SESSION 6.2
NOVATECH 2007 1227
Fractionation of Infiltration and Inflow (I/I)
components in urban sewer systems with
regression analysis
D?termination de l'origine de l'infiltration et des apports dans un
syst?me d'assainissement urbain par une analyse de r?gressions
Christian Karpf, Torsten Franz, Peter Krebs
Dresden University of Technology
Institute for Urban Watermanagement
Email: Christian.karpf@tudresden.de
RESUME
La gestion des syst?mes d?assainissement n?cessite des donn?es sur la variabilit? et
le volume des sources d?eau us?e dans les r?seaux urbains. En particulier, ce sont
l?infiltration de l?eau souterraine et l?entr?e de l?eau superficielle (I/I) qui sont
importantes pour la d?cision de r?habilitation et d?op?ration du r?seau
d?assainissement. Dans cette communication, une m?thode est pr?sent?e qui
soutient l?identification et la quantification des apports I/I. La m?thode est fond?e sur
une combinaison des approches de mod?lisation qui repr?sentent les fractions du
d?bit diff?rentes dans le r?seau d?assainissement. Les param?tres du mod?le sont
d?riv?s par une application de la r?gression lin?aire multiple. La m?thode a ?t?
appliqu?e pour la ville Dresde. Les r?sultats de la m?thode de fraction sont pr?sent?s
et discut?s.
ABSTRACT
The management of urban sewer systems requires data about variability and
discharge of typical waste water sources in urban catchments. Especially the
infiltration of groundwater and the inflow of surface water (I/I) are important for
decisions about rehabilitation and operation of sewer networks. In this paper a new
methodology is presented which supports the identification and quantification of I/I
components. The methodology is based on a combination of model approaches
representing the different flow fractions in sewer networks. Parameters of the models
are deduced by the application of a multiple linear regression. The methodology was
applied for the City of Dresden. Results of the fractionation method are presented and
discussed.
KEYWORDS
Combined water fractionation , infiltration, inflow, I/I, multiple linear regression,
wastewater components.
SESSION 6.2
1228 NOVATECH 2007
1 INTRODUCTION
Fractions of the total discharge in urban sewer systems are sewage of households
and industry, rainwater, infiltrated groundwater, drainage water and eventually the
inflow of surface water courses (e.g. overflows of springs or creeks). The discharges
of domestic and nondomestic wastewater as well as the discharge of rainwater
determine the hydraulic and procedural design of the sewer network and the
wastewater treatment plant (WWTP). But also infiltration of groundwater and inflow of
drainage and surface water sources  also referred to as infiltration/inflow (I/I) 
represent a basic component which influences significantly costs and operation. I/I
induce an increase of the hydraulic load and mostly a lowering of the waste water
treatment efficiency and thus additional costs and a deterioration of the receiving
water (ELLIS, 2001). Furthermore, I/I can cause a broadening of floods in urban
areas and the endangerment of urban infrastructure during flood events. Otherwise,
I/I have some positive impacts on the operational process of sewer networks and the
urban infrastructure. The increased total discharge due to I/I causes advanced
flushing, lower concentrations, and maybe a significant decrease of sewage
temperature and increase of nitrate in the systems. The consequences are reduced
anaerobic processes and the decrease of sedimentation processes, smell
development and corrosion in sewer pipes. Furthermore, the drainage of groundwater
could prevent the groundwater table from rising and wetting urban areas
(GUSTAFFSON, 2000), e.g. in former mining areas.
For the assessment of operation strategies, for the future development of the systems
and for the design of sewage constructions it is necessary to analyse the flow
fractions in sewer systems. Balance methods to assess flow components are usually
applied (DE BENEDITTIS and BERTRANDKRAJEWSKI, 2004). These methods
which require measurements of sewage flow, wastewater discharge and rain
intensities, afford the fractionation of rainwater inflow and I/I. Disadvantageously,
balance methods can not differentiate between the sources of I/I, i.e. groundwater,
drainage water, surface water. In order to get more detailed information about I/I
sources, methods based on chemical characteristics of sewage water were
developed such as isotope methods (KRACHT et al., 2003) or tracer measurements
(KRACHT and GUJER, 2004). However, these methods are costly and are applicable
when certain boundary conditions are fulfilled only, such as a different oxygen isotope
composition of drinking and groundwater. Beside measurements, I/I sources are
assessed by modelling. The models are based on conceptual (BELHADJ, 1995;
GUSTAFFSON et al., 1999) and physical approaches (GUSTAFFSON et al., 1997,
RODRIGUEZ et al., 2004). However, they have a high parameter uncertainty and
extensive data requirements.
In the project presented here it was our aim to develop a method which allows the
fractionation of I/I components based on reproducible mathematical methods and
commonly available data. The method links model approaches for the different I/I
components. It includes the identification of the I/I sources by hydrograph and
correlation analyses, the description of the processes with physicalconceptual
approaches and the calibration of basic parameters with multiple linear regressions.
The developed methodology is applied and tested for the sewer system of the City of
Dresden. The example shows data requirements and results of the methodology.
2 INVESTIGATED CATCHMENT AND DATA
The Dresden catchment covers an area of 98 km? with approximately 470,000
inhabitants. Industrial areas with significant contributions to the waste water discharge
are situated within the city catchment, too. The sewer system consists of 900 km
SESSION 6.2
NOVATECH 2007 1229
