- Email: [email protected]
Modelling of rainfall induced infiltration into separate sewerage
e
Pergamon
W.". ScL T.c1t. Vol. 32, No. I. pp. 161-168, 1995. Copyri,bIOI995IAWQ
0273-1223(95)0055 I-X
Prinled iD Oreal Britain. All ri,hll reoervod. 0273-1223195 $9'50 + 000
MODELLING OF RAINFALL INDUCED INFILTRATION INTO SEPARATE SEWERAGE N. Belhadj, C. Joannis and G. Raimbault Laboratoire Central des Pants et Chaussees, Centre de Nantes, Division Eau. BP 19, 44340 Bouguenais, France
ABSTRACT Aowrate changes in separate wastewater sewerage during wet weather are often attributed to inappropriate connections of runoff water. But these inputs are not the only cause of such behaViour and infiltration through leaking defects or cracks can supply large flows inlD collection pipes. The characterization of these flows is not an easy task since they involve complex processes, depending not only on rainfall events but also on hydrological conditions and seasons. Using 16 months of hourly measurements of rainfall and f10wrates, we developed a six parameter conceptual model to simulate rainfall induced infiltration into a smaIl sewer system. Sensitivity analysis applied ID the proposed model showed good achievements under various calibration conditions but displayed higb parameter interacbons whicb may be a serious drawback for some specific model uses. Model application ID another sewer network Yielded good agreement between observed and simulated flows. The suitability of this model must be further checked on other sites.
KEYWORDS
Drainage; infiltration/inflow; mathematical model; sewer evaluation study. INTRODUCTION Urban storm drainage is a concern not only in combined sewer systems. or separate storm water sewers: separate foul water sewerage also displays special behaviour during rainy periods. Indeed large inputs from inflltration nnd inflow very often cause some trouble for the collection and treatment of wastewater. The two kinds of "extraneous water" quoted above are very different as regards their behaviour nnd their effects. as well as their location in the sewer system nnd the solution which cnn be used to fix them. or to cope with them. - Inflow comes from inappropriate connection of impervious areas to the foul water collecting pipes. It displays high peak flows. directly related to rainfall events. - lnflltration comes from groundwater. seeping into sewerage through cracks. untight joints. and other defects. Its flowrate is supposed to change rather slowly. according to seasonal variations of groundwater levels.
161
N. BELHAD] el al.
162
To address these problems. sewer evaluation studies have been conducted in France for more than fifteen years. They aim to quantify and locate the two kinds of inputs quoted above. so that an assessment can be made about their consequences on sewerage and receiving waters. and solutions be proposed (Ranchet et al. 1982). But some results provide clear evidence for a third kind of extraneous water, somewhat intermediate between infiltration and inflow: that is rainfall induced infiltration. For instance. a survey conducted over 100 catchments investigated during sewer evaluation studies. showed that misconnected impervious areas expected from discharge vs rainfall regression were not conflnned by smoke testing: indeed. on average only one third of so-called "active" surfaces could be identified (Balas & Ruperd. 1993). This may be caused by inputs. which are actually infiltration. but highly temporary and variable along with time. They depend not only on rainfall intensity. but also on underground water level and soil moisture in the vicinity of sewer pipes. They may in some cases react to rainfall in a very similar way as inflow. As a matter of fact. rainfall induced infiltration has been cited since the very beginning of sewer evaluation studies. But it is still seldom addressed specifically (Joannis. 1993). So we tried to learn a bit more about it through field measurements. and developed a model which can help to deal with that kind of input. EXPERIMENTAL STUDY Two small catchments (a few hectares). serviced by separate sewer systems and displaying homogeneous types of urbanization were chosen for experimentation. and provided with facilities to measure rainfall. flowrates in the sewer pipes. and hydraulic potentials in soil (either under green areas or pavement). A nearby meteorological station supplied data for evapotranspiration rates. One of the two sites under investigation. which is the premises of our laboratory (LCPC) is rather rural. with the major part of the sewerage laid under green areas. and fitted with very few connection lines. The other catchment (REZE) is typically a suburban residential estate, with sewerage laid under pavement, and many connections to private properties. Indeed our first site is a bit special. but very well suited to the study of infiltration: we checked that it was free from inflows. and even foulwater is rather scarce. so that infiltration can be observed in its "genuine" state. unspoiled by other inputs. We used 16 months of hourly recordings on that site to get a good view of the variability and magnitude of infiltrations. as well as some insights into processes which might be implied (Breil. 1990). The same data were then used to develop a model. the perfonnances of which have been checked with data coming from the other site. Table I. An example of magnitude of infiltration and other components of discharge collected by sewerage Infiltration
foul water
Storm water (imperviousness ratio 40%) 83
40
SS
0.46
0.22
0.18
1.43 ( 18 mm/d)
0.036
0.024
0.025
0.2 ( 2.5 mm/h)
typical values yearly volume (m3/hab) Q95 daily volume (m3/i/inhab,\ Q99 ~~nrlv vnlnmr. m3/hlinhab.\
Innow (inappropriate connexion of 5% of total catchment area) 10.4
