A direct analysis of flood interval probability using approximately 100-year streamflow datasets

ABSTRACT

Series of observed flood intervals, defined as the time intervals between successive flood peaks over a threshold, were extracted directly from 11 approximately 100-year streamflow datasets from Queensland, Australia. A range of discharge thresholds were analysed that correspond to return periods of approximately 3.7 months to 6.3 years. Flood interval histograms at South East Queensland gauges were consistently unimodal whereas those of the North and Central Queensland sites were often multimodal. The exponential probability distribution (pd) is often used to describe interval exceedence probabilities, but fitting utilizing the Anderson-Darling statistic found little evidence that it is the most suitable. The fatigue life pd dominated sub-year return periods (<1 year), often transitioning to a log Pearson 3 pd at above-year return periods. Fatigue life pd is used in analysis of the lifetime to structural failure when a threshold is exceeded, and this paper demonstrates its relevance also to the elapsed time between above-threshold floods. At most sites, the interval medians were substantially less than the means for sub-year return periods. Statistically the median is a better measure of the central tendency of skewed distributions but the mean is generally used in practice to describe the classical concept of flood return period.

Editor Z.W. Kundzewicz; Associate editor I. Nalbantis     

Estimates of lifetimes against pitch angle diffusion

We consider timescales on which particle distributions respond to pitch angle diffusion. On the longest timescale, the distribution decays at a single rate independent of equatorial pitch angle α₀, even though the diffusion coefficient, and the distribution itself, may vary greatly with α₀. We derive a simple integral expression to approximate this decay rate and show that it gives good agreement with the full expression. The roles of both the minimum and loss cone values of the diffusion coefficient are demonstrated and clarified.     

Topographical effects on the distributions of rainfall and 18O distributions: a case in Miyake Island,Japan

In this paper, we try to calculate precipitation in Miyake Island, Japan. In order to know the temporal and spatial variations of precipitation, we have set 15 rain gauges randomly in the island to collect the monthly precipitation data since June 1994. It is found that the precipitation is very different from point to point. First, we used statistical methods to get the correlations between the monthly precipitation at our survey points and that at the weather station. Next, regression analyses were used to establish formulae to calculate precipitation as a function of altitude, aspect of the geomorphological surface and wind direction. Based on these results, distributions of monthly and yearly precipitation and δ¹⁸O over the island were assessed. The results show that landscape patterns strongly influence precipitation distribution over the island, with the highest precipitation being found on the windward side, about 400–600 m above sea level. Even at places at the same altitude, the precipitation was different because of the aspect of the landscape. At the same time, altitude effects for δ¹⁸O on both the windward and leeward sides were −0·10‰/100 m and −0·15‰/100 m, respectively. Comparing with the distribution of precipitation distribution, it was also found that δ¹⁸O for the windward and leeward sides was different from that for precipitation, which means that both topographical effects must be considered separately. © 1998 John Wiley & Sons, Ltd.     

A meteorological-based crop coefficient model for estimation of daily evapotranspiration

Estimation of daily evapotranspiration (ET) over cloudy regions highly desires models which rely on meteorological data only. Notwithstanding, the conventional crop coefficient (K_c) method requires detailed knowledge of geo/biophysical properties of the coupled land-vegetation system, precipitation, and soil moisture. Six Eddy Covariance (EC) towers in Iowa, California and New Hampshire of the USA (covering corn, soybeans, prairie, and deciduous forest) were selected. Investigation on 6 years (2007–2012) 15-min micrometeorological records of these sites revealed that there is an indubitable strong interaction between relative humidity (RH), reference ET (ET_o), and actual ET at different timescales. This allowed to bypass the need for the non-meteorological inputs and express K_c as a second-order polynomial function of RH and ET_o, the ambient regression evapotranspiration model (AREM). The coefficients of the empirical function are crop-specific and may require calibration over different soil types. The mean absolute percentage error (MAPE) of the regression against daily EC observations was 17% during the growing season, and 32% throughout the year with root mean square error (RMSE) of 0.74 mm day⁻¹ and coefficient of determination of 0.71. The model was fully operational (MAPE of 34% and RMSE of 0.82 mm day⁻¹) over the four Iowan sites based on inputs from local weather stations and NLDAS-2 forcing data of NASA. AREM was capable of capturing the dynamics of ET at 15-min and daily timescales irrespective of varying complexities associated with biophysical, geophysical and climatological states.     

