Extreme Rainfall Event Analysis Using Rain Gauges in a Variety of Geographical Situations

About 30 years of measurements made by the rain gauges located in Piedmont (Italy) have been analyzed. Rain gauges have been divided into 4 datasets considering the complex orography near Turin, namely the flatlands, mountains, hills and urban areas. For each group of gauges, the Generalized Extreme Values (GEV) distributions are estimated considering both the entire dataset of available data and different sets of 3 years of data in running mode. It is shown that the GEV estimated parameters temporal series for the 3 years dataset do not present any specific trend over the entire period. The study presented here is preliminary to a future extreme rainfall event analysis using high temporal and spatial resolution X-band weather radar with a limited temporal availability of radar maps covering the same area.


Introduction
Extreme rainfall events analysis could be very significant if it is possible to put in evidence trends related to climate change and their impacts on the society [1] [2].
A large number of theoretical modelling and empirical analyses have been performed suggesting that changes in frequency and intensity of extreme events, including also extreme floods, may occur even in relations to small changes in climate [3]- [8] making extreme rainfall events analysis even more important.
Extreme rainfall event analyses have been made almost all over the world considering in particular rain gauges data or climatological models (e.g.[1] [9]- [11]).But up to now, very few analyses have been performed exploiting weather radars.The most important example of extreme rainfall event analysis using radar data is related to a Dutch region and presented in a set of papers of A. Overeem [12]- [15].A climatological analysis is presented exploiting C-band Doppler radar data with a spatial resolution of 2.4 km and 10 years of historical data.The Generalized Extreme Value (GEV) distributions are evaluated as well as the radar depth-duration curves over small selected basins demonstrating that radar systems may be a useful tool to analyze extreme events.Of course, in this case the orography is homogeneous.
In particular in the Piedmont region (North-Western part of Italy), the orography is extremely complex and flash floods in small basins are causing large damages.Consequently it is important to evaluate the extreme distribution functions of such events and to find out if there are climatological trends causing significant changes in the distribution parameters.
In the present paper, the available data from a set of rain gauges are examined to this end as well as preliminary study for a future analysis using X-band weather radar installed in Turin.

Rain Gauges Data
In Piedmont, around the town of Turin, a set of meteorological stations, managed by ARPA Piemonte, are installed.They are equipped with a set of different sensors including rain gauges.Measured data are available and can be downloaded freely on internet.They have been used in the in the statistical analysis of extreme events reported in the following.In particular it is used the cumulative daily rainfall data available for each day.
Seventeen fully operative weather stations equipped with rain gauges have been identified in a 30 km radius circle around Turin.

Rain Gauges Groups
The rain gauges have been divided into 4 homogeneous groups, taking into account their installation environment.
The 4 zones are the following (see also in the following Tables 1-4 and  • Mountains area.

Temporal Availability of Rain Gauges Data
The rain data are available on the archive accessible on internet since 1988.Since we ended the analysis the 30 th June 2014, it means that some rain gauges have been operative for more than 26 years.However, due to maintenance reasons and newer installations, each meteorological station has its own period of operation often smaller than 26 years, as reported in the following table (Table 5).

GEV Distribution and Parameters
The extreme rainfall event analysis using rain gauges data has been performed by estimating the GEV distribu- tion parameters.Therefore it has been assumed that the hypothesis of the GEV theory is satisfied, which is a common choice when an extreme event analysis is performed.The expression of the common GEV distribution is reported Equation (1): k is the shape factor, σ is the scale parameter and μ is called location parameter.
( ) It is well known that the GEV distribution parameters can be made using two different methods: the maximum likelihood (ML) estimation method and the L-moment method.Since the ML method is more robust also for a small number of data [16], GEV parameters (k, σ, μ) estimations were obtaining using a MATLAB © routine implementing such method.

