Transcript
Blockwoche Visualisierung Raum-Zeit-Würfel
Raum-Zeit-Würfel
Peter Löwe, GFZ Potsdam ploewe@gfz-potsdam.de
Übersicht
• Einführung Raum-Zeit-Würfel
• Anwendungsbeispiele 2D->3D
– Wetterradar
– Küstenschutz
– Tsunami-Frühwarnsystem
• Anwendungsbeispiel 5D->3D
– Qualitätssicherung Wetterradar
Motivation
„Time is often considered as the fourth cartographic or geographic dimension“
[Wikipedia:“Time“]
Zeitgeographie
• 1960er: Torsten Hägerstrand begründet die Zeitgeographie:
– Raum-Zeit-Modell
– Raum-Zeit-Pfad
– Raum-Zeit-Würfel
• Raum-Zeit-Würfel:
– X/Y: Geographischer Raum
– Z: Zeit
• Zeigt die Beziehungen zwischen Zeit, Raum und weiteren Variablen
• Aufzeigen von Raum-Zeit-Pfaden für Objekte/Individuen
• Explorative Datenanalyse
• Option: Real Time Monitoring
http://www.svgopen.org/2005/papers/abstract_neumann_thematic_navigation_in_space_and_time/
Umsetzung mit GIS
„Modelling and visualizing time and spatio-temporal navigation in GIS is truly a multidisciplinary research topic, including domains such as • geography, • social and live sciences, • psychology, • philosophy, • GIScience, • GIS, • cartography, • computer science, • information visualization, • multimedia design, • mathematics, statistics, etc.
Substantial input is currently contributed from information visualization, a discipline that deals a lot with interactive graphics, visualizing large data sets and data mining issues“
[Card et al 1999 in A. Neumann, 2005]
Beispiel: Minard‘s Karte
• Der französische Bauingenieur Charles Joseph Minard veröffentlichte 1869 eine Grafik zu den Verlusten der französischen Armee während Napoleons Russlandfeldzug, die Carte figurative des pertes successives en hommes de l'Armée Française dans la campagne de Russie 1812–1813.
[Wikipedia]
Carte figurative des pertes successives en hommes de l'Armée Française dans la campagne de Russie 1812–1813
[Wikipedia]
2D -> 3D
Darstellung als Raum-Zeit-Würfel Minards Karte ist Sankey Diagramm (Darstellungen mit mengenproportionalen Pfeilen).
Kraak 2003
Praxisbeispiele
1. Wetterradar
2. Küstenentwicklung
3. Tsunamimodellierung
Beispiel 1: Wetterradar
Datenbasis
• Dreidimensionale Volumenscans der Atmosphäre.
• Frequenz: 5 Minuten
• Auflösung: 1km
• Eingangsdaten: Constant Altitude Plan Position Indicator (CAPPI) (zweidimensionale „Schnitte“)
• Maximales Echo über alle Schnittebenen: MaxCAPPI
• Produkt: – Niederschlagskarten
– „Pluviogramme“
• Abgeleitete Größe: Niederschlagserosivität
2D
Rainfall Data
Erosivity Model
Erosivity
Pulses
Erosivity Maps
Rainfall
Maps
Visualization
Lower Atmosphere
Processing: High Level View MRL-5 Radar,
SAWS Large Amounts
of 3D Data
A complete scan of the lower
atmosphere (up to 18km, 200km
radius) takes 5 minutes:
●288 data sets daily
●8,064 – 8928 data sets monthly
●195,120 data sets per year
24h total
erosive
16:18:50 Hours 16:43:30 Hours 16:59:56 Hours
Erosivity
Reflectivity
Σ
Σ
Left: Reflectivity Centre: Rainfall Right: Erosivity
MaxCAPPI
Erosivität
The Challenge
● Can we trust the 2D rainfall data ?
– Metadata appears correct.
– [are the rainfall fields correct ?]
● Weather Radar provides 3D data.
– [3D->2D transformation: Correctly done?]
Garbage in, Garbage out
● Can we trust the rainfall information of the weather radar ?
● Model results are based on rainfall data.
● Errors and Biases in the rainfall data will affect all derived
products.
● What about transient biases which might vary in time or
space?
● One should have a close look at the data !
