Estimation of High Floods by Three Rainfall-Runoff Models with Short Rainfall-Runoff Series (Alzette River Basin, Luxembourg)

Transcription

1 Estmaton of Hgh Floods by Three Ranfall-Runoff Models wth Short Ranfall-Runoff Seres (Alzette Rver Basn, Luxembourg) El Idrss, A. 1 Drogue, G. 1,2, Pfster, L. 1, Iffly, J. F. 1, Hoffmann, L. 1, Hngray, B. 3, Guex, F. 3 1 CREBS-Cellule de Recherche en Envronnement et Botechnologes, Centre de Recherche Publc Gabrel Lppmann, 162a, Avenue de la Faïencere, L-1511 Luxembourg, Grand-duchy of Luxembourg. 2 Centre d'ecologe Végétale et d'hydrologe, UMR-MA 12 ENGEES-ULP, 1, qua Koch, F-677 Strasbourg cedex, France. 3 Ecole Polytechnque Fédérale, IATE - HYDRAM, CH-115 Lausanne, Swtzerland. (drss@crpgl.lu) Abstract: Ths paper presents a comparson of hourly hgh runoff smulatons usng short dscharge seres for three parsmonous ranfall-runoff models that dffer substantally n ther conceptualsaton (two reservor models and one physcally-based model). The models were appled to eght montored sub-basns charactersed by dfferent physographcal propertes and hydrologcal behavour, located n the expermental Alzette rver basn (Luxembourg). The model calbraton procedure conssts n selectng only ranfall-runoff events wth hghest peak flows and hghest runoff producton that occurred durng the avalable measurement perod ( ). Smulated extreme values of peak flow and stormflow volumes were analysed and compared to observed runoff seres. Results show that the models are able to provde good fts to the ranfall-runoff event s hydrographs. Nevertheless, the physcally-based MHM model gves the best results n terms of predctve accuracy. Keywords: ranfall-runoff; modellng peak flows; stormflow volume; Alzette rver basn; Luxembourg. 1. INTRODUCTION Ranfall-runoff models are mportant tools n operatonal hydrology and can dffer n terms of mathematcal representaton of processes, spatal dscretsaton of the basn and data requrements. In practce, the superorty of dstrbuted physcally based models over smpler models for operatonal purposes s currently an open queston. Ths queston s mportant for users of models, who may need to judge whether the ncreased costs of obtanng and processng spatally-dstrbuted basn data can be justfed n terms of ncreased relablty of model predctons [Donnelly- Makoweck and Moore, 1999]. Therefore, a comparson of models s requred to provde a bass for choosng a model that wll yeld an adequate performance n a specfc applcaton for the lowest cost. The purpose of ths paper s to compare the outputs of three ranfall-runoff models usng short observaton data seres. 2. METHODS 2.1 Study area and data The three models were appled to eght sub-basns (Fgure 1, Table 1), located n the expermental Alzette basn (1176 km 2, Grand-duchy of Luxembourg). The selected sub-basns were chosen to be representatve of the varablty of basn szes, geologcal condtons, physographcal propertes, as well as the avalablty and qualty of streamflow data (Table 1). Three sub-basns are homogeneous from a lthologcal pont of vew wth essentally marls (Merbech, Mess, Esch). Except for the Alzette n, all other sub-basns can be consdered as rural and forested. Note that former mnng actvtes n the rght bank trbutares dsturb the hydrologcal behavour of the Alzette n. 47

