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1.
Modelling raindrop size distribution (DSD) is a fundamental issue to connect remote sensing observations with reliable precipitation products for hydrological applications. To date, various standard probability distributions have been proposed to build DSD models. Relevant questions to ask indeed are how often and how good such models fit empirical data, given that the advances in both data availability and technology used to estimate DSDs have allowed many of the deficiencies of early analyses to be mitigated. Therefore, we present a comprehensive follow-up of a previous study on the comparison of statistical fitting of three common DSD models against 2D-Video Distrometer (2DVD) data, which are unique in that the size of individual drops is determined accurately. By maximum likelihood method, we fit models based on lognormal, gamma and Weibull distributions to more than 42.000 1-minute drop-by-drop data taken from the field campaigns of the NASA Ground Validation program of the Global Precipitation Measurement (GPM) mission. In order to check the adequacy between the models and the measured data, we investigate the goodness of fit of each distribution using the Kolmogorov–Smirnov test. Then, we apply a specific model selection technique to evaluate the relative quality of each model. Results show that the gamma distribution has the lowest KS rejection rate, while the Weibull distribution is the most frequently rejected. Ranking for each minute the statistical models that pass the KS test, it can be argued that the probability distributions whose tails are exponentially bounded, i.e. light-tailed distributions, seem to be adequate to model the natural variability of DSDs. However, in line with our previous study, we also found that frequency distributions of empirical DSDs could be heavy‐tailed in a number of cases, which may result in severe uncertainty in estimating statistical moments and bulk variables.  相似文献   

2.
Multifractal comparison of the outputs of two optical disdrometers   总被引：1，自引：1，他引：0  
ABSTRACT

In this paper a universal multifractals comparison of the outputs of two types of collocated optical disdrometers installed on the roof of the Ecole des Ponts ParisTech is performed. A Campbell Scientific PWS100 which analyses the light scattered by the hydrometeors and an OTT Parsivel2 which analyses the portion of occluded light are deployed. Both devices provide a binned distribution of drops according to their size and velocity. Various fields are studied across a range of scales: rain rate (R), liquid water content (ρ), polarimetric weather radar quantities such the horizontal reflectivity (Zh) and the specific differential phase (Kdp), and drop size distribution (DSD) parameters such as the total drop concentration (Nt) and the mass-weighted diameter (Dm). For both devices, good scaling is retrieved on the whole range of available scales (2?h–30?s), except for the DSD parameters for which the scaling only holds down to few minutes. For R, the universal multifractal parameters are found to equal 1.5 and 0.2 for α and C1, respectively. Results are interpreted with the help of the classical Zh–R and R–Kdp radar relations.
Editor D. Koutsoyiannis; Associate editor E. Volpi  相似文献   

3.
ABSTRACT

Throughfall drop size distributions (DSDs) are important for plant–soil interactions. This is the first known study to quantify differences in throughfall DSDs with the presence and absence of foliage. Employing a disdrometer, three parameters solely representing throughfall drip were measured and calculated: maximum drop diameter (DMAX), median volume diameter of drops (D50DR) and relative volume percentage of drops (pDR). Beneath Liriodendron tulipifera L. in Maryland (USA), DMAX, D50DR and pDR were substantially larger when the canopy was unfoliated. In fact, the presence or absence of foliage was one of the primary factors affecting all three throughfall DSDs along with air temperature, according to the boosted regression tree analysis. Experimental results were attributed to differing physical properties of intercepted water between foliated and unfoliated periods and differential water behavior on leaves and bark. Future work should examine the effects of concentrated drip points on the development of throughfall-induced hot spots.
Editor M.C. Acreman; Associate editor F. Hattermann  相似文献   

