- Email: [email protected]
A rationale for using local and regional point rainfall data for design and analysis of urban storm drainage systems
~
Pergamon
PH: S0273-l223(98)OO310-2
Waf. Sci. r~ch. Vol. 37, No.1\, pp. 7-14.1998. C 1998 IAWQ . Published by Elsevier Science Ud . Printed in Great Britain. All rights reserved 0273 -1223198 $19 '00 + 0 '00
A RATIONALE FOR USING LOCAL AND REGIONAL POINT RAINFALL DATA FOR DESIGN AND ANALYSIS OF URBAN STORM DRAINAGE SYSTEMS P. S. Mikkelsen*, H. Madsen**, K. Arnbjerg-Nielsen*, H. K. Jergensen'"?", D. Rosbjerg** and P. Harremoes" • DepartmentofEnvironmental Scienceand Engineering, Technical University of Denmark. Building 115. 2800 Lyngby. Denmark •• Departmentof Hydrodynamics and WaterResources. TechnicalUniversity of Denmark. Building I 15,2800 Lyngby,Denmark ••• Weatherand ClimateInformation Division, Danish Meteorological Institute, Lyngbyvej 100, 2100 Copenhagen East. Denmark
ABSTRACf The Danish measuring network for high-resolutlon rainfall data cons ists of approximately 70 tipping bucket ram gauges of which 41 have been operated for more than 10 years . The gauges are separated by one to 300 km and cover an area of 43.000 km2. Significant geographical variations of extreme rainfall characteristics have been observed. Part of these variations can be explained by correlation with the mean annual rainfall and the existence of a metropolitan effect in the Greater Copenhagen area. The remaining variation may be attnbuted to sampling errors and small-scale spatial variations close to the gauges. Engineering methodologies all require rain data of some kind. ranging from design storms based on idf-curves for use in simple calculations to high-resolution time series for use in detailed simulation studie s. A comprehensive regional analys is was carried out 10 account for the geographical variat ion and to improve estimation for large return periods exceeding the actual length of the measured time series . Ideally. rainfall data used as input to urban drainage calculations should always be based on regional rain information. Regional design storms can be made readily available based on theory developed In this study. However, a satisfactory framework for generating synthetic rain series from regional rain information is not yet available. Thus . there will still be a need for using historical rain series in the near future. To improve the basis for choosing representative historical rain series all the Danish gauges have been classified according to their deviations from the regional distribution. @ 1998 IAWQ. Published by Elsevier Science Ltd. All rights reserved
KEYWORDS Urban drainage; rainfall; local data; regional data; time series, idf-curves. INTRODUCTION Until 20 years ago urban drainage systems were designed and analysed on the basis of design storms. The assumption for the design storm concept is that the relevant detrimental effects (flooding. overload and pollution) have statistical properties similar to those of the rain. This is true for linear systems, but because 7
8
P. S. MIKKELSEN et al.
urban runoff is a non-linear system it was proposed instead to use historical rain series as input to computer models of urban drainage, e.g. (Johansen and Harremoes, 1979; Johansen et al., 1984). Then, statistics can be generated directly on the calculated detrimental effects as a basis for analysing compliance with respect to return period. Since then it has become established practice to use historical rain series as input to hydrological model packages for detailed simulation of urban drainage systems. The performance indices looked at typically include both rarely occurring phenomena such as flooding related to extreme rainfall events, and more frequent phenomena related to accumulated rainfall over long time scales, e.g. discharge of nutrients to receiving waters. However, due to lack of suffic iently long data series measured in or nearby the catchment in question, simulations are often based on an available rain series from another location . So far, this has been considered good engineering practice and possible errors caused by geographical variation of the rainfall pattern have been virtually overlooked. In many countries rainfall is now measured at an increasing number of stations, and the length of the time series (the record lengths) are slowly approaching the return periods chosen as design criteria. The motivation for using the new data as input to simulations is growing with this development. However, it is not obvious how the new data may be best utilised for different purposes and on what basis decisions should be made when several candidate rain series are available. A large number of measuring stations and acceptable record lengths make a comprehensive statistical analysis of rainfall data possible. Such analysis may, or may not, support the prejudiced opinion that runoff simulations should be based on local rain data measured within the catchment, or in an area with similar physiographic characteristics. The large number of measuring stations may also improve the ability to pred ict rainfall characteristics corresponding to return periods exceeding the actual record lengths. This requires introduction of regionalisation procedures not employed so far within the urban drainage community, and for some applications the conventional historical (measured) rain series may have to be supplemented with design storms, or with synthetic (artificial) rain series, generated from regional rain information. The Danish national measuring system for rain data relevant within urban hydrology was introduced in 1979 by the Danish Water Pollution Control Committee (DWPCC) and the Danish Meteorological Institute (DMI). After several years of debate a project was initiated in 1996 that aims at setting up a decision scheme for using data from the measuring network. This paper explains the background of the project, discusses different types of rainfall data, summarises the results obtained when analysing the data in detail and outlines a rationale for using local and regional rainfall data, that is proposed as a national Danish guideline.
TERMINOLOGY Rainfall characteristics. A set of parameters that may be used to characterise rainfall on an event basis. Common examples are maximum intensities calculated as an average over a defined duration or total rainfall depths of events. Other examples with specific reference to urban hydrology are overflow volumes and necessary detention basin volumes for defined catchment characteristics. T-year event. The magnitude of a rainfall characteristic that on average will be exceeded once per Tyears. Tyear events can be estimated from extreme value statistics such as the partial duration series (PDS) method. Sampling uncertainty. Uncertainty in estimation of e.g. T-year events due to a limited sample size (few observation years). Geographical variation. Variation of rainfall characteristics from one location to another. Sometimes this type of variation is also referred to as regional variation (variation from one site in a region to another).
Urban storm drainagesystems
9
Region. An area classification according to geography and/or relevant physiographic and climatic characteristics. Sub-regions may be defined when heterogeneity is present within a region.
