# Return Period of Characteristic Discharges from the Comparison between Partial Duration and Annual Series, Application to the Walloon Rivers (Belgium)

^{*}

## Abstract

**:**

_{0.625}computed with partial series. Annual series computations allow Q

_{100}discharge determination and extreme floods recurrence interval estimation. A comparison of data from the literature allowed for the confirmation of the value of Myer’s rating at 18, and this value was used to predict extreme floods based on the area of the watershed.

## 1. Introduction

_{a}) or partial series (T

_{p}); (2) which threshold flow should be used to select floods for the partial series method. Annual series do not allow for an estimation of recurrence intervals of bankfull discharge of less than 1 year. This is a problem because such recurrences occur regularly on many rivers in Wallonia, particularly in the Ardenne [7].

_{a}and T

_{p}) for predicting a flood with low recurrence [8]. To determine this threshold, a literature review was conducted in order to compare the different threshold values and to confidently select a reliable method based on a series of comparisons and tests.

_{100}-flood discharge. Moreover, extreme events have also been compiled, analyzed and compared to Q

_{100}estimates. Maximum probable extreme floods were estimated from the catchment area by Guilcher [20] and Réméniéras [21]. Recent data has been compiled using their methodology in order to propose a robust value for the Myer–Coutagne equation [22] for the rivers of Wallonia.

## 2. Materials and Methods

#### 2.1. Study Sites

^{2}. The oldest station recording hourly data was installed in 1967; 37 stations offer data starting before 1990, 24 between 1990 and 2000, and 15 after 2000 (Table 1).

#### 2.2. Bankfull Discharges of a Selection of Rivers in the Meuse and Scheldt Basins

_{b}values for selected rivers.

_{b}ranges between 1 and 2 years, expressed in annual series [27,32,33,34,35,36]. Dury [37] considered that the return period of Q

_{b}was equal to 1.58 years, the value corresponding to the most probable value of the annual maximum in the Gumbel distribution. Tricart [38] assumed a recurrence of Q

_{b}equivalent to 1.5 years. However, Petit and Daxhelet [12] demonstrated that it increases with catchment size, annual rainfall, contrast of the hydrologic regime, while it decreases with bed load sediment grain size. Amoros and Petts [39] and Edwards et al. [40] estimate the recurrence of Q

_{b}at 1.5 years but closer to one year for rivers with an impervious substrate and closer to 2 years in permeable terrain area. Wilkerson [41] also postulates that the 2-year recurrence flood (Q

_{2}) can be a good estimate of Q

_{b}in absence of field observations.

#### 2.3. Methods for Flood Return Period Estimation

#### 2.3.1. Graphical Method and Gumbel Distribution

_{[r]}the value correspoding to the rank r and c a coefficient, usually fixed to 0.5 after Hazen [57] and recommended by Brunet-Moret [58].

_{0}is a position parameter which corresponds to the distribution mode and is calculated from the mean annual discharge (Q

_{m}) of the series (Equation (6)).

_{1}and T

_{2}, respectively the upper and lower limits of the interval [65]

_{i}, the theoretical discharge of a flood with a return period of i years and σ the standard deviation of the floods sample used.

_{a}), corresponding to the maximum annual flood, and the partial flood series (T

_{p}) whose flow is greater than a given threshold were analyzed.

#### 2.3.2. Flood Return Period Calculation in Annual Series

#### 2.3.3. Flood Return Period Calculation in Partial Series

_{b}, encompassing the 0.6 Q

_{b}value proposed by Petit and Pauquet [7]); (3) a wide range of specific discharges (from 0.025 to 0.2 m

^{3}·s

^{−1}·km

^{−2}); (4) several characteristic discharges estimated from hydrologic series; and (5) a discharge threshold defined to obtain around 5 independent flood peaks per year [78].

_{b}) is not suitable in the absence of field observations, as the data sometimes do not exist. (3) Specific discharges as threshold for POT calculations are not suitable because permeable and impervious watersheds will show major differences in their specific discharges [83]. (4) A characteristic discharge value such as Q

_{2.33}could be set as threshold but it is also dependent on the length of the hydrologic series and the type of fluvial regime and substratum. (5) The best series-length independent estimator we have used is the number of average flood peaks. Adamowski [78] suggests using 2–5 peaks while Cunnane [76] opts for a threshold a number of 1.65 N of flood peaks where N represents the number of years recorded in the discharge series while Lang et al. [68] utilize an equation which will test both the dispersion and the stationarity of the number of floods. We have chosen to set a threshold that gives a value of around 5 independent peak floods after POT selection. As the selection algorithm computer software takes time to run, another type of algorithm has been conceived in order to count all peak floods (dependent and independent) in real time. The threshold that gives 5.5 dependent and independent peak floods per year for each station has been sought; it corresponds to about 5 independent flood peaks per year and does not require the complete operational run of the algorithm (Table 3). This script (see Appendix C) is available in the Supplementary Materials.

## 3. Results

#### 3.1. Bankfull Discharge Return Period Analysis

^{2}in Wallonia while summer floods require hourly discharge values for a catchment area of less than 100 to 250 km

^{2}, depending on the area and the fluvial regime.

_{b}by region needs at first an overview of the regional specific bankfull discharge. The lowest values are observed in rivers from Hesbaye with an average specific Q

_{b}of 0.063 m

^{3}·s

^{−1}·km

^{−2}. Rivers from Brabant, Hainaut, and Condroz regions show average values of 0.096, 0.098, and 0.100 m

^{3}·s

^{−1}·km

^{−2}respectively. The rivers from Lorraine exhibit average specific Q

_{b}discharge value of 0.119 m

^{3}·s

^{−1}·km

^{−2}while Entre-Vesdre-et-Meuse and Ardenne regions are showing values of 0.131 and 0.132 m

^{3}·s

^{−1}·km

^{−2}respectively. Larger values are observed in the region of Fagne and Famenne with 0.156 m

^{3}·s

^{−1}·km

^{−2}. Two groups are clearly distinctive: the Fagne–Famenne with systematically higher Q

_{b}values, the Hesbaye with systematically lower Q

_{b}. At river scale, some of them clearly stand out. We can cite the ones with a specific bankfull discharge value above 0.2 m

^{3}·s

^{−1}·km

^{−2}; in Ardenne region: the Eau Noire (no. 5), Hoëgne river (no. 6) and Wayai river (no. 37); in Fagne–Famenne region: Brouffe river (no. 39) and the Ruisseau d’Heure (no. 46). The Hoëgne River at Belleheid (no. 6) appears clearly as an outlier. It is located in a cascade-system reach with a steep profile slope (average: 3.7%) [84]. Its observed Q

_{b}value (~10 m

^{3}·s

^{−1}) is equal to the Q

_{0.625}computed value (9.9 m

^{3}·s

^{−1}). However this value is very different from the 2.4 m

^{3}·s

^{−1}given by the Equation 1 for pebble-bedded rivers on impervious substratum [16]. The Brouffe River located in the Fagne region with a specific Q

_{b}value of 0.250 m

^{3}·s

^{−1}·km

^{−2}correspond to an anthropized reach in the vicinity of the gauging station. The other rivers from Fagne–Famenne region show specific Q

_{b}values in the range 0.1–0.2 m

^{3}·s

^{−1}·km

^{−2}.

_{b}values led the authors to consider that the Q

_{0.625}-flood is the most suitable value, i.e., flood events happening 1.6 times a year. Figure 4 shows that the fit between Q

_{0.625}and Q

_{b}does not exhibit the normal regional pattern because the computation is taking into account both the physical features as well as the hydrological parameters. In addition, with their more extensive watershed catchment areas, Ardenne’s rivers are those with the largest Q

_{b}in this dataset. A few outliers are detected: no. 49 and no. 50, the Bocq River whose stations suffer from rating curve instability, lack of data and concrete-channelized reaches near hydrographic stations.

_{b}return period from 0.3 to 1.3 years. Stations located on the main watercourse of the Ourthe have an average value of 0.8 years while Aisne tributary (stations no. 1 and no. 2) and Lienne tributary (station no. 18) show values of 0.30, 0.68 and 1.28 years respectively.

_{b}return period from 0.3 to 0.7 years.

_{b}discharge return period between 0.3 and 0.5 years (with Ardenne characteristics) while the Eau Blanche River and Brouffe River, tributary of the Viroin and located in the Fagne region, show return period of 1.0 and 1.3 years respectively.

_{b}recurrence interval ranges between 0.2 and 0.4 years, which is consistent with observations and flood alerts from the regional river network manager. The Vire and Ton catchments show bankfull discharge return period from 0.3 to 0.7 years except for the Vire at Ruette (station no. 75) where natural levees increase the value to 2.2 years.

