Visualisierung Raum-Zeit Würfel

Blockwoche Visualisierung Raum-Zeit-Würfel

Raum-Zeit-Würfel

Peter Löwe, GFZ Potsdam [email protected]

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