Multifractal analysis of the rainfall time distribution on the metropolitan area of Barcelona (Spain)

In most of the studies on scale properties in the rainfall process, multifractal behavior has been investigated without taking into account the different rain generation mechanisms involved. However, it is known that rain processes are related to certain scales, determined by climatological characteristics as well as regional and local meteorological features. One of the implications derived from these correspondences is the possibility that the multifractal parameters of the rainfall could depend on the dominant precipitation generation mechanism. Fractal analysis techniques have been applied in this work to rainfall data recorded in the metropolitan area of Barcelona in the period 1994–2001, as well as to a selection of synoptic rainfall events registered in the same city in the period 1927–1992. The multifractal parameters obtained have been significantly different in each case probably showing the influence of the rain generation mechanisms involved. This influence has been revealed also in the analysis of the effects of seasonality on the multifractal behavior of rainfall in Barcelona.     

Rainfall rate distribution in a local scale: The case of Barcelona city

Summary Convective rainfall rate distribution is not very uniform even at a local scale. In order to make an evaluation of it in the urban area of Barcelona, a dense rain gauge network has been stablished in this city. The gauges are of high resolution tilting bucket type. In this paper, preliminary results are presented. The distributions obtained show a strong variation of the rainfall rate for the several parts of the city. The intensity-duration curves for severe storms have been made in the various points of measure together with the areal reduction factors of rainfall. The analysis of raincell movement gives E-W as a predominant direction and a speed in the 3–12 m/s range.With 9 Figures     

Large-scale and spatio-temporal extreme rain events over India: a hydrometeorological study

Frequency, intensity, areal extent (AE) and duration of rain spells during summer monsoon exhibit large intra-seasonal and inter-annual variations. Important features of the monsoon period large-scale wet spells over India have been documented. A main monsoon wet spell (MMWS) occurs over the country from 18 June to 16 September, during which, 26.5 % of the area receives rainfall 26.3 mm/day. Detailed characteristics of the MMWS period large-scale extreme rain events (EREs) and spatio-temporal EREs (ST-EREs), each concerning rainfall intensity (RI), AE and rainwater (RW), for 1 to 25 days have been studied using 1° gridded daily rainfall (1951–2007). In EREs, ‘same area’ (grids) is continuously wet, whereas in ST-EREs, ‘any area’ on the mean under wet condition for specified durations is considered. For the different extremes, second-degree polynomial gave excellent fit to increase in values from distribution of annual maximum RI and RW series with increase in duration. Fluctuations of RI, AE, RW and date of occurrence (or start) of the EREs and the ST-EREs did not show any significant trend. However, fluctuations of 1° latitude–longitude grid annual and spatial maximum rainfall showed highly significant increasing trend for 1 to 5 days, and unprecedented rains on 26–27 July 2005 over Mumbai could be a realization of this trend. The Asia–India monsoon intensity significantly influences the MMWS RW.     

Multifractal analysis of 1-min summer rainfall time series from a monsoonal watershed in eastern China

Multifractal analysis can provide parameters associated with different scales of rainfall, which may be useful for setting up parsimonious downscaling models of rainfall, or for revealing climate-specific properties. Time series of rain rate with 1-min resolution collected from ten stations over a monsoon watershed in eastern China were used to study the multifractal properties. The power spectra estimated by fast Fourier transform (FFT) and discrete Haar wavelet transform (DWT) showed three scaling regimes: the sub-hourly scaling regime with β?≈?1.2, the scaling regime from 1 h to 1 day with β close to 0.6, and the low-frequency spectra plateau with β?≈?0.1. From the hyperbolic tails of exceeding probability distributions, the estimated values of parameter q _c are in 2–2.5, which were consistent with the critical order of K(q) curves. The statistical moments display two main scaling regimes: the high-frequency regime from 3 min to 5 days and the scaling regime beyond 5 days. The scales of 5–10 days seem a transitional regime. The reason that the regimes, revealed by the power spectra, disagree with the statistical moments may be that both FFT and DWT power spectra have limited abilities of analyzing low-frequency scaling but are sensitive to the properties in high-frequency scales. The H values estimated for the regime of sub-hourly scales are larger than 0.4, and the values for the regime 1 h–1 day are close to 0.1. For the low-frequency scales beyond 1 day, negative H is obtained by DWT power spectra. The parameters of universal multifractal models were also estimated. The values of α for the scaling range of 1 min–5 days are 0.486?±?0.047, and for the low-frequency scaling range, its values are 0.808?±?0.323. For the high- and low-frequency scaling ranges, the values of C ₁ are 0.5 and 0.169, respectively, which is different from the values for daily rainfall series collected at the same rain gages.     

