Dimensionality Reduction-based Interactive Visual Analytics Approach for Investigating Ensemble Weather Simulations

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Dimensionality Reduction-based Interactive Visual Analytics
Approach for Investigating Ensemble Weather Simulations
Go Tamura
PHOTRON LIMITED
Tokyo, Japan
tamurag@photron.co.jp
Sena Kobayashi
Kobe University
Kobe, Japan
239x025x@stu.kobe-u.ac.jp
Naohisa Sakamoto
Kobe University
Kobe, Japan
naohisa.sakamoto@people.kobe-u.ac.jp
Yasumitsu Maejima
Kobe University
Kobe, Japan
maejima@maritime.kobe-u.ac.jp
Jorji Nonaka
RIKEN R-CCS
Kobe, Japan
jorji@riken.jp
Fig. 1: Overview of the visual analytics workow, and related back-end processing, for the interactive visual exploration of the
set of ensemble members, from weather simulations, in addition to the verication truth data, used for data assimilation.
Abstract
Torrential rains causing infrastructure damage and threats to hu-
man lives have unfortunately become more frequent worldwide.
HPC-based numerical weather predictions, by using ensemble sim-
ulation and data assimilation, have become an indispensable tool
for dealing with such extreme weather phenomena. However, en-
semble simulations can generate large time-varying, multivariate,
and multivalued outputs, posing a particular challenge to the vi-
sualization and analysis tasks. In this paper, we present a visual
analytics approach combining unsupervised machine learning and
a combination of 2D and 3D visual representation techniques to
This work is licensed under a Creative Commons Attribution International
4.0 License.
HPCASIA ’25, Hsinchu, Taiwan
©2025 Copyright held by the owner/author(s).
ACM ISBN 979-8-4007-1335-4/25/02
https://doi.org/10.1145/3712031.3712326
assist interactive visual analysis of such HPC-based simulation re-
sults. In addition to the investigation of how ensemble members
evolve over time, this also makes possible the investigation of how
these members compare with the verication truth data, which
can contribute to a better understanding of the simulation models.
We developed a prototype visual analytics system, and through
some experimental evaluations with a domain scientist in numer-
ical weather prediction, we could conrm the usefulness of the
proposed approach in the better understanding of the spatiotem-
poral behavior of the ensemble members themselves, as well as in
comparison to the verication truth data, which was not possible
by using traditional visual analysis based on ensemble mean and
spread.
CCS Concepts
•Human-centered computing
→
Visualization systems and
tools;•Computing methodologies
→
Dimensionality reduction
and manifold learning;Rendering;•Applied computing
→
Earth
and atmospheric sciences.
13
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HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan Go Tamura and Naohisa Sakamoto et al.
Keywords
HPC, ensemble simulation, data assimilation, visual analytics, in-
teractive visual exploration
ACM Reference Format:
Go Tamura, Sena Kobayashi, Naohisa Sakamoto, Yasumitsu Maejima, and Jorji
Nonaka. 2025. Dimensionality Reduction-based Interactive Visual Analytics
Approach for Investigating Ensemble Weather Simulations. In HPC Asia 2025
: Proceedings of the International Conference on High Performance Computing
in Asia-Pacic Region (HPCASIA ’25), February 19–21, 2025, Hsinchu, Taiwan.
ACM, New York, N Y, USA, 10 pages. https://doi.org/10.1145/3712031.3712326
1 Introduction
The intensity and frequency of weather-related natural disasters
have noticeably increased worldwide as some of the probable eects
of climate change and global warming [
23
,
32
]. In addition to the
larger hurricanes, cyclones, and typhoons causing vast devastation
and damage, torrential rains have also caused severe infrastructure
damage and unfortunate human losses due to the consequent ood-
ing and landslides. Such torrential rainstorms include sudden and
heavy downpours, also known as “guerrilla rainstorms” in Japan.
It is worth mentioning that HPC-based Numerical Weather Pre-
diction (NWP) has played an important role in dealing with such
natural phenomena, and it is worth mentioning that its theoretical
foundation related to the physical modeling of Earth’s climate was
recognized and awarded with the 2021 Nobel Prize in Physics.
Ensemble simulation and data assimilation, in addition to high-
resolution models, have become widely used in modern HPC-based
NWP. A set of simulation runs, i.e., ensemble members (hereinafter
referred to as members) with slightly dierent initial conditions
with induced perturbations are performed on ensemble simulations,
and data assimilation is applied to occasionally adjust the simula-
tion parameters with real-world observational data such as from
meteorological radars and satellites [
25
]. Continuous improvements
in HPC systems’ performance have made it possible to perform
larger-scale simulations, and we can cite Kondo et al.’s work [
11
]
as an example of large-scale ensemble simulation with data assimi-
lation, using over 10,000 members on the former Japanese agship
supercomputer (K computer). This kind of big data assimilation
has also been conducted on the successor Fugaku supercomputer,
and the recognition came in the form of a nalist nomination in
the ACM Gordon Bell Prize for Climate Modelling at SC’23 [
15
].
On the other hand, this imposes an increased challenge for the
visual analysis of the ensemble simulation outputs because of the
time-varying (
𝑇
), multivariate (
𝑉
), and multivalued (
𝑀
) nature of
the data as shown in Fig. 1.
Domain scientists in NWP have traditionally used the ensemble
mean and spread, i.e., the standard deviation of the members, to
investigate and understand their NWP simulation models. How-
ever, in modern NWP simulations with high-frequency data assim-
ilation [
12
], statistical and quantitative evidence becomes highly
relevant to better understand the simulation models and to nd
potential factors that aect the simulation accuracy. There is an
inherent diculty in analyzing multiple members (values), physical
quantities (variables), and their temporal changes (time steps) at
the same time by using a single visualization method. Therefore, a
combination of visualization and analysis techniques working in
a linked manner has widely been adopted for the visual analysis
of ensemble data as we can verify in the surveys conducted by
Wang et al. [27] and Rautenhaus et al. [20].
We have conducted collaborative work by involving domain
scientists in HPC, NWP, and visualization to investigate the use of
Dimensionality Reduction (DR), an unsupervised machine learning
technique, and a combination of visual representation techniques,
such as “2D Heatmap”, “2D Slice”, and “3D Probability Isosurface”
renderings for investigating ensemble weather simulations. A pro-
totype Graphical User Interface (GUI) for the integrated visual
analytics tool is shown in Fig. 2, and the multiple views (from ato
e) are linked together, that is, an interactive user manipulation in a
view will be propagated to the others by updating them as shown
in Fig. 1. These multiple linked views with dierent information will
enable the overview and detailed spatiotemporal comparison and
analysis of members and ground truth data (verication truth data).
