| Περίληψη: | Rainfall is one of the most representative, significant and dominant climatic variables, since it
considerably affects hydrologic equilibrium, as well as constituting a control parameter in
water management. However, due to its intermittent nature and highly variable character, its
statistical modeling and forecasting under changing climate conditions, is one of the most
pressing and crucial problems in modern Hydrology. In this thesis, we present, critically
assess and compare the most popular approaches which have been used in the literature, in
the fields of: a) extreme rainfall estimation, and b) reproducing rainfall statistics based on
climate models results.
In extreme excess modelling, one fits a generalized Pareto (GP) distribution to rainfall
excesses above a properly selected threshold u. The latter is generally determined using
various approaches, such as non-parametric methods that are intended to locate the changing
point between extreme and non-extreme regions of the data, graphical methods where one
studies the dependence of GP related metrics on the threshold level u, and Goodness of Fit
(GoF) metrics that, for a certain level of significance, locate the lowest threshold u that a GP
distribution model is applicable. In Chapter 1, we review representative methods for GP
threshold detection, discuss fundamental differences in their theoretical bases, and apply
them to 1714 over-centennial daily rainfall records from the NOAA-NCDC database. We
find that non-parametric methods are generally not reliable, while methods that are based on
GP asymptotic properties lead to unrealistically high threshold and shape parameter
estimates. The latter is justified by theoretical arguments, and it is especially the case in
rainfall applications, where the shape parameter of the GP distribution is low; i.e. on the order
of 0.1 ÷ 0.2. Better performance is demonstrated by graphical methods and GoF metrics that
rely on pre-asymptotic properties of the GP distribution. For daily rainfall, we find that GP
threshold estimates range between 2÷12 mm/d with a mean value of 6.5 mm/d, while the
existence of quantization in the empirical records, as well as variations in their size, constitute
the two most important factors that may significantly affect the accuracy of the obtained
results.
Concerning reproduction of the statistical structure of daily rainfall at a basin level based
on climate model (CM) results, two types of statistical approaches have been suggested. One
is statistical correction of CM rainfall outputs based on historical series of precipitation. The
other, usually referred to as statistical rainfall downscaling, is the use of stochastic models to
conditionally simulate rainfall series, based on large-scale atmospheric forcing from CMs. While promising, the latter approach attracted reduced attention in recent years, since the
developed downscaling schemes involved complex weather identification procedures, while
demonstrating limited success in reproducing several statistical features of rainfall. In a
recent effort, Langousis and Kaleris (2014) developed a statistical framework for simulation
of daily rainfall intensities conditional on upper-air variables, which is simpler to implement
and more accurately reproduces several statistical properties of actual rainfall records. In
Chapter 2, we study the relative performance of: i) direct statistical correction of CM rainfall
outputs using non-parametric distribution mapping, and ii) the statistical downscaling scheme
of Langousis and Kaleris (2014), in reproducing the historical rainfall statistics, including
rainfall extremes, at a regional level. This is done for an intermediate-sized catchment in
Italy, i.e. the Flumendosa catchment, using rainfall and atmospheric data from 4 CMs of the
ENSEMBLES project. The obtained results are promising, since the proposed downscaling
scheme is more accurate and robust in reproducing a number of historical rainfall statistics,
independent of the CM used and the characteristics of the calibration period. This is
particularly the case for yearly rainfall maxima.
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