Vaes G.

I-Revues

SESSION 1.2 
NOVATECH 2007  171 
The spatial relevance of extreme rainfall events 
La pertinence de la représentation spatiale des événements 
pluviaux extrêmes 
Vaes G. 
HydroScan, Tiensevest 26/4, 3000 Leuven, guido.vaes@hydroscan.be 
RESUME 
La pluie extrême est un élément clef de la conception des systèmes d’assainissement 
unitaires. Dans la plupart des cas, la pluie utilisée est obtenue par une mesure 
ponctuelle. La question à poser est le choix de la période de retour. Cette question a 
aussi une dimension spatiale. Chaque système ou conduite individuelle peut être 
calculé pour résister à des inondations pour une certaine période de retour T. Quand 
et où l’événement extrême aura lieu est une loterie. Pour l’assainissement urbain, les 
orages estivaux sont les plus critiques. Ces orages peuvent être très locaux avec un 
diamètre de seulement quelques kms. Si un système d’assainissement est dessiné 
pour ne pas avoir des inondations avec une période de retour de T ans, la 
conséquence est que dans ce système un événement avec cette période de retour T 
va arriver plusieurs fois, mais à des endroits différents. La question pour l’exploitant 
du système est : combien de fois je peux avoir un événement avec un période de 
retour T quelque part dans mon système. 
ABSTRACT 
 
Extreme rainfall is a key element in the design of urban drainage systems.  For most 
design work, the rainfall used is obtained from point rainfall measurements.  
A question for the design of urban drainage systems is the return period for which the 
design is to be carried out.  This question has also a spatial component.  
Every individual drainage system or part of it can be designed to resist flooding for 
a certain return period T.  When and where an extreme event will happen is a lottery.  
For urban drainage systems, the severe summer thunderstorms are the most critical 
(in Western Europe climate conditions).  These summer thunderstorms can be very 
local with a diameter of only a few km.  When an urban drainage system is designed 
to have no flooding with a return period T, this has the consequence that within this 
system an event with this return period T will take place several times within T years, 
but generally at different locations over the catchment.  The question for a drainage 
system manager is then : how many times can I get a T year event somewhere in my 
system ? 
 
KEYWORDS 
Design criteria, flooding, rainfall, return period, spatial distribution 
SESSION 1.2 
172 NOVATECH 2007  
1 INTRODUCTION 
 
Extreme rainfall is a key element in the design of urban drainage systems.  For most 
design work, the rainfall used is obtained from point rainfall measurements.  
With respect to the required accuracy in time and magnitude this is the only option for 
design purposes.  This rainfall is assumed to be uniform over the catchment, which is 
of course only a good approximation for small catchments (up to a few km2 : for the 
bias in function of the area see figure 1).  When more measurement locations are 
available within a short range, spatial partitioning methods as e.g. the Thiessen 
polygons can be applied, eventually a spatial correction factor can be used as 
a function of the area of the Thiessen polygons (figure 1 : Vaes et al.,2005).  Also for 
design purposes areal rainfall correction coefficients can be used, based on statistical 
analysis of long series of spatial variable rain fields (Vaes et al., 2005).  
Besides a static bias, there is also the dynamic effect of storms moving over the 
catchment in specific directions and with specific speed.  This dynamic effect might 
be significant e.g. when the main flow direction in the urban drainage system is the 
same as the moving direction of the rainfall and the cumulative effect is larger the 
slower the storm moves over the catchment with a speed similar to the velocities in 
the drainage system (Vaes et al., 2002b). 
 
2 SPATIAL RELEVANCE OF EXTREME RAINFALL EVENTS 
 
2.1 Questions arising 
 
An important question for the design of urban drainage systems is the return period 
for which the design is to be carried out. This should be an economic trade off 
between costs for extra investments and damage that can be prevented by these 
extra investments.  This question has also a spatial component.  Each individual 
drainage system or part of it can be designed to resist flooding for a certain return 
period T.  This should assure that at each location there is certainly not more frequent 
a flooding than on average every T year.  For urbanised areas the design return 
periods are more and more elevated nowadays, because the risks (damage) become 
larger.  When and where an extreme event will happen is a lottery.  For urban 
drainage systems, the severe summer thunderstorms are the most critical (in Western 
Europe climate conditions).  These summer thunderstorms can be very local with 
a diameter of only a few km and for larger urban drainage systems, they may affect 
only part of it.  When a large urban drainage system is designed to have no flooding 
with a return period T, this has the consequence that within this system an event with 
this return period T will take place several times within T years, but at different 
locations over the catchment.  The question for a drainage system manager is then : 
how many times can I get a T year event in my system ? 
 
