Monthly rain amounts (MRA) recorded at Fabra Observatory (Barcelona, NE Spain) since 1917–2010, are analysed from two complementary points of view. First, mono- and multifractal characteristics of MRA are compared with those corresponding to the monthly Western Mediterranean Oscillation index (WeMOi), which affects the rainfall regime at the western Mediterranean region. Monofractality is analysed through Hurst and Hausdorff exponents, and a power law describing the dependence of MRA power spectra on frequency. The reconstruction theorem permits to quantify the complexity of the physical process by means of the correlation dimension and the Kolmogorov entropy. In agreement with this theorem, the predictive instability is also evaluated through the Lyapunov exponents. The multifractality is characterized by the critical Hölder exponent, as well as by the asymmetry and spectral width of the multifractal spectrum. Second, three predictive processes for MRA are tested. One of them is based on the assumption that MRA could be simulated by fractional Gaussian noise. The other two are, by one hand, an ARIMA(p,1,0) process for MRA; on the other hand, an adaptation of the ARIMA process for MRA taking as arguments preceding WeMOi. Finally, relationships between MRA and WeMOi confirm that outstanding MRA use to be coincident with negative WeMOi. An explanation is also proposed for the non-negligible number of MRA corresponding to positive WeMOi.
Dry spell lengths, DSL, defined as the number of consecutive days with daily rain amounts below a given threshold, may provide relevant information about drought regimes. Taking advantage of a daily pluviometric database covering a great extension of Europe, a detailed analysis of the multifractality of the dry spell regimes is achieved. At the same time, an autoregressive process is applied with the aim of predicting DSL. A set of parameters, namely Hurst exponent, H, estimated from multifractal spectrum, f(a), critical Hölder exponent, a0, for which f(a) reaches its maximum value, spectral width, W, and spectral asymmetry, B, permits a first clustering of European rain gauges in terms of the complexity of their DSL series. This set of parameters also allows distinguishing between time series describing fine- or smooth-structure of the DSL regime by using the complexity index, CI. Results of previous monofractal analyses also permits establishing comparisons between smooth-structures, relatively low correlation dimensions, notable predictive instability and anti-persistence of DSL for European areas, sometimes submitted to long droughts. Relationships are also found between the CI and the mean absolute deviation, MAD, and the optimum autoregressive order, OAO, of an ARIMA(p,d,0) autoregressive process applied to the DSL series. The detailed analysis of the discrepancies between empiric and predicted DSL underlines the uncertainty over predictability of long DSL, particularly for the Mediterranean region.
A spatial analysis of partial duration series, PDS, of the dry spell lengths, DSL, is applied to 267 European stations during years 1951–2000. A DSL is defined as the number of consecutive days with precipitation below 0.1 mm/day. For every station, PDS are made of DSL longer than those corresponding to 95th empirical percentile. The L-skewness and L-kurtosis diagram of the PDS distributions shows that most of the stations fit well a generalised Pareto, GP, model. Only four rain gauge records at the southeast Mediterranean coast notably depart from this model. In addition, DSL maps for return periods of 2, 5, 10, 25 and 50 years are introduced by taking into account GP parameters, which are estimated by fitting the GP distribution to empirical PDS distributions of DSL. A comparative study with those obtained in a previous paper, for the whole DSL series and the corresponding best distribution model (Pearson type III), shows that the differences of DSL for the different return periods keep within ±10 % in most of rain gauges. Moreover, a principal component analysis, PCA, is applied to the four first L-moments of the 267 rain gauges. Then, a regionalization in 11 groups is obtained after the clustering process. Finally, a regional frequency analysis is attempted, being possible to assign a GP parent distribution with different parameters to 7 out of the 11 groups.
The complexity, predictability and predictive instability of the Western Mediterranean Oscillation index (WeMOi) at monthly scale, years 1856-2000, are analysed from the viewpoint of monofractal and multifractal theories. The complex physical mechanism is quantified by: (1) the Hurst exponent, H, of the rescaled range analysis; (2) correlation and embedding dimensions, mu* and d(E), together with Kolmogorov entropy, kappa, derived from the reconstruction theorem; and (3) the critical Holder exponent, alpha(o), the spectral width, W, and the asymmetry of the multifractal spectrum, f(alpha). The predictive instability is described by the Lyapunov exponents, lambda, and the Kaplan-Yorke dimension, D-KY, while the self-affine character is characterized by the Hausdorff exponent, H-a. Relationships between the exponent beta, which describes the dependence of the power spectrum S(f) on frequency f, and the Hurst and Hausdorff exponents suggest fractional Gaussian noise (fGn) as a right simulation of empiric WeMOi. Comparisons are made with monthly North-Atlantic Oscillation and Atlantic Multidecadal Oscillation indices. The analysis is complemented with an ARIMA(p,1,0) autoregressive process, which yields a more accurate prediction of WeMOi than that derived from fGn simulations.