combined sewers, 380 km foul water pipes and 340 km storm water pipes. The city is
situated along the river Elbe. The average runoff of the river yields 327 m?/s. During
flood events the river water may enter the sewer system via flooded manholes and
leaky CSOgates which should cut off sewer and river system when the water level in
the latter is higher. In the past, sewerage technology included the flushing of the
sewer pipes by runoff from creeks or springs, which were connected to the system.
Some of these surface water sources are still connected with the network. Parts of
the sewer system are temporary or permanently influenced by the aquifer (KARPF
and KREBS, 2004).
For the following investigations flow data of the WWTP, rain intensity, air temperature,
groundwater levels, water levels of the river Elbe and flow measurements in a local
creek were used. The data were available from 1995 to 1999 with a resolution of 1
day except for groundwater measurements which were measured every 8 days.
Additional water supply data of the year 1999 were used for verification purposes.
3 IDENTIFICATION OF I/I COMPONENTS
The dry weather flow (DWF) in urban sewer systems, which can be deduced by the
exclusion of rain water and snow melt runoff by statistical or by hydrological methods
(WEISS et al., 2002; WITTENBERG and BROMBACH, 2002), is characterised by the
variations of the different input sources. The daily and weekly and in some
catchments also seasonal variations of the DWF depend mainly on the drinking water
consumption and thus on the domestic and industrial waste water discharge.
Seasonal and yearly variations are often induced by groundwater and surface water
sources. Peak flows during dry weather could be induced by floods or rain derived
infiltration (RDI)  also referred to as fast infiltration component which describes an
increased inflow after rain events.
In order to investigate the dynamics of waste water discharge the Dresden data of
DWF for the year 1999 were classified by months and week days (Figure1, left).
Thus, the influences of industry and tourism and other seasonal and weekly
differences can be identified. It can be seen, that the weekly variation is small. There
is no significant difference between working and weekend days. Furthermore, the
monthly flow differs. The increased values from February to March apparently are
induced by I/I sources. Drinking water supply data support the assumption, that
seasonal variations are not induced by varying drinking water consumption and
sewage discharge, respectively (Figure 1, right).
0
2000
4000
6000
8000
10000
12000
mo tue we thu fri sa su
ru
n
o
f
f
se
we
r
syst
e
m
(m
?
h
1
)
Jan Feb Mar Apr
May Jun Jul Aug
Sep Okt Nov Dez
0
1000
2000
3000
4000
5000
123456789101112
month
dri
n
k
i
n
g
w
a
t
e
r
c
ons
umpt
i
on
(m
?
h
1
)
mean monthly value
maximal daily value
minimal daily value
Figure 1: Total discharge in the sewer system of the city of Dresden classified by weekday and
month (left) and drinking water supply (right) in 1999
The relationship between flow in the sewer systems and hydrological data is
assessed by a correlation analysis. Figure 2 illustrates correlations between
measured DWF, water level measurements of the river Elbe, runoff measurements of
SESSION 6.2
1230 NOVATECH 2007
a local creek, summarised rain heights of 7 days before the considered dryweather
day and the mean distance between groundwater level and sewer pipe inverts.
class
num
b
e
r
of
d
a
t
a
class
nu
mbe
r
of
d
a
ta
class
nu
mbe
r
of
data
class
n
u
m
be
r
of
da
t
a
class
nu
mbe
r
of d
a
t
a
dry w eather flow
sewer system
water level river Elbe
local creek runoff
distance
groundw ater  sew er system
precipitation
7 days before dry w eather
R = 0.82
R = 0.16
R = 0.72
R = 0.82
Figure 2: Distribution and correlation of DWF, water level in the river Elbe, runoff in a local creek,
distance between groundwater and sewer system and summarized precipitation 7 days before
dry weather
A strong correlation between the flow in the sewer system and the groundwater and
local and regional surface water courses can be observed, whereas the river and
groundwater shows a closer correlation with the sewage flow than the correlation
between the local creek and sewage flow. The precipitation shows a low correlation
with the DWF. It is concluded, that surface water courses and groundwater are much
more important for the sewage flow during dryweather periods than local rainfall
before these dry weather periods. This conclusion can also be confirmed by the
investigation of rain derived infiltration (RDI).
0
2000
4000
6000
8000
10000
12000
DWF 1 day
before
rain event DWF 1 day
after
DWF 2 days
after
r
unoff
(
m
?h
1
)
19950815
19951118
19970204
19970318
19970418
19970912
19971107
19980216
19980420
19981215
19990906
mean value
Figure 3: Flow in the sewer system of the City of Dresden before and after rain events
SESSION 6.2
NOVATECH 2007 1231
RDI was investigated by the comparison of flow rates before, during and after rain
events. The result is illustrated in Figure 3. The DWF 2 days after the rain events
have similar magnitudes as before rain events, i.e. an influence of the events is not
longer detectable. This result, which can be observed in different seasons, is
apparently independent of the climate conditions. It is concluded that RDI has a low
importance in the considered catchment and that RDI can be neglected by using two
dry days after the rain event for DWFexaminations.
4 METHODS
4.1 Approaches to model I/I components
According to the correlation and hydrograph analysis, groundwater and surface water
sources were identified as main contributors to I/I in the catchment of the City of
Dresden. The approaches applied for the various components are described in the
following.
The approach for groundwater infiltration is based on the law of Darcy (equation 1).
The factor k
in
represents the permeability of the pipes in (m
3
?m
2
?s
1
). It is assumed,
that the pipe reacts like an ideal drain. That means, the area A
