GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus GmbHGöttingen, Germany10.5194/gmd-8-2329-2015Three-dimensional visualization of ensemble weather forecasts – Part 1: The visualization tool Met.3D (version 1.0)RautenhausM.marc.rautenhaus@tum.deKernM.SchäflerA.https://orcid.org/0000-0002-6165-6623WestermannR.Computer Graphics & Visualization Group, Technische Universität München, Garching, GermanyDeutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, GermanyM. Rautenhaus (marc.rautenhaus@tum.de)31July201587232923534February201527February201523June201525June2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/articles/8/2329/2015/gmd-8-2329-2015.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/8/2329/2015/gmd-8-2329-2015.pdf
We present “Met.3D”, a new open-source tool for the interactive three-dimensional (3-D) visualization of numerical ensemble weather predictions. The
tool has been developed to support weather forecasting during
aircraft-based atmospheric field campaigns; however, it is applicable
to further forecasting, research and teaching activities. Our work
approaches challenging topics related to the visual analysis of
numerical atmospheric model output – 3-D visualization, ensemble
visualization and how both can be used in a meaningful way suited
to weather forecasting. Met.3D builds a bridge from proven 2-D
visualization methods commonly used in meteorology to 3-D
visualization by combining both visualization types in a 3-D
context. We address the issue of spatial perception in the 3-D view
and present approaches to using the ensemble to allow the user to
assess forecast uncertainty. Interactivity is key to our approach.
Met.3D uses modern graphics technology to achieve interactive
visualization on standard consumer hardware. The tool supports
forecast data from the European Centre for Medium Range Weather
Forecasts (ECMWF) and can operate directly on ECMWF hybrid sigma-pressure
level grids. We describe the employed visualization algorithms, and
analyse the impact of the ECMWF grid topology on computing 3-D
ensemble statistical quantities. Our techniques are demonstrated
with examples from the T-NAWDEX-Falcon 2012 (THORPEX – North Atlantic Waveguide and Downstream Impact Experiment) campaign.
Introduction
Weather forecasting requires meteorologists to explore large amounts
of numerical weather prediction (NWP) data, and to assess the
uncertainty of the predictions. Visualization methods that facilitate
fast and intuitive exploration of the data hence are of particular
importance. In practice, the forecasting process for the most part
relies on two-dimensional (2-D) visualization methods. Meteorologists
use weather maps, vertical cross sections and a multitude of
meteorological diagrams to depict the data. From these image sources,
they build “mental models” of the three-dimensional (3-D),
time-varying forecast atmosphere inside their heads
.
Despite the 3-D nature of the atmosphere, 3-D visualization methods
have not found widespread usage, even though there have been promising
attempts in the 1990s and early 2000s that suggested added value
.
Various hindering factors are discussed in the literature, including
resistance of forecasters to adapt to new 3-D visualization methods
that are decoupled from their “familiar” 2-D products
, problems with spatial
perception in 3-D renderings , as well as issues
due to limited performance and the need
for dedicated graphics workstation hardware .
In addition to 3-D space and time, forecast visualization has in
recent years become more challenging through the increased use of
ensemble weather predictions – sets of forecast runs whose
distribution provides information on forecast uncertainty
e.g..
The development of visualization methods that depict the uncertainty
derived from ensemble data is an active topic of research not only for
weather forecast ensembles . Yet again,
ensemble visualization techniques related to weather forecasting
published so far mainly focus on two dimensions as well
e.g..
In this paper we introduce a new open-source visualization tool,
“Met.3D”, that provides interactive 3-D visualization techniques
for ensemble prediction data. There has been an immense progress in
mainstream graphics hardware capabilities in recent years. Making use
of these developments, Met.3D facilitates interactive visualization of
present-day NWP data sets on consumer hardware. The tool has been
developed as a new effort to demonstrate the feasibility of using 3-D
visualization for forecasting, this time also considering uncertainty
information from ensemble data sets. It is intended to be used for
actual forecasting tasks, as well as a platform to implement and
evaluate new 3-D and ensemble visualization techniques.
The work presented in this paper has been inspired by a particular
application, forecasting the weather situation to plan research flights
during aircraft-based field campaigns. We focus on this
application throughout the paper at hand. However, Met.3D is
applicable to a broader range of forecasting and visual data analysis
tasks. Both fast exploration and uncertainty assessment play a major
role in campaign forecasting:
When investigating suitable meteorological conditions to specify
the route of a research flight (that is, waypoints in 3-D space and
time), the forecaster is required
to quickly identify atmospheric features relevant to the flight and to communicate
findings to colleagues.
Upper-level features typically important to
flights with high-flying aircraft are of an inherently
3-D nature (for example, clouds, jet streams or the
tropopause). From our experience in campaigns with DLR (German
Aerospace Centre) involvement, visualization used during campaigns has
been solely based on 2-D methods, typically with limited
interactivity. We are hence interested in investigating how 3-D
visualization methods and interactivity (to quickly navigate the data
space) can be used to aid the exploration.
Assessing the forecast's uncertainty has become indispensable as
flights frequently have to be planned multiple days before take off
(typically 3–7 days; the medium forecast range) to obtain
the required approval from air traffic authorities.
While the use of ensemble predictions has been reported for recent field
campaigns e.g.,
they have, to the best of our knowledge, not been used to create specific interactive forecast
products for flight planning.
However, ensembles provide valuable information; for example, 3-D
probability fields for the occurrence of a targeted atmospheric
process or feature can be derived. Potential flight routes can be
planned in regions in which the probability is high.
An open question,
however, is how can the ensemble data be visualized to improve flight
planning in the medium forecast range.
Our objective is to use
interactive 3-D visualization of ensemble predictions
from the European Centre for Medium Range Weather Forecasts (ECMWF)
to improve the
forecast process for field campaigns. The work has been stimulated by
the forecast requirements of a specific field campaign, the
international T-NAWDEX-Falcon campaign (THORPEX – North Atlantic
Waveguide and Downstream Impact Experiment – Falcon, hereafter
TNF). TNF took place in October 2012 with the objective to take
in situ measurements in warm conveyor belts (WCBs), airstreams in
extratropical cyclones that lift warm and moist air from near the
surface to the upper troposphere e.g..
provided details on the campaign and its
flight planning. The major forecasting challenge was to predict the
likelihood of WCB occurrence within aircraft range. This was
expressed by a number of forecast questions that guided the
development of Met.3D:
How will the large-scale weather situation develop over
the next week, and will conditions occur that favour WCB formation?
How uncertain are the weather predictions?
Where and when, in the medium forecast range and within the spatial range of the aircraft, is a WCB most likely to occur?
How meaningful is the forecast of WCB occurrence?
Where will the WCB be located relative to cyclonic and dynamic features?
In a recent ECMWF newsletter article , we provided
a brief overview of our work. It is the purpose of this publication to describe
the techniques we have developed in detail and to present our solutions to particular
challenges.
We split our work into two parts, structured as follows.
In this paper, we introduce Met.3D.
We discuss challenges related to interactive 3-D visualization and present techniques that
address questions A and B.
To put our work in the context of the
literature, we review recent work in meteorological and ensemble visualization
in Sect. .
Section presents Met.3D's visualization capabilities.
When introducing 3-D visualization to forecasting,
we need to consider that the 2-D visualization methods commonly used in meteorology
provide many advantages (for example, spatial perception) and that meteorologists are
used to working with them. In a 3-D forecast tool to be used in practice, we hence have
to be careful not to replace proven 2-D methods, but to put them into a 3-D context and
to use 3-D visualization to add value.
We address the challenges of creating such a “bridge” from 2-D to 3-D
visualizations, of improving spatial perception of 3-D renderings and of designing
interactive methods that provide fast and easy visual access to ensemble information.
A supplementary video containing real-time screen recordings of examples shown
in Sect. demonstrates the performance of Met.3D on mid-range consumer hardware.
To avoid
time-consuming pre-processing of the forecast data prior to
visualization, Met.3D operates directly on the ECMWF hybrid sigma-pressure
model grid. The characteristics of the data and resulting
challenges for visualization are discussed along with Met.3D's
visualization algorithms and system architecture in
Sect. .
Section discusses
the efficient yet accurate computation of statistical quantities from the ensemble
predictions.
When computing statistical quantities on
a per grid-point basis an error is introduced, since the vertical
positions of the ECMWF model grid points vary between members. Regridding to
a common grid is a solution, albeit time-consuming and hence
undesirable for real-time visualization. We analyse the error
introduced when ignoring such a regridding and provide advice on how
to handle the issue.
Section provides information on code
availability, before the paper is concluded in Sect. .
