  This work proposes a new procedure for estimating the non-stationary spatial
covariance function for Spatial-Temporal Deformation. The proposed procedure is
based on a monotonic function approach. The deformation functions are expanded
as a linear combination of the wavelet basis. The estimate of the deformation
guarantees an injective transformation. Such that two distinct locations in the
geographic plane are not mapped into the same point in the deformation plane.
Simulation studies have shown the effectiveness of this procedure. An
application to historical daily maximum temperature records exemplifies the
flexibility of the proposed methodology when dealing with real datasets.