An ensemble simulation of localized torrential rain with record
heavy precipitation within a range of tens of kilometers occurred
at Kobe City in Japan, was used for practical evaluations.
Our main contribution is the new visual analytics approach,
which enables interactive investigation of the spatiotemporal be-
haviors of the members in comparison to the verication truth
data that was not possible by using the traditional approach based
on ensemble mean and spread. Following are the new proposed
techniques behind the implemented integrated visual analytics
environment for interactive exploration of large-scale ensemble
weather simulation results by using multiple linked views:
•
Express the ensemble simulation data, and its related veri-
cation truth data, as fourth-order tensor data with members,
variables,time, and space as the reference axes, for subse-
quent processing which includes slicing, attening, dimen-
sionality reduction, and probability isosurface.
•
Heatmap-based comparative visualization combined with
MDS-based dimensionality reduction plot to enable overview
of spatiotemporal behavior of the members, with respect to
the verication truth data, based on the selected variable of
interest.
•
Isosurface-based comparative visualization method to iden-
tify spatial regions with low or high discrepancies between
isosurfaces from the members and from the verication truth
data.
2 Related Works
As mentioned earlier, there is an extensive survey focusing on
visualization techniques and analytics tasks for ensemble data [
27
],
as well as an extensive survey focusing on meteorological data
analysis, which also includes ensemble data visualization [
20
]. We
can also cite an interesting visualization viewpoint categorizing the
ensemble visualization approaches onto feature-based and location-
based visualization [
16
]. It is worth noting that a variety of visual
analytics tools for handling ensemble data have also been proposed
so far [
4
,
6
,
9
,
17
,
22
,
24
,
26
,
29
,
31
]. Most of those existing visual
analytics tools have coordinated multiple linked views to enable
intuitive user interaction. However, most of them have focused
on the investigation of the spatiotemporal behaviors among the
members and did not take into account how these members evolve
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DR-based Interactive Visual Analytics Approach for Investigating Ensemble Weather Simulations HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan
Fig. 2: Overview of the integrated visual analytics tool for
interactive exploration of members and verication truth
data. The linked views are composed of: (a) Dimensionality
reduction plot view; (b) Timeline heatmap plot view; (c,d)
Cross-sectional plot view; and (e) Probability isosurface plot
view. This visualization example uses ensemble simulation
data of a torrential rain occurred at Kobe City.
over time in comparison to the real-world data or other kinds of
ground truth data. This is highly desired from domain scientists
in high-resolution NWP, using high-frequency data assimilation
such as those focusing on short-range NWP simulations targeting
torrential downpours as guerrilla rainstorms [
13
] targeted in this
work. As related works to realize this, we focused on visualization
techniques from three perspectives: Overview;Comparative; and
Temporal visualization of members.
Overview visualization is useful for examining the overall spa-
tiotemporal distribution of the members. This can facilitate the
understanding of how the entire set of members behaves spatially
and temporally and can provide some clues for further analysis.
Whitaker et al. [
30
] proposed an abstraction method for curvilin-
ear data of contour groups extracted from ensemble data. In this
method, the boxplot drawing was extended to calculate the shape
features of the contour lines, based on the concept of data depth,
and visualize its statistics in the form of median and interquartile
ranges. There is also an extended work [
14
] applied to streamlines
and pathlines. For ensemble data represented as 3D scalar data,
there is a method to extract isosurfaces, and visualize their spatial
statistical distribution. Pöthkow et al. [
19
] extended the Marching
Cubes method to calculate the probability for the set of extracted
isosurfaces that pass through the grid cells, and proposed the Prob-
abilistic Marching Cubes to visualize the spatial distribution of the
probability of existence of these isosurfaces. In this work, we used
this method as a pre-processing to obtain the probability isosur-
face plot (Fig. 2(e)) used to present the existence probability of the
members’ isosurfaces.
Comparative visualization is useful for investigating and under-
standing similarities or dissimilarities between members. For this
purpose, juxtaposition can be applied to simultaneously compare
dierent rendering results, such as those visual analytics systems
for ensemble data described in [
5
,
22
,
24
]. Wang et al. [
28
] utilized
juxtaposition and superimposition of parallel coordinates plots in
a single view to visualize multi-resolution ensemble simulation
results. It is worth mentioning that they used observational data
from meteorological satellites, as verication truth data, for eval-
uating the members’ quality, which is similar to our target goal.
Some approaches estimate the distance between objects to be used
as a comparison metric (similarity). Fofonov et al. [
8
] proposed
a method in which the dierences in the shape of the extracted
isosurfaces from the members are used as the distance. There is an
extension to this work, named Projected Field Similarity [
7
], which
was proposed to eliminate the distance uctuation problem depend-
ing on the user-selected threshold. In this work, we applied this
technique as a pre-processing for obtaining the heatmap (Fig. 2(b))
plot.
Temporal visualization is useful for investigating and understand-
ing temporal trends within the members. For instance, Wang et al. [
28
]
used juxtaposition for visualizing daily contour diagrams of the
entire month (30 juxtaposed views) from a single member for
analyzing the spatiotemporal evolution of the selected member.
Shu et al. [
24
] proposed a 2D time series plot, in which the hor-
izontal axis represents the time, and the vertical axis represents
arbitrary physical quantity (variable) obtained from the ensemble
data. Poco et al. [
17
] proposed a matrix view to compare spatiotem-
poral correlations among dierent ensemble simulation models
to facilitate similarity comparison. Fofonov et al. [
8
] applied di-
mensionality reduction for comparing the time evolution of the
members. They used Multidimensional Scaling (MDS) projection
to represent members as polylines in the projected view and dis-
play the changes over time, and we adopted this approach in the
dimensionality reduction plot (Fig. 2(a)).
3 Methodology
3.1 Design Concept
The proposed visual analytics workow (Fig. 1) was designed to
assist domain scientists in investigating the spatiotemporal behav-
ior of the members and verication truth data in ensemble weather
simulations. For instance, to nd potential factors that aected the
simulation accuracy based on statistical and quantitative evidence.
This is expected to be useful for better understanding the under-
lying simulation phenomena and for the optimization process of
NWP simulation models. To enable this, it was focused on fullling
the following three requirements:
R-1
Which members follow, or not, the verication truth data ?
R-2
When did the members start or stop, following the veri-
cation truth data ?
R-3
Where are the spatial regions showing high or low dis-
crepancies between members and verication truth data ?
