final_program_abstracts[1]

11 IMSC Session Program
A functional data approach for climate zones identification
Tuesday - Parallel Session 5
Edmondo Di Giuseppe 1 , Giovanna Jona Lasinio 2 , Stanislao Esposito 1 and
Massimiliano Pasqui 3
1 CRA-Cma, Roma, Italy
2 Uniroma1, Roma, Italy
3 CNR-Ibimet, Roma, Italy
In order to correctly describe atmospheric variability and clear trends, homogeneous
climate regions should be identified. A combination of Functional Data Analysis
(FDA) and Partioning Around Medoids (PAM) clustering technique is applied in Italy
for surface temperature and precipitation fields. The analysed dataset is composed of
daily precipitation and daily minimum and maximum temperature data collected for
the period 1961-2007 from 96 Italian stations. First, minimum and maximum
temperatures were averaged to obtain medium temperature. Then Monthly Mean of
Medium Temperature (Tmed-MM) and Monthly Cumulated Rainfall (Prec-MC) were
calculated. Thus, 96 time series of 564 monthly values concerning a set of 2 climatic
variables form the basis for the classification.
FDA is a collection of techniques to model data from dynamic systems in terms of
some set of basis functions, which are a linear combination of known functions. FDA
consists of converting observations gathered at discrete time into functional data.
Tmed-MM and Prec-MC time series can be considered as realizations of continuous
processes recorded in discrete time. As each time series is representative of station
location climate variability, they are converted into functional data through the
estimation of spline coefficients. The main advantage of functional data is the
reduction of many observations to few coefficients, preserving the information about
temporal pattern of the time series. B-splines system of basis with a fixed number of
knots is adopted for functional data conversion, which guarantees a comparability of
responses from 96 time series. Fixed interior knots are 45 plus 2 knots corresponding
to the edges of observations interval, piece-wise polynomials degree is 3 for a total
number of 51 estimated coefficients. A Generalized Cross Validation (GCV)
procedure is applied for determining the λ weight of penalty matrix. Finally the
number of estimated coefficients is reduced by means of Principal component
analysis (PCA). Thus, the Pc’s of estimated coefficients are partitioned by PAM
classification technique to obtain climate zones.
PAM algorithm clusters objects around k medoids where k is specified in advance.
Medoids are chosen at each iteration as representative items rather than calculate the
mean of the items in each cluster. As an alternative the coordinates of k medoids can
be established as initial medoids. A comparison between the average distance of
object i from all other objects in the same cluster and the minimum distance of object
i from all other objects not in the same cluster composes an index defined as
silhouette. A plot of silhouettes for all objects is a method both to determine the
number of clusters and also to determine which objects lie well within their clusters
and which do not.
Once a final grouping of the stations is established, a cross validation procedure is
applied in order to quantify those stations correctly classified. An assessment based
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