Local raindata. Rain measured at a specific location close to the catchment in question. Regionalrain data. Rain data measured at one or more locations different from the one in question. Filteredrain data. Rain data that have been treated to extract important characteristics (cf', above). A typical example of filtered rain data is intensity-duration-frequency (idf) curves. Historical rain series. Measured un-filtered time series of rain data, typically stored in a file for use as input to hydrological simulation software. Synthetic rain series. Generated time series of rain data with the same statistical properties and format as historical series. BACKGROUND Denmark covers a total area of 43,000 km2 and is a relatively flat country situated between 55° and 58° northern latitude and 8° and 13° eastern longitude in a coastal, Northern climate. The mean annual precipitation varies geographically between 550 and 850 mm, mainly governed by the dominant westerly wind direction, proximity to the coast and orography. The elevation is everywhere less than 200 m, and the physiographic and climatic characteristics vary relatively smooth. The measuring network consists of 75 gauging stations separated by one to 300 km, The locations of the gauges are mainly dictated by economy since they are placed in those of the Danish municipalities that contribute financially to the network. This is the reason for a large concentration of gauges around Greater Copenhagen. All stations are based on tipping bucket gauges with high resolution in time and volume and now, the longest records include 19 years of data starting from 1979. The measuring system and the data quality control is described in detail by Jergensen et al. (1998). r
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Figure I. Left: Map of Denmark indicatingthe locationof the 43 gaugingstations from the DWPCC network that were part of the first study of data from 1979-87(Harremoesand Mikkelsen. 1995). Right: Extreme value series for each of the 43 stauons, plotted using T .. obl.period/rank.
10
P.S. MIKKELSEN et al.
Already the first studies of data from the DWPCC system based on 43 stations with up to 9 years of data showed large variations between data recorded at different stations. Figure I shows the locations of the gauges and extreme valueseries of the total volume of individual rain storms for each gauge. The variation implies that e.g. the input to calculatethe volume of a detention basindesigned to overflow on average once per year could be anywhere between 20 and 30 mm of rainfall. Such a dramatic variation is of coursecritical to the result of computerised urban storm drainage calculations (Arnbjerg-Nielsen and Harrernoes, 1996). However, a substantial part of the observed variation may originate from sampling errors, in whichcase the variation is of limited practical consequence. This cannotbe revealed by traditional non-parametric methods for estimating T-year events but more advanced statistical treatment of the data may refine the conclusions in this respect. Several other methods for estimating T-year events and the associated sampling uncertainty were later tested, including both non-parametric and parametric methods, and it readily appeared that sampling errors are of considerable magnitude for large return periods. As a consequence, the geographical variation was proven statistically significant for small Tbut not for large'T (Arnbjerg-Nielsen et al., 1994; Madsen et al., 1994). Two regional co-variates were identified using regional regression and principal components analysis: the meanannualrainfall and an extremevalueof daily precipitation corresponding to T =0.2 years. However, the two variables only described a significant part of the variation for very small return periods. The analysis illustrated on the one hand the effect of sampling errors for large return periods and on the other hand a metropolitan effect in the Copenhagen area where extreme rainfalls tend to last longerthan in other parts of the country, less influenced by an urban environment. Such effects were not included in the regression model, Arnbjerg-Nielsen et al. (1996). In a separate study Mikkelsen et al. (1996) found that inter-site correlation, caused by spatial coverage and movement of individual rain storms, has a major influence on regional modelling and thus, the motivation was strongfor analysing the data in moredetail. TYPES OF POINTRAINFALL DATAUSED FORDESIGN AND ANALYSIS Two issuesare of criticalimportance to the DWPCC guideline project. J. The rain gauges are placed irregularly throughout the country. It is not clear which gauges providedata that fit with the perception of a smooth regional variation in Denmark and which gauges providedata that doesnt, Data fromoutlier-stations shouldof courseonly be usedaftercarefully checking the possible reasons for differing statistical behaviour. Also,on what basisshouldrain data be choosen in practical cases where no local rain gauge is available?
2. The European Committee for Standardisation is introducing new guidelines soon, that recommend which return periods should be used for design and analysis relative to different problems, e.g. T = 2Q..30 years for flooding of city areas (CEN, 1995). These return periods are much larger than what is normally recognised and they exceed the length of the longestrecorded data series from the modem Danish measuring network. This implies that commonly used engineering methodologies based on historical rain data as input to simulations cannot be useddirectly. These two issues illustrate exactly the two main purposes of regionalisation. On the one hand, regionalisation may help understanding and accounting for geographical variation by estimating e.g, a regression model that correlates significant geographical variations of extreme rainfall characteristics with available information on regional physiographic andclimaticcharacteristics. On the other hand, regionalisation makes it possible to utilise information from all gauging stations to improve estimation for large return periods. This is done by scaling data from different stations according to the chosen regional model and adjusting for the available information level (that governs the sampling uncertainty) by accounting for the spatial intersite correlation in the region(Madsen and Rosbjerg, 1997). In Fig. 2 some common types of point rainfall data are classified according to their main features. Highresolution time series are used today as direct input to simulations when analysing complex hydrologic or
11
Urban stonn drainage systems
hydraulic problems where detrimental effects may occur at many different time scales. The advantage of such time series is that they reflects all relevant rainfall characteristics from peak intensities with short duration to variations in annual rainfall. Historical rain series are commonly used but synthetic rain series may well be the solution for the future. Ambjerg-Nielsen et al. (1998) give details about a rain series generator based on Markov chain theory that has been used to simulate rain series in Denmark. Essentially, historical rain series are un-filtered data, whereas synthetic rain series are filtered according to the chosen generator model.
Local data
High-resolution time series
Design storms
Historical time series
idf-eurves
Synthetic time series
CDS rain storms Idf-curves
Regional data
Synthetic time series
CDS rain storms
Figure 2. Classification of different types of point rainfall data used for design and analyses.
