# Occurrence Probabilities of Wet and Dry Periods in Southern Italy through the SPI Evaluated on Synthetic Monthly Precipitation Series

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{4}years of monthly precipitation for each rain gauge was generated by means of a Monte Carlo technique. Then, dry and wet periods were analyzed through the application of the standardized precipitation index (SPI) over 3-month and 6-month timespan (short-term) and 12-month and 24-month period (long-term). As a result of the SPI application on the generated monthly precipitation series, higher occurrence probabilities of dry conditions than wet conditions have been detected, especially when long-term precipitation scales are considered.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study

^{2}, is a large portion of southern Italy, ranging from Campania and Apulia in the North, to Sicily in the South (Figure 1).

^{2}(Figure 1 and Table 1).

#### 2.2. Stochastic Modeling of Monthly Precipitation

_{ij}(j = month; i = year) the sequence of random variables which describes the cumulated precipitation from a non-specified origin i = 0, and defining N

_{j}as the number of days of the j-month and I

_{0}as a generic reference value of the daily precipitation intensity (assumed in this work equal to 1 mm/day), the dimensionless random variables:

_{ij}> 0), finalized to the gaussianisation of the process, the sequence of random variables Z

_{k}:

_{k}. If this correlation is significant, it can be modelled as an autoregressive process of order p. Being Z

_{k}standardized Gaussian variables and considering a white noise standardized Gaussian process W

_{k}, it can be written:

_{Z}

_{,l}of the autocorrelation coefficients of lag l (l = 1, .., p) of the sequence Z

_{k}, by solving the Yule-Walker system it is possible to estimate the parameters ${\varphi}_{l}$ and consequently ${\psi}_{0}$ with the following relation [67]:

_{0,k}= Z

_{k}and w

_{0,k}= z

_{k}, in order to verify the hypothesis that the process Z

_{k}can be considered as a white noise.

#### 2.3. Standardized Precipitation Index

_{0}, c

_{1}, c

_{2}, d

_{1}, d

_{2}and d

_{3}are mathematical constants.

## 3. Results

_{k}showed low linear correlation coefficients, but not low enough to consider the process Z

_{k}uncorrelated. In fact, the application of the Anderson test, with a lag v

_{max}= 24, to the z

_{k}series evidenced that only for 18 rain gauges the process Z

_{k}can be considered as a white noise (p = 0), while for the other 28 precipitation series, it is sufficient to adopt an autoregressive model of order p = 1.

^{4}years long synthetic series have been generated for each rain gauge through a Monte Carlo procedure, and the SPI data were evaluated both for short (SPI3 and SPI6) and long (SPI12 and SPI24) time scales. Considering the SPI classification (Table 2), the occurrence probabilities of the various classes of dry and wet conditions were evaluated for each rain gauge. The results were also spatially interpolated using a spline technique.

## 4. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Maps of the monthly occurrence probabilities of Extreme drought (

**a**), Severe drought (

**b**), Moderate drought (

**c**), Extremely wet (

**d**), Severely wet (

**e**) and Moderately wet (

**f**) conditions for the 3-month SPI.

**Figure 3.**Box-plots of the regional occurrence probabilities of Extreme, Severe and Moderate drought and wet conditions for the 3-month (

**a**), 6-month (

**b**), 12-month (

**c**) and 24-month (

**d**) SPI. The lines indicate the theoretical values proposed by McKee et al. [32].

**Figure 4.**Maps of the monthly occurrence probabilities of Extreme drought (

**a**), Severe drought (

**b**), Moderate drought (

**c**), Extremely wet (

**d**), Severely wet (

**e**) and Moderately wet (

**f**) conditions for the 6-month SPI.

**Figure 5.**Maps of the monthly occurrence probabilities of Extreme drought (

**a**), Severe drought (

**b**), Moderate drought (

**c**), Extremely wet (

**d**), Severely wet (

**e**) and Moderately wet (

**f**) conditions for the 12-month SPI.

**Figure 6.**Maps of the monthly occurrence probabilities of Extreme drought (

**a**), Severe drought (

**b**), Moderate drought (

**c**), Extremely wet (

**d**), Severely wet (

**e**) and Moderately wet (

**f**) conditions for the 24-month SPI.

ID Code | Rain Gauge | Region | Longitude | Latitude | No. of Years of Observation |
---|---|---|---|---|---|