2 Basn Outlet Area (km 2 ) Impervous formatons (%) Pervous formatons (%) Cultvated land (%) Grassland (%) Forested land (%) Urbansed land (%) Merbech Pall Nederpallen Mess Pontperre Roudbach Esch Mamer Attert Rechlange Alzette Impervous formatons: Impermeable geology s substratum wth domnance of marls, schsts, clay or slt Pervous formatons: Permeable geology s substratum wth domnance of sandstone Table 1. Physographcal characterstcs of the selected sub-basns A dense hydrologcal observaton network has been set up n the expermental Alzette basn snce streamgauges are recordng water levels at a 15-mnute tme step. N Y Rechlange Nederpallen Y Pontperre Y Ettelbruck Y Stream gauge Y Hourly ran gauge Daly ran gauge Klometers Rver network Natonal boundares Fgure 1. Study area and measurement networks Total ranfall (Pt) was collected va 19 nonrecordng daly rangauges and 4 rangauges recordng at an hourly tme-step, coverng the study areas and avalable for the modellng perod. To compute hourly ranfall for each sub-basn, the daly areal ranfall (nterpolated va Thessen polygons) was tme dsaggregated accordng to the temporal structure of ranfall of the 5 hourly reference rangauges. Potental evapotranspraton (PET) was estmated usng the Penman-Monteth formula [Monteth and Unsworth, 199] wth daly meteorologcal data measured at the Luxembourg arport. The same clmatologcal data seres were unformly appled to the whole study area. Data sets used n ths study come from the hydroclmatologcal database bult-up and valdated by the CRP-GL (CREBS laboratory). 2.2 Hydrologcal model descrpton Three parsmonous ranfall-runoff models, smulatng hourly mean dscharge were tested. They dffer substantally n ther runoff producton and routng functons (Table 2). The Hydrologcal Recursve Model, HRM, [Levander et al., 1994] s called recursve because the reservor structure at order n s obtaned from reservor structure at order n-1 by a smple transformaton (namely, routng + lateral nput). In the followng, the HRM model was appled n ts sem-dstrbuted verson, whch accounts for the permeablty of lthologcal formatons. In ths case, sx free parameters must be optmsed by the Rosenbrock method. The lumped SOCONT model [Guex, 21] has three parameters to be ftted. The SOCONT parameters have no physcal meanng even though sgnfcant relatonshps wth specfc basn characterstcs could be found. The thrd model, the Meshed Hydrologcal Model, MHM [Batardy, 1984] s a storm runoff event model. For runnng ths model, physcal characterstcs of the basns (Table 2) were spatally dstrbuted nto regular squared grd cells by usng a Geographcal Informaton System; the grd sze used for ths study s 1 m. In vew of ranfall-runoff modellng, total dscharge (Qt) s separated va the Base Flow Index (BFI) software [Kaden, 1994] nto two components representng the storm runoff (Qr) and 471

3 MHM HRM SOCONT Type of the model Dstrbuted Sem-dstrbuted Lumped determnstc Producton functon Runoff coeffcent (constant) Sol reservor Sol reservor Routng functon Iso-chronal map Geometrcal sochrones Dranage reservor Base flow Not consdered Dranage reservor Dranage reservor Calbraton procedure Tral-error (manual) Automatc Two steps (automatc) Calbraton crteron Nash-Sutclffe coeffcent 1-Nash-Sutclffe coef. Nash-Sutclffe coef. Hydroclmatc nputs Pt, Qt, Qr, Qb Pt, PET Pt, PET Geographcal nputs Grded maps: geology, rver Geology, dranage area, Dranage area network, slope, flow drectons sochronal zones Outputs Qr, sochronal map Qt Qt, Qb, PET Parameters meanng Physcal meanng Physcal meanng No physcal meanng Table 2. Man characterstcs of the three tested models for ths case study the base flow (Qb). To produce stormflow (Qr), the MHM uses two matrces combnng two geologcal classes and three slope classes: the frst matrx contans the stormflow coeffcents (2x3=6 parameters) and the second one contans the runoff veloctes (2x3=6 parameters). To obtan the total dscharge, the Qr values are added to the estmated Qb. MHM model calbraton conssts n fttng manually the 12 parameters values [El Idrss et al., 1999]. 2.3 Modellng calbraton procedure The avalable streamflow measurement perod extends over 4.5 years from January 1997 to March 21; snce the number of hgh flood events s lmted, the seres are not long enough to perform a statstcal analyss of hgh floods. However, t s possble to calbrate the model parameters by extractng medum and hgh flood events from the avalable data seres. In the frst step, only hydrographs wth the hghest peak flows are retaned; a threshold s arbtrarly selected for a gven sub-basn (Fgure 2). Recorded peak flow (m 3 /s) Selected events Unselected events Total ranfall (mm) Fgure 2. Selecton of events accordng to the peak flow crteron (Mamer at ) Next, events that have the lowest runoff producton volumes are rejected (Fgure 3). The ranfallrunoff events fnally retaned (no more than 4 to 5 per sub-basn) present smlar saturated sol mosture condtons. In the second step, the model parameters were optmsed accordng to three dfferent methods: ) all ranfall-runoff events were aggregated nto a unque sequence preceded by a one month perod for ntalsng storage reservors; ) each event was separately calbrated wth an ntal warm-up perod for base flow. Optmal model parameters were averaged; ) usng the contnuous data seres (usual applcaton of the SOCONT and the HRM models). The 3 methods gve results wth slght dfferences and wll be thus consdered as comparable. Stormflow volume (mm) Selected events Unselected events Total ranfall (mm) Fgure 3. Selecton of events accordng to the stormflow volume crteron (Esch at ) 2.4 Crtera for model performance Both numercal and graphcal crtera were consdered to provde a good overall ndcaton of the model s capabltes. The accuracy crtera concern the stormflow shape (Qr), peak flows and stormflow volumes. 472

