WO2008110909A2

WO2008110909A2 - Measurement method for measuring the peak flow discharges and the channel bed roughness in a natural or artificial water course and related system

Info

Publication number: WO2008110909A2
Application number: PCT/IB2008/000599
Authority: WO
Inventors: Tullio Tucciarelli
Original assignee: Universita' Degli Studi Di Palermo
Priority date: 2007-03-15
Filing date: 2008-03-14
Publication date: 2008-09-18
Also published as: WO2008110909A3; ITRM20070134A1

Abstract

Measurement system for measuring peak flow discharges comprising at least two water level measurement instruments, including radar sensors or other suitable sensors placed outside the stream flow, located at suitable distance from each other in correspondence with respective channel sections; the shape of the channel between the sections varying gradually or, however, with known law. The synchronous acquisition of the water levels allows, by means of a numerical analysis of the unsteady-state process, to compute both the peak flow discharge and the average bed roughness at the flood time.

Description

MEASUREMENT METHOD FOR MEASURING THE PEAK FLOW DISCHARGE AND THE CHANNEL BED ROUGHNESS IN A NATURAL OR ARTIFICIAL WATER COURSE AND RELATED SYSTEM Field of the invention

The present invention refers to a measurement method for measuring discharges in channels or natural or artificial rivers at the peak flow time and to a related system, that allows to get both the peak flow discharge and the average channel bed roughness at the flood time. State of the art

The discharge measurement in channels is fundamental for the validation of all the rainfall-runoff models, as well as of the flow routing models on fixed and mobile beds.

In the case of channels having small size, artificial structures have been built in which the stream flow to realize the critical status condition is forced and water depth changes are induced; with these changes it is possible to measure with high precision the transient discharge value. Document US5824916 describes one of these structures, but in case of rivers of large or medium size it is obviously totally unfeasible.

Most of the channel discharge measurements are still now carried out by means of: continuos recording of water depths in single sections, assuming an uni- vocal relationship between water depth and discharge, also called water depth-discharge relation; - velocity measurement recording.

The second methodology is usually adopted for the calibration of the water depth-discharge relation. With the first methodology, disadvantageously, the water depth - discharge relation is assumed often constant for long time periods, without taking into account the progressive change of the bed geometry, of the channel banks and of the bed roughness, said change being due to the deposition or erosion processes, as well as to the vegetation growth. Numerical calibration procedures have been proposed to evaluate, by means of the optimal control theory, the Manning roughness coefficient starting from sequential water depth measurements. This has been done without any particular reference to the discharge measurement in specific channel sections. Otherwise, the discharge measurement is always carried out assuming a known channel bed roughness.

For example, document DE2935015 describes a method that, by means of the water level gradient measurement, allows the discharge computation in unsteady state conditions without the direct velocity measurement, but only for a given value of the channel bed roughness.

Discharge measurements have been more rarely carried out by means of updating the river section geometry and measuring local flow velocities obtained by mechanical or electromagnetic probes merged in the stream flow. More recently, use of the Acoustic Doppler Velocity (ADV) sensors allows to obtain local velocity measurements by locating the sensors in points of the stream flow different from the measurement ones.

Usually, the discharge measurement by means of direct velocity measurements happens to be, other than expensive, also inefficient when discharges at the peak flow time should be measured. This is due to the following reasons: in order to measure the peak flow discharge a continuous monitoring system is required; this becomes very expensive when human assistance is needed,

- velocity measurements become imprecise when strong turbulences occur,

- turbulence and, above all, the solid transport associated to the flood event can provide damage to the instrumentation located inside the stream flow.