4.
Forest canopies present irregular surfaces that alter both the quantity and spatiotemporal variability of precipitation inputs. The drop size distribution (DSD) of rainfall varies with rainfall event characteristics and is altered substantially by the forest stand properties. Yet, the influence of two major European tree species, European beech (Fagus sylvatica L.) and Norway spruce (Picea abies (L.) H. Karst), on throughfall DSD is largely unknown. In order to assess the impact of these two species with differing canopy structures on throughfall DSD, two optical disdrometers, one above and one below the canopy of each European beech and Norway spruce, measured DSD of both incident rainfall and throughfall over 2 months at a 10‐s resolution. Fractions of different throughfall categories were analysed for single‐precipitation events of different intensities. While penetrating the canopies, clear shifts in drop size and temporal distributions of incoming rainfall were observed. Beech and spruce, however, had different DSD, behaved differently in their effect on diameter volume percentiles as well as width of drop spectrum. The maximum drop sizes under beech were higher than under spruce. The mean ± standard deviation of the median volume drops size (D50) over all rain events was 2.7 ± 0.28 mm for beech and 0.80 ± 0.04 mm for spruce, respectively. In general, there was a high‐DSD variability within events indicating varying amounts of the different throughfall fractions. These findings help to better understand the effects of different tree species on rainfall partitioning processes and small‐scale variations in subcanopy rainfall inputs, thereby demonstrating the need for further research in high‐resolution spatial and temporal properties of rainfall and throughfall.  相似文献   

5.
TeleseismicP-waves of some large earthquakes that occurred in the eastern Mediterranean region have been analysed by using an iterative maximum entropy technique in order to obtain the independent spectral parameters, the long-period spectral level 0 and the corner frequencyf 0 of the far-field displacement spectra.Based on these parameters, the seismic source parameters seismic momentM 0, source dimensionr, fault lengthl, average displacement u, shear stress drop , radiated energyE s and apparent stressn are calculated for the considered earthquakes by using Brune's and Madariaga's models.The striking feature of the source parameters obtained in this study is the low stress drop value which varies between 5 and 15 bars. If Madariaga's model had been used, higher stress drop values would have been obtained.The low stress drop earthquakes in the eastern Mediterranean region might be interpreted either by the possible presence of low strength material near the source or by the partial stress drop model.  相似文献   

6.
Abstract

Rainfall simulators have often been used to mimic natural rainfall for studies of various land-surface and water interaction processes. The characteristics of the simulated rainfall are the main indicators used to judge the performance of the rainfall simulators. The aim of this study is to investigate the potential of piezoelectric transducers for measuring and evaluating a dripper-type simulated rainfall drop-size distribution (DSD) and kinetic energy (KE). The directly measured KE was significantly correlated with the estimated KE using the drop-size distribution and empirical rain drop fall velocity relationships. This result emphasizes the potential use of the piezoelectric sensor to directly measure and evaluate rainfall kinetic energy. Also, the relationship between rainfall intensity and KE showed good patterns of agreement between simulated rainfall and natural rainfall.

Citation Abd Elbasit, M. A. M., Yasuda, H. & Salmi, A. (2011) Application of piezoelectric transducers in simulated rainfall erosivity assessment. Hydrol. Sci. J. 56(1), 187–194.  相似文献   

7.
Drop size distribution (DSD) over the tropical region exhibit pronounced variations during different monsoon seasons. Measurements from an impact type Joss–Waldovgel disdrometer is used for characterization of drop size distribution and its integral parameters over a tropical coastal station (Thiruvananthapuram, 8.31°N, 76.54°E, 20 m asl). Rain events were identified during the winter, premonsoon, summer monsoon and postmonsoon seasons from 8 years, computed rain duration (min) and accumulated rain water (mm). Rain intensity (mm h?1), mean drop diameter (Dm, mm) and total number concentration of raindrops (NT, m?3) were calculated on each sampling interval and classified in to different bins. The different range bins of rain intensity and their relative contributions towards total rainfall are different for different seasons. Maximum events were reported on the R2 (heavy drizzle/light rain) type, but the contribution of rainfall (mm) is mainly registered on R4 (heavy rain) type. Similarly, the NT and Dm are also showing different characteristics during different monsoon seasons. Frequency of occurrence of Dm is higher in Dm2 (1–2 mm) followed by Dm1 (Dm < 1 mm) and then Dm3 (2–3 mm) with difference in magnitudes for different seasons. On analysing relative rainfall contribution from different mean diameter bins, it can be observed that Dm2 and Dm3 (1–3 mm) are the major contributors to the total rainfall. In the case of NT, both frequency and accumulated water are almost same or comparable for the different bins during all the seasons. The Dm and NT are positively related with different intensity bins. The lower rainfall intensity bins show higher duration during the summer monsoon season and lower duration during the premonsoon season, the higher intensity range bins show lower duration for the premonsoon season and higher duration for the postmonsoon season.  相似文献   

