tsk {ltsk}

Ordinary Global Time and Space Kriging

Description

Function for ordinary kriging in time and space based on the product-sum variogram model, kriging in a local neighbourhood.

Usage

tsk(query, obs, subset = T, nmin = 3, nmax = 20, xcoord = "x", 
    ycoord = "y", tcoord = "t", zcoord = "z", 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

subset

logical; for local kriging; if TRUE only observations within the distances of estimated spatial and temporal sills from the prediction location are used for prediction

nmin

for local kriging: if the number of neighbors after subset is less than nmin, a missing value will be generated

nmax

for local kriging: the number of nearest observations that should be used for a kriging prediction, by default all observations are used.

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

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 kriging based on a product sum model and support kriging in a local neighborhood.

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 list of a matrix krig, containing the prediction and prediction standard error 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

a list of estimated time space variogram, and a list of fitted parameter values of the product sum variogram model.

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'])
## run kriging
system.time(out <- tsk(ex2.query[1:2,],obs,zcoord='pr_pm25',Large=400))
out$krig