"Acoustic Doppler Current Profilers" (ADCPs) are also used for a direct velocity measurement in the channel. The ADCP devices are suitable to measure the velocity profile along a given direction starting from the position of a transducer, located either on one stream flow border to get horizontal profiles or on the bottom of a boat to get vertical profiles. This transducer measures the "Doppler" time lag of the acoustic signal reflected by the suspended particles moving with the stream flow. The same instrument can provide the water depth by measuring the return time of the acoustic signal reflected by the channel bed. ADCP instruments can be located inside the stream flow more easily and safely than the traditional probes, obtaining velocity profiles in several points of the same direction, not close to the water surface and to the instrument itself. Among ADCP there are also some instruments with the transducer located on a small catamaran-boat, moving from one to the other bank of the river. This avoids the displacement in the water of a boat and, thus, the direct human personnel intervention. Disadvantageously the discharge measurement by means of ADCP instruments remains anyway very expensive, specially if applied to very large rivers, and often very difficult to apply, for example in poor security conditions because of a flood event occurrence.

At the present time, the only data possible to get by means of instruments located outside the stream flow are the water depths and the water surface velocities, that instead can be very different from the average value of the velocity in the section. These instruments use either "Particle Image Velocity" (PIV) techniques or techniques based on radar impulses.

The "Particle Image Velocity" (PIV) technique for the laboratory measurement of the velocity is a not-intrusive technique for the surface velocity measurement based on the analysis of sequential images of the solid particles carried on by the stream flow. From this technique the Large Scale Particle Image Velocity (LSPIV) has been derived; the LSPIV is the application of the PiV analysis to the natural images of the free surface of a water course at a specified section. More information and analysis are anyway required to pass from the surface velocity measurements to the estimation of the vertical velocity profile. Other measurement techniques, that do not require the placement of any instrument inside the water, provide, in order to measure the discharge in a given section, the surface velocity measurement in several points by means of a high frequency Doppler radar impulse, emitted from a radar located outside the stream flow. The channel cross section can be measured by hanging a low frequency Ground Penetrating Radar (GPR) above the water surface, from a bridge or a cable. If the bridge or the cable are not available, the GPR system and the radar can be located on a helicopter, following from above the water course. Very large uncertainties still exist on the accuracy provided by these instruments in the velocity and water depth measurements during flood events. It is therefore clear the need of providing a method and a related system for the peak flow discharge measurement that allows to overcome the above mentioned inconveniences. Summary of the invention

The main purpose of the present invention is to provide a method that allows to measure the peak flow discharges in a water course and, at the same time, to update the bed roughness and thus the related water depth-discharge relation, along with the biological condition changes of the channel bed, without carrying out any velocity measurement.

A further purpose of the invention is to provide a related system that allows to carry out the above mentioned measurements in a simple, fast and inexpensive way with respect to the currently adopted devices.

The present invention, therefore, is aimed to realize the above-mentioned goals by performing a measurement method for measuring the peak flow discharge q_maχ in a water course, in which there is provided the definition of at least two water course sections, said method comprising according to claim 1 the following steps: a) acquiring the water depths h*i(tj), h*_p(tj), at times tj, in a first upstream section and in at least a second downstream section p of the water course channel bed, by means of respective measurement instruments located at said sections and detecting the time t*_p in which the water depth measured in the second section p attains a predetermined value h^* _p; b) computing the water depths h_p(n,t_t) in said second downstream section p and computing the discharges q-i(n, tj,) in said first upstream section in function of generic values of average channel bed roughness coefficient n by means of a monodimensional numerical model of flood flow routing; c) detecting the time t_p(n) corresponding to a predetermined value of the computed water depth h_p(n) ; d) computing the optimal value n* of the average channel bed roughness coefficient, as root of the equation t_p{h_p (n))=t_ρψ_ρ); 3) computing the peak flow discharge q_max corresponding to the maximum discharge qim_ax(n, tj), computed by the numerical model, by changing the generic value of the average roughness coefficient n with the optimum value n*. According to a first embodiment of the method, said predetermined values h*_p and h_p(n) are the maximum values of the water depths respectively measured and computed in said second downstream section p.

According to a second embodiment of the method, said predetermined values h*_p and h_p{n) are set equal to each other and their value is selected among those values occurring in said second downstream section p during the most rapid rising phase of the water depth.

