linesmodel {ProbForecastGOP} | R Documentation |
Computes the value of the parametric variogram model at given distances.
linesmodel(distance, variog.model="exponential", param)
distance |
numeric vector of distances. |
variog.model |
character string giving the name of the parametric variogram model. Implemented models are: exponential, spherical, gauss, gencauchy and matern. |
param |
numeric vector containing the values of the variogram parameters.
If the parametric model specified is exponential, spherical or gauss, param is a vector of length 3 containing, in order: the nugget effect (non negative number), the variance and the range (both positive numbers). If the parametric model specified is gencauchy, param is a vector of length 5 whose entries are, in order: the nugget effect (non negative number), the variance, the range (both positive numbers), the smoothness parameter a (a number in (0,2]), and the long-range parameter b (a positive number). If the parametric model specified is matern, param is a vector of length 4 whose entries are, in order: the nugget effect (a non-negative number), the variance, the range, and the smoothness parameter a (all three, positive numbers). |
The function calculates the value of the parametric variogram at given distances using the following equations:
- If the parametric model is exponential
gamma(d) = rho+σ^{2} cdot (1-exp(- frac{d}{r}))
where rho is the nugget effect, σ^2 is the variance, r is the range, and d is the distance.
- If the parametric model is spherical
gamma(d) = rho+σ^{2} cdot (frac{3}{2}cdotfrac{d}{r}-frac{1}{2}cdot frac{d^3}{r^3})
where rho is the nugget effect, σ^2 is the variance, r is the range, and d is the distance.
- If the parametric model is gauss
gamma(d) = rho+σ^{2} cdot (1-exp(- frac{d^2}{r^2} ))
where rho is the nugget effect, σ^2 is the variance, r is the range, and d is the distance.
- If the parametric model is gencauchy
gamma(d) = rho+σ^{2} cdot (1-(1+frac{d^a}{r^a})^{- frac{b}{a}})
where rho is the nugget effect, σ^2 is the variance, r is the range, and d is the distance.
- If the parametric model is matern
gamma(d) = rho+σ^{2} cdot (1-(frac{2^{1-a}}{Γ(a)}cdot frac{d^a}{r^a} cdot K_{a}(frac{d}{r}))
where rho is the nugget effect, σ^2 is the variance, r is the range, and d is the distance.
The function returns a numeric vector with the values of the parametric variogram model at the bin midpoints.
Gel, Y., Raftery, A. E., Gneiting, T., Berrocal, V. J. veronica@stat.washington.edu.
Gel, Y., Raftery, A. E., Gneiting, T. (2004). Calibrated probabilistic mesoscale weather field forecasting: The Geostatistical Output Perturbation (GOP) method (with discussion). Journal of the American Statistical Association, Vol. 99 (467), 575–583.
Cressie, N. A. C. (1993). Statistics for Spatial Data (revised ed.). Wiley: New York.
Gneiting, T., Schlather, M. (2004). Stochastic models that separate fractal dimension and the Hurst effect. SIAM Review 46, 269–282.
Stein, M. L. (1999). Interpolation of Spatial Data - Some Theory for Kriging. Springer-Verlag: New York.
## Loading data data(slp) day <- slp$date.obs id <- slp$id.stat coord1 <- slp$lon.stat coord2 <- slp$lat.stat obs <- slp$obs forecast <- slp$forecast ## Computing empirical variogram variogram <- Emp.variog(day=day,obs=obs,forecast=forecast,id=id,coord1=coord1, coord2=coord2,cut.points=NULL,max.dist=NULL,nbins=NULL) ## Estimating variogram parameters ## Without specifying initial values for the parameters param.variog <- Variog.fit(emp.variog=variogram,variog.model="exponential",max.dist.fit=NULL, init.val=NULL,fix.nugget=FALSE) ## Plotting the empirical variogram with the estimated parametric variogram superimposed plot(variogram$bin.midpoints,variogram$empir.variog,xlab="Distance",ylab="Semi-variance") lines(variogram$bin.midpoints,linesmodel(distance=variogram$bin.midpoints,variog.model="exponential",param=c(param.variog$nugget, param.variog$variance,param.variog$range)))