# The Influence of the Annual Number of Storms on the Derivation of the Flood Frequency Curve through Event-Based Simulation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Stochastic Rainfall Series Generation and Storm Identification

^{−2}); and (7) a vector of scale factors, one for each rain gauge (-). Generally, the available observed data in the basin consist of daily rainfall series. From these data, the model is calibrated by applying the Shuffled Complex Evolution algorithm [47], in order to adjust the model rainfall time-series statistic characteristics to the behavior of the observed daily rainfall series. A detailed description of the RainSimV3 can be found in Burton et al. [39]. The stochastic rainfall model validation was performed comparing both the annual maximum daily rainfall frequency curve from observed data in each rain gauge and simulated from the model at the same location. We obtained the daily modeled values by aggregating the hourly simulated time-series.

#### 2.2. Estimation of the Peak Flow Frequency Curves

_{R}). We performed the rainfall–runoff simulations for storms selected under all three criteria. For each criterion, we identified the order of storm event that generated the maximum peak flow in that year, and compared the storm orders obtained for each criterion and for the entire period analyzed. We selected as the best criterion the one that required lower storm orders for obtaining the peak-flow annual maxima (as will be shown later, in this study, the selected criterion was the total rainfall depth). Then, based on the selected criterion, we calculated different FFCs varying the number of storm events considered each year. First, we selected the largest storm each year (storm of order 1); second, we considered the two largest storms of each year (order 1 + order 2) and so on until covering the total number of selected storms per year. Finally, we compared the FFCs and determined the minimum number of storms to be considered each year in order to ensure the inclusion of the annual maximum peak flow.

#### 2.3. Case Studies

^{2}), a tributary of the Targus River in the central region of mainland Spain. The studied basins were: Santillana (211 km

^{2}), El Pardo (495 km

^{2}) and Manzanares (1294 km

^{2}). The sub-basin determination was conducted according to Sordo-Ward et al. [27]. The main characteristics are summarized in Table 1 and Figure 3.

_{1}), second the storms of order 1 + 2 (FFC

_{2}), and so on until considering 25 storms each year. This was considered the reference flood frequency curve (FFC

_{R}). In all cases, for each year, the annual maximum peak-flow was identified and the corresponding FFC was estimated by applying the Gringorten non-parametric formula. The basin characteristics, sub-basin determination, topology, deterministic average initial conditions and parameters were selected from Sordo-Ward et al. [27]. In addition, for comparison purposes, we used hourly data from six storm events in the Manzanares basin recorded by five rain gauges and the corresponding observed hydrographs at the Manzanares basin outlet (gauge station 3182E). We simulated the storm events and compared the peak flows with the observed ones.

#### 2.4. Limitations of the Methodology

## 3. Results and Discussion

#### 3.1. Rainfall Model Calibration/Validation and Rainfall Events Identification/Characterisation

#### 3.2. FFCs Estimation and Effect of Considering Different Number of Storms Each Year

_{1}). Second, we calculated the FFC

_{2}considering the two largest storms of each year (order 1 + order 2). This was repeated until a maximum of 25 storms were selected. The FFC calculated with all 25 storm events was considered the reference FFC (FFC

_{R}). The procedure was repeated for the three analyzed basins. Figure 9 (left) shows the FFCs obtained for each basin and different storm orders. Results evidenced a general similarity among the different FFCs for all cases. However, a deeper analysis showed that the behavior of the FFCs changed according to the Tr of the peak flow considered. In order to quantify it, Figure 9 (right) shows the ratio between de FFCs for different cumulated orders (order 1, 1 + 2, 1 + 2 + 3, …, 1 + 2 + 3 + … 24) and the reference FFC

_{R}(order 1 + 2 + 3 …. + 25). The fewer storms considered per year and/or the lower the Tr analyzed, the lower the ratio becomes. The difference between the FFC

_{1}and the FFC

_{R}was higher than 6% (up to 22%) for Tr ≤ 10 years. For 10 ≤ Tr ≤ 1000 years, the difference stabilized between 2% and 6%. The difference between the FFC

_{2}and the FFC

_{R}was around 3%–30% for Tr ≤ 10 years. For 10 ≤ Tr ≤ 500 years, the difference stabilized between 1.5% and 3% and, for 500 ≤ Tr ≤ 1000 years, it decreased to around 1%–2%. The difference was lower than 5% for Tr ≤ 10 years for the comparison between the FFC

_{4}and FFC

_{R}. For 10 ≤ Tr ≤ 1000 years, the difference stabilized around 1%–2%. In all cases, the higher the basin area, the lower the difference. In addition, the difference when comparing the FFCs among them (i.e., FFC

_{1}, FFC

_{2}, …, FFC

_{24}) decreased significantly when increasing the Tr analyzed. For example, for 100 ≤ Tr ≤ 1000, the difference between FFC

_{1}and FFC

_{4}was around 5%. We observed that for FFC

_{3}and higher and for Tr ≥ 50 years, the difference among them were lower than 3%. As it regards the effect of basin area, the behavior of the FFCs and the ratio analysis for the three basins were found to be similar.