R-1 focuses on identifying members that follow the verication
truth data by computing their similarity based on the distance to
the reference. R-2 focuses on identifying temporal regions of time
when the members have the best or worst match compared to the
verication truth data. The timeline heatmap plot (Fig. 2(b)) in com-
bination with the dimensionality reduction plot (Fig. 2(a)) is used
for the overview visualization to meet the requirements R-1 and
R-2.R-3 focuses on identifying spatial regions where the members
show signicant discrepancies compared to the verication truth
data, indicating the regions where the simulation accuracy was
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HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan Go Tamura and Naohisa Sakamoto et al.
Fig. 3: Ensemble data
𝑬
with
𝑁𝑚
members. Each member
𝑴
has a set of simulation elds
𝑭
with
𝑁𝑔
grid points and
𝑁𝑡
time
steps. A set of numerical data
𝑽
composed of
𝑁𝑣
variables is
assigned to each grid point
𝑔𝑖
for the corresponding variable
𝑣𝑖and time step 𝑡𝑖.
low. The probability isosurface plot (Fig. 2(e)) is used to enable the
identication of such spatial regions to meet the requirement R-3.
3.2 Ensemble Data
Ensemble data used in this work comprises a set of outputs from
multi-run simulations, in addition to the verication truth data. The
conceptual diagram is shown in Fig. 3, where the ensemble data
𝑬
is composed of a set of members
𝑴
, where each of them having a
simulation eld
𝑭
with a set of time steps
𝑻
, and a set of numerical
data
𝑽
. The simulation eld treated in this work comprises 3D
grid cells, and each grid cell is composed of a set of grid points
𝑔𝑖
.
Assuming that the number of members is represented as
𝑁𝑚
, then
the ensemble data 𝑬can be represented as:
𝑬={𝑴1,𝑴2, . . . , 𝑴𝑁𝑚}(1)
Assuming the total number of the simulation time steps as
𝑁𝑡
,
the number of grid points constituting the simulation eld as
𝑁𝑔
,
and the number of variables as
𝑁𝑣
, then the components of the
ensemble data can be represented as:
𝑴={𝑭1,𝑭2, . . . , 𝑭𝑁𝑡}(2)
𝑻={𝑡1, 𝑡2, . . . , 𝑡𝑁𝑡}(3)
𝑭={𝑔1, 𝑔2, . . . , 𝑔𝑁𝑔}(4)
𝑽𝑔𝑖={𝑣1, 𝑣2, . . . , 𝑣𝑁𝑣}(5)
These components are then arranged as a 4D array of data by
using the above four components as the reference axes (
𝑚
,
𝑓
,
𝑡
, and
𝑣
). By applying the Kolda et al.’s notation [
10
] to express tensor
data, the ensemble data
𝑬
can be represented as a 4
𝑡ℎ
order tensor
data
𝑬𝑚𝑓 𝑡 𝑣
, where the indexes
(𝑚, 𝑓 , 𝑡, 𝑣)
represent each of the four
axes. As shown in the visual analytics workow (Fig. 1), slicing and
attening operations are carried out to the tensor data to extract
partial tensor data of interest and to rearrange it for dimensionality
reduction processing.
3.2.1 Slicing. The slicing operation is conducted with respect to
a user selected variable of interest. By representing this variable
of interest as
𝑣𝑖
, where
𝑖≤𝑁𝑣
, slicing will be carried out to every
member of set
𝑴
, with respect to the
𝑽
axis, as shown in Fig. 4. If we
arrange these sliced planes as stacked slices, the resulting data will
be a 3
𝑟𝑑
order tensor data, and can be represented as
𝑬:::𝒊
, where
the subscript colon “:” indicates that all elements of the marked
axis are used.
Fig. 4: Slicing a 4
𝑡ℎ
order tensor data
𝑬
with respect to the
𝑉
axis, and the user selected variable of interest
𝑣𝑖
will be
extracted. By stacking up the sliced data, this will result in a
3𝑟𝑑 order tensor data 𝑬:::𝒊.
3.2.2 Flaening. The attening operation is conducted on the pre-
vious sliced data in order to rearrange it on a time and member basis.
Fig. 5 shows this attening operation on the 3
𝑟𝑑
order tensor data
𝑬:::𝒊
carried out by slicing it along the
𝑴
axis, and by rearranging
the extracted slices with respect to the
𝑻
axis in sorted order. The
resulting 2𝑛𝑑 order tensor data will be represented as 𝑿.
Fig. 5: Flattening process of a 3
𝑟𝑑
order tensor data
𝐸:::𝑖
by
slicing it along the
𝑀
axis, and rearranging with respect to
the 𝑇axis.
3.3 DR-based Overview Visualization
2D visual representations in the form of connected scatterplot
(Fig. 2(a)) and heatmap plot (Fig. 2(b)) will be used to give an
overview of the members’ evolution behavior over time among
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DR-based Interactive Visual Analytics Approach for Investigating Ensemble Weather Simulations HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan
themselves, and also in comparison to the verication truth data.
For this purpose, slicing (Fig. 4) and attening (Fig. 5) are applied
to the input 4
𝑡ℎ
order tensor data to obtain the simulation elds in
the form of 2
𝑛𝑑
order tensor data
𝑿=𝑬𝒋:𝒌 𝒊
, composed of
𝑭(𝑗, 𝑘 )
elements from the member
𝑴𝒋
and time step
𝑡𝑘
. This 2
𝑛𝑑
order
tensor data 𝑿can be represented as follows:
𝑿={𝑭(1,1), . . . , 𝑭(1, 𝑁𝑡), . . . ,
𝑭(𝑁𝑚,1), . . . 𝑭(𝑁𝑚, 𝑁𝑡)} (6)
DR will then be applied to
𝑿
, and the resulting dimensional-
ity reduced
𝑿′
will be a set of 2D vector
𝑭′
as shown in Fig. 6.
Among dierent DR techniques, we opted for using Multidimen-
sional Scaling (MDS) [
3
] since it is well known for maintaining the
relationships between distances among elements within the data as
much as possible. This pair-wise distance between elements can be
considered as an index to quantify similarity among the elements.
