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Wat. Sci. Tecla. VDI. 31.ND.I. pp. 209-215.1995. Copyriabt 11:1 1995 IA WQ

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SPACE-TIME HETEROGENEITIES OF RAINFALLS ON RUNOFF OVER URBAN CATCHMENTS

Christian ROllX,* Anne Guillon** and Anne Comblez* • Centre d'Enseignement et de Recherche sur la Gestion des Ressources Naturelles et de l'Environnemen4 &ole Nationale des Ponts et Chaussees, La Courtine, 93167 Noisy-Ie-Grand Cedex, France •• Conseil General de Seine-Saint-Denis, Direction de I'Eau et de l'Assainissement, 199. avo de Generale de Gaul/e, 93110 Rosny-s/s-Bois Cedex, France

ABSTRACT

Simulated outlet flow series are compared downstream of a 14 sq. km. urban watershed. They are aenerated either with design rainfall, with long-term point rainfall series. or with long-term space distributed rainfall series (measured with 3 raingauges or with radar). The use of the double-triangle shaped byelOgrapb as design rainfall provides the same T-year flow as the long term 3 raingauge series. if it is used with a areal reduction factor and uniformly applied 10 the watershed. For the same T-year mean areal precipitation depth during the time of concentration, the rainfall spatial and temporal beterOgenities may induce differences up 10 +/- 30% on the peak flow, compared 10 the T-year peak flow.

KEYWORDS

Hyetograph shape: long-term series: peak-flow: rainfall: spatial heterogeneity: urban hydrology.

INTRODUcnON

Sewer networks are designed. in France, to provide protection against events of a given return period. This event can be a water level. a peak flow. a hydrograph volume. a discharge. etc. In practice. as runoff measurements are scarcely available. they are estimated with a rainfall-runoff model.

Regarding the T-year watershed peal flow. it is often considered as the result of a T-year rainfall for a duration equivalent to the watershed time of concentration. This rainfall is represented by point hyetograph. sometimes reduced by an areal reduction factor (ARP) or a storm reduction factor (SRF).

Brunelle (1991) has shown by simulations of theoretical rainfalls on a 240 ha catchment that for the same mean areal rainfall. spatial heterogeneity induces deviations up to ± 10-20% on peak flow estimated. Blanchet (1993) obtained similar results on the same watershed. but with real rainfalls. Niemczynowicz (1988). studying the rainfall space-time distribution on a small urban catchment, reaches the conclusion that not only the space-time repartition is important but also the rainfall movement.

209

210 C. ROUX tt al.

The main purpose of this work is to study, using a real case, the effects of space-time heterogeneities of the T-year rainfalls on the T-year peak flow estimates. A long term series of peak flows is generated, other things being equal (initial conditions, system parameters, etc.), by means of a long term series of rainfall data and a sewer network model. Relations between these variables are described and results are compared with those of the double-triangle shaped design hyetograph (Desbordes et al., 1976) which is often used in France.

We discuss firstly the methodology, secondly the data being used and, finally, the main results from which conclusions and prospects are drawn.

METHODOLOGY

This work is based on a dense rainguage network associated for several years with a meteorological radar, allowing the spatial distribution of rainfall to be estimated. The sewer network is modelled with CEDRE, the urban rainfall-runoff model developed by the "Laboratoire Methodes" of INSA, LYON.

Rainfall-runoff simulations on the watershed

The simulations are performed with four sets of data:

- point rainfall long-term series; - three rainguage long-term series; - radar measured rainfall series; - design hyetograph (double triangle shaped).

The point rainfall data are those observed on each rainguage being used for the three rainguage simulations (same raingauges and same events). They are uniformly applied to the whole watershed area. The Thiessen polygons are employed for the three rainguage simulations: each sub-watershed receives the rainfall measured on the nearest raingauge. Radar data only used for a comparison purpose as the available sample remains short regarding the number of strong events.

Data processinl:

For each simulation set, the outlet peak flow is compared with the maximum 60-minute-mean rainfall intensity. In this way, for the same mean rainfall depth over the watershed area during its time of concentration (60 minutes), one can observe the peak flow variability induced firstly, by the time distribution of the hyetographs (case of one raingauge rainfall being uniformly applied to the watershed area) and secondly, by the time-space distribution of the rainfalls (case of three raingauge and radar rainfalls).