_{R}that considers all 25 storms every year (Figure 9).

#### 3.3. Joint Analysis of Maximum Annual Peak Flow and Hydrograph Volume

#### 3.4. Sensitivity Analysis of Inter-Event Time Determination

## 4. Conclusions

- The degree of alignment between the calculated flood frequency curves and the reference flood frequency curve depends on the return period of the peak flow considered.
- Considering the criterion of the total rainfall depth to define when one storm is larger than another, a strong correlation was found between this criterion and the corresponding peak flow. Considering the three largest storms each year, the probability of achieving the maximum annual peak flow ranges between 83% and 92% depending on the analyzed basin.
- The flood frequency curve for high return period (50 ≤ return period ≤ 1000 years) generated by considering the three largest storms each year can be estimated with a difference lower than 3% regarding the reference flood frequency curve.
- By using the largest storm each year, for return periods higher than 10 years, the derived flood frequency curve determines which storms of order 1 show a difference lower than 10% regarding the reference flood frequency curve (considering all the identified storms).
- Basins with larger catchment areas would require more annual largest storms than in smaller basins in order to achieve the maximum peak flow each year.
- Considering the three largest storms each year, the probability of achieving simultaneously a hydrograph with the maximum annual peak flow and the maximum annual volume for a return period higher than 100 years is 94%, the return period being calculated from the maximum annual peak flows series. If we calculated the return period from the maximum annual hydrograph volume series, the probability would increase to 98%.
- The inter-storm time shows low influence on determining the minimum number of largest storms to be considered for achieving the maximum annually peak flow. Considering a wide range of inter-storm time (3 to 33 h) for the identification of storm events, the difference of the probability of including the maximum peak flow for a specific number of storms considered each year is lower than 3% in all cases.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CF | Cumulative frequency distribution |

CV | Coefficient of variation |

FFCi | Peak-flow frequency curve considering the i largest storms of each year |

FFC_{R} | Reference peak-flow frequency curve considering a maximum of 25 largest storms of each year |

IDF | Intensity–Duration–Frequency curves |

MIT | Minimum inter-event time (hours) |

NS | Nash–Sutcliffe coefficient |

RF | Relative frequency distribution |

Rq | Ratio between the FFCs for different maximum storm orders and the reference FFCR |

