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Visualization-Driven Structural and Statistical Analysis of Turbulent Flows

Abstract and Figures

Knowledge extraction from data volumes of ever increasing size requires ever more flexible tools to facilitate interactive query. Interactivity enables real-time hypothesis testing and scientific discovery, but can generally not be achieved without some level of data reduction. The approach described in this paper combines multi-resolution access, region-of-interest extraction, and structure identification in order to provide interactive spatial and statistical analysis of a terascale data volume. Unique aspects of our approach include the incorporation of both local and global statistics of the flow structures, and iterative refinement facilities, which combine geometry, topology, and statistics to allow the user to effectively tailor the analysis and visualization to the science. Working together, these facilities allow a user to focus the spatial scale and domain of the analysis and perform an appropriately tailored multivariate visualization of the corresponding data. All of these ideas and algorithms are instantiated in a deployed visualization and analysis tool called VAPOR, which is in routine use by scientists internationally. In data from a 10243 simulation of a forced turbulent flow, VAPOR allowed us to perform a visual data exploration of the flow properties at interactive speeds, leading to the discovery of novel scientific properties of the flow, in the form of two distinct vortical structure populations. These structures would have been very difficult (if not impossible) to find with statistical overviews or other existing visualization-driven analysis approaches. This kind of intelligent, focused analysis/refinement approach will become even more important as computational science moves towards petascale applications.
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Visualization-Driven Structural and Statistical
Analysis of Turbulent Flows
Kenny Gruchalla1, Mark Rast2, Elizabeth Bradley1, John Clyne3, and Pablo
Mininni4
1Department of Computer Science, University of Colorado, Boulder, Colorado
2Laboratory for Atmospheric and Space Physics, Department of Astrophysical and
Planetary Sciences, University of Colorado, Boulder, Colorado
3Computational and Information Systems Laboratory, National Center for
Atmospheric Research, Boulder, Colorado
4Departamento de F´ısica, Facultad de Ciencias Exactas y Naturales, Universidad de
Buenos Aires, Argentina and Geophysical Turbulence Program, National Center for
Atmospheric Research, Boulder, Colorado
Abstract. Knowledge extraction from data volumes of ever increasing
size requires ever more flexible tools to facilitate interactive query. In-
teractivity enables real-time hypothesis testing and scientific discovery,
but can generally not be achieved without some level of data reduction.
The approach described in this paper combines multi-resolution access,
region-of-interest extraction, and structure identification in order to pro-
vide interactive spatial and statistical analysis of a terascale data volume.
Unique aspects of our approach include the incorporation of both local
and global statistics of the flow structures, and iterative refinement fa-
cilities, which combine geometry, topology, and statistics to allow the
user to effectively tailor the analysis and visualization to the science.
Working together, these facilities allow a user to focus the spatial scale
and domain of the analysis and perform an appropriately tailored mul-
tivariate visualization of the corresponding data. All of these ideas and
algorithms are instantiated in a deployed visualization and analysis tool
called VAPOR, which is in routine use by scientists internationally. In
data from a 10243simulation of a forced turbulent flow, VAPOR allowed
us to perform a visual data exploration of the flow properties at interac-
tive speeds, leading to the discovery of novel scientific properties of the
flow, in the form of two distinct vortical structure populations. These
structures would have been very difficult (if not impossible) to find with
statistical overviews or other existing visualization-driven analysis ap-
proaches. This kind of intelligent, focused analysis/refinement approach
will become even more important as computational science moves to-
wards petascale applications.
1 Challenges to data analysis
A critical disparity is growing in the field of computational science: our abil-
ity to generate numerical data from scientific computations has in many cases
exceeded our ability to analyze those data effectively. Supercomputing systems
have now reached petaflop performance [1], supporting numerical models of ex-
traordinary complexity, fidelity, and scale. In supercomputing centers, terabyte
data sets are now commonplace and petabyte data sets are anticipated within a
few years. However, analysis tools and the computational machinery that sup-
ports them have not been able to scale to meet the demands of these data.
For many computational scientists, this lack of analysis capability is the largest
barrier to scientific discovery.
