| Title: | Estimates, Plots and Evaluates Leaf Angle Distribution Functions, Calculates Extinction Coefficients |
|---|---|
| Description: | Leaf angle distribution is described by a number of functions (e.g. ellipsoidal, Beta and rotated ellipsoidal). The parameters of leaf angle distributions functions are estimated through different empirical relationship. This package includes estimations of parameters of different leaf angle distribution function, plots and evaluates leaf angle distribution functions, calculates extinction coefficients given leaf angle distribution. Reference: Wang(2007)<doi:10.1016/j.agrformet.2006.12.003>. |
| Authors: | Wei-Min Wang <[email protected]> |
| Maintainer: | Wei-Min Wang <[email protected]> |
| License: | GPL |
| Version: | 1.0 |
| Built: | 2025-03-03 04:32:41 UTC |
| Source: | https://github.com/cran/RLeafAngle |
Compute the Beta distribution of leaf zenith angle.
BetaDis(meu, neu)BetaDis(meu, neu)
meu |
One of the parameters for Beta function. |
neu |
One of the parameters for Beta function. |
The Beta distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-BetaDis(1.616,2.188) plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-BetaDis(1.616,2.188) plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
Compute the parameter of Beta function given leaf angle distribution mearuements.
computeBeta(LeafAngles)computeBeta(LeafAngles)
LeafAngles |
The measurements of leaf angle distribution. |
The two parameters of Beta function given leaf angle distribution mearuements.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
data(Pisek) computeBeta(Pisek[[2]])data(Pisek) computeBeta(Pisek[[2]])
Compute the mean projection of unit leaf area on the plane perpendicular to beam direction, namely, G parameter.
computeG(LeafAngleZ, FractionZ, LeafAngleA, FractionA, theta, alpha)computeG(LeafAngleZ, FractionZ, LeafAngleA, FractionA, theta, alpha)
LeafAngleZ |
The center angles list of leaf zenith angle intervals. |
FractionZ |
The leaf area fraction list given leaf zenith angle intervals list. |
LeafAngleA |
The center angles list of leaf azimuth angle intervals. |
FractionA |
The leaf area fraction list given leaf azimuth angle intervals list. |
theta |
The zenith angle of beam direction. |
alpha |
The azimuth angle of beam direction. |
The mean projection of unit leaf area on the plane perpendicular to beam direction, namely, G value.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
angleZ<-c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5) angleA<-c(10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350) sADis<-sysAziDis() sZDis<-sphericalDis() for(solarZenith in 10:80) { print(computeG(angleZ,sZDis,angleA,sADis,solarZenith,40)) }angleZ<-c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5) angleA<-c(10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350) sADis<-sysAziDis() sZDis<-sphericalDis() for(solarZenith in 10:80) { print(computeG(angleZ,sZDis,angleA,sADis,solarZenith,40)) }
Compute the G value given lamda (the parameter of ellipsoidal function) and beam direction.
computeGEllip(lambda, theta)computeGEllip(lambda, theta)
lambda |
The parameter of ellipsoidal function given leaf angle distribution mearuements. |
theta |
The zenith angle of beam direction. |
The G value.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
computeGEllip(1.0, 30)computeGEllip(1.0, 30)
Compute the parameter of ellipsoidal function given leaf angle distribution mearuements.
computeLambda(LeafAngles)computeLambda(LeafAngles)
LeafAngles |
The measurements of leaf angle distribution. |
The parameter of ellipsoidal function given leaf angle distribution mearuements.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
data(Pisek) computeLambda(Pisek[[2]])data(Pisek) computeLambda(Pisek[[2]])
Compute the parameter of rotated-ellipsoidal function given leaf angle distribution mearuements.
computeLambdaR(LeafAngles)computeLambdaR(LeafAngles)
LeafAngles |
The measurements of leaf angle distribution. |
The parameter of ellipsoidal function given leaf angle distribution mearuements.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
data(Pisek) computeLambdaR(Pisek[[2]])data(Pisek) computeLambdaR(Pisek[[2]])
Compute the fraction of sunlit folige given solar position, LAI and G value with the assumption of the symmetric distribution of leaf azimuth angle.
computeSunlit(Theta, G, LAI)computeSunlit(Theta, G, LAI)
Theta |
Solar zenith angle. |
G |
The G value, namely the projection of foliage area. |
LAI |
Leaf area index. |
The fraction of sunlit foliage.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
computeSunlit(30, 0.5, 2.0)computeSunlit(30, 0.5, 2.0)
Compute the parameter of Verhoef's leaf angle distribution given leaf angle distribution mearuements.
