Visualizing 2D probability distributions from EOS satellite image-derived data sets: a case study

Abstract

Maps of biophysical and geophysical variables using Earth Observing System (EOS) satellite image data are an important component of Earth science. These maps have a single value derived at every grid cell and standard techniques are used to visualize them. Current tools fall short, however, when it is necessary to describe a distribution of values at each grid cell. Distributions may represent a frequency of occurrence over time, frequency of occurrence from multiple runs of an ensemble forecast or possible values from an uncertainty model. We identify these "distribution data sets" and present a case study to visualize such 2D distributions. Distribution data sets are different from multivariate data sets in the sense that the values are for a single variable instead of multiple variables. Data for this case study consists of multiple realizations of percent forest cover, generated using a geostatistical technique that combines ground measurements and satellite imagery to model uncertainty about forest cover. We present two general approaches for analyzing and visualizing such data sets. The first is a pixelwise analysis of the probability density functions for the 2D image while the second is an analysis of features identified within the image. Such pixel-wise and feature-wise views will give Earth scientists a more complete understanding of distribution data sets. See www.cse.ucsc.edu/research/avis/nasa is for additional information.

Visualization techniques for spatial probability density function data

“…Animations of the different instances of spatial data are used to help the user gain insight to the uncertainty at the different pixels. Kao, Dungan & Pang (2001) have developed techniques to study probability density functions (pdfs) in greater detail. They estimate the pdfs from the samples in the probability datasets, and then use various statistical summaries of the pdfs, e.g., mean, variance, skewness, kurtosis, inter-quartile distance etc.…”

“…The user has to probe each point to visualize the estimated pdf. Figure 1 shows a visualization from (Kao et al, 2001). The lower layer shows a colormap of the mean of the Landsat dataset described in Section 3.…”

“…Values range from 0 to 255, re-scaled from percentage forest-cover (Kao et al, 2002). A visualization of this dataset from (Kao et al, 2001) is shown in Figure 1. Different clustering results for this dataset are shown in Figure 3.…”

“…Different clustering results for this dataset are shown in Figure 3. (Kao et al, 2001). The dataset is described in Section 3.…”

“…A quick comparison between Figures 1 and 3 will show the difference between the pixel-wise visualization approach and the clustering approach. Figure 1 is a pixel based visualization of the Landsat dataset from (Kao et al, 2001), while Figure 3 shows clustering results of the same data.…”