# A Stochastic Approach for the Analysis of Long Dry Spells with Different Threshold Values in Southern Italy

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## Abstract

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## 1. Introduction

^{th}century at a seasonal time scale based on daily precipitation data at 104 gauge stations. Pérez-Sánchez and Senent-Aparicio [32] analyzed meteorological droughts and dry spells in a semiarid region (Segura Basin, SE Spain). After an overview of the statistical distributions mostly used to model dry (wet) spell durations, Zolina et al. [33] analyzed the changes in the duration of wet and dry periods over Europe.

## 2. Materials and Methods

## 3. Application

#### 3.1. Study Area and Data Base

^{2}with a coastline of 738 km which reaches the Tyrrhenian Sea on the west side and the Ionian Sea on the southeast side of the region (Figure 2). Due to its position within the Mediterranean Sea and to its orography (42% of the regional area is over 500 m a.s.l. high) the climate of the region is typically Mediterranean but presents a high spatial variability of its climatic features and of extreme hydrological phenomena such as flood and drought [48]. In particular, rainfall deficits are not unusual in the region and thus, drought analysis is particularly important in Calabria where agriculture is one of the largest sectors of the tradable economy. In fact, several drought events hit the region in the 1980’s [49,50] and many industries suffered from drought, including the production of fodder for livestock, vegetables, cereals, fruit growing, viticulture, beekeeping products, and other livestock sectors.

#### 3.2. Intensity Function Modelled through Truncated Fourier Series

^{th}and 150

^{th}day, that are days in the month of May). Figure 3 also presents evidence that there was a low increase of the maximum values of the expected values for both the stations, passing from the first sub-period to the second one. As an example, for the Cassano station, fixing a 5-mm threshold, the maximum value for the 1951–1980 sub-period was equal to 20.7 days (about 1.31 on the y-axis) increases to 22.3 days (about 1.35 on the y-axis) for the successive sub-period.

#### 3.3. Test on the Statistical Significance of the Variation of Dry Spells between the Two Periods

#### 3.4. Occurrence Probability of Long Dry Spells

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Sketch of the dry spells sequence k’Δt of rainfall events h, each lower than the threshold h

_{s}.

**Figure 3.**Expected and observed values of the dry spells sequences ${k}^{\prime}$ with thresholds 2 mm for the Cosenza rain gauge and 5 mm for the Cassano rain gauge in the 30-year periods 1951–1980 and 1981–2010.

**Figure 4.**Behaviour of the Fourier parameter ${a}_{0}^{*}$ for the different threshold values. The values in blue and red refer to 1951–1980 and 1981–2010 sub-periods, respectively. The ticks evidenced on the x-axis are the threshold values, expressed by the equation ln(1+h

_{s}).

**Figure 5.**Comparison between simulated (boxplots) and observed values (blue dots) of the maximum dry spell length evaluated for the different thresholds for each 30-year period for the Cosenza rain gauge. (Bottom and top of the box: first and third quartiles. Band inside the box: median, second quartile. Ends of the whiskers: 5% and 95% percentiles. Yellow color: values below the median. Red color: values above the median.).

**Figure 6.**Estimated values of the dry spells duration ${k}_{\mathrm{max}}^{\prime}$ (days) for different 30-year periods and thresholds for the Cosenza rain gauge. (

**a**) 1951–1980 and (

**b**) 1981–2010.

Rain Gauge | Latitude | Longitude | Altitude (m a.s.l.) | Proximity to Sea Side (km) | % Missing Data | Mean Annual Rainfall (mm) | Mean Dry Spell Length (days) |
---|---|---|---|---|---|---|---|

Cosenza | 39°46’56” | 16°19’08” | 251 | 14.452 | 1.4 | 1014.6 | 6.9 |

Cassano allo Jonio | 39°17’11” | 16°15’55” | 242 | 18.257 | 1.9 | 734.2 | 6.7 |

San Pietro in Guarano | 39°20’42” | 16°18’48” | 660 | 23.435 | 1.1 | 992.9 | 6.5 |

Campotenese | 39°52’19” | 16°04’05” | 965 | 23.672 | 0.2 | 1465.3 | 5.7 |

Threshold | Rain Gauges | 1951–1980 | 1981–2010 | ||||
---|---|---|---|---|---|---|---|

