Statistical distribution and spectral analysis of rainfallanomalies for Barcelona (NE Spain)

Summary  Rainfall anomaly patterns are obtained for the city of Barcelona from a statistical and a spectral point of view. The time series consists of monthly rainfall amounts recorded over 128 years without interruption. Monthly positive and negative anomalies, obtained as the difference between monthly amounts and monthly threshold values, are used for both types of analyses. The threshold levels are derived form the deciles of theoretical monthly rainfall distributions, which have been previously modelled by the gamma distribution. Positive and negative anomalies of the monthly rain amounts are investigated for these threshold levels. The statistical analysis is applied to each decile considered, yielding empirical exponential laws that can be used to forecast the cumulative number of episodes of consecutive months with either positive or negative anomalies equalling or exceeding a fixed length. A set of linear laws, relating the expected rainfall amount cumulated during an episode of a fixed length, is also deduced. It is worthy of mention that, independently of the decile considered, all the exponential and linear laws have satisfactory regression coefficients. At the same time, it has also been possible to establish the evolution of the coefficients of these laws with respect to the different deciles considered. The exponential laws for episodes of positive and negative anomalies are the starting point, together with two hypotheses, to model probabilities of repeated long episodes over an arbitrary number of years and their return periods in terms of the Poisson distribution model. Moreover, power spectra are derived for anomalies relative to the 50% decile at monthly and seasonal scale. The spectral estimates obtained are then compared with theoretical spectra deduced from possible Markovian or random behaviour of the time series of anomalies. Finally, the significant spectral peaks are discussed and compared with other significant spectral components deduced for some areas of the Mediterranean domain. Received November 11, 1999 Revised February 28, 2000     

Extreme normalised residuals of daily temperatures in Catalonia (NE Spain): sampling strategies, return periods and clustering process

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.     

Spatial and temporal patterns of dry spell lengths in the Iberian Peninsula for the second half of the twentieth century

Summary Daily pluviometric records of 43 meteorological stations across the Iberian Peninsula have permitted a detailed analysis of dry spell patterns for the period 1951–2000 by distinguishing daily amount thresholds of 0.1, 1.0, 5.0 and 10.0 mm/day. The analyses are based on three annual series, namely the number of dry spells, N, the average dry spell length, L, and the extreme dry spell length, L _max. First, the statistical significance of local trends for the annual series of N, L and L _max has been investigated by means of the Mann-Kendall test and significant field trends have been established by means of Monte Carlo simulations. Clear signs of negative field trends are detected for N (1.0 and 10.0 mm/day) and L (0.1 mm/day). Second, the Weibull model fits well the empirical distributions of dry spell lengths for all the rain gauges, whatever the daily amount threshold, with a well ranged spatial distribution of their parameters u and k. On the basis of the Weibull distribution, return period maps for 2, 5, 10, 25 and 50 years have been obtained for dry spell lengths with respect to the four daily threshold levels. While for 0.1 and 1.0 mm/day the longest dry spells are expected at the south of the Iberian Peninsula, for 5.0 and 10.0 mm/day they are mostly detected at the southeast. Finally, the elapsed time between consecutive dry spells has been analysed by considering the same rain amount thresholds and different dry spell lengths at increasing intervals of 10 days. This analysis makes evident a significant negative field trend of the elapsed time between consecutive dry spells of lengths ranging from 10 to 20 days for daily amount thresholds of 1.0, 5.0 and 10.0 mm/day. Authors’ addresses: X. Lana, C. Serra, Departament de Física i Enginyeria Nuclear, ETSEIB, Universitat Politècnica de Catalunya, Av. Diagonal 647 planta 11, 08028 Barcelona, Spain; M. D. Marínez, Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain; A. Burgue?o, Departament de Meteorologia i Astronomia, Universitat de Barcelona, 08028 Barcelona, Spain; J. Martín-Vide, L. Gómez, Grup de Climatologia, Universitat de Barcelona, 08028 Barcelona, Spain.     