The imbalance of scale between numerical simulation and data analysis is
largely due to their contrasting demands on computational resources. Large-
scale numerical simulation is typically a batch processing operation that proceeds
without human interaction on parallel supercomputers. Data analysis, in con-
trast, is fundamentally an interactive process with a human investigator in the
loop, posing questions about the data and using the responses to progressively
refine those questions[2]. While some data analyses certainly can be performed
in batch mode, this is only practical for completely predetermined investiga-
tions. Exploratory analysis depends on hypothesis generation and testing, which
requires an interactive environment that can provide timely and meaningful feed-
back to the investigator. Unfortunately, this kind of interactive workflow is not
well-suited to batch access on a parallel supercomputer. Another key bottleneck
in the analysis process is data storage. If the data exceeds the size of the available
random access media, one must manage its storage and exchange across differ-
ent media. Disk transfer rates are generally inadequate to support interactive
processing of large-scale computational data sets.
These dilemma can be addressed by data reduction, and a variety of schemes
have been developed to reduce data volumes while maintaining essential proper-
ties. Their methods and results depend on the scientific goals of the simulation
and analysis. For example, in the investigation of turbulent flows, analysis of
strictly statistical or spectral properties can enable significant reduction in data
dimensionality, while analysis of local flow dynamics, thermodynamics, or stabil-
ity does not. In the later cases, the only solution is to reduce the physical volume
under analysis. There are two general classes of methods for this. First, one can
isolate and extract local sub-regions from the global domain. The success of this
strategy depends on locating those regions in the solution that are of particu-
lar scientific importance or interest, which is a real challenge to intelligent data
analysis. There has been some very interesting work in the IDA community on
dimensional reduction for this purpose[3, 4]. The visualization-driven approach
described in this paper extracts regions of interest using an iterative interactive
filtering technique that employs a combination of global and local flow statistics.
The second class of data-volume reduction techniques uses a coarsened global
approximation of the discrete solution to subsample the data over the entire do-
main. The obvious challenge here is selecting an appropriate coarsening (method
and scale) to maintain accuracy — and confidence in the results.
Both of these data-reduction techniques have been implemented in VAPOR,
an open-source desktop visualization-driven analysis application (available at
http://www.vapor.ucar.edu). It closely couples advanced visualization with quan-
titative analysis capabilities, and it handles the complexities of large datasets
using a hierarchical data model. It is designed to support a multi-phase analysis
process, allowing the investigator to control a speed-and-memory versus a locus-
and-quality trade off. This is an ideal context within which to explore intelligent
data reduction. Using the ideas described in the previous paragraph, we have
extended VAPOR’s capabilities to include definition, manipulation, and refine-
ment of feature sub-spaces based on multi-scale statistics of turbulent structures
contained within the data. The user can explore the data volume at a coarsened
resolution to gain a qualitative understanding and identify regions/structures of
interest. Those regions/stuctures can then be investigated at progressively higher
resolutions with computationally intensive visualization and analysis performed
on progressively smaller sub-domains or structure populations. The base func-
tionality of VAPOR provides data coarsening in the form of multi-resolution
access via wavelet decomposition and reconstruction [5]. VAPOR’s data coars-
ening approach coupled with a simple a simple sub-domain selection capabil-
ity and has a successful track record in the analysis of large-scale simulation
data using only modest computing resources [6]. With the addition of intelligent
region-of-interest extraction, VAPOR can now provide interactive, scientifically
meaningful explorations of tera-scale data volumes.
The following Section describes VAPOR’s visualization-driven analysis ca-
pabilities; Section 3 demonstrates their power using data from a 10243forced
incompressible hydrodynamic simulation.
2 VAPOR: A desktop analysis and visualization
application
Many applications have been developed specifically for the visualization and
analysis of large-scale, time-varying numerical data, but all of them have signifi-
cant limitations in terms of visualization, analysis, and/or scalability. In many of
these tools, the emphasis is on the algorithms and the generation of aesthetic im-
ages, rather than on scientific discovery [7]. Visualization-oriented applications,
like Paraview [8], Visit [9], and Ensight, lack quantitative analysis capabilities,
and many of them demand specialized parallel computing resources. High-level,
fourth-generation data languages such as ITT’s IDL and Mathworks’s Matlab
are on the opposite end of the analysis-visualization spectrum. They provide a
rich set of mathematical utilities for the quantitative analysis of scientific data
but only limited visualization capabilities, and they do not scale well to very
large data sets.