In the second part of this study hereafter “Part 2”,
we address forecast questions C to E.
A method to compute 3-D WCB probabilities from Lagrangian particle
trajectories is introduced and evaluated, and Met.3D is extended by a technique to
visually analyse the derived probabilities.
To demonstrate the added value of 3-D visualization for forecasting, we present
a comprehensive case study with detailed meteorological interpretations of
a forecast case of TNF.
The case study uses methods from both papers and illustrates how Met.3D can
be used in practice.
Readers primarily interested in the application of Met.3D should read
Sect. in this part, skip the technical sections and
proceed to the case study in Part 2.
3-D and ensemble visualization in meteorology
Our work is related to 3-D visualization in meteorology and to
uncertainty and ensemble visualization.
3-D visualization in meteorology
Visualization tools in meteorology can be distinguished with respect to
application in a research setting and application in an operational forecast
setting . As point out, a tool in an operational setting
should offer techniques tailored to the specific forecasting task and not
confuse the forecaster with large sets of parameters that need to be configured.
A research setting, on the other hand, demands a tool that is flexible to adapt
to different exploration tasks and data formats. Its visualizations should be
highly configurable by the user.
In forecasting, 2-D visualization systems prevail.
With respect to field campaigns with DLR involvement, the Mission Support System (MSS) is frequently used, a tool that generates horizontal and vertical 2-D
sections
of the forecast data upon user request . This tool motivated
the design of our proposed bridge from 2-D to 3-D that we describe in Sect. .
Further 2-D systems that have been applied include the German Weather Service (DWD) NinJo
workstation and the ECMWF Metview
software .
The few reports on the usage of 3-D visualization of atmospheric model data
in forecasting date to the 1990s and early 2000s.
, and
reported on experiments with 3-D visualization for local forecasting during the 1996
Olympic Games in Atlanta. They concluded that an advantage of their 3-D methods was “that
they virtually eliminated the need to laboriously evaluate numerous two-dimensional
images”, however, noted a lack of interactivity due to limitations in computational
performance.
, and presented
“RASSIN”
and its successor “VISUAL”, a 3-D forecasting system for usage within the DWD.
Discussing their experience with an operational test of the software, , too, point
out the importance of system performance for user acceptance. They furthermore
highlight the need for common concepts of operations (user interface and workflow)
when forecasters are asked to transition from a 2-D to a 3-D environment.
presented “D3D” (Display 3D), a 3-D software built at the United
States Forecast Systems Laboratory (FSL) on top of the “Vis5D” tool
. D3D's user interface was designed to match that of the 2-D
“D2D” (Display 2D) software in use at the National Weather Service Weather Forecast Offices
(WFOs). “Real-time forecast exercises” were conducted to evaluate the value of 3-D
visualization, and the software was installed at a number of WFOs.
A few case studies were presented, including usage of D3D for the examination
of tropical cyclones , the usage of 3-D trajectories
, and the analysis of the synoptic situation during a
tornado outbreak .
reported on experiences gained with the system. They not only discuss the
reluctance of forecasters to switch from 2-D to 3-D, but also confidently state that for
forecasters trained with D3D it is “hard to deny that examining the atmosphere using
a 3-D tool is not more effective and complete than using 2-D displays”.
also positively reported on the interactivity introduced by
their system. Interactively moveable vertical soundings and cross sections, for example,
were very well perceived by the forecasters.
There was also an approach to ensemble visualization with D3D.
suggest to interpret the ensemble dimension as the vertical coordinate in Vis5D and
to view a 2-D map of an ensemble product as a 3-D isosurface.
Subsequently, reported on the application of 3-D techniques in
a WFO to visualize observed radar data in the forecast process, using the “GR2Analyst” software.
With respect to research environments, 3-D visualization is more frequently
used.
Early approaches in the 1970s and 1980s used mainframe computers to create 3-D views or animations
of atmospheric observations and numerical model output
e.g.and references therein.
For example, created an award-winning cf.
animation movie of a numerically modelled storm, a project that at that time still required
multiple months and a large amount of computer time .
Since around 1990, a number of workstation and desktop visualization tools have appeared.
Vis5D, mentioned above, became a major 3-D visualization tool in meteorology and
was widely used into the 2000s .
However, its development was discontinued.
A number of other, mostly general-purpose, systems that have been used in the
atmospheric sciences are listed by ,
and . They include the commercial systems
“Application Visualization System” ,
“Iris Explorer” ,
the “IBM Data Explorer” later renamed to
“OpenDX” and made open source; discontinued in 2007,
and “amira” (Stalling et al., 2005; now “Avizo”).
More recently, prominent tools include “Vapor” and the Unidata “Integrated Data Viewer” (IDV)
. Vapor is an open-source 3-D visualization software developed at the
United States National Centre for Atmospheric Research. It features a number of 3-D
visualization techniques to view time-varying gridded data sets; however, it does not provide
techniques for ensemble data or forecasting functionality.
IDV is a comprehensive Java application for the analysis and visualization of geosciences data.
It is based on the “Visualization for Algorithm Development” (VisAD) library
e.g.
and supports a variety of visualization methods, including some 3-D support. For example,
use IDV's 3-D capabilities for interactive immersion
learning. On a broader scope, “Paraview” is
an open-source, general-purpose visualization tool that can also be used with meteorological
data. In the context of a graduate university course,
investigated how Paraview can be used in
a meteorological setting.
Also, commercial general-purpose systems with 3-D capabilities that are frequently
used in the atmospheric domain include “Interactive Data Language” (IDL)
e.g., cf.
and “Avizo Green” e.g..
3-D visualization has also been used for virtual reality applications in teaching
e.g..
A major reason why 2-D methods are often preferred in the atmospheric sciences
is that they are well suited to convey quantitative information, as
point out in a survey of visualization in
meteorology. 2-D contour lines and colour mappings can be used to
convey a large range of data values. In a 3-D depiction, only a small number of
isosurfaces can be displayed without cluttering and occlusion. However, a 3-D
image is able to convey spatial structure in all three dimensions, a distinct
advantage compared to 2-D methods. On the downside, spatial perception is more
challenging in 3-D. Determining the location of a data feature displayed in
a 2-D image is usually not an issue. In a 3-D projection, achieving good spatial
perception can be difficult. Major influencing factors are, for example, shadows
and illumination models e.g.and references
therein.
The issue is also noted by . As an approach, they have implemented
a switch to an overhead view and a vertically moveable map in D3D to enable the forecaster
to better judge the spatial position of a 3-D feature.
Ensemble visualization
Ensemble visualization aims at identifying variability, similarities and differences
among ensemble members. It is closely related to uncertainty
visualization, of which and
provide early overviews. In the atmospheric sciences, 2-D visualizations of
statistical quantities that summarize the ensemble distribution or that
represent relative frequencies for events are frequently used. ch.
7.6.6 lists a number of techniques.
For example, current products provided in ECMWF's “ecCharts” system
include maps of mean and standard deviation (SD), maps of
threshold probabilities (for example, the probability of precipitation exceeding
a critical threshold) and of derived statistical measures for example, the extreme
forecast index;.
In a recent survey – also including applications outside the atmospheric
domain – classify ensemble visualization methods
described in the literature into “location-based methods” and
“feature-based methods”. Location-based methods compare ensemble properties
at fixed locations in the data set. In the simplest case, this includes the
ensemble mean, SD or probability as computed at a given grid
point. Such statistical quantities have been visualized via colour maps,
opacity, texture and animation . Also, glyphs have been used to display, for example,
uncertainty in wind fields . Feature-based methods,
on the other hand, extract features from each ensemble member and aim at
visually comparing the detected features. Examples include spaghetti plots
(where the isolines are the features), the joint display of detected cyclonic
features and visualization techniques for the
prediction of hurricane tracks . Recently,
have generalized box plots to contour box plots to enable
an improved quantitative and qualitative analysis of ensembles of 2-D isocontours
and level sets. In 3-D, the effect of uncertainty on the position of 3-D
isosurfaces has been the topic of a number of studies. It has been approached
with, for instance, geometric displacements and
surface animation . In a study concerning the reconstruction of
the Earth's subsurface model, visualize confidence
intervals around an isosurface using additional transparent surfaces as well as
lines connecting the surfaces. Recently, techniques have used stochastic
modelling of uncertainty in scalar ensembles to quantify and visualize the
possible occurrences of isosurfaces . The latter studies all
include examples from the atmospheric domain.
