Research Article
A Hidden Markov Model Applied to the Daily Spring
Precipitation over the Danube Basin
Constantin Mares,
1
Ileana Mares,
1
Heike Huebener,
2
Mihaela Mihailescu,
3
Ulrich Cubasch,
4
and Petre Stanciu
1
1
National Institute of Hydrology and Water Management, 013686 Bucharest, Romania
2
Hessian Centre on Climate Change, 65203 Wiesbaden, Germany
3
University of Agronomic Sciences and Veterinary Medicine, 011464 Bucharest, Romania
4
Institute of Meteorology, Free University Berlin, 12165 Berlin, Germany
Correspondence should be addressed to Constantin Mares; constantin mares ro@yahoo.com
Received 12 August 2013; Revised 20 November 2013; Accepted 26 December 2013; Published 19 February 2014
Academic Editor: Klaus Dethlof
Copyright © 2014 Constantin Mares et al. his is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
he main goal of this study is to obtain an improvement of the spring precipitation estimation at local scale, taking into account
the atmospheric circulation on the Atlantic-European region, by a statistical downscaling procedure. First we have itted the
precipitation amounts from the 19 stations with a HMM with 7 states. he stations are situated in localities crossed by the Danube or
situated on the principal tributaries. he number of hidden states has been determined by means of BIC values. A NHMM has been
applied then to precipitation occurrence associated with the information about atmospheric circulation over Atlantic-European
region. he atmospheric circulation is quantiied by the irst 10 components of the decomposition in the EOFs or MEOFs. he
predictors taking into account CWTs for SLP and the irst summary variable from a SVD have also been tested. he atmospheric
predictors are derived from SLP, geopotential, temperature, and speciic and relative humidity at 850 hPa. As a result of analyzing
the multitude of the predictors, a statistical method of selection based on the informational content has been achieved. he test of
the NHMM performances has revealed that SLP and geopotential at 850 hPa are the best predictors for precipitation.
1. Introduction
Hidden Markov models (HMM) were irst described in [1]
and in other series of statistical papers in the second half of
the 1960s. he most cited publication regarding the solutions
of practical and theoretical problems that appear related to
HMM application is that of Rabiner [2]. Although the irst
applications of HMM in meteorology, hydrology, or climate
change studies appeared relatively late ater the 1960s, a
substantial increasing of the investigations based on itting by
HMM has been noted lately.
Considering that precipitation, as it is known, represents
the most important predictor in hydrological studies, we will
focus on the modeling of these meteorological variables. If
at the beginning of the 1990s the precipitation modeling was
achieved using a HMM, then the number of investigations
where precipitation modeling using HMM is associated
with precipitation modeling using nonhomogenous HMM
(NHMM) by introducing atmospheric factors as inputs has
increased. he atmospheric factors (or other predictors)
modify the transition matrix of HMM, and this modeling
clearly approaches the reality best.
Among the irst applications of HMM and NHMM for
generating precipitation, there is the one described in [3].
Paper [4] presents the relation between the transition matrix
of a NHMM which is dependent of time and the transition
matrix of a HMM which is independent on time. he variable
that realizes this transformation is the input variable. As it is
shown in [5], the HMMs are utilized both as diagnostic and
as prognostic tools.
Regarding the predictors (inputs) in NHMM, their selec-
tion is a rather diicult problem. As it is presented in [6] the
selection of suitable predictors is crucial when developing a
statistical downscaling model. he basic demand for a pre-
dictor refers to the given information that may be emphasized
Hindawi Publishing Corporation
Advances in Meteorology
Volume 2014, Article ID 237247, 11 pages
http://dx.doi.org/10.1155/2014/237247