The goal of the VAPOR project was to address these shortcomings. It pro-
vides an integrated suite of advanced visualization capabilities that are specif-
ically tailored to volumetric time-varying, multivariate numerical data. These
capabilities, coupled with the intelligent data reduction strategies introduced in
the previous sections, allow investigators to rapidly identify scientifically mean-
ingful spatial-temporal regions in large-scale multivariate data. VAPOR’s design
— both its functionality and its user interface — is guided by a steering com-
mittee of computational physicists to ensure that it truly meets the needs of
the end-user community. Scalability is addressed through a multi-phase analysis
process that is based on a combination of region-of-interest isolation, feature
extraction (with our extensions), and a hierarchical data model. Finally, VA-
POR interfaces seamlessly with high-level analysis languages like IDL, allowing
its user to perform rigorous quantitative analyses of regions of interest.
2.1 Visualization
VAPOR incorporates a variety of state-of-the-art volume rendering and flow-
visualization techniques, including both direct and indirect volume rendering [10].
Direct volume rendering describes a class of techniques, which generate images
directly from volumetric data without any intermediate geometric constructions,
while indirect volume rendering constructs geometric isosurfaces. To support the
visualization of vector fields, VAPOR provides both sparse and dense particle-
tracing methods [11]. The former render the geometry of individual trajectories
of particles seeded in a flow field, and can support both steady (time-invariant)
and unsteady (time-varying) trajectory integration. Dense particle-tracing meth-
ods synthesize textures that represent how the flow convolves input noise.
VAPOR’s integrated design allows these volume rendering and flow-visualization
techniques to be used in different combinations over a single analysis run, in con-
cert with the intelligent data reduction strategies described in Section 2.3, as the
investigator progressively isolates and refines scientifically meaningful regions of
the data. The hierarchical data model that supports this is described in the next
Section. By utilizing the optimized data-parallel streaming processors of modern
graphics processing units (GPUs), VAPOR can effectively work with volumes of
the order of 15363[6].
2.2 Hierarchical data model
The VAPOR data storage model is based on wavelet decomposition [5, 12]. Data
are stored as a hierarchy of successively coarser wavelet coefficients; each level
in this hierarchy represents a halving of the data resolution along each spatial
axis, corresponding to an eight-fold reduction in data volume. In this manner,
VAPOR maintains a series of useful coarsened approximations of the data, any
of which can be accessed on demand during an analysis run, without an undue
increase in storage requirements. Wavelet data are organized into a collection
of multiple files: one binary file containing the wavelet coefficients for each time
step, each variable, and each wavelet transformation level, and a single metadata
file that describes the attributes of the field data (e.g., the grid type, the time
steps, the spatial resolution, the field names, etc.).
This storage model naturally supports intelligent, interactive data decom-
position. It allows VAPOR to operate on any subset of time steps, variables,
and wavelet transformation levels, which has a variety of important advantages,
including iterative focus and refinement of the analysis effort. An investigator
can control the level of interactivity by regulating the fidelity of the data, first
browsing a coarsened representation across the global spatial-temporal domain
to identify regions or features of interest and then examining those reduced do-
mains in greater detail. The hierarchical data/metadata combination also allows
VAPOR to work with very large data collections, as data components can be
stored off-line until required, handling incomplete data sets smoothly.
2.3 Multivariate feature extraction
The VAPOR volume rendering capability forms the basis for the multivariate
feature extraction technique we have implemented to isolate structures of inter-
est in large data sets. A multidimensional transfer function is used to define a
mapping from data values to the color and opacity values in the volume render-
ing. The opacity component of this function visually separates the volume into
opaque features. VAPOR users can construct and refine these functions itera-
tively, and use them in different thresholding schemes to visually separate the
volume into opaque regions.
Once these regions have been visually identified using the transfer function,
the individual structures are extracted and tagged using a connected-component
labeling algorithm [13], an image-processing technique that assigns groups of ǫ-
connected data points5a unique feature label. Once the features have been iden-
tified in this manner, they can be visualized and analyzed as individual features
oppose to a set of opaque voxels. The individual features can be visualized in
isolation or as members of sub-groups, and the data points and geometry of each
can exported to external analysis packages for further analysis, as described in
Section 2.4. This allows any user-defined physical property to be computed on
the associated data points contained in each feature, over any field or combina-
tion of fields in the data. VAPOR presents the resulting values and distributions
to the user as a table of feature-local histograms and property values, as shown
in Figure 1. Using this table, the set of features can be culled based on the central
moments of their distributions to further focus the study. The entire reduction
process—including the transfer function design and feature definition—can be it-
erated to progressively refine the analysis, providing insight into the multivariate
properties of structures across multiple scales.