As such, the distance between the same data will be 0, and as the
distance increases, it means that the elements proportionately dier
from each other. for the MDS calculation, Projected Field Similar-
ity (PFS) [
7
] will be used as a pre-processing to obtain pair-wise
distance between elements, and PFS-based distance
𝐷𝑓(𝑭𝐴,𝑭𝐵)
between elds 𝑭𝐴and 𝑭𝐵will be obtained as follows:
𝐷𝑓(𝑭𝐴,𝑭𝐵)=1−Í𝑁𝑔
𝑖=1(1−max(𝑣′
𝑗𝑎𝑖, 𝑣 ′
𝑗𝑏𝑖))
Í𝑁𝐹
𝑖=1(1−min(𝑣′
𝑗𝑎𝑖, 𝑣 ′
𝑗𝑏𝑖)) (7)
Here,
𝑣′
𝑗𝑎𝑖
,
𝑣′
𝑗𝑏𝑖
represent the normalized
𝑗
th numerical data
dened for the grid points
𝑔𝑎𝑖
and
𝑔𝑏𝑖
from the elds
𝐹𝐴
and
𝐹𝐵
,
respectively. By evaluating the PFS-based distance
𝐷𝑓
for all el-
ements of the tensor data
𝑿
(Eq. 6), we can obtain the distance
matrix Das follows:
D=©«
𝐷𝑓(𝐹(1,1),𝐹 (1,1)) ··· 𝐷𝑓(𝐹(𝑁𝑚,𝑁𝑡),𝐹 (1,1))
.
.
.....
.
.
𝐷𝑓(𝐹(1,1),𝐹 (𝑁𝑚,𝑁𝑡)) ··· 𝐷𝑓(𝐹(𝑁𝑚,𝑁𝑡),𝐹 (𝑁𝑚,𝑁𝑡)) ª®¬(8)
This distance matrix Dwill be used as the input data for the
MDS calculation, and the resulting dimensionality reduced
𝑿′
will
be a set of 2D vector
𝑭′
, as shown in Fig. 6, and can be represented
as follows:
𝑿′
={𝑭′(1,1), . . . , 𝑭′(1, 𝑁𝑡), . . . ,
𝑭′(𝑁𝑚,1), . . . 𝑭′(𝑁𝑚, 𝑁𝑡)} (9)
Fig. 7 shows a visualization of the dimensionality reduced
𝑿′
as a connected scatterplot. The pair-wise
𝑭′
values are used as the
spatial coordinates for the scatterplot, and the plots belonging to the
same member are then connected in chronological order to generate
polygonal lines. By superimposing these polygonal lines, from each
of the members, in the same 2D plotting space, it becomes possible
to compare how the distance, i.e., similarity, between members
changes over time. However, such superimposed polygonal lines
may suer from visual cluttering on regions where multiple points
or lines are densely plotted. To overcome this problem, and to
facilitate quantitative analysis, we opted to visualize
𝑿′
also in
the form of timeline heatmap, as shown in Fig. 8. In this plot, the
Fig. 6: MDS-based dimensionality reduction of a 2
𝑛𝑑
order
tensor data 𝑿into 𝑿′, which is a set of 2D vector 𝑭′.
degree of similarity between the member and verication truth
data is used as an index (
𝐶
) to determine the color in the timeline
heatmap. This is obtained by calculating the distance
𝐷𝑓
between
the eld
𝐸𝑖 𝑓 𝑗 𝑣
, of member
𝑀𝑖
at time step
𝑡𝑗
, in comparison to the
eld
𝑶=𝐸𝑡:𝑗𝑣
from the verication truth data at each of the time
steps, as follows:
𝐶=𝐷𝑓(𝑂, 𝐸𝑖 𝑓 𝑗 𝑣 ).(10)
The obtained minimum and maximum values for the
𝐶
will be
used to dene the colormap range for coloring the timeline heatmap.
3.4
Isosurface-based Comparative Visualization
3D visual representation in the form of a probabilistic isosurface
plot (Fig. 2(e)) will be used for comparative visualization to identify
spatial regions with high or low discrepancies between members in
comparison to the verication truth data. Probabilistic Isosurface
can be dened as the probability of the existence of the isosurfaces
from the members when comparing the same 3D spatial location.
For this purpose, as shown in Fig. 9, the 3
𝑟𝑑
order tensor data
𝑬:::𝒊
,
used for the previous overview visualization, will be applied for
slicing along the
𝑻
axis, and this will result in a 2
𝑛𝑑
order tensor
data
𝑷=𝐸::𝑡𝑣
. It is worth mentioning that this
𝑷
will also be used
for the 2D slice rendering in the cross-sectional plot view (Fig. 2(c,
d)). For the probabilistic isosurface, isosurfaces for a given isovalue
will be extracted from each of the members, and will be used to
calculate their statistical distribution (Probabilistic Isosurface) by
using the Probabilistic Marching Cubes [
19
]. We assume that the
shape corresponds to 3D Cartesian grid cells, where each grid cell
Fig. 7: Visualization of the DR-based
𝑿′
by using connected
scatterplot, in the form of polygonal lines.
17
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HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan Go Tamura and Naohisa Sakamoto et al.
Fig. 8: Distance between member and verication truth data
is used as an index for coloring the timeline heatmap.
has eight grid points (
𝑔(𝑖), 𝑖 =
1
,
2
, . . . ,
8), and also assume that
𝜇𝑖
is the average of variable values v
(𝑖)
from all members at the
eight grid points, and
𝜎𝑖 𝑗
is the covariance of v
(𝑖)
and v
(𝑗)
from
all members. In addition, we also assume that the distribution of
variable values v
𝐺≡ {
v
(1),
v
(2), . . . ,
v
(8)}
at grid cell
𝐺
follows
the multivariate normal distribution:
𝑓(v𝐺)=
1
√2𝜋8√𝚺
exp(− 1
2(v𝐺−𝝁)′𝚺−1(v𝐺−𝜇)) (11)
Here, the mean
𝝁
and the variance-covariance matrix
𝚺
are given
as follows:
𝝁=(𝜇1, 𝜇2, . . . 𝜇8);𝚺=©«
𝜎11 ··· 𝜎81
.
.
.....
.
.
𝜎81 ··· 𝜎88 ª®®¬
(12)
Then, the probability
𝑃𝐺(𝜃)
, meaning if an isosurface with iso-
value 𝜃∈IR exists in the grid cell 𝐺, will be as follows:
𝑃𝐺(𝜃)=1−∫𝑑v(1)1∫𝑑v(2). . . ∫𝑑v(8)𝑓(v𝐺),(13)
where
∀𝛼∈ {1,2. . . , 8},v(𝛼)≤𝜃∨ ∀𝛼∈ {1,2. . . , 8},v(𝛼)≥𝜃 . (14)
Monte Carlo integration is applied to solve Eq. 13, and for this
purpose, a sequence of random numbers (satisfying Eq. 11) will be
generated, and the probability (satisfying the condition of Eq. 14)
will be estimated. The sequence of random numbers v, following
the multivariate normal distribution, is generated by using an initial
Fig. 9: Probabilistic Isosurface is obtained by applying Proba-
bilistic Marching Cubes to the isosurfaces extracted from all
members.
