^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

A methodology to estimate the discharge along rivers, even poorly gauged ones, taking advantage of water level measurements derived from satellite altimetry is proposed. The procedure is based on the application of the Rating Curve Model (RCM), a simple method allowing for the estimation of the flow conditions in a river section using only water levels recorded at that site and the discharges observed at another upstream section. The European Remote-Sensing Satellite 2, ERS-2, and the Environmental Satellite, ENVISAT, altimetry data are used to provide time series of water levels needed for the application of RCM. In order to evaluate the usefulness of the approach, the results are compared with the ones obtained by applying an empirical formula that allows discharge estimation from remotely sensed hydraulic information.

To test the proposed procedure, the 236 km-reach of the Po River is investigated, for which five

River discharge is the variable of interest for many scientific and operational applications related to water resources management and flood risk mitigation. Unfortunately, it is not a direct measure, and it is normally expressed in terms of water level variations using mathematical formulas or calibrated relationships, referred to as rating curves. A rating curve is established by simultaneous measurements of velocity and water levels, and a curve is fitted through the measured hydraulic variables [

In addition to these inherent issues, the need to develop new procedures for river discharge estimation based on remote sensing technology is also motivated by: (1) the recent decrease in the hydraulic monitoring network observed all over the world [

Radar altimetry measures the distance between satellite and instantaneous water surface. The differences between the satellite altitude, relative to a reference ellipsoid determined through precise orbit computation, and the distance from the satellite to the water provides a measurement of the water level above the datum. In order to obtain the height of the water, various corrections have to be added, such as the time delay related to the propagation of the pulse through the atmosphere (dry and wet tropospheric correction) and the ionosphere (ionospheric correction) and the correction for solid tidal effects on the Earth (the solid tide correction) [

Due to the size of the footprint, the radar altimetry technology has been widely applied to large rivers, such as the Amazon River [

The accuracy of altimeter water level time series over river and floodplains has been discussed in several previously published papers (

The high accuracy of altimetry data provided by the latest spatial missions and the convincing results obtained in the previous applications suggest that these data may also be employed for hydrological model calibration [

Based on the above insights, this work proposes a simple methodology to estimate the discharge along rivers, even those poorly gauged, taking advantage of water level measurements derived from satellite altimetry and of the application of the Rating Curve Model (RCM) [

A long branch of the Po River, in northern Italy, is selected as a case study. It represents one of the up-to-date stream gauged networks in Italy, and so far, studies that use satellite altimetry data do not exist. Five gauged stations, with daily observations of water levels, located along the selected reach and water level time series (35-day time step) at four VSs, are available, derived from ERS-2 and ENVISAT tracks from May 1995 to August 2010.

Two different analyses are carried out. At first, the water levels derived by altimetry and

A comparison between the discharges estimated by RCM and by the empirical equation proposed by Bjerklie

The validation of the altimetry data is performed by comparing them with the ground-based water level data from gauged stations. At first, a preliminary analysis is carried out by investigating the coefficients of correlation calculated between the satellite data and the

Considering the temporal resolution of the altimetry sensor and the distance between the gauged stations and the satellite track,

The Rating Curve Model (RCM) is a simple approach for discharge assessment at local sites where only the stage is monitored, while the river flow and the stage are known at another river section some distance away. Therefore, RCM allows rating curve estimation at hydrometric sites where flow velocity measurements cannot be carried out or are available only for low stage values. RCM was originally developed for downstream discharge estimation when the flow hydrograph is recorded at an upstream site [_{u}_{d}_{u}_{d}_{L}

The effective flow area is that part of the wetted section that conveys the water flow, and in principle, it can be different from the surveyed one, due both to the morphological characteristics and the interaction with hydraulic structures. The wave travel time is assumed as the time shift necessary to overlap the rising limb and the peak region of the two dimensionless stage hydrographs [_{L}_{L}

When RCM is applied to simulate continuous flood events, the model parameters, α and β, can be derived through _{d}

The discharge assessment at the river site of interest through RCM by using altimetry satellite data can be carried out if an upstream gauged site, for which a rating curve is available, is present, and topographical surveys are executed at both end sections for _{u}_{d}

In the present study, it is assumed that no level-discharge records are available at the downstream river site (ungauged site) where the discharge assessment is of interest, and hence,

Bjerklie ^{3}/s) is the discharge,

The comparison between the two approaches, RCM and BJ03, is carried out considering the VSs where the altimetry data are available.

