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1.
High-biomass red tides occur frequently in some semi-enclosed bays of Hong Kong where ambient nutrients are not high enough to support such a high phytoplankton biomass. These high-biomass red tides release massive inorganic nutrients into local waters during their collapse. We hypothesized that the massive inorganic nutrients released from the collapse of red tides would fuel growth of other phytoplankton species. This could influence phytoplankton species composition. We tested the hypothesis using a red tide event caused by Mesodinium rubrum (M. rubrum) in a semi-enclosed bay, Port Shelter. The red tide patch had a cell density as high as 5.0×105 cells L?1, and high chlorophyll a (63.71 μg L?1). Ambient inorganic nutrients (nitrate: \(\rm{NO}_3^-\), ammonium: \(\rm{NH}_4^+\), phosphate: \(\rm{PO}_4^{3-}\), silicate: \(\rm{SiO}_4^{3-}\)) were low both in the red tide patch and the non-red-tide patch (clear waters outside the red tide patch). Nutrient addition experiments were conducted by adding all the inorganic nutrients to water samples from the two patches followed by incubation for 9 days. The results showed that the addition of inorganic nutrients did not sustain high M. rubrum cell density, which collapsed after day 1, and did not drive M. rubrum in the non-red-tide patch sample to the same high-cell density in the red tide patch sample. This confirmed that nutrients were not the driving factor for the formation of this red tide event, or for its collapse. The death of M. rubrum after day 1 released high concentrations of \(\rm{NO}_3^-\), \(\rm{PO}_4^{3-}\), \(\rm{SiO}_4^{3-}\), \(\rm{NH}_4^+\), and urea. Bacterial abundance and heterotrophic activity increased, reaching the highest on day 3 or 4, and decreased as cell density of M. rubrum declined. The released nutrients stimulated growth of diatoms, such as Chaetoceros affinis var. circinalis, Thalassiothrix frauenfeldii, and Nitzschia sp., particularly with additions of \(\rm{SiO}_4^{3-}\) treatments, and other species. These results demonstrated that initiation of M. rubrum red tides in the bay was not directly driven by nutrients. However, the massive inorganic nutrients released from the collapse of the red tide could induce a second bloom in low-ambient nutrient water, influencing phytoplankton species composition.  相似文献   

2.
Effects of temporally correlated infiltration on water flow in an unsaturated–saturated system were investigated. Both white noise and exponentially correlated infiltration processes were considered. The moment equations of the pressure head (ψ) were solved numerically to obtain the variance and autocorrelation functions of ψ at 14 observation points. Monte Carlo simulations were conducted to verify the numerical results and to estimate the power spectrum of ψ (S ψψ ). It was found that as the water flows through the system, the variance of the ψ (\( \sigma_{\psi }^{2} \)) were damped by the system: the deeper in the system, the smaller the \( \sigma_{\psi }^{2} \), and the larger the correlation timescale of the infiltration process (λ I ), the larger the \( \sigma_{\psi }^{2} \). The unsaturated–saturated system gradually filters out the short-term fluctuations of ψ and the damping effect is most significant in the upper part of the system. The fluctuations of ψ is non-stationary at early time and becomes stationary as time progresses: the larger the value of λ I , the longer the non-stationary period. The correlation timescale of the ψ (λ ψ ) increases with depth and approaches a constant value at depth: the larger the value of λ I , the larger the value of λ ψ . The results of the estimated S ψψ is consistent with those of the variance and autocorrelation function.  相似文献   

3.
During the ruptures of an earthquake,the strain energy.△E,.will be transferred into,at least,three parts,i.e..the seismic radiation energy(E_s),fracture energy(E_g),and frictional energy(E_f),that is,△E = E_s + E_g + E_f.Friction,which is represented by a velocity- and state-dependent friction law by some researchers,controls the three parts.One of the main parameters of the law is the characteristic slip displacement.D_c.It is significant and necessary to evaluate the reliable value of D_c from observed and inverted seismic data.Since D_c controls the radiation efficiency.η_R = E_s/(E_s+ E_g),the value of η_r is a good constraint of estimating D_c.Integrating observed data and inverted results of source parameters from recorded seismograms.the values of E_s and E_g of an earthquake can be measured,thus leading to the value of η_R.The constraint used to estimate the reliable value of D_c will be described in this work.An example of estimates of D_c.based on the observed and inverted values of source parameters of the September 20,1999 M_S 7.6 Chi-Chi(Ji-Ji).Taiwan region,earthquake will be presented.  相似文献   