Design storms are typically used for simple design problems. For example, block rain storms taken from empirical idf-eurves are well suited for sizing pipe diameters with the rational method. A more advanced type of design storm is e.g. the Chicago design storm (CDS) which reflects maximum intensities for a range of durations and presupposes a general synthetic shape of heavy rain storms (Chow et al., 1988). In some cases CDS are used as input to simulations to analyse the hydraulic capacity of up-stream sewer networks. The motivation is mostly economic since the computational costs associated with using CDS is small compared with using high-resolution time series of rain data. However, any type of design storm should be used with care because they capture only specifically defined rainfall characteristics. Using CDS e.g. for analysing the hydraulic capacity of complex non-linear sewer networks or assessment of detention basin sizes and pollution runoff may lead to questionable results.
It sounds intuitively reasonable to use local rain data when dealing with catchments where measurements are available. In principle, local time series can be filtered to provide idf-curves or CDS. It can also be used un-filtered as input to simulations and if the available historical time series is too short, longer synthetic time series may be generated based on the available data (Ambjerg-Nielsen et al., 1998). Local data can be readily used when simulation models are calibrated with e.g. local flow data, but there are numerous problems associated with using local data for off-line design and analysis, cf. the two issues emphasised at the beginning of this chapter. As mentioned earlier, regional rain data makes it possible to account for geographical variation and to utilise information from all gauging stations in a region. The next section outlines the regional analysis carried out in the DWPCC project. SYSTEMATIC REGIONAL ANALYSIS A systematic regional analysis based on all data collected until the beginning of 1997 and newly developed regionalization procedures was conducted to form the best possible basis for deciding on a rationale for the future regarding use of data from the DWPCC network. Historical rain series from a total of 41 gauging stations each with more than 10 years of observations were included in the investigation, corresponding to a total of 650 station years. Each rain series was filtered to extract the following rainfall characteristics. maximum average intensities per event for the following range of durations; 10, 30 and 60 minutes, and 3, 6, 12, 24 and 48 hours total rainfall depths per event and per day necessary detention basin volumes and overflow volumes per event for two simplified catchments with defined interceptor capacities of 0.1 and 1.0 J.Lm s')
P. S. MIKKELSEN et at.
12
These rainfall characteristics were chosen to reflect the most important features of rainfall with respect to urbanstorm drainage. T-year events wereestimated for each rainfall characteristic using the partialduration series method where only events exceeding a defined threshold level are included in the analysis. The number of threshold exceedances was described by a Poisson distribution with intensity A.. corresponding to the expected number of annual threshold exceedances, The exceedance magnitudes were described by the generalized Pareto distribution (GPO) which has two parameters, the mean value of the exceedance magnitudes, u, and a shape parameter, le. The regional analysis is described in detail by Madsen et al. (1998) and thus,only the mainfindings are summarised below. I. The frequency of extreme events (A) varies significantly in the region, and a large part of this variation can be explained by the mean annual rainfall (MAR); the largerMARthe moreextreme events are observed. The degree of explanation is generally much larger for rainfall characteristics related to volume over large durations than for peak intensities.
2. For the average magnitude of extreme events ~), the region can be considered homogeneous for peak intensities. For rainfall characteristics relatedto volume over largedurations a significant metropolitan effect was observed, the average magnitude beinglargerin the Copenhagen area than in the rest of the country, but the variation could not be explained by variation of the MAR. Thus, in this case it was necessary to divide the region into two sub-regions: (I) the Copenhagen area,and (2) the rest of the country. 3. For higherorder statistical moments, reflecting the shape of the extremevaluedistribution (lC), the region can generally be considered homogeneous. In this case a regional probability distribution with a common shapeparameter can be used to parameterise extreme rainfall characteristics. Figure3 (left) illustrates an application wherelocalestimates of the Poisson parameter (Ai) for the maximum average intensity per event for 24 hoursduration (i24h) are correlated with the mean annual rainfall (MAR) obtained from a map from OMI. The 95% confidence limits reflect the prediction uncertainty, e.g, the sum of the sampling variance (related with at-site estimation and with estimation of the regression parameters) and the residual model error variance, when using a generalised least squares (GLS) regression model to predict Aat un-gauged locations. Figure 3 (right) i1lustrates the impactof the regression model on regional estimation of i24h in the sub-region outside Copenhagen. For different levels of MAR T-year event estimates are drawn and it appears that the lines are almost parallel, due to the fact that only the Poisson parameter Acould be explained with the regression model.
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Figure3. Lefl:Regression of localestimates of the Poisson parameter (Ai> for i24h withthe meanannualrainfall (MAR), including 95%confidence limits. Right: T-year eventestimates of i24h for varying levelsof MARin mm.