A few articles in the visualization literature have presented software tools
that put special emphasis on ensembles in earth science applications.
present the “Ensemble-Vis” tool and
investigated the usage of multiple linked views to visualize 2-D weather
simulation ensembles. They conclude that the combination of standard statistical
displays (spaghetti plots, maps of mean and SD) with
user interaction facilitates clearer presentation and simpler exploration of
the data. In their “Noodles” tool, enhanced
spaghetti plots by glyphs and confidence ribbons to highlight the Euclidean
spread of 2-D contour ensembles. They describe the usage of their methods by
atmospheric researchers investigating different parametrizations in the Weather
Research and Forecasting (WRF) model. also
highlighted the positive effect of interactivity and linked views on the user and
note the challenge of potential generalization of their work to three
dimensions. Recently, have presented “Ovis”,
a system for the visualization of 2-D ocean height-field ensemble data. They again
use linked views of maps, statistical plots and 3-D renderings and demonstrate
the use of time-series glyphs for the comparative visualization of the ensembles
at two different positions over time. discussed the
application of their tool to off-shore oil operations and the planning of
underwater glider paths.
The 3-D ensemble visualization tool Met.3D
Met.3D has been developed to support ensemble data exploration during forecasting, in particular for field campaigns (at the time of writing this paper). Beside this primary objective, we
have designed the software in a way that it can be used as a framework into which new
ensemble visualization techniques can be implemented and evaluated with respect to their
use in forecasting.
We note that Met.3D is not intended to be a full-featured meteorological
workstation; this would be beyond the scope of our work.
At the time of writing, Met.3D supports forecast data from the ECMWF
Ensemble Prediction System (ENS), comprising 50 perturbed forecast
runs and an unperturbed control run .
These 51 forecast members approximate the distribution of possible future weather
scenarios .
Real-world context for the T-NAWDEX-Falcon case used for the
examples: visible Meteosat satellite image of Europe and the North
Atlantic of 12:00 UTC, 19 October 2012 (Meteosat operated by
EUMETSAT, image processing by DLR-IPA). Important features are the
narrow trough to the west of the British Isles (dark red line), the
former Hurricane Rafael and the WCB manifest in the cloud
band east of the trough.
The visualization examples shown in this paper
use data from the TNF forecast case of 19 October 2012.
The satellite image in Fig. provides a real-world observation of
major features that appear in the visualizations: a distinct narrow trough was located to
the west of the British Isles. Upstream of the trough the former Hurricane Rafael
transformed into a strong mid-latitude cyclone. East of the trough, ascending WCB
air masses
formed a cloud band extending from Spain to the British Isles. The clouds further stretch
along a jet stream over southern Scandinavia and the Baltic Sea.
The static images shown in the following sections are complemented by
video clips contained in the
Supplement to this paper, helping to illustrate the interactive capabilities
of Met.3D. The videos are screen recordings realized on hardware consisting of
a consumer-class six-core Intel Xeon running at 2.67 GHz, equipped with 24 GB of RAM,
a 512 GB solid state drive and an Nvidia GeForce GTX 560Ti graphics card with 2 GB of
video memory.
User interface
The main user interface of Met.3D. We apply 2-D and 3-D
visualization techniques to explore ensemble weather
forecasts. (a) Isosurfaces of cloud cover fraction of 0.5
coloured by elevation (hPa), and a vertical section of potential
vorticity (PVU). (b) Horizontal section with contour lines
of the mean geopotential height field (m) and filled contours of
its SD (m). (c) Normal curves applied to
the wind field to visualize the jet core. The white isosurface shows
45 ms-1. Colour coding in ms-1. (d–f)
See text for details.
Figure shows the graphical user interface (GUI) of Met.3D.
The forecast data fields can be displayed in multiple 3-D views
(Fig. a, b, c).
In the horizontal, a cylindrical longitude–latitude projection is used. As common in
meteorology, the logarithm of pressure serves as the vertical coordinate. Vertical scale,
i.e. the proportion of vertical to horizontal units, can be specified for each view
individually.
Time navigation is provided for the forecast initialization (or base, or run) time and the
forecast valid time (Fig. d). This way,
subsequent forecast runs can be checked for consistency by keeping the valid time fixed
and changing the initialization time.
A distinct feature is the ensemble navigation. The user can select a specific forecast
member for exploration, animate over members and toggle the ensemble mean for all
currently displayed data fields (Fig. e).
Visual entities such as a horizontal or vertical cross section, the base map or a 3-D
isosurface are represented by “actors” and are assigned to a “scene”. A scene,
in other words a collection of actors, can be assigned to one of the views for rendering.
An actor can be part of multiple scenes. For example, a cross section could be viewed as
a traditional 2-D image in one view, and be combined with a 3-D isosurface in another. If
the section is relocated, its position is updated in both views.
To keep the user interface simple, properties that the user can modify for a particular
actor (e.g. the isovalue of an isosurface, the forecast variable displayed by an actor,
the associated colour palette) are arranged in a tree-like structure on the left of the
Met.3D window and are easily accessible (Fig. f).
If used in a forecast setting, only the uppermost tree nodes are required by the
user to, for instance, load pre-defined forecast products.
point out the importance of visual comparisons in the
forecasting process. Met.3D's actors can be synchronized in time and ensemble dimension,
its views can be synchronized to the same camera viewpoint. Thus, side-by-side
comparison of different data sets is facilitated.
A bridge from 2-D to 3-D
Bridge from 2-D to 3-D visualization. (a) Horizontal
section of geopotential height (contour lines) and horizontal wind
speed (colour) at 250 hPa, as obtained from the DLR Mission
Support System. ECMWF deterministic forecast from 00:00 UTC, 17 October 2012, valid at 18:00 UTC, 19 October 2012. (b)
The same data, rendered by Met.3D and mapped into the 3-D
context. The section can be interactively moved by the
user. (c) Vertical section of horizontal wind speed
(colour) and potential temperature (contour lines) in Met.3D,
amended by a 50 ms-1 isosurface of wind speed, coloured
by pressure (hPa). Note how spatial perception of the 3-D isosurface
is aided by rendering shadows and labelled vertical poles (animated
version of this figure in the Supplement at 00:05 min).
To help forecasters transition to the 3-D visualization environment, we have
implemented horizontal and vertical 2-D sections.
The sections reproduce the look of the corresponding
products in the DLR MSS , providing filled and
line contours, wind barbs, coast lines and graticule.
In Met.3D, the sections are embedded into the 3-D context and can be interactively
moved in space by the user in real time.
This provides a very fast means to explore the atmosphere's vertical structure (by
sliding a horizontal section up and down), or the change in forecast variables along
a flight track when a waypoint is relocated (by moving a vertical section).
Also, the camera can be moved interactively to zoom in, pan or tilt the view – for
instance, to view multiple sections stacked on each other from an angled viewpoint.
Figure illustrates the concept.
The forecast wind field is visualized by means of a horizontal and vertical section. The
horizontal map – largely resembling the corresponding product from
the MSS – is stacked
on top of surface level contours displaying the mean sea level pressure
(Fig. b).
The vertical section is augmented by a 3-D isosurface of wind speed (Fig. c); the isovalue is
chosen such that the strongest winds of the jet stream, an important indicator
for the large scale flow of the upper troposphere, are captured.
The 3-D display allows us to locate the vertical section in space and additionally
provides information on the spatial structure of the jet.
We approach the challenge of spatial perception by drawing projections of all
rendered structures to the surface to imitate shadows generated by a light source above
the scene. As illustrated in Fig. b and c, the shadows
help to qualitatively judge the elevation of a feature, and also show its horizontal
location. To improve the quantitative judgement of elevation, the user can colour
the isosurface according to pressure elevation, and place vertical poles in the scene
that provide labelled pressure axes (Fig. c). The poles
can be interactively moved in the scene (by picking and dragging handles that appear in an
“interaction mode”), so that different locations can be probed.
Vertical sections can be drawn along an arbitrary number of waypoints
(Fig. c).
Analogous to vertical poles, each waypoint and section segment displays a handle in
interaction mode that the user can drag to move the waypoint or segment.
They can also be moved
synchronously in multiple scenes, as illustrated in
Fig. . Displayed are sections of potential vorticity
(Fig. a, the red colours around values of 2 PVU (potential vorticity unit) show
the dynamic tropopause) and cloud cover fraction
(Fig. b). Wind barbs overlain on a horizontal
section can be configured to automatically scale in size and
density. In Fig. , the horizontal section of
equivalent potential temperature shows the different character of
air masses transported by Rafael. When the user zooms into the view,
Met.3D increases the density of the wind barbs
(Fig. b). The frontal zone along which the typical
change in wind direction occurs can now be well perceived.