_{b}return period of 1.9 and 1.8 years respectively. The other rivers have not-often experienced bankfull discharge events: the Petite Gette River with a Q

_{b}return period of 8.9 years, the Rhosnes at Amougies with 5.4 years and the Bocq River at two locations (4.5 and 3.0 years). These discharge patterns are directly linked to the high values of the specific discharges values described earlier. The station corresponding to the Vesdre River at Chaudfontaine (no. 32) is not represented in graphs and tables. The calculated return period of its discharges is disturbed by hydroelectric and drinking water dams (Eupen and Gileppe dams).

#### 3.2. Discharge and Return Period of Extreme Floods

_{a100}, computed with Gumbel method’s of moments) and watershed area (see Equation (14)).

_{max}is the maximum discharge (in m

^{3}·s

^{−1}), A the watershed area, C the Myer’s rating which relates to the physical parameters of the watershed and to the morphoclimatic system and the exponent a = 0.5; the value of this exponent is justified by the fact that, in the presence of a uniform downpour, the total volume flow is proportional to the area of the basin and the concentration time is schematically equivalent to the length of the watercourse [2,92,93]. Myer’s ratings, which were recorded following extreme floods in the High Fens range from 16 to 18 [94,95], with pluri-centennial return periods. In Corsica, Gob et al. [96] computed a Coutagne–Myer coefficient close to 30 for the extreme flooding in 1973 in these Mediterranean mountains with their steep slopes. This coefficient exceeds 100 in the Ardèche River and its tributaries during ‘Cévenoles’ episodes, because it is related both to meteorological and topoclimatological parameters, with the energy of the topographic relief inducing a particular fluvial regime. Differences are partly explained by the more important role attributed to the surface of the basin in Myer’s formula, thus accentuating the size differences between watersheds [93].

^{3}·s

^{−1}) with A, the area of the watershed (in km

^{2}), Q

_{0}= 10

^{6}and A

_{0}= 10

^{8}. The parameter k is a regionalized parameter and it is equal to 3.5 in the northern oceanic zone.

^{2}) and a huge variability appears in their resulting plot points. They have identified, for any catchment with less than 10, 20-square-kilometre areas, a limit named the “downpour phenomenon” where heavy rainfall associated with runoff can lead to a specific discharge of 10 m

^{3}·s

^{−1}·km

^{−2}[97]. Indeed, Francou & Rodier’s equation seems most unsuitable for modelling extreme floods for any catchment area below ~100 km

^{2}with k = 3.5 (Figure 6). A value of 3.9 is needed in order to fit with the extreme discharge values that were observed in watercourses of Wallonia.

_{100}envelope curve from our selection of 76 stations. Their estimate of Q

_{100}discharge is obviously related to the length of the series of observations and to the extreme events that occurred in the watersheds in this study, given the large spatial disparity in storm precipitation or snowmelt associated with the highest floods. With an average of 31 years of data gathered by the 76 stations studied, the highest floods have an average recurrence of 80 years. Several maximum flow rates are considered as a pluri-centennial flood. The limited length of the hydrologic series does not allow a more robust recurrence interval estimate. As mentioned earlier, Francou and Rodier’s envelope curve significantly underestimates the discharge of the flash-floods which occurred in Belgium in both small and large watersheds. These events are markedly better modeled by the Myer’s formula.

## 4. Discussion

_{a}= T

_{p}+ 0.5. In the analysis of a selection of rivers in different geographical regions in Wallonia (Belgium), this equation turns into T

_{a}= T

_{p}+ 0.83 (± 0.10 as standard deviation) for bankfull discharge. The flood threshold in partial series has been defined—thanks to a complete analysis of the evolution of the return period value—depending on the average number of flood events per year. Each station has a graphic representation of the area where the calculated return period is stable and corresponds, in our subset, to around five events per year. Comparing this to other studies (see Table 2) which mention a threshold corresponding to a flow rate of either a defined partial return period [77,80] or linked to a number of flood events per year [76,78], we use a threshold (T

_{p}~ 0.2 years) lower than daily series studies (T

_{p}from 1.15 to 2 years).

_{b}determination in hourly series and a threshold of T

_{p}~0.2 years, we have observed that Q

_{b}value could be accurately estimated in absence of field data as the Q

_{0.625}discharge in partial series. Wilkerson [41] listed the published Q

_{b}return period of a variety of authors from Europe, USA and Australia. They range from 0.46 to 10 years depending on localization, with average or mode values often reported as being between 1.0 and 2.0 years because annual series are mainly used. Petit [95] mentions that the use of partial series give a better estimation of the reccurence interval of Q

_{b}and this is in the range from 0.4 to 0.7 years in Ardenne rivers with any watershed area of less than 500 km

^{2}. With the same hydrologic series, annual series give for our subset (field-observed data excluding anthropized stations) an average Q

_{b}return period value of 1.5 years (range: 1–2.6 yr) for 59 stations. Later studies have confirmed this value in Southern Italy [98] in annual series. However recent literature lacks values in partial series over a wide selection of stations [7,99,100].

^{2}in annual series was of the order of 1 year, very close to the value limit which one can obtain by using annual series and values around 1.5 to 2 years in the case of larger Ardenne type rivers [7]. Fagne and Famenne rivers, often characterized by small catchment area due to the morphology of the lithologic depression, show a large specific Q

_{b}. This is a consequence of the fact that they flow over soft shales which are not very resistant to erosion [17,101], and this tends to incise the river more deeply into its bed. However, these rivers exhibit T

_{p}values of around 0.7 years. Bankfull discharge frequency is just a bit more important than that of either the Ardenne rivers (0.6 years) or the Entre-Vesdre-et-Meuse rivers (0.5 years). In the rivers of Hesbaye, a generalized weakness of the flows (e.g., Gette and Geer Rivers) is observed, because precipitation is much lower and anthropogenic withdrawals are far from negligible. Average bankfull discharge return period reaches 2.7 years despite low specific Q

_{b}.

_{b}return period (2.16 years). Due to their similar substrate to Ardenne watercourses, the rivers of Brabant— which is incised in Cambro-Ordovico-Silurian formations—do not deviate from the relationship defined for the Ardenne. However, rivers such as the Senne, the Dyle are nevertheless very different from the Ardenne rivers, even if they incise the substratum very locally. Very different land use in their catchment can modify the hydrological response to precipitation [102].

_{100}-flood discharge and the return period of extreme floods were analyzed through envelope-curve based on maximum hourly discharges recorded during the hydrological data series in the one hand, as well as literature detailing the available data for flash-floods and extreme floods in Wallonia and surrounding areas. A majority of flood time series are shorter than 50 years. This leads to a mismatch between the length of the flood records and the need for an adequate estimate of the return period, in order to achieve effective and efficient infrastructure design [10]. Increased imperviousness of the landscape tends to increase watershed response to rainfall [102] and heightens the risk of extreme flash-floods [88].

^{2}. The difference between the Q

_{100}floods observed in gauged stations and the maximum discharge (Q

_{max}) estimated with the Myer’s rating varies with the size of the catchments and the length of the hydrographic series.

_{100}, …) and the problem linked to changes in climatological normal—that have to be reassessed over the last 30 years [105]—as prescribed by the World Meteorological Organization.

## 5. Conclusions

_{b}recurrence intervals required an overview of regional characteristics, such as specific bankfull discharge. Sand- or silted-rivers from Hesbaye region present the lowest values of specific bankfull discharge. Pebble-bedded and/or silted rivers from Brabant, Hainaut, and Condroz regions have average specific Q

_{b}around 0.100 m

^{3}·s

^{−1}·km

^{−2}. Sand-bedded rivers in the Lorraine region and pebble-bedded rivers from Entre-Vesdre-et-Meuse and Ardenne regions present values around 0.125 m

^{3}·s

^{−1}·km

^{−2}. Rivers on impervious schistose substratum in Fagne and Famenne regions present the highest values (specific Q

_{b}around 0.156 m

^{3}·s

^{−1}·km

^{−2}).

_{a}= T

_{p}+ 0.83 (± 0.10) for bankfull discharge of rivers of Wallonia, which could be estimated—in the absence of field data—as the Q

_{0.625}discharge in partial series.

_{p}) and a greater dispersion of data points cloud when compared with older studies in the same area and the same rivers with datasets of daily series. Fagne and Famenne rivers exhibit T

_{p}values of Q

_{b}around 0.7 years while Ardenne rivers show average values of 0.6 years. Entre-Vesdre-et-Meuse rivers (0.5 years) and Hesbaye rivers (2.7 years), are respectively the most frequent and less frequent overbank-flooded rivers. Whilst Lorraine rivers, with their complex substratum, show very different T

_{p}values—according to the local materials—and whether or not there are natural levees present.

_{100}discharge and to compare the dimensions of the watershed area. Information on extreme floods was gathered in Wallonia (in both gauged and ungauged catchments) and this was used to compute the value of C, the Myer’s rating which relates to the physical parameters of the watershed and to the morphoclimatic system. We could confirm the value of C = 18 with new data over a wide range of watershed area. Difference between the Q

_{100}envelope-curve and Myer’s curve is best seen in small watersheds because flash-floods are more prone to affecting small catchments with the resulting extreme discharges.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{1.5}, Q

_{2.33}, Q

_{5}, Q

_{10}, Q

_{20}, and Q

_{50}) calculated with the Gumbel’s ordinary moments method for all the studied stations and the Q

_{10/365}, i.e., the flood discharge that is reached 10 days a year. Table A5 presents the equations of annual and partial recurrence interval calculated with the same method.