Table I provides some figures which allow us to compare infiltration flowrates (either rainfall induced or not) with foulwllter flows, and typical inflows. and even with total storm water which can be collected on an urban catchment. For that purpose. we used data from LCPC as far as infiltration is concerned. but we combined them with synthesized data for foulwater. inflows and storm water. in order to correct the special
Rainfall induced infiltration Imo separate sewerage
163
features of the site. The figures encompass time scales ranging from one hour to one year. For the shorter time scales, we chose as references the values for Qj9S (daily flowrate not exceeded more than 18 days a year) and Qb99 (hourly flowrate not exceeded more than 82 hours a year). For these timescales, infiltration displays flowrates higher than foul water peak flows, but still much lower than regular storm water. They are however significantly higher than typical inflows, especially on a daily basis. DEVELOPMENT OF A MODEL (BELHADJ, 1994) We intended to develop a model which could simulate infiltration, and especially its behaviour related to rainfall. according to the following objectives: - to provide a means to analyse data from the field, basically to allow dependable identification and quantification of different components contributing to the total discharge. One can see that this objective is related to the evaluation tasks; - to provide a means to extrapolate results coming from measurements conducted over a fairly short period (typically a few weeks) to a variety of hydrological conditions. For instance it can be interesting to quantify infiltration over a year, under standardized hydrological conditions. This is useful for evaluation purposes, but also for designing and dimensioning new facilities (transport. storage. treatment) which could cope with present flowrates. This may be used for actual projects. when it is not practically sound to reduce extraneous inputs, or as a reference for economic calculations; - if possible. to provide a means to forecast the effects of rehabilitation works on the discharges which are to be expected in the future. For these objectives, the kind of conceptual models which is classically used by hydrologists seemed to be suitable. especially for the second one: indeed the first and third objectives need to give some kind of physical meaning to the features of the model. Methods and criteria used to calibrate the model The process used for the development of the model was to start from an initial simple version, and to explore the ways by which it could be improved, according to the results yielded. For that purpose. we had to choose criteria to assess the "fitness" of the model. and to measure the improvements introduced by modification and sophistication of successive releases. For our needs. we extensively used the classical Nash criterion that is complementary to one of the ratio between the sum of squared differences between measured and simulated values. and the variancy of measured values. This criterion is often expressed as a percentage, and is an evaluation for a good reproduction of flowrates. including their distribution over time. The same criterion was used for automated calibration of the parameters of the different issues of the model. Indeed it was important to use an objective method to calibrate the models in order to compare them. This was best achieved with the methods of simplex. which has been shown by experience to be more efficient than Rosenbrock's method. During the first step of model development, we used all the available data to calibrate the parameters, and compare the results of different model structures. Once the best structure was identified, we took a second step, during which we investigated wether the model could be calibrated with less data. and how it succeeded in sim ulating data not included in the calibration process. Buildjnf: of the mode! The building of our model started from a modification of a former model. GR2. developed by CEMAGREF (Technical Centre for Agriculture) to simulate runoff on rural catchments (Edijatno. 1991). This model features two reservoirs, and 3 parameters. and operates on a one-hour time-step. The first reservoir is called
N. BELHADJ er al.
164
the production reservoir. and provides an efficiency factor for gross rainfall. It integrates several processes involved in losses affecting rainfall which reach ground level ( interception. evapotranspiration. surface storage... ). and provides an estimation of the depth of rainwater which will actually contribute to the discharge at the outfall of the sewer network. The second reservoir, which is called the transfer reservoir. processes net rainfall intensity into a properly shaped hydrograph. Results given by this fIrst model showed that it could not display all the dynamic behaviour of real infIltration: all versions underestimated peak flows. and overestimated recession rates. A close examination of discharge curves suggests that infIltration is the sum of two components one of them is rapidly responding to rainfall. the other one is more damped. So we searched for a model structure with two outputs. Finally, the best configuration is pictured in Fig.l. This model has two inputs: rainfall and evapotranspiration. and two outputs "slow" infUtration and "fast" infIltration. These are expressed as mmlh. so one has to multiply them by a scale factor. Sac. with the units of a surface area. Production function is managed by the level in the production reservoir. and involves two parameters a and b. Repartition of efficient rainfall between the two transfer reservoirs is controlled by the level in reservoir S (Slow) and parameter c. Finally both components of drainage discharge are calculated from the levels in each transfer reservoir by means of a quadratic law. using parameters Smax and Fmax.
Rg (gross rainfall)
J,
Rn (net rainfall) En
(l-k).Rn
i L---]
Re = k.Rn
(efficient rainfall)
k =1/11+exp(a-b,P»)
L
kl.Re
(l-kl).Re
kl = SIc
P (production)
D S(Slow~ 1-
D J F(Fast)
q 1=Sac*IS I(S+Smax»)
q2=Sac*IF I(F+Fmax))
Figure I. Best model structure.