sequence of random numbers r
={𝑟1, 𝑟2, . . . , 𝑟 8}
, that follows the
normal distribution, and the Cholesky decomposed matrix A, from
the variance-covariance matrix
𝚺
, is applied to obtain v
=
Ar
+
𝝁
. Assuming that a random sampling is performed by using
𝑛
random numbers, then the probability 𝑃𝐺(𝜃)can be calculated by
approximation as follows:
𝑃𝐺(𝜃) ≈ 1−1
𝑛
𝑛

𝑘=1
𝑆(v𝑘),(15)
where
𝑆(v)=1if vfulll the Eq. 14
0otherwise
The eld data for the probabilistic isosurface will then be ob-
tained by calculating this probability for all grid cells, from the
𝑁𝑚
elds that constitute the 2
𝑛𝑑
order tensor data
𝑷
. To quantify the
probability of the existence of members’ isosurface in comparison
to the verication truth data, we calculate the probability quantica-
tion index for coloring the isosurface. For this purpose, we focus on
the grid cell
𝐺
, which contains the point Xon the isosurface from
verication truth data. The eight grid points that constitute the grid
cell
𝐺
are represented as
𝑔(𝑘), 𝑘 =
1
,
2
, ..,
8, and the probability for
the existence of the isosurface on the grid points can be dened as
𝑃𝑔(𝑘)
. The probability
𝑃X(𝜃)
for the isosurface, of isovalue
𝜃
, that
will pass through the point X, can be then calculated by using linear
interpolation. By assuming that (𝑥 , 𝑦, 𝑧)represents the coordinate
value of point Xon the isosurface, located in the global coordinate
system, then the corresponding coordinate value
(𝑝, 𝑞, 𝑟 )
of a point
X′on the local coordinate system can be obtained as follows:
𝑝=2𝑥−𝑥1
Δ𝑥−1; 𝑞=2𝑦−𝑦1
Δ𝑦−1; 𝑟=2𝑧−𝑧1
Δ𝑧−1(16)
Here,
Δ𝑥, Δ𝑦, Δ𝑧
represent the grid spacing in each of the 3D carte-
sian axes, and the probability quantication index
𝑃X
for the mem-
bers’ isosurface with isovalue 𝜃, can be calculated as follows:
𝑃X(𝜃)=
8

𝑘=1
𝑁𝑘(𝑝, 𝑞, 𝑟 )𝑃𝑔(𝑘)(𝜃)(17)
Here,
𝑁𝑘
represents the interpolation function for the grid cell
𝐺
,
and is calculated from the local coordinates
(𝑝𝑘, 𝑞𝑘, 𝑟𝑘)
of the grid
points, from the grid cell, as follows:
𝑁𝑘(𝑝, 𝑞, 𝑟 )=
1
8(1+𝑝𝑘𝑝)(1+𝑞𝑘𝑞)(1+𝑟𝑘𝑟).(18)
Here,
(𝑝𝑘, 𝑞𝑘, 𝑟𝑘)
is given as the local coordinates of the grid points
constituting the grid cells.
In this work, we extended the probabilistic isosurface plot by
also providing how the members’ mean behave compared to the
verication truth data. For this purpose, we will use another color
mapping index named certainty quantication index
𝐶X
to present
how certain the members’s mean isosurface is compared to the
verication truth data’s isosurface with the same isovalue
𝜃
. As
shown in Fig. 10, we used the averaged eld from all members
since the centrally located isosurface will be proportional to the
isosurface extracted from the averaged eld data, as explained
in [
18
]. As shown in the gure, the distance between a point X, on
the verication truth data’s isosurface, with respect to the isosurface
18
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DR-based Interactive Visual Analytics Approach for Investigating Ensemble Weather Simulations HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan
𝑆𝑚𝑒𝑎𝑛
, from the averaged eld data, can be obtained by searching
for the shortest distance between the vertices constituting both
isosurfaces. This distance can be represented as
𝐷𝑠(𝑆𝑚𝑒𝑎𝑛,
X
)
, and
will be used to calculate the certainty quantication index
𝐶X
, for
the point X, as follows:
𝐶X=
𝑃X(𝜃)
𝐷𝑠(𝑆𝑚𝑒𝑎𝑛,X) + 1(19)
These probability (
𝑃X
) and certainty (
𝐶X
) quantication indexes
are used for coloring in the probabilistic isosurface plot view (Fig. 2(e)).
Fig. 10: Distance
𝐷
, between the point Xon the verication
truth data’s isosurface with respect to the average isosurface,
is calculated by searching for the shortest distance, and used
for obtaining the certainty quantication index applied for
coloring the isosurface.
3.5 Visual Analytics System
We implemented a prototype visual analytics system by integrating
the back-end processing and rendering functionalities to realize the
visual analytics workow detailed in Fig. 1. For this purpose, we
used KVS (Kyoto Visualization System) [
21
], a C++-based integrated
development framework for visualization application development.
We also used the Qt6 [
1
] framework to implement the graphical user
interface (GUI) shown in Fig. 2. Through this GUI, users are able to
interact, for instance, to select a region, member, or time of interest,
as well as to visually explore the 2D and 3D rendering results. In the
DR plot view (Fig. 2(a)), labeling is applied to the polygonal lines
to facilitate its identication, and depending on the user-selected
member, automatic enlargement (zoom in) or reduction (zoom out)
will be carried out to improve its recognition. Through the timeline
heatmap plot view (Fig. 2(b)), users can select a member and time
of interest, and this will update the DR plot. The member chosen
will be colored in red, and the members’ label will move to the
corresponding time position to facilitate their identication and
comparison. In the probability isosurface plot view (Fig. 2(e)), the
probability isosurface for the selected time step will be visualized
as a 3D rendering, and users can also freely navigate through the
rendering results. In the same manner, in the cross-sectional plot
views (Fig. 2(c,d)), 2D rendering will be updated every time the user
selects a dierent time of interest. Users can also freely navigate
through the cross-sectional views by modifying the z-coordinate
value using the attached slider.
4 Experimental Evaluations
Practical experiments were conducted with a domain expert to eval-
uate the eectiveness of the proposed visual analytics approach.
For this purpose, we used a computational server composed of
Dual Intel Xeon Gold 6238R (28 cores / 2.20 GHz each) CPU, 384GB
of DRAM, and an NVIDIA Quadro RTX 8000 GPU. Although we
used a hardware system located far from an HPC site, it is worth
mentioning that the visual analytics can be carried out in the visu-
alization environment usually provided at HPC sites, such as the
pre/post-processing system on the Fugaku supercomputer environ-
ment [2].