Partial Series | Annual Series | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

ID | River | Location | Q_{1.5} (m^{3}·s^{−1}) | Q_{2} (m^{3}·s^{−1}) | Q_{2.33} (m^{3}·s^{−1}) | Q_{5} (m^{3}·s^{−1}) | Q_{10} (m^{3}·s^{−1}) | Q_{20} (m^{3}·s^{−1}) | Q_{50} (m^{3}·s^{−1}) | Q_{10/365} (m^{3}·s^{−1}) |

1 | Aisne | Erezée | 12.0 | 12.7 | 13.1 | 15.3 | 17.8 | 20.3 | 23.4 | 4.9 |

2 | Aisne | Juzaine | 30.2 | 32.4 | 33.6 | 40.0 | 48.4 | 56.4 | 66.8 | 11.0 |

3 | Amblève | Targnon | 117.4 | 124.7 | 128.6 | 146.8 | 171.9 | 196.1 | 227.3 | 54.0 |

4 | Amblève | Martinrive | 172.7 | 184.3 | 190.4 | 226.1 | 271.1 | 314.2 | 370.1 | 72.8 |

5 | Eau Noire | Couvin | 53.4 | 57.5 | 59.7 | 70.0 | 84.3 | 98.0 | 115.8 | 15.4 |

6 | Hoëgne | Belleheid | 12.3 | 13.0 | 13.4 | 16.1 | 18.8 | 21.5 | 25.0 | 2.7 |

7 | Hoëgne | Theux | 60.2 | 64.1 | 66.2 | 73.9 | 88.0 | 101.5 | 119.0 | 14.6 |

8 | Lembrée | Vieuxville | 10.1 | 10.9 | 11.3 | 13.8 | 16.7 | 19.4 | 23.0 | 2.6 |

9 | Lesse | Resteigne | 51.9 | 56.2 | 58.4 | 73.0 | 88.1 | 102.5 | 121.2 | 24.7 |

10 | Lesse | Hérock | 154.0 | 164.9 | 170.7 | 212.6 | 257.3 | 300.1 | 355.6 | 66.5 |

11 | Lesse | Gendron | 167.3 | 179.7 | 186.3 | 224.9 | 271.7 | 316.5 | 374.6 | 71.7 |

12 | Lesse | Eprave | 49.6 | 53.0 | 54.8 | 65.6 | 78.8 | 91.5 | 107.9 | 26.0 |

13 | Lhomme | Grupont | 21.5 | 22.8 | 23.6 | 28.7 | 34.3 | 39.6 | 46.6 | 9.1 |

14 | Lhomme | Forrières | 31.5 | 33.6 | 34.8 | 43.9 | 53.0 | 61.8 | 73.1 | 14.2 |

15 | Lhomme | Jemelle | 37.6 | 40.1 | 41.4 | 49.5 | 58.8 | 67.7 | 79.3 | 16.4 |

16 | Lhomme | Rochefort | 69.1 | 74.4 | 77.3 | 98.7 | 120.2 | 140.8 | 167.5 | 22.8 |

17 | Lhomme | Eprave | 72.2 | 76.3 | 78.5 | 92.0 | 106.2 | 119.8 | 137.4 | 29.1 |

18 | Lienne | Lorcé | 22.2 | 23.8 | 24.7 | 28.2 | 34.0 | 39.5 | 46.7 | 9.8 |

19 | Mellier | Marbehan | 18.0 | 19.5 | 20.3 | 25.1 | 30.6 | 35.9 | 42.7 | 6.9 |

20 | Our | Ouren | 61.3 | 65.8 | 68.2 | 79.3 | 93.6 | 107.3 | 125.1 | 29.7 |

21 | Ourthe | Durbuy | 138.8 | 148.0 | 152.9 | 182.9 | 218.5 | 252.6 | 296.8 | 72.4 |

22 | Ourthe | Tabreux | 177.9 | 191.3 | 198.3 | 242.2 | 292.5 | 340.9 | 403.4 | 91.1 |

23 | Ourthe | Sauheid | 341.7 | 365.5 | 378.1 | 456.6 | 546.3 | 632.4 | 743.8 | 175.6 |

24 | Ourthe orientale | Houffalize | 23.8 | 25.7 | 26.7 | 33.0 | 40.4 | 47.4 | 56.5 | 10.9 |

25 | Ruisseau des Aleines | Auby-sur-Semois | 13.7 | 14.4 | 14.7 | 16.7 | 19.1 | 21.4 | 24.3 | 8.1 |

26 | Rulles | Habay-la-Vieille | 18.7 | 20.1 | 20.8 | 25.0 | 29.5 | 33.8 | 39.4 | 8.5 |

27 | Rulles | Tintigny | 39.3 | 41.7 | 43.0 | 48.1 | 54.5 | 60.6 | 68.6 | 19.9 |

28 | Ry du Moulin | Vresse-sur-Semois | 12.6 | 13.6 | 14.1 | 17.8 | 21.1 | 24.2 | 28.3 | 5.6 |

29 | Semois | Tintigny | 81.7 | 87.8 | 91.0 | 109.7 | 132.3 | 154.0 | 182.1 | 35.5 |

30 | Semois | Membre Pont | 219.6 | 237.2 | 246.6 | 304.3 | 365.0 | 423.3 | 498.8 | 113.9 |

31 | Sûre | Martelange | 40.4 | 44.2 | 46.1 | 57.9 | 70.0 | 81.5 | 96.4 | 16.9 |

32 | Vesdre | Chaudfontaine | 127.0 | 135.9 | 140.6 | 164.1 | 194.1 | 222.9 | 260.2 | 40.7 |

33 | Vierre | Suxy | 34.7 | 37.7 | 39.3 | 49.7 | 60.0 | 69.9 | 82.7 | 17.9 |

34 | Viroin | Olloy-sur-Viroin | 114.4 | 123.3 | 128.0 | 149.0 | 181.1 | 211.8 | 251.7 | 35.9 |

35 | Viroin | Treignes | 102.0 | 109.4 | 113.4 | 138.7 | 168.0 | 196.1 | 232.5 | 36.5 |

36 | Wamme | Hargimont | 24.9 | 26.6 | 27.5 | 31.0 | 38.8 | 46.3 | 56.0 | 7.5 |

37 | Wayai | Spixhe | 25.4 | 27.2 | 28.1 | 35.0 | 41.8 | 48.4 | 56.8 | 6.3 |

38 | Biran | Wanlin | 11.7 | 12.7 | 13.2 | 16.7 | 20.1 | 23.3 | 27.5 | 2.2 |

39 | Brouffe | Mariembourg | 20.8 | 22.4 | 23.2 | 28.5 | 33.9 | 39.0 | 45.7 | 5.5 |

40 | Eau Blanche | Aublain | 19.1 | 20.5 | 21.2 | 26.7 | 32.0 | 37.0 | 43.5 | 7.4 |

41 | Eau Blanche | Nismes | 41.4 | 44.0 | 45.4 | 52.9 | 63.5 | 73.7 | 86.8 | 16.0 |

42 | Hantes | Beaumont | 20.6 | 22.4 | 23.3 | 30.4 | 37.6 | 44.6 | 53.5 | 4.8 |

43 | Hermeton | Romedenne | 22.2 | 23.8 | 24.7 | 27.7 | 33.2 | 38.5 | 45.4 | 6.0 |

44 | Hermeton | Hastière | 26.4 | 28.5 | 29.5 | 35.9 | 43.0 | 49.8 | 58.6 | 7.9 |

45 | Marchette | Marche-en-Famenne | 13.0 | 13.9 | 14.3 | 16.3 | 18.8 | 21.3 | 24.4 | 2.8 |

46 | Ruisseau d’Heure | Baillonville | 14.7 | 15.9 | 16.5 | 19.3 | 22.6 | 25.7 | 29.7 | 3.5 |

47 | Wimbe | Lavaux-Sainte-Anne | 14.7 | 15.7 | 16.2 | 19.0 | 22.1 | 25.0 | 28.8 | 5.3 |

48 | Biesme l’Eau | Biesme-sous-Thuin | 13.8 | 15.0 | 15.7 | 19.6 | 24.4 | 29.0 | 35.0 | 2.6 |