O.O~::::::I::f.;t::::::::::::::::::~~:::::::}]F:::::I::::::I~:lr:I:::::rli:T~~~#:::::::::::::;::::::\:::~ ~:: ~-................................. . ..................................................................................................
10 A
20 .0 110.0
................................................ : ..................... : ............
..
. ..:::: ........................ ...
~~iri;6ii i~~i6h):::::::::::: ~~ ~~ ~ ~~~ ~~ ~~~ ~~ ~~ ~~~:~~~ ~~ ~ ~ ~~~ ~~~~ ~~ ~ ~~~~~~~:~~~ ~~::~~~ ~ ~ ~~~~~~::~~ ~ .. ~~~~~~~. ~~~~~~:~~~ ~~ ~ ~~~~~~~ ~~ ~ ~ ~~~~~~~~~ ~~: d~cnarg.
(m3/h)
20.0 10.0
10
-
NOV
ZD
....
'meuured'totalln',ltrallOn
10
20
DEC
10
JAN
•••• .lmulal8d 1D1al1n',ltralion
20
ao
10
FEI
20
CJ .imulal8d .Iow component
Figure 2. Simulated and measured infiltration !lowrates on LCPC site (6-bour time·step).
0' Infiltration
Rainfall Induced Infiltration Into separate sewerage
165
As we can see in Fig. 2, results are fairly satisfying for the site of LCPC. The Nash criterion is about 90% for the whole simulated period. BEHAVIOUR OF THE MODEL Calibration periods and validation results Once a model structure had been chosen, we used only a part of the available measured data to calibrate the model, and checked the quality of simulation on the remaining data, which were then used for validation purposes. So we could investigate the influence of calibration period on model efficiency. We used calibration periods varying in length between 3 and 12 months, which of course included neither the same hydrological conditions, nor the same quantity of information. Table 2 shows that the time length of the calibration period is not the most important feature for the quality of simulation: good results have been obtained with fairly short calibration periods, provided these are representative of discharge variability. This occurs especially in winter. Moreover, a longer calibration period does necessarily mean a better quality for simulation, either during the calibration period or the validation period. Indeed, a calibration period including autumn, when drainage is starting again after a much less productive season. does provide poor results. A more typical calibration period is to be preferred as far as infiltration is concerned. But summer measurements are useful too, to calibrate inputs from inflows. So measurements over one year are the most suitable way to deal with all aspects of wastewater collection. Table 2. Effects of calibration period on model efficiency Validation period
Calibration period
Whole period
time-length NASH(%) time-length NASH(%) NASH(%)
N°
Dates
I
18/09 - 18/12187
3 months
70,1
13 months
58,7
62,9
2
18/12187 - 18/03/88
3 months
93,7
13 months
84,S
89,8
3
18/03/87- 18/09/87
6 months
89,6
10 months
80,2
84,3
4
18/03/87 - 18/12187
81,S
7 months
66,S
69,1
9 months
Sensitivity and interrelationships between parameters The sensitivity of the model to the values of each parameter is an interesting feature for model calibration. To investigate this sensitivity we used as references the highest value of criterion and the corresponding set of parameters from the calibration process. In the fltst step, the optimum value of each parameter has been changed in tum by a fixed proportion, and corresponding new values for adjustment criterion have been calculated. This showed that for total discharge. production parameters (a and b) were the most influential. Transfer parameters (Smax, Fmax and c) had some influence on the distribution of total discharge between slow and fast components. Of course Sac is a very sensitive parameter, as all outputs are directly proportional to its value (see Fig. 3).
In a second step, we calibrated the model again by tuning either one. or all parameters but the one which had been shifted during the fltst step. This gave an indication of the interrelationships between parameters, and the possibility to achieve some kind of predetermination of parameter sets suited for one or another field situation. It appeared that parameters were quite dependent on one another, and that a shift in one parameter
N. BELHADJ
166
el
al.
could be fairly well compensated by an appropriate re-tuning of the other ones. This could apply even to "contributing surface" Sac, which can be compensated by a and b. So it seems difficult to derive typical values for each parameter in a given situation, as several sets may be convenient, and one or another of them can be selected by a calibration process. Moreover, we observed in some cases that two sets of parameter values could produce nearly the same output for total discharge, whereas its distribution between its two components was different (for instance 40%/60% vs 60%/40% on a yearly basis). This may limit the potential use of the model as a tool for analysing measured data.
value of NASH criterion 100
(%)
politivo IIIift
• reference - - optimum without porturbolioo
b
Smox
Fomx
So.
Shift 01 the value of one parameter: ~
_
without recalibration of other parameters after recalibration of other parameters
Figure 3. Sensitivity of the model to variations in parameter values and compensation effects among parameters.