Periodicities and irregularities of indices describing the daily pluviometric regime of the Fabra Observatory (NE Spain) for the years 1917–1999

Summary Several patterns of a daily pluviometric regime are obtained from an homogeneous set of daily rainfall recorded at the Fabra Observatory (NE Spain) for the period 1917–1999. Power spectral analyses of four annual pluviometric indices, determined from different daily rain amount percentiles, are performed. Periodicities of the quasi-biannual oscillation (QBO), North Atlantic Oscillation (NAO) and sunspot cycles are correlated in some cases with empirical spectral peaks of the indices exceeding Markov red-noise with a confidence level of 95%. Depending on the rainy day percentiles, a set of short periods (2.1–4.6 years), a second group of intermediate periods (5.5 and 9.2 years) and, finally, a third group of long periods of 11.8, 20.8 and 41.5 years can be distinguished. These periods are compared with those derived for other European and African emplacements. Additionally, the consecutive irregularity of every annual series is quantified by means of a concept similar to the entropy.     

Principal Component Analysis of precipitation and rainfall regionalization in Spain

Summary A T-mode Principal Component Analysis (PCA) based on a network including 68 pluviometric gauges and their 12 mean monthly amounts of rainfall is attempted in order to describe the main patterns governing precipitation in Spain. The procedure is applied to a 12 × 12 intermonth covariance matrix; the unrotated components and two additional solutions deduced after varimax and oblimin rotations are presented and discussed. In all cases component scores are computed and their spatial distribution is discussed. Two regionalizations of Spanish rainfall are then obtained and compared in terms of group homogeneity. There follows a discussion concerning the main pluviometric characteristics of each region deduced from the best division.With 7 Figures     

Spatial and temporal analysis of dry spells in Greece

Summary ?A spatio-temporal analysis of the dry spells that occur in the Greek area is carried out for an extended period of 40 years (1958–1997). The dry spells can be defined as a number of consecutive days with no rain. The number of days defines the length of the dry spells. The longest spells are identified in central (Cyclades) and the south-east Aegean Sea whereas dry spells with the minimum length are shown over the north-west of the Greek area that reflects the significance of the latitude and the topography. Negative Binomial Distribution and Markov Chains of second order have been used to fit the duration of the dry spells of different lengths. The study of the seasonal and annual distribution of the frequency of occurrence of dry spells revealed that the dry spells in Greece depict a seasonal character, while medium and long sequences are associated with the duration and hazards of drought. Received February 20, 2002; revised September 5, 2002; accepted October 6, 2002     

Some Statistical Characteristics of Monthly and Annual Pluviometric Irregularity for the Spanish Mediterranean Coast

Summary  Seven series of monthly pluviometric amounts, sometimes exceeding recording periods of 100 years and compiled by the Instituto Nacional de Meteorología (Spain), are used to study the irregularity of the pluviometric regime along the Spanish Mediterranean coast and nearby Atlantic coast. First of all, three statistical functions (gamma, log-normal and a combination of Poisson and gamma distributions) and moment-ratio diagrams are used to model the monthly and annual empirical distributions of precipitation amounts, each distribution being tested by means of the Kolmogorov-Smirnov test. It is noteworthy that, whereas most of the monthly cases require the gamma distribution, the pluviometric behaviour of the summer months is well described by the Poisson-gamma distribution. Moreover, both the log-normal and the gamma distributions satisfactorily model empirical annual amounts. Consequently, rainfall amounts are not identically distributed along a year for each gauge tested. Second, temporal trends deduced for annual and seasonal amounts are computed and their statistical significance evaluated. The most notable fact is that, although some linear trends are close to 1 mm/year, their significance levels exceed the assumed threshold value and, excepting the winter season for Barcelona, they are considered non-significant from a statistical point of view. Finally, by again using monthly and annual amounts, three temporal irregularity indexes are computed for each pluviometric series, the temporal disparity of the rainfall patterns of the Mediterranean region being enhanced as a result. It addition to the temporal irregularity, a change with latitude is observed both in the parameters of the statistical distributions and the temporal irregularity indexes for the rain gauges analysed. The two most southerly rain gauges constitute a special case in comparison with the remaining stations, because they also receive the Atlantic influences due to their proximity to this ocean. Received February 25, 1999/Revised August 2, 1999     

Buoyant plume rise in a Lagrangian framework

For the dispersion of buoyant material, the interaction with the environment by entrainment forms a serious obstacle for a formulation in a Lagrangian framework. Nevertheless an outline is given here on how buoyant plume rise in a Lagrangian sense could be described. Though the method contains a number of heuristic elements, it has all the advantages of a Lagrangian formulation. It is shown that it is possible to formulate a Lagrangian model which both is able to recover the classical formulations for plume rise in a calm environment and to accomodate more recent Eulerian formulations in a turbulent environment. Moreover, the method offers excellent possibilities to include the turbulent characteristics of the plume's environment and arbitrary stratifications of the boundary layer. These facts make it attractive for various practical applications. Some examples are given which illustrate this.     