Urbanstorm drainagesystems
13
Based on the regional model r-year events and a measure of the associated uncertainty can be estimated at an arbitrary location in the region, and it can e.g. be used to calculate idf-curves as illustrated by Madsen et al. (1998). Generally, larger T-year events are obtainedin the Copenhagen sub-region than in the rest of the country. and there is a tendency that peak intensities are more uncertain than intensities with long duration for small return periods while the uncertainty increases with the duration for large return periods. As a supplement to the regional analysis of filtered data each of the historical rain series from the DWPCC measuring network were compared with the regional model. For all rainfall characteristics and a range of selectedreturn periodsthe following statisticwas computed:
U= BAS -BREG ~Var{BREG
(I)
)
where SAS refers to a local estimate, SREO is a regional estimate for the relevant sub-region and the same MAR and Var{SREO) is the variance of the regional estimate. U is approximately normal distributed and describes in probabilistic terms how much each historical rain series differs from the regional distribution. Thus, it can be used to assess how well each series fits with the regional model. As the final part of the regional analysis all rain series were classified according to their values of U for different rainfall characteristics and return periods. This classification turned out to be highly dependent on the problem in question (the rainfall characteristic lookedat) and on the return periodconsidered. thus makingit difficult to point out individual historical rain series that performequally well compared with the regional model in all cases. A RATIONALE FOR FUTURE USE OF LOCALANDREGIONAL DATA The engineering profession uses a variety of methods for solving different urban drainage problems. and each method is directly connected with the use of some kind of rainfall data. Methods range from simplistic procedures based on idf-curves to use of complex simulation tools that typically take rainfall time series as direct input. In principle.there is a potential for using all types of rain data mentioned in Fig. 2. However.all typesof data are not necessary and some are presently not available. Imaginethat the regional modelcan be trusted ideallyin all cases. This would imply that the residual model error is caused by shelter-conditions close to the gauges, other spatial variations on a relatively small scale compared with the physical extent of sewer catchments or even by measurement errors. Such variations shouldnot motivateuse of local rain data. Instead,they should be accounted for by addinga safety marginto designlevels based on regionalrain data, see Mikkelsen et al. (1997) for moredetails. However, in spite of the obvious advantages of regionalisation, it can not be used in every practical case. Regionalisation is normallycarriedout on filtered rain data and nobody has come up with a regionalised rain series generator that captures all relevantcharacteristics of a historical rain series. The performance of the generator described by Ambjerg-Nielsen et al. (1998) is generally good but there is a tendency to underestimate heavy rainfall accumulated over long durations. Furthermore, no steps have yet been taken to regionalise the generator; e.g. to scale it according to the metropolitan effect and the MAR in accordance with the resultsof the regional analysis. At the present time regionalisation of filtered data such as idf-curves and CDS is possible and feasible. and there is no reason to use filtered data based on local measurements. even if a rain gauge is placed nearby. Regionalisation of un-filtered data (synthetic time series) is not yet possible and thus, there is a need to continue using historical rain series in the near future, both for gauged and un-gauged catchments. Classification of historical rain series using Eq. (I) is a necessary tool when choosing among the available historical data series. The suggestion is to choose a series from the relevant sub-region (with or without metropolitan effect) with approximately the same MAR as the catchment in question. and with a value of U
14
P.S. MIKKELSEN et al.
for a range of rainfall characteristics and return periods looked at, that corresponds to a desired safety level of the rainfall input. The final guideline will take shape as a decision matrix in which the recommendations regarding the use of rainfall data will depend highly on the problem in question, the methodology chosen, and the return period considered. However, it is of primary importance that the variety of methodologies in use today is acknowledged and that new methodologies are allowed to evolve in the future. Ideally. the choice of engineering methodology should be based on the available information level about rainfall and other input, and on general knowledge about the reliability of the methodology. This new perception calls for an increased use of statistical concepts in urban drainage engineering practice in addition to the more commonly used pragmatic choices.
REFERENCES Arnbjerg-Nielsen, K.• Harremoes, P. and Spliid, H. (1994). Non-parametric statistics on extreme rainfall. Nordic Hydrol.• 25(4). 267-278. Arnbjerg-Nielsen, K. and Harrernoes, P. (1996). The importance of inherent uncertainties in state-of-the-art urbanstormdrainage modelling fromungauged smallcatchments, J. Hydrol., 179.305-319. Ambjerg-Nielsen, K., Harremoes, P. and Spliid, H. (1996). Interpretation of regional variation of extreme values of point precipitation in Denmark. Atmos. Res., 42. 99-111 . Arnbjerg-Nielsen , K., Madsen, H. and Harremoes, P. (1998). Formulating and testing a rain series generator based on tipping bucketgauges. Wat. Sci. Tech., 37(11), (thisissue). CEN (1995). Drain and sewer systems outside buildings, Part 4 Hydraulic design and environmental considerations. European Committee forStandardization, final draftpro EN 752·4:1995, CENrrcl65, WG22N317E. Chow, V. T.• Maidment, D. R. and Mays,L. W. (1988). Applied hydrology. McGraw Hill. USA. Harremoes, P. and Mikkelsen. P. S. (1995). Properties of extreme point rainfall I: Results froma rain gaugesystemin Denmark. Atmos.Res.. 37, 277-286. Johansen. L. and Harremoes, P. (1979). The use of historical storms for urban drainage design. In: International Symposium on Urban Storm Runoff, University of Kentucky. Lexington. KY. July 23·26. 1979. pp. 61-70. OES Pub]. Lexington. KY. USA. Johansen, N. B., Harremoes, P. and Jensen, M. (1984). Methods for calculation of annual and extreme overflow events from combined sewersystems. War. Sci. Tech., 16(819), 311-325. Jargensen, H. K.. Rosenern, S.• Madsen, H. and Mikkelsen. P. S. (1998). Quality control of rain data used for urban runoff systems. War. Sci. Tech., 37(11), (this issue). Madsen, H.• Rosbjerg, D. and Harremoes, P. (1994). PDS-modelling and regional Bayesian estimation of extreme rainfalls. Nordic Hydrol., 25(4).279·300. Madsen, H. and Rosbjerg,D. (1997). Generalized leastsquares and empirical Bayesestimation in regional partialduration series index-flood modeling. Water Resour. Res.• 33(4).771 -781. Madsen, H., Mikkelsen. P. S.• Rosbjerg, D. and Harremoes, P. (1998). Estimation of regional intensity-duration-frequency curves forextremeprecipitation. Wat. Sci. Tech., 37(11). (thisissue). Mikkelsen, P. S., Madsen. H., Rosbjerg, D. and Harremoes, P. (1996). Properties of extreme rainfalllU: Identification of spatial inter-site correlation structure. Almas. Res., 40. 77·98. Milclcelsen. P. S., Arnbjerg-Nielsen, K. and Harremoes, P. (1997). Consequences for established design practice fromgeographical variation of historical rainfall data. Waf. Sci. Tech.,36(8-9), 1-6.