8.
Precipitation types in winter storms   总被引：2，自引：0，他引：2  
The characteristics of and the evolution between snow, rain, ice pellets, and freezing rain are discussed. Precipitation type and the nature of its size distribution and extent are related to the melting behaviour of snow. Model calculations of this melting show the progression of precipitation type from freezing rain to ice pellets and finally to snow, as melting systematically erodes an upper level inversion within about 5 h for a precipitation rate of 1mm h–1. The increase in temperature of the low level subfreezing region associated with ice pellet formation (up to 1°C) should furthermore be detectable. These phase transitions between the various precipitation types, as affected by atmospheric cooling by melting, are predicted to occur over mesoscale distances.  相似文献   

9.
During volcanic eruptions, volcanic ash transport and dispersion models (VATDs) are used to forecast the location and movement of ash clouds over hours to days in order to define hazards to aircraft and to communities downwind. Those models use input parameters, called “eruption source parameters”, such as plume height H, mass eruption rate Ṁ, duration D, and the mass fraction m63 of erupted debris finer than about 4 or 63 μm, which can remain in the cloud for many hours or days. Observational constraints on the value of such parameters are frequently unavailable in the first minutes or hours after an eruption is detected. Moreover, observed plume height may change during an eruption, requiring rapid assignment of new parameters. This paper reports on a group effort to improve the accuracy of source parameters used by VATDs in the early hours of an eruption. We do so by first compiling a list of eruptions for which these parameters are well constrained, and then using these data to review and update previously studied parameter relationships. We find that the existing scatter in plots of H versus Ṁ yields an uncertainty within the 50% confidence interval of plus or minus a factor of four in eruption rate for a given plume height. This scatter is not clearly attributable to biases in measurement techniques or to well-recognized processes such as elutriation from pyroclastic flows. Sparse data on total grain-size distribution suggest that the mass fraction of fine debris m63 could vary by nearly two orders of magnitude between small basaltic eruptions ( 0.01) and large silicic ones (> 0.5). We classify eleven eruption types; four types each for different sizes of silicic and mafic eruptions; submarine eruptions; “brief” or Vulcanian eruptions; and eruptions that generate co-ignimbrite or co-pyroclastic flow plumes. For each eruption type we assign source parameters. We then assign a characteristic eruption type to each of the world's  1500 Holocene volcanoes. These eruption types and associated parameters can be used for ash-cloud modeling in the event of an eruption, when no observational constraints on these parameters are available.  相似文献   

10.
The earthquake inter-event time distribution is studied, using catalogs for different recent aftershock sequences. For aftershock sequences following the Modified Omori’s Formula (MOF) it seems clear that the inter-event distribution is a power law. The parameters of this law are defined and they prove to be higher than the calculated value (2–1/p). Based on the analysis of the catalogs, it is determined that the probability densities of the inter-event time distribution collapse into a single master curve when the data is rescaled with instantaneous intensity, R(t; M th ), defined by MOF. The curve is approximated by a gamma distribution. The collapse of the data provides a clear view of aftershock-occurrence self-similarity.  相似文献   