4.
During the last 15 years, more attention has been paid to derive analytic formulae for the gravitational potential and field of polyhedral mass bodies with complicated polynomial density contrasts, because such formulae can be more suitable to approximate the true mass density variations of the earth (e.g., sedimentary basins and bedrock topography) than methods that use finer volume discretization and constant density contrasts. In this study, we derive analytic formulae for gravity anomalies of arbitrary polyhedral bodies with complicated polynomial density contrasts in 3D space. The anomalous mass density is allowed to vary in both horizontal and vertical directions in a polynomial form of \(\lambda =ax^m+by^n+cz^t\), where m, n, t are nonnegative integers and a, b, c are coefficients of mass density. First, the singular volume integrals of the gravity anomalies are transformed to regular or weakly singular surface integrals over each polygon of the polyhedral body. Then, in terms of the derived singularity-free analytic formulae of these surface integrals, singularity-free analytic formulae for gravity anomalies of arbitrary polyhedral bodies with horizontal and vertical polynomial density contrasts are obtained. For an arbitrary polyhedron, we successfully derived analytic formulae of the gravity potential and the gravity field in the case of \(m\le 1\), \(n\le 1\), \(t\le 1\), and an analytic formula of the gravity potential in the case of \(m=n=t=2\). For a rectangular prism, we derive an analytic formula of the gravity potential for \(m\le 3\), \(n\le 3\) and \(t\le 3\) and closed forms of the gravity field are presented for \(m\le 1\), \(n\le 1\) and \(t\le 4\). Besides generalizing previously published closed-form solutions for cases of constant and linear mass density contrasts to higher polynomial order, to our best knowledge, this is the first time that closed-form solutions are presented for the gravitational potential of a general polyhedral body with quadratic density contrast in all spatial directions and for the vertical gravitational field of a prismatic body with quartic density contrast along the vertical direction. To verify our new analytic formulae, a prismatic model with depth-dependent polynomial density contrast and a polyhedral body in the form of a triangular prism with constant contrast are tested. Excellent agreements between results of published analytic formulae and our results are achieved. Our new analytic formulae are useful tools to compute gravity anomalies of complicated mass density contrasts in the earth, when the observation sites are close to the surface or within mass bodies.  相似文献   

5.
Recent publications on the regression between earthquake magnitudes assume that both magnitudes are affected by error and that only the ratio of error variances is known. If X and Y represent observed magnitudes, and x and y represent the corresponding theoretical values, the problem is to find the a and b of the best-fit line \(y = a x + b\). This problem has a closed solution only for homoscedastic errors (their variances are all equal for each of the two variables). The published solution was derived using a method that cannot provide a sum of squares of residuals. Therefore, it is not possible to compare the goodness of fit for different pairs of magnitudes. Furthermore, the method does not provide expressions for the x and y. The least-squares method introduced here does not have these drawbacks. The two methods of solution result in the same equations for a and b. General properties of a discussed in the literature but not proved, or proved for particular cases, are derived here. A comparison of different expressions for the variances of a and b is provided. The paper also considers the statistical aspects of the ongoing debate regarding the prediction of y given X. Analysis of actual data from the literature shows that a new approach produces an average improvement of less than 0.1 magnitude units over the standard approach when applied to \(M_{w}\) vs. \(m_{b}\) and \(M_{w}\) vs. \(M_{S}\) regressions. This improvement is minor, within the typical error of \(M_{w}\). Moreover, a test subset of 100 predicted magnitudes shows that the new approach results in magnitudes closer to the theoretically true magnitudes for only 65 % of them. For the remaining 35 %, the standard approach produces closer values. Therefore, the new approach does not always give the most accurate magnitude estimates.  相似文献   

6.
Rapid magnitude estimation relations for earthquake early warning systems in the Alborz region have been developed based on the initial first seconds of the P-wave arrival. For this purpose, a total of 717 accelerograms recorded by the Building and Housing Research Center in the Alborz region with the magnitude (Mw) range of 4.8–6.5 in the period between 1995 and 2013 were employed. Average ground motion period (\( \tau_{\text{c}} \)) and peak displacement (\( P_{\text{d}} \)) in different time windows from the P-wave arrival were calculated, and their relation with magnitude was examined. Four earthquakes that were excluded from the analysis process were used to validate the results, and the estimated magnitudes were found to be in good agreement with the observed ones. The results show that using the proposed relations for the Alborz region, earthquake magnitude could be estimated with acceptable accuracy even after 1 s of the P-wave arrival.  相似文献   

