The distribution of foliage density with foliage angle estimated from inclined point quadrat observations

1965 ◽  
Vol 13 (2) ◽  
pp. 357 ◽  
Author(s):  
JR Philip
Keyword(s):  
Integral Equation ◽  
Standard Deviation ◽  
Leaf Angle ◽  
Frequency Data ◽  
Sampling Errors ◽  
Contact Frequency ◽  
Foliage Density ◽  
The Mean ◽  
Point Quadrat ◽  
The Given

Estimation of the distribution of foliage density with foliage angle from contact frequency data for a number of quadrat inclinations involves solution of a Fredholm integral equation of the first kind. The kernel is known from the work of Warren Wilson and Reeves, and the observed contact frequencies constitute the given function f(β). The solution is g(α), the foliage angle density function. f (β) is known at only a finite number of points, and each value contains inevitable sampling errors. The structure of the solution is such that g(β) is consequently subject to serious errors. A technique involving smoothing of the data is developed with the aim of minimizing this difficulty. The technique is critically discussed and applied to observations of Warren Wilson on lucerne leaves. The analysis indicates that the distribution of leaf angle is roughly symmetrical about the mean angle, with a standard deviation of about 15°.

scholarly journals A low-cost acoustic permeameter

2017 ◽  
Vol 6 (1) ◽  
pp. 199-207 ◽  
Author(s):  
Stephen A. Drake ◽  
John S. Selker ◽  
Chad W. Higgins
Keyword(s):  
Standard Deviation ◽  
Relative Error ◽  
Low Cost ◽  
Low Frequency ◽  
Environmental Noise ◽  
Intrinsic Permeability ◽  
Sampling Errors ◽  
Resonance Frequencies ◽  
The Mean ◽  
Frequency Approximation

Abstract. Intrinsic permeability is an important parameter that regulates air exchange through porous media such as snow. Standard methods of measuring snow permeability are inconvenient to perform outdoors, are fraught with sampling errors, and require specialized equipment, while bringing intact samples back to the laboratory is also challenging. To address these issues, we designed, built, and tested a low-cost acoustic permeameter that allows computation of volume-averaged intrinsic permeability for a homogenous medium. In this paper, we validate acoustically derived permeability of homogenous, reticulated foam samples by comparison with results derived using a standard flow-through permeameter. Acoustic permeameter elements were designed for use in snow, but the measurement methods are not snow-specific. The electronic components – consisting of a signal generator, amplifier, speaker, microphone, and oscilloscope – are inexpensive and easily obtainable. The system is suitable for outdoor use when it is not precipitating, but the electrical components require protection from the elements in inclement weather. The permeameter can be operated with a microphone either internally mounted or buried a known depth in the medium. The calibration method depends on choice of microphone positioning. For an externally located microphone, calibration was based on a low-frequency approximation applied at 500 Hz that provided an estimate of both intrinsic permeability and tortuosity. The low-frequency approximation that we used is valid up to 2 kHz, but we chose 500 Hz because data reproducibility was maximized at this frequency. For an internally mounted microphone, calibration was based on attenuation at 50 Hz and returned only intrinsic permeability. We found that 50 Hz corresponded to a wavelength that minimized resonance frequencies in the acoustic tube and was also within the response limitations of the microphone. We used reticulated foam of known permeability (ranging from 2 × 10−7 to 3 × 10−9 m2) and estimated tortuosity of 1.05 to validate both methods. For the externally mounted microphone the mean normalized standard deviation was 6 % for permeability and 2 % for tortuosity. The mean relative error from known measurements was 17 % for permeability and 2 % for tortuosity. For the internally mounted microphone the mean normalized standard deviation for permeability was 10 % and the relative error was also 10 %. Permeability determination for an externally mounted microphone is less sensitive to environmental noise than is the internally mounted microphone and is therefore the recommended method. The approximation using the internally mounted microphone was developed as an alternative for circumstances in which placing the microphone in the medium was not feasible. Environmental noise degrades precision of both methods and is recognizable as increased scatter for replicate data points.

A formula for average foliage density

1967 ◽  
Vol 15 (1) ◽  
pp. 141 ◽  
Author(s):  
JB Miller
Keyword(s):  
Fourier Analysis ◽  
Density Function ◽  
Frequency Function ◽  
Contact Frequency ◽  
Foliage Density ◽  
Point Quadrat

Point quadrat readings, taken to assess density of foliage in a plant, determine a contact frequency function f. A formulais given expressing the average foliage density of the plant in terms of f. This is compared with the work of Philip, who determined from f using a foliage angle density function g and an approximate Fourier analysis.

scholarly journals A low-cost acoustic permeameter

2016 ◽  
Author(s):  
Stephen A. Drake ◽  
John S. Selker ◽  
Chad W. Higgins
Keyword(s):  
Standard Deviation ◽  
Relative Error ◽  
Low Cost ◽  
Low Frequency ◽  
Environmental Noise ◽  
Intrinsic Permeability ◽  
Sampling Errors ◽  
Resonance Frequencies ◽  
The Mean ◽  
Frequency Approximation