APPLICATION OF THE MODEL ON THE SITE OF REZE As mentioned above. flowrates on this site are much better balanced between foul water and infiltration than for LCPC. Besides these two contributions. we discovered a few inappropriate connections of runoff water. thus the calibration of a model for infiltration needed first an extraction of infiltration flowrates from total discharge measurements. To achieve this, we used rainfall events occurring during the dry season to get an accurate estimation of impervious areas improperly connected to wastewater sewerage. Hourly runoff flowrates were then calculated for all rainfall events by the very simple "rational" formula. For foulwater flowrates, we tried to derive typical 24-hour patterns from measurements during dry periods. and used these patterns over the whole period. Infiltration records show a behaviour similar to LCPC. although the configuration of the site is quite different: variable flowrates. which are rather large when compared with foul water on a yearly basis, and depending on rainfall event~ and on seasons. Some evidence exist~ that pavements are fairly pervious, and that the superposition of different pavement layers may be important to accumulate infiltration water and convey it towards the trench into which sewer pipes were laid (Raimbault and Sylvestre, 1990). As can be seen in Fig. 4, the model previously developed provided good results, as infiltration flowrates calculated from rainfall and evapotranspiration alone closely follow the minima of total measured discharge. the difference coming from the foul water daily pattern. On that site, dynamic behaviour of infiltration seems to be more damped than on the LCpc site. As a comparison we give a curve for "extrapolated" runoff misconnection. These data come from a separate storm sewer on the same site, which has been monitored during the same period. A ratio has been applied to rough data, because the limits of the catchment are not the same, and because misconnection is only a rather small part of total runoff. It appears that during the very wet period under consideration, infiltration peak flows were quite similar to those for misconnected runoff. But volumes are much more important. This may be surprising, as infiltration should concern
Rainfall induced infiltration into separate sewerage
167
stonnwater pipes as well. Indeed foulwater pipes are laid a little deeper than stonnwater pipes. but the difference is small. The main reason for such different behaviour may be that wastewater from houses is connected to public sewerage by the means of regular connection lines. whereas runoff is lead to gullies along sidewalks: connection lines might well be responsible for much infiltration.
REZE 1/12/93 -28/2/94
days - - typical runoff connections (extrapolated)
simulated infiltration
- - - - total discharge (measured)
Figure 4. Simulated and measured infiltration flowrates on Rezc site (I bour lime-step). compared willl total discbarge and typical runoff misconnection.
CONCLUSION Monitoring of two sites showed that infiltration can display very dynamic behaviour. and that their contribution to total discharge at the output of a separate foul water sewerage can be important, even on an hourly basis. By the means of classical hydrological modelling. we succeeded in building a model which is able to simulate infiltration and its relationships with rainfalls and seasons. It seems that the calibration of this model can be achieved with a limited amount of measured data. provided they include significant events and hydrological situations: one regular year must be sufficient. Compensation effects between parameters put some limitations on the use of the model as a tool for detailed sewer evaluation: indeed it can provide an overall quantification of infiltration under standard conditions. but the distribution between slow and fast components is questionable. So more investigations are needed about the different types and locations of infiltration processes. and about the effects of rehabilitation techniques. but in its present state. the model can be used to design facilities. which can cope with observed flowrates. ACKNOWLEDGEMENT This study has been funded by the French Ministry of the Environment. REFERENCES Belbadj. N. (1994). Variations par temps de pluie des debits dans les reseaux d'eaux "sies de type separatl/: Identification des composantes et model/sation des illfiltrations. Tb~se de Doctoral, ENPC. 289 p.
N. BELHADJ el aI.
168
Breil, P. (1990). Drainage des eaux claires parasites par les riseaux sarntaires. Micanismes et approche quantitative. 1b~se de Doctoral, L. H. M. Montpelliec n, 311 p. Edijatno (1990). Mise au point d'un modele eUmentaire pluie-dibit au pas de temps journa/ier. Th~ de Doctoral, Univcrsi~ Louis Pasteur, Strasbourg, 242 p. Joannis, C. (1993). Les etudes diagnostic de riseaux d'ossainissement: analyse retrospective et propositions. EllIdes et Recherches des Laboratoires des Poots et Chaus~es, S&ie Environoement et ~nie Urbain, 009, 132 p. Raimbaull, G. and Sylvestre, P. (1990)_ Analyse des variations d'~tat hydJique dans 1es cbaus*s. BulL Liaison Labo P. et Cia. 167
mai-juin.
Rancbet J., Renard, D. and Vicq, A. (1982). Analyse et d~tection des eaux parasites dans les reseaux d'assainissemenl TSM de l'Eau. 4,173-183. Balas, E. and Rupecd, Y. (1993). Les contr61es de branchement au riseau d'/gouts par tests d lafumee, Etudes et Rechercbes des Laboratoires des Poots et Chauss~s, S&ie Eoviroooement et G~oie Urbain, EG8, SO p.