4 For assessng hourly global model effcency, the Nash and Sutclffe [197] coeffcent was computed for each sub-basn: n ( Qsm Qobs ) = 1 CNS = 1 (1) n = 1 2 ( Qobs Qobs) where n s the number of dscharge values of the selected events hydrographs, Qsm and Qobs are the smulated and the observed stormflow values respectvely, and Qobs s the average of observed stormflow values. CNS s less than 1 (equal to 1 when Qsm = Qobs). To assess goodness of ft and accuracy of smulated peak flows and stormflow volumes, mean absolute error (MAE), expressed n percentage was determned for each sub-basn : 1 n MAE (%) = ( Ysm Yobs )/Yobs (2) n = 1 where n s the number of dscharge values of the selected events hydrographs, Ysm stands for the computed values and Yobs stands for the measured values. The nearer the MAE s to zero the better the method. To quantfy the mportance of the dfference between observed and smulated stormflow volume, bas or magntude of mean errors (MBE), expressed n mm, was determned for each subbasn : 1 n MBE = ( Ysm Yobs ) (3) n = 1 3. RESULTS 3.1 Model effcency The CNS varaton for the tested sub-basns s depcted n Fgure 4. In terms of general performance, the MHM model gves slghtly better results than SOCONT and HRM. The average CNS s of.76,.73 and.72 respectvely. However, MHM seems to be less effcent on the largest sub-basns (Attert at Rechlange and Alzette at ). The three models obtan ther worst CNS for the Mess sub-basn. It s possble that the nfluence of a hghway on the natural hydrologcal behavour of ths homogeneous sub-basn does not permt an accurate smulaton of observed hydrographs. 2 The most homogeneous and the less homogeneous tested sub-basns (Merbech and Alzette n ) have an unexpected sgnfcant nfluence on model performance. The best results are obtaned for the less homogeneous one. Ths could be explaned by Mosley [1981]: where a number of hydrologcal factors are equally mportant n controllng hydrologc regme, and where the heterogenety dffers from one property to another, a complex mosac of hydrologcally apparent homogeneous areas may result. CNS Fgure 4. Comparson of model effcency (Nash and Sutclffe coeffcent) The MAE and MBE crtera are used to characterse the stormflow volume (SFV) varatons for the eght chosen sub-basns. The comparson of the results provded by the three models concernng SFV s shown n Fgure 5. MAE (%) Nederpallen Nederpallen MHM MHR SOCONT Pontperre Rechlange MHM HRM SOCONT Pontperre Rechlange Fgure 5. MAE crteron for smulated stormflow volumes Averaged MAE values obtaned by MHM and SOCONT are close and thus comparable (21.4 and 22.5 respectvely). Excepted for the contrasted result recorded for the Roudbach at subbasn, no specfc tendency s observed for the remanng sub-basns. 473