Tr | Return period (years) |

## References

- Smith, A.; Sampson, C.; Bates, P. Regional flood frequency analysis at the global scale. Water Resour. Res.
**2015**, 51, 539–553. [Google Scholar] - Botto, A.; Ganora, D.; Laio, F.; Claps, P. Uncertainty compliant design flood estimation. Water Resour. Res.
**2014**, 50, 4242–4253. [Google Scholar] [CrossRef] - Nguyen, C.; Gaume, E.; Payrastre, O. Regional flood frequency analyses involving extraordinary flood events at ungauged sites: Further developments and validations. J. Hydrol.
**2014**, 508, 385–396. [Google Scholar] [CrossRef] - Laio, F.; Ganora, D.; Claps, P.; Galeati, G. Spatially smooth regional estimation of the flood frequency curve (with uncertainty). J. Hydrol.
**2011**, 408, 67–77. [Google Scholar] [CrossRef] - Merz, R.; Blöschl, G. Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information. Water Resour. Res.
**2008**, 44. [Google Scholar] [CrossRef] - Goñi, M.; López, J.J.; Gimena, F.N. Reservoir rainfall–runoff geomorphological model. I: Application and parameter analysis. Hydrol. Process.
**2013**, 27, 477–488. [Google Scholar] [CrossRef] - Goñi, M.; López, J.J.; Gimena, F.N. Reservoir rainfall-runoff geomorphological model. II: Analysis, calibration and validation. Hydrol. Process.
**2013**, 27, 489–504. [Google Scholar] [CrossRef] - Hadadin, N. Evaluation of several techniques for estimating storm water runoff in arid watersheds. Environ. Earth Sci.
**2012**, 69, 1773–1782. [Google Scholar] [CrossRef] - Beven, K.J. Rainfall-Runoff Modelling: The Primer, 2nd ed.; Wiley-Blackwell: Hoboken, NJ, USA, 2008; p. 488. [Google Scholar]
- Singh, V.P.; Frevert, D.K. Mathematical Models of Small Watershed Hydrology and Applications; Water Resources Publication: Highlands Ranch, CO, USA, 2002; p. 950. [Google Scholar]
- Singh, V.P.; Frevert, D.K. Mathematical Models of Large Watershed Hydrology; Water Resources Publication: Highlands Ranch, CO, USA, 2002; p. 891. [Google Scholar]
- Raines, T.; Valdés, J. Estimation of flood frequencies for ungaged catchments. J. Hydraul. Eng.
**1993**, 119, 1138–1154. [Google Scholar] [CrossRef] - Hadadin, N. Modeling of Rainfall-Runoff Relationship in Semi-Arid Watershed in the Central Region of Jordan. Jordan J. Civ. Eng.
**2016**, 10, 209–218. [Google Scholar] [CrossRef] - Blazkova, S.; Beven, K. A limits of acceptability approach to model evaluation and uncertainty estimation in flood frequency estimation by continuous simulation: Skalka catchment, Czech Republic. Water Resour. Res.
**2009**, 45. [Google Scholar] [CrossRef] - Samuel, J.M.; Sivapalan, M. Effects of multiscale rainfall variability on flood frequency: Comparative multisite analysis of dominant runoff processes. Water Resour. Res.
**2008**, 44. [Google Scholar] [CrossRef] - Aronica, G.; Candela, A. Derivation of flood frequency curves in poorly gauged Mediterranean catchments using a simple stochastic hydrological rainfall-runoff model. J. Hydrol.
**2007**, 347, 132–142. [Google Scholar] [CrossRef] - Arnaud, P.; Lavabre, J. Coupled rainfall model and discharge model for flood frequency estimation. Water Resour. Res.
**2002**, 38. [Google Scholar] [CrossRef] - Loukas, A. Flood frequency estimation by a derived distribution procedure. J. Hydrol.
**2002**, 255, 69–89. [Google Scholar] [CrossRef] - Rahman, A.; Weinmann, P.E.; Hoang, T.M.T.; Laurenson, E.M. Monte Carlo simulation of flood frequency curves from rainfall. J. Hydrol.
**2002**, 256, 196–210. [Google Scholar] [CrossRef] - Wagener, T.; Wheater, H.S.; Gupta, H.V. Rainfall-Runoff Modelling in Gauged and Ungauged Catchments; Imperial College Press: London, UK, 2004; p. 332. [Google Scholar]
- Berthet, L.; Andréassian, V.; Perrin, C.; Javelle, P. How crucial is it to account for the antecedent moisture conditions in flood forecasting? Comparison of event-based and continuous approaches on 178 catchments. Hydrol. Earth Syst. Sci.
**2009**, 13, 819–831. [Google Scholar] [CrossRef] - Sivapalan, M.; Wood, E.; Beven, K. On hydrologic similarity: 3. A dimensionless flood frequency model using a generalized geomorphic unit hydrograph and partial area runoff generation. Water Resour. Res.
**1990**, 26, 43–58. [Google Scholar] [CrossRef] - Natural Environment Research Council (NERC). Flood Studies Report; Natural Environment Research Council (NERC): London, UK, 1975. [Google Scholar]
- Flores-Montoya, I.; Sordo-Ward, A.; Mediero, L.; Garrote, L. Fully stochastic distributed methodology for multivariate flood frequency analysis. Water
**2016**, 8. [Google Scholar] [CrossRef] - De Michele, C.; Salvadori, G. On the derived flood frequency distribution: Analytical formulation and the influence of antecedent soil moisture condition. J. Hydrol.
**2002**, 262, 245–258. [Google Scholar] [CrossRef] - Silveira, L.; Charbonier, F.; Genta, J. The antecedent soil moisture condition of the curve number procedure. Hydrol. Sci. J.
**2000**, 45, 3–12. [Google Scholar] [CrossRef] - Sordo-Ward, A.; Bianucci, P.; Garrote, L.; Granados, A. How safe is hydrologic infrastructure design? Analysis of factors affecting extreme flood estimation. J. Hydrol. Eng.
**2014**, 19. [Google Scholar] [CrossRef] - Viglione, A.; Blöschl, G. On the role of storm duration in the mapping of rainfall to flood return periods. Hydrol. Earth Syst. Sci.