An other aspect of the invention is to provide a system for the peak flow discharge measurement in a water course that, according to claim 9, comprises at least two water depth measurement instruments, placed outside the water course at a predetermined distance from each other in correspondence with two sections of the water course, data processing means suitable to process the data detected by said measurement instruments and to compute the peak flow discharge in correspondence with one of the two sections, wherein said measurement instruments are provided with synchronization means suitable to synchronize the instruments each other.

Advantageously, due to the synchronization of the acquisition of the water depths in at least two channel sections, the system and the method of the invention allow to get the simultaneous estimation of both the flood peak flow discharge and the average channel bed roughness at the flood time. Possible velocity measurements can be used, when available, to reduce the estimation error.

A further advantage is given by the fact that the discharge and roughness measurements are obtained in a fast, safe and inexpensive way with respect to the known systems and methods. In fact, with respect to the current technologies, the discharge estimation is carried out by means of water depth measurements carried out with instruments located outside the stream flow, that can continuously work or be activated with a long distance control without the presence of a human operator. It is known in fact that, during the flood event, the instruments for the velocity measurement, located inside the stream flow, either provide totally wrong measures or have high probabilities of being seriously damaged.

The flood peak flow discharge measurement is fundamental for the validation of the rainfall/runoff models, the recording and the study of the discharge time series, the flood early warning in rivers with a large hydrographic basins. The method of the invention requires the knowledge of the river bed topography in the zone between the two measurement sections. The topography is obtained by means of the acquisition of digital maps, obtained by means of air born images integrated with direct measurements, specially in the areas submerged by the water at the air borne picture time. The topography can also be obtained by carrying out some simple direct topography survey in the mentioned area.

The dependent claims describe preferred embodiments of the invention. Brief Figures description

Further features and advantages of the invention will be more evident in reason of the detailed description of a preferred, but not exclusive, embodiment of a system and a method for the discharge measurement shown, as example and without any delimitation purpose, with the help of the enclosed figures where: Fig. 1 represents a graph with an example of water depth hydrograph measured in two different channel sections;

Fig. 2 represents schematically an example of the system of the invention; Detailed description of preferred embodiments of the invention The measurement system, object of the present invention, comprises at least two water depth measurement instruments 10,11 located outside the water course 14, at suitable distance from each other, at the respective channel sections. Between said sections the shape of the channel changes gradually or anyway with known law, through the use of digital maps. The "water depth" is meant to be the maximum water depth value along a section of the water course.

The measurement instruments 10, 11 , equipped with a sensor 15, for example a radar or any other suitable sensor, can be located at a distance ranging from about 1 and 20 km. Smaller distances are appropriate for small water depths, of the order of few tens of centimetres, while the larger distances are appropriate for water depths of the order of meters. Between the sections where measurement instruments are installed important inflows from other water courses must be missing.

In the case of artificial channels the distance between the measurement instruments can be also smaller than 1 km.

Advantageously the measurement instruments, including the main instrument 10 and at least one auxiliary instrument 11 , are synchronized with a maximum error of few seconds, either by means of an immediate radio communication of the data recorded by the auxiliary instrument to the main instrument, or by means of continuous recording of the absolute measurement time in the measurement instrument dataloggers. The absolute time is measured with high precision, possibly radio-controlled clocks.

The measurement instruments 10, 11 can comprise then, along with the sensor 15, a high precision clock, a telephone device and/or a radio transmitter- receiver. The telephone device can send the data on the public GSM network or, preferably, on the GPRS network. If the locations of the measurement instruments are not covered by any telephone network, it is possible to use a satellite device. The datalogger, always present in the main instrument, can be not provided in the auxiliary instrument if equipped with radio transmitter. The synchronous acquisition of the water depths in the predetermined measurement sections allows, by means of a numerical analysis of the unsteady state process carried out by means of data processing means comprising a suitable software, to compute both the peak flow discharge and the average channel bed roughness at the flood time.