2.4 Coupled visual, quantitative, and statistical analysis
Understanding large-scale simulation data is an exploratory process that can be
greatly facilitated by combining highly interactive, qualitative visual examina-
tion with quantitative numerical analysis. Visualization can be used to motivate
analysis through the identification of structures in the data, giving rise to hy-
potheses that can be validated or rejected through numerical study. Likewise,
the analysis can be used to drive the visualization, identifying salient quanti-
tative characteristics of the data through numerical study, and then visualiz-
ing their associated geometric shapes and physical properties. VAPOR’s design
5i.e., those that are connected by an ǫchain
Fig. 1. The VAPOR structure analysis dialog, which displays feature-local histograms
of user-selected field distributions.
seamlessly combines qualitative visual and quantitative numerical investigation,
enabling its users to interactively transition between the two. Its multi-resolution
visualization and region-of-interest isolation capabilities, in conjunction with its
hierarchical data representation, allow its users to cull data intelligently and pass
appropriate subsets to an external quantitative analysis package.
Smooth integration of all of these capabilities required some interesting de-
sign decisions. VAPOR performs GPU-accelerated visualization natively, as de-
scribed in Section 2.1, and hands numerical analysis off to IDL. VAPOR and
IDL sessions are run simultaneously; after regions of interest are identified in
the former, the associated data volumes are exported via metadata descriptors
to the latter for further study. The tight coupling between IDL and VAPOR is
accomplished by a library of data-access routines, which allow IDL access to the
wavelet-encoded data representation. (This approach is readily generalizable to
other analysis packages, complementing and enhancing existing user capabili-
ties.) The qualitative/quantitative tandem is very effective: IDL, as mentioned
at the beginning of Section 2, does not scale well to large data sets [12], but VA-
POR’s ability to focus the study neatly bypasses that problem, and the results
of IDL analysis on focused regions can be seamlessly imported back into the
VAPOR session for visual investigation. By repeating this process, very large
data sets can be interactively explored, visualized, and analyzed without the
overhead of reading, writing, and operating on the full data volume.
3 Application to vortical structures in Taylor-Green flow
As an illustration of the power of the ideas described in the previous sections,
we use VAPOR to explore data from an incompressible Taylor-Green forced tur-
bulence simulation with a microscale Reynolds number of Rλ1300 [14]. The
particular structures in this data that are of scientific interest involve vortic-
ity, but the volume contains so many of these structures, of different sizes and
strengths, as to pose a truly daunting analysis problem. The small-scale struc-
tures are particularly hard to isolate, so that is what we set out to analyze with
VAPOR.
Fig. 2. A volume rendering of areas of strong vorticity in Taylor-Green turbulence
isolates tens of thousands of vortical structures.
3.1 Global vorticity and structure identification
Vortices play important roles in the dynamics and transport properties of fluid
flows, but they are surprisingly hard to define, which complicates the task of de-
signing a vortex extraction method. Jiang et al. [15] provide an extensive survey
of current techniques. As a working definition, we treat a vortex filament, tube,
or sheet as a connected region with a higher relative amplitude of vorticity than
its surrounding [16]. Many vortex detection and visualization methods use the
same definition, and most of them operationalize it by thresholding the magni-
tude of the vorticity. This is the starting point for our analysis, but VAPOR’s
capabilities allowed us to add other scientifically meaningful analysis steps and
iteratively focus the process. In this particular case, it allowed us to investigate
the correlation between vorticity and helicity across multiple scales and discover
important structural properties that were previously unknown.
The first step in the process is to threshold the vorticity of the Taylor-Green
data using the opacity contribution of the multidimensional tranfer function.
The fields in the data include the simulated velocity vector field and two derived
fields: a vorticity vector field and a normalized helicity field. Vorticity is defined
as the curl of a velocity field, ω=∇ × v, characterizing the pointwise rotation
of fluid elements. Helicity is a scalar value, Hn=v·ω
|v||ω|, the cosine of the angle
between velocity and vorticity. An initial vorticity threshold was chosen to begin
separating the tube-like vortical structures in the data volume. This step isolates
tens of thousands of vortical structures, as shown in Figure 2. Using VAPOR’s
iterative refinement capabilities, we focus the study by further considering the
helicity within these structures. A global analysis across the entire data volume,
Figure 3, shows that both helicity and its pointwise correlation with vorticity
are distributed in a nearly uniform fashion—i.e., that all angles between velocity
and vorticity vectors occur with similar frequencies across all values of vorticity.