49 | Bocq | Spontin | 14.9 | 16.4 | 17.1 | 22.1 | 28.2 | 34.1 | 41.6 | 3.8 |

50 | Bocq | Yvoir | 19.3 | 21.2 | 22.2 | 28.2 | 36.2 | 43.9 | 53.9 | 6.5 |

51 | Samson | Mozet | 13.6 | 14.6 | 15.1 | 17.0 | 20.2 | 23.3 | 27.3 | 3.7 |

52 | Berwinne | Dalhem | 24.4 | 26.3 | 27.4 | 31.9 | 38.7 | 45.3 | 53.7 | 4.7 |

53 | Bolland | Dalhem | 4.4 | 4.6 | 4.8 | 5.9 | 7.2 | 8.5 | 10.2 | 1.0 |

54 | Gueule | Sippenaken | 23.0 | 24.5 | 25.3 | 29.1 | 33.4 | 37.5 | 42.8 | 5.1 |

55 | Dyle | Florival | 20.1 | 20.8 | 21.2 | 22.6 | 24.7 | 26.7 | 29.3 | 8.3 |

56 | Samme | Ronquières | 18.9 | 20.2 | 20.9 | 25.3 | 30.3 | 35.1 | 41.3 | 4.1 |

57 | Senne | Steenkerque | 24.2 | 25.9 | 26.8 | 29.9 | 35.0 | 39.9 | 46.3 | 5.1 |

58 | Senne | Quenast | 27.2 | 29.1 | 30.1 | 33.7 | 39.4 | 44.9 | 52.0 | 5.8 |

59 | Sennette | Ronquières | 10.3 | 11.0 | 11.4 | 11.2 | 13.2 | 15.1 | 17.6 | 1.9 |

60 | Anneau | Marchipont | 11.1 | 12.3 | 12.9 | 15.9 | 20.2 | 24.4 | 29.8 | 1.5 |

61 | Grande Honnelle | Baisieux | 17.2 | 18.7 | 19.4 | 23.2 | 28.7 | 34.0 | 40.9 | 3.7 |

62 | Rhosnes | Amougies | 17.0 | 17.6 | 17.9 | 18.7 | 21.0 | 23.2 | 26.0 | 6.7 |

63 | Ruisseau des Estinnes | Estinnes-au-Val | 4.4 | 4.9 | 5.1 | 6.8 | 8.8 | 10.7 | 13.3 | 0.6 |

64 | Trouille | Givry | 6.0 | 6.6 | 6.9 | 8.0 | 10.3 | 12.5 | 15.4 | 1.1 |

65 | Burdinale | Marneffe | 3.0 | 3.2 | 3.3 | 3.9 | 4.8 | 5.6 | 6.7 | 0.5 |

66 | Geer | Eben-Emael | 11.5 | 12.0 | 12.2 | 13.5 | 15.0 | 16.4 | 18.2 | 4.9 |

67 | Grande Gette | Sainte-Marie-Geest | 12.6 | 13.7 | 14.3 | 18.1 | 22.5 | 26.7 | 32.2 | 2.4 |

68 | Mehaigne | Ambresin | 15.5 | 16.3 | 16.7 | 17.9 | 20.7 | 23.3 | 26.8 | 5.7 |

69 | Mehaigne | Wanze | 17.8 | 18.9 | 19.5 | 22.5 | 26.6 | 30.6 | 35.6 | 9.0 |

70 | Petite Gette | Opheylissem | 6.5 | 7.0 | 7.2 | 8.9 | 11.2 | 13.4 | 16.3 | 1.6 |

71 | Semois | Chantemelle | 16.2 | 17.1 | 17.6 | 19.6 | 22.8 | 25.9 | 29.9 | 6.4 |

72 | Semois | Etalle | 21.8 | 22.8 | 23.3 | 25.5 | 29.1 | 32.5 | 36.9 | 9.9 |

73 | Ton | Virton | 7.6 | 8.0 | 8.1 | 8.4 | 9.4 | 10.4 | 11.6 | 3.1 |

74 | Ton | Harnoncourt | 34.0 | 36.6 | 37.9 | 42.6 | 52.7 | 62.4 | 75.0 | 13.3 |

75 | Vire | Ruette | 19.6 | 20.9 | 21.6 | 24.0 | 28.0 | 31.8 | 36.7 | 5.4 |

76 | Vire | Latour | 19.7 | 20.8 | 21.5 | 24.3 | 28.2 | 32.0 | 36.8 | 6.9 |

ID | River | Location | Annual Series Equation | Partial Series Equation |
---|---|---|---|---|

u = a (Q − Q_{0}) | ||||

1 | Aisne | Erezée | u = 0.30 (Q − 10.23) | u = 0.44 (Q − 7.55) |

2 | Aisne | Juzaine | u = 0.09 (Q − 23.25) | u = 0.14 (Q − 16.31) |

3 | Amblève | Targnon | u = 0.03 (Q − 96.49) | u = 0.04 (Q − 70.50) |

4 | Amblève | Martinrive | u = 0.02 (Q − 136.17) | u = 0.03 (Q − 100.69) |

5 | Eau Noire | Couvin | u = 0.05 (Q − 41.47) | u = 0.07 (Q − 26.01) |

6 | Hoëgne | Belleheid | u = 0.27 (Q − 10.47) | u = 0.41 (Q − 7.41) |

7 | Hoëgne | Theux | u = 0.05 (Q − 45.66) | u = 0.08 (Q − 33.75) |

8 | Lembrée | Vieuxville | u = 0.26 (Q − 7.95) | u = 0.38 (Q − 4.84) |

9 | Lesse | Resteigne | u = 0.05 (Q − 42.96) | u = 0.07 (Q − 26.32) |

10 | Lesse | Hérock | u = 0.02 (Q − 123.25) | u = 0.03 (Q − 83.01) |

11 | Lesse | Gendron | u = 0.02 (Q − 131.40) | u = 0.02 (Q − 86.35) |

12 | Lesse | Eprave | u = 0.06 (Q − 39.21) | u = 0.09 (Q − 28.02) |

13 | Lhomme | Grupont | u = 0.13 (Q − 17.44) | u = 0.22 (Q − 12.44) |

14 | Lhomme | Forrières | u = 0.08 (Q − 25.65) | u = 0.14 (Q − 18.43) |

15 | Lhomme | Jemelle | u = 0.08 (Q − 30.84) | u = 0.12 (Q − 21.56) |

16 | Lhomme | Rochefort | u = 0.04 (Q − 55.80) | u = 0.06 (Q − 33.60) |

17 | Lhomme | Eprave | u = 0.05 (Q − 63.60) | u = 0.07 (Q − 45.50) |

18 | Lienne | Lorcé | u = 0.13 (Q − 16.67) | u = 0.19 (Q − 12.39) |

19 | Mellier | Marbehan | u = 0.14 (Q − 14.12) | u = 0.21 (Q − 8.80) |

20 | Our | Ouren | u = 0.05 (Q − 50.72) | u = 0.07 (Q − 32.51) |

21 | Ourthe | Durbuy | u = 0.02 (Q − 111.73) | u = 0.03 (Q − 79.98) |

22 | Ourthe | Tabreux | u = 0.01 (Q − 141.54) | u = 0.02 (Q − 95.65) |

23 | Ourthe | Sauheid | u = 0.01 (Q − 277.26) | u = 0.01 (Q − 198.68) |

24 | Ourthe orientale | Houffalize | u = 0.10 (Q − 18.36) | u = 0.16 (Q − 12.09) |

25 | Ruisseau des Aleines | Auby-sur-Semois | u = 0.32 (Q − 12.01) | u = 0.43 (Q − 9.28) |

26 | Rulles | Habay-la-Vieille | u = 0.17 (Q − 16.07) | u = 0.22 (Q − 10.38) |

27 | Rulles | Tintigny | u = 0.12 (Q − 35.35) | u = 0.12 (Q − 23.11) |

28 | Ry du Moulin | Vresse-sur-Semois | u = 0.23 (Q − 11.20) | u = 0.33 (Q − 7.50) |

29 | Semois | Tintigny | u = 0.03 (Q − 64.46) | u = 0.05 (Q − 41.32) |

30 | Semois | Membre Pont | u = 0.01 (Q − 182.82) | u = 0.02 (Q − 107.00) |

31 | Sûre | Martelange | u = 0.06 (Q − 33.89) | u = 0.08 (Q − 16.74) |

32 | Vesdre | Chaudfontaine | u = 0.02 (Q − 104.10) | u = 0.03 (Q − 68.43) |

33 | Vierre | Suxy | u = 0.07 (Q − 29.03) | u = 0.10 (Q − 15.97) |

34 | Viroin | Olloy-sur-Viroin | u = 0.02 (Q − 84.88) | u = 0.03 (Q − 55.41) |

35 | Viroin | Treignes | u = 0.03 (Q − 80.07) | u = 0.04 (Q − 52.40) |

36 | Wamme | Hargimont | u = 0.10 (Q − 15.30) | u = 0.18 (Q − 13.71) |

37 | Wayai | Spixhe | u = 0.11 (Q − 21.47) | u = 0.17 (Q − 13.74) |

38 | Biran | Wanlin | u = 0.22 (Q − 9.98) | u = 0.32 (Q − 5.40) |

39 | Brouffe | Mariembourg | u = 0.14 (Q − 17.83) | u = 0.19 (Q − 10.30) |

40 | Eau Blanche | Aublain | u = 0.14 (Q − 16.27) | u = 0.22 (Q − 10.00) |

41 | Eau Blanche | Nismes | u = 0.07 (Q − 31.83) | u = 0.12 (Q − 24.15) |

42 | Hantes | Beaumont | u = 0.10 (Q − 15.99) | u = 0.17 (Q − 8.84) |

43 | Hermeton | Romedenne | u = 0.14 (Q − 16.63) | u = 0.19 (Q − 11.35) |

44 | Hermeton | Hastière | u = 0.11 (Q − 21.77) | u = 0.15 (Q − 12.75) |

45 | Marchette | Marche-en-Famenne | u = 0.29 (Q − 11.17) | u = 0.37 (Q − 7.45) |