Pergamon
W.". ScL T.c1t. Vol. 32, No. I. pp. 161-168, 1995. Copyri,bIOI995IAWQ
0273-1223(95)0055 I-X
Prinled iD Oreal Britain. All ri,hll reoervod. 0273-1223195 $9'50 + 000
MODELLING OF RAINFALL INDUCED INFILTRATION INTO SEPARATE SEWERAGE N. Belhadj, C. Joannis and G. Raimbault Laboratoire Central des Pants et Chaussees, Centre de Nantes, Division Eau. BP 19, 44340 Bouguenais, France
ABSTRACT Aowrate changes in separate wastewater sewerage during wet weather are often attributed to inappropriate connections of runoff water. But these inputs are not the only cause of such behaViour and infiltration through leaking defects or cracks can supply large flows inlD collection pipes. The characterization of these flows is not an easy task since they involve complex processes, depending not only on rainfall events but also on hydrological conditions and seasons. Using 16 months of hourly measurements of rainfall and f10wrates, we developed a six parameter conceptual model to simulate rainfall induced infiltration into a smaIl sewer system. Sensitivity analysis applied ID the proposed model showed good achievements under various calibration conditions but displayed higb parameter interacbons whicb may be a serious drawback for some specific model uses. Model application ID another sewer network Yielded good agreement between observed and simulated flows. The suitability of this model must be further checked on other sites.
KEYWORDS
Drainage; infiltration/inflow; mathematical model; sewer evaluation study. INTRODUCTION Urban storm drainage is a concern not only in combined sewer systems. or separate storm water sewers: separate foul water sewerage also displays special behaviour during rainy periods. Indeed large inputs from inflltration nnd inflow very often cause some trouble for the collection and treatment of wastewater. The two kinds of "extraneous water" quoted above are very different as regards their behaviour nnd their effects. as well as their location in the sewer system nnd the solution which cnn be used to fix them. or to cope with them. - Inflow comes from inappropriate connection of impervious areas to the foul water collecting pipes. It displays high peak flows. directly related to rainfall events. - lnflltration comes from groundwater. seeping into sewerage through cracks. untight joints. and other defects. Its flowrate is supposed to change rather slowly. according to seasonal variations of groundwater levels.
161
N. BELHAD] el al.
162
To address these problems. sewer evaluation studies have been conducted in France for more than fifteen years. They aim to quantify and locate the two kinds of inputs quoted above. so that an assessment can be made about their consequences on sewerage and receiving waters. and solutions be proposed (Ranchet et al. 1982). But some results provide clear evidence for a third kind of extraneous water, somewhat intermediate between infiltration and inflow: that is rainfall induced infiltration. For instance. a survey conducted over 100 catchments investigated during sewer evaluation studies. showed that misconnected impervious areas expected from discharge vs rainfall regression were not conflnned by smoke testing: indeed. on average only one third of so-called "active" surfaces could be identified (Balas & Ruperd. 1993). This may be caused by inputs. which are actually infiltration. but highly temporary and variable along with time. They depend not only on rainfall intensity. but also on underground water level and soil moisture in the vicinity of sewer pipes. They may in some cases react to rainfall in a very similar way as inflow. As a matter of fact. rainfall induced infiltration has been cited since the very beginning of sewer evaluation studies. But it is still seldom addressed specifically (Joannis. 1993). So we tried to learn a bit more about it through field measurements. and developed a model which can help to deal with that kind of input. EXPERIMENTAL STUDY Two small catchments (a few hectares). serviced by separate sewer systems and displaying homogeneous types of urbanization were chosen for experimentation. and provided with facilities to measure rainfall. flowrates in the sewer pipes. and hydraulic potentials in soil (either under green areas or pavement). A nearby meteorological station supplied data for evapotranspiration rates. One of the two sites under investigation. which is the premises of our laboratory (LCPC) is rather rural. with the major part of the sewerage laid under green areas. and fitted with very few connection lines. The other catchment (REZE) is typically a suburban residential estate, with sewerage laid under pavement, and many connections to private properties. Indeed our first site is a bit special. but very well suited to the study of infiltration: we checked that it was free from inflows. and even foulwater is rather scarce. so that infiltration can be observed in its "genuine" state. unspoiled by other inputs. We used 16 months of hourly recordings on that site to get a good view of the variability and magnitude of infiltrations. as well as some insights into processes which might be implied (Breil. 1990). The same data were then used to develop a model. the perfonnances of which have been checked with data coming from the other site. Table I. An example of magnitude of infiltration and other components of discharge collected by sewerage Infiltration
foul water
Storm water (imperviousness ratio 40%) 83
40
SS
0.46
0.22
0.18
1.43 ( 18 mm/d)
0.036
0.024
0.025
0.2 ( 2.5 mm/h)
typical values yearly volume (m3/hab) Q95 daily volume (m3/i/inhab,\ Q99 ~~nrlv vnlnmr. m3/hlinhab.\
Innow (inappropriate connexion of 5% of total catchment area) 10.4
Table I provides some figures which allow us to compare infiltration flowrates (either rainfall induced or not) with foulwllter flows, and typical inflows. and even with total storm water which can be collected on an urban catchment. For that purpose. we used data from LCPC as far as infiltration is concerned. but we combined them with synthesized data for foulwater. inflows and storm water. in order to correct the special
