Corato G. 1 , Moramarco T. 1 , Tucciarelli T. 2

1. River discharge estimation using water levels hydrographs and 1D shallow water modelling Corato G.1, Moramarco T.1, Tucciarelli T.2 1Research Institute for Geo-Hydrological Protection, CNR, Via Madonna Alta 126, 06128 Perugia, Italy - email: g.corato@irpi.cnr.it 2Department of Civil,Environmental and Aerospace Engineering, University of Palermo, Italy, Viale delle Scienze, 90128, Palermo, Italy

2. Velocity measurements are costy in terms of time or equipments During high floods it is difficult to carry out velocity measurements Discharge can be estimated by using water level measurements Ponte San Giovanni (PG): flood eventofNovember 2005 Introduction Discharge is traditionally obtained through spatial integration of local velocity measurement.

3. I. Hydrometric river site with knownrating curve II. Hydrometric river site with unknown rating curve Jones Formula (Henderson, 1966), Fenton (Fenton, 1999), Marchi (Marchi, 1976) Level observations III. Equipped river reach with rating curve known at one of the ends Rainfall-runoff modeling, RCM (Moramarco et al. 2005) IV.Equipped River reach with level observations only Dyrac (Dottori et al., 2009), MAST (Aricò et al., 2009), VPMS (Perumal et al., 2007; 2010) Significant lateral flows Rating Curve Level observations Introduction Level observations Negligible lateral flows Level observations

4. To assess the discharge hydrograph at channel ends by a simple hydraulic model starting from water level measurements only. The analysis is also addressed for the case of significant lateral inflow along the river reach. level observation Significant Lateral Inflow level observation Purpose

5. Hydraulic Model Diffusive form of Saint Venant Equation: H: Water level R: Hydraulic radius A: Flow area n: Manning’s roughness QuL: lateral Inflow for unit channel length Boundary Conditions (BC) Upstream BC hu(t) is the observed water level Downstream BC zero diffusion condition To minimize error given by approximated downstream BC channel has to extend over the second gauged section

6. Lateral Inflow Modeling Continuity equation: Along the characteristic line: Total lateral Inflow TL wave travel time, c celerity, L channel length If the celerity wave c is constant and is negligible Au upstream flow area, Ad downstream flow area

7. Lateral Inflow Modeling Wave travel time estimation TL has been computed as the time shift needed to overlap the rising limb of two dimensionless stage hydrographs (Moramarco et al. 2005):

8. QL t Once QL estimated and n is calibrated, the discharge at gauged sites can be calculated by Dora Solver Manning coefficient is calibrated by minimizing MSE between computed and observed Area Hydrographs at 2nd gauged site: Manning Coefficient Calibration upstreamgauged site Dora Solver (Noto and Tucciarelli, 2001) is used to propagate water levels Middle pointchannel downstreamgauged site

9. Pierantonio Bas. Area: 1805 km2 Ponte Felcino Bas. Area: 2040 km2 Distance: 20.5 km Modeled channel: 25.5 km Bed slope: 0.16 % No significant lateral Inflow Intermediate basin - 10% upstream basin Ponte Felcino Bas. Area: 2040 km2 Ponte Nuovo Bas. Area: 4135 km2 Distance: 22.5 km Modeled Channel: 28 Km Bed slope: 0.16 % Significant Lateral Inflow Intermediate basin - 100% upstream basin Area Study

10. Area Study Pierantonio Site Ponte Felcino Site Ponte Nuovo Site

11. Results: Pierantonio - Ponte Felcino No Significant Lateral Inflows

12. Results: Ponte Felcino - Ponte Nuovo Significant Lateral Inflows TL = 4.75 TL = 3.33

13. Results: Ponte Felcino - Ponte Nuovo Significant Lateral Inflows flooding

14. Conclusions The water levels hydrograph analysis is suitable both for manning coefficient calibration and for lateral inflow modelling The method is able to estimate with a fair accuracy at channel ends discharge hydrograph by using only water levels measurements also when significant lateral inflows take place. Therefore, the proposed method can be conveniently adopted for the rating curve assessment at river sites just starting from stage records. Future Developments Lateral Inflow representation: Variable wave celerity Non-Prismatic term Sketch lateral inflow

15. References Aricò, C., Nasello, C. and Tucciarelli, T., Using unsteady water level data to estimate channel roughness and discharge hydrograph, Adv Water Resour, 2009; 32(8):1223-1240. Dottori, F., Martina, L. V. & Todini, E., A dynamic rating curve approach to indirect discharge measurements, Hydrol. Earth Syst. Sci., 2009, 13, 847-863. Fenton, J. D., Calculating hydrographs from stage records, Proc. 28th IHAR Congress, Graz, Austria,1999. Henderson, F. M., Open channel flow, Macmilliam Series in Civil Engigneering, Macmilliam Eds., 1966, New York, USA, pp. 522. Moramarco T., Barbetta S., Melone F. & Singh V.P., Relating local stage and remote discharge with significant lateral inflow, Journal of Hydrologic Engineering, 2005, 14(1), 51-62. Marchi, E., La propagazione di onde di piena, Atti Accademia Nazionale dei Lincei, 1976, 64, 594-602. The DORA algorithm for network flow models with improved stability and convergence properties. JOURNAL OF HYDRAULIC ENGINEERING, vol. 127 (5); p. 380-391, ISSN: 0733-9429, doi: 10.1061/(ASCE)0733-9429(2001)127:5(380) Perumal, M., Moramarco, T., Sahoo, B. & Barbetta, S., A methodology for discharge estimation and rating curve development at ungauged river sites, WaterResour. Res., 2007; 43, W02412. Perumal, M., T. Moramarco, B. Sahoo, and S. Barbetta, On the practical applicability of the VPMS routing method for rating curve development at ungauged river sites, Water Resour. Res., 2010, doi:10.1029/2009WR008103, in press. Thanks for your attention