46 | Ruisseau d’Heure | Baillonville | u = 0.23 (Q − 12.80) | u = 0.25 (Q − 6.93) |

47 | Wimbe | Lavaux-Sainte-Anne | u = 0.25 (Q − 12.86) | u = 0.32 (Q − 8.61) |

48 | Biesme l’Eau | Biesme-sous-Thuin | u = 0.16 (Q − 9.94) | u = 0.25 (Q − 5.60) |

49 | Bocq | Spontin | u = 0.12 (Q − 9.86) | u = 0.22 (Q − 6.20) |

50 | Bocq | Yvoir | u = 0.09 (Q − 12.22) | u = 0.17 (Q − 7.66) |

51 | Samson | Mozet | u = 0.23 (Q − 10.58) | u = 0.33 (Q − 7.45) |

52 | Berwinne | Dalhem | u = 0.11 (Q − 18.28) | u = 0.16 (Q − 11.60) |

53 | Bolland | Dalhem | u = 0.56 (Q − 3.24) | u = 1.04 (Q − 2.40) |

54 | Gueule | Sippenaken | u = 0.18 (Q − 20.49) | u = 0.20 (Q − 12.92) |

55 | Dyle | Florival | u = 0.36 (Q − 18.50) | u = 0.39 (Q − 14.84) |

56 | Samme | Ronquières | u = 0.15 (Q − 15.28) | u = 0.23 (Q − 10.23) |

57 | Senne | Steenkerque | u = 0.15 (Q − 19.74) | u = 0.18 (Q − 13.14) |

58 | Senne | Quenast | u = 0.13 (Q − 22.20) | u = 0.16 (Q − 14.80) |

59 | Sennette | Ronquières | u = 0.38 (Q − 7.29) | u = 0.42 (Q − 5.47) |

60 | Anneau | Marchipont | u = 0.17 (Q − 7.21) | u = 0.26 (Q − 3.39) |

61 | Grande Honnelle | Baisieux | u = 0.14 (Q − 12.07) | u = 0.21 (Q − 7.32) |

62 | Rhosnes | Amougies | u = 0.33 (Q − 14.16) | u = 0.50 (Q − 12.89) |

63 | Ruisseau des Estinnes | Estinnes-au-Val | u = 0.37 (Q − 2.70) | u = 0.70 (Q − 1.59) |

64 | Trouille | Givry | u = 0.32 (Q − 3.37) | u = 0.54 (Q − 2.27) |

65 | Burdinale | Marneffe | u = 0.84 (Q − 2.10) | u = 1.29 (Q − 1.39) |

66 | Geer | Eben-Emael | u = 0.51 (Q − 10.62) | u = 0.70 (Q − 8.61) |

67 | Grande Gette | Sainte-Marie-Geest | u = 0.17 (Q − 9.31) | u = 0.27 (Q − 5.77) |

68 | Mehaigne | Ambresin | u = 0.27 (Q − 12.34) | u = 0.37 (Q − 9.92) |

69 | Mehaigne | Wanze | u = 0.18 (Q − 14.37) | u = 0.28 (Q − 10.93) |

70 | Petite Gette | Opheylissem | u = 0.32 (Q − 4.20) | u = 0.59 (Q − 3.04) |

71 | Semois | Chantemelle | u = 0.23 (Q − 13.09) | u = 0.34 (Q − 10.16) |

72 | Semois | Etalle | u = 0.21 (Q − 18.42) | u = 0.30 (Q − 14.90) |

73 | Ton | Virton | u = 0.77 (Q − 6.49) | u = 0.93 (Q − 5.48) |

74 | Ton | Harnoncourt | u = 0.07 (Q − 22.32) | u = 0.12 (Q − 17.48) |

75 | Vire | Ruette | u = 0.19 (Q − 16.10) | u = 0.23 (Q − 10.82) |

76 | Vire | Latour | u = 0.19 (Q − 16.56) | u = 0.26 (Q − 11.74) |

_{0}) where u is a double transformation of the cumulated frequency F(Q), and expressed as u = −ln(−ln F(Q)). The variable a is the scale parameter estimated through the system of Equations (5) and (6). Q

_{0}is the form parameter. Available hourly data have been used, from station installation date to 31 December 2018.

## Appendix B. Visual Basic Code for the Estimation of the Number of Dependent and Independent Peaks over Threshold

## Appendix C. Visual Basic Code for the Calculation of the Partial Series Return Periods

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**Figure 2.**Convergence of annual and partial series—comparison of the method of ordinary moments and the graphical method (example on the Aisne River at Juzaine—station no. 2).

**Figure 4.**Fit between the discharge value of Q

_{0.625}in partial series and the field-observed Q

_{b}.

**Figure 5.**Return period of the observed bankfull discharge (expressed in partial series for values below 5 years and in annual series beyond).

**Figure 6.**Extreme recorded discharge between 1968 and 2018 in gauged Walloon rivers and the comparison between Myer’s formula (with C = 18) and different flash flood in ungauged watershed (Sart-Tilman flash flood, Chefna watercourse and High Fens watercourses) as well as Meuse 1925-26 large inundation; envelope curve of Q

_{100}values computed for the 76 studied stations. Francou & Rodier’s formula for northern oceanic zone maximum discharge is also shown as well as the optimized k parameter fitting with extreme floods of Walloon rivers.

ID | River | Location | A (km^{2}) | Station Code | Station Start Date | N_{y} | Q_{b} (m^{3}·s^{−1}) | Specific Q_{b} (m^{3}·s^{−1}·km^{−2}) | Sources of Q_{b} Observation |
---|---|---|---|---|---|---|---|---|---|

ARDENNE Region | |||||||||

1 | Aisne | Erezée | 67.4 | L6690 | 1998–12 | 20 | 7.3 | 0.108 | Houbrechts (2000) [14] |

2 | Aisne | Juzaine | 183 | L5491 | 1975–03 | 34 | 23.8 | 0.130 | Houbrechts (2000) [14] |

3 | Amblève | Targnon | 802.9 | S6671 | 1968–06 | 20 | 87.3 | 0.109 | New observation |

4 | Amblève | Martinrive | 1062 | S6621 | 1968–10 | 45 | 140 | 0.132 | Houbrechts (2005) [42] |

5 | Eau Noire | Couvin | 176 | S9071 | 1968–03 | 33 | 36.9 | 0.210 | New observation (2008) |

6 | Hoëgne | Belleheid | 20 | S6526 | 1993–06 | 25 | 10 | 0.500 | New observation (2019) |

7 | Hoëgne | Theux | 189 | L5860 | 1979–02 | 36 | 36.8 | 0.195 | Deroanne (1995) [43] |

8 | Lembrée | Vieuxville | 51 | L6300 | 1991–09 | 26 | 7.9 | 0.155 | Houbrechts (2005) [42] |

9 | Lesse | Resteigne | 345 | L5021 | 1992–06 | 46 | 33 | 0.096 | Franchimont (1993) [44] |

10 | Lesse | Hérock | 1156 | L6610 | 1996–05 | 23 | 105 | 0.091 | Bioengineering techniques report (2016) |

11 | Lesse | Gendron | 1286 | S8221 | 1968–01 | 51 | 131 | 0.102 | Bioengineering techniques report (2016) |

12 | Lesse | Eprave | 419 | L5080 | 1969–01 | 41 | 37 | 0.088 | Petit et al. (2015) [45] |

13 | Lhomme | Grupont | 179.9 | L6360 | 1991–10 | 22 | 20 | 0.111 | Franchimont (1993) [44] |

14 | Lhomme | Forrières | 247 | L6310 | 1991–10 | 24 | 24.5^{1} | 0.099 | Computed Q_{0.625} |

15 | Lhomme | Jemelle | 276 | S8527 | 1969–01 | 50 | 29.7^{1} | 0.108 | Computed Q_{0.625} |

16 | Lhomme | Rochefort | 424.9 | L6650 | 1996–07 | 22 | 51.8^{1} | 0.122 | Computed Q_{0.625} |

17 | Lhomme | Eprave | 478 | L6360 | 1992–07 | 24 | 60 | 0.126 | Petit et al. (2015) [45] |