1 | Benevento (Genio Civile) | Campania | 14.769 | 41.117 | 72 |

2 | Bisaccia | Campania | 15.380 | 41.008 | 82 |

3 | Casalvelino | Campania | 15.102 | 40.184 | 76 |

4 | Caserta (Genio Civile) | Campania | 14.319 | 41.067 | 81 |

5 | Nusco | Campania | 15.088 | 40.886 | 84 |

6 | S. Angelo a Fasanella | Campania | 15.336 | 40.451 | 80 |

7 | Salerno (Genio Civile) | Campania | 14.736 | 40.667 | 79 |

8 | Cersosimo | Basilicata | 16.348 | 40.051 | 65 |

9 | Grassano | Basilicata | 16.270 | 40.632 | 61 |

10 | Lagopesole | Basilicata | 15.737 | 40.804 | 83 |

11 | Maratea | Basilicata | 15.717 | 39.984 | 62 |

12 | Pisticci | Basilicata | 16.735 | 40.295 | 67 |

13 | Vaglio di Lucania | Basilicata | 15.916 | 40.667 | 68 |

14 | Altamura | Apulia | 16.554 | 40.824 | 86 |

15 | Bari (Osservatorio) | Apulia | 16.873 | 41.118 | 86 |

16 | Biccari | Apulia | 15.191 | 41.393 | 84 |

17 | Brindisi | Apulia | 17.938 | 40.629 | 86 |

18 | Cerignola | Apulia | 15.906 | 41.264 | 85 |

19 | San Marco in Lamis | Apulia | 15.637 | 41.711 | 87 |

20 | Santa Maria di Leuca | Apulia | 18.356 | 39.800 | 85 |

21 | Taranto | Apulia | 17.251 | 40.465 | 86 |

22 | Vieste | Apulia | 16.176 | 41.881 | 86 |

23 | Campotenese | Calabria | 16.068 | 39.873 | 79 |

24 | Capo Spartivento | Calabria | 16.056 | 37.927 | 68 |

25 | Cassano allo Ionio | Calabria | 16.319 | 39.783 | 74 |

26 | Cecita | Calabria | 16.538 | 39.400 | 70 |

27 | Cittanova | Calabria | 16.078 | 38.352 | 77 |

28 | Cosenza | Calabria | 16.265 | 39.287 | 79 |

29 | Filadelfia | Calabria | 16.293 | 38.787 | 76 |

30 | Isola di Capo Rizzuto | Calabria | 17.094 | 38.961 | 67 |

31 | Joppolo | Calabria | 15.905 | 38.592 | 68 |

32 | San Pietro in Guarano | Calabria | 16.314 | 39.346 | 72 |

33 | Scilla | Calabria | 15.720 | 38.252 | 64 |

34 | Tiriolo | Calabria | 16.510 | 38.940 | 58 |

35 | Acireale | Sicily | 15.159 | 37.599 | 85 |

36 | Castelbuono | Sicily | 14.079 | 37.929 | 81 |

37 | Castronuovo di Sicilia | Sicily | 13.599 | 37.679 | 82 |

38 | Chiaramonte Gulfi | Sicily | 14.699 | 37.029 | 86 |

39 | Floresta | Sicily | 14.909 | 37.979 | 85 |

40 | Leonforte | Sicily | 14.379 | 37.629 | 81 |

41 | Noto | Sicily | 15.059 | 36.879 | 82 |

42 | Palermo Oss. Astronomico | Sicily | 13.349 | 38.099 | 61 |

43 | Palma di Montechiaro | Sicily | 13.759 | 37.199 | 81 |

44 | San Saba | Sicily | 15.499 | 38.279 | 69 |

45 | Sciacca | Sicily | 13.079 | 37.499 | 85 |

46 | Trapani | Sicily | 12.499 | 38.009 | 84 |

**Table 2.**Climate classification according to the Standardized Precipitation Index (SPI) values [32].

SPI Value | Class | Probability (%) |
---|---|---|

SPI ≥ 2.0 | Extremely wet | 2.3 |

1.5 ≤ SPI < 2.0 | Severely wet | 4.4 |

1.0 ≤ SPI < 1.5 | Moderately wet | 9.2 |

0.0 ≤ SPI < 1.0 | Mildly wet | 34.1 |

−1.0 ≤ SPI < 0.0 | Mild drought | 34.1 |

−1.5 ≤ SPI < −1.0 | Moderate drought | 9.2 |

−2.0 ≤ SPI < −1.5 | Severe drought | 4.4 |

SPI < −2.0 | Extreme drought | 2.3 |

**Table 3.**Values of the transformation parameter λ, number of harmonics ${N}_{h}^{\left(\mu \right)}$ and ${N}_{h}^{\left({\sigma}^{2}\right)}$ for the mean and the variance functions, respectively, and p-order of the autoregressive model, estimated for each rain gauge.