„Flattening
“ Overall
Trust
Trust
3D data
2D information
From single drawings
1 2 3
„Radar Rain Flip-Book“
„Erosivity Peaks Flip-
Book“
Boredom in, Boredom out
● Large data archives exist and more data are
added every day (288 data sets in our example).
● How can we easily identify time intervals
when „some interesting weather“ has
occurred?
● We could watch it all in 4D (3D over time):
– Takes too much time, is incredibly boring
– Problem to watch the right things at the right
time.
time
1
2D Space: Rainfall field
2
3
Yellow: Rainfall
Red: Erosivity
Data Errors
(ground targets)
Not real
clouds !
1
2
3
Flip-book Volume
Ce n'est pas un nuage!
Painting of a pipe
Quality Control
A precipitation field and its resulting erosivity pulses shown in side-view.
The height of a rainfall track tells
us how long it did rain at a
certain location
Rods of
eternal
soaking:
Data errors
Beispiel 2: Küstenschutz
[Materialien von Prof. Helena Mitasova, 2011]
Analysis of barrier islands vulnerability
and evolution:
Airborne lidar surveys since 1996
Analysis of DEM time series
Space-time cube
Datenbasis
• Datenquelle: LIDAR Scans
• Auflösung: 0.3-1.0m
• Frequenz: Jährlich
Barrier islands
Dynamic topography:
sand is redistributed by wind, waves,
storm surge
Vulnerable:
coastal erosion, sea level rise,
inundation
First line of defense against storms
Cape Hatteras
0 10km
Nags Head
N
Vulnerability: Dune ridgeline Vulnerability: function of dune ridge and toe position
Least cost path method for ridgeline extraction:
Continuous line, robust to elevation anomalies, highly automated
Elevation surface Cost surface
Vulnerability: Dune toeline Dune toe extraction: elastic sheet, cost surface and least cost path
Cost Surface
0 4km
Nags Head
N
Evolution metrics from DEM series
Core surface z-min for each cell
Envelope surface z-max for each cell
Dynamic layer: bounds terrain evolution for a
given period
Shoreline band: defined by shoreline from core
and envelope, bounds shoreline dynamics for
given period
t1
t2
t3
.
.
tn
result
core, envelope, DEM
0 100m
1999
2001
2004
2008
1999
2001
2004
2005
2007
2008
1999 2008
min
max
2001
2005
2007
2008
Orthophoto and shoreline band
Time of maximum
c
0 50m
Evolution metrics
Y[m]
X[m]
Time
[year]
space-time cube
t1
t2
t3
tn ...
15
7
0 m
z=f(x,y,t)
Terrain evolution in space-time cube
How does evolution pattern change with elevation?
What is the direction of fastest elevation change?
Time series of (x,y,z) point clouds interpolated to voxel model
Elevation: 10 11 12 m
0 100m
2008
2005
2001
1999
Time
Y
X
Contour evolution as isosurface
Isosurface representation of 10, 11 and 12m
elevation contours for time series
Time
[year]
Y[m]
X[m]
2005
2003
2001
1999
1997 0 200m
Elevation
4.5m
Time
[year]
2005
2003
2001
1999
1997
2005 shoreline
4.6 m contours
beach
beach
z = 4.5m 0 200m
DEM [year]
2005
2003
1997
Contour evolution with overwash
Dynamics at different elevations Different spatial pattern of dynamics at different elevations:
0.3m shoreline, 1.5m upper beach, 4.5m mid-dune, 7.5m dune ridge
stable dune peaks
2005 dune rebuilt
2003 dune overwash
sand disposal
Time
[year]
Y[m] X[m]
0 200m
2005
2003
2001
1999
1997 z=1.5m
z=0.3m
2005
2003
2001
1999
1997
2005
2003
2001
1999
1997
z=4.5m
z=7.5m
2005
2003
2001
1999
1997
Beispiel 3: Tsunamiwarnung
Tsunamifrühwarnsysteme
• Tsunami Early Warning Systems (TEWS) basieren auf online Sensoren und Modelldaten.
• Tsunamiausbreitungs-modelle werden in Bibliotheken für den Ernstfall vorgehalten.