For each simulation set, peak flow series and maximum 60-minute-mean rainfall intensity series are sorted in a descending order. In these two sorted series, observations of the same rank have the same empirical return period (plotting pOSition). In this way, one can estimate peak flows of the same return period as the rainfalls which allows the assessment of the relationship existing between the point rainfalls, the areally distributed rainfalls and the peak flows (see Fig. I).

THE DATA

The rainfall data

Rainfall data are those from the dense raingauge network of Seine-Denis County (just east from Paris) and from the RODIN-type Radar of Trappes, managed by the national meteorological office (Meteo-France) and calibrated by CALAMAR, a software developed by the RHEA Co .. The rainfall database inCludes about 250

Space-time heterogeneities of rainfalls 211

station-years of validated data with a time resolution of 1 minute and a depth resolution of 0.1 or 0.2 mm depending on the raingauge. The raingauge mean failure rate does not exceed 10%. and has been dramatically reduced these last years to less than 5%. About fifty events have been recorded by radar.

The raingauge network includes data since 1076. which allows the use of 19 year records on several raingauges (7). However. such point or three raingauge series are too short for estimating events of return period up to 20-50 years. In order to increase the sample sizes, data from different raingauges have been aggregated to build a regional sample. Roux et al. (1994) showed in fact that the spatial homogeneity hypothesis cannot be rejected on the Seine-Saint-Denis area (236 sq. km.), which allows the mixing of data from different sites. As regards spatial dependence between the at-site data it can be estimated that the regional sample is equivalent to an at-site sample of about 120 years at a 5 minute time step, of about 50 years at a 4 hour time step, and of about 70 years at a 60 minute time step. the time of concentration of our watershed.

The sewer network

The site and its modelisation are briefly described hereafter:

Site description. The sewer network is the Ru Sainte-Baudile which flows into the River Maeve at NeuillysIMarne. It has an area of 1400 ha and an impervious coefficient of 30%. The sewer network mean slope varies between 2% upstream and 0.4% downstream. The watershed consists mainly of individual and small collective residences.

Hydrological nwdel. The watershed has been discretized into 21 sub-watersheds. on which the rainfall•runoff transformation is performed with the linear-storage model. The model unique parameter, K, the time lag, is estimated with a multi-parameter expression fitted by Desbordes (1975), depending on the area. the impervious coefficient, and the length and the mean slope of the longest path on the watershed.

Hydrograph routeing nwdel. The hydrograph routeing is performed with the Muskingum conceptual model. with limitation of the flow to the pipe capacity. In other words, when the pipe capacity is reached. the water excess is stored until the flow decreased. This method slightly under-estimated the peak flow because in fact. during the confined flow period. the water pressure increase is neglected. In the present work. this simpler approach has been used in lieu of a full dynamic routeing model.

Model parameters. The network topology is known. as well as the weir positions and the roughness parameter of the pipes. The Strickler coefficient is set to 60.

The rainfall space-time distribution effects on the runoff are studied. other things being equal (initial conditions. system parameters. etc.). on a "real" case, very similar to the reality. but not necessarily identical. In other words, this study analyses the sensibility of a given model to the space-time distribution of rainfall. We make the hypothesis that the general behaviour of the system would not be very different if its parameters showed small departures from the reality. In fact, flow data were available for one event: the measured peak flow was 16 m3/s and the modelled peak flow was 13 m3/s. Measurement errors as well as the hydrograph routeing methodology may explain the difference.

RESULTS

Figure 1 relates T-year peak flow and T-year 60-minute-areal-mean rainfall intensities. These areal mean intensities are either uniformly distributed (point rainfalls) over the watershed or not (3 raingauge rainfalls). One can see that in both cases, the observed T-year peak flow is about the same. with less than ±3.S% error around a mean value.

212 C. ROUX el al.

Then the results are given for each simulation set. showing the dispersion induced on the peak flow by respectively, the hyetograph shape of areally uniform rainfalls and the space-time heterogeneity of areally distributed rainfalls.

Ru Ste-Baudlle outlet peak flows vs. same T-year mean areal rainfalls

~~: I E 14 t i 12 t i 10 t

.. . ...•. rl

R :L--~ o 10 20 30 40 50

areal max. mean-60-mn intensity mmlh

\- 3 raingauges • point • design hyet.