${\mathit{a}}_{0}^{*}$ | ${\mathit{a}}_{1}^{*}$ | ${\mathit{b}}_{1}^{*}$ | ${\mathit{a}}_{0}^{*}$ | ${\mathit{a}}_{1}^{*}$ | ${\mathit{b}}_{1}^{*}$ | ||

h_{s} = 1 mm | Cosenza | 0.2568 | 0.0521 | 0.0237 | 0.2308 | 0.0533 | 0.0190 |

Cassano allo Ionio | 0.2692 | 0.0499 | 0.0160 | 0.2359 | 0.0401 | 0.0136 | |

San Pietro in Guarano | 0.2734 | 0.0597 | 0.0253 | 0.2332 | 0.0557 | 0.0232 | |

Campotenese | 0.3124 | 0.0528 | 0.0147 | 0.2730 | 0.0551 | 0.0123 | |

h_{s} = 2 mm | Cosenza | 0.2333 | 0.0495 | 0.0224 | 0.2133 | 0.0497 | 0.0177 |

Cassano allo Ionio | 0.2409 | 0.0452 | 0.0148 | 0.2092 | 0.0385 | 0.0120 | |

San Pietro in Guarano | 0.2456 | 0.0514 | 0.0247 | 0.2156 | 0.0495 | 0.0200 | |

Campotenese | 0.2895 | 0.0455 | 0.0130 | 0.2524 | 0.0477 | 0.0114 | |

h_{s} = 5 mm | Cosenza | 0.1949 | 0.0407 | 0.0177 | 0.1762 | 0.0401 | 0.0133 |

Cassano allo Ionio | 0.1923 | 0.0409 | 0.0109 | 0.1708 | 0.0257 | 0.0112 | |

San Pietro in Guarano | 0.2073 | 0.0408 | 0.0216 | 0.1816 | 0.0409 | 0.0166 | |

Campotenese | 0.2403 | 0.0341 | 0.0110 | 0.2103 | 0.0355 | 0.0102 | |

h_{s} = 10 mm | Cosenza | 0.1560 | 0.0373 | 0.0166 | 0.1417 | 0.0367 | 0.0092 |

Cassano allo Ionio | 0.1532 | 0.0389 | 0.0100 | 0.1344 | 0.0235 | 0.0101 | |

San Pietro in Guarano | 0.1775 | 0.0390 | 0.0191 | 0.1496 | 0.0387 | 0.0151 | |

Campotenese | 0.1987 | 0.0300 | 0.0105 | 0.1693 | 0.0227 | 0.0098 | |

h_{s} = 20 mm | Cosenza | 0.1296 | 0.0292 | 0.0130 | 0.1059 | 0.0267 | 0.0066 |

Cassano allo Ionio | 0.1151 | 0.0324 | 0.0066 | 0.0924 | 0.0158 | 0.0088 | |

San Pietro in Guarano | 0.1333 | 0.0317 | 0.0138 | 0.1120 | 0.0318 | 0.0127 | |

Campotenese | 0.1427 | 0.0222 | 0.0086 | 0.1212 | 0.0102 | 0.0089 |

**Table 3.**Results of the test about the statistically significant differences between the two 30-year periods.

Rain Gauge | $\mathit{d}$ | ${\mathit{\delta}}_{0.95}$ | ${\mathit{F}}_{\mathsf{\Delta}}\left(\mathit{d}\right)$ | ${\mathit{H}}_{0}$ |
---|---|---|---|---|

Cosenza | 18.34 | 18.28 | 0.954 | Rejected |

Cassano allo Jonio | 19.45 | 18.90 | 0.968 | Rejected |

San Pietro in Guarano | 17.72 | 17.43 | 0.961 | Rejected |

Campotenese | 16.32 | 15.44 | 0.982 | Rejected |

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**MDPI and ACS Style**

Sirangelo, B.; Caloiero, T.; Coscarelli, R.; Ferrari, E. A Stochastic Approach for the Analysis of Long Dry Spells with Different Threshold Values in Southern Italy. *Water* **2019**, *11*, 2026.
https://doi.org/10.3390/w11102026

**AMA Style**

Sirangelo B, Caloiero T, Coscarelli R, Ferrari E. A Stochastic Approach for the Analysis of Long Dry Spells with Different Threshold Values in Southern Italy. *Water*. 2019; 11(10):2026.
https://doi.org/10.3390/w11102026

**Chicago/Turabian Style**

Sirangelo, Beniamino, Tommaso Caloiero, Roberto Coscarelli, and Ennio Ferrari. 2019. "A Stochastic Approach for the Analysis of Long Dry Spells with Different Threshold Values in Southern Italy" *Water* 11, no. 10: 2026.
https://doi.org/10.3390/w11102026