Vertical sections can be moved interactively in Met.3D to
explore the vertical structure of the atmosphere, for example along
potential flight track segments. (a) Potential vorticity
(colour coding in PVU), (b) cloud cover fraction. Red
colours in (a) mark the 2-PVU surface and thus the dynamic
tropopause. Note the low tropopause along the trough. Same forecast
as in Fig. (animated version of
this figure in the Supplement at 01:24 min).
With respect to colours used in the visualizations, it is important to address
perceptual issues .
To map scalar value to colour, we have implemented the
perceptually based hue–chroma–luminance (HCL) colour space. Following
and , the user can create colour palettes
by specifying ranges in hue, chroma and luminance.
Alternatively, colours can be explicitly specified to reproduce colour bars the user is
familiar with. An example is the colour palette for potential vorticity shown in Fig. .
Ensemble support
Met.3D enables the forecaster to explore variation in the ensemble, to
identify regions in which the forecast is uncertain, and to explore
possible forecast scenarios. The user can interactively navigate
through the ensemble members to judge the variability in the
forecast. Each member can also be explored individually. Statistical
measures including threshold probabilities, mean, minimum, maximum and
SD can be derived on demand. For threshold
probabilities (for example, wind speed exceeding 45 ms-1
or cloud cover fraction being below 0.2) the threshold value can be
adjusted interactively.
Figure shows an example of exploring the
upper-level ensemble wind field of the forecast from Monday, 15 October 2012, 00:00 UTC, valid at Friday, 19 October 2012,
18:00 UTC. To visualize the jet stream, two wind speed isosurfaces
are rendered. The large variation of the ensemble regarding position,
structure and strength of the jet stream over the Atlantic highlights
high uncertainty in this area. On the other hand, the strong jet
extending from Spain to Scandinavia is predicted with higher
certainty; while in the mean wind field the 45 ms-1
signal over the Atlantic is largely smoothed out, it is present over
Europe (Fig. d). However, adding
a horizontal section of wind speed SD
(Fig. e) to the isosurface of mean wind
speed reveals that the position of the jet is uncertain in particular
on its northern side.
Figure shows the probability of wind speed
exceeding 45 ms-1. A high probability of over 70 % can again be found over
northern Europe (Fig. a). The large horizontal extent of the area
of low (10 %) probability above the Atlantic reflects the uncertainty. The actual jet can
occur anywhere in this region. Two days later, with decreasing forecast lead
time, the ensemble has significantly converged and the uncertainty has decreased
(Fig. b).
Figure c and d show the
probability of the Schmidt–Appleman criterion , an indicator for
the occurrence of contrails aircraft-induced clouds that also have been
the target of research flights;.
Visualization of the probability of the Schmidt–Appleman criterion being fulfilled shows
that contrails, in the example, can only occur between about 400 and 200 hPa. In the
given case, a high probability can be observed on the leading downstream edge of the jet.
Normal curves
Met.3D automatically scales size and density of wind barbs
overlain on horizontal sections. (a and b)
Equivalent potential temperature (colour coded in K) at
850 hPa, overlain with contour lines of geopotential
height. Same forecast as in Fig.
(animated version of this figure in the Supplement at 01:54 min).
Navigation through the ensemble. Visualized are the
50 ms-1 (green opaque) and 30 ms-1 (yellow
transparent) isosurfaces of horizontal wind speed (forecast from
00:00 UTC, 15 October valid at 18:00 UTC, 19
October 2012). (a) Control run, members (b) 27 and
(c) 33, (d) ensemble mean, (e) ensemble
mean augmented by a horizontal section of SD
(ms-1), (f) ensemble maximum (animated version
of this figure in the Supplement at 02:26 min).
Probability fields computed from the ensemble, valid at 18:00 UTC, 19
October 2012. (a and b) Probability
of horizontal wind speed exceeding 50 ms-1, as computed
from the forecast initialized (a) at 00:00 UTC, 15
October 2012 and (b) at 00:00 UTC, 17 October 2012. Shown are the
70 % (red opaque) and 10 % (white transparent)
isosurfaces. Note how the ensemble converges. (c
and d) Probability of contrail occurrence
(Schmidt–Appleman criterion fulfilled and relative humidity greater
than 80 %), as viewed from different camera positions (80 %
red opaque and 50 % white transparent) (animated version of this
figure in the Supplement at 03:23 min).
In the volume visualizations shown in Figs. and
, the structure of the scalar fields inside the transparent
isosurfaces cannot easily be inferred.
As stated in Sect. , this is a disadvantage of 3-D visualization:
while an isosurface allows for inference on the 3-D spatial structure of the
displayed data field, it only displays a single data value. Although two or three
isosurfaces can be rendered in a single image using transparency, the image quickly
becomes illegible when more surfaces are used.
“Normal curves” were suggested by
to estimate the spatial distance between two isosurfaces. For our application, we
propose to use “3-D normal curves”
as an intermediate means between a 2-D section and a 3-D isosurface
to visualize the structure of scalar fields in the interior of an isosurface.
The curves are started on a transparent isosurface and proceed
along the field's gradient direction, i.e. normal to the isosurface.
The spacing of the curves can be controlled by the user (cf. Sect. ).
We colour the curves
according to the scalar value. This way, we achieve a visual sampling of a subdomain of
the volume. In contrast to a 2-D section that samples a planar subdomain, the normal
curves
sample a 3-D subdomain enclosed by an isosurface via a discrete set of lines.
Following the gradient, the curves converge at local extrema of the data field.
This way, the user can at a glance identify the locations and strengths of present
extrema, and judge the strength and direction of the gradient between an extremum
and the outer isosurface.
Normal curves help to analyse the topology of 3-D scalar
fields. They reveal the distribution of data values in a subdomain
enclosed by a 3-D isosurface and enable fast identification and
tracking of local extrema. (a–c) Probability of cloud ice
water content exceeding 0.01 gkg-1. The white
transparent isosurface shows 40 % probability. Colour coding in
%. (d) Details of the identified maximum are inspected
with a horizontal section at 250 hPa. Forecast from
00:00 UTC, 17 October 2012 valid at 12:00 UTC, 20 October 2012
(animated version of this figure in the Supplement at 04:28 min).
Figure illustrates the approach. The goal is to
identify regions of maximum probability of cloud ice water content exceeding
0.01 gkg-1, and to track the regions' evolution over time. The normal curves
immediately show a maximum in the upper part of the transparent 40 % isosurface
(Fig. b and c).
The corresponding shadows reveal that the maximum is approximately located above the
Pyrenees.
Interaction with the vertical axis shows a vertical position between 300 and 200 hPa.
Further visual aids can now be added to obtain more quantitative information.
In the example, the horizontal section can be immediately placed in the region of
interest, without the need to search the entire vertical extent of the model atmosphere
(Fig. d).
While extrema can also be identified with an inner opaque isosurface (cf. Fig. ) or by interacting with 2-D sections, the normal curve
approach requires less interaction steps.
This is advantageous if the absolute values of the extrema are not known
beforehand (with isosurfaces the user needs to search over isovalues), and if
the extrema shall be visually tracked over ensemble members or time. Concerning time,
in particular probability values tend to decrease with increasing forecast lead
time;
hence, a fixed isosurface is not well suited to visualize the temporal evolution of
a maximum.
Hybrid sigma-pressure levels used by the ECMWF
model. (a) The elevation of the model levels (green lines;
the example shows levels from the 31 level model; level indices k
in green) changes with surface pressure (black curve at the
bottom). The data value for a given pressure value p can be
located at different levels in the grid (the red line marks the
location of p= 600 hPa). (b) Example of how
the surface orography affects the vertical displacement of the grid
points in a vertical section.
In Fig. c (also shown in the video at 05:40 min),
the method is applied to the
upper-level wind field shown in Fig. . Here, the normal
curves inside the 45 ms-1 isosurface converge to the string-like line of local
maxima in the wind field – the curves are used to identify the position of the jet
core and its strength.
Visualization algorithms and system architecture
Response time, the time required to display a new image after the user has interacted
with, for example, camera or time step, is crucial to the acceptance of an interactive
visualization tool, as and emphasize.
To achieve low response times, we make extensive use of modern graphics processing units
(GPUs). These highly parallel processors provide high computational throughput
and memory bandwidth and are well suited to accelerate visualization algorithms.