11.
The interannual variability of monthly mean January and July precipitation and its possible change due to global warming are assessed using a five-member ensemble of climate for the period 1871–2100, simulated by the CSIRO Mark 2 global coupled atmosphere–ocean model. In the 1961–1990 climate, for much of the middle to high latitudes the standard deviation of precipitation for both months is roughly proportional to the mean, with the coefficient of variation (C) typically 0.3–0.5. The variability there is shown to be largely consistent with that from a first-order Markov chain model of the daily rainfall occurrence, with the distribution of wet-day amounts approximated by a gamma distribution. Global distributions of Mark 2-based parameters of this stochastic model, commonly used in weather generators, are presented. In low latitudes, however, the variability from the coupled model is typically double that anticipated by the stochastic model, as quantified by an ‘overdispersion ratio’. C often exceeds one at subtropical locations, where rain is less frequent, but sometimes relatively heavy.The standard deviation of monthly mean precipitation S generally increases as the global model warms, with the global mean S in 2071–2100 in January (July) being 9.0% (11.5%) larger than in 1961–1990. Decreases in some subtropical locations occur, particularly where mean precipitation decreases. The global pattern of overdispersion is largely unchanged, however, and the changes in S can be related to those in the stochastic model parameters. Much of the increase in S is associated with increases in the scale parameter of the gamma distribution of wet-day amounts. Changes in C, which is unaffected by this parameter, are generally small. Increases in C in several subtropical bands and over northern midlatitude land in July are related to a decreased frequency of precipitation, and (to a lesser degree) changes in the gamma shape parameter. Some potential applications of the results to downscaling are discussed, and illustrated using observed rainfall from southeast Australia.  相似文献   

12.
Martin Hanel  Petr Máca 《水文研究》2014,28(6):2929-2944
Rain event characteristics are assessed in a 10‐year (1991–2000) record for 122 stations in the Czech Republic. Individual rain events are identified using the minimum interevent time (mit) concept. For each station, the optimal mit value is estimated by examining the distribution of interevent times. In addition, various mit values are considered to account for the effect of mit on rain event characteristics and their interrelationships. The interdependence between rain event characteristics and altitude, average rainfall depth, and geographic location are explored using simple linear models. Most rain event characteristics can be to some extent explained by average total rainfall or altitude, although models including the former significantly outperformed models using the latter. Significant correlation was found among several pairs of monthly mean characteristics often including event rain rate (with event duration, depth, maximum intensity, and fraction of intraevent rainless periods). Moreover, strong correlation was revealed between number of events, interevent time, event depth, and duration. In general, correlation decreases in absolute value with mit. Strong spatial correlation was found for the mean monthly interevent time and number of events. Spatial correlation was considerably smaller for other characteristics. In general, spatial dependence was smaller for larger mit values. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

13.
The generalized gamma (GG) distribution has a density function that can take on many possible forms commonly encountered in hydrologic applications. This fact has led many authors to study the properties of the distribution and to propose various estimation techniques (method of moments, mixed moments, maximum likelihood etc.). We discuss some of the most important properties of this flexible distribution and present a flexible method of parameter estimation, called the generalized method of moments (GMM) which combines any three moments of the GG distribution. The main advantage of this general method is that it has many of the previously proposed methods of estimation as special cases. We also give a general formula for the variance of theT-year eventX T obtained by the GMM along with a general formula for the parameter estimates and also for the covariances and correlation coefficients between any pair of such estimates. By applying the GMM and carefully choosing the order of the moments that are used in the estimation one can significantly reduce the variance ofT-year events for the range of return periods that are of interest.  相似文献   