广东地区雷电活动的气候分布特征

利用地闪定向仪(DF)和时间到达法(TOA)定位技术,1997年3月～1998年6月在研究范围内共计得到404431次地闪资料.分析了地闪的雷电流强度、回击数的气候概率分布特征以及雷电参数的日变化及其空间分布的气候规律.正闪占总闪的比例仅为5.03%,正负闪密度的高值中心均在(114.E,23.N)附近.总体日变化特征明显,全天有两个高值时段,分别为00～06时和12～18时.与北方地区的雷电特征不同.结果表明雷电活动特征可以基本揭示本地区天气活动的时空分布的规律.     

Statistical assessment of trends and oscillations in rainfall dynamics: Analysis of long daily Italian series

Since the 18th century systematic measurements of rainfall have been collected in Italy. The daily rainfall series observed in Milan (1835–2001), Genoa (1833–2000), Bologna (1813–2001) and Palermo (1797–1999) are examples of available long rainfall records. These data series can help analyzing the evolution of precipitation. The present paper deals with long term evolution of: (i) annual rainfall amount; (ii) annual number of rainy events; (iii) intensity of rainfall, (iv) inter-annual rainfall partitioning, i.e. the duration of wet and dry periods, and (v) maximum annual values of daily rainfall amount, duration of wet and dry periods. The evolution is studied analyzing the first two order statistics and the 30-year return period quantiles via moving window analysis. Confidence intervals are introduced to check the statistical significance of the estimated statistics and quantiles. The results are compared with those provided by the traditional Mann-Kendall test. The analysis shows how the annual precipitation exhibits a negative trend in the first half of 20th century, with a subsequent positive trend in northern Italy (Genoa, Milan and Bologna). Conversely, the dataset for Palermo (southern Italy) displays only a negative trend. Because the number of precipitation episodes is found to decrease in the investigated period, the average rain rate is significantly increasing especially in northern Italy. This is also associated with shorter duration of rain episodes with an evident effect on rainfall extremes. Dry periods tend to be longer with increasing variability. The Mann-Kendall test and its progressive form have shown to be well suited for monotonic trend, but the confidence interval analysis, introduced here, is more appropriate if oscillations are significant.     

Impact of drought on wildland fires in Greece: implications of climatic change?

An increasing trend and a statistically significant positive correlation between wildfire occurrence, area burned and drought (as expressed by the Standardized Precipitation Index, SPI) have been observed all over Greece, during the period 1961?C1997. In the more humid and colder regions (Northern and Western Greece) the number of fires and area burned were positively correlated to both summer (SPI6_October) and annual drought (SPI12_September), whereas in the relatively more dry and hot regions (Southern and Central Greece) the number of fires and area burned were correlated only to summer drought. In 1978, Greece entered a period of prolonged drought, possibly as a result of the global climatic change. Data analysis of the period 1978?C1997 revealed a statistically significant increase in the mean annual number of fires, the area burned and the summer and annual drought episodes in the relatively more humid and colder regions (Northern and Western) of Greece (which in the past were characterized by less fires and area burned) compared to the more dry and hot regions (Southern and Eastern Greece), which always presented high fire activity. Additionally, analyzing the two sub-periods (1961?C1977, 1978?C1997) separately, drought was significantly correlated only to fire occurrence during the years 1961?C1977, whereas during 1978?C1997 drought was significantly correlated mainly to area burned. It became obvious that drought episodes, although they are not solely responsible for fire occurrence and area burned, they exert an increasingly significant impact on wildfire activity in Greece.     