7.
ADCP and temperature chain measurements have been used to estimate the rate of energy input by wind stress to the water surface in the south basin of Windermere. The energy input from the atmosphere was found to increase markedly as the lake stratified in spring. The efficiency of energy transfer (Eff), defined as the ratio of the rate of working in near-surface waters (RW) to that above the lake surface (P 10), increased from ～0.0013 in vertically homogenous conditions to ～0.0064 in the first 40 days of the stratified regime. A maximum value of Eff～0.01 was observed when, with increasing stratification, the first mode internal seiche period decreased to match the diurnal wind period of 24 h. The increase in energy input, following the onset of stratification was reflected in enhancement of the mean depth-varying kinetic energy without a corresponding increase in wind forcing. Parallel estimates of energy dissipation in the bottom boundary layer, based on determination of the structure function show that it accounts for ～15% of RW in stratified conditions. The evolution of stratification in the lake conforms to a heating stirring model which indicates that mixing accounts for ～21% of RW. Taken together, these estimates of key energetic parameters point the way to the development of full energy budgets for lakes and shallow seas.  相似文献   

8.
Microstructure measurements were performed along two sections through the Halmahera Sea and the Ombai Strait and at a station in the deep Banda Sea. Contrasting dissipation rates (??) and vertical eddy diffusivities (K z ) were obtained with depth-averaged ranges of \(\sim [9 \times 10^{-10}-10^{-5}]\) W kg??1 and of \(\sim [1 \times 10^{-5}-2 \times 10^{-3}]\) m2 s??1, respectively. Similarly, turbulence intensity, \(I={\epsilon }/(\nu N^{2})\) with ν the kinematic viscosity and N the buoyancy frequency, was found to vary seven orders of magnitude with values up to \(10^{7}\). These large ranges of variations were correlated with the internal tide energy level, which highlights the contrast between regions close and far from internal tide generations. Finescale parameterizations of ?? induced by the breaking of weakly nonlinear internal waves were only relevant in regions located far from any generation area (“far field”), at the deep Banda Sea station. Closer to generation areas, at the “intermediate field” station of the Halmahera Sea, a modified formulation of MacKinnon and Gregg (2005) was validated for moderately turbulent regimes with 100 < I < 1000. Near generation areas marked by strong turbulent regimes such as “near field” stations within strait and passages, ?? is most adequately inferred from horizontal velocities provided that part of the inertial subrange is resolved, according to Kolmogorov scaling.  相似文献   

9.
The first part of this paper reviews methods using effective solar indices to update a background ionospheric model focusing on those employing the Kriging method to perform the spatial interpolation. Then, it proposes a method to update the International Reference Ionosphere (IRI) model through the assimilation of data collected by a European ionosonde network. The method, called International Reference Ionosphere UPdate (IRI UP), that can potentially operate in real time, is mathematically described and validated for the period 9–25 March 2015 (a time window including the well-known St. Patrick storm occurred on 17 March), using IRI and IRI Real Time Assimilative Model (IRTAM) models as the reference. It relies on foF2 and M(3000)F2 ionospheric characteristics, recorded routinely by a network of 12 European ionosonde stations, which are used to calculate for each station effective values of IRI indices \(IG_{12}\) and \(R_{12}\) (identified as \(IG_{{12{\text{eff}}}}\) and \(R_{{12{\text{eff}}}}\)); then, starting from this discrete dataset of values, two-dimensional (2D) maps of \(IG_{{12{\text{eff}}}}\) and \(R_{{12{\text{eff}}}}\) are generated through the universal Kriging method. Five variogram models are proposed and tested statistically to select the best performer for each effective index. Then, computed maps of \(IG_{{12{\text{eff}}}}\) and \(R_{{12{\text{eff}}}}\) are used in the IRI model to synthesize updated values of foF2 and hmF2. To evaluate the ability of the proposed method to reproduce rapid local changes that are common under disturbed conditions, quality metrics are calculated for two test stations whose measurements were not assimilated in IRI UP, Fairford (51.7°N, 1.5°W) and San Vito (40.6°N, 17.8°E), for IRI, IRI UP, and IRTAM models. The proposed method turns out to be very effective under highly disturbed conditions, with significant improvements of the foF2 representation and noticeable improvements of the hmF2 one. Important improvements have been verified also for quiet and moderately disturbed conditions. A visual analysis of foF2 and hmF2 maps highlights the ability of the IRI UP method to catch small-scale changes occurring under disturbed conditions which are not seen by IRI.  相似文献   