14.
From the events synthesized from the one-dimensional dynamical mass-spring model proposed byBurridge andKnopoff (1967), the relation between rupture length and earthquake momentM is studied for various model parameters. The earthquake moment is defined to be the total displacement of a connected set of mass elements which slide during an event. A parameter stiffness ratios is defined as the ratio of the spring constant between the two mass elements to that between one mass element and the moving plate. The velocity-dependent friction law (including weakening and hardening processes) is taken to control the sliding of a mass element. The distribution of the breaking strengths over the system is considered to be a fractal function. The cases for severals values and different velocity-dependent friction laws with different decreasing ratesr w of the frictional force with sliding velocity are studied numerically. The weakening process of the frictional force from the static one to the dynamic one obviously affects theM– relation. Meanwhile, a rapid weakening process rather than a slow weakening process can result in aM– relation, which is comparable to the observed one. Although an increase in thes value can yield an increase in the upper bound of the value and the number of events with largeM and values, the scaling of theM– relation is not affected by the change of thes value. For the cases in this study, the theoretical –M relations for small events withM<1 are almost in the form: M 1/2, while those for large events withM>1 have a scaling exponent less than but close to 1. In addition, the fractal dimension, the friction drop ratio and the roughness of the distribution of the breaking strengths over the fault surface are the minor parameters influencing the –M relation. A comparison between the theoreticalM– relation and the observed one for strike-slip earthquakes shows that for large events the theoreticalM– relation is quite consistent with the observed one, while for small events there is a one-order difference in the two relations. For the one-dimensional model, the decreasing rate of the dynamic frictional force with velocity is the main factor in affecting the characteristic value of the earthquake moment, at which the scaling of theM– relation changes.  相似文献   

15.
The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a – fora minaa max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ –1 decays in proportion tok –1 in the high frequency range and its growth is proportional tok 2 in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ –1 has a broader peak as increases and/ora min/a max decreases. The nondimensional peak wave numberk p a max at whichQ –1 takes the peak value is almost independent ofa min/a max for =1 and 2 while it considerably depends ona min/a max for =3. The phase velocity is almost independent ofk in the rangeka max<1 and increases monotonically ask increases in the rangeka max>1. While the magnitude ofQ –1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ –1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk p a max, the probable range ofa max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a max is estimated to range from 2 to 5 km. We cannot estimatea max in a narrow range for =3.  相似文献   

16.
David Dunkerley 《水文研究》2008,22(22):4415-4435
In hydrology and geomorphology, less attention has been paid to rain event properties such as duration, mean and peak rain rate than to rain properties such as drop size or kinetic energy. A literature review shows a lack of correspondence between natural and simulated rain events. For example, 26 studies that report event statistics from substantial records of natural rain reveal a mean rain rate of just 3·47 mm h?1 (s.d. 2·38 mm h?1). In 17 comparable studies dealing with extreme rain rates including events in cyclonic, tropical convective, and typhoon conditions, a mean maximum rain rate (either hourly or mean event rain rate) of 86·3 mm h?1 (s.d. 57·7 mm h?1) is demonstrated. However, 49 studies using rainfall simulation involve a mean maximum rain rate of 103·1 mm h?1 (s.d. 81·3 mm h?1), often sustained for > 1 h, exceeding even than of extreme rain events, and nearly 30 times the mean rain rate in ordinary, non‐exceptional, rain events. Thus rainfall simulation is often biased toward high rain rates, and many of the rates employed (in several instances exceeding 150 mm h?1) appear to have limited relevance to ordinary field conditions. Generally, simulations should resemble natural rain events in each study region. Attention is also drawn to the raindrop arrival rate at the surface. In natural rain, this is known to vary from < 100 m?2 s?1 to > 5000 m?2 s?1. Arrival rate may need to be added to the list of parameters that must be reproduced realistically in rainfall simulation studies. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

17.
This paper presents a model that simulates the size distribution and erosivity of raindrops and throughfall drops. It utilizes existing models of rainfall drop size distribution and fall velocity and combines them with newly collated evidence of throughfall drop size distributions. A sensitivity analysis reveals that the model is sensitive to parameters that are easily measured or estimated: rainfall intensity, the mean volume drop diameter of the intercepted throughfall, canopy cover, and canopy height. The results of the model may be used at two levels. Firstly, to calculate specifically the size and fall velocity of individual drops, parameters that are needed in studies examining the response of soil surfaces to forces applied by rainfall. Secondly, to produce erosivity indices, based on rainfall intensity but which take account of the effects of a vegetation canopy. The paper shows that while the kinetic energy of rainfall (E(0), J mm?1 m?2) may be calculated from an equation of the familiar form: the kinetic energy of throughfall under any canopy may be calculated by combining this equation with another that relates the energy of drops under a 100 per cent canopy cover (E(100)) and the canopy height: .  相似文献   