Potential energy for slantwise parcel motion

Two formulations for the potential energy for slantwise motion are compared: one which applies strictly only to two-dimensional flows (SCAPE) and a three-dimensional formulation based on a Bernoulli equation. The two formulations share an identical contribution from the vertically integrated buoyancy anomaly and a contribution from different Coriolis terms. The latter arise from the neglect of (different) components of the total change in kinetic energy along a trajectory in the two formulations. This neglect is necessary in order to quantify the potential energy available for slantwise motion relative to a defined steady environment.     

Theoretical derivation of precipitation coverage probability from a set of heterogeneous point probabilities

Various meteorological studies require probabilistic modeling such as the flood, drought, and wet and dry spell occurrences. The most commonly employed approaches are based on the binomial probability distribution function (pdf), which is valid for homogeneous temporal and spatial probabilities. However, in practice, heterogeneous probabilities are very common, and in this case, the classical binomial pdf cannot be employed. This paper presents a rigorous probabilistic methodology for heterogeneous probabilities by considerations from the random field concept. The general form of the binomial pdf is derived and it is shown that for homogeneous probabilities it yields the classical binomial pdf exactly. The necessary analytical formulations are derived with the assumption that the meteorological occurrences at a set of sites or time periods (day, month, and year) are independent from each other. The probability statements derived in this paper are helpful in predicting the regional and temporal probable potential future meteorological occurrences. The application of the proposed methodology is presented for annual precipitation occurrences at six meteorology stations around Istanbul, Turkey.     

Climatological aspects of extreme precipitation in Europe, related to mid-latitude cyclonic systems

Climatic aspects of extreme European precipitation are studied. Daily pluviometric data from 280 stations across Europe, covering the period from 1958 to 2000, are used. First, the criteria for extreme precipitation cases and episodes are communicated using threshold and spatial definitions. The cases and episodes meeting these criteria are grouped according to their area of appearance. Most of them are located in three major areas: Greece, the Alps, and the Iberian Peninsula. The existence of trends in the annual and seasonal time series of these extreme events is examined. Decreasing trends are found in most of the cases, for Greece, the Iberian Peninsula, and Europe, as a whole. The Alps present a different behavior, with no trend at all in the southern part, and a possible increasing trend in the northern part. Finally, the positive impact of altitude in the frequency of occurrence of extreme precipitation episodes in Europe is discussed.     

A comparison of the flood precipitation episode in August 2002 with historic extreme precipitation events on the Czech territory

The hydro-meteorological characteristics of the flood from August 2002, which affected a great part of the Czech territory, particularly the Vltava and Labe river basin, were compared with corresponding conditions during similar flood events in the summer seasons of 1997, 1890, 1897 and 1903. The comparison shows analogies in synoptic conditions and causal precipitation heights. The heaviest precipitation fell in the area of a considerable horizontal pressure gradient on the rearward side of the cyclone which advanced very slowly to the north-east across Central Europe and created conditions for the transport of moist air as well as for an organized long-term updraft enhanced in orographically exposed regions. The varying features of the individual events were based on the spatial–temporal distribution of causal precipitation and also on the very different saturation of the catchments. It was chiefly the extraordinary time concentration of precipitation together with the highest catchment saturation that made the flood in 2002 the most extreme.The extremeness of meteorological fields during two episodes in July 1997 was compared with two episodes in August 2002 with the aid of the reanalysis data from ECMWF. The first episode in 1997 and the second episode in 2002 were the most similar and more extreme in terms of the large-scale fields of basic meteorological quantities. The similar features of these episodes are specifically an intensive influx of moisture into Central Europe and intensive upward motions in the precipitation area. The extremeness of upper- and low-level potential vorticity fields was evaluated to diagnose the behavior of the cyclone and frontal precipitation bands accompanying it. The suitable spatial configuration of positive upper- and low-level potential vorticity anomalies induced an additional amplification of upward motions in the precipitation area that apparently contributed to triggering the heavy precipitation over Central Europe. On the whole, quantities reached more extreme values during the second episode in 2002.     