GPU acceleration is implemented with OpenGL 4 and the OpenGL Shading Language
(GLSL)
https://www.opengl.org/documentation/glsl/
, using vertex, geometry, fragment and compute
shaders. These small GPU programs allow the parallel execution of operations on the
level of a graphics vertex or of an output fragment (i.e. a single pixel in the
generated image), the generation of new geometry by the graphics subsystem, or the
general parallel execution of operations. We will not go into detail of
graphics technology here, for an introduction to GPU-based visualization we refer the
reader to, for example, or
. On the CPU side, Met.3D is implemented in C++.
A second important factor influencing response time is the way data are read from disk and
whether and how it needs to be processed prior to visualization. We have designed an
ensemble data pipeline to handle this task efficiently.
In this section, we discuss the methods used to achieve high visualization
performance in Met.3D. After describing the
data that can be handled by the tool (Sect. ), we discuss the ensemble
data pipeline (Sect. ) and the GPU-based visualization
algorithms (Sect. and ).
Forecast data
The data upon which we have based our visualization methods are
obtained from the ECMWF global ensemble weather prediction system ENS and the
high-resolution deterministic integrated forecast system (IFS).
One of our system design goals was to support the forecast data in the format they can
be retrieved from the ECMWF Meteorological Archive and Retrieval System (MARS).
MARS outputs the data interpolated in the horizontal to a regular latitude–longitude
grid. In the vertical, the data are available on either a set of pre-defined pressure
levels (PLs), or, higher resolved and thus better suited for 3-D visualization, on the
native model grid levels (MLs).
For the latter, the model uses terrain following hybrid sigma-pressure
coordinates, as illustrated in Fig. . The vertical-pressure coordinate pk of a grid point at level k is defined
by a set of fixed coefficients ak and bk and the surface pressure
psfc below the grid point : pk=ak+bk×psfc. With increasing altitude the influence of psfc decreases.
During TNF, the operational ensemble forecast was available with 62 levels (91 levels
for the deterministic forecast, increased by the time of writing to 137 levels). At this
resolution, levels are constant in pressure above approximately 64 hPa (70 hPa)
. In
the horizontal, a spectral truncation of T639 (T1279) is available, corresponding to
a regular latitude–longitude grid of approx. 0.28∘× 0.28∘ (0.15∘× 0.15∘).
Forecasts are available twice daily (starting at 00:00 and 12:00 UTC) at a time step
of 3 h up to 144 h forecast lead time and 6 h up to 240 h
forecast lead time.
For the examples in this paper, we use ENS data interpolated
horizontally to 1∘× 1∘ and to
0.25∘× 0.25∘;
1∘× 1∘ is the grid spacing we were able to
operationally retrieve during TNF, as permitted by the available
internet bandwidth and interpolation time required by
MARS. Deterministic data are used at
0.15∘× 0.15∘ grid spacing. In the vertical,
all 62 and 91 levels are used.
The forecast domain used in the examples encompasses 100∘ in
longitude by 40∘ in latitude, resulting in
101 × 41 × 62 grid points for ENS data fields at
1∘× 1∘ grid spacing,
401 × 161 × 62 points at
0.25∘× 0.25∘ grid spacing and
669 × 268 × 91 points for the deterministic forecast
at 0.15∘× 0.15∘ grid spacing. Using floating
point precision (4 bytes per value), the data fields require
approximately 1, 16 and 62 MB per member, time step and forecast
parameter in graphics memory. For visualizations using multiple
forecast parameters and the entire ensemble, the required memory
quickly adds up.
Forecast data can be read directly from GRIB files output by MARS or
from NetCDF-CF
http://cfconventions.org/
files. Our
goal was to minimize the time span between data availability at ECMWF
and visualization. Hence, no pre-processing of the data prior to usage
in Met.3D is required. Forecast parameters not output by the ECMWF
model, however, need to be computed first. For this purpose, Met.3D
can be connected to the data processing system of the DLR MSS, which
derives additional quantities (for example, relative humidity and
potential vorticity) from the forecast parameters output by ECMWF.
Ensemble processing pipeline
To process the ensemble data prior to rendering, we have designed a data
processing pipeline composed of modules (“data sources”) that create, read
or process data and that can be combined in flexible ways.
Figure illustrates the concept. Algorithms in the data
sources (for example, ensemble statistics or trajectory filtering; cf. Part 2)
can be implemented to execute on either CPU or GPU (the latter via compute
shaders). All data sources are connected to a memory manager that caches intermediate
results. The actors that implement the visualization methods are placed at the end of
a pipeline. They send “requests” into the pipeline to obtain a specific data
item. These requests are composed of multiple key/value pairs similar to the Web Map Service requests used in the MSS seefor details.
A request emitted into a pipeline propagates from data source to data source. Each
data source interprets the keys it requires. If the requested operation has been executed
before and the result has been cached, no action is taken. Otherwise, the data source
defines a processing task to perform the requested operation. The task, however, is not
executed immediately. If applicable, remaining keys are passed on to the data source's
input(s). If a data source requires additional input, it can also append keys to the
request.
All processing tasks defined this way are assembled into a task graph that is passed to
a scheduler for execution. Based on the dependencies provided by the graph
structure and information carried by the tasks, the scheduler can process the
tasks. For example, tasks that have to be performed for all members of the
ensemble can be executed in parallel.
As an example, consider the pipeline depicted in Fig. b.
The volume actor at the end of the pipeline emits a request for a scalar field
containing the probability of horizontal wind speed exceeding 45 ms-1. The
module computing the probability field requires the wind field of each ensemble
member, regridded to a common grid. Hence, requests for regridded data fields
containing the members' wind speed are emitted and a task is set up to compute
the probability from these fields. The regridding module, in turn, requests that
the wind speed fields are read from disk by the reader module. For an ensemble
of size M, the resulting task graph (Fig. c) contains
M tasks to read the wind field of a single member, M tasks to regrid these
fields to a common grid and one task to compute the probabilities. The
regridding tasks are well suited to be executed in parallel.
To indicate an order of magnitude of the response times that Met.3D achieves
on our test hardware when the displayed data field is changed,
Table lists timings for
changing the forecast time in the horizontal section in Fig. .
Timings are provided for displaying a single member of the ensemble and for displaying
the ensemble mean (the latter as an example of a statistic that requires all members of
all variables when computed on demand),
both when data need to be read from disk and when it is available in cache.
If the data to be visualized are available in cache, no task graph needs to be
executed and the response time is of the order of a few milliseconds.
If data need to be read from disk, the response time is bounded by the disk's bandwidth.
This becomes noticeable in particular when ensemble statistical quantities are derived
on demand. For the TNF data set at 0.25∘ grid spacing, all members of the
ensemble encompass approximately 3.2 GB that need to be read from disk. Our test hardware
requires about 17 s for this task.
One possibility to decrease this time is to pre-compute frequently used statistical
quantities. In our set-up, this can be done with the MSS data processing system. However,
the interactivity to change, for example, the threshold for a probability field is lost
with this solution.
Alternatively, the system performance can be increased by using pre-loading techniques
to hide disk access. Here, the data for an anticipated subsequent time step are read
in the background while the user explores the current time step.
The current Met.3D architecture is prepared to implement such techniques. However,
comprehensive optimizations of the system performance were outside the scope
of this project and are left for future work.
Order of magnitude of response times achieved by Met.3D to display a new image after the
user has advanced the forecast time for the horizontal section in
Fig. b, displaying either data of a single member or of
the ensemble mean (the latter an example of a statistic that requires all members of
all variables when computed on demand).
Timings are measured on the test hardware described in Sect.
and given for both forecast data at 1∘ grid spacing and at 0.25∘ grid
spacing;
12 parallel threads are used by the scheduler for task graph execution.
Fig. b uses four forecast variables, reading all
ensemble members (for computation of the mean) from the disk hence involves
reading 4×51×1MB at
1∘ grid spacing and 4×51×16MB at
0.25∘ grid spacing.
Met.3D's visualization algorithms support data fields on both hybrid sigma-pressure
levels and on pressure levels. The difference is how the data fields are sampled on the
GPU to obtain a value at a particular position in longitude–latitude-pressure space – an
operation required by all visualization algorithms. In the horizontal, data fields on
a regular longitude–latitude grid are supported.
To use the data on the GPU, a single forecast variable of a single member is stored in
a 3-D texture (i.e. a 3-D data array) in GPU memory. We assume that these data fields fit
into GPU memory. Longitude–latitude axes, as well as pressure
levels for PL grids, are stored in an additional 1-D texture. For ML grids, the
corresponding 2-D psfc field and the coefficients ak and bk are stored.
This allows for computation of the pressure coordinate of a grid point on the fly, without the
need to use additional graphics memory for a 3-D texture with pressure values.
