Direct method to remove trend of spatio  temporal data througth median polish.
1  removetrendMPst(MPST,eps=0.01, maxiter=10L)

MPST 
object of class 
eps 
real number greater than 
maxiter 
the maximum number of iterations. Default 10. 
Robust method introduced for Cressie(1993) and enhanced by Berke(2001) to remove trend of a space  time process with data ≤ft\{y(\mathbf{s}_{abc},t), a=1,...,U; b=1,...,V; c=1,...,W, t=1,...,n \right\}
Y(\mathbf{s}_{abc},t)= μ_{y}(\mathbf{s}_{abc},t) + δ _{abct}
where
μ _{y}(\mathbf{s}_{abc},t)= μ +α _{a} + β _{b} + ξ _{c} + τ _{t}
and δ _{abct} is a fluctuation arising from natural variability and from the measurement process. Additionally, μ is an overall mean, α_{a} is the ath row effect, β_{b} is the effect bth column effect, ξ_{c} is the cth layer effect, τ _{t} is the tth time effect.
data.frame with the following fields:
ET 
indicate the time of a observation 
x 
spatial coordinates x 
y 
spatial coordinates y 
z 
spatial coordinates z 
Trend 
trend calculated through median polish space  time 
Value 
observed values 
Residual 
Residual = ValueTrend 
Berke, O. (2001). Modified median polish kriging and its application to the wolfcamp  aquifer data. Environmetrics, 12(8):731748.[link]
Cressie, N. (1993). Statistics for spatial data. Wiley series in probability and statistics.[link]
1 2 3 4 5 6 7 8 9 10 11 12  ## Not run:
data(Metadb)
x<matrix(0,1,37)
for(i in 1:37){
x[,i] < 2007 + (seq(0, 36)/12)[i]
}
x<as.Date (as.yearmon(x), frac = 1)
time = as.POSIXct(x, tz = "GMT")
MPST<ConstructMPst(Metadb[,c(1:4)],time,pts=Metadb[,2:4],Delta=c(7,6,5))
residuals<removetrendMPst(MPST,eps=0.01, maxiter=2)
## End(Not run)

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