Development of a Methodology for Parameterization of Time scale and Space scale in Hydrological Systems Based on Wavelet Theory (I)

For the heterogeneous subsurface system,
the heterogeneity and the spatial variability are
the intrinsic properties of porous media which
affects the water and pollutant transport process
directly. A key factor of simulating results
depends on whether the parameters of the
subsurface system were parameterized properly
or not. In this study, a wavelet based analysis is
applied to evaluate the scale effects of
parameters and to develop a quantitative
method of parameter scales. First, the wavelet
kernel function is used to derive the theoretical
relationship between the wavelet spectrum of
piezometric head and hydraulic conductivity in
a one-dimensional heterogeneous system.
Furthermore, by solving forward problem, the
relationship between the wavelet spectrum
energy of nonstationary hydraulic conductivity
field that is generated artificially and the actual
energy is analyzed. Finally, the scale effects
that contribute to wavelet spectrum energy in
the heterogeneous groundwater system are
investigated. A general theoretical solution for
tackling both stationary and nonstationary
process was developed. The numerical
examples showed that wavelet-based approach
was able to identify both discontinuity and
pattern of heterogeneous for the nonstationary
hydraulic conductivity of subsurface
groundwater system.