In the case of instantaneous transmission of the data recorded by the measurement instruments, said data processing means can be directly in cooperation with at least one of the measurement instruments, or with the data acquisition server. In the case of only local recording of the data detected in each measurement instrument, the processing of these data will be carried out after the flood event.

The system of the invention can also be provided with an further sensor for each measurement instrument, for example a further radar sensor, suitable to penetrate the liquid medium for a synchronous acquisition of the channel bed elevations. This also allows the instantaneous discharge measurement in mobile bed conditions.

Advantageously, the system of the invention can work continuously or anyway being activated from a long distance control, without providing the presence of a human operator. This can be done by means of suitable long distance control instruments, for example a GPRS unit provided in at least one of the measurement instruments.

The energy supplying means of the measurement instruments can comprise solar panels or batteries, when the first are easily subject to rubbery or vandalism. As an accurate analysis of the recorded water depths requires measurements with the frequency of the order of minutes, in the case of battery power supply it is better to prevent their exhaustion by means of an acquisition frequency regulation. The increase of the acquisition frequency, to be realized by means of automatism or long distance control; can be provided in this way only in the time period of few hours in which the peak flow of the flood is forecasted. In Fig. 2, as example, a scheme of the system with two measurement instruments 10, 11 located at two bridges 12, 13 along the water course 14 is shown. The method of the invention is based on the observation that the dynamic process taking place around the peak flow time, in correspondence with very severe hydrological events, is strongly not stationary.

The measurement method of the invention, carried out by means the previously said software, adopts as input:

- the time series, that is the hydrographs of the water depths h^*-ι(tj), h*₂(tj) in two measurement sections, an upstream section 1 and a downstream section 2, and eventually of a further water depth h^* ₃(t,-) in a measurement section 3 intermediate between said sections 1 and 2, with i=1 ,... ,N; said hydrographs being provided by the corresponding measurement instruments in the sections;

- the geometry of some sections of the reach of channel included between the measurement instruments 10, 11 respectively of the upstream section 1 and of the downstream section 2.

The further measurement section 3 can be intermediate between the upstream section 1 and the downstream section 2 or, when only two measurement sections are available, it is the same downstream section 2. From the channel bed topographic data it is possible to obtain, for each computational section j adopted by the numerical simulation model of the software, the approximated trend of the functions σ/h), R_j(h), T_j(h), where h is the water depth, σ is the cross section area, R is the hydraulic radius and T is the free surface width. Such numerical model provides simultaneously, along with the water depths h_j computed in the different computational sections, also the discharges q_j (tj, n) in all the computational sections, including also the predetermined measurement sections, at the times tj with i = 1 , ..., N. After the insertion of the input data, the software is able to optimize the value of the Manning coefficient n, that is the average roughness coefficient of the channel bed, by computing the root of the equation: t_p (h_p (n))= t;(h; ) (1), where: h_p(n) and h_p ^* are the maximum values of the water depths, respectively computed and measured in the measurement section 3; t_p is the time in which the computed water depth h attains the Rvalue in the measurement section 3, t^* is the time in which the measured water depth h^* attains the /Rvalue in the same measurement section 3.

Alternatively, if the peak time t_p' of the measured hydrographs is not precisely identifiable because of small amplitude oscillations, it is possible to set a unique value for h_p(n) and h_p ^* ; this value is selected among the values attained in the measurement section 3 during the most rapid rising phase of the water depth. In order to compute the water depth values in the measurement section 3, corresponding to generic values of the Manning coefficient n, the software adopts a numerical model solving the Saint-Venant equations written in monodimen- sional form with the following boundary and initial conditions. If the stream flow in the upstream section 1 is subcritical, the only boundary condition to set at the upstream measurement section 1 is the one given by the measured water depth values. If the stream flow is supercritical (Froude number greater than one) in the upstream measurement section 1 , a second boundary condition will be set according to the kinematic hypothesis, that is according to the hypothesis of water depth gradient dh/dx equal to zero, where x is the water flow direction.