Abstract. Intrinsic permeability is an important parameter that regulates air exchange through porous media such as snow. Standard methods of measuring snow permeability are inconvenient to perform outdoors, fraught with sampling errors and require specialized equipment, while bringing intact samples back to the laboratory is also challenging. To address these issues, we designed, built, and tested a low-cost acoustic permeameter that allows computation of volume-averaged intrinsic permeability for a homogenous medium. Permeameter elements were designed for use in snow but the measurement methods are not snow-specific. The electronic components, consisting of a signal generator, amplifier, speaker, microphone and oscilloscope, are inexpensive and easily obtainable. The system is suitable for outdoor use when it is not precipitating but the electrical components require protection from the elements in inclement weather. The permeameter can be operated with a microphone either internally mounted or buried a known depth in the medium. The calibration method depends on choice of microphone positioning. For an externally located microphone, calibration was based on a low-frequency approximation applied at 500 Hz that provided an estimate of both intrinsic permeability and tortuosity. The low-frequency approximation that we used is valid up to 2 kHz but we chose 500 Hz because data reproducibility was maximized at this frequency. For an internally mounted microphone, calibration was based on attenuation at 50 Hz and returned only intrinsic permeability. We found that 50 Hz corresponded to a wavelength that minimized resonance frequencies in the acoustic tube and was also within the response limitations of the microphone. We used reticulated foam of known permeability (ranging from 2 × 10−7 m2 to 3 × 10−9 m2) and estimated tortuosity of 1.05 to validate both methods. For the externally mounted microphone the mean normalized standard deviation was 6 % for permeability and 2 % for tortuosity. The mean relative error from known measurements was 17 % for permeability and 2 % for tortuosity. For the internally mounted microphone the mean normalized standard deviation for permeability was 10 % and the relative error was also 10 %. Permeability determination for an externally mounted microphone is less sensitive to environmental noise than is the internally mounted microphone and is therefore the recommended method. The approximation using the internally mounted microphone was developed as an alternative for circumstances in which placing the microphone in the medium was not feasible. Environmental noise degrades precision of both methods and is recognizable as increased scatter for replicate data points.

scholarly journals THE STUDY OF THE DEPENDENCE OF SIZES OF MEASURED MICROSCOPIC OBJECTS AT THE POSITION OF THE SLICE PLANE

2019 ◽  
Vol 27 (4) ◽  
pp. 55-60
Author(s):  
A. E. Lun'kov ◽  
U. A. Gladilin ◽  
K. E. Ibragimova
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Cross Sections ◽  
Mean Value ◽  
Distribution Functions ◽  
Distribution Law ◽  
The Mean ◽  
The Cross ◽  
The Difference ◽  
The Given

For microscopic objects in the form of spheres of different radii have been calculated the functions of distribution of the cross sections radii, taking into account the dependence on the position of the plane of the slice. Taking into account this dependence, the distribution functions of the cross sections radii of the spheres whose radii were given by the normal distribution law with the variation of its parameters were calculated. It is found that the difference between the given distribution function of the radii of spheres and the distribution function of their sections in the plane of the slice depends on the ratio of the standard deviation to the mean value of the radii. Depending on this relation, two simple algorithms are proposed to reconstruct the distribution function of the radii of objects by the distribution function of the radii of their sections. It is shown that these algorithms can be used to correct the experimental curve of the size distribution of micro-objects in the form of ellipsoid.

The use of pont quadrats, with specieal reference to stem-like organs.

1966 ◽  
Vol 14 (1) ◽  
pp. 105 ◽  
Author(s):  
JR Philip
Keyword(s):  
Integral Equations ◽  
Sampling Error ◽  
Practical Implementation ◽  
Relative Standard Error ◽  
Sampling Errors ◽  
Relative Variance ◽  
Axial Angle ◽  
Relative Standard ◽  
Contact Frequency ◽  
Foliage Density