5 The MHM and SOCONT models have slghtly postve (3.5 mm) and negatve bas averages (-4.6 mm), respectvely. However, HRM largely underestmates the volume (-14.2 mm), especally for the smaller sub-basns (Fgure 6). MBE (mm) Nederpallen MHM HRM SOCONT Pontperre Fgure 6. Bas recorded by the three models (MBE crteron) For the storm peak flow (SPF) values, MHM gves better results than the two other models and the dfference s rather sgnfcant (Fgure 7). Note that the smulated peak flow values were extracted n a wndow of ± 3 hours around the observed peak flow values. MAE (%) Nederpallen Fgure 7. Comparson of smulated peak flow (MAE crteron) The MHM leads to a MAE of 16.3% on average. Ths value reaches 29.9% and 28.5% for HRM and SOCONT, respectvely. The same, but less pronounced tendency s found for the MBE crteron. The manually orented calbraton method and the smulaton of only net runoff can partally explan the observed dfferences. But the better results recorded for the CNS and the SFV confrm the overall better accuracy of MHM. The best averagng MAE results of SFV smulatons are obtaned on the Mamer (13.1%) and Attert (13.8%) sub-basns. These are medum Rechlange MHM HRM SOCONT Pontperre Rechlange szed sub-basns wth a relatvely homogeneous spatal dstrbuton of geologcal formatons: n the upstream-downstream sense for the Mamer and north-south sense for the Attert. As the number of sampled ranfall-runoff events does not exceed 5 for each chosen sub-basn t s nadequate to use them to carry out any trend concernng the very hgh peak flows and volumes. In Fgure 8 (page down) are represented for the three models, scatter plots of observed and smulated storm peak flows of all selected subbasns. Observed peak flow values rangng from 35 m 3 /s to 5 m 3 /s are lackng. The SOCONT model shows a systematc underestmaton for the entre range of peak flows (Fgure 8). HRM smulates well low observed peak flow values and slghtly overestmates measured peak flow values superor to 4 m 3 /s (Fgure 8). Model predctons towards extreme values mght be exaggerated. On the contrary, the SOCONT model wll systematcally underestmated extreme values (Fgure 8). MHM model results suggest a slght trend towards an underestmaton of peak flows superor to 25 m 3 /s. In terms of stormflow volume (Fgure 9), both HRM and SOCONT show progressve underestmaton of volume from low to hgh values. However, MHM gves a good trend estmaton of observed volume dscharge and provdes a better tendency for volumes of extreme events. 4. CONCLUSIONS AND PERSPECTIVES A procedure to analyse and compare hourly hgh floods smulated by three ranfall-runoff models wth short ranfall-runoff seres s presented. The results based on the CNS crteron show that the three tested models are well suted to assess the smulaton of hgh event s dscharges for the eght selected sub-basns n terms of general shape of the observed storm hydrographs. The results based on the MAE and MBE crtera suggest that the MHM model s best suted for dentfyng the peak flows and stormflow volumes wthn the study area, regardless of the sub-basn s scale and characterstcs. The SOCONT model shows a systematc under-estmaton of both peak flow and stormflow volumes and should not be used for extreme values. The accuracy of the calbraton procedure would be better f suffcent hgher ranfall-runoff observed events would exst. In the future, each sub-basn wll be separately examned. Concernng the method verfcaton, the lack of hourly Intensty-Duraton-Frequency curves n the Alzette basn does not allow the use of a range of desgned storm events wth adequate return perods. 474

6 Modelled peak flow (m 3 /s) MHM R 2 =.95 Modelled peak flow (m 3 /s) HRM R 2 =.97 Modelled peak flow (m 3 /s) SOCONT R 2 = Observed peak flow (m 3 /s) Observed peak flow (m 3 /s) Observed peak flow (m 3 /s) Fgure 8: Comparson of observed and smulated peak flow Modelled stormflow volume (mm) 6 MHM 5 R 2 = Observed stormflow volume (mm) Modelled stormflow volume (mm) 6 HRM 5 R 2 = Observed stormflow volume (mm) Modelled stormflow volume (mm) 6 SOCONT 5 R 2 = Observed stormflow volume (mm) Fgure 8: Comparson of observed and smulated stormflow Acknowledgement Thanks to Levander T. for provdng the HRM model and for hs comments. 5. REFERENCES Batardy, J., L élaboraton d un modèle hydrologque conceptuel mallé pour la prévson des débts en temps réel. Applcaton au bassn versant de la Lesse à Daverdsse. Rapport fnal, S.A. LGR N.V., Athus, 254 pp., Belgque, Donnelly-Makoweck, L.M., and R.D. Moore, Herarchcal testng of three ranfall-runoff models n small forested catchments, Journal of Hydrology, 219, , El Idrss, A., I. Ruthy, P. Hang, M. VanClooster, E. Persoons, Regonalzaton of ranfall-runoff parameters n the catchment of the Dyle (Belgum), Act of: Internatonal conference on Modellng of transport process n sols at varous scales n tme and space, Edted by J., Feyen & K. Wyo, Leuven, Belgum, November 24-26, Guex, F., Modélsaton hydrologque dans le bassn versant de l Alzette (Luxembourg), régonalsaton des paramètres d un modèle global, Traval pratque de Dplôme, Ecole Polytechnque Fédérale de Lausanne, 67 p., 21. Kaden, U., Etude de la séparaton des écoulements sur dfférents bassns d Alsace. Applcaton et automatsaton de la technque du Base Flow Index (BFI), Master thess, Unversté Lous Pasteur, Strasbourg, 55 pp., Levander, T., G. Mantlla-Moralles, A. Zerman, Etude comparatve de la résoluton spatale des modèles hydrologques sur le bassn de la Charente. Symposum sur les relatons contnent-zones côtères, GIP Hydrosystèmes, La Rochelle, 17 pp., Monteth, J. L. and M. Unsworth, Prncples of Envronmental Physcs, 2 nd ed., Edward Arnold, London, 199. Mosley, M.P., Delmtaton of New Zealand hydrologc regons, Journal of Hydrology, 49, , Nash, J.E., and J.V. Sutclffe, Rver flow forecastng through conceptual models. Part I: a dscusson of prncples, Journal of Hydrology, 1, ,