The approximation of the downstream boundary condition, that is the condition in the intermediate measurement section 3 or in the downstream section 2, is necessary only in the case of downstream subcritical stream flow. If the measurement sections are two and the stream flow, downstream the upstream section 1 , is subcritical (Froude number smaller than one), the measurement section 3 will be the same downstream section 2 and the corresponding boundary condition can be given by the kinematic hypothesis or by other approximation of the unknown condition.

If the available sections are three and the stream flow is subcritical the measurement section 3 will be the intermediate one between the upstream section 1 and the downstream section 2 and the downstream boundary condition will be given by the measured water depth values.

The initial condition will be the steady state one corresponding to the discharge satisfying the initial value of both the boundary conditions. The method, object of the present invention, advantageously comprises the following steps: a) acquisition at three measurement sections 1 , 2 and 3 of the water depths h*i(tj), h^* ₂(tj) and h*₃(tj) and detection of the time t_p defined in equation (1); b) computation of the water depths h_p(n,t_j) in the measurement section 3, intermediate between sections 1 and 2 or coincident with the downstream section 2, by means of the numerical integration of the Saint Venant momentum and continuity equations, written in monodimensional form; c) detection of the time t_p(n) corresponding to the water depth h_p{n) , defined in equation (1); d) computation of the optimal Manning coefficient n* as root of equation (1); e) computation of the peak flow discharge q_maχ corresponding to the maximum discharge qi_max(n) computed by the model in the upstream section 1 adopting the optimal value n* of the Manning coefficient. The above said software or computer program comprises program coding means, suitable to realize steps from b) to e) when such program runs on a computer. Such program can be memorized on means readable by a computer, like as example cd, pen drive, ecc. In the step b) the computation of the water depths h_p{n,t^) in the measurement section 3, intermediate between sections 1 and 2 or coincident with the downstream section 2, is carried out by means of numerical integration of the Saint Venant momentum and continuity equations along the examined channel reach. A flow routing numerical model suitable to solve the above said Saint Venant equations is adopted. In the monodimensional case, the PDE (partial differential equations) system is the following one:

dt dx (5)

l ^ϊ+÷dx-P\^-y K^^gστfc+^gσ\fdx^~+^+~^¥^ϊϊ) =^~o^{X} (δa)}

where x is the flow direction, t is the time, g the gravity acceleration and z is the known topographic elevation.

The equation system (5)-(6a) is solved in the unknowns h and q for given boundary and initial conditions, previously discussed, and for a simulation time interval below defined.

In order to save computational time and to be able to adopt quite simple and reliable numerical codes, it is possible to adopt the so called diffusive hypothesis and to use in the above said system, instead of equation (6a), the following momentum equation: dH(xj) n²q q

(6b), dx σ^>Rⁱⁿ where H(x,t) is the free surface elevation with respect to an horizontal plane in the water section with abscissa x at the time t. In the diffusive model the boundary conditions are always those already mentioned in the case of sub- critical upstream and downstream flow. The steady state condition, that is with constant discharge, is set as initial condition along the channel bed. In order to fit the initial boundary conditions with ihe desired ones, a specific part of the code computes different steady-state water depth profiles, each one corresponding to a different discharge and to the water depth of the upstream section at the initial time T1 of the simulation. The calibration of the above said discharge is such that the initial water depth profile in proximity of the downstream section satisfies the downstream boundary condition previously specified.

In order to reduce the computation time, the simulation time must be limited to a short time interval comprising the maximum water depth in the upstream and downstream sections; on the other hand, in order to reduce the effect of the initial condition estimation error, particularly large in the central sections of the investigated bed reach, it is important to start the simulations at an initial time in which, in the channel bed, water depth and discharge values are much smaller than those corresponding to the peak values.

In order to get good measurements with a reduced computational time, step b) and the following ones are run starting from a predetermined time T1 obtained with the following procedure:

- selecting a time TM corresponding to the maximum water depth h*_3maχ in the measurement section 3;

- starting from this value, moving backward in time up to the time T1 in which the first local minimum h^*i_min of the measured water depth h-i* occurs in the upstream section 1.