Bias and precision of percentiles of bulk grain size distributions

Percentiles such as D₅₀ and D₈₄, calculated from weights retained on different sieves, are widely used to characterize grain size distributions (GSDs) of bulk samples of sedimentary deposits or sediment fluxes. The sampling variability of such percentiles is not well known, and few sampling guidelines exist for reliable characterization of GSDs. We report results from computer sampling experiments on the variability of sample percentiles in different-sized samples from populations with a log-normal GSD by weight and different sorting coefficients. Sample sizes are scaled by the volume of a median-sized grain so that results can be applied to any log-normal GSD. Sampling is random for the GSD by number that is equivalent to a specified GSD by weight. Results show important differences from standard sampling theory applicable to pebble-count GSDs. In small bulk samples all percentiles, including the median, are underestimated (more so for smaller samples, coarser percentiles and poorer sorting), and precision does not improve with the square root of sample size until fairly large sample sizes are exceeded. Non-dimensional equations fitted by eye to the results give good approximations to expected bias and precision in any percentile from 50 to 95 for any given sample size and population sorting coefficient. They are inverted to estimate the sample size required to avoid significant bias, or achieve specified precision, in any percentile of interest given estimates of the population D₅₀ and sorting coefficient. Target sample sizes are sometimes considerably smaller, but in other circumstances larger, than suggested by previous guidelines relating to estimation of the entire grain size distribution. Bias is likely in small samples of river bedload and good precision requires very large samples of poorly sorted gravel deposits. © 1997 John Wiley & Sons, Ltd.     

Seismic anisotropy of shales

Shales are a major component of sedimentary basins, and they play a decisive role in fluid flow and seismic‐wave propagation because of their low permeability and anisotropic microstructure. Shale anisotropy needs to be quantified to obtain reliable information on reservoir fluid, lithology and pore pressure from seismic data, and to understand time‐to‐depth conversion errors and non‐hyperbolic moveout. A single anisotropy parameter, Thomsen's δ parameter, is sufficient to explain the difference between the small‐offset normal‐moveout velocity and vertical velocity, and to interpret the small‐offset AVO response. The sign of this parameter is poorly understood, with both positive and negative values having been reported in the literature. δ is sensitive to the compliance of the contact regions between clay particles and to the degree of disorder in the orientation of clay particles. If the ratio of the normal to shear compliance of the contact regions exceeds a critical value, the presence of these regions acts to increase δ, and a change in the sign of δ, from the negative values characteristic of clay minerals to the positive values commonly reported for shales, may occur. Misalignment of the clay particles can also lead to a positive value of δ. For transverse isotropy, the elastic anisotropy parameters can be written in terms of the coefficients W₂₀₀ and W₄₀₀ in an expansion of the clay‐particle orientation distribution function in generalized Legendre functions. For a given value of W₂₀₀, decreasing W₄₀₀ leads to an increase in δ, while for fixed W₄₀₀, δ increases with increasing W₂₀₀. Perfect alignment of clay particles with normals along the symmetry axis corresponds to the maximum values of W₂₀₀ and W₄₀₀, given by and . A comparison of the predictions of the theory with laboratory measurements shows that most shales lie in a region of the (W₂₀₀, W₄₀₀)‐plane defined by W₄₀₀/W₂₀₀≤W^max₄₀₀/W^max₂₀₀ .     

Explanatory analysis of the relationship between atmospheric circulation and occurrence of flood‐generating events in a coastal city

