# Investigating the Reliability of Stationary Design Rainfall in a Mediterranean Region under a Changing Climate

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The island’s topography ranges from sea level to over 3000 m a.s.l. at the Etna volcano. Precipitation exhibits notable spatial and temporal fluctuations. The MAP ranges from approximately 360 mm in the southeastern part of the island to roughly 1300 mm in the northeast region [30], with an overall mean of approximately 700 mm. In terms of temporal variation, rainfall is predominantly concentrated in the winter season, with the summer months (i.e., June, July, and August) mostly dry.

#### 2.2. SIAS Rainfall Dataset and Regional DDFs

#### 2.3. Methodology

#### 2.3.1. Regional Quantile Exceedance Detection

_{24}and n for the evaluation of the scale factor. The ${h}_{reg}$ have been derived for the reference durations and the return periods of 5, 10, and 20 years. We decided to consider a maximum return period of 20 years since SIAS data length is equal to 21 years, spanning the period from 2002 to 2022, which is not sufficient to apply a reliable probabilistic model for a return period greater than that.

^{−1}. The PDF of the binomial distribution, which is valid only if the probability of more than one occurrence per year is null, provides the probability that y T-year events occur exactly in n successive years. Assuming T = 5, the mode value is 4 in a period of 20 years.

#### 2.3.2. Quantile Comparison and Revision of the Return Periods

## 3. Results and Discussion

#### 3.1. Regional Quantile Exceedance

#### 3.2. Revision of the Return Periods Defined with the Regional Approach

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Location of the gauges of the Servizio Informativo Agrometeorologico Siciliano (SIAS) used for the presented analyses, overlaid onto the DEM of Sicily.

**Figure 2.**At-site comparison between the h

_{reg}for the 1 h duration and the 5-year return period and the aggregated data series of the SIAS rain gauge named “Palermo” (upper panel) and spatial distribution of the number of exceedances for different durations (rows) and return periods (columns) over the entire region (lower panel).

**Figure 3.**Probability density functions of the binomial statistical distribution, in blue, and of the number of h

_{reg}exceedances, in red, for the reference durations (rows) and return periods (columns). What might look like a third different color in the figure is due to the overlap of the two histograms. The small panels represent the respective cumulative distribution function.

**Figure 4.**Spatial distribution of p-value for the K–S test for the reference durations. High p-values indicate greater significance in not rejecting the null hypothesis that the sample belongs to the theoretical Gumbel distribution.

**Figure 5.**Empirical density distribution of the T

_{SIAS}of all 72 considered SIAS rain gauges, compared to the corresponding T

_{reg}(red dashed line). Results are expressed for all the reference durations (rows) and the return periods of 5, 10, and 20 years (columns).

**Figure 6.**Spatial representations of the T

_{SIAS}for the 72 considered SIAS rain gauges. Results are expressed for all reference durations (rows) and the T

_{reg}of 5, 10, and 20 years (columns).

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**MDPI and ACS Style**

Treppiedi, D.; Cipolla, G.; Francipane, A.; Cannarozzo, M.; Noto, L.V.
Investigating the Reliability of Stationary Design Rainfall in a Mediterranean Region under a Changing Climate. *Water* **2023**, *15*, 2245.
https://doi.org/10.3390/w15122245

**AMA Style**

Treppiedi D, Cipolla G, Francipane A, Cannarozzo M, Noto LV.
Investigating the Reliability of Stationary Design Rainfall in a Mediterranean Region under a Changing Climate. *Water*. 2023; 15(12):2245.
https://doi.org/10.3390/w15122245

**Chicago/Turabian Style**

Treppiedi, Dario, Giuseppe Cipolla, Antonio Francipane, Marcella Cannarozzo, and Leonardo Valerio Noto.
2023. "Investigating the Reliability of Stationary Design Rainfall in a Mediterranean Region under a Changing Climate" *Water* 15, no. 12: 2245.
https://doi.org/10.3390/w15122245