European dry spell length distributions, years 1951–2000

Daily precipitation records of 267 European rain gauges are considered to obtain dry spell length (DSL) series along the second half of the twentieth century. A dry spell consists of consecutive days with daily rain amount below a given threshold, R ₀. Four DSL series are obtained for R ₀ values equal to 0.1, 1.0, 5.0, and 10.0 mm/day, and their empirical distributions are properly fitted to different statistical models: Pearson type III (PE3), Weibull (WEI), generalised Pareto, (GPA) and lognormal distributions. The parameters of every model are estimated by L-moments, and the goodness of fit is assessed by quantifying discrepancies between empirical and theoretical distributions in the L-skewness–kurtosis diagrams. The most common best-fitting model is PE3, especially for 0.1 and 1.0 mm/day. Nevertheless, a few stations in southern Europe are better modelled by the WEI distribution. For 5.0 and 10.0 mm/day, the spatial distribution of the best-fitting model is more heterogeneous than for the lowest thresholds. While PE3 is still the preferred model for Western Europe, some DSL series are better fitted to WEI or GPA models. Maps of DSL average and standard deviation and expected lengths for return periods of 2, 5, 10, 25, and 50 years show some common features. Whereas for thresholds of 0.1 and 1.0 mm/day, a N–S gradient is detected, especially in Mediterranean areas; for 5.0 and 10.0 mm/day, a NW–SE gradient is observed in the Iberian Peninsula and a SW–NE gradient in the Scandinavian Peninsula. Then, the vicinity to Atlantic and Arctic Oceans and the Mediterranean Sea, as well as orographic features, are more determining factors than the latitude in patterns associated with the highest R ₀ thresholds. Finally, a regional frequency analysis based on a clustering algorithm is attempted for the four thresholds R ₀, with the PE3 model as the parent distribution for the largest clusters.     

Increasing trend of northeast monsoon rainfall over the equatorial Indian Ocean and peninsular India

Peninsular India and Sri Lanka receive major part of their annual rainfall during the northeast monsoon season (October–December). The long-term trend in the northeast monsoon rainfall over the Indian Ocean and peninsular India is examined in the vicinity of global warming scenario using the Global Precipitation Climatology Project (GPCP) dataset available for the period 1979–2010. The result shows a significant increasing trend in rainfall rate of about 0.5 mm day^?1 decade^?1 over a large region bounded by 10 °S–10 °N and 55 °E–100 °E. The interannual variability of seasonal rainfall rate over peninsular India using conventional rain gauge data is also investigated in conjunction to the Indian Ocean dipole. The homogeneous rain gauge data developed by Indian Institute of Tropical Meteorology over peninsular India also exhibit the considerable upward rainfall trend of about 0.4 mm day^?1 decade^?1 during this period. The associated outgoing longwave radiation shows coherent decrease in the order of 2 W?m^?2 decade^?1 over the rainfall increase region.     

Polarimetric rainfall retrieval from a C-Band weather radar in a tropical environment (The Philippines)

We evaluated the potential of polarimetric rainfall retrieval methods for the Tagaytay C-Band weather radar in the Philippines. For this purpose, we combined a method for fuzzy echo classification, an approach to extract and reconstruct the differential propagation phase, Φ _DP , and a polarimetric self-consistency approach to calibrate horizontal and differential reflectivity. The reconstructed Φ _DP was used to estimate path-integrated attenuation and to retrieve the specific differential phase, K _DP . All related algorithms were transparently implemented in the Open Source radar processing software wradlib. Rainfall was then estimated from different variables: from re-calibrated reflectivity, from re-calibrated reflectivity that has been corrected for path-integrated attenuation, from the specific differential phase, and from a combination of reflectivity and specific differential phase. As an additional benchmark, rainfall was estimated by interpolating the rainfall observed by rain gauges. We evaluated the rainfall products for daily and hourly accumulations. For this purpose, we used observations of 16 rain gauges from a five-month period in the 2012 wet season. It turned out that the retrieval of rainfall from K _DP substantially improved the rainfall estimation at both daily and hourly time scales. The measurement of reflectivity apparently was impaired by severe miscalibration while K _DP was immune to such effects. Daily accumulations of rainfall retrieved from K _DP showed a very low estimation bias and small random errors. Random scatter was, though, strongly present in hourly accumulations.     