The simulation period will be comprised between T1 and T2, where T2 is enough greater than TM. T2 is set greater than TM to allow, for each value of the Manning coefficient n, the computation of the time f_p(n) in equation (1). Said value of Manning coefficient n, used for the simulation of the water depths, will be set within the range of the physically admissible minimum and maximum values (thereby also greater or smaller that the optimal value n*). The detection of the time f_p(n) requires, in fact, to extend the simulation until the water depth value h_p is attained in the measurement section 3. A possible choice is T2 = T1 + 2*(TM-T1). B2008/000599

13

It is possible to further reduce time T1, and thus to extend the simulation period, if the first local minimum of the water depth in the upstream section 1 is followed shortly by other smaller local minima.

For the numerical solution of the simulation problem the methodologies DORA and MAST proposed by Noto V. and T. Tucciarelli (2001), "The DORA algorithm for network flow models with improved stability and convergence properties", Journal of Hydraulic Engineering (ASCE), 127(5), 380-391 and Tucciarelli T., "A new algorithm for a robust solution of the fully dynamic De Saint Venant equations", Journal of Hydraulic Research (IAHR), 41 (3), 239-246, 2003, can be used.

After the numerical relationship between the Manning coefficient n and the time ^(77) is set, the root of equation (1) can be numerically computed using a standard technique for the numerical solution of algebraic equations. Because high resolution and computation velocity are not required, the use of a robust algorithm, like the Brent one, is recommended.

In an embodiment of the method of the invention, in the case in which the entire channel reach comprised between the upstream section 1 and the downstream section 2 has a slope i of at least 1%, we can neglect the inertia forces and the water depth gradient (the so called kinematic hypothesis) in the entire investigated reach and compute the Manning coefficient n and the peak flow discharge q_max as roots of the system:

c_max =~^d^ dσ n {_Hκjr _\ ^ HKJL) f ^dσ\ J (3). where q_maχ is the maximum discharge, that is the peak flow discharge corresponding to the maximum water depth h_max, i is the slope of the channel bed, n is the Manning coefficient, , σ(hmax) and R(h_max) are respectively the area and the hydraulic radius values of the channel bed section at the maximum water depth in each of the two sections. The celerity c_max is the propagation celerity corresponding to the maximum discharge q_max. It can be shown that, in the kinematic hypothesis, only one value of the product

PR = σ %^2l*4ϊ (4) corresponds to each discharge in a channel bed with homogeneous roughness. It is then possible to approximate the maximum celerity as the ratio between the distance of the upstream section 1 from measurement section 3 and the difference t_p-t-i between the time t_p in which the maximum product PR in the measurement section 3 is measured and the time ti in which the maximum product PR in the upstream section 1 is measured.

In the kinematic case the measurement of the time lag between the two water depth hydrographs measured at the two channel sections, as can be seen for example in the graph of Fig.1 , allows to evaluate directly the propagation celerity Cm_ax of the maximum discharge. From the celerity it is possible to derive then not only the discharge, but also the channel bed roughness. In particular, after c_max is computed, the value of the Manning coefficient n is obtained from equation (3) and, then, from equation (2) the maximum discharge is obtained, that is the peak flow discharge qm_ax (as in the step e) previously described).

By solving this two equations system, including the Manning equation and the kinematic celerity expression (see Henderson F. M. (1966) - "Open channel flow" Macmilliam Series in Civil Engineering, Macmilliam eds., New York), the computation of the root of equation (1) can be avoided. This allows to compute the sought unknowns without the need of knowing the channel morphology in the sections intermediate between the sections where the water depths are measured.

The sensitivity analysis of the model given by equations (2) and (3) also shows that the estimation error of n and qm_ax is smaller, as percentage, than the error committed in the measurement of h_maχ and c_max.