**2009**, 13, 205–216. [Google Scholar] [CrossRef] - Alfieri, L.; Laio, F.; Claps, P. A simulation experiment for optimal design hyetograph selection. Hydrol. Process.
**2008**, 22, 813–820. [Google Scholar] [CrossRef] - Blazkova, S.; Beven, K. Flood frequency estimation by continuous simulation of subcatchment rainfalls and discharges with the aim of improving dam safety assessment in a large basin in the Czech Republic. J. Hydrol.
**2004**, 292, 153–172. [Google Scholar] [CrossRef] - Bocchiola, D.; Rosso, R. Use of a derived distribution approach for extreme floods design: A case study in Italy. Adv. Water Resour.
**2009**, 32, 1284–1296. [Google Scholar] [CrossRef] - Andres-Domenech, I.; Montanari, A.; Marco, J.B. Stochastic rainfall analysis for storm tank performance evaluation. Hydrol. Earth Syst. Sci.
**2010**, 14, 1221–1232. [Google Scholar] [CrossRef] - Arnaud, P.; Fine, J.; Lavabre, J. An hourly rainfall generation model applicable to all types of climate. Atmos. Res.
**2007**, 85, 230–242. [Google Scholar] [CrossRef] - Wilks, D.; Wilby, R. The weather generation game: A stochastic weather models. Prog. Phys. Geogr.
**1999**, 23, 329–357. [Google Scholar] [CrossRef] - Candela, A.; Brigandì, G.; Aronica, G.T. Estimation of synthetic flood design hydrographs using a distributed rainfall–runoff model coupled with a copula-based single storm rainfall generator. Nat. Hazards Earth Syst. Sci.
**2014**, 14, 1819–1833. [Google Scholar] [CrossRef] [Green Version] - Vandenberghe, S.; Verhoest, N.E.C.; Buyse, E.; De Baets, B. A stochastic design rainfall generator based on copulas and mass curves. Hydrol. Earth Syst. Sci.
**2010**, 14, 2429–2442. [Google Scholar] [CrossRef] - Kao, S.C.; Govindaraju, R.S. Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resour. Res.
**2008**, 44. [Google Scholar] [CrossRef] - Grimaldi, S.; Serinaldi, F. Design hyetograph analysis with 3-copula function. J. Sci. Hydrol.
**2006**, 51, 223–238. [Google Scholar] [CrossRef] - Burton, A.; Fowler, H.J.; Kilsby, C.G.; O’Connell, P.E. A stochastic model for the spatial-temporal simulation of nonhomogeneous rainfall occurrence and amounts. Water Resour. Res.
**2010**, 46. [Google Scholar] [CrossRef] - Burton, A.; Kilsby, C.G.; Fowler, H.J.; Cowpertwait, P.S.P.; O’Connell, P.E. RainSim: A spatial–temporal stochastic rainfall modelling system. Environ. Model. Softw.
**2008**, 23, 1356–1369. [Google Scholar] [CrossRef] - Salsón, S.; García-Bartual, R. A space-time rainfall generator for highly convective Mediterranean rainstorms. Nat. Hazards Earth Syst. Sci.
**2003**, 3, 103–114. [Google Scholar] [CrossRef] - Cowpertwait, P.; Kilsby, C.; O’Connell, P. A space-time Neyman-Scott model of rainfall: Empirical analysis of extremes. Water Resour. Res.
**2002**, 38. [Google Scholar] [CrossRef] - Dunkerley, D. Identifying individual rain events from pluviograph records: A review with analysis of data from an Australian dryland site. J. Hydrol. Process.
**2008**, 22, 5024–5036. [Google Scholar] [CrossRef] - Aryal, R.K.; Furumai, H.; Nakajima, F.; Jinadasa, H.K.P.K. The role of inter-event time definition and recovery of initial/depression loss for the accuracy in quantitative simulations of highway runoff. Urban Water J.
**2007**, 4, 53–58. [Google Scholar] [CrossRef] - Bonta, J.V.; Rao, A.R. Factors affecting the identification of independent storm events. J. Hydrol.
**1988**, 98, 275–293. [Google Scholar] [CrossRef] - Restrepo-Posada, P.J.; Eagleson, P.S. Identification of inde-pendent rainstorms. J. Hydrol.
**1982**, 55, 303–319. [Google Scholar] [CrossRef] - Duan, Q.; Soorooshian, S.; Gupta, V. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour. Res.
**1992**, 28, 1015–1031. [Google Scholar] [CrossRef] - Campo, M.A.; Sordo, A.; González-Zeas, D.; Cirauqui, D.; Garrote, L.; López, J. Application of a stochastic rainfall model in flood risk assessment. Geophys. Res. Abstr.
**2009**, 11. [Google Scholar] [CrossRef] - Sordo-Ward, A.; Garrote, L.; Bejarano, M.D.; Castillo, L.G. Extreme flood abatement in large dams with gate-controlled spillways. J. Hydrol.
**2013**, 498, 113–123. [Google Scholar] [CrossRef] - Sordo-Ward, A.; Garrote, L.; Martín-Carrasco, F.; Bejarano, M.D. Extreme flood abatement in large dams with fixed-crest spillways. J. Hydrol.
**2012**, 466–467, 60–72. [Google Scholar] [CrossRef] [Green Version] - Bianucci, P.; Sordo-Ward, A.; Moralo, J.; Garrote, L. Probabilistic-Multi objective Comparison of User-Defined Operating Rules. Case Study: Hydropower Dam in Spain. Water
**2015**, 7, 956–974. [Google Scholar] [CrossRef] - United States Soil Conservation Service. National Engineering Handbook, Section 4: Hydrology; U.S. Department of Agriculture: Washington, DC, USA, 1972; p. 127.
- McCarthy, G.T. The Unit Hydrograph and Flood Routing; US Army Corps of Engineers: Providence, RI, USA, 1939. [Google Scholar]
- Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models, Part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Flores-Montoya, I.; Requena, A.; Sordo-Ward, A.; Mediero, L.; Garrote, L. Deriving bivariate flood frequency distributions for dam safety evaluation. In Proceedings of the 8th International Conference of European Water Resources Association (EWRA): Water Resources Management in an Interdisciplinary and Changing Context, Porto, Portugal, 26–29 June 2013.