1215号“布拉万”台风暴雨及降水非对称性分布的成因分析

利用中尺度非静力模式WRF对2012年第15号台风“布拉万”在中国东北地区造成的暴雨过程进行了数值模拟,结合观测资料对模拟结果进行了验证,利用模式输出的高分辨率资料,对“布拉万”台风造成的强降水及其非对称性分布的成因进行了诊断分析。结果表明,模式很好地再现了台风登陆过程中的路径、强度变化和降水分布,受中纬度西风槽带来的干冷空气影响,“布拉万”台风登陆后的降水和环流结构具有明显的不对称性,降水主要集中在台风中心西北侧的能量锋区附近。水汽散度通量和水汽螺旋度能够较好地描述强降水过程的发生、发展及其非对称性分布的时空特征,在强降水区,水汽散度通量表现为正值强信号,而水汽螺旋度表现为负值强信号,在非降水区和弱降水区,两者均表现为弱信号。等熵位涡分析显示,对流不稳定只是此次台风暴雨前期和初始阶段的不稳定条件,而湿位涡(MPV)的湿斜压项(MPV₂)则是暴雨增强和出现非对称性分布的主要机制。在暴雨形成过程中,由于冷空气侵入造成了在台风环流西北侧湿等熵面的陡立倾斜和水平风垂直切变的增强,导致了气旋性涡度的显著增强,气旋性涡度增强造成的强烈上升运动将降水区东南侧输送过来的暖湿空气向上输送,从而导致了暴雨的发生,这其中条件性对称不稳定是降水得以加强的一种重要不稳定机制。     

Multifractal analysis of daily rainfall from a monsoon watershed in Eastern China

The multifractal behavior of daily rainfall was investigated for a watershed in Eastern China to better understand the temporal structure of rainfall under monsoonal climate. In this study, over periods of up to 46 years, daily rainfall recorded in 1962 to 2007 at 10 meteorological stations in the administrative area of Lin-Yi City in Shandong province were analyzed with focus on features of power spectra, standard statistical moments, and exceedance probability tails of these daily rainfall time series. Spectral analysis and study of the moments of the rainfall intensity showed that a scaling range from 1 day to 1 year is present. Empirical moment scaling functions of the rainfall intensity calculated for different moments of order suggested that the values of universal multifractal parameters α and C ₁ for all stations were approximated to 0.7 and 0.37, respectively. Comparing with the parameters estimated in other literatures, our results showed higher values for α but lower values for C ₁ in general, which suggested that the rainfall series in the study watershed influenced by the East-Asia monsoon climate have similarities to that in France, but are spikier and smoother than that in the semi-arid region in Portugal. The parameter H values were estimated as vary from ?0.18 to ?0.22, which is similar to the result obtained by Tessier et al. (J Geophys Res-Atmos 101:26427–26440, 1996).     

A methodology to classify extreme rainfall events in the western mediterranean area

Summary From a large data set (1927–1992) of rainfall rate in Barcelona, the relationship between maximum rainfall rates for time intervals between 5 minutes and 24 hours has been investigated. Intensity-Duration-Frequency (IDF) curves and their master equation for every return period in Barcelona have been obtained. A cluster analysis has yielded four main classes of extreme rainfall events in this area, corresponding to durations shorter than 35 minutes, 1 hour, 2–6 hours and those longer than 6 hours respectively. An index to classify extreme rainfall events has been proposed. This index gives some information about the severity of storms taking into account the contribution of different scales implied in rainfall processes.     