Because the hydraulic propagation process has, in most of the channel beds in proximity of the discharge measurement sections, features similar to those typical of the kinematic hypothesis, similar conclusions can be qualitatively generalized also to not strictly kinematic cases.

Claims

1. Measurement method for measuring the peak flow discharge (q_maχ) in a water course, in which there is provided the definition of at least two water course sections, comprising the following steps: a) acquiring the water depths h*i(t,), h^* _p(tj), at times tj, in a first upstream section (1) and in at least a second downstream section (p) of the water course channel bed, by means of respective measurement instruments (10,11) located at said sections, and detecting of the time t^* _p in which the water depth measured in the second section (p) attains a predetermined value h*_p; b) computing the water depths h_p(n,t_j) in said second downstream section (p) and computing the discharges q-ι(n, tj,) in said first upstream section (1) in function of generic values of average channel bed roughness coefficient (n) by means of a monodimensional numerical model of flood flow routing; c) detecting the time t_p{n) corresponding to a predetermined value of the computed water depth h_p(n) ; d) computing the optimal value (n^*) of the average channel bed roughness coefficient as root of the equation t_p ψ_p (n))= t_p ^* [h_p ^* j; e) computing the peak flow discharge (q_maχ) corresponding to the maximum discharge qim_aχ(n, tj), computed by the numerical model, by changing the generic value of the average roughness coefficient (n) with the optimum value

(n^*).

2. Method according to claim 1 , wherein the predetermined values h*_p and h_p (n) are the maximum values of the water depths respectively measured and computed in said second downstream section (p).

3. Method according to the claim 1 , wherein the predetermined values h*_p and h_p(n) are set equal to each other and their value is selected among those values attained in said second downstream section (p) during the most rapid rising phase of the water depth.

4. Method according to any of the claims from 1 to 3, wherein said monodimensional numerical model of flood flow routing solves the Saint-Venant equations with predetermined boundary and initial conditions. U

5. Method according to claim 3, wherein the Saint-Venant equations are:

dt dx

where "x" is the water flow direction, "t" is the time, "g" is the gravity acceleration and "z" is the topographic elevation, "R" is the hydraulic radius and "σ" is the area of the section.

6. Method according to claim 3, wherein the Saint-Venant equations are:

J^ + ^ - O dt dx

where H(x,t) is the elevation, with respect to an horizontal plane, of the free surface in the water section with abscissa x at time t, "R" is the hydraulic radius and "σ" is the area of the section.

7. Method according to claim 1 , wherein the steps b) and the following ones are run from a predetermined time (T1) obtained with the following procedure:

- selecting a first time (TM) corresponding to the maximum water depth value measured in said second downstream section (p);

- starting from this first time (TM), proceeding backward in time up to said predetermined time (T1) defined as the time in which it is attained the first local minimum of the water depth measured in the first upstream section (1).

8. Method according to claim 7, wherein the steps b) and the following ones can be stopped at an other time (T2) defined by the equation T2=T1 +2*(TM-T1).

9. System for measuring the peak flow discharge in a water course comprising at least two water depth measurement instruments (10,11), placed outside the water course at a predetermined distance from each other in correspondence with two sections of the water course, data processing means suitable to process the data detected by said measurement instruments (10,11) and to compute the peak flow discharge in correspondence with one of the two sections, wherein said measurement instruments (10, 11) are provided with synchronization means suitable to synchronize the instruments each other.

10. System according to claim 9, wherein said synchronization means comprise a high precision clock, a telephone device and/or a radio transmitter/receiver.

11. System according to claim 10, wherein at least one of the measurement instruments is provided with a data logger.

12. System according to claim 9, where the measurement instruments are provided with a radar sensor (15).

13. System according to claim 9, wherein said predetermined distance ranges between about 1 and 20 km.

14. System according to any of the claims from 9 to 13, wherein said processing means are in cooperation with at least one of the measurement instruments.

15. System according to any of the claims from 9 to 13, wherein each measurement instrument can be provided with a further sensor suitable to penetrate the water for a synchronous recording of the channel bed elevations.