While this is a useful result, it lumps the whole data volume together, possibly
obscuring important local differences. Using VAPOR to generate feature-local
histograms, we find that different high-vorticity regions do indeed have distinct
helicity distributions, Figure 3(c). Three populations of structures are conspic-
uously evident: those whose helicity distributions span the full range with no
distinct peak, those with a peak at high absolute values of helicity (i.e., domi-
nated by nearly aligned or anti-aligned velocity and vorticity vectors), and those
whose helicity distributions peak near zero (i.e., dominated by nearly orthogonal
velocity and vorticity).
Fig. 3. The relationship between vorticity and helicity in Taylor-Green Turbulence a)
the histogram of global normalized helicity, indicating helicity, measured point wise in
the domain, has a nearly uniform distribution; b) the scatter plot of vorticity magni-
tude versus normalized helicity, showing that helicity has a nearly uniform distribution
across all values of vorticity; c) a selected subset of the feature-local helicity histograms
from features defined by high vorticity that show individual regions of strong vorticity
have distinct helicity distributions.
Using VAPOR’s intrinsic capabilities, we have thus effectively differentiated
the regions of strong vorticity into three structure populations, based on their
helicity distributions. In order to investigate the statistics and local dynamics
of these structures, we next extend the analysis through a combination of vi-
sualization in VAPOR and focused study in the coupled quantitative analysis
package. By visualizing individual features in isolation, we find that the wide
noisy distributions belong to composite structures that were not well separated
into individual components by the original vorticity thresholding, while the other
two populations are those of individual tube-like structures. This result allows
us to further cull the dataset and focus on the tube-like structures with either
high or low helicity magnitude. Both populations have similar geometries, but
streamlines seeded in these regions, as shown in Figure 5, reveal that their flow
properties are quite different. In the low-helicity tubes, the streamlines twist
around the core; in the high-helicity tubes the streamlines more closely follow
the writhe of the tube.
Further interactive analysis of these distinct vortex structures can proceed
either by examining the statistical properties of the population or the detailed
dynamics of any one of them. Looking first at statistics of the population of
vortical structures as a whole, we note that, while structures with all values of
helicity exist, there seems to be a small deficit of those with high absolute mean
value compared to the point-wise helicity distribution (Figure 4a). Moreover,
the helicty of any given structure is well defined and symetrically distributed
about its mean value (Figure 4b and 4c). The helicity distribution within a
great majority of the structures has both small variance and skewness.
Fig. 4. Distributions of the first three central moments of the feature-local helicity
distributions.
The detailed dynamics underlying any single vortex structure is also acces-
sible. By exporting planar cross sections through tubes using VAPOR’s cross-
section capability, average radial profiles of the helicity and vorticity can be
constructed (Figure 5c & 5d). Distinct differences between the maximally and
minimally helical structures are apparent. The maximally helical structure has
one sign helicity throughout, while the minimally helical twisted structure shows
a change in the sign of helicity near its border (Figure 5c). This appears to be
associated with inward (toward the pinched section midway along the tube )
axial flow surrounding the outside of the vortex tube and outward (diverging
from a pinched section midway along the tube) axial flow in its core, (Figure 6).
A temporal history of these flows would be critical in confirming what looks
to be a significant vorticity amplification mechanism in this minimally helical
vortex filament. Also critical in future analysis would be the ability to combine
the statistical and dynamical analyses presented here to determine how common
this mechanism is and whether particular dynamical processes are statistically
linked to specific structure populations.
Fig. 5. Local dynamics of two strucutures with different helicity distributions showing:
a) streamlines seeded within segmented region; b) the feature-local helicity histogram;
c) an average radial helicity profile; d) an average radial vorticity profile. The shaded
region of the radial profiles represents the inside of the visualized structure.
The primary advantage of coupling visual data investigation with a data
analysis language is the ability to defer expensive calculations of derived quan-
tities until they are needed and then perform them only over sub-domains of
interest. The computational requirements for computing such variables in ad-
vance, across the entire domain, is often impratical, overwhelming the available
analysis resources. Furthermore, some quantities, as was shown by our analysis
of the Taylor-Green flow, can only be computed with reference to the location
of a flow structure and are therefore not in principle a priori computable. The
coupling between VAPOR and IDL facilitates the calculation of derived quanti-
ties as needed over sub-regions of the domain, realizing considerable savings in
storage space and processing time.