Regional intensity–duration–frequency analysis in the Eastern Black Sea Basin,Turkey, by using L-moments and regression analysis

The analysis of rainfall frequency is an important step in hydrology and water resources engineering. However, a lack of measuring stations, short duration of statistical periods, and unreliable outliers are among the most important problems when designing hydrology projects. In this study, regional rainfall analysis based on L-moments was used to overcome these problems in the Eastern Black Sea Basin (EBSB) of Turkey. The L-moments technique was applied at all stages of the regional analysis, including determining homogeneous regions, in addition to fitting and estimating parameters from appropriate distribution functions in each homogeneous region. We studied annual maximum rainfall height values of various durations (5 min to 24 h) from seven rain gauge stations located in the EBSB in Turkey, which have gauging periods of 39 to 70 years. Homogeneity of the region was evaluated by using L-moments. The goodness-of-fit criterion for each distribution was defined as the Z^DIST statistics, depending on various distributions, including generalized logistic (GLO), generalized extreme value (GEV), generalized normal (GNO), Pearson type 3 (PE3), and generalized Pareto (GPA). GLO and GEV determined the best distributions for short (5 to 30 min) and long (1 to 24 h) period data, respectively. Based on the distribution functions, the governing equations were extracted for calculation of intensities of 2, 5, 25, 50, 100, 250, and 500 years return periods (T). Subsequently, the T values for different rainfall intensities were estimated using data quantifying maximum amount of rainfall at different times. Using these T values, duration, altitude, latitude, and longitude values were used as independent variables in a regression model of the data. The determination coefficient (R ²) value indicated that the model yields suitable results for the regional relationship of intensity–duration–frequency (IDF), which is necessary for the design of hydraulic structures in small and medium sized catchments.     

Mechanism of high rainfall over the Indian west coast region during the monsoon season

The mechanism responsible for high rainfall over the Indian west coast region has been investigated by studying dynamical, thermodynamical and microphysical processes over the region for the monsoon season of 2009. The European Centre for Medium-Range Weather Forecasts wind and NCEP flux data have been used to study the large scale dynamical parameters. The moist adiabatic and multi-level inversion stratifications are found to exist during the high and low rainfall spells, respectively. In the moist adiabatic stratification regime, shallow and deep convective clouds are found coexisting. The Cloud Aerosol Interaction and Precipitation Enhancement EXperiment aircraft data showed cloud updraft spectrum ranging from 1 to 10 m s^?1 having modal speed 1–2.5 m s^?1. The low updrafts rates provide sufficient time required for warm rain processes to produce rainfall from shallow clouds. The low cloud liquid water is observed above the freezing level indicating efficient warm rain process. The updrafts at the high spectrum end go above freezing level to generate ice particles produced due to mixed-phase rainfall process from deep convective clouds. With aging, deep convection gets transformed into stratiform type, which has been inferred through the vertical distribution of the large scale omega and heating fields. The stratiform heating, high latent heat flux, strong wind shear in the lower and middle tropospheric levels and low level convergence support the sustenance of convection for longer time to produce high rainfall spell. The advection of warm dry air in the middle tropospheric regions inhibits the convection and produce low rainfall spell. The mechanisms producing these spells have been summarized with the block diagram.     

Multi-decadal scale variability in autumn-winter rainfall in south-western Australia since 1655 AD as reconstructed from tree rings of Callitris columellaris

We present the first tree-ring based reconstruction of rainfall for the Lake Tay region of southern Western Australia. We examined the response of Callitris columellaris to rainfall, the southern oscillation index (SOI), the southern annular mode (SAM) and surface sea temperature (SST) anomalies in the southern Indian Ocean. The 350-year chronology was most strongly correlated with rainfall averaged over the autumn-winter period (March–September; r = ?0.70, P < 0.05) and SOI values averaged over June–August (r = 0.25, P < 0.05). The chronology was not correlated with SAM or SSTs. We reconstructed autumn-winter rainfall back to 1655, where current and previous year tree-ring indices explained 54% of variation in rainfall over the 1902–2005 calibration period. Some variability in rainfall was lost during the reconstruction: variability of actual rainfall (expressed as normalized values) over the calibration period was 0.78, while variability of the normalized reconstructed values over the same period was 0.44. Nevertheless, the reconstruction, combined with spectral analysis, revealed that rainfall naturally varies from relatively dry periods lasting to 20–30 years to 15-year long periods of above average rainfall. This variability in rainfall may reflect low-frequency variation in the El Niño-Southern Oscillation rather than the effect of SAM or SSTs.     