4.1 Utilized Dataset
Output from an ensemble weather simulation, with data assimila-
tion, using 20 members, carried out on the Fugaku supercomputer,
was used as the target ensemble data. The weather simulation
model corresponds to a torrential rain on July 28, 2008, in Kobe
City, which caused a rapid rise in the Toga River’s water level,
causing unfortunate human losses. It is worth mentioning that
pseudo-observational data was used as the verication truth data,
since the Phased Array Weather Radar (PAWR), currently operating
at the Suita Campus of Osaka University, did not exist at that time.
The simulation model is from the Japan Meteorological Agency
Nonhydrostatic Model (JMA-NHM). In this model, 11 variables
are utilized for the numerical simulation. The model domain has
120
×
120 horizontal grids at 1-km resolution and 50 vertical lay-
ers. The vertical grids have non-equal intervals ranging from 20
m to 22
,
244 m. The center of the model domain corresponds to
the location of the PAWR in Osaka University, and the simulation
domain covers the entire region of Kobe-city as shown in Fig. 11.
The main variables of interest for the evaluations were the mixing
ratio of water vapor (QV), which is one of the main factors for the
development of cumulonimbus clouds that cause heavy rain, and
the mixing ratio of rainwater (QR), which indicates the amount of
heavy rain.
4.2 Visual Analytics Case Study
Fig. 12 shows the members’ distribution when selecting QV as the
variable of interest in the DR plot view. It is worth mentioning that
the gure on the right side (b) is the same as that shown in Fig. 2(a).
The green line represents the verication truth data, the blue lines
represent the members, and the red line represents the selected
member. From these plots, it becomes straightforward to gure out
that the similarity between the members and verication truth data
Fig. 11: Simulation region (120Km
×
120Km), with Kobe City
in the center (Images were obtained from Google Maps).
19
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HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan Go Tamura and Naohisa Sakamoto et al.
is smaller than the similarity among the members. This can also be
conrmed by visualizing the corresponding cross-sectional views
as shown in Fig. 2 (c,d).
Fig. 12: DR plot view when selecting QV as the variable of
interest. Ensemble members with (a) and without (b) veri-
cation truth data. The green colored plots represent the
verication truth data, and the red colored plots represent
the selected member (member “0” in the example).
From Fig. 12(b), we could also identify 13 members (from 7 to
19) that are closely arranged. From the domain expert point of
view, this similar behavior among many members indicates that the
ensemble simulation shows an ideal state for the variable QV. In
addition, it also becomes easy to identify distribution bias among the
members, thus enabling a better understanding of the distribution
Fig. 13: Timeline heatmap plot showing the similarity (dis-
tance) of each member, for the variable QV, when compared
to the verication truth data. The horizontal axis represents
the simulation time steps, and the vertical axis represents
the members.
Fig. 14: Timeline heatmap plot showing the similarity of QR.
of the members during the simulation. The timeline heatmap plot
view (Fig. 13) shows how the similarity among the members, for
the variable QV, compared to the verication truth data evolve
over time. The smaller the distance (representing higher similarity),
the closer it will be to the blue color. From this kind of visual
representation, it becomes easy to observe that the similarity of
all members proportionately decreases over time, and the domain
scientist explained that it is in line with what is expected.
On the other hand, Fig. 15 shows the DR and timeline heatmap
plots when selecting the variable QR. From the timeline heatmap
plot, it becomes easy to identify that in the beginning they are
plotted in blue color, indicating a high degree of similarity, and
this can be easily conrmed on the DR plot since the members
are densely plotted in the top portion. However, in the middle of
the simulation, the heatmap plot changes from yellow to orange,
indicating relatively low similarity with respect to the verication
truth data. This can also be conrmed from the DR plot since the
members become separately plotted. In addition, we can observe
high similarity at the right end of the time steps. This kind of
information was not possible to gure out by using traditional
visual analysis based on ensemble mean and spread, and much
richer information becomes possible to obtain via interactive visual
analysis, bringing an immediate response (update) to the actions.
Fig. 15: DR plot view when selecting QR.
We used the variable QV To evaluate the probability isosurface
plot view. We set the isovalue as
𝜃=
0
.
001
𝑔/𝑘𝑔
, and the result-
ing spatial distribution of certainty (accuracy) and probability are
shown in Fig. 16. This isovalue corresponds to the region where it
is raining. Plot (a) shows the visualization results when selecting
“Certainty” in the radio button (Fig. 2(e)), and the isosurface from
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DR-based Interactive Visual Analytics Approach for Investigating Ensemble Weather Simulations HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan
verication truth data will be colored by using the certainty quan-
tication index (Eq. 19). In this plot, the most accurate regions will
be displayed in red, and the less accurate regions will be displayed
in blue. This plot was helpful to the domain expert to understand
that although most of the region is red, there is a band-shaped
blue region in the center. A possible explanation was that this can
be caused by ascending air currents and clouds resulting in high
variability to the simulation results, thus reducing the accuracy of
the simulation model. Plot (b) shows the results when selecting
“Probability” in the radio button (Fig. 2(e)), which will superimpose
the probability distribution by using the probability quantication
index (Eq. 17). Plot (c) shows the regions with a higher probabil-
ity (yellow), and plot (d) regions with a lower probability (purple).
From plot (c), it is possible to observe that the isosurface is hidden
in the high probability region; that is, it corresponds to most of the
members being close to the verication truth data. On the other
hand, we can observe from plot (d) that the lower probability region
is located at a lower altitude than the isosurface. An explanation for
this is the existence of a specic member (member 0), which shows
distinct behavior from other members as shown in Fig. 12(b). From
these practical evaluations, we could conrm the eectiveness of
the proposed visual analytics workow, which can bring much
richer information to the domain scientists to better understand
the ensemble simulation behavior, which was not possible to obtain
by using traditional visual analysis based on ensemble mean and
spread.
Fig. 16: Probability isosurface plot showing (a) the isosur-
face from the verication truth data colored by using the
certainty quantication index (Eq. 19), and (b, c, d) when
superimposing with the spatial distribution of probability
quantication index (Eq. 17).
4.3 Pre-processing
It is worth mentioning that part of the computation was executed as
pre-processing to enable quick response during interactive visual
exploration. The pre-processing was applied to the calculations
related to dimensionality reduction (DR) and probabilistic marching
cubes (PMC). To make clear the involved computational cost, we
set the number of Monte Carlo sampling during the PMC as 100
and measured the processing time when changing the number of
time steps or the number of members. Table 1 shows the processing
time, in seconds, when changing the number of members by xing
the number of time steps as 15. Table 2 shows the processing time
when changing the number of time steps by xing the number of
members as 10. Considering that the target is HPC-based ensemble
simulations, we are investigating the possibility of applying in-situ
processing on the HPC side.