Fig. 6. Top: Streamlines colored by y-component velocity, which approximates the
axial velocity. Bottom: vorticity magnitude and Y-component velocity cross-sections
taken at positions a, b, & c (extents of the structure are bounded by the dotted line)
4 Conclusions
VAPOR’s tight integration of visualization with traditional techniques like statis-
tics, fourth-generation data languages, and effective information-management
strategies meets the challenges that are inherent in visual exploration of com-
plex turbulence data. This will only become more important as data volumes
increase. The Taylor-Green flow simulation described in the previous section,
which has 10243degrees of freedom, can be readily computed on today’s ter-
aflop supercomputing platforms. The emergence of petaflop-capable machines
will enable simulations at vastly greater scales, resulting in substantially larger
data volumes. 40963simulations have already been conducted on existing su-
percomputers [17] and the recent NSF Track 1 Petascale computing solicitation
calls for a system capable of executing a homogeneous turbulence simulation
with 12,2883degrees of freedom [18]. The interactive analysis model in this pa-
per, with its reliance on progressive data refinement, visual data browsing, and
region/structure-of-interest isolation, is intrinsically highly scalable. We have
described our experiences with this analysis model in the context of investigat-
ing numerically simulated turbulence. However, we believe that these techniques
have applicability across a broad spectrum of data-intensive sciences.
5 Acknowledgements
We wish to thank the National Science Foundation and the National Center for
Atmospheric Research for their computational support.
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... To evaluate the utility of the techniques described in this paper in the analysis of turbulent structures, we have implemented them in the open-source VAPOR [21, 22] visualization and analysis environment, which is a widely deployed toolset in the turbulence community that specifically targets time-varying, multivariate, large-scale data sets. Our technique can be divided into four steps: selection, clustering, attribute calculation, and quantization. ...
... These vortical structures are dominated by writhe. While both of these regions have high helicity values along the core, the twisting feature is dominated by low helicity values (see Gruchalla et al. [22] for futher analysis). By iterating our visualization and analysis pipeline, we can further deconstruct the complex features with the broad noisy helicity distributions into substructures and investigate their individual local distributions (seeFigure 2). ...
Conference Paper
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We introduce an iterative feature-based transfer function design that extracts and systematically incorporates multivariate feature-local statistics into a texture-based volume rendering process. We argue that an interactive multivariate feature-local approach is advantageous when investigating ill-defined features, because it provides a physically meaningful, quantitatively rich environment within which to examine the sensitivity of the structure properties to the identification parameters. We demonstrate the efficacy of this approach by applying it to vortical structures in Taylor-Green turbulence. Our approach identified the existence of two distinct structure populations in these data, which cannot be isolated or distinguished via traditional transfer functions based on global distributions.
... Standard scientific visualization tooling, such as Paraview [1], and YT provide efficient volume rendering pipelines, with a number of features that can be used to tease out various aspects of the data. In the case of YT, for example, transfer functions for the volume renderer are multidimensional, and thus gives great control and option to the visualization scientist [10]. However, these tools do not provide more advanced rendering capabilities, like scattering, global illumination, and reflections, which can be useful in highlighting data characteristics [2,14]. ...
... The use of wavelet-based compression schemes is becoming increasingly popular in the data visualization domain, see for example Gruchalla [9], Gruchalla et al. [10], and Gruchalla et al. [11]. We fully expect this trend to continue with their inclusion as the default compression tool in the VAPOR software package [6]. ...
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... Last version April-2002.Figure 1 is an example of Vis5D visualization of isosurfaces and vertical planes of air pollution produces by the air quality system MM5-CMAQ run by the authors.Figure 1. Example of visualization with Vis5D VAPOR (Visualization and Analysis Platform for Ocean, Atmosphere, and Solar Researchers) is a software package developed at the National Center for Atmospheric Research in collaboration with U.C. Davis and Ohio State University. It can produce images and movies from very large mesh-based datasets, such as wind velocity and other physical fields in two and three dimensions [4]. VAPOR has its own input file format, VDF, but it supports conversion from other formats, such as NetCDF, in particular the files output by Weather Research and Forecasting model (WRF). ...
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