An analysis of the normalised rainfall intensity curves in Barcelona (NE Spain) has been undertaken from selected rain rate episodes recorded by an urban network of tipping buckets applying a 5-min integration time along the years 1994–2009. These curves, based on cumulative amount and time distributions, are modelled by a power law, this fact suggesting fractal behaviour. Four parameters characterise these curves. One of them is the exponent of the power law. Another one quantifies the intermittency of the rainfall along the episode. The other two are the coordinates of cumulative
amount and time distribution from which the power law fits well the normalised curve. The total rainfall amount of the episode, its length and the coefficient of variation of the 5-min amounts are also considered as complementary parameters. Taking advantage of these seven parameters, patterns of rainfall intensity are determined for every episode. These patterns, together with the statistical distribution of 5-min amounts, maximum intensity and rainfall intermittence,
should increase the knowledge on the urban rainfall regime with the aim of improving drainage design. In addition to present results, flood prevention should be complemented with extreme value analyses and quantification of return periods.
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.
M. Carmen Casas-Castillo; Rodriguez, R.; Navarro, J.; Russo, B.; Lastra, A.; González, P.; Redaño, A. Theoretical and applied climatology DOI: 10.1007/s00704-016-1998-0 Data de publicació: 2016-11-11 Article en revista
The fractal behavior of extreme rainfall intensities registered between 1940 and 2012 by the Retiro Observatory of Madrid (Spain) has been examined, and a simple scaling regime ranging from 25 min to 3 days of duration has been identified. Thus, an intensity-duration-frequency (IDF) master equation of the location has been constructed in terms of the simple scaling formulation. The scaling behavior of probable maximum precipitation (PMP) for durations between 5 min and 24 h has also been verified. For the statistical estimation of the PMP, an envelope curve of the frequency factor (k m ) based on a total of 10,194 station-years of annual maximum rainfall from 258 stations in Spain has been developed. This curve could be useful to estimate suitable values of PMP at any point of the Iberian Peninsula from basic statistical parameters (mean and standard deviation) of its rainfall series.
This is a copy of the author 's final draft version of an article published in the journal Theoretical and applied climatology.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00704-016-1998-0
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.
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.
Pérez, N.; M. Carmen Casas-Castillo; Rodriguez, R.; Peña, J.; Rius, A.; Solé, J. Germán; Redaño, A. Theoretical and applied climatology Vol. 124, num. 3-4, p. 935-944 DOI: 10.1007/s00704-015-1476-0 Data de publicació: 2015-04-25 Article en revista
Relationship between maximum rainfall rates for time intervals between 5 minutes and 24 hours has been studied from almost a century (1905-2003) of rainfall data registered in the Ebre Observatory (Tarragona, Spain). Intensity-duration-frequency (IDF) curves and its master equation for every return period in the location have been obtained, as well as the probable maximum precipitation (PMP) for all the considered durations. In particular, the value of the 1-day PMP has resulted 415 mm, very similar to previous estimations of this variable for the same location. Extreme rainfall events recorded in this period have been analyzed and classified according to their temporal scale. Besides the three main classes of cases corresponding to the main meteorological scales, local, mesoscale and synoptic, a fourth group constituted by complex events with high intense rates for a large range of durations has been identified also, indicating the contribution of different scale meteorological processes acting together in the origin of the rainfall. A weighted intensity index taking into account the maximum rainfall rate in representative durations of every meteorological scale has been calculated for every extreme rainfall event in order to reflect their complexity.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00704-015-1476-0
The rainfall spatial organization in the metropolitan area of Barcelona (Spain) has been studied from records of an urban rain gauge network in the period 1994–2009. Using
statistical and regional analysis techniques, correlation between data recorded by the different rain gauges has been calculated, and the effective number of independent stations (neq) equivalent to the used network has been determined. It has been found out that for durations longer than 20 min, the areal rainfall return period observed for a storm registered by
the network approximately decreases by a factor of 1/neq in relation to the current point rainfall intensity–duration–frequency
relationships for the metropolitan area of Barcelona.
Using objective analysis techniques, continuous precipitation fields have been generated on a regular grid with a spatial
resolution of 300×300 m for the storms registered by the rain gauges from 1994 to 2009, for durations from 10 min to 24 h.
The precipitation fields obtained have been useful to estimate the characteristic areal reduction factors in the metropolitan
area of Barcelona. A direct relationship has been found between the areal reduction factor for all the area corresponding
to the urban rainfall network of Barcelona and the effective number of neq for every duration considered
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.
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.