Horizontal 2-D sections on a pressure surface p are rendered by placing the vertices of
a grid of triangles horizontally at the positions of the data grid points and vertically
at p (Fig. a). Data sampling only needs to be done when p is
changed.
Executed in parallel for each vertex, a binary search in the vertex shader yields the
model levels (or pressure levels) k and k+1 enclosing p in the corresponding grid
column. Following the ECMWF FULLPOS interpolation routines ,
interpolation between these two levels is done linearly in ln(p). The results are
cached in a 2-D texture.
Filled contours are rendered by assigning colour to each fragment within
a triangle in the fragment shader, using the horizontally hardware-interpolated scalar
value. To obtain a colour, colour palettes (cf. Sect. ) are stored as
1-D transfer functions in 1-D textures. These textures
are used as lookup tables (LUTs), mapping a scalar value to a colour.
Line contours are generated by a marching squares
e.g.ch. 1 implementation in a geometry shader. Each
grid cell of the cached 2-D cross section texture is examined in parallel and, if
applicable, a line segment is drawn.
Graticule, coast and border lines are overlain on each horizontal section to improve
spatial perception (cf. Fig. b).
Wind barbs are also generated in a geometry shader. It takes the horizontal wind
field's u and v components as input and generates the geometry of the barbs, again
exploiting GPU parallelism.
Pipeline concept of Met.3D: (a) data sources are
connected to form a pipeline, into which a visualization
“actor” sends data requests; (b) sample pipeline to
visualize the probability of horizontal wind speed exceeding
45 ms-1. A request for the probability triggers further
requests up the pipeline; (c) Task graph generated by the
pipeline in (b).
Vertical sections are rendered with a similar grid of triangles. A triangle vertex is
drawn for each vertical (model or pressure) level and each of a number of intermediate
horizontal points along a line connecting the waypoints the user has specified
(Fig. b). The distance between the intermediate points can be specified.
A vertex shader computes the vertical position of each vertex and places it accordingly.
This operation is
a simple lookup for PL data and involves interpolation of psfc and
computation of the model level pressure for ML grids. Scalar values
are interpolated horizontally, also in the vertex shader, on the level on which the
vertex is placed. They are also cached in a 2-D texture that is updated if a waypoint is
moved. Filled and line contours are generated equivalently to those in the horizontal
sections.
Three-dimensional isosurfaces are rendered with front-to-back raycasting
implemented in the fragment shader. For
each fragment (pixel) of the output image, a ray is cast through the data volume,
sampling it at regular intervals and thus finding isosurface crossings.
For this type of visualization algorithm, sampling the scalar volume is more expensive,
as we need to interpolate in all three spatial dimensions to an arbitrary position in
longitude–latitude-pressure space.
For PL data, the grid is rectilinear (Fig. b) and can be sampled
using texture mapping e.g., thus benefiting from the fast trilinear
hardware interpolation provided by modern GPUs. By mapping the
longitude–latitude-pressure coordinates of the sampling position to texture
coordinates (tlon,tlat,tp) on the unit cube, the GPU interpolates the 3-D
texture at an arbitrary position.
For regular grids, this mapping is a simple linear scaling.
Since, however, PL grids retrieved from MARS are irregularly spaced in the vertical, we
need a method to map pressure to tp. This is realized by means of an LUT stored in an
additional 1-D texture.
The level indices k can be linearly scaled to tp,k∈(0…1). Since we know
the pressure values pk at the levels k, we can compute a continuous k̃ for
intermediate p by linearly interpolating in ln(p) (Fig. b).
k̃ can subsequently be scaled to tp.
These mappings from p to tp are pre-computed for a number, say 2048, of pressure
values and stored in the LUT that can be accessed in the shader.
Sampling data fields in GPU shaders. (a) For each
vertex of a horizontal section, model levels k and k+1 are found
by binary search. The scalar value is linearly interpolated in
ln(p) between these two levels. (b) PL grids are
rectilinear (left), allowing for the usage of trilinear hardware
interpolation between the grid points surrounding a sample position
(red dot). For ML grids (right), the sample position can be located
between different model levels k for two adjacent grid columns,
thus prohibiting hardware interpolation.
ML grids are not rectilinear and thus sampling becomes more complicated. As illustrated
in Fig. b, the continuous level index k̃ in general is
not the same for adjacent grid columns. In the worst case, a given p is located between
different model levels in its four surrounding grid columns.
Trilinear hardware interpolation requires k̃ to be the same in all surrounding
grid columns, it hence cannot be used.
Consequently, we need to split the interpolation into four vertical interpolations in the
grid columns and a subsequent bilinear horizontal interpolation.
A naïve approach is to use the binary search used for the horizontal sections for
the
vertical interpolations; however, our experiments showed that rendering times can be
reduced by a factor of about 2 when again making use of an LUT approach for hardware
interpolation.
However, the horizontal interpolation needs to be implemented in software. ML sampling is
hence over 4 times more expensive than PL sampling.
To use hardware interpolation for the ML in the vertical, we need to extend the LUT approach.
First, the horizontal texture coordinates tlon and tlat are set to the horizontal
position of the grid columns.
Since the model level pressure varies with psfc, we in principle need to pre-compute
one LUT for every psfc value that occurs in the forecast field. We instead make use
of a 2-D LUT, containing LUTs for discrete values of psfc reflecting the expected
range of psfc in the data. Using bilinear hardware interpolation, this LUT is used
to interpolate in both psfc and ln(p) to obtain a mapping from ln(p) to tp.
The additional memory requirement is reasonable: for an LUT using 2048 entries in the
vertical and 600 entries for psfc between 1050 and 450 hPa, approximately 9 MB
of GPU memory are required in float precision (i.e. 4 bytes/value). The table can be
shared among variables on the same grid.
The traversal of the data volume is accelerated with an empty-space skipping strategy
. The longitude–latitude-pressure space covered by a data
field is divided uniformly into a regular grid of Ni×Nj×Nk cells. For
each cell, minimum and maximum data values are computed. In the shader, the information
is used to skip cells in which an isosurface cannot possibly be located. Due to the
different horizontal and vertical scales, care has to be taken when choosing the step
size for traversing non-empty cells. Depending on the factor that is used to scale
ln(p) to a z coordinate in visualization space, the vertical distance between two grid
points often is considerably smaller than the horizontal distance. The step size chosen needs to
be small enough to ensure that no grid point is skipped during traversal.
Once an isosurface crossing has been identified, the isosurface normal (equivalent to the
gradient of the scalar field at the crossing position) is computed via central
differences. The pixel colour is subsequently determined using the commonly used
Blinn–Phong lighting model e.g. Colour can be pre-defined or
obtained from a transfer function. Also, a second scalar field can be mapped to the
isosurface to colour, for example, a wind speed isosurface by temperature.
Order of magnitude of rendering times achieved by Met.3D for selected
visualizations from this paper.
Timings are measured on the test hardware described in Sect. .
ECMWF ENS data at a grid spacing of 1∘ in both
longitude and latitude are used. The data fields are available in GPU memory.
ML refers to visualizations from hybrid sigma-pressure model levels (62 levels),
PL refers to visualizations from data fields regridded to 62 pressure levels
chosen equal to the levels of an ML grid defined by a constant surface pressure
of 1000 hPa.
Timings are average values of continuous
rendering over 30 s. A Met.3D window of 1600 by 900 pixels is used (the size used
for the video in the Supplement, corresponding to a viewport of 1192 by 864 pixels).
“Animated” for cross sections refers to vertically sliding a horizontal
section or moving a waypoint of a vertical section.
Table lists typical rendering times for images shown in
this paper.
Note that the performance of the raycaster depends on the visualized data as well as on
camera viewpoint. In particular the effectiveness of the empty-space skipping strategy
for a selected isovalue depends strongly on the spatial distribution of the data values.
During user interaction, the step size used by the raycaster to sample the data fields
can be reduced (cf. Table ). While this temporarily reduces
image quality, rendering time is also reduced.
Two-dimensional sections are rendered at the same performance for ML and PL data sets, as the same number
of interpolation operations needs to be performed for both grid types.
For raycasted images, Table
provides timings for ML data sets and PL data sets with the same number of vertical
levels. Due to the reduced number of vertical interpolation operations, PL data are
typically rendered by a factor of two to three faster than ML data.
We note that as for the data pipeline, comprehensive optimizations of the visualization algorithms were
outside the scope of our work. In particular with respect to the raycaster, further
optimizations are possible, for example, by integrating an adaptive step size strategy.
Computation of normal curves
Normal curve computation is implemented in a compute shader.