Pergamon
PH: S0273-l223(98)OO310-2
Waf. Sci. r~ch. Vol. 37, No.1\, pp. 7-14.1998. C 1998 IAWQ . Published by Elsevier Science Ud . Printed in Great Britain. All rights reserved 0273 -1223198 $19 '00 + 0 '00
A RATIONALE FOR USING LOCAL AND REGIONAL POINT RAINFALL DATA FOR DESIGN AND ANALYSIS OF URBAN STORM DRAINAGE SYSTEMS P. S. Mikkelsen*, H. Madsen**, K. Arnbjerg-Nielsen*, H. K. Jergensen'"?", D. Rosbjerg** and P. Harremoes" • DepartmentofEnvironmental Scienceand Engineering, Technical University of Denmark. Building 115. 2800 Lyngby. Denmark •• Departmentof Hydrodynamics and WaterResources. TechnicalUniversity of Denmark. Building I 15,2800 Lyngby,Denmark ••• Weatherand ClimateInformation Division, Danish Meteorological Institute, Lyngbyvej 100, 2100 Copenhagen East. Denmark
ABSTRACf The Danish measuring network for high-resolutlon rainfall data cons ists of approximately 70 tipping bucket ram gauges of which 41 have been operated for more than 10 years . The gauges are separated by one to 300 km and cover an area of 43.000 km2. Significant geographical variations of extreme rainfall characteristics have been observed. Part of these variations can be explained by correlation with the mean annual rainfall and the existence of a metropolitan effect in the Greater Copenhagen area. The remaining variation may be attnbuted to sampling errors and small-scale spatial variations close to the gauges. Engineering methodologies all require rain data of some kind. ranging from design storms based on idf-curves for use in simple calculations to high-resolution time series for use in detailed simulation studie s. A comprehensive regional analys is was carried out 10 account for the geographical variat ion and to improve estimation for large return periods exceeding the actual length of the measured time series . Ideally. rainfall data used as input to urban drainage calculations should always be based on regional rain information. Regional design storms can be made readily available based on theory developed In this study. However, a satisfactory framework for generating synthetic rain series from regional rain information is not yet available. Thus . there will still be a need for using historical rain series in the near future. To improve the basis for choosing representative historical rain series all the Danish gauges have been classified according to their deviations from the regional distribution. @ 1998 IAWQ. Published by Elsevier Science Ltd. All rights reserved
KEYWORDS Urban drainage; rainfall; local data; regional data; time series, idf-curves. INTRODUCTION Until 20 years ago urban drainage systems were designed and analysed on the basis of design storms. The assumption for the design storm concept is that the relevant detrimental effects (flooding. overload and pollution) have statistical properties similar to those of the rain. This is true for linear systems, but because 7
8
P. S. MIKKELSEN et al.
urban runoff is a non-linear system it was proposed instead to use historical rain series as input to computer models of urban drainage, e.g. (Johansen and Harremoes, 1979; Johansen et al., 1984). Then, statistics can be generated directly on the calculated detrimental effects as a basis for analysing compliance with respect to return period. Since then it has become established practice to use historical rain series as input to hydrological model packages for detailed simulation of urban drainage systems. The performance indices looked at typically include both rarely occurring phenomena such as flooding related to extreme rainfall events, and more frequent phenomena related to accumulated rainfall over long time scales, e.g. discharge of nutrients to receiving waters. However, due to lack of suffic iently long data series measured in or nearby the catchment in question, simulations are often based on an available rain series from another location . So far, this has been considered good engineering practice and possible errors caused by geographical variation of the rainfall pattern have been virtually overlooked. In many countries rainfall is now measured at an increasing number of stations, and the length of the time series (the record lengths) are slowly approaching the return periods chosen as design criteria. The motivation for using the new data as input to simulations is growing with this development. However, it is not obvious how the new data may be best utilised for different purposes and on what basis decisions should be made when several candidate rain series are available. A large number of measuring stations and acceptable record lengths make a comprehensive statistical analysis of rainfall data possible. Such analysis may, or may not, support the prejudiced opinion that runoff simulations should be based on local rain data measured within the catchment, or in an area with similar physiographic characteristics. The large number of measuring stations may also improve the ability to pred ict rainfall characteristics corresponding to return periods exceeding the actual record lengths. This requires introduction of regionalisation procedures not employed so far within the urban drainage community, and for some applications the conventional historical (measured) rain series may have to be supplemented with design storms, or with synthetic (artificial) rain series, generated from regional rain information. The Danish national measuring system for rain data relevant within urban hydrology was introduced in 1979 by the Danish Water Pollution Control Committee (DWPCC) and the Danish Meteorological Institute (DMI). After several years of debate a project was initiated in 1996 that aims at setting up a decision scheme for using data from the measuring network. This paper explains the background of the project, discusses different types of rainfall data, summarises the results obtained when analysing the data in detail and outlines a rationale for using local and regional rainfall data, that is proposed as a national Danish guideline.
TERMINOLOGY Rainfall characteristics. A set of parameters that may be used to characterise rainfall on an event basis. Common examples are maximum intensities calculated as an average over a defined duration or total rainfall depths of events. Other examples with specific reference to urban hydrology are overflow volumes and necessary detention basin volumes for defined catchment characteristics. T-year event. The magnitude of a rainfall characteristic that on average will be exceeded once per Tyears. Tyear events can be estimated from extreme value statistics such as the partial duration series (PDS) method. Sampling uncertainty. Uncertainty in estimation of e.g. T-year events due to a limited sample size (few observation years). Geographical variation. Variation of rainfall characteristics from one location to another. Sometimes this type of variation is also referred to as regional variation (variation from one site in a region to another).
Urban storm drainagesystems
9
Region. An area classification according to geography and/or relevant physiographic and climatic characteristics. Sub-regions may be defined when heterogeneity is present within a region.