10.
Vegetation is known to influence the hydrological state variables, suction \( \left( \psi \right) \) and volumetric water content (\( \theta_{w} \)) of soil. In addition, vegetation induces heterogeneity in the soil porous structure and consequently the relative permeability (\( k_{r} \)) of water under unsaturated conditions. The indirect method of utilising the soil water characteristic curve (SWCC) is commonly adopted for the determination of \( k_{r} \). In such cases, it is essential to address the stochastic behaviour of SWCC, in order to conduct a robust analysis on the \( k_{r} \) of vegetative cover. The main aim of this study is to address the uncertainties associated with \( k_{r} \), using probabilistic analysis, for vegetative covers (i.e., grass and tree species) with bare cover as control treatment. We propose two approaches to accomplish the aforesaid objective. The univariate suction approach predicts the probability distribution functions of \( {\text{k}}_{\text{r}} \), on the basis of identified best probability distribution of suction. The bivariate suction and water content approach deals with the bivariate modelling of the water content and suction (SWCC), in order to capture the randomness in the permeability curves, due to presence of vegetation. For this purpose, the dependence structure of \( \psi \) and \( \theta_{w} \) is established via copula theory, and the \( k_{r} \) curves are predicted with respect to varying levels of \( \psi - \theta_{w} \) correlation. The results showed that the \( k_{r} \) of vegetative covers is substantially lower than that in bare covers. The reduction in \( k_{r} \) with drying is more in tree cover than grassed cover, since tree roots induce higher levels of suction. Moreover, the air entry value of the soil depends on the magnitude of \( \psi - \theta_{w} \) correlation, which in turn, is influenced by the type of vegetation in the soil. \( k_{r} \) is found to be highly uncertain in the desaturation zone of the relative permeability curve. The stochastic behaviour of \( k_{r} \) is found to be most significant in tree covers. Finally, a simplified case study is also presented in order to demonstrate the impact of the uncertainty in \( k_{r} \), on the stability of vegetates slopes. With an increment in the parameter \( \alpha \), factor of safety (FS) is found to decrease. The trend of FS is reverse of this with parameter \( n \). Overall FS is found to vary around 4–5%, for both bare and vegetative slopes.  相似文献   

11.
Theory of wave boundary layers (WBLs) developed by Reznik (J Mar Res 71: 253–288, 2013, J Fluid Mech 747: 605–634, 2014, J Fluid Mech 833: 512–537, 2017) is extended to a rotating stratified fluid. In this case, the WBLs arise in the field of near-inertial oscillations (NIOs) driven by a tangential wind stress of finite duration. Near-surface Ekman layer is specified in the most general form; tangential stresses are zero at the lower boundary of Ekman layer and viscosity is neglected below the boundary. After the wind ceases, the Ekman pumping at the boundary becomes a linear superposition of inertial oscillations with coefficients dependent on the horizontal coordinates. The solution under the Ekman layer is obtained in the form of expansions in the vertical wave modes. We separate from the solution a part representing NIO and demonstrate development of a WBL near the Ekman layer boundary. With increasing time t, the WBL width decays inversely proportional to \( \sqrt{t} \) and gradients of fields in the WBL grow proportionally to \( \sqrt{t} \); the most part of NIO is concentrated in the WBL. Structure of the WBL depends strongly on its horizontal scale L determined by scale of the wind stress. The shorter the NIO is, the thinner and sharper the WBL is; the short-wave NIO with L smaller than the baroclinic Rossby scale LR does not penetrate deep into the ocean. On the contrary, for L?≥?LR, the WBL has a smoother vertical structure; a significant long-wave NIO signal is able to reach the oceanic bottom. An asymptotic theory of the WBL in rotating stratified fluid is suggested.  相似文献   