The aim of this study is to enhance the understanding of the occurrence of flood‐generating events in urban areas by analysing the relationship between large‐scale atmospheric circulation and extreme precipitation events, extreme sea water level events and their simultaneous occurrence, respectively. To describe the atmospheric circulation, we used the Lamb circulation type (LCT) classification and re‐grouped it into Lamb circulation classes (LCC). The daily LCCs/LCTs were connected with rare precipitation and water‐level events in Aarhus, a Danish coastal city. Westerly and cyclonic LCCs (W, C, SW and NW) showed a significantly high occurrence of extreme precipitation. Similarly, for extreme water‐level events westerly LCCs (W and SW) showed a significantly high occurrence. Significantly low occurrence of extreme precipitation and water‐level events was obtained in easterly LCCs (NE, E and SE). For concurrent events, significantly high occurrence was obtained in LCC W. We assessed the change in LCC occurrence frequency in the future based on two regional climate models (RCMs). The projections indicate that the westerly directions in LCCs are expected to increase in the future. Consequently, simultaneous occurrence of extreme water level and precipitation events is expected to increase in the future as a result of change in LCC frequencies. The RCM projections for LCC frequencies are uncertain because the representation of current LCCs is poor; a large number of days cannot be classified and the frequencies of the days that can be classified differ from the observed time series. Copyright © 2015 John Wiley & Sons, Ltd.     

Identification of changes in heavy rainfall events in Ontario,Canada

To assess whether changes in the frequency of heavy rainfall events are occurring over time, annual maximum records from 21 rainfall gauges in Ontario are examined using frequency analysis methods. Relative RMSE and related boxplots are used to characterize assessment for selecting distributions; the Gumbel distribution is verified as one of the most suitable distributions to provide accurate quantile estimates. Records were divided into two time periods, and tested using the Mann-Kendall test and lag-1 autocorrelations to ensure that data in each period are identically distributed. The confidence intervals of design rainfalls for each return period (2, 5, 10, and 25-year) are derived by using resampling method, and compared at 90 % confidence levels. The changes in heavy rainfall intensities are tested at gauges across the Province of Ontario. Several significant decreases in heavy rainfall intensities are identified in central and southern Ontario. Increases in heavy rainfall intensities are identified in gauges at Sioux Lookout and Belleville. The sensitivity analysis of changes identified with respect to the year of splitting indicates changes are occurring during the 1980s and 1990s.     

Dimensionality reduction in drought modelling

For monitoring hydrological events characterized by high spatial and temporal variability, the number and location of recording stations must be carefully selected to ensure that the necessary information is collected. Depending on the characteristics of each natural process, certain stations may be spurious or redundant, whereas others may provide most of the relevant data. With the objective of reducing the costs of the monitoring system and, at the same time, improving its operational effectiveness, three procedures were applied to identify the minimum network of rain gauge stations able to capture the characteristics of droughts in mainland Portugal. Drought severity is characterized by the standardized precipitation index applied to the timescales of 1, 3, 6 and 12 consecutive months. The three techniques used to reduce the dimensionality of the network of rain gauges were as follows: (i) artificial neural networks with sensitivity analysis, (ii) application of the mutual information criterion and (iii) K‐means cluster analysis using Euclidean distances. The results demonstrated that the best dimensionality reduction method was case dependent in the three regions of Portugal (northern, central and southern) previously identified by cluster analysis. All the reduction techniques lead to the selection of a subset of rain gauges capable of reproducing the original temporal patterns of drought. For specific severe drought events in Portugal in the past, the comparison between drought spatial patterns obtained with the original stations and the selected subset indicated that the subset produced statistically satisfactory results (correlation coefficients higher than 0.6 and efficiency coefficients higher than 0.5). Copyright © 2012 John Wiley & Sons, Ltd.     

Sums, products, and ratios for downton’s bivariate exponential distribution

Motivated by environmental applications, we derive the exact distributions of R = X+Y, P = X Y and W = X/(X+Y) and the corresponding moment properties when X and Y follow Downton’s bivariate exponential distribution. The expressions turn out to involve several special functions. For practical purposes, we also provide extensive tabulations of the percentage points associated with the distributions.     

Probability distribution of annual,seasonal and monthly precipitation in Japan

Abstract

The method of L-moment ratio diagrams and the average weighted distance (AWD) are used to determine the probability distribution type of annual, seasonal and monthly precipitation in Japan. For annual precipitation, the log-Pearson type III (LP3) distribution provides the best fit to the observations with the generalized-extreme value (GEV), three-parameter lognormal (LN3) and Pearson type III (P3) distributions as potential alternatives. For seasonal precipitation, the P3 distribution shows the best fit to the observations of spring precipitation; the LP3 the best fit for summer and winter precipitation; and the LN3 the best fit for autumn precipitation with the LP3 as a potential alternative. For monthly precipitation, the P3 distribution fits the precipitation best for January, February, March, May, July, October and December; the LP3 for June; and the LN3 for April, August, September and November. The identified probability distribution types of annual, seasonal and monthly precipitation are basically consistent. Overall, the P3 and LP3 distributions are acceptable distribution types for representing statistics of precipitation in Japan with the LN3 distribution as a potential alternative.     