Local raindata. Rain measured at a specific location close to the catchment in question. Regionalrain data. Rain data measured at one or more locations different from the one in question. Filteredrain data. Rain data that have been treated to extract important characteristics (cf', above). A typical example of filtered rain data is intensity-duration-frequency (idf) curves. Historical rain series. Measured un-filtered time series of rain data, typically stored in a file for use as input to hydrological simulation software. Synthetic rain series. Generated time series of rain data with the same statistical properties and format as historical series. BACKGROUND Denmark covers a total area of 43,000 km2 and is a relatively flat country situated between 55° and 58° northern latitude and 8° and 13° eastern longitude in a coastal, Northern climate. The mean annual precipitation varies geographically between 550 and 850 mm, mainly governed by the dominant westerly wind direction, proximity to the coast and orography. The elevation is everywhere less than 200 m, and the physiographic and climatic characteristics vary relatively smooth. The measuring network consists of 75 gauging stations separated by one to 300 km, The locations of the gauges are mainly dictated by economy since they are placed in those of the Danish municipalities that contribute financially to the network. This is the reason for a large concentration of gauges around Greater Copenhagen. All stations are based on tipping bucket gauges with high resolution in time and volume and now, the longest records include 19 years of data starting from 1979. The measuring system and the data quality control is described in detail by Jergensen et al. (1998). r
r
,r
80
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Figure I. Left: Map of Denmark indicatingthe locationof the 43 gaugingstations from the DWPCC network that were part of the first study of data from 1979-87(Harremoesand Mikkelsen. 1995). Right: Extreme value series for each of the 43 stauons, plotted using T .. obl.period/rank.
10
P.S. MIKKELSEN et al.
Already the first studies of data from the DWPCC system based on 43 stations with up to 9 years of data showed large variations between data recorded at different stations. Figure I shows the locations of the gauges and extreme valueseries of the total volume of individual rain storms for each gauge. The variation implies that e.g. the input to calculatethe volume of a detention basindesigned to overflow on average once per year could be anywhere between 20 and 30 mm of rainfall. Such a dramatic variation is of coursecritical to the result of computerised urban storm drainage calculations (Arnbjerg-Nielsen and Harrernoes, 1996). However, a substantial part of the observed variation may originate from sampling errors, in whichcase the variation is of limited practical consequence. This cannotbe revealed by traditional non-parametric methods for estimating T-year events but more advanced statistical treatment of the data may refine the conclusions in this respect. Several other methods for estimating T-year events and the associated sampling uncertainty were later tested, including both non-parametric and parametric methods, and it readily appeared that sampling errors are of considerable magnitude for large return periods. As a consequence, the geographical variation was proven statistically significant for small Tbut not for large'T (Arnbjerg-Nielsen et al., 1994; Madsen et al., 1994). Two regional co-variates were identified using regional regression and principal components analysis: the meanannualrainfall and an extremevalueof daily precipitation corresponding to T =0.2 years. However, the two variables only described a significant part of the variation for very small return periods. The analysis illustrated on the one hand the effect of sampling errors for large return periods and on the other hand a metropolitan effect in the Copenhagen area where extreme rainfalls tend to last longerthan in other parts of the country, less influenced by an urban environment. Such effects were not included in the regression model, Arnbjerg-Nielsen et al. (1996). In a separate study Mikkelsen et al. (1996) found that inter-site correlation, caused by spatial coverage and movement of individual rain storms, has a major influence on regional modelling and thus, the motivation was strongfor analysing the data in moredetail. TYPES OF POINTRAINFALL DATAUSED FORDESIGN AND ANALYSIS Two issuesare of criticalimportance to the DWPCC guideline project. J. The rain gauges are placed irregularly throughout the country. It is not clear which gauges providedata that fit with the perception of a smooth regional variation in Denmark and which gauges providedata that doesnt, Data fromoutlier-stations shouldof courseonly be usedaftercarefully checking the possible reasons for differing statistical behaviour. Also,on what basisshouldrain data be choosen in practical cases where no local rain gauge is available?
2. The European Committee for Standardisation is introducing new guidelines soon, that recommend which return periods should be used for design and analysis relative to different problems, e.g. T = 2Q..30 years for flooding of city areas (CEN, 1995). These return periods are much larger than what is normally recognised and they exceed the length of the longestrecorded data series from the modem Danish measuring network. This implies that commonly used engineering methodologies based on historical rain data as input to simulations cannot be useddirectly. These two issues illustrate exactly the two main purposes of regionalisation. On the one hand, regionalisation may help understanding and accounting for geographical variation by estimating e.g, a regression model that correlates significant geographical variations of extreme rainfall characteristics with available information on regional physiographic andclimaticcharacteristics. On the other hand, regionalisation makes it possible to utilise information from all gauging stations to improve estimation for large return periods. This is done by scaling data from different stations according to the chosen regional model and adjusting for the available information level (that governs the sampling uncertainty) by accounting for the spatial intersite correlation in the region(Madsen and Rosbjerg, 1997). In Fig. 2 some common types of point rainfall data are classified according to their main features. Highresolution time series are used today as direct input to simulations when analysing complex hydrologic or
11
Urban stonn drainage systems
hydraulic problems where detrimental effects may occur at many different time scales. The advantage of such time series is that they reflects all relevant rainfall characteristics from peak intensities with short duration to variations in annual rainfall. Historical rain series are commonly used but synthetic rain series may well be the solution for the future. Ambjerg-Nielsen et al. (1998) give details about a rain series generator based on Markov chain theory that has been used to simulate rain series in Denmark. Essentially, historical rain series are un-filtered data, whereas synthetic rain series are filtered according to the chosen generator model.
Local data
High-resolution time series
Design storms
Historical time series
idf-eurves
Synthetic time series
CDS rain storms Idf-curves
Regional data
Synthetic time series
CDS rain storms
Figure 2. Classification of different types of point rainfall data used for design and analyses.