Refinement of point quadrat techniques leads to three integral equations. (A) relates the variation of contact frequency with quadrat angle, f(β), to the distribution of foliage deiisity with foliage angle, &(α) (Philip 1965a). (B), app!icab!e to stems or stem-like organs, relates f (β) to the distribution of foliage (stem surface) density with axial angle h(γ); and (C) connects g(α) and h(γ). A trio of integral equations analogous to (A), (B), (C) holds for any class of axisymmetrical organs whose members are geometrically similar. The utility nf these equations in practice depends on the differential order of their solutions: the higher the order, the greater the amplification of errors. The order is 2½ for (A) and 3 for (B). Reliable results on the distribution of stem axial angles thus require very accurate data (and hence a great deal of labour). The kernels entering (A), (B), and (C) are basic, not only to "integral equation" studies of the problem, but also to less ambitious approaches. Data on these kernels are therefore presented. They are used to illustrate the inherent difficulties in estimating h(γ). Simple methods are developed for estimating foliage density for stems from quadrat observations at one, two, or three angles. These are appreciably more accurate than the similar formulae (for foliage in general) developed by Warren Wilson (1960, 1963). The reason for this is indicated. The latter sections of the paper deal with some statistical aspects of the use of point quadrats. For a given "relative variance" the accuracy of any f(β) observation depends solely on the number of quadrat contacts, N. The relative variance is typically of order unity, and it follows that the relative standard error of f(β) is of order N-½. The accuracy of f(β) observations may therefore be determined a priori by fixing minimum contact numbers rather than by fixing quadrat numbers. Practical implementation of procedures of this type is discussed. Optimal strategies for simple estimates of foliage density are considered, the criterion being maximum accuracy for a given quantity of observational labour. Accuracy may be improved markedly by proper distribution of contact numbers amongst the quadrat angles. The optimal distribution is indicated. A basis for the choice between one-, two-, and three-angle formulae is developed. The accuracy of alternative formulae depends on the total variance arising from (i) sampling error in the observations, and (ii) intrinsic error in the formula. The method is arbitrary in the sense that a ruie is required to distinguish between the labour needed to observe a fixed total number of contacts at one, two, and three quadrat angles. The approach is illustrated by applying it to Warren Wilson's formulae. It may be used also for the corresponding "stem" formulae and for formulae involving f(0°) and f(90°), which are better adapted to give estimates of "mean" foliage or axial angle as well. The errors in estimates of "mean" foliage and axial angles due to sampling errors in f(0°) and f(90°) are examined. The determination of "mean" axial angle (even if the assumption of a uniform angle were valid) is inherently rather inaccurate, especially for small values of the angle.

At Least One Standard Deviation Above the Mean

1969 ◽  
Vol 14 (9) ◽  
pp. 470-471
Author(s):  
M. DAVID MERRILL
Keyword(s):  
Standard Deviation ◽  
The Mean

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

PENGARUH PENDIDIKAN KESEHATAN REPRODUKSI PADA PEER GROUP (TEMAN SEBAYA) TERHADAP PENGETAHUAN DAN PERSEPSI REMAJA TENTANG PENDEWASAAN USIA PERKAWINAN DI SMA NEGERI 1 KECAMATAN NAMORAMBE KAB. DELI SERDANG 2018

2020 ◽  
Vol 1 (2) ◽  
pp. 56-66
Author(s):  
Irma Linda
Keyword(s):  
Standard Deviation ◽  
Health Education ◽  
Reproductive Health ◽  
Peer Group ◽  
Peer Groups ◽  
A Value ◽  
Significant Difference ◽  
Reproductive Health Education ◽  
The Mean ◽  
Adolescent Perceptions

Background: Early marriages are at high risk of marital failure, poor family quality, young pregnancies at risk of maternal death, and the risk of being mentally ill to foster marriage and be responsible parents. Objective: To determine the effect of reproductive health education on peer groups (peers) on the knowledge and perceptions of adolescents about marriage age maturity. Method: This research uses the Quasi experimental method with One group pre and post test design, conducted from May to September 2018. The statistical analysis used in this study is a paired T test with a confidence level of 95% (α = 0, 05). Results: There is an average difference in the mean value of adolescent knowledge between the first and second measurements is 0.50 with a standard deviation of 1.922. The mean difference in mean scores of adolescent perceptions between the first and second measurements was 4.42 with a standard deviation of 9.611. Conclusion: There is a significant difference between adolescent knowledge on the pretest and posttest measurements with a value of P = 0.002, and there is a significant difference between adolescent perceptions on the pretest and posttest measurements with a value of p = 0.001. Increasing the number of facilities and facilities related to reproductive health education by peer groups (peers) in adolescents is carried out on an ongoing basis at school, in collaboration with local health workers as prevention of risky pregnancy.

Some Explicit Results for the Mean Spherical Approximation for Mixtures of Yukawa Fluids

2008 ◽  
Vol 73 (3) ◽  
pp. 424-438 ◽  
Author(s):  
Douglas J. Henderson ◽  
Osvaldo H. Scalise
Keyword(s):  
Integral Equation ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Inverse Temperature ◽  
Temperature Expansion ◽  
Yukawa Fluid ◽  
The Mean ◽  
Full Solution ◽  
Insight Into ◽  
Reasonable Model

The mean spherical approximation (MSA) is of interest because it produces an integral equation that yields useful analytical results for a number of fluids. One such case is the Yukawa fluid, which is a reasonable model for a simple fluid. The original MSA solution for this fluid, due to Waisman, is analytic but not explicit. Ginoza has simplified this solution. However, Ginoza's result is not quite explicit. Some years ago, Henderson, Blum, and Noworyta obtained explicit results for the thermodynamic functions of a single-component Yukawa fluid that have proven useful. They expanded Ginoza's result in an inverse-temperature expansion. Even when this expansion is truncated at fifth, or even lower, order, this expansion is nearly as accurate as the full solution and provides insight into the form of the higher-order coefficients in this expansion. In this paper Ginoza's implicit result for the case of a rather special mixture of Yukawa fluids is considered. Explicit results are obtained, again using an inverse-temperature expansion. Numerical results are given for the coefficients in this expansion. Some thoughts concerning the generalization of these results to a general mixture of Yukawa fluids are presented.

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