Direct relationships of discharges to the mean and standard deviation of the intervals between their exceedences

Abstract

This article paves a way for assessing flood risk by the use of two-parameter distributions, for the intervals between threshold exceedences rather than by the traditional exponential distribution. In a case study, the apparent properties of intervals between exceedences of runoff events differ from those anticipated for exponentially distributed series. A procedure is proposed to relate two statistical parameters of the intervals to threshold discharges. It considers partial duration series (PDS) with thresholds equal to all high enough observed discharges. To avoid unnecessary assumptions on the behaviour of those parameters and effects of dependence between parameters for different PDS, a non-parametric trend-free pre-whitened scheme is applied. It leads to power-law relationships between a discharge and the mean and standard deviation of the intervals between its exceedences. Predicted mean inter-exceedence intervals, for the highest observed discharges at the stations, are closer to the observational periods than those predicted by GEV distributions fitted to AMS, and by GP distributions to fitted PDS. In the present case, the latter predictions are longer than the observational periods whereas some of the predicted mean inter-exceedences are shorter than the corresponding observational periods and some others are longer.

Citation Ben-Zvi, A. & Azmon, B. (2010) Direct relationships of discharges to the mean and standard deviation of the intervals between their exceedences. Hydrol. Sci J. 55(4), 565–577.     

Simulated changes due to global warming in the variability of precipitation, and their interpretation using a gamma-distributed stochastic model

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.     

Roving revisited,towards an optimum throughfall sampling design

Additional aspects regarding the optimum fixed and roving sampling techniques, to those already explored in a previous authors’ throughfall study, are further investigated here. The roving technique consists in the random repositioning, with a frequency f_r, of N throughfall gauges among M positions (M > N), oppositely to the fixed or stationary arrangement where N = M. Both fixed and roving optimum sampling techniques of 100 monitored throughfall events sampled with 200 fixed gauges under a semideciduous tropical rain forest in Panama were investigated by means of Monte‐Carlo numerical experiments. Mean dispersion was shown to be always smaller in the roving versus the fixed gauge arrangement, independently of the relocation frequency studied (f_r = 0.1, 0.2, 0.5, 1), such that all roving schemes with N ≥ 50 gauges lay within ±5% of the mean cumulative throughfall. Results indicated that a low variability, high precision, and accuracy are obtained with a modest relocation frequency f_r = 0.2 (i.e. a relocation every five episodes of the original 100 measured events) and N = 30 roving gauges, with no significant improvement worth the extra field work beyond f_r > 0.2 and N >30. Only by increasing the number of roving positions from M < < 200 to M = 200, the precision and accuracy of the mean estimate were improved without comprising additional labour. Hence, a roving sampling scheme which relocates gauges over completely new fresh sites each roving cycle is recommended for future throughfall studies. Finally, we designed an a priori sampling strategy which permitted us to conclude that using only the first 20 out of the total 100 measuring events, for the remaining 80 throughfall field measurements, N = 40 roving gauges (i.e. five time less than the originally 200 gauges displayed) would have been sufficient for ensuring ≤5% error, expressed as percentage of the mean cumulative throughfall. Copyright © 2012 John Wiley & Sons, Ltd.     

