SSN (version 1.1.7)

Torgegram: Empirical Semivariogram Based on Hydrologic Distance and flow connection

Description

Torgegram computes the empirical semivariogram from the data based on hydrologic distance. The results are presented separately for flow-connected and flow-unconnected sites.

Usage

Torgegram(object, ResponseName, maxlag = NULL, nlag = 6,
	inc = 0, nlagcutoff = 15, EmpVarMeth = "MethMoment")

Arguments

object

an object of class SpatialStreamNetwork-class or influenceSSN-class

ResponseName

a response or residual variable name in the data.frame of observed data in the SpatialStreamNetwork or influenceSSN object.

maxlag

the maximum lag distance to consider when binning pairs of locations by the hydrologic distance that separates them. The default is the median distance between all pairs of locations.

nlag

the number of lag bins to create. The distance between endpoints that define a bin will have equal lengths for all bins. The bin sizes are then determined from the minimum lag in the data, and the specification of maxlag.

inc

the bin distance between endpoints. It is possible to specify the bin distance rather than nlag. In this case, the number of bins is determined by the bin distance and the distance between the mininum and maximum (maxlag) lag in the data

nlagcutoff

the minimum number of pairs needed to estimate the semivariance for a bin. If the sample sizes is less than this value, the semivariance for the bin is not calculated.

EmpVarMeth

method for computing semivariances. The default is "MethMoment", the classical method of moments, which is just the average difference-squared within bin classes. "Covariance" computes covariance rather than semivariance, but may be more biased because it subtracts off the simple mean of the response variable. "RobustMedian" and "RobustMean" are robust estimators proposed by Cressie and Hawkins (1980). If v is a vector of all pairwise square-roots of absolute differences within a bin class, then "RobustMedian" computes median(v)^4/.457. "RobustMean" computes mean(v)^4/(.457 + .494/length(v)).

Value

A list of six vectors describing the semivariance values for each bin and the hydrologic distances and number of pairs used to estimate those values. These data are presented separately for flow-connected and flow-unconnected sites.

distance.connect

the mean hydrologic distance separating pairs of flow-connected sites used to calculate the semivariance for each bin

gam.connect

the mean semivariance for flow-connected sites in each bin

np.connect

the number of pairs of flow-connected sites used to calculate the semivariance for each bin

distance.unconnect

the mean hydrologic distance separating pairs of flow-connected sites used to calculate the semivariance for each bin

gam.unconnect

the mean semivariance for flow-connected sites in each bin

np.unconnect

the number of pairs of flow-connected sites used to calculate the semivariance for each bin

Details

The Torgegram function creates a list of hydrologic distances and empirical semivariogram values, along with number of pairs of points in each bin, for both flow-connected and flow-unconnected sites. Flow-connected locations lie on the same stream network (share a common downstream junction) and water flows from one location to the other. Flow-unconnected locations also lie on the same stream network, but do not share flow. The output is of class Torgegram.

See Also

A generic plot operates on the object created here.

Examples

	library(SSN)
	data(mf04p)
	#make sure mf04p has the correct path, will vary for each users installation
	mf04p@path <- system.file("lsndata/MiddleFork04.ssn", package = "SSN")

	ESVF <- Torgegram(mf04p, "Summer_mn")
	plot(ESVF)

	ESVF <- Torgegram(mf04p, "Summer_mn", maxlag = 20000, nlag = 10)
	plot(ESVF, sp.relationship = "fc", col = "red", main = "Flow-connected Torgegram")
	plot(ESVF, sp.relationship = "fu", min.cex = .4, max.cex = 8,
		   main = "Flow-unconnected Torgegram")
	plot(ESVF, min.cex = .4, max.cex = 8, col = c("darkgray", "black"),
		   main = "", xlab = "Stream Distance (m)")

	# generate and plot an empirical semivariogram based on model residuals
	data(modelFits)
	#make sure fitSp has the correct path, will vary for each users installation
	fitSp$ssn.object@path <- system.file("lsndata/MiddleFork04.ssn", package = "SSN")
	resids <- residuals(fitSp)
	names(resids$ssn.object)
	ESVF <- Torgegram(resids, "_resid_", maxlag = 20000,
		  nlag = 10)
	plot(ESVF, xlim = c(0,10000))