Figure 1. T -year peak flow vs T -year mean areal rainfall.

One rain&au&e area!ly uniform rainfalls

For the same maximum 60-minute-mean intensity. deviations up to ±8% around a mean value are observed for 2 to 20 year rainfalls (see fig.2). They have been analysed using a hyetograph heterogeneity criterion, the ratio of the maximum mean intensity over respectively 30 and 60 minuted (Imax30IImax60). It is shown that 60% of the deviation variance is explained by this criterion. The optimal value of this ratio should be close to 1.6. in order to find the peak flow with the same return period as the rainfall (see fig.3).

Ru Ste-Baudlle outlet peak flows vs. areally uniform rainfalls

18 ~ - .---.. -----.--------- .--.-.-----I

~ 16 t , 14 T ~ 12 + 8 i

~ 10 T R 81

6 1

o

...•. • •• ....... ,.. ..... y-

. . .,,-... . .. ~ ....... .

• •

• • • ..

10 20 30 40 50 areal max. mean 60-mn-intensity - mmlh

I • 1 raingauge - uniformly distributed I Figure 2. H yewgrapb shape effect on the peak flow.

Space-lime heterogeneities of rainfalls

Hyetograph shape effect on peak flow deviation from the T -year peak flow

fI. 15 t

.5 10 -;-- .. :8 5 i_ .~ 0.;...1 ---,:-..-.~ ..... -----...... '--!::~~~---.....!!:...----=:-r -8

CD -5.,.··· i?! • -'iii -10 : ._

i-15: -- -,- --1.2 1.4 1.6 1.8 2

hyetograph shape erit. Im30 / ImOO

I • observed deviations I Figure 3. relative deviation from die T-year peak flow vs a byetograpb shape ailetion.

Three rain&AUB' areany distributed rainfalls

213

The simulated peak flows related to 2 to 20 year rainfalls are mainly observed within a ±12-IS9b interval around a mean value, the same as in the case of uniformly distributed point rainfalls. Some observations however show deviations up to ±309b (see fig.4).

Compared to areally unifonn rainfalls, spatial heterogeneity does not necessarily induce deviations on the peak flows. The most important ones result from very heterogeneous rainfalls; a heterogeneity between upstream and downstream. When it is marked between right bank and left bank of the main runoff direction, heterogeneity seems to have weaker effects (see fig.S).

Ru Ste-Baudlle outlet peak flows vs. areally distributed rainfalls

18

~ 16 , 14

~ 12 .lC 10

i8 6

o 10 20 30 40 50 areal max. mean 60-mn-lntensity - mmlh

I- 3 ralngauges • radar (14 pixels) I Figure 4. The rainfall space-time distribution effect on die peak flow.

214 C. KUUA el QI.

Ru Ste-Baudlle outlet peak flows VS. spatial heterogeneity

25 '1 ----------~ ,

:.e 151. . .. .... j

t~ \_' __ ~_::_ .••• _ •••• _ •••• _ •.•• _.~.~:_ •. _ ..• _-_-_:~:--_------.Jj Upstream Left/Right Bank Downstream

area with the strongest rainfall

I-+- Mean deviation 1 standard error conf. lim. I Figure 5. Relative deviation from the T-year peak flow vs. the spatial heterogeneity.

For the same mean rainfall depth over the watershed, strong rainfalls over the downstream area result in stronger peak flows than strong rainfalls over the upstream area. The same behaviour was observed by Blanchet (1993). The main phenomenon driving this is the routeing attenuation effect of the flood. In our case the presence of two discharge weirs situated in the middle of the network may have induced additional effecl~.

Radar areaUy distributed rainfalls

No significant differences are observed with the three raingauge simulation. Observed deviation do not exceed ±12-15% (see fig.4). The sample did not contain strong and very heterogeneous evenl~.

DQuble-trian~le shaped desj~n byeto~raph

We consider here the peak flow resulting from double-triangle shaped design hyetographs with a core triangle duration equal to 60 minutes, the time of concentration. They are compared with those of firstly, the point rainfall long-term series simulations and secondly, the three raingauge long-term series simulations. In the two cases, and for return periods between 2 and 20 years, observed deviation from the T -year peak flow do not exceed ±5% (see Fig. I). This design hyetograpb appears to be valid for estimating T-year peak flows in our case, but the conclusion is limited to this hydrograph feature.