Prediction of concentrated flow width in ephemeral gully channels

Empirical prediction equations of the form W = aQ^b have been reported for rills and rivers, but not for ephemeral gullies. In this study six experimental data sets are used to establish a relationship between channel width (W, m) and flow discharge (Q, m³ s^?1) for ephemeral gullies formed on cropland. The resulting regression equation (W = 2·51 Q^0·412; R² = 0·72; n = 67) predicts observed channel width reasonably well. Owing to logistic limitations related to the respective experimental set ups, only relatively small runoff discharges (i.e. Q < 0·02 m³s^?1) were covered. Using field data, where measured ephemeral gully channel width was attributed to a calculated peak runoff discharge on sealed cropland, the application field of the regression equation was extended towards larger discharges (i.e. 5 × 10^?4m³s^?1 < Q < 0·1 m³s^?1). Comparing W–Q relationships for concentrated flow channels revealed that the discharge exponent (b) varies from 0·3 for rills over 0·4 for gullies to 0·5 for rivers. This shift in b may be the result of: (i) differences in flow shear stress distribution over the wetted perimeter between rills, gullies and rivers, (ii) a decrease in probability of a channel formed in soil material with uniform erosion resistance from rills over gullies to rivers and (iii) a decrease in average surface slope from rills over gullies to rivers. The proposed W–Q equation for ephemeral gullies is valid for (sealed) cropland with no significant change in erosion resistance with depth. Two examples illustrate limitations of the W–Q approach. In a first example, vertical erosion is hindered by a frozen subsoil. The second example relates to a typical summer situation where the soil moisture profile of an agricultural field makes the top 0·02 m five times more erodible than the underlying soil material. For both cases observed W values are larger than those predicted by the established channel width equation for concentrated flow on cropland. For the frozen soils the equation W = 3·17 Q^0·368 (R² = 0·78; n = 617) was established, but for the summer soils no equation could be established. Copyright © 2002 John Wiley & Sons, Ltd.     

Comparing satellite derived precipitation datasets using the Hillslope River Routing (HRR) model in the Congo River Basin

In this paper, three satellite derived precipitation datasets (TRMM, CMORPH, PERSIANN) are used to drive the Hillslope River Routing (HRR) model in the Congo Basin. The precipitation data are compared spatially and temporally in two forms: (1) precipitation magnitudes, and (2) resulting streamflow and water storages. Simulated streamflow is assessed using historical monthly discharge data from in situ stream gauges and recent stage data based on water surface elevations derived from ENVISAT radar altimetry data. Simulated total water storage is assessed using monthly storage change values derived from GRACE data. The results show that the three precipitation datasets vary significantly in terms of magnitudes but generally produce a reasonable hydrograph throughout much of the basin, with the exception of the equatorial regions of the watershed. The satellite datasets provide unreasonably high values for specific periods (e.g. all three in Oct–Nov; only CMORPH and PERSIANN in Mar–Apr) in the equatorial regions. Overall, TRMM (3B42) provides the best spatial and temporal distributions and magnitudes or rainfall based on the assessment measures used here. Both CMORPH and PERSIANN tend to overestimate magnitudes, especially in the equatorial regions of the Basin. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation of the gravitational potential energy of the earth based on different density models

The estimation of the Earth’s gravitational potential energy E was obtained for different density distributions and rests on the expression E = − (W_min + ΔW) derived from the conventional relationship for E. The first component W_min expresses minimum amount of the work W and the second component ΔW represents a deviation from W_min interpreted in terms of Dirichlet’s integral applied on the internal potential. Relationships between the internal potential and E were developed for continuous and piecewise continuous density distributions. The global 3D density model inside an ellipsoid of revolution was chosen as a combined solution of the 3D continuous distribution and the reference PREM radial piecewise continuous profile. All the estimates of E were obtained for the spherical Earth since the estimated (from error propagation rule) accuracy σ_E of the energy E is at least two orders greater than the ellipsoidal reduction and the contribution of lateral density inhomogeneities of the 3D global density model. The energy E contained in the 2nd degree Stokes coefficients was determined. A good agreement between E = E_Gauss derived from Gaussian distribution and other E, in particular for E = E_PREM based on the PREM piecewise continuous density model and E-estimates derived from simplest Legendre-Laplace, Roche, Bullard and Gauss models separated into core and mantle only, suggests the Gaussian distribution as a basic radial model when information about density jumps is absent or incomplete.     