18.
Zusammenfassung Das Gebiet um die Ostsee ist als erdmagnetisch stark gestört bekannt. Die Karte zeigt die Verteilung der intensiven Anomalien, wo Z 2000 and 5000 überschreitet. Der Gruppierung dieser Anomalien kann man eine ung.N Richtung zuschreiben.
Summary The area around the Baltic Sea is known as magnetically intensely disturbed. The map shows the distribution of most intensive anomalies, where Z is more than 2000 and 5000 . The direction of the group of these intensive anomalies can be as appr.N supposed.
  相似文献   

19.
New equations and techniques for dealing with drop breakups are developed and applied to the modelling of the evolution of raindrop spectra in rainshafts. Breakup experiments byMcTaggart-Cowan andList (1975) served as data base.No matter what the original size distribution, the spectrum evolution will always lead to a Marshall-Palmer type equilibrium di tributionN=N 0e–D, with =constant andN 0 proportional to the rainfall rateR. (D stands for raindrop diameter.) ForR29 mm h–1 and an original Marshall-Palmer distribution, the required fall height to reach equilibrium is 2 km.The equilibrium distributions are characterized by linear relationships betweenR, the radar reflectivity factorZ, the liquid water content LWC and theN 0 of the Marshall-Palmer distribution. Possible explanations for the discrepancy with observations are given.The fact that the all-water processes cannot produce drops withD2.5 mm (as confirmed by observations) leads to the conclusion that observed large raindrops withD5 mm represent melted hailstones and have not yet reached an equilibrium distribution. These latter conclusions were reached within the original assumption of videspread, steady state precipitation.  相似文献   

20.
This article deals with the right-tail behavior of a response distribution \(F_Y\) conditional on a regressor vector \({\mathbf {X}}={\mathbf {x}}\) restricted to the heavy-tailed case of Pareto-type conditional distributions \(F_Y(y|\ {\mathbf {x}})=P(Y\le y|\ {\mathbf {X}}={\mathbf {x}})\), with heaviness of the right tail characterized by the conditional extreme value index \(\gamma ({\mathbf {x}})>0\). We particularly focus on testing the hypothesis \({\mathscr {H}}_{0,tail}:\ \gamma ({\mathbf {x}})=\gamma _0\) of constant tail behavior for some \(\gamma _0>0\) and all possible \({\mathbf {x}}\). When considering \({\mathbf {x}}\) as a time index, the term trend analysis is commonly used. In the recent past several such trend analyses in extreme value data have been published, mostly focusing on time-varying modeling of location or scale parameters of the response distribution. In many such environmental studies a simple test against trend based on Kendall’s tau statistic is applied. This test is powerful when the center of the conditional distribution \(F_Y(y|{\mathbf {x}})\) changes monotonically in \({\mathbf {x}}\), for instance, in a simple location model \(\mu ({\mathbf {x}})=\mu _0+x\cdot \mu _1\), \({\mathbf {x}}=(1,x)'\), but the test is rather insensitive against monotonic tail behavior, say, \(\gamma ({\mathbf {x}})=\eta _0+x\cdot \eta _1\). This has to be considered, since for many environmental applications the main interest is on the tail rather than the center of a distribution. Our work is motivated by this problem and it is our goal to demonstrate the opportunities and the limits of detecting and estimating non-constant conditional heavy-tail behavior with regard to applications from hydrology. We present and compare four different procedures by simulations and illustrate our findings on real data from hydrology: weekly maxima of hourly precipitation from France and monthly maximal river flows from Germany.  相似文献   

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