Feasibility of estimating total stem volume and aboveground biomass from measurement on the largest trees in even-aged pure stands

2001 ◽  
Vol 31 (11) ◽  
pp. 2042-2048 ◽  
Author(s):  
A Osawa ◽  
A P Abaimov ◽  
T Kajimoto
Keyword(s):  
Distribution Function ◽  
Aboveground Biomass ◽  
Power Distribution ◽  
Present Method ◽  
Size Distribution Function ◽  
Stem Volume ◽  
Systematic Bias ◽  
Type Distribution ◽  
Predicted Values ◽  
Paired T Test

Feasibility was tested of estimating the total stem volume and aboveground biomass from data of only the largest trees in even-aged pure stands. We applied a method of fitting a size-distribution function to data that exclude information of smaller individuals in a stand and compared the predicted stem volume and aboveground biomass with those calculated with data of all living trees in the stand. The paired t test showed that the predicted values of the total stem volume and aboveground biomass were not different (p = 0.05) from those observed even if only the largest 10% of the trees were used for estimation with the –3/2 power distribution. Results were similar with the beta-type distribution; however, data from at least the largest 30% of the trees in the stand must be included. Absolute values of the relative error of the predicted total stem volume or aboveground biomass were generally in the range 10–20%, indicating that the present method is accurate enough to be used for calculation of these variables. However, there is systematic bias in the predictions of the total stem volume and aboveground biomass of a stand. Possible causes of the indicated biases and potential ways for improvement of the predictions were discussed.

Feasibility of estimating stem size distribution from measurement on the largest trees in even-aged pure stands

2001 ◽  
Vol 31 (5) ◽  
pp. 910-918 ◽  
Author(s):  
Akira Osawa ◽  
Anatoly P Abaimov
Keyword(s):  
Size Distribution ◽  
Power Distribution ◽  
Environmental Changes ◽  
Stand Structure ◽  
Size Variation ◽  
Stand Density ◽  
Distribution Functions ◽  
Stem Volume ◽  
Type Distribution ◽  
Stem Size

Reconstruction of the size distribution of trees in stands provides critical information for assessing the effects of environmental changes on forests and for forest management. For furthering a method of such reconstruction, feasibility of estimating size distribution in stem volume from measurement of the largest trees was examined for even-aged pure stands of Pinus banksiana Lamb.and Larix gmelinii (Rupr.) Rupr. We tested what percentage of the largest trees should be included in obtaining a frequency distribution in stem volume that is not statistically different from the observed size distribution patterns. The –3/2 power, beta-type, and adjusted beta-type distribution functions were applied. Comparison of the observed stem frequencies and those estimated from measurement of the largest trees in a stand suggested that (i) the –3/2 power distribution, beta-type distribution, or adjusted beta-type distribution may be used for reconstruction of stem size variation in pure stands, if the overall size variation could be approximated by one of these functions; (ii) we can be at least 95% sure that the tree size pattern be expressed successfully with the –3/2 power distribution with tree samples of only the largest 20% in the stand, or with the beta-type distribution with the largest 30% in the stand; and (iii) the reliability decreases somewhat for the adjusted beta-type distribution. The second observation implies that reconstruction of the temporal changes in stand structure may be reliable up to the time when the stand density was about five times that of the trees used for fitting the –3/2 power distribution curve. Reliability may be warranted up to the stand density of about three times as the number of trees used for fitting the beta-type distribution. Other considerations and limitations are also discussed.

scholarly journals The mass of the Milky Way out to 100 kpc using halo stars

2020 ◽  
Author(s):  
Alis J Deason ◽  
Denis Erkal ◽  
Vasily Belokurov ◽  
Azadeh Fattahi ◽  
Facundo A Gómez ◽  
...  
Keyword(s):  
Distribution Function ◽  
Mass Concentration ◽  
Milky Way ◽  
Function Analysis ◽  
Large Magellanic Cloud ◽  
Systematic Bias ◽  
Cosmological Simulations ◽  
Halo Stars ◽  
Systematic Effects ◽  
Mass Estimate

Abstract We use a distribution function analysis to estimate the mass of the Milky Way out to 100 kpc using a large sample of halo stars. These stars are compiled from the literature, and the vast majority ($\sim \! 98\%$) have 6D phase-space information. We pay particular attention to systematic effects, such as the dynamical influence of the Large Magellanic Cloud (LMC), and the effect of unrelaxed substructure. The LMC biases the (pre-LMC infall) halo mass estimates towards higher values, while realistic stellar halos from cosmological simulations tend to underestimate the true halo mass. After applying our method to the Milky Way data we find a mass within 100 kpc of M( < 100kpc) = 6.07 ± 0.29(stat.) ± 1.21(sys.) × 1011M⊙. For this estimate, we have approximately corrected for the reflex motion induced by the LMC using the Erkal et al. model, which assumes a rigid potential for the LMC and MW. Furthermore, stars that likely belong to the Sagittarius stream are removed, and we include a 5% systematic bias, and a 20% systematic uncertainty based on our tests with cosmological simulations. Assuming the mass-concentration relation for Navarro-Frenk-White haloes, our mass estimate favours a total (pre-LMC infall) Milky Way mass of M200c = 1.01 ± 0.24 × 1012M⊙, or (post-LMC infall) mass of M200c = 1.16 ± 0.24 × 1012 M⊙ when a 1.5 × 1011M⊙ mass of a rigid LMC is included.

Informational Measures of the Shape of the Amoroso Distributions for the Research of Dispersed Materials

2021 ◽  
Vol 1031 ◽  
pp. 58-66
Author(s):  
Vitaly Polosin
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Applied Research ◽  
Particle Distribution ◽  
Size Distribution Function ◽  
Distribution Model ◽  
Information Uncertainty ◽  
Particle Size Distribution Function

For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. The article proposes a uniform model for setting the interval of information uncertainty of non-symmetric particle size distributions. Based on the analysis of statistical and information uncertainty intervals, new shape coefficients of distribution models are constructed, these are the entropy coefficients for shifted and non shifted distributions of the Amoroso family. Graphics of dependence of entropy coefficients of non-symmetrical distributions show that distributions well-known are distinguish at small of the shapes parameters. Also it is illustrated for parameters of the form more than 2 that it is preferable to use the entropy coefficients for the unshifted distributions.The material contains also information measures for the well-known logarithmic normal distribution which is a limiting case of distribution Amorozo.

scholarly journals Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

2021 ◽  
Author(s):  
Irina Alexandrova ◽  
Alexander Ivanov ◽  
Dmitri Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Initial Distribution ◽  
Size Distribution Function ◽  
Superheated Liquid ◽  
Balance Equations ◽  
The Laplace Transform ◽  
And Shifts ◽  
Initial Distribution Function

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering-Volmer and Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.

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