Table 1: Processing times (sec.) of DR and Probabilistic March-
ing Cubes (PMC) when xing the number of time steps as 15.
5 members 10 members 20 members
DR 2.42 4.12 10.89
PMC 309.44 318.52 329.26
Table 2: Processing times (sec.) of DR and PMC when xing
the number of members as 10.
5 steps 10 steps 20 steps 60 steps
DR 0.63 1.79 6.01 49.9
PMC 106.04 210.35 421.66 1,267.37
5 Conclusion
In this work, we proposed an interactive visual analytics approach
to enable interactive visual exploration of ensemble data composed
of ensemble simulation output and its related verication truth data.
It is expected to facilitate the investigation of ensemble weather sim-
ulations, using verication truth data for data assimilation, which
has become increasingly common. In the proposed approach, the
target ensemble data is expressed as fourth-order tensor data with
members, variables, time, and space as the reference axes for nec-
essary subsequent processing. The GUI is composed of multiple
linked views to enable overview as well as comparative visualiza-
tion of spatiotemporal features among the members themselves
and in comparison with the verication truth data. The timeline
heatmap plot was designed to facilitate the search for members
and time of interest and to assist the analysis of the dimensionality
reduction plot, especially when visual cluttering occurs in densely
plotted regions. The probability isosurface plot has proven helpful
for easily identifying spatial regions with low or high discrepancies
between isosurfaces from members and verication truth data. The
proposed visual analytics tool has been developed to fulll the three
main requirements from the domain expert side, and the experimen-
tal evaluations conrmed that the proposed visual analytics system
could be helpful for better understanding the ensemble members’
spatiotemporal behavior compared to the verication truth data,
which was not possible by using traditional visual analysis based on
ensemble mean and spread. A deeper understanding of ensemble
members’ behavior compared to the verication truth data is ex-
pected to contribute to the improvements in the simulation models,
thus increasing their accuracy and assisting in mitigating weather-
related natural disasters caused by torrential rains. In future work,
we plan to investigate other DR-based techniques and work on the
variable axis of the ensemble data to enable more detailed analysis
and exible visual exploration.
21
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HPCASIA ’25, February 19–21, 2025, Hsinchu, Taiwan Go Tamura and Naohisa Sakamoto et al.
Acknowledgments
This work was partially supported by JSPS KAKENHI (Grant Num-
bers: 20H04194, 21H04903, 22H03603). This work was partially
supported by MEXT as “Program for Promoting Researches on
the Supercomputer Fugaku” (Drastic acceleration of the industrial
applications of HPC through AI and research and development of
new computational methods for the next era, JPMXP1020230321).
This work used computational resources of the supercomputer Fu-
gaku provided by the RIKEN Center for Computational Science
(Project ID: ra000007, rccs-hud).
References
[1] [n. d.]. Qt6. https://www.qt.io. (accessed on 2024.11.10).
[2]
[n. d.]. Towards an Easy-to-Use Visualization Environment on the Fugaku. https:
//www.sc-asia.org/2023/wp-content/uploads/2023/02/post121s2-le2.pdf . (ac-
cessed on 2024.11.10).
[3]
Michael AA Cox and Trevor F Cox. 2008. Multidimensional Scaling. In Handbook
of Data Visualization. Springer, 315–347.
[4]
Carolina VeigaFerreira de Souza, Priscila da Cunha Luz Barcellos, Lhaylla Crissa,
Marcio Cataldi, Fabio Miranda, and Marcos Lage. 2022. Visualizing Simulation
Ensembles of Extreme Weather Events. Computers & Graphics (2022). doi:10.
1016/j.cag.2022.01.007
[5]
Ismail Demir, Christian Dick, and Rüdiger Westermann. 2014. Multi-Charts for
Comparative 3D Ensemble Visualization. IEEE Transactions on Visualization and
Computer Graphics 20, 12 (2014), 2694–2703.
[6]
Marina Evers, Karim Huesmann, and Lars Linsen. 2021. Uncertainty-aware
Visualization of Regional Time Series Correlation in Spatio-temporal Ensembles.
Computer Graphics Forum (2021). doi:10.1111/cgf.14326
[7]
Alexey Fofonov and Lars Linsen. 2019. Projected Field Similarity for Comparative
Visualization of Multi-Run Multi-Field Time-Varying Spatial Data. In Computer
Graphics Forum, Vol. 38. Wiley Online Library, 286–299.
[8]
Alexey Fofonov, Vladimir Molchanov, and Lars Linsen. 2015. Visual Analysis of
Multi-run Spatio-temporal Simulations using Isocontour Similarity for Projected
Views. IEEE Transactions on Visualization and Computer Graphics 22, 8 (2015),
2037–2050.
[9]
Thomas Höllt, Ahmed Magdy, Peng Zhan, Guoning Chen, Ganesh Gopalakrish-
nan, Ibrahim Hoteit, Charles D Hansen, and Markus Hadwiger. 2014. Ovis: A
Framework for Visual Analysis of Ocean Forecast Ensembles. IEEE Transactions
on Visualization and Computer Graphics 20, 8 (2014), 1114–1126.
[10]
Tamara G Kolda and Brett W Bader. 2009. Tensor Decompositions and Applica-
tions. SIAM review 51, 3 (2009), 455–500.
[11]
Keiichi Kondo and Takemasa Miyoshi. 2016. Impact of Removing Covariance
Localization in an Ensemble Kalman Filter: Experiments with 10,240 Members
using an Intermediate AGCM. Monthly Weather Review 144, 12 (2016), 4849 –
4865. doi:10.1175/MWR-D- 15-0388.1
[12]
Yasumitsu Maejima and Takemasa Miyoshi. 2022. A Control Simulation Experi-
ment for August 2014 Severe Rainfall Event Using a Regional Model. In American
Meteorological Society 102𝑛𝑑 Annual Meeting, Session 4-2.
[13]
Yasumitsu Maejima, Takemasa Miyoshi, Masaru Kunii, Hiromu Seko, and Kae
Sato. 2019. Impact of Dense and Frequent Surface Observations on 1-Minute-
Update Severe Rainstorm Prediction: A Simulation Study. Journal of the Meteoro-
logical Society of Japan. Ser. II 97 (2019), 253–273.
[14]
Mahsa Mirzargar, Ross T Whitaker, and Robert M Kirby. 2014. Curve Boxplot:
Generalization of Boxplot for Ensembles of Curves. IEEE Transactions on Visual-
ization and Computer Graphics 20, 12 (2014), 2654–2663.