A century of precipitation variability along the pacific coast of North America and its impact

Precipitation data at seven stations along the west coast of North America, dating back to 1851 at some stations, are synthesized by means of empirical orthogonal function analysis. Characteristics of runs of generally wet and generally dry conditions are quantified. A significant change in precipitation regime, lasting 41 yrs, occurred in the middle of this century and could return in the future. Drought occurrences, similar to midwestern United States episodes, appear in the data, but are not statistically verifiable. A single example of the interaction of precipitation variability and society is given. Man's actions amplify the impact of variability on hydroelectric power generation in two ways: Society adapts itself rapidly to transient beneficial conditions, creating a false sense of well-being; technology expands to consume maximum available resources, decreasing system resilience.     

Rainfall characterisation by application of standardised precipitation index (SPI) in Peninsular Malaysia

The interpretations of trend behaviour for dry and wet events are analysed in order to verify the dryness and wetness episodes. The fitting distribution of rainfall is computed to classify the dry and wet events by applying the standardised precipitation index (SPI). The rainfall amount for each station is categorised into seven categories, namely extremely wet, severely wet, moderately wet, near normal, moderately dry, severely dry and extremely dry. The computation of the SPI is based on the monsoon periods, which include the northeast monsoon, southwest monsoon and inter-monsoon. The trends of the dry and wet periods were then detected using the Mann–Kendall trend test and the results indicate that the major parts of Peninsular Malaysia are characterised by increasing droughts rather than wet events. The annual trends of drought and wet events of the randomly selected stations from each region also yield similar results. Hence, the northwest and southwest regions are predicted to have a higher probability of drought occurrence during a dry event and not much rain during the wet event. The east and west regions, on the other hand, are going through a significant upward trend that implies lower rainfall during the drought episodes and heavy rainfall during the wet events.     

Changes in exceptional hydrological and meteorological weekly event frequencies in Greece

The aim of the present study is, primarily, to compare the frequencies of exceptional hydrological and meteorological weekly events, employing the self-calibrated versions of Palmer’s drought indices (PDSI and PHDI, respectively), from 17 stations across Greece in the decade 1997–2006 with these of 1961–1990; on second level, to identify the trends and define the time lags between these two indices for the study period 1961–2006. The changes in the spatial distribution of exceptional weekly event frequencies between the most recent decade and the baseline period were similar for both drought indices. When 1997–2006 was compared with 1961–1990, the number of stations with a frequency of exceptionally dry weekly events >93rd percentile, increased by seven stations (41%) for PDSI and nine (53%) for PHDI, at the expense of exceptionally moist weekly spells. PDSI was found to lead PHDI by three to 20?weeks. If exceptional weekly events continue to be more frequent in the future, major implications for natural water resources are expected.     

Frequency Changes of Weather Types in the Alpine Region since 1945

Summary The annual occurrence of different weather types of Schüepp’s synoptic classification in the Alpine region has significantly changed since the beginning of its recording in 1945. The annual frequency (number of days per year) has shifted towards more convective and less advective weather types. Since 1945 the number of long-lasting convective episodes rose and the number of long-lasting advective episodes lessened. Most of these changes took place in winter. The annual frequencies of weather types and the annual mean of certain local meteorological parameters are significantly correlated. On the large scale there is a strong interdependence between the high pressure weather type and the North Atlantic Oscillation (NAO) index which is based on the sea-level pressure difference between Portugal and Iceland. Received July 28, 1997 Revised November 18, 1997     

Spatial and temporal analysis of dry spells in Croatia

Systematic statistical analysis of dry day sequences, which are defined according to 0.1, 1, 5 and 10 mm of precipitation-per-day thresholds, is performed on seasonal and yearly basis. The data analysed come from 25 Croatian meteorological stations and cover the period 1961–2000. Climatological features of the mean and maximum dry spell durations, as well as the frequency of long dry spells (>20 days) are discussed. The results affirm the three main climatological regions in Croatia, with the highlands exhibiting shorter dry spells than the mainland, and the coastal region exhibiting longer dry spells. The prevailing positive trend of both mean and maximal durations is detected during winter and spring seasons, while negative trend dominate in autumn for all thresholds. Positive field significant trends of mean dry spell duration with 5 and 10 mm thresholds are found during spring and the same is valid for annual maximum dry spell duration with a 10 mm threshold. It is found that the Discrete Autoregressive Moving Average (DARMA(1,1)) model can be used to estimate the probabilities of dry spells in Croatia that are up to 20–30 days long.