Visual Analysis of Relevant Fields in Geoscientific Multifield Data - Towards an Interdisciplinary Approach in Earth System Science - page 205

apply dimension visualization for the analysis of multi elds. Similar to the dual-

space approaches, we apply MDS to dimensions. However, we consider spatial data
visualizations to be more appropriate for this scenario than the data item projections
of other dual-space approaches.

3 Field Similarity Plot

Our approach focuses on the uniform qualitative comparison of the fields present in

a dataset, which requires all fields to be normalized. In the following, we assume

that all fields are normalized to the unit interval.

First, a number of commonly studied and newly derived

fields are included in

the analysis. Speci cally, we add gradient magnitudes, Hessian determinants, and

fields based on the gradient similarity measure (GSIM) introduced by Sauber et al.
( 2006 ). For two gradients gi i and g j , GSIM is de ned as

r

s ð g i ; g j Þ ¼ ð s d ð g i ; g j Þ s m ð g i ; g j ÞÞ ð 1 Þ

;

2

g i g j
k g i kk g j k

s d ð g i ; g j Þ ¼ ð 2 Þ

;

k g i kk g j k
ðk g i kþk g j kÞ

s m ð g i ; g j Þ ¼ 4 ð 3 Þ

2 ;

where s d is the direction similarity, is m is the magnitude similarity, and r regulates
sensitivity of the measure (set to 1

3 as recommended (Sauber et al. 2006 )).

:

first-order similarity between gradi-
ents, second-order similarity between eigenvectors of the principal eigenvalue of
the Hessians, and mixed similarity between the

The following GSIM fields are computed:

first- and the second-order deriv-
atives estimate (i.e. gradients and Hessian eigenvectors, respectively). In the set of
derived

fields, the gradients and their similarities carry first-order relationships,

while other fields might indicate more complex relationships. All derived fields are

normalized as well.
Next, for each data field, we interpret the vector of its values at all spatial

locations as a multidimensional data point and compute integrated differences
between pairs of

fields. In the following, we use the global Euclidean distance

measure de ¼n x n y n z ,andn x , n y , n z

are respective sizes of the spatial grid in x, y, z dimensions. This distance is
computed as

ned on the *-dimensional space, where

s

X

2

d ij ¼

½v j xyz v i xyz ð 4 Þ

;

xyz