Figure illustrates the proposed normal curve
algorithm. To generate a set of seed points, rays aligned with the three world
space axes (longitude, latitude, pressure) are cast through the data volume. The rays are
started at regularly spaced points (grey arrows; the spacing can be adjusted by the user).
To avoid the regular pattern of these initial start points being reflected by the
normal curves,
we disturb the ray positions by a random factor (black arrows).
The intersection points of the rays with the selected outer isosurface are then used as
initial seed points for the normal curves
(green dots). In particular in regions of high curvature, multiple rays
can hit the isosurface at close-by points on the surface.
To prevent normal curves from being started close together, a regular volume with
a grid size of the average initial ray distance is placed over the scene (yellow grid).
Only one seed is allowed per grid cell. Hence, if a seed point falls into a cell
already occupied, it is discarded (illustrated in the orange grid cell). The
normal curves are integrated in parallel in the direction of the scalar field's gradient,
using a fourth-order Runge–Kutta scheme. The gradient is computed with the same method used
for isosurface shading. If present, the integration can be stopped at an inner
opaque isosurface (illustrated by the red isosurface in Fig. ).
Computation of normal curves. Seeding points for the curves
(green dots) are placed at the intersections between axis aligned
rays (black arrows) and the outer isosurface (only rays from two
directions are shown for illustration). Only a single seed is
allowed in each grid box of the yellow volume.
Impact of (not) regridding on ensemble statistical quantities
A challenge that arises from aiming at interactive ensemble visualization is
the efficient yet accurate computation of statistical quantities from the ensemble
predictions.
We compute statistical quantities per grid point.
Probabilities, for example, are computed by evaluating for every member and for each grid
point a given probability criterion (for instance, wind speed exceeding a given
threshold). The evaluation of the criterion yields for every member a binary
volume, with the bits set when the criterion is fulfilled.
Probabilities are computed by counting the number of members with a set
bit for each grid point. Other statistical measures are computed similarly for each
grid point over the ensemble dimension.
For 2-D grids, this is common procedure and also for
3-D grids not an issue as long as a given grid point is located at the
same spatial position in all members. However, due to surface pressure
varying between ensemble members, this is not the case for data on ML
grids. Hence, depending on the vertical gradient of the forecast
variable from which a statistical quantity is computed, an error is
introduced. One approach to this issue is to vertically regrid all
ensemble members to a common grid, for example, the one defined by the
mean surface pressure (as done in the example pipeline in
Fig. ). This, however, introduces an
additional interpolation step and demands computational resources.
In this section, we investigate the visual and quantitative differences between
statistical quantities computed from the original ML grids and those computed from
data fields regridded to a common grid. The differences are compared to an additional
error that is introduced by linearly interpolating the statistical quantities. At ECMWF,
maps of statistical quantities on pressure levels are computed from the individual
member's forecast data on these pressure levels. This implies that a forecast
meteorological variable is first interpolated to the target vertical position for each
member using linear interpolation in p or ln(p); cf.,
followed by the computation of the statistical quantity. If, on the contrary, we first
compute the statistical quantity on the 3-D model grid and then linearly interpolate to
the target vertical position, an error is introduced due to the non-linear
nature of most statistical measures. The same problem arises in the horizontal dimensions.
(a) SD of surface pressure,
σ(psfc). Forecast from 00:00 UTC, 15 October 2012,
valid at 18:00 UTC, 19 October 2012. Red contour lines show mean
sea level pressure. (b) Vertical section of the pressure
difference (yellow-blue-black colour bar in hPa) between highest and
lowest ensemble member, rendered on top of a wireframe map of
σ(psfc).
Visual differences between statistical quantities computed
from a vertically regridded ensemble to those computed from the
original ensemble. Horizontal section at 950 hPa
(approx. model levels 51–55 in
Figs. and
) of (a–c)p(|v|>20ms-1) (%) and (d–f)σ(RH). Same forecast as in
Fig. . Shown is (a)
the probability and (d) SD computed from
the original model grid, (b and e) computed from
members regridded to the grid defined by the mean psfc,
and (c and f) the difference between both fields.
Distribution of differences between statistical quantities
computed from a vertically regridded ensemble to those computed from
the original ensemble. Plots are generated from all 256 742 grid
points of the data field. Same forecast as in
Fig. . Shown are (a
and d) μ(|v|), (b and e)
σ(|v|) and (c and f) p(|v|>20ms-1); (a–c) distribution and vertical
occurrence of absolute values of the quantities. (d–f)
Distribution and vertical occurrence of differences due to
regridding (denoted by regridΔ); note the
logarithmic scale of the histograms in (d–f). Probability
values are discrete due to the size of the ensemble (51 members).
The same as Fig. but for
variables depending on moisture; (a and d)
SD of relative humidity; (b and e)
probability of potential vorticity exceeding 2 PVU; (c
and f) Probability of grid box cloud cover fraction falling
below 0.05.
Histogram of σ(psfc), overlain with the
bin-averaged difference of σ(psfc) against the
differences between σ(|v|) computed from a vertically
regridded ensemble and computed from the original member grids.
Same forecast as in
Fig. .
Distribution of errors due to vertical linear interpolation
(denoted by interpΔ) of statistical
quantities. (a) Distribution of errors of
σ(|v|) (top), and vertical occurrence of the errors
(bottom). (b) The same for p(|v|>20ms-1). (c) Vertical profile of level
average differences due to regridding (crosses) and interpolation
(dots). Same forecast as in
Fig. .
In the following, we analyse regridding and interpolation error for
the forecast data we had available from TNF. We present results from
the forecast initialized at 00:00 UTC, 15 October 2012 and valid at
114 h lead time at 18:00 UTC, 19 October 2012. This case is
representative for the data set, results for other time steps of the TNF
data set are similar.
Variation in grid-point pressure
First, we estimate typical vertical grid-point displacements that can
be observed between ensemble
members. Figure a shows the
SD of psfc for the example case. It
reaches values of 8 to 10 hPa in the uncertain regions of the
forecast. This particularly applies to the low-pressure systems over
the Atlantic and the northern British
Isles. Figure b shows a vertical
cross section of the maximum pressure difference between any two
members per grid point in these two areas. Close to the surface, the
difference reaches 40 hPa, corresponding (at low altitudes) to
an elevation offset of about 400 m. In most other regions,
however, differences are smaller. Also, as expected from the model
grid topology, differences vanish in upper atmospheric levels.
Difference due to vertical regridding
Vertical regridding is implemented as a data source that can be
integrated into the Met.3D ensemble processing pipeline
(cf. Fig. ). The user can toggle between
visualizations from original and from regridded data fields, and, if
required, permanently enable regridding. If statistical quantities
are computed from the original member grids, the resulting field is
interpreted on a grid defined by the mean surface pressure.
On our test hardware (cf. Sect. ), the cost of
single-threaded CPU regridding on average is about 60 ms per
member and variable for the TNF ENS forecast at 1∘ grid spacing
(256 742 grid points per 3-D field) and about 1 s at
0.25∘ grid spacing (4 997 262 grid points). Even though
multiple ensemble members can be processed in parallel on a multi-core
machine and the regridding process could be further sped up using the
GPU, there is a delay in particular for high-resolution data sets and
visualizations using multiple variables.
We have visually inspected a number of 2-D and 3-D renderings of
statistical quantities of several meteorological variables. As
expected, the largest visual differences appear close to the
surface. They become most manifest in horizontal sections, which are
most sensitive to vertical variations in a 3-D data field.
Figure shows two typical low-altitude
examples, the probability of horizontal wind speed exceeding
20 ms-1, p(|v|>20ms-1), and the
SD of relative humidity, σ(RH). From our
inspection we find that differences tend to be larger for variables
that depend on moisture and variables derived thereof; however, we
could not find any examples in which visualized structures were
significantly altered. For example, while there is some visible
difference in σ(RH) along Rafael's warm front, the
structure itself is not significantly altered.
Visual differences strongly depend on the employed colour palette and
visualized data range. Depending on the range of values covered by
a single colour, small changes might simply not be reflected in the
visualization. To ensure that differences in general are small, we
have performed a statistical analysis of the entire TNF
data set. Figure shows results for
three statistical quantities computed from the wind field of the
example case: mean μ(|v|), SD
σ(|v|), and p(|v|>20ms-1). The
scatter plots show that for all three quantities the largest
differences appear at lower altitudes (higher model level indices).
Also, differences mostly are small compared to absolute values of the
quantities. For example, at only a few grid points the difference in
σ(|v|) and p(|v|>20ms-1) exceeds
1 ms-1 and 10 %, respectively. The range of
differences observed in Fig. is well
reflected in the histogram.