18 | Lienne | Lorcé | 147 | L6240 | 1992–09 | 25 | 21.3 | 0.145 | Houbrechts (2005) [42] and new authors observation (2008) |

19 | Mellier | Marbehan | 62 | L5500 | 1974–06 | 39 | 8.8 | 0.142 | New observation (2008) |

20 | Our | Ouren | 386 | L6330 | 1991–09 | 26 | 29.2 | 0.076 | New observation (2005) |

21 | Ourthe | Durbuy | 1285 | S5953 | 1994–12 | 24 | 100 | 0.078 | New observation |

22 | Ourthe | Tabreux | 1597 | S5921 | 1970–12 | 48 | 160 | 0.100 | Petit & Daxhelet (1989) [12] |

23 | Ourthe | Sauheid | 2910 | S5826 | 1974–01 | 45 | 300 | 0.103 | Pauquet & Petit (1993) [46] |

24 | Ourthe orientale | Houffalize | 179 | L5930 | 1979–02 | 37 | 21 | 0.117 | Petit et al. (2015) [45] |

25 | Ruisseau des Aleines | Auby-sur-Semois | 88.4 | L6990 | 2003–09 | 15 | 13.3 | 0.150 | New observation (2018) |

26 | Rulles | Habay-la-Vieille | 96 | L5970 | 1981–11 | 33 | 11 | 0.115 | Petit and Pauquet (1997) [7] |

27 | Rulles | Tintigny | 219 | L5220 | 1971–02 | 39 | 24.3 | 0.111 | New observation (2008) |

28 | Ry du Moulin | Vresse-sur-Semois | 61.8 | L7000 | 2003–09 | 15 | 5.8 | 0.094 | Jacquemin [47] |

29 | Semois | Tintigny | 380.9 | S9561 | 1974–01 | 45 | 40 | 0.105 | New observation (2008) |

30 | Semois | Membre Pont | 1235 | S9434 | 1968–01 | 51 | 130 | 0.105 | Petit & Pauquet (1997) [7], Gob et al. (2005) [48] |

31 | Sûre | Martelange | 209 | L5610 | 1975–03 | 40 | 32 | 0.153 | Peeters et al. (2018) [19] |

32 | Vesdre | Chaudfontaine | 683 | S6228 | 1975–06 | 43 | 120 | 0.176 | Petit & Daxhelet (1989) [12] |

33 | Vierre | Suxy | 219.8 | L7140 | 2003–12 | 15 | 19 | 0.086 | New observation (2008) |

34 | Viroin | Olloy-sur-Viroin | 491 | L6380 | 1992–01 | 26 | 55 | 0.112 | New observation (2011) |

35 | Viroin | Treignes | 548 | S9021 | 1968–01 | 45 | 62 | 0.113 | New observation (2009) |

36 | Wamme | Hargimont | 80 | L6370/L7640 | 2011–06 | 13 | 12.1 | 0.151 | New observation (2008) |

37 | Wayai | Spixhe | 93.8 | L6790 | 2002–03 | 17 | 25 | 0.267 | New estimate |

FAGNE–FAMENNE Region | |||||||||

38 | Biran | Wanlin | 51.9 | L7190 | 2004–09 | 14 | 6.3 | 0.121 | New observation (2008) |

39 | Brouffe | Mariembourg | 80 | S9111 | 1981–01 | 38 | 20 | 0.250 | New observation (2009) |

40 | Eau Blanche | Aublain | 106.2 | L6530 | 1994–03 | 24 | 17 | 0.160 | New observation (2011) |

41 | Eau Blanche | Nismes | 254 | S9081 | 1968–01 | 50 | 29 | 0.114 | Vanderheyden [49] and new observation (2013) |

42 | Hantes | Beaumont | 92.4 | L6880 | 2003–03 | 15 | 15 | 0.162 | New observation |

43 | Hermeton | Romedenne | 115 | L5060 | 1969–02 | 48 | 17.3 | 0.150 | New observation (2008) |

44 | Hermeton | Hastière | 166 | S8622 | 1967–09 | 50 | 20 | 0.120 | New observation (2008) |

45 | Marchette | Marche-en-Famenne | 48.9 | L7120 | 2003–12 | 15 | 7.2 | 0.147 | Petit & Daxhelet (1989) [12] |

46 | Ruisseau d’Heure | Baillonville | 68 | L6050 | 1984–06 | 29 | 14 | 0.206 | Louette (1995) [13] |

47 | Wimbe | Lavaux-Sainte-Anne | 93 | L6270 | 1991–08 | 26 | 11.7 ^{1} | 0.125 | Computed Q_{0.625} |

CONDROZ Region | |||||||||

48 | Biesme l’Eau | Biesme-sous-Thuin | 79.8 | L7180 | 2004–09 | 14 | 6 | 0.075 | New observation |

49 | Bocq | Spontin ^{2} | 163.6 | L7320 | 2006–04 | 40 | 18.3 | 0.112 | Petit et al. (2015) [45] |

50 | Bocq | Yvoir | 230 | L5800 | 1979–02 | 39 | 26.3 | 0.114 | Peeters et al. (2013) [50] |

51 | Samson | Mozet | 108.2 | L5980 | 1982–10 | 26 | 10.6 ^{1} | 0.098 | Computed Q_{0.625} |

ENTRE–VESDRE–ET–MEUSE Region | |||||||||

52 | Berwinne | Dalhem | 118 | L6390 | 1991–12 | 24 | 17 | 0.144 | Houbrechts et al. (2015) [51] |

53 | Bolland | Dalhem | 29.3 | L6770 | 2001–12 | 17 | 3.4 | 0.116 | New observation |

54 | Gueule | Sippenaken | 121 | L6660 | 1996–06 | 22 | 16 | 0.132 | Mols (2004) [52] |

BRABANT Region | |||||||||

55 | Dyle | Florival | 430 | L6160 | 1992–07 | 23 | 20.5 | 0.048 | New observation (2011) |

56 | Samme | Ronquières | 135 | S2371 | 1971–08 | 30 | 15 | 0.111 | Denis et al. (2014) [53] |

57 | Senne | Steenkerque | 116 | L5660 | 1996–06 | 40 | 14 | 0.121 | SPW data |

58 | Senne | Quenast | 169 | 1977–03 | 40 | 19.5 | 0.115 | New observation (2011) | |

59 | Sennette | Ronquières | 70 | L5670 | 1977–07 | 28 | 6 | 0.086 | SPW data |

HAINAUT Region | |||||||||

60 | Anneau | Marchipont | 78.2 | L6870 | 2003–03 | 15 | 7.3 ^{1} | 0.094 | Computed Q_{0.625} |

61 | Grande Honnelle | Baisieux | 121 | L5170 | 1971–01 | 40 | 12.4 ^{1} | 0.103 | Computed Q_{0.625} |

62 | Rhosnes | Amougies | 165 | L5412 | 1972–02 | 38 | 19 | 0.115 | SPW data |

63 | Ruisseau des Estinnes | Estinnes-au-Val | 28.7 | L7080 | 2003–11 | 15 | 3.0 ^{1} | 0.105 | Computed Q_{0.625} |

64 | Trouille | Givry | 55.7 | L6710 | 2000–05 | 19 | 4.2 ^{1} | 0.075 | Computed Q_{0.625} |

HESBAYE Region | |||||||||

65 | Burdinale | Marneffe | 26.8 | L6461 | 2008–09 | 10 | 2.2 ^{1} | 0.082 | Computed Q_{0.625} |

66 | Geer | Eben-Emael | 452.3 | L6340 | 1991–08 | 23 | 11.9 | 0.026 | Mabille & Petit (1987) [54] |

67 | Grande Gette | Sainte-Marie-Geest | 135 | L5720 | 1978–01 | 41 | 10 | 0.074 | New observation (2011) |

68 | Mehaigne | Ambresin | 194.7 | L6470 | 1991–12 | 25 | 12 | 0.062 | Peeters et al. (2018) [19] |

69 | Mehaigne | Wanze | 352 | L5820 | 1978–12 | 39 | 18.1 | 0.051 | Perpinien (1998) [55] at Moha |

70 | Petite Gette | Opheylissem | 134 | L6280 | 1991–08 | 25 | 4.8 ^{1} | 0.081 | Computed Q_{0.625} |

LORRAINE Region | |||||||||

71 | Semois | Chantemelle | 89 | L5880 | 1979–01 | 40 | 11.1 | 0.125 | New observation (2001) |

72 | Semois | Etalle | 123.9 | L6180 | 1992–09 | 25 | 15.2 | 0.123 | New observation (2008) |

73 | Ton | Virton | 89 | L6440 | 1991–08 | 25 | 6.5 | 0.073 | New observation (2007) |

74 | Ton | Harnoncourt | 293 | L5520 | 1974–03 | 44 | 27.6 | 0.094 | New observation (2008) |

75 | Vire | Ruette | 104 | L5600 | 1975–07 | 39 | 21.3 | 0.205 | SPW data and new estimate |

76 | Vire | Latour | 125 | L6030 | 1983–10 | 34 | 12 | 0.096 | New observation (2008) |

^{2}) is the catchment area at the station location; Q

_{b max}(m

^{3}·s

^{−1}) is field-observed bankfull discharge expressed in hourly flow,

^{1}except for values computed from partial series (Q

_{0.625}).