**Figure 2.**Methodological scheme for the determination of the storm event durations and the storm event definition for each sub-basin: (

**a**) independent storm identification and extraction from the mean hourly time-series for the entire basin and period of analysis; (

**b**) mean storm event for each defined sub-basin from the identified event periods.

**Figure 3.**Location of the case studies. Black circles show the basin outlets and the dots characterized by an alphanumeric code representing the rainfall gauge stations considered in this study.

**Figure 4.**Validation of the spatial–temporal stochastic rainfall model. Dots represent the annual maxima of the daily rainfall frequency curve from observed data. Grey lines represent frequency curves of annual maxima of daily rainfall from 60 simulated series of 100 years.

**Figure 5.**Comparison of the Intensity-Duration-Frequency curves (IDF) obtained from observed data (station ID-3195, 5-min time-step) and from the results of the RainSimV3 model (hourly time-step).

**Figure 6.**Main characteristics of the entire set of storm events and the set of maximum annual rain depth storm events extracted from the continuous spatially-averaged rainfall series: (

**a**) total rainfall depth in mm; (

**b**) storm duration in hours; (

**c**) storm mean intensity in mm/hours; and (

**d**) inter-event time in hours. Dotted lines represent the cumulative frequency distributions of non-exceedance for the entire set and crossed dashed lines do the same for the subset of the maximum annual rain depth storms. Dark bars show the relative frequency for the entire set and light bars do it for the subset of the maximum annual rain depth storms.

**Figure 7.**Comparison among the three criteria for identifying the highest annual storms. Percentage of occurrence that a storm of a specific order generates the annual maximum peak flow: (

**Left**) Santillana sub-basin; (

**Centre**) El Pardo sub-basin; and (

**Right**) Manzanares basin.

**Figure 8.**Comparison among the observed peak flow and corresponding simulated peak flow (hourly time-step) at the outlet of Manzanares basin.

**Figure 9.**(

**Left**) FFCs obtained for each basin and different storm orders; and (

**Right**) ratio between the FFCs for different maximum storm orders and the reference FFC

_{R}: (

**a**) Santillana sub-basin; (

**b**) The Pardo sub-basin; and (

**c**) Manzanares basin. Thin black lines show the results (the FFC and ratio) for the largest rainfall depth each year, the wide black lines considering the two largest rainfall depths each year, the thin grey lines the three largest rainfall depths each year, the wide grey lines the 10 largest rainfall depths rainfall each year and the dashed black lines shows the reference FFC.