SESSION 1.2 
NOVATECH 2007  173 
2.2 Methodology 
 
In order to assess this spatial relevance of extreme rainfall events, following 
methodology is used.  With the spatial rainfall generator of (Willems, 2000) (valid for 
the rainfall conditions in Flanders, Belgium), a large (time) series of spatial rain fields 
have been generated.  Based on these rain fields areal rainfall correction coefficients 
were calculated (figure 1) (Vaes et al., 2005).  These areal rainfall correction 
coefficients are function of the diameter of the considered area, the rainfall intensity 
(or the return period via point Intensity/Duration/Frequency(IDF)-relationships) and 
the duration of the rainfall (aggregation level).   
 
 
spatial integrated rainfall intensity / measured point rainfall intensity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
radius drainage area (km)
m
ea
n 
ar
ea
l c
or
re
ct
io
n 
co
ef
fic
ie
nt
5
10
20
50
limit
measured
intensity
(mm/h)
aggregation level = 10 minutes
 
Figure 1 : Areal rainfall correction coefficients for an aggregeation level of 10 minutes 
(Vaes et al., 2005). 
 
When the areal rainfall correction coefficients are calculated for a storm with rainfall 
intensities with a return period of 100 years in the central location, the mean rainfall 
intensity over each larger area can be derived.  These lower values of mean rainfall 
over a larger area can be recalculated in terms of return period based on the statistics 
of the point rainfall IDF-relationships (i.e. for Flanders (Vaes, 1999)).  This calculated 
return period gives an estimation of the probability that in this larger area somewhere 
a 100 year event will take place.   
 
Translated to a more mathematical formulation this means the following. 
A point rainfall intensity ip over a duration ∆t has a certain return period Tp through the 
IDF-relationships.  When this rainfall is taken representative over an area with 
a radius R, an areal correction coefficient φ can be calculated as function of the 
aggregation level ∆t, the point rainfall intensity ip and the radius R (see figure 1).  
The representative rainfall intensity for the total area with radius R is then iR = ip × φ.   
SESSION 1.2 
174 NOVATECH 2007  
Based on the point rainfall IDF-relationships, the return period TR of this intensity iR 
can be calculated as a function of ∆t.  This return period TR will be (much) smaller 
than the return period Tp.  This means that on average every TR years in an area with 
radius R there will be a subarea where the rainfall intensity will have a return period of 
at least Tp. 
 
2.3 Results 
 
For the range of areal rainfall correction coefficients for aggregation levels between 
10 and 180 minutes and diameters of circular areas up to 30 km, this probability is 
calculated (based on the areal rainfall correction coefficients) and visualised in 
figure 2. This is generally the range of areas and concentration times that covers 
urban drainage systems. 
In this way for the mean 100 year (spatial distributed) rainfall the return period can be 
calculated (based on statistics of point rainfall measurements) in terms of rainfall 
volumes over areas with different magnitude.  This will typically lead to decreasing 
return periods for larger areas.  When an extreme event has a return period of 
100 year in the centre of the storm and the return period over an area with e.g. 
a diameter of 16 km is only 10 years (as calculated in figure 2), it can be roughly 
concluded that a similar event will occur on average 10 times in this area with 16 km 
diameter in 100 years.  This kind of magnitude of area corresponds to a large city as 
Brussels (Belgium).  When this is further extrapolated to Flanders (approximately 
13000 km2) a 100 year summer storm would take place somewhere (even at different 
places) in Flanders approximately every year. The accuracy of the calculations 
however decreases significantly for increasing areas, certainly above 30 km diameter, 
because certain larger scale effects are not taken into account in the spatial rainfall 
generator used. 
 
0.1
1
10
100
0 5 10 15 20 25 30 35
diameter area (km)
re
tu
rn
 p
er
io
d 
(y
ea
r)
100 year local rainfall
10 year local rainfall
Brussels
 
Figure 2 : Average return period of a 100 respectively 10 year rainfall event somewhere 
in a larger area (average for aggregation levels between 10 and 180 minutes). 
SESSION 1.2 
NOVATECH 2007  175 
If based on figure 2 the number of occurrences is calculated of a T year event in 
T years, this gives the values as shown in figure 3.  From this graph it seems that the 
more extreme the rainfall is, the more often (relatively to the global period of T years) 
it will occur and as a consequence the smaller the spatial extend must be.  
The average diameter Devent of the event is related to the total catchment diameter 
Darea as : 
occurencesofnumber
DD areaevent =  
 
1
10
100
0 5 10 15 20 25 30 35
diameter area (km)
nu
m
be
r o
f o
cc
ur
en
ce
s
100 year local rainfall
10 year local rainfall
Brussels
 
Figure 3 : Number of occurrences of a T year event in a larger area in a period of T years 
(average for aggregation levels between 10 and 180 minutes). 
 
2.4 Further remarks 
 
This analysis is based on the rainfall that is valid for Flanders and specific for extreme 
summer storms with large intensities during short periods, which mostly have 
a limited spatial extent.  These storms are most critical for small and local water 
systems, e.g. urban drainage systems and small water courses. 
For areas larger than 30 km diameter the original rainfall generator is not accurate 
enough, but an extension of it has been made towards larger areas (Willems 
& Berlamont, 2002); this could be used to further expand this analysis to larger areas. 
Further research with the original (spatial and temporal distributed) rain fields in stead 
of on the processed data (i.e. areal rainfall correction coefficients) can point out to 
which extent the variability is accurately enough taken into account. 
 