The accuracy of the discharge estimates is determined by using four performance measures: RMSE and NS, the relative root mean square error, RRMSE, and the relative error, RE, these two latter defined as follows:
_{sim}_{obs}_{obs}

In order to test the proposed methodology for river discharge estimation by satellite altimetry data, the Po River in northern Italy is selected as a case study. It is located in the center of a large flat alluvial plain, the Pianura Padana (Po Valley), and this avoids some issue tied to the presence of mountains that may affect the altimeter echoes. For this study, five gauged river stations along the river, continuously monitoring the water level, are used: Piacenza (basin area equal to 42,030 km^{2}), Cremona (50,726 km^{2}), Borgoforte (62,450 km^{2}), Sermide (68,724 km^{2}) and Pontelagoscuro (70,091 km^{2}) (

The stage and discharge recorded

As regards the flow regime, the values of maximum, mean and minimum discharge of the period 1995–2010 are reported in

At present, various databases are available, enabling the retrieval of water level altimetry time series for large basins, such as Hydroweb [

In this section, first, the comparison between satellite and

As the first step, both the water level measurements from gauged stations and satellite sensors are referred to the same ellipsoid in order to allow data comparison. As expected, the VSs do not correspond with the gauged stations (see

The correlations between the water levels recorded in all the gauged stations and provided at the VSs from altimetry data are reported in _{L}

In order to evaluate the quantitative accuracy of the satellite data, the water levels derived by satellite altimetry are simulated by using linear regression between satellite observations and

The estimated accuracy is consistent with previous studies, as, for example, by Birkinshaw

The same conclusions can be drawn by examining the NS coefficient values that are found higher for ENVISAT (0.85 for both the stations) than for ERS-2 (0.73 and 0.78 for Sermide and Pontelagoscuro, respectively) for the VS3. Moreover, the NS coefficients for VS3 (ERS-2 and ENVISAT) are much higher than the ones for VS2, despite RMSE being the same. This is ascribed to the variance of the altimetry series belonging to VS2 that is equal to 0.98 m and 1.04 m for Sermide and Pontelagoscuro, respectively, whereas for the VS3, it is found to be almost twice (in the range 1.99–2.39 m).

The accuracy of RCM to estimate discharge by using satellite data is carried out by comparison with the observed discharge at the closest gauged stations. To this end, we analyze two river reaches: Piacenza-VS2 and Piacenza-VS3. The gauged stations of Sermide and Pontelagoscuro are used as benchmarks, assuming that the contribution of the intermediate drainage area is negligible (see

The hydraulic quantities involved in

The analysis is performed by assuming the section geometry available at both river reach ends, while the _{L}^{3}·s^{−1}) observed in the upstream station in the entire period by using _{L}_{obs}, Q_{RCM}) overlap the bisector line for both the gauged stations, demonstrating the good agreement of the discharge derived by RCM with

A further analysis is carried out by considering the river reach, Piacenza-VS3. The conditions are the same as the previous case, but the T_{L} is 28 h for a reach of 207 km. The results are shown in _{obs}, Q_{RCM}) are below the bisector. RMSE is higher than the one estimated for VS2 (equal to 453 m^{3}·s^{−1} and 497 m^{3}·s^{−1}), but NS increases up to 0.85 and 0.82, for Sermide and Pontelagoscuro station, respectively (see

If we compare the observed and simulated discharge considering only ERS-2 altimetry data, RCM works better for VS2 (ERS-2) with RMSE, RRMSE and RE errors lower than the ones computed for VS3 (ERS-2).

The use of constant and uncalibrated values for the parameters, _{obs}_{RCM}

Generally, RCM provides satisfactory results, confirming the potential usefulness of the method to be used with satellite data for the estimation of the discharge. Moreover, these errors are consistent with the ones of the study carried out by Getirana

For the application of the empirical equation, BJ03, the slope, _{0}

In ^{3}·s^{−1} and 834 m^{3}·s^{−1} for Sermide and Pontelagoscuro, respectively) and the RRMSE values (70.5% and 55.3%) are quite high, whereas negative NS values are obtained. This result is due to an important overestimation of BJ03, clearly visible in

Furthermore, by considering the VS3 (ERS-2 and ENVISAT), errors are found to be higher than the ones referring to RCM, above all for the Sermide section, with RMSE, RRMSE and NS equal to 755 m^{3}·s^{−1}, 54.3% and 0.59, respectively. For Pontelagoscuro section, the performance measures are slightly better, with RMSE, RRMSE and NS values of 670 m^{3}·s^{−1}, 45% and 0.66, respectively. Additionally, in this case, altimetry data from ENVISAT are better than ERS-2 ones, as shown in

It is worth noting that RCM takes into account the discharge recorded at the upstream section, whereas BJ03 does not consider this input data. Furthermore, also, the application of the BJ03 in Italy should be preceded by a calibration of the coefficients by using the

In this study, river discharge is estimated for two gauged sites on the Po River by using altimetry data from ERS-2 and ENVISAT satellites. The comparison between the satellite and

The study uses two methods for the discharge estimation in the ungauged river site, where only the geometry of the cross-sections is required. The proposed simplified routing model, named RCM, applied with altimetry data, is able to estimate the discharge in a river site narrower than the one usually considered for altimetry applications [

Moreover, the RCM method outperformed the empirical formula proposed by Bjerklie

The obtained results suggest that the radar altimetry observations can be used to estimate discharge at ungauged river sites. An open issue that has still to be addressed is related to the assessment of the cross-section geometry [

Future investigations will be performed to integrate altimetry-derived water levels and velocity data derived by Moderate Resolution Imaging Spectroradiometer, MODIS [

The authors wish to thank the European Space Agency for furnishing the altimetry data, ARPA (Agenzia Regionale Prevenzione e Ambiente) Emilia Romagna and, in particular, Eng. Federica Pellegrini, for providing the analyzed data for the Po River basin.