Larger differences appear for statistical quantities computed from
moist variables (Fig. ). Again, the
histogram for σ(RH) confirms the range of differences
shown in Fig.
(Fig. d). For probabilities of
potential vorticity and cloud cover, differences of up to 30 % can
occur (Fig. e and f). However, for
most grid points, differences are smaller.
Figure shows a histogram of
σ(psfc) of the example case, overlain with the
bin-averaged difference in σ(|v|). As can be expected,
larger differences on average occur in regions with high
σ(psfc). However, even for large
σ(psfc), most differences are small (not shown). We
hence cannot state that large σ(psfc) in general
accounts for large differences.
Error due to vertical interpolation of statistical quantities
Example of vertically interpolating statistical quantities. Consider an ensemble of three members and corresponding scalar
quantities s1 .. s3 at the two vertical levels k and k+1. While the mean value μ(s), interpolated to the mid-level
between k and k+1, equals the mean of the interpolated scalar values, this is not true for the SD σ(s) and the
probability that a scalar value exceeds 1.5, p(s>1.5). The subscript i refers to “interpolated”.
The error introduced by vertical linear interpolation of a statistical
quantity depends on the quantity. Consider the example given in
Table . Due to the linear nature of
the ensemble mean, there is no difference whether we first compute the
mean at the grid points and then interpolate to the sample location or
vice versa. For non-linear quantities including SD and
probability, the results are different.
Figure shows distributions of the interpolation errors
for σ(|v|) and p(|v|>20ms-1).
Note that in contrast to the differences caused by regridding, the largest errors due to
interpolation occur in upper atmospheric levels, where the vertical distance
between model levels becomes larger.
Between the surface and approximately model level 10 (approximately 100 hPa), the order
of magnitude of the interpolation errors is comparable to that of the differences due to
regridding.
At middle atmospheric levels, both errors are at a minimum, as shown by the vertical
profile of horizontally averaged differences. At the upper boundary of the model
atmosphere, interpolation errors become significantly larger, These regions, however, are
not relevant for the forecast cases we are interested in.
Discussion
The examples show that the errors introduced by computing the statistical
quantities from the original member grids are of comparable magnitude to the
errors introduced by vertically interpolating the computed quantities. For most
grid points, both are negligible and result in only little difference in the
visualization. However, for some variables and cases (in particular moist
variables), differences can be of the same order of magnitude as the statistical
quantity itself.
We conclude that for general exploration of the forecast data, it is sufficient
for the user to use the “fast” option and visualize quantities computed from
the original member grids. However, if the result is crucial for an important
decision, our advice is to switch to regridded quantities and accept the
additional compute time. The “best” results and those most comparable to
products obtained from ECMWF can be achieved by first interpolating
each member to the desired vertical pressure and then computing the statistical
quantities. In this case, neither regridding nor vertical interpolation of the
quantity corrupts the result. In Met.3D, this is possible for horizontal sections.
Conclusions
We have presented Met.3D, a new open-source tool that provides
interactive 3-D visualization techniques for numerical ensemble
weather prediction data in a way suitable for weather forecasting.
The development of Met.3D has been motivated by the application of
forecasting during aircraft-based atmospheric field campaigns, in
particular, by the requirements of the T-NAWDEX-Falcon 2012 campaign.
However, we see the tool applicable to a wider range of applications,
including the analysis of ensemble simulation output in atmospheric
research and the usage of Met.3D to support teaching in meteorology
classes.
Our work is concerned with meaningful 3-D depiction and ensemble visualization,
two challenging topics of weather forecast visualization.
We have addressed a number of challenges that have been discussed in the literature,
including prevention of a decoupling between commonly used 2-D and new 3-D
visualization methods, spatial perception in 3-D scenes, suitable
uncertainty visualization techniques, and system performance.
Interactivity is key to our approach. It is facilitated by exploiting the
computational power provided by modern graphics processing units and by means of
a flexible, modular system architecture.
We have built a bridge from proven 2-D visualization methods commonly used in meteorology
to 3-D visualization; 2-D products are rendered in a 3-D context, a product's position can
be changed interactively. When 3-D elements are visualized, spatial perception is improved
by displaying shadows on the Earth's surface, enabling the user to judge the horizontal
position and relative elevation of an element. Quantitative height information can be
obtained by means of interactive vertical axes. We have proposed normal curves,
a novel visualization technique to reveal the structure inside a transparent 3-D isosurface
of a scalar field. With normal curves, the locations and magnitudes of local extrema in
the visualized data can be identified at a glance.
To visually provide information on forecast uncertainty, Met.3D implements support for
ensemble forecasts.
The tool is designed to allow for integration of both feature-based and location-based
ensemble visualization techniques. In the presented version,
forecast products can be animated over the ensemble dimension, and
statistical quantities can be derived and visualized on demand. Concerning the
computation of statistical quantities from forecast data on hybrid sigma-pressure grids,
we have shown that ignoring the variation in grid-point pressure between the ensemble
members has little impact on the visualization.
The paper at hand is the first of a two-part study. We have focussed on Met.3D's
functionality, system architecture and visualization algorithms.
In Part 2, we focus on the specific forecast requirements
of T-NAWDEX-Falcon and use Met.3D to predict warm conveyor belt situations.
Ensemble particle trajectories are employed to predict a probability of
warm conveyor belt occurrence.
In particular, a case study, revisiting a forecast case from T-NAWDEX-Falcon,
demonstrates the practical application of Met.3D and highlights
the potential of the software to improve the weather forecasting process.
Future work needs to include careful evaluation of the presented visualization
techniques to study their impact on tasks performed by meteorologists and
atmospheric researchers in their daily work.
We discuss our point of view on the added value of interactive 3-D ensemble
visualization for forecasting after the presentation of the case study
in the conclusions of Part 2.
For example,
in our experience, the provided
interactivity for 2-D sections and the ability to add features as 3-D elements
helps to much faster build a mental model of the atmosphere. This, of course,
reflects our personal perception. We plan to evaluate the issue with a user
study in the near future.
We will actively use Met.3D during upcoming field campaigns, including a future
NAWDEX campaign scheduled for 2016.
We also see much potential for further research in meteorological
visualization.
With respect to 3-D visualization, further improvement of spatial perception is very
important. In the Met.3D version presented here, shadows are only rendered on the Earth's
surface. Global illumination techniques e.g.
that, for example, allow 3-D elements to mutually cast shadows on each other,
may further improve the user's judgement of spatial relationships.
Also, the impact of different projections on perceived spatial distance needs
to be studied.
Met.3D currently is restricted to a cylindrical map projection in the horizontal.
Additional challenges include the efficient rendering from further native model grid
topologies and real-time placement of text labels to convey quantitative information. The
latter applies in particular to 2-D and 3-D contour lines and surfaces.
Due to the employed GPU implementation of the 2-D marching squares contouring
algorithm, continuous line geometry is not easily available. Hence, it is
difficult to compute positions for labels.
With respect to ensemble and uncertainty visualization, open questions are abundant, as
reflected by the literature surveyed in Sect. . In Part 2, we
introduce a feature-based approach for WCBs.
Further approaches, both feature based and location based,
can be implemented in Met.3D to study their feasibility and applicability in
meteorology.
With the development of Met.3D, we have demonstrated how we envision 3-D and ensemble
techniques to become a part of standard meteorological visualization. The tool provides
a solid software infrastructure that opens the door to investigate the above-listed and
other research questions, thus enabling the further advancement of meteorological
visualization.
Code availability
To facilitate ease of deployment and of future research and
developments, we have made the source code of Met.3D available as
open-source under the GNU General Public License, version 3. Please
enter the following into your web browser to go to the software repository:
https://bitbucket.org/wxmetvis/met.3d; here you can
obtain an up-to-date version of the software. We welcome user
feedback as well as contributions that help with the further
development of the code. If you are interested, please contact us.
The Supplement related to this article is available online at doi:10.5194/gmd-8-2329-2015-supplement.
Acknowledgements
Access to ECMWF prediction data has been kindly provided in the context of the ECMWF special project “Support Tool for HALO
Missions”. This work was supported by the European Union under the ERC Advanced Grant 291372 – SaferVis – Uncertainty
Visualization for Reliable Data Discovery. M. Rautenhaus was supported by a grant from Ev. Studienwerk Villigst e.V. C. M. Grams and
A. Schäfler were supported by the German Research Foundation (DFG) as part of the research unit PANDOWAE
(FOR896).This work was supported by the German Research Foundation (DFG) and the Technische Universität München
within the funding programme Open Access Publishing.Edited by: H. Tost
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