Definition of Extreme Rainfall Event
It is necessary to establish when a rainfall event is considered "extreme" and, therefore, which is the dataset to use for the estimation of the GEV distribution parameters.
Three different methods have commonly been used to identify extreme rainfall events: • The Peaks Over Threshold (POT) using rainfall depth thresholds over a specified time interval.
• The Peaks Over Threshold (POT) using probabilistic thresholds, such as the 90 th and 99 th percentiles of precipitation, over a specified time interval.In this way it is possible to define and discriminate heavy and very heavy events.• The Block Maxima (BM), calculating the return periods of the event based on a specific interval maximum on 24 hours precipitation series.
For the analysis of extreme event reported in this paper, the POT approach is followed and two different defi-nitions of extreme events are considered: • Threshold T 1 = 40 mm/day: an event is considered as extreme, for a single rain gauge, when during 24 hours more than 40 mm of cumulated rain are measured.It corresponds to almost the 90 th percentile of the precipitation distribution.• Threshold T 2 = 50 mm/day: an event is considered as extreme, for a single rain gauge, when during 24 hours more than 50 mm of cumulated rain are measured.It corresponds to almost the 95 th percentile of the precipitation distribution.

Data Processing and Results
The GEV distribution parameters were estimated examining the entire period of available rain gauges data corresponding to 26 years that is from 1998 to 2014.However there is a general feeling that the climate is changing, and in particular the "extremes" may be significantly affected.Therefore it is of great interest to be able to put in evidence any change in the GEV distribution, possibly over not so long time interval.For this reason, we subdivided the available data set in 3 years groups, in order to see if some systematic changes in the GEV distribution may be put in evidence, well aware of the poor significance of any results that could be obtained in this way.
The 3 years groups of rain gauges data were examined in "running mode" for both rain thresholds, T 1 and T 2 over the entire period 1988-2014.
As reported in Section 2, the rain gauges were divided in the four geographical areas (Mountains area, Hills area, Flatlands area and Turin area) and the corresponding GEV distributions parameters were evaluate.
Table 6 (for T 1 = 40 mm/day) and Table 7 (for T 2 = 50 mm/day) report the GEV distributions parameters k, σ, μ.In both tables it is possible to note that most of k parameters are positive.It means that the GEV distributions are Frechét distribution (or EV2, Extreme Value type 2, distribution) which are very common in hydrology research and applications.3 report the GEV parameters estimations: the green lines are the values of the corresponding parameters estimated by using all the available rain measurements during the 26 years interval.As appears also from the tables, the GEV parameters are not extremely different from one to the other geographical area, except for the value of σ significantly larger in the mountains area with respect to the others, as it can be expected due to the large variability of wind current and rain fields between the mountains.
In the same figures, the diagrams report the same parameters estimated over the 3 years intervals.It is quite evident that there are no significant trends in such estimates and no significant correlation from area to area.

Conclusions and Outlooks
The data analysis has shown that the parameters estimated over a long time period (26 years)  are not significantly different for the 4 orographic regions examined (Mountain area, Hills, Flatlands, Town of Turin).However, even a relatively dense gauge network is not able to put in evidence "extremes" distribution changes over a short time interval correlated with climatic changes: a different approach should be considered.
In the near future, we intend to use meteorological radar data hoping to get more significant results for short time variations, possibly exploiting the high temporal and spatial resolution of a small X-band weather radar present in the area [17] [18].

Figure 1 Figure 1 .
Figure 1.Rain gauges grouped identified in each area within a 30 km radius circle.

Figure 2 .
Figure 2. Variation of GEV distribution estimated parameters k, σ, μ for threshold T 1 = 40 mm/day, considering groups of 3 years in "running mode".In each of the 3 plots, x axis represents the progressive group of 3 years (according to Table6).

Figure 3 .
Figure 3. Variation of GEV distribution estimated parameters k, σ, μ for threshold T 2 = 50 mm/day, considering groups of 3 years in "running mode".In each of the 3 plots, x axis represents the progressive group of 3 years (according to Table7).

Table 1 .
Rain gauges in the "Mountains area".

Table 4 .
Rain gauges in the "Turin area".

Table 5 .
Operational interval of each rain gauge (date in dd/mm/yy format).