ID Code | Rain Gauge | λ | ${\mathit{N}}_{\mathit{h}}^{\left(\mathit{\mu}\right)}$ | ${\mathit{N}}_{\mathit{h}}^{\left({\mathit{\sigma}}^{2}\right)}$ | p |
---|---|---|---|---|---|

1 | Benevento (Genio Civile) | 0.436 | 2 | 1 | 1 |

2 | Bisaccia | 0.546 | 2 | 1 | 1 |

3 | Casalvelino | 0.490 | 2 | 3 | 0 |

4 | Caserta (Genio Civile) | 0.473 | 2 | 2 | 1 |

5 | Nusco | 0.510 | 2 | 2 | 1 |

6 | S.Angelo a Fasanella | 0.429 | 2 | 2 | 1 |

7 | Salerno (Genio Civile) | 0.433 | 2 | 2 | 0 |

8 | Cersosimo | 0.359 | 2 | 1 | 0 |

9 | Grassano | 0.429 | 2 | 2 | 1 |

10 | Lagopesole | 0.469 | 2 | 2 | 1 |

11 | Maratea | 0.461 | 2 | 2 | 0 |

12 | Pisticci | 0.352 | 2 | 1 | 1 |

13 | Vaglio Di Lucania | 0.444 | 2 | 3 | 0 |

14 | Altamura | 0.431 | 2 | 2 | 0 |

15 | Bari (Osservatorio) | 0.413 | 2 | 2 | 0 |

16 | Biccari | 0.488 | 2 | 2 | 1 |

17 | Brindisi | 0.393 | 2 | 2 | 0 |

18 | Cerignola | 0.407 | 2 | 1 | 1 |

19 | San Marco in Lamis | 0.431 | 2 | 2 | 0 |

20 | Santa Maria di Leuca | 0.383 | 2 | 3 | 1 |

21 | Taranto | 0.374 | 2 | 2 | 1 |

22 | Vieste | 0.392 | 2 | 1 | 1 |

23 | Campotenese | 0.466 | 2 | 2 | 1 |

24 | Capo Spartivento | 0.338 | 3 | 2 | 0 |

25 | Cassano allo Ionio | 0.473 | 2 | 2 | 0 |

26 | Cecita | 0.442 | 2 | 2 | 1 |

27 | Cittanova | 0.401 | 2 | 1 | 1 |

28 | Cosenza | 0.477 | 2 | 2 | 1 |

29 | Filadelfia | 0.477 | 2 | 3 | 1 |

30 | Isola di Capo Rizzuto | 0.315 | 2 | 3 | 1 |

31 | Joppolo | 0.498 | 2 | 1 | 0 |

32 | San Pietro in Guarano | 0.513 | 2 | 2 | 1 |

33 | Scilla | 0.484 | 2 | 1 | 1 |

34 | Tiriolo | 0.405 | 2 | 2 | 1 |

35 | Acireale | 0.299 | 2 | 1 | 0 |

36 | Castelbuono | 0.390 | 3 | 2 | 0 |

37 | Castronuovo Di Sicilia | 0.389 | 2 | 1 | 0 |

38 | Chiaramonte Gulfi | 0.371 | 2 | 1 | 1 |

39 | Floresta | 0.378 | 3 | 2 | 0 |

40 | Leonforte | 0.363 | 2 | 1 | 1 |

41 | Noto | 0.320 | 2 | 1 | 1 |

42 | Palermo Oss. Astronomico | 0.431 | 3 | 2 | 0 |

43 | Palma di Montechiaro | 0.333 | 2 | 3 | 0 |

44 | San Saba | 0.381 | 2 | 2 | 1 |

45 | Sciacca | 0.331 | 2 | 1 | 1 |

46 | Trapani | 0.408 | 3 | 2 | 1 |

© 2018 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**

Caloiero, T.; Sirangelo, B.; Coscarelli, R.; Ferrari, E.
Occurrence Probabilities of Wet and Dry Periods in Southern Italy through the SPI Evaluated on Synthetic Monthly Precipitation Series. *Water* **2018**, *10*, 336.
https://doi.org/10.3390/w10030336

**AMA Style**

Caloiero T, Sirangelo B, Coscarelli R, Ferrari E.
Occurrence Probabilities of Wet and Dry Periods in Southern Italy through the SPI Evaluated on Synthetic Monthly Precipitation Series. *Water*. 2018; 10(3):336.
https://doi.org/10.3390/w10030336

**Chicago/Turabian Style**

Caloiero, Tommaso, Beniamino Sirangelo, Roberto Coscarelli, and Ennio Ferrari.
2018. "Occurrence Probabilities of Wet and Dry Periods in Southern Italy through the SPI Evaluated on Synthetic Monthly Precipitation Series" *Water* 10, no. 3: 336.
https://doi.org/10.3390/w10030336