Synthesjs

The same mean T-year rainfall depth over the watershed, either uniformly distributed or not, provides on average the same outlet peak flow. the T-year peak flow.

The T-year double-triangle shaped design hyetograph, with a core triangle duration equal to the time of concentration. provides the T-year peak flow with less than ±5% deviation. It should be uniformly applied to the watershed area, using an Areal Reduction Factor (ARP) if the T-year rainfall depth of the core triangle is estimated on point data.

This ARF is defined by Bronet-Moret et al. (1966) and allows. for a given time step and a given area, the estimation of the T-year mean rainfall depth over the area from the T-year point rainfall depth. It is a ratio between two quantities; quantities from. respectively, areal and point data. The ARP has been estimated at D.HO in our case (60 minutes. 1400 hal. in good agreement with a general expression we found from the data

l:ipace-time heterogeneities of rainfalls 215

of Seine-Denis: ARF(S,t..t) = S- £ + Ii Ln(4t) (to be published), where S is the watershed area, Dt the time step and II and E. two parameters.

A T-year mean rainfall depth, if it is spatially distributed over the watershed, and especially if it is balanced between upstream and downstream, can induce deviations on peak flows up to ±30% around the T-year peak flow. In this way, and in our case, a lO-year rainfall can result as easily in a 2-year peak flow as in a SO-year peak flow.

CONCLUSION

Using long term series simulations on a particular case has shown, that on average, T-year rainfall results in T-year peak flows, and that the double-triangle shaped design hyetograph is able to provide the T-year peak flow, with less than ±5% error.

However, for the same T-year mean rainfall intensity over the watershed and during the time of concentration, time-space distribution may induce significant deviations in the peak flow. In our case, they are mainly situated between ±lS% around the mean but can reach ±30%. It is therefore highly recommended to use space-time information when analysing a particular event Simple criteria have proved to be relevant to explain some of these deviations and should be improved. In addition to them, and in the same way, assessing the rainfall movement could be fruitful.

Developing long-term series simulation would be realistic for practical use under the following conditions:

- long term rainfall series should be available: either historic series or simulated series, generated by a stochastic rainfall generator;

- the rainfall-runoff simulation model should be able to deal with long term rainfall series.

ACKNOWLEDGEMENT

The authors gratefully acknowledge the "Laboratoire M6thodes" of lNSA, Lyon for loaning the software CEDRE (Conception, Evaluation et Dessin des R6seaux d'Egout) used for the simulations

REFERENCES

Blancbet, F. (1993). Elaboration d'une mesure de reftrence de la lame d'eau en bydrologie urbaine. Thise de Docloral de l'Universilt de Paris XIII, Ins/.Galilee, 285 p.

Brunelle, D. (1991). ElUde de I'innuence de I'htu!rogtntili! spatiale de Ia luie sue Ie comportement bydrologique du bassin versant de Livry-Gargan. Memoire de Mat/rise en Sciences Appliqutes de rEeole Polylechnique de Montrial, 189 p.

Brunet-Moret, Y., Rocbe, M. (1966). ElUde Ibtorique et mtthodologique de I'abauememnt des pluies, Cahiers de rORSTOM No.41,3-13.

Desbordes, M. (1975). Un essai de modtlisation des pbtnom~nes de ruissellement luvlal urbain. Techniques el Sciences Manicipales (T.S.M.) No 3, 121-126.

Desbordes, M., Raous. P. (1976). Un exemple de I'inu!n!t des ~tudes de sensibilJ~ des modllies bydrologiques. La Houille Blanche No.1, 37-43.

Niemczynowicz. J., (1988). The rainfall movement - a valuable complement to short-term rainfall data. Journal of Hydrology, 104,311-326.

Roux, C., Desbordes, M. (1944). Rainfall frequency curves with a recent urban dense raingauge nelwotk. Closing Ihe gap between Iheory and praclice in urban raitlfall applicalions, SI·Mor/iz. SwlJzerland, Ediled by Nlemczynow/cz. Un/v. of Lund, 77-90.