computeTrig(LeafAngles)computeTrig(LeafAngles)
LeafAngles |
The measurements of leaf angle distribution. |
The two parameters of Verhoef's leaf angle distribution.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
data(Pisek) computeTrig(Pisek[[2]])data(Pisek) computeTrig(Pisek[[2]])
Compute the ellipsoidal distribution of leaf zenith angle.
ellipsoidalDis(lambda)ellipsoidalDis(lambda)
lambda |
The parameter of ellipsoidal function. |
The ellipsoidal distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-ellipsoidalDis(1) plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-ellipsoidalDis(1) plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
Compute the rotated ellipsoidal distribution of leaf zenith angle.
ellipsoidalRDis(lambdaR)ellipsoidalRDis(lambdaR)
lambdaR |
The parameter of rotated-ellipsoidal function. |
The rotated ellipsoidal distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-ellipsoidalRDis(1) plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-ellipsoidalRDis(1) plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
Estimate the parameters of Beta distribution given leaf angle measurements.
estBeta(LeafAngles)estBeta(LeafAngles)
LeafAngles |
The leaf angle measurements. |
the parameters of Beta distribution.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
angleZ<-c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5) angleA<-c(10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350) sADis<-sysAziDis() sZDis<-sphericalDis() for(solarZenith in 10:80) { print(computeG(angleZ,sZDis,angleA,sADis,solarZenith,40)) }angleZ<-c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5) angleA<-c(10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350) sADis<-sysAziDis() sZDis<-sphericalDis() for(solarZenith in 10:80) { print(computeG(angleZ,sZDis,angleA,sADis,solarZenith,40)) }
Compute the extremophile distribution of leaf zenith angle.
extremophileDis()extremophileDis()
The extremophile distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-extremophileDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-extremophileDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
Leaf angle distribution data measured in two sites of Ku-ringgai Chase National Park, Sydney, Australia and provided by Dr. D.S. Falster of Macquarie University, Australia
data(Falster)data(Falster)
A list with 39 arrays where one array for tree specy name and 38 array of leaf angle distribution for each specy.
Leaf angle distribution measurements provided by D.S. Falster
W.-M. Wang (wmwangATgmail.com)
Falster, D. and Westoby, M., 2003. Leaf size and angle vary widely across species: what consequences for light interception? New Phytol.158, 509-525.
data(Falster) Falster[1]data(Falster) Falster[1]
Compute the fraction leaf area given leaf angle intervals (in degree) and the parameters of Beta function.
interBeta(AngleLower, AngleUpper, meu, neu)interBeta(AngleLower, AngleUpper, meu, neu)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
meu |
One of the parameters for Beta function. |
neu |
One of the parameters for Beta function. |
Compute the fraction leaf area of Beta function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interBeta(40,50,1.616,2.188)interBeta(40,50,1.616,2.188)
Compute the fraction leaf area given leaf angle intervals (in degree) and the parameters of ellipsoidal function.
interEllip(AngleLower, AngleUpper, lambda)interEllip(AngleLower, AngleUpper, lambda)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
lambda |
The parameter of ellipsoidal function. |
Compute the fraction leaf area of ellipsoidal function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interEllip(40,50,1.1)interEllip(40,50,1.1)
Compute the fraction leaf area given leaf angle intervals (in degree) and the parameters of rotated-ellipsoidal function.
interEllipR(AngleLower, AngleUpper, lambdaR)interEllipR(AngleLower, AngleUpper, lambdaR)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
lambdaR |
The parameter of rotated-ellipsoidal function. |
Compute the fraction leaf area of rotated-ellipsoidal function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interEllipR(40,50,1.1)interEllipR(40,50,1.1)
Compute the fraction leaf area of Erectophile distribution given leaf angle intervals (in degree).
interErectophile(AngleLower, AngleUpper)interErectophile(AngleLower, AngleUpper)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
Compute the fraction leaf area of Erectophile function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interErectophile(40,50)interErectophile(40,50)
Compute the fraction leaf area of Extremophile distribution given leaf angle intervals (in degree).
interExtremophile(AngleLower, AngleUpper)interExtremophile(AngleLower, AngleUpper)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
Compute the fraction leaf area of Extremophile function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interExtremophile(40,50)interExtremophile(40,50)
Compute the fraction leaf area of Plagiophile distribution given leaf angle intervals (in degree).
interPlagiophile(AngleLower, AngleUpper)interPlagiophile(AngleLower, AngleUpper)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
Compute the fraction leaf area of Plagiophile function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interPlagiophile(40,50)interPlagiophile(40,50)
Compute the fraction leaf area of Planophile distribution given leaf angle intervals (in degree).