Daily precipitation forecast of ECMWF verified over Iran

In this paper, the performance of the Centre for Medium Range Weather Forecast (ECMWF) model (t?+?27 h to t?+?51 h) in predicting precipitation is discussed. This model is the first, which has been verified over Iran. The spatial resolution of the model is 0.351° and the 24-h forecasts are compared with daily observations. The study concentrates on year 2001 and the precipitation measurements were collected from the data of 2,048 rain gauges in Iran. The accuracy of four different interpolation methods (nearest neighborhood, inverse distance, kriging, and upscaling) was investigated. Using cross-validation, the inverse distance method (IDM) with minimum mean error was applied. Verification results are given in terms of difference fields (mean error?=?0.46 mm/day), rank–order correlation coefficients (0.70), as well as accuracy scores (false alarm ratio?=?0.50 and probability of detection?=?0.60) and skill scores (true skill statistics [TSS]?=?0.45) in year 2001. The position of the rain band was only partly captured by the ECMWF model; however, the position of maximum precipitations agrees with the observations well. The results show that the high values of TSS are associated with the large amounts of precipitation (over 25 mm). Slight to moderate precipitation events have been underforecasted by the model (bias?<?1) and it leads to a small value of TSS for these thresholds (5–25 mm/day). The ECMWF model has better performance in high and mountainous regions than over flat terrain and in deserts. Comparing TSS over the Alborz and the Zagros Mountains, it is obvious that the ability of the model to predict the convective precipitation events needs some improvement. The amount of daily precipitation has been also slightly overestimated over Iran. From the beginning of January up to 21 March 2001, the ECMWF time series indicates an obvious phase shift of 1 day, although in other months, no phase shift is noticed.     

Long-term variation of rainfall erosivity in Calabria (Southern Italy)

The changes in rainfall erosivity have been investigated using the rainfall erosivity factor (R) proposed for USLE by Wischmeier and Smith (R _W-S ) and some simplified indexes (the Fournier index modified by Arnoldus, F, a regional index spatial independent, R _Fr , and a regional index spatial dependent, R _Fs ) estimated by indirect approaches. The analysis has been carried out over 48 rainfall stations located in Calabria (Southern Italy) using data collected in the period 1936–2012 and divided in three sub-periods. The series of the erosivity indexes and of some precipitation variables have been analyzed for evidence of trends using standard methods. The simplified indexes suggested a general underestimation of the rainfall erosivity with respect to R _W-S . The mean underestimation ranged between 23 and 54 % for R _Fr and from 10 to 15 % for R _Fs . Both the sign and the magnitude of the trends were different for the different stations depending on the variable and sub-period considered. In general, the erosivity increased during the period 1936–1955 (1^st sub-period) and during the more recent sub-period (1992–2012, 3^rd sub-period), whereas it decreased during 1958–1977 (2^nd sub-period). The evidence of trends was generally higher for R _W-S than for R _Fr and R _Fs . Focusing on the most recent sub-period (3^rd sub-period), all the variables analyzed showed mainly increasing trends but with different magnitude. More particularly, R _W-S showed a mean increment of 29 %; F, R _Fr and R _Fs increased by 11, 15 and 18 %, respectively; the maximum intensity of 0.5-h precipitation increased by 5 %; and the annual precipitation increased by 22 %. Consequently, it remains difficult to define which precipitation variable plays the dominant role in the temporal variation of rainfall erosivity in the region. However, the overall results suggest that the indexes estimated by indirect procedures (F, R _Fr , and R _Fs ) should be used with caution for climate change analysis, despite they are used for practical purposes considering they are based on easily available information.     