Processes controlling rapid temperature variations on rock surfaces

In arid environments, thermal oscillations are an important source of rock weathering. Measurements of temperature have been made on the surface of rocks in a desert environment at a sampling interval of 0·375 s, with simultaneous measurements of wind speed, air temperature, and incoming shortwave radiation. Over timescales of hours, the temperature of the rock surface was determined primarily by shortwave radiation and air temperature, while rapid temperature variations, high dT/dt, at intervals of seconds or less, were determined by wind speed. The maximum values of temperature change and time spent above 2°C min^?1 increased at high measurement rates and were much higher than previously reported. The maximum recorded value of dT/dt was 137°C min^?1 and the average percentage time spent above 2°C min^?1 was ～70 ± 13%. Maximum values of dT/dt did not correlate with the maximum values of time spent above 2°C min^?1. Simultaneous measurements of two thermocouples 5·5 cm apart on a single rock surface had similar temperature and dT/dt values, but were not correlated at sampling intervals of less than 10 s. It is suggested that this is resulting from rapid fluctuations due to small spatial and timescale wind effects that are averaged out when data is taken at longer sampling intervals, ～10 s or greater. Published in 2010 by John Wiley & Sons, Ltd.     

Field experiments constraining the probability distribution of particle travel distances during natural rainstorms on different slope gradients

Rain splash erosion is an important soil transport mechanism on steep hillslopes. The rain splash process is highly stochastic; here we seek to constrain the probability distribution of splash transport distances on natural hillslopes as a function of hillslope gradient and total precipitation depth. Field experiments were conducted under natural precipitation events to observe splash travel on varying slope gradients. The downslope fraction of splash transport on 15°, 25° and 33° gradients were 85%, 96% and 96%, respectively. Maximum splash transport (L_max) was related to the rain splash detachment of soil particles and slope gradient. An empirical relationship of L_max to the precipitation depth and gradient was obtained; it is linearly proportional to hillslope gradient and logarithmically related to precipitation depth. Measured splash distances were calibrated to the fully two‐dimensional (2D) model of splash transport of Furbish et al. (Journal of Geophysical Research 112 : F01001, 2007) that is based on the assumption that radial splash distances are exponentially distributed; calibrated values of mean splash transport distances are an order of magnitude greater than those previously determined in a controlled laboratory setting. We also compared measured data with several one‐dimensional (1D) probability distributions to asses if splash transport distances could be better explained by a heavy‐tailed probability distribution rather than an exponential probability distribution. We find that for hillslopes of 15° and 25°, although a log‐normal probability distribution best describes the data, we find its likelihood is nearly indistinguishable from an exponential distribution based on computing maximum likelihood estimators for all 1D distributions (exponential, log‐normal and Weibull). At 33°, however, we find stronger evidence that measured travel distances are heavy‐tailed. Copyright © 2011 John Wiley & Sons, Ltd.     

The effect of intensity of turbulence in umbrella cloud on tephra dispersion during explosive volcanic eruptions: Experimental and numerical approaches

During an explosive volcanic eruption, tephra fall out from the umbrella region of the eruption cloud to the ground surface. We investigated the effect of the intensity of turbulence in the umbrella cloud on dispersion and sedimentation of tephra by performing a series of laboratory experiments and three dimensional (3-D) numerical simulations. In the laboratory experiments, spherical glass-bead particles are mixed in stirred water with various intensities of turbulence, and the spatial distribution and the temporal evolution of the particle concentration are measured. The experimental results show that, when the root-mean-square of velocity fluctuation in the fluid (W_rms) is much greater than the particle terminal velocity (v_t), the particles are homogeneously distributed in the fluid, and settle at their terminal velocities at the base of the fluid where turbulence diminishes. On the other hand, when W_rms is as small as or smaller than v_t, the particle concentration increases toward the base of the fluid during settling, which substantially increases the rate of particle settling. The results of the 3-D simulations of eruption cloud indicate that W_rms is up to 40 m/s in most of the umbrella cloud even during a large scale plinian eruption with a magma discharge rate of 10⁹ kg/s. These results suggest that relatively coarse pyroclasts (more than a few mm in diameter) tend to concentrate around the base of the umbrella cloud, whereas fine pyroclasts (less than 1/8 mm in diameter) may be distributed homogeneously throughout the umbrella cloud during tephra dispersion. The effect of the gradient of particle concentration in the umbrella cloud explains the granulometric data of the Pinatubo 1991 plinian deposits.