Rainfall induced infiltration Imo separate sewerage
163
features of the site. The figures encompass time scales ranging from one hour to one year. For the shorter time scales, we chose as references the values for Qj9S (daily flowrate not exceeded more than 18 days a year) and Qb99 (hourly flowrate not exceeded more than 82 hours a year). For these timescales, infiltration displays flowrates higher than foul water peak flows, but still much lower than regular storm water. They are however significantly higher than typical inflows, especially on a daily basis. DEVELOPMENT OF A MODEL (BELHADJ, 1994) We intended to develop a model which could simulate infiltration, and especially its behaviour related to rainfall. according to the following objectives: - to provide a means to analyse data from the field, basically to allow dependable identification and quantification of different components contributing to the total discharge. One can see that this objective is related to the evaluation tasks; - to provide a means to extrapolate results coming from measurements conducted over a fairly short period (typically a few weeks) to a variety of hydrological conditions. For instance it can be interesting to quantify infiltration over a year, under standardized hydrological conditions. This is useful for evaluation purposes, but also for designing and dimensioning new facilities (transport. storage. treatment) which could cope with present flowrates. This may be used for actual projects. when it is not practically sound to reduce extraneous inputs, or as a reference for economic calculations; - if possible. to provide a means to forecast the effects of rehabilitation works on the discharges which are to be expected in the future. For these objectives, the kind of conceptual models which is classically used by hydrologists seemed to be suitable. especially for the second one: indeed the first and third objectives need to give some kind of physical meaning to the features of the model. Methods and criteria used to calibrate the model The process used for the development of the model was to start from an initial simple version, and to explore the ways by which it could be improved, according to the results yielded. For that purpose. we had to choose criteria to assess the "fitness" of the model. and to measure the improvements introduced by modification and sophistication of successive releases. For our needs. we extensively used the classical Nash criterion that is complementary to one of the ratio between the sum of squared differences between measured and simulated values. and the variancy of measured values. This criterion is often expressed as a percentage, and is an evaluation for a good reproduction of flowrates. including their distribution over time. The same criterion was used for automated calibration of the parameters of the different issues of the model. Indeed it was important to use an objective method to calibrate the models in order to compare them. This was best achieved with the methods of simplex. which has been shown by experience to be more efficient than Rosenbrock's method. During the first step of model development, we used all the available data to calibrate the parameters, and compare the results of different model structures. Once the best structure was identified, we took a second step, during which we investigated wether the model could be calibrated with less data. and how it succeeded in sim ulating data not included in the calibration process. Buildjnf: of the mode! The building of our model started from a modification of a former model. GR2. developed by CEMAGREF (Technical Centre for Agriculture) to simulate runoff on rural catchments (Edijatno. 1991). This model features two reservoirs, and 3 parameters. and operates on a one-hour time-step. The first reservoir is called
N. BELHADJ er al.
164
the production reservoir. and provides an efficiency factor for gross rainfall. It integrates several processes involved in losses affecting rainfall which reach ground level ( interception. evapotranspiration. surface storage... ). and provides an estimation of the depth of rainwater which will actually contribute to the discharge at the outfall of the sewer network. The second reservoir, which is called the transfer reservoir. processes net rainfall intensity into a properly shaped hydrograph. Results given by this fIrst model showed that it could not display all the dynamic behaviour of real infIltration: all versions underestimated peak flows. and overestimated recession rates. A close examination of discharge curves suggests that infIltration is the sum of two components one of them is rapidly responding to rainfall. the other one is more damped. So we searched for a model structure with two outputs. Finally, the best configuration is pictured in Fig.l. This model has two inputs: rainfall and evapotranspiration. and two outputs "slow" infUtration and "fast" infIltration. These are expressed as mmlh. so one has to multiply them by a scale factor. Sac. with the units of a surface area. Production function is managed by the level in the production reservoir. and involves two parameters a and b. Repartition of efficient rainfall between the two transfer reservoirs is controlled by the level in reservoir S (Slow) and parameter c. Finally both components of drainage discharge are calculated from the levels in each transfer reservoir by means of a quadratic law. using parameters Smax and Fmax.
Rg (gross rainfall)
J,
Rn (net rainfall) En
(l-k).Rn
i L---]
Re = k.Rn
(efficient rainfall)
k =1/11+exp(a-b,P»)
L
kl.Re
(l-kl).Re
kl = SIc
P (production)
D S(Slow~ 1-
D J F(Fast)
q 1=Sac*IS I(S+Smax»)
q2=Sac*IF I(F+Fmax))
Figure I. Best model structure.