^{2}The Bocq station at Spontin presents incomplete hydrological data. A correlation with the SETHY station from Bocq at Yvoir was used to complete the data between 1978 and 2018.

**Table 2.**Flow thresholds and time intervals between floods considered as independent in partial series

Threshold | Time Interval | Author(s) |
---|---|---|

Threshold corresponding to a flow rate with a T_{p} of 1.15 years | - | Dalrymple, 1960 [80] |

Threshold defining a number of 1.65 N of floods where N represents the number of years recorded in the discharge series | Two successive peaks considered as independent if the flow drops to less than two-thirds of the first peak. Interval greater than three times the duration of the flood rise of the first five ‘clear’ hydrographs in the series | Cunnane, 1973 [76] |

Lowest annual maximum flood of the series | - | Dunne and Leopold, 1978 [70] |

Two successive peaks considered as independent if flow rate drops below 75% of the discharge of the lowest peak | Peaks separated by at least 5 days + the natural logarithm of the watershed surface (in miles²) | USWRC, 1976 [74] |

Threshold depending on the interval optimized by autocorrelation test | Selection by statistical self-correlation test of flood duration | Miquel, 1984 [73] |

Threshold corresponding to a flow rate with partial return period in the range 1.2-2 years | - | Irvine and Waylen [77] |

0.6 Q_{b} | Time interval between two successive maximum flow rates equals to at least four days, separated by a minimum whose value is less than or equal to 50% of the value of the lower of these two maximums | Pauquet and Petit, 1993 [46]; Petit and Pauquet, 1997 [7] |

Several methods for estimating the threshold based on a stationarity test of the number of defined floods | - | Lang et al., 1999 [68] |

Threshold and time interval defined to obtain between 2 to 5 floods peaks per year | Adamowski, 2000 [78] | |

Threshold = µ_{q} + 3σ_{q} where µ_{q} is the mean daily flow rate of the series and σ_{q} is the standard deviation of the daily flow rate according to Rosbjerg et al. [79] | Iterative high-pass filtering of the daily flow rates in order to detect independent peaks | Claps and Laio, 2003 [81] |

Threshold = average daily flow rate | 3 days | Brodie and Khan, 2016 [75] |

- | 10 to 15 days depending on watershed area | Karim et al., 2017 [66] |

**Table 3.**Return period of characteristic discharges computed for the selection of hydrologic stations

Annual Series | Partial Series | T_{a}/T_{p} Conver-Gence Point (yr) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

ID | River | Location | Q_{b} (m^{3}·s^{−1}) | Annual Lowest Flood (m^{3}·s^{−1}) | T_{a} Q_{b} (yr) | Q_{100} (m^{3}·s^{−1}) | T_{a} Q_{hmax} (yr) | Threshold for 5.5 Events/yr (m^{3}·s^{−1}) | T_{p} Q_{b} (y) | Q_{0.625} (m^{3}·s^{−1}) | |

ARDENNE Region | |||||||||||

1 | Aisne | Erezée | 7.3 | 7.1 | 1.1 | 25.8 | 32 | 6.30 | 0.30 | 9.7 | 4.0 |

2 | Aisne | Juzaine | 23.8 | 11.0 | 1.6 | 74.6 | >100 | 13.15 | 0.68 | 23.0 | 4.0 |

3 | Amblève | Targnon | 87.3 | 78.1 | 1.4 | 250.7 | 75 | 60.00 | 0.51 | 93.6 | 5.0 |

4 | Amblève | Martinrive | 140 | 74.4 | 1.6 | 411.9 | 54 | 84.15 | 0.70 | 134.9 | 4.5 |

5 | Eau Noire | Couvin | 36.9 | 26.9 | 1.4 | 129.1 | 37 | 20.68 | 0.52 | 40.1 | 5.3 |

6 | Hoëgne | Belleheid | 10 | 6.1 | 1.5 | 27.6 | 44 | 6.05 | 0.62 | 9.9 | 3.5 |

7 | Hoëgne | Theux | 36.8 | 24.2 | 1.3 | 132.2 | 45 | 25.80 | 0.33 | 47.5 | 7.0 |

8 | Lembrée | Vieuxville | 7.9 | 3.8 | 1.6 | 25.7 | 70 | 3.62 | 0.71 | 7.5 | 4.0 |

9 | Lesse | Resteigne | 33 | 13.4 | 1.2 | 135.2 | 68 | 20.39 | 0.47 | 38.1 | 3.4 |

10 | Lesse | Hérock | 105 | 80.5 | 1.3 | 397.2 | 52 | 69.39 | 0.46 | 118.6 | 3.4 |

11 | Lesse | Gendron | 131 | 58.1 | 1.6 | 418.1 | 65 | 70.00 | 0.67 | 127.3 | 3.8 |

12 | Lesse | Eprave | 37 | 14.0 | 1.5 | 120.1 | >300 | 22.70 | 0.55 | 38.6 | 3.8 |

13 | Lhomme | Grupont | 20 | 7.9 | 2.0 | 51.8 | 29 | 10.59 | 1.12 | 17.0 | 3.2 |

14 | Lhomme | Forrières | 24.5 ^{1} | 15.7 | 1.5 | 81.6 | 35 | 15.90 | 0.62 | 24.5 | 3.0 |

15 | Lhomme | Jemelle | 29.7 ^{1} | 12.4 | 1.4 | 87.9 | 30 | 17.77 | 0.62 | 29.7 | 3.9 |

16 | Lhomme | Rochefort | 51.8 ^{1} | 34.2 | 1.5 | 187.5 | 32 | 28.11 | 0.62 | 51.7 | 3.0 |

17 | Lhomme | Eprave | 60 | 45.7 | 1.4 | 150.7 | 28 | 35.70 | 0.68 | 58.7 | 3.4 |

18 | Lienne | Lorcé | 21.3 | 10.5 | 2.4 | 52.1 | 47 | 10.49 | 1.28 | 17.0 | 6.0 |

19 | Mellier | Marbehan | 8.8 | 6.8 | 1.1 | 47.8 | 64 | 6.96 | 0.32 | 13.3 | 3.7 |

20 | Our | Ouren | 29.2 | 31.4 | 1.0 | 138.4 | 37 | 22.10 | 0.28 | 46.6 | 5.5 |

21 | Ourthe | Durbuy | 100 | 61.9 | 1.4 | 329.9 | 74 | 64.96 | 0.50 | 108.8 | 3.8 |

22 | Ourthe | Tabreux | 160 | 68.1 | 1.9 | 450.2 | 77 | 73.80 | 1.03 | 134.5 | 3.7 |

23 | Ourthe | Sauheid | 300 | 148.9 | 1.8 | 827.3 | 49 | 159.92 | 0.92 | 263.9 | 3.7 |

24 | Ourthe orientale | Houffalize | 21 | 9.9 | 1.9 | 63.3 | ~100 | 9.61 | 1.01 | 17.5 | 3.8 |

25 | Ruisseau des Aleines | Auby-sur-Semois | 13.3 | 7.6 | 1.0 | 26.5 | 23 | 7.82 | 1.30 | 11.3 | 4.0 |

26 | Rulles | Habay-la-Vieille | 11 | 6.9 | 1.1 | 43.5 | 32 | 7.80 | 0.38 | 14.1 | 3.7 |

27 | Rulles | Tintigny | 24.3 | 20.3 | 1.0 | 74.5 | 30 | 17.40 | 0.33 | 31.3 | 20.0 |

28 | Ry du Moulin | Vresse-sur-Semois | 5.8 | 7.3 | 1.0 | 31.4 | 55 | 6.02 | 0.31 | 9.5 | 2.7 |

29 | Semois | Tintigny | 40 | 34.6 | 1.1 | 203.1 | >100 | 34.80 | 0.29 | 62.0 | 4.0 |

30 | Semois | Membre Pont | 130 | 89.0 | 1.2 | 555.3 | ~100 | 80.90 | 0.41 | 162.3 | 3.5 |

31 | Sûre | Martelange | 32 | 13.9 | 1.5 | 107.6 | 73 | 11.27 | 0.81 | 28.3 | 3.6 |

32 | Vesdre | Chaudfontaine ^{2} | 120 | 35.4 | 2.0 | 288.1 | 71 | 53.14 | 1.20 | 98.1 | 5.0 |

33 | Vierre | Suxy | 19 | 15.3 | 1.1 | 92.3 | 33 | 11.52 | 0.41 | 24.7 | 3.3 |

34 | Viroin | Olloy-sur-Viroin | 55 | 41.3 | 1.2 | 281.5 | 26 | 42.38 | 0.29 | 85.6 | 5.8 |