GW
, which is wetted by
groundwater, is permeable. The hydraulic slope depends on the pressure height (?h),
represented by the difference of groundwater level and pipe water level, and the
mean distance (?d) between leakage area A
GW
and groundwater level.
d
h
AkQ
GWinin
?
?
??=
equation 1
Thus the upper limit of infiltration Q
in
is k
in
?A
GW
. For the assessment of permanent and
temporary surface water inflows several approaches were used depending on data
availability. The calculation of surface water inputs during flood events is described
with equation 2 based on the approach of Toricelli. The inflow (Q
flood
) of surface water
depends on the pressure height (?h
SW
), the leaky area (A) and a coefficient
describing the shape of the openings (?). In order to simplify equation 2 the
parameters are combined to one factor (k
flood
).
SWfloodSWflood
hkhgAQ ??=?????= 2?
equation 2
Permanent inflows of surface water courses (Q
inflow
) are modelled by a simple
conceptual approach (equation 3) consisting of a coefficient (k
SW
) and the runoff in a
local creek (Q
SW
).
SWSWlow
QkQ ?=
inf
equation 3
4.2 Multiple linear regression
The approaches of the I/Icomponents were combined in equation 4, by which the
DWF for a certain time step (in our case: one day) is estimated.
()
??
+?+??+
?
?
?
?
?
?
?
?
?
??=
j
WSWSWjSWflood
i ik
i
iGWGWDW
QQkhk
d
h
AkQ
5.0
,
,
,
d
ependen
t
var
i
abl
e
in
f
ilt
r
a
t
i
on
coef
f
i
cient
in
f
ilt
r
a
t
i
on
var
i
able
sur
f
ace
w
a
t
e
r
coef
f
i
cient 1
su
rfa
c
e
w
a
te
r
var
i
able
1
sur
f
ace
w
a
t
e
r
c
oef
f
i
c
i
ent
2
sur
f
ace
w
a
t
e
r
var
i
able 2
con
s
t
ant
i? index sewer pipe
j ?index sewer manhole/ CSO
equation 4
SESSION 6.2
1232 NOVATECH 2007
A multiple linear regression method was used to identify the coefficients k
GW,
k
SW
, k
flood
(equations 1  3). The constant value of Q
W
, also estimated with the regression,
represents the waste water discharge. The DWF (Q
DW
) is the dependent variable.
Inputs of the linear regression method are datasets of the dependent and
independent variables. These sets stand for different process phenomena
represented by the fluctuating water levels of aquifer and surface water and the
reaction of the sewer system. The dependent and independent variables were
provided by preprocessing.
4.3 Preprocessing
Except for the surface water variable 2 in equation 4, which is based on flow
measurements in a certain small local creek, the linear regression requires data pre
processing.
The determination of DWF Q
DW
is based on flow measurements of sewage flow at the
waste water treatment plant inlet, rain intensity measurements in the catchment and
additional measurements of the air temperature. Days of DWF are defined by a
maximum rainfall intensity of 0.3 mm?d
1
at the considered day and one day before in
order to exclude RDI (see above). Furthermore, 3 days before and on the respective
DWFday the air temperature should not be in the range of ?2?C and +2?C. By using
this condition the runoff of snow melt water in the sewer system is excluded.
The calculation of the infiltrationbased variable requires the estimation of the
groundwater level near the sewer system elements and the waste water level in each
pipe of the considered area. Hence, groundwater level measurements were
spatiotemporally interpolated and linked to the sewer pipe location. Waste water
levels in the sewer pipes were simulated with a hydrodynamic network model.
Surface water variable 1 (equation 4), representing the temporary influence of the
river Elbe, was identified by the linkage of river water levels and the levels of sewer
network elements (manholes, CSOgates, CSOweirs) in a geographic information
system.
5 RESULTS
The results of the multiple linear regression are summarised in Figure 4.
datasets 420
correlation coefficient of
the regression model R 0.91
pniveau of the
regression model <0.0001
calculated coefficients
partial
correlation pniveau
kin
0.67
<0.0001
kflood
0.33
<0.0001
kSW
0.41
<0.0001
constant QW (m?h
1
) 3347
pniveau of the constant <0.0001
measured QW (waste
water flow in m?h
1
) 2928
54321012345
standardised residuals
0
20
40
60
80
100
120
140
160
numb
e
r
of
da
ta
expected normal distribution
(residuals of the regression model = difference of
calculated and measured DWF)
Figure 4: Assessment of the quality of the linear regression method and the deduced coefficients
of the regression model for DWF estimation
SESSION 6.2
NOVATECH 2007 1233
The comparison of calculated values and the measured data of DWF shows a strong
correlation (R = 0.91). Furthermore, the regression model and the individual
coefficients have a high significance (p < 0.0001). The partial correlation coefficients
give an idea about the relevance of I/I components. The residuals between calculated
DWF and the measured DWF yield a good approximation of the normal distribution.
The comparison of measured waste water discharge and the constant value support
the assumption that the constant value can be interpreted as waste water discharge.
It can be concluded, that the deduced model (equation 4) is applicable to predict the
DWF and variations of single I/I components in the investigated catchment.
The modelled hydrographs of the I/I components between 1995 and 1999 are
illustrated in Figure 5. A comparison with measured values shows, that seasonal
fluctuations of the DWF are well described by the regression model (Figure 5, left).
With an average value of 74 % of the I/I volume the infiltration component Q
in
is the
most important contributor to I/I (Figure 5, top right). Permanent surface water input
yields about 23% and temporal inflows of surface water induced by flood represents
3% of the I/I volume. However, in a shortterm run the surface water sources may
dominate I/I. This is shown by the peak flow of a spring flood event in 1999, where
more than 50% of the I/Ivolume was induced by surface water courses (Figure 5,
bottom right).
0
2000
4000
6000
8000
10000
12000
1995