interPlanophile(AngleLower, AngleUpper)interPlanophile(AngleLower, AngleUpper)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
Compute the fraction leaf area of Planophile function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interPlanophile(40,50)interPlanophile(40,50)
Compute the fraction leaf area of Spherical function given leaf angle intervals (in degree).
interSpherical(AngleLower, AngleUpper)interSpherical(AngleLower, AngleUpper)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
Compute the fraction leaf area of Spherical function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interSpherical(40,50)interSpherical(40,50)
Compute the fraction leaf area of Uniform distribution given leaf angle intervals (in degree).
interUniform(AngleLower, AngleUpper)interUniform(AngleLower, AngleUpper)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
Compute the fraction leaf area of Uniform function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
interUniform(40,50)interUniform(40,50)
Compute the fraction leaf area given leaf angle intervals (in degree) and the parameters of Verhoef's leaf angle distribution function.
intervalTrig(AngleLower, AngleUpper, ap, bp)intervalTrig(AngleLower, AngleUpper, ap, bp)
AngleLower |
The lower limit of leaf angle intervals in degree. |
AngleUpper |
The upper limit of leaf angle intervals in degree. |
ap |
One of the parameters of Verhoef's leaf angle distribution function. |
bp |
One of the parameters of Verhoef's leaf angle distribution function. |
Compute the fraction leaf area of Verhoef's leaf angle distribution function.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
intervalTrig(40,50, -0.325, -0.173)intervalTrig(40,50, -0.325, -0.173)
Retrieve the density of leaf area given leaf angle measurements.
LADdensity(LeafAngles)LADdensity(LeafAngles)
LeafAngles |
The measurements of leaf angle distribution. |
Leaf area density given leaf angle intervals (0,10,20,30,40,50,60,70,80,90).
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
data(Falster) LADdensity(Falster[[2]])data(Falster) LADdensity(Falster[[2]])
Leaf angle distribution data provided by Dr. Tartu Observatory, Department of Remote Sensing, Estonia
data(Pisek)data(Pisek)
A list with 55 arrays where one array for tree specy name and 54 array of leaf angle distribution for each specy.
Leaf angle distribution measurements provided by Jan Pisek
W.-M. Wang (wmwangATgmail.com)
Pisek, Jan, et al. "Is the spherical leaf inclination angle distribution a valid assumption for temperate and boreal broadleaf tree species?." Agricultural & Forest Meteorology 169.3(2013):186-194.
data(Pisek) Pisek[1]data(Pisek) Pisek[1]
Compute the plagiophile distribution of leaf zenith angle.
plagiophileDis()plagiophileDis()
The plagiophile distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-plagiophileDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-plagiophileDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
Compute the planophile distribution of leaf zenith angle.
planophileDis()planophileDis()
The planophile distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-planophileDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-planophileDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
Plot the density of leaf area given leaf angle measurements.
plotdensity(LeafAngles, main = "Leaf angle distribution", type = "l", pch = 20)plotdensity(LeafAngles, main = "Leaf angle distribution", type = "l", pch = 20)
LeafAngles |
The measurements of leaf angle distribution. |
main |
An overall title for the plot. |
type |
The type of plot. |
pch |
The symbol of plot. |
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
data(Pisek) plotdensity(Pisek[[2]])data(Pisek) plotdensity(Pisek[[2]])
Retrieve the density of leaf area given leaf angle measurements.
selectClassic(LeafAngles)selectClassic(LeafAngles)
LeafAngles |
The measurements of leaf angle distribution. |
The classic leaf angle distribution type
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
data(Falster) selectClassic(Falster[[2]])data(Falster) selectClassic(Falster[[2]])
Compute the spherical distribution of leaf zenith angle.
sphericalDis()sphericalDis()
The spherical distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-sphericalDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-sphericalDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
Compute the symmetric distribution of leaf azimuth angle.
sysAziDis()sysAziDis()
The symmetric distribution of leaf azimuth angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
aDis<-sysAziDis() plot(c(10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350), aDis, xlab=expression(Leaf~azimuth~angle~~(""^"o")), ylab="Leaf area freqency")aDis<-sysAziDis() plot(c(10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350), aDis, xlab=expression(Leaf~azimuth~angle~~(""^"o")), ylab="Leaf area freqency")
Compute the uniform distribution of leaf zenith angle.
uniformDis()uniformDis()
The uniform distribution of leaf zenith angle.
Wei-Min Wang (wmwang AT gmail.com)
Wang, W. M., Li, Z. L., & Su, H. B. (2007). Comparison of leaf angle distribution functions: effects on extinction coefficient and fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
sDis<-sphericalDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")sDis<-sphericalDis() plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis, xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")