Design storms are typically used for simple design problems. For example, block rain storms taken from empirical idf-eurves are well suited for sizing pipe diameters with the rational method. A more advanced type of design storm is e.g. the Chicago design storm (CDS) which reflects maximum intensities for a range of durations and presupposes a general synthetic shape of heavy rain storms (Chow et al., 1988). In some cases CDS are used as input to simulations to analyse the hydraulic capacity of up-stream sewer networks. The motivation is mostly economic since the computational costs associated with using CDS is small compared with using high-resolution time series of rain data. However, any type of design storm should be used with care because they capture only specifically defined rainfall characteristics. Using CDS e.g. for analysing the hydraulic capacity of complex non-linear sewer networks or assessment of detention basin sizes and pollution runoff may lead to questionable results.
It sounds intuitively reasonable to use local rain data when dealing with catchments where measurements are available. In principle, local time series can be filtered to provide idf-curves or CDS. It can also be used un-filtered as input to simulations and if the available historical time series is too short, longer synthetic time series may be generated based on the available data (Ambjerg-Nielsen et al., 1998). Local data can be readily used when simulation models are calibrated with e.g. local flow data, but there are numerous problems associated with using local data for off-line design and analysis, cf. the two issues emphasised at the beginning of this chapter. As mentioned earlier, regional rain data makes it possible to account for geographical variation and to utilise information from all gauging stations in a region. The next section outlines the regional analysis carried out in the DWPCC project. SYSTEMATIC REGIONAL ANALYSIS A systematic regional analysis based on all data collected until the beginning of 1997 and newly developed regionalization procedures was conducted to form the best possible basis for deciding on a rationale for the future regarding use of data from the DWPCC network. Historical rain series from a total of 41 gauging stations each with more than 10 years of observations were included in the investigation, corresponding to a total of 650 station years. Each rain series was filtered to extract the following rainfall characteristics. maximum average intensities per event for the following range of durations; 10, 30 and 60 minutes, and 3, 6, 12, 24 and 48 hours total rainfall depths per event and per day necessary detention basin volumes and overflow volumes per event for two simplified catchments with defined interceptor capacities of 0.1 and 1.0 J.Lm s')
P. S. MIKKELSEN et at.
12
These rainfall characteristics were chosen to reflect the most important features of rainfall with respect to urbanstorm drainage. T-year events wereestimated for each rainfall characteristic using the partialduration series method where only events exceeding a defined threshold level are included in the analysis. The number of threshold exceedances was described by a Poisson distribution with intensity A.. corresponding to the expected number of annual threshold exceedances, The exceedance magnitudes were described by the generalized Pareto distribution (GPO) which has two parameters, the mean value of the exceedance magnitudes, u, and a shape parameter, le. The regional analysis is described in detail by Madsen et al. (1998) and thus,only the mainfindings are summarised below. I. The frequency of extreme events (A) varies significantly in the region, and a large part of this variation can be explained by the mean annual rainfall (MAR); the largerMARthe moreextreme events are observed. The degree of explanation is generally much larger for rainfall characteristics related to volume over large durations than for peak intensities.
2. For the average magnitude of extreme events ~), the region can be considered homogeneous for peak intensities. For rainfall characteristics relatedto volume over largedurations a significant metropolitan effect was observed, the average magnitude beinglargerin the Copenhagen area than in the rest of the country, but the variation could not be explained by variation of the MAR. Thus, in this case it was necessary to divide the region into two sub-regions: (I) the Copenhagen area,and (2) the rest of the country. 3. For higherorder statistical moments, reflecting the shape of the extremevaluedistribution (lC), the region can generally be considered homogeneous. In this case a regional probability distribution with a common shapeparameter can be used to parameterise extreme rainfall characteristics. Figure3 (left) illustrates an application wherelocalestimates of the Poisson parameter (Ai) for the maximum average intensity per event for 24 hoursduration (i24h) are correlated with the mean annual rainfall (MAR) obtained from a map from OMI. The 95% confidence limits reflect the prediction uncertainty, e.g, the sum of the sampling variance (related with at-site estimation and with estimation of the regression parameters) and the residual model error variance, when using a generalised least squares (GLS) regression model to predict Aat un-gauged locations. Figure 3 (right) i1lustrates the impactof the regression model on regional estimation of i24h in the sub-region outside Copenhagen. For different levels of MAR T-year event estimates are drawn and it appears that the lines are almost parallel, due to the fact that only the Poisson parameter Acould be explained with the regression model.
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Figure3. Lefl:Regression of localestimates of the Poisson parameter (Ai> for i24h withthe meanannualrainfall (MAR), including 95%confidence limits. Right: T-year eventestimates of i24h for varying levelsof MARin mm.