A compilation of daily extreme temperatures recorded at the Fabra Observatory (Catalonia, NE Spain) since 1917 up to 2005 has permitted an exhaustive analysis of the fractal behaviour of the daily extreme temperature residuals, DTR, defined as the difference between the observed daily extreme temperature and the daily average value. The lacunarity characterises the lag distribution on the residual series for several thresholds. Hurst, H, and Hausdorff, Ha, exponents, together with the exponent beta of the decaying power law, describing the evolution of power spectral density with frequency, permit to characterise the persistence, antipersistence or randomness of the residual series. The self-affine character of DTR series is verified, and additionally, they are simulated by means of fractional Gaussian noise, fGn. The reconstruction theorem leads to the quantification of the complexity (correlation dimension, mu*, and Kolmogorov entropy, kappa.) and predictive instability (Lyapunov exponents, lambda, and Kaplan-Yorke dimension, D-KY) of the residual series. All fractal parameters are computed for consecutive and independent segments of 5-year lengths. This strategy permits to obtain a high enough number of fractal parameter samples to estimate time trends, including their statistical significance. Comparisons are made between results of predictive algorithms based on fGn models and an autoregressive autoregressive integrated moving average (ARIMA) process, with the latter leading to slightly better results than the former. Several dynamic atmospheric mechanisms and local effects, such as local topography and vicinity to the Mediterranean coast, are proposed to explain the complex and instable predictability of DTR series. The memory of the physical system (Kolmogorov entropy) would be attributed to the interaction with the Mediterranean Sea.
Aiming to improve the knowledge of droughts in Europe, three indices related to dry spells, DS, regime have been analysed: the number of DS per year, N; the longest annual DS, L-max; and the mean DS length per year, L, for different daily rainfall thresholds (0.1, 1.0, 5.0 and 10.0 mm/day) at annual and seasonal scales. The database consists of daily records from 267 rain gauges, along the years 1951-2000. First, the mean values at annual and seasonal scales of these three indices are represented for the four thresholds. For 0.1 and 1.0 mm/day, spatial patterns suggest a strong N-S gradient for latitudes south of 45 degrees N, especially at annual scale and in summer season. For 5.0 and 10.0 mm/day, the patterns are different, with a strong gradient in the Scandinavian Peninsula and the largest L-max and L at NE Europe, except for summer. Second, a principal component analysis, PCA, is applied to the 60 variables (three indices at five time scales and four thresholds) characterising the DS regime of every gauge. A clustering process leads to a classification of the 267 rain gauges into 20 spatial clusters, on the basis of five selected principal components replacing the original variables. Most of clusters are spatially coherent, with greater spatial variability on DS regimes towards the south and west than to the north and east of Europe. And third, time trends on the three indices are quantified by the Kendall-tau algorithm, and statistical significances at 95% confidence level are assessed by the Mann-Kendall test. For all thresholds and seasons, there is a clear predominance of significant negative trends for N. Specifically, the highest number of rain gauges with significant negative trends corresponds to summer and winter, with average percentages from -2.7 to -8.1% per decade. In summer, significant negative trends are observed in Western Europe at 40 degrees-60 degrees N and between 10 degrees W and 20 degrees E. In annual and winter periods, negative trends are detected also at Western Europe for 0.1 and 1.0 mm/day and at latitudes south of 45 degrees N for the two highest thresholds. Spring, and especially autumn, are characterised by a low number of negative trends, particularly for 1.0, 5.0 and 10.0 mm/day. In summer, L-max depicts remarkable positive trends in Western Europe, at 40 degrees N-60 degrees N and between 0 degrees E and 20 degrees E, with high average values close to +10% per decade. Positive trends on L are dominant at annual scale and winter for 0.1 mm/day, and in summer for 0.1 and 1.0 mm/day, with average trends ranging from +4.8 to +8.1% per decade. Spring and autumn are characterised by numerous negative trends on L for all thresholds. (C) 2013 Elsevier BM. All rights reserved.
The multifractal character of the daily extreme temperatures in Catalonia (NE Spain) is analyzed by means of the multifractal detrended fluctuation analysis (MF-DFA) applied to 65 thermometric records covering years 1950–2004. Although no clear spatial patterns of the multifractal spectrum parameters appear, factor scores deduced from Principal Component analysis indicate some signs of spatial gradients. Additionally, the daily extreme temperature series are classified depending on their complex time behavior, through four multifractal parameters (Hurst exponent, Hölder exponent with maximum spectrum, spectrum asymmetry and spectrum width). As a synthesis of the three last parameters, a basic measure of complexity is proposed through a normalized Complexity Index. Its regional behavior is found to be free of geographical dependences. This index represents a new step towards the description of the daily extreme temperatures complexity.