020
2
1995

060
2
1995
10
0
2
1996

020
2
1996
06
0
2
1996

100
2
1997

020
2
1997

060
2
1997

100
2
1998

020
2
19
98
060
2
1998
10
0
2
199
9
020
2
1999
06
0
2
1999
10

0
2
fl
ow (m
?
?
h
1
)
temporal surface water inflow (Qflood)
groundwater infiltration (Qin)
permanent surface water inflow (Qinflow)
waste water discharge (Qw)
measured DWF
23%
69% 1%
7%
mean volume of I/I fractions 19951999
33%
14%22%
31%
I/Ifractions 19990304 (spring flood event)
Figure 5: Dynamic fractionation of the DWF in the City of Dresden, long term and short term
balance
6 CONCLUSIONS
The combination of model approaches to simulate I/I processes and the calibration of
the parameters with multiple linear regression methods offer opportunities to quantify
the various components of I/I. The approaches which are linked in a regression
equation must be reduced to linear or quasi linear models. This is a disadvantage for
a detailed process representation. On the other hand, such simplified physical and
conceptual model approaches yield satisfying results regarding general statements
about the components,. An important requirement of the described methodology is
the availability of groundwater and surface water data. Furthermore, flow data of the
sewer network at least in the WWTP inflow, rain intensity in the catchment and
temperature measurements are necessary to separate DWF from the total discharge.
The deduced regression model for the City of Dresden illustrates a high significance
of estimated coefficients. These results underline the influence of numerous I/I
components on the variation of the DWF. With a fraction of 74 % of the total I/I
volume groundwater infiltration is the most important contributor to I/I in the study.
SESSION 6.2
1234 NOVATECH 2007
The annual input volume of permanent and temporary surface water yields about
26 %. But, surface water fractions increase rapidly and may become dominant during
flood events.
With the introduced methodology it is possible to analyse quantities and variations of
I/Icomponents. The deduced regression model can be used for the investigation of
present, past and future hydrological scenarios.
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ACKNOWLEDGEMENTS
This work was supported by the German Ministry of Education and Research (BMBF) within the
project ?Development of a 3zonemodell for groundwater and infrastructure management after
extreme flood events in urban areas? (FKZ: 02WH0558) and by the German Research
Foundation (DFG) within the project ?Modelling of sewerage exfiltration with indicator parameters?
(GZ: KR 2337/31). Also, the support of the City of Dresden is greatly acknowledged.