[15]
Takemasa Miyoshi, Arata Amemiya, Shigenori Otsuka, Yasumitsu Maejima, James
Taylor, Takumi Honda, Hirofumi Tomita, Seiya Nishizawa, Kenta Sueki, Tsuyoshi
Yamaura, YutakaIshikawa, Shinsuke Satoh, Tomoo Ushio, Kana Koike, and Atsuya
Uno. 2023. Big Data Assimilation: Real-time 30-second-refresh Heavy Rain
Forecast Using Fugaku During Tokyo Olympics and Paralympics. In Proceedings
of the International Conference for High Performance Computing, Networking,
Storage and Analysis (Denver, CO, USA) (SC ’23). Association for Computing
Machinery, New York, NY, USA, Article 8, 10 pages. doi:10.1145/3581784.3627047
[16]
Harald Obermaier and Kenneth I Joy. 2014. Future Challenges for Ensemble
Visualization. IEEE Computer Graphics and Applications 34, 3 (2014), 8–11.
[17]
Jorge Poco, Aritra Dasgupta, Yaxing Wei, William Hargrove, Christopher
Schwalm, Robert Cook, Enrico Bertini, and Claudio Silva. 2014. Similarity-
Explorer: A Visual Inter-Comparison Tool for Multifaceted Climate Data. In
Computer Graphics Forum, Vol. 33. Wiley Online Library, 341–350.
[18]
Kai Pöthkow and Hans-Christian Hege. 2010. Positional Uncertainty of Iso-
contours: Condition Analysis and Probabilistic Measures. IEEE Transactions on
Visualization and Computer Graphics 17, 10 (2010), 1393–1406.
[19]
Kai Pöthkow, Britta Weber, and Hans-Christian Hege. (2011). Probabilistic March-
ing Cubes. In Computer Graphics Forum, Vol. 30. Wiley Online Library, 931–940.
[20]
Marc Rautenhaus, Michael Böttinger, Stephan Siemen, Robert Homan, Robert M.
Kirby, Mahsa Mirzargar, Niklas Röber, and Rüdiger Westermann. 2018. Visual-
ization in Meteorology — A Survey of Techniques and Tools for Data Analysis
Tasks. IEEE Transactions on Visualization and Computer Graphics 24, 12 (2018),
3268–3296.
[21]
Naohisa Sakamoto and Koji Koyamada. 2015. KVS: A Simple and Eective
Framework for Scientic Visualization. Journal of Advanced Simulation in Science
and Engineering 2, 1 (2015), 76–95.
[22]
Jibonananda Sanyal, Song Zhang, Jamie Dyer, Andrew Mercer, Philip Amburn,
and Robert Moorhead. 2010. Noodles: A Tool for Visualization of Numerical
Weather Model Ensemble Uncertainty. IEEE Transactions on Visualization and
Computer Graphics 16, 6 (2010), 1421–1430.
[23]
S.I. Seneviratne, X. Zhang, M. Adnan, W. Badi, C. Dereczynski, A. Di Luca, S.
Ghosh, I. Iskandar, J. Kossin, S. Lewis, F. Otto, I. Pinto, M. Satoh, S.M. Vicente-
Serrano, M. Wehner, and B. Zhou. 2021. Weather and Climate Extreme Events in
a Changing Climate. Cambridge University Press, Cambridge, United Kingdom
and New York, NY, USA, 1513–1766. doi:10.1017/9781009157896.013
[24]
Qingya Shu, Hanqi Guo, Jie Liang, Limei Che, Junfeng Liu, and Xiaoru Yuan. 2016.
Ensemblegraph: Interactive Visual Analysis of Spatiotemporal Behaviors in En-
semble Simulation Data. In 2016 IEEE Pacic Visualization Symposium (PacicVis).
IEEE, 56–63.
[25]
Tadashi Tsuyuki and Takemasa Miyoshi. 2007. Recent Progress of Data Assimila-
tion Methods in Meteorology. Journal of the Meteorological Society of Japan. Ser.
II 85B (2007), 331–361. doi:10.2151/jmsj.85B.331
[26]
Dominik Vietingho, Christian Heine, Michael Böttinger, Nicola Maher, Johann
Jungclaus, and Gerik Scheuermann. 2021. Visual Analysis of Spatio-Temporal
Trends in Time-Dependent Ensemble Data Sets on the Example of the North
Atlantic Oscillation. In 2021 IEEE 14th Pacic Visualization Symposium (PacicVis).
71–80. doi:10.1109/PacicVis52677.2021.00017
[27]
Junpeng Wang, Subhashis Hazarika, Cheng Li, and Han-Wei Shen. 2018. Visual-
ization and Visual Analysis of Ensemble Data: A Survey. IEEE Transactions on
Visualization and Computer Graphics 25, 9 (2018), 2853–2872.
[28]
Junpeng Wang, Xiaotong Liu, Han-Wei Shen, and Guang Lin. 2016. Multi-
Resolution Climate Ensemble Parameter Analysis with Nested Parallel Coor-
dinates Plots. IEEE Transactions on Visualization and Computer Graphics 23, 1
(2016), 81–90.
[29]
Keita Watanabe, Naohisa Sakamoto, Jorji Nonaka, and Yasumitsu Maejima. 2022.
Angular-based Edge Bundled Parallel Coordinates Plot for the Visual Analysis of
Large Ensemble Simulation Data. In 2022 IEEE 12th Symposium on Large Data
Analysis and Visualization (LDAV). 1–10. doi:10.1109/LDAV57265.2022.9966393
[30]
Ross T Whitaker, Mahsa Mirzargar, and Robert M Kirby. 2013. Contour Boxplots:
A Method for Characterizing Uncertainty in Feature Sets from Simulation En-
sembles. IEEE Transactions on Visualization and Computer Graphics 19, 12 (2013),
2713–2722.
[31]
Mingdong Zhang, Li Chen, Quan Li, Xiaoru Yuan, and Junhai Yong. 2021.
Uncertainty-Oriented Ensemble Data Visualization and Exploration using Vari-
able Spatial Spreading. IEEE Transactions on Visualization and Computer Graphics
27, 2 (2021), 1808–1818. doi:10.1109/TVCG.2020.3030377
[32]
Wenxia Zhang, Tianjun Zhou, Lixia Zhang, Kexin Gui, Tingyu Zhang, Lan Li,
Pan Rongyun, Yongjun Chen, Shijie Tang, Shuai Hu, Robin Clark, Laurent Li,
Chao Li, Juan Rivera, and Xin Huang. 2024. 2023: Weather and Climate Extremes
Hitting the Globe with Emerging Features. Advances in Atmospheric Sciences 41
(04 2024), 1–16. doi:10.1007/s00376- 024-4080- 3
22
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