35 | Viroin | Treignes | 62 | 47.4 | 1.3 | 259.8 | 141 | 43.79 | 0.37 | 78.1 | 3.7 |

36 | Wamme | Hargimont | 12.1 | 9.8 | 1.3 | 63.3 | 89 | 11.76 | 0.26 | 19.4 | 6.0 |

37 | Wayai | Spixhe | 25 | 14.4 | 2.0 | 63.1 | >100 | 11.22 | 1.41 | 19.7 | 3.0 |

FAGNE–FAMENNE Region | |||||||||||

38 | Biran | Wanlin | 6.3 | 4.2 | 1.1 | 30.6 | 14 | 3.96 | 0.35 | 8.7 | 3.0 |

39 | Brouffe | Mariembourg | 20 | 7.3 | 1.9 | 50.6 | 75 | 7.47 | 1.30 | 15.7 | 3.5 |

40 | Eau Blanche | Aublain | 17 | 9.3 | 1.7 | 48.4 | 37 | 8.03 | 1.00 | 14.5 | 3.2 |

41 | Eau Blanche | Nismes | 29 | 20.1 | 1.4 | 96.6 | >300 | 19.70 | 0.43 | 33.1 | 4.3 |

42 | Hantes | Beaumont | 15 | 10.9 | 1.5 | 60.2 | 30 | 6.42 | 0.63 | 14.9 | 3.5 |

43 | Hermeton | Romedenne | 17.3 | 9.0 | 1.7 | 50.5 | 75 | 8.61 | 0.66 | 17.0 | 7.5 |

44 | Hermeton | Hastière | 20 | 11.3 | 1.4 | 65.2 | 87 | 9.53 | 0.64 | 19.9 | 4.0 |

45 | Marchette | Marche-en-Famenne | 7.2 | 6.3 | 1.0 | 26.8 | 34 | 5.63 | 0.27 | 10.3 | 6.0 |

46 | Ruisseau d’Heure | Baillonville | 14 | 6.9 | 1.9 | 32.7 | 23 | 4.45 | 1.28 | 10.7 | 8.0 |

47 | Wimbe | Lavaux-Sainte-Anne | 11.7 ^{1} | 7.8 | 1.3 | 31.7 | 40 | 6.68 | 0.62 | 11.7 | 4.0 |

CONDROZ Region | |||||||||||

48 | Biesme l’Eau | Biesme-sous-Thuin | 6 | 4.1 | 1.2 | 39.5 | 20 | 4.24 | 0.32 | 9.8 | 4.0 |

49 | Bocq | Spontin | 18.3 | 4.3 | 3.3 | 47.3 | >150 | 5.09 | 2.99 | 10.3 | 4.0 |

50 | Bocq | Yvoir | 26.3 | 5.7 | 4.3 | 61.3 | >150 | 6.81 | 4.53 | 13.3 | 4.0 |

51 | Samson | Mozet | 10.6 ^{1} | 6.3 | 1.5 | 30.3 | 21 | 6.00 | 0.62 | 10.6 | 6.5 |

ENTRE-VESDRE-ET-MEUSE Region | |||||||||||

52 | Berwinne | Dalhem | 17 | 13.3 | 1.5 | 60.1 | >100 | 8.72 | 0.53 | 18.3 | 5.5 |

53 | Bolland | Dalhem | 3.4 | 1.7 | 1.7 | 11.4 | >150 | 2.07 | 0.62 | 3.4 | 3.7 |

54 | Gueule | Sippenaken | 16 | 14.6 | 1.1 | 46.8 | 39 | 9.30 | 0.44 | 18.1 | 5.7 |

BRABANT Region | |||||||||||

55 | Dyle | Florival | 20.5 | 13.5 | 2.6 | 31.2 | 16 | 12.70 | 1.77 | 17.6 | 20.0 |

56 | Samme | Ronquières | 15 | 9.5 | 1.5 | 46.0 | >100 | 8.28 | 0.66 | 14.7 | 4.0 |

57 | Senne | Steenkerque | 14 | 8.8 | 1.1 | 51.0 | ~100 | 9.18 | 0.32 | 18.9 | 9.0 |

58 | Senne | Quenast | 19.5 | 9.9 | 1.3 | 57.4 | ~100 | 10.39 | 0.49 | 21.3 | 9.0 |

59 | Sennette | Ronquières | 6 | 4.2 | 1.2 | 19.4 | 68 | 3.94 | 0.34 | 7.9 | >50.0 |

HAINAUT Region | |||||||||||

60 | Anneau | Marchipont | 7.3 ^{1} | 2.6 | 1.8 | 33.9 | 79 | 2.96 | 0.62 | 7.3 | 5.0 |

61 | Grande Honnelle | Baisieux | 12.4 ^{1} | 3.3 | 1.6 | 46.1 | 44 | 5.46 | 0.62 | 12.4 | 4.8 |

62 | Rhosnes | Amougies | 19 | 7.3 | 5.4 ^{3} | 28.2 | 50 | 10.90 | 3.98 | 15.0 | 9.0 |

63 | Ruisseau des Estinnes | Estinnes-au-Val | 3.0 ^{1} | 0.6 | 1.9 | 15.2 | >100 | 1.26 | 0.62 | 3.0 | 3.6 |

64 | Trouille | Givry | 4.2^{1} | 1.1 | 1.8 | 17.6 | 51 | 1.69 | 0.62 | 4.2 | 6.2 |

HESBAYE Region | |||||||||||

65 | Burdinale | Marneffe | 2.2 ^{1} | 0.9 | 1.8 | 7.6 | 30 | 0.92 | 0.62 | 2.2 | 5.5 |

66 | Geer | Eben-Emael | 11.9 | 6.4 | 2.5 | 19.6 | 67 | 7.59 | 1.90 | 10.1 | 3.8 |

67 | Grande Gette | Sainte-Marie-Geest | 10 | 3.1 | 1.7 | 36.3 | 50 | 4.68 | 0.81 | 8.8 | 4.0 |

68 | Mehaigne | Ambresin | 12 | 5.8 | 1.5 | 29.4 | 22 | 7.43 | 0.49 | 12.8 | 10.4 |

69 | Mehaigne | Wanze | 18.1 | 7.2 | 2.5 | 39.4 | >100 | 9.10 | 1.63 | 14.2 | 4.5 |

70 | Petite Gette | Opheylissem | 4.8 ^{1} | 2.2 | 8.9 ^{4} | 18.5 | >300 | 2.64 | 18.46 | 4.8 | 4.0 |

LORRAINE Region | |||||||||||

71 | Semois | Chantemelle | 11.1 | 6.7 | 1.3 | 32.9 | 44 | 8.05 | 0.35 | 13.3 | 6.4 |

72 | Semois | Etalle | 15.2 | 12.8 | 1.2 | 40.2 | 38 | 12.48 | 0.31 | 18.4 | 6.5 |

73 | Ton | Virton | 6.5 | 4.7 | 1.6 | 12.5 | 26 | 4.64 | 0.59 | 6.6 | ~30.0 |

74 | Ton | Harnoncourt | 27.6 | 11.4 | 2.0 | 84.4 | 376 | 15.31 | 0.75 | 25.8 | 7.0 |

75 | Vire | Ruette | 21.3 | 6.7 | 3.2 | 40.4 | 41 | 8.01 | 2.16 | 15.3 | 15.0 |

76 | Vire | Latour | 12 | 10.0 | 1.1 | 40.4 | 56 | 9.69 | 0.30 | 15.8 | 5.8 |

_{b}is the bankfull discharge expressed in hourly flow,

^{1}except for values computed from partial series (Q

_{0.625}).

^{2}The Vesdre River at Chaudfontaine (no. 32) is disturbed by human dams upstream so return periods are not consistent with surrounding stations’ values.

^{3}The Rhosnes River at Amougies and the

^{4}Petite Gette River at Opheylissem are located in anthropized reaches.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Van Campenhout, J.; Houbrechts, G.; Peeters, A.; Petit, F.
Return Period of Characteristic Discharges from the Comparison between Partial Duration and Annual Series, Application to the Walloon Rivers (Belgium). *Water* **2020**, *12*, 792.
https://doi.org/10.3390/w12030792

**AMA Style**

Van Campenhout J, Houbrechts G, Peeters A, Petit F.
Return Period of Characteristic Discharges from the Comparison between Partial Duration and Annual Series, Application to the Walloon Rivers (Belgium). *Water*. 2020; 12(3):792.
https://doi.org/10.3390/w12030792

**Chicago/Turabian Style**

Van Campenhout, Jean, Geoffrey Houbrechts, Alexandre Peeters, and François Petit.
2020. "Return Period of Characteristic Discharges from the Comparison between Partial Duration and Annual Series, Application to the Walloon Rivers (Belgium)" *Water* 12, no. 3: 792.
https://doi.org/10.3390/w12030792