The Dry Day Since Last Rain index, DDSLR,
quantifies for every recording day the number of consecutive
preceding days with daily rainfall below a threshold. In
essence, DDSLR may quantify the hydrologic stress generated
by consecutive days of rainfall deficit taking into account
some daily rainfall thresholds associated with the
resolution of the pluviometer, evapotranspiration, runoff
and thin layer saturation processes. A detailed analysis of
DDSLR at daily and annual scales and for the whole recording
period permits a complete description of the daily
rainfall deficit regime and induced hydrologic stress. These
characteristics have been derived for 0.1, 1.0, 5.0 and
10.0 mm/day thresholds for 93 years (1917–2009) of continuous
daily rainfall records at the Fabra Observatory
(Barcelona, NE Spain). Time trends on chronological series
of DDSLR are determined and statistically tested for every
calendar day. Fourier series analysis applied to four calendar
day statistics (number of non-null DDSLR, average,
standard deviation and maximum of DDSLR) leads to
detection of the dominant periodicities, taking as fundamental
periodicity the 365 days of the year. The best statistical
model reproducing the empirical distribution of DDSLR,
year by year, for every calendar day and for the whole
recording period, is also investigated. Whatever the time
scale considered, the Poisson-gamma model is assumed due
to the non-negligible number of null DDSLR. Finally, time
trends on extreme series of annual DDSLR, the appropriate
statistical model for these series (the generalised logistic
distribution, GLO), together with an estimation of DDSLR
for several return periods, permit the description of the
expected main future patterns of this index. In this way,
current and next future hydrologic stress at the Fabra Observatory
and neighbouring areas become characterised.
The complex spatial and temporal characteristics
of European dry spell lengths, DSL, (sequences of consecutive
days with rainfall amount below a certain threshold)
and their randomness and predictive instability are analysed
from daily pluviometric series recorded at 267 rain gauges
along the second half of the 20th century. DSL are obtained
by considering four thresholds, R0, of 0.1, 1.0, 5.0
and 10.0 mm/day. A proper quantification of the complexity,
randomness and predictive instability of the different DSL
regimes in Europe is achieved on the basis of fractal analyses
and dynamic system theory, including the reconstruction theorem.
First, the concept of lacunarity is applied to the series
of daily rainfall, and the lacunarity curves are well fitted to
Cantor and random Cantor sets. Second, the rescaled analysis
reveals that randomness, persistence and anti-persistence
are present on the European DSL series. Third, the complexity
of the physical process governing the DSL series is quantified
by the minimum number of nonlinear equations determined
by the correlation dimension. And fourth, the loss of
memory of the physical process, which is one of the reasons
for the complex predictability, is characterized by the values
of the Kolmogorov entropy, and the predictive instability
is directly associated with positive Lyapunov exponents. In
this way, new bases for a better prediction of DSLs in Europe,
sometimes leading to drought episodes, are established. Concretely,
three predictive strategies are proposed in Sect. 5. It
is worth mentioning that the spatial distribution of all fractal
parameters does not solely depend on latitude and longitude
but also reflects the effects of orography, continental climate
or vicinity to the Atlantic and Arctic Oceans and Mediterranean
Extreme normalised residuals, defined as departures from the average values, of 65 daily maximum, T max, and minimum, T min, temperature series recorded in Catalonia (NE Spain) during 1950–2004 are analysed. Similarly to the sampling strategies applied to long dry spells, the partial duration series (PDS) offer some advantages in comparison with the annual extreme series. Instead of using a common percentile threshold for all temperature series, PDS are chosen according to the mean excess plot procedure. Series of extreme residuals are modelled, in terms of the L-moments formulation, by the generalised Pareto distribution. Extreme residuals of T max and T min are estimated for return periods ranging from 2 to 50 years and their spatial distribution is represented for selected return periods of 2, 5, 10, 25 and 50 years. Two daily extreme temperatures events, a hot episode (in August) and a cold episode (in February), are simulated taking into account the average T max (T min) for a day in August (February), their standard deviations and the extremes for a 50-year return period. Both simulations are compared with outstanding real episodes recorded on August 13th 2003 and February 11th 1956. Additionally, a spatial regionalisation of Catalonia in several clusters, in terms of the extreme residuals for return periods from 2 to 50 years, is done. A principal component analysis is applied to the extreme residual curves characterising every temperature series and, using as variables the principal components, the regionalisation is obtained by applying the average linkage clustering algorithm. Finally, each cluster is characterised by its average extreme residual curve for return periods ranging from 2 to 50 years at 1-year interval.
Martinez, M.D.; Lana, F.J.; Burgueño, A.; Serra, C. Annual Meeting European Meteorological Society organised with European Conference on Aplications of Meteorology p. 106 Data de presentació: 2009-09-28 Presentació treball a congrés
Lana, F.J.; Burgueño, A.; Martinez, M.D.; Serra, C. Tethys: revista del temps i el clima de la Mediterrània occidental num. 6, p. 15-30 DOI: 10.3369/tethys.2009.6.02 Data de publicació: 2009 Article en revista