O.O~::::::I::f.;t::::::::::::::::::~~:::::::}]F:::::I::::::I~:lr:I:::::rli:T~~~#:::::::::::::;::::::\:::~ ~:: ~-................................. . ..................................................................................................
10 A
20 .0 110.0
................................................ : ..................... : ............
..
. ..:::: ........................ ...
~~iri;6ii i~~i6h):::::::::::: ~~ ~~ ~ ~~~ ~~ ~~~ ~~ ~~ ~~~:~~~ ~~ ~ ~ ~~~ ~~~~ ~~ ~ ~~~~~~~:~~~ ~~::~~~ ~ ~ ~~~~~~::~~ ~ .. ~~~~~~~. ~~~~~~:~~~ ~~ ~ ~~~~~~~ ~~ ~ ~ ~~~~~~~~~ ~~: d~cnarg.
(m3/h)
20.0 10.0
10
-
NOV
ZD
....
'meuured'totalln',ltrallOn
10
20
DEC
10
JAN
•••• .lmulal8d 1D1al1n',ltralion
20
ao
10
FEI
20
CJ .imulal8d .Iow component
Figure 2. Simulated and measured infiltration !lowrates on LCPC site (6-bour time·step).
0' Infiltration
Rainfall Induced Infiltration Into separate sewerage
165
As we can see in Fig. 2, results are fairly satisfying for the site of LCPC. The Nash criterion is about 90% for the whole simulated period. BEHAVIOUR OF THE MODEL Calibration periods and validation results Once a model structure had been chosen, we used only a part of the available measured data to calibrate the model, and checked the quality of simulation on the remaining data, which were then used for validation purposes. So we could investigate the influence of calibration period on model efficiency. We used calibration periods varying in length between 3 and 12 months, which of course included neither the same hydrological conditions, nor the same quantity of information. Table 2 shows that the time length of the calibration period is not the most important feature for the quality of simulation: good results have been obtained with fairly short calibration periods, provided these are representative of discharge variability. This occurs especially in winter. Moreover, a longer calibration period does necessarily mean a better quality for simulation, either during the calibration period or the validation period. Indeed, a calibration period including autumn, when drainage is starting again after a much less productive season. does provide poor results. A more typical calibration period is to be preferred as far as infiltration is concerned. But summer measurements are useful too, to calibrate inputs from inflows. So measurements over one year are the most suitable way to deal with all aspects of wastewater collection. Table 2. Effects of calibration period on model efficiency Validation period
Calibration period
Whole period
time-length NASH(%) time-length NASH(%) NASH(%)
N°
Dates
I
18/09 - 18/12187
3 months
70,1
13 months
58,7
62,9
2
18/12187 - 18/03/88
3 months
93,7
13 months
84,S
89,8
3
18/03/87- 18/09/87
6 months
89,6
10 months
80,2
84,3
4
18/03/87 - 18/12187
81,S
7 months
66,S
69,1
9 months
Sensitivity and interrelationships between parameters The sensitivity of the model to the values of each parameter is an interesting feature for model calibration. To investigate this sensitivity we used as references the highest value of criterion and the corresponding set of parameters from the calibration process. In the fltst step, the optimum value of each parameter has been changed in tum by a fixed proportion, and corresponding new values for adjustment criterion have been calculated. This showed that for total discharge. production parameters (a and b) were the most influential. Transfer parameters (Smax, Fmax and c) had some influence on the distribution of total discharge between slow and fast components. Of course Sac is a very sensitive parameter, as all outputs are directly proportional to its value (see Fig. 3).
In a second step, we calibrated the model again by tuning either one. or all parameters but the one which had been shifted during the fltst step. This gave an indication of the interrelationships between parameters, and the possibility to achieve some kind of predetermination of parameter sets suited for one or another field situation. It appeared that parameters were quite dependent on one another, and that a shift in one parameter
N. BELHADJ
166
el
al.
could be fairly well compensated by an appropriate re-tuning of the other ones. This could apply even to "contributing surface" Sac, which can be compensated by a and b. So it seems difficult to derive typical values for each parameter in a given situation, as several sets may be convenient, and one or another of them can be selected by a calibration process. Moreover, we observed in some cases that two sets of parameter values could produce nearly the same output for total discharge, whereas its distribution between its two components was different (for instance 40%/60% vs 60%/40% on a yearly basis). This may limit the potential use of the model as a tool for analysing measured data.
value of NASH criterion 100
(%)
politivo IIIift
• reference - - optimum without porturbolioo
b
Smox
Fomx
So.
Shift 01 the value of one parameter: ~
_
without recalibration of other parameters after recalibration of other parameters
Figure 3. Sensitivity of the model to variations in parameter values and compensation effects among parameters.
