Yield and overflow from a finite stochastic reservoir

The paper discusses the overflow (spillage) and yield rates and the total overflow and total yield over a specified time from a finite discrete stochastic reservoir, in which the yieldY _t during the working interval (t,t+1) is a function of the storageZ _t at timet, the inflow sequence {X _t } being IID.The distribution vector of the spillage rate at timet is a telescoped version of the distribution of a certain Markovian variable whose transition matrix is derived. Formulae are given for the distribution of the total spillageW _h given suitable initial conditions, forh=1,2,3; and a simple expression derived forE(W _h ).     

Ein Spektrograph für Niederschlagstropfen mit automatischer Auswertung

Summary A new spectrometer which gives a continuous record of the size distribution of raindrops is described. The basic principe is the automatic compensation of the force, produced by a raindrop falling upon the rigid receiving system.The spectrometer is able to record the drop-size distribution of very weak as well as very heavy showers (more than 200 mm/h). Up to 200 drops per second with diameters ranging from 0.3 to 5.3 mm sorted into 20 groups can be recorded.An analog computer calculates and integrates simultaneously the rain intensityR, the water content in the airW and the radar reflectivityZ. The precision of the radar reflectivityZ, calculated from the raindrop spectrum, depends on the rain intensity, the receiving area and the timet during exposure. The precision ofZ is calculated for different timest as a function of the rain intensity.     

Multifractal comparison of the outputs of two optical disdrometers

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 (Z_h) and the specific differential phase (K_dp), and drop size distribution (DSD) parameters such as the total drop concentration (N_t) and the mass-weighted diameter (D_m). 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 Z_h–R and R–K_dp radar relations.

Editor D. Koutsoyiannis; Associate editor E. Volpi     

A multiple distribution Markovian model for annual hydrologic time series

Nonlinear serial dependence and skewness of annual hydrologic time series {X _t } have been challenging the classical theory of Gaussian stochastic processes, particularly if the study of extremes (dry or wet years) is required as it is often the case. In this paper, a new and general model is proposed assuming that the geophysical system which is responsible forX _t can take different states and that this state process is modeled by a Markov chain. At each time,X _t is generated from a statistical distribution which depends on the state that has occurred. This model can preserve non-linear structures of serial dependence and it can produce a skewed marginal distribution ofX _t without any transformation. A successful application of this model to the study of annual rainfall at Fortaleza (Northeast of Brazil) is also presented.     

网湖鲫鱼的生长与资源评估

根据1984—1986年在湖北省网湖进行渔业资源调查的资料,应用Von Bertalanffy生长方程描述该湖鲫鱼的生长模式,同时按照Joneo体长股分析模型和Thompson-Bell体长预测模型分别推算鲫鱼资源量和不同捕捞强度下资源量和渔获量的理论值,并求得最大持续渔获量。据此,对该湖鲫鱼资源的合理开发和利用进行了分析和讨论,并提出渔业对策。     

Mathematical model for evaluation of the effect of soil erosion on soil productivity

This paper is concerned with the development of a stochastic model for evaluating the long-term effect of soil erosion on soil productivity. Due to random variations in annual crop yield, the effect of erosion on crop production is not easily detectable in the short run, but becomes gradually evident over a sufficiently long time period. Under these circumstances, it seems that an experimental approach to this problem may be very difficult. The long period of time over which such an experiment has to be conducted may result in prohibitively high costs. In addition, it also means that eventual resolution of this problem must be postponed until a distant future time. The stochastic model formulated here provides us with a useful tool to assess the trend in quantitative changes in crop production due to erosion and to project future crop losses. The model is a discrete parameter stochastic process. Its derivation is based on a single assumption that the annual loss rates form a sequence of independent random variables {Z_i}₁∞ (in this paper, we consider only two particular cases: (a) {Z_i}₁∞ is a sequence of constants; (b) {Z_i}₁∞ is a sequence of independent identically distributed random variables). For these particular cases, we obtained its marginal n-dimensional distribution function and correlation function. One of the principal model features is its simple structure and remarkable lack of restrictive and unrealistic assumptions.     

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.     