**Figure 10.**For each analyzed basin, the figure shows the storm order that corresponds to every Tr, represented as grey dots: (

**a**) Santillana sub-basin; (

**b**) The Pardo sub-basin; (

**c**) Manzanares basin. The numbers on the right represent the probability that a storm of a specific order generates the maximum peak flow of given a year.

**Figure 11.**For each analyzed basin, the plot shows the probability to generate the maximum peak flow of a year simulating only storms of a specific order or lower: (

**a**) Santillana sub-basin; (

**b**) The Pardo sub-basin; (

**c**) Manzanares basin. The black lines represent the maximum annual peak-flows with 1 ≤ Tr < 10 years, the dark dashed grey lines for 10 ≤ Tr < 50 years, the thin dashed black lines for 50 ≤ Tr < 100 years, the dark grey lines for 100 ≤ Tr < 500 years and the light grey lines for 500 ≤ Tr < 1000 years.

**Figure 12.**Maximum storm order required to include the maximum peak flow each year for different probabilities. Dot and dashed line corresponds to the Santillana sub-basin, dotted line to the Pardo sub-basin and dashed line to the Manzanares basin.

**Figure 13.**Maximum storm order required to achieve, simultaneously, the event of maximum annual peak flow and hydrograph volume for different cumulated probabilities and Tr ranges. (

**a**) Tr calculated from the maximum peak flow each year (Manzanares); (

**b**) Tr calculated from the maximum hydrograph volume each year (Manzanares). The black lines represent the maximum annual peak flows with 1 ≤ Tr < 10 years, the dark dashed grey lines for 10 ≤ Tr < 50 years, the thin dashed black lines for 50 ≤ Tr < 100 years, the dark grey lines for 100 ≤ Tr < 500 years and the light grey lines for 500 ≤ Tr < 1000 years.

**Figure 14.**Maximum storm order required to achieve the maximum peak flow each year for different probabilities and MITs (Manzanares basin). The line with a circle corresponds to MIT 3 h, the line with the rectangle to MIT 6 h, the dark line with the cross to MIT 9 h, the dashed line to MIT 12 h, the grey line with a cross to MIT 24 h and the light grey line with a solid circle correspond to MIT 33 h.

Name | Area (km^{2}) | N° Sub-Basins | Sub-Basin Area (km^{2}) | |
---|---|---|---|---|

Average | Range | |||

Santillana | 211 | 5 | 42 | 6.4/89 |

Pardo | 495 | 7 | 71 | 6.4/196 |

Manzanares | 1294 | 14 | 92 | 6.4/255 |

**Table 2.**Maximum storm order required to obtain 95% and 99% probability of achieving the maximum peak flow for a specific year.

Probability (%) | Tr (Years) | Maximum Storm Order to Be Considered | ||
---|---|---|---|---|

Santillana | Pardo | Manzanares | ||

95/99 | 1 ≤ Tr < 10 | 5/11 | 4/9 | 6/10 |

95/99 | 10 ≤ Tr < 50 | 2/5 | 2/5 | 3/6 |

95/99 | 50 ≤ Tr ≤ 100 | 2/5 | 2/5 | 3/6 |

95/99 | 100 ≤ Tr ≤ 500 | 2/5 | 2/5 | 2/5 |

95/99 | 500 ≤ Tr ≤ 1000 | 1/2 | 2/3 | 2/5 |

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## Share and Cite

**MDPI and ACS Style**

Sordo-Ward, A.; Bianucci, P.; Garrote, L.; Granados, A.
The Influence of the Annual Number of Storms on the Derivation of the Flood Frequency Curve through Event-Based Simulation. *Water* **2016**, *8*, 335.
https://doi.org/10.3390/w8080335

**AMA Style**

Sordo-Ward A, Bianucci P, Garrote L, Granados A.
The Influence of the Annual Number of Storms on the Derivation of the Flood Frequency Curve through Event-Based Simulation. *Water*. 2016; 8(8):335.
https://doi.org/10.3390/w8080335

**Chicago/Turabian Style**

Sordo-Ward, Alvaro, Paola Bianucci, Luis Garrote, and Alfredo Granados.
2016. "The Influence of the Annual Number of Storms on the Derivation of the Flood Frequency Curve through Event-Based Simulation" *Water* 8, no. 8: 335.
https://doi.org/10.3390/w8080335