 
SESSION 1.2 
176 NOVATECH 2007  
3 REAL EXTREME EVENTS 
 
In September 2005, heavy rainfall poured down above Brussels (figure 4).  
The maximum rainfall volume measured in one of the 13 measurement locations in 
30 minutes was 49 mm (98 mm/h = 272 l/s/ha).  This is approximately twice the 
maximum amount that was ever measured by the Belgian Royal Meteorological 
Institute (at Uccle) during more than a century (Vaes et al., 2002a).  A network of 
13 pluviographic stations is available in Brussels.  Based on these measurements 
an assessment is made on the spatial pertinence of the return period for this extreme 
rainfall event. 
 
 
 
Figure 4 : Network of pluviographic stations in the Brussels Region and the maximum hourly 
rainfall volumes (provided by the Water Administration of the Brussels Region). 
 
The result of the calculation of the spatial relevance is shown in figure 5 for the 
different subareas (and combinations of them) defined as Thiessen polygons around 
the rainfall measurement locations.  The series indicated as “return period of rainfall 
volumes” show the return periods as calculated based on the point IDF-relationships 
for the combination of the different subareas (combined from most severe to less 
severe rainfall).  The series indicated as “return period of the rainfall variability” take 
into account the relative area of the subcatchments.  This series shows that although 
the total rainfall volume over the total area will take place every 11 years, the high 
variations and extremes in certain subareas still are very extreme for this total 
catchment (still once in about 300 years when taking into account the spatial 
relevance). 
 
SESSION 1.2 
NOVATECH 2007  177 
10
100
1000
10000
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
area (ha)
re
tu
rn
 p
er
io
d 
(y
ea
r)
return period of rainfall volumes
return period of the rainfall variability
 
Figure 5 : Return periods of having an extreme event like this of September 2005 
somewhere in Brussels. 
 
4 HOW TO DEAL WITH THESE EXTREME EVENTS ? 
 
It is not feasible to take into account this kind of extreme events in the design of urban 
drainage systems.  However, one can assess the effects of these extreme events and 
calculate the corresponding risks.  When using traditional hydrodynamic models, 
the simulation results become incorrect because the superficial flow over the streets 
is not taken into account.  The water is mostly stored locally at the flooded nodes and 
this creates artificial storage and underestimation of the downstream peak flows.  
With the traditional hydrodynamic models it is however possible also to take into 
account the street flow by introducing a network of wide and shallow canals 
that represent the streets on top of the pipe network (e.g. Vaes et al., 2004).  
Although these hydrodynamic models are not really developed for this kind of 
simulations and the accuracy might be lower as for the pipes, it still gives a more 
realistic assessment then without this street layer.  The main problem for this kind of 
modelling with the extra street layer is the availability of topographical data and 
details.  For example, if the curb stones are equal with the street level at the entrance 
of a garage in the basement of a house, this influences the risks largely.  As the flood 
risk is the product of the probability with the damage, it is logical that for dense 
populated urban areas and for special structures not the same probabilities of 
flooding can be accepted as for zones with lower impact in terms of damage. 
 
SESSION 1.2 
178 NOVATECH 2007  
5 CONCLUSIONS 
 
If we design our urban drainage systems to have no flooding at each location for 
a certain return period T and the design is accurate, we will have not more than once 
in T years a flooding at each location.  However, this will not occur at the same time 
at each location e.g. in a large city, because of the limited spatial extent of the 
extreme rainfall events.  For that reason in a larger urban area an extreme event with 
a return period of T years will occur much more frequent than once in T years.  
Urban water managers often observe more frequent flooding than the design return 
periods, but are most often not aware of this space/frequency-relationship caused by 
the large variability of the rainfall in space and time. It is a challenge to take this into 
account in urban water risk management plans. 
 
ACKNOWLEDGMENTS 
 
The author is grateful to the Water Administration of the Brussels Region that 
supplied the rainfall data for the case study.  Furthermore, P. Willems of the 
K.U.Leuven is acknowledged for the use of the results of the spatial rainfall generator. 
 
LIST OF REFERENCES  
Vaes G. (1999). The influence of rainfall and model simplification on combined sewer system 
design. PhD, K.U.Leuven, Belgium. 
Vaes G., Willems P. and Berlamont J. (2002a). 100 years of rainfall registration : are there 
trends ? Water Science and Technology, 45(2). 
Vaes G., Willems P. and Berlamont J. (2002b). Moving design storms for combined sewer 
systems. 9th international conference on urban drainage, Portland, USA. 
Vaes G., Bouteligier R., Herbos P. and Berlamont J. (2004). Modelling of floods caused by urban 
drainage systems. 6th international Conference on Urban Drainage Modelling, Dresden, 
Germany. 
Vaes G., Willems P. and Berlamont J. (2005). Areal rainfall correction coefficients for small urban 
catchments. Atmospheric Research, 77(1). 
Willems P. (2000). Probabilistic immission modeling of receiving surface waters. PhD, 
K.U.Leuven, Belgium. 
Willems P. and Berlamont J. (2002). Accounting for the spatial rainfall variability in urban 
modelling applications. Water Science and Technology, 45(2). 


La pertinence de la représentation spatiale des événements pluviaux extrêmes

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La pertinence de la représentation spatiale des événements pluviaux extrêmes

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