网湖似剌鳊鮈年龄与生长的研究

对湖北省阳新县网湖所采得的862尾似刺鳊鮈的年龄与生长的研究表明,其年轮特征主要为切割型和碎裂型。其体长与鳞径呈直线相关:L=5.6784+4.3056R;体长与体重呈幂函数的增长关系:W=2.8026×10~(-2)L~(2.8754)。应用Van Bertalanffy生长方程拟合该鱼的一般生长规律,其生长参数为:L_∞=25.0143cm,W_∞=277.8876g,K=0.4668,t_0=-1.3886,拐点年龄t_i=1龄,拐点体长L_i=16.42cm,拐点体重W_i=82.82g。     

Real-time prediction of the peak suspended sediment concentration and sediment yield of the Lao-Nung River during storms

Based on rainfall erosion of soil and suspended sediment transport in storm events, a method is proposed to predict peak suspended sediment concentration and suspended sediment yield in watersheds based on rainfall characteristics prior to peak rainfall intensity. The rainfall characteristics factors that dominate peak suspended sediment concentration C_p are rainfall erosion factor R_ef, first peak rainfall intensity of area-average rainfall i_p1 and antecedent precipitation index I_ap; the rainfall characteristics factors that dominate suspended sediment yield Y_ss in storm events are total rainfall P, suspended sediment yield factor R_sf and antecedent precipitation index I_ap. This research focuses on watersheds in Liau-Kwei observation station along Lao-Nung River in southern Taiwan as the research object, and adopts the PSED-model to simulate the discharge hydrograph, suspended sediment concentration hydrograph and suspended sediment yield in 11 storm events for analysis. The analytical results show that there is a good correlation between the above-mentioned rainfall characteristics factors and C_p as well as Y_ss, thus enabling C_p and Y_ss to be predicted by using Expressions (13) and (14). These two expressions are utilized to predict C_p and Y_ss of Typhoon Morakot in 2009, and the results are compared with those from simulation by using the PSED-model. The result of comparison shows there is a good capability in predicting. For the watersheds where it is necessary to predict C_p and Y_ss of a storm event for the benefit of effective operation of water resource facilities, the aforesaid rainfall characteristics factors can be utilized to establish applicable models for prediction.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

The Displacement and Strain Field of Three-dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains ε_xx (r, t), ε_yy (r, t) and ε_zz (r, t) and the bulk strain θ (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (α, β, γ) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.     

Globalstrahlung und Sonnenaktivität

Summary Using the highest global irradiance values (Sun plus sky) at noon derived from the records gathered during the years 1958 to 1963 at Genova, Monte Capellino and Sauze d'Oulx, it is demonstrated that the thermal energy which the Earth receives from the Sun is dependent from the Sun activity. Precisely, an increase of the thermal energy withR _Z occurs up toR _Z=160–170, whereas for greater values ofR _Z the thermal energy received decreases with the increase ofR _Z.

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Herrn Prof. Dr.Hans Ertel zu seinem 60. Geburtstag gewidmet.     

Effects of solar and geomagnetic activity in long-term variations in the ionospheric parameters of the auroral zone in 1963–1986

A stable linear relation between foF2 and W with a correlation coefficient of 0.68–0.96 has been revealed as a result of a joint analysis of the foF2 critical frequencies and the virtual minimal heights (h’F) obtained from the data of vertical sounding (VS) of the ionosphere at Dixon Island auroral station, Wolf numbers (W), and PC geomagnetic index from 1963 to 1986. A significant linear relation exists between foF2 and the PC index with a correlation coefficient of r = 0.18–0.67. The correlation between the PC index and W is low in winter and autumn and is r = 0.50 and 0.74 at a significance level of ss = 0.96–0.99 in spring and summer. When the correlation between PC and foF2 is analyzed, it is necessary to consider the effect of solar activity (SA) on both parameters. The multiple correlation coefficients between these parameters have been calculated with regard to the effect of W. They were R = 0.75−0.98; however, the standardized regression coefficients β _W and β _PC indicated that W and PC considerably and insignificantly affect multiple correlation with foF2, respectively, and this effect depends on the season and time of day. It has been detected that the cyclic variations in foF2 and h’F are asymmetric. The amplitudes of these parameters in cycle 20 are smaller than in cycle 21.     

Lg amplitude ratios H/Z and station terms in the six eastern provinces of China

Using the data set of about 1 Hz Lg amplitudes from 80 stations in the six eastern provinces of China, the ratios of horizontal to vertical amplitude of Lg waves,H/Z are determined. The mean lg(H/Z)-value is equal to 0.13. For the station bases of soft deposit,granite and sedimentary rock, lg(H/Z)-values average 0.55, 0.04 and 0.10, respectively. For the three kinds of station bases, the station terms of horizontal amplitude,C _h average 0.65, −0.09 and 0.00; that of vertical amplitude,C _z average 0.32, −0.04 and 0.00, respectively. There are the relations betweenC _h ,C _z and lg(H/Z):C _h =0.01+2.10C _z andC _h =−0.15+1.46 lg(H/Z). The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 281–286, 1991. Project sponsored by the Chinese Joint Seismological Science Foundation.     