The authors declare no conflict of interest.

Geographical location of the study area. Spatial distribution of

Water level time series of available

Scatter plot of the water level for

Piacenza-VS2 river reach: comparison between the discharge simulated by using the Rating Curve Model (RCM) and the Bjerklie formula and the observed

Piacenza-VS3 river reach: comparison between the discharge simulated by using RCM and the Bjerklie formula and the observed

Characteristics of the gauged stations of the Po River: basin area (_{b}_{max}_{min}_{m}

_{b}^{2}) |
_{max}^{3}·s^{−1}) |
_{min}^{3}·s^{−1}) |
_{m}^{3}·s^{−1}) | |||
---|---|---|---|---|---|---|

Piacenza | 42,030 | 213 | 18.01 | 12,800 | 125 | 958 |

Cremona | 50,726 | 278 | 12.86 | 13,750 | 200 | 1,115 |

Borgoforte | 62,450 | 266 | 10.47 | 12,047 | 209 | 1,373 |

Sermide | 68,724 | 493 | 11.19 | 10,100 | 123 | 1,358 |

Pontelagoscuro | 70,091 | 302 | 18.73 | 10,300 | 156 | 1,501 |

Distance in km between

VS1 | 124 | 77 | −20 | −77 | −112 |

VS2 | 190 | 144 | 47 | −11 | −46 |

VS3 | 207 | 160 | 63 | 6 | −29 |

VS4 | 264 | 217 | 120 | 63 | 28 |

Coefficient of correlation between water levels recorded at the

VS1 (ERS-2 and ENVISAT) | 1995–2010 | 0.37 | 0.38 | 0.42 | 0.43 | |

VS1 (ERS-2) | 1995–2003 | 0.35 | 0.37 | 0.42 | 0.44 | |

VS1 (ENVISAT) | 2002–2010 | 0.40 | 0.39 | 0.41 | 0.42 | |

VS2 (ERS-2) | 1995–2003 | 0.79 | 0.83 | 0.83 | 0.82 | |

VS3 (ERS-2 and ENVISAT) | 1995–2010 | 0.81 | 0.85 | 0.90 | 0.91 | |

VS3 (ERS-2) | 1995–2003 | 0.75 | 0.81 | 0.87 | 0.89 | |

VS3 (ENVISAT) | 2002–2010 | 0.89 | 0.90 | 0.92 | 0.92 | |

VS4 (ERS-2) | 1995–2003 | 0.31 | 0.32 | 0.31 | 0.35 |

Root mean square error (RMSE) and Nash Sutcliffe coefficient (NS) between the water levels measured at the

VS2 (ERS-2) | 72 | 0.80 | 0.63 | 0.75 | 0.67 |

VS3 (ERS-2 and ENVISAT) | 148 | 0.76 | 0.79 | 0.69 | 0.82 |

VS3 (ERS-2) | 72 | 0.87 | 0.73 | 0.75 | 0.78 |

VS3 (ENVISAT) | 76 | 0.59 | 0.85 | 0.61 | 0.85 |

VS2 and VS3: comparison between the discharge derived from RCM and the empirical equation derived by Bjerklie

| ||||||||
---|---|---|---|---|---|---|---|---|

^{3}·s^{−1}) |
^{3}·s^{−1}) |
|||||||

VS2 (ERS-2) | 396 | 29.0 | 0.73 | −2.7 | 962 | 70.5 | −0.61 | 52.9 |

VS3 (ERS-2 and ENVISAT) | 453 | 32.6 | 0.85 | −20.2 | 755 | 54.3 | 0.59 | 29.6 |

VS3 (ERS-2) | 530 | 33.4 | 0.84 | −17.3 | 892 | 56.2 | 0.54 | 29.2 |

VS3 (ENVISAT) | 365 | 30.3 | 0.87 | −23.9 | 597 | 49.6 | 0.64 | 30.2 |

| ||||||||
---|---|---|---|---|---|---|---|---|

^{3}·s^{−1}) |
^{3}·s^{−1}) |
|||||||

VS2 (ERS-2) | 405 | 26.9 | 0.73 | −12.1 | 834 | 55.3 | −0.14 | 38.3 |

VS3 (ERS-2 and ENVISAT) | 497 | 33.3 | 0.82 | −25.8 | 670 | 44.9 | 0.66 | 20.6 |

VS3 (ERS-2) | 526 | 31.2 | 0.82 | −22.3 | 794 | 47.0 | 0.60 | 21.3 |

VS3 (ENVISAT) | 467 | 35.7 | 0.80 | −30.1 | 527 | 40.3 | 0.74 | 19.8 |