ltsk (version 1.0.1)

lk: local space kriging

Description

This function implements ANN neighbor search, automatic variogram estimation and ordinary Kriging to predict spatial data at multiple query locations.

Usage

lk(query, obs, th, xcoord = "x", ycoord = "y", zcoord = "z",  vlen = 15)

Arguments

query

data frame containing query spatial locations

obs

data frame containing spatial locations and observed data

th

a priori chosen distance thresholds for neighbor search

xcoord

field name for x coordinate in both query and obs

ycoord

field name for y coordinate in both query and obs

zcoord

field name for data in obs

vlen

number of bins to compute local spatial variogram

Value

• Kriging mean and standard error and quality flags.ll{ krig predictive mean sigma predictive standard error Hs estimated range nugget estimated nugget psill estimated partial sill model variogram model } where the variogram model are ll{ 1 Spherical 2 Gaussian 3 Exponential 4 Matern }

Details

With the development of GIS and remote sensing, data sets are available over large spatial domain. Ordinary kriging which involves the O(n^3) matrix operation, becomes computationally in-feasible for prediction. In addition to the computational issues, the stationarity assumption underlying ordinary kriging is usually violated for environmental data over large domain.

In addition to Bayesian spatial modeling, local method offers a computational efficient approach for spatial prediction. This function implements a local Kriging method for spatial prediction from large data sets. At each location where prediction is required (termed as query point), a plausible and concervative distance threshold is used to select neighboring locations with observed spatial data. A local variogram is estimated to enable ordinary kriging within this neighborhood.

Implementation of the local Kriging requires specifying a distance threshold (th). It is an upper bound within which spatial auto-correlation is believed to exist. The distance threshold may be obtained from variogram estimates plus knowledge of the underlying spatial process. For the given threhold, ANN tree is used to efficiently identify neighbors.

Remote sensed data are dense within a small distance. Dense data lead to computational issue for variogram estimation and kriging even for local methods. In senarios when the number of neighbors exceeds a user-specified upper limit (Large), neighbors are sub-sampled in a spatially balanced way to reduce the neighborhood size. Sub-sampling leads to improved computational efficiency without loss of predictive accuracy due to the strong spatial autocorrelation within short distances.

In remote sensed applications, cloud cover could lead to missing data. This poses challenges in the subsequent variogram estimation and Kriging. Without further knowledge of the spatial process, query points within the area with sparse data are excluded. This function does not perform local kriging when the neighborhood contains less than five distinct spatial locations with observed data in the neighborhood. But we recommend at least 20 data points for varioram estimation and Kriging.

Local empirical variogram is calculated using method of moments within the neighborhood. Four variogram models: Gaussian, exponential, spherical and Matern are fit to the empirical variogram. The range parameter is estimated from the first distance lag where the empirical variogram exceeds 80 Ordinary kriging is used to predict the spatial process at each query point. The estimated range parameter is used to reduce the neighborhood. Only initial neighbors that are spatially correlated with the process at the query point are used in prediction. In case the estimated range is small, indicating a locally weak spatial process, a sample of 10

Examples

data(epa_cl)
data(ex)
out <- lk(ex1.grid,ex1.data,0.25)
if(require(fields))
	quilt.plot(ex1.grid$x,ex1.grid$y,out$krig,
		nrow=10,ncol=10,main='predicted PM[2.5] 01/01/2005')