Plasma pressure distribution in the equatorial plane of the Earth’s magnetosphere at geocentric distances of 6–10<Emphasis Type="Italic">R</Emphasis><Subscript><Emphasis Type="Italic">E</Emphasis></Subscript> according to the international THEMIS mission data

The structure of the averaged plasma pressure distribution in the plasma ring around the Earth at geocentric distances of ∼6–10R _E has been determined. The distribution function moments measured on the international THEMIS mission satellites have been used. The plasma pressure distribution in the equatorial plane at 15R _E > X_SM > −15R _E and 15R _E > Y_SM > −15R _E has been statistically studied. The radial dependence of the plasma pressure at the day-night and morning-evening meridians has been analyzed. It has been indicated that the plasma ring around the Earth has a structure, which is close to being azimuthally symmetric. The achieved results have been compared with the pressure distributions obtained previously. It has been indicated that in the overlapping regions, the achieved results agree with the previously obtained data within the pressure determination errors.     

Dynamic characteristics of soil-foundation interaction system detected from forced vibration test and earthquake observation

This paper presents some results on the following subjects obtained from in-situ forced vibration tests and earthquake observations. (1) The characteristics of the radiation damping of soil-foundation interaction systems vs. non-dimensional frequency a₀ (=ωr/V_s) were experimentally estimated by the equivalent damping ratios h_H ( = K′_H/2K_H) and h_R ( = K′_R/2K_R), which were defined by complex stiffnesses 1K_H (= K_H + iK_H) and 1K_R (= K_R + iK′_R) of soil. The results for h_H and h_R of base rock were compared with those of soft soil. (2) A comparative study of experimental and theoretical results was made. The theoretical results were obtained from elastic half-space theory. (3) A semi-empirical equation to estimate the equivalent S-wave velocity for the elastic half-space model is proposed here, considering the effects of layered media. (4) Various comparisons of the results of 1 K_H, 1 K_R, h_H and h_R of forced vibration tests and earthquake observations were made.     

Depth of detection of buried resistive targets with some electrode arrays in electrical prospecting

Assuming the minimum detectable anomaly to be 10%, depths of detection of a 2D vertical resistive sheet of thickness t are found to be 4.0t, 3.0t, 4.0t and 4.0t with Wenner, two-electrode, three-electrode and dipole-dipole (β-Wenner) arrays, respectively, when the array spread is in-line. On the other hand, the depths of detection obtained with a broadside spread of the arrays right over the sheet are much less and are correspondingly 2.5t, 2.0t, 2.5t and 2.5t. An increase in the depth extent W of the sheet from 10t to 20t does not increase its depth of detection with the arrays. The depths of detection of an infinitely resistive horizontal cylinder of radius R are respectively 1.5R, 1.8R, 2.0R and 2.0R with the above-listed arrays when the array spread is in-line. With broadside spread of any of the arrays, the depth of detection is seen to be 2.5R. In the case of a spherical target of radius R, the detection depths of any of the arrays are found to be small and to vary between 0.8R and 1.1R. Comparatively, the detection depths of resistive targets are much lower than those of conductive targets of the same size and shape, with any electrode array. Among all the arrays studied, the two-electrode array performs worst in the detection of resistive targets while it performs best in detecting conducting targets of limited lateral extent. In the case of a spherical target, either resistive or conductive, there is no distinct change in its detection depth with array.     

Scale factor for lengths of the geopotential model

Summary Using the data in[1], the scale factor for lengths is derived of the geopotential model R ₀ =GM/W ₀ (W ₀ is the potential on a generalized geoid). The resulting value, R ₀ ==6 363 672.9 m, which is2 m less than the original value[5], is practically the same as that in[6].     

Attenuation characteristics of coda waves and estimation of Q c values in eastern China

For short-period near-earthquake records in eastern China, from the empirical attenuation formula of coda ground motion amplitudeA with timeτ: lgA=G−2. 235 lgτ, using the single scattering theory modified with epicentral distance, we obtain the curve family of corrected coda amplitudeA _c(r,t), andω/2Q _c values for each time interval of coda. From this,Q _c(f,h) values, which correspond to each observational average frequency and sampling depth, are calculated. The results substantially agree with those observationalQ _c values in Yunnan, Beijing and central Asia.