Estimation of sub-hourly DDF curves using scaling properties of hourly and sub-hourly data at partially gauged site

In urban drainage systems, knowledge of short-duration rainfall events can be considered as one of the most critical elements when their hydrological behaviour wants to be investigated. The temporal resolution of rainfall data usually available for practical applications is often lower than the data requested for the design procedures or mathematical models application, greatly affecting their reliability. Moreover, when high resolution rain gauges are available in the catchment, the registration period cannot be sufficiently long for obtaining practically usable statistical analyses. The present study proposes a method for estimating the distribution of sub-hourly extreme rainfalls at sites where data for time interval of interest do not exist, but rainfall data for longer duration are available. The proposed method is based on the “scale-invariance” (or “scaling”) theory whose concepts imply that statistical properties of the extreme rainfall processes for different temporal scales are self-related by a scale-changing operator involving only the scale ratio. The methodology is applied to extreme rainfall data from a rain gauge network within the metropolitan area of Palermo (Italy). Following the application, it is shown that the statistical properties of the rainfall series have a simple scaling property over the range of duration 10 min–24 h. A simple parsimonious analytical formulation for the DDF curves, which embodies the scaling behaviour, is presented.     

Spatio-temporal variability and predictability of summer monsoon onset over the Philippines

The spatio-temporal variability of boreal summer monsoon onset over the Philippines is studied through the analysis of daily rainfall data across a network of 76 gauges for the period 1977 to 2004 and the pentad Merged Analysis of Precipitation from the US Climate Prediction Center from 1979 to 2006. The onset date is defined using a local agronomic definition, namely the first wet day of a 5-day period receiving at least 40 mm without any 15-day dry spell receiving <5 mm in the 30 days following the start of that period. The onset is found to occur rather abruptly across the western Philippines around mid-May on average and is associated with the set-up of a “classical” monsoonal circulation with low-level easterlies subsequently veering to southerly, and then southwesterly. The onset manifests itself merely as a seasonal increase of rainfall over the eastern Philippines, where rainfall occurs throughout most of the year. Interannual variability of the onset date is shown to consist of a spatially coherent large-scale component, rather similar over the western and eastern Philippines, with a moderate to high amount of local-scale (i.e. station scale) noise. In consequence, the large-scale signal can be easily retrieved from any sample of at least 5–6 stations across the network although the local-scale coherence and fingerprint of the large-scale signal of the onset date are found to be stronger over the central Philippines, roughly from Southern Luzon to Northern Mindanao. The seasonal predictability of local onset is analyzed through a cross-validated canonical correlation analysis using tropical Pacific and Indian Ocean sea surface temperature in March and the 850 hPa May wind field from dynamical forecast models as predictors. The regional-scale onset, defined as the average of standardized local-scale anomalies in onset date, shows good predictive skill (r ≈ 0.8). Moreover, most of the stations show weak to moderate skill (median skill = 0.28–0.43 depending on the scheme) with spatial averaging across stations typically increasing skill to >0.6.     

Comparison of a simple logarithmic and equivalent neutral wind approaches for converting buoy-measured wind speed to the standard height: special emphasis to North Indian Ocean

The difference between the transferred wind speed to 10-m height based on the equivalent neutral wind approach (U _n) and the logarithmic approach (U _log) is studied using in situ observations from the Indian, Pacific, and Atlantic Oceans, with special emphasis given to the North Indian Ocean. The study included U _n ? U _log variations with pressure, relative humidity, wind speed, air temperature, and sea surface temperature (SST). U _n ? U _log variation with respect to air temperature (T _a) reveals that U _n ? U _log is out of phase with air temperature. Further analysis found that U _n ? U _log is in phase with SST (T _s) ? T _a and varies between ?1.0 and 1.0 m/s over the North Indian Ocean, while for the rest of the Oceans, it is between ?0.3 and 0.8 m/s. This higher magnitude of U _n ? U _log over the North Indian Ocean is due to the higher range of T _s ? T _a (?4 to 6 °C) in the North Indian Ocean. Associated physical processes suggested that the roughness length and friction velocity dependence on the air–sea temperature difference contributes to the U _n ? U _log difference. The study is further extended to evaluate the behavior of U _n ? U _log under cyclonic conditions (winds between 15 and 30 m/s), and it was found that the magnitude of U_n ? U _log varies 0.5–1.5 m/s under the cyclonic wind conditions. The increasing difference with the wind speed is due to the increase in the momentum transfer coefficient with wind speed, which modifies the friction velocity significantly, resulting in U _n higher than U _log. Thus, under higher wind conditions, U _n ? U _log can contribute up to half the retrieval error (5 % of the wind speed magnitude) to the satellite validation exercise.