APPLICATION OF THE MODEL ON THE SITE OF REZE As mentioned above. flowrates on this site are much better balanced between foul water and infiltration than for LCPC. Besides these two contributions. we discovered a few inappropriate connections of runoff water. thus the calibration of a model for infiltration needed first an extraction of infiltration flowrates from total discharge measurements. To achieve this, we used rainfall events occurring during the dry season to get an accurate estimation of impervious areas improperly connected to wastewater sewerage. Hourly runoff flowrates were then calculated for all rainfall events by the very simple "rational" formula. For foulwater flowrates, we tried to derive typical 24-hour patterns from measurements during dry periods. and used these patterns over the whole period. Infiltration records show a behaviour similar to LCPC. although the configuration of the site is quite different: variable flowrates. which are rather large when compared with foul water on a yearly basis, and depending on rainfall event~ and on seasons. Some evidence exist~ that pavements are fairly pervious, and that the superposition of different pavement layers may be important to accumulate infiltration water and convey it towards the trench into which sewer pipes were laid (Raimbault and Sylvestre, 1990). As can be seen in Fig. 4, the model previously developed provided good results, as infiltration flowrates calculated from rainfall and evapotranspiration alone closely follow the minima of total measured discharge. the difference coming from the foul water daily pattern. On that site, dynamic behaviour of infiltration seems to be more damped than on the LCpc site. As a comparison we give a curve for "extrapolated" runoff misconnection. These data come from a separate storm sewer on the same site, which has been monitored during the same period. A ratio has been applied to rough data, because the limits of the catchment are not the same, and because misconnection is only a rather small part of total runoff. It appears that during the very wet period under consideration, infiltration peak flows were quite similar to those for misconnected runoff. But volumes are much more important. This may be surprising, as infiltration should concern
Rainfall induced infiltration into separate sewerage
167
stonnwater pipes as well. Indeed foulwater pipes are laid a little deeper than stonnwater pipes. but the difference is small. The main reason for such different behaviour may be that wastewater from houses is connected to public sewerage by the means of regular connection lines. whereas runoff is lead to gullies along sidewalks: connection lines might well be responsible for much infiltration.
REZE 1/12/93 -28/2/94
days - - typical runoff connections (extrapolated)
simulated infiltration
- - - - total discharge (measured)
Figure 4. Simulated and measured infiltration flowrates on Rezc site (I bour lime-step). compared willl total discbarge and typical runoff misconnection.
CONCLUSION Monitoring of two sites showed that infiltration can display very dynamic behaviour. and that their contribution to total discharge at the output of a separate foul water sewerage can be important, even on an hourly basis. By the means of classical hydrological modelling. we succeeded in building a model which is able to simulate infiltration and its relationships with rainfalls and seasons. It seems that the calibration of this model can be achieved with a limited amount of measured data. provided they include significant events and hydrological situations: one regular year must be sufficient. Compensation effects between parameters put some limitations on the use of the model as a tool for detailed sewer evaluation: indeed it can provide an overall quantification of infiltration under standard conditions. but the distribution between slow and fast components is questionable. So more investigations are needed about the different types and locations of infiltration processes. and about the effects of rehabilitation techniques. but in its present state. the model can be used to design facilities. which can cope with observed flowrates. ACKNOWLEDGEMENT This study has been funded by the French Ministry of the Environment. REFERENCES Belbadj. N. (1994). Variations par temps de pluie des debits dans les reseaux d'eaux "sies de type separatl/: Identification des composantes et model/sation des illfiltrations. Tb~se de Doctoral, ENPC. 289 p.
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Breil, P. (1990). Drainage des eaux claires parasites par les riseaux sarntaires. Micanismes et approche quantitative. 1b~se de Doctoral, L. H. M. Montpelliec n, 311 p. Edijatno (1990). Mise au point d'un modele eUmentaire pluie-dibit au pas de temps journa/ier. Th~ de Doctoral, Univcrsi~ Louis Pasteur, Strasbourg, 242 p. Joannis, C. (1993). Les etudes diagnostic de riseaux d'ossainissement: analyse retrospective et propositions. EllIdes et Recherches des Laboratoires des Poots et Chaus~es, S&ie Environoement et ~nie Urbain, 009, 132 p. Raimbaull, G. and Sylvestre, P. (1990)_ Analyse des variations d'~tat hydJique dans 1es cbaus*s. BulL Liaison Labo P. et Cia. 167
mai-juin.
Rancbet J., Renard, D. and Vicq, A. (1982). Analyse et d~tection des eaux parasites dans les reseaux d'assainissemenl TSM de l'Eau. 4,173-183. Balas, E. and Rupecd, Y. (1993). Les contr61es de branchement au riseau d'/gouts par tests d lafumee, Etudes et Rechercbes des Laboratoires des Poots et Chauss~s, S&ie Eoviroooement et G~oie Urbain, EG8, SO p.