1. Erdbeben-Lokation -> Auswahl „passender“ Tsunamimodelle
2. Reduktion der in Frage kommenden Simulationen anhand von online-Sensoren.
3. Informationslogistik auf Basis des prognostizierten Tsunamiverlaufs.
Datenbasis
• Tsunamimodellrechnungen – Vergangenheit
– „What-If“
• Inhalte: – Wellenhöhenraster
– Mareogramme („Fieberkurven“)
• Frequenz: 2-5 Minuten
• Abgeleitete Daten: – Maximale Wellenhöhen
• Kritisch: Validität der Simulation
Maximale Wellenhöhen des Tohoku-Tsunami 2011 (GFZ)
Validität der Simulation
• Wellenausbreitungen sind dynamisch
• Verifikation an historischen Testfällen ist „schwierig“
• Beurteilung der Stabilität/Belastbarkeit der Simulationen :
– Räumliches Verhalten
– Zeitliches Verhalten
– Informationsgehalt
Beispiel: Kreta 356n.Chr.
Wellenaus-breitung
Maximale Wellenhöhen
Datenfehler
Tohoku Tsunami 11.3.2011
• Magnitude 9 Beben
• Bruchlänge: 400 km
• 27m Gesamt-Versatz
• 7m Vertikalbewegung
• „Live-Übertragung“ via KML
Tohoku Raumzeitwürfel
Negative Wellen
Positive Wellen
Einladung: Lange Nacht der Wissenschaften
2. Juni 2011. • Raumzeitwürfel in
3D im Visiolab des GFZ.
5D -> 3D
• Kollabieren höherdimensionaler Daten am Beispiel Wetterradar
Datenkollaps der Höheninformation
(Wurde schon gezeigt)
The 2D (xy) rainfall field was „squeezed“ out of the 3D (xyz) weather
radar data, implicitly „collapsing“ the vertical dimension.
The stacking of the time frame „flip-book“ pages substituted the altitude (z) dimension by the time dimension.
Next Step: Spatial Collapse
This approach can be followed further:
● In the previous example we collapsed the z-
dimension
● Now we collapse the horizontal (xy)
dimension.
● The resulting diagram is a preview format:
„Contoured Altitude by Frequency
Diagram“ (CFAD).
Contoured Frequency by Altitude
Diagrams (CFAD) ● CFAD can be created from 3D radar reflectivity data (original
airspace radar scan). The 3D data set is sliced vertically.
● Histograms of the reflectivities (1D) are generated for each
slice/layer.
● Stacking the histograms gives us a 2D synopsis of the current
situation in the scanned airspace.
● This tells us a lot about the weather and potential measurement
errors.
CFAD – An Example
Contoured Frequency by Altitude Diagram (CFAD).
Numbers on contour lines give the number of voxels in the observation area
with a given radar reflectivity.
The CFAD gives a snapshot of weather intensity at different altitudes in the lower atmosphere.
Largest count of
hydrometeors
CFATD = Raum-Zeit-Würfel
● Contoured Frequency Altitude by Time
Diagram adds the time dimension, resulting in
a volume body -> .
● The shape of the CFATD makes it easy to
identify:
● periods of high radar reflectivity, i.e. intense
weather, and
● Errors in the radar or processing chain.
Beispiel
Altitude
Iso Surfaces resemble
levels of droplet
counts (a few, many,
lots)
Critical threshold: If the inner
layer (many droplets) of the
„loaf“ exceeds it, then there is
heavy downpour or even hail.
Visual Quality Control
● CFATD gives a convenient and reliable quality measure for observations not to use ● If the CFATD structure appears blocky, or „non-organic“: discard the data
Faulty data
Faulty
data
Better data, better models
● 4D previews for „Live Quality Control“ in sensor systems:
– Weather Radar does „now-casting“
● It looks into the distance (right now)
● but not into the future
– Real-time generation of CFATD „loaves“ could be used for radar system
calibration and maintenance.
What level of quality
do we get RIGHT NOW ?
Fazit
• Raum-Zeit-Würfel können in verschiedenen Szenarien eingesetzt werden
• Sie vermitteln Übersicht über zeitlich/räumlich fluktuierende Datensätze für Analyse und Diskussion
• Möglichkeit zur Analyse von räumlich/zeitlichen Fehlern
• Nutzung ist retrospektiv und in „real-time“ möglich.
• In Verbindung mit Datenreduktionsmethoden (CFAD) können auch höherdimensionale Daten genutzt werden.
Danke für die Aufmerksamkeit
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