12.
Seismicity has been identified as an example of a natural, nonlinear system for which the distribution of frequency and event size follow a power law called the “Gutenberg–Richter (G-R) law.” The parameters of the G-R law, namely b- and a-values, have been widely used in many studies about seismic hazards, earthquake forecasting models, and other related topics. However, the plausibility of the power law model and applicability of parameters were mainly verified by statistical error σ of the b-value, the effectiveness of which is still doubtful. In this research, we used a newly defined p value developed by Clausetet al. (Power-Law Distributions in Empirical Data, SIAM Rev. 51, 661–703, 2009) instead of the statistical error σ of the b-value and verified its effectiveness as a plausibility index of the power-law model. Furthermore, we also verified the effectiveness of K–S statistics as a goodness-of-fit test in estimating the crucial parameter \(M_{\text{c}}\) of the power-law model.  相似文献   

13.
A semiempirical mathematical model of iron and manganese migration from bottom sediments into the water mass of water bodies has been proposed based on some basic regularities in the geochemistry of those elements. The entry of dissolved forms of iron and manganese under aeration conditions is assumed negligible. When dissolved-oxygen concentration is <0.5 mg/L, the elements start releasing from bottom sediments, their release rate reaching its maximum under anoxic conditions. The fluxes of dissolved iron and manganese (Me) from bottom sediments into the water mass (J Me) are governed by the gradients of their concentrations in diffusion water sublayer adjacent to sediment surface and having an average thickness of h = 0.025 cm: \({J_{Me}} = - {D_{Me}}\frac{{{C_{Me\left( {ss} \right)}} - {C_{Me\left( w \right)}}}}{h}\) (D Me ≈ 1 × 10–9 m2/s is molecular diffusion coefficient of component Me in solution; C Me(ss) and C Me(w) ≈ 0 are Me concentrations on sediment surface, i.e., on the bottom boundary of the diffusion water sublayer, and in the water mass, i.e., on the upper boundary of the diffusion water sublayer). The value of depends on water saturation with dissolved oxygen (\({\eta _{{O_2}}}\)) in accordance with the empiric relationship \({C_{Me\left( {ss} \right)}} = \frac{{C_{_{Me\left( {ss} \right)}}^{\max }}}{{1 + k{\eta _{{O_2}}}}}\) (k is a constant factor equal to 300 for iron and 100 for manganese; C Me(ss) max is the maximal concentration of Me on the bottom boundary of the diffusion water sublayer with C Fe(ss) max ≈ 200 μM (11 mg/L), and C Mn(ss) max ≈ 100 μM (5.5 mg/L).  相似文献   

14.
Fine structured multiple-harmonic electromagnetic emissions at frequencies around the equatorial oxygen cyclotron harmonics are observed by Van Allen Probe A outside the core plasmasphere(L~5) off the magnetic equator(MLAT~.7.5°)during a geomagnetic storm. We find that the multiple-harmonic emissions have power spectrum density(PSD) peaks during 2–8equatorial oxygen gyroharmonics( f ~ n fO+, n=2–8), while the fundamental mode(n=1) is absent, implying that the harmonic waves are generated near the equator and propagate into the observation region. Additionally, these electromagnetic emissions are linearly polarized. Different from the equatorial noise emission that propagates considerably obliquely, these emissions have moderate wave normal angles(approximately 40°–60°), which predominately increase as the harmonic number increases.Considering their frequency and wave normal angle characteristics, it is suggested that these multiple-harmonic emissions play an important role in the dynamic variation of radiation belt electrons.  相似文献   

15.
Conditional risk based on multivariate hazard scenarios   总被引：1，自引：1，他引：0  
We present a novel methodology to compute conditional risk measures when the conditioning event depends on a number of random variables. Specifically, given a random vector \((\mathbf {X},Y)\), we consider risk measures that express the risk of Y given that \(\mathbf {X}\) assumes values in an extreme multidimensional region. In particular, the considered risky regions are related to the AND, OR, Kendall and Survival Kendall hazard scenarios that are commonly used in environmental literature. Several closed formulas are considered (especially in the AND and OR scenarios). An application to spatial risk analysis involving real data is discussed.  相似文献   

