Using unsteady-state water level data to estimate channel roughness and discharge hydrograph Costanza Aricò * , Carmelo Nasello, Tullio Tucciarelli Dipartimento di Ingegneria Idraulica ed Applicazioni Ambientali, Università di Palermo Viale delle Scienze, 90128 Palermo, Italy article info Article history: Received 27 November 2008 Received in revised form 30 April 2009 Accepted 2 May 2009 Available online 10 May 2009 Keywords: Flow meter Discharge estimation Flow routing Calibration Shallow waters Diffusive model abstract A novel methodology for simultaneous discharge and channel roughness estimation is developed and applied to data sets available at three experimental sites. The methodology is based on the synchronous measurement of water level data in two river sections far some kilometers from each other, as well as on the use of a diffusive flow routing solver and does not require any direct velocity measurement. The methodology is first analyzed for the simplest case of a channel with a large slope, where the kinematic assumption holds. A sensitivity and a model error analysis are carried out in this hypothesis in order to show the stability of the results with respect to the error in the input parameters in the case of homoge- neous roughness and to analyze the effect of unknown roughness heterogeneity on the estimated dis- charges. The methodology is then extended to the more general case of channels with mild slope and validated using field data previously collected in three Italian rivers: the Arno (in Tuscany), the Tiber (in Latium) and the Vallo di Diana, a small tributary of the Tanagro river (in Southern Italy). The perfor- mance of the proposed algorithm has been investigated according to three performance criteria estimat- ing the quality of the match between the measured and the computed stage and discharge hydrographs. Results of the field tests can be considered good, despite the uncertainties of the field data and of the measured values. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Direct measurement of discharge in rivers is traditionally ob- tained through spatial integration of measured local velocities. The velocity values can be obtained with instruments like mechan- ical or electromagnetic probes, in full contact with the water at the measured point. More recently, the all velocity profile along a given radius starting from the instrument transducer can be obtained from Acoustic Doppler Current Profilers (ADCPs) [14,17,18,26], measuring the Doppler shift of the backscattered acoustic signal re- flected by the solid particles moving within the stream flow. These and also other instruments fully immerged in the water are easily subject to damage and usually require direct personnel assistance. The Large Scale Particle Image Velocity (LSPIV) is used to get a measurement of the 2D plane surface velocity field, applying image analysis to two subsequent natural images of the water surface around a given section [12]. Further information and analysis is obviously required in order to estimate the velocities at different depths from the water surface. Because of the abovementioned difficulties for direct discharge measurements, gauged sections in natural rivers and artificial channels are usually equipped with water level sensors and the measured water levels are related to the discharges by means of so-called stage–discharge (SD) relation. This relation assumes a one-to-one relationship between water depth and discharge, an hypothesis that is strictly true only according to the kinematic assumption. This assumption holds in many gauged sections, lo- cated upstream of the urbanized areas; in this case the error in the discharge estimation, for given water depth, is a few percent units. In spite of this, the use of the SD relation has several drawbacks. The SD is difficult to compute, because for almost all natural rivers it requires direct velocity measurements. The hydraulic resistance and the geometry sections are subject to frequent changes, due to erosion/deposition processes, as well as to seasonal vegetational changes [4,8]; this implies the need for a frequent reconstruction of the SD relation. Most importantly, direct velocity measurement is very unlikely to occur during significant hydrological events. For almost all the available SD relations, the higher stage–discharge points are obtained via simple extrapolation of real measured values. To partially cope with this difficulty, the use of two water level sensors located in two different river sections has been proposed since about ten years ago. Most of the authors have proposed more or less simplified models to relate directly the downstream rating curve with the measured stage hydrograph in both sections and 0309-1708/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2009.05.001 * Corresponding author. E-mail addresses: arico@idra.unipa.it (C. Aricò), nasello@idra.unipa.it (C. Nasello), tucciar@idra.unipa.it (T. Tucciarelli). Advances in Water Resources 32 (2009) 1223–1240 Contents lists available at ScienceDirect Advances in Water Resources journal homepage: www.elsevier.com/locate/advwatres