tsbk: Ordinary Global Time and Space Block Kriging

In ltsk: Local Time Space Kriging

Ordinary Global Time and Space Block Kriging

Description

Function for block kriging in time and space based on the product-sum variogram model.

Usage

tsbk(query, obs, xcoord = "x", ycoord = "y", tcoord = "t", zcoord = "z",
	bcoord='block', gcoord='g',vth = NULL, vlen = NULL, 
    llim = c(3, 3), verbose = T, Large = 2000, future = T)

Arguments

query	a data frame containing query spatiotemporal locations
obs	a data frame containing spatiotemporal locations and observed data
xcoord	field name for x coordinate in both query and obs
ycoord	field name for y coordinate in both query and obs
tcoord	field name for time coordinate in both query and obs
zcoord	field name for data in obs
bcoord	field name for block in query
gcoord	field name identifying each unique query point
vth	thersholds for local spatiotemporal varigoram (default 75% max lag difference)
vlen	numbers of bins for local spatiotemporal varigram(default,space 15, temporal for each day)
llim	lower limits for number of data points to calculate Kriging (default 3 spatial, 3 temporal neighbors)
verbose	boolean whether print details information
Large	upper limit of neighbor points, beyond which subsampling was done
future	include observed points in future relative to query points.

Details

Function implements global time space block kriging based on a product sum model.

If the number of neighbors exceeds a user-specified upper limit (Large), neighbors are sub-sampled in a balanced way to reduce the neighborhood size.

Four variogram models: Gaussian, exponential, spherical and Matern are automatically fit to the empirical space and time variogram in the first lag. The range parameter is estimated from the first distance lag where the empirical variogram exceeds 80% of the maximum. Weighted least square is then used to estimate the nugget and partial sill parameters. Model with minimal residual sum of squares between the empirical and fitted variogram is chosen as the variogram model.

Field names for geographic coordinates and time stamps must match between query and observed data frames.

Value

a matrix containing the prediction and prediction standard error for each block, and a flag denoting the reason for un-successful prediction:

0	valid prediction
1	not enough temporal neighbors
2	not enough spatial neighbors
3	not enough neighbors
4	variogram could not be fit

Author(s)

Naresh Kumar ([e-mail]) Dong Liang ([e-mail])

References

Iaco, S. De & Myers, D. E. & Posa, D., 2001. "Space-time analysis using a general product-sum model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 21-28, March.

Kumar, N., et al. (2013). "Satellite-based PM concentrations and their application to COPD in Cleveland, OH." Journal of Exposure Science and Environmental Epidemiology 23(6): 637-646.

Liang, D. and N. Kumar (2013). "Time-space Kriging to address the spatiotemporal misalignment in the large datasets." Atmospheric Environment 72: 60-69.

See Also

krigeST in gstat

Examples

## load the data
data(ex)
data(epa_cl)
## apply log transformation
obs[,'pr_pm25'] = log(obs[,'pr_pm25'])
ex2.query$block <- 1 ## a single block
ex2.query$g <- 1:nrow(ex2.query)
## run kriging
## system.time(out <- tsbk(ex2.query[1:2,],obs,zcoord='pr_pm25',Large=400))

ltsk documentation built on Sept. 3, 2023, 1:06 a.m.