|Spatial Statistical Estimation and Classification ---
Theory and Applications from Centimeter to Continental Scale
Ute Herzfeld, Ph.D Cooperative Institute for Research in Environmental Sciences, and Department of Applied Mathematics, University of Colorado, Boulder.
Monday, September 8, 2008
4:00 p.m. 223 Weber
The objectives of spatial statistical estimation are the spatial structure analysis, interpolation,
extrapolation and related error analysis of a primary variable. In the first part of the talk, statistical
methods such as ordinary and advanced kriging and their mathematical relationship to inverse
theory will be discussed.
The topic of the second part of the presentation will be the retrieval of hidden or secondary information on complex spatial variables from geophysical data. Typical situations of obscured geological
or geophysical information are the following: (1) Noise may disturb the signal for a variable for
which measurements have been collected. (2) The variable of interest may be obscured by other
geophysical processes. (3) The information of interest may formally be captured in a secondary
variable, whereas data may have been collected for a primary variable only, that is related to
the geophysical process of interest. As a solution, we introduce a new form of spatial statistical
characterization and classification, which proceeds by the following steps: (1) calculation of vario
functions (which may be of higher order or residual type or combinations of both), (2) derivation
of classification parameters from vario functions, and (3) characterization, classification or segmentation, depending on the applied problem. In some situations, spatial surface roughness is utilized
as an auxiliary variable. For example, ice surface roughness measured in the Greenland inland ice
provides (1) the basis for statistical analysis of glaciologic processes, (2) high-resolution informa-
tion for satellite observations of Greenland, and (3) conclusions relevant to recent melting of the
Greenland ice sheet.
The statistical analysis of large data sets as typically arise in satellite remote sensing leads to
interesting problems in mathematical computation, the solutions of some of those will be discussed in
the talk. In an ongoing project supported by NASA's cryospheric sciences, simulation of scale-
dependent fractal fields is applied to derive measurement requirements for a future ice observations satellite.