16.
The celebrated Boltzmann-Gibbs (BG) entropy, S BG = ?kΣ i p i ln p i , and associated statistical mechanics are essentially based on hypotheses such as ergodicity, i.e., when ensemble averages coincide with time averages. This dynamical simplification occurs in classical systems (and quantum counterparts) whose microscopic evolution is governed by a positive largest Lyapunov exponent (LLE). Under such circumstances, relevant microscopic variables behave, from the probabilistic viewpoint, as (nearly) independent. Many phenomena exist, however, in natural, artificial and social systems (geophysics, astrophysics, biophysics, economics, and others) that violate ergodicity. To cover a (possibly) wide class of such systems, a generalization (nonextensive statistical mechanics) of the BG theory was proposed in 1988. This theory is based on nonadditive entropies such as \(S_q = k\frac{{1 - \sum\nolimits_i {p_i^q } }}{{q - 1}}\left( {S_1 = S_{BG} } \right)\). Here we comment some central aspects of this theory, and briefly review typical predictions, verifications and applications in geophysics and elsewhere, as illustrated through theoretical, experimental, observational, and computational results.  相似文献   

17.
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18.
The relation of the Kp index of geomagnetic activity to the solar wind electric field (E SW) and the projection of this field onto the geomagnetic dipole has been estimated. An analysis indicated that the southward component of the IMF vector (B z < 0) is the main geoeffective parameter, as was repeatedly indicated by many researchers. The presence of this component in any combinations of the interplanetary medium parameters is responsible for a high correlation between such combinations and geomagnetic activity referred to by the authors of different studies. Precisely this field component also plays the main role in the relation between the Kp index and the relative orientation of E SW and the Earth’ magnetic moment.  相似文献   

19.
Analysis of the frequency dependence of the attenuation coefficient leads to significant changes in interpretation of seismic attenuation data. Here, several published surface-wave attenuation studies are revisited from a uniform viewpoint of the temporal attenuation coefficient, denoted by χ. Theoretically, χ( f) is expected to be linear in frequency, with a generally non-zero intercept γ?=?χ(0) related to the variations of geometrical spreading, and slope dχ/df = π/Q e caused by the effective attenuation of the medium. This phenomenological model allows a simple classification of χ( f) dependences as combinations of linear segments within several frequency bands. Such linear patterns are indeed observed for Rayleigh waves at 500–100-s and 100–10-s periods, and also for Lg from ~2 s to ~1.5 Hz. The Lg χ( f) branch overlaps with similar linear branches of body, Pn, and coda waves, which were described earlier and extend to ~100 Hz. For surface waves shorter than ~100 s, γ values recorded in areas of stable and active tectonics are separated by the levels of \(\gamma _{D} \approx 0.2 \times 10^{-3}\) s???1 (for Rayleigh waves) and 8 ×10???3 s???1 (for Lg). The recently recognized discrepancy between the values of Q measured from long-period surface waves and normal-mode oscillations could also be explained by a slight positive bias in the geometrical spreading of surface waves. Similarly to the apparent χ, the corresponding linear variation with frequency is inferred for the intrinsic attenuation coefficient, χ i , which combines the effects of geometrical spreading and dissipation within the medium. Frequency-dependent rheological or scattering Q is not required for explaining any of the attenuation observations considered in this study. The often-interpreted increase of Q with frequency may be apparent and caused by using the Q-based model of attenuation and following preferred Q( f) dependences while ignoring the true χ( f) trends within the individual frequency bands.  相似文献   

20.
This paper introduces a portfolio approach for quantifying pollution risk in the presence of PM\(_{2.5}\) concentration in cities. The model used is based on a copula dependence structure. For assessing model parameters, we analyze a limited data set of PM\(_{2.5}\) levels of Beijing, Tianjin, Chengde, Hengshui, and Xingtai. This process reveals a better fit for the t-copula dependence structure with generalized hyperbolic marginal distributions for the PM\(_{2.5}\) log-ratios of the cities. Furthermore, we show how to efficiently simulate risk measures clean-air-at-risk and conditional clean-air-at-risk using importance sampling and stratified importance sampling. Our numerical results show that clean-air-at-risk at 0.01 probability level reaches up to \(352\,{\mu \hbox {gm}^{-3}}\) (initial PM\(_{2.5}\) concentrations of cities are assumed to be \(100\,{\mu \hbox {gm}^{-3}}\)) for the constructed sample portfolio, and that the proposed methods are much more efficient than a naive simulation for computing the exceeding probabilities and conditional excesses.  相似文献   

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