3. Motivation
„Time is often considered as the fourth
cartographic or geographic dimension“
[Wikipedia:“Time“]
4. Zeitgeographie
• 1960er: Torsten Hägerstrand • Raum-Zeit-Würfel:
begründet die Zeitgeographie: – X/Y: Geographischer Raum
– Z: Zeit
– Raum-Zeit-Modell • Zeigt die Beziehungen
– Raum-Zeit-Pfad zwischen Zeit, Raum und
weiteren Variablen
– Raum-Zeit-Würfel
• 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/
5. 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, Substantial input is currently contributed
from information visualization, a discipline
• information visualization, that deals a lot with interactive graphics,
• multimedia design, visualizing large data sets and data mining
• mathematics, statistics, etc. issues“
[Card et al 1999 in A. Neumann, 2005]
6. 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]
7. Carte figurative des pertes successives en hommes de l'Armée
Française dans la campagne de Russie 1812–1813
[Wikipedia]
8. 2D -> 3D
Minards Karte ist Sankey Diagramm Darstellung als Raum-Zeit-Würfel
(Darstellungen mit
mengenproportionalen Pfeilen).
Kraak 2003
11. 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
12. Processing: High Level View
Lower Atmosphere MRL-5 Radar,
SAWS
Large Amounts
of 3D Data
2D Rainfall
Rainfall Data Maps
Erosivity Model
A complete scan of the lower
atmosphere (up to 18km, 200km Erosivity
radius) takes 5 minutes: Pulses
●288 data sets daily
●8,064 – 8928 data sets monthly Visualization
Erosivity Maps
●195,120 data sets per year
14. 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?]
15. 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 !
3D data
Trust „Flattening
Overall
“
Trust
2D information
17. 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.
18. Data Errors
Flip-book Volume (ground targets)
3
3
2
2 time
1
1
2D Space: Rainfall field
Not real Yellow: Rainfall
clouds ! Red: Erosivity
20. Quality Control
Rods of
The height of a rainfall track tells eternal
us how long it did rain at a soaking:
certain location Data errors
A precipitation field and its resulting erosivity pulses shown in side-view.
21. 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
23. Barrier islands
Dynamic topography:
Nags Head 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
N
24. 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
26. Evolution metrics from DEM series
t1
Core surface z-min for each cell
t2 Envelope surface z-max for each cell
tNags Head
.
3
Dynamic layer: bounds terrain evolution for a
.
tn
given period
Shoreline band: defined by shoreline from core
result and envelope, bounds shoreline dynamics for
given period
0 4km
N
27. Evolution metrics
core, envelope, DEM
1999
0 100m
2001
2004
Orthophoto and shoreline band
2008 1999
2008
c
1999
2001 min
2004 max
2005 2001
2007 2005
2008 2007
0 50m 2008
Time of maximum
28. 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
tn
... space-time cube
t3
t2
z=f(x,y,t)
t1
Time
[year]
15
7
Y[m]
0m
X[m]
29. Contour evolution as isosurface
Isosurface representation of 10, 11 and 12m
elevation contours for time series
Elevation: 10 11 12 m
2008
2005
2001
1999
Time
Y
0 100m
X
30. Contour evolution with overwash
DEM [year] z = 4.5m 0 200m
2005
2005 2003
2001
1999
1997 beach
2003
2005 shoreline
1997
4.6 m contours
Time
[year]
2005 Time
2003 [year]
2001 beach Y[m]
1999 Elevation
0 200m X[m]
1997 4.5m
31. 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 2005
2003
2001
1999
z=4.5m 1997
z=1.5m
2005
2003
2001 2005 dune rebuilt
1999 2003 dune overwash
1997 2005
2003
sand disposal 2001
1999
z=7.5m 1997
z=0.3m
2005
2003
2001
1999 Time
1997 [year]
0 200m
stable dune peaks
X[m] Y[m]
33. Tsunamifrühwarnsysteme
• Tsunami Early Warning Systems 1. Erdbeben-Lokation -> Auswahl
(TEWS) basieren auf online „passender“ Tsunamimodelle
Sensoren und Modelldaten. 2. Reduktion der in Frage
kommenden Simulationen
• Tsunamiausbreitungs-modelle
anhand von online-Sensoren.
werden in Bibliotheken für den
3. Informationslogistik auf Basis
Ernstfall vorgehalten.
des prognostizierten
Tsunamiverlaufs.
35. Validität der Simulation
• Wellenausbreitungen sind dynamisch
• Verifikation an historischen Testfällen ist
„schwierig“
• Beurteilung der Stabilität/Belastbarkeit der
Simulationen :
– Räumliches Verhalten
– Zeitliches Verhalten
– Informationsgehalt
42. Einladung:
Lange Nacht der Wissenschaften
2. Juni 2011.
• Raumzeitwürfel in
3D im Visiolab des
GFZ.
43. 5D -> 3D
• Kollabieren
höherdimensionaler
Daten am Beispiel
Wetterradar
44. 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.
45. 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).
46. 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.
47. CFAD – An Example
Largest count of
hydrometeors
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.
48. 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.
49. Beispiel
Iso Surfaces resemble
levels of droplet
counts (a few, many,
Altitude lots)
Critical threshold: If the inner
layer (many droplets) of the
„loaf“ exceeds it, then there is
heavy downpour or even hail.
50. 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
51. 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 ?
52. 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.
