of a rainstorm over a catchment can have a large in¯uence. For example, if the main ¯ow in a sewer system occurs in the same direction as the main moving direction of the rain storm, a cumulative eect occurs. This can lead
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to an increasing risk of ¯ooding or to larger over¯ow emissions (Luyckx et al., 1998). Often, dierences in geography and land use can lead to a local microclimate, as around cities, hills and large rivers. Because of the high variability of the rainfall and the limited data availability, it is dicult to prove such eects and to assess the dierences. In addition, also the measuring equipment and environment are dierent and changing in time, so that measured dierences and changes do not necessarily correspond to climate differences and changes. 9. Conclusions The temporal variability of the rainfall is studied intensively around the world. As computers become continuously faster, more possibilities arise in order to take into account this temporal variability. Depending on the application and the system's behaviour it might be necessary to use other types of rainfall input as the standard design storms in order to obtain accurate simulation results. Dierent types of rainfall input are investigated and proposed as there are: selected short rainfall series for design and impact calculations and modi®ed single storm events for design calculations including upstream storage. In many cases the optimum between model and input uncertainty is leading towards simpli®ed models using continuous long-term simulations. This especially holds for capacitive systems, which behave non-linearly. In these cases physically based conceptual models can lead to very accurate simulation results. The spatial variability however is studied less intensively, mainly because of a lack of accurate data. Most rainfall data is obtained using point rainfall measurements. Further research is necessary to investigate the relationships between point rainfall data and spatial distributed rainfall for modelling purposes. There is a large need for methodologies to incorporate the spatial variability of the rainfall in the standard modelling practice. References Dahl, A., Harremoes, P., & Jacobsen, P. (1996). Joint probability of ¯ooding. In Seventh international conference on urban storm drainage, Hannover, Germany. Harremoes, P., Jensen, M., & Johansen, N. B. (1984). A staged approach to application of rainfall data to urban runo calculations. Water Science & Technology, 16(8/9). Keifer, C. J., & Chu, H. H. (1957). Synthetic storm patterns for drainage design. ASCE Journal of Hydraulic Engineering, 83(4). Luyckx, G., Willems, P., & Berlamont, J. (1998). In¯uence of the spatial variability of rainfall on sewer system design. Hydrology in a Changing Environment. In Proceedings of the British hydrological society international conference, Exeter, UK.
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Petrovic, J., & Despotovic, J. (1998). Historical rainfall for urban storm drainage design. Water Science & Technology, 37(11). Vaes, G. (1999). The in¯uence of rainfall and model simpli®cation on combined sewer system design. Ph.D. Thesis, University of Leuven, Belgium. Vaes, G., & Berlamont, J. (1998a). Conceptual modelling of over¯ow emissions. In IAWQ 19th biennial international conference on water quality, Vancouver, Canada. Vaes, G., & Berlamont, J. (1998b). Modelling of over¯ow emissions in Flanders. Water Science & Technology, 38(10). Vaes, G., & Berlamont, J. (1999). Emission predictions with a multilinear reservoir model. Water Science & Technology, 39(2). Vaes, G., & Berlamont, J. (2000a). Selection of appropriate short rainfall series for design of combined sewer systems. In 1st International conference on urban drainage on internet, Hydroinform, Czech Republic. Vaes, G., & Berlamont, J. (2000b). The eect of rain water storage tanks on design storms. In 1st international conference on urban drainage on internet, Hydroinform, Czech Republic.
Vaes, G., Willems, P., & Berlamont, J. (1998). Assessment of combined sewer over¯ow emissions. In UDM`98, 4th international conference on developments in urban drainage modelling, London, UK. Willems, P. (1998). Hydrological applications of extreme value analysis, Hydrology in a Changing Environment. In Proceedings of the British hydrological society international conference, Exeter, UK. Willems, P. (2000a). Compound intensity/duration/frequency-relationships of extreme precipitation for two seasons and two storm types. Journal of Hydrology, 233. Willems, P. (2000b). Probabilistic immission modelling of receiving surface waters. Ph.D. Thesis, University of Leuven, Belgium. Willems, P., Vaes, G., & Berlamont, J. (1999). Compound IDFrelationships and design storms for two seasons and storm types. In 8th international conference on urban storm drainage, Sydney, Australia.