IEEE Geoscience and Remote Sensing Magazine - December 2021 - 204

Spatial
Ratio
Temporal
(a)
-0.5
-1
-1.5
-2
-2.5
0.5
Ratio
(b)
1
0.5
-0.5
-1
0.5
Ratio
(c)
-1.25
-1.5
-1.75
-2
-2.25
-2.5
-2.75
0.5
Ratio
(d)
FIGURE 11. (a) The entropy measurement for different spatiotemporal
configurations in the ESDC variables. The IT Venn diagram
represents Figure 10 and how it relates to measuring entropy: the
expected uncertainty. The measured entropy for (b) precipitation,
(c) SH, and (d) evaporation from the ESDC [56] changes with different
spatial-temporal representations, ranging from fully spatial
(ratio = zero) to fully temporal (ratio = one).
204
1
4
9
16
25
36
49
1
4
9
16
25
36
49
1
4
9
16
25
36
49
high probability (e.g., the east-west U.S. gradient) emerge
[45]. Studying precipitation in the fully temporal configuration
translates into a clear ruling of the winter season in the
Amazon, Indonesia, and northern Europe. Yet a comparison
of temporal versus spatial information in Figure 12 (bottom
row) reveals that spatial information dominates in desert
areas (e.g., Australia, the Iberian Peninsula, the Sahara, and
Mexico), which are reasonably independent of time, and that
temporal information dominates in the Sahel (savanna),
northern latitudes, and southwest China, which are generally
characterized by high rain factors, seasons, and moisture.
The transfer of SH into the air is dependent on the temperature
gradient between the surface and the space above.
SH information patterns stand out clearly. While (fully)
spatial information dominates in the northern hemisphere,
(fully) temporal information patterns appear in the tropics,
where rainfall is present across larger regions and longer
seasons. The global spatial distribution of SH information
shows the largest values in subtropical, dry regions, where
available energy is preferentially partitioned to SH rather
than latent heat [50], and it seems to be anticorrelated with
the amplitude of the mean seasonal cycle. These results reveal
the most SH information in tropical and subtropical
deserts, where a high surface temperature conducts much
heat into the air above, and the least information near the
poles, where surface temperatures are much lower. The information
is mainly concentrated in the tropics, too, and
shows patterns similar to those of precipitation, with the
exception of clear spatial information in India.
Evaporation maps reveal that spatial information dominates
in deserts and dry regions, where evaporation is limited,
while temporal information (with more interannual
variability) resides in northern latitudes. This is mainly due
to low temperatures and radiation, equating to little evaporation
throughout the year. Temperate areas show increased
evaporation information in purely spatial and temporal configurations,
coinciding with increasing temperatures above
ground moistened by winter rains. Cooler winter temperatures
in the southern hemisphere reduce evaporation, which
is also captured in the spatial-versus-temporal divergence
maps. Note that, in very dry regions, there is more information
(a lower evaporative fraction), while, conversely, for very
humid regions, the information agrees with [50].
CONCLUSIONS
This article introduced a Gaussianization method and illustrated
how to use it for multivariate density estimation in
the context of Earth system science. The problem is highly
relevant given the advent of all kinds of Earth data (both
remotely sensed and in situ observations), novel products,
and model simulations. Density estimation is a long-standing,
unresolved problem in statistics and machine learning,
mainly because of the curse of dimensionality. Data in remote
sensing and geosciences pose additional problems for
PDF estimation: high-dimensional data, nonlinear feature
relations, many noise sources, and distinct spatial-temporal
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
Entropy
Entropy
Entropy
IEEE Geoscience and Remote Sensing Magazine - December 2021

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2021