Urbanstorm drainagesystems
13
Based on the regional model r-year events and a measure of the associated uncertainty can be estimated at an arbitrary location in the region, and it can e.g. be used to calculate idf-curves as illustrated by Madsen et al. (1998). Generally, larger T-year events are obtainedin the Copenhagen sub-region than in the rest of the country. and there is a tendency that peak intensities are more uncertain than intensities with long duration for small return periods while the uncertainty increases with the duration for large return periods. As a supplement to the regional analysis of filtered data each of the historical rain series from the DWPCC measuring network were compared with the regional model. For all rainfall characteristics and a range of selectedreturn periodsthe following statisticwas computed:
U= BAS -BREG ~Var{BREG
(I)
)
where SAS refers to a local estimate, SREO is a regional estimate for the relevant sub-region and the same MAR and Var{SREO) is the variance of the regional estimate. U is approximately normal distributed and describes in probabilistic terms how much each historical rain series differs from the regional distribution. Thus, it can be used to assess how well each series fits with the regional model. As the final part of the regional analysis all rain series were classified according to their values of U for different rainfall characteristics and return periods. This classification turned out to be highly dependent on the problem in question (the rainfall characteristic lookedat) and on the return periodconsidered. thus makingit difficult to point out individual historical rain series that performequally well compared with the regional model in all cases. A RATIONALE FOR FUTURE USE OF LOCALANDREGIONAL DATA The engineering profession uses a variety of methods for solving different urban drainage problems. and each method is directly connected with the use of some kind of rainfall data. Methods range from simplistic procedures based on idf-curves to use of complex simulation tools that typically take rainfall time series as direct input. In principle.there is a potential for using all types of rain data mentioned in Fig. 2. However.all typesof data are not necessary and some are presently not available. Imaginethat the regional modelcan be trusted ideallyin all cases. This would imply that the residual model error is caused by shelter-conditions close to the gauges, other spatial variations on a relatively small scale compared with the physical extent of sewer catchments or even by measurement errors. Such variations shouldnot motivateuse of local rain data. Instead,they should be accounted for by addinga safety marginto designlevels based on regionalrain data, see Mikkelsen et al. (1997) for moredetails. However, in spite of the obvious advantages of regionalisation, it can not be used in every practical case. Regionalisation is normallycarriedout on filtered rain data and nobody has come up with a regionalised rain series generator that captures all relevantcharacteristics of a historical rain series. The performance of the generator described by Ambjerg-Nielsen et al. (1998) is generally good but there is a tendency to underestimate heavy rainfall accumulated over long durations. Furthermore, no steps have yet been taken to regionalise the generator; e.g. to scale it according to the metropolitan effect and the MAR in accordance with the resultsof the regional analysis. At the present time regionalisation of filtered data such as idf-curves and CDS is possible and feasible. and there is no reason to use filtered data based on local measurements. even if a rain gauge is placed nearby. Regionalisation of un-filtered data (synthetic time series) is not yet possible and thus, there is a need to continue using historical rain series in the near future, both for gauged and un-gauged catchments. Classification of historical rain series using Eq. (I) is a necessary tool when choosing among the available historical data series. The suggestion is to choose a series from the relevant sub-region (with or without metropolitan effect) with approximately the same MAR as the catchment in question. and with a value of U
14
P.S. MIKKELSEN et al.
for a range of rainfall characteristics and return periods looked at, that corresponds to a desired safety level of the rainfall input. The final guideline will take shape as a decision matrix in which the recommendations regarding the use of rainfall data will depend highly on the problem in question, the methodology chosen, and the return period considered. However, it is of primary importance that the variety of methodologies in use today is acknowledged and that new methodologies are allowed to evolve in the future. Ideally. the choice of engineering methodology should be based on the available information level about rainfall and other input, and on general knowledge about the reliability of the methodology. This new perception calls for an increased use of statistical concepts in urban drainage engineering practice in addition to the more commonly used pragmatic choices.
REFERENCES Arnbjerg-Nielsen, K.• Harremoes, P. and Spliid, H. (1994). Non-parametric statistics on extreme rainfall. Nordic Hydrol.• 25(4). 267-278. Arnbjerg-Nielsen, K. and Harrernoes, P. (1996). The importance of inherent uncertainties in state-of-the-art urbanstormdrainage modelling fromungauged smallcatchments, J. Hydrol., 179.305-319. Ambjerg-Nielsen, K., Harremoes, P. and Spliid, H. (1996). Interpretation of regional variation of extreme values of point precipitation in Denmark. Atmos. Res., 42. 99-111 . Arnbjerg-Nielsen , K., Madsen, H. and Harremoes, P. (1998). Formulating and testing a rain series generator based on tipping bucketgauges. Wat. Sci. Tech., 37(11), (thisissue). CEN (1995). Drain and sewer systems outside buildings, Part 4 Hydraulic design and environmental considerations. European Committee forStandardization, final draftpro EN 752·4:1995, CENrrcl65, WG22N317E. Chow, V. T.• Maidment, D. R. and Mays,L. W. (1988). Applied hydrology. McGraw Hill. USA. Harremoes, P. and Mikkelsen. P. S. (1995). Properties of extreme point rainfall I: Results froma rain gaugesystemin Denmark. Atmos.Res.. 37, 277-286. Johansen. L. and Harremoes, P. (1979). The use of historical storms for urban drainage design. In: International Symposium on Urban Storm Runoff, University of Kentucky. Lexington. KY. July 23·26. 1979. pp. 61-70. OES Pub]. Lexington. KY. USA. Johansen, N. B., Harremoes, P. and Jensen, M. (1984). Methods for calculation of annual and extreme overflow events from combined sewersystems. War. Sci. Tech., 16(819), 311-325. Jargensen, H. K.. Rosenern, S.• Madsen, H. and Mikkelsen. P. S. (1998). Quality control of rain data used for urban runoff systems. War. Sci. Tech., 37(11), (this issue). Madsen, H.• Rosbjerg, D. and Harremoes, P. (1994). PDS-modelling and regional Bayesian estimation of extreme rainfalls. Nordic Hydrol., 25(4).279·300. Madsen, H. and Rosbjerg,D. (1997). Generalized leastsquares and empirical Bayesestimation in regional partialduration series index-flood modeling. Water Resour. Res.• 33(4).771 -781. Madsen, H., Mikkelsen. P. S.• Rosbjerg, D. and Harremoes, P. (1998). Estimation of regional intensity-duration-frequency curves forextremeprecipitation. Wat. Sci. Tech., 37(11). (thisissue). Mikkelsen, P. S., Madsen. H., Rosbjerg, D. and Harremoes, P. (1996). Properties of extreme rainfalllU: Identification of spatial inter-site correlation structure. Almas. Res., 40. 77·98. Milclcelsen. P. S., Arnbjerg-Nielsen, K. and Harremoes, P. (1997). Consequences for established design practice fromgeographical variation of historical rainfall data. Waf. Sci. Tech.,36(8-9), 1-6.